On exponential stability of nonlinear Volterra difference equations in phase spaces

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.     

Physical and chemical analysis of elemental sulfur formation during galena surface oxidation

The surface oxidation of sulfide minerals, such as galena (PbS), in aqueous solutions is of critical importance in a number of applications. A comprehensive understanding of the formation of oxidation species at the galena surface is still lacking. Much controversy over the nature of these oxidation products exists. A number of oxidation pathways have been proposed, and experimental evidence for the formation of elemental sulfur, metal polysulfides, and metal-deficient lead sulfides in acidic conditions has been shown and argued. This paper provides further insight into the electrochemical behavior of galena at pH 4.5. Utilizing a novel experimental system that combines in situ electrochemical control and AC mode atomic force microscopy (AFM) surface imaging, the formation and growth of nanoscopic domains on the galena surface are detected and examined at anodic potentials. AFM phase images indicate that these domains have different material properties to the underlying galena. Continued oxidation results in nanoscopic pitting and the formation of microscopic surface domains, which are confirmed to be elemental sulfur by Raman spectroscopy. Further clarification of the presence of elemental sulfur is provided by Cryo-XPS. Polysulfide and metal-deficient sulfide could not be detected within this system.     

Variational sets: Calculus and applications to nonsmooth vector optimization

We develop elements of calculus of variational sets for set-valued mappings, which were recently introduced in Khanh and Tuan (2008) [1] and [2] to replace generalized derivatives in establishing optimality conditions in nonsmooth optimization. Most of the usual calculus rules, from chain and sum rules to rules for unions, intersections, products and other operations on mappings, are established. Direct applications in stability and optimality conditions for various vector optimization problems are provided.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

Optical stark spectroscopy of the D1Π-X1Σ+(0,0) band of scandium monohydride

The laser induced fluorescence (LIF) spectra of the D(1)Π-X(1)Σ(+)(0,0) band of a rotationally cold (<20 K) molecular beam sample of scandium monohydride, ScH, and scandium monodeuteride, ScD, were recorded without and in the presence of a static electric field. The fine and magnetic hyperfine parameters for the X(1)Σ(+)(v=0) and D(1)Π(v=0) states of ScH and ScD were determined from the analysis of the field-free spectra. An unexpected isotopic dependence of the (45)Sc(I=7/2) magnetic hyperfine interaction was observed. The lowest J-levels of the D(1)Π( v=0) state of ScH are not perturbed, but the corresponding levels for ScD are strongly perturbed. The observed electric field induced splitting, broadenings, and shifts were analyzed to produce permanent electric dipole moments, μ(e), of 1.74 ± 0.15 and 2.177 ± 0.006 D for the X(1)Σ(+)(v=0) and D(1)Π(v=0) states, respectively. The trend in μ(e) for the 3d-metal monohydrides is discussed.     

A novel implicit finite difference method for the one-dimensional fractional percolation equation

In this paper, a novel implicit finite difference method for the one-dimensional fractional percolation equation is proposed. Consistency, stability and convergence of the method are established. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.     

On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling

Mathematical Programming -     

Any nilpotence degree occurs in mod-<Emphasis Type="Italic">p</Emphasis> cohomology rings of <Emphasis Type="Italic">p</Emphasis>-groups

Let p be an odd prime number and let n be an arbitrary positive integer. We prove that there exists a p-group whose mod-p cohomology ring has a nilpotent element H²() satisfying ⁿ0,^n+p–1=0. As a corollary, we exhibit a p-group whose mod-p cohomology ring contains an element of nilpotency degree n+1.Mathematical Subject Classification (2000): 20J06, 20D15, 55R40To Phuong and Nin