The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

Malaysia implemented a movement control order (MCO) to curb the spread of the SARS-CoV-2 virus in March 2020. Despite healthcare services remaining operational, rising COVID-19 infections and MCO restrictions have forced healthcare professionals to seek a compromise between service capacity and standard operating procedure compliance. A cross-sectional survey was conducted among public and private sector doctors, dentists and pharmacists to determine how lockdown measures impacted healthcare services. Responses from 413 doctors, 193 dentists, and 163 pharmacists were analysed. Pharmacy services remained mostly unaffected throughout the MCO. In contrast, operational capacities for surgical and dental services were severely affected during the MCO. All service sectors reported restricting patients or accompanying individuals at the workplace, reductions in staffing capacity, and shortened patient contact time at various degrees. Many pharmacy and medical participants reported supplying extended medication supplies to patients. Adoption of virtual healthcare services was generally poor. All private service sectors suffered financial losses ranging between 59 to 75%. Periodic assessments of the healthcare system throughout the pandemic are required to identify which patients have their treatment compromised so that healthcare managers and policy makers can plan and implement appropriate interventions that help alleviate pressure within the health system.

We introduce poly-symplectic extension of Souriau Lie groups Thermodynamics based on higher-order model of statistical physics introduced by R.S. Ingarden. This extended model could be used for small data analytics and Machine Learning on Lie groups. Souriau Geometric Theory of Heat is well adapted to describe density of probability (Maximum Entropy Gibbs density) of data living on groups or on homogeneous manifolds. For Small Data Analytics (Rarified Gases , sparse statistical survey,…), density of maximum entropy should consider Higher Order Moments constraints (Gibbs density is not only defined by first moment but fluctuations request 2nd order and higher moments) as introduced by R.S. Ingarden. We use Poly-sympletic model introduced by Christian Günther, replacing the symplectic form by a vector-valued form. The poly-symplectic approach generalizes the Noether theorem, the existence of momentum mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. The formalism is covariant, i.e. no special coordinates or coordinate systems on the parameter space are used to construct the Hamiltonian equations. We underline the contextures of these models, and the process to build these generic structures.

In the field of computational fluid dynamics (CFD) for rotorcraft, two significant challenges are resolving the complex vortex structures in rotor wakes, and representing the moving rotor blades in the ambient airflow. This study addresses the first challenge by using a third-order unstructured finite volume solver, which, compared to its second-order counterpart, has substantially lower dissipation. Consequently, even relatively coarse meshes are capable of resolving small vortices. With this background flow field solver, the second challenge is addressed by modeling each rotor as an Actuator Disk Model (ADM), or describing individual rotor blades as actuator lines, designated as the Actuator Line Model (ALM). Both of these models are equipped with an improved correction for aerodynamic losses at blade tips, which is thoroughly presented in the methodology section. The numerical experiments section centers on analyzing errors linked to various sampling approaches. Additionally, the article discusses comparisons between vortex theory and ALM, specifically regarding calculations for fixed-wing aircraft. Furthermore, high-order precision and parallel efficiency are exemplified in scenarios encompassing rotors engaged in both hovering and forward flight rotors. The results in this paper demonstrate that the combination of the ALM/ADM with the improved tip loss correction and the third-order finite volume solver presents a new way of developing efficient tools for the aerodynamic analysis of helicopter rotors.

End-of-life electric vehicle (EV) batteries can be reused to reduce their environmental impact and economic costs. However, the growth of a second-life market is limited by the lack of information on the characteristics and performance of these batteries. As the volume of end-of-life EVs may exceed the amount of batteries needed for stationary applications, investigating the possibility of repurposing them in mobile applications is also necessary. This article presents an experimental test that can be used to collect the data necessary to fill a battery passport. The proposed procedure can facilitate the decision making process regarding the suitability of a battery for reuse at the end of its first life. Once the battery passport has been completed, the performance and characteristics of the battery are compared with the requirements of several mobile applications. Mobile charging stations and forklift trucks were identified as relevant applications for the reuse of high capacity prismatic cells. Finally, a definition of a state of health (SoH) is proposed to track the suitability of the battery during use in the second life application considering not only energy but also power and efficiency of the battery. This SoH shows that even taking into account accelerated ageing data, a repurposed battery can have an extended life of 11 years at 25~°C. It has also been shown that energy fade is the most limiting performance for lifetime and that cell-to-cell variation should be tracked as it has been shown to have a significant impact on battery life.

Proteomic analysis revealed the preservation of many proteins in the “Heslington brain” (which is at least 2,600-year-old brain tissue uncovered within the skull excavated in 2008 from a pit in Heslington, Yorkshire, England). Five of these proteins (“main proteins”), heavy, medium, and light neurofilament proteins (NFH, NFM, and NFL), glial fibrillary acidic protein (GFAP), and myelin basic (MBP) protein are engaged in the formation non-amyloid protein aggregates, such as intermediate filaments and myelin sheath. We used a wide spectrum of bioinformatics tools to evaluate the prevalence of functional disorder in several related sets of proteins, such as “main proteins” and their 44 interactors, as well as all other protein identified in the Heslington brain. These analyses revealed that all five “main proteins”, half of their interactors and almost one third of the Heslington brain proteins are expected to be mostly disordered. Furthermore, most of the remaining proteins are expected to contain sizable disordered regions. This is in contrary the expected substantial (if not complete) elimination of the disordered proteins from the Heslington brain. Therefore, it seems that the intrinsic disorder of NFH, NFM, NFL, GFAP, and MBP, their interactors and many other proteins might play a crucial role in preserving the Heslington brain by forming tightly folded brain protein aggregates, in which different parts are glued together via the disorder-to-order transitions.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

In this paper, we concentrate on the study of the properties of residual Tsallis entropy for order statistics. Order statistics have an important role in reliability structural engineering for example for modelling lifetimes of series and parallel systems. The residual Tsallis entropy of ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of ith order statistics from a uniform distribution is investigated. In a mathematical framework, a method to express the residual Tsallis entropy of the ith order statistic from a continuous distribution in terms of the residual Tsallis entropy of the ith order statistic from a uniform distribution is provided. This approach may provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. Further, we study the monotonicity properties of the residual Tsallis entropy of order statistics under dierent conditions. By studying these properties, deeper understanding of the relationship between the position of order statistics and the resulting residual Tsallis entropy is gained.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

With simple but rigorous arguments we prove that the ordinary second quantization of bosonic and fermionc fields is formally equivalent to constraining the elementary degrees of freedom of the classical fields to have intrinsically periodic dynamics in time. This result confirms and extends the formal equivalence obtained in previous papers for general Hamiltonian systems in terms of canonical quantization, for elementary relativistic particles also in terms of the Feynman Path Integrals, as well as other remarkable correspondences of both phenomenological and theoretical fundamental interest.

Motivated by Kurt's work [Filomat 30 (4) 921-927, 2016], we first consider a class of a new generating function for (p, q)-analog of Apostol type polynomials of order a including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order a. By making use of their generating function, we derive some useful identities. We also introduce (p, q)-analog of Stirling numbers of second kind of order v by which we construct a relation including aforementioned polynomials.

Enhancing the acoustical quality in learning environments is mandatory, especially for Hearing Aids (HAs) users. When in-field evaluations cannot be performed, Virtual Reality (VR) can be adopted for the acoustical quality assessment of existing and new buildings, contributing to the acquisition of subjective impressions in lab settings. To ensure an accurate spatial reproduction of the sound field in VR also for HAs users, multispeaker-based systems can be employed to auralize a given environment. However, most systems are effortful due to costs, size and construction. This work deals with the validation of a VR-system based on a 16-speaker-array synced with a VR-headset, arranged to be easily replicated in small non-anechoic spaces and suitable for HAs users. Both objective and subjective validations are performed against a real university lecture room of 800 m3 and with 2.3 s of Reverberation Time at mid-frequencies. Comparisons of binaural and monoaural room acoustic parameters are performed between measurements in the real lecture room and its lab reproduction. To validate the AudioVisual experience, 32 normal-hearing subjects were administered the Igroup Presence Questionnaire (IPQ) on the overall sense of perceived presence. The outcomes confirm that the system is a promising and feasible tool to predict the perceived room acoustical quality.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

^{We consider the collective pricing orders in a minimum supply chain that is composed of a monopolistic manufacturer and many retailers that belong to the same chain store firm. The retailers have the freedom to raise or lower the local price. The chain store firm sets up the commercial rules for local retail stores to maximize its total payoff. The monopolistic manufacturer firm controls the total quantity supplied for the market to achieve maximum benefits. We applied the two dimensional Ising model in statistical physics to map the collective distribution of microscopic strategy of local retailers into the macroscopic total payoff of the chain store firm. The local stores choose to raise the price or lower the price based their own mind when the supply in market surpasses the demand. When the supply in market is far less than the demand, the stores synchronously raise prices, even though a local store only have the incomplete information of their nearest neighboring supermarket. We find the critical equation for the balance point between the action of supplier and the action of chain store management based on game theory and statistical physics. The critical equation can identify the Nash equilibrium point of the non-cooperative game between the manufacturer and the chain-store seller, and reveal different levels of collective operations. This statistical physics method also holds for more complicate supply chains and economic systems.}

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

In deaths and diseases attributed to tobacco smoke cardiovascular events exceed cancer and respiratory diseases. Second hand smoke (SHS) promotes the development of arteriosclerosis and can also trigger acute changes of endothelial function and of blood coagulability. Indoor smoking bans reduced coronary syndrome and myocardial infarction 10-20% within one year and were followed by sustainable decreases of stroke and diabetes. With a smoke-free hospitality industry people recognized tobacco smoke as an air pollutant, smoking in public was denormalized and social acceptance of smoking in front of children and pregnant women decreased also in homes and in cars. Combined effects with ambient air pollution are proven for active smoking and suspected for SHS. Contamination with third hand smoke (THS, “cold smoke”) persists for months in homes and cars, creating secondary pollutants that in some cases are more toxic (e.g., tobacco-specific nitrosamines). Remnants found in air, dust, and on surfaces (carpets, wallpapers, upholstery, soft toys) were associated with their metabolites in saliva and urine of children and with elevated levels of nicotine on hands and cotinine in urine of nonsmokers residing in homes previously occupied by smokers. In animal experiments effects of THS were found on thrombogenesis, insulin resistance through oxidative stress, on the developing immune system, lipid metabolism and alterations in liver, lung, skin and behavior. Much less is known about health effects for bystanders from the aerosols exhaled during “vaping” of e-cigarettes, but nicotine and other toxins from e-cigarettes are certainly a hazard, which should be prevented by the use of dermal and oral nicotine products, which are safer for nicotine replacement and without risk for bystanders.

Elucidating physicochemical processes in the degradation of pollutants may optimize their removal from water sources. This work presents a set of elementary steps in the photocatalytic degradation of carbamazepine (CBZ), assuming a steady state approximation in an Advanced Oxidation Process (AOP) combining short-wave ultraviolet radiation (UVC), homogeneous reagent (H₂O₂) and heterogeneous (TiO₂) catalyst. Elementary steps include excitation of both reagent/catalysts by UVC photons, adsorption of CBZ on the excited TiO₂, or its oxidation by hydroxyl radicals. Assuming the steady state approximation on the intermediate products (excited TiO₂, CBZ- excited TiO₂ complex, and hydroxyl radicals), leads to rate laws for degradation of CBZ, in which UVC radiation, TiO₂, and H₂O₂ are pseudo first order at all concentrations or intensities having no direct influence on CBZ pseudo-order, whereas CBZ shifts from pseudo first order at low concentrations to pseudo-zero order at high concentrations. Several experiments to test the mechanism were conducted, by varying CBZ, H₂O₂, and TiO₂ concentrations, and UVC radiation intensities. Measured results indeed fit the suggested mechanism for the first three, but irradiation intensity appears to shift CBZ influence from pseudo-second to pseudo-first order with increased intensities. Corrected elementary steps are proposed to fit the results.

We continue to analyze basic constraints on human's decision making from the viewpoint of quantum measurement theory (QMT). As has been found, the conventional QMT based on the projection postulate cannot account for combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarm signal for quantum-like modeling of decision making. Recently, it was shown that this objection to quantum-like modeling can be removed on the basis of the general QMT based on quantum instruments. In the present paper we analyse the problem of combination of QOE, RRE, and the famous QQ-equality (QQE). This equality was derived by Busemeyer and Wang and it was shown (in the joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfies it. Now, we construct quantum instruments satisfying QOE, RRE, and QQE. The general features of our approach are formalized with postulates which generalize {\it Wang-Busemeyer} postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the famous Clinton-Gore Poll data with a prior belief state independent of the question order. This model successfully removes the order effect from the data to determine the genuine distribution of the opinions in the Poll. The paper also provides a psychologist-friendly introduction to the theory of quantum instruments - the most general mathematical framework for quantum measurements. We hope that this theory will attract attention of psychologists and will stimulate further applications.

The licensing of new reactors implies the use of verified and validated neutronics codes. Numerical validation can rely on sensitivity and uncertainty studies but they require repeated execution of time-consuming neutron flux and depletion calculations. The computational costs can be shortened by using perturbation theories. However, Depletion Perturbation Theory is restricted to single integral values such as a nuclide density. Relying on reduced basis approaches, which reconstruct the whole nuclide densities at once, is one way to get around this restriction. Furthermore, the adjoint-based reduced-order model uses the direct and adjoint equations for the projection. For diffusion or transport calculations, Exact-to-Precision Generalized Perturbation Theory has been developed. Still, no models for depletion calculations are readily available. Therefore, this paper describes a novel adjoint-based reduced order model for the Bateman equation. It uses a range-finding algorithm to create the basis and the Depletion Perturbation Theory for the reconstruction of the nuclide densities at first order. Our paper shows that for several perturbed cases, the depletion reduced-order model successfully reconstructs the nuclide densities. As a result, this serves as a proof of concept for our adjoint-based reduced order model which can perform sensitivity and uncertainty burn-up analysis in a shorter time.

Data obtained by Direct Numerical Simulations (DNS) of pressure-driven turbulent channel flow are studied in the range 180 ≤ Reτ≤ 10,000. Reynolds number effects on the Mean Velocity Profile (MVP) and second order statistics are analyzed with a view of finding logarithmic behavior in the overlap region or even further from the wall, well in the boundary layer’s outer region. Values of Kármán constant for the MVPs and the Townsend-Perry constants for the streamwise and spanwise fluctuation variances are determined for the Reynolds numbers considered. A data-driven model of the MVP, proposed and validated for zero pressure gradient flow over a flat plate, is employed for pressure-driven channel flow by appropriately adjusting Coles’ strength of the wake function parameter, Π. There is excellent agreement between the analytic model predictions of MVP and the DNS-computed MVP as well as of the Reynolds shear stress profile. The skin friction coefficient Cf is calculated analytically. The agreement between the analytical model predictions and the DNS-based computed discrete values of Cf is excellent.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

District heating networks have become widespread due to their ability to distribute thermal energy efficiently, which leads to reduced carbon emissions and improved air quality. The characteristics of these networks vary remarkably depending on the urban layout and system amplitude. Moreover, extensive data about the energy distribution and thermal capacity of different areas are seldom available. Design, optimization and control of these systems are enabled by the availability of fast and scalable models of district heating networks. This work addresses this issue by proposing a novel method to develop a scale-free model of large-scale district heating networks. Starting from coarse data available at the main substations, a physics-based model of the system aggregated regions is developed by identifying the heat capacity and heat loss coefficients. The model validation on the network of Västerås, Sweden, shows compatibility with literature data and can therefore be exploited for system design, optimization and control-oriented applications. In particular, the possibility to estimate the heat storage potential of network regions allows new smart management strategies to be investigated.

In this work we present the results obtained with an artificial neural network (ANN) which we trained to predict the expected output of high-order harmonic generation (HHG) process, while exploring a multi-dimensional parameter space. We argue on the utility and efficiency of the ANN model and demonstrate its ability to predict the outcome of HHG simulations. In this case study we present the results for a loose focusing HHG beamline, where the changing parameters are: the laser pulse energy, gas pressure, gas cell position relative to focus and gas cell length. The physical quantity which we predict here using ANN is directly related to the total harmonic yield in a specified spectral domain (20-40 eV). We discuss the versatility and adaptability of the presented method.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

The thick functionally graded material (FGM) circular cylindrical shells with advanced varied shear correction coefficient and third-order shear deformation theory (TSDT) under advanced thermal vibration are studied by the method of generalized differential quadrature (GDQ). The coefficient of displacement model of TSDT is applied to derive the equations of motion for the thick FGM circular cylindrical shells. The stiffness in simpler forms of thick FGM circular cylindrical shells and temperature rise in linear expression of the heat conduction equation are used. The differential equations in dynamic equilibrium state of thick FGM circular cylindrical shells can be obtained and rewritten into displacements and shear rotations in partial derivative expressions under dynamic thermal loads in partial derivative expressions. Parametric effect studies including advanced nonlinear varied shear correction coefficient, nonlinear coefficient c1 value, power law index and thermal temperature difference of external heating loads on the displacements and stresses of thick FGM cylindrical shells under thermal dynamic vibration are investigated.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

This work investigates spatial and temporal distributions of hydroxyl, OH, in laser-plasma in laboratory air at standard ambient temperature and pressure. Of interest are determination of temperature and density of OH and establishment of a correlation of molecular OH emission spectra with shadow graphs for time delays of 50 to 100 microsecond, analogous to previous work on shadow graph and emission spectroscopy correlation for cynaide, CN, in gas mixtures and for time delays of the order of 1 microsecond. Wavelength- and sensitivity- corrected spatiotemporal data analysis focuses on temperature inferences using molecular OH emission spectroscopy. Near-ir radiation from a Q-switched laser device initiates optical breakdown in laboratory air. The laser device provides 6 nanosecond, up to 850 milli Joule pulses at a wavelength of 1064 nanometer, and focal irradiance in the range of 1 to 10 Tera Watt per centimeter-squared. Frequency doubled beams are utilized for capturing shadow graphs for visualization of the breakdown kernel at time delays in the range of 0.1 to 100 microsecond. OH emission spectra of the laser plasma, spatially resolved along the slit dimension, are recorded in the wavelength range of 298 nm to 321 nm, and with gate widths adjusted to 10 microsecond for the intensified charge-coupled device that is mounted at the exit plane of a 0.64 m Czerny-Turner configuration spectrometer. Diatomic OH signals occur due to recombination of the plasma and are clearly distinguishable for time delays larger than 50 microsecond, but are masked by spectra of N2 early in the plasma decay.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

We here investigate the dynamical behavior of a fractional-order predator-prey system with anti-predator behavior and Holling IV type functional response. First we study the non-negativity, existence, uniqueness, and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, and prove the existence of a supercritical Hopf bifurcation in the system. After providing numerical simulations to illustrate the conclusions theoretically derived, by summarizing those various analytical results obtained, we finally present three interesting conclusions that can contribute to better understanding and preservation of ecological systems.

The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane BnHm+n is extended here, with the B3LYP/cc-pVDZ model, to pure conjugated carbon systems with the example of buckminsterfullerene C60 with the corresponding icosahedral isoelectronic system closo-borane B60H60, and the fluorine substituted systems B60F30H30 and B60F60 , all with icosahedral Ih symmetry. All systems correspond to energy minima in the potential energy hypersurface, except for B60(F30)in(H30)out . Selected electronic structure methods are used to characterize all systems: molecular electrostatic potentials (MEP), atomic charges, bond orders, and topological properties of the electron density within quantum theory of atoms-in-molecules (QTAIM) and electron-localization function (ELF) theory. In the particular case of B60H60 we use the recently developed Hückeloid model to characterize this system. The stability of the energy minimum icosahedral structure B60F60 could have an origin in F···F attractive interactions of the inner fluorine atoms of the cage.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and triggered the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

This author is not a philosopher nor historian of science, but an engineering thermodynamicist. In that regard and in addition to various philosophical “why & how” treatises and existing historical analyses, the physical and logical “what it is” reflections, as successive Key Points, where a key reasoning infers the next one, along with novel contributions and original generalizations, are presented. We need to keep in mind that in Sadi Carnot’s time (early 1800s) the steam engines were inefficient (below 5%, so the heat in and out were comparable within experimental uncertainty), the conservation of caloric flourished (might be a fortunate misconception), and many critical thermal-concepts, including the conservation of energy (The First Law) were not even established. If Clausius and Kelvin were "fathers of thermodynamics" then Sadi Carnot was the "grandfather" [Kostic, 2023 July 24], or better yet, Sadi Carnot was the "Forefather of Thermodynamics-to-become" [Kostic, 2023 October 29].

We delve into the axion-dilaton model within the supergravity framework, with a specific focus on the intricacies of domain wall construction and stability. Employing holographic vitrification, we unravel the dynamics of domain wall formation in gauge theories featuring periodic vacuum structures. Our model, incorporating a QCD-like axion term and a stabilizing dilaton, undergoes scrutiny for conductivity variations under weak disorder. The investigation reveals the model's resilience, manifesting near-perfect conductivity under mild disorder conditions. However, the rigorous mathematical motivation for the holographic setup demands further elucidation. The scattered nature of our results prompts the necessity for a more systematic interpretation of QCD phenomena and conductivity transitions. This study contributes to the mathematical understanding of the axion-dilaton model's behavior, highlighting the imperative for a refined holographic framework and a more coherent interpretation of observed phenomena.

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein-Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole's tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration's thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system's stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple, straightforward with reliable first order overall approximations. The spectral norm is used throughout the investigation and numerical stability is proven. Simulation experiments are given to illustrate our results.

In this paper we compare the effects of forecasting demand using individual (disaggregated) components versus first aggregating the components either fully or into several clusters. Demand streams are assumed to follow autoregressive moving average (ARMA) processes. Using individual demand streams will always lead to a superior forecast compared to any aggregates, however we show that if several aggregated clusters are formed in a structured manner then these subaggregated clusters will lead to a forecast with minimal increase in mean-squared forecast error. We show this result based on theoretical MSFE obtained directly from the models generating the clusters as well as estimated MSFE obtained directly from simulated demand observations. We suggest a pivot-algorithm, that we call Pivot Clustering, to create these clusters. We also provide theoretical results to investigate sub-aggregation, including for special cases such as, aggregating MA(1) streams and ARMA streams with similar or same parameters.

For effective warehouse management, various criteria should be taken into consideration in terms of inventory management, demand, transportation distance, usage area, delivery-waiting times, and minimizing the costs that may arise from them. Because, the purpose of the product assignment problem is to minimize the total transport distance during storage and to reduce the space required for product assignment. However, the storage location assignment problem (SLAP) occurs simultaneously with production planning activities in real life. In this study, an integrated mixed-integer nonlinear (MINLP) mathematical model is proposed, which includes the assignment of products to storage areas and production planning, using the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) class based policy for storage systems where multiple criteria are important. In the TOPSIS class-based policy, weight and waiting time criteria are taken into account, as well as the COI (Cube-per-order index index), which is widely used in the literature. In addition, a decision support system flow has been proposed that takes into account the single criterion, multiple criteria and COI index criteria of the developed model and provides its integration with different product assignment policies. Detailed literature research; It has been revealed that the proposed mathematical model and decision support system flow have the feature of applying an existing field of science to a new problem.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

In addition to the canonical loss-of-function mutations, mutations in proteins may additionally result in gain-of-function through the binary activation of cryptic ‘structural capacitance elements’. Our previous bioinformatic analysis allowed us to propose a new mechanism of protein evolution - structural capacitance – that arises via the generation of new elements of microstructure upon mutations that cause a disorder-to-order (DO) transition in previously disordered regions of proteins. Here we propose that the DO transition is a necessary follow-on from expected early codon-anticodon and tRNA acceptor stem-amino acid usage, via the accumulation of structural capacitance elements - reservoirs of disorder in proteins. We develop this argument further to posit that structural capacitance is an inherent consequence of the evolution of the genetic code.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Humans are incapable of judging the temporal order of visual events at brief temporal separations with perfect accuracy. Their performance---which is of much interest in visual cognition and attention research---can be measured with the temporal-order judgment task, which typically produces S-shaped psychometric functions. Occasionally, researchers reported plateaus within these functions, and some theories predict such deviation from the basic S shape. However, the centers of the psychometric functions result from the weakest performance at the most difficult presentations and therefore fluctuate strongly, leaving existence and exact shapes of plateaus unclear. This study set out to investigate whether plateaus disappear if the data accuracy is enhanced, or if we are ``stuck on a plateau'', or rather with it. For this purpose, highly accurate data were assessed by model-based analysis. The existence of plateaus is confidently confirmed and two plausible mechanisms derived from very different models are presented. Neither model, however, performs well in the presence of a strong attention manipulation, and model comparison remains unclear on the question which of the models describes the data best. Nevertheless, the present study includes the highest accuracy in visual TOJ data and the most explicit models of plateaus in TOJ studied so far.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

Large lithium-ion batteries (LIBs) in electric vehicles and energy storage systems demonstrate different performance and lifetime compared to small LIB cells, owing to the size effects generated by the electrical configuration and property imbalance. However, the calculation time for performing life predictions with three-dimensional (3D) cell models is undesirably long. In this paper, a lumped cell model with equivalent resistances (LER cell model) is proposed as a reduced order model of the 3D cell model, which enables accurate and fast life predictions of large LIBs. The developed LER cell model is validated via the comparisons with results of the 3D cell models by simulating a 20-Ah commercial pouch cell (NCM/graphite) and the experimental values. In addition, the LER cell models are applied to different cell types and sizes, such as a 20-Ah cylindrical cell and a 60-Ah pouch cell.

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

(1) Background: Since fullerene C60 is insoluble in water and is toxic, it is not applicable in biomedicine and cosmetics. For this reason, the first derivative FD-C60 (fullerenol) was synthesized, which solved the problem of solubility in water and partially reduced toxicity. In order to maximally reduce toxicity and increase biomedical efficiency, the second derivative SD-C60 (3HFWC- Hyper-Harmonized-Hydroxylated Fullerene Water Complex), was created. (2) Methods: In order to obtain the most reliable data, several different methods are applicable in the characterization of FD-C60 and SD-C60 with water layers (NIR, FTIR, 13C-NMR,  1H-NMR, TGA/DTA, XRD, AFM/MFM etc.). (3) Results: FD-C60 as an individual structure is about 1.3 nm in size, while SD-C60 as an individual structure is 1030 nm in size. The aforementioned methods showed that SD-C60 contains water layers, which explains the difference between those two structures in the physicochemical properties, and their effects on biomolecules. (4) Conclusions: Based on the above methods and techniques, FD-C60 and SD-C60 are two different substances in terms of size, structure, and physicochemical properties; FD-C60 at 100C has endothermic characteristics and SD-C60 at 133C has exothermic characteristics, FD-C60 possesses water molecules only from humidity, while SD-C60 has water molecules from both humidity and extra water molecules in layers, the zeta potential of FD-C60 is -25.85 mV, while it is -43.29 mV for SD-C60.

Thermally-assisted-occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Besides, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

The capacity and the mechanism of the adsorption of aqueous barium (Ba), cobalt (Co), strontium (Sr) and zinc (Zn) by Ecuadorian (NatAllo) and synthetic (SynAllo-1 and SynAllo-2) allophanes were studied as a function of contact time, pH and metal ion concentration using kinetic and equilibrium experiments. The mineralogy, nano-structure and chemical composition of the allophanes were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, transmission electron microscopy and specific surface area analyses. The evolution of adsorption fitted to a pseudo-first-order reaction kinetics, where equilibrium between aqueous metal ions and allophane was reached within < 10 min. The metal ion removal efficiencies varied from 0.7 to 99.7 % at pH 4.0 to 8.5. At equilibrium, the adsorption behavior is better described by the Langmuir model than by the Dubinin-Radushkevich model, yielding sorption capacities of 10.6, 17.2 and 38.6 mg/g for Ba^(2+), 12.4, 19.3 and 29.0 mg/g for HCoO_2^-, 7.2, 15.9 and 34.4 mg/g for Sr^(2+) and 20.9, 26.9 and 36.9 mg/g for Zn^(2+), respectively, by NatAllo, SynAllo-2 and SynAllo-1. The uptake mechanism is based on a physical adsorption process. Allophane holds great potential to remove aqueous metal ions and could be used instead of zeolites, montmorillonite, carbonates and phosphates for wastewater treatment.

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

Multiphoton microscopy (MPM) is a cutting-edge nonlinear microscopy technique known for its exceptional capabilities in imaging dense tissues, making it an ideal tool for exploring human kidney tissue. This study delves into the application of MPM in evaluating renal cell tumors and characterizing tumor capsules. MPM encompasses two core methods: two-photon excitation fluorescence (TPEF) and second harmonic generation (SHG). It leverages femtosecond lasers to provide deep tissue imaging while minimizing phototoxicity, making it well-suited for live tissue analysis. The study analyzed 100 formalin-fixed paraffin-embedded (FFPE) kidney tissue samples, ensuring compliance with ethical standards. Using a Ti:Sapphire laser for femtosecond pulses and a variety of optical components and filters, the researchers captured TPEF and SHG signals, facilitating image analysis. Normal kidney tissue exhibited distinctive structures like glomeruli and tubules under MPM. Renal cell carcinoma (ccRCC) displayed unique TPEF patterns with eccentrically located nuclei and indistinct cytoplasmic membranes. Papillary RCC (pRCC) exhibited a papillary pattern with dark nuclei, while chromophobe RCC (chRCC) showcased distinct features like thick cell membranes, strong TPEF signal in nuclei, and granular cytoplasm. Renal oncocytoma (RO) presented strong TPEF signals in cuboidal cells with microcyst-like arrangements. Overall, MPM proved invaluable in assessing human kidney tissue, offering distinct TPEF patterns for different renal cell tumor types. This non-invasive technique has the potential to enhance pathological examinations and advance our understanding of complex biological processes, ultimately contributing to improved diagnostics and treatment strategies for renal diseases.

The critical period (CP) phenomenon in language development ranks among the 125 conundrums facing scientists in the 21st century, according to Science. While the phenomenon itself has been noncontroversial in first language acquisition, it still warrants an adequate explanation. Predicated on language acquisition as a complex process, questions among the first to be raised include: How do children accomplish this remarkable feat in such a short amount of time? And how do nature and nurture come together to influence language learning? In second language acquisition, however, both the notion of CP, albeit popular, and its empirical evidence have remained contested to this date - among the questions, whether the observed evidence counts as CP-specific and/or whether or not it warrants an isomorphic attribution to maturational constraints. Entwined in this debate are two well-established facets of inter-learner differential attainment. The first is that there exists a stark difference in ultimate attainment between younger and older learners. A second facet is the vast differences in ultimate attainment among older learners. In this article, adopting a social physics approach, we mathematically establish both the relationship between nature and nurture contributions and the presence of a critical period, and, at once, tender a parsimonious and probable theory for the twin phenomena of inter-learner differential attainment.

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampéde Fériet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a qparameter and the Hermite based λ -Stirling polynomials of the second kind.

This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and misleading issues in thermodynamics; since now, we have the advantage to look at the historical developments more comprehensively and objectively than the pioneers. Starting from Carnot (grand-father of thermodynamics-to-be) to Kelvin and Clausius (fathers of thermodynamics), and other followers, the most relevant issues are critically examined and put in historical and contemporary perspective. From original reasoning of energy forcing and displacement to logical-proofs of the fundamental laws, to ubiquity of thermal motion and heat, and indestructibility of entropy, including new concept of “thermal roughness” and inevitability of dissipative irreversibility, to “dissecting Carnot true reversible-equivalency” and critical concept of “Carnot-Clausius heat-work equivalency (CCHWE)” regarding interchangeability of heat and work, and to demonstrating “no hope” for the “challengers” of the Second Law of thermodynamics, among others, are offered. It is hoped that the novel contributions presented will enhance comprehension and resolve some of the fundamental issues, as well as promote collaboration and future progress.

Results from a behavioral economic laboratory experiment are used to enhance our understanding of public health decisions made during the COVID-19 pandemic. The identification of systematic biases from optimal decision theory found in controlled experiments could help inform public policy design for future public health crises. The laboratory and the shelter-in-place decisions made during COVID-19 included elements of risk, uncertainty and ambiguity. The lab findings found individuals adopt different decision rules depending on both personal attributes and on the context and environment in which the decision task is conducted. Key observations to consider in the context of the COVID-19 decision environment include the importance of past experience, the ability to understand and calculate the odds of each action, the size and differences in economic payoffs given the choice, the value of information received, and how past statistical independent outcomes influence future decisions. The academic space encompassing both public health and behavioral economics is small, yet important, particularly in the current crisis. The objective of continued research in this area would be to develop a more representative model of decision-making processes, particularly during crisis, that would serve to enhance future public health policy design.

Heat pump-based renewable energy and waste heat recycling has become the mainstay of the Clean Heating Plan. Still, configuring a fit control system for that remains a worthwhile research topic. In order to address the problems that arose in the previous heating period, this study configures a Smith-predictor-based PID cascade control system with an advanced fireworks algorithm that adaptively tunes the structural parameters of controllers. Simulation and live measures demonstrate that the upgraded control scheme counters the adverse effects of time lag, reduces overshoot, and shortens the settling time. Further, benefiting from a delicate balance between heating demand and supply, the heating system with upgraded management increases the average exergetic efficiency by 11.4% and decreases the complaint rate by 76.5%. Note that the advanced fireworks algorithm mitigates the adverse effect of capacity lag and simultaneously accelerates the optimizing and converging processes, exhibiting its comprehensive competitiveness among this study’s three intelligent optimization algorithms. Nonetheless, the forecast and regulation of the return water temperature of the heating system are independent of each other in this research. Configuring an integral predictive control structure for the return water temperature of heating systems is worthwhile in the future.

The performance of laser beams in tracking Lissajous scan trajectories is severely limited by beam jitter. To enhance the performance of fast steering mirror (FSM) control in tracking Lissajous scan trajectories, this paper proposed a fractional order active disturbance rejection controller (FOADRC) and verified its effectiveness in improving system scanning tracking accuracy. A dynamic mathematical model of fast steering mirror was studied and the design of parameters for the control mode of the closed-loop system was determined. A reduced order linear active disturbance rejection controller suitable for FSM systems was designed and the corresponding fractional order proportional differentiation (FOPD) controller were determined according to the mathematical model. The use of the designed controller enabled high-performance tracking of high-frequency Lissajous scanning curves (X-axis 500 Hz, Y-axis 350 Hz) and met the need for high-frequency repetitive scanning. The controller has the characteristics of simple implementation and low computational complexity and is suitable for closed-loop control applications in engineering.

The paper draws attention and opens the debate on major societal issues that concern not only Muslims but human societies, at large, because of their profound implications, afflictions, and their present and future transitive dimensions. The paper discusses two major issues that have attracted a great deal of attention in the recent past: wealth and income disparities, and global indebtedness. Four remedies have stressed upon and/or proposed to eradicate and/or lessen some of the burdens of these problems have been thoroughly examined. These are: - Stripping commercial banks of their power to create money out of thin air (i.e., Ex Nihilo). Thus, reviving financial reform in line with the spirit of the call for the “Establishment of a National Bank [in England]” in the 1820s by the renowned British economist David Ricardo (1772-1823). The Bank of England was a private commercial entity at that time. - Prohibiting of ‘harmful’ speculation activities in financial and economic transactions and/or imposing hefty taxes on transactions relating to such activities. The implementation of such a policy requires and clear-cut distinction between the ‘harmful’ and ‘non-harmful’ speculative activities in financial and non-financial markets. - Levying adequate and fair taxes on the wealthiest upper class at the global scene. Calls for such a policy is on rise in the past few years. For instance, “Speakers at the European Development Days summit in Brussels, [in 2017], said that a just tax system should be “at the heart” of the development debate, and that more transparency is needed to ensure that companies pay their fair share. Tax avoidance schemes used by multinational companies, such as moving profits to tax havens, result in global losses of around $650 billion a year in tax receipts — with developing countries losing $200 billion, according to a study from the International Monetary Fund”, (Edwards, 2017; Crivello et al., 2015, p. 21) - Establishing a neutral legislative and tax regimes for different modes of financing. Thus, providing ‘a level playing field’ for equity and debt modes of financing due to the current biasness of the tax regimes to debt-based financing instruments as it has been documented in various studies carried out by the IMF, the European Commission, and other international prominent bodies.

The search for new materials that could improve the energy density of Li-ion batteries (LIB) is one of today’s most challenging issues. Recently, cation-disordered lithium-excess metal oxides have emerged as a promising new class of cathode materials for LIB, due to their high reversible capacities and nice structural stability. However, a full structural model of the Li-transition metal (TM) sharing sublattice and the origin of short range ordering (SRO) of cation ions requires further investigation. In this work, we put forward a Monte Carlo strategy of building a cation-disordered rocksalt material supercell model. The cation ions of Li_1.0Ti_0.5Ni_0.5O₂ (LTNO) are placed at the FCC sublattice sites with the constraint of Pauling’s electroneutrality rule, instead of a random way. This constraint causes the Li-Ti and Ni-Ni clustering (the cation short range ordering). Based on this model, we discussed the relationship between the short range ordering, the local distorting, the theoretic capacity and the order-disorder strengths. A unified understanding of these factors in cation-disordered materials may enable a better design of disordered-electrode materials with high capacity and high energy density.

Materials design for processing and application requires fundamental understanding of their properties based interatomic interaction. The use of the novel concept of total bond order density (TBOD) as a single quantum mechanical metric to characterize the internal cohesion of a crystal and correlate with the calculated physical properties is particularly appealing. This requires detailed first-principles calculation of the electronic structure, interatomic bonding and related properties. In this article, we use this new concept and apply it to chalcogenide crystals based on data obtained from 25 crystals: Ag₂S, Ag₂Se, Ag₂Te, As₂S₃, As₂Se₃, As₂Te₃, As₄Se₄, Cu₂S, Cu₂Se, Cu₂Te, Cu₄GeS₄, Cu₂SnS₃, Cu₂SnSe₃, GeS₂, GeSe₂, Ge₄Se₉, Sb₂S₃, Sb₂Se₃, Sb₂Te₃, SnS, SnSe, CdSe, CdTe, ZnSe, and ZnTe. Together with the calculated optical and mechanical properties, we demonstrate the efficacy of using this novel approach for materials design that could facilitate the exploration and development of new chalcogenide crystals and glasses. Moreover, the TBOD and its partial components (PBOD) could be the key descriptors in machine learning protocol for broader scale design when a large database is available.

Sustainability in material purchasing is a growing area of research. Goods purchasing decisions strongly affect transportation path flows, vehicle consolidation, inventory levels and related obsolescence costs. Within a global sourcing context, companies experience the need of new decision making approaches capable to consider a large variety of factors, also linked with society and environment. Environmental impact assessment has become a key requirement for materials purchasing and transportation decisions since global warming is a rising concern both in academic and industrial researches. In fact, it is well known that the freight transport industry is responsible for large amounts of carbon emissions contributing to global warming. In this paper, we initially analyse and compare the environmental economic policies established by the International Governments in relation to the carbon trading systems adopted. Then, we develop a multi-objective lot sizing approach useful in practice to define the sustainable quantity to purchase when a Cap and Trade mitigation policy is present. We further analyse the model behaviour according to different carbon price values by demonstrating that carbon prices are still far too low to motivate managers towards sustainable purchasing choices.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

In the last two decades, the development of high-throughput diagnostic methods and availabil-ity of effective treatments has increased interest in newborn screening for lysosomal storage disorders. However, long-term follow-up experience is needed to clearly identify risks, benefits and challenges. We report our 8-year experience of screening and follow up on about 250,000 neonates screened for four lysosomal storage diseases (Pompe disease, mucopolysaccharidosis type I, Fabry dis-ease, Gaucher disease), using enzyme activity assay by tandem mass spectrometry, and bi-omarker quantification as second tier test. Among the 126 positive newborns (0.051%), 51 infants were confirmed as affected (positive pre-dictive value 40%), with an overall incidence of 1:4,874. Of these, 3 infantile-onset Pompe dis-ease, 2 neonatal-onset Gaucher disease and 4 mucopolysaccharidosis type I patients were imme-diately treated. Furthermore, another four Gaucher disease patients needed treatment in the first years of life. Our study demonstrated the feasibility and effectiveness of newborn screening for lysosomal storage diseases. Early diagnosis and treatment allow the achievement of better patient out-comes. Challenges such as false positive rates, the diagnosis of variants of uncertain significance or late-onset forms, and the lack of treatment for neuronopathic forms, should be addressed.

An overview of the chemical compounds forming the rare smectic T phases is cited with references to the historical context. Thermodynamics (transition temperatures, enthalpies) along with the factors (stereochemical constraints, electrostatic interactions, aliphatic chain stacking, intermolecular forces) contributing to the adoption of tetragonal scaffolds are also discussed. Characteristic optical microscopy textures and x-rays diffraction patterns are presented. In parallel, a comparison of the geometrical parameters such as distances between atoms, molecular areas, volumes, and lattice parameters with the closest two-dimensional and three-dimensional organizations, is performed.

The theory of Ismail's non-extensive maximum entropy solution (NME) is described in detail. It is used as an inductive inference technique for heavy-tailed queues with a non-robust mean queue length and a non-extensive "long-range" interaction. In our novel method, we substitute the non-robust mean queue length for the conventional Pollaczeck-Khinchin mean queue length. In other words, the new non-extensivity parameter q will be included in the resulting state probability function. Numerical portraits are provided to capture the influential effect of the derived formalism, , on the stable M//1 queue with heavy tails. More potentially, some applications of Hurst Exponent to social computing and connected health are provided. Conclusion with some challenging open problems and possible future research pathways are given.

Different types of resonators are used to create acoustic metameterials and metasurfaces. Recent studies focused on the use of multiple resonators of dipole, quadrupole, octupole and even hexadecapole types. This paper considers the theory of an acoustic metasurface, which is a flat surface with a periodic arrangement of multiple resonators. The sound field reflected by the metasurface is determined. If the distance between the resonators is less than a half the wavelength of the incident plane wave, the far field can be described by a reflection coefficient that depends on the angle of incidence. This allows to characterize the acoustic properties of the metasurface by a homogenized boundary condition, which is a high order tangential impedance boundary condition. The tangential impedance depending on the multiple order of the resonators is introduced. In addition, we analyze sound absorption properties of these metasurfaces, which are a critical factor in determining their performance. The paper presents a theoretical model that accounts for the multiple orders of resonators and their impact on sound absorption. The maximum absorption coefficient for a diffuse sound field, as well as the optimal value for the homogenized impedance, are calculated for arbitrary multipole orders.

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest only is considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

This paper combines the Good Regulator Theorem with the Law of Requisite Variety and seven other requisites that are necessary and sufficient for a cybernetic regulator to be effective and ethical. The resulting Ethical Regulator Theorem provides a basis for systematically evaluating and improving the adequacy of existing or proposed designs for systems that make decisions that can have ethical consequences; regardless of whether the regulators are human, machines, cyberanthropic hybrids, organizations, corporations, or government institutions. The theorem is then used to define an ethical design process that has potentially far-reaching implications for society. A six-level framework is proposed for classifying cybernetic and superintelligent systems, which highlights the existence of a possibility-space bifurcation in our future time-line. The implementation of “super-ethical” systems is identified as an urgent imperative for humanity to avoid the danger that superintelligent machines might lead to a technological dystopia. Third-order cybernetics is defined as the cybernetics of ethical systems. Concrete actions, a grand challenge, and a vision of a super-ethical society are proposed to help steer the future of the human race and our wonderful planet towards a realistically achievable minimum viable cyberanthropic utopia.

Soft-Core architecture for Analogue to Digital Converter (ADC) sampling is useful for mixed signal applications. Soft-core architecture for cutting edge odd or even ADC sampling with interface to block RAM memory has not been found. Soft-core architecture as a concept has become popular due to the advantage of customization for different applications as compared to general-core architecture suited for single application. The latest generation of piece wise sampling is odd sampling and was introduced in the second decade of the 20th century. Odd and even order sampling techniques are analogue in nature driven by a tuned (tuned for odd or even) mixer. This paper proposes a third-generation piece wise sampling with soft-core architecture that enables an option to select both odd and even while interfacing to memory mapping. The proposed odd/even has superior SNR performance of 6 dB as compared to existing architecture such as Mod-∆ which recorded worst performance of 18 dB. Advances in soft-core technology have allowed a niche odd/even switching field to be identified and studied, the study has also been extended to include memory architecture.

Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

Below T_CO=157 K the quasi-one-dimensional charge-transfer salt (TMTTF)_2SbF_6 undergoes a pronounced phase transition to a charge-ordered ground state. We have explored the non-linear and photoconductive behavior as a function of applied voltage, laser pulse energy and temperature. Besides a decay of the photoconductive signal in a double exponential fashion in the millisecond range, we discover current oscillations in the kHz range induced by the application of short laser pulses. While the resonance frequencies do not depend on voltage or laser intensity and vary only slightly with temperature, the amplitude changes linearly with the laser intensity and voltage. The findings are discussed and compared to comparable phenomena in other low-dimensional electron systems.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

The United Nations' sustainable development goals have underscored the importance of enhancing supply chain sustainability while appropriately distributing orders. This study proposes a novel framework involving Z-number, game theory, indifference threshold-based attribute ratio analysis (ITARA), and combined compromise solution method (CoCoSo) to evaluate the sustainability of suppliers and order allocations. To better reflect the decision makers’ current choices for the sustainability of assessed suppliers and order allocations; enhance the comprehensiveness of decision-making, the importance parameter of the supplier is obtained through game theory objectively for transforming supplier performance into order allocation performance. The Z-numbers are involved in ITARA (so-called ZITARA) and CoCoSo (so-called ZCoCoSo) to overcome the issue of information uncertainty in the process of expert evaluation. ZITARA and ZCoCoSo are applied to assess the objective weight of criteria and the ranking of assessed order allocations, respectively. Afterwards, a case study of China’s company is illustrated the utility of the proposed framework and inform their decision-making process regarding the orders to be assigned to the assessed suppliers.

In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices $A$ and $B$. $A$ is said to be C-S orthogonal to $B$ if $A^{\tiny\textcircled{S}}B=0$ and $BA^{\tiny\textcircled{S}}=0$, where $A^{\tiny\textcircled{S}}$ is the generalized core inverse of $A$. The characterizations of C-S orthogonal matries and the C-S additivity are also provided. And the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.

The cell concentration measurement on a culture assay using bioimpedance is a very useful tool, but it is complex to translate impedance to cell concentration values. The purpose of this work is to find a method to obtain in real time the cell concentration values for a given cell-culture assay using an oscillator as the measurement circuit. From a basic cell-electrode model, enhanced models of the cell culture immersed in a saline solution (culture medium) can be derived. These models can be used in a fitting routine to real time estimation of the cell concentration in a cell culture, using the oscillation frequency and amplitude delivered by measurement circuits proposed by the authors. Based on real experimental data (frequency and amplitude of oscillations) obtained by connecting the cell culture to an oscillator as a load, the fitting routine is simulated, and real time data of cell concentration is achieved. These results are compared with concentration data found by traditional optical methods for counting. In addition, the error obtained is divided and analyzed in two parts: in the first part of the experiment (when the few cells are adapting to the culture medium) and the second part of the experiment (when the cells grow exponentially until they completely cover the well).Low error values are obtained in the growth phase of the cell culture (the relevant phase), therefore the results obtained are considered to be promising, proving that the fitting routine is valid, and that the cell concentration can be measured in real time using an oscillator.

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.

As a matter of course, the first gene must be formed in the absence of gene. On the other hand, many biopolymers including gene are produced under the genetic system in extant organisms. Thus far, no idea explaining how the first gene was formed in the absence of gene, has been proposed except the idea based on the GADV hypothesis. GADV means four amino acids; Gly [G], Ala [A], Asp [D] and Val [V]. In this article, a reliable answer to the question, how the first gene was generated, is provided. The idea is as follows. The first gene (genetic information) was formed by random joining of anticodons, GNCs, which were carried by primeval anticodon stem-loop (AntiC-SL) tRNAs produced during repeated cycles of random joining of nucleotides and degradation of oligonucleotides. However, it might be difficult for many persons to accept the idea, because tRNAs and metabolic pathways using various proteins, which are produced under genetic functions, must be used to form the first gene. Then, it is reconsidered based on definition of genetic information and minimum necessary things to generate the first gene in this article, how the first gene was generated. Consequently, it could be reconfirmed that five prototypes of members (genetic code, tRNA, metabolism, cell structure and protein) composing the fundamental life system, except gene, are certainly necessary to generate the first gene. Namely, it can be concluded that the first gene was formed through nucleotide metabolism with immature [GADV]-proteins, primeval AntiC-SL tRNA formation with immature [GADV]-proteins, formations of single-stranded (GNC)n codon sequence by random joining of anticodons, GNCs, carried by AntiC-SL tRNAs, double-stranded (ds)-(GNC)n RNA and maturation of an immature [GADV]-protein, which was produced from one strand of the ds-RNA. Thus, the first gene was formed using the five primitive or prototypes of members, which were produced in the absence of gene. There would be no other way for generating the first gene.

Proteins having a variety of functions play many essential roles in maintaining various life activities in organisms. Various methods, by which new protein functions can be artificially produced, have progressed rapidly upon development in recombinant DNA technology and effective screening techniques. However, the obtainable scope of the new functions has been restricted in a narrow range, because only functions of presently existing proteins can be used. On the other hand, it has been considered that it would be impossible to create an entirely new protein, which does not show any meaningful homology with any other amino acid sequences of previously existing proteins. The reason is because one amino acid sequence for a protein cannot be selected out from an extraordinary large amino acid sequence diversity as ~10130. As a matter of course, it is impossible to design an amino acid sequence of a protein in advance and a gene encoding the protein cannot be also formed through random process. Nevertheless, extant organisms have generated a variety of entirely new proteins in some way to make full use of them. This means that extant organisms have equipped a mechanism with which entirely new proteins can be produced under the present core life system composed of protein, tRNA (genetic code) and gene. In this article, first I introduce the mechanism, with which entirely new proteins are created in extant organisms, and further propose a novel strategy for application of the mechanism to protein engineering through creation of entirely new proteins, which could contribute to development of various industries.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining the individual bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that it features patterns that can be used to determine the shortest addition chain for certain N. We show that a string with the smallest assembly index can be assembled by an elegant trivial program of length equal to this index if the length of the string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index that could assemble this string. We conjecture that a black hole surface is defined by a balanced distinct string that satisfies the upper bound of a distinct string assembly index. The results confirm that four Planck areas provide a minimum information capacity that provides a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that the problem of determining the assembly index of a given binary string is NP-complete, while the problem of creating the string so that it would have a predetermined maximum assembly index is NP-hard. Therefore, once the new information is assembled by a dissipative structure or by a human, increasing the information entropy according to the second law of infodynamics, it is subject to the second law of thermodynamics, and nature seeks to optimize its assembly pathway.

The paper describes a new formula for calculating the mutual inductance between a thin conical sheet inductor and a filamentary circular loop, which are coaxial. The presented formula is derived semi-analytically using the complete elliptic integrals of the first, second, and the third kind, along with the integral term which will be solved numerically. The results are validated using double and single integration methods, as well as the semi-analytical formula. The mutual inductance between a thin wall solenoid and a filamentary circular loop can be obtained using the new formula for the conical coil and circular loop. Presented formulas can be useful in various applications, such as broadband RF and wireless power transfer systems that utilize conical inductors. Overall, the paper presents a valuable contribution to the field of inductor design and can be useful in various applications involving conical inductors.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

This article presents a unique set of voltage and current data from a public building and acquired using a hybrid measurement solution that combines Python and Grafana. The transversal purpose consists of contributing to the community with a vision of the quality of the supply more oriented to the monitoring of the state of the network, providing a more realistic vision, which allows a better understanding, and the adoption of the best decisions to achieve the efficient energy management and thus optimize the operation and maintenance of power systems. The work focuses on higher order statistical estimators that, combined with exploratory data analysis techniques, improve the characterization of the shape of the stress signal. These techniques and data, together with the acquisition and monitoring system, present a unique combination in the line of low-cost measurement solutions. It also incorporates the underlying benefit of the contribution to industrial benchmarking. The paper also includes a computational comparison between Python and LabVIEW to elicit the performance of the measurement solution.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

This paper offers an integrated approach for correlated storage assignment strategy (CSAS) to optimize travel distance by considering item correlation, picking frequency, zoning, and slot constraints to improve operational efficiency in distribution centers. We simplify the mixed integer non-linear programming (MINLP) model and incorporate integrated heuristic procedures for faster convergence. We introduce positive and negative centroid deviations as techniques to guide the model convergence and explore different scenarios. In the second stage of item assignment, we prioritize items within zones using a ranking formula that is optimal for both single-item and multiple-item orders. By analyzing the distribution of correlated item across zones and the impact of their picking frequency on optimizing travel distance, we propose an improved CSAS that minimize travel distance by strategically placing items based on their proximity to the depot. Our model reduces trips in distant zones by prioritizing larger average order sizes, while maximizing trips for frequently ordered smaller lists in closer zones. This method significantly reduces travel distance by minimizing the need for pickers in distant zones to frequently travel to the depot. Simulation results show reductions of up to 36.75% for fitted data and 33.59% for recent data.