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Altun Emrah Khan Naushad Mamode 《Methodology and Computing in Applied Probability》2022,24(3):1735-1751
Methodology and Computing in Applied Probability - In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced.... 相似文献
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Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire 下载免费PDF全文
Malik Mamode 《advances in applied mathematics and mechanics.》2011,3(6):689-701
The exact analytical expression of the period of a conservative nonlinear
oscillator with a non-polynomial potential, is obtained. Such an oscillatory
system corresponds to the transverse vibration of a particle attached to the center of a
stretched elastic wire. The result is given in terms of elliptic functions and validates the
approximate formulae derived from various approximation procedures as the
harmonic balance method and the rational harmonic balance method usually
implemented for solving such a nonlinear problem. 相似文献
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The length of instability intervals is investigated for the Hill equation y′′+ω(ω− 2∈p(x)y = 0, where p(x) has an infinite Fourier series of coefficients c
n. For any small ∈ it is shown that these lengths are completely characterized by the c
n's. 相似文献
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Malik Mamode 《Journal of mathematical chemistry》2017,55(3):734-751
A new method of computing the Madelung constants for hypercubic crystal structures in any dimension \(n\ge 2\) is given. It is shown for \(n\ge 3\) that the Madelung constant may be obtained in a simple, efficient and unambiguous way as the Hadamard finite part of the integral representation of the potential within the crystal which is divergent at any point charge location. Such a regularization method fails in the bidimensional case due to the logarithmic nature of singularities for the potential. In that case, a specific approach is proposed taking in account the scale invariance of the Poisson equation and the existence of a finite horizon for each point charge in the plane. Since a closed-form exact solution for the 2D electrostatic potential may be derived, one shows that the Madelung constant may be defined via an appropriate limit calculation as the mean value of potential energies of charges composing the unit cell. 相似文献
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Malik Mamode 《Applied mathematics and computation》2009,215(1):276-282
The variational iterative method is revisited for initial-value problems in ordinary or partial differential equation. A distributional characterization of the Lagrange multiplier - the keystone of the method - is proposed, that may be interpreted as a retarded Green function. Such a formulation makes possible the simplification of the iteration formula into a Picard iterative scheme, and facilitates the convergence analysis. The approximate analytical solution of a nonlinear Klein-Gordon equation with inhomogeneous initial data is proposed. 相似文献
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