A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Viscoelastic properties of nanostructured natural rubber/polystyrene interpenetrating polymer networks

The effects of the blend ratio and initiating system on the viscoelastic properties of nanostructured natural rubber/polystyrene‐based interpenetrating polymer networks (IPNs) were investigated in the temperature range of ?80 to 150 °C. The studies were carried out at different frequencies (100, 50, 10, 1, and 0.1 Hz), and their effects on the damping and storage and loss moduli were analyzed. In all cases, tan δ and the storage and loss moduli showed two distinct transitions corresponding to natural rubber and polystyrene phases, which indicated that the system was not miscible on the molecular level. However, a slight inward shift was observed in the IPNs, with respect to the glass‐transition temperatures (T_g's) of the virgin polymers, showing a certain degree of miscibility or intermixing between the two phases. When the frequency increased from 0.1 to 100 Hz, the T_g values showed a positive shift in all cases. In a comparison of the three initiating systems (dicumyl peroxide, benzoyl peroxide, and azobisisobutyronitrile), the dicumyl peroxide system showed the highest modulus. The morphology of the IPNs was analyzed with transmission electron microscopy. The micrographs indicated that the system was nanostructured. An attempt was made to relate the viscoelastic behavior to the morphology of the IPNs. Various models, such as the series, parallel, Halpin–Tsai, Kerner, Coran, Takayanagi, and Davies models, were used to model the viscoelastic data. The area under the linear loss modulus curve was larger than that obtained by group contribution analysis; this showed that the damping was influenced by the phase morphology, dual‐phase continuity, and crosslinking of the phases. Finally, the homogeneity of the system was further evaluated with Cole–Cole analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1680–1696, 2003     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

On the number of curves of genus 2 over a finite field

In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in , the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in .     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Use of ab initio pseudopotentials for the assignment of boundary conditions of clusters modeling MgO

Conclusions The work reported in this article was aimed at determining the feasibility and desirability of using ab initio core pseudopotential anionic centers and cluster models of ionic crystals of the type of a cluster implanted in a crystal. The results presented herein, from calculations of a number of clusters of magnesium oxide, demonstrate the promise of this approach for compensation of bond rupture effects. In particular, such a model offers a means for a substantial reduction of the artifact-introduced nonequivalence of the partial ionic densities and the effective charges. The comparatively high reliability of the cluster scheme proposed in this work is also supported by results from calculations of the geometric parameters of the crystal.Branch of Institute of Chemical Physics, Russian Academy of Sciences. Institute of Chemistry of Natural Organic Raw Materials, Siberian Branch, Russian Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 2, pp. 3–7, March–April, 1992.     

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Synthesis of Esters of Dioxane Alcohols and Their Performance as Plasticizers for Polyvinyl Chloride Compounds

A procedure was developed for preparing a plasticizer for polyvinyl chloride compounds from the fraction of dioxane alcohols. The main physicochemical properties of the new plasticizer were determined. Items prepared from formulations containing the new plasticizer were fabricated and tested in laboratory.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 6, 2005, pp. 972–976.Original Russian Text Copyright © 2005 by Glazko, Gur’yanova, Levanova, Kozlova, Neiman.     

Comparative preparations of homoleptic hydridic anions of iron and ruthenium using solution-based organometal hydrogenation techniques

A study of the preparations of the complex hydridic anions [MH(6)](4)(-) (M = Fe and Ru) reveals a number of distinctive features. Here a soluble homoleptic ruthenium hydride has been prepared for the first time. For example, both FeX(2) and [Ru(eta(4)-1,5-COD)X(2)], X = Cl and Br, react with PhMgBr solutions under hydrogen to produce the title compounds. The benzene liberated in these reactions is more readily hydrogenated in the case of a homogeneous room temperature ruthenium hydride preparation to both cyclohexane and cyclohexene. The (1)H NMR spectroscopic data show that the two complex anions have hydride absorptions in the low-frequency region, delta -20.3 and -14.7, respectively. Further, (1)H spin-lattice relaxation times (T(1)) for M-H are longer in the case of Ru vs Fe.