We investigate a class of combinatorial sums involving reciprocals of central binomial coefficients , employing generating functions as the primary solution technique to formulate and analyze series involving the Catalan's constant. Using a direct approach, we derive new identities through integral techniques.

This paper deals with developing a new class of quaternions, called hyper-dual Horadam quaternions which are constructed from the quaternions whose components are hyper-dual Horadam numbers. We investigate the algebraic properties of these quaternions.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

We examine the extensions of the basic arithmetical operations of addition and multiplication on the natural numbers into higher-rank hyper-operations also on the natural numbers. We go on to define the concepts of prime and composite numbers under these hyper-operations and derive some results about factorisation, resulting in fundamental theorems analogous to the Fundamental Theorem of Arithmetic.

Elevated immunoglobulin E (IgE) levels are commonly associated with allergies. However, high IgE levels are also found in several other infectious and non-infectious disorders. Elevated IgE levels typically suggest allergies, eczema, or recurrent skin infections. Very high IgE levels are uncommon in patients with active eczema but typically reflect a monogenic atopic condition or inborn immune defects with an atopic phenotype. The aim of our research is to identify if the possible cause of high IgE levels is also dependent on external factors, age, or associated recurrent pathologies such as infections. To answer this question, we performed a one-year retrospective study that included 200 hospitalized children who had at least two viral or bacterial infections in the six months preceding hospitalization. Measurements of IgE and allergen panels (respiratory and digestive) using blood samples revealed that individuals who tested positive for the body’s synthesis of hyperimmunoglobulin E were not observably allergic to any potential allergens despite having higher total serum IgE. According to the results, there was a strong correlation between elevated IgE serum levels and a history of infectious diseases among the patients.

The proper hydrogenation of Hyper-coal (HPC) using 1, 2, 3, 4-tetrahydroquinoline (THQ) was able to decrease the oxygen content and adjust the molecular structure of HPC for preparing the spinnable pitch with high softening point (SP). The spinnable pitch prepared from the THQ-soluble (QS) fraction of HPC as a precursor consisted more naphthenic carbon groups than that prepared from the 1-methylnaphthalene (1-MN) soluble (MNS) fraction of HPC. The HPC-QS derived pitch showed excellent spinnability even the SP of 260°C, and the tensile strength of the resultant carbon fiber was up to 1350 MPa with a diameter around 8 µm by only heat treatment at 800°C for 5 min.

Shaped surfaces are increasingly used in the field of mould making for casting or injection moulding, where future products include shapes with different curvatures. These are surfaces that form convex curves, concave curves, or a combination thereof. Given these machined surfaces, it is important to know the impact of the finishing strategies on these surfaces. This paper deals with the comparison of finishing milling strategies in the production of shaped surfaces and the analysis of different methods for the evaluation of surface topography, surface roughness and the evaluation of deviations. The material used for the experiments was AlCu4Mg aluminium alloy, and Constant Z, Spiral and Spiral circle strategies were chosen for the finishing strategies. The evaluation of surface topography and surface roughness was carried out at three different sample heights with respect to the tool contact with the machined surface. The results showed changes in the toolpaths due to the variation of the effective diameter of the tool cutter to the machined surface as well as the choice of strategy. To produce specimens with corresponding shapes in terms of topography, the Constant Z strategy was the most suitable, in which uniform toolpaths were obtained over the whole height of the sample.

In this work, we apply ensemble formalism to a geometric agents model to study the effect of saving propensity in a system with money, credit, and debt. We calculate the partition function to obtain the total money of the system, with which we give an interpretation of the economic temperature in terms of the different payment methods available to the agents. We observe an interplay between the fraction of money that agents can save and the debt that can be financed. We also observe that the system’s entropy increases as the saved proportion increases and increases, even more, when debt is present.

YG-13A represents the highest level of Chinese SAR satellites to date. In this paper, we report on experiments conducted to improve and validate ranging accuracy with YG-13A. We analyze the error sources in the YG-13A ranging system, such as atmospheric path delay, and transceiver channel delay. A real-time atmospheric delay correction model is established to calculate the atmospheric path delay, considering the troposphere delay and ionosphere delay. Six corner reflectors (CRs) were set up to ensure the accuracy of validation methods. Pixel location accuracies of up to 0.479-m standard deviation can be achieved after a complete calibration. We further demonstrate that the adjustment of the CRs can cause a marginal loss of ranging precision. After eliminating this error, the ranging accuracy is improved to 0.237 m. For YG-13A, a single frequency GPS receiver is used and the orbital nominal accuracy is 0.3 m, which is the biggest factor restricting its ranging accuracy. Our results show that the ranging accuracy of YG-13A can achieve decimeter-level, which is lower than centimeter-level accuracy with TerraSAR-X loading a dual frequency GPS. YG-13A has great convenience in terms of access to control points and target location that does not depend on ground equipment.

In the extended malfatti problem, the numbers of circles in the triangle are triangle numbers, because the tangency properties among the internal circles and 3 sides of the triangle have special type of structure. That is, the corner circle tangent to two sides of the triangle and two boundary circles, the boundary circles tangent to one side of the triangle and 4 other circles, and the inner circles always tangent to 6 other circles. The circles we find in extended general Malfatti’s problem has the property that the smallest radius and the largest radius for the circle has big difference. In this paper, we proposed algorithms to solve the problem that the tangency properties among circles and sides of triangle is not fixed, so that the number of circles in the triangle is not necessary a triangle numbers. The purpose of this change is try to find the radii of the circles in the triangle is within a small range.

The spectrums of one type of object under different conditions have the same features (up, down, protruding, concave) at the same spectral positions, which can be used as primary parameters to evaluate the difference among remotely sensed pixels. Wavelet-feature correlation ratio Markov clustering algorithm (WFCRMCA) for the remotely sensed data is proposed based on an accurate description of abrupt spectral features and an optimized Markov clustering in the wavelet feather space. The peak points can be captured and identified by applying a wavelet transform to spectral data. The correlation ratio between two samples is a statistical calculation of the matched peak point positions on the wavelet feature within an adjustable spectrum domain or a range of wavelet scales. The evenly sampled data can be used to create class centers, depending on the correlation ratio threshold at each Markov step, accelerating the clustering speed by avoiding the computation of Euclidean distance for traditional clustering algorithms, such as K-means and ISODATA. Markov clustering applies several strategies, such as a simulated annealing method and gradually shrinking the clustering size, to control the clustering convergence. At each clustering tempera-ture, it can obtain the best class centers quickly. The experimental results of the Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS) and Thermal Mapping (TM) data have verified its ac-ceptable clustering accuracy and high convergence velocity.

This paper explores the geometric impossibility of angle trisection within Euclidean geometry, with a particular focus on the 90° angle. It presents a rigorous proof that highlights the fundamental limitations of various approaches to angle trisection, highlighting their failure to achieve universality. The paper critiques modern proofs that allow for the trisection of certain angles while dismissing others, arguing that such methods are inherently flawed due to their lack of geometric consistency. The paper introduces a new perspective through a new property named “inconsistent property”, a concept derived from geometric operations involving proportional magnitudes. This property reveals contradictions within the framework of Euclidean geometry, paralleling the logical challenges faced in proving the impossibility of trisecting an arbitrary angle. By drawing comparisons between traditional and contemporary proofs, the paper demonstrates that inconsistencies arise not only from specific cases but also from broader geometric principles. The findings reaffirm the robustness of Euclidean geometry in addressing the trisection problem and challenge the validity of alternative proofs that do not adhere to universal geometric principles. This paper contributes to a clearer understanding of the limitations of angle trisection methods and encourages further investigation into the technical implications and broader impact of the angle impossibility proof.

This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for these angles, demonstrating the enduring strength of Euclidean principles from classical to modern times. The presented workflow goes beyond Euclidean geometry to examine non-Euclidean methods, particularly analytical approaches, revealing misconceptions that compromise the genetic and geometric rigor of Euclidean principles. The paper exposes incongruities when algebraic proofs related to angle constructability are applied to the Euclidean system, emphasizing the misalignment of fundamental geometric concepts. A notable result in the paper is the construction of a angle, introducing the “ angle chord” as a novel geometric property. This property challenges assumptions made by non-Euclidean methods and highlights the nuanced geometric properties crucial for rigorous constructions. The paper refutes the fallacy of relying solely on algebra for solutions to angles multiples of , emphasizing the necessity of embracing Euclidean geometry for geometric discoveries. The paper underscores the merits and resilience of Euclidean geometry, showcasing its independence and depth across historical and modern perspectives. The newly presented geometric construction not only resolves a longstanding question but also emphasizes the intrinsic strength and uniqueness of Euclidean principles in contrast to alternative methodologies.

Gastrointestinal (GI) tract disorders, ranging from benign polyps to aggressive forms of cancer, pose significant health challenges globally. Early detection and precise classification of these conditions are crucial for effective treatment and improving patient survival rates. This study employs the Hyper-Kvasir dataset, a comprehensive collection of endoscopic images, to develop deep learning models that harness the power of the YOLO (You Only Look Once) architecture for real-time detection and classification of GI abnormalities. The focus is on overcoming inherent challenges such as class imbalance and limited annotated data availability. Advanced machine learning strategies, including data augmentation and semi-supervised learning, are utilized to enhance the model's performance. Our experiments demonstrate notable improvements in the detection of pre-cancerous lesions and other GI abnormalities, confirming the potential of integrating AI into endoscopic practices to support clinicians, reduce diagnostic errors, and contribute to more accurate and timely diagnoses. The implications of these findings are significant, offering a pathway to more reliable diagnostic processes and ultimately, better patient management in gastroenterology.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Identification of the honey bee (Apis mellifera) subspecies is an important aspect of bee breeding and biodiversity conservation. The identification can be based on molecular or morphological markers. For some markers, including the cytochrome c oxidase subunit, there is a well-established methodology allowing consistent subspecies identification in different laboratories. In the case of morphological markers, identification is hindered by a lack of reference data and a standardized methodology to reuse it. We show here that reference data for the identification of honey bees based on geometric morphometrics can be saved in an XML file. The information in this file can be easily extracted by other users for the identification of unknown samples. We illustrate this procedure using ten samples from north India. The samples were identified as A. mellifera; next, they were identified as lineage C; and finally, most of the samples had high similarity to honey bees from Croatia and Slovenia. We explained what data is required for such identification and how it can be reused. The method described here can be applied not only to honey bee wings but also to all data based on landmark coordinates.

This article presents the results of the consideration of the Bertrand paradox in terms of geometric probability theory. Although the method and conclusions of this article are straightforward, no equivalent studies were found when reviewing the relevant literature. This could be conditioned by the fact that the hypotheses presented in this research have low intuitive obviousness and, in contrast, could be due to the historically established agreement regarding the issue. This article shows that out of three classical solutions to the problem described by Bertrand, two methods are inconsistent with the claimed relative objectivity. Although the remaining solution (1/4) seems to be the most correct, we cannot claim that we have exhaustively ruled out all aspects that could reduce its adequacy to solve the problem.

The first hyperpolarizability of graphene quantum dots (GQDs) suspended in water was determined using the hyper-Rayleigh scattering (HRS) technique. To the best of our knowledge, this is the first application of the HRS technique to characterize GQDs. Two commercial GQDs (Acqua-Cyan and Acqua-Green) with different compositions were studied. The HRS experiments were performed with an excitation laser at 1064 nm. The measured hyperpolarizabilities were (1.0±0.1) × 10^(-27) esu and (0.9±0.1) × 10^(-27) esu for Acqua-Cyan and Acqua-Green, respectively. The results were used to estimate the hyperpolarizability per nanosheet obtained by assuming that each GQDs has five nanosheets with 0.3 nm thickness. The two-level model, used to calculate the static hyperpolarizability per nanosheet, provides the values of (2.4±0.1) × 10^(-28) esu (Acqua-Cyan) and (0.5±0.1) × 10^(-28) esu (Aqua-Green). The origin of the nonlinearity is discussed on the basis of polarized resolved HRS experiments, and an electric quadrupolar behavior with a strong dependence on surface effects is found. The nontoxic characteristics and order of magnitude indicate that these GQDs may be useful for biological microscopy imaging.

We have particularly investigated the correlation law of the effect of different carbon black fillings on the hyper-elastic mechanical behavior of natural rubber by conducting uniaxial tensile tests over a wide range of deformations with different volume fractions of carbon black fillings (0%, 4.7%, 8.9%, 12.8%, 16.4%, 19.7%, 22.7%, 25.2%). The results show that the stress-strain curve for carbon black filled rubber increases with the amount of filling, meaning that the rubber gradually becomes "harder". We explore the correlation between the carbon black filling volume and the parameters of the Yeoh constitutive model by examining the Yeoh constitutive model to characterize the hyper-elastic mechanical behavior of rubber with different carbon black fillings. A quantitative relationship between the material parameters and the carbon black filling volume in the Yeoh constitutive model is presented. A method for calculating the material parameters of the Yeoh constitutive model is developed and it predicts the correlation between the hyper-elastic properties of rubber and the volume fraction of carbon black filling.

A wealth of Full Waveform (FW) LiDAR data are available to the public from different sources, which is poised to boost the extensive application of FW LiDAR data. However, we lack a handy and open source tool that can be used by potential users for processing and analyzing FW LiDAR data. To this end, we introduce waveformlidar, an R package dedicated to FW LiDAR processing, analysis and visualization as a solution to the constraint. Specifically, this package provides several commonly used waveform processing methods such as Gaussian, adaptive Gaussian and Weibull decompositions, and deconvolution approaches (Gold and Richard-Lucy (RL)) with users’ customized settings. In addition, we also developed functions to derive commonly used waveform metrics for characterizing vegetation structure. Moreover, a new way to directly visualize FW LiDAR data is developed through converting waveforms into points to form the Hyper Point cloud (HPC), which can be easily adopted and subsequently analyzed with existing discrete-return LiDAR processing tools such as LAStools and FUSION. Basic explorations of the HPC such as 3D voxelization of the HPC and conversion from original waveforms to composite waveforms are also available in this package. All of these functions are developed based on small-footprint FW LiDAR data, but they can be easily transplanted to the large footprint FW LiDAR data such as Geoscience Laser Altimeter System (GLAS) and Global Ecosystem Dynamics Investigation (GEDI) data analysis. It is anticipated that these functions will facilitate the widespread use of FW LiDAR and be beneficial for better estimating biomass and characterizing vegetation structure at various scales. The package and code examples can be found at https://github.com/tankwin08/waveformlidar.

Validation of the TROPOspheric Monitoring Instrument (TROPOMI) SIF product is a necessity to evaluate its feasibility in various applications. A few validation works have been conducted through direct comparison with in-situ SIF retrievals or cross-comparison with similar satel-lite-based SIF or vegetation index (VI) products. Nevertheless, the influence of the geolocation mismatch between the validation pixel and reference data on validation results was never con-sidered. This study, for the first time, quantifies the geolocation shift of the TROPOMI validation pixel based on a geometric location matching method and then the uncertainty caused by the ge-olocation mismatch. The results indicate that the geolocation shift of the TROPOMI pixel shows large temporal variations, with a standard deviation of 2.45 km and 1.96 km in the across- and along-track directions. The mean shifts are 0.07 km and 0.25 km in the across- and along-track directions respectively, indicating eastward shifts in the across-track direction and northward shifts in the along-track direction in general. More than half (42/54) of the time periods showed relative uncertainty larger than 5%, with the maximum even reaching 55.7%. Hence, the uncertainty caused by geolocation mismatch should be fully considered in the validation of satellite SIF products, especially over heterogeneous surfaces.

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

The hyper-arid environment is characterized by high inter-annual climatic fluctuations. The yearly average rainfall can change substantially for several years, forming wet or dry sub-periods. Observing rainfall trends over a sub-period can lead to a false perception of a change in the trend but may in fact represent a periodic cycle when examined on a larger time scale. We aimed to better characterize the rainfall regime prevailing in the hyper-arid Arava Valley (Israel/Jordan), and to examine the response of vegetation to annual rainfall. We hypothesized that annual and perennial vegetation would respond differently to wet and dry sub-periods, and that grazing activities will impact vegetation growth. We used a time series of monthly rainfall, from which we calculated Standard Precipitation Index (SPI), and calculated proxies of perennial and annual vegetation over the last four decades using Landsat-derived Normalized Difference Vegetation Index (NDVI). We found no clear trend in rainfall amounts during this period, however we did identify wet and dry sub-periods which were statistically distinct in rain and in vegetation patterns from each other. The highest levels of correlation between rainfall and the NDVI derived proxies were found when examining average rainfall over a period of two- three years for the annual vegetation and over four years for perennial vegetation. Using the Mann-Kendall test, we identified a time lag of two to four years, with the proxies of annual vegetation responding faster than the proxies of perennial vegetation, to shifts between wet and dry sub-period. In addition, we found a consistent difference between natural vegetation cover in Jordan (grazed) and Israel (non-grazed), favoring the development of natural vegetation on the Israeli side. We conclude that integrating between long-term remote sensing satellite imagery and climatic records revealed the greater resilience of perennial vegetation in the hyper-arid region to climatic fluctuation, and enabled us to identify the vegetation’s sensitivity to anthropogenic impact.

The expansion of copper mining on the hyper-arid pacific slope of southern Peru has precipitated growing concern for scarce water resources in the region. Located in the headwaters of the Torata river, in the department of Moquegua, the Cuajone mine, owned by Southern Copper, provides a unique opportunity, in a little-studied region, to examine the relative impact of the landscape-scale mining on water resources in the region. Principal component analysis and cluster analysis of the water chemistry data from 16 sites, collected over three seasons during 2017 and 2018, show distinct statistical groupings indicating that, above the settlement of Torata, water geochemistry is a function of chemical weathering processes acting upon underlying geological units, and confirming that the Cuajone mine does not significantly affect water quality in the Torata river. Impact mitigation strategies that firstly divert channel flow around the mine and secondly divert mine waste to the Toquepala river and tailings dam at Quebrada Honda, below the Toquepala mine, in the department of Tacna, secure water quality in the Torata river for the foreseeable future. In the greater Moquegua river catchment, our results further suggest that water quality has been more significantly impacted by urban effluents and agricultural runoff than the Cuajone mine. The increase in total dissolved solids in the waters of the lower catchment reflects the cumulative addition of dissolved ions through chemical weathering of the underlying geological units, supplemented by rapid recharge of surface waters contaminated by residues associated with agricultural and urban runoff through the porous alluvial aquifer. Concentrations in some of the major ions exceeded internationally recommended maxima for agricultural use, especially in the coastal region. Occasionally, arsenic and manganese contamination also reached unsafe levels for domestic consumption. In the lower catchment, below the Cuajone mine, data and multivariate analyses point to urban effluents and agricultural run-off rather than weathering of exposed rock units, natural or otherwise, as the main cause of contamination.

This paper describes and demonstrates an autonomous robotic team that can rapidly learn the characteristics of environments that it has never seen before. The flexible paradigm is easily scalable to multi-robot, multi-sensor autonomous teams, and is relevant to satellite calibration/validation and the creation of new remote sensing data products. A case study is described for the rapid characterisation of the aquatic environment, over a period of just a few minutes we acquired thousands of training data points. This training data allowed our machine learning algorithms to rapidly learn by example and provide wide area maps of the composition of the environment. Along side these larger autonomous robots two smaller robots that can be deployed by a single individual were also deployed (a walking robot and a robotic hover-board), observing significant small scale spatial variability.

Hypergravity accelerators are a type of large machinery used for gravity training or medical research. A failure of such large equipment can be a serious problem in terms of safety or costs. This paper proposes a prediction model that can proactively prevent failures that may occur in a hy-pergravity accelerator. The method proposed in this paper was to convert vibration signals to spectograms and perform classification training using a deep learning model. An experiment was conducted to evaluate the performance of the method proposed in this paper. A 4-channel accel-erometer was attached to the bearing housing, which is a rotor, and time-amplitude data were obtained from the measured values by sampling. The data were converted to a two-dimensional spectrogram, and classification training was performed using a deep learning model for four conditions of the equipment: Unbalance, Misalignment, Shaft Rubbing, and Normal. The ex-perimental results showed that the proposed method had a 99.5% F1-Score, which was up to 23% higher than the 76.25% for existing feature-based learning models.

The identification of bloodstain is one of the most important approaches in obtaining evidence in criminalistics. A threshold method based on spectral co-efficient and interclass variance is proposed in this paper, it is a non-contact, non-destructive method for quickly identifying bloodstains. The spectra of bloodstains and other suspected substances were all extracted from their hyper-spectral image. Then calculate the correlation coefficients of these spectral and interclass variances, analyze the differences between substances. The best blood recognition threshold was determined as 0.9. After preprocessing for eliminating systematic errors, experiments with the threshold 0.9 are carried out to identify bloodstains on the calico and red T-shirt. The method can remarkably identify the bloodstain from other non-blood substances both quickly and efficiently. The blood extraction rate can reach to 93.35% and 89.19%, respectively. It is an important step toward the implementation of bloodstain non-contact and non-destructive identification in forensic casework.

With the rapid advancement of urbanization, the problem of traffic congestion in cities has become increasingly severe. Effectively managing traffic congestion is crucial for sustainable urban development. Previous studies have indicated that fluid dynamics theory can be applied to address flow problems in transportation, and this article aims at utilize CFD to solve congestion issues in urban road traffic. Firstly, a similarity analysis is conducted between fluids and traffic flow at the theoretical level. By converting parameters, the formula of fluid is derived into the formula of traffic flow, thus demonstrating the feasibility of using CFD in traffic flow research. On this basis, targeting recurrent congestion and non-recurrent congestion scenarios, 2D road fluid domains and constraints are constructed based on the common characteristics of each congestion type area. By using Fluent software to analyze the flow conditions under different congestion characteristics, use the smoothness of fluid motion to find out the problems causing traffic congestion and conduct analysis to reveal the microscopic mechanism behind congestion formation. For different types of congestion, in order to clarify the effectiveness of congestion mitigation measures, the geometric design of road intersections and diversion measures are discussed in depth. The traffic pressure is analyzed by adjusting the vehicle inlet angle at intersections or controlling the vehicle flow speed. Finally, the optimal design scheme is obtained by comparative analysis. The work of this article provides new ideas for optimizing urban road design and solving vehicle traffic congestion problems. The optimization measures can effectively reduce the accident rate and improve the efficiency of traffic flow.

The overall comfort experienced by an individual in an n-dimensional space can be theoretically constructed using a mathematical equation, that relates the comfort experienced by an individual in a particular point in space with spatial points associated with higher comfort attributes and the desirable factors affecting the current environmental space.

Outliers seriously affect the accuracy in geometric model fitting. Previous works in coping with outliers involve threshold selection and scale estimation. However most scale estimators suppose the inlier distribution as a Gaussian model, which usually poorly meets the cases in geometric model fitting. Outliers, considered as the points with big residuals to all the true models, share common items with big values in quantized residual preferences, thus making the outliers gather away from the inliers in quantized residual preference space. In this paper we make use of this outlier consensus in quantized residual preference space by extending the usage of energy minimization to combine the model error and the spatial smoothness in quantized residual preference space for outlier detection. The energy minimization based outlier detection process follows an alternate sampling and labeling framework. After the outlier detection, an ordinary energy minimization method is employed to optimize the inlier labels, which also follows the framework of alternate sampling and labeling. The experimental results in this study show that the energy minimization based outlier detection method can detect most of the outliers in the data. Furthermore, the proposed energy minimization based inlier segmentation process segments the inliers into different models quite accurately. Overall, the performance of the proposed method is better than most of the state-of-the-art methods.

Quantum physics is intrinsically probabilistic. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such state. The degrees of freedom of a quantum state are position and spin, and upon their specification Born's rule in phase space defines randomness. We focus on the spin degree of freedom and elucidate the spin entropy. Then, we present some of its properties and show how entanglement increases spin entropy. Some speculative predictions on the decay of the $Z^0,W^{+,-}$ gauge bosons conclude the paper.

Although the similarity laws were widely used in impact fields, the scaling relations of anisotropic elastic structures often were broken when the geometric distortion (not equal scaling in different spatial directions) and the material distortion (different materials used for scaled model and full-size prototype) were considered. To overcome the difficulty of geometric and material distortion, a directional framework of similarity laws, termed as oriented-density-length-velocity (ODLV) system, is proposed for the anisotropic elastic structure under impact loads. Different from previous similarity law systems using scalar dimensional analysis, the directional similarity law framework mainly considers spatial anisotropy for structural geometry and material parameters. Based on the oriented dimensional analysis and the orthotropic Hooke's law, directional dimensionless numbers and directional scaling relations with geometric power properties for the elastic modulus and the Poisson's ratio are presented systematically. By selecting the dominant material parameters controlling similarity, three important scaling techniques with correction of geometric width and thickness are proposed to compensate for the difficulty of distortion. A clamped square plate with different anisotropic and isotropic elastic materials subjected to dynamic pressure pulse is verified numerically and discussed in detail. The results show that the thin square plate prototype must be scaled to be the thinner/thicker rectangular plate, and the components of displacement, stress and strain between scaled model and full-scale prototype behave good consistency in both spatial and temporal fields.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

Classical Optimal Power Flow (OPF) is one of the complex and challenging problem in power system that includes non-convex, nonlinear and large-scale structure. With the use of incorporation of uncertain and intermittent wind energy sources in the OPF problem, the complexity of the problem escalates. In a power system, Flexible Alternating Current Transmission Systems (FACTS) devices can mitigate most of the problems associated with power quality and overload in the network. However, determining the placement and sizing of facts devices is an additional problem to minimize the total cost of production of the power system. As a result, in order to solve OPF problem which includes all of these conditions, an artificial intelligence based optimization algorithm needs to have an unusual exploration ability as well as exploitation–exploration balance. Weighted mean of vectors (INFO) is a new heuristic optimizer, which can help finding a more effective solutions in engineering design optimization problems. In this study, firstly, INFO algorithm was improved by using the Fitness–Distance Balance (FDB) method with its abilities. Then, the algorithm developed with a hyper-heuristic method to create the beginning optimal population by using Linear Population Reduction Success-History based Adaptive Differential Evolution (LSHADE). Finally, the developed algorithm has been applied for solving optimal placement and sizing of facts devices for optimal power flow problem incorporating wind energy source. The obtained results showed that the proposed algorithm is more effective solver for the problems cases while compared to the literature.

Flexible surgical robots are emerging as advanced tools for minimally invasive surgeries, offering greater versatility compared to traditional rigid robots. Unlike commercial endoscopes, the overtube should remain fixed to maintain stability, ensure a clear field of view, and allow surgical tools to perform tasks efficiently. While constant curvature bending of the overtube is sufficient for some lesions, certain lesions require the overtube to bend into specific shapes to achieve appropriate positioning. Various methods for creating different bending shapes have been proposed in previous research, typically involving connecting multiple segments. However, this approach complicates control and reduces both space and cost efficiency. This study proposed a conceptual method for adding a shaping tendon to control the bending shape and mathematically analyzed the effect of this shaping tendon, inserted along an arbitrary path in addition to the main driving tendons for constant curvature bending, on the bending shape of the hyper-redundant manipulator with rolling joints. The overall system was modeled and analyzed from an energy perspective, and the validity of the proposed mathematical modeling was verified through comparison with results obtained from physical experiments. In addition, it was identified that the design parameter determining the tendon path is significant element in defining bending shape of the overtube.

The hyperspectral vegetation index was defined based on the distinctive features of the spectral curve. In alignment with the growth and development characteristics of cotton, the spectral reflectivity of the cotton canopy was computed at different growth stages. The aim of this study was to clarify the association between cotton yield and canopy spectral indices and to develop yield estimation models utilizing hyperspectral imaging. The ASD Field Spec Pro VNIR 2500 spectrometer radiometer was employed to collect spectral reflectance data from cotton canopies at various growth stages. Using spectral analysis techniques, quantitative models were developed based on hyper-spectral vegetation indices, including Normalized Difference Vegetation Index (NDVI) (NDVI) and Radar Vegetation Index (RVI) to extract characteristic information from the cotton canopies. Following thorough testing and precise monitoring of the estimation models, the most optimal models representing cotton canopy structure parameters were identified. Results demonstrate that the power function model, relying on NDVI, provides the most accurate forecasting for Leaf Area Index (LAI)). Additionally, the exponential function model based on RVI proves to be the most effective for predicting cotton unit area above-ground fresh biomass, while another exponential function model based on RVI is identified as the best for predicting cotton unit area above-ground fresh biomass. Clearly, the application of hyper-spectral remote sensing technology enables the analysis, simulation, assessment, and providing scientific basis for precision cotton planting and cotton field management strategies.

In this paper, a relatively new hyper convolution spectra for characterization liquid, viscoelastic and solid samples is presented. Special attention is paid to the biophysical characterization of epithelial tissues and early detection of cancer of the skin, cervix, colon, and oral cavity. The method is based on the use of two types of white light, diffuse and polarized, from the same LED light sources. Based on the subtraction of the intensity values of these two lights and using the hyper convolution algorithm, the ratio of paired and unpaired electrons of tissue is obtained. This ratio correlates well with the state of the tissue: normal, irritating, precancerous, and cancerous. First, a proof-of-concept studies were performed, and later clinical studies on samples from one thousand two hundred fifteen people were performed. It showed that hyper Opto-Magnetic Imaging Spectroscopy (OMIS) can detect epithelial tissue cancers with an accuracy of 85-96%. Bearing in mind that the OMIS method also acquires the biophysical characteristics of the deeper skin layers (epidermis, basement membrane, dermis) by analysing convolution spectra of RGB channels of both diffuse and polarized white light, it is possible to apply this method in cosmetics (skin hydration, collagen, and elastin states, etc.). During OMIS applications, we noticed places where improvements could be made to increase method’s accuracy using advanced machine learning methodologies.

Hyper duplex stainless steels, HDSS, are a new alloy group of duplex stainless steels with the highest corrosion resistance and mechanical properties among the existing modern stainless steel. Due to the addition of extra high content of alloying elements, e.g. Cr, Ni, Mo, etc., the crystallization behavior of the δ-ferrite from the liquid is of vital importance for controlling the steel properties. In this work, the effect of cooling rate (i.e. 4°C/min and 150 °C/min) on the growth process of δ-ferrite in S33207 during the solidification process was investigated using high-temperature confocal scanning laser microscopy (HT-CLSM) in combination with electron microscopes and thermodynamic calculation. The results showed that the solidification mode of S33207 steel was a ferrite-austenite type (FA mode). L→δ transformation occurred at a certain degree of supercooling, and merging occurred during the growth of δ phase dendrites. Similar microstructures were observed after solidification under these two different cooling rates. The variation of area fraction of δ ferrite at the free surface and temperature as well as time during solidification of S33207 steels were calculated at different cooling rates of 4 °C/min and 150 °C/min, respectively. The current HT-CLSM study provides in-situ experimental evidence to confirm that a low cooling rate favored the growth of primary δ-ferrite, whereas a high cooling rate favored the nucleation of primary δ-ferrite during the solidification process. The post-microstructure as well as composition evolution is also briefly investigated. This work shed light on the real time insights for the crystallization behavior of hyper duplex stainless steels during solidification, which aims to contribute to the process control of manufacturing of this steel grade.

Low pressure fluid transport (1) applications often require low and precise volumetric flow rates (2) including low leakage to reduce additional costly and complex sensors. A peristaltic pump de-sign (3) was realized, with the fluid’s flexible transport channel formed by a solid cavity and the wobbling plate comprising a rigid and a soft layer (4). In operation, the wobbling plate is driven externally by an electric motor, hence, the soft layer is contracted and unloaded (5) during pump-cycles transporting fluid from low to high pressure sides. A thorough characterization of the pump system is required to design and dimension the components of the peristaltic pump. To capture all these parameters and their dependencies on various operation-states, often complex and long-lasting dynamic 3D FE-simulations are required. We present, here, a holistic design methodology (6) including analytical as well as numerical calculations, and experimental valida-tions for a peristaltic pump with certain specifications of flow-rate range, maximum pressures, and temperatures. An experimental material selection process is established and material data of candidate materials (7) (liquid silicone rubber, acrylonitrile rubber, thermoplastic-elastomer) are directly applied to predict the required drive torque. For the prediction, a semi-physical, analyti-cal model was derived and validated by characterizing the pump prototype.

The increasing prevalence of spinal disorders and the subsequent rise in spinal fusion surgeries stress the necessity for optimizing spinal fusion cages, crucial for stabilizing the spine and supporting osseointegration. Despite the widespread attempts at material modifications and surface enhancements to improve these devices, failure rates and complications remain significant. This research explores an imaginitive approach to enhancing spinal fusion cages through the application of geometric tiling designs, a method scarcely employed . The study systematically investigates the potential of triangular, diamond, and hexagonal tiling patterns to improve the structural integrity and capability for osseointegration of spinal fusion cages. Through a finite element analysis simulation, each design's ability to withstand multi-directional loads and effectively distribute stress was tested under simulated conditions that mimic the complexities of spinal motion. Preliminary findings in fields of engineering indicate that geometric tiling can significantly enhance the load-bearing capabilities and stress distribution of spinal fusion cages, potentially reducing the likelihood of implant subsidence and failure. The triangular and hexagonal designs, in particular, demonstrate superior performance in maintaining structural stability under axial and anterior compressive forces compared to traditional cage designs. This research opens a new pathway for the development of more durable and efficient spinal fusion cages. By leveraging the structural advantages of geometric tiling, future spinal implants could achieve better clinical outcomes, leading to improved patient recovery and reduced rates of complications.

Liquidity providers for asset-pair pools with constant value distri- bution, such as Balancer pools, experience some impermanent loss whenever there is price divergence in the tokens’ fiat values. In this paper, we model this impermanent loss for geometric mean invariant pools by deriving a function of two parameters. We analyze our function graphically, showing that unevenly distributed pools with large weighting disparities best mitigate the risk of impermanent loss. We conclude by providing a general protocol for liquidity providers to choose a suitable pool based on their risk tolerance and profit goals.

Visual inertial SLAM algorithms enable robots to autonomously explore and navigate in unknown scenes. However, most of the current SLAM systems highly rely on static environment assumptions, which fails in the exsitence of motional objects in the real environment. To improve the robustness and localization accuracy of SLAM systems in dynamic scenes, this paper proposes a visual-inertial SLAM framework that fuses semantic and geometric information, called DA-VINS. First, this paper presents a dynamic object classification method based on feature’s current motion state, which obtains temporary static features in the environment. Secondly, a features dynamics check module based on IMU prior and adjacent frame’s geometry constraint is designed to calculate dynamic factors. It also verifies the classification results of temporary static features. Finally, a dynamic adaptive bundle adjustment module based on the features’ dynamic factors is designed to adjust the weights of features in nonlinear optimization. We evaluated our method in public and our dataset. The results show that D-VINS is one of the most real-time, accurate, and robust systems in dynamic scenes.

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

Correlation between the category richness (CR) and morphological diversity (MD) of some communities at a local scale was found pendent, however, examination of a whole category using a large dataset are lacking. In this study, 1119 jewel species from around the world representing all existing subfamilies and 33.78% of Buprestidae genera were selected as a test group. A geometric morphometric analysis on the contour of homologous traits: pronotum and elytra was conducted to quantify morphological diversity. Correlations between MD and CR among subfamilies were found to be consistently positive with the exceptions of a pronotum genus-level test on the subfamily category. The correlation was also found to be higher at the genus-level than it on the species-level, in both pronotum and elytron measurements. Based on our analyses the hypothesis of positive correlations was expected in the genus-level test of jewel beetles but rejected in species-level test. The inconsistent correlation between morphological diversity and species richness revealed convergent morphological variation of pronotum under the similar functional diversity in Buprestidae. In addition, our test revealed variable correlation between MD and CR based on different groups and characters, which might be caused by morphological changes under coevolution with different ecological factors.

The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler-Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations.

Membrane materials are most widely applied in construction engineering with small mass and high flexibility, it presents strong geometric nonlinearity in the process of vibration. In the paper, an improved multi-scale perturbation method is used to solve the aeroelastic stability of closed and open membrane roofs for quantify the effect of geometric nonlinearity on the single-mode aeroelastic instability wind speed of membrane roofs. The results show that the critical wind speed values of the two models are small when the geometrical nonlinearity of membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of membrane on the aerodynamic stability of roof can be neglected, However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of membrane roof. The results obtained in this paper have important theoretical reference value for the design the membrane structures.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.

Within the genus Macrolophus (Heteroptera: Miridae), the species M. costalis (Fieber), M. melanotoma (Costa) and M. pygmaeus (Rambur) are present in the Mediterranean region on a wide variety of plant species. While M. costalis can easily be separated from the other two by the black tip at the scutellum, M. pygmaeus and M. melanotoma are cryptic species, extremely similar to one another in external traits, which have resulted in misidentifications. M. pygmaeus is an efficient biological control agent, both in greenhouse and field crops. The misidentification of these cryptic species could limit the effectiveness of biological control programs. Although morphology of the left paramere of the male genitalia has been used as a character for identification of these two cryptic species, there is controversy on the reliability of this character as a taxonomic tool for these species. Using geometric morphometric techniques, which are a powerful approach in detecting slight shape variations, the left parameres from these three Macrolophus species were compared. The paramere of M. costalis was larger and had a different shape than that of M. melanotoma and M. pygmaeus; however, no differences in size or shape were found between the left paramere of M. melanotoma and that of M. pygmaeus. Therefore, our results confirm that this character is too similar and it cannot be used to discriminate between these two cryptic species.

This paper aims to explore the relationship between airfoil deformation and airfoil aerial-aquatic adaptation. The form of “flexible skin and rigid drive structura” holds immense potential for various applications. In this study, we utilize the B-spline method to parametrically describe the airfoil shape. An airfoil deformation parameterization method is proposed based on the isogeometric method. This method allows us to depict airfoil deformation as the position and displacement of the driving point, enabling an expression of the flexible skin's deformation driven by the internal structure. We utilize the Xfoil application and Gaussian regression method to elucidate the relationship between driving point position and displacement and the airfoil's dynamic performance. Additionally, we employ the Sobol method to assess the sensitivity of the driving point variables to the airfoil's dynamic performance. Our findings indicate that the attack angle of the airfoil exhibits the highest sensitivity index to the airfoil's dynamic performance. Furthermore, variables of the driving point situated at the leading and trailing edges of the lower surface significantly impact the airfoil lift coefficient, those located at the mid-section of the upper surface have a considerable effect on the airfoil drag coefficient.

In this article it is shown, first, that a change of basis in Minkowski space is equivalent to a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. Second, that such mixed bases can be interpreted as a measurement system used by local, flat observers whose direct distance measurements are restricted to an (n−1)-dimensional submanifold in an n-dimensional Euclidean space. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean space measures a Minkowski spacetime. This interpretation could be useful for theories in special relativity and related fields that rely on spacetime concepts, as it offers a more intuitive geometric understanding of the Minkowski metric.

A two-way coupled model between polydisperse particle phases with compressible gases and a density-based coupling implicit solution method combining the third-order MUSCL with QUICK spatial discretization scheme and the second-order temporal discretization scheme are constructed based on the discrete-phase model (DPM) and the stochastic wander model (DRWM) in the Eu-lerian-Lagrangian framework in conjunction with a unitary particulate source (PSIC) approach and the SST k-ω turbulence model. The accuracy of the numerical prediction method is verified using previous supersonic nozzle gas-solid two-phase flow experiments. Numerical simulation of two-phase jet of dry powder extinguishing agent gas with pilot-type supersonic nozzle was carried out to analyze the influence of geometrical parameters such as length ratio rL and area ratio rA of main nozzle on the two-phase flow field as well as on the jet performance indexes such as particle mean velocity vp,a, velocity inhomogeneity Φvp, particle dispersion Ψp, particle mean acceleration ap,a and so on. By analyzing the parameters, we indicate the requirements for the combination of jet performance metrics for different flame types such as penetrating, spreading, and dispersing.

Cantilever beams are the most widely used form of strain-driven energy harvesting, which uses piezoelectric materials. Although researchers are constantly seeking improved power output from cantilever-beam-driven piezoelectric energy harvesters, a systematic and fundamental analysis of the effect of beam geometry on the power capacity of energy harvesters warrants further investigation. Most of the previous research accounts for beams that are fully coated with piezoelectric material. While a larger coating area increases energy output, it also escalates costs as piezoelectric materials are very expensive. Considering the high cost of piezoelectric materials when dealing with limited piezoelectric material, enhancing power output can be achieved by employing a larger base beam and coating a portion of it at the fixed end. As such, the aim of this work is to investigate a wide variety of cantilever beam shapes (e.g., trapezoidal, triangular, V-cut, concave, and convex) with partial piezoelectric material coating on the base beam to maximize the power output capacity of the harvester. To ascertain a comparable argument, the surface area, volume, and mass of all the considered beam shapes are kept consistent, as these parameters influence the power output of the harvester. The geometry of each shape is systematically varied to understand the effect of geometric configuration on the output power density. Finally, the power capacities of all types of beams are compared, and a design is proposed to obtain the maximum power output. It was found that when the surface area of both the beam and piezoelectric material is kept constant and piezoelectric material is located at the fixed end, a trapezoidal beam with a smaller base width and larger free end width is the most efficient in generating power as long as the structural integrity is maintained. The finding is completely opposite as was suggested by previous studies, which proposed that a trapezoidal beam with a smaller free end yields higher output. Instead, this study demonstrates that an inverted trapezoidal beam produced higher output, considering partial coating compared to the full beam coating used in previous studies. Additionally, a correlation is presented on how the beam resonance frequency shifts with variation in beam parameters.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

Radiation Fireballs are singular phenomena which involve severe thermal radiation and consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects have frequently posed a difficult analytical instance, mainly due to its specific configuration. In this article, since the usual solving equations for the said cases are impractical, the authors propose a novel graphic-algorithm method that sorts the problem efficiently for different kinds of obstructions and relative positions of the fireball and the defenses. Adequate application of this method may improve the safety of a significant number of facilities exposed to such risks.

Deficient wound healing is frequently observed in patients diagnosed with diabetes, a clinical complication that compromises mobility and leads to limb amputation, decreasing patient autonomy and family lifestyle. Fibroblasts are crucial for secreting the extracellular matrix to pave the wound site for endothelial and keratinocyte regeneration. The biosynthetic pathways for collagen production are one of the main components of the extracellular matrix, as the crosslinking of extracellular collagen fibers is intimately related to fibroblast redox homeostasis. In this study, human dermic fibroblasts were cultured with 1 mM sodium selenite (inorganic) and 1 mM of two selenium amino acids (organic), Se-cysteine and Se-methionine. This concentration was compatible with long-term exposure necessary for extracellular matrix production and allowed us to examine the impact of these three compounds on the state and response of the thiol-based HyPer biosensor expressed in the cytoplasm. In addition, the abundance of extracellular matrix and ultrastructural properties were evaluated by Picrus Sirius red staining and scanning electronic microscopy, respectively. We also evaluated whether these selenium compounds effectively ameliorated the perturbations induced by culturing fibroblasts at high glucose levels (25 mM) regarding cytoplasmic redox, extracellular matrix, and glycation on collagen fibers. Our results indicate that cytoplasm protein oxidation was sensitive to selenium compound supplementation. Selenium amino acids increased the sensitivity to protein oxidation, and only Se-cysteine increased the disulfide bond reduction in fibroblasts maintained in high glucose. Despite the lack of effect of selenium compounds on the glu-cose-induced increase in matrix fiber thickness, we found that endothelial migration improved in the matrix generated by high glucose-cultured fibroblasts.

The soil and groundwater of Bhagobangola I block of Murshidabad district, West Bengal, India is severely arsenic contaminated. A bacterium was isolated from the garden soil of Mahishasthali village, which could tolerate 36.49 mM arsenic (III), 280.44 mM arsenic (V) and 63 mM chromium (III), which makes it arsenic (III & V) and chromium (III) hyper-tolerant bacterium. The growth pattern of this bacterium does not show much alteration in presence of 10 mM arsenic (III) and chromium (III), emphasizing its resistance to these heavy metals. Scanning electron microscopy depicted the size of this bacterium to be ~1.45 µm. 16S rDNA sequencing followed by subsequent phylogenetic analysis established the identity of this bacterium as Microbacterium paraoxydans. The bacterium is capable of bioremediation of arsenic and showed 30.8% & 22.6%, and 35.2% and 30.5% of bioremediation over a period of 24 and 48 hours in 1 mM and 4 mM arsenite, respectively. Microbacterium paraoxydans also exhibit plant growth promoting properties like nitrogen fixation, phosphate solubilization, indole-3-acetic acid production and production of siderophores. Therefore, the heavy metal resistance, bioremediation potential and plant growth promoting potential of the bacterium could be utilized not only for reduction of arsenic toxicity in soil and groundwater but also for plant growth promotion by using it as a biofertilizer.

Genetic Programming (GP) is a powerful Machine Learning (ML) algorithm that can produce readable white-box models. Although successfully used for solving an array of problems in different scientific areas, GP is still not well known in Remote Sensing. The M3GP algorithm, a variant of the standard GP algorithm, performs Feature Construction by evolving hyper-features from the original ones. In this work, we use the M3GP algorithm on several sets of satellite images over different countries to create hyper-feature from satellite bands to improve the classification of land cover types. We add the evolved hyper-features to the reference datasets and observe a significant improvement of the performance of three state-of-the-art ML algorithms (Decision Trees, Random Forests and XGBoost) on multiclass classifications and no significant effect on the binary classifications. We show that adding the M3GP hyper-features to the reference datasets brings better results than adding the well-known spectral indices NDVI, NDWI and NBR. We also compare the performance of the M3GP hyper-features in the binary classification problems with those created by other Feature Construction methods like FFX and EFS.

Hyper spectral imaging (HSI) is a technique that is used to obtain the spectrum for each pixel in the image. It helps in finding objects and identifying materials etc. Such an identification is very difficult using other imaging techniques. It allows the researchers to investigate the documents without any physical contact. Nowadays detection of unequal Ink mismatch based on HSI has shown vast improvement in distinguishing the inks. Detection of unequal Ink mismatch is an unbalanced clustering problem. This paper used K-means Clustering for ink mismatch detection. K-means Clustering find same subgroups in the data based on Euclidean distance. This paper demonstrates performance in unequal Ink mismatch based on HSI.

. Interconnected control systems (ICS) widely apply to various technical systems. ICS has a complex description. Therefore, simplified models use, which the specifics of an object do not always reflect. So, the problem of synthesizing mathematical models is topical. The work purpose is to develop an approach to obtaining models in conditions of incomplete a priori information. We use an adaptive approach. As examples, two-channel systems (TCS) with cross-links and identical channels consider, and a method for mathematical model design. We consider the system with asymmetric cross-links and evaluate their impact on properties of an adaptive identification system. Approach proposed to assessing the TCS identifiability with cross-links. The excitation constancy influence on TСS parameter estimates is studied. A generalization of the proposed approach is given for an interconnected system.

The structural identification (SI) problem of control objects has not been solved. The formalization and interpretation complexity of the structure concept is the main problem. In identification systems, the form of the model (its structure) choice is intuitive and bases on the experience and knowledge of the researcher in most cases. The task of parametric identification is often interpreted as SI. It introduces certain confusion in understanding of the task and decision-making. This is two different areas of research. The structural identification problem is multifaceted and includes many subtasks, and their solution gives the final result. Some tasks have been solved. The purpose of this work is to review existing approaches and methods to the structural identification problem of control objects from a system perspective. It is necessary to give the SI problem statement at the multiple-informational level to reflect the difficulties of formalizing SI. New directions to analyse that were not SI areas until now.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

Rare-earth tetraborides RB4 are of great interest due to the occurrence of geometric magnetic frustration and corresponding unusual magnetic properties. While the Gd3+ spins in GdB4 align along the ab plane, Er3+ spins in the isomorphic ErB4 are confined to the c–axis. The magnetization in the latter exhibits a plateau at the midpoint of the saturation magnetization. Therefore, solid solutions of (Gd, Er)B4 provide an excellent playground for exploring the intricate magnetic behavior in these compounds. Single crystals of Gd(1-x)Erx B4 (x = 0, 0.2, and 0.4) were grown in aluminum flux. X-ray diffraction scans revealed single phase materials, and a drop in the unit cell volume with increasing Er content, suggesting the partial substitution of Er at the Gd sites. Heat capacity measurements indicated a systematic decrease of the Néel temperature (TN) with increasing Er content. The effective magnetic moment determined from the magnetization measurement agreed with the calculated free-ion values for Gd3+ and Er3+, providing further evidence for the successful substitution of Er for Gd. The partial substitution resulted in an anomalous ferromagnetic phase below TN, exhibiting significant anisotropy, predominantly along the c-axis. This intriguing behavior merits further studies of the magnetism in the Gd(1-x)ErxB4 borides.

Owing to the advantages of cost-effectiveness, compactness, and the avoidance of complicated camera synchronization, single-camera three-dimensional (3D) digital image correlation (DIC) techniques have gained increasing attention for deformation measurement of materials and structures. In the traditional single-camera 3D-DIC system, the left and right view images can be recorded by a single camera using a diffraction grating, a bi-prism or a set of planar mirrors. To further improve the measurement accuracy of single-camera 3D-DIC, this paper introduces a single-camera four-view imaging technique by installing a pyramidal prism in front of the camera. The 3D reconstruction of the measured points before and after deformation is realized with eight governing equations induced by four views, and the strong geometric constraints of four views can help to improve the measurement accuracy. A static experiment, a rigid body translation experiment and a four-point bending experiment show that the proposed single-camera 3D-DIC method can achieve higher measurement accuracy than the dual-view single-camera 3D-DIC techniques and has advantages in reducing both random error and systematic error.

Reasonable trajectory planning is the precondition for the parafoil airdrop system to achieve autonomous accurate homing and safe landing. In order to successfully realize the self-homing of the parafoil airdrop system, a new trajectory optimization design scheme is proposed in this paper. The scheme is based on the parafoil's unique flight and control characteristics and adopts a segmented homing design. Compared with the current common trajectory design method, its core feature is to avoid the problem that the straight-line flight distance before landing is limited by the radius of the height-reducing area and ensure landing accuracy and safety. Firstly, the different starting states of the parafoil airdrop system and the landing requirements were comprehensively considered, and the homing trajectory is reasonably segmented. Based on the requirements of energy control, stable flight, and landing accuracy, the optimal objective function of the trajectory was established, and the trajectory parameters, calculation methods, and constraints were given. Secondly, the cuckoo search algorithm was applied to optimize the objective function to obtain the final home trajectory. Finally, the trajectory planning under different airdrop conditions was simulated and verified. The results showed that the planned trajectories could reach the target point accurately and meet the flight direction requirements, proving the proposed scheme's correctness and feasibility.

During the few years, various algorithms have been developed to extract features from high-resolution satellite imagery. For the classification of these extracted features, several complex algorithms have been developed. But these algorithms do not possess critical refining stages of processing the data at the preliminary phase. Various satellite sensors have been launched such as LISS3, IKONOS, QUICKBIRD, and WORLDVIEW etc. Before classification and extraction of semantic data, imagery of the high resolution must be refined. The whole refinement process involves several steps of interaction with the data. These steps are pre-processing algorithms that are presented in this paper. Pre-processing steps involves Geometric correction, radiometric correction, Noise removal, Image enhancement etc. Due to these pre-processing algorithms, the accuracy of the data is increased. Various applications of these pre-processing of the data are in meteorology, hydrology, soil science, forest, physical planning etc. This paper also provides a brief description of the local maximum likelihood method, fuzzy method, stretch method and pre-processing methods, which are used before classifying and extracting features from the image.

This paper introduces new improvements to the modified version of the BIRECT (BI secting RECTangles) algorithm referred to as BIRECTv. We explore various approaches, by first including a grouping strategy for hyper-rectangles having almost the same sizes by categorizing them into different classes. Therefore constraining them not to exceed a certain pre-defined threshold (a small positive value to define the tolerance level). This approach allows for more efficient computation and can be particularly useful when dealing with a large number of hyper-rectangles with varying sizes. To avoid over-sampling, and preventing redundant or excessive sampling, at some shared vertices in descendant subregions, a particular vertex database is used to limit the number of samples taken within each subregion to two. The experimental investigation shows that these improvements have a positive impact on the performance of the BIRECTv(imp.) algorithm and the proposal is a promising global optimization algorithm compared to the original BIRECTv algorithm and its variants. Additionally, the BIRECTv(imp.) algorithm showed particular efficacy in solving high-dimensional problems.

U-Net, based on a deep convolutional neural network (CNN), has been clinically used to au-to-segment normal organs and potentially target volumes. However, CNNs with local geometric dependencies may limit the accuracy of segmentation. Additionally, the performance of CNNs can vary depending on the selection of network hyper-parameters, which was mitigated by the proposition of nnU-Net. We chose a vision transformer architecture called VT U-Net, which features a self-attention excluding the convolution layer, to overcome the limitations of CNNs by utilizing global geometric information of images. The VT U-Net v.2 became more powerful thanks to the adaptive hyper-parameter optimizer embedded in nnU-Net. However, despite leveraging the benefits of nnU-Net, VT U-Net v.2 still had additional network hyper-parameters that needed to be optimally chosen. Accordingly, among various hyper-parameters, this study attempted to find the optimal combination of the patch size and the embedded dimension regarding the transformer. From the 4-fold cross-validation, the modified VT U-Net v.2 showed the highest average performance for planning target volume (PTV) segmentation among the investigated networks. Though nnU-Net was based on convolution layers, the adaptive hyper-parameter optimizers turned out to enhance the performance. It was also confirmed that network hyper-parameters affected the segmentation accuracy of vision transformers.

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

This research paper presents a deep learning approach to early detection of skin cancer using image augmentation techniques. The authors propose a two-stage image augmentation technique that involves the use of geometric augmentation and generative adversarial network (GAN) to classify skin lesions as either benign or malignant. This research utilized the public HAM10000 dataset to test the proposed model. Several pre-trained models of CNN were employed, namely Xception, Inceptionv3, Resnet152v2, EfficientnetB7, InceptionresnetV2, and VGG19. Our approach achieved accuracy, precision, recall, and F1-score of 96.90%, 97.07%, 96.87%, 96.97%, respectively, which is higher than the performance achieved by other state-of-the-art methods. The paper also discusses the use of SHapley Additive exPlanations (SHAP), an interpretable technique for skin cancer diagnosis, which can help clinicians understand the reasoning behind the diagnosis and improve trust in the system. Overall, the proposed method presents a promising approach to automated skin cancer detection that could improve patient outcomes and reduce healthcare costs.

Understanding the binding behavior and conformational dynamics of intrinsically disordered proteins (IDPs) is crucial for unraveling their regulatory roles in biological processes. However, their lack of stable 3D structures poses challenges for analysis. To address this, we propose an algorithm that explores IDP binding behavior with protein complexes by extracting topological and geometric features from the protein surface model. Our algorithm identifies a geometrically favorable binding pose for the IDP and plans a feasible trajectory to evaluate its transition to the docking position. We focus on IDPs from Homo sapiens and Mus-musculus, investigating their interaction with the Plasmodium Falciparum (PF) pathogen associated with malaria-related deaths. We compare our algorithm with HawkDock and HDOCK docking tools for quantitative (computation time) and qualitative (binding affinity) measures. Our results indicate that our method outperforms the compared methods in computation performance and binding affinity of experimental conformations.

Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and potentially accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.

Cryptocurrencies like Bitcoin rely on a proof-of-work system to validate transactions and prevent attacks or double-spending. A new proof-of-work is introduced which seems to be the first number theoretic proof-of-work unrelated to primes: it is based on a new metric associated to the Collatz algorithm whose natural generalization is algorithmically undecidable: the inflation propensity is defined as the cardinality of new maxima in a developing Collatz orbit. It is numerically verified that the distribution of inflation propensity slowly converges to a geometric distribution of parameter $0.714 \approx \frac{(\pi - 1)}{3}$ as the sample size increases. This pseudo-randomness opens the door to a new class of proofs-of-work based on congruential graphs.

Vascular endothelial growth factors (VEGFs) are regarded as the key vasculogenic mediators in the human body, of which VEGF-A is considered as one of the important types. It is the major growth factor possessing increasing vascular permeability as well as angiogenesis properties. This article provides intuition into the different effects of VEGF-A on vessels in ovarian hyper stimulation syndrome (OHSS) which is defined as a complication of in-vitro fertilization for infertility treatment, and obesity, a universally health problem. These are two dissimilar pathways outcomes for VEGF-A effects, thereby This article reviews updated information about the mentioned disorders and reveals that how this kind of growth factor yields different results on vasculature by activating distinct intracellular signaling in endothelial cells.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

This paper presents an advanced methodology for processing radar imagery stacks using Persistent Scatterer and Distributed Scatterer Interferometry (PSDS) to enhance spatial coherence and improve displacement detection accuracy. The workflow leverages Level 2 Coregistered Single Look Complex (L2-CSLC) images generated by the open-source COMPASS (COregistered Multi-temPorAl Sar SLC) framework in combination with the Combined eigenvalue maximum likelihood Phase Linking (CPL) approach as implemented in MiaplPy. Starting the analysis directly from Level 2 products offers a significant advantage to end-users, as they simplify processing by being pre-geocoded and ready for immediate analysis. Additionally, the open-source nature of the workflow and the use of L2-CSLC products simplify the processing pipeline, making it easier to distribute directly to users for practical applications in monitoring infrastructure stability in dynamic environments. The ISCE3-MiaplPy workflow is compared against ISCE2-MiaplPy and the European Ground Motion Service (EGMS) to assess its performance in detecting infrastructure deformation in dynamic environments, such as the Algeciras port. Results indicate that ISCE3-MiaplPy delivers significantly denser measurements, albeit with increased noise, compared to its counterparts. This higher resolution enables a more detailed understanding of infrastructure stability and surface dynamics, which is critical for environments with ongoing human activity or natural forces.

The Range–Doppler (R-D) model is extensively employed for the geometric processing of Synthetic Aperture Radar (SAR) images. Refining the sensor motion state and imaging parameters is the most common method for achieving high-precision geometric processing using the R-D model, comprising a process that involves numerous parameters and complex computations. In this study, we introduce a novel approach to improve the positioning accuracy of the R-D model, implementing a low-order polynomial to compensate for the original imaging errors without altering the initial positioning parameters. We also design low-order polynomial compensation models with different parameters. The models are evaluated on various SAR images from different platforms and bands, including spaceborne TerraSAR-X and GF3-C images, manned airborne SAR-X images, and unmanned aerial vehicle-mounted miniSAR-Ku images. Furthermore, image positioning experiments involving the use of different polynomial compensation models and various numbers and distributions of Ground Control Points (GCPs) are conducted. The experimental results demonstrate that geometric processing accuracy comparable to that of the classical rigorous positioning method can be achieved even when applying only an affine transformation model to the images. Compared to classical refinement models, however, the proposed image-compensated R-D model is much simpler and easy to implement. Thus, this study provides a convenient, robust, and widely applicable method for the geometric positioning processing of SAR images, offering a potential approach for the joint-positioning processing of multi-source SAR images.

More than fifty million people over the age of fifty have osteoporosis issues due to low bone mass, disease contribution, and not exercising continuously. Certain most important risk factors and causes of osteoporosis contain age, gender, hormones, visits to inexperienced doctors, and certain medical conditions. In this manuscript, we diagnosed certain frank operational laws under the availability of complex intuitionistic fuzzy (CIF) information. Furthermore, using the evaluated operational laws, we pioneered the theory of CIF frank weighted averaging (CIFFWA), CIF frank ordered weighted averaging (CIFFOWA), CIF frank hybrid averaging (CIFFHA), CIF frank weighted geometric (CIFFWG), CIF frank ordered weighted geometric (CIFFOWG), CIF frank hybrid geometric (CIFFHG) operators, and described their beneficial and valuable results with certain useful properties. Moreover, we aim to evaluate the most dangerous type of osteoporosis based on their symptoms, causes, and risk factors using diagnosed approaches. Finally, to enhance the worth of the evaluated operators, we compare the diagnosed result with certain prevailing results and illustrated their geometrical representation with the help of MATLAB.

Today’s purchasing companies demand an advanced buyer equal of enactment from their supplier while the two parties maintain a respectful connection. Although the supplier selection (SC) product life cycle cost (SCPLCC) is an important consideration among corporations, SCPLCC problem has become associated with deciding how one supplier should be selected from possible alternatives. In this study, we applied two types of goal programming, multiobjective linear programming and revised multichoice goal programming to develop a PLCC-based concept to solve the SCPLCC problem and construct a decision-making tool for application to a case of supply chain management in a Taiwanese light-emitting diode company in the high-tech industry. Our study main contribution Company managers can easily use the two approaches of the SCPLCC model with different parameters to solve SCPLCC model problems. Finally, we comparing five models found RMCGP with weighted linear goal programming had an adequate effect for application to the PLCC concept for high-technology comapny; this cloud make company decision–makers focus on low PLCC and select better supplier.

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e. in all real world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.

Full waveform (FW) LiDAR holds great potential for retrieving vegetation structure parameters at a high level of detail, but this prospect is constrained by practical factors such as lack of available handy processing tools and technical intricacy of waveform processing. This study introduces a new product, named the Hyper Point Cloud (HPC) derived from FW LiDAR data, and explore its potential applications such as tree crown delineation using the HPC-based intensity and percentile height (PH) surfaces, which show a promising solution to the constraints of using FW LiDAR data. Results of the HPC present a new direction to handle FW LiDAR data and offer prospects for studying the mid-story and understory of vegetation with high point density (~ 182 points/m2). The intensity-derived digital surface model (DSM) generated from the HPC shows that the ground region has larger maximum intensity (MAXI) and mean intensity (MI) than the vegetation region while having smaller total intensity (TI) and number of intensities (NI) at the given grid cell. Our analysis of intensity distribution contours at individual tree level exhibit similar patterns, indicating that the MAXI and MI are decreasing from the tree crown center to tree boundary while a rising trend is observed for TI and NI. These intensity variable contours provide a theoretical justification for using HPC-based intensity surfaces to segment tree crowns and exploit their potential for extracting tree attributes. The HPC-based intensity surfaces and the HPC-based PH Canopy Height Models (CHM) demonstrate promising tree segmentation results comparable to the LiDAR derived CHM for estimating tree attributes such as tree locations, crown widths and tree heights. We envision that products such as the HPC and the HPC-based intensity and height surfaces introduced in this study can open new perspectives to use FW LiDAR data and alleviate the technical barrier of exploring FW LiDAR data for detailed vegetation structure characterization.

If "quantization is an art" then it can be greatly rened by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we can demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.

We explore several ways, in order to include fermionic structures naturally in a physical theory in C⁴. We begin with the standard Dirac formalism and we proceed by using Cartan's property of triality as a second option. Afterwards, we suggest a new approach (in a preliminary basis), by introducing an 1-linear form, as the "square root of the geometry" derived by the usual 2-linear forms (quadratic forms). Keeping this way, we introduce n-linear forms, in order to formulate a new geometric structure, which could be suitable for the formulation of a pure geometric unied theory.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

To cope with the complexity, the digital transformation of cyber-physical and socio-technology systems demands the utilization of heterogeneous tailorable development environments with dynamic configuring ability and transparent integration of independently developed dedicated frameworks. Hyper-frameworks, aka Framework-of-Frameworks, correspond to the System-of-Systems paradigm and designate a software-supported, meta-model-based generator of executable configurations. Armed with a meta-modeling layer, the incremental development of hybrid architecture instances focuses on language-based models and their transformations into functional, interpretable environments. Data-driven reasoning and decision support for the entire life cycle of digitally transformed systems critically depends on the effectiveness of involved generative mechanisms and the trustworthiness of related information resources. The Architecture, Meta-Configuration, and Information Resource Handling are the essential segments of the initial version of the proposed evolution prototype. In this article, we formulate five essential hypotheses founding the proposed digital transformation hyper-framework project that integrates the framework model with a meta-configuration-based generative mechanism. The Life Cycle Modeling component framework creatively integrates System, Software, and Operation Engineering. Specification and development of the additional component frameworks, in compliance with specified generative mechanisms, direct further refinements of the proposed Hyper-framework.

Hyper-radiosensitivity (HRS) is the increased sensitivity to low doses of ionizing radiation observed in most cell lines. We previously demonstrated that HRS is permanently abolished in cells irradiated at a low dose rate (LDR), in a mechanism dependent on transforming growth factor β3 (TGF-β3). In this study, we aimed to elucidate the activation and receptor binding of TGF-β3 in this mechanism. T-47D cells were pre-treated with inhibitors of potential receptors and activators of TGF-β3, along with addition of small extracellular vesicles (sEVs) from LDR primed cells, before their radiosensitivity was assessed by the clonogenic assay. The protein content of sEVs from LDR primed cells was analyzed with mass spectrometry. Our results show that sEVs contain TGF-β3 regardless of priming status, but only sEVs from LDR primed cells remove HRS in reporter cells. Inhibition of the matrix metalloproteinase (MMP) family prevents removal of HRS, suggesting an MMP-dependent activation of TGF-β3 in the LDR primed cells. We demonstrate a functional interaction between TGF-β3 and activin receptor like kinase 1 (ALK1), by showing that TGF-β3 removes HRS through ALK1 binding, independent of ALK5 and TGF-βRII. These results are an important contribution to a more comprehensive understanding of the mechanism behind TGF-β3 mediated removal of HRS.

This study presents an extensive collection of data on the aerodynamic behavior at a low Reynolds number and geometric coefficients for 2900 airfoils obtained through the class shape transformation (CST) method. By employing a verified OpenFOAM-based CFD simulation framework, lift and drag coefficients were determined at a Reynolds number of 10^5. Considering the limited availability of data on low Reynolds number airfoils, this dataset is invaluable for a wide range of applications, including unmanned aerial vehicles (UAVs) and wind turbines. Additionally, the study offers a method for automating CFD simulations that could be applied to obtain aerodynamic coefficients at higher Reynolds numbers. The breadth of this dataset also supports the enhancement and creation of machine learning (ML) models, further advancing research into the aerodynamics of airfoils and lifting surfaces.

This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation was located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the Piecewise-Linear Interface Calculation (PLIC) scheme of the VOF method was performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface was accounted for using the continuum interfacial force (CSF) model. To solve the Navier-Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software were employed. The 3D PLIC-VOF HiG-Flow algorithm was used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation was evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found on the scientific literature. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm was found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. Lastly, the 3D bubble rising problem was simulated for different fluid densities and viscosity’s ratios. Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and the OpenFOAM, DROPS and NaSt3D software. The bubble’s rise velocity and evolution of the bubble’s center of mass is also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with these software.

Since large articulated vehicles have uncertainties in trailer articulation angle as well as dynamic complexity, it is not easy to accurately establish a reliable motion plan. In this paper, two geometric path plans constructed based on the empirical rules of driving experts are presented so that articulated vehicles can automatically perform perpendicular parking on a reverse path. By analyzing the empirical parking methods of professional drivers, these path plans were constructed by appropriately combining several standardized simple basic motions to facilitate implementation in real vehicles. In addition, path plans included appropriate complementary motions to effectively respond to uncertainties arising from articulation angles, etc. The complementary motions developed in this study are based on the results of qualitative analysis on the behavior of articulated vehicles. The usefulness of the proposed articulated vehicle parking method has been proven through hundreds of experimental tests using a 1:10 ratio model automated vehicle.

The search algorithm based on symbiotic organisms’ interactions is a relatively recent bio-inspired algorithm of the swarm intelligence field for solving numerical optimization problems. It is meant to optimize applications based on the simulation of the symbiotic relationship among the distinct species in the ecosystem. The modified SOS algorithm is developed to solve independent task scheduling problems. This paper proposes a modified symbiotic organisms search based scheduling algorithm for efficient mapping of heterogeneous tasks to access cloud resources of different capacities. The significant contribution of this technique is the simplified representation of the algorithm's mutualism process, which uses equity as a measure of relationship characteristics or efficiency of species in the current ecosystem to move to the next generation. These relational characteristics are achieved by replacing the original mutual vector, which uses an arithmetic mean to measure the mutual characteristics with a geometric mean that enhances the survival advantage of two distinct species. The modified symbiotic organisms search algorithm (G_SOS) aimed to minimize the task execution time (Makespan), response, degree of imbalance and cost and improve the convergence speed for an optimal solution in an IaaS cloud. The performances of the proposed technique have been evaluated using a Cladism toolkit simulator, and the solutions are found to be better than the existing standard (SOS) technique and PSO.

Using the PLCC advantages generates revenue and lowers costs more than might be anticipated. It ensures better decisions by using a more perfect and practical assessment of revenues and costs. Although the supplier selection (SC) product life cycle cost (SCPLCC) is an important consideration among corporations, SCPLCC problem has become associated with deciding how one supplier should be selected from possible alternatives. In this study, we applied two types of goal programming, multiobjective linear programming and revised multichoice goal programming to develop a PLCC-based concept to solve the SCPLCC problem and construct a decision-making tool for application to a case of supply chain management in a Taiwanese light-emitting diode company in the high-tech industry. Our study main contribution Company managers can easily use the two approaches of the SCPLCC model with different parameters to solve SCPLCC model problems. Finally, we comparing five models found RMCGP with weighted linear goal programming had an adequate effect for application to the PLCC concept for high-technology company; this cloud make company decision–makers focus on low PLCC and select better supplier.

After developed the formulation of a "general relativity" in C⁴ [2], we proceed with the formulation of a Hamilton-Jacobi equation in C⁴. We argue that in this consideration, the usual problems of the ADM formalism, do not exist, due to the complex time as it exists in our consideration. Specically, we can derive a suitable dispersion relation in order to work with and nd a generalised super Hamiltonian

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

Using Drone Cells to optimize Radio Access Networks is an exemplary way to enhance the capabilities of terrestrial Radio Access Networks. Drones fitted with communication and relay modules can act as Drone Cells. The multi Drone Cell placement problem is solved using an adapted Dispersive Flies Optimization alongside with other meta-heuristic algorithms such as Particle Swarm Optimization and Differential Evolution. A home-brewed simulator has been used to test the effectiveness of the different implemented algorithms. Specific environment respective parameter tuning have been explored to better highlight possible advantages of one algorithm over other in any particular environment. Algorithmic diversity has been explored, leading to several modifications and improvements in the implemented models. The results show that using tuned parameters there is a performance uplift in coverage probability when compared to the default meta-heuristic parameters while still remaining within the constraints implied by the problem’s requirements and resource limitation. The paper concludes by offering a study between multiple meta-heuristic approaches and comparison between the methods, investigating the impact of parameter-tuning as well as analyzing the impact of intermittent restart for algorithms persistent diversity.

A series of derivatives, involving two dithienylethene (DTE), groups, connected by several molecular linkers (bis(ethylene-1,2-dithiolato)Ni- (NiBDT), naphthalene, quasilinear oligothiophene chains) are investigated with the aid of computational quantum chemistry methods. This involves the computation of the second- and third-order nonlinear optical properties, i.e. molecular hyperpolarizabilities of the designed/selected derivatives. These properties can be efficiently controlled by DTE switches, in connection with light of appropriate frequency. We found that NiBDT, as a linker, is associated with a greater contrast, in comparison to naphthalene, between the first and second hyperpolarizabilities of the “open-open” and the “closed-closed” isomers. This is explained by invoking the low lying excited states of NiBDT. It has been found that the second hyperpolarizability can be used as an index, which follows the structural changes induced by photochromism. The two-photon absorption, which is related to the imaginary part of second hyperpolarizability, has also been investigated for the S0S1 transition. Furthermore, the intramolecular excited-state energy transfer (EET) is studied as well as the overlap between the absorption and emission spectra of the donor and acceptor groups of the molecules. The electronic coupling, VDA, between the donor and acceptor fragments, as well as the emission spectrum of the donor and the absorption spectrum of the acceptor have been computed, assuming a Förster type transfer mechanism. EET is a critical factor governing the photochromism. Two methods were used to compute VDA, one based on linear response and one based on the distributed multipole analysis (DMA); both techniques give very similar results for the dominating Coulomb contribution. For NiBDT as the linker a low VDA value has been computed. We found that VDA is affected by the molecular geometry. Our results clearly show that the linker strongly influences the communication between the open-closed DTE groups and thus, photochromism. The present computations show that full photochromism is attained in derivatives where two DTE groups are linked by a tetrathiophene chain, in agreement with experiment. The sensitivity of molecular linear and nonlinear optical properties upon photochromism can assist with the identification of the molecular isomers.