Toda brackets and cup-one squares for ring spectra

In this paper we prove the laws of Toda brackets on the homotopy groups of a connective ring spectrum and the laws of the cup-one square in the homotopy groups of a commutative connective ring spectrum.Comment: 22 page

Frustrated quantum-spin system on a triangle coupled with ege_g lattice vibrations - Correspondence to Longuet-Higgins et al.'s Jahn-Teller model -

We investigate the quantum three spin model $({\bf S_1},{\bf S_2},{\bf S_3})$ of spin$=1/2$ on a triangle, in which spins are coupled with lattice-vibrational modes through the exchange interaction depending on distances between spin sites. The present model corresponds to the dynamic Jahn-Teller system $E_g\otimes e_g$ proposed by Longuet-Higgins {\it et al.}, Proc.R.Soc.A.{\bf 244},1(1958). This correspondence is revealed by using the transformation to Nakamura-Bishop's bases proposed in Phys.Rev.Lett.{\bf 54},861(1985). Furthermore, we elucidate the relationship between the behavior of a chiral order parameter ${\hat \chi}={\bf S_1\cdot(S_2\times S_3)}$ and that of the electronic orbital angular momentum ${\hat \ell_z}$ in $E_g\otimes e_g$ vibronic model: The regular oscillatory behavior of the expectation value $$for vibronic structures with increasing energy can also be found in that of$$. The increase of the additional anharmonicity(chaoticity) is found to yield a rapidly decaying irregular oscillation of $$

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

Reductions of the Volterra and Toda chains

The Volterra and Toda chains equations are considered. A class of special reductions for these equations are derived.Comment: LaTeX, 6 page

Rotor eddy-current loss in permanent magnet brushless machines

This paper presents an analysis of the rotor eddy-current loss in modular and conventional topologies of permanent magnet brushless machine. The loss is evaluated both analytically and by time-stepped finite-element analysis, and it is shown that it can be significant in both machine topologies. It is also shown that the loss can be reduced significantly by segmenting the magnets

Integrable Discretizations of Chiral Models

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is achieved via a deformation of the ordinary differential calculus. In particular, the nonlinear Toda lattice results in this way from the linear (continuum) wave equation. The method is applied to several further examples. We also construct Lax pairs and B\"acklund transformations for the class of models considered in this work.Comment: 14 pages, Late

On Discrete Symmetries of the Multi-Boson KP Hierarchies

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce a concept of the square-root lattice leading to a family of new pseudo-differential operators with covariance under additional B\"{a}cklund transformations.Comment: 11 pgs, LaTeX, IFT-P/75/93, UICHEP-TH/93-1

Whisper-to-speech conversion using restricted Boltzmann machine arrays

Whispers are a natural vocal communication mechanism, in which vocal cords do not vibrate normally. Lack of glottal-induced pitch leads to low energy, and an inherent noise-like spectral distribution reduces intelligibility. Much research has been devoted to processing of whispers, including conversion of whispers to speech. Unfortunately, among several approaches, the best reconstructed speech to date still contains obviously artificial muffles and suffers from an unnatural prosody. To address these issues, the novel use of multiple restricted Boltzmann machines (RBMs) is reported as a statistical conversion model between whisper and speech spectral envelopes. Moreover, the accuracy of estimated pitch is improved using machine learning techniques for pitch estimation within only voiced (V) regions. Both objective and subjective evaluations show that this new method improves the quality of whisper-reconstructed speech compared with the state-of-the-art approaches

A Nonrelativistic Chiral Soliton in One Dimension

I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one direction. Relation to higher-dimensional Chern--Simons theory is indicated. The theory is quantized and results for the two-body quantum problem agree at weak coupling with those coming from a semiclassical quantization of the soliton.Comment: 11 pages, Latex2