Holonomic rank of A-hypergeometric differential-difference equations

We introduce A-hypergeometric differential-difference equation and prove that its holonomic rank is equal to the normalized volume of A with giving a set of convergent series solutions.Comment: 16 page

A Note on Stable States of Dipolar Systems at Low Temperatures

In the past several years, many important innovations in nanotechnology were made. Today it becomes possible to make nanosize magnetic particles, and development of high storage-density magnetic device is desired. In such a magnetic particle system, dipole interaction plays the main role. In this note, we consider stable states of dipolar systems at low temperature: Some systems show ``antiferromagnetic structure'', and others show magnetic domain structure, depending on lattice shapes.Comment: 5 pages including 5 eps figures, to appear in "Computer Simulation Studies in Condensed Matter Physics XVIII", Eds. D. P. Landau, S. P. Lewis, and H.-B. Sch\"{u}ttler (Springer Verlag, Heidelberg, Berlin

Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.Comment: 23 pages, 1 figur

Holonomic rank of A-hypergeometric differential-difference equations

金沢大学理工研究域　数物科学系We introduce A-hypergeometric differential-difference equation HA and prove that its holonomic rank is equal to the normalized volume of A with the Gröbner basis theory and giving a set of convergent series solutions. © 2008 Elsevier B.V. All rights reserved

Finite dipolar hexagonal columns on piled layers of triangular lattice

We have investigated, by the Monte Carlo simulation, spin systems which represent moments of arrayed magnetic nanoparticles interacting with each other only by the dipole-dipole interaction. In the present paper we aim the understanding of finite size effects on the magnetic nanoparticles arrayed in hexagonal columns cut out from the close-packing structures or from those with uniaxial compression. In columns with the genuine close-packing structures, we observe a single vortex state which is also observed previously in finite 2-dimensional systems. On the other hand in the system with the inter-layer distance set $1/\sqrt{2}$ times of the close-packing one, we found ground states which depend on the number of layers. The dependence is induced by a finite size effect and is related to a orientation transition in the corresponding bulk system.Comment: 3 pages, 2 figures. Proceedings of the International Conference on Magnetism 2006 (ICM2006) conference. To appear in a special volume of Journal of Magnetism and Magnetic Material

Opposing effects of estradiol and progesterone on the oxidative stress-induced production of chemokine and proinflammatory cytokines in murine peritoneal macrophages

In inflammatory and oxidative liver injury, virus proteins and reactive oxygen species are involved in the regulation of proinflammatory cytokine production by macrophages. This study investigated the effects of estradiol (E2) and progesterone on the unstimulated and oxidative stress-stimulated production of tumor necrosis factor (TNF)-α, interleukin (IL)-1β, macrophage inflammatory protein (MIP)-2, and macrophage chemotactic protein (MCP)-1 by peritoneal macrophages isolated from male and female mice. E2 inhibited the cytokine production of TNF-α, IL-1β, MIP-2, and MCP-1 by the unstimulated macrophages from males and females, which was then further stimulated by progesterone. The exposure to hydrogen peroxide in the macrophages from both sexes induced the production of cytokine. The hydrogen peroxide-stimulated cytokine production was suppressed by E2 and enhanced by progesterone. The sex hormone effects on the unstimulated and stimulated macrophages were blocked by their receptor antagonists and showed no significant difference between male and female subjects. These findings suggest that E2 may play a favorable role in the course of persistent liver injury, by inhibiting proinflammatory cytokine production, which, in addition, progesterone may counteract the favorable E2 effects through their receptors