Results 61 to 70 of about 78,766 (164)
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
, 1999 A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials,
Granovskii Ya. I. +6 more
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On an extension of a recurrent relation from combinatorics
Electronic Journal of Qualitative Theory of Differential Equations, 2017 The following recurrent relation/partial difference equation $$w_{n,k}=aw_{n-1,k-1}+bw_{n-1,k},$$ where $k,n,a,b\in\mathbb{N}$, appears in a problem in combinatorics. Here we show that an extension of the recurrent relation is solvable on, the, so called,
Stevo Stevic
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Jarzynski equation for a simple quantum system: Comparing two definitions of work
, 2007 The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated.
Engel, A., Nolte, R.
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Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation [PDF]
Advances in Difference Equations, 2010 The authors consider the nonlinear neutral delay difference equation \[ \Delta(a_{kn}\cdots\Delta(a_{2n}\Delta(a_{1n}\Delta(x_n+b_n x_{n-d})))) +f(n,x_{n-r_{1n}},x_{n-r_{2n}},\dots,x_{n-r_{sn}})=0,\quad n\geq n_0, \] where \(d,k,s\in\mathbb{N}\), \(a_i,b\) are real sequences, \(r_{jn}\) are integers, and \(f:\{n_0,n_0+1,\dots\}\times\mathbb{R}^s\to ...
Liu Min, Guo Zhenyu
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Non-polynomial extensions of solvable potentials a la Abraham-Moses [PDF]
, 2013 Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics.
Darboux G., Ryu Sasaki, Satoru Odake
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Exactly solvable models of nuclei [PDF]
, 2014 In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well ...
Heyde, K., Van Isacker, P.
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Eigenvalue problem for differential Cauchy-Riemann operator with nonlocal boundary conditions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 We consider the reduced spectral problem for the Cauchy-Riemann operator with nonlocal boundary conditions to Fredholm linear integral equation of the second kind with a continuous kernel. The corresponding Fredholm determinant is defined for all spectral
Nurlan N Imanbaev
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On a solvable difference equations system
FilomatIn this paper, we study three dimensional system of difference equations. Firstly, we examine the solutions of the mentioned system depending on whether the parameters are equal to zero or non-zero. In addition, the solutions of this system are obtained in closed form.
Ömer Aktaş, Merve Kara, Yasin Yazlik
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Symmetric nonlinear solvable system of difference equations
Electronic Journal of Qualitative Theory of Differential EquationsWe show the theoretical solvability of the system of difference equations x n + k = y n + l y n − c d y n + l
Stevo Stević +2 more
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Solvable Optimal Velocity Models and Asymptotic Trajectory
, 1996 In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density.
B. S. Kerner +18 more
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