THE INVERSE EIGENPROBLEM WITH RANK-ONE UPDATING AND ITS STABLITY

Let ∑, Г be two n-by-n diagonal matrices with σi,γi as their diagonals. For the inverse eigenvalue problem: look for y∈Rn such that Г + yyT is similar to ∑, we prove thatu also the sufficient condition for the solvability of this inverse problem. Its solution (set) is given explicitly. In some case, the problem is unstable. But we prove that the sums of the square of some contigious components keep stable, i.e., small sum keeps small, large sum has a small relative perturbation, see Theorem 3.

DYNAMIC STABILITY OF SPINDLE BLADE IN RING SPINNING Zhou Bingrong(Department of Mechanical Engineering)

It is discussed that a tangential force T induces a self-excited vibration in the motion ofspindle blades of a ring spinning frame.Depending on the relative magnitude of the tangentialforce compared with the tangential damping force the motion of blade is either stable orunstable.The chief factors causing the self-excited vibration can also be traced from the charac-ter of the experimental locus.

Preparation of MMA-BA-DMAEMA Nanosized Latex

The terpolymer latex of methyl methacrylate (MMA)/butyl acrylate (BA)/ dimethyl aminoethyl methacrylate (DMAEMA) with diameter of less than 100 nm was prepared by seeding semi-continuous emulsion copolymerization using APS (ammonium persulfate) / TMEDA (N,N,N, N-tetramethylethylenediamine) as the redox initiators and SDS (sodium dodecylsulfate) and OP (P-octylpolyethylene glycol phenylether) as co-emulsifiers. The factors that influenced the process stability of the copolymerization and the particle size of the latex were investigated. The addition of aqueous ammonia as coagulation inhibitor provided better process stability of the copoly- merization. The addition of acetic acid as the acidification agent caused a remarkable reduction of the latex particle size.

What can routh table offer in addition to stability?

Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a little beyond, the number of unstable roots of a polynomial in terms of the signs of certain entries of the Routh table constructed from the coefficients of the polynomial. The use of the Routh table, as far as the common textbooks show, is only limited to this function. We will show that the Routh table can actually be used to construct an orthonormal basis in the space of strictly proper rational functions with a common stable denominator. This orthonormal basis can then be used for many other purposes, including the computation of the H2 norm, the Hankel singular values and singular vectors, model reduction, H∞ optimization, etc. Keywords Routh stablity criterion - Orthonormal basis - Root-mean-squared value - Hankel operater - Nehari problem - Model reduction This work was supported by the Hong Kong Research Grants Council.

An Experimental Analysis of Stability in Human Walking

Biped locomotion has excellent environment adaptability due to natural selection and evolution over hundreds of millions years. However, the biped walking stability mechanism is still not clear. In this paper, an experimental analysis of walking stability in human walking is carried out by using a motion capture system. A new stability analysis method is proposed based on Zero Moment Point （ZMP） and Sliding Time Window （STW）. The influences of ground friction coefficient, ground slope angle and contact area of support polygon on human walking stability are investigated. The experiment is carried out with 12 healthy subjects, and 53 passive reflective markers are pasted to each subject to obtain moving trajectory and to calculate lower limb joint variation during walking. Experimental results show that ground friction coefficient, ground slope angle and contact area have significant effects on the stride length, step height, gait cycle and lower limb joint angles. When walking with small stability margin, subjects modulate gait to improve the stability, such as shortening stride length, reducing step height, and increasing the gait cycle. These results provide insights into the stability mechanism of human walking, which is beneficial for locomotion control of biped robots.

Oscillation of Numerical Solution in the Runge-Kutta Methods for Equation x'(t)=ax(t)+a_0x([t])

The paper de ls with oscillation of Runge-Kutta methods for equation x＇（t） = ax（t） ＋ aox（[t]）. The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given.

Mathematical modeling with optimal control analysis of social media addiction

In this paper,we developed a deterministic mathematical model of social media addiction(SMA)with an optimal control strategy.Major qualitative analysis like the social media addiction free equilibrium point(E_(0)),endemic equilibrium point(E^(*)),basic reproduction number eR0T,were computed.From the stability analysis,we found that the social media addiction free equilibrium point(SMAFEP)is locally asymptotically stable if R_(0)<1.The global asymptotic stablity of SMAFEP is stablished using Castillo-Chavez theorem.If R_(0)>1 the unique endemic equilibruim is locally assymptotically stable.Also using Center Manifold theorem,the model exhabits a forward bifurcation at R_(0)=1.The sensitivity of model parameters is done using the normalized forward sensitivity index definition.Secondly,we introduced two time dependent controls on the basic model and formulated an optimal control model.Then,we used the Pontryagin’s maximum principle to find the optimal system of the model.Numerical simulations,on the optimal control problem using the fourth-order Range-Kutta forward-backward sweep method,on the suggested strategies for SMA is performed.We found that to effectively control SMA at a specified period of time,stakeholders and policymakers must apply the integrated control strategies C.