This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the L-centroid body, and their polars. Examples are the Blaschke-Santaló inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodie...

An orbit geometry where the central projection ray of the detector is not constrained to pass through the center-of-rotation for all projection angles can be useful to reduce uniformity artifacts and to avoid truncation when imaging non centrally located organs. We present a backprojection filtering algorithm for parallel geometry with an elliptical orbit acquisition and verify the algorithm by...

The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie group G in the following manner. We consider the adjoint action of G on its Lie algebra L(G). If T is a maximal torus of G and W its Weyl group, then it is well known that W-orbits in L(T) correspo...

Let A be a C*-algebra, L a closed left ideal of A and p the closed projection related to L. We show that for an xp in A∗∗p (∼= A∗∗/L∗∗) if pAxp ⊂ pAp and px∗xp ∈ pAp then xp ∈ Ap (∼= A/L). The proof goes by interpreting elements of A∗∗p (resp. Ap) as admissible (resp. continuous admissible) vector sections over the base space F (p) = {φ ∈ A∗ : φ ≥ 0, φ(p) = ‖φ‖ ≤ 1} in the notions developed by ...

Projection and intersection bodies define continuous and GL(n) contravariant valuations. They played a critical role in the solution of the Shephard problem for projections of convex bodies and its dual version for sections, the Busemann– Petty problem. We consider the question whether ΦK ⊆ ΦL implies V (K) ≤ V (L), where Φ is a homogeneous, continuous operator on convex or star bodies which is...

The MAX-LABEL-COVER(K,L) Problem: An instance to the MAX-LABEL-COVER(K,L) problem comprises of a bipartite graph G(U, V, E) with U and V being the two partitions, and a projection function πv→u : L → K on each edge (u, v). The objective is to obtain a labeling of the vertices (a function f : U → K, V → L) which satisfies maximum fraction of the edges. Edge (u, v) is satisfied by labeling f if a...

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, have been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to loca...

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...

Let be a nest and let be a subalgebra of L(H) containing all rank one operators of alg . We give several conditions under which any derivation δ from into L(H) must be inner. The conditions include (1) H− ≠H, (2) 0+ ≠ 0, (3) there is a nontrivial projection in which is in , and (4) δ is norm continuous. We also give some applications.