In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Fina...

In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix multiplication: most other fast approximant basis algorithms basically aim at efficiently reducing the input instance to instances for which PMBasis is fast. Such red...

Introduction: In most oscillators, the close-to-the-carrier amplitude modulation (AM) noise is usually lower than the phase modulation (PM) noise and does not pose serious problems. However, in highperformance systems where every decibel of PM noise is important, the AM noise cannot be neglected. Numerous applications consider AM noise effects on the overall performance of an oscillator or a sy...

We do not think that the relativistic Morse potential problem has been correctly formulated and solved by A. D. Alhaidari. Key-words: Dirac equation; Dirac-Morse problem; Exact solution. PACS numbers: 03.65.Pm 03.65.Ge ∗To be submitted for publication in Phys. Rev. Lett. †Permanent address: Departamento de Ciências Exatas e da Natureza, Universidade Federal da Paráıba, Cajazeiras PB, 58.900-000...

We give a combinatorial proof for a second order recurrence for the polynomials pn(x), where pn(k) counts the number of integer-coordinate lattice points x = (x1, . . . , xn) with ‖x‖ = ∑n i=1|xi| ≤ k. This is the main step to get finiteness results on the number of solutions of the diophantine equation pn(x) = pm(y) if n and m have different parity. The combinatorial approach also allows to ex...

We write the master equation describing the Parrondo’s games as a consistent discretization of the Fokker–Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondo’s games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials corre...

We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...

The ternary lanthanum sulfide selenide β -LaS1.86(1)Se0.14(1) was obtained by reaction of the elements in an NaCl flux. The new compound adopts the β -LnS2 structure type and crystallizes in the orthorhombic space group Pnma (no. 62) with lattice parameters of a = 814.77(1), b = 1638.46(1) and c = 413.88(1) pm. Raman lines indicate the presence of mixed (S1−ySey)2− dianions with y ≈ 0.14, besid...

The analytical solutions of the Schrödinger equation with position-dependent mass for the Morse potential are obtained by the series expansion method. The Morse potential and the position-dependent mass themselves are expanded in the series about the origin. As an example, the analytical series solutions of the Morse potential with the position-dependent mass m=m0eλr are given.  2004 Elsevier ...

We study the eigenvalues En` of the Salpeter Hamiltonian H = β √ m2 + p2 +vr, v > 0, β > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula En` ≈ min r>0 { v(Pn`/r) 2 + β √ m2 + r2 } provides both upper and lower energy bounds for all the eigenvalues of the problem. PACS: 03.65.Ge, 03.65.Pm, 11.10.St En...