Studies on structure property relationship in a polymer–clay nanocomposite film based on (PAN)8LiClO4

A new combination of ionically conducting polymer–clay nanocomposites based on (PAN)₈LiClO₄ + x wt % montmorillonite (unmodified) clay has been prepared using the standard solution cast process. X-Ray diffraction (XRD) analysis reveals strong interaction of polymer salt complex (PS) with the montmorillonite matrix evidenced by changes in d₀₀₁ spacing of the clay and enhancement in the clay gallery width on composite formation possibly due to intercalation of polymer–salt complex into nanometric clay galleries. Evidences of such an interaction among polymer–ion–clay components of the composite matrix has also been observed in the Fourier transform infrared (FTIR) spectrum results. FTIR results clearly indicated cation (Li⁺) coordination at nitrile (CN) site of the polymer backbone along with appearance of a shoulder suggesting strong evidence of polymer–ion interaction. Addition of clay into the PS matrix has been observed to affect ion–ion interaction resulting from ion dissociation effect at low clay loading in the PNC films. Complex impedance spectroscopy (CIS) analysis has provided a response comprising of a semicircular arc followed by a spike attributed respectively, to the bulk conduction and electrode polarization at the interfaces. Electrical transport appears to be predominantly ionic (t_ion = 0.99) with significant improvement in the electrical conductivity and thermal stability properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2577–2592, 2008     

Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations

An analysis of the discrete shallow‐water equations using the Raviart–Thomas and Brezzi–Douglas–Marini finite elements is presented. For inertia–gravity waves, the discrete formulations are obtained and the dispersion relations are computed in order to quantify the dispersive nature of the schemes on two meshes made up of equilateral and biased triangles. A linear algebra approach is also used to ascertain the possible presence of spurious modes arising from the discretization. The geostrophic balance is examined and the smallest representable vortices are characterized on both structured and unstructured meshes. Numerical solutions of two test problems to simulate gravity and Rossby modes are in good agreement with the analytical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Highly fluorescent mono‐substituted poly(arylacetylene)s containing tolane chromophores

A new class of highly fluorescent mono‐substituted polyarylacetylenes ( P1–P3 ) has been successfully prepared with good yields and high molecular weights from a series of phenylethynylene‐substituted arylacetylenes ( M1–M3 ), using W‐based catalyst. These polymers are readily soluble in common organic solvents (e.g., THF, toluene, and chloroform) and thermally stable up to ～350 °C. Both ¹H NMR and IR studies confirmed that all the monomers were selectively polymerized at the terminal triple bond. The ¹H NMR results showed that both P1 and P2 have essentially trans‐polyene backbone structures, while P3 contains significant amounts of both cis‐ and trans‐structures. Coincidently, the photoluminescence (PL) intensity of P3 is also much lower than both P1 and P2 . Nevertheless, the PL intensity of P1–P3 are all much higher than that of PPA , suggesting that the introduction of phenylethynylene group to the phenyl rings of PPA s have made the in general nonemissive PPA s to become highly photoluminescent. Most interestingly, although P1 did not contain any substituent group on its tolane pendant group, it is already highly soluble in common organic solvent and emitting blue fluorescence (416 nm) with a reasonably good quantum yield (0.36). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5483–5498, 2008     

Braid groups in genetic code

For every genetic code with finitely many generators and at most one relation, a braid group is introduced. The construction presented includes the braid group of a plane, braid groups of closed oriented surfaces, Artin— Brieskorn braid groups of series B, and allows us to study all of these groups from a unified standpoint. We clarify how braid groups in genetic code are structured, construct words in the normal form, look at torsion, and compute width of verbal subgroups. It is also stated that the system of defining relations for a braid group in two-dimensional manifolds presented in a paper by Scott is inconsistent. Supported by RFBR grant No. 02-01-01118. __________ Translated from Algebra i Logika, Vol. 45, No. 2, pp. 131–158, March–April, 2006.     

On orthogonal polynomials with respect to the form -(x - c)S'

Summary A form (linear functional) $u$ is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){\mathbf S}',$ where ${\mathbf S}$ is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration.     

一族二阶导数计值迭代方法的收敛性

从带一个参数的三阶迭代族(其中包括Halley迭代,Chebyshev迭代和超Halley迭代)出发,推出避免二阶导数计算的带两个参数的迭代族.在Newton-antorovich型的假设条件下,通过用一个递推关系证明了此迭代族的三阶收敛性,并给出了非线性算子方程解的存在惟一性定理.     

提升现代民营企业管理水平的对策

现代民营企业是最具普遍意义的企业组织形态,其自身的众多特点为企业的建立和初期的发展具有功不可没的作用,但随着社会分工的精细化和经营的国际化,现代民营企业要想永葆青春、不断飞跃,必须做好改革与创新。     

Quasicontinuum Models of Dynamic Phase Transitions

We propose a series of quasicontinuum approximations for the simplest lattice model of a fully dynamic martensitic phase transition in one dimension. The approximations are dispersive and include various non-classical corrections to both kinetic and potential energies. We show that the well-posed quasicontinuum theory can be constructed in such a way that the associated closed-form kinetic relation is in an excellent agreement with the predictions of the discrete theory.     

‘Classical’ convergence theorems for generalized continued fractions

In this paper the classical convergence theorems by Śleszyński-Pringsheim, Worpitzky and Van Vleck for ordinary continued fractions will be generalized to continued fractions generalizations (along the lines of the Jacobi–Perron algorithm) with four-term recurrence relations.