Exponent of a finite group with a fixed-point-free four-group of automorphisms

Let e be a positive integer and G a finite group acted on by the four-group V in such a manner that C _G (V) = 1. Suppose that V contains an element v such that the centralizer C _G (v) has exponent e. Then the exponent of G″, the second derived group of G, is bounded in terms of e only.     

Appearance of New Parametric Resonances in Time-Dependent Harmonic Oscillator

In this paper, we establish that in time-dependent harmonic oscillator under an oscillatory decreasing perturbation the parametric resonances, which do not exist in an ordinary harmonic oscillator under the same perturbation, may occur.     

Homogeneous nucleation of droplets from supersaturated vapor in a closed system

Kinetic equations describing homogeneous nucleation kinetics within standard model are solved numerically under the condition of a constant number of molecules in the considered system. It has consequences to decrease the supersaturation of the supersaturated vapor during the process of the formation of small droplets of a new phase. The decrease of supersaturation occurs in a short time and reaches some value which remains unchanged for a relatively long time (quasistationary regime), especially at lower initial supersaturations. This time interval decreases with increasing value of the initial supersaturation. In the quasistationary regime the nucleation rate reaches its stationary value. At higher initial supersaturation, the rate of formation of nuclei goes to some maximum value corresponding to the stationary nucleation rate and then decreases with time due to the decrease of supersaturation.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Chaotic synchronization of coupled electron-wave systems with backward waves

The chaotic synchronization of two electron-wave media with interacting backward waves and cubic phase nonlinearity is investigated in the paper. To detect the chaotic synchronization regime we use a new approach, the so-called time scale synchronization [Chaos 14, 603-610 (2004)]. This approach is based on the consideration of the infinite set of chaotic signals' phases introduced by means of continuous wavelet transform. The complex space-time dynamics of the active media and mechanisms of the time scale synchronization appearance are considered.     

Calix[4]tubes: An Approach to Functionalization

Adamantylcalix[4]arenes decorated with ester groups and calix[4]arene tetratosylates were used to prepare a series of calix[4]tubes bearing 3-methoxycarbonyl- and 3-methoxycarbonylmethyl-1-adamantyl units (up to eight) in good yield. These compounds were subjected to further chemical transformations giving a wide set of novel ester-, acid-, hydroxy-, amine-, and urea-functionalized calix[4]tubes. Introduction of urea groups into the calixtube core led not only to anion-targeted receptors, but also provided heteroditopic behavior of the hosts, which enriches the well-established potassium-uptake ability of calix[4]tubes.     

Large n Limit of Gaussian Random Matrices with External Source, Part I

We consider the random matrix ensemble with an external sourcedefined on n×n Hermitian matrices, where A is a diagonal matrix with only two eigenvalues ±a of equal multiplicity. For the case a>1, we establish the universal behavior of local eigenvalue correlations in the limit n, which is known from unitarily invariant random matrix models. Thus, local eigenvalue correlations are expressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum. We use a characterization of the associated multiple Hermite polynomials by a 3×3-matrix Riemann-Hilbert problem, and the Deift/Zhou steepest descent method to analyze the Riemann-Hilbert problem in the large n limit.Dedicated to Freeman Dyson on his eightieth birthdayThe first author was supported in part by NSF Grants DMS-9970625 and DMS-0354962.The second author was supported in part by projects G.0176.02 and G.0455.04 of FWO-Flanders, by K.U.Leuven research grant OT/04/24, and by INTAS Research Network NeCCA 03-51-6637.