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...

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...

Additive fuzzy systems can filter impulsive noise from signals. Alpha-stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter ct ranges through the interval (0, 2] and gives the Gaussian bell curve when 0t = 2 and gives the Cauchy bell curve when ~t = 1. The impulsiveness grows as ~ falls and the bell...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, Lorentz Transformation(LT) is derived by an alternate method, using photon clocks, placed at the locations of the concerned events, which are initially synchronised using a light signal(Einstein synchrony). Then, it is shown that the second term in the time dilation equation of the LT, is the term responsible for time travel and further it is shown that this term arises merely du...

We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy– Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motiv...