Phytoecdysteroids of Plants of the Silene Genus. 2-Deoxyecdysterone-25-Acetate from Silene wallichiana

The new ecdysteroid 2-deoxyecdysterone-25-acetate was isolated from roots of Silene wallichiana Klotzsch.     

Electrocatalytic properties of Au(111)-Pd quasi-single-crystal film electrodes as probed by ATR-SEIRAS

Electrochemical and electrocatalytic properties of thin films Au(111-25 nm), which are quasi-single-crystal electrodes 25 nm thick made of gold with the (111) preferential orientation, and same electrodes modified with a monolayer (ML) of palladium are studied in 0.1 M solutions of HClO₄ and H₂SO₄ employing voltammetric techniques and surface enhanced infrared reflection absorption spectroscopy (ATR-SEIRAS). Spectroscopic experiments demonstrate strong adsorption of electrolyte species (H₂O, OH_ads, anions) on the Pd surface. The weak and reversible adsorption of CO on Au(111-25 nm) does not change the interfacial-water structure. Adsorption of CO on the Pd-modified film results in an irreversibly adsorbed CO adlayer stabilized by co-adsorbed isolated water species. Various electrooxidation mechanisms are discussed. Electrochemical and spectroscopic investigations on the adsorption and electrooxidation of HCOOH on bare and 1 ML Pd-Au(111-25 nm) electrodes reveal that electrooxidation proceeds in both cases via a direct or dehydrogenation pathway. This mechanism involves the formation of formate as intermediate, which is detected by in situ ATR-SEIRAS. The reactivity on Pd-modified surfaces is higher than on bare gold. The specifically adsorbed anions (sulfate/bisulfate) and the oxide formation on the substrate surface lower the reactivity for CO and HCOOH on both surfaces. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 11, pp. 1312–1329. Based on the report delivered at the 8th International Frumkin Symposium “Kinetics of the Electrode Processes,” October 18–22, 2005, Moscow. The text was submitted by the authors in English.     

匐枝马尾藻的化学成分研究

首次报道从中国北海匐枝马尾藻Sargassum polycystcum分离得到3个纯化合物 ，经过MS，IR，~1H NMR，~(13)C NMR（DEPT），HMQC和HMBC等波谱技术鉴定为： 豆甾-3β-羟基-5，23，25-三烯(1)，3-二下五烷氧基-1，2-丙二醇(2)，24ξ-甲 基胆甾-3β，5α，6β，25-四醇-25-乙酸酯(3)，其中化合物1为新化合物。     

A remark on a maximal function over a Cantor set of directions

LetM _e ⁰ be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL ². We consider a sequence of operators over finite sets of directions converging toM _e ⁰ . We improve the previous estimate for the (L ²,L ²)-norm of these particular operators. We also prove thatM _e ⁰ is bounded from some subsets ofL ² toL ². These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip. Partially supported by Spanish DGICYT grant no. PB90-0187.     

Smooth projective translation planes

A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or .Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

Reflected Brownian motion in a cone: Semimartingale property

Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1     

Shape-preserving approximation inL p

We prove a direct theorem for shape preservingL _p -approximation, 0p, in terms of the classical modulus of smoothnessw ₂(f, t _p ¹ ). This theorem may be regarded as an extension toL _p of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.Communicated by Ron DeVore.     

On extension theory inL 2-spaces

We present the first steps towards a general extension theory inL ²-spaces. By this theory it is possible to construct all perturbations of the Laplacian supported by a closed setN even if the classical capacity ofN equals zero.     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.