Determinations of Uranium(VI) Binding Properties with some Metalloproteins (Transferrin,Albumin, Metallothionein and Ferritin) by Fluorescence Quenching

The interactions between uranium and four metalloproteins (Apo-HTf, HSA, MT and Apo-EqSF) were investigated using fluorescence quenching measurements. The combined use of a microplate spectrofluorometer and logarithmic additions of uranium into protein solutions allowed us to define the fluorescence quenching over a wide range of [U]/[Pi] ratios (from 0.05 to 1150) at physiologically relevant conditions of pH. Results showed that fluorescence from the four metalloproteins was quenched by UO₂²⁺. Stoichiometry reactions, fluorescence quenching mechanisms and complexing properties of metalloproteins, i.e. binding constants and binding sites densities, were determined using classic fluorescence quenching methods and curve-fitting software (PROSECE). It was demonstrated that in our test conditions, the metalloprotein complexation by uranium could be simulated by two specific sites (L₁ and L₂). Results showed that the U(VI)–Apo-HTf complexation constant values (log K₁ = 7.7, log K₂ = 4.6) were slightly higher than those observed for U(VI)–HSA complex (log K₁ = 6.1, log K₂ = 4.8), U(VI)–MT complex (log K₁ = 6.5, log K₂ = 5.6) and U(VI)–Apo-EqsF complex (log K₁ = 5.3, log K₂ = 3.9). PROSECE fitting studies also showed that the complexing capacities of each protein were different: 550 moles of U(VI) are complexed by Apo-EqSF while only 28, 10 and 5 moles of U(VI) are complexed by Apo-HTf, HSA and MT, respectively.     

Weighted Bergman Kernels and Quantization}

Let Ω be a bounded pseudoconvex domain in C ^N , φ, ψ two positive functions on Ω such that − log ψ, − log φ are plurisubharmonic, and z∈Ω a point at which − log φ is smooth and strictly plurisubharmonic. We show that as k→∞, the Bergman kernels with respect to the weights φ ^{k ψ} have an asymptotic expansion

Bryuno Function and the Standard Map

For the standard map the homotopically non-trivial invariant curves of rotation number ω satisfying the Bryuno condition are shown to be analytic in the perturbative parameter ε, provided |ε| is small enough. The radius of convergence ρ(ω) of the Lindstedt series – sometimes called critical function of the standard map – is studied and the relation with the Bryuno function B(ω) is derived: the quantity |log ρ(ω) + 2 B (ω)| is proved to be bounded uniformly in ω. Received: 8 February 2000/ Accepted: 2 March 2001     

3d Monte Carlo simulation of site-bond continuum percolation of spheres

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ( φ_e), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres 1 - φ_e is the porosity. The bond percolation threshold (p _b) can be described in terms of φ_e by a simple analytical expression: log(φ_e)/log(φ_ec) + log(p _b)/log(p _bc) = 1, with p _bc = 0.12 independent of the bond range and φ_ec a constant that decreases with increasing bond range. Received: 10 March 2003 / Accepted: 23 April 2003 / Published online: 21 May 2003 RID="a" ID="a"e-mail: jean-christophe.gimel@univ-lemans.fr     

Investigations of electronic minority charge carrier conductivity in La0.9Sr0.1Ga0.8Mg0.2O2.85

The perovskite structured material LaGaO₃ doped with 10 mol-% strontium and 20 mol-% magnesium was prepared by two different wet-chemical synthesis routes. The total conductivity was measured in air and under an oxygen partial pressure of 10⁻²⁰ bar. There was a decrease by 10 % in 4 days when the atmosphere was changed from air to 10⁻²⁰ bar. This process is reversible. Hebb-Wagner measurements resulted in values for the electronic minority charge carrier conductivities in pure oxygen of log σ_h [S/cm]=−4.02 and log σ_e [S/cm]=−15.5 for the holes and electrons, respectively, at 600 °C. In the partial pressure range 10⁻³ bar≤p(O₂)≤1 bar, a slope of +1/4 was observed for d(log (σ_h)) / d(log (p(O₂)) at T=600, 650 and 700 °C. That is in agreement with the assumption of a large number of oxygen vacancies. The diffusion coefficient of the holes was evaluated from the relaxation curves to be 1.1*10⁻⁷ cm²/s at 600 °C. Degradation effects were observed under highly reducing conditions which are attributed to the formation of gallium-platinum alloys and the loss of gallium oxide if O₂ is available in the gas phase. Paper presented at the 6th Euroconference on Solid State Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.     

Ionic conductivity of silver chalcogenide glasses

The dynamic response by electrical spectroscopy of ionically conducting chalcogenide glasses (Ag₂S)_x(GeS₂)_1–x has been studied. The activation energies E_d.c deduced from the Arrhenius plots are temperature dependent. Fitting the curves to log(σ_a.c)=f(log ω) leads to values of characteristic parameters that are dependent both on temperature and frequency. The obtained experimental results are compared with a theoretical model based on the concept of “free volume” fluctuations. A new approch is proposed leading to acceptable hopping distances. Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, 11–18 Sept. 1994.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

The Mixing Time Evolution of Glauber Dynamics for the Mean-Field Ising Model

We consider Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime (β < 1) has order n log n, whereas the mixing-time in the case β > 1 is exponential in n. Recently, Levin, Luczak and Peres proved that for any fixed β < 1 there is cutoff at time with a window of order n, whereas the mixing-time at the critical temperature β = 1 is Θ(n ^3/2). It is natural to ask how the mixing-time transitions from Θ(n log n) to Θ(n ^3/2) and finally to exp (Θ(n)). That is, how does the mixing-time behave when β = β(n) is allowed to tend to 1 as n → ∞. In this work, we obtain a complete characterization of the mixing-time of the dynamics as a function of the temperature, as it approaches its critical point β _c  = 1. In particular, we find a scaling window of order around the critical temperature. In the high temperature regime, β = 1 − δ for some 0 < δ < 1 so that δ ² n → ∞ with n, the mixing-time has order (n/δ) log(δ ² n), and exhibits cutoff with constant and window size n/δ. In the critical window, β = 1± δ, where δ ² n is O(1), there is no cutoff, and the mixing-time has order n ^3/2. At low temperature, β = 1 + δ for δ > 0 with δ ² n → ∞ and δ = o(1), there is no cutoff, and the mixing time has order . Research of J. Ding and Y. Peres was supported in part by NSF grant DMS-0605166.     

Superdiffusivity of Occupation-Time Variance in 2-dimensional Asymmetric Exclusion Processes with Density ρ = 1/2

We compute that the growth of the occupation-time variance at the origin up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least tlog (log t) for general rates, and at least t(log t)^1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of “second-class” particles.Research supported in part by NSA H982300510041 and NSF-DMS 0504193     

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1/ε ² we consider the asymptotic regime ε → 0 with the angular velocity Ω proportional to (ε ²|log ε|)⁻¹. We prove that if Ω = Ω₀(ε ²|log ε|)⁻¹ and Ω₀ > 2(3π)⁻¹ then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary ‘hole’ around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.     

Low-lying Gamow-Teller transitions in spherical nuclei

The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 ⩽ A ⩽ 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying β decay log(ft) values have been calculated for the nuclei under consideration.     

Sharpenings of Li's Criterion for the Riemann Hypothesis

Exact and asymptotic formulae are displayed for the coefficients λ _n used in Li's criterion for the Riemann Hypothesis. For n → ∞ we obtain that if (and only if) the Hypothesis is true, λ _n ∼ n(A log n + B) (with A > 0 and B explicitly given, also for the case of more general zeta or L-functions); whereas in the opposite case, λ _n has a non-tempered oscillatory form. ^★Institut de Mathématiques de Jussieu-Chevaleret (CNRS UMR 7586), Université Paris 7, F-75251 Paris CEDEX 05, France.     

Biological activity of aldose reductase and lipophilicity of pyrrolyl-acetic acid derivatives

Quantitative Structure-Activity Relationship modeling is a powerful approach for correlating an organic compound to its lipophilicity. In this paper QSAR models are established for estimation of correlation of the lipophilicity of a series of pyrrolyl-acetic acid derivatives, inhibitors of the aldose reductase enzyme, in the n-octanol-water system with biological activity of aldose reductase. Lipophilicity, expressed by the logarithm of n-octnol-water partition coefficient log P and biological activity of aldose reductase inhibitory activity by log it. Result obtained by QSAR modeling of compound series reveal a definite trend in biological activity and a further improvement in quantitative relationships are established if, beside log P, Hammett electronic constant σ and connectivity index chi-3 (³ χ) term included in the regression equation.     

A Farey Fraction Spin Chain

We introduce a new number-theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation-invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and a phase transition occurs for positive inverse temperature β= 2. The free energy is the same as that of related, non-translation-invariant number-theoretic spin chain. Using a number-theoretic argument, the low-temperature (β > 3) state is shown to be completely magnetized for long chains. The number of states of energy E= log(n) summed over chain length is expressed in terms of a restricted divisor problem. We conjecture that its asymptotic form is (n log n), consistent with the phase transition at β= 2, and suggesting a possible connection with the Riemann ζ-function. The spin interaction coefficients include all even many-body terms and are translation invariant. Computer results indicate that all the interaction coefficients, except the constant term, are ferromagnetic. Received: 20 August 1998/ Accepted: 17 December 1998     

Renormalisation-Induced Phase Transitions for Unimodal Maps

The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential −t log | Df |. Multiple and indeed infinitely many phase transitions at positive t can occur for some quadratic maps. All unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum. The author was supported by the EU training network “Conformal Structures and Dynamics”.     

The running BFKL: Resolution of Caldwell’s puzzle

The HERA data on the proton structure function F ₂(x,Q ²) at very small x and Q ₂ show a dramatic departure of the logarithmic slope ∂F ₂/∂log Q ² from theoretical predictions based on the DGLAP evolution. We show that the running BFKL approach provides a quantitative explanation for the observed x and/or Q ² dependence of ∂F ₂/∂log Q ². Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 92–97 (25 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles

We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. Our model is macroscopically described by an inhomogeneous Smoluchowski’s equation in the low ε limit provided that the initial number of particles N is of order |log ε|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low ε limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation.     

Random Matrix Theory and ζ(1/2+it)

We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of |Z| and Z/Z ^*, and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log Z as N→∞. In the limit, we show that these two distributions are independent and Gaussian. Costin and Lebowitz [15] previously found the Gaussian limit distribution for Im log Z using a different approach, and our result for the cumulants proves a conjecture made by them in this case. We also calculate the leading order N→∞ asymptotics of the moments of |Z| and Z/Z ^*. These CUE results are then compared with what is known about the Riemann zeta function ζ (s) on its critical line Re s= 1/2, assuming the Riemann hypothesis. Equating the mean density of the non-trivial zeros of the zeta function at a height T up the critical line with the mean density of the matrix eigenvalues gives a connection between N and T. Invoking this connection, our CUE results coincide with a theorem of Selberg for the value distribution of log ζ(1/2+iT) in the limit T→∞. They are also in close agreement with numerical data computed by Odlyzko [29] for large but finite T. This leads us to a conjecture for the moments of |ζ(1/2+it) |. Finally, we generalize our random matrix results to the Circular Orthogonal (COE) and Circular Symplectic (CSE) Ensembles. Received: 20 December 1999 / Accepted: 24 March 2000     

Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel

Let stand for the integral operators with the sine kernels acting on L ²[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of are given by

A Generic C1 Expanding Map¶has a Singular S–R–B Measure

We show that for a generic C¹ expanding map T of the unit circle, there is a unique equilibrium state for − log T′ that is an S–R–B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of whether a generic C¹ expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure. Received: 8 December 2000 / Accepted: 27 March 2001