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Graph B Martin Schmidt b studied Mathematics and Computer Science at the Leibniz Universität Hannover and received his PhD in 2013 in the area of algorithmic optimization. Her main research area is discrete optimization, including graph theory and integer optimization problems and with a particular emphasis on location and network design problems. His research topics include optimization under uncertainty, network optimization with a focus on energy networks, as well as combinatorial and algorithmic optimization. [Extracted from the article]

Nowadays, there has been a rapidly increasing number of scientific submissions in multiple research domains. A large number of journals have various acceptance rates, impact factors, and rankings in different publishers. It becomes time-consuming for many researchers to select the most suitable journal to submit their work with the highest acceptance rate. A paper submission recommendation system is more critical for the research community and publishers as it gives scientists another support to complete their submission conveniently. This paper investigates the submission recommendation system for two main research topics: computer science and applied mathematics. Unlike the previous works (Wang et al., 2018; Son et al., 2020) that extract TF–IDF and statistical features as well as utilize numerous machine learning algorithms (logistics regression and multiple perceptrons) for building the recommendation engine, we present an efficient paper submission recommendation algorithm by using different bidirectional transformer encoders and the Mixture of Transformer Encoders technique. We compare the performance between our methodology and other approaches by one dataset from Wang et al. (2018) with 14012 papers in computer science and another dataset collected by us with 223,782 articles in 178 Springer applied mathematics journals in terms of top K accuracy (K = 1 , 3 , 5 , 10). The experimental results show that our proposed method extensively outperforms other state-of-the-art techniques with a significant margin in all top K accuracy for both two datasets. We publish all datasets collected and our implementation codes for further references. 1 1 https://github.com/BinhMisfit/PSRMTE. • Bidirectional transformer encoders can improve the performance of the paper submission recommendation system. • The Mixture of Transformer Encoders framework shows the efficiency in the paper submission recommendation problem. • Proposed techniques can surpass other recent techniques on two datasets related. [ABSTRACT FROM AUTHOR]

A constant focus in planning the conference was a strong commitment to excellence in the technical program, a hallmark of this series of conferences. The American Nuclear Society (ANS) 2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2021) continued the rich tradition of this biennial conference series, showcasing preeminent computational science research for nuclear applications. Mathematics and computational methods are of fundamental importance in the design and analysis of nuclear systems. [Extracted from the article]

The time and spatial complexities are HT ht and HT ht , respectively. Published Papers This is a Special Issue of I Mathematics i belonging to the section "Mathematics and Computer Science", which was closed on 30 June 2022. This Special Issue was mainly concerned with quantum algorithms, the mathematics underlying them, and those complexity issues arising from them. [Extracted from the article]

Several properties of the products of finite maximal prefix, maximal biprefix, semaphore, synchronous, maximal infix and maximal outfix codes are discussed respectively. We show that, for two nonempty subsets X and Y of A * such that the product XY being thin, if XY is a maximal biprefix code, then X and Y are maximal biprefix codes. Also, it is shown that, for two finite nonempty subsets X and Y of A * such that the product XY being unambiguous, if XY is a semaphore code then X and Y are semaphore codes. Finally, two open problems to the product of finite semaphore and maximal infix codes are presented. [ABSTRACT FROM AUTHOR]

Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [[1]], economics [[3]], medicine [[5]], ecology [[7]], education [[9]], etc. Conclusions The purpose of this Special Issue was to attract high-quality new papers in the field of applied and computational mathematics for digital environments, offering original solutions to various problems that are relevant and in demand in various fields of human activity. 10.3390/math10224297 21 Demidova L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. I hope that these selected research papers are recognized as important and meaningful by the international scientific community and can form the basis for further research in the field of applied and computational mathematics for digital environments, solving complex problems in various disciplines and application areas. [Extracted from the article]

The purpose of this paper is to present and discuss pedagogical frameworks and approaches to developing, delivering, and evaluating a new interdisciplinary course within the domain of energy informatics at both Master's and PhD levels. This study is needed because many papers on sustainable energy engineering education concentrate on course content but provide very little information on the pedagogical methods employed to deliver that content. The proposed new course is called "smart energy and power systems modelling" and is aimed at discussing how mathematical optimization, in the context of computer science, can contribute to more effectively managing smart energy and power systems. Different pedagogical frameworks are discussed and adapted for the specific domain of energy informatics. An ASSURE model coupled with Bloom's taxonomy is presented for the design of the course and identification of learning objectives; self-regulated learning strategies are discussed to enhance the learning process; a novel model called GPD (Gaussian Progression of Difficulty) for lecture planning was proposed; a teaching-research nexus is discussed for the course planning and enhancement. Adopting qualitative analyses and an inductive approach, this paper offers a thorough reflection on the strengths and weaknesses of the new course, together with improvement possibilities based on fieldwork and direct experience with the students and colleagues. Opportunities and challenges of interdisciplinary teaching are presented in light of real-world experience, with a particular focus on the interaction between mathematics and computer science to study the specific application of energy and power systems. [ABSTRACT FROM AUTHOR]

Provides an overview of the articles which were submitted and processed through the regular "Parallel Processing Letters," review process in 2004. Discussion on the nearest load balancing schemes on processor networks; Presentation of a novel systolic algorithm for generating all the well-formed parenthesis strings in lexicographical order; Proposal of a parallel unconditionally stable solver for three-dimensional convection-diffusion equations by applying the upwind Crank-Nicolson difference schemes combined with alternating bar parallelization.

This editorial introduces the special issue, Resources for Undergraduate Cryptology. We begin by describing possible roles for cryptology in the undergraduate mathematics curriculum together with a brief overview of the subject. We conclude with a brief preview of each paper included in this issue. [ABSTRACT FROM AUTHOR]

The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper. [ABSTRACT FROM AUTHOR]

The SIAM Journal on Applied Mathematics has published a special section on the life sciences, highlighting the use of mathematical models and analysis in understanding biological systems. The section showcases a range of topics, including population dynamics, genetics, neuroscience, epidemics, and various physiological systems. The papers in the section focus on providing biological insights or suggesting novel experiments, and they incorporate practical issues, data-driven modeling, and uncertainty quantification. The special section reflects the growing interest and activity in the fields of mathematical and computational biology, which have been driven by real-world applications in health, medicine, and bioengineering. [Extracted from the article]

Unconstrained optimization problems have a long history in computational mathematics and have been identified as being among the crucial problems in the fields of applied sciences, engineering, and management sciences. In this paper, a new variant of the conjugate descent method for solving unconstrained optimization problems is introduced. The proposed algorithm can be seen as a modification of the popular conjugate descent (CD) algorithm of Fletcher. The algorithm of the proposed method is well-defined, and the sequence of the directions of search is shown to be sufficiently descending. The convergence result of the proposed method is discussed under the common standard conditions. The proposed algorithm together with some existing ones in the literature is implemented to solve a collection of benchmark test problems. Numerical experiments conducted show the performance of the proposed method is very encouraging. Furthermore, an additional efficiency evaluation is carried out on problems arising from signal processing and it works well. [ABSTRACT FROM AUTHOR]

Taming next-generation HPC systems: Run-time system and algorithmic advancements In the first one, the parallel algorithm control runs on top of the popular graph partitioning METIS tool. This special issue of I Concurrency and Computation: Practice and Experience i contains revised and extended versions of selected papers presented at the 13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019, which was held on September 8-11, 2019 in Bialystok, Poland. [Extracted from the article]

The article presents the discussion on exploring new foundational and translational research towards enabling exascale computing for emerging scientific and societal challenges. Topics include high-performance computing (HPC) simulations, artificial intelligence (AI), and extreme data-driven computing; and advances in applications, programming environments, runtimes, libraries, innovative algorithms, domain-specific frameworks, and systems architecture.

The problems of constructing accurate and stable algorithms for solving inverse problems of mathematical physics are at the forefront of modern computational mathematics due to the ever-increasing number of applications of such problems in physics and technology, as well as to the properties of these problems, which greatly complicate their numerical solution. In this paper, we consider the problem of numerical solution of one of such problems, known as the inverse problem of heat transfer. The numerical method for solving the inverse problem of heat transfer uses the apparatus of hypersingular integral equations. As far as the authors know, this approach to the construction of methods for solving the inverse problem of heat transfer is used for the first time. The numerical method described in the paper makes it possible to successfully find an approximate solution to the inverse problem of heat transfer, including the case of significant errors in the initial data. The solution of a model example demonstrates the efficiency of the method proposed. [ABSTRACT FROM AUTHOR]

The scope of computation has expanded dramatically beyond the rubric of discrete, deterministic sequential computation under which it has been studied for many decades. That focus, of course, led to a great deal of deep and beautiful theory, but our focus in this special issue of Mathematical Structures in Computer Science is on new directions that have emerged from the study of computational phenomena in other settings, and thus on a celebration of the diversity of ideas, methods, new applications and novel sources of inspiration that have marked the modern era. The papers in this issue come from sources extending far beyond the core of computer science, yet using many of the central ideas that have evolved within computer science and mathematics. The nexus of all this activity has been, on the one hand, the boundary between logic and computation, and, on the other hand, the natural sciences, particularly physics and biology. The papers in this collection are expanded versions of selected papers from the DCM 2010 workshop, which was held in Edinburgh in July 2010. The theme of the workshop was Causality, Computation and Physics. [ABSTRACT FROM AUTHOR]

Based on a dynamic discrete model of an out-of-plane curved beam with a constant curvature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent section reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated. [ABSTRACT FROM AUTHOR]

This special issue of the Journal of Optimization Theory & Applications focuses on the work of Professors Cornelis Roos and Florian A. Potra in the field of optimization. The issue includes a biographical sketch of both professors, highlighting their achievements. The papers in the special issue cover various topics such as conic optimization, interior point methods, proximal methods, convex optimization, and stochastic optimal control. The authors of the papers have close connections to Professors Roos and Potra, either as students, visitors, or co-authors. The document is a compilation of research papers on interior-point methods (IPMs) and their applications in optimization and conic programming. The papers cover theoretical developments of IPMs, algorithms for linear complementarity problems (LCPs), weighted LCPs, and sufficient linear complementarity problems. There are also papers on new computational approaches for IPMs, applications of IPMs in different fields such as mechanics and support vector machines, and the theory and application of conic optimization. The document also includes papers on proximal methods for convex and non-convex problems, as well as papers on convexity and convex optimization. The volume concludes with acknowledgments to the authors, reviewers, and editor-in-chief. [Extracted from the article]

The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating CT and mathematics in current empirical studies published from 2015 to 2021. The review showed that most of the studies implemented CT-intensive Math-connected integration. Five major types of CT tools had been identified, i.e., digital tangibles, apps and games, programming languages, formative or summative assessments, and other technological tools. In many instances, the tools also provide functions of assessment of CT skills. The most assessed CT competencies were including algorithms and algorithmic thinking, abstraction, testing and debugging, loops, and sequences. Geometry and Measurement was the most assessed mathematics topic. Our scoping review is beneficial in the investigation of the literature on CT and mathematics education, as well as guides those who are interested in developing curriculum, programs, or assessments that involve the integration of CT and mathematics. [ABSTRACT FROM AUTHOR]

This paper presents a groundbreaking numerical technique for solving nonlinear time fractional differential equations, combining the conformable continuity equation (CCE) with the Non-Polynomial Spline (NPS) interpolation to address complex mathematical challenges. By employing conformable descriptions of fractional derivatives within the CCE framework, our method ensures enhanced accuracy and robustness when dealing with fractional order equations. To validate our approach's applicability and effectiveness, we conduct a comprehensive set of numerical examples and assess stability using the Fourier method. The proposed technique demonstrates unconditional stability within specific parameter ranges, ensuring reliable performance across diverse scenarios. The convergence order analysis reveals its efficiency in handling complex mathematical models. Graphical comparisons with analytical solutions substantiate the accuracy and efficacy of our approach, establishing it as a powerful tool for solving nonlinear time-fractional differential equations. We further demonstrate its broad applicability by testing it on the Burgers–Fisher equations and comparing it with existing approaches, highlighting its superiority in biology, ecology, physics, and other fields. Moreover, meticulous evaluations of accuracy and efficiency using ( L 2 and L ∞ ) norm errors reinforce its robustness and suitability for real-world applications. In conclusion, this paper presents a novel numerical technique for nonlinear time fractional differential equations, with the CCE and NPS methods' unique combination driving its effectiveness and broad applicability in computational mathematics, scientific research, and engineering endeavors. [ABSTRACT FROM AUTHOR]

One of the challenges of university mathematics courses in secondary teacher preparation is incorporating pedagogical discussions. The focus in a mathematics course is—and should be—on mathematics. But research also suggests that without addressing pedagogical implications these content courses are not meaningful to secondary teachers' future classroom practice. The thrust of this paper is exploring ideas for how to leverage mathematical practice in university mathematics courses—and, in particular, what have been described as Pedagogical Mathematical Practices (PMPs). The paper reports on a study of (n = 10) pre- and in-service mathematics teachers that explored the viability of the PMP construct, with the intent of specifying particular PMPs. Drawing on interviews with teacher participants who had recent experiences in an inquiry-oriented discrete mathematics course, the study reports on the ways in which they identified a set of mathematical practices as being productive pedagogically. The study contributes a teacher-perspective on the construct of PMPs, including the identification of four PMPs from the study data: explicit visualization; multiple approaches; concrete exemplification; and informal justification. Implications for their potential use in university mathematics courses with regard to teacher education are discussed. [ABSTRACT FROM AUTHOR]

With the improvement of people's living standards, people's pursuit of art is also getting higher and higher. Ceramic products are artistic works whose meanings contain thousands of stories including mountains, waters, and rivers. Ceramic products include vases, tea sets, flower pots, plates, and rice bowls. A vase is a vessel, mostly made of ceramic or glass, with a beautiful and smooth appearance. The bottom of the vase usually holds water, which keeps the plants alive and beautiful. Tea utensils refer to tea-drinking utensils such as tea cups, teapots, tea bowls, tea cups, saucers, and tea trays in a narrow sense. There are many kinds of tea sets in China, with beautiful shapes. In addition to practical value, they also have high artistic value, so they are well known at home and abroad and are favored by tea lovers in all dynasties. Digital image processing is the use of computers to remove noise and enhance, restore, segment, and extract features from images. Discrete mathematics is a mathematical subject that studies the structure of discrete quantities and their interrelationships and is an important branch of modern mathematics. The meaning of discrete refers to different elements connected together, mainly to study the structure and mutual relationship based on discrete quantities. Its objects are generally limited or countable elements. With the continuous development of digital image processing technology, this technology has also been applied to the shape design of ceramic products. This paper mainly conducts in-depth research on the preprocessing algorithm of digital images, from the initial analysis of the historical culture of the process to the subsequent algorithm research. Then its accuracy is matched to make a comparison, and finally an estimate based on the ceramics studied in this paper will be made. In the experimental part, the public is first investigated and analyzed, and the conclusion shows that the results of the color investigation of ceramic products include the following aspects: There are about 103 people having more needs for light and elegant color feeling, which echoes the needs of modeling. There are around 97 people demanding that the color be combined with the shape to reflect the color difference between the interior and the exterior. Since the internal and external chromatic aberration and mixed colors will bring novelty to the appearance of ceramic products, there are also a large number of people in the demand for mixed colors, about 84 people. Then it is analyzed that the ink-and-wash ceramics in the landscape style are more popular, and then the detailed description is carried out. Finally, the finished product is displayed. [ABSTRACT FROM AUTHOR]

The solution of nonlinear Boolean equations in a binary field plays a crucial part in cryptanalysis and computational mathematics. To speed up the process of solving Boolean equations is an urgent task that needs to be addressed. In this paper, we propose a method for solving Boolean equations based on the Grover algorithm combined with preprocessing using classical algorithms, optimizing the quantum circuit for solving the equations, and implementing the automatic generation of quantum circuits. The method first converted Boolean equations into Boolean expressions to construct the oracle in the Grover algorithm. The quantum circuit was emulated based on the IBM Qiskit framework and then simulated the Grover algorithm on this basis. Finally, the solution of the Boolean equation was implemented. The experimental results proved the feasibility of using the Grover algorithm to solve nonlinear Boolean equations in a binary field, and the correct answer was successfully found under the conditions that the search space was 221 and three G iterations were used. The method in this paper increases the solving scale and solving speed of Boolean equations and enlarges the application area of the Grover algorithm. [ABSTRACT FROM AUTHOR]

This article shares one project, a programmable paper circuit timeline that highlights the use of mathematics and computational thinking practices in the middle school science classroom while students learn science history. Timeline design Students sketch both an artistic version of what they intend their timeline project to look like and a labeled circuit diagram illustrating how they will create functional circuits out of copper tape (see Figure 1). By programmable paper circuit, we refer to a circuit that is created using copper tape and light-emitting diode (LED) lights, but then is connected to a microcontroller so that it becomes programmable (see Figure 1). When teachers engage students in the Lighting Up History Project, students use ratios to represent Jemison's progress over time with a length model (time: length). [Extracted from the article]

This report provides information and summary data for manuscripts submitted, acceptance rates and review times for the I International Journal of Computer Mathematics (IJCM) i from 1st January 2018 to 30th June 2019. All submissions to I IJCM i are processed via ScholarOne Manuscripts at http://mc.manuscriptcentral.com/commat. I IJCM i continues to screen papers for originality using the CrossRef Similarity Check™ software to screen papers for unoriginal material. [Extracted from the article]

Let C k + 1 be a cycle of length k + 1 and C t + 1 be a cycle of length t + 1. A polygon flower with two centers, denoted by F = F (C k + 1 ; P 1 , ... , P k ; C t + 1 ; P k + 1 , ... , P k + t) is obtained by identifying the i th edge of C k + 1 with an edge ei that belongs to an end-polygon of Pi for i = 1 , ... , k , and identifying the j th edge of C t + 1 with an edge ej that belongs to an end-polygon of Pj for j = k + 1 , ... , k + t , where C k + 1 and C t + 1 have a common edge h. In this paper, we determine the order of sandpile group S(F) of F, which can be viewed as generalized of results in paper (Haiyan Chen, Bojan Mohar. The sandpile group of a polygon flower. Discrete Applied Mathematics, 2019). Moreover, the formula and structure for sandpile group of polygon flower can be obtained. Finally, as application of our result, we also present the sandpile group of cata-condensed system with two branched hexagons. [ABSTRACT FROM AUTHOR]

The paper describes in detail a class of educational problems from an elementary school course of mathematics and computer science. This course has been implemented over the past decades by a team led by Academician of the RAS A.L. Semenov. In the problems, it is necessary to find, build, or list all objects that satisfy a certain system of conditions. The student conducts these activities in a visual world of basic objects of discrete mathematics and computer science: strings (finite sequences of symbols), bags (multisets), tables, trees, and statements containing quantifiers. The connections of these problems with problems in computational combinatorics (counting the number of options), with search problems in the theory of computational complexity, with "big ideas," and general cognitive strategies for their formation in education are considered. The content of education in our approach is more adequate to the context of the modern world. [ABSTRACT FROM AUTHOR]

In the modern era, graph theory is considered a useful tool for quantification and simplification of various dynamic components in complex systems. By representing elements as nodes and their connections as edges, graph theory can transform anything from urban planning to computer data into a meaningful mathematical language. Nowadays, numerous practical applications have been designed and developed based on graph theory. Graph theory is a branch of discrete mathematics that aims to describe and solve problems with discrete structures using points and edges. One of the problems concerning graphs is the Eulerian path problem. This research demonstrates that this problem can also be investigated from the perspective of Operations Research (OR). In a more general sense, the Eulerian path problem is a routing problem. This paper presents a pure mathematical model to describe the relationship between the variables of the Eulerian path problem. One of the features of the proposed mathematical model is its solvability by most optimization software. Finally, several numerical examples are provided to enhance the understanding of this model, and they are solved using the proposed approach. All the analyses in this research are conducted using one of the most advanced optimization software, MATLAB. The proposed mathematical model provides a systematic and efficient approach to discover Eulerian paths in specific graphs, contributing to the advancement of graph theory and its practical applications. [ABSTRACT FROM AUTHOR]

Within the existing taxonomy of mathematical proofs, visual proofs distinguish themselves by using representation as a tool for demonstration. This paper explores visual proofs in mathematics and their relationship with architectural representation. Most notably, stereotomy and graphic statics exhibit qualities of visual proofs by demonstrating how forms are generated. [ABSTRACT FROM AUTHOR]

This document is a summary of a special issue of the journal Concurrency and Computation: Practice and Experience, which contains eight selected papers from the 14th International Conference on Parallel Processing and Applied Mathematics (PPAM 2022). The conference focused on topics related to high-performance computing (HPC) and included discussions on emerging technologies, algorithms, and software tools. The selected papers cover a range of subjects, including the convergence of iterative methods for solving nonlinear equations, testing interval arithmetic libraries, automatic performance tuning for symmetric eigenvalue problems, GPU computing, simulation of molecular magnetism, load balancing in distributed memory systems, predicting execution time of computational workloads, and resource selection for cloud-based applications. The papers provide valuable insights and advancements in the field of HPC. [Extracted from the article]

Summary: Luis Raúl Pericchi Guerra was born in Caracas, Venezuela, on 11 March 1952. He completed a B.S. in Mathematics in 1975 at the Universidad Simón Bolívar in Caracas, an M.S. in Statistics at the University of California Berkeley in 1978 and a Ph.D. in Statistics at Imperial College London in 1981. After graduating from Imperial College, Luis Raúl went back to Universidad Simón Bolívar. There, he played a key role in the developing of graduate programmes in Statistics and single handedly built an internationally recognised group focused on Bayesian statistics. In 2001, he moved to the Universidad de Puerto Rico in Rio Piedras to become the Chair of the Mathematics Department. At Universidad de Puerto Rico, he was instrumental in the establishment of a Ph.D. track in Computational Mathematics and Statistics. Luis Raúl has published over 120 papers in statistical and domain‐specific journals, making significant contributions to several areas of Bayesian statistics (especially in the areas of model selection and Bayesian robustness) and their application (especially in hydrology). He is a Fellow of the American Statistical Association, the International Society for Bayesian Analysis, the John Simon Guggenheim Memorial Foundation and an Elected Member of the International Statistical Institute. This conversation took place over multiple sessions during the 2022 O'Bayes meeting in Santa Cruz, California, and the months that followed. [ABSTRACT FROM AUTHOR]

In this paper we study colorings (or tilings) of the two-dimensional grid ℤ 2 . A coloring is said to be valid with respect to a set P of n × m rectangular patterns if all n × m sub-patterns of the coloring are in P. A coloring c is said to be of low complexity with respect to a rectangle if there exist m , n ∈ ℕ and a set P of n × m rectangular patterns such that c is valid with respect to P and |P|≤ nm. Open since it was stated in 1997, Nivat's conjecture states that such a coloring is necessarily periodic. If Nivat's conjecture is true, all valid colorings with respect to P such that |P|≤ mn must be periodic. We prove that there exists at least one periodic coloring among the valid ones. We use this result to investigate the tiling problem, also known as the domino problem, which is well known to be undecidable in its full generality. However, we show that it is decidable in the low-complexity setting. Then, we use our result to show that Nivat's conjecture holds for uniformly recurrent configurations. These results also extend to other convex shapes in place of the rectangle. After that, we prove that the nm bound is multiplicatively optimal for the decidability of the domino problem, as for all ε > 0 it is undecidable to determine if there exists a valid coloring for a given m , n ∈ ℕ and set of rectangular patterns P of size n × m such that |P|≤ (1 + ε)nm. We prove a slightly better bound in the case where m = n, as well as constructing aperiodic SFTs of pretty low complexity. This paper is an extended version of a paper published in STACS 2020 (Kari and Moutot 12). [ABSTRACT FROM AUTHOR]

We say that a space X has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of X is countable. A space X has a zeroset diagonal if there is a continuous mapping f : X2 ! [0, 1] with X = f-1(0), where X = {(x, x) : x 2 X}. In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most c. [ABSTRACT FROM AUTHOR]

In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they applied to the heat equation. In this part of the series, we construct several 2D systems to find how the errors depend on the time step size. Sweeps for other key parameters will be presented in the next part of the series. [ABSTRACT FROM AUTHOR]

This paper introduces the forbidden subgraph conditions for Hamilton-connected graphs. If the degree sequence of the graph is (4 , 2 , 2 , 2 , 2) and it is connected, then it is called hourglass Γ 0 . For integers i ≥ 1 , the graph Z i is paw, which is obtained by attaching one of the vertices of the triangle to one of the end vertices of a path with a number of edges i. We show that every graph G is Hamilton-connected if G is a Γ 0 -free, K 1 , 3 -free, Z 14 -free, and a 3-connected graph. Moreover, we give an example to show the sharpness of a paw-type forbidden subgraph in a 3-connected, Hamilton-connected graph. Our focus on the Hamilton-connected problem can be applied to data center networks (DCNs). In the future, we will remove the forbidden subgraph families from our conclusions when building the network to obtain the optimal communication cost. Our result extends the result of Ryjáček and Vrána (Discrete Mathematics 344: 112350, 2021). [ABSTRACT FROM AUTHOR]

In this paper, a finite spin system corresponding to magnetic molecules with the wheel geometry is discussed in the Ising-like limit of the Heisenberg Hamiltonian. We put stress on the ground state degeneration, which is determined with the use of some discrete mathematics methods, especially investigating some integer sequences, including the famous Fibonacci one. [ABSTRACT FROM AUTHOR]

In this paper, a computer program developed in the computer algebra system Maple is presented, which investigates alienness and strong alienness of linear functional equations. [ABSTRACT FROM AUTHOR]

Graphs are used to solve many problems in mathematics and computer sciences. Many structures can be displayed with the help of graphs. For example, a directed graph can be used to show how websites are related to cach other. Vague graph (VG) is one of the most important graphs in the fuzzy graph (FG)-theory, which can play a significant role in finding the most suitable places in construction and also finding the shortest path in computer networks. Connectivity indices are one of the most widely used topics in graph theory, which are used in other sciences, including computer science and chemistry. One of the most famous indices in the graph is the Wiener index, which belongs to the description of the molecular structure, which is used to design molecules with desirable properties. Therefore, in this paper, we introduce important topological indices such as Wiener index, Wiener absolute index, Randic index, Zegreb index, Harmonic index, and Average Wiener index on VGs and investigate their properties with several examples. Finally, an application of the Wiener index is given to find the most suitable place to build an university. [ABSTRACT FROM AUTHOR]

Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer science in intriguing ways. Behind programming practices is computational thinking (CT), a mode of thinking involved in formulating and solving problems so that the solutions could be represented and carried out by computing means. In this paper, CT is seen as a boundary object connecting mathematics and computer science in a school problem-solving context. In particular, we examine and analyse middle school students' work upon engaging in mathematical problem solving-in a programming environment, taking CT as a boundary object embedded in the block-based programming environment, Scratch. The analysis is guided by observing boundary crossing features of CT in the students' artefacts produced in Scratch while solving mathematical problems related to symmetry and arithmetic sequence. The findings of this study open up new dimensions to explore CT as a boundary object in integrated STEM pedagogy. [ABSTRACT FROM AUTHOR]

This paper focuses on developing and analyzing a new AR-iterative scheme designed for estimating fixed points of generalized non-expansive mappings of the Suzuki kind. The scheme’s stability and convergence properties are rigorously proven, highlighting its superior convergence rate for non-expansive mappings when compared to existing schemes in the literature. Additionally, an application of the AR-iterative scheme to differential equations is presented. These findings underscore the effectiveness and versatility of the proposed scheme in numerical analysis and computational mathematics. [ABSTRACT FROM AUTHOR]

The article highlights the growing importance of computational mathematics in tackling intricate real-world phenomena governed by distributed order fractional dynamics. These dynamics, characterized by memory effects and non-local interactions, are pervasive in various fields such as physics, biology, finance, and engineering. Despite their prevalence, analytical solutions for distributed order fractional differential equations remain difficult to find, necessitating the development of robust numerical methods. The paper explores the effectiveness of Romanovski–Jacobi spectral collocation techniques in this context and provides a thorough analysis of how to use them to solve distributed order fractional differential equations. By leveraging these schemes, researchers gain valuable insights into efficiently analyzing and simulating fractional systems, thereby advancing our understanding of complex dynamics across diverse domains. It provides precise numerical findings by using finite expansion to evaluate residuals. The precision of the approach is illustrated by numerical simulations, especially in distributed order fractional differential equations. Additionally, we provide a few numerical tests to demonstrate the method's ability to preserve the underlying problem's non-smooth solution. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

Topological data analysis (TDA) uses information from topological structures in complex data for statistical analysis and learning. This paper discusses persistent homology, a part of computational (algorithmic) topology that converts data into simplicial complexes and elicits information about the persistence of homology classes in the data. It computes and outputs the birth and death of such topologies via a persistence diagram. Data inputs for persistent homology are usually represented as point clouds or as functions, while the outputs depend on the nature of the analysis and commonly consist of either a persistence diagram, or persistence landscapes. This paper gives an introductory level tutorial on computing these summaries for time series using R, followed by an overview on using these approaches for time series classification and clustering. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and ClassificationData: Types and Structure > Time Series, Stochastic Processes, and Functional DataApplications of Computational Statistics > Computational Mathematics [ABSTRACT FROM AUTHOR]

In 2019, the Department of Mathematics and Statistics at Maynooth University commenced a project which sought to address, through the provision of mathematics learning supports, the issues of poor engagement and retention of computer science students studying mathematics. In this paper, we present preliminary engagement and performance data along with interviews conducted with eight students. We discuss how the quantitative data seemed to indicate that computer science students were engaging at similar levels to their peers, but several factors, including the quality of this engagement and their mathematical backgrounds may explain their poor exam performance. It also emerged that, while students were largely negative about their experiences in large lectures and their awareness of the relevance of mathematics to computer science, they were generally positive about smaller teaching situations such as tutorials, mathematics support drop-in and opportunities to work with their peers. [ABSTRACT FROM AUTHOR]

This paper is a review of our work, an experimental study and simulation of seismic fields in volcanic structures using vibrators as sources of elastic waves. We review the results of experimental studies of mud volcanoes carried out by the Institute of Computational Mathematics and Mathematical Geophysics (ICM&MG) of the Siberian Branch (SB), Russian Academy of Sciences (RAS); by the Institute of Physics of the Earth (IPE), RAS; and by the Kuban State University in the Taman mud-volcanic province using vibrators. We have carried out mathematical simulation in heterogeneous geophysical media to refine the information on the structure of the object under investigation, as well as on the distinguishing features of the seismic field. We have developed a mathematical approach to deal with the simulation of vibroseismic probing of mud volcanoes with arbitrary geometries incorporating knowledge of deep-seated faults, overlapping layers, and so on. Numerical techniques were used to solve sets of equations in elasticity theory and to develop parallel algorithms, program packages, as well as carrying out numerical experiments in high-performance computational systems. We present results from calculations of the seismic field for the source zone of the Shugo mud volcano. This paper describes 3D and 2D geophysical models developed for this study and the results of simulation for the seismic field of the Karabetova Gora mud volcano and for the Elbrus magmatic volcano. It is shown that the approach developed here using active vibroseismic techniques can be successfully used in practice to refine the seismic field, the deep structure of geophysical models, and to study the effects exerted by the geometry of a magma chamber and by the presence of erupting channels on data acquired by an observation system on the ground surface. These studies prove that vibroseismic sources with high accuracies of periodic excitation can be used to study volcanic structures and to conduct active monitoring of volcanic activity. [ABSTRACT FROM AUTHOR]

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66-76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al. (J Photogramm Remote Sens 94:63-69, 2014). [ABSTRACT FROM AUTHOR]