Existence of multiple positive solutions for N-laplacian in a bounded domain in R-N

Let Ohm be a bounded domain in IRN, N greater than or equal to 2, lambda > 0, q is an element of (0, N - 1) and alpha is an element of (1, N/N-1 In this article we show the existence of at least two positive solutions for the following quasilinear elliptic problem with an exponential type nonlinearity:

Observation of the Ωb- baryon and measurement of the properties of the Ξb- and Ωb- baryons

We report the observation of the bottom, doubly-strange baryon Omega^-_b through the decay chain Omega^-_b -> J/psi Omega^-, where J/psi -> mu^+ mu^-, Omega^- -> Lambda K^-, and Lambda -> p pi^-, using 4.2 fb^{-1} of data from p\bar p collisions at sqrt{s}=1.96 TeV, and recorded with the Collider Detector at Fermilab. A signal is observed whose probability of arising from a background fluctuation is 4.0 * 10^{-8}, or 5.5 Gaussian standard deviations. The Omega^-_b mass is measured to be 6054.4 +/- 6.8 (stat.) +/- 0.9 (syst.) MeV/c^2. The lifetime of the Omega^-_b baryon is measured to be 1.13^{+0.53}_{-0.40}(stat.) +/- 0.02(syst.)$ ps. In addition, for the \Xi^-_b baryon we measure a mass of 5790.9 +/- 2.6(stat.) +/- 0.8(syst.) MeV/c^2 and a lifetime of 1.56^{+0.27}_{-0.25}(stat.) +/-0.02(syst.) ps. Under the assumption that the \Xi_b^- and \Omega_b^- are produced with similar kinematic distributions to the \Lambda^0_b baryon, we find sigma(Xi_b^-) B(Xi_b^- -> J/psi Xi^-)}/ sigma(Lambda^0_b) B(Lambda^0_b -> J/psi Lambda)} = 0.167^{+0.037}_{-0.025}(stat.) +/-0.012(syst.) and sigma(Omega_b^-) B(Omega_b^- -> J/psi Omega^-)/ sigma(Lambda^0_b) B(Lambda^0_b -> J/psi Lambda)} = 0.045^{+0.017}_{-0.012}(stat.) +/- 0.004(syst.) for baryons produced with transverse momentum in the range of 6-20 GeV/c.

Molecular structure of Lantadene-B&C, triterpenoids ofantana camara, red variety: Lantadene-B, 22β-angeloyloxy-3-oxoolean-12-en-28-oic acid; Lantadene-C, 22 β-(S)-2′-methyl butanoyloxy-3-oxoolean-12-en-28-oic acid

(I)Lantadene-B: C35H52O5,M r =552.80, MonoclinicC2,a=25.65(1),b=6.819(9),c=18.75(1) Å,beta=100.61(9),V=3223(5) Å3,Z=4,D x =1.14 g cm–3 CuKagr (lambda=1.5418A),mgr=5.5 cm–1,F(000)=1208,R=0.118,wR=0.132 for 1527 observed reflections withF o ge2sgr(F o ). (II)Lantadene-C: C35H54O5·CH3OH,Mr=586.85, Monoclinic,P21,a=9.822(3),b=10.909(3),c=16.120(8)Å,beta=99.82(4),V=1702(1)Å3,Z=2,D x =1.145 g cm–3, MoKagr (lambda=0.7107Å), mgr=0.708 cm–1 F(000)=644,R=0.098, wR=0.094 for 1073 observed reflections. The rings A, B, C, D, and E aretrans, trans, trans, cis fused and are in chair, chair, sofa, half-chair, chair conformations, respectively, in both the structures. In the unit cell the molecules are stabilized by O-HctdotO hydrogen bonds in both the structures, however an additional C-HctdotO interaction is observed in the case of Lantadene-C.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

Crystal and molecular structure of Boc-Phe-Val-OMe; comparison of the peptide conformation with its dehydro analogue

The crystal structure of the peptide Boc-Phe-Val-OMe determined by X-ray diffraction methods is reported in this paper. The crystals grown from aqueous methanol are orthorhombic, space group P2(1)2(1)2(1), a = 11.843(2), b = 21.493(4), c = 26.676(4)Angstrom and V = 6790 Angstrom(3). Data were collected on a CAD4 diffractometer using MoK2 radiation (lambda = 0.7107 Angstrom) up to Bragg angle theta = 26 degrees. The structure was solved by direct methods and refined by a least-squares procedure to an R value of 6.8% for 3288 observed reflections. There are three crystallographically independent peptide molecules in the asymmetric unit. All the three molecules exhibit extended conformation. The sidechain of the Val(2) residue shows two different conformations. The conformation of the peptide Boc-Phe-Val-OMe is compared with the conformation of Ac-Delta Phe-Val-OH. It is observed that while Boc-Phe-Val-OMe exhibits an extended conformation, Ac-Delta Phe-Val-OH shows a folded conformation. The results of this comparison highlight the conformation constraining property of the Delta Phe residue. Interestingly, even though Boc-Phe-Val-OMe and Ac-Delta Phe-Val-OH are conformationally different, they exhibit similar packing patterns in the solid state. (C) Munksgaard 1995.

Structure of 9[alpha],19-dihydroxy-4-androstene-3,17-dione

C19H26O4, M(r) = 318.41, orthorhombic, P2(1)2(1)2(1), a = 10.591 (1), b = 11.133 (1), c = 13.657 (2) angstrom, V = 1610.29 angstrom 3, Z = 4, D(m) (flotation in KI) = 1.301, D(x) = 1.313 g cm-3, Mo K-alpha, lambda = 0.7107 angstrom, mu = 0.85 cm-1, F(000) = 688, T = 293 K, R = 0.057 for 1253 significant reflections. The A ring is disordered with atoms C(2) and O(19) occupying two possible sites. The molecules are held together by a hydrogen bond [O(9)...O(17) = 2.89 angstrom].

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Crystal structure of Boc-LAla-Delta Phe-Delta Phe-Delta Phe-Delta Phe-NHMe: a left-handed helical peptide

alpha,beta-Dehydrophenylalanine residues constrain the peptide backbone to beta-bend conformation. A pentapeptide containing four consecutive (Delta Phe) residues has been synthesised and crystallised. The peptide Boc-LAla-Delta Phe-Delta Phe-Delta Phe-Delta Phe-NHMe (C45H46N6O7, MW = 782.86) was crystallised from an acetonitrile/methanol mixture. The crystal belongs to the orthorhombic space group P2(1)2(1)2(1) With a = 19.455(6), b = 20.912(9), c = 11.455(4) Angstrom and Z = 4. The X-ray (MoKalpha, lambda = 0.7107 Angstrom) intensity data were collected using the Rigaku-AFC7 diffractrometer. The crystal structure was determined by direct methods and refined using the least-squares technique, R = 8.41% for 1827 reflections with \F-o\ > 4 sigma\F-o\. The molecule contains the largest stretch of consecutive dehydrophenylalanine residues whose crystal structure has been determined so far. The peptide adopts left-handed 3(10)-helical conformation despite the presence of LAla at the N-terminus. The mean phi, psi values, averaged across the last four residues are 56.8 degrees and 17.5 degrees, respectively. There are four 4-->1 intramolecular hydrogen bonds, characteristic of the 3(10)-helix. In the crystal each molecule interacts with four crystallographically symmetric molecules with one hydrogen bond each.

Limiting ionic conductance of symmetrical, rigid ions in aqueous solutions: Temperature dependence and solvent isotope effects

Limiting ionic conductance (Lambda(0)) of rigid symmetrical unipositive ions in aqueous solution shows a strong temperature dependence. For example, Lambda(0) more than doubles when the temperature is increased from 283 to 318 K. A marked variation also occurs when the solvent is changed from ordinary water (H2O) to heavy water (D2O). In addition, Lambda(0) shows a nonmonotonic size dependence with a skewed maximum near Cs+. Although these important results have been known for a long time, no satisfactory theoretical explanation exists for these results. In this article we present a simple molecular theory which provides a nearly quantitative explanation in terms of microscopic structure and dynamics of the solvent. A notable feature of this theory is that it does not invoke any nonquantifiable models involving solvent-berg or clatherates. We find the strong temperature dependence of Lambda(0) to arise from a rather large number of microscopic factors, each providing a small but nontrivial contribution, but all acting surprisingly in the same direction. This work, we believe, provides, for the first time, a satisfactory explanation of both the anomalous size and temperature dependencies of Lambda(0) of unipositive ions in molecular terms. The marked change in Lambda(0) as the solvent is changed from H2O to D2O is found to arise partly from a change in the dielectric relaxation and partly from a change in the effective interaction of the ion with the solvent.

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-1/2 fermions in three dimensions at a finite density (rho similar to k(F)(3)) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector lambda equivalent to (lambda(x),lambda(y),lambda(z)), whose magnitude lambda determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k(F)vertical bar a(s)vertical bar less than or similar to 1), the ground state in the absence of the gauge field (lambda = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (lambda = 0). For large gauge couplings (lambda/k(F) >> 1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)-we call these bosons ``rashbons.'' In the absence of interactions (a(s) = 0(-)), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling lambda(T). For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of lambda near lambda(T). In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

Unsteady MUD rotating flow over a rotating sphere near the equator

The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid lambda greater than or equal to lambda(0). The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.

Relation Between the Diffusivity, Viscosity, and Ionic Radius of LiCl in Water, Methanol, and Ethylene Glycol: A Molecular Dynamics Simulation

A molecular dynamics (MD) investigation of LiCl in water, methanol, and ethylene glycol (EG) at 298 K is reported. Several; structural and dynamical properties of the ions as well as the solvent such as self-diffusivity, radial distribution functions, void and neck distributions, velocity autocorrelation functions, and mean residence times of solvent in the first solvation shell have been computed. The results show that the reciprocal relationship between the self-diffusivity of the ions and the viscosity is valid in almost all solvents with the exception of water. From an analysis of radial distribution functions and coordination numbers the nature of hydrogen bonding within the solvent and its influence on the void and neck distribution becomes evident. It is seen that the solvent solvent interaction is important in EG while solute solvent interactions dominate in water and methanol. From Voronoi tessellation, it is seen that the voids and necks within methanol are larger as compared to those within water or EG. On the basis of the void and neck distributions obtained from MD simulations and literature experimental data of limiting ion conductivity for various ions of different sizes we show that there is a relation between the void and neck radius on e one hand and dependence of conductivity on the ionic radius on the other. It is shown that the presence of large diameter voids and necks in methanol is responsible for maximum in limiting ion conductivity (lambda(0)) of TMA(+), while in water in EG, the maximum is seen for Rb+. In the case of monovalent anions, maximum in lambda(0) as a function ionic radius is seen for Br- in water EG but for the larger ClO4- ion in methanol. The relation between the void and neck distribution and the variation in lambda(0) with ionic radius arises via the Levitation effect which is discussed. These studies show the importance of the solvent structure and the associated void structure.

PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

用于掺钛蓝宝石激光系统的高反膜的激光损伤

用电子束蒸发制备了用于掺钛蓝宝石啁啾脉冲放大激光系统的TiO2/HfO2/SiO2高反膜，其带宽约为176nm（R>98%, λ0=800nm），激光损伤阈值（LIDT）为2.4 J/cm2。通过TiO2和HfO2单层膜的透过光谱计算了这两种材料的折射率和消光系数。高反膜的性能主要由高折射率材料决定：折射率越高，反射带越宽；消光系数越小，薄膜吸收越小，LIDT越高。最后，讨论了高反膜的激光损伤机制。

Effect of incorporating nonlanthanoidal indium on optical properties of ferroelectric Bi4Ti3O12 thin films

Bi4Ti3O12 (BTO) and Bi3.25In0.75Ti3O12 (BTO:In) thin films were prepared on fused quartz and LaNiO3/Si (LNO) substrates by chemical solution deposition (CSD). Their microstructures, ferroelectric and optical properties were investigated by X-ray diffraction, scanning electron microscope, ferroelectric tester and UV-visible-NIR spectrophotometer, respectively. The optical band-gaps of the films were found to be 3.64 and 3.45 eV for the BTO and BTO:In films, respectively. Optical constants (refractive indexes and extinction coefficients) were determined from the optical transmittance spectra using the envelope method. Following the single electronic oscillator model, the single oscillator energy E-0, the dispersion energy E-d, the average interband oscillator wavelength lambda(0), the average oscillator strength S-0, the refractive index dispersion parameter (E-0/S-0), the chemical bonding quantity beta, and the long wavelength refractive index n(infinity) were obtained and analyzed. Both the refractive index and extinction coefficient of the BTO:In films are smaller than those of the BTO films. Furthermore, the refractive index dispersion parameter (E-0/S-0) increases and the chemical bonding quantity beta decreases in the BTO and BTO:In films compared with those of bulk. (C) 2007 Published by Elsevier B.V.