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ON THE SOLUTION OF NONLINEARTWOPOINT BOUNDARY VALUE PROBLEM──u" + g(t.u) = f(t),u(0) = u(2π) = 0

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Applied Mathematics and Mechanics(English Edition) 1998年第9期19卷 889-894页

作者：黄文华曹菊生沈祖和 Wuxi Univ of Light Industry Wuxi China

In this paper, a non-variational version of a max-min principle is proposed, andan existence and uniqueness result is obtained for the nonlinear two-point boundaryvalue problenl u' + g(t.u) = f(t),u(0) = u(2π) = 0

关键词： Hilbert space diffeomorphism nonlinear two-point boundaryvalue problem unique solution

Finite Determinacy of High Codimension Smooth Function Germs

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Applied Mathematics(A Journal of Chinese Universities) 2019年第1期34卷 92-99页

作者： GAN Wen-liang PEI Dong-he LI Qiang GAO Rui-mei School of Mathematics and Statistics Northeast Normal University School of Mathematics and Statistics Guizhou University of Finance and Economics School of Science Qiqihar University Department of Science Changchun University of Science and Technology

Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.

关键词： function germ Jacobian ideal diffeomorphism right equivalence

Vacuum Black Hole Mass Formula Is a Vanishing Noether Charge

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Communications in Theoretical Physics 2002年第3期38卷 309-312页

作者： WU Xiao-Ning GUO Han-Ying HUANG Chao-Guang WU Ke Institute of Theoretical Physics the Chinese Academy of Sciences P.O. Box 2735 Beijing 100080 China Institute of Theoretical Physics the Chinese Academy of Sciences P.O. Box 2735 Beijing 100080 China Institute of High Energy Physics the Chinese Academy of Sciences P.O. Box 9184 Beijing 100039 China Institute of Theoretical Physics the Chinese Academy of Sciences P.O. Box 2735 Beijing 100080 China Institute of Theoretical Physics the Chinese Academy of Sciences P.O. Box 2735 Beijing 100080 China Departrnent of Mathematics Capital Normal University Beijing 100037 China

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.

关键词： black hole, mass formula, Noether charge, diffeomorphism invariance

Existence of Invariant Tori in Reversible Mappings

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Acta Mathematica Sinica,English Series 2019年第9期35卷 1419-1452页

作者： Sheng Qing HU School of Mathematical Sciences Peking University

In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently clos... 详细信息

关键词： Reversible diffeomorphism invariant tori non-degeneracy conditions KAM method

Geometric Structures of Stable Time-Variant State Feedback Systems

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Journal of Beijing Institute of Technology 2007年第4期16卷 500-504页

作者：仲锋惟孙华飞张真宁 School of Science Beijing Institute of Technology

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.

关键词： geometric structure state feedback immersion diffeomorphism

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ON A MIN-MAX THEOREM

Applied Mathematics(A Journal of Chinese Universities) 1997年第3期12卷 293-298页

作者： WUGUANGRONG HUANGWENHUA SHENZUHE DepartmentofMathematics NanjingUniversityNanjing210093. WuxiUniversityoflightindustry wuxi214036 DepartmentofMathematics NanjingUniversityNanjing210093

In this paper we prove a nonvariational form of a rain-max problem in [l] and give its application to a periodical problem.

关键词： Min-max diffeomorphism solution

FREDHOLM AND COMPACT MAPPINGS SHARING A VALUE

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Applied Mathematics and Mechanics(English Edition) 2001年第6期22卷 682-686页

作者： J.M.Soriano Departmento de Anlisis Matemtico

Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.

关键词： zero point continuation methods C 1 homotopy surjective implicit function theorem compact mapping Fredholm mapping index zero injective diffeomorphism

On the Approaching Domain Obtained by Finite Element Method

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Northeastern Mathematical Journal 2002年第3期18卷 273-282页

作者：邹青松李永海 AcademyofMathemasticsandSystemsSciences ChineseAcademyofSciencesBeijing100080 SchoolofMathematics JilinUniversityChangchun130012

The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the a... 详细信息

关键词： nonconforming isoparametric finite element method approaching do-main diffeomorphism

Reconsidering “Does the Sum Rule Hold at the Big Bang?” with Pre Planckian HUP, and Division Algebras

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Journal of High Energy Physics, Gravitation and Cosmology 2017年第4期3卷 539-557页

作者： Andrew W. Beckwith Physics Department College of Physics Chongqing University Chongqing China

In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.

关键词： Quantum Measures Spatial diffeomorphism Cylinder Sets Caratheodary-Hahn-Huvanek Theorem Big Bang Singularity Causal Sets Modified Pre Planckian Heisenberg Uncertainty Principle HUP Division Algebras