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...

We first prove a general gluing theorem which creates new nondegenerate constant mean curvature surfaces by attaching half Delaunay surfaces with small necksize to arbitrary points of any nondegenerate CMC surface. The proof uses the method of Cauchy data matching from [8], cf. also [10]. In the second part of this paper, we develop the consequences of this result and (at least partially) chara...

We introduce a quantization map and study the quantization of Schubert and Grothendieck polynomials, monomials, elementary and complete polynomials. Our construction is based on the quantum Cauchy identity. As a corollary, we prove the Lascoux–Schützenberger type formula for quantum Schubert polynomials of the flag manifold. Our formula gives a simple method for computation of quantum Schubert ...

Let L be an unbounded linear operator in a real Hilbert space H, a generator of a C0 semigroup, and let g : H → H be a C2 loc nonlinear map. The DSM (dynamical systems method) for solving equation F (v) := Lv+ g(v) = 0 consists of solving the Cauchy problem u̇ = Φ(t, u), u(0) = u0, where Φ is a suitable operator, and proving that i) ∃u(t) ∀t > 0, ii) ∃u(∞), and iii) F (u(∞)) = 0. Conditions on L...

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regu...

We compute the spectra of the Tanaka type Laplacians = ∂̄ Q∂̄Q + ∂̄Q∂̄ ∗ Q and △ = ∂ ∗ Q∂Q+ ∂Q∂ ∗ Q on the Rumin complex Q, a quotient of the tangential Cauchy-Riemann complex on the unit sphere S in Cn. We prove that Szegö map is a unitary operator from a subspace of (p, q− 1)-forms on the sphere defined by the operators △ and the normal vector field onto the space of L-harmonic (p, q)-forms on th...

In this article, we present various new results on Cauchy tensors and Hankel tensors. We first introduce the concept of generalized Cauchy tensors which extends Cauchy tensors in the current literature, and provide several conditions characterizing positive semi-definiteness of generalized Cauchy tensors with nonzero entries. Furthermore, we prove that all even order generalized Cauchy tensorsw...

in this paper, a novel matched filter based on a new kernel function with cauchy distribution is introduced to improve the accuracy ofthe automatic retinal vessel detection compared with other available matched filter‑based methods, most notably, the methods builton gaussian distribution function. several experiments are conducted to pick the best values of the parameters for the new designedfi...