Homotopic properties of confluent maps in the proper category

We establish some properties of homotopical nature for confluent maps in the proper category. We analyze in this setting the characterization of tree-like continua by J.H. Case and R.E. Chamberlin as well as the theorem by T.B. McLean on the preservation of tree-likeness under confluent maps. We give counterexamples for the corresponding proper analogues and we extend results of several authors in classical continuum theory to non-compact spaces. Finally, we describe the behavior of these maps with respect to the fundamental pro-group, generalizing results of J. Grispolakis and other authors. Two questions of interest are still open (Open Question 15 and Conjecture 24).     

高速转发引擎设计分析与实现

高速转发引擎是核心路由器设计中的重要难点和关键技术,基于FPGA技术,分析了高速转发引擎设计中的挑战,并给出了一种基于并行流水线机制的10Gbps转发引擎设计方案.     

Best approximation theorems for nonexpansive and condensing mappings in hyperconvex spaces

In hyperconvex metric spaces we consider best approximation, invariant approximation and best proximity pair problems for multivalued mappings that are condensing or nonexpansive.     

Cancellation for two-dimensional unique factorization domains

We show that if A and B are finitely generated two-dimensional unique factorization domains over an algebraically closed field, then A[x]≅B[x] implies A≅B. The proof is an application of an algebraic technique involving the AK invariant which has previously been used to obtain other cancellation theorems.     

Normal toric ideals of low codimension

Every normal toric ideal of codimension two is minimally generated by a Gröbner basis with squarefree initial monomials. A polynomial time algorithm is presented for checking whether a toric ideal of fixed codimension is normal.     

The integral operator with logarithmic kernel has only one positive eigenvalue

The aim of this short note is to show that the integral operator with the kernel log(x + y) being indefinite has only one positive eigenvalue.     

Ring structures on groups of arithmetic functions

Using the theory of Witt vectors, we define ring structures on several well-known groups of arithmetic functions, which in another guise are formal Dirichlet series. The set of multiplicative arithmetic functions over a commutative ring R is shown to have a unique functorial ring structure for which the operation of addition is Dirichlet convolution and the operation of multiplication restricted to the completely multiplicative functions coincides with point-wise multiplication. The group of additive arithmetic functions over R also has a functorial ring structure. In analogy with the ghost homomorphism of Witt vectors, there is a functorial ring homomorphism from the ring of multiplicative functions to the ring of additive functions that is an isomorphism if R is a Q-algebra. The group of rational arithmetic functions, that is, the group generated by the completely multiplicative functions, forms a subring of the ring of multiplicative functions. The latter ring has the structure of a Bin(R)-algebra, where Bin(R) is the universal binomial ring equipped with a ring homomorphism to R. We use this algebra structure to study the order of a rational arithmetic function, as well the powersfα for α∈Bin(R) of a multiplicative arithmetic function f. For example, we prove new results about the powers of a given multiplicative arithmetic function that are rational. Finally, we apply our theory to the study of the zeta function of a scheme of finite type over Z.     

A class of weighted multivariate normal distributions and its properties

This article proposes a class of weighted multivariate normal distributions whose probability density function has the form of a product of a multivariate normal density and a weighting function. The class is obtained from marginal distributions of various doubly truncated multivariate normal distributions. The class strictly includes the multivariate normal and multivariate skew-normal. It is useful for selection modeling and inequality constrained normal mean vector analysis. We report on a study of some distributional properties and the Bayesian perspective of the class. A probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify the distribution and to implement computation, with output readily adapted for the required analysis. Necessary theories and illustrative examples are provided.     

Suzuki cross‐coupling reaction of aryl and heterocyclic bromides and aromatic polybromides on a Pd(II)‐hydrotalcite catalyst

The Suzuki cross‐coupling reaction of various bromine‐containing substrates and phenylboronic acid in toluene at 90 °C on a Pd(AcO)₂Py₂ catalyst supported on an Mg? Al hydrotalcite, using K₂CO₃ as the base, was studied. The conversion and selectivity results obtained for many of the substrates were excellent and similar to those provided by more active or even homogeneous catalysts. The reactions of aryl polybromides and phenylboronic acid gave the corresponding polyaromatic compounds in variable yields depending on the particular substrate. Arylation occurred in a consecutive manner by substitution of the different Br atoms. ICP‐MS measurements of the palladium content of the catalyst performed prior to and after the reaction revealed that part of the metal is incorporated into the bulk solution; therefore, the catalytic process is not purely heterogeneous. Copyright © 2008 John Wiley & Sons, Ltd.     

Geometric interpolation in symmetrically-normed ideals

The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in a symmetrically-normed ideal J_?⊆B(H) defined by a ? symmetric norming function (s.n.f.). The norms considered define Finsler metrics in a certain manifold of positive operators, and can be regarded as weighted ?-norms, the weight being a positive invertible operator.