This lectures were given by Florian Enescu at the mini-course on classical problems in commutative algebra held at University of Utah, June 2004. The references listed were used extensively in preparing these notes and the author makes no claim of originality. Moreover, he encourages the reader to consult these references for more details and many more results that had to be omitted due to time...

By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear m-point boundary value problem for the following second-order boundary value problem on time scales φ uΔ ∇ a t f t, u t 0, t ∈ 0, T , φ uΔ 0 ∑m−2 i 1 aiφ uΔ ξi , u T ∑m−2 i 1 biu ξi , where φ : R → R is an increasing homeomorphism and homomorphism and φ 0 0. Some new results are obta...

In this study, nearness near-ring, subnearness M-group and ideal are introduced. By considering operations on the set of all near left weak cosets, near-ring cosets homomorphism also presented. Moreover, some properties these structures investigated.

Suppose that M,N are von Neumann algebras acting on a Hilbert space and M is hyperfinite. Let ρ : M → N be an ultraweakly continuous ∗-homomorphism and let δ : M → N be a ∗-ρ-derivation such that δ(I) commutes with ρ(I). We prove that there is an element U in N with ‖U‖ ≤ ‖δ‖ such that δ(A) = Uρ(A)− ρ(A)U for all A ∈ M. c © Electronic Journal of Theoretical Physics. All rights reserved.

A linear deformation of a Meyer set M in R is the image of M under a group homomorphism of the group [M ] generated by M into R. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the orginal set M is pure point diffractive. AMS Cl...

Suppose that y is a continuous homomorphism of a locally compact group G into another such group, H, then ¡p induces in a natural way a homomorphism 9>* of the measure algebra of G, called M(G), into M(H). The action of <p* on the subspace M0(G) is studied in this paper. The space M0(G) is the nonabelian analogue to the space of measures on a locally compact abelian group whose Fourier-Stieltje...

1. Introduction Let B be a commutative Banach algebra, and let 6 be a homomorphism from B into a Banach algebra A. In this paper we are concerned with establishing conditions on A and B which ensure that 6 is continuous. If A is semisimple, it is well known that any such homomorphism must be continuous, and therefore we shall be interested in cases where A is not semisimple. Questions of this n...

Given a Young diagram λ and the set Hλ of partitions of {1, 2, . . . , |λ|} of shape λ, we analyze a particular S|λ|-module homomorphism QH λ → QHλ ′ to show that QHλ is a submodule of QHλ ′ whenever λ is a hook (n, 1, 1, . . . , 1) with m rows, n ≥ m, or any diagram with two rows.