We provide a unique normal form for rank two irregular connections on the Riemann sphere. In fact, we birational model where introduce apparent singular points and bundle has fixed Birkhoff–Grothendieck decomposition. The essential poles parabolic structures. first one only depends formal type of points. latter determines connection (accessory parameters). As consequence, an open set correspond...

Statistical methods based on ranking are known to be versatile and powerful techniques. Nonparametric rank tests for two-way analysis of variance have been studied by several authors, for example: rank transform (RT ) proposed by Conover and Iman (1981); asymptotic theory of RT discussed by Hora and Conover (1984), Akritas (1990) and Thompson and Ammann (1990). McKean and Vidman (1994) suggeste...

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion

In this paper, we present a robust normal estimation algorithm based on the low-rank subspace clustering technique. The main idea is based on the observation that compared with the points around sharp features, it is relatively easier to obtain accurate normals for the points within smooth regions. The points around sharp features and smooth regions are identified by covariance analysis of thei...

Multivariate normal probabilities, which are used for statistical inference, must be computed numerically. This article describes a new rank-1 lattice quadrature rule and its application to computing multivariate normal probabilities. In contrast to existing lattice rules the number of integrand evaluations need not be speciied in advance. When compared to existing algorithms for computing mult...

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.