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The response-to-intervention approach was initially proposed to solve a problem associated with the identification of learning disabled children. Over time, it evolved into an approach intended to prevent learning disabilities and a multi-tiered system of support for learners. The goal of the present paper is to describe the main steps of this evolution and the main components of a multi-tiered system of support. We also relate this approach explicitly to the other papers in this special issue, namely the management of its implementation and the inclusion of mathematics as a teaching subject and behaviour regulation. Finally, we briefly discuss the contribution of the response-to-intervention framework to the field of education. [ABSTRACT FROM AUTHOR]

Problems in mathematics are a frequent major complaint in neuropediatric departments, for which there are two explanatory theoretical models: the hypothesis of a genetic and modular origin (with a number sense deficit) and a multidetermined origin. The purpose of this paper is to review the mathematical difficulties described in Turner syndrome and Fragile X syndrome, because a specific mathematical disorder is usually reported in these populations, supporting the existence of a number sense. Analysis of the literature reveals highly variable cognitive phenotypes in these populations, especially regarding mathematical abilities. Performance heterogeneity might be related to different factors such as the abilities needed to perform the task, the variability of definitions, the different tests used in the studies and the heterogeneity of the syndromes themselves. A number sense deficit is usually described in these syndromes, but variable cognitive impairments are also observed. The idea of a modular functioning is then debated and we argue for the necessity of a global cognitive evaluation approach. [ABSTRACT FROM AUTHOR]

Let N be the set of positive integers and A a subset of N. For n∈N, let p(A,n) denote the number of partitions of n with parts in A. In the paper J. Number Theory 73 (1998) 292, Nicolas et al. proved that, given any N∈N and B⊂{1,2,…,N}, there is a unique set A=A0(B,N), such that p(A,n) is even for n>N. Soon after, Ben Saı¨d and Nicolas (Acta Arith. 106 (2003) 183) considered σ(A,n)=∑d∣n,d∈Ad, and proved that for all k≥0, the sequence (σ(A,2kn) mod 2k+1)n≥1 is periodic on n. In this paper, we generalise the above works for any formal power series f in F2[z] with f(0)=1, by constructing a set A such that the generating function fA of A is congruent to f modulo 2, and by showing that if f=P/Q, where P and Q are in F2[z] with P(0)=Q(0)=1, then for all k≥0 the sequence (σ(A,2kn) mod 2k+1)n≥1 is periodic on n. [Copyright &y& Elsevier]

In this paper, we study the most popular book of recreational mathematics published in the second half of the 18th century: The Nouvelles Récréations by Guyot. We indicate the motivations of the author, a simple postman, and the conditions which led him to write this book. We describe the spirit of the book and the public at which it aims. The success of the Nouvelles Récréations illustrates the rise of a science in polite society whose main goal is to amaze and amuse. Then, we examine the place of mathematics in this project and analyze the repertoire of problems and tricks. We focus on problems of combinatorics proposed by Guyot, like anagrams and card shuffles, which inspired some real mathematical work on the part of Monge and Gergonne. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we define the notion of “graded algebra with symmetries”. This notion is a generalization of the extended differential forms. We prove that for a graded algebra with symmetries T, we associate a subalgebra which generalizes the noncommutative differential forms. Using this algebra , we can define the Hochschild and cyclic homologies, cup i-products and the Steenrod squares. [Copyright &y& Elsevier]

Let ΦΦ( x) be the number of the integers n such that φφ( n) ≤≤ x, where φφ denotes the Euler function. In this paper we give an explicit form of Bateman's theorem for the remainder term ΦΦ( x) -- Ax where A == ζζ(2) ζζ(3)/ ζζ(6). [ABSTRACT FROM AUTHOR]

At the beginning of the 1890s, Schwarz and Peano (independently of each other) showed that Serret’s definition of the area of a surface was flawed. This paper first aims at describing the various methods that the mathematicians have used for correcting Serret’s reasoning; its second goal is to compare and to present more in detail two solutions: Lebesgue’s notorious construction and Peano’s definition. [ABSTRACT FROM AUTHOR]

In [Breuil et Schneider, J. reine angew. Math. 610: 149–180, 2007] is formulated a conjecture on the equivalence of the existence of invariant norms on certain locally algebraic representations of GL d+1( L) and the existence of certain de Rham representations of Gal(/ L), where L is a finite extension of ℚ p. In this paper, we prove the “easy” direction of the conjecture: the existence of invariant norms implies the existence of admissible filtrations. [ABSTRACT FROM AUTHOR]

Abstract: The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley–Harrison cohomology operator for . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in . [Copyright &y& Elsevier]

Abstract: In this paper we study the centered and non-centered Hardy–Littlewood maximal functions, M and , for a wide class of non-doubling measure μ defined on cusped manifolds. In particular, we give a class of manifolds with exponential volume growth on which M is of weak type and is bounded on for all . [Copyright &y& Elsevier]

Abstract: In this paper, we define in the framework of noncommutative differential forms the notion of cup i-product introduced by Steenrod in [N.E. Steenrod, Product of cocycles and extensions of mappings, Ann. Math. 48 (2) (1947)]. This cup i-product permits to define an operator who will be a generalisation of the operator b defined in Hochschild and cyclic homology. With the operator we define in an explicitly way the Steenrod and Thomas–Pontrjagin squares. [Copyright &y& Elsevier]

Abstract: In this paper, we use p-adic families of automorphic forms for a unitary group in three variables, containing some non-tempered forms constructed by Rogawski, to prove some cases of the Bloch–Kato conjectures. [Copyright &y& Elsevier]

This paper presents an axiomatic description in a base free way of infinite root systems as those found in the study of Kac–Moody–Borcherds' algebras. In 1979, R. Moody [Adv. Math. 33 (1979) 144] posed the problem of finding such a description. In [Comm. Algebra 23 (1995) 4791], J.G. Bliss has already presented two answers to this question with his notions of “geometric root systems” and “rational root systems.” This new answer to Moody's question fits into the framework of the earlier axiomatic theory of the « syste`mes ge´ne´rateurs de racines » developed in [N. Bardy, Me´m. Soc. Math. Fr. (N.S.) 65 (1996)]. [Copyright &y& Elsevier]

Let Ω⊂RN be an open set. We consider on Ω the competitors (U,K) for the reduced Mumford–Shah functional, that is to say the Mumford–Shah functional in which the L2-norm of U term is removed, where K is a closed subset of Ω and U is a function on Ω&z.drule;K with gradient in L2. The main result of this paper is the following: there exists a constant c for which, whenever (U,K) is a quasi-minimizer for the reduced Mumford–Shah functional and B(x,r) is a ball centered on K and contained in Ω with bounded radius, the HN−1-measure of K∩B(x,r) is bounded above by crN−1 and bounded below by c−1rN−1. [Copyright &y& Elsevier]

In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global Lp convergence of the Navier–Stokes vorticity ων to the Eulerian vorticity ω, with p>1. To cite this article: T. Hmidi, C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]

Application of the fuzzy set theory to the biometric evaluation of the species Nummulites millecaput in the western part of the Tethys. The goal of this paper is to demonstrate the ability of the fuzzy-set theory to contribute to the evaluation of paleontological problems. As an example, the species Nummulites millecaput, Boube´e has been chosen. One hundred specimens of this species, collected from four localities (Arrimblar, Adelholzen, Dudar, and Mount-Kotuc) have been prepared (equatorial sections) for the biometric measurement of the external and internal characteristics. First a traditional statistical evaluation was performed, followed by the construction of membership functions, the latter ones expressing in the best way the transitions from one locality to the other. The results of this evaluation confirmed that from Aquitaine (France) to Armenia, the same species – Nummulites millecaput – was distributed during the Eocene. To cite this article: G. Ba´rdossy et al., C. R. Palevol 2 (2003). [Copyright &y& Elsevier]

This paper concerns a generalization of the “Single Index Model” when the explanatory variable is valued in an infinite dimensional space. Such model will be called the “Single Functional Index Model”. The main contribution of this study is to propose a functional framework which includes the classical vectorial case. Pointwise asymptotic properties are stated under less restrictive conditions on the law of the explanatory variable than what it is usually assumed in the vectorial case. To cite this article: F. Ferraty et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]

In this paper, we define all the random measures Z whose image by a certain homomorphism f is equal to a given random measure Z′. This means that we solve the equation f(Z)=Z′ where the random measure Z is unknown. The obtained results are applied to interpolation problems. To cite this article: A. Boudou, C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]

The purpose of this paper is to obtain a CLT with rate for the left random walk on the affine group of Rd. We make weak assumptions under which the operator associated with the random walk is not quasi-compact. The method consists in using recent results of C. Jan [5] about the CLT for martingales. [Copyright &y& Elsevier]

The paper deals with an intellectual and historical approach to the changing meanings of the term “model” in life sciences. The author 1st tries to understand how modeling has gradually spread over life sciences then he particularly focus on the birth of mathematical modeling in this field. This quite new practice offers new insights on the old debate concerning the mathematization of life sciences. Nowadays, through computers, mathematics not only analyze or quantify but model things: what does it mean? The question turns out to be dramatic as far as digital simulation is concerned. That is the reason why he choosed to study a particular case: the history of the individual plant mathematical modeling. On this case, one may discern various epistemological standpoints that caused various reactions to the emergence of computer simulation, from the 50s to the 90s. The author shows that philosophical views often play a role in the history of sciences, especially in the choice of supposed proper mathematical formalisms. This will indicate that contemporary discourses tend to echo each other. That is the reason why he feels authorized to address the Foucault’s concept—épistémè—to denote these convergences between the scientific and the philosophical discourses. Finally, it is suggested that this épistémè gradually is changing because one can currently observe the emergence of a “graphical” thought through these simulation experiments, which tends to replace a more functionalist thought. [Copyright &y& Elsevier]