SU(1, 1) Random Polynomials

We study statistical properties of zeros of random polynomials and random analytic functions associated with the pseudoeuclidean group of symmetries SU(1, 1), by utilizing both analytical and numerical techniques. We first show that zeros of the SU(1, 1) random polynomial of degree N are concentrated in a narrow annulus of the order of N ^–1 around the unit circle on the complex plane, and we find an explicit formula for the scaled density of the zeros distribution along the radius in the limit N. Our results are supported through various numerical simulations. We then extend results of Hannay⁽¹⁾ and Bleher et al. ⁽²⁾ to derive different formulae for correlations between zeros of the SU(1, 1) random analytic functions, by applying the generalized Kac–Rice formula. We express the correlation functions in terms of some Gaussian integrals, which can be evaluated combinatorially as a finite sum over Feynman diagrams or as a supersymmetric integral. Due to the SU(1, 1) symmetry, the correlation functions depend only on the hyperbolic distances between the points on the unit disk, and we obtain an explicit formula for the two point correlation function. It displays quadratic repulsion at small distances and fast decay of correlations at infinity. In an appendix to the paper we evaluate correlations between the outer zeros |z _j |>1 of the SU(1, 1) random polynomial, and we prove that the inner and outer zeros are independent in the limit when the degree of the polynomial goes to infinity.     

Discrete Dynamical Systems with W(A (1) m−1 × A (1) n−1) Symmetry

We give a birational realization of affine Weyl group of type A ⁽¹⁾ _m–1 × A ⁽¹⁾ _n–1. We apply this representation to construct some discrete integrable systems and discrete Painlevé equations. Our construction has a combinatorial counterpart through the ultra-discretization procedure.     

Comparative study of (1 0 0) and (1 1 1)B InGaAs single quantum well laser diodes

In this work, a series of identical In_xGa_1−xAs/Al_yGa_1−yAs single quantum well laser diodes, grown on (1 0 0) and (1 1 1)B GaAs substrates, have been thoroughly studied. For all samples, clear evidence of reduced threshold current densities in the (1 1 1)B substrate has been observed in electroluminescence spectra at 17 and 300 K. Modelling of the devices, based on a self-consistent solution of Schrödinger–Poisson's equations, was utilised in order to reproduce the experimental results. The model incorporates strain and piezoelectric effects on the quantum well states, free carrier screening, overlap integral computation, and optical gain calculation. The underlying mechanism, that explains the threshold reduction observed in the (1 1 1)B laser diodes, is discussed based on the results of the modelling.     

Some perturbation calculations for 1s2p, 1s 22p,and 1s 22s

The Dalgarno interchange theorem is used, together with the U function approach, to evaluate the first order perturbation corrections to <r ₁ ^-1+r ₂ ^-1> and <r ₁ + r ₂> for the two-electron states 1s2p ¹ P and 1s2p ³ P. The results for <r ₁ + r ₂> are extended by using a screening approximation, and are compared with the results of accurate variational calculations. The first order perturbation correction to spin-weighted expectation values of type <ΣV(r_j )s_zj > is given for the three-electron states 1s ²2p ² P and 1s ²2s ² S. The case V(r_j ) = r _j ^-1 is treated in detail.     

Comparative dynamical study of the HD and isotopomers interacting with Pd(1 1 1) and Cu(1 1 0) surfaces

We study the dynamics of HD and H₂ molecules interacting with Pd(1 1 1) and Cu(1 1 0) using the classical trajectory method based on potential energy surfaces obtained from Density Functional Theory calculations. Our results predict a negligible isotopic effect on the dissociative adsorption probability on Pd(1 1 1) whereas on Cu(1 1 0), the adsorption probability for HD(ν_i=0) is slightly lower than for H₂(ν_i=0), mainly due to its lower initial vibrational zero point energy. The final rotational energy distribution of scattered HD and H₂ molecules are very similar. This shows that the asymmetric mass distribution of HD, barely affects the fraction of initial translational energy transferred to rotation during the scattering process. Our calculations point to the larger number of open rotational excitation channels for HD, as the main cause of rotational excitation probabilities larger than for H₂. The theoretical apparent rotational temperature, T_rot, of HD molecules scattered from Pd(1 1 1) at impact energy , is in good agreement with the experimental value. In contrast, for Cu(1 1 0) the theoretical T_rot is much lower than the value measured for Cu(1 0 0). Possible reasons for such a discrepancy between theory and experiments are discussed.     

1H NMR Studies of 1-Ethylimidazole Binding to Cytochrome C

Abstract

Kinetic and equilibrium data for 1-EtIm binding to cyt c at temperature range of 303–319K have been determined at pH 7.0 by using ¹HNMR method. Thermodynamic values (ΔH°=39.5 kJ mol^?1, ΔS° = 154 J mol^?1K^?1 and Ea = 142 kJ mol^?1) are obtained from Van't Hoff and Arrhenius's relations. Some hyperfine shifted resonances of l-EtIm cyt c have been assigned for the first time using 1D saturation transfer experiments. The origin of the asymmetric spin density distribution in heme groups of 1-EtIm cyt c and the reason of low affinity of cytochrome c for 1-EtIm are also discussed move toward upfield from original position. However, Te-2, 4 substituents in cyt c are more electron withdrawing than the propionic acid side chains, which lead to the 5-methyl group going toward downfield.     

Magnetic characteristics of thin Ni films electrodeposited on n-Si(1 1 1)

The nanocrystalline Ni films were grown on n-Si(1 1 1) substrate by pulsed electrodeposition in non-aqueous NiCl₂ + methanol solution. The frequency of potential pulse was modulated during the deposition of Ni onto Si substrates. When the frequency varies from 20 to 900 Hz, the average size of Ni nanocrystallites varied in the ranges from 48 to 130 nm. In these cases, all Ni films have grown through a three-dimensional instantaneous nucleation followed by diffusion-limited growth. From X-ray diffraction measurement, it has been found that Ni(1 1 1) grows preferentially on the Si(1 1 1) substrates. The magnetic hysteresis loops for as-deposited films were measured by using VSM. As the angle θ between film plane and applied magnetic field varies from 0 to 90, the coercivity (H_c) and squareness (S) obtained from the magnetic hysteresis loops showed an opposite behavior. With the increase in θ, H_c increased but S decreased near linearly. We have also investigated the variation of H_c as a function of Ni nanocrystallite’s size. From VSM measurement, we could observe that the coercivities for the magnetic field applied perpendicular and parallel to the film plane increase up to the average size of 86 nm but begin to decrease over this size.     

Glide of dislocations in <1 1 1>{3 2 1} slip system: an atomistic study

Atomistic calculations are performed to investigate plastic slip in the <1?1?1>{3?2?1} system in body-centred cubic iron. Several modern interatomic potentials, developed over the last decade, are applied to compute the stacking fault γ-line energy in the {3?2?1} plane and the results are compared with the ab initio prediction. The applied potentials have shown strong deviations, but several potentials acquired good qualitative agreement with the ab initio data. Depending on the applied potential, the lowest value of the Peierls stress for the edge dislocation (ED) is 50 MPa (Ackland and Bacon from 1997) and the highest is 550 MPa (Dudarev and Derlet from 2005), while for the screw dislocation it is much higher, in the range 1–2 GPa. At finite temperature, however, the flow stress of the ED is found to decrease exponentially reaching a negligible value at about 200 K, irrespective of the applied potential. On the basis of the data obtained using Ackland–Mendelev potential from 2004, we conclude that the slip resistance of the <1?1?1>{3?2?1} system is in between the resistance of the <1?1?1>{1?1?0} and <1?1?1>{1?1?2} slip systems.     

Elementary Systems of (1 + 1) Kinematical Groups: Contraction and Quantization

We present the (algebra) group contraction chain SU(1, 1) → P(1, 1) → G(1, 1), where P(1, 1) and G(1, 1) are the Poincaré and the Galilei groups, respectively, in (1 + 1) dimensions. We have paid attention to the contraction of the pseudo-extended Poincaré group to the central extended Galilei group. Objects like group laws, coadjoint orbits and representations of the contracted groups have been obtained in terms of their noncontracted counterparts. As an application we study the Moyal quantization of classical systems, having those groups as symmetry groups, by means of the contraction of the so called Stratonovich-Weyl kernels which provide such quantization.     

2+1 gravity for genus >1

In [1] we analysed the algebra of observables for the simple case of a genus 1 initial data surface ² for 2+1 De Sitter gravity. Here we extend the analysis to higher genus. We construct for genus 2 the group of automorphismsH of the homotopy group ₁ induced by the mapping class group. The groupH induces a groupD of canonical transformations on the algebra of observables which is related to the braid group for 6 threads.     

Temperature dependent LEED study of Pb{1 1 1}

The thermal behavior of Pb{1 1 1} was studied using low-energy electron diffraction (LEED) in the temperature range 11–323 K. The surface interlayer spacings increase with temperature at about the same rate as the bulk up to 0.5 T_m, and then increase faster. The relaxation of the surface, which is larger than for other fcc {1 1 1} surfaces, is maintained in the temperature range studied. Although Pb has a larger expansion coefficient than other metals, the surface thermal expansion behavior is in line with other surfaces, and is consistent with harmonic interplanar potentials.     

Canonical Representations of Sp(1,n) Associated with Representations of Sp(1)

Canonical representations of Sp(1,n) associated with finite dimensional irreducible representations of Sp(1) are defined using vector-valued Berezin kernels. Their decomposition into irreducible representations is determined by decomposing the corresponding reproducing distributions in terms of positive definite trace spherical functions on Sp(1,n). The canonical representatons are also identified with the restriction to Sp(1,n) of certain maximal degenerate representations of SL(n+1,H). Received: 1 May 1998 / Accepted: 18 November 1998     

Photon-Added SU(1, 1) Coherent States and their Non-Classical Properties

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

     

Invariants of 2+1 gravity

In [1, 2] we established and dicussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genusg with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to 6g-6(g>1) is treated in detail with a precise classification forg=1 andg=2.     

The Proton NMR Assignment of 1-Aminocyclo-propane-1-carboxylic Acid

The two sets of diastereomeric hydrogen atoms cis and trans to the carboxylate of 1-aminocyclopropane-1-carboxylic acid (ACC) were differentiated by a ¹H-nmr study. The measurement of the ¹H-nmr spectrum of ACC at pH 3.8 during the successive addition of non-chiral lanthanide reagents such as Eu(NO₃)₃, Pr(NO₃)₃ or Gd(NO₃)₃ demonstrated that the hydrogen atoms cis to the carboxylate function of ACC resonate at δ=1.42 and that the hydrogen atoms trans to the carboxylate function of ACC resonate at δ=1.20. The mono-substituted cyclopropanes, cyclo-propanecarboxylic acid (CPC) and cyclopropyl-amine (CPA) were used in complementary lanthanide-reagent shift titrations along with the back titration of an ACC-Eu⁺⁺⁺ complex with DCl to further substantiate the assignment. This assignment allows for the non-destructive, nonisotopic diluting analysis of various biosynthetically derived deuterated ACC's formed from the corresponding deuterated S-adenosyl-L-methionine.     

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity.The fundamental field variables are the tetrad fields e i μ and the gravity is attributed to the torsion.A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived.The energy associated with this solution is calculated using the two-dimensional gravitational energy-momentum formula.     

Twists in Hopf algebras andRT 1 T 2=T 2 T 1 relations

LetR be a matrix unitary quasi-classical solution of the Yang-Baxter equation. Considering an associative algebra defined by the relationRT ₁ T ₂=T ₂ T ₁ we find a universal twistF such thatR is the image ofR=F ₂₁ F ⁻¹ in the vector representation. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Dispersion of cerebral on-resonanceT 1 in the rotating frame (T 1ρ) in global ischaemia

T ₁ in the rotating frame (T _1ρ) has been recently shown to be an early magnetic resonance imaging index of ongoing pathology in vivo. Dispersion ofT _1ρ at aB ₁ range from 620 to 160500 rad/s was quantified in the rat brain to study the effects of ischaemia onT _1ρ relaxation and to elude the role of physico-chemical mechanisms underlying the relaxation changes. The results show a biphasic effect of the dispersion ofR _1ρ (1/T _1ρ) in ischaemic brain. In the lowB ₁ region (less than 5000 rad/s), an increase was detected, while at the highB ₁ end of the experiments,R _1ρ was reduced. This was accompanied by a change in the fitted values describing the dispersion characteristics. Injection of a superparamagnetic contrast agent, AMI-227, before ischaemia shifted theR _1ρ curve upwards by 4% but showed no effect on the shape of theR _1ρ dispersion curve. The present results argue for a specific effect of endogenous susceptibility on cerebralR _1ρ in the early moments of ischaemia due to a relaxation enhancement in the blood pool. Our results confirm that quantitativeR _1ρ dispersion nuclear magnetic resonance (NMR) improves the sensitivity ofR _1ρ NMR to detect ischaemia in vivo. Simple empirical linear or exponential fits proved to be efficient ways to describe dispersion data in the limitedB ₁ range, as more detailed models may not offer additional information in a physically relevant manner for complex systems, such as the brain.     

Letter: O(d + 1, d + n + 1)-Invariant Formulation of Stationary Heterotic String Theory

We present a pair of symmetric formulations of the matter sector of the stationary effective action of heterotic string theory that arises after the toroidal compactification of d dimensions. The first formulation is written in terms of a pair of matrix potentials Z ₁ and Z ₂ which exhibits a clear symmetry between them and can be used to generate new families of solutions on the basis of either Z ₁ or Z ₂; the second one is an O(d + 1, d + n + 1)-invariant formulation which is written in terms of a matrix vector W endowed with an O(d + 1, d + n + 1)-invariant scalar product which linearizes the action of the O(d + 1, d + n + 1)symmetry group on the coset space O(d + 1, d + n + 1)/[O(d + 1) × O(d + n + 1)]; this fact opens as well a simple solution-generating technique which can be applied on the basis of known solutions.