http://repository.enu.kz/handle/enu/20210 2026-04-04T00:27:30Z http://repository.enu.kz/handle/enu/30733 WEAK GROTHENDIECK COMPACTNESS PRINCIPLE FOR SYMMETRIC SPACES MATIN, DAUREN; NESSIPBAYEV, YERLAN; SUKOCHEV, FEDOR; ZANIN, DMITRIY We strengthen and simplify the weak Grothendieck compactness principle for symmetric sequence spaces, and extend it to both symmetric function spaces and noncommutative symmetric spaces of measurable operators. 2024-01-01T00:00:00Z http://repository.enu.kz/handle/enu/30732 ULYANOV INEQUALITIES FOR THE MIXED MODULI OF SMOOTHNESS IN MIXED METRICS Simonov, B.V.; Jumabayeva, A.A. In this paper, mixed moduli of smoothness of functions of two variables are studied. We prove Ulyanov-type inequalities between mixed moduli of smoothness of positive orders in different metrics. Estimates for the mixed moduli of smoothness of the derivative of a function are also obtained in terms of the mixed moduli of smoothness of the function itself. 2024-01-01T00:00:00Z http://repository.enu.kz/handle/enu/30731 Towards robust security in WSN: a comprehensive analytical review and future research directions Zhukabayeva, Tamara; Zholshiyeva, Lazzat; Ven-Tsen, Khu; Mardenov, Yerik; Adamova, Aigul; Karabayev, Nurdaulet; Abdildayeva, Assel; Baumuratova, Dilaram One of the most important aspects of the effective functioning of wireless sensor network (WSN) is their security. Despite significant progress in WSN security, there are still several unresolved issues. Many review studies have been published on the problems of possible attacks on WSN and their identification. However, due to the lack of their systematic analysis, it is not possible to fully substantiate practical recommendations for the effective application of the proposed solutions in the field of WSN security. In particular, the creation of methods that provide a high degree of security while minimizing computational effort and costs, and the development of effective methods for detecting and preventing attacks on WSN. The purpose of this document is to fill this gap. The article presents the results of the study in the form of a systematic analysis of the literature with a targeted selection of sources to identify the most effective methods for detecting and preventing attacks on WSN. By identifying the security of WSN, which has not yet been addressed in research works, the review aims to reduce its impact. As a result, our extended taxonomy is presented, including attack types, datasets, effective WSN attack detection methods, countermeasures, and intrusion detection systems (IDS). 2024-01-01T00:00:00Z http://repository.enu.kz/handle/enu/30730 The Approximation of Functions of Several Variables with Bounded p-Fluctuation by Polynomials in the Walsh System Akhazhanov, Talgat; Matin, Dauren; Baituyakova, Zhuldyz This paper presents direct and inverse theorems concerning the approximation of functions of several variables with bounded p-fluctuation using Walsh polynomials. These theorems provide estimates for the best approximation of such functions by polynomials in the norm of the space under consideration. The paper investigates the properties of the Walsh system, which includes piecewise constant functions, and builds on earlier work on trigonometric and multiplicative systems. The results are theoretical and have potential applications in such areas as coding theory, digital signal processing, pattern recognition, and probability theory. 2024-01-01T00:00:00Z