Let (Wt)0≤t≤1 be an r-dimensional Wiener process defined on a probability space (Ω, , P) and let ( t)0≤t≤1 denote the natural filtration of (Wt) such that 0 contains all P-null sets of . Let ξ be an 1-measurable d-dimensional square-integrable random variable. Let f be an Rd-valued process defined on R+ ×Ω×Rd ×Rd×r with values in Rd such that for all (y,z) ∈ Rd ×Rd×r , the map (t,ω) → f (t,ω, y...

In the spirit of the Genetics of the Regular Figures, by L. Fejes Tóth [FT, Part 2], we prove the following theorem: If 2n points are selected in the n-dimensional Euclidean ball Bn so that the smallest distance between any two of them is as large as possible, then the points are the vertices of an inscribed regular cross-polytope. This generalizes a result of R.A. Rankin [R] for 2n points on t...

For the class of locally compact groups P that can be written as the semidirect product of a locally compact subgroup P0 and a oneparameter group R+ of automorphisms of P0, a new model of representations of the current groups P is constructed. The construction is applied to the maximal parabolic subgroups of all simple groups of rank 1. In the case of the groups G = SO(n, 1) and G = SU(n, 1), a...

Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆h is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynomial of degree ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...

extended abstract 1. introduction nazek al-malaike (1923-2007) is among the contemporary poets in whose works the themes of romanticism such as loneliness, grief, despair, traveling to a fantasy world, and love can be seen. she is an emotional poet with breadth of imagination who under the influence of romanticism, at times through digressing toward the past and remembering memories and at othe...

the value of clinical use of tumor markers cea and ca15-3 for early detection of recurrent breast cancer still is a controversial. this study was investigated relationship between tumor markers cea and ca15-3 and recurrence breast cancer. data regarding 147 women who had breast cancer were entered into the study. patients were reviewed for 120 months after treatment. maximum time for relapse wa...