Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

Commutative Moufang Loops with Finite Conjugacy Classes of Subloops

It is proved that the following conditions are equivalent for an arbitrary commutative Moufang loop :1) the loop is finite over the center;2) every subloop of defines a finite conjugacy class of subloops;3) every associative subloop of defines a finite conjugacy class of subloops;4) every infinite associative subloop of defines a finite conjugacy class of subloops.     

The Dirac-Ramond operator on loops in flat space

In this paper, a rigorous construction of the S¹-equivariant Dirac operator (i.e., Dirac-Ramond operator) on the space of (mean zero) loops in is given and its equivariant L²-index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra.     

Holomorphic K-Theory, Algebraic Co-cycles, and Loop Groups

In this paper we study the holomorphic K-theory of a projective variety. This K-theory is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory is built out of studying algebraic bundles over a variety up to algebraic equivalence. In this paper we will give calculations of this theory for flag like varieties which include projective spaces, Grassmannians, flag manifolds, and more general homogeneous spaces, and also give a complete calculation for symmetric products of projective spaces. Using the algebraic geometric definition of the Chern character studied by the authors we will show that there is a rational isomorphism of graded rings between holomorphic K-theory and the appropriate morphic cohomology groups, in terms of algebraic co-cycles in the variety. In so doing we describe a geometric model for rational morphic cohomology groups in terms of the homotopy type of the space of algebraic maps from the variety to the symmetrized loop group U(n)/ _n where the symmetric group _n acts on U(n) via conjugation. This is equivalent to studying algebraic maps to the quotient of the infinite Grassmannians BU(k) by a similar symmetric group action. We then use the Chern character isomorphism to prove a conjecture of Friedlander and Walker stating that if one localizes holomorphic K-theory by inverting the Bott class, then rationally this is isomorphic to topological K-theory. Finally this will allows us to produce explicit obstructions to periodicity in holomorphic K-theory, and show that these obstructions vanish for generalized flag mani-folds.     

On the Evaluation of the Evolution Operator Z Reg( R 2, R 1) in the Diakonov–Petrov Approach to the Wilson Loop

We evaluate the evolution operator Z _Reg(R ₂,R ₁) introduced by Diakonov and Petrov for the definition of the Wilson loop in terms of a path integral over gauge degrees of freedom. We use the procedure suggested by Diakonov and Petrov (Physics Letters B 224 (1989) 131) and show that the evolution operator vanishes. PACS numbers: 11.10.-z; 11.15.-q; 12.38.-t; 12.38.Aw; 12.90.+b.     

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介绍了EAST托卡马克逆磁线圈加补偿线圈的逆磁测量。该方法的优点是补偿线圈有效地消除了纵场线圈产生的磁通变化,而调节机构能降低来自极向场的误差信号。详细地叙述了逆磁线圈工程设计中考虑的材料选择和结构设计对逆磁线圈的影响。最后给出了次测量系统的误差分析。     

气体火焰驻波演示实验的理论分析

对通过声场使可燃气体产生火焰驻波的波形进行研究,得出火焰驻波在波节处(固定反射端)出现火焰,在波腹处几乎不出现火焰的结论,理论分析与实验观测相符.     

Incidence properties of cosets in loops

We study incidence properties among cosets of infinite loops, with emphasis on well‐structured varieties such as antiautomorphic loops and Bol loops. While cosets in groups are either disjoint or identical, we find that the incidence structure in general loops can be much richer. Every symmetric design, for example, can be realized as a canonical collection of cosets of a infinite loop. We show that in the variety of antiautomorphic loops the poset formed by set inclusion among intersections of left cosets is isomorphic to that formed by right cosets. We present an algorithm that, given a infinite Bol loop S, can in some cases determine whether |S| divides |Q| for all infinite Bol loops Q with S?Q, and even whether there is a selection of left cosets of S that partitions Q. This method results in a positive confirmation of Lagrange's Theorem for Bol loops for a few new cases of subloops. Finally, we show that in a left automorphic Moufang loop Q (in particular, in a commutative Moufang loop Q), two left cosets of S?Qare either disjoint or they intersect in a set whose cardinality equals that of some subloop of S.     

偏振模色散对非线性光纤环镜微波光子开关的影响及其补偿

建立了考虑PMD在内的NOLM微波光子开关光波传输方程,给出了基于耦合非线性薛定谔方程的分步傅里叶法,三维庞加莱球理论和琼斯传输矩阵法的数值分析模型.仿真获得在光子开关中微波直接强度调制光载波的传输过程,以及在不同调制带宽下一阶和二阶PMD对光波信号和NOLM功率传输函数的影响.指出PMD造成NOLM开关性能钝化和消光比严重恶化,并引起信号信噪比下降和旁瓣泄漏.当调制带宽大于40GHz时,二阶PMD的影响比一阶PMD更加严重.最后讨论了NOLM中的PMD补偿问题.