A note on fermionic flows of the N=(1|1) supersymmetric Toda lattice hierarchy

We extend the Sato equations of the N=(1|1) supersymmetric Toda lattice hierarchy by two new infinite series of fermionic flows and demonstrate that the algebra of the flows of the extended hierarchy is the Borel subalgebra of the N=(2|2) loop superalgebra.Comment: 4 pages LaTe

Hot-pressed silicon nitride with various lanthanide oxides as sintering additives

The effects of addition of various lanthanide oxides and their mixture with Y2O3 on the sintering of Si3N4 were investigated. The addition of simple and mixed lanthanide oxides promoted the densification of Si3N4 in hot-pressing at 1800 C under 300-400kg/ centimeters squared for 60 min. The crystallization of yttrium and lanthanide-silicon oxynitrides which was observed inn the sintered body containing yttrium-lanthanide mixed oxides as additives led to the formation of a highly refractory Si3N4 ceramic having a bending strength of 82 and 84 kg/millimeters squared at room temperature and 1300 C respectively. In a Y2O3+La2O3 system, a higher molar ratio of La2O3 to Y2O3 gave a higher hardness and strength at high temperatures. It was found that 90 min was an optimum sintering time for the highest strength

The correspondence between Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches in random matrix theory: the Gaussian case

Two approaches (TW and ASvM) to derivation of integrable differential equations for random matrix probabilities are compared. Both methods are rewritten in such a form that simple and explicit relations between all TW dependent variables and $\tau$-functions of ASvM are found, for the example of finite size Gaussian matrices. Orthogonal function systems and Toda lattice are seen as the core structure of both approaches and their relationship.Comment: 20 pages, submitted to Journal of Mathematical Physic

Abelian Conformal Field theories and Determinant Bundles

The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichm\"uller space of an oriented pointed surface gives the vectorspace the modular functor associates to the oriented pointed surface. However the connection on the sheaf of vacua is only projectively flat, so we need to find a suitable line bundle with a connection, such that the tensor product of the two has a flat connection. We shall construct a line bundle with a connection on any family of pointed curves with formal coordinates. By computing the curvature of this line bundle, we conclude that we actually need a fractional power of this line bundle so as to obtain a flat connection after tensoring. In order to functorially extract this fractional power, we need to construct a preferred section of the line bundle. We shall construct the line bundle by the use of the so-called $bc$-ghost systems (Faddeev-Popov ghosts) first introduced in covariant quantization [FP]. We follow the ideas of [KNTY], but decribe it from the point of view of [TUY].Comment: A couple of typos correcte

Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories

The $u$-plane integrals of topologically twisted $N = 2$ supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an interpretation of these contact terms from the point of view of integrable hierarchies and their Whitham deformations. This is inspired by Mari\~no and Moore's remark that the blowup formula of the $u$-plane integral contains a piece that can be interpreted as a single-time tau function of an integrable hierarchy. This single-time tau function can be extended to a multi-time version without spoiling the modular invariance of the blowup formula. The multi-time tau function is comprised of a Gaussian factor $e^{Q(t_1,t_2,...)}$ and a theta function. The time variables $t_n$ play the role of physical coupling constants of 2-observables $I_n(B)$ carried by the exceptional divisor $B$. The coefficients $q_{mn}$ of the Gaussian part are identified to be the contact terms of these 2-observables. This identification is further examined in the language of Whitham equations. All relevant quantities are written in the form of derivatives of the prepotential.Comment: latex, 17 pages, no figures; final version for publicatio

Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1+1 dimensions

The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1+1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents in the long-wavelength limit. The RG analysis reveals that the RG flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed point with increasing the strength of the noise. This is supplemented by the numerical simulations of the KS equation with a stochastic noise, in which the scaling behavior of the KPZ equation can be easily observed even in the moderate system size and time.Comment: 12pages, 7figure

Detection of Minimum-Ionizing Particles and Nuclear Counter Effect with Pure BGO and BSO Crystals with Photodiode Read-out

Long BGO (Bismuth Germanate) and BSO (Bismuth Silicate) crystals coupled with silicon photodiodes have been used to detect minimum-ionizing particles(MIP). With a low noise amplifier customized for this purpose, the crystals can detect MIPs with an excellent signal-to-noise ratio. The NCE(Nuclear Counter Effect} is also clearly observed and measured. Effect of full and partial wrapping of a reflector around the crystal on light collection is also studied.Comment: 18 pages, including 5 figures; LaTeX and EP

Toda Lattice Hierarchy and Zamolodchikov's Conjecture

In this letter, we show that certain Fredholm determinant $D(\lambda;t)$, introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit of soliton solution for the Toda lattice hierarchy with 2-periodic reduction condition.Comment: 6 pages, LaTeX file, no figure