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.

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

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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.

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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)偷拍日韩无码一区，可分為三部分：第一部分運(yùn)用極值原理亚洲欧美中文无修、上下解方法和錐映射不動點(diǎn)指標(biāo)理論得到正平衡解存在的充分條件；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)男女av网站有那些，并討論了局部分歧解的穩(wěn)定性怎么能看aAA片；第三部分利用特征值擾動理論、標(biāo)準(zhǔn)橢圓正則化理論又紧又爽视频、Sobolev嵌入定理及指標(biāo)理論討論了正平衡解的多重性国产操屄、唯一性及穩(wěn)定性，并討論了參數(shù)對解的影響亚洲美女偷拍视频。

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.

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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...

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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.

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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.

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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.

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