We obtain a flagged form of the Cauchy determinant and establish a correspondence between this determinant and nonintersecting lattice paths, from which it follows that Cauchy identity on Schur functions. By choosing different origins and destinations for the lattice paths, we are led to an identity of Gessel on the Cauchy sum of Schur functions in terms of the complete symmetric functions in t...

In this paper, by using a special family of filters $mathcal{F}$ on an EQ-algebra $E$, we construct a topology $mathcal{T}_{mathcal{mathcal{F}}}$ on $E$ and show that $(E,mathcal{T}_{mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we o...

This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with Lipschitz boundary. It completes the results obtained in [4] for domains of class C. This estimate is established by using an interior Carleman estimate and a technique based on a sequence of balls which approach the boundary. This technique is inspired f...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

The internal structure of a charged spherical black hole is still a topic of debate. In a nonrotating but aspherical gravitational collapse to form a spherical charged black hole, the backscattered gravitational wave tails enter the black hole and are blueshifted at the Cauchy horizon. This has a catastrophic effect if combined with an outflux crossing the Cauchy horizon: a singularity develops...

Formulæ are derived for expressing Cauchy and Hilbert transforms of a function f in terms of Cauchy and Hilbert transforms of f(xr). When r is an integer, this corresponds to evaluating the Cauchy transform of f(xr) at all choices of z1/r. Related formuæ for rational r result in a reduction to a generalized Cauchy transform living on a Riemann surface, which in turn is reducible to the standard...

Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space. Nuray 2 proved the inclusion relations between the set of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. Kwon and Shim 3 studied statistical convergence and lacunary statistical convergence of sequences of fuzzy ...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

Principal Component Analysis (PCA) aims to learn compact and informative representations for data and has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Principal Compo...