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The International Sirius Mathematics Center, located on the Black Sea coast, was founded in 2019 by the Talent and Success Foundation for organizing mathematical conferences and other events promoting the development of mathematics in Russia. In 2024, the Center has acquired its own Russian-language journal for publication of original research papers by participants of conferences held at the Center. The authors are invited to submit papers to the journal at https://ef.msp.org/submit/sirius [ABSTRACT FROM AUTHOR]

Example-generation tasks have been suggested as an effective way to both promote students’ learning of mathematics and assess students’ understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we investigate students’ responses to a particular sequence of example-generation tasks, posed either on paper or through e-assessment. We identify a striking difference in students’ example-generation strategies and success, for e-assessment and paper-based versions of the same tasks. This suggests the use of example-generation tasks in e-assessment may not be straightforward, and we conclude by discussing the implications for teaching and research. [ABSTRACT FROM AUTHOR]

Comparative studies on paper and pencil– and computer-based tests principally focus on statistical analysis of students' performances. In educational assessment, comparing students' performance (in terms of right or wrong results) does not imply a comparison of problem-solving processes followed by students. In this paper, we present a theoretical tool for task analysis that allows us to highlight how students' problem-solving processes could change in switching from paper to computer format and how these changes could be affected by the use of one environment rather than another. In particular, the aim of our study lies in identifying a set of indexes to highlight possible consequences that specific changes in task formulation have, in terms of task comparability. Therefore, we propose an example of the use of the tool for comparing paper-based and computer-based tasks. [ABSTRACT FROM AUTHOR]

This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches. [ABSTRACT FROM AUTHOR]

This letter from the editors introduces Vol. 24(3) of the Nexus Network Journal, which is the second special issue of selected papers from the Nexus 20/21 conference. The papers in this issue are categorised into four themes: (i) spatial distortion and perception, (ii) computational design methods, (iii) design concepts in historical examples and (iv) stereotomy, vaults and domes. In addition, papers in the Didactics section of the journal are dedicated to research about pedagogical advances which connect architecture and mathematics. [ABSTRACT FROM AUTHOR]

The paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education. [ABSTRACT FROM AUTHOR]

Nexus 2018, the 12th international, interdisciplinary conference for architecture and mathematics, took place in Pisa in June 2018. From among the 43 presentations, 12 papers were selected for publication in the Nexus Network Journal. In what follows the conference directors the papers that make up vol. 22, no. 1 (2020). [ABSTRACT FROM AUTHOR]

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation. [ABSTRACT FROM AUTHOR]

This letter from the editor presents Vol. 25(2) of the Nexus Network Journal. This issue has two connected themes, the first is about the role of regular modules, patterns, or proportions in architecture, and the second, the ways rules or systems underpin architectural form. The papers in this issue address either regularity, rules, or in most cases, both, because spatial and formal patterns are typically derived from rules. Collectively, the eleven research contributions in this issue have topics that span chronologically from the thirteenth century to the present day, and geographically from Asia to Africa and Europe. [ABSTRACT FROM AUTHOR]

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685-696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536-546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives. [ABSTRACT FROM AUTHOR]

Invites authors to submit papers for a special issue of “Journal of Mathematics Teacher Education” on the nature and role of tasks in mathematics teachers' education.

In this survey paper, we describe the state of the field of research on teaching mathematics with technology with an emphasis on the secondary school phase. We synthesize themes, questions, results and perspectives emphasized in the articles that appear in this issue alongside the relevant foundations of these ideas within the key journal articles, handbooks and conference papers. Our aim is to give an overview of the field that provides opportunities for readers to gain deeper insights into theoretical, methodological, practical and societal challenges that concern teaching mathematics with technology in its broadest sense. Although this collection of articles was developed prior to the global coronavirus pandemic, we have taken the opportunity to survey the contributing authors to provide some country perspectives on the impact the pandemic has had on mathematics teaching with technology in the period January–July 2020. We conclude the survey paper by identifying some areas for future research in this increasingly relevant topic. [ABSTRACT FROM AUTHOR]

In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565-577 ) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors. [ABSTRACT FROM AUTHOR]

In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ and $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ in the cyclotomic field ℚ(ζ n), 2 ∤ n, for a ∈ ℤ, ( a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]

Presents several Origami-based mathematical problems. Application of the activity of paper folding in solving math puzzles using the angles, geometric shapes and creases of the paper; Construction of paper shapes based on mathematical rules and parameters provided by the puzzle.

The article presents papers of the "Czech-Taiwanese Workshop on the Intermediate- and High-Energy Physics," that was held in Prague, Czech Republic from March 3-5, 2003, organized by Academy of Sciences of the Czech Republic, National Science Council of Taiwan, Czech Physical Society (Section of the Union of Czech Mathematicians and Physicists) and Physical Society of the Republic of China (Taiwan).

This paper illustrates how years 1 and 2 students were guided to engage in data modelling and statistical reasoning through interdisciplinary mathematics and science investigations drawn from an Australian 3-year longitudinal study: Interdisciplinary Mathematics and Science Learning (https://imslearning.org/). The project developed learning sequences for 12 inquiry-based investigations involving 35 teachers and cohorts of between 25 and 70 students across years 1 through 6. The research used a design-based methodology to develop, implement, and refine a 4-stage pedagogical cycle based on students' problem posing, data generation, organisation, interpretation, and reasoning about data. Across the stages of the IMS cycle, students generated increasingly sophisticated representations of data and made decisions about whether these supported their explanations, claims about, and solutions to scientific problems. The teacher's role in supporting students' statistical reasoning was analysed across two learning sequences: Ecology in year 1 and Paper Helicopters in year 2 involving the same cohort of students. An explicit focus on data modelling and meta-representational practices enabled the year 1 students to form statistical ideas, such as distribution, sampling, and aggregation, and to construct a range of data representations. In year 2, students engaged in tasks that focused on ordering and aggregating data, measures of central tendency, inferential reasoning, and, in some cases, informal ideas of variability. The study explores how a representation-focused interdisciplinary pedagogy can support the development of data modelling and statistical thinking from an early age. [ABSTRACT FROM AUTHOR]

In K-12 education, Computational Thinking (CT) has been a trendy issue in mathematics education, but the approach and results of CT + Math are not yet clear enough. This paper systematically reviewed 22 SSCI journal papers from three perspectives: the current status, outcomes, and implications of mathematics and CT integration. Results indicate that: (1) The empirical studies were more inclined to be carried out in primary school; (2) The sample size inversely proportional to the duration, the same as the duration and the learning phase; (3) the integration of mathematics and CT were gradually emerging in kindergartens, while the empirical studies in junior and senior high schools still needs to be improved; (4) The experimental type prioritizes case studies and lacks mixed research; (5) Most research designs employ a variety of measuring instruments but limited in multimodal data; (6) Through the teaching model of plug-in programming, the integration of mathematics and CT was centred on the field of geometry and number operations; and (7) The CT skills involved are mainly Problem decomposition, Pattern recognition, Abstraction, Algorithm design and Debugging. The limitations and future directions are also discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper describes a Lesson Study in which in-service mathematics secondary-school teachers, collaborating with researchers, involve grade 10 students in tessellation problems. The data are collected by an experiment carried out in the context of the "Liceo Matematico" project, with three volunteer teachers. The experiment goal was to craft a collaborative design of the research lesson between teachers and researchers. The research aim of the paper is to examine the use of Lesson Study in the institutional and cultural context of Italian secondary school with the use of Cultural Transposition as a theoretical framework. The research is qualitative with idiographic aims, based on video research. The educational aim of the research is to provide a solid basis for a revamped in-service teacher education first in the context of the project, then in curricular context. Semiotic mediation is used to provide, within Lesson Study, the conceptual framework for teachers and researchers collaborative design of the research lesson. The results show that Lesson Study, as a foreign practice, is an opportunity for teachers to confront their teaching practices, to enrich their professional development, resulting in more awareness on their didactical action in and outside the classroom. [ABSTRACT FROM AUTHOR]

Abstract  We generalize a result of F. Luca and A. Sankaranarayanan by proving that the set of n for which ϕ(1) ⃛ ϕ(n) is squareful is of zero density. A similar statement holds for σ (n) instead of ϕ(n) and for some other multiplicative functions. [ABSTRACT FROM AUTHOR]

It is proved that the set of those natural numbers which cannot be written as n-Ω( n) is of positive lower density. Here Ω( n) is the number of the prime power divisors of n. This is a refinement of a theorem of F. Luca. [ABSTRACT FROM AUTHOR]

It is shown that an approach earlier used by the author for classification of closed simply connected 6-manifolds (reduction to the problem of calculating certain bordism groups) can also be applied for easily obtaining the results by Barden (1965) on classification of closed simply connected 5-manifolds. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

This letter from the guest editors introduces Vol. 25(4) of the Nexus Network Journal: Architecture and Mathematics. In this special issue, 11 research contributions examine the influence of geometry on the process of making in architecture and vice versa. From fabrication experiments with industrial robots and investigations of geometry and material constraints to the development of the theoretical framework of shape rules and making grammars, the contributions in this issue present the research potential that translates architectural geometry into physical objects in architecture. [ABSTRACT FROM AUTHOR]

In this paper, as an improvement of the paper (Ishige et al. in SIAM J Math Anal 49:2167–2190, 2017), we obtain the higher order asymptotic expansions of the large time behavior of the solution to the Cauchy problem for inhomogeneous fractional diffusion equations and nonlinear fractional diffusion equations. [ABSTRACT FROM AUTHOR]

This article provides instructions in preparing a paper for publication in the "Journal of Optimization Theory and Applications." Some of these guidelines are the following: 1)submission of manuscripts in triplicate; 2) reference to English as the official language of the journal; 3) inclusion of an abstract of at least 50 to 100 words in each contribution; and, 4) the abstract should be followed by a list of four to five key words identifying the subject.

Provides instructions for contributing authors of the "Journal of Optimization Theory and Applications." Overall style of the journal; Language to be used; Inclusion of abstracts and key words in the papers.

Provides instructions for contributing authors to the "Journal of Optimization Theory and Applications." Official language to be used; Inclusion of abstracts and key words in the papers; Format for writing mathematical formulas.

We fill a gap in the proof of one of the central theorems in Epp’s paper, concerning p-cyclic extensions of complete discrete valuation rings. [ABSTRACT FROM AUTHOR]

Uncertainty theory, founded in 2007, has become a branch of mathematics to model uncertainty rather than randomness. As an indispensable part of uncertainty theory, uncertain graph and uncertain network optimization has received the wide attention of many scholars. Naturally, a series of original research achievements have been obtained on uncertain graph and uncertain network optimization. This paper aims to present a state-of-the-art review on the recent advance in uncertain graph and uncertain network optimization. Furthermore, it hopes to predict the possible future research directions. Based on Web of Science database, this paper retrieves 144 related papers from 2011 to 2021 to analyze the features of published articles. More precisely, we analyze the annual number of publications, key topics and sub-fields, journals, and most-cited articles. In addition, the main results and models for uncertain graph and uncertain network optimization are summarized. Furthermore, the limitations of existing literature and the possible development trend are discussed. [ABSTRACT FROM AUTHOR]

We give in this paper two explicit examples of nonsolvable weakly hyperbolic operators with real coefficients in two-space-dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we explore the consequences of a distinction between ‘live' and ‘dead' network nodes; ‘live' nodes are able to acquire new links whereas ‘dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network. [ABSTRACT FROM AUTHOR]

The article announces the selection of the study "Decomposition Algorithms for Stochastic Programming on a Computational Grid," written by Jeff Linderoth and Stephen Wright by the editorial board of the periodical "Computational Optimization and Applications," for the Best Paper Award 2004. The paper describes research carried out by the authors at the Argonne National Laboratory which was supported by the National Science Foundation (NSF). The research involved the development of middleware software, the discovery of new algorithms that could exploit the power of grid platforms while not being affected too seriously by its less felicitous features and the implementation of these algorithms using the resulting codes to solve touchstone problems in optimization.

In this paper, we consider sums related to the floor function. We improve previous results for some special arithmetic functions considered by O. Bordellès [On certain sums of number theory, Int. J. Number Theory, 18(9):2053– 2074, 2022], J. Stucky [The fractional sum of small arithmetic functions, J. Number Theory, 238:731–739, 2022], and J. Wu [Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski, Period. Math. Hung., 80(1):95–102, 2020]. It is worth emphasizing that we use much simpler methods to give much better results than previous. [ABSTRACT FROM AUTHOR]

The paper lists the main open questions left in the area both theoretically and practically, mainly related with the inherent tension between communication efficiency and quality of assumptions in proof systems. This special issue of Designs, Codes and Cryptography on the topic Mathematics of Zero-Knowledge aims at encouraging mathematicians and computer scientists with a strong interest in Mathematics to contribute to the burgeoning topic of zero-knowledge proofs. [Extracted from the article]

Mathematics, as a subject dealing with abstract concepts, poses a special challenge for educators. In students' experience, the subject is often associated with (potentially) unflattering adjectives — “austere”, “remote”, “depersonalized”, and so forth. This paper describes a computer program named HyperGami whose purpose is to alleviate this harsh portrait of the mathematical enterprise. HyperGami is a system for the construction of decorated paper polyhedral. shapes; these shapes may be combined into larger polyhedral sculptures, which we have dubbed “orihedra.” In this paper, we illustrate the methods by which orihedra may be created from HyperGami solids (using the construction of a particular sculpture as an example); we describe our experiences with elementary- and middle-school students using HyperGami to create orihedra; we discuss the current limitations of HyperGami as a sculptural medium; and we outline potential directions for future research and software development. [ABSTRACT FROM AUTHOR]

Abstract  This paper addresses the dialectical relation between theoretical thinking and technique, as they co-emerge in a combined computer algebra (CAS) and paper-and-pencil environment. The theoretical framework in this ongoing study consists of the instrumental approach to tool use and an adaptation of Chevallard’s anthropological theory. The main aim is to unravel the subtle intertwining of students’ theoretical thinking and the techniques they use in both media, within the process of instrumental genesis. Two grade 10 teaching experiments are described, the first one on equivalence, equality and equation, and the second one on generalizing and proving within factoring. Even though the two topics are quite different, findings indicate the importance of the co-emergence of theory and technique in both cases. Some further extensions of the theoretical framework are suggested, focusing on the relation between paper-and-pencil techniques and computer algebra techniques, and on the issue of language and discourse in the learning process. [ABSTRACT FROM AUTHOR]

In this note, we make two revisions of the paper [2]. The first one is the asymptotic behavior of the energy functional as t → T (see [2, Theorem 1.6]), where T is the blow-up time. The second one is the equivalent conditions for the solutions blowing up in finite time or existing globally (see [2, Theorem 1.8]). [ABSTRACT FROM AUTHOR]

Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their ability to summarize large amounts of unstructured text into coherent themes or topics allows researchers in any field to keep an overview of state of the art by creating automated literature reviews. In this article, we apply topic modeling in the context of mathematics education and showcase the use of this data science approach for creating literature reviews by training a model of all papers (n = 336) that have been presented in Thematic Working Groups related to technology in the first eleven Congresses of the European Society for Research in Mathematics Education (CERME). We guide the reader through the stepwise process of training a model and give recommendations for best practices and decisions that are decisive for the success of such an approach to a literature review. We find that research in this period revolved around 25 distinct topics that can be grouped into four clusters: digital tools, teachers and their resources, technology experimentation, and a diverse cluster with a strong focus on student activity. Finally, a temporal analysis of these topics reveals a correlation between technology trends and research focus, allowing for reflection on future research in the field. [ABSTRACT FROM AUTHOR]

Mathematicians frequently attend their peers' lectures to learn new mathematical content. The goal of this paper is to investigate what mathematicians learned from the lectures. Our research took place at a 2-week workshop on inner model theory, a topic of set theory, which was largely comprised of a series of lectures. We asked the six workshop organizers and seven conference attendees what could be learned from the lectures in the workshop, and from mathematics lectures in general. A key finding was that participants felt the motivation and road maps that were provided by the lecturers could facilitate the attendees' future individual studying of the material. We conclude by discussing how our findings inform the development of theory on how individuals can learn from lectures and suggest interesting directions for future research. [ABSTRACT FROM AUTHOR]

In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré's works leading to this conjecture has not been carefully discussed or described, and some other historical aspects about it have not been addressed either. For example, one question is how it fits into the overall work of Poincaré in topology, and what are some other related questions that he had raised. Since Poincaré did not state the Poincaré conjecture as a conjecture but rather raised it as a question, one natural question is why he did this. In order to address these issues, in this paper, we examine Poincaré's works in topology in the framework of classifying manifolds through numerical and algebraic invariants. Consequently, we also provide a full history of the formulation of the Poincaré conjecture which is richer than what is usually described and accepted and hence gain a better understanding of overall works of Poincaré in topology. In addition, this analysis clarifies a puzzling question on the relation between Poincaré's stated motivations for topology and the Poincaré conjecture. [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]

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]

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]

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]

In this paper, I report the results of a study of a large-scale implementation of an evidence-based, objective-oriented approach to teaching via digital platforms among mathematics teachers in Denmark. The aim of the study was to investigate how these platforms affect the work of mathematics teachers and how emergent problems in this process can be addressed from an implementation perspective. This objective was achieved by applying concepts from the theory of instrumental genesis to analyze ethnographical data of teachers' platform usage and data from participatory workshops. The results of the study indicate that the design of platforms is likely to conflict with the needs of mathematics teachers and thus I argue for the need of addressing such issues by supporting teachers in enacting innovations rather than by redesigning them. Furthermore, in the paper I suggest that future workshop is an adequate format to support such enactments. [ABSTRACT FROM AUTHOR]

This paper discusses different approaches to constructing approximate mathematical models. [ABSTRACT FROM AUTHOR]

Abstract Transformer differential protection is exposed to faulty operation related to abnormal operation conditions (inrush, overexcitation, etc.). In this paper a new approach to improve the relay security and dependability is proposed, based on the space-vector analysis of the differential signal, and on their time characteristic shapes in Parks plane. The approach is supported by an introductory formulation and later validated. The technique has been shown to be robust and very simple for the purpose of detecting internal faults. [ABSTRACT FROM AUTHOR]

A recent paper (hereafter referred to as the "Paper"), Bermingham (2003), presented what appeared to be an analytical review of current situation of declining population growth rates in many parts of the world. The Paper suggested that the increasing growth rates before about 1970 constituted exponential growth, but that the currently declining growth rates were not exponential growth. Hence, the paper asserted that we should not use the terms "exponential growth" and "doubling times" in describing the current situation. Many of the suggestions in the paper are contrary to established mathematics. These suggestions are examined here in some detail. [ABSTRACT FROM AUTHOR]

This article discusses Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups. The results of the paper were completed in the Summer 98 and reported by the authors at a number of conferences and seminars. In this version of the paper researchers decided to leave the material of Section 5 in the form close to the preliminary text written in 1998. In particular, researchers did not try to match the quantum group description of finite-difference Toda lattices given in Section 5 with the construction that has become standard since then due to the paper by writer P. Etingof.