Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

空气比热容比实验的非绝热问题

通过一系列的实验数据分析，发现空气比热容比实验中非绝热现象不可以忽略．     

Hydrodynamical limit for a drift-diffusion system modeling large-population dynamics

In this paper we study the stability of the following nonlinear drift-diffusion system modeling large population dynamics ∂_tρ+div(ρU−ε∇ρ)=0, divU=±ρ, with respect to the viscosity parameter ε. The sign in the second equation depends on the attractive or repulsive character of the field U. A proof of the compactness and convergence properties in the vanishing viscosity regime is given. The lack of compactness in the attractive case is caused by the blow-up of the solution which depends on the mass and on the space dimension. Our stability result is connected, depending of the character of the potentials, with models in semiconductor theory or in biological population.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Diphenylmethane transformations over boron trifluoride modified alumina and silica-alumina

Transformations of diphenylmethane were investigated in a flow system in the presence of alumina and silica-alumina modified with boron trifluoride at atmospheric pressure and elevated temperatures. Hydrogen transfer reaction was observed on addition of tetralin to the substrate stream. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

The adsorption of toluene on V-Sb oxides. Theoretical aspects

Toluene adsorption reactions on the (1 1 0) surface of VSbO₄ have been analyzed following the changes in the electronic structure of the hydrocarbon molecule and metal cation sites of the oxide using the Just Another Extended Hückel Molecular Orbital Program (JAEHMOP) code. The bonding character of these interactions has also been studied in the same theoretical framework. The calculations indicate that the exothermic hydrocarbon parallel interaction on Sb-V sites results in the weakening of one of the C-H bonds of the methyl fragment. This leads to a H-abstraction that involves the participation of a Sb-cation. Both methyl and phenyl fragments decrease their electronic population and so does the V-cation site. Most of these electrons are transferred to other V atoms in the bulk solid. As a result the LUMO of the toluene-oxide system fully populates. The analysis reveals that methyl-Sb bonding interactions mainly involve C_2px and H_1s orbitals with Sb_5s orbital, while non-bonding phenyl-V interactions involve C_2px orbitals with V_3dx²−y² orbital. This last interaction facilitates the desorption of the benzyl species after H-abstraction.     

Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.