DSpace Collection: Volume 9 Number 1
http://hdl.handle.net/10525/2473
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On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions
http://hdl.handle.net/10525/2485
Title: On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions<br/><br/>Authors: Kyurkchiev, Nikolay; Markov, Svetoslav<br/><br/>Abstract: We introduce a modification of the familiar cut function byreplacing the linear part in its definition by a polynomial of degree p + 1obtaining thus a sigmoid function called generalized cut function of degreep + 1 (GCFP). We then study the uniform approximation of the (GCFP)by smooth sigmoid functions such as the logistic and the shifted logisticfunctions. The limiting case of the interval-valued Heaviside step functionis also discussed which imposes the use of Hausdorff metric. Numericalexamples are presented using CAS MATHEMATICA.Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths
http://hdl.handle.net/10525/2484
Title: Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths<br/><br/>Authors: Baicheva, Tsonka; Topalova, Svetlana<br/><br/>Abstract: Dedicated to the memory of the late professor Stefan Dodunekovon the occasion of his 70th anniversary.We classify up to multiplier equivalence maximal (v, 3, 1) opticalorthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1)OOCs with v ≤ 99.There is a one-to-one correspondence between maximal (v, 3, 1) OOCs,maximal cyclic binary constant weight codes of weight 3 and minimum distance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binarycyclically permutable constant weight codes. Therefore the classification of(v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs areperfect and they are equivalent to cyclic Steiner triple systems of order vand (v, 3, 1) cyclic difference families.Model Mining and Efficient Verification of Software Product Lines
http://hdl.handle.net/10525/2483
Title: Model Mining and Efficient Verification of Software Product Lines<br/><br/>Authors: Soleimanifard, Siavash; Gurov, Dilian; Schaefer, Ina; Østvold, Bjarte; Markov, Minko<br/><br/>Abstract: Software product line modeling aims at capturing a set of software productsin an economic yet meaningful way. We introduce a class of variability modelsthat capture the sharing between the software artifacts forming the productsof a software product line (SPL) in a hierarchical fashion, in terms of commonalitiesand orthogonalities. Such models are useful when analyzing and verifying all productsof an SPL, since they provide a scheme for divide-and-conquer-style decompositionof the analysis or verification problem at hand. We define an abstract class of SPLsfor which variability models can be constructed that are optimal w.r.t. the chosenrepresentation of sharing.We show how the constructed models can be fed into a previously developedalgorithmic technique for compositional verification of control-flow temporal safetyproperties, so that the properties to be verified are iteratively decomposed intosimpler ones over orthogonal parts of the SPL, and are not re-verified overthe shared parts. We provide tool support for our technique, and evaluateour tool on a small but realistic SPL of cash desks.On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations
http://hdl.handle.net/10525/2482
Title: On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations<br/><br/>Authors: Valchanov, Nikola; Golev, Angel; Iliev, Anton<br/><br/>Abstract: This paper is dedicated to Prof. Nikolay Kyurkchievon the occasion of his 70th anniversaryThis paper gives sufficient conditions for kth approximations ofthe zeros of polynomial f (x) under which Kyurkchiev’s method fails on thenext step. The research is linked with an attack on the global convergencehypothesis of this commonly used in practice method (as correlate hypothesisfor Weierstrass–Dochev’s method). Graphical examples are presented.Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)
http://hdl.handle.net/10525/2481
Title: Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)<br/><br/>Authors: Akritas, Alkiviadis<br/><br/>Abstract: Given the polynomials f, g ∈ Z[x] of degrees n, m, respectively,with n > m, three new, and easy to understand methods — along withthe more efficient variants of the last two of them — are presented for thecomputation of their subresultant polynomial remainder sequence (prs).All three methods evaluate a single determinant (subresultant) of anappropriate sub-matrix of sylvester1, Sylvester’s widely known and usedmatrix of 1840 of dimension (m + n) × (m + n), in order to compute thecorrect sign of each polynomial in the sequence and — except for the secondmethod — to force its coefficients to become subresultants.Of interest is the fact that only the first method uses pseudo remainders.The second method uses regular remainders and performs operationsin Q[x], whereas the third one triangularizes sylvester2, Sylvester’s littleknown and hardly ever used matrix of 1853 of dimension 2n × 2n.All methods mentioned in this paper (along with their supporting functions)have been implemented in Sympy and can be downloaded from the linkhttp://inf-server.inf.uth.gr/~akritas/publications/subresultants.py