A CHARACTERIZATION OF CONVEX FUNCTIONS AND ITS APPLICATION TO OPERATOR MONOTONE FUNCTIONS
We give a characterization of convex functions in terms of dier- ence among values of a function. As an application, we propose an estimation of operator monotone functions: If A > B 0 and f is operator monotone on (0,1), then f(A) f(B) f(kBk+ ) f(kBk) > 0, where = k(A B) 1 k 1 .
FURUTA INEQUALITY AND ITS RELATED TOPICS
This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Lowner-Heinz inequality to Furuta inequality, 2. Ando-Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order.
Immersive haptic interaction with media
New 3D video representations enable new modalities of interaction, such as haptic interaction, with 2D and 3D video for truly immersive media applications. Haptic interaction with video includes haptic structure and haptic motion for new immersive experiences. It is possible to compute haptic structure signals from 3D scene geometry or depth information. This paper introduces the concept of haptic motion, as well as new methods to compute haptic structure and motion signals for 2D video-plus-depth representation. The resulting haptic signals can be rendered using a haptic cursor attached to a 2D or 3D video display.