Volume 19, No. 2 (2009)
Articles
SMOOTH DEPENDENCE ON RIEMANNIAN METRIC OF EIGENVALUES OF HODGE-DE RHAM OPERATORS
MIHAELA ALBICI
Let M be an oriented, closed and smooth manifold of dimension n, Ak(M) the space of smooth differential forms on M, and Μ(M) the space of all Riemannian metrics on M, endowed with the canonical structure of smooth Fréchet manifold. Using an idea of J. Wenzelburger [10], [11], we prove that the eigenvalues of the Hodge-de Rham operator Δ(k): Ak(M) → Ak(M) depend smoothly on the Riemannian metric g ∈ Μ(M), for each k ∈ {1,2,…n}. Minimax principle (see Theorem 2.2 of M. Craioveanu, M. Puta and Th. M. Rassias [5], p. 286) imply the smoothly dependence on Riemannian metric of eigenvalues of Hodge-de Rham operators and of restrictions of these operators on spaces of differential exact forms, respectively of coexact forms. It is also shown that some Hodge-de Rham decompositions smoothly depend on the Riemannian metric.
CONTROLS FOR RFID IN SUPPLY CHAIN PROCESSES AUDIT
CRISTIAN AMANCEI(1), BOGDAN AMANCEI(2)
The increasing use Radio Frequency Identification (RFID) systems to provide real-time visibility of inventory from the point of manufacture to the point of sale expand the capabilities of organizations by enabling companies to achieve a greater visibility and flexibility in their supply chain processes. This environment requires the auditor to identify the associated risks and the controls that mitigate those risks, in order to help the organization to provide certified services in collaboration with their partners. In addition, this paper presents aspects of the audit mission for RFID systems in supply chain processes.
THE LAMELLAR DIFFRACTION GRATING PROBLEM: A SPECTRAL METHOD BASED ON SPLINE EXPANSION
ANA MARIA ARMEANU(1, 2), KOFI EDEE(2), GERARD GRANET(2), PATRICK SCHIAVONE(1)
Our aim is to solve the electromagnetic problem of the diffraction of a plane wave by a one dimensional lamellar grating. In that case the solution to Maxwell's equations can be split into two canonical cases : the so-called transverse magnetic (TM) and transverse electric (TE) polarizations. These cases can be treated separately, reducing the problem to a scalar one. In this paper we only consider the TE polarization case in which the only non null component of the electric field is parallel to the grating grooves. Since the grating is invariant in one direction the Maxwell's equations reduce to an eigenvalue problem for which a numerical solution is obtained by using the method of moments. First the unknown function is expanded in a series of spline functions and then the operator deduced from the Maxwell's equations is projected onto a set of test functions after a suitable inner product has been defined. The choice of the basis and test functions and their properties have an essential impact for the rate of convergence. One of the reasons for choosing splines functions is that they were successfully used in the signal processing field. We can take advantage of their analytical definition as piecewise polynomials and their compact support. Concerning the test functions, we compare three possible choices : Dirac, gate or spline functions. Thanks to their attractive properties, these functions allow calculating analytically the matrix coefficients deduced from the inner product. The computational effort is therefore drastically minimized.
CONTROLLING CHAOTIC DYNAMICAL SYSTEMS THROUGH FIXED POINT ITERATIVE TECHNIQUES
VASILE BERINDE
An extremely simple and effcient controlling mechanism has been developed to stabilize discrete dynamical systems. The new technique is essentially based on considering controllers taken from typical fixed point iterative methods. Theoretical analysis as well as computer simulations have been provided to show the simplicity, great power, effectiveness and eficiency of this new method in practice.
MATRIX MATHEMATICAL MODELS USED IN THE REPRESENTATION OF MOLECULAR STRUCTURES
ZOIŢA-MĂRIOARA BERINDE
Mathematics is very useful in chemistry, among other things, to produce models. In this paper we propose a brief description of a mathematical model of the chemical structures using matrices associated to the molecular graphs. These matrices provide a source for obtaining some important molecular descriptors that can be used in QSPR (Quantitative Structure - Property Relationship) and QSAR (Quantitative Structure − Activity Relationships). Using the notions of weighted electronic distance (w.e.d.) introduced by the author in [11], we present the weighted electronic connectivity matrix (CEP), associated to a chemical graph and also illustrate the calculation technique of ZEP index.
INFINITESIMAL MOTIONS OF THE 2 − π STRUCTURES ON THE TANGENT BUNDLE
VICTOR BLĂNUŢĂ(1), MANUELA GÎRŢU(1), VALENTIN GÎRŢU(2)
We define the motion of an almost 2 − π structure on the tangent bundle and study the main properties of these. We study here the existence and arbitrariness of d-connection DΓ(N) determining all these connections. Finally we determine the infinitesimal motions of this structure and we study the properties of these motions.
INFINITESIMAL MOTIONS OF THE METRICAL 2 − π STRUCTURES ON THE TANGENT BUNDLE
VICTOR BLĂNUŢĂ, VALER NIMINEŢ
We define the notion of almost metrical 2 − π structure on the tangent bundle and study the main properties of such a structure. We study here the existence and arbitrariness of a d-connection FΓ(N) and determine all these connections. Finally we determine the infinitesimal motions of this structure and study the properties of these motions.
COMPUTER-BASED ITERATIVE AND INCREMENTAL TEACHING OF MATHEMATICS
DORIN BOCU(1), DORINA BOCU(2)
Mathematics is the subject that may legitimate a certain affinity between the humans and the dimension of gods. The high level of abstraction that mathematics exhibits may turn down the most genuine intentions of understanding and using the truths that are based on sophisticated paradigms regarding the organization and interpretation of numbers. In this paper, we propose a first attempt to answer the question: “Is it possible to use the computer in order to attenuate the difficulties one may encounter when learning mathematics?”
MATHEMATICS AND ART
MIHAI BRESCAN
The present study focuses on the analysis, under various aspects, of the relation between mathematics, literature (mainly poetry) and the plastic arts (mainly painting). The first part presents the similarity of the creative act in mathematics and in art, from the point of view of several remarkable creators, both mathematicians and artists. The second part emphasizes the relation between mathematics and poetry exemplified in the vision of some great mathematicians and poets. The work of the outstanding mathematician-poet Dan Barbilian-Ion Barbu represents the main focus. The third part outlines the connection between mathematics and painting, illustrated in the works and ideas of some representative personalities of the world culture.
A HYBRID GENETIC ALGORITHM FOR BALANCING ASSEMBLY LINES WITH COMPATIBILITY CONSTRAINTS
OCTAV BRUDARU(1), DIANA POPOVICI(2), CINTIA COPACEANU(3)
The paper presents a hybrid genetic algorithm for deterministic assembly line balancing (ALB) problem with a single model and an additional constraint, which requires that the workstations are compatible with a given cover of the assembly tasks. The performance criteria are the minimizing of the idle time and the smoothing index. The algorithm includes a special procedure to generate the cover sets and a special mutation operator preserving the topological order. It is also combined with an efficient greedy procedure proper to the problem. All genetic operators are applied with dynamic probabilities that favour the creating and preserving of good constructive blocks. The experimental investigation proves the ability of the hybrid method to find good solutions to this type of balancing problem.
OPTIMIZING DISTRIBUTION NETWORKS WITH NESTED GENETIC ALGORITHMS
O. BRUDARU(1, 2), B. VALMAR(2)
This paper deals with the optimizing of distribution networks with a central depots and a prescribed number of intermediate depots that supply groups of clients. A two levels metaheuristic is described for solving it. On the first level, a genetic algorithm used for finding the feasible group of consumers and the corresponding intermediate depots, like in the p-median problem. For such a partitioning of the clients, the interior provisioning circuits are obtained by invoking a hybrid genetic algorithm, and this task represents the second level of the metaheuristic. This second level completes the partial solutions from the first level and computes the fitness function of the genetic algorithm on the first level. The performance of the metaheuristic containing the two nested genetic algorithms is experimentally evaluated.
THE MAXMIN ALGORITHM FOR THE MAXIMUM FLOW
ELEONOR CIUREA(1), MIHAI - STEFAN IOLU(2)
In this paper we study maximum flow algorithms by using a new approach.
KNOWLEDGE MINING FROM WEB CUSTOMER OPINIONS TO IMPROVE ENTERPRISE PRODUCT
DOMENICO CONSOLI, CLAUDIA DIAMANTINI, DOMENICO POTENA
Nowadays, for the enterprise, the customer is a very important strategic resource. The opinions of a customer about a particular product/service helps top management to introduce improvements in processes and products, thus the enterprise gains competitive advantages. So, it is very important to define a bidirectional communication channel, supported from collaborative tools, between the customer and the enterprise. In this paper we introduce a customer oriented framework that after gathering and polarizing web customer opinions, with an algorithm of sentiment analysis, is able to route dysfunctions about product/service to competence center. This framework can be considered a Customer-Centred Information System that crosses many internal business functions.
SOME OPEN PROBLEMS IN THE THEORY OF ALMOST PERIODIC FUNCTIONS
C. CORDUNEANU
The theory of almost periodic functions is a well established branch of modern mathematics, with roots in the work of mathematicians as H. Poincare, P. Bohl and E. Esclangon. The essentials of the theory have been published by H. Bohr (1922{1926), whose work immediately attracted the interest of many distinguished mathematicians like V. Stepanov, S. Bochner, H. Weyl, N. Wiener, A.S. Besicovitch, J. von Neumann, N.N. Bogolinbov, with significant contributions to the field.
PSEUDO-ATOMS OF FUZZY MULTISUBMEASURES
ANCA CROITORU, ALINA GAVRILUT
In this paper we establish some decomposition results using pseudo-atoms of fuzzy multisubmeasures with respect to the Hausdorff topology. We also point out several properties of fuzzy set multifunctions.
OMEGA AND RELATED POLYNOMIALS IN NANOSTRUCTURES
MIRCEA V. DIUDEA
Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count opposite, topologically parallel, edges in graphs, particularly to describe the polyhedral nanostructures. Basic definitions are given and clear relations with other three related polynomials are discussed. These relations are supported by close formulas and appropriate examples. Close formulas for the calculation of Omega and its relative polynomials and derived single numbers, in several classes of nanostructures are given.
CONSIDERATIONS ON TIME MINIMIZATION IN TRANSPORTATION PROBLEM WITH IMPURITIES
GHEORGHE DOGARU(1), CRISTINA NISTOR(2)
The transportation problems with impurities in goods are very important from practical point of view because of higher frequency. An extension of time transportation problem is considered when goods can have some impurities and the final mixture of goods arrived at destination have some specifications. This time transportation problem is in connection with linear lexicographical transportation problem with impurities. In this paper is also presented an algorithm to solve bottleneck transportation problem making a connection with linear lexicographical transportation problem with impurities. The algorithm optimality conditions are similar to those given by H. Issermann, but there are some modifications caused by impurities.
THE CENTENNIAL OF CONVERGENCE IN MEASURE
LIVIU C. FLORESCU
In this work we recall the classical definitions and results about the topology of convergence in measure, but we also present some recent ones.
NEW HYBRID GENETIC ALGORITHM WITH ADAPTIVE OPERATORS AND VARIABILITY TARGET FOR OPTIMIZING VARIABLE ORDER IN OBDD
I. FURDU(1), O. BRUDARU(2)
Reduced Ordered Binary Decision Diagrams are one of the most powerful data structure for boolean manipulation on switching functions as top process in digital circuits design. The size of ROBDDs is very sensitive to the ordering choices of input variables. A new genetic algorithm is described for optimizing the variable order. It uses adaptive operators and includes a mechanism based on information energy for controlling the variability of the population. Experimental investigations of the performance of this genetic algorithm are described.
ANALYSIS OF ENTROPY MEASURES
ANGEL GARRIDO
Our paper to develop some useful analytical tools for the foundations of Uncertainty Measures. Because we need to obtain new ways to model adequate conditions or restrictions, constructed from vague pieces of information. For this, it is necessary to classify more efficiently the distinct types of measures; in particular, the fuzzy measures. Now, we complete this study by the analysis on Entropy and other Measures of Uncertainty, with their relationships. So, we attempt to go on, advancing by this paper.
A SET-VALUED LUSIN TYPE THEOREM
A. C. GAVRILUŢ
In this paper, we present a Lusin type theorem under a suitable type of measurability for regular multisubmeasures in Hausdorff topology.
ON TOTALLY-MEASURABLE FUNCTIONS
A. GAVRILUŢ, A. CROITORU
In this paper, we study different basic problems concerning real valued functions which are totally-measurable with respect to the variation of a (multi)submeasure. As applications, special considerations on their relation with Gould type integrability and additional problems are given (e.g., a Fatou lemma type, the Banach structure of a Lp space).
INTELLIGENT AGENT-BASED MEDICAL SYSTEMS
BARNA IANTOVICS
The development of efficient and flexible agent-based medical diagnosis systems represents a recent research direction. Medical multiagent systems may improve the efficiency of traditionally developed medical computational systems, like the medical expert systems. In our previous researches, a novel cooperative medical diagnosis multiagent system called CMDS (Contract Net Based Medical Diagnosis System) was proposed. CMDS system can flexibly solve a large variety of medical diagnosis problems. In this paper we analyze the increased intelligence of the CMDS system, which motivates its use for different medical problems solving.
SOME CURVATURE PROPERTIES IN RANDERS SPACES
OTILIA LUNGU
In this paper we get a condition for Randers spaces to be simultaneously with scalar flag curvature and with constant E-curvature.
AN APPLICATION OF AN INTEGRAL OPERATOR USING BRIOT - BOUQUET DIFFERENTIAL SUPERORDINATION
ANAMARIA GEANINA MACOVEI
The notion of differential superordination was introduced as a dual concept of differential subordination by the S. S. Miller and P. T. Mocanu. In this paper we give applications to Briot-Bouquet differential superordination and we prove a sandwich theorem, generalizing some results from [7] and [8].
A GENERALIZATION OF ORLICZ-SOBOLEV CAPACITY IN METRIC MEASURE SPACES
MARCELINA MOCANU
Given a Banach function space B and a metric measure space X, we investigate continuity and regularity properties of the B-capacity, that we introduced in [13] by means of a Sobolev-type space N1,B(X). It was proved that B-capacity is an outer measure, which represents the correct gauge for distinguishing between two functions in N1,B(X) [13] . In the case when B is reflexive we show that B-capacity is continuous on increasing sequences of arbitrary subsets of X. Assuming that B has absolutely continuous norm, that every function in B is dominated by a semicontinuous function in B and that continuous functions are dense in N1,B(X), we prove that B-capacity is outer regular. As consequences of this outer regularity we obtain the continuity of B-capacity on decreasing sequences of compact subsets of X and the coincidence between the B-capacity and another usual capacity.
ON THE VEHICLE ROUTING PROBLEM WITH TIME WINDOWS AND MULTIPLE USE OF VEHICLES
ELENA NECHITA
Due to the energy crisis and to the new types of demands from customers, nowadays transportation and logistics environment require computational and simulation methods in order to reduce costs and improve performances. In this paper, the solutions for vehicle routing problems with time windows and multiple use of vehicles are reviewed. Also, competitiveness of Ant Colony Optimization algorithms, when compared with other metaheuristic techniques or exact algorithms for this problem, are considered.
SOME CLASSES OF GL-METRICS ON TM
VALER NIMINEŢ
In the present paper we continue the investigations of GL-space and study the geometry of such GL-metrics on TM by means the nonlinear connection.
STOCHASTIC ORDERING OF SUMS OF TWO INDEPENDENT EXPONENTIAL RANDOM VARIABLES
EUGEN PĂLTĂNEA
In this paper, we formulate a necessary and sufficient condition for ranking in the convex order the sums of two independent exponential random variables. This characterization is added to a series of recent results in the field.
INTELLIGENT AGENTS FOR MONITORING SYSTEMS
BOGDAN PĂTRUŢ
This paper’s aim is to define the concepts of s-agent and multiagent monitoring system we used for constructing the MageLan and ContTest systems. We used formal language theory to present the environment and the abstract architecture for constructing multi-agent systems.
MATHEMATICAL MODEL OF LARGE FOREST FIRE INITIATION
VALERIY PERMINOV
The great interest of the concerned problem is explained by the influence of large forest fires on the ground level layer of the atmosphere, which causes medium temperature drop due to the area smoke screen and leads to the damage or delay of agricultural plant ripening and to various ecological disasters. Considering that, natural investigations of these problems are merely impossible and methods of mathematical modeling are urgent. This paper, inscribed in the context of the general mathematical model of forest fires, gives a new mathematical setting and a method of numerical solution of a problem of a large forest fire initiation. The objective of the present research is to define dimensions of the ignition zone and to study photochemical processes which are taking place.
THE RODIN MODULAR LANGUAGE V. 21 AUG 2009 – USER MANUAL AND REPORT
DAN POPA
The scope of this paper is to provide news concerning The Rodin Project (http://www.haskell.org/haskellwiki/Rodin) – a national specific modular didactic language actually used as a helping tool in teaching base of computer science in high school and universities. The problem of producing enough programmers is actual and is a necessary step in order to assure the future development of the IT industry, services and software infrastructure. Rodin is dedicated to the teaching of C-like language's concepts, a wide used set of languages. The Rodin Language is specific designed to cross the language barrier which appears when students without any knowledge of English Language are supposed to quickly learn structured programming. The Rodin Language was release in August 2008. Teachers and students are encouraged and invited to contribute in order to build a corpus of Rodin Programs, based on the model of Free Software Groups. The sources written using Rodin are actually available free of charges from its website [5]. Rodin is used by The Faculty of Mathematics of Bacău University and also by some high schools from Bacău and Iasi area. The papers contains information concerning several aspects of the project, visible at users level: syntax, examples, differences, notes. This community project dedicated to teachers – The Rodin Language – and, of course, the Rodin Language itselfis are presented below.
THE RODIN TECHNICAL REPORT - COMPUTING THE EXPRESSION OF A PSEUDOCONSTRUCTOR OVER MONADIC VALUES USABLE AS MODULAR SEMANTIC AUTOEVALUATOR BY EQUATIONAL REWRITING
DAN POPA
The paper focuses on the act of computing the expression of a pseudoconstructor over monadic values (actions) - usable as a modular semantic autoevaluator - by using equational rewriting. After that, the syntax is represented by it's semantic. This paper is a part of The Rodin Technical Report.
SOME GENERAL FIXED POINT THEOREMS FOR OCCASIONALLY WEAKLY COMPATIBLE D- MAPPINGS
VALERIU POPA
In this paper some general fixed point theorems for owc D-mappings satisfying an implicit relation are proved by generalizing some results in [1], [4] and [6].
EFFICIENCY AND MULTIFUNCTIONS
VASILE POSTOLICĂ
This research paper is focused on the common concepts of the efficiency and set-valued map. After a short introduction, we propose some questions regarding the notion of efficiency and we emphasize the Pareto optimality as one of the first finite dimensional illustrative examples. We present the efficiency and the multifunctions in the infinite dimensional ordered vector spaces following also our recent results concerning the most general concept of approximate efficiency, as a natural generalization of the efficiency, with implications and applications in vector optimization and the new links between the approximate efficiency, the strong optimization - by the full nuclear cones - and Choquet’s boundaries by an important coincidence result. In this way, the efficiency is strong related to the multifunctions and Potential theory through the agency of optimization and conversely. Several pertinent references conclude this study.
NUMBER OF JUMPS FOR SAMPLE FUNCTIONS OF LEVY PROCESSES
NADIA MIRELA STOIAN
The structure of jumps of a Levy process is determined by its Levy (or characteristic) measure. For an n-dimensional Levy process, the Levy measure of D ⊂ Rn is given by the expected number, per unit time, of jumps whose size belongs to D.
THE NORMAL GRAPH CONJECTURE IS TRUE FOR MINIMAL UNBREAKABLE GRAPHS
MIHAI TALMACIU
A graph is normal if there exists a cross-intersecting pair of set families one of which consists of cliques while the other one consists of stable sets, and furthermore every vertex is obtained as one of these intersections. It is known that perfect graphs are normal. Korner and de Simone observed that C5, C7 and complement of C7 are minimal, not normal and conjectured, as generalization of the Strong Perfect Graph Theorem, that every (C5, C7, complement of C7)-free graph is normal (Normal Graph Conjecture). In this paper we prove this conjecture for the class of minimal unbreakable graphs. As it turns out, unbreakable graphs find natural applications to wireless network security. These applications, detailed in ([15], [22], [24]), range from increasing network resilience, to enhancing confidentiality, to reducing interference. An intriguing new development, documented in ([11], [12], [14], [18]), show direct relevance of unbreakable graphs to social and peer-to-peer networks.
CONNECTED GRAPHS OF DIAMETER TWO HAVING SMALL DEGREE DISTANCES
IOAN TOMESCU
Topological indices, like degree distance, introduced by Dobrynin and Kochetova and Gutman were studied in mathematical chemistry. In this paper it is proved that in the class of connected graphs G of order n ≥ 4 and diameter equal to 2 such that G not ≅K1,n-1, the minimum degree distance is reached by K1,n-1 + e and it is conjectured that the bistar consisting of vertex disjoint stars K1,n-3 and K1,1 with central vertices joined by an edge has minimum degree distance in the class of connected graphs G of order n such that G not ≅ K1,n-1.
F# MODULES INTEGRATION IN DISTRIBUTED APPLICATIONS DEVELOPMENT PROCESS
COSMIN TOMOZEI(1), MARIUS VETRICI(2)
The objective of this paper is to analyze distributed systems development process with special emphasis on F# modules integration. Functions and classes written in F# prove to be valuable resources for a higher level of security, execution speed and accuracy. The .NET integration support makes the selection of this functional language for distributed applications development rather straightforward. Examples of architectures which implement modules written in F# will be given.
PUBLIC KEY INFRASTRUCTURE OVERVIEW
NICUŞOR VATRĂ
Public key infrastructures have become the starting point for modern security mechanisms on the Internet, PKI is closely linked to the asymmetric key encryption, digital signatures, digital certificate and encryption services. The purpose of this paper is to briefly describe the general and essential concepts of the PKI to persons interested in security and secure commerce but with a low knowledge level about the Internet security. That's why this study begins by introducing some basic security concepts, which are needed to understand the PKI topics. This document intends to be a good starting point for those interested in the PKI concepts, without analyzing particular implementations.
PARALLEL ALGORITHMS FOR FINANCIAL DERIVATIVES EVALUATION IN GENERALIZED HESTON MODEL
TIBERIU SOCACIU(1), ILIE PARPUCEA(2), BAZIL PÂRV(3), MARIA PÂRV(4)
This paper shows how can be estimated the value of an option if we assume the Heston model on a message-based architecture. We use two methods: first, a Monte Carlo method, then a parallelization of a recurrence obtained from a generalized Merton-Garman equation.
COMBINATORIAL OPTIMIZATION ALGORITHMS FOR POLAR GRAPHS AND THEIR APPLICATIONS IN FINANCE
D. PACURARI(1), M. MUNTEANU(1), M.TALMACIU(2)
Many natural problems in finance involve partitioning assets into natural groups or identifying assets with similar properties. Building a diversified portfolio is somehow dual to clustering. An approach to clustering constructs an similarity graph, where elements i and j are connected by an edge if and only if i and j are similar that they should/can be in the same cluster. If the similarity measure is totally correct and consistent, the graph will consist of disjoint cliques, one per cluster. A graph is (s, k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph and B a disjoint union of at most k cliques. Recognizing a polar graph is known to be NP-complete. In this paper we determine the density and the stability number for (s,k)-polar graphs with algorithms that are comparable, while respect to computing time, with the existing ones and we give some applications in finance.