Embedding polynomial matrices of one variable

A non square matrix with coefficients in K[z] can (if a condition on its minors is satisfied) be embedded into a square matrix with determinant 1. Finding theoretically and in an algorithmic way an embedding of small degree is solved by a construction with vector bundles on the projective line over K.     

Extensions of p-adic vector measures

For R being a separating algebra of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m: R → E a bounded finitely additive measure, it is shown that:

a If m is σ-additive and strongly additive, then m has a unique σ-additive extension m^σ on the σ-algebra R^σ generated by R.

b If m is strongly additive and τ-additive, then m has a unique τ-additive extension m^τ on the α-algebra R^bo of all τ_R-Borel sets, where τ_R is the topology having R as a basis.

Also, some other results concerning such measures are given.     

Parallel algorithms for variational inequalities over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings

This paper presents a framework of iterative algorithms for the variational inequality problem over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings in real Hilbert spaces. Strong convergence theorems are established under a certain contraction assumption with respect to the weighted maximum norm. The proposed framework produces as a simplest example the hybrid steepest descent method, which has been developed for solving the monotone variational inequality problem over the intersection of the fixed point sets of nonexpansive mappings. An application to a generalized power control problem and numerical examples are demonstrated.     

Spectral multipliers for Laplacians with drift on Damek–Ricci spaces

We prove a multiplier theorem for certain Laplacians with drift on Damek–Ricci spaces, which are a class of Lie groups of exponential growth. Our theorem generalizes previous results obtained by W. Hebisch, G. Mauceri and S. Meda on Lie groups of polynomial growth.     

广义Pell方程Ax^2-By^2=4的通解公式

主要运用 Lucas 数的奇偶性,讨论了当 A, B 是适合 A〉1,2-AB 且 AB 非平方数的正整数时,广义 Pell 方程的整数解（x, y）,即给出了方程 Ax^2 -By^2=4适合gcd（x, y）=1的整数解（x, y）的通解公式。     

Metric complements of overt closed sets

We show that the set of points of an overt closed subspace of a metric completion of a Bishop‐locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop‐compact. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Invariant generators for generalized distributions

The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.     

Chain homogeneous Souslin algebras

Assuming Jensen's principle ?⁺ we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todor?evi?.     

A Note on degree antiregular graphs

This note proves a conjecture of Merris that the minimal value of entries of the doubly stochastic matrix of the degree antiregular graph E_n of order n ≥ 3 is equal to (l/2(n + l)).