Results 31 to 40 of about 88 (55)
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case [PDF]
, 2015 The 'relativistic' Heun equation is an 8-coupling difference equation that generalizes the 4-coupling Heun differential equation. It can be viewed as the time-independent Schrödinger equation for an analytic difference operator introduced by van Diejen ...
Simon N.M. Ruijsenaars
core +2 more sources
Demonstratio MathematicaThis article is devoted to exploring the solutions of several systems of the first-order partial differential difference equations (PDDEs) with product type u(z+c)[α1u(z)+β1uz1+γ1uz2+α2v(z)+β2vz1+γ2vz2]=1,v(z+c)[α1v(z)+β1vz1+γ1vz2+α2u(z)+β2uz1+γ2uz2]=1 ...
Liu Xiao Lan +3 more
doaj +1 more source
Spectral equations for the modular oscillator [PDF]
, 2017 Motivated by applications for non-perturbative topological strings in toric Calabi--Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of Faddeev) Harper type operators, corresponding to a special case of the quantized mirror curve of local $\mathbb{P}^1\times\mathbb{P}^1$ and complex values of Planck'
arxiv +1 more source
, 2022 The equation $f^n+g^n=1$, $n\in\mathbb{N}$ can be regarded as the Fermat Diophantine equation over the function field. In this paper we study the characterization of entire solutions of some system of Fermat type functional equations by taking $e^{g_1(z)}
Haldar, Goutam
core +1 more source
Hyers-Ulam stability of the first order difference equation generated by linear maps [PDF]
arXiv, 2021 Hyers-Ulam stability of the difference equation $ z_{n+1} = a_nz_n + b_n $ is investigated. If $ \prod_{j=1}^{n}|a_j| $ has subexponential growth rate, then difference equation generated by linear maps has no Hyers-Ulam stability. Other complementary results are also found where $ \lim_{n \rightarrow \infty} \left(\prod_{j=1}^{n}|a_j| \right)^{\frac{1}{
arxiv
Hyers-Ulam Stability For A Type Of Discrete Hill Equation [PDF]
arXiv, 2023 We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both homogeneous and non-homogeneous, we also establish a Hyers-Ulam stability constant.
arxiv
Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint [PDF]
arXiv, 2010 Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its Galois Group G has finite determinant group and is reductive.
arxiv
Mahler equations and rationality [PDF]
arXiv, 2016 We give another proof of a result of Adamczewski and Bell concerning Mahler equations: A formal power series satisfying a $p-$ and a $q-$Mahler equation over ${\mathbb C}(x)$ with multiplicatively independent positive integers $p$ and $q$ is a rational function.
arxiv
Best constant for Ulam stability of first-order h-difference equations with periodic coefficient [PDF]
arXiv, 2020 We establish the best (minimum) constant for Ulam stability of first-order linear $h$-difference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples.
arxiv
Zero Entropy for Some Birational Maps of C^2 [PDF]
arXiv, 2017 This work deals with a special case of family of birational maps f : C2 -> C2 dynamically classified in [9]. In this work we study the zero entropy sub families of f. The sequence of degrees dn associated to the iterates of f is found to grow periodically, linearly, quadratically or exponentially. Explicit invariant fibrations for zero entropy families
arxiv