A scientific investigation into visual preferences of rural recreation path landscapes is crucial for enhancing visual qualities and visitors' experience. Taking Baofeng, a representative traditional village in Yunlong, as an example, this study analyzed the visual preference of three typical linear recreational paths with different landscape attributes. We used eye-tracking technology to collect eye movement data and conducted a subjective semantic differential evaluation. Our findings manifest a general inclination amongst individuals to favor closer views and paths with clear trajectories and rich elevation changes while walking, despite preference differences on different types of paths. Regarding group diversity, more inclusive design should be made to meet the sensory needs of different groups. Moreover, despite the limited level of correlation between subjective and objective evaluation methods, combining these two approaches remains indispensable. This synthesis advances prior quantitative landscape evaluation with a specific focus on rural path landscapes and upholds the integrity of results by combining objectivity with subjectivity. It also provides relevant design suggestions for further rural renewal and path planning of Baofeng village.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

This work assesses the dietary use of two insect meals of Tenebrio molitor (TM) larvae reared in conventional (TM-10) or MAPs-enriched substrates (MAP-TM-10) as fish meal replacements (10%) in the diets of gilthead seabream (Sparus aurata). Fish (n=4,500; 207.19 ± 1.47 g) were divided into three groups with triplicates: Control (fed conventional diet), TM-10 and MAP-TM-10 groups.The fish were reared in floating cages for 12 weeks and The dietary effects on white blood cell ac-tivation, heat shock proteins, MAPKs, and apoptosis of the fish were evaluated. The MAP-TM-10 group exhibited the highest eosinophilic induction and plasma cells. Phosphorylated levels of p38 MAPK; p44/42 MAPK; HSP70 and HSP90 increased in the TM-10 and MAP-TM-10. In terms of apoptosis, Bax levels were lower in the TM groups compared to the Control, and the MAP-TM-10 group showed even lower levels than the TM-10 group. Bcl-2 levels increased in the TM-10 compared to the Control, and further increased in the MAP-TM-10 group. The Bax/Bcl-2 ratio, an apoptosis indicator, decreased in the TM groups, with the MAP-TM-10 group showing a further decrease compared to TM-10. These findings suggest that insects breeding substrate enriched with MAPs modulated the effect of TM on cellular stress and apoptosis.

A new green-validated and highly sensitive electrochemical method for the determination of molnupiavir (MOV) has been developed using cyclic voltammetry. The proposed analytical platform involves the use of disposable screen-printed reduced graphene oxide 2.5% electrode (SPrGOE 2.5%) for the first time to measure MOV with high specificity. The surface morphology of the sensor was investigated by using a scanning electron microscope armed with an energy-dispersive X-ray probe. The fabricated sensor attains improved sensitivity when sodium dodecyl sulfate (SDS) surfactant was added to the supporting electrolyte solution. Thus, various factors were investigated in order to select the best supporting electrolyte for voltammetric determination of MOV, and the optimum conditions were achieved by employing 0.04 M Britton-Robinson at pH 2, 10-4 M SDS, and SPrGOE 2.5%. Well-defined MOV oxidation peaks were obtained with no reduction peaks in cyclic voltammetry using diffusion-controlled pathways. The method was validated using differential pulse voltammetry according to ICH guidelines, providing it to be precise, accurate, specific, and robust with linearity over a concentration range of 50-6017 ng/mL. The incorporation of the reduced graphene nanoparticles supported the in situ interaction between electrode surface and MOV, improved the selectivity, and reduced the detection limit to the concentration level of 15.98 ng/mL. The stability investigation demonstrated that SPrGOE 2.5% can provide high-stability behavior throughout a three-month period under refrigeration. The fabricated SPrGOE 2.5% was successfully employed for the measurement of MOV in pharmaceutical capsules and human bio-fluids without the interference of endogenous matrix components as well as the commonly used excipient.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

Real-world optimization problems are often gov- erned by one or more constraints. Over the last few decades, extensive research has been performed in Constrained Opti- mization Problems (COPs) fueled by advances in computational power. In particular, Evolutionary Algorithms (EAs) are a preferred tool for practitioners for solving these COPs within practicable time limits. We propose a novel hybrid Evolutionary Algorithm based on the Differential Evolution algorithm and Adaptive Parameter Gaining Sharing Knowledge-based algo- rithm to solve global real-world constrained parameter space. The proposed CHAGSKODE algorithm leverages the power of multiple adaptation strategies concerning the control parameters, search mechanisms, as well as uses knowledge sharing between junior and senior phases. We test our method on the benchmark functions taken from the CEC2020 special session & competition on real-world constrained optimization. Experimental results indicate that CHAGSKODE is able to achieve state-of-the- art performance on real-world constrained global optimization when compared against other well-known real-world constrained optimizers.

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

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

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

Molecular mechanisms associated with the pathogenesis of Vesicular stomatitis virus (VSV) in livestock remain poorly understood. Several studies have highlighted the relevant role of macrophages in controlling the systemic dissemination of VSV during infection in different animal models, including mice, cattle and pigs. To gain more insight on the molecular mechanisms used by VSV to impair the immune response in macrophages, we used microarrays to determine the transcriptomic changes produced by VSV infection in primary cultures of porcine macrophages. The results indicated that VSV infection induced the massive expression of multiple anorexic, pyrogenic, proinflammatory and immunosuppressive genes. Overall, the interferon (IFN) response appeared suppressed, leading to the absence of stimulation of interferon-stimulated genes (ISG). Interestingly, VSV infection promoted the expression of several genes known to downregulate the expression of IFNb. This represents an alternate mechanism for VSV control of the IFN response, beyond the recognized mechanisms mediated by the matrix protein. Although there was no significant differential gene expression in macrophages infected with a highly virulent epidemic strain compared to a less virulent endemic strain, the endemic strain consistently induced higher expression of all upregulated cytokines and chemokines. Collectively, this study provides novel insights into VSV molecular pathogenesis and immune evasion that warrants further investigation

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

The Pashmina and Barbari are two famous goat breeds found in the wide areas of the Indo-Pak region. Pashmina is famous for its long hair-fiber (Cashmere) production while Barbari is not-selected for this trait. So, the mRNA expression profiling in the skin samples of both breeds would be an attractive and judicious approach for detecting putative genes involved in this valued trait. Here, we performed differential gene expression analysis on publicly available RNA-Seq data from both breeds. Out of 44,617,994 filtered reads of Pashmina and 55,995,999 of Barbari which are 76.48% and 73.69% mapped to the ARS1 reference transcriptome assembly respectively. A pairwise comparison of both breeds resulted in 47,159 normalized expressed transcripts while 8,414 transcripts are differentially expressed above the significant threshold. Among these, 4,788 are upregulated in Pashmina while 3,626 transcripts are upregulated in Barbari. Fifty-nine transcripts harbor 57 genes including 32 LOC genes and 24 are annotated genes which were selected on the basis of TMM counts > 500. Genes with ectopic expressions other than uncharacterized and LOC symbol genes are Keratins (KRT) and Keratin Associated Proteins (KRTAPs), CystatinA&6, TCHH, SPRR4, PPIA, SLC25A4, S100A11, DMKN, LOR, ANXA2, PRR9 and SFN. All of these genes are likely to be involved in keratinocyte differentiation, sulfur matrix proteins, dermal papilla cells, hair follicles proliferation, hair curvature, wool fiber diameter, hair transition, hair shaft differentiation and its keratinization. These differentially expressed reported genes are critically valuable for enhancing the quality and quantity of the pashmina fiber and overall breed improvement. This study will also provide important information on hair follicle differentiation for further enrichment analyses and introducing this valued trait to other goat breeds as well.

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

The hydrodynamic behavior of the air-acetic acid system in a bubble column is studied using a differential pressure transmitter, double probe optical fiber probe, and the electrical resistance tomography (ERT) technique. The superficial gas velocity ranges from 0.016 to 0.094 m/s under ambient temperature and pressure. The influences of viscosity and surface tension on gas holdup, bubble rising velocity, and bubble chord distribution in the column are discussed with different mass fractions of an acetic acid solution. The results show that as the mass fraction of acetic acid increases, the surface tension of the liquid phase decreases, and the viscosity first increases and then decreases. This causes the gas holdup in the column to first increase and then decrease, and reaches the maximum value at an acetic acid mass fraction of 55% to 60%. The rising velocity of the bubbles in the column is high in the central region and has a low-value distribution near the wall. The bubble chord length distribution is concentrated, and the distribution of the bubble chord length in the column becomes narrow with any decrease in surface tension. Studying the hydrodynamic behavior of a bubble column with the air-acid system is of great significance considering the absence of data on air-organic acid systems.

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses an extension of Haebara linking by proposing a flexible class of robust linking functions for comparisons of many groups. These robust linking functions are particularly suited to item response data that are generated under partial invariance. In a simulation study, it is shown that the newly proposed robust Haebara linking approach outperforms existing approaches of Haebara linking. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

In the present paper, we introduced and study a new class of harmonic univalent functions on unit disc U. also we obtain coefficient conditions, extreme points, convolution condition for the above class of harmonic univalent functions.

This paper describes the dielectric relaxation spectroscopy (DRS) method for obtaining glass transition temperature and the onset of crystallinity of skim milk powder (SMP). The methodology consists of exposing SMP samples to numerous constant temperatures, T, and water activities, a_w, and measuring the relaxation time. Measurements are based on changes in the loss-tangent height at its peak frequency. Glass transition times are identified at peaks in the loss-tangent height versus time curve and the onset of crystallinity times are identified when the loss-tangent height collapses. The analysis leads to two boundary curves: glass transition T_g, a_w curve and the onset of crystallinity T_c, a_w curve. They separate the SMP stable (long shelf life) and unstable (short shelf life) regions. Two curve fitting algorithms were developed for (a) a_w², t_g curve where t_g is the time to glass transition and a_w², t_c curve where time t_c is the time to onset of crystallinity and (b) T_g, a_w and T_c, a_w boundary curves. Finally, the DRS data are compared to differential scanning calorimetry (DSC) results.

A simple in vitro biosensor for the detection of β-amyloid 42 in phosphate-buffer saline (PBS) and undiluted human serum was fabricated and tested based on our platform sensor technology. The bio-recognition mechanism of this biosensor was based on the effect of the interaction between antibody and antigen of β-amyloid 42 to the redox couple probe of K₄Fe (CN) ₆ and K₃Fe (CN) ₆. Differential pulse voltammetry (DPV) served as the transduction mechanism measuring the current output derived from the redox coupling reaction. The biosensor was a three-electrode electrochemical system, and the working and counter electrodes were 50 nm thin gold film deposited by sputtering technique. The reference electrode was a thick-film printed Ag/AgCl electrode. Laser ablation technique was used to define the size and structure of the biosensor. Cost-effective roll-to-roll manufacturing process was employed in the fabrication of the biosensor making it simple and relatively inexpensive. Self-assembled monolayers (SAM) of 3-Mercaptopropionic acid (MPA) was employed to covalently immobilize the thiol group on the gold working electrode. A carbodiimide conjugation approach using N-(3-dimethylaminopropyl)-N’-ethylcarbodiimide hydrochloride (EDC) and N–hydroxysuccinimide (NHS) was undertaken for cross-linking antibody of β-amyloid 42 to the carboxylic groups on one end of the MPA. The antibody concentration of β-amyloid 42 used was 18.75µg/mL. The concentration range of β-amyloid 42 in this study was from 0.0675µg/mL to 0.5µg/mL for both PBS and undiluted human serum. DPV measurements showed excellent response in this antigen concentration range. Interference study of this biosensor was carried out in the presence of Tau protein antigen. Excellent specificity of this β-amyloid 42 biosensor was demonstrated without interference by other species such as T-tau protein.

This paper presents a two-stage ADC based on pseudo-differential operational transconductance amplifier (OTA), which is designed for the readout circuit of X-ray linear array sensor. This hybrid ADC employs an incremental sigma-delta ADC and a cyclic ADC, achieving a good trade-off between accuracy and conversion speed. The two stages share the same hardware to reduce power consumption and die area. A common-mood feedback module is used to suppress the influence of charge injection, and the effectiveness is demonstrated by detailed theoretical analysis. A test chip of 14-bit ADC is fabricated in 0.35μm CMOS technology. The measured root mean square (RMS) value of DNL is 0.254 LSB, and the maximum value of INL is -0.776/+1.56 LSB. The measured effective number of bits (ENOB) is 13.43 bits.

To address the issue of GNSS receivers being unable to function properly in tunnels due to the loss of Global Navigation Satellite System(GNSS) signals, this paper proposes a two-dimensional differential positioning system for tunnel environments, based on dual leaky coaxial(LCX) cables with GNSS signal frequency relay forwarding. The system receives mixed GNSS signals from open environments and utilizes the frequency selection capabilities of the MAX2769E chip to separate and generate radio frequency signals at different frequencies corresponding to GPS, BDS, and GLONASS. These signals are then used to drive three ports of the LCX cables, which are laid in parallel within the tunnel. By leveraging the uniform radiation characteristics of the LCX cables, stable GNSS signal coverage is achieved throughout the tunnel. On the receiving end, the GNSS receiver achieves two-dimensional positioning by utilizing inter-satellite pseudorange differences and reference point error correction. Simulation results indicate that the dual T-shaped radiating LCX cables configuration offers excellent positioning accuracy and noise resistance, achieving meter-level positioning accuracy in tunnel environments.

Psychiatric disorders, characterized by complex and fluctuating patterns of thoughts, emotions, and behaviors, can be effectively modeled and visualized using mathematical wave equations. This study explores the representation of three major psychiatric conditions— Psychosis, Bipolar Disorder and Obsessive Compulsive Disorder (OCD)—through the application of differential equations, damping factors, and noise perturbations. Psychosis is modeled using Lissajous figures with high-frequency components, damping, and noise, symbolizing the irregular and erratic thought patterns characteristic of this condition. The inclusion of random perturbations and varying frequencies illustrates the chaotic and unpredictable nature of psychotic episodes, while damping effects reflect the temporary reductions in symptom intensity. For bipolar disorder, a system of partial differential equations simulates the cyclical nature of manic and depressive episodes. The model captures high-energy manic phases with periodic disturbances and the subsequent transition to lower-energy depressive states through damping effects. This representation highlights the oscillatory behavior and recurring episodes inherent to bipolar disorder. OCD is represented with Circumferential Complex Equations in Mult directions. The resulting graphical representations provide intuitive visual insights into the dynamics of these psychiatric disorders. By leveraging wave equations and mathematical modeling, this approach offers a novel perspective on understanding and analyzing the complex behaviors associated with OCD, bipolar disorder and psychosis. This method not only aids in the conceptualization of psychiatric phenomena but also underscores the potential of mathematical tools in the study of mental health conditions.

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established, when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.

In our study we investigated the accelerated aging process of PLA under 253.7 nm UV-C irradiation with the use of GPC, NMR, FTIR, DSC methods and formal kinetic analysis. The results of GPC and DSC indicated a significant degree of destructive changes in PLA macromol-ecules, while spectroscopic methods NMR and FTIR showed maintenance of PLA main structural elements even after a long time of UV exposure. In addition to that, the GPC method displayed the formation of a high-molecular fraction starting from 24 hours of irradiation, and an increase in its content after 144 hours of experiment. It has been showed for the first time that a distinctive feature of prolonged UV exposure is the occurrence of intra- and intermolecular radical recom-bination reactions, leading to the formation of a high-molecular fraction of PLA decomposition products. This causes the observed slowdown of the photolysis process. It was concluded that photolysis of PLA is a complex of physicochemical processes, the mechanism of which depends on morphological changes in a solid phase of the polymer under UV radiation.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*>0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

The influence of polysialic acid (PSA) and sialic acid (SA) on the gut microbial community composition and metabolites in healthy human was investigated using a bionic gastrointestinal reactor. The results indicated that PSA and SA significantly changed the gut microbiota and metabolites in different degrees. PSA can increase the relative abundances of Faecalibacterium and Allisonella, whereas SA can increase those of Bifidobacterium and Megamonas. Both can significantly increase the content of short-chain fatty acids. The results of metabolome analysis showed that PSA can upregulate ergosterol peroxide and gallic acid and downregulate the harmful metabolite N-acetylputrescine. SA can upregulate 4-pyridoxic acid and lipoic acid. PSA and SA affect gut microbiota and metabolites in different ways and have positive effects on human health. These results will provide reference for the further development of PSA- and SA-related functional foods and health products.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

Key thermophysical properties necessary for the successful design and use of CoCrFeNi alloy in thermophysical applications have been measured experimentally, and the results have been compared with literature values and results previously obtained for commercial Ni-Cr alloys and equiatomic CoCrFeNi alloy. In particular, the thermal diffusivity, coefficient of thermal expansion (CTE), and specific heat capacity were measured for the as-cast and homogenized equiatomic CoCrFeNi alloy over a temperature range allowing the thermal conductivity to be calculated up to 1173 K. The thermal conductivity and thermal diffusivity of the equiatomic CoCrFeNi alloy were found to deviate from monotonic behavior in the temperature range from 773 to 1100 K. Such a deviation was previously observed in the behavior of the temperature dependence of CTE and specific heat capacity of the equiatomic CoCrFeNi alloy. The non-linear behavior is primarily the result of order/disorder phenomena for the as-cast and homogenized sample, as well as additionally for the as-cast sample, non-equilibrium solidification under arc melting conditions. The measured data of thermophysical properties are provided for thermally differently treated samples, and it is shown that there is a difference in the behavior of the temperature dependences of CTE, thermal diffusivity, and heat capacity.

The main object of this work is to establish the existence and uniqueness of a solution to the 3D Navier-Stokes (NS) system for an incompressible fluid with viscosity. The nonlinearity of the NS system, as well as the need to estimate velocity and pressure for every value of the viscosity parameter [1] make them challenging to solve. In this regard, in the present work, we study the Navier-Stokes system, which describe the flow of a viscous incompressible fluid and the solution was obtained for velocity and pressure in an analytical form. In addition, the found pressure distribution law, which is described by a Poisson type equation and plays a fundamental role in the theory of Navier-Stokes systems in constructing analytic smooth (conditionally smooth) solutions.

In order to solve the problems of complicated steering control of unmanned vehicles in the field and difficult steering on complex roads, we designed a wheel-track composite vehicle equipped with a novel power differential steering mechanism with dual driving, which drove the steering of the vehicle through the differential rotation of the rear two wheels. The unmanned vehicle was simple to control, small in size, and able to work under the conditions of complex roads, such as hills, mountains, and muddy land. Firstly, a steering mechanism with both differential speed and force was designed to prevent the vehicle from skidding into muddy land and stopping motionless. Secondly, the kinematics model and dynamics model of the two drive shafts and the two output shafts (wheel shafts) were established. Thirdly, according to the relationship between the rotational speed of the two output shafts and the steering radius of the vehicle, the kinematic model of the rotational speed of the two input shafts and the steering radius of the wheel-track composite vehicle was obtained. Finally, according to the test data, the mathematical model of rotational speeds of the two input shafts and the actual steering radius of the vehicle was obtained by neural network fitting, and the maximum relative error between the model results and the actual steering radius value was 3.53%. The combination of power differential steering mechanism and wheel-track composite unmanned vehicle increased the adhesion with the ground and could better adapt to the complex road environment. In conclusion, the unmanned vehicle had the advantages of continuous radius steering, deceleration and torsion increase, differential lock, etc. It was suitable for all-terrain military and civilian vehicles and various special equipment mobile platforms of the walking device, and the research results could provide theoretical references for the steering control and structural optimization of the wheel-track composite vehicle under the environment of complex road surface.

In a previous paper, we solved the partial differential equation of Mullins problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed 〖y'〗^2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

In a power plant that uses seawater as a coolant, a debris filter is required to remove foreign substances from the seawater, and differential pressure leads to a decrease in the coolant flow rate, leading to a decrease in power generation efficiency. In this study, analysis was performed under different initial flow velocity conditions of 1.5m/s, 2.0m/s, and 2.5m/s for a debris filter used in a power plant to understand flow characteristics in CTCS. The flow and differential pressure characteristics of a CTCS with an installed debris filter were considered in a comparative analysis of velocity, pressure, and turbulent kinetic energy distribution. The results confirmed that a vortex was generated in the pipe with the debris filter, apparently due to the collision of the flow with the bracket of the debris filter. As the flow rate increased, the range of the vortex increased, causing a loss in flow.

The deep energy method (DEM), a type of physics-informed neural network, is evolving as an alternative to finite element analysis. This method employs the principle of minimum potential energy to predict deformations under static loading conditions. However, the model’s accuracy is contingent upon choosing the appropriate architecture for the model, which can be challenging due to the high interactions between hyperparameters, large search space, difficulty in identifying objective functions, and non-convex relationships with the objective functions. To improve DEM’s accuracy, we first introduce random Fourier feature (RFF) mapping. RFF mapping helps with the training of the model by reducing bias towards high frequencies. The effects of six hyperparameters are then studied under compression, tension, and bending loads in planar linear elasticity. Based on this study, a systematic automated hyperparameter optimization approach is proposed. Due to the high interaction between hyperparameters and the non-convex nature of the optimization problem, Bayesian optimization algorithms are used. The models trained using optimized hyperparameters and having Fourier feature mapping can accurately predict deflections compared to finite element analysis. Additionally, the deflections obtained for tension and compression load cases are more sensitive to variations in hyperparameters than bending.

To guide analysts to select the right tool and parameters in differential gene expression analysis of single-cell RNA sequencing (scRNA-seq) data, we developed a novel simulator that recapitulates the data characteristics of real scRNA-seq datasets while accounting for all the relevant sources of variation in a multi-subject, multi-condition scRNA-seq experiment: the cell-to-cell variation within a subject, the variation across subjects, the variability across cell types, the mean/variance relationship of gene expression across genes, library size effects, group effects, and covariate effects. By applying it to benchmark 12 differential gene expression analysis methods (including cell-level and pseudo-bulk methods) on simulated multi-condition, multi-subject data of the 10x Genomics platform, we demonstrated that methods originating from the negative binomial mixed model such as glmmTMB and NEBULA-HL outperformed other methods. Utilizing NEBULA-HL in a statistical analysis pipeline (https://github.com/interactivereport/scRNAseq_DE) for single cell analysis will enable scientists to better understand cell-type specific transcriptomic response to disease or treatment effects and to discover new drug targets. Further, application to two real datasets showed the outperformance of our differential expression (DE) pipeline, with unified findings of differentially expressed genes (DEG) and a pseudo-time trajectory transcriptomic result. In the end, we made recommendations of filtering strategies of cells and genes based on simulation results to achieve optimal experimental goals.

A gold nanostructured film modified glassy carbon electrode (Au_film/GCE) was developed for the determination of chromium (VI) in water sample. GCE was immersed into HAuCl₄ solution (10^-3M) and electrodeposition of thin gold layer was conducted at –0.4 V (vs Ag/AgCl) for 10 min. The strong affinity between Au and Cr species resulted with increasing of Cr (VI) signal, compared with the bare glassy carbon electrode. The electrodepositing time, type of supporting electrolyte, pH, the scan rate, modulation amplitude, and modulation time were optimized using differential pulse anodic stripping voltammetry (DP-ASV). The calibration graph using accumulation time of 120 s was linear from 10 to 120 µgL^-1 with a sensitivity 1.3 x 10^-2 µA/µgL^-1. Under optimum experimental conditions, a good correlation coefficient R²=0.9971, and a low detection limit 5.5 µg/L Cr (VI) was obtained. The signal was reproducible with a relative standard deviation ±4.5 %. The developed Au_film/GCE sensor was applied for the Cr (VI) determination of in sewage water samples.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

Extracellular vesicles (EVs) are membranous vesicles secreted by both prokaryotic and eukaryotic cells and play a vital role in intercellular communication. EVs are classified into several subtypes based on their origin, physical characteristics, and biomolecular makeup. Exosomes, a subtype of EVs, are released by the fusion of multivesicular bodies (MVB) with the plasma membrane of the cell. Several methods have been described in literature to isolate exosomes from biofluids including blood, urine, milk, and cell culture media among others. While differential ultracentrifugation (dUC), has been widely used to isolate exosomes, other techniques including ultrafiltration, precipitating agents such as poly-ethylene glycol (PEG), immunoaffinity capture, microfluidics and size exclusion chromatography (SEC) have emerged as credible alternatives with pros and cons associated with each. In this review, we provide a summary of commonly used exosomal isolation techniques with a focus on SEC as an ideal methodology. We evaluate the efficacy of SEC to isolate exosomes from an array of biological fluids, with a particular focus on its application to adipose tissue-derived exosomes. We argue that exosomes isolated via SEC are relatively pure and functional, and that this methodology is reproducible, scalable, inexpensive, and does not require specialized equipment or user expertise.

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

In the environments of all kinds open coal storage sites , mining-affected coalbeds, and goafs, parts of coal body at low moisture content (≤8%) are prone to spontaneous combustion under the influence of some external environmental factors. In order to examine the influence effect of low moisture content on the spontaneous combustion tendency of coals with different metamorphic grade, we conducted temperature programmed oxidation (TPO) experiment and differential scanning calorimetry (DSC) experiment to study the spontaneous combustion characteristics of coals with different metamorphic grade at four different low moisture content, and comparatively analyzed the change laws of the characteristic parameters of four different metamorphic grade coals at four different low moisture content. The experimental results indicate that: 1) Compared other low moisture content, anthracite and fat coal at low moisture content of 1.2% show stronger tendency to undergo spontaneous combustion, long flame coal and lignite at low moisture content of 3.4% and 5.6% are more prone to spontaneous combustion. 2) Four different metamorphic grade coals at low moisture content of 7.8% are less prone to spontaneous combustion; 3) Coals with different metamorphic grade have different tendency to undergo spontaneous combustion.

By defining a constant probabilistic orbit of and iterated functions, the stability dynamics of these functions in possible interactions through connectivity provides the formation of a dynamic fixed point as a metric space between both iterated functions. The presence of a dynamic fixed point identifies qualitatively phases of iteration time lengths and interaction orbits of the event. Qualitative results show that the greater the average distance from one of the functions to the fixed point of the other (all possible solutions), the higher the iteration expression on time (false asymptotic effect) of one of the functions and in the opposite hand, the lower the average distance, the higher orbit’s interactions proximity between iterated functions (stability). This feature reveals asymptotic (well-defined) behavior between functions f and g within a well-defined Lyapunov stability.

A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the c.d.f. of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of processes’ measure.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

This study investigates the solution of a boundary value problem using two numerical methods: the Rayleigh-Ritz method and the finite element method (FEM). The aim is to compare the performance of these methods and assess the reliability of FEM as a generalization of the Rayleigh-Ritz approach for more complex problems. The Rayleigh-Ritz method and the linear element formulation of the finite element method were employed to solve the boundary value problem. A detailed comparison of the results obtained from both methods was performed. Graphical illustrations were used to present the solutions, and potential sources of error were analyzed, including element and domain approximation errors, round-off errors, and the impact of using linear rather than quadratic elements in FEM. The solutions generated by both methods were found to be in close agreement, demonstrating that FEM is a viable alternative to the Rayleigh-Ritz method for solving boundary value problems. The minor discrepancies observed can be attributed to approximation errors and the choice of linear elements in the finite element analysis. This work highlights the applicability and effectiveness of both the Rayleigh-Ritz method and FEM in solving boundary value problems. It underscores the finite element method’s flexibility, especially in handling more complex boundary conditions and geometries, and contributes to the understanding of the factors influencing the accuracy of numerical methods in structural analysis.

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

Heavy metals represent a class of chemical elements that includes metalloids, bases and transition metals, lanthanides and actinides. They are distinguished for their toxicity in small concentrations and for their negative effects on the environment and human health. They are present in various samples, mainly in water, industrial waste and food. The determination of heavy metals is carried out mainly by analytical methods, using spectroscopy, spectrometry and electroanalysis, while studies are being carried out for the development of new and faster methodologies and techniques for their analysis, with particular emphasis on voltammetry. This review deals with the determination of heavy metals mainly in environmental samples (water) using voltammetry. In particular, the methods of their determination are evaluated in terms of sensitivity, selectivity and applicability.

Sensory descriptive analysis was used to evaluate the aged Feng-flavored baijiu. The results indicated that there are notable differences in the samples of different ages. The samples with shorter storage times and fresh distilled Baijiu present bran flavor, and fresh green flavor. with the increase of storage time, the fragrance of honey, sweetness, flowers, and aging gradually increases. The samples of Feng-flavored baijiu were dected by Headspace solid-phase microextraction (HS-SPME) combined with comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC–TOFMS) , in total, 496 sustances were identified in all samples, mainly containing 14 types of substances, such as esters, aldehydes etc., of which 42 substances were found in Feng-flavored baijiu for the first time. Chemometrics was used to analyze the key differential compounds. 143 differential compounds closely related to aging were preliminarily screened, and principal component analysis revealed that these samples were separated by year. 65 differential compounds were selected out by partial least squares discriminant analysis(PLS-DA). Furthermore, 43 key differential compounds were selected from the aged Feng-flavored baijiu combined with variable importance in projection and Pearson correlation coefficients. Partial least squares regression (PLSR) was used to research the correlation of sensory properties and key differential compounds, and the results indicated that most compounds were closely related to the aged Baijiu . This study afford theoretical basis and reference for flavor research of Feng-flavored baijiu.

The susceptible-infected-recovered/removed-vaccinated (SIRV) epidemics model is an important generalization of the SIR epidemics model as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemics outbreaks. Additional to the time-dependent infection ($a(t)$) and recovery ($\mu (t)$) rates, regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively, the time-dependent vaccination rate $v(t)$ accounts for the transition between the compartments $S\to V$ of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections $J(t)\ll 1$. As vaccination campaigns automatically reduce the rate of new infections by transferring susceptible to vaccinated persons, the limit $J(t)\ll 1$ is even better fulfilled than in the SIR-epidemics model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections $\jt(t)=a(t)S(t)I(t)$, the corresponding cumulative fraction $J(t)$, and $V(t)$, respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction $\jinf $ after infinite time allows us to check the validity of the original assumption $J(t)\le \jinf \ll 1$.

The energy-intensive sector of the cement industry needs to find technologically advanced methods to produce cement with as little energy as possible, without polluting the environment and without sacrificing the quality (fineness) of the cement. In addition, the stress on the machines changes the behavior of the data. By combining the k-means method, two (2) feature selection methods, nine (9) machine learning methods, and the differential evolution (DE) method, a dynamic system is created where the user determines the key performance indicators (KPIs) each time. The user has the potential to control the distribution of the data, the input of machine learning models, and the ability to switch the system to the suggested values without damage. The selection of the best-performing models is based on the normalized root mean squared error (NRMSE). The DE method optimizes the dynamic objective function. The optimal values of the manipulated variables are evaluated compared to the value of the objective function from the actual values of the variables. In all experiments, the recommendations are acceptable. The final results show an improvement in the operation of both the cement mill and kiln compared to the current operating condition.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

Pea (Pisum sativum L.), like most legumes, forms mutualistic symbioses with nodule bacteria and arbuscular mycorrhizal (AM) fungi. The positive effect of inoculation is partially determined by the plant genotype, thus, pea varieties with high and low symbiotic responsivity have been described, but the molecular genetic basis of this trait remains unknown. Here, we compare the symbiotically responsive breeding line ‘Triumph’ of grain pea with its parental cultivars ‘Vendevil’ (a donor of high symbiotic responsivity) and ‘Classic’ (a donor of agriculturally valuable traits) using genome and transcriptome sequencing. We show that ‘Triumph’ inherited one-fourth of its genome from ‘Vendevil’, including the genes related to AM and nodule formation, and reveal that under combined inoculation with nodule bacteria and AM fungi, ‘Triumph’ and ‘Vendevil’, in contrast to ‘Classic’, demonstrate similar up-regulation of the genes related to solute transport, hormonal regulation and flavonoid biosynthesis in their roots. We also identify the gene PsGLP2, whose expression pattern distinguishing ‘Triumph’ and ‘Vendevil’ from ‘Classic’ correlates with difference within the promoter region sequence, making it a promising marker for the symbiotic responsivity trait. The results of the study may be helpful for future molecular breeding programs aimed at creation of symbiotically responsive cultivars of pea.

A systematic and comprehensive review of critical applications of Blockchain Technol-ogy with Differential Privacy integration lies within the privacy and security enhancement. This paper aims to highlight the research issues in the e-health domain (e.g., Electronic Medical Rec-ords) and to review the current research directions in Differential Privacy integration with Blockchain Technology.(1) Background: The current state of the art in the e-health domain is identified as follows: (a) healthcare information poses a high level of security and privacy concerns due to its sensitivity; (b) due to vulnerabilities surrounding the healthcare system, a data breach is common and presents a risk for attacks by an adversary; and (c) the current privacy and security apparatus needs further fortification. (2) Methods: The methodology uses a systematic literature review (SLR) to identify and select relevant research papers and academic journals in DP and BT. (3) Results: The results are categorized into: e-Health Record Privacy, Real-Time Health Data, and Health Survey Data Protection to identify inherent issues with Differential Privacy integra-tion with Blockchain and technical challenges.(4) Conclusion: This review thoroughly surveyed and summarized Differential Privacy mechanisms in EMR privacy, real-time health data, and health survey data protection while highlighting challenges.

Quantitative differential phase contrast (qDPC) imaging has become an important method of optical measurement and life science research in microscopy because of its high reconstruction resolution and non-invasive, high-contrast and quantitative imaging of biological samples. Despite the continuous development of the principle and algorithm, the frame rate of the existing qDPC algorithm is still much lower than that of camera acquisition, so it is hardly applied to real-time image the fast-moving biological samples. In this paper, based on color-coded multiplexing strategy, a compact real-time quantitative phase imaging system is designed to realize multi-mode imaging. The system employs a programmable LED array to illuminate directly, and the phase reconstruction algorithm is deployed in the graphics processing unit (GPU) of the laptop to accelerate the calculation. The system can achieve high-speed quantitative phase imaging of non-stained biological samples, and the frame rate can reach 60fps. The device has the advantages of compact structure, low cost and portability. Thus, it is suitable for mobile medical applications.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often deviates from strict deterministic patterns due to stochastic factors such as genetic variation and environmental fluctuations. In this study, we extend a general model for ontogenetic growth proposed by West et al. to stochastic models for ontogenetic growth by incorporating stochasticity using white noise. According to data variance fitting for stochasticity, we propose two stochastic models for ontogenetic growth, one is for determinate growth and one is for indeterminate growth. To develop a universal stochastic process for ontogenetic growth across diverse species, we approximate stochastic trajectories of two stochastic models and apply random time change and obtain a geometric Brownian motion with a multiplier of an exponential time factor. We conduct detailed mathematical analysis and numerical analysis for our stochastic models. Our stochastic models predict well not only average growth, but also variations of growth within species. This stochastic framework may be extended to studies of other growth phenomena.

Our objective in this work is to demonstrate how Physics-Informed Neural Networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a prismatic cantilever beam that is exposed to triangular loading, and comprehending its mechanical behavior is of utmost importance in the aerospace field. PINNs utilize the physical information, including differential equations and boundary conditions, within the loss function of the neural network to approximate the solution. Our approach determines the overall loss by aggregating the losses from the differential equation, boundary conditions, and data. We employed a Physics-Informed Neural Network (PINN) and an Artificial Neural Network (ANN) with equivalent hyperparameters to solve a fourth-order differential equation. By comparing the performance of the PINN model against the analytical solution of the equation and the results obtained from the ANN model, we have conclusively shown that the PINN model exhibits superior accuracy, robustness, and computational efficiency when addressing high-order differential equations that govern physics-based problems. In conclusion, the study demonstrates that PINN offers a superior alternative for addressing solid mechanics problems with applications in the aerospace industry.

In this work, we study a boundary control problem for the evolutionary Stokes equations, under mixed boundary conditions, in two and three dimensions. The Stokes equation is a valuable tool in cardiovascular biomechanics, especially for modeling blood flow in low-velocity and high-viscosity conditions. Its application in the microvasculature, the design of medical devices, and the study of cardiovascular diseases helps improve the understanding and treatment of various pathological conditions. We provide a comprehensive theoretical framework to address the analysis and the derivation of a system of first-order optimality conditions that characterizes the solution of the control problem. Finally, solution-finding algorithm is proposed and illustrated with some simulations.

This research paper is divided into two aspects: first part describes the modelling techniques which are referred for handling infectious diseases in public health domain, second part describes the modelling techniques which are referred for building epidemiology cases in public health domain. To illustrate further, first part helps in understanding various modeling ordinary differential equations have been defined to develop the definition, described to know the terminologies involved in developing the equations and henceforth established to understand the end-to-end process. Second part helps in understanding various aspects of epidemiology in public health domain and how they help in addressing the public health domain policy-making.

This study aims to refine our understanding of evolutionary processes, particularly as they apply to complex organisms, using an innovative graph-based simulation approach. We model the topological evolution of simple (5-node ring graph) and complex (20-node dense random graph) organisms over 10 generations, applying different mutation rates to reflect biological realities. Our results provide intriguing insights into the potentially different evolutionary dynamics at play in simple versus complex organisms. While simple organisms demonstrate high topological flexibility and rapid adaptability, aligning with classical evolutionary models, complex organisms exhibit a surprising degree of structural stability. This stability persists even under mutation rates that would typically drive significant changes in simpler systems. The simulation highlights an important consideration: the intricate, interdependent networks characteristic of complex organisms may create a form of evolutionary buffering. This buffering could modulate the impact of random mutations and natural selection – processes that are cornerstones of evolutionary theory. Our findings suggest that the high degree of complexity in advanced life forms may necessitate a more nuanced view of how evolutionary processes operate across different levels of biological organization. Furthermore, the emergence of new structural motifs in simple organisms, contrasted with the relative conservation in complex topologies, indicates that evolutionary mechanisms may manifest differently across the spectrum of biological complexity. This observation invites a more detailed exploration of how evolutionary principles apply to diverse life forms.These results contribute to the ongoing refinement of evolutionary theory, especially in its application to complex organisms. They suggest that additional mechanisms, such as constrained mutations, epigenetic changes, or higher-order organizational principles, may play significant roles alongside random mutations and natural selection in the evolution of complex life forms.

In the face of rising global demand and unsustainable production methods, cultivated crustacean meat (CCM) is proposed as an alternative means to produce delicious lobster, shrimp and crab products. Cultivated meat requires starting stem cells that may vary in terms of potency, and propensity to proliferate or differentiate into myogenic (muscle-related) tissues. We suggest that regenerating crustacean limbs harbor a range of stem cells suitable for cultivated meat production and present a humane tissue source because they can be accessed non-lethally. To investigate stem cell activity in this model, we have conducted RNA-Seq analysis across six stages of claw regeneration in the crayfish Cherax quadricarinatus (four pre-molt and two post-molt stages), along with histology and real time quantitative PCR (qPCR). Differential expression analysis revealed expression patterns of significantly up- or down-regulated genes in 14 functional categories. Relative expression of select stem cell target genes (including endocrine, myogenic, cell cycle and pluripotency factors) highlighted two growth peaks during pre-molt regeneration and limited stem cell activity after the molt. Histology and qPCR results support the overall finding that pre-molt limb regeneration stages harbor more stem cell activity, likely making them a more prolific cell source for CCM development.

The paper describes the new method for image compression based on coordinated group signal transformation. The algorithm is a type of difference coding. Coordinated processing significantly simplifies the difference signal conversion scheme using a single group codec for all signals. The described method considers color channels as correlated signals of a multi-channel communication system. The specifics of the processed data required modification of the coordinated group processing algorithm. First, we changed how to calculate the difference signals to prevent data loss. Secondly, the group codec was supplemented with a neural network to improve the quality of reconstructed images. We considered the following types of neural networks: fully connected, recurrent, convolution, and convolution in the Fourier space. Based on the simulation results, it is best to use fully connected neural networks if the goal is to minimize processing delay time. These networks have a response time of 13 ms. On the other hand, if the priority is to improve quality in cases where delays are not critical, then convolution neural networks in the Fourier space should be used. These networks have a response time of 140 ms and are of significant interest.

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we obtained, analytically, the corresponding solutions for the conditional moment generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case. We believe that the The aforementioned model encompasses a range of processes similar to that produced by a bivariate square-root process in which entries are correlated in the standard way, i.e., via a constant correlation coefficient. Note that, for the latter, closed-form solutions for the conditional characteristic functions are not available. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices via a Fourier cosine series method.

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.

In this paper, we derive Jeffreys divergence, generalized Fisher divergence and corresponding De Bruijn identities on space-time random field. First, we determine the relation between Fisher information on the space-time random field in one of the space-time points and the ratio of Jeffreys divergence on a space-time random field at distinct space-time positions to the square of coordinate difference. In addition, we also find identities between the partial derivative of the Jeffreys divergence and the generalized Fisher divergence with respect to space-time variables, i.e. the De Bruijn identities, between two space-time random fields obtained by different parameters under the same Fokker-Planck equations. At the end of this paper, we present three examples of the Fokker-Planck equations on space-time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and accompanying De Bruijn identities.

A patient in her early 20s presented with constant and progressive lower abdominal and back pain, mainly on the right side of the abdomen, purulent vaginal discharge and pyrexia. Radio-logical assessment revealed a possible tuboovarian abscess and incidental diagnosis of ipsilateral renal agenesis. The patient was treated for pelvic inflammatory disease (PID), however after antibiotic administration and since the symptoms were not resolving, an abdominal MRI was requested which revealed a uterus didelphys with two cervices, an obstructed haemivagina and evidence of haematocolpos. The diagnosis of OHVIRA syndrome was confirmed and the patient underwent an excision of the vaginal septum, drainage of the haematopyocolpos and laparoscopic drainage of the tuboovarian abscess. She achieved a good recovery.

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black-Scholes-Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath-Jarrow-Morton model and adapting the Hull-White interest rate model to fit BMM. The study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

In this paper we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra. Making use of this we construct two examples of transposed Poisson superalgebra. One of them is the graded differential algebra of differential forms on a smooth finite dimensional manifold, where we use the Lie derivative as an even degree derivation. The second example is the commutative superalgebra of basic fields of the quantum Yang-Mills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We prove several identities, which hold in a transposed Poisson superalgebra.

(1) Background: Motor neuron diseases (MNDs) are fatal neurodegenerative diseases. Biomarkers could help in defining patients’ prognosis and stratification. Beyond neurofilaments, chitinases are a promising family of possible biomarker, which correlate with neuroinflammatory status. We evaluated plasmatic levels of CHI3L1 in MNDs, MND mimics and healthy controls (HCs); (2) Methods: We used Sandwich ELISA to quantify CHI3L1 in plasma samples from 44 MNDs, 7 HSP, 9 MND mimics and 19 HCs. We collect also ALSFRSr scale, MRC scale, spirometry, mutational status, progression rate (PR), blood sampling, neuropsychological evaluation; (3) Results: Plasma levels of CHI3L1 resulted to be different among groups (p= 0.005). Particularly, MND mimics showed higher CHI3L1 levels compared to MNDs and HCs. CHI3LI levels did not differ among PMA, PLS and ALS and we do not find correlation among CHI3L1 levels and clinical scores, spirometry parameters, PR, and neuropsychological features. Of note, red blood cells count and haemoglobin correlated with CHI3L1 levels (respectively, p<0.001, r=0.63; p= 0.022, r=0.52); (4) Conclusions: CHI3L1 plasma levels resulted to be increased in the MND mimics cohort when compared to MNDs. The increase of CHI3L1 in neuroinflammatory processes could explain our findings. We confirmed that CHI3L1 plasma levels did not differentiate between ALS and HCs and nor correlate with neuropsychological impairment.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

In this work, we studied the Green’s functions of the second order differential operators with involution. Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution is obtained. Basicity of eigenfunctions of the second-order differential operator operator with complex-valued coefficient is established.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

Traditional potential transformers have problems of large volume, difficulty in insulation, iron core saturation, ferroresonance overvoltage and poor transient response characteristics. The voltage sensor based on the principle of electric field coupling and differential input structure does not need to contact the measured object or ground, and can avoid the above problems. However, it requires a sufficiently high capacitance between the differential electrodes to obtain sufficient accuracy and a high voltage division ratio. The existing method of using mutual capacitance between the differential electrodes will cause many problems and fail to meet the practical needs. To solve the above problems, this paper innovatively uses multi-layer ceramic capacitor to replace the mutual capacitance and designs a new type of voltage sensor. In addition, by using single bypass small resistance grounding method to increase the input impedance of the differential signal processing circuit, error of the sensor is further reduced. The experimental results show that the sensor has excellent accuracy and great transient response characteristics. The ratio error under power frequency is within ±0.5% and the phase error is within 1. The ratio error in the range of 500 Hz∼30 kHz is within ±5% and the phase error is within 5. Moreover, it has the advantages of low cost, miniaturization, flexible shape and easy to adjust the voltage division ratio. These characteristics indicate that the sensor has good voltage measurement and sensor network potential.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

Inequality of health service for different specialty categories not only occurs in different areas inequality of health service for different specialty categories in the world, but also happens in the online service platform. In the online health community (OHC), health service was often of inequality for different specialty categories, including both online views and medical consultation for offline registered service. Moreover, how the factor city-level impacts the inequality of health service in OHC is still unknown. We designed a causal inference study with data on distributions of serviced patients and online views in over 100 distinct specialty categories on one largest OHC in China. To derive the causal effect of the city-levels (two levels inducing 1 and 0) on the Gini coefficient, we matched the focus cases in cities of rich healthcare resources with the potential control cities. For the Gini coefficient of serviced patients in over 100 specialty categories, the average treatment effect of level-1 cities is 0.470, which is 0.029 higher than that of the matched group. Similarly, for the Gini coefficient of online views, the average treatment effect of Level-1 cities is 0.573, which is 0.016 higher than that of the matched group. For each of the specialty categories, we also estimated the average treatment effect the specialty category’s Gini coefficient ( ) with the balanced covariates. The results support the argument that the total Gini coefficient of all the doctors in OHC shows that the inequality of health service is still very serious. This study contributes to the development of the theoretically grounded understanding of the causal effect of city-level on the inequality of health service in an online to offline healthcare service setting.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

Metabolomics studies require a deep understanding of enzyme dynamics and their responses to environmental disturbances within a complex metabolic network. This paper presents a novel approach to modeling enzyme activity as a dynamic topological manifold, where each enzyme is represented as a node, and their interactions are described by differential equations. These equations account for both compensatory interactions and external perturbations, simulating how enzymes dynamically stabilize their activities in response to varying conditions. We explore the application of this model to visualize enzyme interactions, using graph theory to represent the network structure and color gradients to illustrate interaction intensities. Multiple disturbances are introduced to analyze the network's resilience and adaptability over time. The results provide insights into the compensatory mechanisms within enzymatic networks, offering a comprehensive visualization through both static and dynamic representations. Our approach allows for a better understanding of how enzymatic systems buffer against mutations and environmental stressors, contributing to the broader field of systems biology and metabolomics.

Differential Evolution (DE) is an evolutionary algorithm that has become increasingly popular due to its effectiveness and efficiency. However, its adaptation for multi-objective optimization requires further investigation. To address this issue, a novel algorithm called ILSDEMO has been proposed, which incorporates indicator-based selection and local search into a self-adaptive DE. ILSDEMO employs an archive population to store non-dominated solutions, generating an initial population uniformly distributed over the feasible solution space using orthogonal design. Additionally, two variants of DE are used to expedite convergence, while q-Gaussian mutation is utilized to exploit better trial individuals. The k-nearest neighbor rule is used to eliminate crowded solutions, and indicator-based selection is employed to generate a new parent population without diversity preservation. The performance of ILSDEMO was investigated on the test instances from the ZDT series and DTLZ series in terms of the selected indicators. The results suggest that ILSDEMO accurately and evenly approximates the true Pareto front compared to NSGAII, IBEA, and DEMO.

A methodology for selecting rational parameters of atmospheric aircrafts at the initial stages of design using an optimization algorithm of differential evolution and numerical mathematical modeling of aerodynamics problems is proposed. The technique involves the implementation of weight and aerodynamic balance in the main flight modes, has the ability to consider atmospheric aircrafts with one or two lifting surfaces, apply parallel calculations and automatically generate a three-dimensional geometric model of aircraft appearance based on the optimization results. A method for accelerating the process of optimizing the parameters of an aircraft in terms of take-off weight by more than three times by introducing a objective function into a set of design variables is proposed and demonstrated. The results of assessing the reliability of the used mathematical models of aerodynamics and the correctness of the calculation the objective function, taking into account various constraints, are presented. A comprehensive test of the performance and efficiency of the methodology is considered by solving demonstration problems to optimize more than ten main design parameters the appearance of two existing heavy-class unmanned aerial vehicles with known characteristics from open sources.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.

Purpose – Extend the Blade Element Momentum Theory (BEMT) such that rotors with pronounced cone and axis angle (tilt or yaw) can be calculated. Derive an equation for the speed ratio (lambda) as a function of Tip Speed Ratio (TSR), radius, blade, cone and axis angle. This converts the BEMT into an Unsteady BEMT or UBEMT. Present the Wagner rotor as one such rotor geometry. --- Methodology – Literature review and calculations. --- Findings – The UBEMT can be used to calculate highly unconventional rotor geometries. --- Research Limitations – Although the aerodynamic coefficients used in the UBEMT are from measurements in steady flow conditions, they can be used with success. --- Practical Implications – Also conventional Horizontal Axis Wind Turbines (HAWT) with noticeable cone and axis angle should be calculated with the UBEMT. The accuracy of power calculations of these HAWTs can be slightly improved. --- Originality – Analytic equations for rotors with cone and axis angle have barely been discussed.

This research presents the design and characteristics of new wideband polarizer based on the square waveguide with irises. Matching and polarization characteristics of the polarizer have been simulated and optimized. Frequency dependences of the characteristics are presented. Developed polarizer can be applied in satellite information systems.

Bone cement, mainly based in PMMA, is commonly used in different arthroplasty surgical proce-dures, and its use is essential for prosthesis fixation. However, its manufacturing process reaches high temperatures that can produce necrosis in the patients' surrounding tissues. In order to con-tribute to avoid this problem, the addition of graphene could delay the polymerisation of the MMA and, simultaneously, contribute to the optimisation of the composite material's properties. This article analysed the effect of the addition of different percentages of Highly Reduced Graphene Oxide (HRGO) with different wt. % (0,10, 0,50 and 1,00) and surface densities (150, 300, 500 and 750 m2/g) on the physical, mechanical, and thermal properties of commercial PMMA-based bone cement and its processing. It was noticed that a lower sintering temperature would be reached with this addition, making it less harmful to use in surgery and as it reduces its adverse effects. In contrast, the materials' density does not show significant changes, which indicates that the addi-tion of HRGO does not significantly increase its porosity. Lastly, the mechanical properties are re-duced by almost 20 %. Nevertheless, these properties are high enough so that these new materials can still fulfil their structural function.

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.

The circuitry of the summarized "floating" differential stages (FDS) based on complementary field-effect transistors with a control p-n junction (CJFET), intended for use in low-noise analog microcircuits, for example, operational amplifiers. The results of modeling the flow characteristics of one of the CJFET FDSs in the LTSpice XVII environment at low temperatures (down to -197 ⁰С) and exposure to a neutron flux in the range of 1e13 ÷ 1e15 n / cm² are presented.

Prebiotic oligosaccharides are widely used as human and animal feed additives for their beneficial effects on the gut microbiota. However, there are limited data to assess the direct effect of such functional foods on the transcriptome of intestinal epithelial cells. The purpose of this study is to describe the differential transcriptomes and cellular pathways of colonic cells directly exposed to galacto-oligosaccharides (GOS) and fructo-oligosaccharides (FOS). We have examined the differential gene expression of polarized Caco-2 cells treated with GOS or FOS and their respective mock-treated cells using mRNA sequencing (RNA-seq). A total of 89 significant differentially expressed genes were identified between GOS and mock-treated groups. For FOS treatment, a reduced number of 12 significant genes were observed to be differentially expressed relative to the control group. KEGG and Gene Ontology functional analysis revealed that genes up-regulated in the presence of GOS were involved in digestion and absorption processes, fatty acids and steroids metabolism, potential antimicrobial proteins, energy-dependent and -independent transmembrane trafficking of solutes and amino acids. Using our data, we have established complementary non-prebiotic modes of action for these frequently used dietary fibers.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

This study compares the rheological, thermal, and textural characteristics of four types of chocolate—white, milk, ruby, and dark—produced by the same manufacturer. White, milk, and ruby chocolates contain 36% fat, while dark chocolate has 39%. Cocoa content varies: from 28% in white, 33% in milk, 47% in ruby, to 70% in dark chocolate. Rheological properties were assessed with a rotational rheometer, while density was measured with a gas pycnometer. Particle size distribution (PSD) was evaluated using laser diffraction, and thermal properties were analyzed with differential scanning calorimetry (DSC). DSC results indicated that enthalpy increased with cocoa content, whereby dark chocolate showed the highest value (55.04 J g⁻¹) and white chocolate the lowest (35.3 J g⁻¹). PSD followed a monomodal pattern; dark chocolate had the smallest particles leading to the highest hardness. Density ranged from 1.2773 to 1.2067 g cm⁻³. Results from classical rotational rheological measurements were in accordance with oscillatory measurements. Rheological measurements confirmed that the Casson yield stress was highest for milk chocolate (17.61 Pa). The viscosity values decrease with increasing shear rate for all chocolates. All chocolate samples showed strong shear-thinning behavior up to 100 s.1 shear rate. Oscillatory measurements showed paste-like nature of all samples, i.e. storage modulus G’ dominates loss modulus G’’ at small shear stress values, and that complex modulus G*, which represents the stiffness varied as follows: milk > white > dark > ruby.