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

Solution of the generalized periodic discrete Toda equation II; Theta function solution

We construct the theta function solution to the initial value problem for the generalized periodic discrete Toda equation.Comment: 11 page

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

Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution

Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between B\"acklund transformations for discrete and ultradiscrete KdV equations.Comment: 11 page

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

Differential regulation of proopiomelanocortin (POMC) mRNA expression in hypothalamus and anterior pituitary following repeated cyanamide with ethanol administration

Background/Aim. We have investigated proopiomelanocortin (POMC) mRNA expression in the arcuate nucleus of the hypothalamus (ARC) and the anterior lobe of the pituitary (AL) following repeated cyanamide-ethanol reaction (CER). Methods. Adult male Sprague -Dawley rats (250 −290 gr) were housed in a temperature and humidity controlled environment with free access to food and water. Four experimental groups were used as follows: saline (as control), cyanamide alone, ethanol alone and ethanol with cyanamide. The animals received daily intraperitoneal injections (i.p.) of cyanamide (10mg/kg, 60 min before ethanol dosing) with or without ethanol (1g/kg) for 5 consecutive days, and were sacrificed 60 min after the last dosing of ethanol. The results were presented as the mean ± SEM for each group. All groups within each data set were compared by one-way ANOVA followed by Fisher PLSD test for multiple comparisons. A value of p<0.05 was considered significant. Results. The POMC mRNA levels in ARC were significantly decreased with cyanamide compared to the control and ethanol alone (p<0.05 and p<0.05 respectively), but increased in AL following repeated CER. Conclusion. We speculate that this differential regulation of POMC mRNA expression may be partially involved in the preventive effects on alcohol intake in response to CER

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

Similitude and scale effects of air entrainment in hydraulic jumps

A hydraulic jump is characterised by some strong turbulence and air entrainment in the roller. New measurements were performed in two channels in which similar experiments with identical inflow Froude numbers and relative channel widths were conducted with a geometric scaling ratio of 2:1. Void fraction distributions showed the presence of an advection/diffusion shear layer in which the data followed an analytical solution of the diffusion equation for air bubbles. The data indicated some scale effects in the small channel in terms of void fraction and bubble count rate. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding to lesser overall aeration of the jump roller. Dimensionless bubble count rates were significantly lower in the smaller channel especially in the mixing layer. The study is believed to be the first systematic investigation of scale effects affecting air entrainment in hydraulic jumps using an accurate air-water measurement technique

Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112--124) with inelastic scattering of 400-MeV $\alpha$ particles in the angular range $0^\circ$--$8.5^\circ$. We find that the experimentally-observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in $^{208}$Pb and $^{90}$Zr very well. From the GMR data, a value of $K_{\tau} = -550 \pm 100$ MeV is obtained for the asymmetry-term in the nuclear incompressibility.Comment: Submitted to Physical Review Letters. 10 pages; 4 figure