We study the spectral properties of the transition semigroup of the killed onedimensional Cauchy process on the half-line (0,∞) and the interval (−1, 1). This process is related to the square root of one-dimensional Laplacian A = − √ − d dx with a Dirichlet exterior condition (on a complement of a domain), and to a mixed Steklov problem in the half-plane. For the half-line, an explicit formula ...

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

We study inhomogeneous Dirichlet boundary value problems associated to a linear parabolic equation dudt=Au with strongly elliptic operator A on bounded and unbounded domains white noise data. Our main assumption is that the heat kernel of corresponding homogeneous problem enjoys Gaussian type estimates taking into account distance boundary. Under mild assumptions about domain, we show generates...

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. 

Determinantal point processes (DPPs) are a class of repulsive processes, popular for their relative simplicity. They traditionally defined via marginal distributions, but subset DPPs called “L-ensembles” have tractable likelihoods and thus particularly easy to work with. Indeed, in many applications, more naturally based on the L-ensemble formulation rather than through kernel. The fact that no...

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entrop...

Observations of the multi-TeV spectra of the nearby BL objects Mkn 421 and Mkn 501 exhibit the high energy cutoffs predicted to be the result of intergalactic annihilation interactions, primarily with infrared photons having a flux level as determined by various astronomical observations. After correction for this absorption effect, the derived intrinsic spectra of these multi-TeV sources can b...

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a given matrix by a Cauchy matrix with a particular focus on the recovery of Cauchy points from noisy data. We derive an approximation algorithm of optimal com...

*Correspondence: [email protected] Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran Abstract In this paper, an effective numerical method to solve the Cauchy type singular Fredholm integral equations (CSFIEs) of the first kind is proposed. The collocation technique based on Bernstein polynomials is used for approximation the solution of various cases of CSFIE...