In previous work, the second author and others have found conditions on a homogeneous space G/H which imply that, up to stabilization, all vector bundles over admit Riemannian metrics of non-negative sectional curvature. One important ingredient their approach is Segal’s result that set form $$G\times _H V$$ for representation V H contains inverses within class. We show this cannot work biquoti...

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of G∖{1} is called minimal if 〈S〉=G and there exists some s∈S such that 〈S∖{s,s−1}〉≠G. In this paper, we characterize distance-regular Cayley graphs Cay(G,S) under the condition minimal.

This is an integral of a differential of first kind on C which does not vanish at ∞. The integral converges everywhere. If g = 0 the inverse funcion of (1.2) is −1/ sin(u). As is well-known, if g = 1 the inverse function of (1.2) is just the Weierstrass function ℘(u) with ℘(u) = 4℘(u) − 4 (or ℘(u) = 4℘(u) − 4). The Bernoulli numbers {B2n} are the coefficients of the Laurent expansion of −1/ sin...

Some genomic evaluation models require creation and inversion of a genomic relationship matrix (G). As the number of genotyped animals increases, G becomes larger and thus requires more time for inversion. A single-step genomic evaluation also requires inversion of the part of the pedigree relationship matrix for genotyped animals (A(22)). A strategy was developed to provide an approximation of...

We shall consider generated pseudo-operations of the following form: x⊕ y = g(−1) (g(x) + g(y)) , x ̄ y = g(−1) (g(x)g(y)) , where g is a positive strictly monotone generating function and g(−1) is its pseudo-inverse. Using this type of pseudo-operations, the Riemann-Stieltjes type integral will be introduced and investigated.

Definition. A group G consists of a set G together with a binary operation ∗ for which the following properties are satisfied: • (x ∗ y) ∗ z = x ∗ (y ∗ z) for all elements x, y, and z of G (the Associative Law); • there exists an element e of G (known as the identity element of G) such that e ∗ x = x = x ∗ e, for all elements x of G; • for each element x of G there exists an element x′ of G (kn...

T HIS INTRODUCTORY section applies to general binary rate k/n convolutional codes. In Section II we specialize to rate one-half to describe a class of codes that allows an interesting mod ification of the stack decoding algorithm [l]-[2]. Section III presents our simulation results. Let G be a conventional convolutional encoder [3] whose rows are the first k rows of a polynomial n X n matrix B ...

Consider any nilpotent group G of finite odd order. We ask if we can always find a galois extension K of Q such that Gal(K/Q) ∼= G. This is the famous Inverse Galois Problem applied to nilpotent groups of finite odd order. By solving the Group Extension Problem and the Embedding Problem, two problems that are related to the Inverse Galois Problem, we show that such a K always exists. A major re...

The generalized inverse has many important applications in aspects of the theoretical research matrices and statistics. One core problems is finding necessary sufficient conditions reverse order laws for operator product. In this paper, we study law g-inverse an product T1T2T3 using technique matrix form bounded linear operators. particular, some inclusion T3{1}T2{1}T1{1} ⊆ (T1T2T3){1} presente...