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We are examining a mathematical model of second-grade Casson fluid flow over a Riga surface. This analysis takes into account the effects of heat generation on a second-grade Casson fluid. Additionally, we have discussed the impacts of Soret and Dufour in the presence of thermal radiation. The study also includes an analysis of the influences of thermal and concentration slip. By considering these factors in the fluid flow, we have constructed a set of partial differential equations. Furthermore, these differential equations have been transformed into dimensionless ordinary differential equations. We have presented the influences of relevant parameters through tables and graphs. Velocity curve reveals declining behavior due to larger values of magnetic field factor. A high magnetic field coefficient means a strong magnetic field. As a result, the force acting on the charged particle increases, causing it to slow down or change direction. This change in force can cause the particle's velocity to decrease. [ABSTRACT FROM AUTHOR]

In order to study the breakup and atomization mechanisms of the fuel-jet in air crossflow and realize the accurate and controllable atomization effect of fuel, this paper proposes a method by coupling the large eddy simulation method and the VOF to DPM method. The results show that the breakup and atomization of the fuel-jet are mainly caused by the Rayleigh–Taylor (R–T) unstable surface wave and the Kelvin–Helmholtz (K–H) instability. The density of fuel-particles is higher near the central region of the fuel jet trajectory, decreasing as distance from the central region increases. As the momentum ratio increases, the penetration depth of the fuel-jet column also increases, resulting in a more concentrated spatial distribution of fuel particles. Conversely, with a lower momentum ratio, the spatial distribution of fuel particles becomes more uniform. For the spatial distribution of fuel particles, a new mathematical model is established to characterize the spatial distribution boundary of fuel particles. At the same momentum ratio, the higher the air velocity, the smaller the average particle diameter. At the same Weg number, the higher the fuel-jet velocity, the higher the average particle diameter. The relative error of the average particle diameter between the experiment and numerical simulation is very small, which is 6.4%. [ABSTRACT FROM AUTHOR]

The correlation filter object tracking algorithm has gained extensive attention from scholars in the field of tracking because of its excellent tracking performance and efficiency. However, the mathematical modeling relationships of correlation filter tracking frameworks are unclear. Therefore, many forms of correlation filters are susceptible to confusion and misuse. To solve these problems, we attempted to review various forms of the correlation filter and discussed their intrinsic connections. First, we reviewed the basic definitions of the circulant matrix, convolution, and correlation operations. Then, the relationship among the three operations was discussed. Considering this, four mathematical modeling forms of correlation filter object tracking from the literature were listed, and the equivalence of the four modeling forms was theoretically proven. Then, the fast solution of the correlation filter was discussed from the perspective of the diagonalization property of the circulant matrix and the convolution theorem. In addition, we delved into the difference between the one-dimensional and two-dimensional correlation filter responses as well as the reasons for their generation. Numerical experiments were conducted to verify the proposed perspectives. The results showed that the filters calculated based on the diagonalization property and the convolution property of the cyclic matrix were completely equivalent. The experimental code of this paper is available at https://github.com/110500617/Correlation-filter/tree/main. [ABSTRACT FROM AUTHOR]

The effective operation of model-based control strategies in modern energy systems, characterized by significant complexity, is contingent upon highly accurate large-scale models. However, achieving such precision becomes challenging in complex energy systems rife with uncertainties and disturbances. Controlling different parts of the energy system poses a challenge to achieving optimal power system efficiency, particularly when employing model-based control strategies, thereby adding complexity to current systems. This paper proposes a novel model-independent control approach aimed at augmenting transient stability and voltage regulation performance in multi machine energy systems. The approach involves the introduction of an optimized model-free fractional-order-based excitation system stabilizer for synchronous generators in a multi machine energy system. To overcome the limitations associated with complex system model identification, which add degrees of simplification at defined operating conditions and assume the system model remains fixed despite high uncertainty and numerous disturbances, an optimal model-independent fractional-order-based excitation control strategy is introduced. The efficacy of the proposed approach is validated through comparative numerical analyses using the MATLAB/Simulink environment. These simulations were conducted on a two-area, 12-bus multi-machine power system. Simulation results demonstrate that the presented excitation system stabilizer outperforms conventional controllers in terms of transient and small-signal stability. It also suppresses the low-frequency electromechanical oscillations within the multimachine energy system. [ABSTRACT FROM AUTHOR]

The Allen-Cahn (AC) model is a mathematical equation that represents the phase separation process. The AC equation has numerous applications in various disciplines, such as image processing, physics, and biology. It models phase transitions, such as solidification and grain growth in materials, pattern formation in chemical reactions, and domain coarsening in biological systems like lipid membranes. Numerical methods are crucial for solving the AC equation due to its complexity and nonlinear nature. Analytical solutions are often extremely difficult to obtain. Therefore, the development of efficient numerical techniques is indispensable for approximating solutions and studying phase transitions, material behavior, and pattern formation accurately. We investigate the stability of an explicit finite difference method (FDM) used to numerically solve the two-dimensional (2D) AC model with a high-order polynomial potential, which was recently proposed to preserve a more intricate structure of interfaces. To demonstrate the precision and optimal estimate of our stability constraints, we conduct various computational tests using the derived time step formulas that ensure the maximum principle. [ABSTRACT FROM AUTHOR]

Thermal and fluid-flow characteristics were numerically analyzed for ultra-thin heat pipes. Many studies have been conducted for ultra-thin heat pipes with a centered wick structure, but this study focused on separated wick structures to increase the evaporation/condensation surface areas within the heat pipe and to reduce the concentration of heat flux within the wick structure. A mathematical heat-pipe model was made in the three-dimensional coordinate system, and the model consisted of three regions: a vapor channel, liquid-wick, and container wall regions. The conservation equations for mass, momentum, and energy were solved numerically with boundary conditions by using a code developed by one of the authors. The numerical results with the separated wick structures were compared with those with the centered, which confirmed the effectiveness of the separation of the wick structure. However, the effectiveness of the separation was affected by the position of the separated wick structure. A simple equation was presented to determine the optimum position of the separated wick structures. Numerical analyses were also conducted when the width of the heat pipe was increased with the cooled section, which clarified that the increase in the cooled-section width with the addition of wick structures was more effective than the increase in the cooled-section length. A 44% reduction in the total temperature difference of the heat pipe was obtained under the present numerical conditions. Furthermore, a comparison was made between experimental results and numerical results. [ABSTRACT FROM AUTHOR]

The Barzilai-Borwein method offers efficient step sizes for large-scale unconstrained optimization problems. However, it may not guarantee global convergence for nonquadratic objective functions. Simulated annealingbased on Barzilai-Borwein (SABB) method addresses this issue by incorporating a simulated annealing rule. This work proposes a novel step-size strategy for the SABB method, referred to as the SABBm method. Furthermore, we introduce two stabilized variants: SABBstab and SABBmstab. SABBstab combines a simulated annealing rule with a stabilization step to ensure convergence. SABBmstab builds upon SABBstab, incorporating the modified step size derived from the SABBm method. The effectiveness and competitiveness of the proposed methods are demonstrated through numerical experiments on CUTEr benchmark problems. [ABSTRACT FROM AUTHOR]

An analytical study of two different models of rectangular porous fins are investigated using a new approximate analytical method, the Ananthaswamy-Sivasankari method. The obtained results are compared with the numerical solution, which results in a very good agreement. The impacts of several physical parameters involved in the problem are interlined graphically. Fin efficiency and the heat transfer rate are also calculated and displayed. The result obtained by this method is in the most explicit and simple form. The convergence of the solution determined is more accurate as compared to various analytical and numerical methods. [ABSTRACT FROM AUTHOR]

In this paper, we transform the given nonlocal boundary condition problem into a manageable local equation. By introducing an additional transformation of the variables, we can simplify this equation into conformable Burgers' equation. Thus, the Keller Box method is used as a numerical scheme to solve the equation. A comparison is made between numerical results and the analytic solution to validate the results of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit. [ABSTRACT FROM AUTHOR]

Running time analysis of evolutionary algorithms for continuous optimization is one research challenge in the field of evolutionary algorithms (EAs). However, the theoretical analysis results have rarely been applied to evolutionary algorithms for continuous optimization in practice, let alone their variants for evolution strategy. In this paper, we regarded the first hitting time of evolution strategy as the stopping time of the renewal process on the basis of the renewal process and in combination with Wald's inequality and stopping time theory. Afterwards, to demonstrate the application of the proposed model in the first hitting time analysis of (1 + 1) ES, we analyzed it with different mutation operators on the sphere function. First, we significantly improved the lower bound on the first hitting time of (1 + 1) ES with a uniform mutation operator, i.e., from Ω (n) to Ω (e c n) . Next, O (n 2 n) was the upper bound on the first hitting time of (1 + 1) ES with a Gaussian mutation operator from the initial distance R to half of the initial distance R /2. The numerical experimental results showed that the theoretical calculation was consistent with the actual running time, which provides a novel method for analyzing the first hitting time of EAs. [ABSTRACT FROM AUTHOR]

The acquisition time of magnetic resonance imaging (MRI) is relatively long. To achieve high-quality and fast reconstruction of magnetic resonance (MR) images, we proposed a non-convex regularization model for MR image reconstruction with the modified transformed l 1 total variation (MTL1TV) regularization term. We addressed this new model using the alternating direction method of multipliers (ADMM). To evaluate the proposed MTL1TV model, we performed numerical experiments on several MR images. The numerical results showed that the proposed model gives reconstructed images of improved quality compared with those obtained from state of the art models. The results indicated that the proposed model can effectively reconstruct MR images. [ABSTRACT FROM AUTHOR]

The authors present a new mathematical model for solving a static symmetric boundary-value problem for a layer weakened by a through hole with ends covered with a diaphragm. A new method based on a system of three singular integral equations is developed and tested numerically. A high-precision numerical analysis shows that as the thickness of the layer increases, relative circumferential stress increases as well. If one of the radii of the elliptical hole decreases, relative circumferential stress also increases. The corresponding graphs are presented. [ABSTRACT FROM AUTHOR]

Although the probability of a rollover accident is lower than that of other forms of collision, rollover is a serious accident that can break the symmetry of the vehicle and cause serious loss of life and property. There are many factors affecting rollovers, such as the environment, the vehicle, and the driving control. A coach comprises a complex dynamic system; as such, the accuracy and rationality of the used mathematical model are decisive in the study of coach rollover warning and control. By analogy with the modeling method of an automobile collision accident, the general process of a coach rollover accident is analyzed in this study in combination with the contact form and freedom of motion characteristic of the coach body and external environment. According to the principle of conservation of energy, the mathematical models of critical rollover impact force in a collision between vehicles and obstacles and in a collision between two vehicles are established, allowing for analysis of the relationships between the critical tripped rollover impact forces required for a 90° rollover and the continuous action time and collision point height. During the collision between the vehicle and the obstacle, the occurrence of a vehicle rollover is related not only to the impact force in the collision process but also to the collision duration time. Even if the impact force is relatively small, the collision lasts long enough that a second collision may occur until the vehicle rolls over. In the process of a two-vehicle collision, the critical rollover impact force is not only related to the vehicle mass but also to the vehicle wheelbase and the height of the collision point. Based on the law of conservation of momentum, the mathematic models of 90-degree rollover and 180-degree rollover are established, and the critical rollover velocities are calculated. The purpose of this study is to provide reference and guidance for the research methods of vehicle rollover stability and anti-rollover control in the intelligent vehicle era. [ABSTRACT FROM AUTHOR]

We introduce a model to describe the evolution of bacterial meningitis epidemics in a non-constant population. We derive the value of the basic reproduction number of our model. We analyze the local and global stability of the disease-free and endemic equilibria. We confirm the results by a numerical analysis of the model. [ABSTRACT FROM AUTHOR]

Cliodynamics is a still a relatively new research area with the purpose of investigating and modelling historical processes. One of its first important mathematical models was proposed by Turchin and called "Demographic-Fiscal Model" (DFM). This DFM was one of the first and is one of a few models that link population with state dynamics. In this work, we propose a possible alternative to the classical Turchin DFM, which contributes to further model development and comparison essential for the field of cliodynamics. Our "Demographic-Wealth Model" (DWM) aims to also model link between population and state dynamics but makes different modelling assumptions, particularly about the type of possible taxation. As an important contribution, we employ tools from nonlinear dynamics, e.g., existence theory for periodic orbits as well as analytical and numerical bifurcation analysis, to analyze the DWM. We believe that these tools can also be helpful for many other current and future models in cliodynamics. One particular focus of our analysis is the occurrence of Hopf bifurcations. Therefore, a detailed analysis is developed regarding equilibria and their possible bifurcations. Especially noticeable is the behavior of the so-called coexistence point. While changing different parameters, a variety of Hopf bifurcations occur. In addition, it is indicated, what role Hopf bifurcations may play in the interplay between population and state dynamics. There are critical values of different parameters that yield periodic behavior and limit cycles when exceeded, similar to the "paradox of enrichment" known in ecology. This means that the DWM provides one possible avenue setup to explain in a simple format the existence of secular cycles, which have been observed in historical data. In summary, our model aims to balance simplicity, linking to the underlying processes and the goal to represent secular cycles. [ABSTRACT FROM AUTHOR]

Measles, a highly contagious viral disease, spreads primarily through respiratory droplets and can result in severe complications, often proving fatal, especially in children. In this article, we propose an algorithm to solve a system of fractional nonlinear equations that model the measles disease. We employ a fractional approach by using the Caputo operator and validate the model's by applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation methods (HWCM). Furthermore, we evaluate the system's stability by implementing the Ulam-Hyers approach. The model takes into account multiple factors that influence virus transmission, and the HWCM offers an effective and precise solution for understanding insights into transmission dynamics through the use of fractional derivatives. We present the graphical results, which offer a comprehensive and invaluable perspective on how various parameters and fractional orders influence the behaviours of these compartments within the model. The study emphasizes the importance of modern techniques in understanding measles outbreaks, suggesting the methodology's applicability to various mathematical models. Simulations conducted by using MATLAB R2022a software demonstrate practical implementation, with the potential for extension to higher degrees with minor modifications. The simulation's findings clearly show the efficiency of the proposed approach and its application to further extend the field of mathematical modelling for infectious illnesses. [ABSTRACT FROM AUTHOR]

The infection caused by Rift Valley fever (RVF) virus is a dangerous vector-borne disease found in humans, domestic, and wild animals. It is transferred through insect vectors to ruminant host and then spread through direct contact of infected animals with their body fluid or organs. In this paper, a fractal-fractional model for the transmission of RVF in the Caputo's sense was presented. We analyzed the model and determined the basic reproduction number through the next-generation matrix technique, indicated by R0. The global sensitivity technique is used for the sensitivity test of R0 to find out the most sensitive input-factors to the reproduction parameter R0. The existence and uniqueness results of the proposed fractal-fractional model were established. Then, we presented the fractal-fractional dynamics of the proposed RVF model through a novel numerical scheme under the fractal-fractional Caputo operator. In the end, the recommended model of RVF was highlighted numerically with the variation of different input parameters of the system. The key factors of the system were highlighted to the policymakers for the control and prevention of the infection. [ABSTRACT FROM AUTHOR]

The article focuses on the control of an omni-tracked vehicle in a symmetrical fully overlapping track system. The vehicle in question is equipped with four independently controlled tracks. The links of each crawler are equipped with a single rolling roller, fixed at an angle to the direction of the vehicle main axis. The authors propose mathematical description to determine the direction and speed of movement of a single pair of omni-tracks with oppositely arranged rolling rollers. Numerical tests were carried out, the results of which were compared with the mathematical model. The numerical studies were then subjected to experimental verification, using a full-scale prototype. A dynamic direction correction algorithm was also proposed with its effectiveness proved experimentally. [ABSTRACT FROM AUTHOR]

Interference fits are very common shaft–hub connections due to their low manufacturing costs and excellent technical properties. The Plastic Conditioning of this machine element is a new and not very well-known method. During the development of this method, it was discovered that Reverse Yielding occurs in certain applications and has a negative impact on the result. This paper examines the effects of Reverse Yielding on the technology of Plastic Conditioning of interference fits in Power Transmission Engineering. Based on the Shear Stress Hypothesis (SH), the Plane Stress State (PSS), and the ideal plastic behavior of materials, established stress–mechanical relationships are used to find the influencing parameters of Reverse Yielding on the technology of Plastic Conditioning and their limits. As a result, a new computational concept is developed that allows the user to maximize Plastic Conditioning while avoiding Reverse Yielding. Analytical calculation suggestions and diagrams for practical application are provided. Furthermore, the deviations in the obtained results, taking into account other material models such as the Von Mises Yield Criterion (VMYC) and material hardening, as well as the Bauschinger effect, are examined in comparison with our own numerical results from the development of Plastic Conditioning, and the resulting need for further research is defined. In addition, the method of Plastic Conditioning of interference fits is introduced and its basic principles are briefly explained. [ABSTRACT FROM AUTHOR]

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on qualitative and numerical solutions to ordinary differential equations between the customary sections on differentiation and integration. This material serves as a bridge between the topics as well as a motivation for integration. [ABSTRACT FROM AUTHOR]

We prove a universal approximation property (UAP) for a class of ODENet and a class of ResNet, which are simplified mathematical models for deep learning systems with skip connections. The UAP can be stated as follows. Let $ n $ and $ m $ be the dimension of input and output data, and assume $ m\leq n $. Then we show that ODENet of width $ n+m $ with any non-polynomial continuous activation function can approximate any continuous function on a compact subset on $ \mathbb{R}^n $. We also show that ResNet has the same property as the depth tends to infinity. Furthermore, we derive the gradient of a loss function explicitly with respect to a certain tuning variable. We use this to construct a learning algorithm for ODENet. To demonstrate the usefulness of this algorithm, we apply it to a regression problem, a binary classification, and a multinomial classification in MNIST. [ABSTRACT FROM AUTHOR]

Our work proposes a new numerical method for finding the solution of three-dimensional Volterra-Hammerstein integral equations by using three-dimensional hybrid block-pulse functions and Legendre polynomials. Our integral equation is converted to a system of nonlinear equations. An error bound for the suggested method is established. Eventually, some numerical examples illustrate that our method is feasible and efficient. [ABSTRACT FROM AUTHOR]

The decrease in gas pressure within the bore of hollow fibers in membrane separation has received considerable interest. Typically, such complex problems are commonly addressed by the utilization of numerical methods. The pure numerical approaches are inadequate in providing a comprehensive understanding of the influence of physical features of fibers (such as length, inner diameter, and intrinsic gas permeance) and operating parameters (such as membrane pressure) on the pressure drop. Another approach is to present the pressure profile by an analytical expression. The integral equation derived from this approach requires a calculation of an improper integral. The improper integral is numerically estimated by a commercial mathematical package or by consulting tables from handbooks, which limit the application and is also implicit in nature. In this study, a simple technique is proposed so that the improper integral is easily and explicitly evaluated by any numerical integration scheme. The effect of fiber length, intrinsic gas permeance on the pressure profile at the permeate side of membrane are also discussed. The pressure profiles serve as a first indication for the design of hollow fiber membrane module. [ABSTRACT FROM AUTHOR]

For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller than the size of the surrounding tissues. Here, we consider the scenario that the cell or the vesicle releases the diffusive compounds to the immediate environment, which is modelled by the diffusion equation. Typically, one separates the intracellular and extracellular environment and uses homogeneous Neumann boundary condition for the cell boundary (so-called spatial exclusion model), while the point source model neglects the intracellular environment. We show that extra conditions are needed such that the solutions to the two models are consistent. We prove a necessary and sufficient condition for the consistency. Suggested by the numerical results, we conclude that an initial condition in the form of Gaussian kernel in the point source model compensates for a time-delay discrepancy between the solutions to the two models in the numerical solutions. Various approaches determining optimal amplitude and variance of the Gaussian kernel have been discussed. [ABSTRACT FROM AUTHOR]

Typhoid fever is an infectious disease that affects humanity worldwide; it is particularly dangerous in areas with communities of a lower socio-economic status, where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and the obtained results indicate that the overall combination of the control measures eradicates typhoid fever in the population, but the controls are more optimal in higher socio-economic status communities. [ABSTRACT FROM AUTHOR]

The primary benefit of metamaterials is that their physical and mechanical properties can be controlled by changing the structure geometry. Numerical analysis tools used in this work offer a few advantages over full-scale testing, consisting of an automated process, as well as lower material and time costs. The investigation is concerned with the behavior of unit cells of the tetrachiral mechanical metamaterial under uniaxial compression. The base material is studied within an elastic mathematical model. The influence of topological defects of the unit cell on the metamaterial properties is studied for the first time. Defects, and especially topological defects, play a decisive role in the mechanical behavior of materials and structures. The unit cell without defects reveals orthotropy of properties. Torsion of a cell with a chiral structure is induced by the rotation of all tetrachiral walls, and therefore it is sensitive to the introduction of defects. There are cases of increased torsion as well as of no compression–torsion coupling effect. In the latter case, the unit cell experiences only shear. The effective Young's modulus is calculated to vary in the range from 23 to 57 MPa for unit cells of different topologies. With the successive introduction of defects in two walls, the studied characteristics increase, correlating with each other. A further increase in the number of defects affects the characteristics in different ways. The introduction of two more defects in the walls decreases torsion and increases Young's modulus, after which both characteristics decrease. The introduction of topological defects in all walls of the unit cell leads to the orthotropic behavior of the cell with the opposite sign of torsion. [ABSTRACT FROM AUTHOR]

In this article, we construct a new sequence of Sz'asz-Mirakjan-Kantorovich operators denoted as Kn;g (f; x), which depending on a parameter g. We prove direct and local approximation properties of Kn;g (f; x). We obtain that, if g > 1, then the operators Kn;g (f; x) provide better approximation results than classical case for all x 2 [0;¥). Furthermore, we investigate the approximation results of Kn;g (f; x), graphically and numerically. Moreover, we introduce new operators from Kn;g (f; x) that preserve affine functions and bivariate case of Kn;g (f; x). Then, we study their approximation properties and also illustrate the convergence of these operators comparing with their classical cases. [ABSTRACT FROM AUTHOR]

In this paper, we present some generalizations and further refinements for the numerical radii of sectorial matrices and Schatten p-norms inequalities of accretive-dissipative matrices, which generalized some results of Kittaneh et al. Moreover, we also give some n-tuple power inequality for sectorial matrices by Yang [22]. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in generalized numerical radius inequalities for the off-diagonal part of a positive semidefinite block matrix. These inequalities produce a new set of inequalities for products and sums of matrices and some inequalities related to sectorial matrices. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

The main idea of this work is an application of probabilistic entropy and also relative entropy in the numerical analysis of uncertainty propagation in the homogenization of some composite materials. The homogenization method is based on the determination of deformation energy for the representative volume elements computed with the use of some specific finite element method experiments. Uncertainty propagation concerns material and geometrical design parameters of particulate composites and is performed thanks to an application of polynomial responses; probabilistic moments of the effective tensor are computed via the iterative generalized stochastic perturbation technique and the semi‐analytical probabilistic method. Probabilistic entropy is determined according to Shannon theory, while relative entropies equations employed here follow mathematical models created by Kullback & Leibler, Jeffreys, Hellinger, and Bhattacharyya. Deterministic analyses have been performed with the use of the system ABAQUS, while all the remaining procedures have been programmed in the computer algebra system MAPLE. [ABSTRACT FROM AUTHOR]

Background: This paper discusses the optimization of a novel fuzzy hierarchical location-routing problem, taking into consideration reliability. The mathematical model presented aims to determine the optimal locations of production centers and warehouses, as well as the optimal routing of vehicles, in order to minimize total costs. Methods: Because of the uncertainty surrounding the demand and transportation cost parameters, a fuzzy programming method was employed to control the model. To solve the mathematical model, both GA and PSO algorithms were used. Results: The results show that as the uncertainty rate increases, the total costs also increase. Additionally, the results indicate that the maximum relative difference percentage between the solutions of the GA and PSO, and the optimal solutions are 0.587 and 0.792, respectively. On the other hand, analysis of numerical examples demonstrates that the Baron Solver is unable to solve large-scale numerical examples. Conclusions: By comparing the results of GA and PSO, it is observed that PSO was able to solve numerical examples in less time than GA, while GA obtained better results than PSO. Therefore, the TOPSIS method was used to rank the different solution methods, which resulted in GA being recognized as an effective algorithm with a utility weight of 0.972. [ABSTRACT FROM AUTHOR]

Axial load carrying capacity for wide range of short concrete filled steel tubular (CFST) members with different cross-sectional profiles has been evaluated in the presented manuscript. Numerical studies are carried out through Finite-Element based demonstration and it has been accomplished in ABAQUS 6.13 package for relevancy of analytically predicted axial load carrying capacity by Unified Formula. To validate the results from the Unified Formula with the experimentally available literature, finite element-based models have been generated for hollow and solid sections of CFST columns. These sections are circular, octagonal, and square in profiles. A total of 31 hollow and 24 solid circular columns, 9 hollow and 9 solid octagonal columns and in last 9 hollow and 38 solid square CFST columns are examined for the persistence of the results. Obtained results through simulated models has been evaluated and validated with the existing results of different researchers. Through close inspection it is found that the proposed Unified formula predicts satisfactory results when compared with the result of established models. Further it is concluded that displacement in the direction of applied load is not uniform throughout the length of CFST columns. Therefore, using ring confinement technique for those regions, applied forces may be distributed more uniformly throughout the length of the members. [ABSTRACT FROM AUTHOR]

By using the principle of coupling of continua of different dimensions, we propose an approach to the mathematical modeling of deformable thread-like inhomogeneities. The proposed approach is based on the conditional partition of the analyzed problem into three partially coupled subproblems: a) external for a medium with conditionally given (a priori unknown) functions of influence on the space curves L ; b) intermediate in the form of the conditions of contact interaction of the medium with inhomogeneities, and c) internal, which is reduced to the construction of a mathematical model of inhomogeneity, which relates the function of influence directly on the surface of the inclusion with the distribution of physical and mechanical fields inside this inclusion. In the case of perfect thermomechanical interaction between the inhomogeneity and the medium, we construct integral relations for the external problem and mathematical models of thread-like inhomogeneities taking into account their thermal conductivity and deformation. In the case of rectilinear inhomogeneities, we propose a method for the solution of the constructed systems of integral equations based on the use of truncated series in Legendre polynomials for the required functions of influence of thread-like inclusions. The results of numerical analysis clarify the influence of relative thermal conductivity, relative elastic compliance, and linear thermal expansion of the material of inhomogeneity on the functions of influence and thermomechanical fields near the tip of the inclusion. [ABSTRACT FROM AUTHOR]

Implementation of vaccines, mosquito repellents and several Wolbachia schemes have been proposed recently as strategies against dengue. Research showed that the use of vaccine and repellent is highly effective when implemented to individuals who are in area with high transmission rates, while the use of Wolbachia bacteria is strongly effective when implemented in area with low transmission rates. This research is to show a three-strategy combination to cope with the dengue using mathematical model. In dengue mathematical model construction, several parameters are not yet known, therefore a genetic algorithm method was used to estimate dengue model parameters. Numerical simulation results showed that the combination of three strategies were able to reduce the number of infected humans. The dynamic of the human population with the combination of three strategies on average was able to reduce the infected human population by 45.2% in immobility aspect. Furthermore, the mobility aspect in dengue model was presented by reviewing two areas; Yogyakarta and Semarang in Indonesia. The numerical solutions showed that the trend graph was almost similar between the two areas. With the maximum effort given, the combination control values decreased slowly until the 100th day. [ABSTRACT FROM AUTHOR]

A mathematical epidemiological model for the transmission of Hepatitis B virus in the frame of fractional derivative with harmonic mean type incidence rate is proposed in this article. The proposed mathematical model is then fictionalized by utilizing the Atangana–Baleanu–Capotu ( A B C ) operator with vaccination effects. The threshold number R0 is calculated by utilizing the next-generation matrix approach. The existence and uniqueness of solution of the proposed model are proved by utilizing the well-known fixed point theory. For the numerical solution of the proposed model with A B C derivative the well-known Adams–Bashforth–Molton (ABM) method is utilized. Likewise, stability is required in regard of the numerical arrangement. In this manner, Ulam–Hyers stability utilizing nonlinear functional analysis is utilized for the proposed model. [ABSTRACT FROM AUTHOR]

Significance: The study of non-transient heat transport mechanism in mono nano as well as ternary nanofluids attracts the researchers because of their promising heat transport characteristics. Applications of these fluids spread in industrial and various engineering disciplines more specifically in chemical and applied thermal engineering. Due of huge significance of nanofluids, the study is organized for latest class termed as ternary nanofluids along with induced magnetic field. Methodology: The model development done via similarity equations and the properties of ternary nanoparticles, resulting in a nonlinear mathematical model. To analyze the physical results with parametric values performed via RKF-45 scheme. Study findings: The physical results of the model reveal that the velocity F ′ (η) increased with increasing m = 0.1 , 0.2 , 0.3 and λ 1 = 1.0 , 1.2 , 1.3 . However, velocity decreased with increasing δ 1 . Tangential velocity G ′ (η) reduces rapidly near the wedge surface and increased with increasing M 1 = 1.0 , 1.2 , 1.3 . Further, the heat transport in ternary nanofluid was greater than in the hybrid and mono nanofluids. Shear drag and the local thermal gradient increased with increasing λ 1 and these quantities were greatest in the ternary nanofluid. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of the diphtheria out-break among the immunocompromised group of people, the Rohingya ethnic group. Approximately 800,000 Rohingya refugees are living in the Balukhali refugee camp in Cox's Bazar. The camp is densely populated with the scarcity of proper food, healthcare, and sanitation. Subsequently, in November 2017 a diphtheria epidemic occurred in this camp. To keep up with the pace of the disease spread, medical demands, and disaster planning, we set out to predict diphtheria outbreaks among Bangladeshi Rohingya immigrants. We adopted a modified Susceptible-Latent-Infectious-Recovered (SLIR) transmission model to forecast the possible implications of the diphtheria outbreak in the Rohingya camps of Bangladesh. We discussed two distinct situations: the daily confirmed cases and cumulative data with unique consequences of diphtheria. Data for statistical and numerical simulations were obtained from [1]. We used the fourth-order Runge-Kutta method to obtain numerical simulations for varying parameters of the model which would demonstrate conclusive estimates. Daily and cumulative data predictions were explored for alternative values of the parameters, i.e., disease transmission rate (β) and recovery rate (γ). Additionally, the average basic reproduction number for the parameters β and was calculated and displayed graphically. Our analysis demonstrated that the diphtheria outbreak would be under control if the maintenance could perform properly. The results of this research can be utilized by the Bangladeshi government and other humanitarian organizations to forecast disease outbreaks. Furthermore, it might help them to make detailed and practical planning to avoid the worst scenario. [ABSTRACT FROM AUTHOR]

There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black- Scholes model on a single asset is a partial differential equation (PDE) charac- terizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Letter function. The numerical analysis prove that this method is eficacious in solving various problems of financial theory. [ABSTRACT FROM AUTHOR]

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders. [ABSTRACT FROM AUTHOR]

We propose and study a mathematical model governing interactions between cancer and immune system with an oncolytic viral therapy (OVT), wherein cancer cells can activate and inhibit immune cells simultaneously with saturations. When the therapy is not applied, it is shown that the interaction can support at most three hyperbolic positive equilibria where two of them are always asymptotically stable and the other is a saddle point. The reachable stable tumor burden can be either small or large depending on initial tumor size. We analyze the full model by proving global asymptotic stability of the virus‐free equilibrium that corresponds to OVT failure. Sufficient conditions based on model parameters are derived under which the model is uniformly persistent. The proposed system is validated using a mouse model of human pancreatic cancer carried out by Koujima et al. Global sensitivity analysis indicates that the rates of tumor‐mediated killing and immune cell exhaustion are critical for tumor progression and therapy success. Numerical bifurcation analysis reveals that the saddle point can be utilized to estimate the maximum tumor load for eradication by OVT. Moreover, an immunosuppressive microenvironment may enhance viral therapy efficacy. [ABSTRACT FROM AUTHOR]