Volume 33, No. 2 (2023)

s*-REGULARITY IN FUZZY M- SPACES

ANJANA BHATTACHARYYA

This paper deals with a new type of open-like set in fuzzy minimal spaces [2], viz. fuzzy m- s*-open set taking fuzzy m-semiopen sets [3] as a basic tool. Afterwards, we introduce an idempotent operator, viz. fuzzy m- s*-closure operator. With the help of this operator we introduce and study two new types of functions, viz. fuzzy almost (m,m1)-s- continu-ous function and fuzzy almost (m,m1)- s*-continuous function. It is shown that every fuzzy almost (m,m1)- s*-continuous function is fuzzy almost (m,m1)-s- continuous func-tion, but the reverse implication is not necessarily true in general. Furthermore, we intro-duce fuzzy m- s*-regular spaces, in which the above mentioned reverse implication holds and, in addition, the classes of fuzzy m-open sets and fuzzy m- s*-open sets coincide.

SOME GROWTH PROPERTIES OF COMPOSITE ENTIRE FUNCTIONS RELATING TO (α, β, γ) -ORDER AND (α, β, γ) -TYPE

TANMAY BISWAS(1), CHINMAY BISWAS(2), SARMILA BHATTACHARYYA(3)

In this paper, we establish some growth properties of composite entire functions on the basis of their (α, β, γ) -order and (α, β, γ) -type.

A STUDY ON GENERALIZED SPACE-MATTER TENSOR

SANJIB KUMAR JANA(1), KANAK KANTI BAISHYA(2), BIKIRAN DAS(3)

The object of the present study is to determine the effect of space-matter tensor in several types of curvature restrictions on Riemannian manifolds like Einstein manifold, quasi Ein-stein manifold, generalized quasi Einstein manifold and pseudo generalized quasi Einstein manifold.

DIGITAL FRONTIERS IN LOGISTICS: A SCALABLE APPROACH TO WIDE-AREA TRANSPORTATION NETWORK OPTIMIZATION

CEZAR-MARIAN PAPARĂ(1,2)

This paper delves into the academic significance of addressing both the Traveling Sales-man Problem (TSP) and the Vehicle Routing Problem (VRP). It conducts a comparative analysis between a source-driven method and the Nearest Neighbor algorithm, both fall-ing under the category of greedy algorithms, in the context of TSP resolution. Focused on a national-scale transportation network with five logistic centers and sixty-two retail stores, the study illuminates the computational challenges in optimizing wide-area logis-tics. Implementing state-of-the-art technologies, including Docker for containerization and PHP Symfony with Doctrine ORM for backend development, the study introduces a highly scalable application. The system utilizes a MySQL database to store actual road distances between nodes, enabling the determination of the minimum-cost route from lo-gistic centers to multiple stores and back, emphasizing the utilization of real road distanc-es. This research offers valuable insights into addressing real-world computational chal-lenges in Logistics through a practical and scalable application. Emphasizing the scalabil-ity and processing power of the implemented solution, along with the utilization of cut-ting-edge tools and frameworks widely adopted in the IT industry, adds depth to its technological significance.

ON SUPERTOPOLOGICAL MODULES AND SUPERGROUP RINGS

BHASKAR VASHISHTH

Theory of super topological modules and submodules is formulated, which is based on D-supercontinuous functions. In the last section we have used the concept of supertopologi-cal groups and supertopological rings defined in [7] with d-compactness and d-separability to stretch the topologies to their group rings under various conditions.

ON THE DENSITY OF LIPSCHITZ FUNCTIONS IN NEWTONIAN SPACES

MARCELINA MOCANU

Let E be a rearrangement invariant Banach function space over a metric measure space X, where the measure of X is doubling and X supports a (1, E)-Poincaré inequality. We pro-vide sufficient conditions for the local Hölder continuity of a representative of each func-tion in N1,E (X), using a quasiconcavity property of a certain power of the fundamental function of E. Using the properties of a non-centered maximal operator based on E, we give a simple proof for the density of Lipschitz functions in a Newtonian space N1,E (X), under the assumptions that E has an absolutely continuous norm and its fundamental function satisfies a certain lower estimate.