ISSN 1439-8516 CN 11-2039/O1
By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on (4r-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 (4r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on (4r-1)-dimensional manifolds and the Han-Yu rigidity theorem to the (a, b) case.
We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov-Witten invariants can be derived.
Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : Alg L → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B) for all A,B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.
A linear directed forest is a directed graph in which every component is a directed path. The linear arboricity la(D) of a digraph D is the minimum number of linear directed forests in D whose union covers all arcs of D. For every d-regular digraph D, Nakayama and Péroche conjecture that la(D) =d + 1. In this paper, we consider the linear arboricity for complete symmetric digraphs, regular digraphs with high directed girth and random regular digraphs and we improve some wellknown results. Moreover, we propose a more precise conjecture about the linear arboricity for regular digraphs.
For a < r < b, the approach of Li and Zhou (2014) is adopted to find joint Laplace transforms of occupation times over intervals (a, r) and (r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.
We introduce the notion of property (RD) for a locally compact, Hausdorff and r-discrete groupoid G, and show that the set S2l (G) of rapidly decreasing functions on G with respect to a continuous length function l is a dense spectral invariant and Fréchet *-subalgebra of the reduced groupoid C*-algebra Cr* (G) of G when G has property (RD) with respect to l, so the K-theories of both algebras are isomorphic under inclusion. Each normalized cocycle c on G, together with an invariant probability measure on the unit space G0 of G, gives rise to a canonical map τc on the algebra Cc(G) of complex continuous functions with compact support on G. We show that the map τc can be extended continuously to S2l (G) and plays the same role as an n-trace on Cr* (G) when G has property (RD) and c is of polynomial growth with respect to l, so the Connes' fundament paring between the K-theory and the cyclic cohomology gives us the K-theory invariants on Cr* (G).
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball BX* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.
Let Sα* be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class Sα*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in Cn
Let G be a polycyclic group and α a regular automorphism of order four of G. If the map ? : G → G defined by g? = [g,α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that CG(α2) and G/[G, α2] are both abelian-by-finite.
In this paper, three new circulant operator matrices, scaled circulant operator matrices, diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered.
