second variation formula 中文意思是什麼
second variation formula
解釋
第二變分公式-
The second part consist of chapter four. in chapter one, we study the energy density of harmonic map from finsler manifold and generalize classical result in [ se ]. in chapter two, we obtain lower estimates for the first eigenvalue of the laplace operator on a compact finsler manifold, and it generalize lichnerowicz - obata theorem [ li ] [ ob ]. in chapter three, we derive the first and second variation formula for harmonic maps between finsler manifolds. as an application, some nonexistence theorems of nonconstant stable harmonic maps from a finsler manifold to a riemannian manifold are given
第一章討論finsler流形到黎曼流形調和映射的能量密度的間隙性，推廣了[ se ]中的結果。第二章對緊致finsler流形上laplace運算元的第一特徵值的下界作了估計，推廣了黎曼流形上的lichnerowicz - obata定理[ li ] [ ob ] 。 -
In the 3rd section we introduce how to use mathematical model to study financial problems, whose assets running on mixed jump - diffusion process, first we get the famous non - linear feynman - kac formula by fbsde, then let the solution of the bsde be a investor ' s utility function, and it ' s the so - called recurse utility function. second, we can prove that this utility function is a continue viscosity solution of the variation inequality which we get above, and we get the comparison theory. third we can use the result to financial market to study the optimal consumption and portfolio problem or evaluate the american option
第三章介紹了利用金融資產價格運行基於復合跳躍? ?擴散過程的數理模型來研究金融經濟問題，通過結合運用正倒向隨機微分方程，推導得到著名的非線性feynman - - kac公式，並且將相應的倒向隨機微分方程的解記為投資者的值函數，這也就是通常所說的效用值函數；接著我們可以證明此效用值函數為某一偏微積分變差不等式的連續粘性解，並且得到了比較原則；這些結果可以應用到金融領域用於消費投資組合的選擇或是美式期權的估值。 -
One of open problems is to study harmonic maps between finsler manifolds and derive the first and second variation formula for harmonic maps between finsler manifolds. firstly, we define harmonic map between finsler manifold. in fact, it is the harmonic map from projective sphere bundle of source manifold to the projective sphere bundle of target manifold
運算元的第一非零特徵值凡全mk .特別地，當『 ，二二k時， m的直徑為六?當m是黎曼流形時，由moer 「定理的推論直接可知m與半徑為去的球等距
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