On Multiplicative Generators of n-Dimensional Overlap Functions

In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.

Generalized multiple time windows model based parallel machine scheduling for TDRSS

The scheduling efficiency of the tracking and data relay satellite system（TDRSS）is strictly limited by the scheduling degrees of freedom（DoF）,including time DoF defined by jobs＇ flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites（TDRSs）.In this paper,ageneralized multiple time windows（GMTW）model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking（APR）based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.

Application of Multiple Mean Generational Function Method to Typhoon Prediction over the Western North Pacific

[ Objective] The multiple mean generational function （MMGF） method was applied to forecast the annual number of typhoons （TYs） over the Western North Pacific （WNP）. [Method]The method yields a number of predictors by mean generational function based on the rolling 50- year data of TYs frequency and sunspot number, and was repeated to generate forecasts year after year by optimal subset regression. [ Result] The results showed a reasonably high predictive ability dudng period 2000 -2010, with an average root mean square （RMSE） value of 1.92 and a mean absolute error （MAE） value of 1.64. [ Conclusion] Although the MMGF method needs further validation in the practical operation, it already has strong potential for the improvement of skill at forecasting annual frequency of TYs in the WNP.

Creation of radially polarized optical fields with multiple controllable parameters using a vectorial optical field generator

A vectorial optical field generator(VOF-Gen) based on two reflective phase-only liquid crystal spatial light modulators enables the creation of an arbitrary optical complex field. In this work, the capabilities of the VOF-Gen in terms of manipulating the spatial distributions of phase, amplitude, and polarization are experimentally demonstrated by generating a radially polarized optical field consisted of five annular rings, the focusing properties of which are also numerically studied with vectorial diffraction theory. By carefully adjusting the relative amplitude and phase between the adjacent rings, an optical needle field with purely longitudinal polarization can be produced in the focal region of a high numerical aperture lens. The versatile method presented in this work can be easily extended to the generation of a vectorial optical field with any desired complex distributions.

THE MULTIPLICATIVE COMPLEXITY AND ALGORITHM OF THE GENERALIZED DISCRETE FOURIER TRANSFORM(GFT)

In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.