Science topics: Mathematical SciencesAlgebra

Science topic

# Algebra - Science topic

For discussion on linear algebra, vector spaces, groups, rings and other algebraic structures.

Publications related to Algebra (10,000)

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In this paper, we introduce the hyperbolic k-Mersenne and k-Mersenne-Lucas octonions and investigate their algebraic properties. We give Binet's formula and present several interrelations and some well-known identities such as Catalan identity, d'Ocagne identity, Vajda identity, generating functions, etc. of these octo-nions in closed form. Further...

Denote by $\mathbb{F}_p[t_1,t_2,\ldots ,t_h]$ the polynomial algebra on $h$ variables over the field of $p$ elements, $\mathbb F_p$ ($p$ being a prime), and by $GL(h, \mathbb F_p)$ the general linear group of rank $h$ on $\mathbb F_p.$ We are interested in the {\it hit problem}, set up by Franklin Peterson, of finding a minimal system of generators...

Due to the importance of the NTRU public key cryptosystem, many improvements have been made to it by increasing security or speed to keep pace with the process of technological development in exchanging various data. In this paper, we construct a public key cryptosystem called HAQTR using non-commutative quaternion algebra with the change of the ma...

The paper studies the Karoubi envelope of a one-dimensional topological theory with defects and inner endpoints, defined over a field. It turns out that the Karoubi envelope is determined by a symmetric Frobenius algebra K associated to the theory. The Karoubi envelope is then equivalent to the quotient of the Frobenius-Brauer category of K modulo...

Unconventional system that are generally adopted for ship propulsion are Ducted Propellers. These devices have recently been studied with medium-fidelity computational fluid dynamics code (based on the potential flow hypothesis) with promising results. Numerical and experimental comparison of ducted propeller with PBCF, case studies with Propeller...

In this article, algebraic characterizations of J-spaces and C-normal spaces are exhibited. The concept of a Z-connected ideal in C(X) is presented and characterized using certain connected subsets of X. We define the class of JC-spaces and characterize its members via Z-connected ideals. Two more classes of ideals in C(X), namely the coz-free and...

This paper is dedicated to the memory of Professor Alexander Vasilevich Mikhalev one of the most significant representatives of the Moscow School of Algebra and
Computer Science, and was one of the last giants – a real scientific rock of the Department of Higher Algebra of Lomonosov Moscow State University.

Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed braided tensor representation subcategories, namely having automorphisms whose equivalence classes necessarily f...

We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize them by complementary approaches based on topological degeneracy of steady states, topological entropy, and d...

Calculate Multiplication Matrices of algebraic systems via Macaulay style formulae.

Known results about permutation polynomials in connection with coefficients in a finite field extend to algebras of the form Lv = K[X]/(p(X)v)\), where K is a finite field,(p(X) ∈ K[X] is an irreducible polynomial, and v = 1,2,..., and to the algebra of power series L[[Z]], where L = K[X]/(p(X)). Analogues of Dickson polynomials are also studied...

The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case called coboundary mock-Lie bialgebra leads to introducing the mock-Lie Yang-Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang-Baxter equation on a Lie algebra...

Stochastic circuits are used in applications that require low area and power consumption. The computing performed using these circuits is referred to as Stochastic computing (SC). The arithmetic operations in this computing can be realized using minimum logic circuits. The SC system allows a tradeoff of computational accuracy and area; thereby, the...

A multi-step, iterative technique for the local non-parametric identification of the standard linear solid (SLS) material model employing fractional order time differential operators is presented. Test input data consists of a set of identified material complex modulus values estimated at different frequency values, obtained from input–output exper...

A generalized homotopy-based Coiflet-type wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed. Based on the improvement of boundary difference order by Taylor expansion, the accuracy in wavelet approximation is largely improved and the accumulated error on boundary is successfully suppressed in application. A un...

Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices. In addition, we explore the unitary diagonalization of the covariance and generalized complementary covariance. Moreover, we g...

Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for th...

This work analyses the time integration of elastoplastic models using implementation platforms with symbolic algebra capabilities. In such platforms, the variables and state functions involved in solving boundary value problems are considered entities continuous in time, thus the time integration of stresses and hardening parameters is always based...

Hom–Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom–Lie algebras are studied further. In the theory of groups, investigations of the properties of the solvable and nilpotent groups are well-developed. We establish a t...

In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a smooth manifold in the topological dual of its algebra of smooth functions. This is generalised here...

We introduce a definition of the locally trivial G-C*-algebra, which is a noncommutative counterpart of the total space of a locally compact Hausdorff numerable principal G-bundle. To obtain this generalization, we have to go beyond the Gelfand–Naimark duality and use the multipliers of the Pedersen ideal. Our new concept enables us to investigate...

Este estudo apresenta o acompanhamento realizado durante três anos, que vai do quatrième2 ao seconde, de um aluno com muitos problemas de aprendizagem em álgebra. O jovem confundia os escritos de expressões numéricas e algébricas, assim como todos os termos que designavam operações de cálculo a serem feitas. Inicialmente, o acompanhamento consistiu...

Mathematicians began to study a series of properties about numbers a long time ago, and a new field of mathematics, the number theory, was born from this. Some special properties of numbers in the number theory make mathematicians use the knowledge of group theory to make some ingenious answers when considering some problems. In the analytic number...

Na aprendizagem de álgebra durante o Ensino Fundamental 2 (EF-2)2, os alunos enfrentam constantemente uma espécie de parede de vidro: os escritos simbólicos, ou seja, a variedade de expressões que combinam números, letras e símbolos de operações, cujo registro semiótico permite-lhes escrever; bem como a heterogeneidade das operações de substituição...

We prove that the simplest gravitational symmetry-reduced models describing cosmology and black hole mechanics are invariant under the Schrödinger group. We consider the flat FRW cosmology filled with a massless scalar field and the Schwarzschild black hole mechanics and construct their conserved charges using the Eisenhart–Duval (ED) lift method i...

Geography of projective varieties is one of the fundamental problems in algebraic geometry. There are many researches toward the characteristics of Chern number of some projective spaces, for example Noethers inequalities, the theorem of Chang-Lopez, and the Miyaoka-Yau inequality. In this paper, we compute the Chern numbers of any smooth complete...

Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using a locally defined potential function, we unravel the spectral-collapse mechanism from Bloch to non-Bloch band...

This is an attempt to extend to algebraic K-theory our approach to group actions in homological algebra that could be called an introduction to Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...

In this paper, we consider the following nonlinear Schrödinger equation: (0.1) −Δu+V(|x|)u=Q(|x|)up,u>0inℝN,u∈H1ℝN,$$ -\Delta u+V\left(|x|\right)u=Q\left(|x|\right){u}^p,\kern0.30em u>0\kern0.20em \mathrm{in}\kern0.20em {\mathrm{\mathbb{R}}}^N,u\in {H}^1\left({\mathrm{\mathbb{R}}}^N\right), $$ where N≥3,p∈1,N+2N−2$$ N\ge 3,p\in \left(1,\frac{N+2}{N...

We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that...

This review article provides a comprehensive overview of the fascinating field of noncommutative probability theory, tracing its evolution from its inception in the early 1980s by Romanian-American mathematician Dan Voiculescu to its current state of prominence in mathematics. Through a meticulous examination of seminal works and recent advancement...

In order to prove the ElGamal CCA(Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group where ICDH(Interactive Computational Diffie Hellman) assumption holds. Until now, only bilinear group with complex algebraic structure has been known as the ICDH group. In this paper, we introduce the ICDH group with sim...

We compute the Bonahon-Wong-Yang quantum invariant for self-diffeomorphisms of the four-puncture sphere explicitly, based on the representation theory of the Checkov-Fock algebra. As an application of the computation, we verify the volume conjecture proposed by Bonahon-Wong-Yang for the four puncture sphere bundles with some technical conditions. T...

A bstract
We find a (1 + 1)-dimensional metric solution for a background hosting various supersymmetric field theories with a single non-chiral real supercharge. This supersymmetric background is globally hyperbolic even though it contains a naked null singularity. In this regard, we show that scalar wave propagation on the background is well-defin...

The well-known Fibonacci sequence has several generalizations, among them, the k-generalized Fibonacci sequence denoted by F (k) . The ﬁrst k terms of this generalization are 0, . . . , 0, 1 and each one afterward corresponds to the sum of the preceding k terms. For the Fibonacci sequence the formula F_{n+1}^{2}-F_{n-1}^2=F_{2n} holds for every n ≥...

In many countries around the world, due to varied administrative goals and perspectives, different departments often produce overlapping spatial plans for the same region. The presence of these multiple plans can lead to conflicts, potentially making some land parcels inapplicable. Thus, establishing a unified spatial planning system by integrating...

The relation between local and global solution of an equation can be discussed with the method of class field theory and algebraic number theory. In this piece of writing, the author will introduce the behavior of both local and global m-th power in some specific number field. Of course, the result in this paper can be extended into the function fi...

El cálculo diferencial es una de las áreas de las matemáticas que presenta mayor complejidad, de ahí que, en muchos casos, constituya un verdadero reto para los estudiantes. Una de las razones por las que esto ocurre se debe a que para abordar el cálculo diferencial es necesario tener conocimientos sólidos en áreas previas de la matemática, como lo...

In this paper we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomple-mented De Morgan algebra endowed with two tense operators G and H satisfying additional...

A (k, m)-Furstenberg set is a subset \(S \subset {\mathbb {F}}_q^n\) with the property that each k-dimensional subspace of \({\mathbb {F}}_q^n\) can be translated so that it intersects S in at least m points. Ellenberg and Erman (Algebra Number Theory 10(7), 1415–1436 (2016)) proved that (k, m)-Furstenberg sets must have size at least \(C_{n,k}m^{n...

Complex projective algebraic varieties with C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {C}}}^*$$\end{document}-actions can be thought of as geometric c...

The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial t-structures, and in particular, full abelian subcategories need not arise as hearts of a t-structure. The purpose of this paper is to investigate full abelian subcategories of triangulated categories whose exact structures are related, and more...

Oriented elements are part of geometry, and they come in two complementary types: intrinsic and extrinsic. Those different orientation types manifest themselves by behaving differently under reflection. Projective dualization in geometric algebras can encode them, or conversely, orientation types inform the interpretation of dualization. Oriented e...

We suggest the usage of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and Ushakov with some examples in ascending HNN-extensions of free-abelian groups and discuss their resistance to length and distance based attacks. We also introduce severa...

Objective
The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction–diffusion problem to produce more accurate solutions.
Results
Quasilinearization technique is used to linearize the semilinear term. The scheme is formulated with discretizing the solution domain piecewis...

A generalized implication on a distributive lattice A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{A}$$\end{document} is a function between A×A\documentclass[...

We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework in which quantum mechanics can be constructed in a complete mathematically consi...

In this lecture, we will study families of Appell-type polynomials, particularly Bernoulli polynomials and Euler polynomials, together with their generalizations, as well as their degenerate version, which have been studied over time. In addition, we will explore the degenerate sine and cosine functions. On this basis, we will introduce the degener...

Let K⟨Xd⟩ be the free associative algebra of rank d≥2 over a field, K. In 1936, Wolf proved that the algebra of symmetric polynomials K⟨Xd⟩Sym(d) is infinitely generated. In 1984 Koryukin equipped the homogeneous component of degree n of K⟨Xd⟩ with the additional action of Sym(n) by permuting the positions of the variables. He proved finite generat...

In the development of the theory of autometrized algebra, various types of research have been conducted. However, there are some properties like convex subalgebra, prime convex subalgebra, meet closed sets, regular convex subalgebra, and convex spectral topology on autometrized algebras that have not been studied yet. In this paper, we define the n...

Given a group G and a partial factor set σ of G, we introduce the twisted partial group algebra κ σ par G, which governs the partial projective σ-representations of G into algebras over a filed κ. Using the relation between partial projective representations and twisted partial actions we endow κ σ par G with the structure of a crossed product by a...

We formulate a notion of jet bundles over a possibly noncommutative algebra A equipped with a torsion-free connection. Among the conditions needed for third-order jets and above is that the connection also be flat and its ‘generalised braiding tensor’ $$\sigma :\Omega ^1\mathop {{\otimes }}_A\Omega ^1\rightarrow \Omega ^1\mathop {{\otimes }}_A \Ome...

A bstract
As a series of work about 5D (spacetime) topological orders, here we employ the path-integral formalism of 5D topological quantum field theory (TQFT) established in Zhang and Ye, JHEP 04 (2022) 138 to explore non-Abelian fusion rules, hierarchical shrinking rules and quantum dimensions of particle-like, loop-like and membrane-like topolog...

We introduce a family of quantum field theories for fields carrying monopole and dipole charges. In contrast to previous realizations, fields have quadratic two-derivative kinetic terms. The dipole symmetry algebra is realized in a discretized internal space and connected to the physical space through a background gauge field. We study spontaneous...

We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\widehat{\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and Wang. In particular, we establish a "factorization formula", expressing the commuting "affine Cartan"-type operato...

Introduction
Teachers’ knowledge and positive attitudes significantly impact educational settings. This study aimed to assess teachers’ mathematical knowledge for teaching (MKT) and their pedagogical content knowledge (PCK) attitudes.
Methodology
It was conducted on all 23 mathematics teachers from Rwandan teacher training colleges (TTCs). Employi...

A new method namely, algebraic elimination method is proposed for finding a complementarity feasible solution to the Symmetric Trapezoidal Intuitionistic fuzzy linear complementarity problem which has applications in non-linear programming. Then, the algebraic elimination method is extended to Symmetric Trapezoidal Intuitionistic fuzzy quadratic pr...

Plantlet is a new variant of Sprout lightweight stream cipher. It uses 61 bit LFSR and 40 bit NFSR. This paper presents a study of Plantlet stream cipher with probability based approach for making algebraic attack on Plantlet. In this paper, we have used low degree multiple of Boolean function to apply algebraic attack. The low degree multiple of B...

We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e., with total Betti number of the maximal possible order. We show how similar ideas can be used to produce real algebraic projective hypersurfaces with a rich structure of umbilical points.

Background: In a culture where teachers follow the textbook prescriptively, Malawian students perform low in mathematics, and no students reach the problem-solving levels.Aim: To explore reasons for students’ low performance, this study aims at investigating opportunities to learn problem-solving in Malawian mathematics textbooks.Setting: This stud...

New possibilities of Gramian computation by using canonical transformations into diagonal, controllable and observable canonical forms are shown. With the help of such a technique the Gramian matrices can be represented in the form of products of Hadamard matrices of multipliers and matrices of the transformed right-hand side of Lyapunov equations....

The synchronization of fractional-order chaotic systems (FOCSs) plays an important role in modern control theory, the projective synchronization (PS) as a class of synchronization problems, also has huge applications and has attracted much attention. It is, however, shown in the obtained literature that the results on the PS of FOCSs either loss th...

Frame is a fundamental notion in the study of vector spaces; they offer
redundancy and flexibility, which favor their application in various fields of
mathematics. This article aims to collect important results of frames in Hibert
pro-C∗-modules: Frame, ∗-frame, ∗-K-frame, g-frame, ∗-g-frame, ∗-K-g-frame,
operator frame, ∗-operator frame, ∗-K-opera...

We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric and double-symmetric analytic functions on Banach spaces ℓp(Cn) and the homomorphisms of these algebr...

p>The increasing penetration of converter-interfaced generators (CIGs) in power systems has posed great challenges in frequency stability analysis, as the frequency dynamics of CIGs may be strongly coupled with voltage dynamics. However, existing analytical models for system frequency generally cannot precisely account for the impact of voltage dyn...

In this study, we present Taylor series solutions for steady‐state non‐isothermal diffusion–reaction problems pertaining to porous catalyst pellets exhibiting arbitrary kinetics. Using the Damkohler relation, the system of two nonlinear differential equations is reduced to a single differential equation subject to the algebraic constraint. We deriv...

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier–Stokes (NS) equations. The development of surrogate models relies on involved algebra and several assumptions. Here, we present a data-driven workflow where a handful of detailed N...

We explore TT¯ deformations of warped conformal field theories (WCFTs) in two dimensions as examples of TT¯ deformed nonrelativistic quantum field theories. WCFTs are quantum field theories with a Virasoro×U(1) Kac-Moody symmetry. We compute the deformed symmetry algebra of a TT¯ deformed holographic WCFT, using the asymptotic symmetries of AdS3 wi...

We establish a version of Turrittin's result on normal forms of linear systems of meromorphic ODEs when the base field K is real and closed. Both the proposed normal forms and the transformations used have coefficients in K. Our motivation comes from applications to the study of trajectories of real analytic vector fields (already treated in the li...

If X is a variety with an additional structure $$\xi $$ ξ , such as a marked point, a divisor, a polarization, a group structure and so forth, then it is possible to study whether the pair $$(X,\xi )$$ ( X , ξ ) is defined over the field of moduli. There exists a precise definition of “algebraic structures” which covers essentially all of the obvio...

We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux Y(s1,…,sk) with k≥2 rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applie...

Mathematics is the mother of all the sciences, engineering and technology, and a normed division algebra of all finite dimensions is the mathematical holy grail. In search of a real three-dimensional, normed, associative, division algebra, Hamilton discovered quaternions that form a non-commutative division algebra of quadruples. Later works showed...

This paper is a follow-up to [J. High Energy Phys. 06, 025 (2020)] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. T...

In this paper, we define three types of 2‐ruled hypersurfaces in the Minkowski 4‐space 𝔼14. We obtain Gaussian and mean curvatures of the 2‐ruled hypersurfaces of type‐1 and type‐2 and some characterizations about its minimality. We also deal with the first Laplace–Beltrami operators of these types of 2‐ruled hypersurfaces in 𝔼14. Moreover, the imp...

Developing a theory for quantum gravity is one of the big open questions in theoretical high-energy physics. Recently, a tensor model approach has been considered that treats tensors as the generators of commutative non-associative algebras, which might be an appropriate interpretation of the canonical tensor model. In this approach, the non-associ...

Several operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product). Using elementary techniques, we prove that this set equipped with the termwise sum and the aforementioned products is an R -algebra, given any commutative ring R with ide...

Let Q and P be the position and momentum operators of a particle in one dimension. It is shown that all compact operators can be approximated in norm by linear combinations of the basic resolvents (aQ+bP-ir)-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepa...

In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar characterization for the analogous coherent structures in the bicategory of spans of sets. We show that commutative and F...

In the realm of program analysis, algebraic invariants play a vital role in verifying the correctness and proper es of programs. An algebraic invariant is a set of polynomial equa ons that hold for all possible values of the program variables at each program loca on. These invariants provide valuable insights into the behavior of the program and ca...

Let n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 2$$\end{document} be a natural number, and denote by Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \...

We study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects of these objects. In particular, we focus our attention on the corresponding invariant subspaces and generalise...

Known results on permutation polynomials with coefficients in a finite field are extended to algebras of the form Lv=K[X]/(p(X)v)), where K is a finite field, p(X) belongs to K[X] and is an irreducible polynomial, v = 1,2..., and to the algebra of power series L[[Z]]. Finally analogues of Dickson polynomials in these algebras are studied.

The first goal of this paper is to find a representation of the Fock space on Cn in terms of the weighted Bergman spaces of the projective spaces CPn−1; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on CPn−1. Also, we study the C* algebras generated by Toeplitz operators where the symbol...

This paper presents a continuous-time subspace identification method utilizing prior information and generalized orthonormal basis functions. A generalized orthonormal basis is constructed by a rational inner function, and the transformed noises have ergodic properties. The lifting approach and the Hambo system transform are used to establish the e...

Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I 1 , and L m : A → A is a Lie-type higher derivation. In continuation of the rigorous and versatile framework for investigating the structure and properties of operators on Hilbert spaces, more facts are needed to characterize Lie-type...

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 to create and analyze a problem involving proportional reasoning within a probabilistic context. For...

Cryptography with DNA sequences is a newly emerging technique that helps for the secured transmission of data. With the help of the biological properties of the DNA sequences, it is possible to enhance the security of a message with minimum cost and reduced computational time. DNA cryptography shows how powerfully the cryptographic methods can be u...

Knowing what first-time freshmen in mathematics believe to be true about themselves as they arrive on a college campus provides valuable perspectives about freshman mathematics learners. We investigated how gender, high school mathematics course history, and university mathematics course placement are related to first-time freshmen’s mathematical m...

The purpose of this paper is to introduce the concept of the so-called modified Dirac operator over the algebra of 3−split numbers, denoted by M. By the mean of this operator we provide a generalization of monogenic functions and we show some of their properties. Moreover, we establish some Fischer-type decomposition theorems for the operator M and...

We present a study on systems of single-molecule magnet systems using semiclassical analysis and catastrophe theory. Separatrices in the parameter space are constructed, which are useful for determining the structure of the Hamiltonian energy levels. In particular the Maxwell set separatrix determines the behavior of the ground state of the system....

The algebraic framework of the interacting boson model with configuration mixing is employed to demonstrate the occurrence of intertwined quantum phase transitions (IQPTs) in the _{40} 40 Zr isotopes with neutron number 52-70. The detailed quantum and classical analyses reveal a QPT of crossing normal and intruder configurations superimposed on a Q...

A bstract
We construct a simple Lorentz-invariant action for maximally supersymmetric self-dual Yang-Mills theory that manifests colour-kinematics duality. We also show that this action double-copies to a known action for maximally supersymmetric self-dual gravity. Both actions live on twistor space and illustrate nicely the homotopy algebraic pers...

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof system for a target logic by enriching a proof system for another, typically simpler, logic with an algebra of cons...

A bstract
In this paper, we propose a novel way to construct off-shell actions of d -dimensional Carrollian field theories by considering the null-reduction of the Bargmann invariant actions in d +1 dimensions. This is based on the fact that d -dimensional Carrollian symmetry is the restriction of the ( d + 1)-dimensional Bargmann symmetry to a nul...

An analysis of the realizations of the ladder operators for the Rosen-Morse and Pöschl-Teller quantum systems is carried out. The failure of the algebraic method of construction in the general Rosen-Morse case is exposed and explained. We present the reduction of a recently obtained set of (2n ± 1) ( 2 n ± 1 ) -th-order Rosen-Morse ladder operators...