This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over L, where L is a finite extension of a field K. This is a generalization of the case where K = Fq and L = Fqm of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by K...

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras assoc...

In this paper we prove that the vertex algebra V + L is rational if L is a negative definite even lattice of finite rank , or if L is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices L, we show that the Zhu algebras of the vertex algebras V + L are semisimple. This extends the result of Abe from [A2] wh...

Let L be a finite geometric lattice of rank r, and for i =0, I, •• •» r, let W. denote the number of elements of L with rank i. F or 1 < k < r 2, we have W, + W. + • • • + V, < W ,+•••+ W ., + W , 12 fe r—k r—l r—1 with equality if and only if the lattice L is modular. We give two further results concerning matchings of lattice elements of rank < k into those of rank > r — k, and observe that a...

In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization crisp in fuzzifying view with distance between ordinary points. For aim, first present concept by considering as non-negative, upper semi-continuous, normal and convex numbers giving examples. We obtain some useful inequalities under restrictions spaces. Then discuss relationships other struct...

The generalization of binary operation in the classical algebra to fuzzy is an important development field algebra. paper proposes a new vector spaces over field, which called M-hazy field. Some fundamental properties spaces, and subspaces are studied, some results also proved. Furthermore, linear transformation studied their Finally, it shown that M-fuzzifying convex induced by subspace space.

the presence of noise in geophysical measurements has undesirable effects on the seismic data. one of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. in some of the receivers the no...

Dedicated to the memory of Bernard Dwork 1. Introduction In this series of two papers, we prove the p-adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal, as conjectured by Dwork 6]. More precisely, we prove a suitable extension of Dwork's conjecture in our more general setting of-modules, see section 2 for precise deen...