MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

Molecular and Electronic Structure of the Peptide Subunit of Geobacter sulfurreducens Conductive Phi from First Principles

The respiration of metal oxides by the bacterium Geobacter sulfurreducens requires the assembly of a small peptide (the GS pilin) into conductive filaments termed pili. We gained insights into the contribution of the GS pilin to the pilus conductivity by developing a homology model and performing molecular dynamics simulations of the pilin peptide in vacuo and in solution. The results were consistent with a predominantly helical peptide containing the conserved a-helix region required for pilin assembly but carrying a short carboxy-terminal random-coiled segment rather than the large globular head of other bacterial pilins. The electronic structure of the pain was also explored from first principles and revealed a biphasic charge distribution along the pilin and a low electronic HOMO-LUMO gap, even in a wet environment. The low electronic band gap was the result of strong electrostatic fields generated by the alignment of the peptide bond dipoles in the pilin's alpha-helix and by charges from ions in solution and amino acids in the protein. The electronic structure also revealed some level of orbital delocalization in regions of the pilin containing aromatic amino acids and in spatial regions of high resonance where the HOMO and LUMO states are, which could provide an optimal environment for the hopping of electrons under thermal fluctuations. Hence, the structural and electronic features of the pilin revealed in these studies support the notion of a pilin peptide environment optimized for electron conduction.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Production of K*(892)(0) and phi(1020) in pp collisions at root s=7 TeV

The production of K*(892)(0) and phi(1020) in pp collisions at root s = 7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra d(2)N/dydp(T) at midrapidity vertical bar y vertical bar < 0.5 in the range 0 < p(T) < 6 GeV/c for K*(892)(0) and 0.4 < p(T) < 6 GeV/c for phi(1020) are reported and compared to model predictions. Using the yield of pions, kaons, and Omega baryons measured previously by ALICE at root s = 7 TeV, the ratios K*/K-, phi/K*, phi/ K-, phi/pi(-), and (Omega + <(Omega)over bar>)/phi are presented. The values of the K*/K-, phi/K* and phi/K- ratios are similar to those found at lower centre-of-mass energies. In contrast, the phi/pi(-) ratio, which has been observed to increase with energy, seems to saturate above 200 GeV. The (Omega + (Omega) over bar)/phi ratio in the p(T) range 1-5 GeV/ c is found to be in good agreement with the prediction of the HIJING/B (B) over bar v2.0model with a strong colour field.

Hard Thermal Loops in the n-Dimensional phi(3) Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional I center dot (3) theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.