Topological Tail Pressure for Asymptotically Sub-additive Continuous Potentials

We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail pressure without any additional assumptions.

Solutions of the Duffin-Kemmer-Petiau equation in the presence of Hulthn potential in(1+2) dimensions for unity spin particles using the asymptotic iteration method

The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.

Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.

Asymptotic iteration approach to supersymmetric bistable potentials

We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method （AIM）. It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.

The Asymptotic Iteration Method for the Eigenenergies of the a Novel Hyperbolic Single Wave Potential

By using the asymptotic iteration method, we have calculated numerically the eigenvalues En of the hyperbolic single wave potential which is introduced by H. Bahlouli, and A. D. Alhaidari. They found a new approach (the “potential parameter” approach) which has been adopted for this eigenvalues problem. For a fixed energy, the problem is solvable for a set of values of the potential parameters (the “parameter spectrum”). This paper will introduce a related work to complete the goal of finding the eigenvalues, the Schr?dinger equation with hyperbolic single wave potential is solved by using asymptotic iteration method. It is found that asymptotically this method gives accurate results for arbitrary parameters, V0, γ, and λ.

Exact Solutions of Klein-Gordon Equation with Scalar and Vector Rosen-Morse-Type Potentials

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.

Relativistic treatment of the spin-zero particles subject to the second Pschl Teller-like potential

The three-dimensional Klein-Gordon equation is solved for the case of equal vector and scalar second Poschl-Teller potential by proper approximation of the centrifugal term within the framework of the asymptotic iteration method. Energy eigenvalues and the corresponding wave function are obtained analytically. Eigenvalues are computed numerically for some values of n and It is found that the results are in good agreement with the findings of other methods for short-range potential.

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrodinger equation with the mulfiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l （states） quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.

Bound states of the Dirac equation with position-dependent mass for the Eckart potential

Studying with the asymptotic iteration method, we present approximate solutions of the Dirac equation for the Eckart potential in the case of position-dependent mass. The centrifugal term is approximated by an exponential form, and the relativistic energy spectrum and the normalized eigenfunctions are obtained explicitly.

Relativistic symmetries with the trigonometric Pschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

SUB-ADDITIVE PRESSURE ON A BOREL SET

The goal of this paper is to investigate topological conditional pressure of a continuous transformation as defined for sub-additive potentials. This study presents a vari- ational inequality for sub-additive topological conditional pressure on a closed subset, which is the other form of the variational principle for the sub-additive topological pressure pre- sented by Cao, Feng, and Huang in [9]. Moreover, under some additional assumptions, this result can be generalized to the non-compact case.

Revised Iterative Solution of Ground State of Double-Well Potential

The revised new iterative method for solving the ground state of Schroedingerequation is deduced. Based on Green functions defined by quadratures along a single trajectory thisiterative method is applied to solve the ground state of the double-well potential. The result iscompared to the one based on the original iterative method. The limitation of the asymptoticexpansion is also discussed.

The Analytic Solution of Schrdinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.

ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.

Inverse Spectral Theory for a Singular Sturm Liouville Operator with Coulomb Potential

We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.

ASYMPTOTIC BEHAVIOR FOR A CLASS OF ELLIPTICEQUIVALUED SURFACE BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS INTERFACE CONDITIONS

Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process:when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.

THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE

We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu),p>1,θ>−p,and T is a half-space{x_(1)>0}.When λ>Θ(where Θ is the Hardy constant),we show that under suitable conditions on f andθ,the equation has a unique positive solution.Moreover,the exact behavior of the unique positive solution as x_(1)→0^(+),and the symmetric property of the positive solution are obtained.

带有位势井的分数阶渐近薛定谔方程的多解性研究

研究分数阶薛定谔方程:(-Δ)^(s)u+V_(λ)(x)u=f(x,u),0<s<1,x∈R^(N),其中N>2s,f满足渐近线性条件,且当λ充分大时位势函数Vλ具有位势井.利用临界点定理得到方程的多解性.

复杂多场景下机械臂避障运动规划方法研究

为提高工业机械臂在狭窄通道、多障碍物等复杂多场景下避障运动规划的成功率和效率,建立了基于圆柱体和球体包围盒机械臂与障碍物之间的碰撞检测模型,并提出了一种基于启发式概率融合人工势场法的改进型RRT^(*)算法(P-artificial potential field-RRT^(*),PAPF-RRT^(*))。采样上引入概率目标偏向与随机采样点优选策略,对采样点进行位置优选约束,增强采样导向性和质量;为改变传统新节点扩展方向和特殊环境下局部最优问题,融合人工势场法的目标引力与障碍物斥力和自适应步长,使算法在APF产生的合力范围下实时引导新节点扩展方向和步长大小,降低过度的探索和碰撞区域扩展;对冗余节点进行删除,并采用三次B样条插值优化,提高机械臂轨迹的柔顺性。仿真结果表明,所提算法较传统RRT^(*)算法在平均路径搜索时间上降低了56.75%,路径长度缩短了17.74%。导入机械臂模型后可视化仿真结果证明,所提算法可使机械臂成功避障且快速平稳运行到目标点。

Existence of Solutions for a Quasilinear Schr?dinger Equation with Potential Vanishing

We study the following quasilinear Schrodinger equation-△u+V(x)u-△(u^(2))u=K(x)g(u),x∈R^(3),where the nonlinearity g(u)is asymptotically cubic at infinity,the potential V(x)may vanish at infinity.Under appropriate assumptions on K(x),we establish the existence of a nontrivial solution by using the mountain pass theorem.