We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that non-exi...

Absfrset. The notion of the Cauchy indexof a real rational scalar function is generalized todefinc the Cauchy index of a real rational symmetric matrix in terms of the behavior of the matrix at real singularities of its elements. Alternative characterizations are obtained which flow from iepresenrations of the real rational matrix using a Laurent series, a matrix fraction description. and a sta...

Abstract. It is well known that the ratio of two independent standard Gaussian random variables follows a Cauchy distribution. Any convex combination of independent standard Cauchy random variables also follows a Cauchy distribution. In a recent joint work [PM16], the author proved a surprising multivariate generalization of the above facts. Fix m > 1 and let Σ be a m × m positive semi-definite...

Hyperbolic equations and inequalities in octants with the lateral Cauchy data at coordinate planes are consdered. Lipschitz stability estimate is established in the case when both the inhomogeneous right hand side and (unknown) initial conditions at {t = 0} have a finite support. This is the first stability estimate for such a Cauchy problem in an infinite domain. Refocusing of time reversal fi...

The accuracy of data diagnosis is important for clinical management, reimbursement, and issues related to healthcare services. Based on preliminary observations, it was found that the inaccuracy code maker with genitourinary disease standard at Sidarjo District Hospital. purpose this study find out comparison coder codes standards sidoarjo district hospital. method used quantitative random samp...

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of the domain, ...

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine’s 2φ1 transformation formula and Sears’ 3φ2 transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator T (bDq). Using this operator, we obtain extensi...

We study the Cauchy problem for the Aw-Rascle-Zhang model for traffic flow with a flux constraint at x = 0. More precisely we consider the Riemann solver, conserving the number of cars at x = 0 but not the generalized momentum, introduced in [9] for the problem with flux constrained. For such a Riemann solver, we prove existence of a solution for the Cauchy problem. The proof is based on the wa...

In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward quasi-cauchy sequences, half Cauchy sequences. Next consider associated idea of continuity namely, ward continuous functions [2] investigated certain intersting results. The entire investigation is perform in (l)-group setting.