ISSN 1439-8516 CN 11-2039/O1
The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered characters in terms of index of Dirac cohomology is calculated explicitly.
In this paper, using the method of blow-up analysis, we obtained a Trudinger–Moser inequality involving Lp-norm on a closed Riemann surface and proved the existence of an extremal function for the corresponding Trudinger–Moser functional.
In this paper, we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue. The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense. Under suitable conditions, we use the substitution formula from Russo and Vallois to find the local solution of this equation. Then, we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.
In this paper, let m ≥ 1 be an integer, M be an m-dimensional compact Riemannian manifold. Firstly the linearized Poincaré map of the Lagrangian system at critical point x
d/(dt)Lq(t, x, ?) - Lp(t, x, ?) = 0
is explicitly given, then we prove that Morse index and Maslov-type index of x are well defined whether the manifold M is orientable or not via the parallel transport method which makes no appeal to unitary trivialization and establish the relation of Morse index and Maslov-type index, finally derive a criterion for the instability of critical point and orientation of M and obtain the formula for two Maslov-type indices.
We calculate the dimensions of Bott–Chern and Aeppli cohomologies associated to a complex structure on S3×S3. We express them in terms mainly of Hogde numbers.
In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor. More precisely, we show that for n ≥ 4, the Cotton tensor of any n-dimensional gradient quasi-Einstein soliton with fourth order f-divergence free Weyl tensor is flat, if the manifold is compact, or noncompact but the potential function satisfies some growth condition. As corollaries, some local characterization results for the quasi-Einstein metrics are derived.
This paper is mainly devoted to proving the four equivalent defining properties of a CBA(κ) space. The proof is based on an interesting tool we established which describes the cyclical five-step deformation procedure for quadrangles in the model 2-plane Sκ2, including the limit shape of each step. As a byproduct we give a complete list of cyclical deformation procedures for all kinds of quadrangles on S12. At last we make a contrast of geometric properties of CBA with CBB spaces, including a comparison between their defining properties and a discussion about Alexandrov’s Lemma.
The skewness of a graph G, denoted by sk(G), is the minimum number of edges in G whose removal results in a planar graph. It is an important parameter that measures how close a graph is to planarity, and it is complementary, and computationally equivalent, to the Maximum Planar Subgraph Problem. For any connected graph G on p vertices and q edges with girth g, one can easily verify that sk(G) ≥ π(G), where π(G) = ?q - g/(g-2) (p - 2)?, and the graph G is said to be π-skew if equality holds. The concept of π-skew was first proposed by G. L. Chia and C. L. Lee. The π-skew graphs with girth 3 are precisely the graphs that contain a triangulation as a spanning subgraph. The purpose of this paper is to explore the properties of π-skew graphs. Some families of π-skew graphs are obtained by applying these properties, including join of two graphs, complete multipartite graphs and Cartesian product of two graphs. We also discuss the threshold for the existence of a spanning triangulation. Among other results some sufficient conditions regarding the regularity and size of a graph, which ensure a spanning triangulation, are given.
Let x : M → ${\Bbb S}$n+p(1) be an n-dimensional submanifold immersed in an (n+p)-dimensional unit sphere ${\Bbb S}$n+p(1). In this paper, we study n-dimensional submanifolds immersed in ${\Bbb S}$n+p(1) which are critical points of the functional S(x) = ∫M S n/2dv, where S is the squared length of the second fundamental form of the immersion x. When x : M → ${\Bbb S}$2+p(1) is a surface in ${\Bbb S}$2+p(1), the functional S(x) = ∫M S n/2dv represents double volume of image of Gaussian map. For the critical surface of S(x), we get a relationship between the integral of an extrinsic quantity of the surface and its Euler characteristic. Furthermore, we establish a rigidity theorem for the critical surface of S(x).
For the Cauchy problem to Keller–Segel system, we show well-posedness and time-decay estimates in the critical scaling-invariant Besov spaces by using Littlewood–Paley analysis together with the decay estimates of heat kernels.
