rss_2.0Mathematics FeedSciendo RSS Feed for Mathematics Feed Subtraction Laws on Semigroups<abstract> <title style='display:none'>Abstract</title> <p>We consider two variants of the sine subtraction law on a semi-group <italic>S</italic>. The main objective is to solve <italic>f</italic>(<italic>xy</italic><italic><sup>∗</sup></italic> ) = <italic>f</italic>(<italic>x</italic>)<italic>g</italic>(<italic>y</italic>) <italic>− g</italic>(<italic>x</italic>)<italic>f</italic>(<italic>y</italic>) for unknown functions <italic>f, g</italic> : <italic>S →</italic> ℂ, where <italic>x</italic> ↦ <italic>x</italic><italic><sup>*</sup></italic> is an anti-homomorphic involution. Until now this equation was not solved even when <italic>S</italic> is a non-Abelian group and <italic>x*</italic> = <italic>x</italic><italic><sup>−</sup></italic><sup>1</sup>. We find the solutions assuming that <italic>f</italic> is central. A secondary objective is to solve <italic>f</italic>(<italic>xσ</italic>(<italic>y</italic>)) = <italic>f</italic>(<italic>x</italic>)<italic>g</italic>(<italic>y</italic>) <italic>− g</italic>(<italic>x</italic>)<italic>f</italic>(<italic>y</italic>), where <italic>σ</italic> : <italic>S → S</italic> is a homomorphic involution. Until now this variant was solved assuming that <italic>S</italic> has an identity element. We also find the continuous solutions of these equations on topological semigroups.</p> </abstract>ARTICLEtrue -Jacobsthal and -Jacobsthal-Lucas Numbers<abstract> <title style='display:none'>Abstract</title> <p>Recently, Bród introduced a new Jacobsthal-type sequence which is called <italic>r</italic>-Jacobsthal sequence in current study. After defining the appropriate <italic>r</italic>-Jacobsthal–Lucas sequence for the <italic>r</italic>-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.</p> </abstract>ARTICLEtrue Barrier Method Via Minorant Function for Linear Semidefinite Programming<abstract> <title style='display:none'>Abstract</title> <p>We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost.</p> <p>Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by some numerical simulations showing the e˙ectiveness of the algorithm developed in this work, which are presented in the last section of this paper.</p> </abstract>ARTICLEtrue -Convexity of Set-Valued Functions<abstract> <title style='display:none'>Abstract</title> <p>In this research we introduce the concept of strong <italic>m</italic>-convexity for set-valued functions defined on <italic>m</italic>-convex subsets of real linear normed spaces, a variety of properties and examples of these functions are shown, an inclusion of Jensen type is also exhibited.</p> </abstract>ARTICLEtrue of the current situation and influencing factors of information technology education in middle school<abstract> <title style='display:none'>Abstract</title> <p>The development of science and technology is becoming more and more rapid, and the educational empowerment of information technology (IT) in middle schools is becoming more and more obvious. The interesting and operational aspects of IT are suitable for middle school students, who are gradually becoming more rational in their thinking and problem-solving skills, and who are curious to discovering new things. This paper analyses the factors influencing the acceptance of IT education among middle school students by reviewing a large amount of literature and compiling technology-related theories. The research variables are determined by combining the characteristics of middle school students, and a structural equation model is constructed to select the factors influencing the acceptance of technology in secondary school IT classrooms, and the hypothesis is proposed, tested and revised, and then the scientific and effective measures are proposed according to the model. By the statistical analysis of variables, it can be seen that the average values of perceived ease of use and social influence (SI) are relatively high, which are 3.9899 and 4.1933, respectively, indicating that SI and subjective initiative have significant positive correlations with the behavioural intentions of middle school students in learning IT. As technological literacy is low, with an average value of only 3.4966, the influence of the technological literacy of IT on middle school students’ learning ability is not significant. This reflects the degree of middle school students’ mastery of the knowledge of IT, which is not enough. Further, the initiative of learning in the network is low and the needs of teachers in IT classes indirectly affect students’ learning initiative. It is hoped middle school students learn IT through the network by their initiative and provide guidance for teachers in teaching, to promote the application and deep popularity of IT in secondary school education.</p> </abstract>ARTICLEtrue and uniqueness of weak solutions of the stochastic differential equations<abstract> <title style='display:none'>Abstract</title> <p>Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available information in order to predict a given filtration. In this paper we define the concept of dependence between stochastic processes and between filtrations, named causal predictability, which is based on the Granger’s definition of causality. This definition extends the ones already given in the continuous time. Then, we provide some properties of the given concept.</p> <p>Finally, we apply the concept of causal predictability to the processes of the diffusion type, more precisely, to the uniqueness of weak solutions of the stochastic differential equations.</p> </abstract>ARTICLEtrue eigenspaces of twisted polynomials over cyclic field extensions<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>K</italic> be a field and <italic>σ</italic> an automorphism of <italic>K</italic> of order <italic>n</italic>. Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial <italic>f</italic> ∈ <italic>K</italic>[<italic>t</italic>; <italic>σ</italic>]. We mainly treat the case that <italic>K/F</italic> is a cyclic field extension of degree <italic>n</italic> with Galois group generated by <italic>σ</italic>.We obtain lower bounds on the dimension of the eigenspace, and compute it in special cases as a quotient algebra. Conditions under which a monic polynomial <italic>f</italic> ∈ <italic>F</italic> [<italic>t</italic>] ⊂ <italic>K</italic>[<italic>t</italic>; <italic>σ</italic>] is reducible are obtained in special cases.</p> </abstract>ARTICLEtrue approximation properties of some non-positive Bernstein-Durrmeyer type operators<abstract> <title style='display:none'>Abstract</title> <p>In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will study the uniform convergence on all continuous functions on [0, 1] as well as a result given in terms of modulus of continuity <italic>ω</italic>(<italic>f, δ</italic>). A Voronovskaja type theorem will be proved as well.</p> </abstract>ARTICLEtrue the explicit geometry of a certain blowing-up of a smooth quadric<abstract> <title style='display:none'>Abstract</title> <p>Using the high symmetry in the geometry of a smooth projective quadric, we construct effectively new families of smooth projective rational surfaces whose nef divisors are regular, and whose effective monoids are finitely generated by smooth projective rational curves of negative self-intersection. Furthermore, the Cox rings of these surfaces are finitely generated, the dimensions of their anticanonical complete linear systems are zero, and their nonzero nef divisors intersect positively the anticanonical ones. And in two special cases, we give efficient ways of describing any effective divisor class in terms of the given minimal generating sets for the effective monoids of these surfaces. The ground field of our varieties is algebraically closed of arbitrary characteristic.</p> </abstract>ARTICLEtrue the B-concavity of functions with many variables<abstract> <title style='display:none'>Abstract</title> <p>The paper deals with the study of the property of B-concavity and BB concavity in the bi-dimesional case and with the relation between these properties and the Bernstein operators defined on a simplex.</p> </abstract>ARTICLEtrue thermoelasticity for double porous materials<abstract> <title style='display:none'>Abstract</title> <p>The main purpose of this paper is to obtain new results in the thermoelasticity for double porous materials, starting from the classical theory of Green-Lindsay’s elasticity. The novelty of the proposed method consists in proving a reciprocal theorem and obtaining the energy equation in the context of Green-Lindsay’s thermoelasticity for double porous materials. The added value in this article is the result regarding the uniqueness of the solution of the problem with mixed data for bodies with double porosity.</p> </abstract>ARTICLEtrue the torsional energy of torus knots under infinitesimal bending<abstract> <title style='display:none'>Abstract</title> <p>The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus knots is considered, and the results show that it is not stationary under infinitesimal bending. The torsional energy variation is determined as well. We prove that there is no infinitesimal bending field that leaves torus curves on the torus. Besides, we define an infinitesimal bending field that does not tear the torus knots while bending. Having in mind the importance of visualization in the infinitesimal bending theory, we observed infinitesimal bending of a curve in that field using independently developed software. The graphs we obtained are presented in the paper and the torus knots are coloured according to their torsional energy. We calculated the numerical value of torsional energy under infinitesimal bending and, finally, the results are discussed using convenient specific examples.</p> </abstract>ARTICLEtrue (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2<abstract> <title style='display:none'>Abstract</title> <p>This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal <italic>I</italic> of a ring <italic>R</italic> is (1,2)-absorbing primary if, whenever non-unit elements <italic>α, β, γ</italic> ∈ <italic>R</italic> with <italic>αβγ</italic> ∈ <italic>I</italic>,then <italic>αβ</italic> ∈ <italic>I</italic> or <italic>γ</italic><sup>2</sup> ∈ <italic>I</italic>. The introduced notion is related to uniformly primary ideals introduced in [5]. The first main objective of this paper is to compare (1,2)-absorbing primary ideals with uniformly primary ideals with order less than or equal 2, as well as to characterize them in many classes of rings. The second part of this paper characterizes, by using (1,2)-absorbing primary ideals, the rings <italic>R</italic> for which all ideals lie between N(<italic>R</italic>) (the nil-radical of <italic>R</italic>)and N(<italic>R</italic>)<sub>2</sub>.</p> </abstract>ARTICLEtrue solutions of Kirchhoff equations with Hartree-type nonlinearity<abstract> <title style='display:none'>Abstract</title> <p>In the present paper, we prove the existence of the solutions (<italic>λ, u</italic>) ∈ ℝ <italic>× H</italic><sup>1</sup>(ℝ<sup>3</sup>) to the following Kirchhoff equations with the Hartree-type nonlinearity under the general mass supercritical settings, <disp-formula> <alternatives> <graphic xmlns:xlink="" xlink:href="graphic/j_auom-2023-0015_eq_001.png"/> <mml:math xmlns:mml="" display="block"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mo>-</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mrow><mml:munder><mml:mo>∫</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:munder><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mrow><mml:mo>∇</mml:mo><mml:mi>u</mml:mi></mml:mrow> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>u</mml:mi><mml:mo>-</mml:mo><mml:mi>λ</mml:mi><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo> <mml:mrow><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mi>α</mml:mi></mml:msub><mml:mo>*</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>K</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow> <mml:mo>]</mml:mo></mml:mrow><mml:mi>K</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mi>u</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:mrow></mml:math> <tex-math>\left\{ {\matrix{{ - \left( {a + b\int\limits_{{\mathbb{R}^3}} {{{\left| {\nabla u} \right|}^2}dx} } \right)\Delta u - \lambda u = \left[ {{I_\alpha }*\left( {K\left( x \right)F\left( u \right)} \right)} \right]K\left( x \right)f\left( u \right),} \hfill \cr {u \in {H^1}\left( {{\mathbb{R}^3}} \right),} \hfill \cr } } \right.</tex-math> </alternatives> </disp-formula> where <italic>a, b &gt;</italic> 0 are prescribed, <italic>I</italic><italic><sub>α</sub></italic> = <italic>|x|</italic><italic><sup>α</sup></italic><sup>−3</sup> is the riesz potential where <italic>α</italic> ∈ (0, 3), <italic>K</italic> ∈ 𝒞<sup>1</sup>(ℝ<sup>3</sup>, ℝ<sup>+</sup>) satisfies an explicit assumption and <italic>f</italic> ∈𝒞 (ℝ, ℝ) satisfies some weak conditions, we develop some new tricks for dealing with the Hartree-type term to overcome the difficulties produced by the appearance of non-constant potential <italic>K</italic>(<italic>x</italic>). This paper extends and promotes the previous results on prescribed <italic>L</italic><sup>2</sup>-norm solutions of the Kirchhoff-type equation.</p> </abstract>ARTICLEtrue inequality for a vector field on Hadamard spaces<abstract> <title style='display:none'>Abstract</title> <p>Our purpose is to study the variational inequality problem for a vector field on Hadamard spaces. The existence and uniqueness of the solutions to the variational inequality problem associated with a vector field in Hadamard spaces are studied.</p> </abstract>ARTICLEtrue skew lattices with modal operator<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we define modal operators in residuated skew lattices and prove some fundamental properties of monotone modal operators on residuated skew lattices (RSL). We prove that the composition of two modal operators is a modal operator if and only if they commute. We investigate strong modal operators in RSL and get a characterization of them. Deductive systems under a modal operator are investigated.</p> </abstract>ARTICLEtrue matrices related to the vector cross product in ℂ<abstract> <title style='display:none'>Abstract</title> <p>Skew-symmetric matrices of order 7 defined through the 2-fold vector cross product in ℂ<sup>7</sup>, and other related matrices, are presented. More concretely, matrix properties, namely invertibility, nullspace, powers and index, are studied. As a consequence, results on vector cross product equations, vector cross product differential equations and vector cross product difference equations in ℂ<sup>7</sup> are established.</p> </abstract>ARTICLEtrue the dynamic coloring problem for direct products of paths with fan graphs<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the <italic>r</italic>-dynamic chromatic problem of the direct product of a path with a fan graph <italic>F</italic><italic><sub>m,n</sub></italic>. The problem is completely solved except for the case <italic>n&lt;r</italic> ∈<italic>{</italic>2<italic>m</italic> +2, 2<italic>m</italic> +3<italic>}</italic>, which is solved under certain assumptions. It enables us to determine in particular the dynamic chromatic number concerning this problem, for all <italic>r ≤</italic> 7, and also, for all <italic>m</italic> ∈<italic>{</italic>1, 2<italic>}</italic>.</p> </abstract>ARTICLEtrue some links between the generalised Lucas pseudoprimes of level<abstract> <title style='display:none'>Abstract</title> <p>Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences. In this paper we first establish new arithmetic properties of the generalized Lucas and Pell-Lucas sequences. Then we study the recent notion of generalized Pell and Pell-Lucas pseudo-primes of level <italic>k</italic>, and find inclusions between the sets of pseudoprimes on different levels. In this process we extend several results concerning Fibonacci, Lucas, Pell, and Pell-Lucas sequences.</p> </abstract>ARTICLEtrue pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation<abstract> <title style='display:none'>Abstract</title> <p>This paper’s main motivation is to study the notion of weighted pseudo almost automorphic (𝒲𝒫𝒜𝒜) functions and establish the existence results of piecewise continuous mild solution of fractional order integro-differential equation with instantaneous impulses. The usual 𝒲𝒫𝒜𝒜 functions may not work since the solution of impulsive differential equations may not be continuous. Thus in order to give a broader spectrum, we introduce this concept. We establish main results by using the Banach contraction mapping principle and Sadovskii’s fixed point theorem. An example is shown to exhibit our analytic findings.</p> </abstract>ARTICLEtrue