Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

<正>This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional(2D) systems.Firstly,the fuzzy modeling method for the usual one-dimensional(1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi-Sugeno(TS) fuzzy model,which is convenient for implementing the stability analysis.Secondly,a new kind of fuzzy Lyapunov function,which is a homogeneous polynomially parameter dependent on fuzzy membership functions,is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system.In the process of stability analysis,the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques.Moreover,the obtained result is formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,a numerical example is also given to demonstrate the effectiveness of the proposed approach.     

From Baecklund Transformation to a Linear System of Sine-Gordon Theory in Superspace

A systematic approach is presented to find a linear system associated with the sine-Gordon equation from a given set of super Riccati systems. The Riccati system is shown to be related to the super B(ae)cklund transformation and the linear eigenvalue problem.     

Explicit Solutions for a （2＋1）-Dimensional Toda Lattice with Two Discrete Variables

An integrable （2＋1）-dimensional Toda lattice with two discrete variables is investigated again, which is produced from a compatible condition of the Lax triad. The Darboux transformation for its spectral problems is found. As an application, explicit solutions of the （2＋1）-dimensional Toda equation with two discrete variables are obtained.     

Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates

We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.     

Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints

This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.     

Pion charge form factor and constraints from space-time translations

The role of Poincaré covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor.It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current,which is most often referred to.The only exception is the front-form approach with q + = 0.How accounting for the related constraints,as well as restoring the equivalence of different RQM approaches in estimating form factors,is discussed.Some extensions of this work and,in particular,the relationship with a dispersion-relation approach,are presented.Conclusions relative to the underlying dynamics are given.     

A Modified Glass Formation Criterion for Various Glass Forming Liquids with Higher Reliability

A modified indicator of the glass forming ability （GFA） from the previous 7 = Tx/（Tl ＋ Tg） for various glass forming liquids is proposed based on a conceptual approach which combines more acceptable physical metallurgy views in terms of the time-temperature-transformation diagrams. It is found that the glass forming ability for glass forming liquids is closely associated mainly with two factors, i.e. （2Tx - Tg） and Tl （wherein Tx is the onset crystallization temperature, Tg the glass transition temperature, and Tl the liquidus temperature）, and could be predicated by a unified parameter γm defined as （2Tx - Tg）/Tl. This approach is confirmed and validated by experimental data in various glass forming systems including oxide glasses, cryoprotectants and metallic glasses, which all shows a higher reliability when their glass forming ability is predicted by the modified parameter.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.     

Wear analysis of revolute joints with clearance in multibody systems

In this work, the prediction of wear for revolute joint with clearance in multibody systems is investigated using a computational methodology. The contact model in clearance joint is established using a new hybrid nonlinear contact force model and the friction effect is considered by using a modified Coulomb friction model. The dynamics model of multibody system with clearance is established using dynamic segmentation modeling method and the computational process for wear analysis of clearance joint in multibody systems is presented. The main computational process for wear analysis of clearance joint includes two steps, which are dynamics analysis and wear analysis. The dynamics simulation of multibody system with revolute clearance joint is carried out and the contact forces are drawn and used to calculate the wear amount of revolute clearance joint based on the Archard’s wear model. Finally, a four-bar multibody mechanical system with revolute clearance joint is used as numerical example application to perform the simulation and show the dynamics responses and wear characteristics of multibody systems with revolute clearance joint. The main results of this work indicate that the contact between the joint elements is wider and more frequent in some specific regions and the wear phenomenon is not regular around the joint surface, which causes the clearance size increase non-regularly after clearance joint wear. This work presents an effective method to predict wear of revolute joint with clearance in multibody systems.     

Pion charge form factor and constraints from space-time translations

The role of Poincaré covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor.It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current,which is most often referred to.The only exception is the front-form approach with q ^＋ = 0.How accounting for the related constraints,as well as restoring the equivalence of different RQM approaches in estimating form factors,is discussed.Some extensions of this work and,in particular,the relationship with a dispersion-relation approach,are presented.Conclusions relative to the underlying dynamics are given.     

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.     

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su（1,1）. The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp（1,2） or B（0,1） in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

A Super mKdV Equation: Bosonization,Painlevé Property and Exact Solutions

The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV(BSmKdV)equation admits Painlevé property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems.     

Exponential synchronization of stochastic impulsive perturbed chaotic Lur''e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Q-Deformed Bosons at Quasi-classical Limit of SO（3）

When a boson interacts with another to form a composite system with SO（3） dynamic symmetry, it is shown that there exists the q-deformed 5osonic excitation satisfying the q-deformed Heisenberg commutation relation in the quasi-classical limit that the angular momentum j for SO（3） is large, but not infinite. In second quantization this quasi-excitation is associated with the boson realization of SO（3） Lie algebra. Physically, the phenomena of q-deformed excitation can happen in many models of quantum dynamics, such as super emission from a system of many identical two-level atoms, the spin wave in Heisenberg chain, the high spin precession and the coherent output of Bose-Einstein atoms in a trap. Especially, in these models, the deformation parameter q is well defined intrinsically by a conservative quantity, such as the total atomic number and the angular momentum.     

Acoustic performance prediction of Helmholtz resonator with conical neck

There is no accurate analytical approach for the acoustic performance prediction of Helmholtz resonator with conical neck,which has broad band acoustic attenuation performance in the low frequency range.To predict the acoustic performance of the resonator accurately,a general theory model based on the one-dimensional analysis approach with acoustic length corrections is developed.The segmentation method is used to calculate the acoustic parameters for sound propagation in conical tubes.And then,an approximate formula is deduced to give accurate correction lengths for conical tubes with difierent geometries.The deviations of the resonance frequency between the transmission loss results obtained by the general theory with acoustic lengths correction and the results from the finite element method and experiments are less than 2 Hz,which is much better than the results from one-dimensional approach without corrections.The results show that the method of acoustic length correction for the conical neck greatly improved the accuracy of the one-dimensional analysis approach,and it will be quick and accurate to predict the sound attenuation property of Helmholtz resonator with conical neck.     

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.     

Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.     

Symmetries and Similarity Reductions of a New （2＋1）-Dimensional Shallow Water Wave System

The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.     

Analysis and demonstration of PID algorithm based on arranging the transient process for adaptive optics

The fastness and robustness of a control algorithm are highly important in the performance of adaptive optics systems. The proportional-integral-derivative control with arranging the transient process, which is designed using a tracking differentiator, is applied into an adaptive optics system. This control algorithm greatly improves the dynamic properties of the control system. To identify the underlying reasons for these improvements, the influence of the control algorithm is theoretically discussed. The control algorithm is verified by a simple adaptive optics system for tip/tilt correction. The experimental results demonstrate that the control algorithm is fast and robust.