The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.

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After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods,the quantum theory of scalar and spinor fields, and then of gauge fields,is developed The emphasis throughout is on functional methods,which have played a large part in modern field theory.

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Thirdly, based on the φ-mapping theory the topological field theory of various topological structures in two-and three-component spinor Bose-Einstein condensates is established.

第三，本文應(yīng)用Φ-映射理論建立了兩分量和三分量旋量玻色-愛(ài)因斯坦凝聚體中包含多種拓?fù)浣Y(jié)構(gòu)的拓?fù)鋱?chǎng)論2021一级A片免费视频。

Bipartite matching is adopted to adjust the relations between the constraint equations and variables, and then the matching result is mapped to a data structure named Engineering Constraint Graph. A solving sequence is achieved by topology sort and strong connected component condensation of ECG.

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It is revealed that in the condensates, the different configurations of order parameters lead to different topological structures-velocity field vortex lines, Mermin-Ho vortex lines and monopoles, and these three topological structures can all be characterized by the Hopf indices and Brouwer degrees of φ-mapping, and their locations and motions also be rigorously determined by φ-mapping theory.

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In this thesis we study largely two problems in the context of the φ-mapping topological current theory proposed by Prof. Yishi Duan, ranging from inner structure of homotopy in algebraic topology to topological excitations in the atomic Bose-Einstein condensates.

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We find that these two kinds of excitations are generated from the zero points of the different vector order parameter fields defined in terms of the Néel vector 〓.

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coherent stack：凝聚層

coherent sheaf 凝聚層 | coherent stack 凝聚層 | coherent topology 凝聚拓撲

coherent topology：凝聚拓?fù)?/p>

coherent stack 凝聚層 | coherent topology 凝聚拓撲 | coherently oriented simplex 協(xié)同定向單形

coherently oriented simplex：協(xié)同定向單形

coherent topology 凝聚拓撲 | coherently oriented simplex 協(xié)同定向單形 | cohomological dimension 上同憚數(shù)

Topological degree of condensing mapping：凝聚場(chǎng)的拓?fù)涠?/p>

拓?fù)潢P(guān)系自動(dòng)建立:Auto-Build Topological Relations | 凝聚場(chǎng)的拓?fù)涠?Topological degree of condensing mapping | 電荷密度拓?fù)浞治?topological analysis of charge density

physical entanglement：物理纏結(jié)

凝聚纏結(jié) cohesional entanglement | 物理纏結(jié) physical entanglement | 拓?fù)淅p結(jié) topological entanglement

topological entanglement：拓?fù)淅p結(jié)

物理纏結(jié) physical entanglement | 拓?fù)淅p結(jié) topological entanglement | 凝聚相 condensed phase

Fixed point theorem of condensing mapping：凝聚映射的不動(dòng)點(diǎn)定理

自縮合乙烯基聚合:self-condensing vinyl polymerization | 凝聚映射的不動(dòng)點(diǎn)定理:Fixed point theorem of condensing mapping | 凝聚場(chǎng)的拓?fù)涠?Topological degree of condensing mapping

coherently scattering region：相干散射區(qū)

coherent | 粘在一起的, 一致的, 連貫的 | coherently scattering region | 相干散射區(qū) | coherenttopology | 凝聚拓撲