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摘要： Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equations of the second degree, and their uses in solving special ordinary differential Equations such as Legendre, Hermite, and Laguerre Equations;moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results obtained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article.

摘要： Dear editor,The main objective of this study is to investigate one type of stochastic optimal control problem for a delayed system using the maximum principle method.The existing research can be categorized into two categories.In the first category,the adjoint equation comprises two backward stochastic differential equations(BSDEs)and one backward ordinary differential equation(BODE),which is assumed to have a zero solution;see e.g.,[1-3].However,there is still scope for improvement in this research direction.Here,a special setting is considered for the system parameters;see e.g.,(3.9)and(3.12)in 21.The BODE is assumed to result in a zero solution when the necessary maximum principle is strictly applied;see e.g.,Theorem 5.1 in 31.In the second category,a typee of anticipated/time-advanced BSDE is introduced as the adjoint equation;see e.g.,[1,4-7].

摘要： INVESTIGATE The scale at the right is balanced,and the bag contains a certain number of blocks.1.Suppose you cannot look in the bag.How can you find the number of blocks in the bag?2.In what way is a balanced scale like an equation?3.What does it mean to solve an equation?To solve an cquation using models,you can use these steps.·You can add or subtract the same number of counters from each side of the mat.·You can add or subtract zero from each side of the mat.ACTIVITY Work with a partner.

摘要： We have obtained approximate bound state solutions of Schrödinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.

摘要： In recent years, a vast amount of work has been done on initial value problems for important nonlinear evolution equations like the nonlinear Schrödinger equation (NLS) and the Korteweg-de Vries equation (KdV). No comparable attention has been given to mixed initial-boundary value problems for these equations, i.e. forced nonlinear systems. But in many cases of physical interest, the mathematical model leads precisely to the forced problems. For example, the launching of solitary waves in a shallow water channel, the excitation of ion-acoustic solitons in a double plasma machine, etc. In this article, we present the PDE (Partial Differential Equation) method to study the following iut = uxx - g|u|pu, g ∈ R, p > 3, x?∈ Ω = [0,L], 0 ≤?t?u (x,0) = u0 (x) ∈?H2 (Ω) and Robin inhomogeneous boundary condition ux (0,t) + αu (0,t) = R1(t), t ≥ 0 and ux (L,t) + αu (L,t) = R2 (t), t ≥ 0 (here?α?is a real number). The equation is posed in a semi-infinite strip on a finite domain Ω. Such problems are called forced problems and have many applications in other fields like physics and chemistry. The main tool of PDE method is semi-group theory. We are able to prove local existence and uniqueness theorem for the nonlinear Schrödinger equation under initial condition and Robin inhomogeneous boundary condition.

摘要： In this article,under suitable conditions on the internal term f(·)and the bound-ary nonlinear term g(·),we prove blow-up results for a class of nonclassical diffusion equations with nonlinear boundary condition.

摘要： In this paper, we construct a class of semi-implicit difference method for time fractional diffusion equations—the group explicit (GE) difference scheme, which is a difference scheme with good parallelism constructed using Saul’yev asymmetric scheme. The stability and convergence of the GE scheme of time fractional diffusion equation are analyzed by mathematical induction. Then, the theoretical analysis is verified by numerical experiments, which shows that the GE scheme is effective for solving the time fractional diffusion equation.

摘要： In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 02s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.

摘要： The implementation of the Grain for Green Program(GGP)has changed the development track of the agricultural eco-economic system in China.In response to the results of a lag study that investigated the coupling between the GGP and the agricultural eco-economic system in a loess hilly region,we used a structural equation model to analyze the survey data from 494 households in Ansai,a district of Yan’an City in Shaanxi Province of China in 2015.The model clarified the direction and intensity of the coupling between the GGP and the agricultural eco-economic system.The coupling benefits were derived through linkages between the program and various chains in the agricultural eco-economic system.The GGP,the agroecosystem of Ansai and their potential coupling effects were in a state of general coordination.The agroecosystem directly affected the coupling effect,with the standardized path coefficient of 0.87,indicating that the agroecosystem in Ansai at this stage provided basic material support for the coupling between the GGP and the agricultural eco-economic system.The direct path coefficient of agroeconomic system impacted on the coupling effect was-0.76,indicating that partial contradictions occurred between the agroeconomic system and the coupling effect.Therefore,although the current agroecosystem in Ansai should be provided sufficient agroecological resources for the benign coupling between the program and the agricultural eco-economic system,agricultural development failed to effectively transform agroecological resources into agricultural economic advantages in this region,which resulted in a relative lag in the development of the agricultural economic system.Thus,the coupling between the GGP and the agricultural eco-economic system was poor.To improve the coupling and the sustainable development of the agricultural eco-economic system in cropland retirement areas,the industrial structure needs to be diversified,the agricultural resources(including agroecological resources,agricultural economic resources and agricultural social resources)need to be rationally allocated,and the chain structure of the agricultural eco-economic system needs to be continuously improved.

摘要： With increasing complexity of today’s electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace’s equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.