We consider a polynomial ring S in n variables over a finite field k of characteristic p and an action of a finite group G on S by homogeneous linear substitutions. This is equivalent to taking the symmetric powers of an n-dimensional kG-module. We want to understand S as a kG-module in a manner as explicit as possible. The ideal solution would be to give a decomposition into indecomposable sum...

Suppose that λ = μ and μ is singular. We consider two aspects of the square property on subsets of λ. First, we have results which show e.g. that for א0 < κ = cf(κ) < μ, the equality cf([μ],⊆) = μ is a sufficient condition for the set of elements of λ whose cofinality is ≤ κ, to be split into the union of μ sets with squares. Secondly, we introduce a certain weak version of the square property ...

In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in [Hy]. We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see [Hy]. 1. Basic definitions and spectrum of stability...

We begin with a definition Definition 1. A one-parameter family T (t) for 0 ≤ t < ∞ of bounded linear operators on a Banach space X is a C 0 (or strongly continuous) Semigroup on X if 1. T (0) = I (the identity on X). 2. T (t + s) = T (t)T (s) (semigroup property) 3. lim t↓0 T (t)v = v for all v ∈ X (This the Strong Continuity at t = 0, i.e., continuous at t = 0 in the strong operator topology)...

let $m_r$ be a non-zero‎ ‎module and ${mathcal f}‎: ‎sigma[m_r]times sigma[m_r]‎ ‎rightarrow$ mod-$bbb{z}$ a bifunctor‎. ‎the‎ ‎$mathcal{f}$-reversibility of $m$ is defined by ${mathcal‎ ‎f}(x,y)=0 rightarrow {mathcal f}(y,x)=0$ for all non-zero $x,y$‎ ‎in $sigma[m_r]$‎. ‎hom (resp‎. ‎rej)-reversibility of $m$ is‎ ‎characterized in different ways‎. ‎among other things‎, ‎it is shown‎ ‎th...

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We present two different types of models where, for certain singular cardinals λ of uncountable cofinality, λ → (λ, ω + 1) 2 , although λ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, ℵω 1 → (ℵω 1 , ω + 1) 2 and consistently, 2 ℵ 0 → (2 ℵ 0 , ω + 1) 2. §0. INTRODUCTION. For regular uncountable κ, the Erdös-Dushni...

A variety of strong and electroweak interaction properties of the pion and the light scalar σ meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the σ meson mass is determined as Mσ = 385.4 MeV. We discuss in detail the gauging of the non-local meson-quark interaction and calculate the electr...

This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how...