Stochastic conservation laws: Weak-in-time formulation and strong entropy condition

This article is an attempt to complement some recent developments on conservation laws with stochastic forcing. In a pioneering development, Feng and Nualart [8] have developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of strong entropy condition. However, the authors' formulation of entropy inequalities are weak-in-space but strong-in-time. In the absence of a priori path continuity for the solutions, we take a critical outlook towards this formulation and offer an entropy formulation which is weak-in-time and weak-in-space.     

Obliquely propagating ion-acoustic shock waves in a degenerate quantum plasma

A theoretical investigation has been carried out on the propagation of non-linear ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system composed of inertial non-relativistic positively charged light and heavy ions, inertialess non-relativistically or ultra-relativistically degenerate electrons and positrons. The reductive perturbation method has been employed to derive the Burgers' equation. It has been observed that under consideration, our plasma model supports only positive potential shock structure. It is also found that the amplitude and steepness of the IASHWs have been significantly modified by the variation of ion kinematic viscosity, oblique angle, number density, and charge state of the plasma species. The results of our present investigation will be helpful for understanding the propagation of IASHWs in white dwarfs and neutron stars.     

1-Soliton solution of the Klein-Gordon-Schrodinger’s equation with power law nonlinearity

This paper obtains the 1-soliton solution of the Klein-Gordon-Schrödinger’s equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. Both 1 + 1, 1 + 2 and 1 + N dimensional cases are considered.     

Vector bundles with holomorphic connection over a projective manifold with tangent bundle of nonnegative degree

For a projective manifold whose tangent bundle is of nonnegative degree, a vector bundle on it with a holomorphic connection actually admits a compatible flat holomorphic connection, if the manifold satisfies certain conditions. The conditions in question are on the Harder-Narasimhan filtration of the tangent bundle, and on the Neron-Severi group.

     

Flat principal bundles over an abelian variety

We prove that a principal G-bundle E_G over a complex abelian variety A, where G is a complex reductive algebraic group, admits a flat holomorphic connection if and only if E_G is isomorphic to all the translations of it by the group structure of A.     

A Criterion for a Vector Bundle Over a Curve to Admit a Connection

Let X be a geometrically connected smooth projective curve defined over a perfect field k. Let E be a vector bundle over X. We prove that E admits a connection if every indecomposable component of E is of degree zero. If the characteristic of k is p, with p > 0, and the rank of each of the indecomposable components of E is not a multiple of p, then E admits a connection if and only if the degree of each indecomposable component of E is a multiple of p. (Received: August 2005)     

A Precious-Metal-Free Hybrid Electrolyzer for Alcohol Oxidation Coupled to CO2-to-Syngas Conversion

Electrolyzers combining CO₂ reduction (CO₂R) with organic substrate oxidation can produce fuel and chemical feedstocks with a relatively low energy requirement when compared to systems that source electrons from water oxidation. Here, we report an anodic hybrid assembly based on a (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) electrocatalyst modified with a silatrane-anchor ( STEMPO ), which is covalently immobilized on a mesoporous indium tin oxide (mesoITO) scaffold for efficient alcohol oxidation (AlcOx). This molecular anode was subsequently combined with a cathode consisting of a polymeric cobalt phthalocyanine on carbon nanotubes to construct a hybrid, precious-metal-free coupled AlcOx–CO₂R electrolyzer. After three-hour electrolysis, glycerol is selectively oxidized to glyceraldehyde with a turnover number (TON) of ≈1000 and Faradaic efficiency (FE) of 83 %. The cathode generated a stoichiometric amount of syngas with a CO:H₂ ratio of 1.25±0.25 and an overall cobalt-based TON of 894 with a FE of 82 %. This prototype device inspires the design and implementation of nonconventional strategies for coupling CO₂R to less energy demanding, and value-added, oxidative chemistry.     

β-Diketonates of Cyclopalladated Arylazonaphthalenes: Synthesis, Characterization and Redox Activity

The synthesis of monomeric mixed species of the type [PdLK] (L = cyclopalladated arylazonaphthalenes) have been achieved by splitting the halogeno-bridge in [Pd₂L₂Cl₂] by β-diketones (HK). The compounds have been characterized on the basis of spectral (IR, UV–VIS, FAB mass, ¹H and ¹³C{¹H}NMR) and elemental analysis data. Some of the [PdLK] cyclometallates occur as isomeric mixtures whose composition have been established by ¹H-NMR data. Electron transfer properties of the cyclopalladates in DMF have been thoroughly examined using cyclic voltammetry.     

Stochastic perturbation of solitons for Alfven waves in plasmas

The stochastic perturbation of solitons due to Alfven waves in plasmas, is studied in this paper, in addition to the deterministic perturbation terms. The Langevin equations are derived and it is proved that the soliton travels through the plasma with a fixed mean velocity.