Curvature Properties of Lorentzian Manifolds with Large Isometry Groups

The curvature of Lorentzian manifolds (M ⁿ ,g), admitting a group of isometries of dimension at least 1/2n(n − 1) + 1, is completely described. Interesting behaviours are found, in particular as concerns local symmetry, local homogeneity and conformal flatness. Second and third authors supported by funds of MURST and the University of Salento.     

A Remark on the Residual Entropy of the Antiferromagnetic Ising Model in the Maximal Critical Field

By means of a transfer matrix method, we show that the residual entropy S of the two-dimensional square lattice antiferromagnetic Ising model in the maximal critical field satisfies (ln λ _n )/(n+1)≤S≤(ln λ _n )/n, where λ _n is the largest eigenvalue of the transfer matrix F _n on a strip of width n. Using these bounds, we numerically calculate the value of S, with precise estimates on the errors, namely, S=0.394198±0.020747.     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M. It is now focused on the quantum state λ _M , of a massless conformally coupled scalar field propagating in M. λ _M is “holographically” induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity of M. It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one, M͂, are globally hyperbolic and M admits future time infinity i ⁺. λ _M coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M, the state λ _M enjoys the following further remarkable properties:

Interaction of ethidium bromide and caffeine with DNA in aqueous solution

Two component (ethidium bromide–caffeine, ethidium bromide–DNA) and three component (ethidium bromide–caffeine–DNA) systems in aqueous saline (0.01 M NaCl) phosphate buffer solutions (pH 6.86, T = 298 K) are studied spectrophotometrically. The equilibrium constants for dimerization of caffeine, K _D  = 1.22 ± 2 M⁻¹, and for heteroassociation of ethidium bromide with caffeine, K = 71 ± 8 M⁻¹, in ethidium bromide–caffeine systems are determined. When the concentration of caffeine is increased, the dynamic equilibrium of the solution shifts toward formation of heterocomplexes which are, presumably, stabilized by dispersive and hydrophobic interactions of chromophores. The equilibrium parameters for ethidium bromide complex formation with DNA are calculated: the coupling constant for the dye with the biopolymer, K ₁ = (232 ± 16)⋅103 M⁻¹, and the number of base pairs of the biopolymer participating in bonding with the ligand, n ₁ = 3.6 ± 0.2, are calculated. Given these values, it is suggested that under these experimental conditions there are two types of bonding between ethidium bromide and the nucleic acid — intercalation and “external” bonds. A McGhee–von Hippel model for a three component system and the numerical values of the parameters for molecular complex formation in two component systems are used to calculate the bonding constant for caffeine with DNA, K ₂ = 127 ± 30 M⁻¹, and the number of base pairs of DNA which bond with caffeine, n ₂ = 1.7 ± 0.2. The concentrations of ethidium bromide and caffeine in the composition of two and three component complexes are calculated as functions of the nucleic acid content in the solution. An analysis of the concentration dependences shows that heteroassociation of ligands has a significant effect on the reduction in the concentration of ethidium bromide–DNA complexes in a three component system for low DNA concentrations, while at high DNA concentrations the bonding of caffeine with the biopolymer has this effect. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 143–151, January–February 2009.     

Photoluminescence of fluoroacrylate polymers impregnated with Eu(bta)<Subscript>3</Subscript> using supercritical CO<Subscript>2</Subscript>

Optical properties (photoluminescence and absorption) of Eu(bta)₃(B) _n (B = H₂O or 1,10-phenanthroline) polycrystalline powders and fluoroacrylate polymers (FAPs) impregnated with these compounds using supercritical CO₂ (SC CO₂) were investigated. It was established that impregnation of Eu(bta)₃phen into the FAPs using an SC CO₂ solution was difficult to achieve. The type of B (ancillary ligand) and the polymer matrix were shown to influence the temperature quenching of photoluminescence of Eu³⁺ ions in the range 25–100°C. A comparative analysis of quantum yields (λ_ex = 300 and 380 nm) and photoluminescence decay times (λ_ex = 337.1 nm) for Eu(bta)₃B _n and for Eu(bta)₃B _n -doped FAPs was performed.     

Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices

We find the limit of the variance and prove the Central Limit Theorem (CLT) for the matrix elements φ _jk (M), j,k=1,…,n of a regular function φ of the Gaussian matrix M (GOE and GUE) as its size n tends to infinity. We show that unlike the linear eigenvalue statistics Tr φ(M), a traditional object of random matrix theory, whose variance is bounded as n→∞ and the CLT is valid for Tr φ(M)−E{Tr φ(M)}, the variance of φ _jk (M) is O(1/n), and the CLT is valid for . This shows the role of eigenvectors in the forming of the asymptotic regime of various functions (statistics) of random matrices. Our proof is based on the use of the Fourier transform as a basic characteristic function, unlike the Stieltjes transform and moments, used in majority of works of the field. We also comment on the validity of analogous results for other random matrices.     

Energy efficiency of femtosecond laser ablation of polymer materials

We present the results of an experimental study of the ablation spectral energy thresholds for a number of polymer materials ((C₂F₄) _n , (CH₂O) _n ) exposed to femtosecond (τ_0.5 ~ 45–70 fs) laser pulses (λ ~ 266, 400, 800 nm) under atmospheric conditions and under vacuum (p ~ 10–2 Pa). We have analyzed the energy thresholds and the efficiency of optical, thermophysical, and gasdynamic processes in laser ablation vs. the laser pulse duration and photon energy.     

Non-Perturbative Heat Kernel Asymptotics on Homogeneous Abelian Bundles

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group G × U(1) over a Riemannian manifold M without boundary. The total connection on the vector bundle naturally splits into a G-connection and a U(1)-connection, which is assumed to have a parallel curvature F. We find a new local short time asymptotic expansion of the off-diagonal heat kernel U(t|x, x′) close to the diagonal of M × M assuming the curvature F to be of order t ⁻¹. The coefficients of this expansion are polynomial functions in the Riemann curvature tensor (and the curvature of the G-connection) and its derivatives with universal coefficients depending in a non-polynomial but analytic way on the curvature F, more precisely, on tF. These functions generate all terms quadratic and linear in the Riemann curvature and of arbitrary order in F in the usual heat kernel coefficients. In that sense, we effectively sum up the usual short time heat kernel asymptotic expansion to all orders of the curvature F. We compute the first three coefficients (both diagonal and off-diagonal) of this new asymptotic expansion.     

Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

Motivated by the study of multivortices in the Electroweak Theory of Glashow–Salam–Weinberg [33], we obtain a concentration-compactness principle for the following class of mean field equations: on M, where (M,g) is a compact 2-manifold without boundary, 0 < a≤K(x)≤b, x∈M and λ > 0. We take with α _i > 0, δ _{p i} the Dirac measure with pole at point p _i ∈M, i= 1,…,m and ψ∈L ^∞(M) satisfying the necessary integrability condition for the solvability of (1)_λ. We provide an accurate analysis for solution sequences of (1)_λ, which admit a “blow up” point at a pole p _i of the Dirac measure, in the same spirit of the work of Brezis–Merle [11] and Li–Shafrir [35]. As a consequence, we are able to extend the work of Struwe–Tarantello [49] and Ding–Jost–Li–Wang [21] and derive necessary and sufficient conditions for the existence of periodic N-vortices in the Electroweak Theory. Our result is sharp for N= 1, 2, 3, 4 and was motivated by the work of Spruck–Yang [46], who established an analogous sharp result for N= 1, 2. Received: 24 September 2001 / Accepted: 7 December 2001     

Modular conformal scaling group evidenced in lepton-quark mass

Lepton-quark mass may reflect a correspondence in spacetime structure described by a modular conformal scaling group. Stemming in part from a spacetime line element correspondenceds → (expλ _n)ds in which the eight quantitiesλ ₀,λ ₁, ...,λ ₇ constitute a closed set under a modular addition, the associated formula for lepton-quark mass (yielding values at the 1 GeV scale for the leptons and lighter quarks and at the physical pole for the top) is conjectured to bem=m _fQ²(exp −λ _n), wherem _f=10.245 TeV is the progenitor fermion mass,Q is the charge number of the lepton or quark, and the modular group parameterλ _n is indexed by a fermion principal quantum numbern that depends on three mutually independent projection operators.     

Curvature tensors unified field equations on SEXn

We study the curvature tensors and field equations in then-dimensional SE manifold SEX_n. We obtain several basic properties of the vectorsS andU and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEX_n and one of its particular solutions is constructed and displayed.     

Caustic Singularity in Ho?ava-Lifshitz Gravity

In this note we search for a family of solutions with Caustic singularity in non relativistic-renormalizable Hořava-Lifshitz (HL) theory without the general covariant. We show that in infrared (IR) limit and with a deviation from λ=1 we have no caustic singularity. Also in ultraviolet (UV) regime and for Ricci flat 3-dimensional (3d) spaces and codimension 1 and for λ≠1 the non linear terms should help bouncing this kind of most dangerous would be caustics. But if 3d curvature does not vanish, higher curvature terms do help caustics even in codimension one. Thus the arguments in (J. Cosmol. Astropart. Phys. 0909:005, 2009) are satisfied correctly.     

Non-steady-state photo-EMF in nanostructured GaN and polypyrrole within porous matrices

We report an experimental investigation of the non-steady-state photoelectromotive force in nanostructured GaN within porous glass and polypyrrole within chrysotile asbestos. The samples are illuminated by an oscillating interference pattern created by two coherent light beams and the alternating current is detected as a response of the material. Dependences of the signal amplitude versus temporal and spatial frequencies, light intensity, and temperature are studied for two wavelengths λ=442 and 532 nm. The conductivity of the GaN composite is measured: σ=(1.1–1.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=442 nm, I ₀=0.045–0.19 W/cm², T=293 K) and σ=(3.5–4.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=532 nm, I ₀=2.3 W/cm², T=249–388 K). The diffusion length of photocarriers in polypyrrole nanowires is also estimated: L _D=0.18 μm.     

Development of Flow Injection Spectrofluorimetric Detection System for the Determination of Homocysteine

In this work, a new simple and sensitive flow injection method is developed for the determination of homocysteine with spectrofluorimetric detection technique. This method is based on the oxidation of homocysteine with Tl (III) in acidic media, producing fluorescence reagent, TlCl₃^2- (λ_ex = 237 nm, λ_em = 419 nm). The effects of chemical parameters (including pH of the solutions, the buffer, Tl (III) and potassium chloride concentrations), instrumental parameters (such as flow rate of the solutions, reaction coil length, and sample loop volume) and temperature on the fluorescence intensity as an analytical signal are studied and optimized. In the optimum conditions of the above variables, homocysteine can be determined in the range 4.0 × 10^-7–40.0 × 10^-6 M with the LDR from 4.0 × 10^-7 to 25.0 × 10^-6 M. The detection limit (with S/N = 3) is 6.0 × 10^-8 M of homocysteine and precision for the injection of 5.0, 10.0 and 15.0 μM of homocysteine are 0.8%, 1.5% and 2.5% (n = 10) respectively. The rate of analysis is 90 samples per hour. The influence of potential interfering substances, including amino acids and carbohydrates is also studied. The proposed method has been successfully used for the determination of homocysteine in the real sample (blood serum and tap water) matrix.     

Spatiotemporal spectroscopic diagnostics of a pulse-periodic strontium vapor laser

Results of spectroscopic investigations into plasma of a pulse-periodic strontium vapor laser operating in the superradiance mode on the infrared transition at λ = 6.45 μm are presented. The method of determining the electron temperature and concentration as well as the gas temperature – T _e , n _e , and T _g – based on measuring the absolute intensities of some SrI and SrII and buffer gas (helium or neon) spectral lines is used. Time dependences of the line intensities during a current pulse (τ = 150 ns) and near afterglow (up to 3 μs) are obtained under conditions of non-equilibrium plasma ionization and recombination. The optical system collects radiation from the entire length of the plasma column by means of separating radial volume zones, includingthe central zone and the zone closer to the walls, with the monochromator slit. The results obtained allow us not only to calculate T _e , n _e , and T _g values, but also to trace the spatiotemporal plasma evolution.     

Mass Under the Ricci Flow

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M, g) be an ALE manifold of dimension n = 3. If m(g) ≠ 0, then the Ricci flow starting at g can not have Euclidean space as its (uniform) limit. Partially supported by NSF and NSFC. The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20060003002.     

Constraints on Vector Unparticle Physics from Cosmic Censorship

Vector unparticle couplings to standard model fields produce repulsive corrections to gravity. From a general relativistic perspective, this leads to an effective Reissner-Nordstr?m-like metric whose “charge” is a function of the unparticle coupling constant λ, and therefore can admit naked singularities. Requiring the system to respect cosmic censorship provides a new method of constraining the value of λ. These limits are extremely loose for stellar-mass black holes, but commensurate with existing bounds for primordial black holes. In the case of theoretical low-mass black holes, the bounds on λ are much stricter than those derived from astrophysical and accelerator phenomenology. Additional constraints on the lower limit of λ are used to estimate the mass of the smallest possible black hole M_BH^minM_{\mathrm {BH}}^{\mathrm{min}} that can be formed in the unparticle framework, as a function of the unparticle parameters (L_U,M_U,d_U,d_BZ\Lambda_{{\mathcal{U}}},M_{{\mathcal{U}}},{d_{\mathcal{U}}},{d_{\mathit{BZ}}}).     

Steady State and Time-Resolved Fluorescence Studies of a Hemagglutinin from Moringa oleifera

The saccharide binding and conformational characterization of a hemagglutinin, a low molecular weight protein from the seeds of Moringa oleifera was studied using steady state and time resolved fluorescence. The lectin binds sugars LacNAc (K _a = 1380 M⁻¹) and fructose (K _a = 975 M⁻¹), as determined by the fluorescence spectroscopy. It has a single tryptophan per monomer which is exposed on the surface and is in a strong electropositive environment as revealed by quenching with iodide. Quenching of the fluorescence by acrylamide involved both static (K _s = 0.216 M⁻¹) and collisional (K _sv = 8.19 M⁻¹) components. The native protein showed two different lifetimes, τ ₁ (1.6 ns) and τ ₂ (4.36 ns) which decrease and get converted into a single one, (2.21 ns) after quenching with 0.15 M acrylamide. The bimolecular quenching constant, k _q was 7.55 × 10¹¹ M⁻¹ s⁻¹. ANS binding studies showed that the native protein has exposed hydrophobic patches which get further exposed at extreme acidic or alkaline pH. However, they get buried in the interior of the protein in presence of 1 M GdnHCl or urea.