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Closed Strong Spacelike Curves, Fenchel theorem and Plateau Problem in the 3-Dimensional Minkowski Space

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Chinese Annals of Mathematics,Series B 2019年第2期40卷 217-226页

作者： Nan YE Xiang MA College of Mathematics and Econometrics Hunan University LMAM School of Mathematical Sciences Peking University

The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacelike condition means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve γ under consideration. The assumption of index 1 is equivalent to saying that γ winds around some timelike axis with winding number 1. This reversed Fenchel-type inequality is proved by constructing a ruled spacelike surface with the given curve as boundary and applying the Gauss-Bonnet formula. As a by-product, this shows the existence of a maximal surface with γ as the boundary.

关键词： Fenchel theorem Spacelike curves Total curvature Maximal surface

Generalization of the optical theorem: experimental proof for radially polarized beams

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Light(Science & Applications) 2018年第1期7卷 708-717页

作者： Alexey V.Krasavin Paulina Segovia Rostyslav Dubrovka Nicolas Olivier Gregory A.Wurtz Pavel Ginzburg Anatoly V.Zayats Department of Physics King’s College LondonStrandLondon WC2R 2LSUK Department of Electronic Engineering Queen Mary University of LondonLondonUK School of Electrical Engineering Tel Aviv UniversityRamat AvivTel Aviv 69978Israel ITMO University St.Petersburg 197101Russia Departamento de Optica CICESECarretera Ensenada-Tijuana 391822860 EnsenadaMexico Laboratory for Optics&Biosciences Ecole PolytechniqueCNRS UMR 7645F-91128 PalaiseauFrance Department of Physics University of North FloridaJacksonville FL 32224USA

The optical theorem,which is a consequence of the energy conservation in scattering processes,directly relates the forward scattering amplitude to the extinction cross-section of the *** derived for planar scalar waves,it neglects the complex structure of the focused beams and the vectorial nature of the electromagnetic *** the other hand,radially or azimuthally polarized fields and various vortex beams,essential in modern photonic technologies,possess a prominent vectorial field ***,we experimentally demonstrate a complete violation of the commonly used form of the optical theorem for radially polarized beams at both visible and microwave *** show that a plasmonic particle illuminated by such a beam exhibits strong extinction,while the scattering in the forward direction is *** generalized formulation of the optical theorem provides agreement with the observed *** reported effect is vital for the understanding and design of the interaction of complex vector beams carrying longitudinal field components with subwavelength objects important in imaging,communications,nanoparticle manipulation,and detection,as well as metrology.

关键词： structure. field. theorem

Contact-pair neighborhood theorem for submanifolds in symplectic pairs

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Frontiers of Mathematics in China 2019年第4期14卷 781-791页

作者： Hai-Long HER Department of Mathematics Jinan University Guangzhou 510632 China

Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q ■M be a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α,β) on Q, which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of β and α, respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.

关键词： Symplectic pair neighborhood theorem contact pair Liouville vector field

LIOUVILLE TYPE theorem FOR THE STATIONARY EQUATIONS OF MAGNETO-HYDRODYNAMICS

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Acta Mathematica Scientia 2019年第2期39卷 491-497页

作者： Simon SCHULZ Mathematical Institute University of Oxford

We show that any smooth solution(u, H) to the stationary equations of magnetohydrodynamics belonging to both spaces L^6(R^3) and BMO^(-1)(R^3) must be identically *** is an extension of previous results, all of which systematically required stronger integrability and the additional assumption ▽u, ▽H∈L^2(R^3), i.e., finite Dirichlet integral.

关键词： Liouville theorem Caccioppoli inequality Navier-Stokes equations MHD

Growth theorem of convex mappings on bounded convex circular domains

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Science China Mathematics 1998年第2期41卷 123-130页

作者：刘太顺任广斌 Department of Mathematics University of Science and Technology of China Hefei China

The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex.

关键词： convex mappings growth and covering theorem convex circular domains.

A mathematical aspect of Hohenberg-Kohn theorem

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Science China Mathematics 2019年第1期62卷 63-68页

作者： Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become the most popular and powerful computational approach to study the electronic structure of *** this article, we study t... 详细信息

关键词： density functional theory electronic structure unique continuation principle Hohenberg-Kohn theorem

On Linnik's almost Goldbach theorem

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Science China Mathematics 1999年第11期42卷 1155-1172页

作者：王天泽 Department of Mathematics Henan University Kaifeng China

It is proved that every sufficiently large even integer can be represented as a sum of two primes and at most 2250 powers of 2.

关键词： almost Goldbach theorem m-twin problem mean value estimate.

On Weyl’s theorem for Functions of Operators

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Acta Mathematica Sinica,English Series 2019年第8期35卷 1367-1376页

作者： Jiong DONG Xiao Hong CAO Lei DAI School of Mathematics and Information Science Shaanxi Normal University Xi'an 710119 P. R. China College of Mathematics and Physics Weinan Normal University Weinan 714000 P. R. China

Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).

关键词： Spectrum Weyl's theorem functions of operators compact perturbation

Generalized Noether theorem and Poincaré-Cartan Integral Invariant for Singular High-order Lagrangian in Fields Theories

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Science China Mathematics 1993年第10期36卷 1212-1225页

作者：李子平 CCAST (World Laboratory) P. O. Box 8730 Beijing 100080 Department of Applied Physics Beijing Polytechnic University Beijing 100022 PRC

A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identities (GNI)) for variant system under the infinite continuous group of field theory in canonical formalism are derived. The strong and weak conservation laws in canonical formalism are also obtained. It is pointed out that some variant systems also have Dirac constraint. Based on the canonical action, the generalized Poincaré-Cartan integral invariant (GPCⅡ) for singular high-order Lagrangian in the field theory is deduced. Some confusions in literafure are clarified. The GPCⅡ connected with canonical equations and canonical transformation are discussed.

关键词： Noether theorem Poincare-Cartan integral invariant high-order derivatives theories in field theories Dirac’s theory of constrained system.