Unruh effect and holography

We study the Unruh effect on the dynamics of quarks and mesons in the context of AdS₅/CFT₄ correspondence. We adopt an AdS₅ metric with the boundary Rindler horizon extending into a bulk Rindler-like horizon, which yields the thermodynamics with Unruh temperature verified by computing the boundary stress tensor. We then embed in it a probe fundamental string and a D7 brane in such a way that they become the dual of an accelerated quark and a meson in Minkowski space, respectively. Using the standard procedure of holographic renormalization, we calculate the chiral condensate, and also the spectral functions for both the accelerated quark and meson. Especially, we extract the corresponding strength of random force of the Langevin dynamics and observe that it can characterize the phase transition of meson melting. This result raises an issue toward a formulation of complementarity principle for the Rindler horizon. We find most of the dynamical features are qualitatively similar to the ones in the thermal bath dual to the AdS black hole background, though they could be quite different quantitatively.     

Effect of Immobilization on Insoluble Collagen Concentration and Type I and Type III Collagen Isoforms of Rat Soleus Muscle

Immobilization is often associated with decreased muscle elasticity. This condition is known as muscle contracture; however, the mechanism remains unclear. The purpose of this study was to clarify the mechanism governing muscle contracture in rat soleus muscle by identifying changes in ankle joint mobility, insoluble collagen concentration and type I and type III collagen isoforms following 1- and 3-week immobilizations. Following a 1-week immobilization, range of motion (ROM) of dorsiflexion declined to 90% of the control value; additionally, ROM dropped to 67.5% of the control value after a 3-week immobilization. This finding suggested that ankle joint mobility decreases in conjunction with extended periods of immobilization. Insoluble collagen concentration in soleus muscles, which was unchanged after 1 week of immobilization, increased 3 weeks after immobilization. These results may be indicative of collagen fibers with strong intermolecular cross-links contained in the muscle was made increased relatively by 3 weeks of immobilization. Therefore, the change in intermolecular cross-links may be significant in terms of progress of muscle contracture with longer periods of immobilization. On the other hand, the ratio of type III to type I collagen isoforms in muscular tissue increased following a 1-week immobilization; moreover, this ratio remained constant after 3 weeks of immobilization. These data suggested that muscle immobilization may induce type III collagen isoform expression. The increase in the ratio of type III to type I collagen isoforms do not change in parallel with the increase in the limitation in ROM; however, this phenomenon probably is not closely related to the progress of muscle contracture. The change of collagen isoform in immobilized muscle may be involved in the mechanism governing the progression of muscle fibrosis.     

Positive Operator Majorization and <Emphasis Type="Italic">p</Emphasis>-hyponormality

In this note we examine the relationships between p-hyponormal operators and the operator inequality . This leads to a method for generating examples of p-hyponormal operators which are not q-hyponormal for any . Our methods are also shown to have implications for the class of Furuta type inequalities.     

Integer Decomposition Property of Free Sums of Convex Polytopes

Let \({\mathcal{P} \subset \mathbb{R}^{d}}\) and \({\mathcal{Q} \subset \mathbb{R}^{e}}\) be integral convex polytopes of dimension d and e which contain the origin of \({\mathbb{R}^{d}}\) and \({\mathbb{R}^{e}}\), respectively. We say that an integral convex polytope \({\mathcal{P}\subset \mathbb{R}^{d}}\) possesses the integer decomposition property if, for each \({n\geq1}\) and for each \({\gamma \in n\mathcal{P}\cap\mathbb{Z}^{d}}\), there exist \({\gamma^{(1)}, . . . , \gamma^{(n)}}\) belonging to \({\mathcal{P}\cap\mathbb{Z}^{d}}\) such that \({\gamma = \gamma^{(1)} +. . .+\gamma^{(n)}}\). In the present paper, under some assumptions, the necessary and sufficient condition for the free sum of \({\mathcal{P}}\) and \({\mathcal{Q}}\) to possess the integer decomposition property will be presented.     

Generalized Aluthge transformation on -hyponormal operators

We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.