Firstly we deduce hyperbolic function transformation and then apply to a class of reaction diffusion equation and brusselator reaction diffusion model which has physics , chemistry and biology significance . thus we obtain many new exact and explicit solutions ( including solitary wave soluiton , peoiodic wave solution and rational functions solutions ) to above equations 推導(dǎo)出了雙曲函數(shù)變換,利用此方法探討了一類反應(yīng)擴(kuò)散方程, brusselator反應(yīng)擴(kuò)散方程這些具有物理、化學(xué)、生物意義的方程的精確解(包括奇性孤波解,周期解和有理函數(shù)解) 。
Therefore , it can be used as an efficient new model for geometric design in the fields of cad / cam . at last , the spatial definition of periodic spline and natural spline constructed by polynomial and hyperbolic functions is given ; the dimension law and zero properties are demonstrated ; and therefore the non - uniform algebraic - hyperbolic period and natural spline curves are obtained . the applications of the low order are given in details 三、給出代數(shù)雙曲周期樣條及自然樣條空間定義,證明其維數(shù)定理和零點(diǎn)定理,構(gòu)造具有最小緊支撐的非均勻代數(shù)雙曲周期及自然樣條函數(shù),進(jìn)而定義非均勻代數(shù)雙曲周期及自然樣條曲線,最后具體給出低階的表示和應(yīng)用
This paper summaries the researches on the new schemes of parameter curves and surfaces modeling - curves and surfaces modeling of trigonometric polynomial , which includes curves and surfaces of t - bezier , t - b - spline , tc - bezier and tc - b - spline . hc - b zier curves and surfaces are also discussed in the space of hyperbolic functions in the end 本文主要對(duì)參數(shù)曲線曲面造型的一種新方法? ?三角多項(xiàng)式曲線曲面進(jìn)行了深入研究,其內(nèi)容主要包括t - b zier曲線曲面、 t - b樣條曲線曲面、 tc - b zier曲線曲面和tc - b樣條曲線曲面。