Stability of a Generalized Quadratic Functional Equation in Schwartz Distributions

We consider the Hyers-Ulam stability problem of the generalized quadratic functional equationuoA＋voB-2woP1 - 2ko P2 =0, which is a distributional version of the classical generalized quadratic functional equation f（x＋y）＋g（x - y） - 2h（x） - 2k（y）=0

Application of adaptive filter in time delay estimation——generalized quadratic interpolation method

The time delay estimation (TDE) of two different received signals from the same source has attracted many interests of researchers in the field of signal processing. A method described for precisely estimating time delay in this paper is based on the assumption that little priori knowledge on statistical characteristics is available for the received signals. The variance of the estimate is derived . The basic architecture of this method is to use the adaptive noise canceller, in the steady state , and to interpolate the weight coefficients by using a generalized quadratic interpolation matrix. The formula of the time delay estimation is presented . The method proposed by F.A. Reed is a special case of this method . The hardware implementation is much easier than that of the conventional time delay estimation method . The results of the system simulation and the experimental results at sea show a good agreement with the theoretical analysis.

On the Fourth Power Mean of the Generalized Quadratic Gauss Sums

The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q （a positive odd number）, and give an exact computational formula for it.

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

Robust Input-Output Energy Decoupling for Uncertain Singular Systems

This paper addresses the robust input-output energy decoupling problem for uncertain singular systems in which all parameter matrices except E exist as time-varying uncertainties. By means of linear matrix inequalities (LMIs), sufficient conditions are derived for the existence of linear state feedback and input transformation control laws, such that the resulting closed-loop uncertain singular system is generalized quadratically stable and the energy of every input controls mainly the energy of a corresponding output, and influences the energy of other outputs as weakly as possible. Keywords Uncertain singular systems - generalized quadratical stability - input-output energy decoupling - linear matrix inequality (LMI) Xin-Zhuang Dong graduated from the Institute of Information Engineering of People’s Liberation Army, China, in 1994. She received the M. S. degree from the Institute of Electronic Technology of People’s Liberation Army, in 1998 and the Ph.D. degree from Northeastern University, China, in 2004. She is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, CAS.Her research interests include singular and nonlinear systems, especially the control of singular systems such as H ∞ control, passive control and dissipative control. Qing-Ling Zhang received the Ph.D. degree from Northeastern University, China, in 1995. He is currently a professor with the Institute of Systems Science, Northeastern University. His research interests include singular systems, fuzzy systems, decentralized control, and H 2/H ∞ control.