Search

• Convolutional code is widely used in communication systems. • NFSR is the main component of the convolutional decoder. • STP is a new mathematical tool with a wide range of applications. • NFSR can be modeled very well with STP, enabling the discussion in mathematics. The nonlinear feedback shift register (NFSR) is the main component of the convolutional decoder. This paper provides a novel method for investigating the driven stability of NFSRs with input via semi-tensor product (STP). By using the STP method, a backward state transition matrix, as well as a backward NFSR, is constructed. Backward NFSRs can help to find the predecessors of any states so that an algorithm for the global stability of autonomous NFSRs is designed. On this basis, two algorithms are proposed for the driven stability of NFSRs with input, and they have lower computational complexity than the existing methods. Meanwhile, some numerical examples are presented to support the results of this paper. Finally, the relationship between stability and connectedness is discussed fully, which derives some interesting results. [ABSTRACT FROM AUTHOR]

This article from New Scientist discusses how mathematics can be used to wrap gifts in a precise and efficient manner. The author explains that when wrapping box-shaped gifts, measuring the length and thickness of the box can help determine the amount of paper needed. For cylindrical gifts, the paper should be slightly wider than the diameter of the gift and the length should be the sum of the diameter and the length of the gift. The article also provides instructions for wrapping equilateral triangular prism gifts and large, flat, square-ish gifts using mathematical methods. The author emphasizes the importance of aligning the pattern on the paper for maximum aesthetic appeal. [Extracted from the article]

The article reports on the author's initiative to design and share fun, paper-based math games for diverse age groups, utilizing tools like LibreOffice Calc, and details the evolution of the Pairs Math Game, its varied versions, and potential uses in educational and community settings. The author also emphasizes promoting playful conversations about numbers and fostering a sense of agency in students to invent their math questions.

A controversial mathematical proof known as the ABC conjecture has sparked bitter divisions among mathematicians. In 2012, Shinichi Mochizuki published a 500-page proof of the conjecture, but many found it incomprehensible. Kirti Joshi at the University of Arizona has now proposed a proof that he claims fixes the problems with Mochizuki's work, but Mochizuki and his supporters remain unconvinced. The debate centers around a part of Mochizuki's proof called Conjecture 3.12, which Joshi believes he has addressed more satisfactorily. However, the paper has not been peer-reviewed, and the controversy continues. [Extracted from the article]

The article discusses the function of folds, from child's play to spacecraft, by way of mathematics and mechanical engineering. Topics discussed include highlights of the International Meeting on Origami in Science, Mathematics and Education, Friedrich Froebel, the first person to suggest the systematic use of folding as a way of teaching geometry and Robert Lang, a former laser physicist greatest hits have been in formalising and building enthusiasm for the mathematics behind origami.

The article examines the value of the scientific works left by scientist Isaac Newton when he died in 1727. Topics covered include his perceptions on mathematics and natural philosophy that are discussed in his works. Also mentioned is the sharing of his scientific works to only few people when he was still devoted to studying optics, physics and mathematics.

The article discusses the steps in designing a better paper helicopter using the response surface methodology (RSM). RSM is a collection of statistical and mathematical techniques to explore efficiently the performance of a system to find ways to improve it. The design of the experiment includes brainstorming, factorial designs, pareto principle and factor screening and fractional factorial designs.

The mid-point quadrature rule is often used to solve the nonlocal integral differentiation equations, in which a central material point is used to calculate the integral of the subdomain in the meshless geometry. However, it can only achieve the linear approximation and the first order convergence rate, and it is only accurate enough when the entire cell overlaps with the neighborhood of a material point. In this paper, to achieve the higher precision and the higher rate of convergence speed, a novel coupling method of reproducing kernel particle method and Gaussian-Legendre quadrature scheme is proposed to solve the nonlocal integral differentiation equations in the meshless geometry, in which the mid-point quadrature scheme is replaced with Gauss quadrature scheme to calculate the integral of the subdomain in the meshless geometry, the reproducing kernel particle method is employed to construct the shape functions for material points in the nonlocal model, and to approximate the value of the Gaussian quadrature node. Moreover, the meshless solution for the peridynamic equation is derived detailedly based on the proposed method. Compared with the traditional meshless solution for the nonlocal equations, the proposed solution has higher precision and higher rate of convergence speed in different problems. The numerical results demonstrate improved results in both mathematics and mechanical problems using the proposed method. [ABSTRACT FROM AUTHOR]

The article focuses on the policy documents published in the first week of December of 2019 in Great Britain. "What School Life Means for Students' Lives," focuses on reading, math and science subjects. "4th Global Report on Adult Learning and Education: Leave No One Behind: Participation, Equity and Inclusion," is a report on adult education provision. "General Election 2019: An Analysis of Manifesto Plans for Education," analyzes the manifesto education plans by British political parties.

In this article author talks about revitalizing learning teams to build collective teacher efficacy, but then teachers complain that they do not have enough time to grade papers or communicate with parents. Topics include examines strategic focus on mathematics instruction pays off with student gains in math proficiency, but lose ground on reading scores.

The article presents the discussion on testing across compulsory education having negative impacts upon children's mathematics education. Topics include encapsulating twelve years of compulsory mathematics education using three examination papers over the course of a few weeks in May/June; and examination question being used for assessing students' engagement with relationships and the interconnectedness of mathematics.

This paper presents a unified framework to generalize the traditional $k$ -core decomposition method for both weighted and unweighted networks. It not only subsumes previous $k$ -core decomposition methods but provides some new ones. With the help of the definition of $n$ -th order h-index, we prove that all $k$ -core indexes can be regarded as some steady state of h-index series with $n$ going to infinity. Furthermore, all $h$ -indexes we obtain in intermediate calculation steps can be used as ranking scores to assess node importance in networks. Finally, we apply the provided new methods as well as two existing ones to four real networks and compare their performances on spreading influences ranking. [ABSTRACT FROM AUTHOR]

The article focuses on the activity programs in education that could lead to deep progress and counter the short term goals and quick delivery that seem to lead to whole terms of revision and no long-term learning. The activity program mentioned in the article is about inequality sign in mathematics. A lot of time was spent on the activity with the students, discussing the number line, the set of solutions and the boundary. Before moving to the idea of solution, there were plenty of opportunities to work on substitution. What students need is to have a depth of understanding of the work, so that they do not spend all their time rehearsing the examination question without anything to hang their learning on.

The article presents an interview with Michael O. Rabin, the 1976 co-winner of the Association for Computing Machinery's A. M. Turing Award. Topics discussed include his interest in mathematics as a high school student in Israel, a paper he co-wrote on automata theory during an internship with International Business Machines, another paper he produced on the degree of difficulty in computable functions, research he has performed on randomization, and the application of that research to cryptography.

In this paper, we introduce the concept of a G -Hausdorff space and show how the results established in the usual metric space can be generalized to the G -metric space. The proven results are used to propose an iterated function system (IFS) called G -IFS. Additionally, the existence of the fractal associated with this construction is demonstrated. This paper shows how non-affine transformations and fractal interpolation functions (FIFs) can be used to approximate fractals by G -IFS. This paper contributes to the understanding of fractal geometry and its applications in mathematics and other fields. • The research paper introduces the concept of a Hausdorff space. • It shows how the results established in the usual metric space can be extended to a more general G metric space. • An iterative function system (IFS) is constructed using the proven results, and a G -IFS is proposed. • The existence of fractals associated with this construction is demonstrated. [ABSTRACT FROM AUTHOR]

Abstract In this paper we continue our study of the shape parameter c contained in the famous multiquadrics (− 1) ⌈ β ⌉ (c 2 + ∥ x ∥ 2) β , β > 0 , and the inverse multiquadrics (c 2 + ∥ x ∥ 2) β , β < 0. The theoretical ground is akin to our previous papers. However, we remove some unnecessary restrictions, making it much more accessible and useful, especially for nonmathematicians [ABSTRACT FROM AUTHOR]

This paper describes the design and implementation of a system for typesetting mathematics. The language has been designed to be easy to learn and to use by people (for example, secretaries and mathematical typists) who know neither mathematics nor typesetting. Experience indicates that the language can be learned in an hour or so, for it has few rules and fewer exceptions. For typical expressions, the size and font changes, positioning, line drawing, and the like necessary to print according to mathematical conventions are all done automatically. For example, the input sum from 1=0 to infinity x sub i = pi over 2 produces ... The syntax of the language is specified by a small context-free grammar; a compiler-compiler is used to make a compiler that translates this language into typesetting commands. Output may be produced on either a phototypesetter or on a terminal with forward and reverse half-line motions. The system interfaces directly with text formatting programs, so mixtures of text and mathematics may be handled simply. This paper was typeset by the authors using the system described. [ABSTRACT FROM AUTHOR]

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Statistical matching aims at combining information available in distinct sample surveys referred to the same target population. The matching is usually based on a set of common variables shared by the available data sources. For matching purposes just a subset of all the common variables should be chosen, the so called matching variables. The paper presents a novel method for selecting the matching variables based on the analysis of the uncertainty characterizing the matching framework. The uncertainty is caused by unavailability of data for estimating parameters describing the association between variables not jointly observed in a single data source. The paper focuses on the case of categorical variables and presents a sequential procedure for identifying the most effective subset of common variables in reducing the overall uncertainty. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to introduce the concept and praxis for eigenform in the context of second-order cybernetics.Design/methodology/approach The paper is designed as a formal (partly mathematical) introduction with excursions into the applications and meanings of these constructions. Mathematics studies what a distinction would be if there could be a distinction. Mathematics is a special form of fictional design. This study raises the question of “What it would mean to go beyond mathematics or for mathematics to go beyond itself?”.Findings This study shows how objects in the author’s experience can be seen to be eigenforms and that in this context such objects are a construct of their interactions, linguistic and otherwise experiential. In this way, the author can investigate scientifically without the need for an assumption of objectivity. The author cocreates the universe through the discovery of distinctions and eigenforms in their dialogue with what can be.Research limitations/implications The implications of this research are profound for the performance and exploration of science. The author can explore their role in that creation and find that what they create is independent of significant subsets of their actions.Practical implications The practical implications of this study are strongest for the logical understanding of the author’s constructions and actions. They have used eigenform and reflexivity to maintain a clear view of their participation in their own worlds.Social implications The social implications are in accordance with the practical implications. The author can now admit that they each produce eigenform models of the others and for themselves. These models have in-depth usage, in that it is understood that one is not identical with their models.Originality/value This paper presents a highly original and very simple way to incorporate second-order cybernetics into all thought and action. [ABSTRACT FROM AUTHOR]

• Introduction of the Common Prime RSA and a brief description of its background mathematics. • An overview and explanation of previous CP-RSA cryptanalytic attacks. • Formulation of new cryptanalytic attack on CP-RSA using Lattice Basis Reduction method. • Explanation and detail description of new Cryptanalytic attack solution on CP-RSA. • CP-RSA Speed and efficiency measures w.r.t practical and asymptotic aspects. • Detail explanation and comparison results with the previous CP-RSA cryptanalytic attacks. Standard RSA cryptosystem becomes vulnerable, when private key d < N 0.292 is used inside CryptoChips of constrained devices, thus an alternate scheme is the Common Prime RSA (CP-RSA) variant, which provides cryptographic (decryption/signing) operations. In this paper, we perform a cryptanalytic attack on CP-RSA using lattice basis reduction method that is used to exploit possible vulnerabilities of RSA small private key attacks. In addition, we performed detail experiments on CP-RSA weak or overestimated bounds and compare results to the past studies. Our implemented cryptanalytic attack implicates more precise and direct method to exploit the CP-RSA existing theoretical and experimental bounds. Also, our results prove that CP-RSA is an effective approach that provides resistance against standard RSA small private key attacks. [ABSTRACT FROM AUTHOR]

The paper by C. Lubich in Numer. Math. 2(52):129–145, 1988 is widely cited for its analysis of convolution quadrature rules for integrals with weakly singular kernels. This analysis depends on a key technical lemma (an upper bound on a discrete convolution sum) whose proof uses some advanced tools. In the present paper it will be shown that this lemma can be quickly proved in an elementary way; moreover, the new proof includes those cases that were excluded from the 1988 paper, and the bounds obtained are shown to be sharp. [ABSTRACT FROM AUTHOR]

The article presents a research paper on the link between hypnagogia sleep and creativity, which references a study by Delphine Oudiette et al., published in an issue of "Science Advances". Topics discussed include the math problem given to the participants and the success rates for participants who stayed awake or progressed to N2 sleep.

In the existing multi-factor one-order (MFOO) forecasting models, each fuzzy logical relation (FLR) has one consequent and more than one premise reflecting the association between the fuzzy values at two consecutive moments, and its premises are related to all the factors involved in forecasting. When using such FLRs to realize prediction, no matched FLR cases happened often and thus no logical prediction can be made. Two shortcomings are found for that: one is that more premises make FLRs matching more difficult; the other is that there are no enough FLRs. To overcome these shortcomings, this paper proposes two kinds of FLRs: short cross-association FLRs and long cross-association FLRs, which mean the influence on the consequent is from a part of the factors instead of all the factors. Specifically, the long cross-association FLRs aim at finding the association between fuzzy values at two non-consecutive moments. Such cross-associations exist in reality, the construction of them allows more FLRs to be mined from history observations. They can raise the possibility of finding available FLRs for forecasting. Based on the proposed FLRs, two MFOO forecasting models are proposed. Experiments show the advantage of the new FLRs and the good performance of the proposed models. [ABSTRACT FROM AUTHOR]

In order to explore a unified theory of three-way decisions proposed by Yao, Hu introduced three-way decision spaces through an axiomatic method, established the corresponding three-way decisions, and proposed two open problems on the changes of decision parameters in definition of three-way decisions. For answering these two questions, this paper firstly discusses the parameter changes in the assumptions from 0 ≤ β < α ≤ 1 to 0 ≤ β ≤ α ≤ 1 and inequality E ( A ) ( x ) ≤ β in the rejection region is replaced by E ( A ) ( x ) < β . Under the circumstance, this paper introduces new type of three-way decisions in three-way decision spaces and discusses properties of the three-way decisions, lower and upper approximations induced by three-way decisions, aggregation three-way decisions over multiple three-way decision spaces and dynamic three-way decisions on three-way decision spaces. Then this paper discusses another question on refusal decision region when the uncertain region is defined by using inequality β < E ( A ) ( x ) < α and gives one example to illustrate the similarity and difference among these three-way decisions based on three-way decision spaces. [ABSTRACT FROM AUTHOR]

In order to solve the problem that previous relation researches in operational task-resource matching are hard to flexible computing for generating a new matching scheme from the existing scheme under the condition of operational tasks or resources adjusted in uncertainty cases, role-based approaches to operational task-resource flexible matching model and algorithm are proposed in the paper for flexible matching operational tasks with resources. Firstly, through introducing the concept of roles, the role-based calculation framework of operational task-resource flexible matching is constructed. Secondly, two aspect indexes about resource utilization ratio (RUR) and time utilization ratio (TUR) are given to reflect operational task-resource matching quality (TRMQ), which can be regarded as the objective function for modeling role-based operational task-resource flexible matching mathematical formulation. On the basis of this, the role-based artificial bee colony (RABC) algorithm, including five specific calculating operators, is put forward for solving the flexible matching problem with double encoding on operational tasks and resources by roles. Finally, via comparing with the previous methods in application cases, it can be validated that role-based model and proposed algorithm are more effective, which can be used to obtain a new incremental scheme from the existing matching scheme for adopting the operational tasks or resources adjustment. Moreover, there are flexible computation advantages of the approaches proposed in this paper to solve the problem about operational task-resource matching in large-scale. [ABSTRACT FROM AUTHOR]

The article discusses the findings of a study by the Google Scholar Team which shows an increase in publication of highly-cited papers by non-elite journals. It notes Google Scholar's analysis of academic publishing by non-elite journals which was posted at 27 percent in 1995 to 47 percent in 2013. It cites that non-elite journals accounted for a 133 percent increase in Computer Science citations, while citations for Physics & Mathematics grew by 204 percent.

The article presents information on what a piece of A4 paper can tell aliens about human beings. Without a common language, it is very difficult to communicate with an alien. Sign language will also be out, because there's no guarantee they'd have arms or eyes. English literature is relevant in English-speaking countries and history on Earth, but it is the maths which applies everywhere. And, if aliens have landed on Earth and a message of peace demonstrating that human beings are a civilized race is to be delivered, then only this piece of paper will work.

Abstract Let X 1 , X 2 , ... be independent and identically distributed random variables with support on non-negative integers and X (n) (n ≥ 1) denote the corresponding sequence of discrete record values. In the present paper, we derive weak and strong limit results for the spacings of discrete record values X (n + m) − X (n) (n → ∞) and discuss generation algorithms of discrete records. [ABSTRACT FROM AUTHOR]

Abstract In Yano et al. (2009), limit theorems (so called, Feynman–Kac penalizations) for the one-dimensional recurrent symmetric α -stable process weighted and normalized by negative (killing) Feynman–Kac functionals with small potential are studied. In this paper, we deal with the same problem for negative potentials diverging at infinity. [ABSTRACT FROM AUTHOR]

Abstract In this short paper we find that the Sobolev inequality 1 p − 2 ∫ f p d μ 2 p − ∫ f 2 d μ ≤ C ∫ | ∇ f | 2 d μ (p ≥ 0) is equivalent to the exponential convergence of the Markov diffusion semigroup (P t) to the invariant measure μ , in some Φ -entropy. We provide the estimate of the exponential convergence in total variation and a bounded perturbation result under the Sobolev inequality. Finally in the one-dimensional case we get some two-sided estimates of the Sobolev constant by means of the generalized Hardy inequality. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to establish two new types of rough set structures associated with the Marcus–Wyse (MW -, for brevity) topology, such as an M -rough set and an MW -topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in Z 2 , where Z is the set of integers. These two rough set structures are related to each other via an M -digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC -, for short) space (U , C) and a subset X of U , we firstly introduce a new neighborhood system on U related to X. Next, we formulate the lower and upper approximations with respect to X , where all of the sets U and X (⊆ U) need not be finite and the covering C is locally finite. Actually, the notion of M -digitization of a 2-dimensional Euclidean space plays an important role in developing an M -rough and MW -topological rough set structures. Further, we prove that M -rough set operators have a duality between them. However, each of MW -topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW -topology. [ABSTRACT FROM AUTHOR]

Abstract The study of properties of gradual evaluation methods in argumentation has received increasing attention in recent years, with studies devoted to various classes of frameworks/ methods leading to conceptually similar but formally distinct properties in different contexts. In this paper we provide a novel systematic analysis for this research landscape by making three main contributions. First, we identify groups of conceptually related properties in the literature, which can be regarded as based on common patterns and, using these patterns, we evidence that many further novel properties can be considered. Then, we provide a simplifying and unifying perspective for these groups of properties by showing that they are all implied by novel parametric principles of (either strict or non-strict) balance and monotonicity. Finally, we show that (instances of) these principles (and thus the group, literature and novel properties that they imply) are satisfied by several quantitative argumentation formalisms in the literature, thus confirming the principles' general validity and utility to support a compact, yet comprehensive, analysis of properties of gradual argumentation. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. Several examples are also presented along with the theory. [ABSTRACT FROM AUTHOR]

Abstract Consider the processes { L t ; t ≥ 0 } and { λ t ; t ≥ 0 } associated with a marked Hawkes process and its conditional intensity. In the present paper, the integration by parts formulas for those processes are constructed, and applied to the study on the absolute continuity for their conditional laws. Moreover, the sensitivity formulas for those processes with respect to the parameters are given. [ABSTRACT FROM AUTHOR]

Abstract This paper develops the asymptotic properties of a recently proposed measure of inequality emphasizing the status of the poor relative to the rich. A simulation confirms the asymptotic results are applicable in practice. [ABSTRACT FROM AUTHOR]

Abstract In intelligent systems, belief function is a common approach to modelling uncertain and imperfect information obtained constantly while knowledge bases are used to encapsulate multiple static information items. In the literature, many different approaches have been proposed for combining belief functions (resp. merging knowledge bases) when there are multiple belief functions (resp. knowledge bases) generated from different sources depicting the same issue of interest. However, the connection between belief function combination and knowledge base merging is not adequately explored. In this paper, we aim to study the correspondence between the two lines of research. By introducing a numerical characteristic function for each knowledge base, we show that there is one to one correspondence between a set of combination rules of belief functions and merging methods of weighted knowledge bases. [ABSTRACT FROM AUTHOR]

Multidomain network classification has attracted significant attention in data integration and machine learning, which can enhance network classification or prediction performance by integrating information from different sources. Despite the previous success, existing multidomain network learning methods usually assume that different views are available for the same set of instances, and thus, they seek a consistent classification result for all domains. However, in many real-world problems, each domain has its specific instance set, and one instance in one domain may correspond to multiple instances in another domain. Moreover, due to the rapid growth of data sources, different domains may not be relevant to each other, which asks for selecting domains relevant to the target/focused domain. A key challenge under this setting is how to achieve accurate prediction by integrating different data representations without losing data information. In this paper, we propose a semisupervised classification approach for a multidomain network based on label propagation, i.e., multidomain classification with domain selection (MCS), which can deal with the cross-domain information and different instance sets in domains. In particular, with sparse weight properties, the proposed MCS can automatically identify those domains relevant to our target domain by assigning them higher weights than the other irrelevant domains. This not only significantly improves a classification accuracy but also helps to obtain optimal network partition for the target domain. From the theoretical viewpoint, we equivalently decompose MCS into two simpler subproblems with analytical solutions, which can be efficiently solved by their computational procedures. Extensive experimental results on both synthetic and real-world data sets empirically demonstrate the advantages of the proposed approach in terms of both prediction performance and domain selection ability. [ABSTRACT FROM AUTHOR]

Purpose Ordinary differential equations (ODEs) are widely used in the engineering curriculum. They model a spectrum of interesting physical problems that arise in engineering disciplines. Studies of different types of ODEs are determined by engineering applications. Various techniques are used to solve practical differential equations problems. This paper aims to present a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages. In this work, the successive differentiation method (SDM) for solving linear and nonlinear and homogeneous or non-homogeneous ODEs is presented. The algorithm uses the successive differentiation of any given ODE to determine the values of the function’s derivatives at a single point, mostly x = 0. The obtained values are used to construct the Taylor series of the solution of the examined ODE. The algorithm does not require any new assumption, hence handles the problem in a direct manner. The power of the method is emphasized by testing a variety of models with distinct orders, with constant and variable coefficients. Most of the symbolic and numerical computations can be carried out using computer algebra systems.Design/methodology/approach This study presents a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages.Findings This method is applied to a variety of well-known equations, such as the Bernoulli equation, the Riccati equation, the Abel equation and the second-order Euler equation, some with constant and variable coefficients. SDM handles linear and nonlinear and homogeneous or nonhomogeneous ODEs in a direct manner without any need to restrictive conditions. The method works effectively to the Volterra integral equations, as will be discussed in a coming work.Originality/value The method can be extended to a wide range of engineering problems that are modeled by differential equations. The method is simple and novel and highly accurate. [ABSTRACT FROM AUTHOR]

Abstract This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Given a convex potential in a space with convex obstacles, an artificial potential is used to navigate to the minimum of the natural potential while avoiding collisions. The artificial potential combines the natural potential with potentials that repel the agent from the border of the obstacles. This is a popular approach to navigation problems because it can be implemented with spatially local information that is acquired during operation time. Artificial potentials can, however, have local minima that prevent navigation to the minimum of the natural potential. This paper derives conditions that guarantee artificial potentials to have a single minimum that is arbitrarily close to the minimum of the natural potential. The qualitative implication is that artificial potentials succeed when either the condition number—the ratio of the maximum and the minimum eigenvalue—of the Hessian of the natural potential is not large and the obstacles are not too flat, or when the destination is not close to the border of an obstacle. Numerical analyses explore the practical value of these theoretical conclusions. [ABSTRACT FROM AUTHOR]

This paper presents a framework for describing users' knowledge of how a simple four-function calculator operates. Differences among novices and experts in their conceptions of "what goes on inside the calculator" for various sequences of button presses are summarized. Individual differences include different views on when an expression is evaluated, different procedures for evaluating a chain of arithmetic, and different rules for evaluating unusual sequences of key presses. [ABSTRACT FROM AUTHOR]

This paper presents a data sublanguage called SQUARE, intended for use in ad hoc, interactive problem solving by non-computer specialists. SQUARE is based on the relational model of data, and is shown to be relationally complete; however, it avoids the quantifiers and bound variables required by languages based on the relational calculus. Facilities for query, insertion, deletion, and update on tabular data bases are described. A syntax is given, and suggestions are made for alternative syntaxes, including a syntax based on English key words for users with limited mathematical back ground. [ABSTRACT FROM AUTHOR]

This paper addresses the robust gradient learning (RGL) problem. Gradient learning models aim at learning the gradient vector of some target functions in supervised learning problems, which can be further used to applications, such as variable selection, coordinate covariance estimation, and supervised dimension reduction. However, existing GL models are not robust to outliers or heavy-tailed noise. This paper provides an RGL framework to address this problem in both regression and classification. This is achieved by introducing a robust regression loss function and proposing a robust classification loss. Moreover, our RGL algorithm works in an instance-based kernelized dictionary instead of some fixed reproducing kernel Hilbert space, which may provide more flexibility. To solve the proposed nonconvex model, a simple computational algorithm based on gradient descent is provided and the convergence of the proposed method is also analyzed. We then apply the proposed RGL model to applications, such as nonlinear variable selection and coordinate covariance estimation. The efficiency of our proposed model is verified on both synthetic and real data sets. [ABSTRACT FROM AUTHOR]

An interview with Marco Ripà. He discusses: geographic, cultural, and linguistic familial background; influence on personal development; pivotal moments; loneliness and associated fear in youth, and its frequency in gifted youth; physique sculpting and personal combat training; B.Econ.Sc., magna cum laude; autodidactic proclivities; expertise and knowledge and its benefit for personal and professional life; contents of the big IQ projects; inspiration for mathematics competitions, papers in number theory, and the creation of integer sequences for OEIS; title, contents, and interest in the discrete mathematics book; academic papers on currency speculation, market failures, social justice, and sub-prime mortgage crisis; common intelligences with lower than expected occurrence and flourishing; a society that provides for the gifted and talented; summarization of the research subjects completed by him; entrance into the high-IQ and ultra-high-IQ world; and the inter-relationship development up to the present between the high-IQ, and ultra-high-IQ, community and himself. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of factor prime factorizations for n-D polynomial matrices and presents a criterion for the existence of factor prime factorizations for an important class of n-D polynomial matrices. As a by-product, we also obtain an algebraic algorithm to check n-D factor primeness in some important cases which partially solves the long-standing open problem of recognizing n-D factor prime matrices. Some problems related to the factorization methods are also studied. Several exam- pies are given to illustrate the results. The results presented in this paper are true over any coefficient field. [ABSTRACT FROM AUTHOR]

A new methodology for the representation of a set of magnetically coupled coils by means of an equivalent circuit is presented in this paper. The proposed method makes use of an equivalent circuit made up of a primary group of RL branches, which are the input terminals-pairs of the model, and a group of RL loops that are magnetically coupled with the primary branches, constituting a multiport model of a system of coupled coils that allows representing its frequency-behavior very accurately. This can be seen as a generalization of the classic methodology for the synthesis of RL driving-point impedances (developed by Foster and Cauer) considering the more general case of having multiple input terminals-pairs. This paper contributes an appropriate tool for the accurate modeling of transformer windings, a historically very difficult. problem due to the frequency-dependence of the inductances and losses. The new method is first applied to the simple case of a single coil and was used afterward to the representation of a coil system, proving in both cases the mathematical validity of the method. The usefulness of the method is shown through its application to the modeling of a transformer winding. [ABSTRACT FROM AUTHOR]

This paper presents new techniques to implement direct digital frequency synthesizers (DDFSs) with optimized piece- wise-polynomial approximation. DUES performances with piece- wise-polynomial approximation are first analyzed, providing theoretical upperbounds for the spurious-free dynamic range (SFDR), the maximum absolute error, and the signal-to-noise ratio. A novel approach to evaluate, with reduced computational effort, the near optimal fixed-point coefficients which maximize the SFDR is de- scribed. Several piecewise-linear and quadratic DDFS are implemented in the paper by using novel, single-summation-tree architectures. The tradeoff between ROM and arithmetic circuits complexity is discussed, pointing out that a sensible silicon area reduction can be achieved, by increasing ROM size and reducing arithmetic circuitry. The Use of fixed-width arithmetic can be combined with the single-summation-tree approach to further increase performances. It is Shown that piecewise-quadratic DDFSs become effective against piecewise-linear designs for an SFDR higher than 100 dBc. Third-order DDFSs are expected to give advantages for an SFDR higher than 180 dBc. The DDFS circuits proposed in this paper compare favorably with previously proposed approaches. [ABSTRACT FROM AUTHOR]

The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most η-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to blind source extraction from convolutive mixtures in multi-input multi-output (MIMO) channels. Two ill-conditioned cases are considered: the number of sensors is less than the number of sources and the number of sensors is greater than or equal to the number of sources but the system is noninvertible. Although there exist several works related to ill-conditioned dynamic MIMO channels, especially on blind channel identification, how to obtain a true source Only from observable convolutive mixtures is still an open problem. In this paper, beginning with introducing two blind ex- traction models for blind deconvolution in ill-conditioned MIMO channels, we discuss the extractability issue. Results from our extractability analysis (a necessary and sufficient condition) show that it is possible to extract individual sources from the outputs. Furthermore, all potentially separable sources (at most equal to the number of sensors) can be extracted sequentially based on these extraction models. A cost function based on cross cumulant is discussed along with the Gauss-Newton algorithm. Finally, a simulation example is presented for illustration. [ABSTRACT FROM AUTHOR]