We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU/R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabri...

Almost a century ago Voronoi [1908] formulated his fundamental algorithm to find the perfect (real positive definite quadratic) forms in n variables. Among these one finds the forms representing the locally extreme lattice packings of spheres. The subject was taken up by M. Koecher [1960], who gave an axiomatic treatment of self-dual cones and a corresponding Voronoi algorithm in this situation...

We investigate self-dual codes from a structural point of view. In particular, we study properties of critical indecomposable codes which appear in the spectrum of a self-dual code. As an application of the results we obtain, we revisit the study of self-dual codes of dimension at most 10.

In this paper, we proposed a tunable graphene-based metamaterial absorber (MA) at dual terahertz band to achieve perfect absorption. The electric field intensity distributions of demonstrated structure is illustrated explain the origin two absorption peaks. Simulation result shows MA owning polarization-insensitive property and wide incident angle tolerance. An inversion algorithm used extract ...

Purpose: Education policy implementation is as important design. This study applies a literature-based, multi-dimensional framework for success factors and barriers to vocational education training (VET) reform in the case of new dual VET law Serbia. We use assess related implementation, then relate these actual progress determine how progress. In this application framework, we examine whether ...

Although nontrivial perfect binary codes exist only for length n = 2m−1 with m ≥ 3 and for length n = 23, many problems concerning these codes remain unsolved. Herein, we present solutions to some of these problems. In particular, we show that the smallest nonempty intersection of two perfect codes of length 2m − 1 consists of two codewords, for all m ≥ 3. We also provide a complete solution to...

We show how to obtain the dual of any lattice model, with inhomogeneous local interactions, based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains disorder loops on the generators of the cohomology group of a particular dimension. An explicit construction for altering the statistical sum to obtain a self...

We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C = R, this recovers the standard projective dimension. We show that three natural definitions of finite Cprojective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results th...

We study the relationship between the projective dimension of a squarefree monomial ideal and the domination parameters of the associated graph or clutter. In particular, we show that the projective dimensions of graphs with perfect dominating sets can be calculated combinatorially. We also generalize the wellknown graph domination parameter τ to clutters, obtaining bounds on the projective dim...

Bent or perfect nonlinear Boolean functions represent the best resistance against the so-called linear and differential cryptanalysis. But this kind of cryptographic relevant functions only exists when the number of input bits m is an even integer and is larger than the double of the number of output bits n. Unfortunately the non-existence cases, the odd dimension (m is an odd integer) or the p...