Gestures,Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization

To improve our understanding of novice students' production of symbolic algebraic expressions, this article contrasts students' presymbolic and symbolic procedures in generalizing activities. Although a significant amount of previous research on the learning of algebra has dealt with students' errors in the mastering of the algebraic syntax, the semiotic cultural theoretical approach presented here focuses on the role that body, discourse, and signs play when students' refer to mathematical objects. Three types of generalizations are identified: factual, contextual, and symbolic. The results suggest that the passage from presymbolic to symbolic generalizations requires a specific kind of rupture with the ostensive gestures and contextually based key linguistic terms underpinning presymbolic generalizations. This rupture means a disembodiment of the students' previous spatial temporal embodied mathematical experience.     

A Numerical Approach to the Repairman Problem with Two Different Types of Machine

In this paper we deal with a heterogeneous machine-interference model under the assumption that the priority machines have pre-emptive priority over the ordinary ones. In each group, machines are characterized by exponentially distributed failure and repair times with different rates. The failed machines are served by a single repairman according to FIFO discipline. The aim of the paper is to give the steady-state operational characteristics of the system, such as operative utilization, expected busy-period length, machine availability, mean waiting times and average number of failed machines. Finally, numerical examples illustrate the problem in question.     

Pattern Generalization with Graphs and Words: A Cross-Sectional and Longitudinal Analysis of Middle School Students' Representational Fluency

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as reading the data, over more distant predictions and generation of abstractions. Performance data also indicate a verbal advantage that shows greater success when working with words than graphs, a replication of earlier findings comparing words to symbolic equations. Surprisingly, students show a marked advantage with patterns presented in a continuous format (line graphs and verbal rules) as compared to those presented as collections of discrete instances (point-wise graphs and lists of exemplars). Student pattern-generalization performance also was higher when words and graphs were combined. Analyses of student performance patterns and strategy use contribute to an emerging developmental model of representational fluency. The model contributes to research on the development of representational fluency and can inform instructional practices and curriculum design in the area of algebraic development. Results also underscore the impact that perceptual aspects of representations have on students' reasoning, as suggested by an Embodied Cognition view.     

Nefness: Generalization to the lc case

This note is devoted to a proof of the b-nefness of the moduli part in the canonical bundle formula for an lc-trivial fibration that is lc and not klt over the generic point of the base. This result is proved in [3, §8] and [4] by using the theory of variation of mixed Hodge structure. Here we present a proof that makes use only of the theory of variation of Hodge structure and follows Ambro's proof of [2, Theorem 0.2].     

A Simple Generalization of the ElGamal Cryptosystem to Non-Abelian Groups

In this article we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the ElGamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equivalent to the ElGamal cryptosystem over finite fields.     

A Generalization of the Conjugate-Gradient Method to Solve Complex Systems

The conjugate-gradient method has gained favour recently, notablyas a procedure for solving large, preconditioned systems ofalgebraic equations. Preconditioning techniques have been developedfor preparing the system for efficient solution by conjugategradients. The basic conjugate-gradient method was developedfor symmetric, positive definite systems. In this paper a generalizationto complex systems is described by developing the work of Fletcher.The methods improve on ‘symmetrization’, solvingthe normal equations for the asymmetric case, and expandingthe complex system to a real one of twice the order. The methodhas already proved to be effective.     

A Generalization of the Hausdorff-Young Theorem

Considering mixed-norm sequence spaces lp,q, p, q 1, C. N. Kellogg proved the following theorem: if 1 < p 2 then lp,2 and lp,2 , where 1/p + 1/p = 1. This result extends the Hausdorff-Young Theorem.We introduce here multiple mixed-norm sequence spaces , examine their properties and characterize the multipliers of spaces of the form lp,[s;n],q, with the index s repeated n times. By an interpolation-type argument we prove that (l,[2;n],2, lp,[1;n],1) for 1 < p 2. Using these results we obtain a further generalization of the Hausdorff-Young Theorem: if 1 < p 2 then lp,[2;n] and lp,[2;n] for each n = 0, 1, 2, ¨. The spaces lp,[2;n] decrease and lp,[2;n] increase properly with n for 1 < p < 2 and 1/p + 1/p = 1. We also extend a theorem of J. H. Hedlund on multiplers of Hardy spaces and deduce other results.     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

均值不等式的一个推广

给出几何-算术均值不等式的一个推广,实例展示其应用,说明与约束极值原理相关的一些问题也可以通过推广的几何-算术均值不等式加以解决.     

Clemens-Schmid序列的推广

本文把Clemens-Schmid正合序列推广到单参数族的奇异纤维具有任意奇性的情况。     

A Structure Preserving Generalization of Independence,Domination and Irredundance

Abstract

The now famous inequality chain ir≤γ≤i≤β ≤ Γ ≤ IR, where ir and IR denote the lower and upper irredundance numbers of a graph, γ and Γ the lower and upper domination numbers, i the independent domination number and β the independence number of a graph, may be seen as the culmination of a process by which we start with independence (a hereditary property of vertex sets); we characterize maximal independence by domination (a superhereditary property of vertex sets), and then characterize minimal domination by irredundance (again a hereditary property). In this paper we generalize independent, dominating and irredundant sets of a graph G to what we will call s-dominating, s-independent and s-irredundant functions (for s a positive integer), which are functions of the type f : V (G) → N, in such a way that the maximal 1-independent, the minimal 1- dominating and the maximal 1-irredundant functions are the characteristic functions of the maximal independent, the minimal dominating and the maximal irredundant sets of G respectively. In addition, we would want to preserve those properties of and relationships between independence, domination and irredundance needed to extend the inequality chain ir≤γ≤i≤β ≤ Γ ≤ IR to one for s-dominating, s-independent and s-irredundant functions by a process similar to that described above.     

A Simple Generalization of the ElGamal Cryptosystem to Non-Abelian Groups II

This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that this MOR cryptosystem has better security than the ElGamal cryptosystem over finite fields.     

A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit

Does relativistic gravity provide arguments against the existence of a preferred frame? Our answer is negative. We define a viable theory of gravity with preferred frame. In this theory, the EEP holds exactly, and the Einstein equations of GR limit are obtained in a natural limit. Despite some remarkable differences (stable “frozen stars” instead of black holes, a “big bounce” instead of the big bang, exclusion of nontrivial topologies and closed causal loops, and a preference for a flat universe) the theory is viable.     

与Murty-Simon猜想相关的一个重要引理的推广

一个图G的无公共邻点的点对集定义为disj(G)={(u,v):N_G(u)∩N_G(v)=Φ}.Füredi在那篇对Murty-Simon猜想取得重大进展的文章中证明了一个重要的引理:对任意具有n个顶点的图G,|E(G)|+|disj(G)|≤「n~2/2」.本文对引理中的和|E(G)|+|disj(G)|做了一些更加深入的研究并对这个引理做了一些推广.     

A Formal,Decision-Theoretic Approach to Flexibility and Robustness

Traditional decision-making techniques only deal with a limited type of uncertainty: that which can be foreseen sufficiently to be expressed as a number of alternate moves between which nature will choose. A plan is formulated which specifies how the decision-maker should respond to nature's moves. Such a plan makes no allowance for uncertainty which could not be foreseen. Unforeseeable uncertainty can only be dealt with if the decision-maker's response to nature's moves is not fixed in advance but is itself uncertain. Flexibility is then defined as the entropy of that uncertainty. It is a measure of both the number of alternative sequences of moves which are open to the decision-maker and his attitude to them. Robustness is a way of trading off flexibility against expected value as estimated under foreseeable uncertainty. The cost of flexibility may be estimated and controlled.