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.     

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.     

Synthesis of functional polymers—Vinylidene fluoride based fluorinated copolymers and terpolymers bearing bromoaromatic side‐group

The radical co‐ and terpolymerization of 4‐[(α,β,β‐trifluorovinyl)oxy]bromo benzene (TFVOBB) with 1,1‐difluoroethylene (or vinylidene fluoride, VDF, or VF₂), hexafluoropropene (HFP), perfluoromethyl vinyl ether (PMVE), and chlorotrifluroroethylene (CTFE) is presented. Although TFVOBB could be thermocyclodimerized, it could not homopolymerize under radical initiation. TFVOBB could be copolymerized in solution under a radical initiator with VDF or CTFE comonomers, while its copolymerization with HFP or PMVE were unsuccessful. The terpolymerization of TFVOBB with VDF and HFP, or VDF and PMVE, or VDF and CTFE also led to original fluorinated terpolymers bearing bromoaromatic side‐groups. The conditions of co‐ and terpolymerization were optimized in terms of the nature of the radical initiators, and of the nature of solvents (fluorinated or nonhalogenated). Various monomer concentrations in the co‐ and terpolymers were assessed by ¹⁹F and ¹H‐NMR spectroscopy. The thermal and physico chemical properties were also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5077–5097, 2004     

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.     

含吡咯烷酮基丙烯酸酯类单体的合成及聚合

轻度交联的聚甲基丙烯酸2-羟乙酯(HEMA)是众所周知的医用水凝胶,即所谓的“Hvdron”。但其吸水率一般在59%(EWC为37%),并不尽人意。近年来,为了提高这类水凝胶的亲水性及生物相容性,常用一些亲水性的烯类单体进行表面改性或通过共聚以达到此目的,N-乙烯基吡咯烷酮是较为常用的这类单体之一。本文合成了含吡咯烷酮基丙烯酸酯类的单体,即丙烯酸2-N-吡咯烷酮基乙酯(PyEA),甲基丙烯酸2-N-吡咯烷酮基乙醋(PyEMA),并研究了这两种单体在甲基丙烯酸二甲氨乙酯(DMAEMA)与过硫酸钾(KPS)所组成的氧化还原引发体系下的聚合。     

Addition of secondary phosphines to N-vinylpyrroles

Secondary phosphines 1-3 react readily with N-vinylpyrroles 4 and 5 under radical initiation to give regiospecifically anti-Markovnikov adducts, diorganyl-2-(1-pyrrolyl)ethylphosphines 6a-d, highly reactive building blocks for organic synthesis, in 88-91% yields.     

Initiation of cationic polymerization of n-butyl vinyl ether by stable cation radicals of substituted phenothiazines

3,7-Diethyl- 10-phenylphenothiazine (DEPPT), a phenothiazine derivative whose 3,7- and 10-positions are blocked, was synthesized. Potentiostatic electrolysis of DEPPT in acetonitrile (ACN) in the presence of 0.1M of LiClO₄ at 0.7 V (vs. Ag/Ag/Cl) yielded the stable cation radical of DEPPT (DEPPT^+·) which was characterized by cyclic voltammetry, UV-visible spectroscopy, and ESR spectrometry. Stable cation radicals of 10-phenylphenothiazine and 3,7-diethyl-10-methylphenothiazine were also prepared. The cationic polymerization of n-butyl vinyl ether was initiated by these cation radicals, including DEPPT^·+. The electron transfer mechanism for the initiation step, which we proposed previously, was supported by the fact that DEPPT^·+ was capable of initiating the polymerization; dimerization of DEPPT^·+ by releasing protons is precluded because 3,7- and 10-positions are all blocked. © 1994 John Wiley & Sons, Inc.