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The irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology. Given a monomial ideal I of a polynomial ring S = k [ x ] over a field k and variables x = { x 1 , ... , x n } , its incidence matrix, is the matrix whose rows are indexed by the variables x and whose columns are indexed by its minimal generators. The main contribution of this paper is the introduction of a novel invariant of a monomial ideal I , termed its signature, which could be thought of as a type of canonical form of its incidence matrix, and the proof that two monomial ideals with the same signature have essentially the same irreducible decomposition. [ABSTRACT FROM AUTHOR]

This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (Comm. Contemp. Math. , 19 (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of a model called the (2 + 1) q -deformed tanh-Gordon model. This model is particularly useful for studying physical systems with violated symmetries, as it provides insights into their behavior. To solve the (2 + 1) q -deformed equation for specific parameter values, the (H + G ′ G 2) -expansion approach is employed. This technique generates analytical solutions that reveal valuable information about the system's dynamics and behavior. These solutions offer insights into the underlying mathematics and deepen the understanding of the system's properties. To validate the accuracy of the analytical solutions, the finite difference technique is also used to find a numerical solution to the q -deformed equation. This numerical approach ensures the correctness of the solutions and enhances the reliability of the results. Tables and graphics are presented in the publication to aid comprehension and comparison. These visuals improve the clarity and interpretability of the data, allowing readers to better understand the similarities and differences between the analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

In the paper, we consider a system of thermoelasticity of type I with viscoelastic damping and nonlinear sources. By using the Galerkin method and the Banach fixed point theorem, we first prove the local existence and uniqueness of weak solution. Secondly, by extending the potential well method, we prove that the local solution exists globally if its initial position starts inside a family of "potential wells." In particular, we also establish an explicit and optimal decay rate of energy driven by the decay rate of the relaxation function which includes exponential, algebraic, and logarithmic decay rates. Finally, by using the continuation theorem and the concavity arguments due to Levine (Trans Am Math Soc 192:1–21, 1974), we show that the local solution blows up at finite time in the sense of Ball (Q J Math Oxf 28(4): 473–486, 1977) if its initial position starts outside the "potential wells." Further, an upper bound for the blow-up time is also given explicitly. Notice that our results imply a sharp result on the global existence and blow-up of the local weak solution and they also allow a relatively large class of relaxation functions that generalize the existing results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple mathematical arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit p → ∞ ; standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic p is more general than standard quantum theory because the latter is a degenerate case of the former in the formal limit p → ∞ . [ABSTRACT FROM AUTHOR]

In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a C^2 open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for Riemannian metrics. This follows from a recent result of Contreras and Mazzucchelli [Duke Math. J. 173 (2024), pp. 347–390]. Furthermore, geodesic flows of Riemannian or Finsler metrics on surfaces are C^2 stably ergodic if and only if they are Anosov. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a two-species reaction–diffusion competition model with Gompertz growth, where the intrinsic growth rates and carrying capacities of environments are heterogeneous. At firstly, assuming two competing species only admit different diffusive rates, we show that 'slower diffuser prevails', which is consistent with the well-known result in Dockery J, Hutson V, Mischaikow K, Pernarowski M. [The evolution of slow dispersal rates: a reaction–diffusion model. J Math Biol. 1998;37(1):61–83; Hastings A. Can spatial variation alone lead to selection for dispersal? Theor Popul Biol. 1983;24:244–251]. Then, for the "weak competition" case, we establish a prior estimate, which combined with the theory of monotone dynamical system and spectral analysis implies that the model admits a unique coexistence steady state, which is globally asymptotically stable. Finally, for the "strong–weak competition" case, we give the expression of critical competition intensity and the weak competitor will be wiped out. [ABSTRACT FROM AUTHOR]

This paper introduces a novel classification method for multi-class multi-label datasets, named multi-class multi-label logistic model tree (MMLMT). Our approach supports multi-label learning to predict multiple class labels simultaneously, thereby enhancing the model's capacity to capture complex relationships within the data. The primary goal is to improve the accuracy of classification tasks involving multiple classes and labels. MMLMT integrates the logistic regression (LR) and decision tree (DT) algorithms, yielding interpretable models with high predictive performance. By combining the strengths of LR and DT, our method offers a flexible and powerful framework for handling multi-class multi-label data. Extensive experiments demonstrated the effectiveness of MMLMT across a range of well-known datasets with an average accuracy of 85.90%. Furthermore, our method achieved an average of 9.87% improvement compared to the results of state-of-the-art studies in the literature. These results highlight MMLMT's potential as a valuable approach to multi-label learning. [ABSTRACT FROM AUTHOR]

Recently, W. Berndt and S. Sra (Hlawka-Popoviciu inequalities on positive definite tensors. Linear Algebra Appl. 2015;486:317–327) proved a Popoviciu type inequality for any arbitrary finite number of positive definite matrices. In this paper, we proved a quantitative Popoviciu type inequality for four positive semi-definite matrices, which is stronger than Berndt-Sra's corresponding result and also a generalization of Hong-Qi's (Refinements of two determinantal inequalities for positive semidefinite matrices. Math Inequal Appl. 2022;25(3):673–678) result. As applications, we partially recovered our early result in F. Wang (A quantitative Popoviciu type inequality, submitted.] and obtained a quantitative Hartfiel inequality. [ABSTRACT FROM AUTHOR]

In this paper, the existence and the uniqueness of an evolutionary anisotropic $ p_i(x) $ p i (x) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the $ L^{\infty } $ L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the $ L^{\infty } $ L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic $ p(x)- $ p (x) − Laplace equation with convection term via $ L^{\infty }- $ L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc. [ABSTRACT FROM AUTHOR]

This research paper delves into the profound interplay between mathematics and visual art, revealing a fundamental correlation rooted in the concept of order. By examining historical periods, particularly the Renaissance and Enlightenment, we illuminate how mathematics catalyzed intellectual and cultural transformations. The Renaissance witnessed a revival of ancient mathematical knowledge, intertwining with the prevailing humanist philosophy. Artists of this era employed mathematical principles, such as perspective and proportion, to bridge the abstract and tangible. In the Enlightenment, mathematical innovation was driven by a commitment to rationality and empirical evidence, mirroring the era's quest for universal truths. Engaging with theoretical and historical literature, we decode the intricate threads connecting mathematics to the pulse of human knowledge and progress. [ABSTRACT FROM AUTHOR]

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The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

The paper aims to propose a two-step iterated method, which is derived from a regularized dynamical system of extragradient-type in terms of time discretizing, for solving an equilibrium problem. We prove that the iterative sequence generated by the method converges strongly to a solution of the equilibrium problem. Some numerical experiments are given to illustrate and compare the behavior of the new method with several other methods. [ABSTRACT FROM AUTHOR]

This paper investigates numerical solutions of pseudomontone variational inequality problems in real Hilbert spaces. Two new algorithms based on the celebrated extragradient method are introduced. Under suitable conditions, it is proved that the two algorithms achieve weak convergence and linear convergence rates. The results extend and improve upon related works in the literature on the associated extragradient algorithms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of solutions of set-valued quasiequilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

The matrix square root is widely encountered in many fields of mathematics. In this paper, based on the properties of M-matrix and quadratic matrix equations, we study the square root of M-matrix, and prove that for a regular M-matrix there always exists a regular M-matrix as its square root. In addition, a structure-preserving doubling algorithm is proposed to compute the square root. Theoretical analysis and numerical experiments are given to show that our method is feasible and is effective under certain conditions. [ABSTRACT FROM AUTHOR]

Nexus Network Journal guest editor Roberta Spallone introduces papers selected from the Nexus Conference 2023 in Turin for detailed review, expansion and development. These papers identify close links between architecture, mathematics, and specific areas of interest related to historical periods, architectural cultures, typological elements, and analysis tools. [ABSTRACT FROM AUTHOR]

As a quantum affinization, the quantum toroidal algebra U q , q ¯ (gl ¨ n) is defined in terms of its "left" and "right" halves, which both admit shuffle algebra presentations (Enriquez in Transform Groups 5(2):111–120, 2000; Feigin and Odesskii in Am Math Soc Transl Ser 2:185, 1998). In the present paper, we take an orthogonal viewpoint, and give shuffle algebra presentations for the "top" and "bottom" halves instead, starting from the evaluation representation U q (gl ˙ n) ↷ C n (z) and its usual R-matrix R (z) ∈ End (C n ⊗ C n) (z) (see Faddeev et al. in Leningrad Math J 1:193–226, 1990). An upshot of this construction is a new topological coproduct on U q , q ¯ (gl ¨ n) which extends the Drinfeld–Jimbo coproduct on the horizontal subalgebra U q (gl ˙ n) ⊂ U q , q ¯ (gl ¨ n) . [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for a class of coupled system of the four-dimensional cubic focusing nonlinear Schrödinger equations was investigated. By exploiting the double Duhamel method and the long-time Strichartz estimate, the global well-posedness and scattering were proven for the system below the ground state. In our proof, we first established the variational characterization of the ground state, and obtained the threshold of the global well-posedness and scattering. Second, we showed that the non-scattering is equivalent to the existence of an almost periodic solution by following the concentration-compactness/rigidity arguments of Kenig and Merle [17] (Invent. Math., 166 (2006), 645–675). Then, we obtained the global well-posedness and scattering below the threshold by excluding the almost periodic solution. [ABSTRACT FROM AUTHOR]

This paper is devoted to dealing with a kind of new Kirchhoff-type problem in RN that involves a general double-phase variable exponent elliptic operator ϕ. Specifically, the operator ϕ has behaviors like |τ|q(x)−2 τ if |τ| is small and like |τ| p(x)−2 τ if |τ| is large, where 1 < p(x) < q(x) < N. By applying some new analytical tricks, we first establish existence results of solutions for this kind of Kirchhoff-double-phase problem based on variational methods and critical point theory. In particular, we also replace the classical Ambrosetti–Rabinowitz type condition with four different superlinear conditions and weaken some of the assumptions in the previous related works. Our results generalize and improve the ones in [Q. H. Zhang, V. D. Rădulescu, J. Math. Pures Appl., 118 (2018), 159–203.] and other related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new family of the generalized k-Leonardo numbers and study their properties. We investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. We obtain combinatorial identities like Binet formula, Cassini’s identity, partial sum, etc. in the closed form. Moreover, we give various generating and exponential generating functions. [ABSTRACT FROM AUTHOR]

A signed graph (G, σ) is called a parity signed graph if there exists a bijective mapping f : V (G) → {1, . . ., |V (G)|} such that for each edge uv in G, f(u) and f(v) have same parity if σ(uv) = +1, and opposite parity if σ(uv) = −1. The rna number σ−(G) of G is the least number of negative edges among all possible parity signed graphs over G. Equivalently, σ−(G) is the least size of an edge-cut of G that has nearly equal sides. In this paper, we show that for the generalized Petersen graph Pn,k, σ−(Pn,k) lies between 3 and n. Moreover, we determine the exact value of σ−(Pn,k) for k ∈ {1, 2}. The rna numbers of some famous generalized Petersen graphs, namely, Petersen graph, Dürer graph, Möbius-Kantor graph, Dodecahedron, Desargues graph and Nauru graph are also computed. Recently, Acharya, Kureethara and Zaslavsky characterized the structure of those graphs whose rna number is 1. We use this characterization to show that the smallest order of a (4n + 1)-regular graph having rna number 1 is 8n + 6. We also prove the smallest order of (4n − 1)-regular graphs having rna number 1 is bounded above by 12n − 2. In particular, we show that the smallest order of a cubic graph having rna number 1 is 10. [ABSTRACT FROM AUTHOR]

Following the increasing impacts on the value of Western play-based pedagogy, early childhood (EC) teachers in China face developmental challenges related to understanding and implementing play-based mathematical education. The purpose of this paper is to explore Chinese EC teachers' perspectives on play-based mathematics teaching. In this qualitative study, semi-structured interviews and lesson plans are collected from six EC teachers in a Chinese kindergarten. Hedegaard's model is applied to frame analysis for capturing EC teachers' views and practices from a holistic perspective. The findings show that all six EC teachers valued play as a pedagogical tool for teaching mathematics, while their pedagogical decisions in applying play to children's mathematics are determined by the various demands from society, parents and children. The multiple demands from different perspectives result in challenges for teachers in designing collective play. This study revealed that only when play activity caters to the possibility of satisfying those demands can teachers pedagogically implement play for children's mathematical learning. The insights emerging from this study might address the pragmatic challenges that teachers face by enhancing teachers' professional development to support the advance of culturally sensitive play-based mathematics teaching in China. [ABSTRACT FROM AUTHOR]

This paper addresses the long-standing question of the predicativity of the Mahlo universe. A solution, called the extended predicative Mahlo universe, has been proposed by Kahle and Setzer in the context of explicit mathematics. It makes use of the collection of untyped terms (denoting partial functions) which are directly available in explicit mathematics but not in Martin-Löf type theory. In this paper, we overcome the obstacle of not having direct access to untyped terms in Martin-Löf type theory by formalizing explicit mathematics with an extended predicative Mahlo universe in Martin-Löf type theory with certain indexed inductive-recursive definitions. In this way, we can relate the predicativity question to the fundamental semantics of Martin-Löf type theory in terms of computation to canonical form. As a result, we get the first extended predicative definition of a Mahlo universe in Martin-Löf type theory. To this end, we first define an external variant of Kahle and Setzer's internal extended predicative universe in explicit mathematics. This is then formalized in Martin-Löf type theory, where it becomes an internal extended predicative Mahlo universe. Although we make use of indexed inductive-recursive definitions that go beyond the type theory |$\mathbf {IIRD}$| of indexed inductive-recursive definitions defined in previous work by the authors, we argue that they are constructive and predicative in Martin-Löf's sense. The model construction has been type-checked in the proof assistant Agda. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spreading behavior of a two-species strong-weak competition system with two free boundaries. The model may describe how a strong competing species invades into the habitat of a native weak competing species. The asymptotic spreading speed of invading fronts has been determined by making use of semi-wave systems in Du et al. (J Math Pures Appl 107:253–287, 2017). Here we give a sharp estimate for the asymptotic spreading speed of invading fronts. Moreover, we prove that the solution of the free boundary problem evolves eventually into a semi-wave solution when the spreading happens, while the solution of the free boundary problem exponentially converges to a semi-trivial solution of such system when the vanishing happens. [ABSTRACT FROM AUTHOR]

In the present paper, we establish an infinite dimensional Kolmogorov–Arnold–Moser (KAM) theorem for reversible systems with double normal frequencies. Applying it, we prove the existence of quasi-periodic solutions for one dimensional coupled nonlinear quantum harmonic oscillators (QHO) with a natural reversible structure. To compensate the lack of smoothing effect of perturbation, we introduce a class of vector fields with polynomial decay which extends the works of Grébert and Thomann (Commun Math Phys 307(2):383–427, 2011) for Hamiltonian QHO. To deal with the reversible, coupled perturbations in the equations, we also introduce a new class of generating vector fields during the KAM iteration. Moreover, the quasi-periodic solutions we obtain may not be linearly stable. This is obviously different from the result in Grébert and Thomann (2011) for Hamiltonian QHO. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness problems of fn(z)L(g) and gn(z)L(f) when they share a non-zero small function α(z) with finite weights, where L(h) represents any one of h(k)(z), h(z + c), h(z + c) - h(z) and h(k)(z + c), k ≥ 1 and c is a non-zero constant. Here f(z) and g(z) are transcendental meromorphic (or entire) functions and α(z) is a small function with respect to both f(z) and g(z). Our results improve and supplement the recent results due to Gao and Liu [Bull. Korean Math. Soc. 59 (2022), 155-166]. [ABSTRACT FROM AUTHOR]

In this paper, we define the zero-divisor graph of a meethyperlattice with respect to a hyperideal. We prove the diameter of a P-hyperlattice and Nakano hyperlattice are at most 3 and 4 respectively. We obtain that the zero-divisor graph with respect to the intersection of two prime hyperideals is complete bipartite. We prove certain properties of these zero-divisor graphs with suitable examples. [ABSTRACT FROM AUTHOR]

This paper focuses on establishing boundedness properties and Parseval–Goldstein-type relations for the generalized Mehler–Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math., 18(3):235–287, 1967). Also, we derive an inversion formula for this transform over Lebesgue spaces. [ABSTRACT FROM AUTHOR]

This paper concerns the bubbling phenomena for the L2$L^2$‐critical half‐wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow‐up solutions concentrating exactly at these singularities. This provides the first examples of multi‐bubble solutions for the half‐wave equation. In particular, the solutions exhibit the mass quantization property. Our proof strategy draws upon the modulation method in Krieger, Lenzmann and Raphaël [Arch. Ration. Mech. Anal. 209 (2013), no. 1, 61–129] for the single‐bubble case, and explores the localization techniques in Cao, Su and Zhang [Arch. Ration. Mech. Anal. 247 (2023), no. 1, Paper No. 4] and Röckner, Su and Zhang [Trans. Amer. Math. Soc., 377 (2024), no. 1, 517–588] for bubbling solutions to non‐linear Schrödinger equations (NLS). However, unlike the single‐bubble or NLS cases, different bubbles exhibit the strongest interactions in dimension one. In order to get sharp estimates to control these interactions, as well as non‐local effects on localization functions, we utilize the Carlderón estimate and the integration representation formula of the half‐wave operator, and find that there exists a narrow room between the orders |t|2+$|t|^{2+}$ and |t|3−$|t|^{3-}$ for the remainder in the geometrical decomposition. Based on this, a novel bootstrap scheme is introduced to address the multi‐bubble non‐local structure. [ABSTRACT FROM AUTHOR]

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. However, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this article, I focus on Macdonald's provocative 1953 paper, "Linguistic Philosophy and Perception," in which she argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. First, it reveals just how far Macdonald's metaphilosophical views diverged from those of many of her contemporaries. Second, the discussion in her article preempts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald's paper is just as likely to provoke discussion today as it was in the 1950s. [ABSTRACT FROM AUTHOR]

Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely P ∗ (n) , M (n) , T ∗ (n) , L (n) , K (n) , A (n) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo 2 a · 5 ℓ for P ∗ (n) , modulo 2 3 for M(n) and T ∗ (n) , where a = 3 , 4 and ℓ ≥ 1 . For instance, we prove that for n ≥ 0 , P ∗ (5 ℓ (4 n + 3) + 5 ℓ - 1) ≡ 0 (mod 2 3 · 5 ℓ). In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: M (5 n + 4) ≡ 0 (mod 5) , T ∗ (5 n + 3) ≡ 0 (mod 5). [ABSTRACT FROM AUTHOR]

The relative advantages and disadvantages of sum scores and estimated factor scores are issues of concern for substantive research in psychology. Recently, while championing estimated factor scores over sum scores, McNeish offered a trenchant rejoinder to an article by Widaman and Revelle, which had critiqued an earlier paper by McNeish and Wolf. In the recent contribution, McNeish misrepresented a number of claims by Widaman and Revelle, rendering moot his criticisms of Widaman and Revelle. Notably, McNeish chose to avoid confronting a key strength of sum scores stressed by Widaman and Revelle—the greater comparability of results across studies if sum scores are used. Instead, McNeish pivoted to present a host of simulation studies to identify relative strengths of estimated factor scores. Here, we review our prior claims and, in the process, deflect purported criticisms by McNeish. We discuss briefly issues related to simulated data and empirical data that provide evidence of strengths of each type of score. In doing so, we identified a second strength of sum scores: superior cross-validation of results across independent samples of empirical data, at least for samples of moderate size. We close with consideration of four general issues concerning sum scores and estimated factor scores that highlight the contrasts between positions offered by McNeish and by us, issues of importance when pursuing applied research in our field. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping (- Δ) 2 θ v t with θ ∈ [ 1 2 , 1 ] . By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and θ ∈ [ 1 2 , 3 4 ] , the polynomial decay rate of the system is t - 1 / (10 - 4 θ) . When the inertia/elasticity ratios are not equal and θ ∈ [ 3 4 , 1 ] , the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent 2 θ from [0, 1] to [1, 2]. [ABSTRACT FROM AUTHOR]

We continue the program first initiated by Laptev, Schimmer, and Takhtajan [Geom. Funct. Anal. 26 (2016), pp. 288–305] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting functions, of functional difference operators H_0 = \mathcal {F}^{-1} M_{\cosh (\xi)} \mathcal {F} with potentials of the form W(x) = \left \lvert {x} \right \rvert ^pe^{\left \lvert {x} \right \rvert ^\beta } for either \beta = 0 and p > 0 or \beta \in (0, 2] and p \geq 0. We provide a new method for studying general potentials which includes the potentials studied by Laptev, Schimmer, and Takhtajan [Geom. Funct. Anal. 26 (2016), pp. 288–305] and [J. Math. Phys. 60 (2019), p. 103505]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics. [ABSTRACT FROM AUTHOR]

In this paper, we study long time behavior of solution to the quantum Zakharov system in two dimensions. We construct a small global solution to the quantum Zakharov system which scatters to a given free solution by using space-time resonance method developed by Gustafson-Nakanishi-Tsai [Commun. Contemp. Math. 11 (2009), pp. 657–707] and Germain-Masmoudi-Shatah [Int. Math. Res. Not. IMRN 3 (2009), 414–432; J. Math. Pures Appl. (9) 97 (2012), pp. 505–543] etc. [ABSTRACT FROM AUTHOR]

Integrating socioscientific issues (SSI) into education is gaining widespread adoption in classrooms due to its positive impact on student's critical thinking, environmental awareness, holistic knowledge and/or the idea of combining science and mathematics. This paper explores the idea of using comics as appropriate media for elementary school students to engage with SSI content. Because of the difficulties in integrating SSI into classrooms, SSI-based learning is more commonly applied in high school and higher education settings, with limited implementation in earlier education. To answer this gap, we developed comics that have SSI content for elementary schools. Comics are chosen as reliable tools for visualising and simplifying complex concepts and making SSI content more accessible and engaging. This paper describes our comics on earthquake-related issues in Indonesia and the principles that guided its design. SSI inherently involves multiple perspectives, so the integration brings together science, and mathematics within the one comic. In integrating different disciplines of comic content, we utilised the rule-of-five framework, widely employed to merge five representational models (experiential, verbal, numerical, visual, and symbolic) commonly used in developing content combining two or more different academic disciplines. [ABSTRACT FROM AUTHOR]

Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

Purpose - The language load within mathematics test items can lead to inaccuracy in assessing Orang Asli pupils' mathematical ability due to their struggle in comprehending the academic language. This study aims to determine the validity of using test accommodations in the form of oral academic language and oral native language when administering mathematics computation and word problem test items among the Orang Asli pupils. Methodology - By employing a quantitative approach, this study utilised random equivalent group design to examine the validity of using oral test accommodations among 334 Grade Four Orang Asli pupils. Three testlets were constructed and used in this study: written test in the academic language (WAL), oral test in the academic language (OAL), and oral test in the native language (ONL). The three testlets comprised Paper 1 and Paper 2, each consisting of 20 mathematics computation and 20-word problem test items, respectively. One-way ANOVA was used to analyse and examine if there were differences in the mathematics performance between the three groups of tests administered to the Orang Asli pupils. Findings - The results indicated that the test scores of the pupils on the oral tests were higher compared to the written test administered to the pupils for both mathematics computation and word problem items. For computation items, the pupils performed better in the OAL testlet, followed by the ONL testlet. On the other hand, the pupils obtained the highest test scores in the ONL testlet compared to the OAL testlet for word problem items. Furthermore, the results illustrate that there is a difference in the mathematics performance of the Orang Asli pupils between the oral tests in both languages and written tests in the academic language. Significant - This study clearly shows that language plays a prominent role in affecting the Orang Asli pupils' mathematics performance. By utilising the oral test as a promising test accommodation, this measure could help address the language barrier faced by the Orang Asli pupils in mathematics testing. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the cyclic-Fibonacci hybrid sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid sequence modulo m, the method will be given to determine the period lengths of this sequence according to the different m values. In the final part of this paper, we study the cyclic-Fibonacci hybrid sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups (2; 2; 2), (2; n; 2) and (n; 2; 2) as applications of the results produced. [ABSTRACT FROM AUTHOR]

The paper dwells on the contributions of APOS theory to the development of teaching and learning of mathematics in school. APOS is an acronym for action, process, object, and schema. The theory emerges as an extension to constructivism but with a more focused and robust learner-centered approach to the teaching and learning of mathematics. Proponents of the theory believed that learning occurs initially as an action or activity in learners' cognitive settings, independent of learners' environment, triggered by cognitive coherence, then it is transformed to process, where learner now waits for internalization of the earlier activity, preparatory to the occurrence of learning. At object level, learner now considers what has been learnt earlier to have been fully internalized into mathematical object(s). Lastly, at schema level, the object learnt is assumed to have been embedded in the learners' schema-a cognitive structure formed as a result of accumulated learning experience, and a complete mental image of what has been learnt is said to have been formed. Against the backdrop of this, the paper looks at how this theory had changed the narrative about teaching and learning of mathematics vis-à-vis the bearing of the theory to other cognitive abilities of the learner such as intelligence and creativity. In the end, the paper suggests the application of APOS theory in teaching and learning mathematics at all levels of learning in Nigeria and beyond. [ABSTRACT FROM AUTHOR]

A binary operation # on Z + is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y −1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played in my mathematical life. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a new class of noncyclic φ-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp'ınola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic φ-contractions as a consequence of our main theorems. [ABSTRACT FROM AUTHOR]

The article deals with the results of mathematics examinations at the University of Finance and Administration in Prague before, during, and immediately after the Covid-19 pandemicrelated restrictions. The first objective is to evaluate whether the non-standard forms of testing (correspondence and online), used on an emergency basis during the pandemic, were adequate compared to the standard form (face-to-face) applied before the pandemic. The second objective is to assess whether and to what extent the results of the examinations have changed after the return of teaching and testing methods to normal. It turns out that the use of non-standard forms, although more challenging for teachers to control, did not lead to better results – the results in the correspondence form were similar to the standard form and even worse in the online form. The results of examinations administered in the standard form after the return to normal teaching were significantly better than in any of the periods studied, including the standard form of examination before the pandemic. Possible reasons for the results are analysed in the paper. [ABSTRACT FROM AUTHOR]

Because the classical art of memory was part of rhetoric, Latin authors did not develop detailed techniques for memorizing numbers. During the Renaissance, some methods for memorizing numerical data were added to the ars memoriae, partly due to the growing readership of memory treatises among merchants. However, the memorization of numerical data remained a marginal topic in memory manuals, and the available techniques were cumbersome when dealing with multiple long numbers. As numerical thinking became prevalent in the “outillage mental” of the time, a specific mnemonic technique was devised in the 17th century. By converting numbers into consonants and then forming words by adding vowels, mnemonists could employ mental images to represent these words and effectively memorize the corresponding numbers. This paper aims to trace the spread of this new technique from France to the Holy Roman Empire and, in the 18th century, to England. Additionally, it will show how new fields of knowledge were incorporated into treatises of the 17th and 18th centuries. Thus, this paper will shed light on how the Scientific Revolution led to the development of new mnemonics by practitioners with sociological backgrounds different from those of Renaissance humanists and orators. [ABSTRACT FROM AUTHOR]

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for the developmental sequence of mathematical drawings and the progression of children's strategies for multiplicative situations were an interpretive lens through which to analyse the drawings. Children used pictographic and iconic drawing types to represent the "story" in the problem and the multiplicative strategies employed to solve the tasks. Exploration of the children's drawings suggested that as children's drawings become more structural, schematic in nature, it may be easier for children to show their understanding of the structural elements of multiplicative relationships. Results revealed that structural elements of multiplicative relationships were more easily seen in iconic representations; however, both pictographic and iconic drawings were useful to observe counting, additive, and multiplicative strategies when mathematical elements of the problem were visible. Additional representations attached to the drawings (e.g. numerical) were needed to confirm children's strategies when their drawings lacked structure. These findings have implications for how young children's drawings are interpreted by classroom teachers. The interpretation of these drawings suggested that some children may not yet realise how their drawings in mathematics need to shift from illustrations of the problem's story context to representing mathematical ideas and processes — which requires intentional teaching of the purpose of drawings for mathematical contexts. [ABSTRACT FROM AUTHOR]

This article introduces some efficient generalized class of factor-type exponential imputation techniques and their corresponding estimators using auxiliary information. Generalized ratio, product, and dual to ratio type exponential estimators are the special cases of our suggested imputation techniques. Biases and mean squared error expressions are derived up to the first order of large sample approximations. The proposed imputation techniques can be viewed as efficient extensions of the work of Singh and Horn [Compromised imputation in survey sampling. Metrika. 2000;51(3):267–276. doi: 10.1007/s001840000054], Singh and Deo [Imputation by power transformation. Statist Papers. 2003;44(4):555–579. doi: 10.1007/BF02926010], Toutenburg and Srivastava [Amputation versus imputation of missing values through ratio method in sample surveys. Statist Papers. 2008;49(2):237–247. doi: 10.1007/s00362-006-0009-4], Kadilar and Cingi [Estimators for the population mean in the case of missing data. Commun Stat Theory Methods. 2008;37(14):2226–2236. doi: 10.1080/03610920701855020], Singh [A new method of imputation in survey sampling. Statistics. 2009;43(5):499–511. doi: 10.1080/02331880802605114], Gira [Estimation of population mean with a new imputation methods. Appl Math Sci. 2015;9(34):1663–1672] and Singh et al. [An improved alternative method of imputation for missing data in survey sampling. J Stat Appl Probab. 2022;11(2):535–543. doi: 10.18576/jsap]. Our proposed estimators are compared with these estimators, including the mean, ratio, and regression imputation techniques. Thereafter, a numerical illustration and simulation study are conducted for a comparative study using real and simulated data sets, and the demonstration shows that our suggested estimators are the most efficient estimators. [ABSTRACT FROM AUTHOR]

Gender disparity in science and mathematics performance is being researched internationally. In a complex education system, like Pakistan, studying the difference in isolation may not generate holistic understanding. Therefore, this paper investigates changes in trends of performance in Science and Mathematics for both genders across public and private schools. Data were gathered from a nationwide sample of elementary grades students (n=15,391) using SATs/MATS. Independent t-test and two-way-ANOVA were employed to analyse data. Results revealed that girls outperformed boys in Science (p<0.01) while no gender differences in performance were observed in Mathematics. Gender and school systems demonstrated significant interaction effect only in mathematics, unveiling that girls perform better in public schools while this difference diminished in the private school system. The results show implications for employing gender-fair policies and practices in science and mathematics education. [ABSTRACT FROM AUTHOR]