Dynamic mechanical properties of epoxy resin/epoxidized rubber blends: Effect of phase separated rubber

The dynamic mechanical properties of blends of diglycidyl ether of bisphenol-A-based epoxy resin and internally epoxidized polybutadiene rubber have been studied. It is shown that the influence of the composition of the continuous phase and of the dispersed phase can be studied not only from the variations of the glass transition temperature but also from the changes in the apparent enthalpy of activation associated with this transition. As the initial rubber content increases, the composition of the dispersed phase remains practically constant while more rubber is able to dissolve in the continuous phase. Analysis of the rubbery plateau region reveals that the shear modulus of the blends is not much affected by the presence of dissolved rubber in the continuous phase but strongly depends on the volume fraction of dispersed phase. This volume fraction can be obtained from the relative drop in shear modulus after modeling the results with the Kerner equation. The results compares well with independent measurements by scanning electron microscopy. © 1994 John Wiley & Sons, Inc.     

Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.     

Fixed point limit behavior ofN-mode truncated Navier-Stokes equations asN increases

The fixed point behavior ofN-mode truncations of the Navier-Stokes equations on a two-dimensional torus is investigated asN increases. FromN=44 on the behavior does not undergo any qualitative change. Furthermore, the bifurcations occur at critical parameter values which clearly tend to stabilize asN approaches 100.     

On diagonally preconditioning the truncated Newton method for super-scale linearly constrained nonlinear programming

We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newton's method. In large-scale programming solving the Newton equation at each iteration can be expensive and may not be justified when far from a local solution. For super-scale problems, the truncated Newton method (where an inaccurate solution is computed by using the conjugate-gradient method) is recommended; a diagonal BFGS preconditioning of the gradient is used, so that the number of iterations to solve the equation is reduced. The procedure for updating that preconditioning is described for LCNP when the set of active constraints or the partition of basic, superbasic and nonbasic (structural) variables have been changed.     

Propagation of partially coherent Gaussian laser beams in graded-index fibres

Using statistical approach the author has solved the equations for the mutual coherence function of partially coherent Gaussian laser beams in graded-index fibres. The expressions for the complex degree of coherence and the intensity distribution have also been shown that the self-focusing length inside the fibre depends upon the degree of coherence. The result have been discussed for both conical and cylindrical guides.     

Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds

Ideas of a simplicial variable dimension restart algorithm to approximate zero points onR ⁿ developed by the authors and of a linear complementarity problem pivoting algorithm are combined to an algorithm for solving the nonlinear complementarity problem with lower and upper bounds. The algorithm can be considered as a modification of the2n-ray zero point finding algorithm onR ⁿ . It appears that for the new algorithm the number of linear programming pivot steps is typically less than for the2n-ray algorithm applied to an equivalent zero point problem. This is caused by the fact that the algorithm utilizes the complementarity conditions on the variables. This work is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply,” which has been approved by the Netherlands Ministry of Education and Sciences.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Polarization Tomography of Quantum Radiation: Theoretical Aspects and Operator Approach

We present theoretical foundations for the quantum tomography of polarization states of light fields as a method for measuring their polarization density operator , which characterizes only the polarization degrees of freedom of the radiation. We mainly attend to the method in which the tomographic observables (the “measurement instruments”) are polarizable in nature. We show that the quantum nature of this method can be adequately expressed using the quasispectral tomographic decompositions of in special operator bases, which are finite sums of partially orthogonal projection operators determining the probability distributions of tomographic observables as the decomposition coefficients. We obtain the matrix versions of such “tomographic” representations of , in particular, by projecting them on semiclassical operator bases determining the polarization quasiprobability functions. We briefly discuss the information aspects of the schemes considered in the paper. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 344–357, December, 2005.     

Szego-Type Limit Theorems for Generalized Discrete Convolution Operators

We study the asymptotic behavior of the averaged f-trace of a truncated generalized multidimensional discrete convolution operator as the truncation domain expands. By definition, the averaged f-trace of a finite-dimensional operator A is equal to , where n is the dimension of the space in which the operator A acts, the set of numbers γ_k, k = 1,..., n, is the complete collection of eigenvalues of the operator A, counting multiplicity; a generalized discrete convolution is an operator from the closure of the algebra generated by discrete convolution operators and by operators of multiplication by functions admitting a continuous continuation onto the sphere at infinity.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 265–277.Original Russian Text Copyright © 2005 by I. B. Simonenko.     

Subdivision of simplices relative to a cutting plane and finite concave minimization

In this article, our primary concern is the classical problem of minimizing globally a concave function over a compact polyhedron (Problem (P)). We present a new simplicial branch and bound approach, which combines triangulations of intersections of simplices with halfspaces and ideas from outer approximation in such a way, that a class of finite algorithms for solving (P) results. For arbitrary compact convex feasible sets one obtains a not necessarily finite but convergent algorithm. Theoretical investigations include determination of the number of simplices in each applied triangulation step and bounds on the number of iterations in the resulting algorithms. Preliminary numerical results are given, and additional applications are sketched.