A - optimal design for duality quadratic polynomial regression models in circle region 圓域上的二元二次多項式回歸模型的最優設計
In the case ( 3 ) . we also have that each critical component and its inverse images under iterations are homeomorphic to the filled julia set of a quadratic polynomial with connected julia set . each of the other components of a ' ( / ) is a single point 對于( 3 ) ,我們進一步有:填充juia集包含臨界點的周期分支及其迭代逆象同胚于一個有連通julia集的二次多項式的填充julia集,而其他分支都是單點。
Yoccoz introduced a powerful puzzle technique and obtained the result that if the quadratic polynomial pc ( z ) with , which has no indifferent cycle , is not infinitely renormalizable , then the julia set j ( pc ) of pc is locally connected while dm is also locally connected at c 利用這個技巧,他得到了對c m ,如果二次多項式pc ( z )不是無窮可重整化的,并且沒有拋物周期點,那么julia集j ( pc )是局部連通的,并且m在c也是局部連通的。
At the end of the last century , c . j . yoccoz is made significant contributions to the theory of complex dynamics , one of which is the study of the local connectivity of the julia sets of quadratic polynomials pc ( z ) = z2 + c and the mandelbrot set m . in his work C yoccoz對復動力系統理論作出了重要的貢獻,其中之一就是對二次多項式pc ( z ) = z ~ 2 + c的julia集和mandelbrot集m的局部連通性的研究。在他的工作中, yoccoz引進了一種強有力的方法? ?拼圖技巧。
In the late part of the active developing period , the temporal variation of sediment concentration and sediment transport ratio of each rainfall can be expressed by exponent function and the variation presents quadratic polynomial function in the stable developing period . the spatial variation character of sediment yields with space of the experimental watershed model . the active position of soil erosion and sediment yield of the experimental watershed model changes from the downside to the upside with the developing process of the watershed model 流域模型侵蝕產沙空間變化特征侵蝕產沙的活躍部位隨流域模型發育過程呈現由流域模型下部逐漸向上部發展特征,其中流域模型下中部為發育初期時段和發育活躍時段侵蝕產沙的活躍部位,流域模型上部是發育穩定時段侵蝕產沙的活躍部位。
In the analysis process , the six main peaks in 88 - 100 kev region , including the y peaks of 234th , the k peaks of th and the k peaks of u , are chosen . the smoothly joined gaussian function and low energy exponential tail is taken as peak shape function and quadratic polynomial is taken as background function . the two functions are fitted to gether to calculate the peak area 在分析過程中,選擇了88 - 100kev能區的~ ( 234 ) th的射線峰, th的k _射線峰以及u的k _射線峰共六個主要能峰,通過采用高斯函數和低能指數尾部光滑聯接的峰形函數和二次多項式本底函數一起擬合,來求出峰面積;而該能區所有能峰的探測效率可以認為是近似相等的,由此得到鈾富集度。
A . douady had suggested to study dynamics of biquadratic polynomials . by definition , a biquadratic polynomial is the composition of two quadratic polynomials , so it is an even quartic polynomials which can be written as f ( z ) = z4 + az2 + 6 , where a , b are parameters . it is easy to see that / has a critical point at 0 and two symmetric critical points at A . douadv曾建議對雙二次多項式的動力系統進行研究,所謂雙二次多項式就是兩個二次多項式的復合,也即偶四次多項式,在一個線型共軛下可以記為fz ) = z ~ 4 + z ~ 2 + b ,這里o , b是參數,點0是它的一個臨界點,另外還有兩個對稱的臨界點( ( - a ) 、 2 ) ~ 2 。