Regularizing effects of some lower order terms in non-uniformly nonlinear elliptic equations

We consider the Dirichlet problem for a class of strongly nonlinear elliptic equations with degenerate coercivity and data in divergence form. We show that some lower order terms have regularizing effects on solutions.     

Uniformities with the same Hausdorff hypertopology

Two uniformities U and V on a set X are said to be H-equivalent if their corresponding Hausdorff uniformities on the set of all non-empty subsets of X induce the same topology. The uniformity U is said to be H-singular if no distinct uniformity on X is H-equivalent to U. The self-explanatory concepts of H-coarse, H-minimal and H-maximal uniformities are defined similarly.It is well known that not all uniformities are H-singular. We show here that there is a property which obstructs H-singularity: Every H-minimal uniformity has a base of finite-dimensional uniform coverings. Besides, we provide an intrinsic characterization of H-minimal uniformities and show that they are H-coarse. This characterization of H-minimality becomes a criterion for H-singularity for all uniformities that are either complete, uniformly locally precompact or proximally fine (e.g., metrizable ones). Some relevant properties which insure H-singularity are introduced and investigated in some aspect.     

Long-Time Behavior for Second Order Lattice Dynamical Systems

Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l ²×l ². For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on ℝ ^m ,m≥1.      

Dirac’s Type Sufficient Conditions for Hamiltonicity and Pancyclicity

Let G = (V, E) be a any simple, undirected graph on n ≥ 3 vertices with the degree sequence . We consider the class of graphs satisfying the condition where , is a positive integer. It is known that is hamiltonian if θ ≤ δ. In this paper,

An uncertainty principle for the basic Bessel transform

The aim of this paper is to prove an uncertainty principle for the basic Bessel transform of order . In order to obtain a sharp uncertainty principle, we introduce and study a generalized q-Bessel-Dunkl transform which is based on the q-eigenfunctions of the q-Dunkl operator newly given by:

Set-valued mapping monotonicity as characterization of D.C functions

In this paper, using a result of Kung-Ching Chang [6], we give a characterization of locally Lipschitz functions which are differences of convex functions defined on a Banach space (not necessarily Asplund) in terms on maximal cyclically monotone set-valued mappings. A subdifferential integration of locally D.C functions. is also given.     

Ultrafast electron diffraction: excited state structures and chemistries of aromatic carbonyls

The photophysics and photochemistry of molecules with complex electronic structures, such as aromatic carbonyls, involve dark structures of radiationless processes. With ultrafast electron diffraction (UED) of isolated molecular beams it is possible to determine these transient structures, and in this contribution we examine the nature of structural dynamics in two systems, benzaldehyde and acetophenone. Both molecules are seen to undergo a bifurcation upon excitation (S(2)). Following femtosecond conversion to S(1), the bifurcation leads to the formation of molecular dissociation products, benzene and carbon monoxide for benzaldehyde, and benzoyl and methyl radicals for acetophenone, as well as intersystem crossing to the triplet state in both cases. The structure of the triplet state was determined to be "quinoidlike" of pipi(*) character with the excitation being localized in the phenyl ring. For the chemical channels, the product structures were also determined. The difference in photochemistry between the two species is discussed with respect to the change in large amplitude motion caused by the added methyl group in acetophenone. This discussion is also expanded to compare these results with the prototypical aliphatic carbonyl compounds, acetaldehyde and acetone. From these studies of structural dynamics, experimental and theoretical, we provide a landscape picture for, and the structures involved in, the radiationless pathways which determine the fate of molecules following excitation. For completeness, the UED methodology and the theoretical framework for structure determination are described in this full account of an earlier communication [J. S. Feenstra et al., J. Chem. Phys. 123, 221104 (2005)].     

Iridoid glucosides from the aerial parts of Globularia alypum L. (Globulariaceae)

From the hydromethanolic extract of the aerial parts of Globularia alypum grown in Morocco, a new chlorinated iridoid glucoside, globularioside has been isolated beside 5 known iridoid glycosides, globularin, globularicisin, globularidin, globularinin and globularimin. This is the first report of a chlorinated iridoid in G. alypum and in the Globulareaceae. Unlike all other known 7-chlorinated iridoid glucosides where the chlorine atom exhibits an alpha configuration, globularioside incorporate the chlorine atom as a 7beta substituent. The structures of the isolated compounds were established on the basis of ESI-MS, MS-MS, 1D and 2D NMR spectral analysis.     

Elastic light scattering from nanoparticles by monochromatic vacuum-ultraviolet radiation

Elastic light scattering is reported using monochromatic vacuum-ultraviolet radiation to study free, spherical silica nanoparticles prepared by approaches from colloidal chemistry, with diameters between 100 and 240 nm. The colloidal nanoparticles of defined size are transferred from an aqueous solution into the gas phase using a particle beam experiment. After focusing of the particle beam by an aerodynamic lens, the scattered light from monochromatic synchrotron radiation is measured. Angle-resolved elastically scattered light is detected, showing a strong forward-scattering component. Additional evidence for the detection of elastically scattered light comes from plotting the scattered light intensity as a function of the dimensionless parameter qR, where q is the magnitude of the scattering wave vector and R is the particle radius. This yields different power-law regimes that are assigned to scattering from the surface and the bulk of the nanoparticles. Furthermore, there is evidence for modulations in the scattered light intensity as a function of scattering angle, which is clearly distinguished from the forward-scattering component. The experimental results are compared to Mie scattering simulations for isolated particles, yielding general agreement with the experimental results. Deviations from Mie simulations are observed for samples consisting of significant amounts of aggregates. The present results indicate that the optical properties of free nanoparticles are sensitively probed by vacuum-ultraviolet radiation.