嵌入定理

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

In differentiable manifolds, one studies for instance differentiable structure, definition of differential manifolds, diffeomorphism, tangent space, Embedding theorem, partitions of unity etc.

微分流形部分主要涉及微分结构，微分流形的定义及例子，可微映射，微分同胚，切空间与余切空间，流形的嵌入，单位分解定理等。

But, by semantic embedding the theorem derivations in object logic usually descends to ones in base logic, which not only requires users know the encoding quite well, but also lower the abstraction level of object logic, and readability and hand-reexecutability of proofs.

但是，语义嵌入方式下目标逻辑定理推导常常向基逻辑下降，这不但要求用户了解编码细节，而且也大大降低了目标逻辑的抽象性以及PVS一向追求的证明可读性和手工可再现性。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

We establish the estimates of positive solutions to a strongly coupled ecological systems in L∞0,T;H1(Ω by energy methods and using Sobolev imbedding theorem and interpolation.

运用能量方法，通过采用嵌入定理、内插不等式建立了非线性强耦合生态系统正解的L∞0，T；H

Then,by using the algebraic method which was introduced by Yang L.and Zhang J.Z.,and the generalized isometric embedding theory,the generalized concept of metric addition is brought forward,a geometric inequality about the generalized metric addition is given,and the main result of Ya...

然后利用杨路和张景中引进的代数方法，应用广义等距嵌入定理，提出了关于两组两个完全同向的n维单形"广义度量加"的概念，并且证明了涉及"广义度量加"的一个几何不等式，它推广了杨路和张景中关于Alexander猜想的结果。

The main aim of this thesis is to study the properties of the maps for Heisenberg group target, which include Lipschitz and Holder continuity, L~#,H~(n , W~(1,p)#,H~(n , BMO and John-Nirenberg estimates, embedded theorems, Poincare inequalities and reverse Poincare inequalities, the regul-arities about the minimizers.

本文的主要目的是系统研究靶流形为Heisenberg群的函数及其空间的性质，其中包括Lipschitz及Hlder连续性、空间L~p及W~(1，p)的性质、空间BMO的性质及其上的John-Nirenberg估计、嵌入定理、Poincare不等式和逆Poincare不等式、能量极小映射的存在性、正则性及用调和函数逼近能量极小映射等问题。

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

We establish several unique embedding results for 3-connected graphs on orientable surfaces which admit relatively large facial walks and representativity and hence generalize Thomassen's uniqueness theorem on LEW-embeddings.

本文给出了几个关于一般可定向曲面上嵌入图的唯一性定理。结果表明：一些具有大的面迹的可定向嵌入仍然具有唯一性。这在本质上推广了C.Thomassen在LEW-嵌入方面的工作。

In this algorithm, the product of two huge primes is the secret information, which is further converted into n natural numbers and then encoded into planted plane cubic tree structures which are embedded into the software codes as software watermark.

水印嵌入的入程是：首先将两个大质数的乘积采取中国剩余定理划分成n个天然数，然后再将这n个天然数编码入n个平面环路树PPCT构造中，将这些构造的构建代码嵌入软件代码中。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。