The matrix representation of the set ∆(d), d = (d1, d2, d3), of the integers which are unrepresentable by d1, d2, d3 is found. The diagrammatic procedure of calculation of the generating function Φ ( d; z ) for the set ∆(d) is developed. The Frobenius number F ( d ) , genus G ( d ) and Hilbert series H(d; z) of a graded subring for non–symmetric and symmetric semigroups S ( d ) are found. The u...

Given a finite ring A which is a free left module over a subring R of A, two types of R-bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric bases, are defined which in turn are used to define duality preserving maps from codes over A to codes over R. Both types of bases are generalizations of similar concepts for fields. Many illustrative examples are given to shed l...

dense medium cyclone is a high capacity device that is widely used in coal preparation. it is simple in design but the swirling turbulent flow, the presence of medium and coal with different density and size fraction and the presence of the air-core make the flow pattern in dmcs complex. in this article the flow pattern simulation of dmc is performed with computational fluid dynamics and fluent...

If every subring of an integral domain is atomic, we say that the latter hereditarily atomic. In this paper, study atomic domains. First, characterize when certain direct limits Dedekind domains are in terms overrings. Then use characterization to determine fields On other hand, investigate hereditary atomicity context rings polynomials and Laurent polynomials, characterizing whose respectively...

Graph mining is an important research area with a plethora of practical applications. Core decomposition in networks, is a fundamental operation strongly related to more complex mining tasks such as community detection, dense subgraph discovery, identification of influential nodes, network visualization, text mining, just to name a few. In this tutorial, we present in detail the concept and pro...

We present an algorithm for graph based saliency computation that utilizes the underlying dense subgraphs in finding visually salient regions in an image. To compute the salient regions, the model first obtains a saliency map using random walks on a Markov chain. Next, k-dense subgraphs are detected to further enhance the salient regions in the image. Dense subgraphs convey more information abo...

This paper concerns the problem of computing the densest k-vertex subgraph of a given graph, namely, the subgraph with the most edges, or with the highest edges-to-vertices ratio. A sequence of approximation algorithms is developed for the problem! with each step yielding a better ratio at the cost of a more complicated solution. The approximation ratio of our final algorithm is O(n0,3””5). We ...

The role of symmetry in ring theory is universally recognized. most directly definable universal relation a symmetric set isomorphism. This article develops certain structure bipolar fuzzy subrings, including quotient ring, homomorphism, and We define (?,?)-cut investigate the algebraic attributions this phenomenon. also support prove various important properties relating to concept. Additional...