On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known integrable systems: one--into a pair of decoupled KdV equations, the other one--into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page

Modeling the Flux-Charge Relation of Memristor with Neural Network of Smooth Hinge Functions

The memristor was proposed to characterize the flux-charge relation. We propose the generalized flux-charge relation model of memristor with neural network of smooth hinge functions. There is effective identification algorithm for the neural network of smooth hinge functions. The representation capability of this model is theoretically guaranteed. Any functional flux-charge relation of a memristor can be approximated by the model. We also give application examples to show that the given model can approximate the flux-charge relation of existing piecewise linear memristor model, window function memristor model, and a physical memristor device

Symmetric Groups and Quotient Complexity of Boolean Operations

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively. Denote by o any binary boolean operation that is not a constant and not a function of one argument only. For m,n >= 2 with (m,n) not in {(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn if and only either (a) m is not equal to n or (b) m=n and the bases (ordered pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in {(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In proving these results we generalize the notion of uniform minimality to direct products of automata. We also establish a non-trivial connection between complexity of boolean operations and group theory

Backlund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations

Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation from the trivial zero solution of this system.Comment: LaTeX, 5 page

Flow prediction for propfan engine installation effects on transport aircraft at transonic speeds

An Euler-based method for aerodynamic analysis of turboprop transport aircraft at transonic speeds has been developed. In this method, inviscid Euler equations are solved over surface-fitted grids constructed about aircraft configurations. Propeller effects are simulated by specifying sources of momentum and energy on an actuator disc located in place of the propeller. A stripwise boundary layer procedure is included to account for the viscous effects. A preliminary version of an approach to embed the exhaust plume within the global Euler solution has also been developed for more accurate treatment of the exhaust flow. The resulting system of programs is capable of handling wing-body-nacelle-propeller configurations. The propeller disks may be tractors or pushers and may represent single or counterrotation propellers. Results from analyses of three test cases of interest (a wing alone, a wing-body-nacelle model, and a wing-nacelle-endplate model) are presented. A user's manual for executing the system of computer programs with formats of various input files, sample job decks, and sample input files is provided in appendices

Chiral symmetry restoration in excited hadrons, quantum fluctuations, and quasiclassics

In this paper, we discuss the transition to the semiclassical regime in excited hadrons, and consequently, the restoration of chiral symmetry for these states. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of the instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. It has been shown recently that the effective single-quark potential is of the Lorentz-scalar nature, for the low-lying hadrons, while, for the high-lying states, it becomes a pure Lorentz vector and hence the model exhibits the restoration of chiral symmetry. We demonstrate explicitly the quantum nature of chiral symmetry breaking, the absence of chiral symmetry breaking in the classical limit as well as the transition to the semiclassical regime for excited states, where the effect of chiral symmetry breaking becomes only a small correction to the classical contributions.Comment: RevTeX4, 20 pages, 4 Postscript figures, uses epsfig.sty, typos correcte

Simple model of self-organized biological evolution as completely integrable dissipative system

The Bak-Sneppen model of self-organized biological evolution of an infinite ecosystem of randomly interacting species is represented in terms of an infinite set of variables which can be considered as an analog to the set of integrals of motion of completely integrable system. Each of this variables remains to be constant but its influence on the evolution process is restricted in time and after definite moment its value is excluded from description of the system dynamics.Comment: LaTeX, 7 page

Frequency and Phase Synchronization in Neuromagnetic Cortical Responses to Flickering-Color Stimuli

In our earlier study dealing with the analysis of neuromagnetic responses (magnetoencephalograms - MEG) to flickering-color stimuli for a group of control human subjects (9 volunteers) and a patient with photosensitive epilepsy (a 12-year old girl), it was shown that Flicker-Noise Spectroscopy (FNS) was able to identify specific differences in the responses of each organism. The high specificity of individual MEG responses manifested itself in the values of FNS parameters for both chaotic and resonant components of the original signal. The present study applies the FNS cross-correlation function to the analysis of correlations between the MEG responses simultaneously measured at spatially separated points of the human cortex processing the red-blue flickering color stimulus. It is shown that the cross-correlations for control (healthy) subjects are characterized by frequency and phase synchronization at different points of the cortex, with the dynamics of neuromagnetic responses being determined by the low-frequency processes that correspond to normal physiological rhythms. But for the patient, the frequency and phase synchronization breaks down, which is associated with the suppression of cortical regulatory functions when the flickering-color stimulus is applied, and higher frequencies start playing the dominating role. This suggests that the disruption of correlations in the MEG responses is the indicator of pathological changes leading to photosensitive epilepsy, which can be used for developing a method of diagnosing the disease based on the analysis with the FNS cross-correlation function.Comment: 21 pages, 14 figures; submitted to "Laser Physics", 2010, 2