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Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 891-901页

作者： yi-hong XU Department of Mathematics School of SciencesNanchang UniversityNanchang 330031China

A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin *** generalized pseudoconvex set-valued functions are *** both the objective function and constraint function are M-derivative,under the assumption of near conesubconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization *** the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.

关键词： strict efficiency near cone-subconvexlikeness set-valued optimization cone

Crust and upper mantle structure in east China and sea areas

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Acta Seismologica Sinica(English Edition) 2001年第5期14卷 503-511页

作者： LI hong-yi 1. Institute of Crustal Dynamics China Seismological Bureau 100085 Beijing China 2. Institute of Geology and Geophysics Chinese Academy of Sciences 100101 Beijing China

Eastern China and vicinal sea areas (98°-150°E, 5°-50°N) are located in the junction zone of Eurasian and Pacific plates, and it is also profoundly influenced by the collision between Indian and Eurasian plates. We utilized surface wave data recorded by 35 digital seismic stations in the area, extracted dispersion curves of fundamental-mode Rayleigh waves along 1252 paths by means of time-frequency analysis based on multiple-filter and other techniques. The study area was divided into a grid of 1°×1°, group velocity distributions of fundamental Rayleigh waves between 10-158 s were determined by Occam's inversion. These velocity distributions roughly depict the lateral variations of shear wave velocities in different depth ranges. With the determined pure path dispersions we further inverted for the S wave velocity structures along two profiles from eastern Tibet to Pacific Ocean and from South China Sea to Mongolia. It is found that the lateral heterogeneity is obvious to 400 km depth, and the velocity structures are correlated with tectonic units in the study area.

关键词： Rayleigh wave group velocity inversion crust-upper mantle velocity structure

On Diagonal P-Representation of Superposition Field of Two Light Modes

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Communications in Theoretical Physics 2006年第5X期45卷 845-848页

作者： FAN hong-yi Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

For the superposition field a^＋1＋aA^＋2 of two light modes we introduce an appropriate diagonal P-representation which is constructed on the common eigenvectors ｜z,x 〉 of （X1 -X2） and al ＋ a2, where Xi = （ai ＋ a^＋i） /√2, [ai, a^＋i] = δij. It is remarkable that ｜z, x〉make up a new quantum mechanical representation.

关键词： superposition fields diagonal P-representation coherent-entangled state representation

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Weyl-Ordered Operator Moyal Bracket by Virtue of Method of Integral Within an Weyl Ordered Product of Operators

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Communications in Theoretical Physics 2006年第2期45卷 245-248页

作者： FAN hong-yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

The Moyal bracket is an exemplification of Weyl＇s correspondence to formulate quantum mechancis in terms of Wigner function. Here we present a formalism of Weyl-ordered operator Moyal bracket by virtue of the method... 详细信息

关键词： Weyl ordering Weyl-ordered operator Moyal bracket IWWOP method

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

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Communications in Theoretical Physics 2008年第10期50卷 935-937页

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation t... 详细信息

关键词： new two-fold integration transform phase space Weyl ordering of operators

A New Differential Formula About Product of Polynomials and Its Application in Multi-electron State Physics

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Communications in Theoretical Physics 2006年第3X期46卷 419-422页

We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representatio... 详细信息

关键词： new differential formula product of polynomials multi-electron state

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

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Communications in Theoretical Physics 2008年第11期50卷 1089-1092页

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl orderedproduct of operators,i.e.,the Weyl correspondence rule can be reconstructed by classical functions' Fourier transfor-mation followed by an inverse Fourier transformation within Weyl ordering of *** an application of thisreconstruction,we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.

关键词： Weyl quantization Weyl ordering of operators angular spectrum of spherical wave

Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

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Communications in Theoretical Physics 2002年第5期38卷 533-536页

作者： FAN hong-yi Department of Physics Shanghai Jiao Tong UniversityShanghai 200030China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

关键词： Wigner function, ensemble average of density operator, matrix element in entangled pure states

“Angle” Operator Conjugate to Photon’s Intrinsic Angular Momentum

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Chinese Physics Letters 2001年第7期18卷 857-859页

作者： FAN hong-yi Department of Applied Physics Shanghai Jiao Tong UniversityShanghai 200030 Department of Material Science and Engineering University of Science and Technology of ChinaHefei 230026

We find the correct“angle”operator conjugate to the intrinsic angular momentum of tne photon by introducing a suitable representation which involves both left-handed and right-handed polarization photon operators.

关键词： conjugate Conjugate momentum