Browsing by Author "Cataranciuc, Sergiu"

Now showing 1 - 20 of 21

ABOUT RATES OF CONVERGENCE IN THE LIMIT THEOREM
(CEP USM, 2011) Munteanu, Bogdan Gheorghe; Leahu, Alexei; Cataranciuc, Sergiu
În lucrare se propune o estimare a ratei de convergenţă a densităţii sumei de variabile aleatoare în raport cu densitatea probabilităţii de repartiţie. Studii similare au fost făcute şi de către alţi matematicieni. Aici putem menţiona lucrarea lui W. Macht şi Wolf W. „On the local central limit theorem” [2], în care aproximarea densităţii probabilităţii unui şir de variabile aleatoare este făcută cu referire la densitatea probabilităţii distribuţiei normale standarde. Principalul rezultat al acestui articol se conţine în teorema 2.1, care stabileşte rata de convergenţă a densităţii probabilităţii unui şir de variabile aleatoare în raport cu densitatea probabilităţii de repartiţie a variantei cu una şi cu trei grade de libertate.
ABSTRACT COMPLEXES, THEIR HOMOLOGIES AND APPLICATIONS
(Institutul de Matematică şi Informatică al AŞM, 2010) Cataranciuc, Sergiu; Soltan, Petru
The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods used for these constructions are for the most part analogous with classical methods [2,32,52], but sometimes they are based on methods from [18,44,58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.
ABSTRACT COMPLEXES, THEIR HOMOLOGIES AND APPLICATIONS
(Institutul de Matematică şi Informatică al AŞM, 2010) Cataranciuc, Sergiu; Soltan, Petru
The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods used for these constructions are for the most part analogous with classical methods [2,32,52], but sometimes they are based on methods from [18,44,58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.
ACOPERIREA CU MULȚIMI d-CONVEXE A GRAFURILOR NEORIENTATE
(2017) Buzatu, Radu; Cataranciuc, Sergiu
Scopul și obiectivele lucrării. Scopul urmărit prin realizarea tezei constă în studierea și soluționarea problemei de acoperire a unui graf neorientat cu mulțimi d-convexe. Pentru atingerea scopului sunt fixate următoarele obiective: examinarea complexității problemei de acoperire a grafului cu un număr p>2 de mulțimi d-convexe; stabilirea condițiilor de existență a unei familii de mulțimi d-convexe, ce formează o acoperire a grafului neorientat; soluționarea problemei de acoperire a grafului cu mulțimi d-convexe netriviale; elaborarea algoritmilor pentru problema de acoperire/divizare a grafului cu mulțimi d-convexe; estimarea numărului de acoperire d-convexă minimă/maximă.
ASUPRA UNOR DISTRIBUŢII FIABILISTE ŞI TEOREMA LIMITĂ POISSON PENTRU ELE
(CEP USM, 2014) Munteanu, Bogdan Gheorghe; Leahu, Alexei; Cataranciuc, Sergiu
Sunt introduse patru noi distribuţii fiabiliste ale minimului şi maximului unui şir de variabile aleatoare independente, identic Erlang distribuite întrun număr aleator, distribuit binomial sau Poisson (zero trunchiate). Sunt abordate proprietăţile şi caracteristicile acestor distribuţii, precum şi condiţiile în careare loc teorema limită Poisson pentru acestea.
CLASE DE SUBGRAFURI STABILE ÎN ORIENTAREA TRANZITIVĂ A GRAFURILOR
(CEP USM, 2015) Cataranciuc, Sergiu; Grigoriu, Nicolae
În articol sunt analizate clasele de subgrafuri stabile, folosite la caracterizarea grafurilor tranzitiv orientabile și la studierea proprietăţilor acestora. Subgrafurile stabile reprezintă un suport în construirea orientării tranzitive a unui graf, precum şi pentru determinarea numărului acestora. De asemenea, sunt prezentate condiţiile necesare şi suficiente pentru ca un graf să fie tranzitiv orientabil.
COERENŢA ELEMENTELOR ÎNTR-UN COMPLEX DE RELAŢII MULTI-ARE
(CEP USM, 2015) Cataranciuc, Sergiu
În articol este generalizată noţiunea de coerenţă simplă a elementelor unui complex de relaţii multi-are. Interpretând elementele complexului de relaţii ca simplexe abstracte, sunt introduse noţiunile de t-coerenţă şi (t q) coerenţă. Sunt demonstrate rezultate ce ţin de relaţia de coerenţă generalizată a simplexelor abstracte.
CONVEX GRAPH COVERS
(Academy of Sciences of Moldova, 2015) Buzatu, Radu; Cataranciuc, Sergiu
We study some properties of minimum convex covers and minimum convex partitions of simple graphs. We establish existence of graphs with fixed number of minimum convex covers and minimum convex partitions. It is known that convex p-cover problem is NP-complete for p\geq3 [5]. We prove that this problem is NP-complete in the case p=2. Also, we study covers and partitions of graphs when respective sets are nontrivial convex.
THE CONVEXITY IN THE COMPLEX OF MULTI-ARY RELATIONS
(Romanian Society of Applied & Industrial Mathematics Universitatea din Pitesti, 2015) Braguţă, Galina; Cataranciuc, Sergiu
For a complex of multi-ary relations [12] it is defined the concept of (k,m)-chain which is a generalization of the concept of chain known from the graph theory. Using (k,m)- chains it is introduced the concept of the distance function and it is proved that this function generate a convexity in the complex of multi-ary relations. It is operating with the concepts of convexity and convex hull, axiomatically defined by F.Levi [29] and we describe the iterative procedure to construct a convex hull for a subset of elements from the complex of multi-ary relations. [ABSTRACT FROM AUTHOR]
DERIVATION OF BOOLEAN FUNCTIONS BY THE BLOCKS METHOD
(Valines SRL, 2014) Bulat, Mihai; Cataranciuc, Sergiu; Ciobanu, Iacob; Izbas, Vladimir; Zgureanu, Aureliu
A method for calculating using blocks of the partial derivatives of the boolean function which are represented in algebraic form { a polynomial form, disjunctive normal form and conjunctive normal form is proposed. The method can be used success- fully for functions which depend on a large number of variables (tens and hundreds). This method can be applied to solve many problems from di®erent areas such as: elaborating of encryption system with variable keys, some problems from discrete mathematics (systems isomorphism problem, problem of determining of chromatic number in graphs ect.).
dm-CONVEX FUNCTIONS IN THE COMPLEX OF MULTI-ARY RELATIONS
(2017) Cataranciuc, Sergiu; Braguța, Galina
In the present work the notions of dm-convexity and dm convex function are defined. Some properties of these functions are mentioned. We study the complexes of multi-ary relations for which the median function is dm-convex.
EULER CHARACTERISTIC OF ABSTRACT CUBES COMPLEX
(Valines SRL, 2014) Cataranciuc, Sergiu
Formula for the Euler characteristics for the In complex is deduced. The formula is expressed by cardinals of the groups of the homologies and by a number of m-dimensional abstract cubes from In.
THE EULER TOUR OFN-DIMENSIONAL MANIFOLDWITH POSITIVE GENUS
(Institutul de Matematică şi Informatică al AŞM, 2008) Cataranciuc, Sergiu; Bujac-Leisz, Mariana; Soltan, Petru
In the paper [1] it is proved that abstract cubicn-dimensional torus[2] possesses a directed Euler tour of the same dimension. The result prompts toa new (virtual) device for transmission and reception of information. In the presentpaper it is shown that every abstract cubicn-dimensional manifold without borders, ofpositive genus possesses an-dimensional directed Euler tour. This result has practicalapplication.
LOCATION PROBLEMS ON d - CONVEX SIMPLE PLANAR GRAPHS
(CEP USM, 2015) Cataranciuc, Sergiu; Macoveiciuc, Elisei
The article examines the center and median problems on graphs with special structure. In scientific works these are frequently called location problems on graphs. Although efficient solutions for graphs with some well-known properties have been found, in general case the problem remains complex. In this paper the structure of median and center in a d-convex simple planargraph Gis studied.We evaluate the connection between median/center of a graph Gwith mentioned properties and median/center of a tree, determined by G.
MATRICELE DE RELAŢII MULTI-ARE ŞI NUMERELE PRIME ÎN CRIPTAREA INFORMAŢIEI
(CEP USM, 2012) Cataranciuc, Sergiu; Zgureanu, Aureliu
Se propune un sistem simetric de criptare a informaţiei, numit Crypto 2. Acest sistem se bazează pe utilizarea numerelor prime mari şi pe dezvoltarea lor polinomială. Un rol deosebit revine matricelor multidimensionale, folositepentru reprezentarea mulţimilor de relaţii multi-are. Se descrie algoritmul de criptare/decriptare a informaţiei, Cripto 2,şi se demonstrează că acest algoritm are o complexitate liniară.
O MODALITATE DE REZOLVARE A PROBLEMELOR DE PROGRAMARE DINAMICĂ
(CEP USM, 2016) Maximilian, Silvestru; Cataranciuc, Sergiu; Căpățână, Gheorghe; Cataranciuc, Emil
În lucrare se propune o metodă eficientă, din punct de vedere practic, pentru soluționarea problemelor de programare dinamică. Procesul de rezolvare este împărțit în etape și reprezintă o schemă de calcul foarte simplă pentru utilizatori. Metoda propusă este expusă prin examinarea problemei de repartiție optimă a investițiiolor între ramuri.Calculele se prezintă sub formă de tabele .
ON NONTRIVIAL COVERS AND PARTITIONS OF GRAPHS BY CONVEX SETS
(Institutul de Matematică şi Informatică al Academiei de Ştiinţe a Moldovei, 2018) Buzatu, Radu; Cataranciuc, Sergiu
In this paper we prove that it is NP-complete to decide whet- her a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a re- cursive formula that establishes the maximum nontrivial convex cover number of a tree.
ON THE DIVISION OF ABSTRACT MANIFOLDS IN CUBES
(Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Mariana; Cataranciuc, Sergiu; Soltan, Petru
We prove that in the class of abstract multidimensional manifolds withoutborders only torusVn1of dimensionn≥1 can be divided in abstract cubes with theproperty: every faceImfromVn1is shared by 2n−mcubes,m= 0,1, . . . , n−1. Theabstract torusVn1is realized inEd, n+1≤d≤2n+1, so it results that in the class ofalln-dimensional combinatorial manifolds [1]onlytorus respects this propriety. Torusis autodual because of this propriety.
SEARCH TREE-BASED APPROACH FOR THE P-MEDIAN PROBLEM USING THE ANT COLONY OPTIMIZATION ALGORITHM
(Academy of Sciences of Moldova, 2014) Bodnariuc, Gabriel; Cataranciuc, Sergiu
In this paper we present an approximation algorithm for the p-median problem that uses the principles of ant colony optimization technique. We introduce a search tree that keeps the partial solutions during the solution process of the p-median problem. An adaptation is proposed that allows ant colony optimization algorithm to perform on this tree and obtain good results in short time.
THE SPECIAL METRICS OF TH E ABSTRACT CUBIC COMPLEX
(CEP USM, 2008) Cataranciuc, Sergiu
Se examinează complexul cubic abstract nK ca un caz particular al G-complexului de relaţii multi-are [2]. Pentru complexul cubic abstract nK se defineşte o funcţie specială ce posedă proprietăţile metricii.