Surface and catalytic properties of doped tin oxide nanoparticles

Mixed oxides composed of Zn-Sn, Ti-Sn and V-Sn were prepared by a co-precipitation method and evaluated as catalysts for methanol oxidation in an ambient fixed-bed reactor. Surface analysis by X-ray photoelectron spectroscopy (XPS) revealed an electronic interaction between dopant and Sn atoms in the oxide structure and showed the formation of surface states associated with the dopants. Oxygen vacancies were present on the Zn-doped oxide, and the oxidation of methanol to carbon oxides was favored. The Ti-doped oxide exhibited a favorable selectivity to dimethyl ether, related to the oxygen anions near Ti centers. Vanadium dopants not only dramatically increased the catalytic activity but also promoted the partial oxidation of methanol to formaldehyde. Results demonstrate that the bridging dopant-O-Sn bond acts as active sites and influences product distribution.     

Fast algorithms for placing large entries along the diagonal of a sparse matrix

Solving a sparse system of linear equations Ax=b is one of the most fundamental operations inside any circuit simulator. The equations/rows in the matrix A are often rearranged/permuted before factorization and applying direct or iterative methods to obtain the solution. Permuting the rows of the matrix A so that the entries with large absolute values lie on the diagonal has several advantages like better numerical stability for direct methods (e.g., Gaussian elimination) and faster convergence for indirect methods (such as the Jacobi method). Duff (2009) [3] has formulated this as a weighted bipartite matching problem (the MC64 algorithm). In this paper we improve the performance of the MC64 algorithm with a new labeling technique which improves the asymptotic complexity of updating dual variables from O(|V|+|E|) to O(|V|), where |V| is the order of the matrix A and |E| is the number of non-zeros. Experimental results from using the new algorithm, when benchmarked with both industry benchmarks and UFL sparse matrix collection, are very promising. Our algorithm is more than 60 times faster (than Duff’s algorithm) for sparse matrices with at least a million non-zeros.     

Restricting the High-Temperature Growth of Nanocrystalline Tin Oxide

The sensitivity of tin oxide is dependent on various factors, one of which is the grain size. Three methods have been investigated with the aim of stabilising the grain size in the nanometer range, namely; (i) encapsulation within a silica matrix, (ii) coating the crystallites with hexamethyldisilazane and (iii) pinning the grain boundaries with a second metal oxide nanocrystal. The resulting materials have been characterised by X-ray powder diffraction (XRPD), Extended X-ray absorption fine structure (EXAFS) and conductivity measurements.     

Envelopes and Covers by Modules of Finite FP-Injective Dimensions

Let R be a ring, n a fixed non-negative integer and ? the class of all left R-modules of FP-injective dimensions at most n. It is proved that all left R-modules over a left coherent ring R have ?-preenvelopes and ?-covers. Left (right) ?-resolutions and the left derived functors of Hom are used to study the FP-injective dimensions of modules and rings.     

On Strongly Copure Flat Modules and Copure Flat Dimensions

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext ⁱ (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings.     

Gorenstein Flat Covers over GF-Closed Rings

We prove that all modules over a left GF-closed ring have Gorenstein flat covers.     

On Copure Projective Modules and Copure Projective Dimensions

Let R be any ring. A right R-module M is called n-copure projective if Ext¹(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext ⁱ (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension.     

Weak Global Dimension of Coherent Rings

In this article, we study the weak global dimension of coherent rings in terms of the left FP-injective resolutions of modules. Let R be a left coherent ring and ? ? the class of all FP-injective left R-modules. It is shown that wD(R) ≤ n (n ≥ 1) if and only if every nth ? ?-syzygy of a left R-module is FP-injective; and wD(R) ≤ n (n ≥ 2) if and only if every (n ? 2)th ? ?-syzygy in a minimal ? ?-resolution of a left R-module has an FP-injective cover with the unique mapping property. Some results for the weak global dimension of commutative coherent rings are also given.     

On Divisible and Torsionfree Modules

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext¹(G, M) = 0 (resp. Tor₁(N, G) = 0) for every divisible left R-module G. It is shown that every left R-module over a left P-coherent ring R has a divisible cover; a left R-module M is D-injective if and only if M is the kernel of a divisible precover A → B with A injective; a finitely presented right R-module L over a left P-coherent ring R is D-flat if and only if L is the cokernel of a torsionfree preenvelope K → F with F flat. We also study the divisible and torsionfree dimensions of modules and rings. As applications, some new characterizations of von Neumann regular rings and PP rings are given.     

The connes spectrums of certain finite non-abelian groups

In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated.