Related papers: On the polar decomposition of circular variables
Through a simple procedure based on the Lu-Chipman decomposition [S-Y. Lu and R. C. Chipman, J. Opt. Soc. Am A 13, 1106 (1996)] any depolarizing Mueller matrix can be transformed into a reduced form which accumulates the depolarization and…
We derive a useful result about the zeros of the $k$-polar polynomials on the unit circle; in particular we obtain a ring shaped region containing all the zeros of these polynomials. Some examples are presented.
We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity…
We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and…
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
We give an alternative proof of a result on the uniform overlap of the algebraic sums of the sets arising from a decomposition of a neighborhood of a circular cone in $\Bbb R^3$. It is known that the uniform overlap result can be applied to…
In this paper, we present a correct proof of an $L_p$-inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
We extend the classical Kadec 1/4 theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation.
We show that Voiculescu's circular operator and, more generally, each circular free Poisson operator has a continuous family of invariant subspaces relative to the von Neumann algebra it generates. The proof relies on upper triangular…
An analog of Picard's little theorem for entire functions of matrices is proved.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
We prove a central limit theorem for the winding number of a directed polymer on a cylinder, which is equivalent with proving the Gaussian fluctuations of the endpoint of the directed polymer in a spatial periodic environment.
We develop a direct derivation for the primary contribution to the vibrational polarizability for molecules, clusters and other finite systems. The vibrational polarizability is then calculated within the generalized gradient approximation…
In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with $q$ a root of unity.
The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here in an analysis of a bar subjected to torsion. Employing a small set of physics-based parameters, which we expect to be approximately…
Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie…
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
We give a proof for the decidability of the HD0L ultimate periodicity problem.
We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.