Contact CR-warped product submanifolds in generalized Sasakian Space Forms
In (4) B. Y. Chen studied warped product CR-submanifolds in Kaehler manifolds. Afterward, I. Hasegawa and I. Mihai (5) obtained a sharp inequality for the squared norm of the second fundamental form for contact CR-warped products in Sasakian space form. Recently Alegre, Blair and Carriago (1) introduced generalized Sasakian space form. The aim of present paper is to study contact CR-warped product submanifolds in generalized Sasakian space form.
On three dimensional generalized Sasakian-space-forms
The object of the present paper is to study Ricci semisymmetric, locally ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document}-symmetric and η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-parallel Ricci tensor in a three dimensional generalized Sasakian-space-form. The three dimensional quasi-Sasakian generalized Sasakian-space-forms have been studied. Besides these, Ricci solitons and gradient Ricci solitons have been studied. Finally, illustrative examples are given.
Investigation of scatter radiation of non-circular X-ray scan trajectories
Modern interventional X-ray devices are highly maneuverable and allow complex 3D imaging trajectories. New scan trajectories enable not only optimized object sampling but also introduce new approaches for dynamic 3D imaging. In this paper, we investigated the scatter radiation of two different scan trajectories. The scatter radiation was sampled by a rail setup with dosimeters at defined positions. After data analysis, contour maps were generated which show for four exemplary heights the scatter radiation distribution. The alternative scan trajectory showed smaller dose exposures at heights correlated to upper torso and head areas of a model physician. Keywords—Image acquisition, alternative scan trajectory, circular tomosynthesis, scatter radiation distribution