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The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.

This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.

Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.

The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.

The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.

Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.

The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

Gas insulated systems, such as gas insulated lines (GIL), use insulating gas, mostly sulfur hexalfluoride (SF₆), to enable a higher dielectric strength compared to e.g. air. However, under high voltage direct current conditions, charge accumulation and electric field stress may occur, which may lead to partial discharge or system failure. Therefore, numerical simulations are used to design the system and determine the electric field and charge distribution. Although the gas conduction shows a more complex current–voltage characteristic compared to solid insulation, the electric conductivity of the SF₆ gas is set as constant in most works. The purpose of this study is to investigate different approaches to address the conduction in the gas properly for numerical simulations.

In this work, two approaches are investigated to address the conduction in the insulating gas and are compared to each other. One method is an ion-drift-diffusion model, where the conduction in the gas is described by the ion motion in the SF₆ gas. However, this method is computationally expensive. Alternatively, a less complex approach is an electro-thermal model with the application of an electric conductivity model for the SF₆ gas. Measurements show that the electric conductivity in the SF₆ gas has a nonlinear dependency on temperature, electric field and gas pressure. From these measurements, an electric conductivity model was developed. Both methods are compared by simulation results, where different parameters and conditions are considered, to investigate the potential of the electric conductivity model as a computationally less expensive alternative.

The simulation results of both simulation approaches show similar results, proving the electric conductivity for the SF₆ gas as a valid alternative. Using the electro-thermal model approach with the application of the electric conductivity model enables a solution time up to six times faster compared to the ion-drift-diffusion model. The application of the model allows to examine the influence of different parameters such as temperature and gas pressure on the electric field distribution in the GIL, whereas the ion-drift-diffusion model enables to investigate the distribution of homo- and heteropolar charges in the insulation gas.

This work presents numerical simulation models for high voltage direct current GIL, where the conduction in the SF₆ gas is described more precisely compared to a definition of a constant electric conductivity value for the insulation gas. The electric conductivity model for the SF₆ gas allows for consideration of the current–voltage characteristics of the gas, is computationally less expensive compared to an ion-drift diffusion model and needs considerably less solution time.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

With the increasing number of mobile applications, efficiently recommending mobile applications to users has become a challenging problem. Although existing mobile application recommendation approaches based on user attributes and behaviors have achieved notable effectiveness, they overlook the diffusion patterns and interdependencies of topic-specific mobile applications among user groups. mobile applications among user groups. This paper aims to capture the diffusion patterns and interdependencies of mobile applications among user groups. To achieve this, a topic-aware neural network-based mobile application recommendation method, referred to as TN-MR, is proposed.

In this method, first, the user representations are enhanced by introducing a topic-aware attention layer, which captures both the topic context and the diffusion history context. Second, it exploits a time-decay mechanism to simulate changes in user interest. Multitopic user representations are aggregated by the time decay module to output the user representations of cascading representations under multiple topics. Finally, user scores that are likely to download the mobile application are predicted and ranked.

Experimental comparisons and analyses were conducted on the actual 360App data set, and the results demonstrate that the effectiveness of mobile application recommendations can be significantly improved by using TN-MR.

In this paper, the authors propose a mobile application recommendation method based on topic-aware attention networks. By capturing the diffusion patterns and dependencies of mobile applications, it effectively assists users in selecting their applications of interest from thousands of options, significantly improving the accuracy of mobile application recommendations.

The primary objective of this study is to tackle the enduring challenge of preserving feature integrity during the manipulation of geometric data in computer graphics. Our work aims to introduce and validate a variational sparse diffusion model that enhances the capability to maintain the definition of sharp features within meshes throughout complex processing tasks such as segmentation and repair.

We developed a variational sparse diffusion model that integrates a high-order L₁ regularization framework with Dirichlet boundary constraints, specifically designed to preserve edge definition. This model employs an innovative vertex updating strategy that optimizes the quality of mesh repairs. We leverage the augmented Lagrangian method to address the computational challenges inherent in this approach, enabling effective management of the trade-off between diffusion strength and feature preservation. Our methodology involves a detailed analysis of segmentation and repair processes, focusing on maintaining the acuity of features on triangulated surfaces.

Our findings indicate that the proposed variational sparse diffusion model significantly outperforms traditional smooth diffusion methods in preserving sharp features during mesh processing. The model ensures the delineation of clear boundaries in mesh segmentation and achieves high-fidelity restoration of deteriorated meshes in repair tasks. The innovative vertex updating strategy within the model contributes to enhanced mesh quality post-repair. Empirical evaluations demonstrate that our approach maintains the integrity of original, sharp features more effectively, especially in complex geometries with intricate detail.

The originality of this research lies in the novel application of a high-order L₁ regularization framework to the field of mesh processing, a method not conventionally applied in this context. The value of our work is in providing a robust solution to the problem of feature degradation during the mesh manipulation process. Our model’s unique vertex updating strategy and the use of the augmented Lagrangian method for optimization are distinctive contributions that enhance the state-of-the-art in geometry processing. The empirical success of our model in preserving features during mesh segmentation and repair presents an advancement in computer graphics, offering practical benefits to both academic research and industry applications.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

This paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.

The analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.

Computational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.

The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.

This investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.

This study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

Financial mathematics is one of the most rapidly evolving fields in today’s banking and cooperative industries. In the current study, a new fractional differentiation operator with a nonsingular kernel based on the Robotnov fractional exponential function (RFEF) is considered for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF).

The homotopy perturbation method (HPM) with the help of the Laplace transform is presented here to check the behaviours of the solutions of the Black–Scholes model. HPM is well known for its accuracy and simplicity.

In this attempt, the exact solutions to a famous financial market problem, namely, the BS option pricing model, are obtained using homotopy perturbation and the LT method, where the fractional derivative is taken in a new YAC sense. We obtained solutions for each financial market problem in terms of the generalized Mittag-Leffler function.

The Black–Scholes model is presented using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact solutions to prove the effectiveness of the proposed work. The different characteristics of the solutions are investigated for different values of fractional-order derivatives.