Volume 24, No. 1 (2014)
Articles
EINSTEIN EQUATIONS IN LIE ALGEBROIDS
MIHAI ANASTASIEI(1), MANUELA GÎRŢU(2)
A Lie algebroid endowed with a Riemannian metric has a canonical connection of Levi-Civita type. We associate to it the Einstein tensor field and using it we construct the Einstein equations. Some particular cases are discussed.
ON (b; μY )-CONTINUOUS FUNCTIONS
V. DHANYA, S. KRISHNAPRAKASH, ENNIS ROSAS
The notion of γ- b -open sets in generalized topological spaces was introduced and studied by Sivagami [5] in 2008: By using the notion of μ-b-open sets, we introduce and study (b; μY )-continuous functions, μ-b-kernel and (μX; μY)-b-open functions in ge-neralized topological spaces. Also some characterizations of (b; μY )-continuous functions are obtained.
SWAN-LIKE REDUCIBILITY FOR TYPE I PENTANOMIALS OVER A BINARY FIELD
RYUL KIM, SU-YONG PAK, MYONG-SON SIN
Swan (Pacific J. Math. 12(3) (1962), 1099-1106) characterized the parity of the number of irreducible factors of trinomials over F2. Many researchers have recently obtained Swan-like results on determining the reducibility of polynomials over finite fields. In this paper, we determine the parity of the number of irreducible factors for so-called Type I pentanomial f(x) = xm + xn+1 + xn + x + 1 over F2 with even n. Our result is based on the Stickelberger-Swan theorem and Newton's formula which is very useful for the computation of the discriminant of a polynomial.
ON CONFORMAL TRANSFORMATION OF A QUARTIC FINSLER SPACE
OTILIA LUNGU, VALER NIMINEŢ
In this paper we consider the conformal transformation of a quartic Finsler space. We obtain the conformal change of Cartan's connection.
DIFFERENTIABILITY OF MONOTONE SOBOLEV FUNCTIONS ON METRIC SPACES
MARCELINA MOCANU
We prove a differentiability result for monotone Sobolev functions on doubling metric measure spaces supporting a Poincaré inequality. This generalizes a result used by Rickman in proving the differentiability of quasiregular mappings. Our main tools are a Stepanov differentiability theorem in doubling metric measure spaces supporting a Poincaré inequality, proved in 2004 by Balogh, Rogovin and Zürcher and a Sobolev embedding theorem on spheres proved by Hajlasz and Koskela. As an application, it is shown that continuous quasiminimizers for the p- energy integral with p>Q-1 are almost everywhere Cheeger differentiable, where Q is the doubling expo-nent of the underlying metric measure space.
PRICE'S THEOREM AND UNCORRELATEDNESS SETS
SOFIYA OSTROVSKA
Price's remarkable theorem on Gaussian random variables was published in 1958 and distinguished by the “Information Theory Society Golden Jubilee Paper Award” in 1988. Nowadays, this theorem remains an important tool used extensively in a wide spectrum of engineering problems, such as those appearing in signal processing, radio and space sciences, as well as information theory and astrophysics. In this paper, Price's theorem is applied to the investigation of possible uncorrelatedness for powers of Gaussian random variables. For zero-mean Gaussian variables the only two possible uncorrelatedness sets has been identified and presented. The study aims to bring into spotlight the celebrated theorem usually disregarded in standard Probability and Statistics courses as well as to initiate further interest in the theorem by demonstrating a series of new applications.
SOME GENERALIZATIONS OF LOCAL CONTINUITY IN IDEAL TOPO-LOGICAL SPACES
ALI OZKURT
In this paper, we consider generalizations of two forms of local continuity of maps between topological spaces, with respect to an ideal of subsets either in the domain or in the codomain. In particular, given an ideal I of subsets of a space Y, one-to-one mappings f : X→Y are investigated such that the restriction of f to X0 is continuous for some closed subset X0 of X. Also we investigate continuity of mappings f : X→Y if X is an ideal topological space. Our results provide some co-rollaries for Baire spaces.
GENERAL FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS OF LATIF - BEG TYPE IN G - METRIC SPACES
ALINA-MIHAELA PATRICIU, VALERIU POPA
In this paper two general fixed point theorems for multivalued mappings in G - metric spaces satisfying a new type of implicit relation which generalizes and improves Theorem 2.1 [1] are proved.
FUNCTIONAL FOLD BASED PROGRAMMING IN SWI-PROLOG
DAN POPA
In this paper the author is completing a gap in the style used by SWI-Prolog programmers. Important notions and theorems from the field of functional programming can now migrate to the logic programming paradigm: foldl, foldr, the universality property, etc.
ASYNCHRONOUS MOTOR SPEED CONTROL BY PRO VIEW OPEN SOURCE SOFTWARE WITHIN A SCADA INTERFACE
PETRU GABRIEL PUIU, IULIAN FURDU
This paper presents the modeling and implementation of an installation designed to control an asynchronous motor within a SCADA interface by a frequency converter. The installation is software controlled by using open source systems. From this perspective the achievement is cheap, yet stable and reliable, ensuring protection of the equipment when leaving the working regime. The surveillance of equipment parameters is done locally through measuring equipment (indicators with precision and digital display) and remotely on a PC with software for monitoring and recording data. The adoption of Pro View as an open source software solution brings the costs down while maintaining a high level of robustness in installations controlling.
COMMON FIXED POINTS FOR MAPS SATISFYING A NEW RATIONAL INEQUALITY IN ORDERED FUZZY METRIC SPACES
K.P.R. RAO, P.R. SOBHAN BABU, G.N.V. KISHORE, B. FISHER
In this paper, we prove some common fixed point results for four and two mappings satisfying a rational contractive condition in a partially ordered fuzzy metric space.
ON {CLAW, ANTENNA, NET}-FREE GRAPHS
MIHAI TALMACIU
In this article, we give a characterization of {claw; antenna; net}-free graphs, a characterization of claw-free graphs, using weakly decomposition. Also, we give a O(n(n + m)) recognition algorithm for {claw; antenna; net}-free graphs, but using weakly decomposition. During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predetermined properties, as well as combinations of such decompositions. In various problems in graph theory, for example in the construction of recognition algorithms, frequently appears the so-called weakly decomposition of graphs.
REMARKS ON THE EXPONENT FUNCTION ASSOCIATED TO A FINITE GROUP
MARIUS TĂRNĂUCEANU
This note deals with the exponent function associated to a finite group. Some classes of finite groups determined by basic properties of this function are investigated.