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Maslov P-Index Theory for a Symplectic Path with Applications

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 441-458页

作者： Chungen LIU School of Mathematics and lpmc Nankai University Tianjin 300071 China.

The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an appli... 详细信息

关键词： Hamiltonian system Symplectic path Maslov P-index Non-periodicboundary problem

Fredholm theory for pseudoholomorphic curves with brake symmetry

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Frontiers of Mathematics in China 2022年第6期17卷 1201-1234页

作者： Beijia ZHOU Chaofeng ZHU Chern Institute of Mathematics Nankai University and LPMCTianjin300071China

We study the pseudoholomorphic curves with brake symmetry in symplectization of a closed contact *** introduce the pseudoholomorphic curves with brake symmetry and the corresponding moduli *** we get the virtual dimen... 详细信息

关键词： Pseudoholomorphic curve brake symmetry moduli space virtual dimension

L(Ω,μ) CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES OF AM-SPACES

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Acta Mathematica Scientia 2007年第2期27卷 225-231页

作者：定光桂 School of Mathematical Sciences Shren Institute of Mathematics and lpmc Nankai University

This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd *** mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particular, there does not... 详细信息

关键词： Isometric mapping odd and subtractive mapping AM-space

Two New Families in the Stable Homotopy Groups of Sphere and Moore Spectrum

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Chinese Annals of Mathematics,Series B 2006年第3期27卷 311-328页

作者： Jinkun LIN College of Mathematical Science and lpmc Nankai University Tianjin 300071 China

This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq ＋ p^mq ＋ q - 3 which are represented by h0（hmbn-1 - hnbm-1） and ie（hohnhm） in the E2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m ＋ 2 ≥ 4, q = 2（p - 1）.

关键词： Stable homotopy groups of spheres Adams spectral sequence Toda spectrum

DISPOSING THE LEFTOVERS UNDER THE CONSIGNMENT CONTRACT WITH REVENUE SHARING:RETAILER VS SUPPLIER

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Journal of Systems Science & Complexity 2012年第2期25卷 262-274页

作者： Wei HU Jianbin LI School of Mathematical Sciences and lpmc Nankai University School of Management Huazhong University of Science and Technology

This paper studies the consignment contract with revenue sharing where the retailer offers two revenue share schemes between himself and his supplier from the viewpoint of inventory ownership: One is that the retailer takes charge of the unsold items,the other one is that the retailer returns the unsold items to the supplier at the end of the selling period,and the supplier disposes those *** each contract,the retailer deducts a percentage from the selling price for each sold item and transfers the balance to the *** supplier solves a two-stage problem:She first chooses contract,then decides retail price and delivery quantity according to the terms of the contract *** an iso-price-elastic demand model,the authors derive the retailer and suppliers’ optimal decisions for both *** addition,the authors characterize how they are affected by disposing *** authors compare the decisions between the two schemes for disposing cost turn out to be holding cost or salvage value,*** authors use numerical examples to show the supplier’s first-stage optimal decision depends critically on demand price elasticity,the disposing cost and the retailer’s share for channel cost.

关键词： Consignment sales revenue sharing stackelberg game supply chain management.

Detection of Some Elements in the Stable Homotopy Groups of Spheres

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Chinese Annals of Mathematics,Series B 2008年第3期29卷 291-316页

作者： Xiugui LIU School of Mathematical Sciences and lpmc Nankai University Tianjin 300071 China

Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.

关键词： Stable homotopy groups of spheres Adams spectral sequence Mayspectral sequence Steenrod algebra

A mod 2 index theorem for pin-manifolds

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Science China Mathematics 2017年第9期60卷 1615-1632页

作者： ZHANG WeiPing Chern Institute of Mathematics&lpmc Nankai UniversityTianjin 300071China

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer(1971)to non-orientable manifolds.

关键词： pin manifolds rood 2 index ^-invariant

Existence of multiple solutions for quasi-linear degenerate elliptic equations

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Science China Mathematics 2022年第5期65卷 971-992页

作者： Yawei Wei School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China

The present paper is concerned with a class of quasi-linear degenerate elliptic *** degenerate operator arises from analysis of manifolds with *** variational methods are applied here to verify the existence of infini... 详细信息

关键词： quasi-linear degenerate operator weighted Sobolev spaces variational method

Geometric simplicity of spectral radius of nonnegative irreducible tensors

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Frontiers of Mathematics in China 2013年第1期8卷 129-140页

作者： Yuning YANG Qingzhi YANG School of Mathematical Sciences and lpmc Nankai University Tianjin 300071 China

We study irreducible tensors. the real and complex geometric simplicity of nonnegative First, we prove some basic conclusions. Based on the conclusions, the real geometric simplicity of the spectral radius of an even- order nonnegative irreducible tensor is proved. For an odd-order nonnegative irreducible tensor, sufficient conditions are investigated to ensure the spectral radius to be real geometrically simple. Furthermore, the complex geometric simplicity of nonnegative irreducible tensors is also studied.

关键词： Nonnegative irreducible tensor Perron-Frobenius theorem,geometrically simple