In 2001, E.D. Gluskin, A.E. Litvak and N. Tomczak-Jaegermann, using probabilistic methods inspired by some earlier work of Gluskin’s, provided an example of a convex body K ⊂ R such that no suitably large rank projection of K is symmetric. We provide an alternate proof of the existence of such a body, the key ingredient of which is a decoupling result due to S.J. Szarek and Tomczak-Jaegermann.

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P 2 g ∧ I ≡ A ∑ 1≤i<j≤3 P 2 g (i, j)A 3 acting on a 3-particle antisymmetric finite dimensional Hilbert space have been found. Here P 2 g denotes the projection operator onto a 2-particle antisymmetric function g, while A denotes the 3-particle antisymmetrizing operator. keywords: spectral decomposition of operators,...

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...

Lutwak introduced the notion of Lp-curvature image and proved an inequality for the volumes of convex body and its Lp-curvature image. In this paper, we first give an monotonic property of Lpcurvature image. Further, we establish two inequalities for the Lp-curvature image and its polar, respectively. Finally, an inequality for the volumes of Lp-projection body and Lp-curvature image is obtained.

Fig. 1. Whole-body maximum intensity projection (MIP) F-FDG PET image (A), performed for restaging in a patient who underwent surgical excision of a vulvar extramammary Paget’s disease three years before, showed multiple areas of increased radiopharmaceutical uptake in the abdomen and pelvis. Fused PET/CT images in axial projection (B–G) showed increased F-FDG uptake corresponding to a vaginal ...

The setting for this paper is n-dimensional Euclidean space Rn. Let n denote the set of convex bodies (compact, convex subsets with nonempty interiors) and n o denote the subset of n that consists of convex bodies with the origin in their interiors. Denote by voli(K | ξ) the i-dimensional volume of the orthogonal projection of K onto an idimensional subspace ξ ⊂Rn. Affine quermassintegrals are ...

Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density-matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density-matrix and the pairing-tensor. The variation of this projected-energy is shown to result in HFB equations with modified express...

Previous studies have suggested that the peptide galanin (GAL) in the hypothalamus is related to the preference of an animal for dietary fat. The present report investigates this relationship further to identify the specific GAL-synthesizing cell groups involved and to characterize their association to circulating glucose or hormones and their possible contribution to body fat deposition. Male ...