We consider Laplace transforms of the Picard-Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms of Gel’fand-KapranovZelevinski hypergeometric systems.

Abstract The paper deals with the problem under which conditions for parameters $$s_1,s_2\in \mathbb R$$ s 1 , 2 ∈ R , $$1\le p,q_1,q_2\le \infty $$ ≤ p</...

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P, Q] = P , where P flows according to the KP hierarchy ∂P/∂t n = [(P n/p) + , P ], with p := ord P ≥ 2; (ii) find a matrix integral representation for the associated τ-function. First we construct an infinite dimensional space W = span C ψ 0 (z), ψ 1 (z),. .. of functions of z ∈ C invariant u...

We introduce a general definition of hybrid transforms for constructible functions. These are integral combining Lebesgue integration and Euler calculus. gives access to well-studied kernels regularity results, while calculus conveys topological information allows compatibility with operations on conduct systematic study such two new ones: the Euler–Fourier Euler–Laplace transforms. show that f...

In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresse...

Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. With the increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very simple approach just like the applications of transfer functions to solve ordinary differential equations. This paper will discuss the applications of Laplace transforms...