in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

We examine a class of binary strings arising from considerations about stream cipher encryption: to what degree can one guarantee that the number of pairs of entries distance k apart that disagree is equal to the number that agree, for all small k? In a certain sense, a keystream with such a property achieves a degree of unpredictability. The problem is also restated combinatorially in terms of...

The struggle of students to solve algebraic equations has been identified as a major challenge in mathematics education. This study investigated the effectiveness Hands-On Equations? early algebra balance model improving equation-solving skills upper elementary and middle school students. Fourth-grade (n = 123) eighth-grade 105) from United States participated this study. A pretest-to-posttest ...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.

We show that if Part(κ, λ) holds for every λ ≥ κ, then κ is strongly compact. Let κ be a regular infinite cardinal, and let λ ≥ κ be a cardinal. Pκ(λ) denotes the set of all subsets of λ of size less than κ. Part(κ, λ) means that for every F : Pκ(λ) × Pκ(λ) → 2, there is a cofinal subset A of (Pκ(λ),⊆) such that F is constant on the set {(a, b) ∈ A × A : a ⊂ b}. This definition is due to Jech [...

ON GRAPHS SATISFYING A STRONG ADJACENCY PROPERTY Y. Ananchuen and L. Caccetta School of Mathematics and Statistics Curtin University of Technology GPO Box U1987 Perth 6001 Western Australia. Dedicated to the memory of Alan Rahilly, 1947 1992 Let m and n be nonnegative integers and k be a positive integer. A graph G is said to have property P*(m,n,k) if for any set of m + n distinct vertices of ...

Stanley [4] showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with the strong Lefschetz property has again the strong Lefschetz property. Introduction Let K be a field, A be a standard graded Artinian K-algebra and a ∈ A a homogeneous form of degree k. The element a is called a ...

The so-called STIT tessellations form the class of homogeneous (spatially stationary) tessellations of R which are stable under the nesting/iteration operation. In this paper, we establish the strong mixing property for these tessellations and give the optimal form of the rate of decay for the quantity |P(A ∩ Y = ∅, ThB ∩ Y = ∅) − P(A ∩ Y = ∅)P(B ∩ Y = ∅)| when A and B are two compact sets, h a...

Eisenstein series play a critical role in number theory. For two hundred years they have been an essential tool in the analysis of automorphic L-functions and in studying properties of quadratic forms in one and several variables. The construction is clear and straightforward, while their properties are sometimes very surprising. The arithmetic of their Fourier coefficients, and their analytic ...