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Some new relations for the Appell function F 1 (a, b, b′; c; w, z) are obtained including differentiation and integration formulas, integral representations, series and recurrence relations. Some integrals are given which can be expressed in terms of F 1 and confluent Appell functions (Humbert fun...
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We study the generalized quantum isotonic oscillator Hamiltonian given by 𝐻 = − 𝑑 2 / 𝑑 𝑟 2 + 𝑙 ( 𝑙 + ...
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The d-dimensional Schrödinger's equation is analyzed with regard to the existence of exact solutions for polynomial potentials. Under certain conditions on the interaction parameters, we show that the polynomial potentials V8(r) = ∑k = 18αkrk,α8>0 and V10(r) = ∑k = 110αkrk,α10>0 are exactly...
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We analyze the polynomial solutions of the linear differential equation p2(x)y″+p1(x)y′+p0(x)y=0 where pj(x) is a jth-degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials pj(x). Special cases are related to known differenti...
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The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using ...
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Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen–Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies Sx and Sp are calculated numerically. Also, we find that S1 x is obtained analyticall...
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A tensorial Green-function treatment of the electronic transmission properties of an atomic wire T-junction is presented within the framework of the tight-binding approximation. The adoption of the tensorial formalism enables overlap effects to be included in a straightforward manner, without the ne...
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We analyze the polynomial solutions of the linear differential equation where is a -degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials . Special cases are related to known differential equations of mathematical physics. Class...
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In this article we study a natural weakening – which we refer to as paratransitivity – of the well-known notion of transitivity of an algebra AA of linear operators acting on a finite-dimensional vector space VV. Given positive integers k and m, we shall say that such an algebra AA is (k,m)(k,m)...
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In this paper, the authors continue the analysis, first undertaken in Livshits et al. (2013) [2], of algebras AA of linear transformations on an n-dimensional complex vector space VV which have the property that if WW is a k-dimensional subspace of VV, then the image of WW under the action of the al...
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In [M.R. Burke, Large entire cross-sections of second category sets in Rn+1Rn+1, Topology Appl. 154 (2007) 215–240], a model was constructed in which for any everywhere second category set A⊆Rn+1A⊆Rn+1 there is an entire function f:Rn→Rf:Rn→R which cuts a large section through A in the sen...
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We consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. Eu...
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The one-dimensional Schr ̈odinger’s equation is analysed w ith regard to the existence of exact solutions for decatic polynomial potentials. Under c ertain conditions on the potential’s pa- rameters, we show that the decatic polynomial potential V ( x ) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2 , a >...
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Let T = {τ1, τ2, ..., τK; p1, p2, ..., pK} be a position dependent random map on [0, 1], where {τ1, τ2, ..., τK} is a collection of nonsingular maps on [0, 1] into [0, 1] and {p1, p2, ..., pK} is a collection of position dependent probabilities on [0, 1]. We assume that the random map T has a ...
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The problem is to determine the number of ‘cops’ needed to capture a ‘robber’ in a game in which the cops always know the location of the robber, and the cops and robber move alternately along edges of a reflexive graph. The cops capture the robber if one of them occupies the same vertex as ...
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Analytic evaluation of Gordon's integral Jj(±p)c(b,b′;λ,w,z)=∫∞0xc+j−1e−λx1F1(b;c;wx)1F1(b′;c±p;zx)dx, are given along with convergence conditions. It shows enormous number of definite integrals, frequently appear in theoretical and mathematical physics applications, easily ded...
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Using the orthonormality of the 2D-Zernike polynomials reproducing kernels, reproducing kernel Hilbert spaces and ensuing coherent states are attained. With the aid of the so obtained coherent states the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized ...
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The electronic structure of quasiperiodic lattices is studied. An alloy theory, including short-range order effects, is used to approximate Fibonacci and Thue–Morse lattices. Short-range order is treated by embedding small clusters in an alloy that itself incorporates a two-site approximation, and...
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McDowell's 1985 electronic bath theory of charge transfer is used to investigate the effect of varying surface temperature on the process of ion scattering from a solid surface. As a specific example, the system of Na+ scattered from W is modeled. The neutralization probability is found to have a si...
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Any pure operator band can be expanded so that each component of the band is reflexive.
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The larval stages of the cynipid wasp Diplolepis rosaefolii induce the formation of single-chambered, lenticular galls on the leaves of the wild shrub rose, Rosa virginiana. The development of galls induced by D. rosaefolii was studied using light and scanning electron microscopy. The gall consists ...
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