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The study of students' use of representations is one of the main topics of physics education research and is guided by the overarching field of semiotics. In this paper we compare two semiotic frameworks, one coming from didactics of mathematics and one from physics education research; "the theory of registers of semiotic representations" and "social semiotics," using the networking of theories methodology. A group of first year university students were audio and video recorded as they discussed concepts relating to thermal energy, a study that will be further explored in an upcoming paper. We find that analyzing the recorded data using two different semiotic perspectives provides a wider interpretation of students' representational use, a descriptive approach to how students use the representations, and an approach to the cognitive aspects of the construction of knowledge. By comparing the theoretical constructs they employ, and how they are employed in the analysis process, we identify constructs that both frameworks have in common, but also where they differ. We have found that each semiotic theory provides a different perspective regarding students' representational use. We also propose that comparing different theories may provide a space for complementing the constructs of each theory and providing a bigger picture to understand students' representational use in physics and other science, technology, engineering, and mathematics education areas.

In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

In this paper, we study variation-inequality initial-boundary value problems with fouth order p(x)-Kirchhoff operators. First, an operator is constructed based on the Leray Schauder principle, and the existence of solutions is obtained. Secondly, the stability and uniqueness of the solution are analyzed after the conditions are appropriately relaxed on the Kirchhoff operators. [ABSTRACT FROM AUTHOR]

Suppose that S T 1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class S T 1 with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional J 2 , 4 f and J 3 , 3 f for the class S T 1 . [ABSTRACT FROM AUTHOR]

In this paper, we define R-norm entropy and conditional R-norm entropy of partitions of algebraic structures, and we establish some of their basic properties. We show that the Shannon entropy and the conditional Shannon entropy of partitions can be derived from the R-norm entropy and the conditional R-norm entropy of partitions, respectively, by letting R tend to 1. Finally, using the notion of entropy for partitions, we define the R-norm entropy of a dynamical system. We prove that the R-norm entropies of isomorphic dynamical systems are equal. [ABSTRACT FROM AUTHOR]

The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra. [ABSTRACT FROM AUTHOR]

Analytical thinking is dominated by binary ideas. From pairwise interactions to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific paradigms. In this paper, we introduce arity as the generic conceptualization of the order of an interaction between a discrete collection of entities and argue that there is a rich universe of higher arity ideas beyond binarity waiting to be explored. To illustrate this, we discuss several higher-order phenomena appearing in a wide range of research areas, paying special attention to instances of ternary interactions. From the point of view of formal sciences and mathematics, higher arity thinking opens up new paradigms of algebra, symbolic calculus and logic. In particular, we delve into the special case of ternary structures, as that itself reveals ample surprises: new notions of associativity (or lack thereof) in ternary operations of cubic matrices, ternary isomorphisms and ternary relations; the integration problem of 3-Lie algebras; and generalizations of adjacency in 3-uniform hypergraphs. All these are open problems that strongly suggest the need to develop new ternary mathematics. Finally, we comment on potential future research directions and remark on the transdisciplinary nature of higher arity science. [ABSTRACT FROM AUTHOR]

In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measures. The Onsager-Machlup function can serve as a density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the "most likely element". The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the "most likely element". This leads to a conundrum - what is the relationship between these two functions? We show both pointwise and G-convergence (which is essentially the convergence of minimizers) of the Onsager-Machlup function under the small-noise limit to the Freidlin-Wentzell function - and give an expression for both. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to path-dependent stochastic differential equations and the law of an infinite system of random algebraic equations. [ABSTRACT FROM AUTHOR]

This paper explores generalized hyper S-acts (GHS-acts) over a hypermonoid S as generalizations of monoid acts within the context of algebraic hyperstructures. Specifically, we extend the definition of C-injectivity to GHS-acts and investigate their internal and homological properties. It is established that to determine the GHS-injectivity of GHS-acts with a fixed element, we only need to consider the inclusions of cyclic GHS-subacts into indecomposable ones. Additionally, we introduce the concepts of semiinjectivity and semi-C-injectivity and give some characterizations of these types of injectivity for quotients of SS. It is demonstrated that, in contrast to the case of ordinary acts over monoids, cyclic GHS-acts are not necessarily a quotient of SS, and injectivity and semi-injectivity do not coincide in the category of GHS-acts with a fixed element. Among other things, we also show that all pure GHS-acts are injective if and only if all pure cyclic GHS-acts are C-injective. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of weak i-hyperfilters of ordered n-ary semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and discuss their related properties. We define Green's relations Mi, J, H and K on ordered n-ary semihypergroups and investigate the relationships between Green's relations and the equivalence relation Wi, which is generated by the weak i-hyperfilters. Also, we give the characterizations of intra-regular ordered n-ary semihypergroups via the properties of weak ihyperfilters. Finally, we introduce the concepts of (i-, Λ-)duo ordered n-ary semihypergroups and establish some interesting properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a split minimization problem with multiple output sets. We propose a new iterative method, which employs the inertial Halpern approximation technique, for a common solution of the split minimization problem and the fixed point problem with a finite family of Bregman relatively nonexpansive mappings in the framework of p-uniformly convex and uniformly smooth Banach spaces. Our iterative method uses the step sizes which do not require prior knowledge of the operators norm, and we prove a strong convergence result under some mild conditions. Moreover, we present some applications of our result and further demonstrate the efficiency and applicability of our algorithm with some numerical examples. The results presented in this paper unify and complement several existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a relaxed CQ algorithm involving the Armijo-line search and the alternated inertial technique to solve the multiple-sets split feasibility problem in infinite dimensional real Hilbert spaces. We prove the convergence of the sequence generated by our method under some mild assumptions. Finally, numerical simulations show the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a class of matrices, namely, Drazin-dagger ma- trices, in which the Drazin inverse and the Moore-Penrose inverse com- mute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore- Penrose inverse, the Drazin inverse and the numerical range of some re- ciprocal matrices are obtained. In particular, the relations between re- ciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP ma- trices are studied. To illustrate the results, some numerical examples are also given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a different approach for algebraic structures. Because, in the concept of ordinary algebraic structures, an algebraic structure consists of a nonempty set of abstract points with one or more binary operations, and it is required to satisfy certain axioms. But, we can use perceptual objects (non-abstract points) on weak nearness approximation space. This is like as a real life. The problem considered in this paper is to determine such features of ideals on weak nearness approximation space. We defined that upper nearness ideal generated by a subset of the ring on weak nearness approximation spaces and introduce some properties of these ideals. In addition to this, it is defined that nearness prime and nearness maximal ideals of the nearness rings and introduce some properties of these ideals. [ABSTRACT FROM AUTHOR]

In the paper (J Math Soc Jpn 72(1):303–331, 2020), Tse-Chung Yang and the first two current authors computed explicitly the number | SSp 2 (F q) | of isomorphism classes of superspecial abelian surfaces over an arbitrary finite field F q of even degree over the prime field F p . There it was assumed that certain commutative Z p -orders satisfy an étale condition that excludes the primes p = 2 , 3 , 5 . We treat these remaining primes in the present paper, where the computations are more involved because of the ramification. This completes the calculation of | SSp 2 (F q) | in the even degree case. The odd degree case was previous treated by Tse-Chung Yang and the first two current authors in (Doc Math 21:1607–1643, 2016). To complete the proof of our main theorem, we give a classification of lattices over local quaternion Bass orders, which is a new input to our previous works. [ABSTRACT FROM AUTHOR]

In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

Let k 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function on a graph G is a function f: V (G) ! f1; 1; 2g such that P u2N(v) f(u) ≥ k for every v 2 V (G), where N(v) is the neighborhood of v, and each vertex u with f(u) = 1 is adjacent to a vertex v with f(v) = 2 or to two vertices w and z with f(w) = f(z) = 1. A set ff1; f2;: ::; fdg of distinct signed total Italian k-dominating functions on G with the property that Pd i=1 fi(v) ≤ k for each v 2 V (G), is called a signed total Italian k-dominating family (of functions) on G. The maximum number of functions in a signed total Italian k-dominating family on G is the signed total Italian k-domatic number of G, denoted by dk stI (G). In this paper we initiate the study of signed total Italian k-domatic numbers in graphs, and we present sharp bounds for dk stI (G). In addition, we determine the signed total Italian k-domatic number of some graphs. [ABSTRACT FROM AUTHOR]

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 in computer-based testing. In order to understand students' cognitive load when answering algebra questions in a computer-based testing environment, three perspectives, element interactivity, practice effect, and individual differences, were investigated in this study. Seven levels of algebra exam questions were created using unary and simultaneous linear equations, and the inverse efficiency scores were employed as a measure of cognitive load in the study. Forty undergraduate and graduate students were tested. There were four findings: (1) As the element interactivity of test materials increased, the cognitive load increased rapidly. (2) The high-efficiency group had a lower cognitive load than the low-efficiency group, suggesting that the high-efficiency group had an advantage in a computer-based testing environment. (3) "Practice" has a considerable effect on reducing cognitive load, particularly in level 6 and 7 test items. (4) The low-efficiency group can reduce but not eliminate the gap with the high-efficiency group; they may require additional experience in a computer-based testing environment in order to improve reducing their cognitive load. [ABSTRACT FROM AUTHOR]

In this paper, the fast synchronization problem of 5D Hindmarsh-Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh-Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh-Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

A family of Bergman-Morrey type spaces in the unit disc are introduced. The boundedness of the embedding from Bergman-Morrey type spaces to a class of tent spaces is studied. The boundedness, compactness, norm and essential norm of Volterra integral operators on Bergman-Morrey type spaces are also investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate various properties and relations involving some general families of double and multiple Hurwitz-Lerch type zeta functions which are associated with the Srivastava-Daoust class of hypergeometric functions in two and more variables. Relevant connections with other (known or new) results for functions of the analytic number theory are also considered. [ABSTRACT FROM AUTHOR]

We investigate in this paper the isolated points of the approximate point spectrum of a closed linear relation acting on a complex Banach space by using the concepts of quasinilpotent part and the analytic core of a linear relation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Charlier statistical Structures. Sufficient and necessary conditions for the existence of consistent estimators of parameters and sufficient and necessary conditions for the existence of consistent criteria for hypotheses testing are given. [ABSTRACT FROM AUTHOR]

In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

We define a q-linear path in a hypergraph H as a sequence (e1,. . ., eL) of edges of H such that |ei nei+1| [[1, q]] and ei n ej = Ø if |i-j| > 1. In this paper, we study the connected components associated to these paths when q = k - 2 where k is the rank of H. If k = 3 then q = 1 which coincides with the well-known notion of linear path or loose path. We describe the structure of the connected components, using an algorithmic proof which shows that the connected components can be computed in polynomial time. We then mention two consequences of our algorithmic result. The first one is that deciding the winner of the Maker-Breaker game on a hypergraph of rank 3 can be done in polynomial time. The second one is that tractable cases for the NP-complete problem of "Paths Avoiding Forbidden Pairs" in a graph can be deduced from the recognition of a special type of line graph of a hypergraph. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of gossiping with interference constraint in radio ring networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and algorithms that attain this makespan. We focus on the case where the transmission network is a ring network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We also suppose that, during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover communication is subject to interference constraints. We use a primary node interference model where, if a node receives a message from one of its neighbors, its other neighbor cannot send at the same time. With these assumptions we completely solve the problem for ring networks. We first show lower bounds and then give gossiping algorithms which meet these lower bounds and so are optimal. The number of rounds depends on the congruences of n modulo 12. [ABSTRACT FROM AUTHOR]

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher's professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra. [ABSTRACT FROM AUTHOR]

Integral Calculus II is a second-year undergraduate course offered by the Department of Pure and Applied Mathematics at Maseno University. It is one of the 20 foundational courses with a high enrolment of about 800 students drawn from the school of Mathematics, Education, Science, and Business. Because of the large number of enrollments in these foundational courses, and the small number of teaching staff, instructors face challenges in providing immediate personalized feedback that can guide learning. Systems for Teaching and Assessment which use Computer Algebra Kernerl, STACK, a computer-aided assessment plug-in that provides a sophisticated assessment in mathematics-related disciplines, was used to deploy Continuous Assessment Tests (CAT) in the course for 370 students. This paper reports on the findings of the course based on a comparison between student test scores in STACK and in the final course exam. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce an abstract notion of determinant which we call quantum determinant, verifying the properties of the classical one. We introduce R--basis and R--solution on rigid objects of a monoidal Ab--category, for a compatibility relation R, such that we require the notion of duality introduced by Joyal and Street, the notion given by Yetter and Freyd and the classical one, then we show that R--solutions over a semisimple ribbon Ab-category form as well a semisimple ribbon Ab--category. This allows us to define a concept of so-called quantum determinant in ribbon category. Moreover, we establish relations between these and the classical determinants. Some properties of the quantum determinants are exhibited. [ABSTRACT FROM AUTHOR]

Each nominal set X can be equipped with a preorder relation ≤ defined by the notion of support, so-called support-preorder. This preorder also leads us to the support topology on each nominal set. We study support-preordered nominal sets and some of their categorical properties in this paper. We also examine the topological properties of support topology, in particular separation axioms. [ABSTRACT FROM AUTHOR]

Consider ideals I of the form \[ I=(x_1^2,\dots, x_n^2)+\operatorname {RLex}(x_ix_j) \] where \operatorname {RLex}(x_ix_j) is the ideal generated by all the square-free monomials which are greater than or equal to x_ix_j in the reverse lexicographic order. We will determine some interesting properties regarding the shape of the Hilbert series of I. Using a theorem of Lindsey [Proc. Amer. Math. Soc. 139 (2011), no. 1, 79–92], this allows for a short proof that any algebra defined by I has the strong Lefschetz property when the underlying field is of characteristic zero. Building on recent work by Phuong and Tran [Colloq. Math. 173 (2023), no. 1, 1–8], this result is then extended to fields of sufficiently high positive characteristic. As a consequence, this shows that for any possible number of minimal generators for an artinian quadratic ideal there exists such an ideal minimally generated by that many monomials and defining an algebra with the strong Lefschetz property. [ABSTRACT FROM AUTHOR]

Let M be a smooth manifold of dimension m ≤ 1 and P be a G-structure on M, where G is a Lie subgroup of linear group GL(m). In [8], it has been defined the prolongations of G-structures related to tangent functor of higher order and some properties have been established. The aim of this paper is to generalize these prolongations to a Weil bundles. More precisely, we study the prolongations of G-structures on a manifold M, to its Weil bundle TAM (A is a Weil algebra) and we establish some properties. In particular, we characterize the canonical tensor fields induced by the A-prolongation of some classical G-structures. [ABSTRACT FROM AUTHOR]

We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs in two different ways: (1) We represent spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam (2004) [1] and Pfaffian matrix tree theorem by Masbaum and Vaintrob (2002) [15]. • We provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper- Hafnians when orders and signs are not considered. • We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam [Advances in Applied Mathematics (2004) Vol. 33: 51-70] and Pfaffian matrix tree theorem by Masbaum and Vaintrob [Internat. Math. Res. Notices (2002) Vol. 27: 1397-1426]. [ABSTRACT FROM AUTHOR]

The low level of mathematical disposition ability of the students in one of the Junior High Schools in Palembang became a special matter during the field experience. It was found that the average percentage of students' mathematical disposition ability was 53.01% in the moderate category. In addition, there were students who had a view of mathematics as a difficult and unpleasant science. In fact, mathematical disposition has a great influence on students' mathematics learning and achievement. Moreover, it will help students to see the beauty of God's creation through mathematics if they have a good mathematical disposition. This makes the Indonesian Realistic Mathematics Approach (PMRI) an alternative solution to the problem of mathematical disposition. The purpose of writing this thesis was to find out whether the application of PMRI could develop the disposition ability of algebra material and to describe the application of PMRI in developing the mathematical disposition ability of students in algebra material using a descriptive qualitative method. The results and conclusions of this paper show that the students' mathematical disposition ability after the application of PMRI increased with an average percentage result to 61.48% in the good category. The increase was caused by the mathematical disposition indicators that were refined in all PMRI syntax. Thus, these indicators can be refined in any syntax. Reflecting on the application of PMRI, it is suggested that the application can be done more than twice and use physical learning media. BAHASA INDONESIA ABSTRACT: Rendahnya kemampuan disposisi matematis siswa di salah satu SMP di Palembang menjadi perhatian khusus saat dilakukannya praktik pengalaman lapangan. Didapatkan rata-rata persentase kemampuan disposisi matematis siswa berada pada 53,01% dengan kategori cukup. Ditambah lagi terdapat siswa yang memiliki pandangan terhadap matematika sebagai suatu ilmu yang sulit dan tidak menyenangkan. Padahal, disposisi matematis sangat berpengaruh terhadap pembelajaran matematika dan prestasi siswa. Apalagi, dengan baiknya disposisi matematis siswa, maka akan mendukung mereka memandang indahnya ciptaan Tuhan melalui matematika. Hal ini menjadikan Pendekatan Matematika Realistik Indonesia (PMRI) menjadi alternatif solusi terhadap permasalahan disposisi matematis. Tujuan dari penelitian adalah untuk mengetahui apakah penerapan PMRI dapat mengembangkan kemampuan disposisi materi aljabar dan mendeskripsikan penerapan PMRI dalam mengembangkan kemampuan disposisi matematis siswa pada materi aljabar dengan menggunakan metode kualitatif deskriptif. Hasil dan simpulan penulisan ini menunjukkan bahwa kemampuan disposisi matematis siswa setelah PMRI diterapkan mengalami peningkatan dengan rata-rata hasil persentase menjadi 61,48% dengan kategori baik. Hasil persentase yang meningkat ini disebabkan oleh indikator disposisi matematis yang terdapat pada keseluruhan sintaks PMRI. Dengan demikian, indikator-indikator tersebut dapat terasah di setiap sintaks. Berkaca dari penerapan PMRI ini, disarankan agar penerapannya dapat dilakukan lebih dari dua kali dan menggunakan media pembelajaran fisik.

We show that R is regular if Tor_{i}^{R}(R^{+},k) = 0 for some i\geq 1 assuming further that R is a \mathbb {N}-graded ring of dimension 2 finitely generated over an algebraically closed equicharacteristic zero field k. This answers a question of Bhatt, Iyengar, and Ma [Comm. Algebra 47 (2019), pp. 2367–2383]. We use almost mathematics over R^{+} to deduce properties of the noetherian ring R and rational surface singularities. Moreover we observe that R^{+} in equicharacteristic zero has a rich module-theoretic structure; it is m-adically ideal(wise) separated, (weakly) intersection flat, and Ohm-Rush. As an application we show that the hypothesis can be astonishingly vacuous for i \ll dim(R). We show that a positive answer to an old question of Aberbach and Hochster [J. Pure Appl. Algebra 122 (1997), pp. 171–184] also answers this question and we use our techniques to study a question of André and Fiorot [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), pp. 81–114] regarding 'fpqc analogues' of splinters. [ABSTRACT FROM AUTHOR]

We prove that over any perfect field, the plane Cremona group is generated by involutions. [ABSTRACT FROM AUTHOR]

We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras and parameterize their cell modules. We give a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product. [ABSTRACT FROM AUTHOR]

For each n = 1, let Xn,1,.. ., Xn, Nn be real random variables and Sn = PNn i=1 Xn, i. Let mn = 1 be an integer. Suppose (Xn,1, . . ., Xn,Nn) is mn-dependent, E(Xni) = 0, E(X2 ni) < 8 and s2n := E(S2n) > 0 for all n and i. Then, dW Sn sn, Z = 30 c1/3 + 12Un(c/2)1/2 for all n = 1 and c > 0, where dW is Wasserstein distance, Z a standard normal random variable and Un(c) = mn s2n XNn i=1 E h X2 n,i 1 { |Xn,i| > c sn/mn i. Among other things, this estimate of dW Sn/sn, Z yields a similar estimate of dTV (Sn/sn, Z) where dTV is total variation distance. [ABSTRACT FROM AUTHOR]

Extensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A0 of a topological *-algebra A[t] are analyzed. It turns out that their maximal extensions as linear functionals or hermitian linear functionals are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [2] is revisited from this point of view. Examples mostly taken from the theory of integration are discussed. [ABSTRACT FROM AUTHOR]

The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We establish some of the foundations of computational spectral theory through the Solvability Complexity Index (SCI) hierarchy, an approach closely related to Smale’s program on the foundations of computational mathematics and McMullen’s results on polynomial root finding with rational maps. Infinite-dimensional problems yield an intricate infinite classification theory, determining which spectral problems can be solved and with what types of algorithms. We provide answers to many longstanding open questions on the existence of algorithms. For example, we show that spectra can be computed, with error control, from point sampling operator coefficients for large classes of partial differential operators on unbounded domains. Further results include: computing spectra of (possibly unbounded) operators on graphs and separable Hilbert spaces with error control; determining if the spectrum intersects a compact set; the computational spectral gap problem and computing spectral classifications at the bottom of the spectrum; and computing discrete spectra, multiplicities, eigenspaces and determining if the discrete spectrum is non-empty. Moreover, the positive results with error control can be used in computer-assisted proofs. In contrast, the negative results preclude computer-assisted proofs for classes of operators as a whole. Our proofs are constructive, yielding a library of new algorithms and techniques that handle problems that before were out of reach. We demonstrate these algorithms on challenging problems, giving concrete examples of the failure of traditional approaches (e.g., “spectral pollution”) compared to the introduced techniques. [ABSTRACT FROM AUTHOR]

The capability of R to do symbolic mathematics is enhanced by the reticulate and caracas packages. The workhorse behind these packages is the Python computer algebra library SymPy. Via reticulate, the SymPy library can be accessed from within R. This, however, requires some knowledge of SymPy, Python and reticulate. The caracas package, on the other hand, provides access to SymPy (via reticulate) but by using R syntax, and this is the main contribution of caracas. We show examples of how to use the SymPy library from R via reticulate and caracas. Using caracas, we demonstrate how mathematics and statistics can benefit from bridging computer algebra and data via R. The caracas package integrates well with Rmarkdown and Quarto, and as such supports creation of teaching material and scientific reports. As inspiration for teachers, we include ideas for small student projects. [ABSTRACT FROM AUTHOR]

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms. [ABSTRACT FROM AUTHOR]

We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by linear equations. The main example of such are affine invariant submanifolds, that is, closures of SL(2, R)-orbits. We prove that the boundary of any linear subvariety is again given by linear equations in generalized period coordinates of the boundary. Our main technical tool is an asymptotic analysis of periods near the boundary of the moduli space of multi-scale differentials which yields further techniques and results of independent interest. [ABSTRACT FROM AUTHOR]

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 school students. We derive suitable content items as well as educational ideas on how to implement them into mathematics classrooms. We build on frameworks from mathematics education research to design a teaching-learning sequence that enables a beneficial learning trajectory across three units—the result is a coherent teaching concept that encompasses Magmas in a hands-on way. It can be used for either extra-curricular activities or advanced courses in mathematics classes, and can be of benefit for mathematics learners. [ABSTRACT FROM AUTHOR]

This article is devoted to the investigation of infinite B*-matrices and linear operators over normed fields. Their structure is studied in the paper. Ideals and centers of the corresponding to them B*-algebras are scrutinized. [ABSTRACT FROM AUTHOR]

The computational capabilities of computer tools expand the student's search capabilities. Conducting computational experiments in the classroom is no longer an organizational problem. This raises the "black box" problem, when the student perceives the computational module as a magician's box and loses conceptual control over the computational process. This article analyses the use of various computer tools, both existing and specially created for "key" computational experiments, that aim at revealing the essential aspects of the introduced concepts using specific examples. This article deals with a number of topics of algebra and calculus that are transitional from school to university, and it shows how computational experiments in the form of a "transparent" box can be used. [ABSTRACT FROM AUTHOR]