Spectral Invariant Subalgebras of Reduced Groupoid C~*-algebras

We introduce the notion of property(RD) for a locally compact, Hausdorff and r-discrete groupoid G, and show that the set S_2~l(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 C_r~*(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 G~0 of G, gives rise to a canonical map τ_c on the algebra C_c(G) of complex continuous functions with compact support on G. We show that the map τ_c can be extended continuously to S_2~l(G) and plays the same role as an n-trace on C_r~*(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 C_r~*(G).     

Nakayama automorphisms of PBW deformations and Hopf actions

Poincaré-Birkhoff-Witt(PBW)deformations of Artin-Schelter regular algebras are skew CalabiYau.We prove that the Nakayama automorphisms of such PBW deformations can be obtained from their homogenizations.Some Calabi-Yau properties are generalized without Koszul assumption.We also show that the Nakayama automorphisms of such PBW deformations control Hopf actions on them.     

Deformations of complex orbifolds and the period maps

We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map.     

Representations of a Class of Associative Algebras Related to the Quantum Torus

1 Introduction The mitivation of this paper comes from the work of[5].We kmow that vertex algebratheory is one of the importans parts in the study of infinte dimensional Lie theory,while thelattice vertex algebras form one of the most important and fundamental classes of vertexalgebras.In they studied the representation theory for certain” half lattice”vertex algebra     

On the density of Birkhoff sums for Anosov diffeomorphisms

Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides of zero, then the set of Birkhoff sums of all the periodic points is dense in R.     

Continuity of Some Classes of Functions Related to Degenerate Parabolic Equations and Its Applications

We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations.     

On ultraproducts of operator algebras

Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups of ultraproduct of C~*-algebras are iso- morphic to the ultraproduct of respective K-groups of C~*-algebras.We also show that the ultraproducts of factors of type Ⅱ_1 are prime,i.e.not isomorphic to any non-trivial tensor product.     

Large deviations for Glauber dynamics of continuous gas

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems.We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology,while it does not satisfy the large deviation principles in the T-topology.     

Stable Stationary Harmonic Maps to Spheres

For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S^k. We show that the singular set of stable-stationary harmonic maps from B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2.     

The local Hlder exponent for the entropy of real unimodal maps In Memory of Lei Tan

We consider the topological entropy h(θ) of real unimodal maps as a function of the kneading parameter θ(equivalently, as a function of the external angle in the Mandelbrot set). We prove that this function is locally Hlder continuous where h(θ) 0, and more precisely for any θ which does not lie in a plateau the local Hlder exponent equals exactly, up to a factor log 2, the value of the function at that point.This confirms a conjecture of Isola and Politi(1990), and extends a similar result for the dimension of invariant subsets of the circle.     

CONTINUOUS AND DISCRETE N-CONVEX APPROXIMATIONS

We show that the best L_p-approximant to continuous functions by n-convex functions isthe limit of discrete n-convex approximations.The techniques of the proof are then used toshow the existence of near interpolants to discrete n-convex data by continuous n-convexfunctions if the data points are close.     

Co cycle Perturbation on Banach Algebras

Letαbe a flow on a Banach algebra(?),and t(?)u_t a continuous function from Rt into the group of invertible elements of(?)such that u_sα_s(u_t)=u_s+t,s,t∈R.Thenβ_t=Adu_t oα_t,t∈R is also a flow on(?),where Adu_t(B)(?)u_tBu_t~(-1)for any B∈(?).βis said to be a cocycle perturbation ofα.We show that ifα,βare two flows on a nest algebra(or quasi-triangular algebra),thenβis a cocycle perturbation ofα.And the flows on a nest algebra(or quasi-triangular algebra)are all uniformly continuous.     

Operator Jensen＇s Inequality on C＊-algebras

A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We give a general formation of Jensen’s inequality for A-convex functions.     

The Spaces ∧_αof Lipschitz Continuous Functions on Complete Riemannian Manifold with Nonnegative Curvature

We consider the spaces∧_αof Lipschitz continuous functions on completeRiemannian manifold with nonnegative Ricci curvature.We first give a characeriza-tion of f∈∧_αin terms of its Poisson integral u(x,t),then we show that the BesselPotential J_βmaPPs∧_αisomorphically onto∧_(α+β).     

Tracial Limit of C^＊-algebras

A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.     

f-ergodicity of Markov Process by Coupling Method北大核心CSCD

We first study the basic coupling and obtain an equation between total variation norm and the basic coupling. Then by use this equation we investigate the ergodicity property of continuous time Markov processes in general state space. For an ergodic continuous-time Markov processes, adding condition π(f) < ∞, by using the coupling method, there exists the full absorption set, such that the continuous time Markov processes are f-ergodic on it. © 2022 Chinese Academy of Sciences. All rights reserved.     

On the core entropy of Newton maps

In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy function is not continuous in this family, which is different from the polynomial case, and describe completely the continuity of the entropy function at the generic parameters.     

On the structure of graded <Emphasis Type="Italic">λ</Emphasis>-Hopf algebras

Let G be an abelian group, B the G-graded λ-Hopf algebra with A being a bicharacter on G. By introducing some new twisted algebras （coalgebras）, we investigate the basic properties of the graded antipode and the structure for B. We also prove that a G-graded λ-Hopf algebra can be embedded in a usual Hopf algebra. As an application, it is given that if G is a finite abelian group then the graded antipode of a finite dimensional G-graded A-Hopf algebra is invertible.     

解一类二阶延迟常微分方程连续RKN方法的P-稳定性

In this paper, we study the P-stability of the continuous Runge-Kutta Nystroem method for solving the delayed second order differential equation that does not depend on y′. A general theorem is presented which can be used to obtain complete characterizations of the P-stability regions of these continuous RungeKutta- Nystroem methods. We use the condition to two given RKN methods.