The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

A theory of tubular neighborhoods for strata in manifold stratified spaces is developed. In these topologically stratified spaces, manifold stratified approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include a multiparameter isotopy extension theorem, neighborhood germ classification and a topological ve...

This is the third in a series of papers aimed at generalizing Siebenmann’s famous PhD thesis [13] so that the results apply to manifolds with nonstable fundamental groups at infinity. Siebenmann’s work provides necessary and sufficient conditions for an open manifold of dimension ≥ 6 to contain an open collar neighborhood of infinity, ie, a manifold neighborhood of infinity N such that N ≈ ∂N ×...

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s(1 ≤ s ≤ n) algebraic hypersurfaces in n-dimensional complex Euclidean space and discuss the Lagrange interpolation along the algebraic manifold of sufficient intersection. By means of some theorems ( such as Bez...

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight co...

In this paper, sliding mode control (SMC) for a bidirectional buck/boost DC-DC converter (BDC) with constant frequency in continuous conduction mode (CCM) is discussed. Since the converter is a high-order converter, the reduced-order sliding manifold is exploited. Because of right-half-plan zero (RHPZ) in the converter’s duty ratio to output voltage transfer function, sliding mode current...

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...

In this paper, we formulate and study the concept of Lp-stability with respect to a set. This robustness concept generalizes the standard Lp-stability notion towards control systems designed to steer the system state into the vicinity of a set rather than of a point. We focus on stable LTI systems with the property that all eigenvalues with zero real part are located in the origin. Employing th...

The stability and Hopf bifurcation of gene expression models with a mechanism delayed state feedback are considered. An effective algorithm for the calculations on delay stable interval equilibrium point, direction, bifurcating periodic solution is also proposed. τ-decomposition strategy applied to tackle issue local stability, explicit formula provided. In addition, asymptotical behaviors solu...