Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. The test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces...

It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an unbounded element then it also has a dense one-sided ideal. In the present paper we obtain analogues of the aforementioned results of Inoue and Fritzsche for r...

in this paper, an approximate axisymmetric method is developed which can reliably calculate fully viscous hypersonic flow over blunt-nosed bodies. in this method, a maslen’s second-order pressure expression is used instead of the normal momentum equation. the combination of maslen’s second-order pressure expression and viscous shock layer equations is developed to accurately and efficiently com...

We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of the Permutation Test for any input size n as well as the optimality of the Circle Test for three input states. In particular, when n = 3, we present a semi-cla...

We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices (i.e., they are given by the sine-kernel in the bulk and the Tracy-Widom distribution at the edge), and we show averaged energy universality (i.e., universality for averages of m-points correl...

A questionnaire was sent to senior partners in all general practices in Scotland designed to elicit experience of patients with gender dysphoria: a subjective experience of incongruity between genital anatomy and gender identity. Responses were received from 73% of practices. The prevalence of gender dysphoria among patients aged over 15 years was calculated as 8.18 per 100,000, with an approxi...

the present study is aimed at assessing the state of national identity among female students of ahwaz islamic azad university and explores the social factors affecting upon it. the statistical society consisted of 8532 students at the three levels of associate diploma undergraduate and master degrees. the research method in this study is a “survey” and collection of data has been carried out by...

Following recent result of L. M. Tóth [Tót21, Annales Henri Lebesgue, Volume 4 (2021)] we show that every 2Δ-regular Borel graph

Distinct elements (F0). In this note we will consider the distinct elements problem, also known as the F0 problem, defined as follows. We are given a stream of integers i1, . . . , im ∈ [n] where [n] denotes the set {1, 2, . . . , n}. We would like to output the number of distinct elements seen in the stream. As with Morris’ approximate counting algorithm, our goal will be to minimize our space...

We present a new approach to multi-dimensional parsing using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. Our approach makes no hard decisions; recognized math expressions are reported to the user in ranked order. A flexible correction mechanism enables users to quickly choose the corre...