Let A be a C*-algebra. Let z be the maximal atomic projection in A∗∗. By a theorem of Brown, x in A∗∗ has a continuous atomic part, i.e. zx = za for some a in A, whenever x is uniformly continuous on the set of pure states of A. Let L be a closed left ideal of A. Under some additional conditions, we shall show that for any x in A∗∗, x has a continuous atomic part modulo L∗∗, i.e. zx + L∗∗ = za ...

Let a, b, c and d be functions in L = L(T, dθ/2π), where T denotes the unit circle. Let P denote the set of all trigonometric polynomials. Suppose the singular integral operators A and B are defined by A = aP + bQ and B = cP + dQ on P, where P is an analytic projection and Q = I − P is a co-analytic projection. In this paper, we use the Helson–Szegő type set (HS)(r) to establish the condition o...

We consider the class of integral operators Qφ on L (R+) of the form (Qφf)(x) = ∫ ∞ 0 φ(max{x, y})f(y)dy. We discuss necessary and sufficient conditions on φ to insure that Qφ is bounded, compact, or in the Schatten–von Neumann class Sp, 1 < p < ∞. We also give necessary and sufficient conditions for Qφ to be a finite rank operator. However, there is a kind of cut-off at p = 1, and for membersh...

LACES DEFINITION. Let P be a finite set of properties. A mapping l that Ž . assigns to any subset S ; P another subset l S is called a lace map if, for all S, G, S , S ; P: 1 2 Ž . Ž . i l S ; S; Ž . Ž . Ž . Ž . ii l S ; G ; S « l G s l S ; Ž . Ž . Ž . Ž . Ž . iii l S s l S « l S j S s l S . 1 2 1 2 1 Ž . Ž . Ž . A set L for which l L s L is called a lace. By applying ii to G s l S , Ž Ž .. Ž ....

background in rhinoplasty, functional and cosmetic problems of the nose are corrected. these problems cause imbalance between the nasal subunit and face. throughout these deformities, there are 4 variants, so there is a need for careful preoperative evaluation either for treatment or prevention of the occurrence. according to functional and aesthetic effects of these variables in rhinoplasty, e...

Backprojection filtering algorithms are presented for three variable orbit fan-beam geometries. Expressions for the fanbeam projection and backprojection operators are given for a flat detector fan-beam geometry with fixed focal length, with variable focal length, and with fixed focal length and off-center focusing. Backprojection operators are derived for each geometry using transformation of ...

This paper deals with a new and systematic method of approximating exact nonlinear lters with nite dimensional lters. The method used here is based on the diierential geometric approach to statistics. The projection lter is derived in the case of exponential families. A characterization of the lters is given in terms of an assumed density principle. An a posteriori measure of the performance of...

Motif detecting in DNA sequences is one of the most popular tasks in computational biology, which is important for people to understand functions of genes. Recently, the motif detecting problem was abstracted as a planted (l,d)-motif problem and many instances of the problem have been proposed as challenges for motif detecting algorithms. In this work, we propose an improved immune genetic algo...

In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrands projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorf...

In this note we investigate the operators associated with frame sequences in a Hilbert space H, i.e., the synthesis operator T : l (N) → H , the analysis operator T ∗ : H → l (N) and the associated frame operator S = TT ∗ as operators defined on (or to) the whole space rather than on subspaces. Furthermore, the projection P onto the range of T , the projection Q onto the range of T ∗ and the Gr...