Narrow Results

Once massless quadratically divergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other divergences into logarithmic form, using partial fraction identities; this includes the case of quadratic divergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to correct numerator factors.

In this paper, a high-order Recursive Quadratic (RQ) algorithm is introduced, and the features of this algorithm are thoroughly studied and illustrated. In addition, a robust RQ algorithm is also developed in the presence of general bounded noisy data to enhance model robustness. A numerical example is included to demonstrate the efficiency of RQ algorithms by comparing the results with both the projection algorithm and the conventional recursive least squares algorithm. Also some simulations are carried out to illustrate the effectiveness of the RQ and robust RQ algorithms.

Emerging switched-mode power supplies incorporated applications demand reliable, less volume and high efficient dc–dc converters. The persistent usage of the dc–dc converters in various applications makes their reliability a significant concern. Hence, this paper deals with a family of non-isolated high gain integrated dc–dc converter topologies derived from a quadratic converter. The reliability analysis is carried out using electronic equipment reliability handbook, MIL-HDBK-217F. For the first time, reliability prediction is done based on the working environment of the power electronic equipments. We developed the reliability prediction for the converters used in the lighting application such as automotive headlamp and aircraft landing lights. The mean time to failure for both the environment is calculated. The reliability comparison is carried out for the proposed topologies and the most reliable converter is chosen. Also, all the converter topologies are simulated using nL5 simulator to confirm their theoretical results. Finally, a laboratory prototype for 40 W with input voltage of 12 V is implemented for the most reliable topology to validate the steady-state analysis.

In this paper we study the nonchaotic and chaotic behavior of all 3D conservative quadratic ODE systems with five terms on the right-hand side and one nonlinear term (5-1 systems). We prove a theorem which provides sufficient conditions for solutions in 3D autonomous systems being nonchaotic. We show that all but five of these systems: (15a, 15b), (18b), (41)(A = ∓1), (43b), and (49a, 49b) are nonchaotic. Numerical simulations show that only one of the five systems, (43b), really appears to be chaotic. If proved to be true, it will be the simplest ODE system having chaos.

In this paper, based on the basic principle of the SPH method’s kernel approximation, a new kernel approximation was constructed to compute first-order derivative through Taylor series expansion. Derivative in Newton’s method was replaced to propose a new SPH iterative method for solving nonlinear equations. The advantage of this method is that it does not require any evaluation of derivatives, which overcame the shortcoming of Newton’s method. Quadratic convergence of new method was proved and a variety of numerical examples were given to illustrate that the method has the same computational efficiency as Newton’s method.