AbstractThis article focuses on different anisotropic models within the framework of a specific modified $$f(\mathcal {R},\mathcal {T}, \mathcal {R}_{\zeta \gamma }\mathcal {T}^{\zeta \gamma })$$ f ( R , T , R ζ γ T ζ γ ) gravity theory. The study adopts a static spherically symmetric spacetime to determine the field equations for two different modified models: (i) $$f(\mathcal {R},\mathcal {T},\mathcal {R}_{\zeta \gamma }\mathcal {T}^{\zeta \gamma })=\mathcal {R}+\eta \mathcal {R}_{\zeta \gamma }\mathcal {T}^{\zeta \gamma }$$ f ( R , T , R ζ γ T ζ γ ) = R + η R ζ γ T ζ γ , and (ii) $$f(\mathcal {R},\mathcal {T},\mathcal {R}_{\zeta \gamma }\mathcal {T}^{\zeta \gamma })=\mathcal {R}(1+\eta \mathcal {R}_{\zeta \gamma }\mathcal {T}^{\zeta \gamma })$$ f ( R , T , R ζ γ T ζ γ ) = R ( 1 + η R ζ γ T ζ γ ) , where $$\eta $$ η is a constant parameter. To address the additional degrees of freedom in the field equations and obtain their corresponding unique solution, the Durgapal-Fuloria spacetime geometry and MIT bag model are utilized. Matching conditions are applied to determine unknown constants within the chosen spacetime geometry. We adopt a certain range of model parameters to analyze the physical characteristics of the developed models in the interior distribution of a particular compact star candidate 4U 1820-30. Energy conditions and some other tests are also implemented to ensure their viability and stability. Additionally, the disappearing radial pressure constraint is employed to find the values of the model parameter, aligning with the observed information of an array of stars. The study concludes that both of our models are well-behaved and satisfy all necessary conditions, and thus we observe them suitable for the modeling of astrophysical objects.

This article focuses on different anisotropic models within the framework of a specific modified f(ℛ,𝒯, ℛ_ζγ𝒯^ζγ) gravity theory. The study adopts a static spherically symmetric spacetime to determine the field equations for two different modified models: (i) f(ℛ,𝒯,ℛ_ζγ𝒯^ζγ)=ℛ+ηℛ_ζγ𝒯^ζγ , and (ii) f(ℛ,𝒯,ℛ_ζγ𝒯^ζγ)=ℛ(1+ηℛ_ζγ𝒯^ζγ) , where η is a constant parameter. To address the additional degrees of freedom in the field equations and obtain their corresponding unique solution, the Durgapal-Fuloria spacetime geometry and MIT bag model are utilized. Matching conditions are applied to determine unknown constants within the chosen spacetime geometry. We adopt a certain range of model parameters to analyze the physical characteristics of the developed models in the interior distribution of a particular compact star candidate 4U 1820-30. Energy conditions and some other tests are also implemented to ensure their viability and stability. Additionally, the disappearing radial pressure constraint is employed to find the values of the model parameter, aligning with the observed information of an array of stars. The study concludes that both of our models are well-behaved and satisfy all necessary conditions, and thus we observe them suitable for the modeling of astrophysical objects.

This article focuses on different anisotropic models within the framework of a specific modified f(R,T,R zeta gamma T zeta gamma) gravity theory. The study adopts a static spherically symmetric spacetime to determine the field equations for two different modified models: (i) f(R,T,R zeta gamma T zeta gamma)=R+eta R zeta gamma T zeta gamma, and (ii) f(R,T,R zeta gamma T zeta gamma)=R(1+eta R zeta gamma T zeta gamma) is a constant parameter. To address the additional degrees of freedom in the field equations and obtain their corresponding unique solution, the Durgapal-Fuloria spacetime geometry and MIT bag model are utilized. Matching conditions are applied to determine unknown constants within the chosen spacetime geometry. We adopt a certain range of model parameters to analyze the physical characteristics of the developed models in the interior distribution of a particular compact star candidate 4U 1820-30. Energy conditions and some other tests are also implemented to ensure their viability and stability. Additionally, the disappearing radial pressure constraint is employed to find the values of the model parameter, aligning with the observed information of an array of stars. The study concludes that both of our models are well-behaved and satisfy all necessary conditions, and thus we observe them suitable for the modeling of astrophysical objects.

This study examines the characteristics of positive solutions for singular semilinear elliptic systems subject to zero Dirichlet boundary conditions. By refining the moving plane technique, we establish the symmetry and monotonicity of solutions within strictly convex symmetric regions.

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.

In this present article, by using the Iterative Laplace Transform Method (ILTM), the diffusion equation of fractional order is solved. The ILTM, which works as a combination of two methods, the iterative method and the other is the Laplace transform method, is applied to several diffusion equations to obtain analytical solutions. The proposed method gives the closed-form of series solutions in terms of the Mittag-Leffler function, which is a queen of functions in fractional calculus. The main aim of this work is to present a simple but reliable algorithm for the solution of diffusion equations of the multi-dimensional type, which clearly describes the materials of density dynamics in the diffusion process. The results obtained by using the ILTM approach indicate that this approach is attractive computationally and implemented easily. Due to its straightforward approach and comfortable way of solving problems, the ILTM can be utilized to solve nonlinear fractional problems in various applied and engineering sciences.

This investigation explores the nature of charged compact stars within the modified theory whose functional depends on the Ricci scalar, Lagrangian density of the matter and trace of the energy–momentum tensor , i.e., f(R,Lm,T) gravity. The methodology involves starting with a static spherical spacetime filled with the isotropic fluid. The field equations are then formulated corresponding to a specific minimal model of this extended theory. While developing these equations, we also take into account different choices of the fluid Lagrangian density. Further, we use the Karmarkar condition to deal with the extra degrees of freedom in equations of motion and construct their corresponding solutions. The metric components obtained from Karmarkar condition possess three constants which are evaluated through the matching conditions of the interior spherical geometry with the exterior vacuum spacetime. Further, we explore the obtained models for different values of the parameters through a comprehensive graphical analysis. Conclusively, our results are well-agreed with the physical conditions and thus advance our understanding of the impact of considered gravity theory on the internal composition of stellar objects.

We study the orbital and oscillatory motion of test particles moving around a rotating Bardeen black hole immersed in perfect fluid dark matter. We obtain the analytical solutions for the radial profiles of specific energy as well as the specific angular momentum of the equatorial stable circular orbits. Using the effective potential approach, we also discuss the stability of circular orbits. We compute the frequencies of radial and latitudinal harmonic oscillations as a function of mass, charge, and angular momentum of the black hole as well as the parameter describing the perfect fluid dark matter. The main characteristics of test particle quasi-periodic oscillations near stable circular orbits are examined in the equatorial plane. Furthermore, we study precessions of Periastron and Lense-Thirring. It is observed that the particle's motion around the black hole is strongly influenced by the model parameters.

This paper is devoted in studying the thermodynamical properties and weak gravitational lensing in the context of a non-commutative charged Schwarzschild black hole surrounded by perfect fluid dark matter. In this context, we study the geometric mass and thermal temperature to discuss the viability of the charged black hole solution by evaluating the specific heat, the phase transition and stability of the configuration. We also study the energy emission process of the black hole. From the thermodynamical properties, we conclude that our studied black hole solution is thermally stable. Moreover, we discuss gravitational lensing in the weak plasma field by considering uniform as well as non-uniform plasma and evaluate the deflection angle where we observe that the deflection angle in the case of uniform plasma is greater than that in non-uniform plasma. We also have studied the image magnification from the source's brightness and observed that in uniform plasma case, the source image is more magnified than the non-uniform plasma.

In this paper, black hole solutions are developed within the framework of f(R, T) gravity through the minimal gravitational decoupling approach. By introducing a new source in the original isotropic matter distribution, the corresponding field equations acquire additional degrees of freedom. Applying the transformation on the radial metric function leads these equations to two distinct sets, each representing the influence of either the seed or additional source exclusively. In order to formulate the black hole solutions, the seed source is considered to be a vacuum, characterized by the Schwarzschild metric. To derive a viable solution for the second system, constraints are imposed on the metric potentials and energy-momentum tensor of the additional source. Three distinct solutions are graphically analyzed based on varying values of the decoupling parameter. The energy conditions are also plotted to determine the nature of the extra source. Finally, it is concluded that two of our developed models agree with the asymptotic flatness criterion and energy bounds in this modified theory.

由于许多物理现象需要建立有两个或多个分量的波动模型用以说明不同的模式、频率和极化现象.此外,只有多分量系统才能从理论和实践上解释一些多个物理场能量的交换.因此,给定一个可积系统,我们如何构造一个非平凡的微分方程系统,使它是可积的并且包含原系统为一个子系统,是可积耦合研究的重要问题之一.利用一个稳定方程推导可积耦合AKNS方程,然后给出一次达布变换,其中的元素可以用两个行列式的商来表示.通过比较一次达布变换的形式和特点,推导出用行列式表示的N次达布变换公式.进而利用种子解,通过N次达布变换进行迭代,可以得到任意阶孤子解.作为达布变换的应用,我们求出了精确显式单孤子解.

将一阶全微分方程与积分因子的概念推广到高阶微分方程情形,并运用积分因子法讨论了一般高阶非线性微分方程的求解问题.

In this study, we explore the Lorentzian and Gaussian distributions. We discuss the wormhole geometry in f(R) gravity with two different exponential models. Both the models for f(R) gravity, i.e., f(R)=R−αΥ(1−e−Λ) and f(R)=R−αΥ∗tanh(Λ), with the concept of non-commutative distribution. We fix the values of unknowns parameters and provide the graphical behavior of the obtained results. It is shown that obtained results fulfill all the necessary conditions of shape function in both cases with both distributions. The inquired wormhole solutions violate the null energy conditions in the background of both models. It is concluded that our obtained results are viable and stable.

行列式展开定理是拉普拉斯定理的特例,拉普拉斯定理是行列式展开定理的推广,利用拉普拉斯定理的推广和证明,对其任意取定的k阶子式进行讨论得到其特例,即为行列式展开定理,运用拉普拉斯定理和行列式性质证明了行列式的乘积,最后将拉普拉斯定理运用到高阶行列式与矩阵行列式的计算中,通过广义对角矩阵行列式进行推广,在分块矩阵行列式计算中进行分类讨论,得到了更一般形式的分块矩阵行列式的计算公式.

讨论了一类广义非线性奇异摄动积分-微分发展方程Robin问题.首先,利用广义Fredholm积分方程求解方法,得到了模型的外部解.其次,引入多重尺度变量,构造了Robin问题解的边界层校正项.然后利用伸长变量,得到了解的初始层校正项,并构造了奇异摄动问题的形式解的合成展开式.最后,用泛函分析不动点理论证明了广义解的渐近展开式的一致有效性.

本文归纳总结了逆矩阵的几种不同的求法,并分析了在什么情况下可以采用什么样的方法,通过具体的例题从定性与定量两个方面进行论证,运用不同的方法得到相同的结果的计算过程的比较,同时在分块矩阵中得到了更一般形式的逆矩阵的计算公式,将有助于教师的教学与学生的学习.

介绍了高阶矩阵逆矩阵的几种不同求法,并通过具体的例题从定性与定量两个方面进行了论证,同时在分块矩阵中得到了更一般形式的逆矩阵的计算公式,将有助于教师的教学与学生的学习.

新升本科院校学生层次差异性较大,运用分层教学是充分体现以学生为主体,教师为主导,激发学生学习兴趣,调动学生学习积极性,因材施教,全面提高教学质量的必要要求.在论述分层教学概念及其理论研究基础上,根据新升格地方本科院校教学模式的共性,分析新升本科院校亳州学院数学教学的现状和采用分层教学模式的必要性,并提出一种学生分层的优化算法,针对学生、教师、教学设计三个层面研究如何实施数学分层模式教学.

In this current study, we explore the modified homogeneous cosmological model in the background of LRS Bianchi type-I space–time. For this purpose, we employ the Homotopy Perturbation Method (HPM). HPM is an analytical-based method. Further, we calculated the main field equations of the cosmological model LRS Bianchi type-I space–time. Furthermore, we discuss the necessary calculations of HPM. Therefore, we investigate the analytical solution of our problem by adopting HPM. In this response, we discuss five different values of parameter n. We also give a brief discussion about solutions. The main purpose of this study is to apply the application of HPM in the cosmological field.

In this paper, a class of systems for epidemic contagion is considered. An epidemic virus ecological model is described. Using the generalized variation iteration method, the corresponding approximate solution to the nonlinear system is obtained and the method for this approximate solution is pointed out. The accuracy of approximate solution is discussed, and it can control the epidemic virus transmission by using the parameters of the system. Thus, it has the value for practical application.