Let $${\mathcal {L}}=\sum _{j=1}^{m}X_{j}^{2}$$ be a Hörmander sum of squares vector fields in $${\mathbb {R}}^{n}$$ , where any $$X_{j}$$ is homogeneous degree 1 with respect to family non-isotropic dilations . Then, {L}}$$ known admit global fundamental solution $$\Gamma (x;y)$$ that can represented as the integral sublaplacian operator on lifting space {R}}^{n}\times {\mathbb {R}}^{p}$$ equi...

One of the numerical methods for solving linear Volterra integral equations is block-by-block method, which is explained in [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985; L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974] and [P.K. Kyte, P. Puri, Computational Methods for Linear Integral Eq...

We evaluate the integral ∞ 0 · · · ∞ 0 1≤i<j≤n (x j − x i) 2 e −x1 dx 1 · · · e −xn dx n using orthogonal polynomials and techniques from linear algebra.

Background Joint work with Fedor Nazarov and Igor Verbitsky (preprint) Start with general functional analysis theorem: Background Joint work with Fedor Nazarov and Igor Verbitsky (preprint) Start with general functional analysis theorem: Given an integral operator T on a σ-finite measure space (Ω, ω) with kernel K : Background Joint work with Fedor Nazarov and Igor Verbitsky (preprint) Start wi...

Let \(\textit{K}\) be a cubic number field. In this paper, we study the Ramanujan sums \(c_{\mathcal {J}}(\mathcal {I})\), where \(\mathcal {I}\) and {J}\) are integral ideals in {O}_\textit{K}\). The asymptotic behaviour of {I})\) over both is investigated.

This paper describes the development of a probabilistic methodology for fracture-mechanics analysis of weld cracks in a center-cracked tension (CCT) specimen. It involves elastic±plastic analyses to predict J-integral, statistical models of uncertainties in loads and material properties, and standard computational methods of structural reliability theory for probabilistic analysis. Eighty-one d...

In [4], Breaz and Breaz gave the univalence conditions of the integral operator Fα,n of the analytic functions belonging to the classes T2, T2,μ and S(p). The purpose of this paper is to generalize the integral operator Fα,n by means of the generalized Al-Oboudi differential operator and investigate univalence conditions of this generalized integral operator considering the classes Tj , Tj,μ an...

In this paper, we aim at establishing certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions, which was introduced and studied by Özergin et al. [J. Comput. Appl. Math. 235(2011), 4601-4610]. All the results derived here are of general character and can yield a number of (known and new) results in the theory of integral transforms and frac...

Using the saddle point method, we obtain from the generating function of the Stirling numbers of the first kind [ n j ] and Cauchy’s integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Goncharov theorem with more precision. In the region j = n− n, α > 1/2, we analyze the dependence of [ n j ] on α.