convex flow 中文意思是什麼
convex flow
解釋
凸岸水流-
This paper is concerned with, the existence and stability of travelling wave solutions for the viscous balance law which is an extension of viscous conservation law where a reaction term g ( u ) is added. l ) the existence of travelling wave solutions by geometric singular perturbation method, we investigate the existence of travelling waves ( a2 ) connecting a saddle point and a sink point and the existence of viscous shock waves c connecting two adjacent or disadjacent saddle points. by giving a detailed analysis of the fast and slow manifolds and verifying the transversality of the intersection of singular stable and unstable manifolds of the reduced problem along the singular heteroclinic orbit, we obtain the existence of travelling waves ( a2 ) in the case of a convex flow function / and that of viscous shock waves c under the assumption that f " is bounded
主要結果如下： 1 ）行波的存在性本文利用[ 37 ]中幾何奇異攝動理論，通過仔細分析= 0時的快流、慢流，驗證= 0時慢流方程的穩定與不穩定流形橫截相交於奇異異宿軌道，先在f為凸的條件下嚴格證明了（ ）存在連接不相鄰的鞍點、結點的行波（ a2 ） ；然後在地f有界的條件下得到（ ）存在連接鞍點（包括相鄰和不相鄰）的粘性沖擊波c ，彌補了[ 11 ]缺少嚴格證明的不足，並推廣了[ 11 ]在f為凸的條件下得到的粘性沖擊波的存在性結果。 -
Under this flow, the convex initial curve will preserve its perimeter, enlarge the enclosed area and make its curvature to be positive definitely. and as the time lasts, it will become more and more circular, and finally, as the time goes to infinity, the curve will converge to a circle in the hausdorff metric
本文證明在這種新的曲線流之下，閉凸曲線周長保持不變、所圍區域的面積不斷增大而曲率保持恆正（從而保持凸性） ，並且，隨著時間的推移曲線變得越來越圓，最終當時間t趨向于無窮大時，曲線在hausdorff度量意義下收斂到一個圓周。 -
First according to the fact that tangential components of the evolution do not affect the geometric shape of the evolving curves, we introduce the evolution equation of geometric quantities for the general planar curves. then we describe the work of gage - hamilton briefly. last we consider a special curvature flow of curve which evolves with speed function of the principal curvatures along the inner norm and show that convexity of the curve is kept and its length and area are contracted if the initial closed curve is smooth and convex. so the final shape of the curve will be a point in finite time
首先根據曲線在切向分量上發展是不影響曲線的發展形狀，我們引入了曲線的一些幾何變量的發展方程；其次我們簡要地回顧gage - hamilton研究曲線發展的一般步驟；最後我們考慮沿曲線的內法線以曲率的函數為發展速度的一類特殊的曲線族，證明了在初始曲線為凸的閉平面簡單曲線條件下，曲線將保持凸的，並且它的面積和周長將同時收縮，並在有限時間內成為一個點。 -
Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature. finally, we will employ the minkowski ' s support function to construct a new kind of non - circular smooth constant breadth curves in order to attack some open problems on the constant width curves ( for example, whether there is a non - circular polynomial curve of constant width, etc. ) in the second part, we will first follow the ideas of gage - hamilton [ 28 ], gage [ 26 ] and the author ' s dissertation [ 47 ] to present a perimeter - preserving closed convex curve flow in the plane, which is from physical phenomena
其次，對雙曲平面上的曲線引入平均測地曲率的概念，並討論雙曲平面上凸曲線的嵌入性與它的平均測地曲率之間的關系，其目的是為了將雙曲平面上曲線的性質與歐氏平面中曲線的性質作一些對比；最後，我們利用minkowski支撐函數構造了一類新的非圓的光滑常寬曲線，其目的是想回答有關常寬曲線的一些未解決問題（如是否存在非圓的多項式常寬曲線 -
Founding that the fr of the tortuous path flow had all changed in longitudinal ( along the circuit ), transverse ( between the sink and convex bank ) and vertical orientation ( from the water surface to the bottom )
結果發現，彎道水流f _ r數在縱向（沿流程） ，橫向（凹凸岸間）和垂向（水面到底板）都是變化的。 -
This report is composed of two main parts, one concerns some geometric inequalities about curves and an application of the minkowski ' s support function, the other deals with the perimeter - preserving flow of closed convex curves in the plane and an application of the curve shortening flow on surfaces
本文主要由兩個部分組成，第一部分涉及曲線的一些不等式以及minkowski支撐函數的一個應用；第二部分討論歐氏平面上閉凸曲線的保長度流和曲面上曲線縮短流的一個應用。
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