一类替换环的偏序$K_{0}$-群的无扭性

A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0（R）^＋, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].     

Refinable bivariate quartic -splines for multi-level data representation and surface display

In this paper, a second-order Hermite basis of the space of -quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a compactly supported super function in terms of the basis functions to facilitate the construction of quasi-interpolants to achieve the highest (i.e., fifth) order of approximation in an efficient way. Due to the small (minimum) support of the basis functions, the refinable mask immediately yields (up to) four-point matrix-valued coefficient stencils of a vector subdivision scheme for efficient display of -quartic spline surfaces. Finally, this vector subdivision approach is further modified to reduce the size of the coefficient stencils to two-point templates while maintaining the second-order Hermite interpolating property.

     

Data-sparse approximation to a class of operator-valued functions

In earlier papers we developed a method for the data-sparse approximation of the solution operators for elliptic, parabolic, and hyperbolic PDEs based on the Dunford-Cauchy representation to the operator-valued functions of interest combined with the hierarchical matrix approximation of the operator resolvents. In the present paper, we discuss how these techniques can be applied to approximate a hierarchy of the operator-valued functions generated by an elliptic operator .

     

Symplectic tori in homotopy 's

This short note presents a simple construction of nonisotopic symplectic tori representing the same primitive homology class in the symplectic -manifold , obtained by knot surgery on the rational elliptic surface with the left-handed trefoil knot . has the simplest homotopy type among simply-connected symplectic -manifolds known to exhibit such a property.

     

First countable, countably compact spaces and the continuum hypothesis

We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of .

     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

On the -torsion of elliptic curves and elliptic surfaces in characteristic

We study the extension generated by the -coordinates of the -torsion points of an elliptic curve over a function field of characteristic . If is a non-isotrivial elliptic surface in characteristic with a -torsion section, then for 11$"> our results imply restrictions on the genus, the gonality, and the -rank of the base curve , whereas for such a surface can be constructed over any base curve . We also describe explicitly all occurring in the cases where the surface is rational or or the base curve is rational, elliptic or hyperelliptic.

     

Spaces on which every pointwise convergent series of continuous functions converges pseudo-normally

A topological space is a -space provided that, for every sequence of continuous functions from to , if the series converges pointwise, then it converges pseudo-normally. We show that every regular Lindelöf -space has the Rothberger property. We also construct, under the continuum hypothesis, a -subset of of cardinality continuum.

     

On tensor products of -very ample line bundles

In this paper, we show that the tensor product of -very ample and -very ample line bundles on a complete algebraic variety is -very ample.

     

-additive families and the invariance of Borel classes

We prove that any -additive family of sets in an absolutely Souslin metric space has a -discrete refinement provided every partial selector set for is -discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps -sets to -sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves -sets, is shown as an application of the previous result.