The proof relies on regular approximation, the fixed point theorem, the embedding theorems, the semigroup theory and a series of complicated estimates.

然后，利用此結(jié)果国产131在线视频免费观看，通過區(qū)域正則化逼近及半群理論獲得各種估計久久铯综合网，并給出了非齊次Liouville-Poisson模型的整體古典解。

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圖的可定向曲面嵌入性質(zhì)国产男女另类裸交一级黄片，通過運用Petersen關(guān)于1-因子的定理久久国产精品免费专区A片，首先證明了對于可定向曲面上的三角剖分圖，其幾何對偶圖具有1-因子九色最新地址；然后在1-因子的導(dǎo)向下可以进的黄网站，通過做一系列增加虧格的手術(shù)，證明了如果一個圖G三角剖分可定向曲面S_g自拍高潮日韩在线视频播放，那么G可以近三角剖分可定向曲面S_h，這里h=g黑鬼操亚洲人，g+1性交一级视频网站，…，「β(G／2」免费在线观看黄的网站，β是指圖G的Betti數(shù)大又大粗又爽又黄w网站，從而得出推論：可定向曲面上的三角剖分圖是上可嵌入的，作為推廣人人人人人人妇人人人干，又研究了一類近四角剖分圖的可定向曲面嵌入性質(zhì)操人人操人人爽爽爽操操操，并得到類似的結(jié)論。

With the help of the Mountain-Pass Theorem lacking Palais-Smale compactness condition (PSc condition and by adoption of the best attained function of Sobolev embedding, the paper proves the existence of nontrivial solutions of two classes of critical biharmonic equations on boundary conditions by overcoming serial difficulties caused by loss of compactness due to Sobolev embedding.

本文借助于沒有 PS 條件的翻山引理久久人人操人人干，并利用 Sobolev 嵌入的最佳達到函數(shù)免费又黄又裸乳的视频网站，克服了由于 Sobolev 嵌入失緊性而帶來的系列困難，證明了含臨界增長的兩類雙調(diào)和方程邊值問題非平凡解的存在性在线欧美日韩视频。

Based on the research work of basic theories including phase space reconstruction,embedding theorem,correlation dimension,local dynamics,Lyapunov exponents,surrogate data etc,based on the research work of general methods such as principal component analysis,correlation dimension GP algorithm,false neighbors method,nonlinear time series prediction,local prediction, adaptive prediction,neural network model,support vector machines regression model, prediction power,nonlinear detection,coarse-graining methodology,conditional entropy and so on,the framework of nonlinear time series analysis are constructed.

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Time series prediction is a very important problem in many applications and the current prediction techniques are nearly all based on the Takens' embedding theorem. Many realistic systems are parameter-varying systems, and the embedding theorems are invalid, predicting the behavior of parameter-varying systems is more difficult.

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For the homoclinics taking on values in the unbounded domain, in order to apply the usual "Mountain Pass " theorem, A compact embedding theorem is proved.

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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.

本文主要有兩章內(nèi)容：第一章研究了該模型正平衡解的性質(zhì)久色入口，可分為三部分：第一部分運用極值原理、上下解方法和錐映射不動點指標(biāo)理論得到正平衡解存在的充分條件色综合精品；第二部分利用分歧理論給出了平衡態(tài)系統(tǒng)正分歧解的結(jié)構(gòu)日韩在线精品福利网页观看视频，并討論了局部分歧解的穩(wěn)定性；第三部分利用特征值擾動理論免费网站9999、標(biāo)準(zhǔn)橢圓正則化理論国产日韩久久综合影院AV、Sobolev嵌入定理及指標(biāo)理論討論了正平衡解的多重性、唯一性及穩(wěn)定性人人爱人人上人人操台湾，并討論了參數(shù)對解的影響日韩午夜一区二区福利影院。

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.

本文給出了幾個關(guān)于一般可定向曲面上嵌入圖的唯一性定理。結(jié)果表明：一些具有大的面跡的可定向嵌入仍然具有唯一性人人人人看人人人人操。這在本質(zhì)上推廣了C.Thomassen在LEW-嵌入方面的工作国产成人高清亚洲影院在线观看。