rss_2.0Tatra Mountains Mathematical Publications FeedSciendo RSS Feed for Tatra Mountains Mathematical Publications Mountains Mathematical Publications Feed Fixed Point Theorems on Complete -Metric Space by Using Rus Contraction Mapping<abstract> <title style='display:none'>Abstract</title> <p>This paper investigates a fixed point over a complete b-metric space for a family of contractive mappings. In this paper, we have discovered new results in the direction of the complete b-metric space by using Rus contraction. Furthermore, we establish a common fixed point theorem between two mappings over complete b-metric space. We also provide some non-trivial examples to display the authenticity of our established results.</p> </abstract>ARTICLEtrue a Non-Convex Lagrange Optimal Control Problem<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we are concerned with an iterative differential inclusion governed by the time-dependent maximal monotone operator with perturbation. The approach to solve our problem is based on the Yosida approximation technique. The theoretical result is applied to prove an existence result for a Lagrange optimal control problem without assumptions concerning convexity.</p> </abstract>ARTICLEtrue of Strumok Cipher Initialization<abstract> <title style='display:none'>Abstract</title> <p>The initialization of the <italic>Strumok</italic> cipher is analyzed in this paper. A modified cipher initialization procedure is constructed for the <italic>Strumok-512</italic> cipher, which allows to show that the cipher initialization is not injective. Security against slide attacks is proved. Furthermore, the Guess-and-Determine attack on the <italic>Strumok-512</italic> cipher is constructed with complexity 2<sup>448</sup>.</p> </abstract>ARTICLEtrue Cryptanalysis of Ascon Using MRHS Equations<abstract> <title style='display:none'>Abstract</title> <p>Ascon is a family of lightweight authenticated encryption and hashing algorithms, which is a finalist in the NIST Lightweight Cryptography competition. We study the Ascon algorithm from the perspective of algebraic cryptanalysis based on the MRHS representation of the cipher. We call such an approach an MRHS cryptanalysis.</p> <p>We represent the system on the gate level (focusing on individual AND-gates) and the S-box level (basing MRHS equations on 5-bit S-boxes). We compare the results from the application of two custom MRHS solvers. The RZ solver is based on linear algebra and exhaustive search. The HC solver is based on adaptive bit-flipping with restarts.</p> <p>We show that both the choice of the solver and the choice of the system representation influence the total complexity of the attack. On the other hand, these choices do not change the fundamental properties of the attack, such as scaling with the amount of information the attacker possesses. A similar assessment holds for using a scaled-down version of Ascon for the experiments. Our method can be used for the experimental evaluation of cipher designs against algebraic attacks.</p> </abstract>ARTICLEtrue Result for a Stochastic Functional Differential System Driven by G-Brownian Motion with Infinite Delay<abstract> <title style='display:none'>Abstract</title> <p>In this article, we are interested in the study of a class of stochastic functional differential systems driven by <italic>G</italic>-Brownian motion with infinite delay. We prove the existence and uniqueness of the solutions when two basic conditions are met: the linear growth condition and the Lipschitz condition.</p> </abstract>ARTICLEtrue Mcshane and Pettis Integrals of Multifunctions<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we present full characterizations of variationally McShane and Pettis integrable multifunctions in terms of the cubic derivative and the variational McShane measure of additive interval multifunctions.</p> </abstract>ARTICLEtrue Nemytskiĭ Operator and Vector Measure Solutions for Non-Linear Initial Value Problems<abstract> <title style='display:none'>Abstract</title> <p>We define and study a Banach-space-valued Nemytskiĭ operator and we find vector measure solutions for associated non-linear initial value problems.</p> </abstract>ARTICLEtrue Alternative Interpretations of Strongly Star Semi-Rothberger and Related Spaces<abstract> <title style='display:none'>Abstract</title> <p>In this article, some under-appreciated characteristics of strongly star-Rothberger subsets are explored. Additionally, with the aid of the SSI property and MSSI property, semi-Rothberger and star semi-Rothberger spaces are represented by families of closed sets. Finally, several selection principle like attributes are produced that can reflect the previously mentioned sequential covering features in an inverted form.</p> </abstract>ARTICLEtrue and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.</p> </abstract>ARTICLEtrue -Lindelöfness Via Hereditary Class<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we define and study the notion of hereditary class on nearly <italic>μ</italic>-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly <italic>μ</italic>-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated.</p> </abstract>ARTICLEtrue Theorems for Nonlinear Second-Order Delay Differential Equations with Some Sublinear Neutral Terms via Canonical Transform<abstract> <title style='display:none'>Abstract</title> <p>New sufficient conditions for oscillation of a second-order nonlinear differential equation with some sublinear neutral terms are established via canonical transform and integral averaging method. Examples are provided to illustrate the significance and novelty of the presented results.</p> </abstract>ARTICLEtrue Simple Computation of Middle Surface Between 3D Point Clouds and/or Discrete Surfaces by Tracking Sources in Distance Function Calculation Algorithms<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance function such as ridges, triple junctions, etc. It requires to compute second order differential characteristics, and also some kinds of heuristics must be applied. Opposite to that, we determine the middle surface just from computing the distance function itself which is a fast and simple approach. We present and compare the results of the fast sweeping method, the vector distance transform algorithm, the fast marching method, and the Dijkstra-Pythagoras method in finding the middle surface between 3D data sets.</p> </abstract>ARTICLEtrue Criteria on the Oscillatory Behaviour of Second Order Nonlinear Differential Equations with Mixed Neutral Terms<abstract> <title style='display:none'>Abstract</title> <p>The authors present some new criteria for the oscillation of second order nonlinear differential equations with mixed nonlinear neutral terms and mixed deviating arguments. The approach used is to linearize the equation under consideration and then to deduce the oscillation from that of the linear form. In so doing, the authors obtain new oscillation criteria via a comparison with the first order equations whose oscillatory behaviors are known. They illustrate their results with some examples.</p> </abstract>ARTICLEtrue of a Special Polybius-Like Cipher Using Hill-Climbing<abstract> <title style='display:none'>Abstract</title> <p>Polybius cipher is a special substitution system widely used during history. In our research, we found several Polybius-like ciphers used in Czecho-slovakia and in the Slovak State from the first half of the 20th century. Various types of this cipher are described in the first Czechoslovak cryptanalysis manual “šifrovací systémy a návod k luštění kryptogramů” by plk. Josef Růžek. It can be also found in the official cryptology directive called G–VII–8 “šifrování” (encryption) from 1938, and another variant in the new version of the same directive from 1946. In this work, we focus on a special Polybius-like cipher inspired by three real ciphers used in Czechoslovakia and in the Slovak State. Two were used during WW2 and one right after the war. We will show how these ciphers were used and how they can be solved with a modern heuristic approach on a personal computer. We evaluate the effectiveness of the Hill-Climbing heuristic methods with restarts. We also investigated several different fitness functions and language models.</p> </abstract>ARTICLEtrue Observations on Ideal Variations of Bornological Covers<abstract> <title style='display:none'>Abstract</title> <p>In this article, we use the notion of ideals to study open covers and related selection principles, and thus, we extend some results in (Caserta et al. 2012; Chandra et al. 2020) where open covers and related selection principles have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notions of ℐ-<italic>γ</italic><sub>ℬ</sub> <italic>s</italic> -cover, ℐ-strong-ℬ-Hurewicz and ℐ-strong-ℬ-groupable cover. Also, in (<italic>C</italic>(<italic>X</italic>),<italic>τ</italic>s<sub>ℬ</sub>), some properties like ℐ-strictly Frèchet Urysohn, ℐ-Reznichenko property are investigated.</p> </abstract>ARTICLEtrue of Sequences<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with density on the set of natural numbers and its connections to the distribution of sequences. Under the assumption of independence, some formulas are derived.</p> </abstract>ARTICLEtrue Transform and Generalized Lipschitz Classes<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to give necessary and sufficient conditions in terms of the Fourier Laguerre-Bessel transform 𝒲<sub><italic>LB</italic></sub><italic>f</italic> of the function <italic>f</italic> to ensure that <italic>f</italic> belongs to the generalized Lipschitz classes <bold>H</bold><sub><italic>α</italic></sub><sup><italic>k</italic></sup> (<bold>X</bold>) and <bold>h</bold><italic><sup>k</sup><sub>α</sub></italic> (<bold>X</bold>), where <bold>X</bold> =[0, +<italic>∞</italic>) <italic>×</italic> [0, +<italic>∞</italic>).</p> </abstract>ARTICLEtrue Strong Porosity of Some Families of Functions<abstract> <title style='display:none'>Abstract</title> <p>The paper deals with the strong porosity of some families of real functions continuous with respect to a given topology 𝒯 or 𝒜-continuous (i.e., continuous with respect to some special family 𝒜 of sets of the real line). Particularly, porosity of those families is investigated in space of the Baire 1 functions or in the space of the Baire 1 and Darboux functions.</p> </abstract>ARTICLEtrue Few Variants of Quasi-Continuity in Bitopological Spaces<abstract> <title style='display:none'>Abstract</title> <p>The purpose of this paper is to introduce a few variants of generalized quasi-continuity of functions defined on a bitopological space and to study their mutual relationship. Moreover, some characterization of sectional quasi-continuous function and its continuity points are investigated.</p> </abstract>ARTICLEtrue Pc-Open Sets and Operation Pc-Separation Axioms in Bitopological Spaces<abstract> <title style='display:none'>Abstract</title> <p>In the present paper, we introduce new types of generalized closed sets called <italic>ij</italic> -pre-generalized closed sets and study some of their properties in bi-topological spaces. Also, we use them to construct new types of separation axioms. Further, we introduce and study the concepts of pairwise operation pc-open sets and pairwise operation pc-separation axioms in bitopological spaces. Several interesting characterizations of different spaces are discussed. The relationships between these spaces are given.</p> </abstract>ARTICLEtrue