hyperbolic functions 中文意思是什麼
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This dissection is mainly to discuss the problems of estimating in the derivation of bounded functions, the coefficients of bounded regular functions and schwarz - pick lemma for the derivation on the hyperbolic metric
本文研究有界正則函數導數和系數的估計問題，以及雙曲度量下關于導數的schwarz - pick不等式。 -
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
推導出了雙曲函數變換，利用此方法探討了一類反應擴散方程， brusselator反應擴散方程這些具有物理、化學、生物意義的方程的精確解（包括奇性孤波解，周期解和有理函數解） 。 -
Secondly, we introduce the recurrence definition of the non - uniform algebraic - hyperbolic b - spline basis using divided differences and the de boor - fix recurrence definition on polynomial functions, and based on the new forms, algebraic - hyperbolic b - spline curves are obtained. they share most of the properties as those of the b - spline curves in the polynomial space. we focus on deducing the calculating and knot inserting formulae for this new kind of curves and then prove that they have the variation diminishing properties
二、利用廣義差商，基於多項式b樣條的deboor - fix遞推定義，給出了任意階非均勻代數雙曲b樣條的遞推定義，由此構造麯線，證明它的幾何不變性、仿射不變性、凸包性、 v . d .性等，重點給出了非均勻代數雙曲b樣條曲線的遞歸求值和節點插入演算法，演算法簡單且穩定，便於在計算機上實現 -
Spline curves defined in the space constructed by polynomial and hyperbolic functions are studied in this paper. the main research contents and achievements are as follow : firstly, we generate the cardinal extended complete chebychevian ( ect ) - systems on the space constructed by polynomial and hyperbolic functions, then introduce the algebraic - hyperbolic b - spline space and identify the dimension law and zero properties. the existence of a basis of splines with minimal compact supports is demonstrated, and functions named non - uniform algebraic - hyperbolic b - splines are obtained by solving certain linear equations with a block matrix
本文主要研究定義在多項式和雙曲函數構成的空間上的樣條曲線，其內容和完成結果如下:一、生成由多項式和雙曲函數構成的空間上的一組典範式ect （ extendedcompletechebychevian ）組及其對偶， ，證明非均勻代數雙曲b樣條空間的維數定理和零點定理，直接通過解塊矩陣線性方程組得到具有最小緊支撐的非均勻代數雙曲b樣條函數，進而構造非均勻代數雙曲b樣條曲線，還具體給出低階的表示 -
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、給出代數雙曲周期樣條及自然樣條空間定義，證明其維數定理和零點定理，構造具有最小緊支撐的非均勻代數雙曲周期及自然樣條函數，進而定義非均勻代數雙曲周期及自然樣條曲線，最後具體給出低階的表示和應用 -
Firstly the formulation arid representation of solutions of the above boundary value problems are given, and then the existence of solutions for the above problems is proved, in which the complex analytic method is applied, namely the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used
先給出這個問題的提法和解的表示式，然後使用一種新的復分析方法，即在橢圓區域上使用復變函數，在雙曲區域上使用雙曲復函數，最後證明了上述混合型方程間斷斜微商問題解的存在性。 -
Hyperbolic k - regular functions
正則函數 -
At last, we construct hyperbolic polynomial curves in the space of hyperbolic functions. we call them as hc - bezier curves
文章最後運用同樣的方法在雙曲函數空間中構造了hc - b zier曲線。 -
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
本文主要對參數曲線曲面造型的一種新方法? ?三角多項式曲線曲面進行了深入研究，其內容主要包括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。
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