algebraic curves 中文意思是什麼
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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 -
The paper applies algebraic geometry, computational geometry, approximation theory to study the following problems : the nother type theory and the riemann - roch type theory of the piecewise algebraic curve ; the number of real intersection points of piecewise algebraic curves ; the real piecewise algebraic variety and the b - net resultant of polynomials
本文應用代數幾何，計算幾何，函數逼近論等學科的基本理論，分別就分片代數曲線的n （ ? ） ther型與riemann - roch型定理；分片代數曲線的實交點數；實分片代數簇以及多項式的b -網結式進行研究。 -
The final nonlinear algebraic equation set is solved using the step - by - step newton - raphson iteration and the deformed curves for the corresponding state of each load increment can be determined
對應每個荷載增量，可求得鋼管混凝土拱在相應狀態下的變形曲線。對各荷載增量進行反復迭代，直至得到荷載的極限值。 -
3. by using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [ 13 ], [ 73 ] ) ; b - net form of bivariate splines function ; discriminant sequence of polynomial ( cf. [ 13 ], [ 73 ] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite. a lower bound of the number of real intersection points is obtained in terms of method of rotation degree of vector field
大連理工大學博士論義：分片代數價線i片代數簇的若十m穴3 ：利用楊路，張景中，侯曉榮在文獻v13 ， 73 ）中關於一元多項式實根的顯式判準，以及二元樣條函數的b網形式，多項式的判別序列和sturm序列的最高次數項系數序列的變號數，本文給出了兩個分片代數曲線的丈交點數（假設公共點是有限的）的計算公式。 -
Three special subspaces of ect spline space : polynomial space, the algebraic trigonometric spline space and hyperbolic spline space are investigated in detail. the generalized p lya polynomials, associated with the three subspaces, are calculated. both of boehm algorithm and oslo algorithm for the ect b spline curves of order 4 over the three special subspaces are displayed
三、在多項式樣條空間、代數三角樣條空間和代數雙曲樣條空間這三個具體的ect空間上，給出了相應典範ect組和廣義p lya多項式的計算和顯示表示，展示了幾個低階ectb樣條曲線各種插入節點演算法的求解全過程 -
In the first part, by using the method of characteristic curves for solving linear partial differential equations, all invariant algebraic surfaces for three nonlinear systems are obtained
第一部分，利用求解線性偏微分方程的特徵曲線法，得到了三個系統的所有不變代數曲面。 -
In this paper the g2 - continuous blending conditions of two algebraic curves implicitly defined based on the construction of algebraic curves that interpolate the geometric constraints are presented
本文在對插值一類幾何約束的隱式代數曲線的構造基礎上，給出了這樣的隱式三次代數曲線二階幾何連續光滑拼接的條件，並給出了實驗結果。 -
Second, combining with the construction principle of geometry - goppa codes, we present a kind of new algebraic - geometry code by using the properties of algebraic curves on finite fields. we determine the value of the code - length n and d imension k, and the lower bound of the minimal distances of the new algebraic - geometry code. the new algebraic - geometry code have the following characteristics : ( l ) the new code is the generalization of geometry - goppa codes and the algebraic - geometry code constructed by chaoping xing and san ling in 2000 ( 2 ) compared with brouwer ' table of the best known codes, we find more new codes, there are at least 60 new codes under two - dimension cases
其次，結合幾何goppa碼的構造原理，利用有限域上代數曲線的特點來構造代數幾何碼，確定了新的代數幾何碼的碼長n和維數k的取值，給出了最小距離d的下限，這類碼的特點是： （ 1 ）新的代數幾何碼是幾何goppa碼和新加坡國立大學chaopingxing和sanling在2000年所構造的代數幾何碼的推廣； （ 2 ）這類碼中有許多種碼的參數優于brouwer碼表，僅二維情形時，就有60多種碼優于brouwer碼表。
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