Templated synthesis of silver nanoparticles in amphiphilic poly(vinylidene fluoride‐co‐chlorotrifluoroethylene) comb copolymer

In this study, poly(vinylidene fluoride‐co‐chlorotrifluoroethylene)‐graft‐poly(oxyethylene methacrylate), P(VDF‐co‐CTFE)‐g‐POEM, an amphiphilic comb copolymer with hydrophobic P(VDF‐co‐CTFE) backbone and hydrophilic POEM side chains at 73:27 wt % was synthesized. The POEM side chains were grafted from the P(VDF‐co‐CTFE) mainchain backbone via atom transfer radical polymerization (ATRP) using direct initiation of the chlorine atoms in CTFE units. Synthesis of microphase‐separated P(VDF‐co‐CTFE)‐g‐POEM comb copolymer was successful, as confirmed by nuclear magnetic resonance (¹H NMR), FTIR spectroscopy, and transmission electron microscopy (TEM). Nanocomposite films were prepared using the comb copolymer as a template film and the in situ reduction of AgCF₃SO₃ precursor to silver nanoparticles under UV irradiation. Silver nanoparticles with 4–8 nm in average size were in situ created in the solid state template film, as revealed by TEM, UV–visible spectroscopy, and wide angle X‐ray scattering (WAXS). Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) presented the selective incorporation and the in situ growth of silver nanoparticles within the hydrophilic POEM domains of microphase‐separated comb copolymer film. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 702–709, 2008     

Analytical application of porphyrins-I Spectrophotometric determination of ultramicro amounts of copper with alpha,beta,gamma,delta-tetra-(3-N-methylpyridyl)porphine

A new water-soluble porphyrin, alpha,beta,gamma,delta-tetra(3-N-methylpyridyl)porphine [T(3-MPy)P], has been synthesized, and its reaction with copper(II) studied spectrophotometrically. Sensitive methods for the determination of copper at ppM level have been established. The spectrophotometric sensitivity and relative standard deviation of the recommended procedure for copper are 0.18 ng/cm(2) (for A = 0.001) and 1.0%, respectively. The interference of 19 ions and 20 salts has been examined, and found to be minimal. The methods established could be applied to the determination of copper in water samples with satisfactory results.     

On the matrix ring over a finite field

Let F_n be the ring of n × n matrices over the finite field F; let o(F_n) be the number of elements in F_n, and s(F_n) be the number of singular matrices in F_n. We prove that $\text{o(F}{}_{\mathrm{n}}\text{)<s(F}{}_{\mathrm{n}}\text{)}{}^{\mathrm{<mtext>1+1</mtext><mtext>n(n-1)</mtext>}}$ if n ? 2, and if n = 2 and o(F) ? 3, then .     

On Poljak's improved subgradient method

Poljak has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a more acute angle with the direction toward the set of optimal solutions than that in the subgradient method.Most of this research has been performed while the first author was visiting the Decision and Information Systems Department, College of Business, Arizona State University, Tempe, Arizona.     

Products of graceful trees

We give some conditions on H and $\text{G}$ for the rooted product H($\text{G}$) to be graceful. These conditions extend and unify previous results.     

A smoothing spline based test of model adequacy in polynomial regression

For the regression model % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa% aajeaWbaGaamyAaaWcbeaakiabeccaGiabg2da9iabeccaGiaabAga% caGGOaGaamiDamaaBaaajeaWbaGaamyAaaWcbeaakiaacMcacaqGGa% Gaey4kaSIaaeiiamaavababeqcbaCaaiaadMgaaSqab0qaaiabew7a% LbaakiaabccacaGGOaGaeqyTduMaai4jaiaadohacaqGGaGaamyAai% aadMgacaWGKbGaaeiiaiaad6eacaGGOaGaam4taiaacYcacaqGGaGa% eq4Wdm3aaWbaaSqabKqaGgaacaaIYaaaaOGaaiykaiaacMcaaaa!57B9!\[y_i = {\rm{f}}(t_i ){\rm{ }} + {\rm{ }}\mathop \varepsilon \nolimits_i {\rm{ }}(\varepsilon 's{\rm{ }}iid{\rm{ }}N(O,{\rm{ }}\sigma ^2 ))\], it is proposed to test the null hypothesis that f is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ^1/2 times an (m–1)-fold integrated Wiener process. For this problem, it is shown that no uniformly (in b) most powerful test exists, but a locally (at b=0) most powerful test does exist. Derivation and calculation of the test statistic is based on smoothing spline theory. Some approximations of the null distribution of the test statistic for the locally most powerful test are described. An example using real data is shown along with a computing algorithm.This author's research was supported by the National Science Foundation under grants numbered DMS-8202560 and DMS-8603083.     

Solid phase synthesis of benzamidine and butylamine-derived hydantoin libraries

We have constructed a number of benzamidine- and butylamine-based hydantoin compounds by means of an efficient route using solid phase synthesis in which neat diisopropylamine was employed for a novel cyclization/traceless cleavage step. All library compounds were obtained in excellent yield and high purity. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the grading numbers of direct products of chains

For a finite lattice L, denote by $\text{l}{}^1\text{(L)}$ and $\text{l}{}_1\text{(L)}$ respectively the upper length and lower length of L. The grading number g(L) of L is defined as $\text{g(L) = l}{}^1\text{(}\text{Sub}\text{(L))-l}{}_1\text{(}\text{Sub}\text{(L))}$ where Sub(L) is the sublattice-lattice of L. We show that if K is a proper homomorphic image of a distributive lattice L, then $\text{l}{}_1\text{(}\text{Sub}\text{(K)) < l}{}_1\text{(}\text{Sub}\text{(L))}$; and derive from this result, formulae for $\text{l}{}_1\text{(}\text{Sub}\text{(L))}$ and g(L) where L is a product of chains.