n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

We use τK to denote the topology of DK (Ω) equipped with such metric. The topology of D (Ω) can be defined precisely. Let β be the collection of all convex balanced sets W ⊂ D (Ω) such that DK (Ω) ∩ W ∈ τK for every compact K ⊂ Ω. Let τ be the collection of all unions of sets of the form φ+W with φ ∈ D (Ω) and W ∈ β. Theorem 1. τ is a topology in D (Ω) and β is a local base for τ . The topology...

Abstract We compute the multiplicative constant in large gap asymptotics of Meijer- G point process. This process generalizes Bessel and appears at hard edge Cauchy–Laguerre multi-matrix models certain product random matrix ensembles.

We develop a canonical Wick rotation-rescaling theory in 3-dimensional gravity. This includes (a) A simultaneous classification: this shows how generic maximal globally hyperbolic spacetimes of arbitrary constant curvature, which admit a complete Cauchy surface, as well as complex projective structures on arbitrary surfaces, are all different materializations of “more fundamental” encoding stru...

Stevan Pilipović, Mirjana Stojanović Abstract. We recall the definition of G–quasiasymptotics at infinity in a framework of Colombeau space G (cf. [8]) and give an application of that notion to a Cauchy problem for a strictly semilinear hyperbolic system. It turns out that quasiasymptotic behaviour at infinity of the solution inherits the quasiasymptotic behaviour at infinity of initial data un...

For the Cauchy problem, gt = u%~, 0 < x < 1, 0 < t < T, ~(0, t) = f(t), 0 < t < T, u.(O, t) = g(t), 0 < t < T, a direct numerical procedure involving the elementary solution of vt = v,, , 0 < x, 0 < t < T, ~(0, t) = g(t), 0 < t < T, v(x, 0) = 0,O < x and a Taylor’s series computed fromf(t) ~(0, t) is studied. Continuous dependence better than any power of logarithmic is obtained. Some numerical...

In this paper, we prove an existence theorem for the pseudo-nonlocal Cauchy problem x′(t) + Ax(t) = f(t, x(t), ∫ t t0 k(t, s, x(s))ds), x0(t0) = x0−g(x), where A is the infinitesimal generator of a C0 semigroup of operator {T (t)}t>0 on a Banach space. The functions f, g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.

Abstract A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that null sequence “becomes” infinitesimal. We signal little-noticed construction system with infinitesimals in 1910 publication by Giuseppe Peano, reversing his earlier endorsement Cantor’s belittli...

In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and Cauchy sequence. this paper, we define $A^{I^{\ast }}$-statistical find under certain conditions, that it is equivalent to $A^{I}$-statistical defined in [Appl. Math. Lett. 2012, 25 733-738]. Moreover, $A^{I}$- sequences some with convergence.