The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic...
To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs. This study presents a formative action in which pre-service teachers are required...
The primary focus of this paper is to extend the concept of pseudospectrum from operators and matrices to elements of a unital complex Banach Jordan algebra, thereby moving from the associative to the non-associative setting. We introduce the notion...
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...
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...
Hedge algebra is a powerful and flexible tool for handling linguistic information, enabling precise quantitative computations and enhancing the effectiveness of multi-criteria decision-making (MCDM). This study proposes a novel integrated fuzzy MCDM...
26 October 2020
An algebraic intermittency model for boundary layer flow transition from laminar to turbulent state, is extended using an experimental data base on boundary layer flows with various transition types and results by large eddy simulation of transition...
A program library for computing pure spin-angular coefficients for any one- and scalar two-particle operators is presented. The method used is based on the combination of the second quantization and quasi-spin techniques with the angular momentum the...
In this study, an extension of the general method [G. Gaigalas, Z. Rudzikas, C. Froese Fischer, J. Phys. B, At. Mol. Phys. (1997). DOI: 10.1088/0953-4075/30/17/006] is described for finding algebraic expressions of the spin-angular parts of the reduc...
A program library, libang77, for computing pure spin-angular coefficients for any one- and scalar two-particle operator is presented. The method is based on the combination of the second quantization and quasi-spin techniques with angular momentum th...
Let
This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for unders...
The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understan...
We present a new look at the classification of real low-dimensional Lie algebras based on the notion of a linear bundle of Lie algebras. Belonging to a suitable family of Lie bundles entails the compatibility of the Lie–Poisson structures with the du...
In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures wit...
The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map
We introduce and study bipolar complex intuitionistic fuzzy Lie algebras (BCIFLAs), a new algebraic framework merging bipolar fuzzy theory, complex-valued membership functions in Cartesian form, and intuitionistic fuzzy Lie algebra theory. Adopting t...
We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but...
The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the...
Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years....
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19 November 2021
The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to alg...
We show that for a finite von Neumann algebra, the states that maximise Segal’s entropy with a given energy level are Gibbs states. This is a counterpart of the classical result for the algebra of all bounded linear operators on a Hilbert space and v...
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...
This paper develops a rigorous algebraic framework for quasi-substructures in Sheffer-based Nelson algebras, extending the landscape of fuzzy algebraic theory. By systematically introducing
In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of
Process algebra is one of the most suitable formal methods to model smart IoT systems for smart cities. Each IoT in the systems can be modeled as a process in algebra. In addition, the nondeterministic behavior of the systems can be predicted by defi...
We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over
This study investigates linear Diophantine fuzzy structures within the framework of Sheffer stroke BCK-algebras (SBCK-algebras). We introduce and characterize linear Diophantine fuzzy SBCK-subalgebras and linear Diophantine fuzzy SBCK-ideals, establi...
The process algebra model has been suggested as an alternative mathematical framework for non-relativistic quantum mechanics (NRQM). It appears to reproduce the wave functions of non-relativistic quantum mechanics to a high degree of accuracy. It pos...
The System for Teaching and Assessment using a Computer Algebra Kernel (STACK) is an open source, computer algebra-based online assessment system for teaching and learning mathematics at university. Although the popularity is increasing around the wo...
The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmo...
To systematically address the intricate multiple criteria decision-making (MCDM) challenges to practical situations where uncertain and hesitant information plays a critical role in guiding optimal choices. In this article, we introduce the concept o...
We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space
This study delves into the convergence of operators and the viscoelastic properties of fractal ladder and tree structures. It proves the convergence of fractal stiffness operators through operator algebra, revealing a fundamental connection between o...
In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras an...
Arnold tongues are wedge-shaped regions in parameter space associated with mode locking and synchronization phenomena in nonlinear dynamical systems. The Caputo fractional standard map extends the classical standard map by incorporating long-memory e...
Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mat...
Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a me...
The Choi–Jamiołkowski correspondence identifies completely positive maps with positive bipartite operators in finite-dimensional quantum information theory. For general von Neumann algebras, the canonical bipartite object is the spatial te...
Computer-based testing is an emerging method to evaluate students’ mathematics learning outcomes. However, algebra problems impose a high cognitive load due to requiring multiple calculation steps, which might reduce students’ performance...
This lecture is a short review on the role entropy plays in those classical dissipative systems whose equations of motion may be expressed via a Leibniz Bracket Algebra (LBA). This means that the time derivative of any physical observable f of the sy...
In this paper, we present a novel concept for an abstract algebra course at the secondary school level. Against the backdrop of findings from mathematics education research, we discuss benefits that arise from teaching abstract algebra to secondary s...
This paper introduces bipolar fuzzy sub-hoops and bipolar fuzzy filters within hoop algebras, extending fuzzy logic to incorporate both positive and negative membership degrees. We define these structures, explore their algebraic properties, and esta...
In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept...
We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences
This study examined the reversal error phenomenon in Chinese students’ algebra word problem-solving, focusing on how sentence structures influence performance and problem representation strategies across educational levels. Using a person-cente...
The mean-variance (MV) portfolio optimization targets higher return for investment period despite the unknown stochastic behavior of the future asset returns. That is why a risk is explicitly considering, quantified by algebraic characteristics of vo...
One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, can help us to meet this goal...
This work considers admissibility-enforcing reconstruction of reaction-channel subgroup levels on prescribed total-subgroup support and probabilities, a setting in which conventional exact reconstruction may produce negative reaction-channel levels....
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