Two dimensional periodic box-ball system and its fundamental cycle

We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of the discrete KP equation. We construct an algorithm to calculate the fundamental cycle, which is an important conserved quantity of the 2-dim. Box-Ball system with periodic boundary condition, by using the tropical curve theory.Comment: 16 pages, 5 figure

Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

Non-Breaking Undular Hydraulic Jump

The discusser performed a large number of experiments on undular hydraulic jumps (CHANSON 1993, 1995a). Most results were reported in CHANSON and MONTES (1995) and CHANSON (1995b, 1995c). The discusser wishes to stress several aspects of undular jump flows and he will show that the work of REINAUER and HAGER did not bring really new information

The effect of different baryons impurities

We demonstrate the different effect of different baryons impurities on the static properties of nuclei within the framework of the relativistic mean-field model. Systematic calculations show that $\Lambda_c^+$ and $\Lambda_b$ has the same attracting role as $\Lambda$ hyperon does in lighter hypernuclei. $\Xi^-$ and $\Xi_c^0$ hyperon has the attracting role only for the protons distribution, and has a repulsive role for the neutrons distribution. On the contrary, $\Xi^0$ and $\Xi^+_c$ hyperon attracts surrounding neutrons and reveals a repulsive force to the protons. We find that the different effect of different baryons impurities on the nuclear core is due to the different third component of their isospin.Comment: 9 page

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

The Coupled Modified Korteweg-de Vries Equations

Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1, ..., M-1$, is studied. We apply a new extended version of the inverse scattering method to this system. It is shown that this system has an infinite number of conservation laws and multi-soliton solutions. Further, the initial value problem of the model is solved.Comment: 26 pages, LaTex209 file, uses jpsj.st

Anyonic behavior of quantum group gases

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.Comment: LaTeX file, 19 pages, two figures ,uses epsf.st

Prostate Cancer Stem Cell-Targeted Efficacy of a New-Generation Taxoid, SBT-1214 and Novel Polyenolic Zinc-Binding Curcuminoid, CMC2.24

Background Prostate cancer is the second leading cause of cancer death among men. Multiple evidence suggests that a population of tumor-initiating, or cancer stem cells (CSCs) is responsible for cancer development and exceptional drug resistance, representing a highly important therapeutic target. The present study evaluated CSC-specific alterations induced by new-generation taxoid SBT-1214 and a novel polyenolic zinc-binding curcuminoid, CMC2.24, in prostate CSCs. Principal Findings The CD133high/CD44high phenotype was isolated from spontaneously immortalized patient-derived PPT2 cells and highly metastatic PC3MM2 cells. Weekly treatment of the NOD/SCID mice bearing PPT2- and PC3MM3-induced tumors with the SBT-1214 led to dramatic suppression of tumor growth. Four of six PPT2 and 3 of 6 PC3MM2 tumors have shown the absence of viable cells in residual tumors. In vitro, SBT-1214 (100nM-1µM; for 72 hr) induced about 60% cell death in CD133high/CD44+/high cells cultured on collagen I in stem cell medium (in contrast, the same doses of paclitaxel increased proliferation of these cells). The cytotoxic effects were increased when SBT-1214 was combined with the CMC2.24. A stem cell-specific PCR array assay revealed that this drug combination mediated massive inhibition of multiple constitutively up-regulated stem cell-related genes, including key pluripotency transcription factors. Importantly, this drug combination induced expression of p21 and p53, which were absent in CD133high/CD44high cells. Viable cells that survived this treatment regimen were no longer able to induce secondary spheroids, exhibited significant morphological abnormalities and died in 2-5 days. Conclusions We report here that the SBT-1214 alone, or in combination with CMC2.24, possesses significant activity against prostate CD133high/CD44+/high tumor-initiating cells. This drug combination efficiently inhibits expression of the majority of stem cell-related genes and pluripotency transcription factors. In addition, it induces a previously absent expression of p21 and p53 (“gene wake-up”), which can potentially reverse drug resistance by increasing sensitivity to anti-cancer drugs

Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.Comment: 27 pages, LaTeX2e (IOP style