In January 2016, a new standard for symmetric block encryption was established in the Russian Federation. The standard contains two encryption algorithms: Magma and Kuznyechik. In this paper we propose to consider the possibility of applying the alge...
Lightweight block ciphers are normally used in low-power resource-constrained environments, while providing reliable and sufficient security. Therefore, it is important to study the security and reliability of lightweight block ciphers. SKINNY is a n...
Cryptographic hash functions play an essential role in various aspects of cryptography, such as message authentication codes, pseudorandom number generation, digital signatures, and so on. Thus, the security of their hardware implementations is an im...
The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the ca...
This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influ...
Algebra as a school subject is ill defined. Students experience algebra quite differently depending on the perspective of algebra taken by authors of the textbooks from which they learn. Through a content analysis of problems (n = 63,174) in the narr...
Claim reserving is one of the most important tasks in non-life insurance, because it directly affects solvency assessment, financial reporting, and risk management. Traditional reserving methods typically rely on assumptions of relatively homogeneous...
Algebraic persistent fault analysis (APFA), which combines algebraic analysis with persistent fault attacks, brings new challenges to the security of lightweight block ciphers and has received widespread attention since its introduction. Threshold Im...
Algebraic persistent fault analysis (APFA) combines algebraic analysis with persistent fault analysis, providing a novel approach for examining block cipher implementation security. Since its introduction, APFA has attracted considerable attention. T...
We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n systems with and without sparse, and show the results of...
Using complex network analysis methods to analyze the internal structure of geographic networks is a popular topic in urban geography research. Statistical analysis occupies a dominant position in the current research on geographic networks. This per...
In modern information technology, research on block cipher security is imperative. Concerning the ultra lightweight block cipher PICO, there has been only one study focused on recovering its complete master key, with a large search space of
Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identifi...
This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and motivations. The first sections deal with model theory. In the first p...
With the particular interest of being implemented in cryptography, the recognition and analysis of image patterns based on Latin squares has recently arisen as an efficient new approach for classifying partial Latin squares into isomorphism classes....
Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the pr...
The output voltage harmonics of electric vehicle (EV) charging converters directly affect grid power quality. This paper proposes a harmonic analysis method based on geometric algebra (GA), which employs a multivector representation of signals and le...
We characterize the dimension of Lie algebras of white noise operators containing the quantum white noise derivatives of the conservation operator. We establish isomorphisms to filiform Lie algebras, Engel-type algebras, and solvable Lie algebras wit...
In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their in...
The study of algebraic invariants associated with Brauer configuration algebras induced by appropriate multisets is said to be a Brauer analysis of the data that define the multisets. In general, giving an explicit description of such invariants as t...
In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle
Many text mining methods use statistical information as a text- and language-independent approach for sentiment analysis. However, text mining methods based on stochastic patterns and rules require many samples for training. On the other hand, determ...
Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist t...
Green and Schroll introduced Brauer configurations to construct Brauer graph algebras and their generalizations, named Brauer configuration algebras, to investigate algebras of tame and wild representation types. It is worth pointing out that giving...
This paper is focused on some algebraic and combinatorial properties of a TMTO (Time–Memory Trade-Off) for a chosen plaintext attack against a cryptosystem with a perfect secrecy property. TMTO attacks aim to retrieve the preimage of a given on...
Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the large-scale...
A novel geometric modeling and calculation method for forward displacement analysis of the 6-3 Stewart platforms is proposed by using the conformal geometric algebra (CGA) framework. Firstly, two formulas between 2-blade and 1-blade are formulated. S...
The transmission problem has emerged as an important component in various application fields, including industry, agriculture, and commerce. Simultaneously, it is also one of the most common challenges encountered in daily activities such as eating,...
There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case of an nth-order ODE that admits an r-parameter Lie group
Persistent homology is a powerful tool in topological data analysis that captures the multi-scale topological features of data. In this work, we provide a mathematical introduction to persistent homology and demonstrate its application to protein&nda...
A detailed sensitivity analysis of ozone density profile retrieval was applied to scattering solar radiance spectra measured with the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument aboard the ENVIronmenta...
This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzz...
This paper describes the evaluation of a single output, online, and time domain modal parameters identification technique based on differential algebra and operational calculus. In addition, an analysis of the frequency response function (FRF) of the...
This paper establishes the existence of unique and multiple solutions to two nonlocal equations with fractional operators. The main results are obtained using the variational method and algebraic analysis. The conclusion is that there exists a consta...
We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad—all these in order t...
With the advent of communication networks, protecting data from security threats has become increasingly important. To address this issue, we present a new text encryption scheme that uses a combination of elliptic curve cryptography and max-plus alg...
This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions f...
This work aims to explore the algebraic and spectral properties of a novel parametric Hermitian non-Pauli spin basis. The primary motivation for this work is to introduce an alternative to the Pauli spin basis for investigating systems where conventi...
This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamental...
This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that un...
This study employs the modified extended direct algebraic method (MEDAM) to investigate the generalized nonlinear fractional
This paper proposes the generalized modified unstable nonlinear Schrödinger’s equation with applications in modulated wavetrain instabilities. The extended direct algebra and generalized Ricatti equation methods are applied to find innovat...
Permutations on a set, endowed with function composition, build a group called a symmetric group. In addition to their algebraic structure, symmetric groups have two metrics that are of particular interest to us here: the Cayley distance and the Kend...
Reliable multivariable control is critical for industrial sectors where processes exhibit severe nonlinearities and interactions. A Continuous Stirred Tank Reactor (CSTR) is a rigorous benchmark for testing control strategies addressing these complex...
Utilizing Multi-Criteria Decision Analysis (MCDA) methods based on environmental, social, and governance (ESG) factors to rank countries according to these criteria aims to evaluate and prioritize countries based on their performance in environmental...
In analysis of problems with parametric spline boundaries that are immersed or inserted into an underlying domain, the discretization on the underlying domain usually does not conform to the inserted boundaries. While the fixed underlying discretizat...
This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wav...
Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and machine le...
We formulate and analyze a 26-dimensional nonlinear dynamical system governing a doubly-fed induction generator (DFIG) wind energy conversion system coupled to an infinite bus through a dynamic transmission line. Seven interacting subsystems—ae...
Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two...
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