Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operators a-1 and a(dagger-1) by their actions on the number states. We show that the squeezed vacuum exp(1/2xia(dagger2)]\0] and squeezed first number state exp[1.2xia(dagger2)]\n = 1] are respectively the eigenstates of the operators (a(dagger-1)a) and (aa(dagger-1)) with the eigenvalue xi.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Two stage iterative wiener filtering for speech enhancement

We formulate a two-stage Iterative Wiener filtering (IWF) approach to speech enhancement, bettering the performance of constrained IWF, reported in literature. The codebook constrained IWF (CCIWF) has been shown to be effective in achieving convergence of IWF in the presence of both stationary and non-stationary noise. To this, we include a second stage of unconstrained IWF and show that the speech enhancement performance can be improved in terms of average segmental SNR (SSNR), Itakura-Saito (IS) distance and Linear Prediction Coefficients (LPC) parameter coincidence. We also explore the tradeoff between the number of CCIWF iterations and the second stage IWF iterations.

LMS versus Wiener filter for a decision feedback equalizer

In this paper we study an LMS-DFE. We use the ODE framework to show that the LMS-DFE attractors are close to the true DFE Wiener filter (designed considering the decision errors) at high SNR. Therefore, via LMS one can obtain a computationally efficient way to obtain the true DFE Wiener filter under high SNR. We also provide examples to show that the DFE filter so obtained can significantly outperform the usual DFE Wiener filter (designed assuming perfect decisions) at all practical SNRs. In fact, the performance improvement is very significant even at high SNRs (up to 50%), where the popular Wiener filter designed with perfect decisions, is believed to be closer to the optimal one.

Discrete Wiener¿Lee transforms

The use of Wiener–Lee transforms to construct one of the frequency characteristics, magnitude or phase of a network function, when the other characteristic is given graphically, is indicated. This application is useful in finding a realisable network function whose magnitude or phase curve is given. A discrete version of the transform is presented, so that a digital computer can be employed for the computation.

An analogue of the Wiener Tauberian Theorem for the Heisenberg Motion group

We show that the Wiener Tauberian property holds for the Heisenberg Motion group TnB

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

A risk-estimation-based formulation for speech enhancement and its relation to Wiener filtering

The goal of speech enhancement algorithms is to provide an estimate of clean speech starting from noisy observations. The often-employed cost function is the mean square error (MSE). However, the MSE can never be computed in practice. Therefore, it becomes necessary to find practical alternatives to the MSE. In image denoising problems, the cost function (also referred to as risk) is often replaced by an unbiased estimator. Motivated by this approach, we reformulate the problem of speech enhancement from the perspective of risk minimization. Some recent contributions in risk estimation have employed Stein's unbiased risk estimator (SURE) together with a parametric denoising function, which is a linear expansion of threshold/bases (LET). We show that the first-order case of SURE-LET results in a Wiener-filter type solution if the denoising function is made frequency-dependent. We also provide enhancement results obtained with both techniques and characterize the improvement by means of local as well as global SNR calculations.

Riesz transforms and multipliers for the Grushin operator

We show that Riesz transforms associated to the Grushin operator G = -Delta - |x|(2 similar to) (t) (2) are bounded on L (p) (a''e (n+1)). We also establish an analogue of the Hormander-Mihlin Multiplier Theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator-valued Fourier multiplier theorem due to L. Weis.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

DIMENSION FREE BOUNDEDNESS OF RIESZ TRANSFORMS FOR THE GRUSHIN OPERATOR

Let G = -Delta(xi) - vertical bar xi vertical bar(2) partial derivative(2)/partial derivative eta(2) be the Grushin operator on R-n x R. We prove that the Riesz transforms associated to this operator are bounded on L-p(Rn+1), 1 < p < infinity, and their norms are independent of dimension n.