Complete Pick positivity and unitary invariance

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S) (z, w) = (1 - z (w) over tilde)(-1) for |z|, |w| < 1, by means of (1/k(S))(T,T*) >= 0, we consider an arbitrary open connected domain Omega in C-n, a complete Pick kernel k on Omega and a tuple T = (T-1, ..., T-n) of commuting bounded operators on a complex separable Hilbert space H such that (1/k)(T,T*) >= 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with T. Moreover, the characteristic function is then a complete unitary invariant for a suitable class of tuples T.

Wigner distribution for angle coordinates in quantum mechanics

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase‐space language is much clarified by this extension.

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

New results on systems with second-class constraints

We show how, for large classes of systems with purely second-class constraints, further information can be obtained about the constraint algebra. In particular, a subset consisting of half the full set of constraints is shown to have vanishing mutual brackets. Some other constraint brackets are also shown to be zero. The class of systems for which our results hold includes examples from non-relativistic particle mechanics as well as relativistic field theory. The results are derived at the classical level for Poisson brackets, but in the absence of commutator anomalies the same results will hold for the commutators of the constraint operators in the corresponding quantised theories.

Detection of edges from projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. The problem of detecting edges from projection data is addressed. It is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

Biorthogonal series method for Oseen type flows

A biorthogonal series method is developed to solve Oseen type flow problems. The theory leads to a new set of eigenfunctions for a specific class of linear non-selfadjoint operators containing the biharmonic one. These eigenfunctions differ from those given earlier in the literature for the biharmonic operator. The method is applied to the problem of thermocapillary flow in a cylindrical liquid bridge of finite length with axial through flow. Flow and temperature distributions are obtained at leading order of an expansion for small surface tension Reynolds number and Prandtl number. Another related problem considered is that of cylindrical cavity flow. Solutions for both cases are presented in terms of biorthogonal series. The effect of axial through flow on velocity and temperature fields is discussed by numerical evaluation of the truncated analytical series. The presence of axial through flow not only convectively shifts the vortices induced by surface forces in the direction of the through flow, but also moves their centers toward the outer cylindrical boundary. This process can lead to significantly asymmetric flow structures.

Kaon B parameter with Wilson fermions

We calculate the kaon B parameter in quenched lattice QCD at beta=6.0 using Wilson fermions at kappa=0.154 and 0.155. We use two kinds of nonlocal (''smeared'') sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for p=(0,0,0) and p=(0,0,1), we show that one can carry out the noperturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral-symmetry-breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for B parameters of the DELTAI = 3/2 part of the electromagnetic penguin operators, and preliminary results for B(K) in the presence of two flavors of dynamical quarks.

Structure of Sesbania Mosaic Virus at 4·7 Å Resolution and Partial Sequence of the Coat Protein

Sesbania mosaic virus (SMV) is a plant virus infecting Sesbania grandiflora plants in Andhra Pradesh, India. Amino acid sequence of the tryptic peptides of SMV coat protein were determined using a gas phase sequenator. These sequences showed identical amino acids at 69% of the positions when aligned with the corresponding residues of southern bean mosaic virus (SBMV).Crystals diffracting to better than 3 Å resolution were obtained by precipitating the virus with ammonium sulphate. The crystals belonged to rhombohedral space group R3 with α = 291·4 Å and α = 61·9°. Three-dimensional X-ray diffraction data on these crystals were collected to a resolution of 4·7 Å, using a Siemens-Nicolet area detector system. Self-rotation function studies revealed the icosahedral symmetry of the virus particles, as well as their precise orientation in the unit cell. Cross-rotation function and modelling studies with SBMV showed that it is a valid starting model for SMV structure determination. Low resolution phases computed using a polyalanine model of SBMV were subjected to refinement and extension by real-space electron density averaging and solvent flattening. The final electron density map revealed a polypeptide fold similar to SBMV. The single disulphide bridge of SBMV coat protein is retained in SMV. Four icosahedrally independent cation binding sites have been tentatively identified. Three of these sites, related by a quasi threefold axis, are also found in SBMV. The fourth site is situated on the quasi threefold axis. Aspartic acid residues, which replace Ile218 of SBMV from the quasi threefold-related subunits are suitable ligands to the cation at this site

Points-to Analysis as a System of Linear Equations

We propose a novel formulation of the points-to analysis as a system of linear equations. With this, the efficiency of the points-to analysis can be significantly improved by leveraging the advances in solution procedures for solving the systems of linear equations. However, such a formulation is non-trivial and becomes challenging due to various facts, namely, multiple pointer indirections, address-of operators and multiple assignments to the same variable. Further, the problem is exacerbated by the need to keep the transformed equations linear. Despite this, we successfully model all the pointer operations. We propose a novel inclusion-based context-sensitive points-to analysis algorithm based on prime factorization, which can model all the pointer operations. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that our approach is competitive to the state-of-the-art algorithms. With an average memory requirement of mere 21MB, our context-sensitive points-to analysis algorithm analyzes each benchmark in 55 seconds on an average.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

Free vibration analysis Of stochastic strings

The free vibration of strings with randomly varying mass and stiffness is considered. The joint probability density functions of the eigenvalues and eigenfunctions are characterized in terms of the solution of a pair of stochastic non-linear initial value problems. Analytical solutions of these equations based on the method of stochastic averaging are obtained. The effects of the mean and autocorrelation of the mass process are included in the analysis. Numerical results for the marginal probability density functions of eigenvalues and eigenfunctions are obtained and are found to compare well with Monte Carlo simulation results. The random eigenvalues, when normalized with respect to their corresponding deterministic values, are observed to tend to become first order stochastically stationary with respect to the mode count.

Holographic c-theorems in arbitrary dimensions

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

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.