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differentiable

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differentiable adj.1.可鑒別的。2.【數學】可微分的。n.-bil...

adj. 1.可鑒別的。 2.【數學】可微分的。 n. -bility “bicontinuously differentiable“ 中文翻譯：   雙連續可微“continuously differentiable“ 中文翻譯：   連續可微的“differentiable atlas“ 中文翻譯：   可微圖“differentiable coordinates“ 中文翻譯：   可微分坐標“differentiable function“ 中文翻譯：   可微分函數; 可微函數“differentiable functional“ 中文翻譯：   可微分泛函“differentiable group“ 中文翻譯：   可微分群“differentiable homeomorphism“ 中文翻譯：   微分同胚“differentiable immersion“ 中文翻譯：   微分浸入“differentiable manifold“ 中文翻譯：   光滑流形; 可微分流形; 可微流形; 微分流形“differentiable manifolds“ 中文翻譯：   微分流行“differenzierbar differentiable“ 中文翻譯：   可微的“non differentiable“ 中文翻譯：   不可微的“non-differentiable“ 中文翻譯：   不可微分的“partially differentiable“ 中文翻譯：   可偏微的“termwise differentiable“ 中文翻譯：   逐項可微的“totally differentiable“ 中文翻譯：   完全可微分的“continuously differentiable function“ 中文翻譯：   連續可微分函數; 連續可微函數“continuously-differentiable function“ 中文翻譯：   連續可微函數“covering differentiable manifold“ 中文翻譯：   覆蓋微分流形“differentiable manifold of class c“ 中文翻譯：   c類微分廖“differentiable random function“ 中文翻譯：   可微隨機函數“doubly differentiable function“ 中文翻譯：   二階可微函數“frechet differentiable function“ 中文翻譯：   弗萊謝可微函數“differentiabilityofapointwisesupremum“ 中文翻譯：   點態上確界的可微性“differentiability property“ 中文翻譯：   可微性性質

differential

Nonlinear operator theorem is now a focus in nonlinear theorem . the study of the ergodic theory for semitopologocal semigroups of nonlinear operators began in the middle of 1970 ' s . it got great development because it was widely used in many problems , such as the numerical solution of differentiable equation , the existence theory of positive solution , contral theory and optimization 非線性算子理論是非線性理論中的熱門話題，它的研究始于上世紀七十年代中期，由于它被廣泛的應用于微分方程的數值解、正解的存在性理論、控制論以及最優化等問題中，因而得到了很大的發展。

To circumvent the non - differentiable difficulty caused by the positive homogeneously function that is involved in an equivalent unconstrained formulation for general inequality constrained optimization problems , we turn to the classical lagrangian function and redefine m ( x ) by a conic optimization problem with the lagrangian as the objective function 為了克服不可微正齊次函數( ? | r _ - ~ m )給約束優化問題的等價無約束形式求解帶來的困難，我們將其目標函數m ( x )重新用一個以經典拉格朗日函數為目標的錐優化問題來表示。

Because this method is a non - linear , non - differentiable and combinatorial - constrained optimization problem , mathematical optimal approaches are not suitable for solving this problem . the genetic algorithm based on natural selection and natural gene mechanism is presented in this paper . it simulates the network structure optimization by simple encoding technique and propagating mechanism 然后，再在本文提出的目標函數(最小化停電區域、最小化開關操作數量、最優化母線電壓降、最優化饋線電流和最優化變壓器負荷)的基礎上，得到整個配電網絡的故障后重構方案。

Furthermore , when replacing the entropy function by a general separate multiplier function , we develop a new regularization approach , referred to as lagrangian regularization approach . this approach does not only provide a unified smoothing technique for the non - differentiable m ( x ) and but also offers a unified framework for constructing penalty functions , whereby building a bridge between the penalty functions and the classical lagrangian 該方法不僅提供了統一光滑不可微函數m ( x )和( ? | r _ - ~ m )的辦法，而且還給出了一種構造罰函數的統一框架，由此將罰函數與經典拉格朗日函數從對偶空間的角度聯系在一起。

Having developed for half an century , the conventional optimization algorithms which are based on the operational research theory and some mathematical programming tools come into mature . such algorithms have been widely used in many fields due to their high efficiency and robustness . however , they usually require the optimized functions to be continuous even high order differentiable 這些在運籌學( operationalresearch )和數學規劃工具( mathematicalprogramming )基礎上形成的最優化算法，具有理論完備、算法效率高、穩定性好等優點，因而在許多需要進行優化計算的場合被廣泛的使用。

Let f ( x ) and f ( x ) stand for the generalized gradients proposed by clarke and xu yihong respectively . three of generalized gradients are compared and the inclusion relation between them is so the set of the generalized gradient defined in this paper is smaller ; they coincide when / is a convex function or f is differentiable 文中對三類廣義梯度進行比較，若以和分別表示clarke和徐義紅定義的廣義梯度，三者之間的包含關系為即本文定義的廣義梯度集合較小；而當f為凸函數或f可微時，三者統一。

We extend this result which is similar to ones of hirsch [ 1l ] and jiang [ 2 ] for 3 - dimensional cooperative system . furthermore , in the paper we discusse the cone of km , and obtain the similar result : theorem b : let f be a continuously differentiable cooperative vector field on d , suppose the following conditions hold : ( a ) d is pm - convex ; ( b ) every forward semi - orbit has compact closure in d ; ( c ) there is not more than one equilibrium p , then there is a unique equilibrium p and it is globally asymptotically stable 此外，本文還將在k _ m錐下討論此問題，并得到平行的結果：定理b ：設f是d上一個連續可微的合作向量場，假設如下條件成立： ( a ) d是p _ m凸的； ( b ) d中的每一個正半軌道有緊閉包； ( c )至多有一個平衡點p ，則一定存在唯一的平衡點p ，并且是全局漸近穩定的。

Because ga possesses the traits of can global random search , the robustness is strong , been use briefly and broadly , it didn ’ t use path search , and use probability search , didn ’ t care inherence rule of problem itself , can search the global optimum points effectively and rapidly in great vector space of complicated , many peak values , cannot differentiable . so it can offset the shortages of nn study algorithm , can reduce the possibility that the minimum value get into local greatly , the speed of convergence can improve , interpolation time shorten greatly , the quantity of training reduce 因為遺傳算法具有全局隨機搜索能力,魯棒性強、使用簡單和廣泛的特點,它不采用路徑搜索,而采用概率搜索,不用關心問題本身的內在規律,能夠在復雜的、多峰值的、不可微的大矢量空間中迅速有效地尋找到全局最優解,所以可以彌補神經網絡學習算法的不足,使陷入局部最小值的可能性大大減少,使得收斂速度提高,訓練量減小。

This paper discusses a variation equation problem in a class of singular stochastic control with stopping time , gives its solution under two different conditions , which is a one order continuous differentiable and concave function , and gives the exact form 摘要討論了一類帶停時的奇異型隨機控制問題中的一個變分方程問題，并且在兩種不同的情況下給出了該變分方程的解，即為一階連續可導凹函數，并在兩種情況下給出了此函數的具體形式。

As a powerful global optimization approach , genetic algorithms ( ga ) can solve a variety of optimization problems in which the objective function is discontinuous , non - differentiable , or highly non - linear , to produce high convergence speed and vast search space 摘要遺傳算法作為一種全局優化算法，可以用來解決在目標函數不連續、不可能、非線性等情況下的復雜問題，且具有較高的收斂效率和廣闊的搜索空間。

We studied the huston - kane method of multibody system theory by the means of differentiable geometry . and point out that huston - kane method can be fully imbedded into lagrange ' s mechanics . huston - kane method is only a transformat 10 、使用微分幾何理論研究了多體系統理論的huston kane方法，指出多體系統理論的huston kane方法完全可以嵌入到lagrange力學體系中，前者只是lagrangc動力學方程的變形。

A distinction of it is that the derivative condition is loosed . especially , we discuss the patch perturbations for a system that the function is only g - differentiable but not f - differentiable . this lays a foundation of discussing the optimal control problems for weak - smooth system 特別是首次對一類g -可微、但不為f -可微的系統的討論，為下一章研究弱光滑系統最優控制的最大值原理奠定了基礎。

It can speed the local rate of convergence and improve the accuracy of solution , and to solve nonlinear constraint optimization problems , coa was combined with exact non - differentiable penalty function 它利用混沌變量的特定內在隨機性和遍歷性跳出局部最優點，并在局部搜索空間經過線性搜索提高解的搜索速度和精度，通過結合精確不可微罰函數以用于求解非線性約束優化問題。

We give a brief but systematic introduction to differentiable geometry and lie group , lie algebra . rigid body motion expressed with the notations from these theories is also introduced . they are the theoretical bases of the subsequent research contents 2 、基本成體系地介紹了微分幾何中的李群、李代數理論，并分析其表達剛體運動的作用，為本文的研究打下基礎。

Using conception of relative rate of change , a definition of probability density function is given based on the class of differentiable monotone function which is bounded on domain of definition , calculation and properties of the mathematical expectation are discussed 摘要對一類單調可微的有界函數，利用相對變化率的概念，定義了一種由該函數生成的概率密度函數。

Continuity , integrability and differentiability of riemann function are discussed ; especially , the non - differentiable properties on [ 0 , 1 ] are proved , and dirichlet ' s function is comparated with it 摘要從黎曼函數的簡單特徵入手討論它的連續性、可積性、可導性，特別是證明了黎曼函數在區間[ 0 ， 1 ]上處處不可導，并結合狄利克雷函數加以引申和推廣。

In the paper , a special class of quasidifferentiable functions - subsuper differentiable functions is introduced , which satisfies the conditions of the existence of high dimensional kernels , and the formula of kernels is deduced 摘要引入了一個特殊的擬可微函數類一次超可微函數，證明了其滿足具有高維核的條件，并且推導出了高維核的計算公式。

In unconstrained optimization , we deal with the standard problem of finding the minimum of a function f : rn - r . if we assume that the function is twice continuously differentiable , many methods can be applied to find the minimum 在無約束最優化中，考慮尋找f ： r ~ n r的極小點。假設f是二次連續可微的，可以有許多方法尋找它的極小點。

We use b - spline smoothing technique to smooth the characteristic function without changing the integral quantity and get a differentiable weight function . the method considerably improves the quality of sampling points 我們用b樣條磨光技術在不改變積分值的前提下磨光特征函數，用可微的權重函數代替特征函數，提高了采樣的質量。