DSpace Collection: Volume 10 Number 3-4
http://hdl.handle.net/10525/2923
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Basic Algorithms for Manipulation of Modules over Finite Chain Rings
http://hdl.handle.net/10525/2929
Title: Basic Algorithms for Manipulation of Modules over Finite Chain Rings<br/><br/>Authors: Georgieva, Nevyana<br/><br/>Abstract: In this paper, we present some basic algorithms for manipulation offinitely generated modules over finite chain rings. We start with analgorithm that generates the standard form of a matrix over a finite chainring, which is an analogue of the row reduced echelon form for a matrix overa field. Furthermore we give an algorithm for the generation of the union oftwo modules, an algorithm for the generation of the orthogonal module to agiven module, as well as an algorithm for the generation of the intersectionof two modules. Finally, we demonstrate how to generate all submodules offixed shape of a given module.ACM Computing Classification System (1998): G.1.3, G.4.Community-Sourcing in Virtual Societies
http://hdl.handle.net/10525/2928
Title: Community-Sourcing in Virtual Societies<br/><br/>Authors: Branzov, Todor<br/><br/>Abstract: The paper studies the approaches to development of goodswith active participation of virtual community members. The concept ofcommunity-sourcing is presented as an alternative to the open source modeland crowdsourcing. On that foundation a conceptual model of resourcemanagement system that use some current good practices of the IT industryis proposed. Results obtained in a virtual community implementing themodel are presented as a validation attempt.ACM Computing Classification System (1998): H.5.3., H.3.5., J.4., K.3.1., K.4.3., K.6.1.Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions
http://hdl.handle.net/10525/2927
Title: Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions<br/><br/>Authors: Bouyuklieva, Stefka; Bouyukliev, Iliya<br/><br/>Abstract: In this article, we study two representations of a Boolean functionwhich are very important in the context of cryptography. We describeMöbius and Walsh Transforms for Boolean functions in details and presenteffective algorithms for their implementation. We combine these algorithmswith the Gray code to compute the linearity, nonlinearity and algebraic degreeof a vectorial Boolean function. Such a detailed consideration will bevery helpful for students studying the design of block ciphers, including PhDstudents in the beginning of their research.ACM Computing Classification System (1998): F.2.1, F.2.2.What is Genselfdual?
http://hdl.handle.net/10525/2926
Title: What is Genselfdual?<br/><br/>Authors: Bouyukliev, Iliya; Bouyuklieva, Stefka; Dzhumalieva-Stoeva, Maria; Monev, Venelin<br/><br/>Abstract: This paper presents developed software in the area of CodingTheory. Using it, all binary self-dual codes with given properties can beclassified. The programs have consequent and parallel implementations.ACM Computing Classification System (1998): G.4, E.4.A Medical Image Denoising Method using Subband Adaptive Thresholding Based on a Shearlet Transform
http://hdl.handle.net/10525/2925
Title: A Medical Image Denoising Method using Subband Adaptive Thresholding Based on a Shearlet Transform<br/><br/>Authors: Petrov, Miroslav<br/><br/>Abstract: The image denoising process is of great importance when analyzingimages and their visualization. A major problem is finding the boundarybetween clearing the noise and keeping the salient features in the images.This paper proposes adaptive subband threshold image denoising in a shearletdomain based on the Shannon entropy. The method does not suppose aspecific type of noise, it does not require data for its spectrum, nor does itlead to highly complex computational algorithms.ACM Computing Classification System (1998): I.5.4, I.4.3, I.4.5.Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]
http://hdl.handle.net/10525/2924
Title: Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]<br/><br/>Authors: Akritas, Alkiviadis G.; Malaschonok, Gennadi I.; Vigklas, Panagiotis S.<br/><br/>Abstract: In this paper we present two new methods for computing thesubresultant polynomial remainder sequence (prs) of two polynomials f, g ∈ Z[x].We are now able to also correctly compute the Euclidean and modifiedEuclidean prs of f, g by using either of the functions employed by ourmethods to compute the remainder polynomials.Another innovation is that we are able to obtain subresultant prs’s inZ[x] by employing the function rem(f, g, x) to compute the remainderpolynomials in [x]. This is achieved by our method subresultants_amv_q(f, g, x), which is somewhat slow due to the inherent higher cost of com-putations in the field of rationals.To improve in speed, our second method, subresultants_amv(f, g,x), computes the remainder polynomials in the ring Z[x] by employing thefunction rem_z(f, g, x); the time complexity and performance of thismethod are very competitive.Our methods are two different implementations of Theorem 1 (Section 3),which establishes a one-to-one correspondence between the Euclidean andmodified Euclidean prs of f, g, on one hand, and the subresultant prs of f, g,on the other.By contrast, if – as is currently the practice – the remainder polynomi-als are obtained by the pseudo-remainders function prem(f, g, x) 3 , thenonly subresultant prs’s are correctly computed. Euclidean and modified Eu-clidean prs’s generated by this function may cause confusion with the signsand conflict with Theorem 1.ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.