Determination of the rheological behavior of epoxy–amine thermosets by dynamic mechanical analysis: Isothermal methods versus nonisothermal methods

The reticulation process of an epoxy resin using an amine as a cure agent was studied at different temperatures and concentrations of the cure agent with dynamic mechanical thermal analysis. The study was performed under both isothermal and nonisothermal conditions, and a temperature–time–transformation diagram was obtained. The measurements from the two modes gave similar results, although the nonisothermal mode required fewer experiments. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1965–1977, 2003     

A general converse theorem for mean‐value theorems in linear elasticity

We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on generalized averaged Gaussian formulas

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.     

Fast Fourier Continuous Cyclic Voltammetry at Gold Ultramicroelectrode in Flowing Solution for Determination of Ultra Trace Amounts of Penicillin G

In this work, for the first time a fast continuous cyclic voltammetry was used as a highly sensitive detection method for Penicillin G in a flow‐injection system. A special computer‐based numerical calculation method (using Fast Fourier Transformation) is introduced here for enhancing the analyte signal and noise reduction. During the measurements, the potential waveform (consists of potential steps for cleaning, stripping and potential ramp) was continuously applied on an Au disk microelectrode (with a radius 12.5 μm in radius). The stripping time was less than 200 ms. Effects of rest potential, sweep rate, and delay time on the sensitivity of the method were investigated. The limit of detection of the method was 1.0 × 10^?11 M. The detection limit of the method is 660 times lower than the most sensitive reported method. The relative standard deviation of the method at 1.0×10^?7 M of Penicillin G was 2.7% for 10 runs.     

应力对La0.83Sr0.17MnO3薄膜输运性能的影响

采用溶胶-凝胶方法在Si(111)上制备了LSMO(x=0.17)薄膜.研究了块体材料和不同厚度薄膜R -T曲线、红外光谱和X射线衍射.结果表明，LSMO薄膜属于正交晶体结构，薄膜取向与膜厚度 有关，当膜厚度为450nm或680nm时，主要取向〈200〉，而膜厚度为900nm时取向为〈020〉 ：根据离子对相互作用能和谐振子模型，得到了红外吸收与Mn—O—Mn键长和键角关系式，6 00cm^-1附近红外吸收与晶格常数b的变化有关；块体与薄膜的金属—绝缘体转变 温度(T_MI)存在较大差别，薄膜转变温度显著低于块体，并与厚度有一定关系. 认为是LSMO薄膜中的应力诱导了晶格常数变化，引起键角改变及JT效应是转变温度变化的主 要原因. 关键词： 单晶硅 晶格常数 金属—绝缘体转变温度 应力诱导     

Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the R-matrices for two-component systems under these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin‘s formalism.For those R-matrices with all required properties,the effects of solution transformations to the six-and eight-vertex systems with open boundary conditions are discussed.these effects can be one of the following types:the Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.