Electron spin resonance absorption in organic metal polyaniline and its blend with PMMA

The electron spin resonance absorption in the synthetic metal polyaniline (PANI) doped with PTSA and its blend with poly(methylmethacrylate) (PMMA) is investigated in the temperature range between 4.2 and 300 K. The observed line shape follows Dyson's theory for a thick metallic plate with slowly diffusing magnetic dipoles. At low temperatures the line shape become symmetric and Lorentzian when the sample dimensions are small in comparison with the skin depth. The temperature dependence of electron spin relaxation time is discussed. (C) 1999 Elsevier Science Ltd. All rights reserved.

Electrical Conductivity and Magneto-Resistance Studies on Polyaniline-Pmma Blends at Very Low Temperature

D.C. electrical conductivity of polyaniline (33%,40%) blended with PMMA was measured from 5K to 300mK. The conductivity behaviour is consistent with fluctuation induced tunneling. Magneto-resistance (MR) was measured between 300K and 2K. From 20K to 2K, a large positive MR was observed. At 2K, for low magnetic fields (<1 Tesla), a deviation from the normal H-2 behaviour was observed.

The connection between Mueller and Jones matrices of polarization optics

A necessary and sufficient condition for the 4 × 4 Mueller matrix to be derivable from the 2 × 2 Jones matrix is obtained. This condition allows one to determine if a given Mueller matrix describes a totally polarized system or a partially polarized (depolarizing) system. The result of Barakat is analysed in the light of this condition. A recently reported experimentally measured Mueller matrix is examined using this condition and is shown to represent a partially polarized system.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Maximum compatible classes from compatibility matrices

A fast algorithm for the computation of maximum compatible classes (mcc) among the internal states of an incompletely specified sequential machine is presented in this paper. All the maximum compatible classes are determined by processing compatibility matrices of progressingly diminishing order, whose total number does not exceed (p + m), where p is the largest cardinality among these classes, and m is the number of such classes. Consequently the algorithm is specially suitable for the state minimization of very large sequential machines as encountered in vlsi circuits and systems.

Scaling behavior of plasmon coupling in Au and ReO3 nanoparticles incorporated in polymer matrices

Polymer nanocomposites containing different concentrations of Au nanoparticles have been investigated by small angle X-ray scattering and electronic absorption spectroscopy. The variation in the surface plasmon resonance (SPR) band of Au nanoparticles with concentration is described by a scaling law. The variation in the plasmon band of ReO3 nanoparticles embedded in polymers also follows a similar scaling law. Sistance dependence of plasmon coupling in polymer composites f metal nanoparticles. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Stabilizing trench's algorithm to invert symmetric toeplitz matrices

Presented here is a stable algorithm that uses Zohar's formulation of Trench's algorithm and computes the inverse of a symmetric Toeplitz matrix including those with vanishing or nearvanishing leading minors. The algorithm is based on a diagonal modification of the matrix, and exploits symmetry and persymmetry properties of the inverse matrix.

Recursive parametrization of quark flavour mixing matrices

We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of U(n) and SU(n) matrices developed earlier. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Robust Formulations for Handling Uncertainty in Kernel Matrices

We study the problem of uncertainty in the entries of the Kernel matrix, arising in SVM formulation. Using Chance Constraint Programming and a novel large deviation inequality we derive a formulation which is robust to such noise. The resulting formulation applies when the noise is Gaussian, or has finite support. The formulation in general is non-convex, but in several cases of interest it reduces to a convex program. The problem of uncertainty in kernel matrix is motivated from the real world problem of classifying proteins when the structures are provided with some uncertainty. The formulation derived here naturally incorporates such uncertainty in a principled manner leading to significant improvements over the state of the art. 1.