A general type of twisted anomaly cancellation formulas

For even-dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the Chern-Simons transgression and we also get some twisted anomaly cancellation formulas.     

Modular Invariance and Anomaly Cancellation Formulas in Odd Dimension Ⅱ

By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.     

A note on generalized twisted anomaly cancellation formulas

In this note, by studying modular invariance properties of some characteristic forms, we get some new twisted anomaly cancellation formulas.     

推广的韩-刘-张反常消去公式

在[Anomaly cancellation and modularity, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics,2014:87-104,World Sci.Publ.,Hackensack,NJ]中,韩-刘-张给出了一个反常消去公式,推广了GreenSchwarz公式和Schwartz-Witten公式.本文研究了两个推广的韩-刘-张公式和一个奇数维的韩-刘-张公式.通过研究一些示性式的模性质,给出了奇数维新的反常消去公式.     

Modular invariance and anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas. As an application, we derive some results on divisibilities on spin manifolds and congruences on spin ^c manifolds.     

Even dimensional manifolds and generalized anomaly cancellation formulas

We give a direct proof of a cancellation formula raised by Han and Zhang (2004) on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among these cancellation formulas are discussed.

     

Anomaly cancellation and the mass spectrum of ε(∞)

The necessary condition for superstrings anomaly cancellation is shown to play the role of a scaling exponent in the mass spectrum of ε^(∞) theory of high energy particle physics.     

Noether theorems and quantum anomalies

A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the explanation of the origin of quantum anomalies can be obtained by using similar formulas for derivatives of functions whose values are measure in the former case and pseudomeasures in the latter.     

Anomaly formulas for the complex-valued analytic torsion on compact bordisms

We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued smooth forms under absolute and relative boundary conditions. In order to define the complex-valued analytic torsion in this situation, we study spectral properties of these generalized Laplacians. Then, as main results, we obtain so-called anomaly formulas for this torsion. Our reasoning takes into account that the coefficients in the heat trace asymptotic expansion associated to the boundary value problem under consideration, are locally computable. The anomaly formulas for the complex-valued Ray–Singer torsion are derived first by using the corresponding ones for the Ray–Singer metric, obtained by Brüning and Ma on manifolds with boundary, and then an argument of analytic continuation. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold.     

Generalized small cancellation theory and applications I. The word problem

In this paper we develop a generalization of the small cancellation theory. The usual small cancellation hypotheses are replaced by some condition that, roughly speaking, says that if a common part of two relations is a big piece of one relation then it must be a very small piece of another. In particular, we show that a finitely presented generalized small cancellation group has a solvable word problem. The machinery developed in the paper is to be used in the following papers of this series for constructing some group-theoretic examples.     

模的弱消去问题和Exchange环的弱稳定条件

本文研究模的弱消去问题和exchange环的弱稳定条件,给出了wsrl条件的新刻划,证明了对具有有限exchange性质的模,外弱消去等价于内弱消去并等价于自同态环满足wsrl条件.     

Anomaly cancellation and modularity,II: The <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> ×<Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> case

In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E ₈ × E ₈ and the Ho?ava-Witten anomaly factorization formula for the gauge group E8 can be derived through modular forms of weight 14. This answers a question of Schwarz. We also establish generalizations of these factorization formulas and obtain a new Ho?ava-Witten type factorization formula.     

Spinc-manifolds and elliptic genera

We present an extension of the “miraculous cancellation” formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. Relations to the Ochanine congruence formula on 8k+4 dimensional Spin^c manifolds are discussed. To cite this article: F. Han, W. Zhang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

考虑预订取消率的酒店退订政策选择演化博弈研究

基于顾客的取消预订行为,在Hotelling模型框架下构建了酒店的博弈模型,分析了两竞争性酒店退订政策选择的问题。研究表明,当顾客对酒店之间水平差异的敏感程度较高时,若两酒店的预订取消率差异较小,则两酒店都将选择宽松的退订政策;若取消率差异较大,则取消率较高的酒店将选择严格的退订政策,而取消率较低的酒店将选择宽松的退订政策。当顾客对酒店之间水平差异的敏感程度较低且两酒店的预订取消率差异较小时,系统存在两个演化稳定策略,酒店只有选择与竞争对手相反的策略才能获得最大收益。本研究能够为酒店的决策制定和收益管理提供一定的支持。     

Multiplication formulas for Apostol-type polynomials and multiple alternating sums

We investigate multiplication formulas for Apostol-type polynomials and introduce λ-multiple alternating sums, which are evaluated by Apostol-type polynomials. We derive some explicit recursive formulas and deduce some interesting special cases that involve the classical Raabe formulas and some earlier results of Carlitz and Howard.     

Stein流形上一个带有算子映射函数的积分公式

本文得到Ｓｔｅｉｎ流形上一个带有算子映射函数Ｓ（ｚ，ζ）和实参数的积分公式，由这个公式不但可以推出Ｓｔｅｉｎ流形上全纯函数和光滑函数的一些已有积分公式和它们相应的拓广式，而且还可以得到一些新的积分公式。     

关于复函数的中值公式及“中间点”的渐近性

讨论几个复函数徽分中值公式的“中间点”渐近性，所得渐近估计式推广了有关文献中相应的结论，然后，建立复函数的积分中值公式及“中间点”的渐近性质，得到与实积分相类似的结果．     

Totally Umbilical Subrnanifolds in a Locally Symmetric Manifold

In this paper we obtain some formulas for totally umbilical submanifolds in a localiy symmetric manifold, and dcrivc some local rcsults on the submanifolds from these formulas.     

局部对称流形的全脐子流形

In this paper we obtain some formulas for totally umbilical submanifolds in a locally symmetric manifold, and derive some local results on the submanifolds from these formulas.     

关于模糊数贴近度问题的研究

利用模糊集和区间数的贴近度理论,讨论了模糊数的贴近度问题.通过区间数与模糊数之间的关系,根据区间数贴近度的一般表示形式,给出了构造一些模糊数贴近度的具体计算公式的方法;并通过实例说明了所得到的贴近度公式的有效性和实用性,解决了常用贴近度公式所不能解决的问题.