A version of Wiener’s and Lévy’s theorems

We obtain weighted algebra analogues of the classical theorems of N. Weiner and P. Lévy on absolutely convergent Fourier series      

A modified inexact implicit method for mixed variational inequalities

In this paper, we suggest and analyze an inexact implicit method with a variable parameter for mixed variational inequalities by using a new inexactness restriction. Under certain conditions, the global convergence of the proposed method is proved. Some preliminary computational results are given to illustrate the efficiency of the new inexactness restriction. The results proved in this paper may be viewed as improvement and refinement of the previously known results.     

Painlevé analysis and integrability of the trapped ionic system

Integrability in the Painlevé sense of the trapped ionic system in the quadrupole field with superpositions of rotationally symmetric hexapole and octopole fields is studied. Five integrable cases of the system are reported. First Integrals of the planar motion are founded. Confirming three-dimensional integrability of the equations of motion, the third explicit integrals of motion are constructed directly for each case. We carried out a numerical study to observe the regularity and chaotic regions via the Poincaré surface of sections, and corroborate the analytical results.     

On hypersurfaces in a Riemannian vector bundle with prescribed Gaussian curvature and convexity

Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and the unit subbundle of E. We prove that there is no radial graph on with a strictly positive Gaussian curvature and that the Gaussian curvature of a convex radial graph must be identically equal to zero. Moreover, by solving on a nonlinear degenerate equation of Monge-Ampère type, we prove the existence of radial graphs having simultaneously a Gaussian curvature identically equal to zero and a prescribed strictly positive vertical Gaussian curvature.Mathematics Subject Classification (2000):35J60, 53C55, 58G30     

Effect of diblock copolymers on dynamic mechanical properties of polyethylene/polystyrene blends

A systematic investigation of the dynamic mechanical properties of high-density polyethylene (HDPE)/high-impact polystyrene (HIPS)/copolymer blends was carried out. Blends of 80/20 weight percent of HDPE/HIPS were prepared in the melt state at 180°C in a batch mixer. Synthesized pure diblock (H77) and tapered diblock (H35) copolymers of hydrogenated polybutadiene (HPB) and polystyrene (PS) were added at different concentrations (1, 3, and 5 wt %), and the dynamic mechanical properties were investigated. The results show that: (1) both the tapered and the pure diblock copolymers enhance the phase dispersion and the interphase interactions; (2) structure and molecular weight are both important parameters in the molecular design of copolymers; (3) important effects occur when only small amounts of copolymer are added (up to the interface saturation concentration SC); (4) a micellar structure formation is possible when the copolymer is in excess in the blend; (5) the effect of the copolymer structure on the SC and the critical micellar concentration (CMC) is more pronounced than the effect of molecular weight. These concentrations are found to be lower for the tapered diblock copolymer. The analysis of the dynamic mechanical thermal analysis (DMTA) results obtained for the 20/80 HDPE/HIPS blend leads to the conclusion that the copolymers also enhance the interactions between heterogeneous phases. Similar conclusions based on electron microscopy were reported in the literature. DMTA shows great potential to relate macroscopic observations to the state of a copolymer in an immiscible blend.     

Rheology and phase separation in polystyrene/poly(vinyl methyl ether) blends

Blends of monodisperse polystyrene and poly(vinyl-methyl-ether) of various compositions were prepared from solution in benzene. Dynamic rheological properties of these blends were studied at different temperatures below, near, and above T_s, the temperature of phase separation, and in a frequency range from 0.05 to 100 rad/s. A flattening in the storage modulus and an initial plateau for the complex viscosity were observed near and above T_s in the low-frequency region; in contrast, below T_s the behavior of the blends was similar to that of the homopolymers. The WLF superposition principle applies only at temperatures below T_s, i.e., in the miscible and homogeneous region. G″ versus G′ representations for the blends were found to be independent of temperature and to vary with composition in the miscible region but are temperature and composition-dependent in the immiscible region. It is also shown that the η″ versus η′ representation is a useful tool for characterizing phase separation of blends and is more sensitive than the classical frequency dependence of the material functions.     

The determination of kinetic data for the reactions of chromium(VI) with glutathione and other thiols

The equations necessary for the determination of the rate constants corresponding to the opposite elementary steps for formation of the oxidant-reductant ester intermediate, as well as that corresponding to its redox decomposition, in the reduction of chromium(VI) by glutathione and other thiols at physiological pH have been deduced. It is shown that those three rate constants can be obtained with a good reproducibility. © 1994 John Wiley & Sons, Inc.     

Pyrrolothieno[1,4]diazepines: Synthesis of alkoxy derivatives

Reactivity of 2-(2-formyl-1H-pyrrol-1-yl)-3-thiophenecarbonitrile and of 2-(2-formyl-1H-pyrrol-1-yl)-3-thiophenecarboxamide was evaluated against various alkoxides. The synthetic pathways involved in these reactions which led to new 4- and 6-alkoxypyrrolothieno[1,4]diazepines are described.     

Behaviour at the non-positive integers of Dirichlet series associated to polynomials of several variables

In this paper, we relate the special values at a non-positive integer \({\underline{\mathbf{s}}=(s_{1},\ldots, s_{r})= -\underline{\mathbf{N}}= (-N_{1},\ldots, -N_{r})}\) obtained by meromorphic continuation of the multiple Dirichlet series \({{Z(\underline{\mathbf{P}}, \underline{\mathbf{s}})=\sum_{\underline{m}\in {\mathbb{N}}^{*n}}{\frac{1}{\prod_{i=1}^{r}{P_{i}^{ s_{i}}(\underline{m})}}}}}\) to special values of the function \({Y(\underline{\mathbf{P}}, \underline{\mathbf{s}})=\int_{[1, +\infty[^{n}} {\prod_{i=1}^{r}{P_{i}^{- s_{i}}(\underline{\mathbf{x}})}\; d{\underline{\mathbf{x}}}}}\) where \({\underline{\mathbf{P}}=(P_{1},..., P_{r}),\; (r\geq 1)}\) are elliptic polynomials in “\({n}\) ” variables. We prove a simple relation between \({Z(\underline{\mathbf{P}}_{\underline{\mathbf{a}}}, -\underline{\mathbf{N}})}\) and \({Y(\underline{\mathbf{P}}_{\underline{\mathbf{a}}}, -\underline{\mathbf{N}})}\), such that for all \({\underline{\mathbf{a}} \in {\mathbb{R}}^{n}_{+}}\), we denote \({\underline{\mathbf{P}}_{\underline{\mathbf{a}}}:=(P_{1 \underline{\mathbf{a}}},\ldots, P_{r \underline{\mathbf{a}}})}\), where \({P_{i\;\underline{\mathbf{a}}}(\underline{\mathbf{x}}):= P_i(\underline{\mathbf{x}}+ \underline{\mathbf{a}})\; (1\leq i\leq r)}\) is the shifted polynomial.     

A new LQP alternating direction method for solving variational inequality problems with separable structure

We presented a new logarithmic-quadratic proximal alternating direction scheme for the separable constrained convex programming problem. The predictor is obtained by solving series of related systems of non-linear equations in a parallel wise. The new iterate is obtained by searching the optimal step size along a new descent direction. The new direction is obtained by the linear combination of two descent directions. Global convergence of the proposed method is proved under certain assumptions. We show the O(1 / t) convergence rate for the parallel LQP alternating direction method.