We define the so-called fully inert socle-regular and weakly Abelian p-groups study them with respect to certain of their numerous interesting properties. For instance, we prove that in case groups length $$\omega $$ , these two group classes coincide, but +1$$ they differ. Some structural characterization results are also obtained. The work generalizes concepts which have been interest recentl...

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...

—A Kleene Semiring (KS) is an algebraic structure satisfying the axioms of Kleene algebra, minus the annihilation axioms x.0 = 0 = 0.x. We show that, like Kleene algebra (KA), KS admits efficient elimination of various kinds of equational hypotheses, in particular Hoare formulas (x = 0). Our method is purely proof-theoretic, and can be used to eliminate Horn hypotheses in any suitable Horn-equa...

In this paper we continue the partition explorations made possible by Omega, the computer algebra implementation of MacMahon’s Partition Analysis. The focus of our work has been partitions associated with directed graphs. The graphs considered here are made up of chains of hexagons, and the related generating functions are infinite products. Somewhat unexpectedly, while the generating functions...

We carefully perform a Hamiltonian Dirac's constraint analysis of the $\ensuremath{\omega}=\ensuremath{-}\frac{3}{2}$ Brans-Dicke theory with Gibbons-Hawking-York boundary term. The Poisson brackets are computed via functional derivatives. After brief summary results for $\ensuremath{\omega}\ensuremath{\ne}\ensuremath{-}\frac{3}{2}$ case [G. Gionti S. J., Canonical addresses inequivalence betwe...

In this work, we show how to implement effective constructions, coding and decoding of algebraic codes by means of Omega, a system specifically designed and programmed for general mathematical computations. For alternant codes, the main class we consider (which includes BCH, RS and classical Goppa codes), we give an implementation of the Euclidean division BM decoding algorithm. For cyclic code...

Let ω \omega be a weight on right cancellative semigroup alttext="upper S"> S encoding="application/x-tex">S</...

Abstract For any congruence subgroup $\Gamma $, we study the vertex operator algebra $\Omega ^{ch}(\mathbb H,\Gamma )$ constructed from $-invariant global sections of chiral de Rham complex on upper half plane, which are holomorphic at all cusps. We construct a basis in terms modular forms $ and compute its character. show that operations determined by modification Rankin–Cohen brackets forms.

Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with cocommutative Hopf algebra structure. We show that if L is a primitive pseudoalgebra over then all finite irreducible L' Cur_H^{H'} L-modules are of form V, where V an L-module, single class exceptions. Indeed, when H(d, \chi, \omega), we introduce non current L'-...