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

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

Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to extract strong coupling results directly from the spectral curve describing the large N master field. We show that the strong coupling limit of the gauge theory corresponds to the so-called tropical limit of the spectral curve. In this limit, the curve degenerates to a planar graph, and matrix model calculations reduce to elementary line integrals along the graph. As an important physical application of these tropical techniques, we study N=3 theories with fundamental matter, both in the quenched and in the unquenched regimes. We calculate the exact spectral curve in the Veneziano limit, and we evaluate the planar free energy and Wilson loop observables at strong coupling by using tropical geometry. The results are in agreement with the predictions of the AdS duals involving tri-Sasakian manifoldsComment: 32 pages, 7 figures. v2: small corrections, added an Appendix on the relation with the approach of 1011.5487. v3: further corrections and clarifications, final version to appear in JHE

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

Uncomputably noisy ergodic limits

V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n f. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given epsilon

Pre-M Phase-promoting Factor Associates with Annulate Lamellae in Xenopus Oocytes and Egg Extracts

We have used complementary biochemical and in vivo approaches to study the compartmentalization of M phase-promoting factor (MPF) in prophase Xenopus eggs and oocytes. We first examined the distribution of MPF (Cdc2/CyclinB2) and membranous organelles in high-speed extracts of Xenopus eggs made during mitotic prophase. These extracts were found to lack mitochondria, Golgi membranes, and most endoplasmic reticulum (ER) but to contain the bulk of the pre-MPF pool. This pre-MPF could be pelleted by further centrifugation along with components necessary to activate it. On activation, Cdc2/CyclinB2 moved into the soluble fraction. Electron microscopy and Western blot analysis showed that the pre-MPF pellet contained a specific ER subdomain comprising "annulate lamellae" (AL): stacked ER membranes highly enriched in nuclear pores. Colocalization of pre-MPF with AL was demonstrated by anti-CyclinB2 immunofluorescence in prophase oocytes, in which AL are positioned close to the vegetal surface. Green fluorescent protein-CyclinB2 expressed in oocytes also localized at AL. These data suggest that inactive MPF associates with nuclear envelope components just before activation. This association may explain why nuclei and centrosomes stimulate MPF activation and provide a mechanism for targeting of MPF to some of its key substrates

On the Use of Quantum Algebras in Rotation-Vibration Spectroscopy

A two-parameter deformation of the Lie algebra u$_2$ is used, in conjunction with the rotor system and the oscillator system, to generate a model for rotation-vibration spectroscopy of molecules and nuclei.Comment: 10 pages, Latex File, published in Modern Group Theoretical Methods in Physics, J. Bertrand et al. (eds.), Kluwer Academic Publishers (1995), 27-3

Sarcomere length-dependent Ca2+ activation in skinned rabbit psoas muscle fibers: coordinated regulation of thin filament cooperative activation and passive force

In skeletal muscle, active force production varies as a function of sarcomere length (SL). It has been considered that this SL dependence results simply from a change in the overlap length between the thick and thin filaments. The purpose of this study was to provide a systematic understanding of the SL-dependent increase in Ca2+ sensitivity in skeletal muscle, by investigating how thin filament “on–off” switching and passive force are involved in the regulation. Rabbit psoas muscles were skinned, and active force measurements were taken at various Ca2+ concentrations with single fibers, in the short (2.0 and 2.4 μm) and long (2.4 and 2.8 μm) SL ranges. Despite the same magnitude of SL elongation, the SL-dependent increase in Ca2+ sensitivity was more pronounced in the long SL range. MgADP (3 mM) increased the rate of rise of active force and attenuated SL-dependent Ca2+ activation in both SL ranges. Conversely, inorganic phosphate (Pi, 20 mM) decreased the rate of rise of active force and enhanced SL-dependent Ca2+ activation in both SL ranges. Our analyses revealed that, in the absence and presence of MgADP or Pi, the magnitude of SL-dependent Ca2+ activation was (1) inversely correlated with the rate of rise of active force, and (2) in proportion to passive force. These findings suggest that the SL dependence of active force in skeletal muscle is regulated via thin filament “on–off” switching and titin (connectin)-based interfilament lattice spacing modulation in a coordinated fashion, in addition to the regulation via the filament overlap

Optimizing of near infrared region reflectance of mix-waste tile aggregate as coating material for cool pavement with surface temperature measurement

The heat generated from dark color asphalt, which is low in surface reflectance mainly contributes to the environmental problem called as urban heat island. Low reflectance at high energy wavelength of sunlight, such as visible light and infrared region will cause the pavement to have high surface temperature, due to high energy absorption from solar radiation. This paper presents the optimization result of cool pavement coating material based on selected tiles aggregate to achieve high near infrared region (NIR) reflectance. Three types of waste tiles were used in this study which are Full Body Porcelain (FBP), Monoporosa (MP) and Porcelain Glaze (PG). All the tiles were prepared in the form of aggregates. A linear model was formed as a function of mix tiles fraction and the analysis of ANOVA suggest that the linear term used for this model is significant. Diagnostics of the model was evaluated using box-cox plot, normal plot of residuals and optimized to predict the mix of the different type of tiles to produce the highest surface NIR reflectance value. The first solution suggests that 100% of MP tile can provide NIR reflectance of 0.53, whereas the second solution suggest that the combination of 50% FBP and 50% of MP tile aggregates could give NIR reflectance value of about 0.51. Experimental work on measuring surface temperature found that optimized samples, M1 and M2 with high NIR reflectance could significantly reduce surface temperature of asphalt pavement at range of 4.1 °C–9.6 °C. In conclusion, the results of optimization is reliable and this method able to provide significant information on optimizing mix of tiles material as to achieve high NIR reflectance value for coating materials of cool-pavement