The focus of the paper is mainly on the existence of limit cycles of a planar system with thirddegree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number of cases with certain restrictions on system...

Currently, reset control focuses on using structures which allow new resetting rules in order to avoid limit cycle to be caused and improve the performance of the system. This paper investigates the properties of some reset strategies, of integer and fractional order, which reset controller states to fixed or variable non-zero values and are able to eliminate or reduce the overshoot in first an...

We study the limit distribution of upper extreme values of i.i.d. exponential samples {ei}i=1 as t →∞, N →∞. Two cases are considered: (A) ess sup X = 0 and (B) ess sup X = ∞. We assume that the function h(x) = − log P{X > x} (case B) or h(x) = − log P{X > −1/x} (case A) is (normalized) regularly varying at ∞ with index 1 < % < ∞ (case B) or 0 < % < ∞ (case A). The growth scale of N is chosen i...

In a “dual” detector a wideband sensitivity is obtained by measuring the differential displacement, driven by the gw wave, of the facing surfaces of two nested massive bodies mechanically resonating at different frequencies. By the use of the recently proposed “selective readout” scheme, capable of specifically selecting the signal contributed by the vibrational modes sensitive to the gravitati...

Once a regression has been fitted to data, it is usually necessary to add confidence intervals to indicate the accuracy of the fitted regression line. This can easily be done for individual explanatory variable values. However sometimes confidence limits are needed simultaneously for the whole range of explanatory variable values of interest. In other words the problem is to construct a confide...

Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in random matrix theory. Though their numerical values are of interest, there is no systematic numerical treatment of Fredholm determinants to be found in the literature. Instead, the few numerical evaluations th...

From high-precision MOST photometry spanning 35 days the existence of two spots rotating with slightly differing periods is confirmed. From the marginal probability distribution of the derived differential rotation parameter k its expectation value as well as confidence limits are computed directly from the data. The result depends on the assumed range in inclination i, not on the shape of the ...

We consider the optimal control problem for a (finite-dimensional) quantum system with an energy-like cost. We explore the limit of small control amplitude and construct an approximation to the two-point boundary value problem resulting from the Maximum Principle. By solving the approximate two-point boundary value problem in two examples, we argue that this limit corresponds to the limit of la...

We demonstrate an amplitude-based bending/displacement sensor that uses a plastic photonic bandgap Bragg fiber with one end coated with a silver layer. The reflection intensity of the Bragg fiber is characterized in response to different displacements (or bending curvatures). We note that the Bragg reflector of the fiber acts as an efficient mode stripper for the wavelengths near the edge of th...

We performed a Monte Carlo study to evaluate the effect of the number of events per variable (EPV) analyzed in logistic regression analysis. The simulations were based on data from a cardiac trial of 673 patients in which 252 deaths occurred and seven variables were cogent predictors of mortality; the number of events per predictive variable was (252/7 =) 36 for the full sample. For the simulat...