Polynomial and polytropic approximations in equation of equilibrium post-Newtonian rotating configurations of degenerate neutron gas

This paper considers the polynomial and polytropic approximations in the equation of equilibrium post-Newtonian rotating configurations of a degenerate neutron gas. The concept of a configuration-averaged polytropic index is introduced.     

Quantum Morphing and the Jones Polynomial

We will explore the experimental observation that on the set of knots with bounded crossing number, algebraically independent Vassiliev invariants become correlated, as noticed first by S. Willerton. We will see this through the value distribution of the Jones polynomial at roots of unit. As the degree of the roots of unit is getting larger, the higher order fluctuation is diminishing and a more organized shape will emerge from a rather random value distribution of the Jones polynomial. We call such a phenomenon “quantum morphing”. Evaluations of the Jones polynomial at roots of unity play a crucial role, for example in the volume conjecture. Received: 15 February 2001 / Accepted: 8 June 2001     

Fermionic Formulas for Level-Restricted Generalized Kostka Polynomials and Coset Branching Functions

Level-restricted paths play an important r?le in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijection between Littlewood–Richardson tableaux and rigged configurations is well-behaved with respect to level-restriction and give an explicit characterization of level-restricted rigged configurations. As a consequence a new general fermionic formula for the level-restricted generalized Kostka polynomial is obtained. Some coset branching functions of type A are computed by taking limits of these fermionic formulas. Received: 9 April 2000 / Accepted: 26 January 2001     

A note on Edwards' hypothesis for zero-temperature Ising dynamics

We give a simple criterion for testing a behavior à la Edwards in certain zero-temperature, ferromagnetic spin-flip dynamics and use it to show that the limiting distributions of those dynamics do not coincide with the uniform distribution over the blocked configurations of the dynamics. We provide explicit examples in dimension one and higher.     

Fluorescence diagnosis of the status of the human lens <Emphasis Type="Italic">in vivo</Emphasis>

We have studied fluorescence spectra of the human lens in vivo for healthy eyes and in different stages of senile cataract development. We propose a spectral criterion, the lens opacity index, allowing us to differentiate between stages of cataract development. We show a high correlation between the stage of cataract development and the opacity index. We propose an empirical expression for determining the stage of senile cataract development from the value of the lens opacity index. The technique has been clinically tested.     

Relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.     

Checking for optimal solutions in some NP-complete problems

For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.     

The( p,q) inflation model

In this paper we propose a new inflation model named( p, q) inflation model in which the inflaton potential contains both positive and negative powers of inflaton field in the polynomial form. We derive the accurate predictions of the canonical single-field slow-roll inflation model. Using these formula, we show that our inflation model can easily generate a large amplitude of tensor perturbation and a negative running of spectral index with large absolute value.     

Affine and polynomial mutual information coregistration for artifact elimination in diffusion tensor imaging of newborns

We have investigated the use of two different image coregistration algorithms for identifying local regions of erroneously high fractional anisotropy (FA) as derived from diffusion tensor imaging (DTI) data sets in newborns. The first algorithm uses conventional affine registration of each of the diffusion-weighted images to the unweighted (b = 0) image for each slice, while the second algorithm uses second-order polynomial warping. Similarity between images was determined using the mutual information (MI) criterion, which is the preferred 'cost' criterion for coregistration of images with significantly different image intensity distributions. We have found that subtle differences exist in the FA values resulting from affine and second-order polynomial coregistration and demonstrate that nonlinear distortions introduce artifacts of spatial extent similar to real white matter structures in the newborn subcortex. We show that polynomial coregistration systematically reduces the presence of erroneous regions of high FA and that such artifacts can be identified by visual inspection of FA maps resulting from affine and polynomial coregistrations. Furthermore, we show that nonlinear distortions may be particularly pronounced when acquiring image slices of axial orientation at the height of the nasal cavity. Finally, we show that third-order polynomial MI coregistration (using the images resulting from second-order coregistration as input) has no observable effect on the resulting FA maps.     

The Tutte polynomial of an infinite family of outerplanar,small-world and self-similar graphs

In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact analytical expression for the Tutte polynomial at several special points     

Efficient solution strategy for the semi-implicit discontinuous Galerkin discretization of the Navier-Stokes equations

We deal with the numerical solution of the system of the compressible Navier–Stokes equations with the aid of the interior penalty Galerkin method. We employ a semi-implicit time discretization which leads to the solution of a sequence of linear algebraic systems. We develop an efficient strategy for the solution of these systems. It is based on a simple adaptive technique for the choice of the time step and a relatively weak stopping criterion for iterative linear algebraic solvers. The presented numerical experiments show that the proposed strategy is efficient for steady-state problems using various grids, polynomial degrees of approximations and flow regimes. Finally, we apply this strategy with a minor modification to an unsteady flow.     

Model fractional quantum Hall states and Jack polynomials

We describe an occupation-number-like picture of fractional quantum Hall states in terms of polynomial wave functions characterized by a dominant occupation-number configuration. The bosonic variants of single-component Abelian and non-Abelian fractional quantum Hall states are modeled by Jack symmetric polynomials (Jacks), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a "squeezing rule" that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks presented in this Letter describe new trial uniform states, but it is yet to be determined to which actual experimental fractional quantum Hall effect states they apply.     

Metastable kinks in the orbifold

We consider static configurations of bulk scalar fields in extra-dimensional models in which the fifth dimension is an S1/Z2 orbifold. There may exist a finite number of such configurations, with the total number depending on the size of the orbifold interval. We perform a detailed Sturm-Liouville stability analysis that demonstrates that all but the lowest-lying configurations--those with no nodes in the interval--are unstable. We also present a powerful general criterion with which to determine which of these nodeless solutions are stable. The detailed analysis underlying the results presented in this Letter, and applications to specific models, are presented in a comprehensive companion paper [M. Toharia and M. Trodden, arXiv:hep-ph/0708.4008].     

Analysis of a qualitative criterion for forecasting off-centre displacement of impurity ions in ionic crystals

Summary With the aid of the Sanderson model for nonmolecular structure a qualitative criterion is derived for forecasting off-centre configurations of monovalent impurity ions (Li⁺, F⁻, Cl⁻, Na⁺, Ag⁺, Cu⁺) in alkali halide crystals. The same criterion is checked for Mn²⁺ impurity ions in some oxides. We also present a critical review of the criteria introduced in the past, as well as of the experimental results up to now known in the literature. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction. Work jointly supported by the Ministero della Pubblica Istruzione and by Consiglio Nazionale delle Ricerche, Gruppo Nazionale di Struttura della Materia.     

Lattice vibrations and local order in substitutional solid solutions. II

The nearest neighbour effect on the mean vibrational state is investigated in solid solutions. It is shown that the possibility of A-B pair bond affection in the closest surrounding of the bond is accounted for, when linear, parabolic or some more complicated dependence of the states of A and B atoms on the relative proportions of both types in their first coordination shell is used. The expression is deduced for the mean vibrational state of atoms in the solid solution under the assumption that the dependence of A and B atom states on the number of unlike atoms in the first coordination shell is given as a polynomial ofi-th order. In the case of the parabolic approximation it follows that the structure of the solid solution (i.e. degree of order) is given by atom interactions, which result in configurations with maximum lattice cohesion. There is no assumption about the nature of atom interaction in the present paper. Therefore the results combined with experimental data can serve as a criterion of availability of different physical models and help in a better understanding of atomic bonds in metal systems.     

SL(2,R) PRINCIPAL PROLONGATION STRUCTURES OF SOLITON EQUATIONS AND THEIR CONSERVATION LAWS

We present the concept of principal prolongation structure (PPS) and a covariant criterion of the completeness of conserva-tion currents for the PPS of class of nonlinear evolution equations (NEES).The SL(2,R) × R'(l) PPS for AKNS systems is constructed, a new set of infinite number of polynomial conservation currents (PCCs) corresponding to the nonlinearity of SL (2,R) group manifold is given. These currents together with the usual PCCS of AKNS systems satisfy a covariant equation for the SL(2,R) × R'(l) PPS. This equation gives rise to a criterion of completeness of these currents. As an example,the sine-Gordon system is analysed.     

Polynomial estimation of probability densities

We propose a new quality criterion and an iterative algorithm for polynomial estimation of probability densities of a random quantity. The properties of the optimal estimate are studied and the conditions and rate of its convergence are found. Antiaircraft Command High School of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1416–1432, November, 1997.     

Determination of the concentration of aerosol particles in a vertical atmospheric column from satellite measurements of the spectral optical depth

We propose a method for fast retrieval of the inhalable particle concentration (PM_2.5 and PM₁₀) in a vertical atmospheric column from satellite measurements of the aerosol optical depth (AOD) without using a priori assumptions concerning the refractive index and the aerosol particle size distribution function. The method is based on a polynomial regression between PM_2.5, PM₁₀, and AOD at the wavelengths 466 nm and 644 nm, established from AERONET data. We have studied the sensitivity of the method to errors in the optical measurements and have estimated the errors in retrieval of PM_2.5 and PM₁₀ for different atmospheric situations. We carry out parametrization of the regressions on the value of the integrated air moisture content.     

Chiral anomaly and nucleon properties in the Nambu-Jona-Lasinio model with vector mesons

We consider the extended SU(3) Nambu and Jona-Lasinio model with explicit vector couplings in the presence of external fields. We study the chiral anomaly in this model and its implications on the properties of the nucleon described as a chiral soliton of three valence quarks bounded in mesonic background fields. For the model to reproduce the QCD anomaly it is necessary to subtract suitable local and polynomial counterterms in the external and dynamical vector and axial-vector fields. We compute the counterterms explicitly in a vector-gauge-invariant regularization, and obtain modifications to the total effective action and vector and axial currents. We study the numerical influence of those counterterms in the two-flavour version of model with dynamical σ, π, , A and ω mesons. We find that, for time-independent hedgehog configurations, the numerical effects in the nucleon mass, the isoscalar nucleon radius and the axial coupling constant are negligibly small.     

Chaos synchronization of coupled neurons with gap junctions

Based on the asymptotic stability theory of dynamical systems and matrix theory, a general criterion of synchronization stability of N coupled neurons with symmetric configurations is established in this Letter. Especially, three types of connection styles (that is, chain, ring and global connections) are considered. As an illustration, complete synchronization of four coupled identical chaotic Chay neurons is investigated. The maximal conditional Lyapunov exponent is calculated and used to determine complete synchronization. As a result, complete synchronization of four coupled identical chaotic Chay neurons can be achieved when the coupling strength is above a critical value, which is dependent on the specific connection style. Numerical simulation is in good agreement with the theoretical analysis.