Volume 34, No. 1 (2024)

G(m)−INVARIANTS AND HOMOTOPY INVARIANTS OF PARTIAL PARALLELIZABLE MANIFOLDS

COSTACHE APREUTESEI

Using a partial and global frame of tangent bundle TM, we construct some G(m)−invariants [M×R^k ] and homotopy classes c_k (M) corresponding to [M×R^k ], k = 1, 2, …, p_0. Some properties of the partial parallelizable and parallelizable manifolds are obtained with the aid of partial trivial structures in tangent bundles and certain homotopy classes.

FUZZY p-b-ALMOST COMPACT SPACES

ANJANA BHATTACHARYYA

This paper deals with some applications of fuzzy p-b-open sets [9]. Here we introduce fuzzy p-b-almost compactness and characterize this concept via fuzzy nets and prefilterbases. We also introduce the notion of fuzzy regularly p-b-open set, for which finite intersection property characterizes fuzzy p-b-almost compactness. It is shown that fuzzy p-b-almost compactness implies fuzzy almost compactness [11] and the converse is true only in fuzzy p-b-regular spaces [9].

A GENERALIZATION OF VUORINEN'S DISTANCE RATIO METRIC IN METRIC SPACES AND BI-LIPSCHITZ EQUIVALENT HYPERBOLIC-TYPE METRICS

MARCELINA MOCANU

We prove in the setting of a general metric space (X, d) the bi-Lipschitz equivalence of generalized versions of Vuorinen's distance ratio metric, Gehring-Osgood metric, Dovgoshey-Hariri-Vuorinen metric, Nikolov-Andreev metric and Ibragimov metric. For the generalized Vuorinen's distance ratio metric j on the complement of a nonempty closed subset M of X we show that the identity map of X\M between (X\M,d) and (X\M,j) is 1-quasiconformal. We also provide su_cient conditions for the completeness of (X\M,j), that is equivalent to the completeness of X\M with each of the above mentioned metrics.

REMARKS ON GENERALIZATIONS OF TOPOLOGICAL SPACES VIA PROPERTIES OF CLOSURE FUNCTIONS

SHYAMAPADA MODAK(1), TAKASHI NOIRI(2)

The fixed points of a closure function are known as closed sets in the corresponding generalized closure space and their complements are called open sets. We identify among the combinations of usual properties of a closure function some that are sufficient (but not necessary, as we show through counterexamples) in order to obtain that the family of open sets is a specific generalization of the notion of topology (namely, weak structure, minimal structure, generalized topology in the sense of Csaszar, supratopology, generalized topology in the sense of Lugojan M-structure). The properties of other operators associated to a closure function (interior, exterior and boundary operators) are also investigated.

NEW UTILITY LIBRARIES FOR LINUX WITH COMPLEX DATA TYPES AND SYSTEM RESOURCES

ALEXANDRU PINTEA

Operating systems have different limitations for every primitive data-type regarding the maximum value that can be stored. For numeric data types, those limitations could be eliminated by converting to string. New C++ utility libraries are provided for both complex data types and system resources. One of the introduced C++ libraries is able to perform operations with numbers stored in string. Another, stores data in its self-defined data type. The last one provides Linux compatibility for C++, taking care of various C++ function definitions.

TWO NEW AXIOMATIZATIONS OF BM-ALGEBRAS

DANIEL A. ROMANO

In this paper two new axiomatizations of the concept of BM-algebra from Algebraic logic are introduced. It is shown how the properties of the BM-algebra can be deduced from the newly designed axiomatizations. The correspondence between ideals and subalgebras is described in this class of algebras.

METRONLIKE STRUCTURES

RAVINDRA KUMAR SONWANE(1), RAM PRASAD(2) and SAMAJH SINGH THAKUR(3)

The simplest tool which man could found to interpret space is the concept of distance. The concept of distance gives a sense of duality and helps us to decide the positional difference between points. Our view is that, if the effect of the observer's point is counted in measuring distances between different points, then the measure may be more relevant. Keeping in mind the properties of metric space, we tried to establish new properties of distance by including the observer's point. Based on properties of angles, Sonwane and Prasad [29] established a mathematical structure called metron as a generalization of metric space. The present paper continues the study of Metron and proposes various metronlike structures by weakening some properties of metrons. The relationships between metron and metron-like structures are discussed by providing appropriate examples and diagrams.

ON THE SUM OF INVERSES OF SUBGROUP ORDERS IN FINITE GROUPS

MARIUS TĂRNĂUCEANU

Let G be a finite group and $f(G)=\sum_{H\leq G}\frac{1}{|H|}$\, i.e. let f(G) be the sum of inverses of the orders of all subgroups H of G. In this note, we study the finite groups G such that f(G) is no greater than 2.