Let G be a connected, simply connected nilpotent Lie group, identified with real algebraic subgroup of UT(n,R), and let Γ lattice in G, π:G→G∕Γ the quotient map. For semialgebraic X⊆G, more generally definable set an o-minimal structure on field, we consider topological closure π(X) compact nilmanifold G∕Γ. Our theorem describes cl(π(X)) terms finitely many families cosets subgroups G. The unde...

In this paper we use the standard terminology and notations of the Riesz spaces theory (see [2]). The Banach lattice of the continuous functions from a compact Hausdorff space into a Banach lattice E is denoted by C(K,E). If E = R then we write C(K) instead of C(K,E). 1 stands for the unit function in C(K). One version of the Banach–Stone theorem states that: Theorem 1. Let X and Y be compact H...

When A = C, H = N is normal and K = G, this is a classical problem which has been studied using a variety of methods (see [3, 8, 1, 12], for example), and its solution for irreducible representations is a crucial ingredient in the Mackey machine [17]. In [10], we considered the problem for C-dynamical systems with H = N normal and K = G, and found a condition on the induced representation IndGN...

Given a permutation π ∈ Sn, let Γ−(π) be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if π(i) > π(j) and there are no integers k, i < k < j, such that π(i) > π(k) > π(j). Let Γ(π) be the graph obtained by dropping the condition that π(i) > π(j), i.e. two vertices are adjacent if the rectangle [i, π(i)] × [j, π(j)] is empty. In the study of the strong order on per...

A syntactic machinery is developed for π-institutions based on the notion of a category of natural transformations on their sentence functors. Rules of inference, similar to the ones traditionally used in the sentential logic framework to define the best known sentential logics, are, then, introduced for π-institutions. A π-institution is said to be rule-based if its closure system is induced b...

in the crystal structure of the title polymeric compound, [c42h38n6o33sr5.2(h2o)]n, five independent metal atoms (sr1-sr5) have different coordination environments. the sr1 and sr5 atoms are nine coordinated and feature distorted tricapped trigonal-prismatic and capped square-antiprismatic geometries, respectively. the rest srii atoms have eight coordination numbers. these units are connected v...

years as a graduate assistant in the physics department. He did additional graduate work at the University of During 1902 to 1906 as a soil physicist at the USDA Bureau of Strasbourg and the University of Leipzig, where he studSoils (BOS), Edgar Buckingham originated the concepts of matric ied under chemist Wilhelm Ostwald, who won the Nobel potential, soil–water retention curves, specific wate...

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type A). One criterion uses totally nonnegative polynomials and the other uses Schur functions. The Bruhat order on Sn is often defined by comparing two permutations π = π(1) · · ·π(n) and σ = σ(1) · · ·σ(n) according to the following criterion: π ≤ σ if σ is obtainable from π by a sequence ...

687 Edgar Buckingham became involved with soil physics for 5 yr at the turn of the twentieth century. His general goal was to advance understanding of moisture movement and evaporation from soils to improve irrigation and crop management. Specifi cally, he was interested in elucidating why evaporation from near the soil surface in arid areas during summer months was self-limiting (Buckingham, 1...

By imposing three semantic constraints on the π-calculus equipped with delayed input, we obtain a variant of the π-calculus. We prove that Hennessy and Riely’s distributed π-calculus can be encoded into this new model, satisfying a full abstraction theorem, which means that one-dimensional mobility can be characterized by communication. We also discuss the difficulties of expressing two-dimensi...