2. Articole
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Item 2D VISUAL MEMBRANE PETRI NETS MODEL OF ALLELIC GENE REGULATION(CEP USM, 2011) Profir, AureliaÎn lucrare este propusă o nouă clasă de Reţele Petri, numită 2D Visual Membrane Petri Nets. În calitate de component de bază al reţelelor, a fost adăugată structura membranară 2D. În plus, este propusă o nouă extensie a formalismului expresiilor descriptive pentru o reprezentare adecvată a componentelor 2D Visual Membrane Petri Nets. În calitate de exemplu de P sisteme cu timp continuu, este analizat modelul P transducerului de reglare a expresiei genelor alele. Componentele modelului de P transducer sunt exprimate prin componentele 2D Visual Membrane Petri Nets şi prin elemente descriptive.Item ABORDAREA SECURITĂȚII INFORMAȚIEI ÎN BAZA STANDARDELOR(CEP USM, 2024) Bragaru, TudorMany people mistakenly believe that information security (SI) and cyber security (SC) are completely different and that SC only boils down to technical-technological issues, settings, firewall rules, etc. In reality SI and SC are very close, and statistics show that the human problem predominates with a weight of about 70 to 95%. The purpose of this paper is to disprove some illusions/myths regarding SI/SC and elucidate their correct approach, with the reorientation from the paradigm based on software-technical-technological problems – towards organizational and management problems, based on generally accepted standards of good practices, without diminishing the importance of IT security and not limited to it. The work is carried out on the basis of an in-depth study of the modern trends in the organization and management of SI/SC with the analysis and synthesis of some recommendations based on bibliographic sources and the standards of best practices for the organization and management of SI/SC. The benefits of the SI/SC approach through the prism of good practice standards are multiple, generally recognized and confirmed by numerous results obtained in research, publications and the increase of the number of certifications of SI/SC management systems.Item ABOUT AN APPLICATION OF GAMES WITH FIXED ORDER OF MOVEMENTS(CEP USM, 2008) Prodan, NicolaeÎn acest articol este descris în forma unui joc de doua persoane cu ordinea fixată a mișcărilor, procesul de ºgestionarea a relațiilor dintre întreprinderile agricole ¸si cele industriale (de prelucrare a producției agricole). Pentru jocul formulat este determinat profitul maxim garantat al jucatorilor.Item ABOUT RATES OF CONVERGENCE IN THE LIMIT THEOREM(CEP USM, 2011) Munteanu, Bogdan Gheorghe; Leahu, Alexei; Cataranciuc, SergiuÎn 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.Item ABSOLUTE ASYMPTOTIC STABILITY OF DISCRETE LINEAR INCLUSIONS(Institutul de Matematică şi Informatică al AŞM, 2006) Cheban, David; Mammana, CristianaThe article is devoted to the study of absolute asymptotic stability of discrete linear inclusions in Banach (both finite and infinite dimensional) space. We establish the relation between absolute asymptotic stability, asymptotic stability, uniform asymptotic stability and uniform exponential stability. It is proved that for asymptotical compact (a sum of compact operator and contraction) discrete linear inclusions the notions of asymptotic stability and uniform exponential stability are equivalent. It is proved that finite-dimensional discrete linear inclusion, defined by matrices {A1,A2, ...,Am}, is absolutely asymptotically stable if it does not admit nontrivial bounded full trajectories and at least one of the matrices {A1,A2, ...,Am} is asymptotically stable. We study this problem in the framework of non-autonomous dynamical systems (cocyles).Item ABSTRACT COMPLEXES, THEIR HOMOLOGIES AND APPLICATIONS(Institutul de Matematică şi Informatică al AŞM, 2010) Cataranciuc, Sergiu; Soltan, PetruThe 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.Item ABSTRACT COMPLEXES, THEIR HOMOLOGIES AND APPLICATIONS(Institutul de Matematică şi Informatică al AŞM, 2010) Cataranciuc, Sergiu; Soltan, PetruThe 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.Item ADAPTAREA LA TEHNOLOGIE: FIGMA VS. SKETCH ÎN DESIGNUL UX/UI PENTRU MEDIUL ONLINE(CEP USM, 2024) Cristei, MariaThe paper describes the concepts, methodology and tools used in UI/UX design, with an emphasis on the online environment, and emphasizes their importance in creating quality design. The article also covers a detailed analysis of Figma with other tools, such as Sketch, highlighting its ability to facilitate team collaboration, flexible project sharing, and efficient integration of the development process.Item ADAPTIVE APPLICATION FOR COMPLEX SYSTEMS MODELING(CEP USM, 2017) Căpățână, Gheorghe; Ciobu, Victor; Paladi, FlorentinThe paper presents a formal system for presentation and measurement of applications adaptability, and describes an original methodology for building adaptive applications from various fields of activity/research, including for computer modeling of complex systems in physics.Item ALGEBRE ECHIVALENTE DE OPERATORI INTEGRALI SINGULARI. CRITERII NOETHERIENE(CEP USM, 2017) Bâclea, Diana; Neagu, VasileÎn prezenta lucrare sunt stabilite condiții necesare și suficiente în care operatorii integrali singulari cu translații de tip Carleman sunt noetherieni, se determină simbolul și se calculează indicele acestor operatori. Aceste rezultate sunt obținute datorită studiului algebrei generate de acești operatori în spațiul Lp cu o anumită pondere, aleasă astfel încât să asigure continuitatea operatorilor. În studiul algebrei respective un rol important are noțiunea de echivalență a algebrelor Banach, introdusă de către matematicienii I.Gohberg și N.Krupnik.Item ALGORITHM FOR THE LOCALIZATION OF SINGULARITIES OF FUNCTIONS DEFINED ON CLOSED CONTOURS(CEP USM, 2017) Capcelea, Maria; Capcelea, TituA numerical algorithm for locating polar singularities of functions defined on a discrete set of points of a simple closed contour in the complex plane is examined. The algorithm uses the Faber-Pad ́e approximation of the function and the fact that the zeros of its denominator give us approximations of the poles of function. The numerical performance of the algorithm is being analyzed on test issues.Item ALGORITHMS FOR SOLVING STOCHASTIC DISCRETE CONTROL PROBLEMS ON NETWORKS WITH VARYING TIME OF STATES’ TRANSITIONS OF THE DYNAMICAL SYSTEM(CEP USM, 2014) Capcelea, MariaThe stochastic versions of discrete optimal control problem on networks with varying time of state transitions of the dinamical system are studied. Polynomial time algorithms for determining the optimal stationary strategies in this problems are proposed.Item ALGORITM CU MODIFICAREA ALEATORIE A COMPONENTELOR GRADIENTULUI PENTRU UN MODEL CONVEX DE OPTIMIZARE(CEP USM, 2008) Balan, PavelA stochastic algorithm is proposed and analyzed, that is a probabilistic generalization of gradient method, for solving convex models. A random change of „old” partial derivatives with „new” ones is performed from one iteration to another. Convergence aspects of this scheme are analyzed for the case when the step is adjusted programmatically. Certain conditions are indicated, that, being respected, ensure the convergence of this scheme to the optimal solution with probability 1.Item ALGORITM EFECTIV PENTRU REZOLVAREA ECUAŢIILOR INTEGRALE SINGULARE(CEP USM, 2007) Capcelea, TituWe present a fast algorithm with O(n log n) computational complexity for the approximate solution of Cauchy 2 singular integral equations with smooth continuous coefficients, defined on the unit circle of the complex plane. In order to obtain this algorithm we adopt Amosov`s idea [1] to the quadrature method. In the case when the approximate method is applicable [2], the solution ϕn of the mentioned fast algorithm satisfies the same convergence rate as the solution n ∗ ϕ of the quadrature method.Item ALGORITM PENTRU DETERMINAREA STRATEGIILOR OPTIME STAŢIONARE ÎNPROBLEMELE STOCASTICE DE CONTROL OPTIMAL DISCRET PE REŢELE DECIZIONALE CU MULTIPLE CLASE RECURENTE(CEP USM, 2015) Capcelea, Maria; Capcelea, TituEste elaborat şi argumentat teoretic un algoritm eficient pentru determinarea strategiilor optime staţionare în problemele stocastice de control optimal discret cu perioada de dirijare infinită, definite pe reţele decizionale cu multiple clase recurente, în care este aplicat criteriul de optimizare a combinaţiei convexe a costurilor medii în clasele recurente. Sunt examinate probleme în care costurile de tranziţie între stările sistemului dinamic şi probabilităţile de tranziţie, definite în stările necontrolabile, sunt constante independente de timp. Algoritmul elaborat este bazat pe modelul de programare liniară pentru determinarea strategiilor optime în problemele de control definite pe reţele decizionale perfecte [3,4].Item ALGORITMI DE SOLUȚIONARE A PROBLEMELOR NELINIARE DE TRANSPORT CU MAI MULȚI INDICI(CEP USM, 2020) Pașa, TatianaÎn articol este formulată și studiată problema neliniară de transport cu funcții concave de cost cu patru indici descrisă de surse, destinații, tipuri de produse și tipuri de tran sport care circulă prin rețea de transport. Tot aici este formulată și studiată problema neliniară de transport cu funcții concave de cost cu cinci indici descrisă de surse, destinații, tipuri de produse și tipuri de transport. Sunt prezentați algoritmi eu ristici care permit soluționarea acestor probleme și rezultatele testărilor pentru algoritmii implementați în limbajul Wolfram.Item ALGORITMI EFICIEN Ţ I PENTRU REZOLVAREA SISTEMELOR DE ECUAŢII CE APAR LA DISCRETIZAREA ECUAŢIILOR INTEGRALE SINGULARE(CEP USM, 2008) Capcelea, Maria; Capcelea, Titu; Lazari, AlexandruIt is marked out the class of iterative algorithms for solvin g of systems of equations which are obtained when discre- tizing SIE with discontinuous coefficients. These algorithms permit essential reducing of computational cost for finding an approximate solution, at that not losing in the quality of other numerical characteristics - they are numerically stable and allow us to check precision in the course of iterations without calculation of approximation of a solution.Item ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF MONOTONE DIFFERENTIAL EQUATIONS WITH A STRICT MONOTONE FIRST INTEGRAL(2020) Ceban, DavidThe paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.Item ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF MONOTONE DIFFERENTIAL EQUATIONS WITH A STRICT MONOTONE FIRST INTEGRAL(Institutul de Matematică şi Informatică al AŞM, 2020) Cheban, DavidThe paper is dedicated to the study of problem of Poisson stability (in particular periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, Levitan almost periodicity, pseudo-periodicity, almost recurrence in the sense of Bebutov, recurrence in the sense of Birkhoff, pseudo-recurrence, Poisson stability) and asymptotical Poisson stability of motions of monotone non-autonomous differential equations which admit a strict monotone first integral. This problem is solved in the framework of general non-autonomous dynamical systems.Item ALMOST PERIODIC SOLUTIONS AND GLOBAL ATTRACTORS OF NON-AUTONOMOUS NAVIER–STOKES EQUATIONS(Springer, 2004) Cheban, David; Duan, JinqiaoThe article is devoted to the study of non-autonomous Navier–Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier–Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic, almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier–Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier–Stokes equations.