Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

Difference Families in Z2d+1⊕Z2d+1 and Infinite Translation Designs in Z⊕Z

We analyse 3-subset difference families of Z_2d+1⊕Z_2d+1 arising as reductions (mod 2d+1) of particular families of 3-subsets of Z⊕Z. The latter structures, namely perfect d-families, can be viewed as 2-dimensional analogues of difference triangle sets having the least scope. Indeed, every perfect d-family is a set of base blocks which, under the natural action of the translation group Z⊕Z, cover all edges {(x,y),(x′,y′)} such that |x−x′|, |y−y′|≤d. In particular, such a family realises a translation invariant (G,K₃)-design, where V(G)=Z⊕Z and the edges satisfy the above constraint. For that reason, we regard perfect families as part of the hereby defined translation designs, which comprise and slightly generalise many structures already existing in the literature. The geometric context allows some suggestive additional definitions. The main result of the paper is the construction of two infinite classes of d-families. Furthermore, we provide two sporadic examples and show that a d-family may exist only if d≡0,3,8,11 (mod 12).     

Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

Considering a plane hyperbolic system with time-periodic coefficients, we construct a version of the direct Lyapunov method with the condition on the derivative of the Lyapunov functional along the trajectories of the system which is weakened by use of periodicity of the coefficients. We exhibit an illustrative example.     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Transversal-Free Translation Nets

Translation planes of order q ² containing non-Desarguesian Baer subplanes are used to construct transversal-free translation nets with very small deficiencies. Also, a generalization of the ideas of Bruen shows that any non-Desarguesian spread in PG(3, q) produces a transversal-free net of small deficiency.     

A new property of Bernstein-Kantorovi? operators

In the present paper, we prove that the Bernstein-Kantorovič operators have the ability of preserving translation property in both C and L^p norms. Supported (in part) by the NSFC(10471130,10371024) of PRC and the Natural Science Foundation (Y604003) of Zhejiang Province.     

IPv4/IPv6翻译网关的研究

In this paper, a model of translation gateway is proposed. The communications between IPv4 network and IPv6 network are realized by using the Microsoft intermediate driver technology in environment of Windows 2000.     

核磁共振法测定高聚物的结构—核磁共振二维谱

介绍了核磁共振(NMR)波谱,尤其是核磁共振二维谱(2D NMR)在最近几年内的进展。内容包括怎样用NMR测定高聚物的序列分布、共聚物结构、聚合物的混溶性、聚合物液晶的取向度、分子量、短链度和长链支化度、凝聚态高聚物的多相结构等。     

Synthesis and characterization of segmented liquid crystal poly(azoxy polyester-co-polyoxypropylene)

In this study a series of a segmented copolyester, poly(4,4′-dioxy-2,2′-dimethyl-azoxybenzene dodecanedioyl) (PMABD)-co-polyoxypropylene 400 (POP), was prepared. The chain length of PMABD studied (n) was varied from 7.8-18.2, and that of POP was unchanged. The intrinsic viscosity of the segmented copolyesters was 1.04-1.30, and the number average molecular weight obtained was 2.53 × 10⁴?3.49 × 10⁴ g/mol. The mesophase texture and thermal properties of the segmented copolyesters were measured as functions of n. It was found that the insert of flexible POP between those liquid crystalline domains of PMABD did affect thermotropic properties of PMABD. As the n value was 9.0 and 7.8 (or 7.4 and 8.6% by weight POP) the texture appeared as cholesteric-like oily streaks. The effect could not be attained by simply copolymerizing a mesogenic moiety with a pair of spacers of different lengths. The fluidity and domain structure of the flexible dodecanedioyl-POP-dodcanedioyl segments are taken into account for the obtained results. © 1995 John Wiley & Sons, Inc.