拟阵的可去圈

本首先用拟阵语言将图论的新概念定义成了拟阵的新概念，然后用拟阵语言将Goddyn和Heuevl所得的图论上的新结果平移成了拟阵的新结果，最后用拟阵的方法对它们给出了新的证明。     

On the process of gaining language as a resource in mathematics education

In this paper, we expand our prior work on mathematics education in contexts of language diversity by elaborating on the three perspectives on language described by Ruiz (NABE J 8(2):15–34, 1984): language-as-right, language-as-resource, and language-as-problem. We illustrate our arguments with data taken from research contexts in Catalonia-Spain and South Africa. In these two parts of the world, the language policy in education has long been an issue, with a monolingual orientation that values one language (i.e., Catalan in Catalonia and English in South Africa) over others. Throughout the introduction of specific examples of policy documents, classroom practices, and participants’ reports, our main point is that the right of using the students’ languages makes sense because it is itself more than an intrinsic human right; it is an option that potentially benefits the creation of mathematics learning opportunities. Especially for the instances of classroom practices, our examples can be considered as representative in that they point to a common situation in our data: despite the fact of the language of learning and teaching being fixed, there is room for the learners and the teacher to take or react to a decision on what language to use, with whom, and how in concrete moments of the interaction. However, on the basis of our studies and drawing on the literature in mathematics education and language diversity, we argue that language rights are not sufficiently connected to language as a pedagogical resource. The enactment of these rights is still contributing in many ways to the social and political construction of problems concerning the role of certain languages in classroom interaction. We conclude the paper by discussing some possibilities for framing language as a resource that provide effective support to all students’ learning of mathematics.     

Program control of operating systems

The traditional job control language becomes superfluous if the existing programming languages are extended slightly. Such extensions also allow drivers and operating systems to be programmed entirely in high level languages. Ultimately, we may see machine independent operating systems. A framework is presented for an extendable operating system which allows a simple, uniform implementation of these language extensions.     

Language and communication in mathematics education: an overview of research in the field

Within the field of mathematics education, the central role language plays in the learning, teaching, and doing of mathematics is increasingly recognised, but there is not agreement about what this role (or these roles) might be or even about what the term ‘language’ itself encompasses. In this issue of ZDM, we have compiled a collection of scholarship on language in mathematics education research, representing a range of approaches to the topic. In this survey paper, we outline a categorisation of ways of conceiving of language and its relevance to mathematics education, the theoretical resources drawn upon to systematise these conceptions, and the methodological approaches employed by researchers. We identify four broad areas of concern in mathematics education that are addressed by language-oriented research: analysis of the development of students’ mathematical knowledge; understanding the shaping of mathematical activity; understanding processes of teaching and learning in relation to other social interactions; and multilingual contexts. A further area of concern that has not yet received substantial attention within mathematics education research is the development of the linguistic competencies and knowledge required for participation in mathematical practices. We also discuss methodological issues raised by the dominance of English within the international research community and suggest some implications for researchers, editors and publishers.     

The Pursuit of an Implication for the Logics L3A and L3B

The authors of Beziau and Franceschetto (New directions in paraconsistent logic, vol 152, Springer, New Delhi, 2015) work with logics that have the property of not satisfying any of the formulations of the principle of non contradiction, Béziau and Franceschetto also analyze, among the three-valued logics, which of these logics satisfy this property. They prove that there exist only four of such logics, but only two of them are worthwhile to study. The language of these logics does not consider implication as a connective. However, the enrichment of a language with an implication connective leads us to more interesting systems, therefore we look for one implication for these logics and we study further properties that the logics obtain when this connective is added to these systems.     

论极限教学的解决方案

首先探讨了极限ε语言的思维复杂性,接着介绍了种种极限教学方案以及笔者自身的实践,在回顾微积分的历史和比较各种方案后,根据教育学原理提出了一种新的极限教学的组合方案.     

Glivenko like theorems in natural expansions of BCK‐logic

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK‐logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK‐logic with negation by a family of connectives implicitly defined by equations and compatible with BCK‐congruences. Many of the logics in the current literature are natural expansions of BCK‐logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one‐variable formula in the language of BCK‐logic with negation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mining information from time series in the form of sentences of natural language

The goal of this paper is to provide a more detailed explanation of the principles how special formulas that characterize properties of trend of time series can be formed and how they are interpreted. Then we show how these formulas can be used in a tectogrammatical tree that construes special sentences of natural language, using which information on behavior of time series is provided. We also outline the principles of mining this information. The last part is devoted to application of the theory of intermediate quantifiers to mining summarized information on time series also in sentences of natural language.     

Effective estimates for unirationality

In this work we refine some estimates that where set up by Morin and Predonzan in [1] and [2]. While the language has been updated, most of the ideas go back to these authors and we have essentially added some observations in the main stream of the proofs.     

An internal language for autonomous categories

We present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus as an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory. We prove that this language is an internal language and show as an application the coherence theorem of Kelly and Mac Lane, which becomes straightforward to state and prove. Finally, we extend the language with the natural numbers and show that this corresponds to a weak Natural Numbers Object in an autonomous category.     

On the restricted Chebyshev–Boubaker polynomials

Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev–Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and we study certain central sequences defined by their coefficient arrays. We give an integral representation for their moments, and we show that the Hankel transforms of these moments have a simple form. We show that the (sequence) Hankel transform of the row sums of the corresponding moment matrix is defined by a family of polynomials closely related to the Chebyshev polynomials of the second kind, and that these row sums are in fact the moments of another family of orthogonal polynomials.     

Semantic contamination and mathematical proof: Can a non-proof prove?

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove.     

一类吸引子的语法复杂性*

本文研究了Feigenbaum吸引子和周期窗口中Feisenbaum吸引子决定的形式语言,讨论了它们的语法复杂性.证明了这类吸引子都是ETOL语言,从而是上下文有关语言(CSL);而不是上下文无关语言(CFL).     

Efficient Management of Multiple Sets to Extract Complex Structures from Mathematical Programs

Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the algebraic formulation is usually sufficient to retrieve different block structures from mathematical programs. These structured problems can then be solved by adequate solution techniques. To illustrate this idea we focus on stochastic programming problems with recourse. Taking into account both time and uncertainty dimensions of these problems, we are able to retrieve different customized structures in their constraint matrices. We applied the Structure Exploiting Tool to retrieve the structure from models built with the GAMS modeling language. The underlying mathematical programs are solved with the decomposition algorithm that applies interior point methods. The optimization algorithm is run in a sequential and in a parallel computing environment.     

Probability,fuzziness and borderline cases

An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is only uncertainty about the relative sharpness or vagueness of the interpretation of the language.     

Patterns in irregular multi-dimensional arrays

In this paper, we study irregular 3D-Arrays with pyramid shapes. Some computation using Maple software and C++ language have been carried out to illustrate some novel and interesting patterns of numbers in these arrays.     

R: A Language for Data Analysis and Graphics

Abstract

In this article we discuss our experience designing and implementing a statistical computing language. In developing this new language, we sought to combine what we felt were useful features from two existing computer languages. We feel that the new language provides advantages in the areas of portability, computational efficiency, memory management, and scoping.