Leaves tufted ; stipes 15 - 30 cm long, densely scaly at base, glabrous above ; sterile lamina about 60 cm long and 20 cm wide, simply pinnate ; pinnae numerous, alternate or subopposite, linear - lanceolate, the largest about 12 cm long and 1 cm wide, base cordate, apex acuminate, margin finely toothed ; veins close, forking once or twice and forming areoles near the midrib ; fertile lamina similar to sterile ones, but somewhat reduced, about 8 cm long and 0. 4 cm wide, lower surface almost entirely covered with sporangia
葉簇生；葉柄長15 - 30厘米，基部密被鱗片，向上近光滑；不育葉片長約60厘米，寬20厘米，一回羽狀；羽片多
數，互生或近對生，線狀披針形，最長者長達12厘米，寬約1厘米，頂端長漸尖，基部心形，邊緣有細密鋸齒；葉脈1 - 2次分
叉，近中脈形成網眼；能育葉與不育葉相似，但較小，長約8厘米，寬約0 . 4厘米，下部滿布孢子囊。
The fractional fourier transform is linear time - frequency transform, and it doesn ’ t have disadvantages of wigner - ville distribution. moreover, the precision of this method is higher, and the performance of antinoise is better
而分
數階傅立葉變換是線性時頻變換，所以它不受交
叉項的干擾，沒有不模糊區間減半的缺點，而且它的估計精度高、抗噪性能好。
Results contrast with the unimproved or some previous models, the features of tumor microvascular networks generated from our model by simulating the angiogenesis in caecum tumor, such as vascular tortuosity, branching and anastomosis, are closer to the physiological facts and more resemble the experimental observations
結果對盲腸腫瘤微血管網進行
數值模擬，與改進前的模型和其他模型比較，本模型生成的腫瘤微血管網結構特徵，如血管的走向、扭曲、分
叉與融合等，更接近生理實際，與實驗觀測圖像的相似度更高。
The chiasmata observed during the later stages of the meiotic prophase are cytological evidence of earlier cross-over events.
在減
數分裂前期末所看到的交
叉是在這以前發生了互換事件的細胞學證據。
It features a data prefetch engine, non - blocking interleaved data cache, dual floating point execution units, and many other goodies
它特有一個
數據預取引擎，無阻塞的交
叉數據緩存，雙浮點執行單元，以及其他一些很好的設計。
5. with the method of apen, we calculated the apen of bifurcate data got from model of r - h. we found the apen of chaos is obviously higher than that of period 2 and 3
用r h模型模擬分
叉數據並進行復雜度計算，以近似嫡為檢測方法，發現在周期二、三之間的混飩
數據的復雜度明顯高於周期節律
數據。
Consequently, there is urgent need of good algorithm for calculating the crossing number of graph
因此，迫切希望有較好的計算機演算法用以計算圖的交
叉數。
Using the algorithm ccn ( calculate crossing number ) invented by us, we investigate the crossing numbers of all graphs for n < 9
利用我們研製的計算圖的交
叉數的演算法ccn （ calculatecrossingnumber ） ，本文對n 9的所有圖的交
叉數進行了研究。
In this article, a algorithm ccn ( calculate crossing number ) is put forward to study the crossing number. it is a very important development in graph planarity issue after planarity - determinant algorithm and embedding algorithm
本文首次給出了較好的計算圖的交
叉數演算法ccn （ calculatecrossingnumber ） ，這是繼圖平面性判定演算法，二連通圖的平面嵌入演算法之後在圖的平面性問題上的一個最重要的進展。
Since the crossing numbers of graph equal the sum of the crossing numbers of all its 2 - connected blocks, we work on the crossing numbers of graphs for n < 9 with unique 2 - connected block.
由於圖的交
叉數等於其所有二連通分支的交
叉數的和，本文計算了n 9的所有單二連通分支圖的交
叉數。
In this paper, three correlative results are given : 1 ) the average crossing number of graph with n vertices and q edges can be signified approximately by quadratic equation of q. 2 ) the average crossing number of graphs with bigger girth is greater than that with smaller girth within given vertices and edges. 3 ) the average crossing number of r - regular graphs greater than that of non - regular graphs within given vertices and edges where n is odd or r < n / 2
並得出相關的規律： 1 ） n個頂點q條邊的單二連通分支圖的平均交
叉數aac （ n ， q ）可近似地表示為q的二次多項式， 2 ）在給定頂點
數n與邊
數q的單二連通分支圖中圍長較大的圖的平均交
叉數大於圍長較小的圖的平均交
叉數， 3 ）在給定頂點
數n與邊
數q的單二連通分支圖中當n為奇
數或r n / 2時， r正則圖的平均交
叉數大於非r正則圖的平均交
叉數。
We also calculate the average crossing number aac ( n ) of all of the 4 - regular graphs for n < 12 and the average crossing number arc ( n ) of some random 4 - regular graphs of degree 4 for n < 16. at the end of the paper, a conjecture that the average crossing number of regular graph of degree 4 is o ( n2 ) is given
同時計算出n 12的所有四正則圖的平均交
叉數aac （ n ） ，和n 16的隨機四正則圖的平均交
叉數arc （ n ） ，並根據計算結果提出四正則圖的平均交
叉數為o （ n ~ 2 ）的猜想。
By the algorithm ccn, we investigate the crossing numbers of regular graphs with small order. we get the crossing numbers of 3 - regular graphs for n < 16 and 4 - regular graphs for n < 12, and the lower bounds of the maximum crossing numbers of 3 - regular graphs for n < 30 and 4 - regular graphs for n < 19, where n is the order of graphs. according to the result, we put forward the conjecture about the maximum crossing numbers of regular graphs
本文還利用演算法ccn （ calculatecrossingnumber ）對頂點
數較小的正則圖的交
叉數進行研究，計算出n 16的三正則圖和n 12的四正則圖的交
叉數，以及n 30的三正則圖和n 19的四正則圖的最大交
叉數的下限（ n為圖的頂點個
數） ，根據計算結果提出關于正則圖最大交
叉數的猜想。
It invests all 3 - regular graphs with order at most 18, all 3 - regular generalized petersen graphs with order at most 30, all 3 - regular graphs with maximum girth and order from 20 to 30, some random 3 - regular graphs with order from 20 to 30, and all circulant graphs cn ( l, k ) with order at most 18. in this article, it is shown that the average crossing number of 3 - regular graphs with biggest girth and order n ( 18 ) is greater than that of all 3 - regular graphs
通過研究n 15的所有三正則的廣義petersen圖p （ n ， k ） ， n 18的所有三正則圖， 20 n 30的隨機三正則圖與具有最大圍長的三正則圖， n 18的所有循環圖c _ n （ 1 ， k ） ，本文得到如下規律：對于給定的頂點
數n （ n 18 ） ，具有最大圍長的三正則圖的平均交
叉數大於所有三正則圖的平均交
叉數。
The crossing number of graph, which is an np - complete problem, has an important theory meaning
圖的交
叉數問題屬于np -困難問題，對它的研究有重要的理論意義。
Using the algorithm ccn ( calculate crossing number ), this article researches on the relation between the crossing number and girth of the 3 - regular graphs
利用計算交
叉數的演算法ccn （ calculatecrossingnumber ） ，本文對三正則圖的交
叉數與圍長的關系進行了深入的研究。
Refers to the traversing graph, we divided it into many traversing of binary tree
對于圖的遍歷，我們將其分開成對多個二
叉數的遍歷。
In addition, erdos and guythe ' s conjecture about graphs with maximal crossing number is proved incorrect
還證明了erdos和guy關于可能有最大的交
叉數的圖的猜想不成立。
Finally, to achieve an windows - like graphical user interface, we save the position, size, and other parameters by defining great deal of data structure, and use binary tree and graph to record the relationship between different graphs
為了實現類windows的圖形用戶界面，我們通過定義大量的
數據結構來保存各個圖像的位置、大小、以及它的各種參
數等
數據，並用二
叉數和圖來記錄各個圖形間的相互關系。
The details are as followings : the most usual problems related to navigation data fusion are studied ( the local navigation sensors export directly navigation parameters and their accuracies without feedbacks and cross data communications ) ; a novel conservative optimal fusion method of non - feedback multi - source correlated estimators is presented, and this method is extended to the case of more than two data sources ; some new theorems are supplied or proved so that our methods are naturally connected to the achievements up to present, and the integrated theory basis of non - feedback multi - source correlated estimators fusion is founded
具體內容如下：研究了最一般的導航數據融合問題（局部導航儀直接輸出導航參數及精度，且無反饋、無局部導航儀之間的交叉數據通訊） ；提出了一種新的無反饋多源相關估計向量的保守最優融合演算法，並將該演算法由兩個數據源推廣到了多個數據源；補充證明了一系列定理，從而將本文方法和前人研究成果有機地融為一體，建立了完整的無反饋多源相關估計向量融合的理論體系。
