Volume 32, No. 2 (2022)

CONVERGENCE IN SOBOLEV SPACES OF SOLUTIONS FOR ELLIPTIC PROBLEMS ON VARYING DOMAINS

ELENA ROXANA ARDELEANU

In this note we discuss results regarding the convergence in the sense of Mosco of a se-quence of open sets. This concept of convergence of sets is a tool in the study of the con-vergence in Sobolev spaces of the solutions of an elliptic boundary value problem, as the domain is varying.

FUZZY PRE-SEMI-CONTINUOUS FUNCTIONS AND FUZZY PRE-SEMI-IRRESOLUTE FUNCTIONS

ANJANA BHATTACHARYYA

This paper deals with a new type of fuzzy open-like set, viz., fuzzy pre-semiopen set, the class of which is strictly larger than that of fuzzy preopen sets and fuzzy s ∗ -open sets. Using this concept as a basic tool, here we introduce fuzzy pre-semiclosure operator which is an idempotent operator. Afterwards, we introduce the notion of fuzzy pre-semi-regular space in which the class of all fuzzy closed sets and that of all fuzzy pre-semiclosed sets coincide. Lastly, we introduce and characterize two types of functions, viz., fuzzy pre-semi-continuous and fuzzy pre-semi-irresolute functions, classes that are strictly larger than that of fuzzy almost s-continuous and fuzzy almost s ∗ -continuous functions, respectively, and establish some applications of these two classes of functions on fuzzy pre-semi-regular spaces.

INTEGRATED SYSTEM FOR SENSING HOME HAZARDS

SORIN IONUȚ CONEA

Optional home insurance covers material losses due to major events that generate signifi-cant, including total, damage to the home. By installing and maintaining the presented system, disasters can be detected immediately and, in some cases, can be automatically mitigated. Homeowners could effectively reduce the hazards effects and massively downsize the recovery costs. The proposed integrated system is designed to be cheap and to have low exploitation costs.

GENERALIZATIONS OF CLOSED FUNCTIONS IN SPACES WITH MINIMAL STRUCTURES

MARCELINA MOCANU

Noiri and Popa introduced and studied the notion of M−closed function between spaces with minimal structures, developing a unified theory of modifications of closedness such as α−closedness, semi-closedness, preclosedness and β−closedness. Using a new notion, that of almost M- closed function, we extend the characterizations of M−closed functions proved by Popa and Noiri to spaces endowed with minimal structures not necessarily closed under arbitrary unions. These minimal structures are useful beyond General Topol-ogy. For bijections between spaces with minimal structure it turns out that almost M- closedness is equivalent to almost M−openness, both being equivalent to the M−continuity of the inverse function. Our main result generalizes a well-known theorem of Long and Herrington showing that θ−open sets in topological spaces are preserved by every function that is both open and closed.

SYSTEMS WITH CONTROL IN DIFFERENTIABLE TANGENT BUNDLE

VALER NIMINEȚ

We study differentiable systems with control in tangent bundle, including the feedback of these systems.

LOW-COST EXPERIMENTS FOR COMPUTER SCIENCE EDUCATION WITH ARDUINO

DAN POPA

Nowadays, the actual post pandemic context of computer science teaching is having some special attributes: big number of students, low budgets, need for STEAM, need of what we can call “pre-robotics” abilities. Otherwise, the costs should be kept low. This paper is a workaround the need of buying expensive Arduino kits. Instead, it is focused on how to teach elementary computer science skills with less accessories added to an Arduino Uno board and is proposing a set of lessons based on this idea and the principle of learn-ing by discovery.

ON QUASI-REGULAR AND NILPOTENT ELEMENTS IN SUPERTOPOLO-GICAL NEAR-RINGS

BHASKAR VASHISHTH(1), DAVINDER SINGH(2)

We study supertopological near-rings in which either the set of quasi-regular element is d-open (called Q-supertopological rings) or the set of nilpotent elements is d-open. We have also characterized Q-supertopological rings among near-rings in terms of right ideals. Sev-eral properties regarding the Jacobson radical of such a supertopological ring are proved. Assuming that the set of nilpotent elements is d-open and the supertopological ring is right d-bounded, it is shown that the Jacobson radical is d-open.