After giving the necessary background in simplicial homology and cohomology, we will state Stokes’s theorem and show that integration of differential forms on a smooth, triangulable manifold M provides us with a homomorphism from the De Rham cohomology of M to the simplicial cohomology of M . De Rham’s theorem, which claims that this homomorphism is in fact an isomorphism, will then be stated a...

Abstract We discuss an extension of Toeplitz quantization based on polyanalytic functions. derive isomorphism theorem for operators between weighted Sobolev-Fock spaces functions, which are images modulation under Bargmann transforms. This generalizes well-known results from the analytic setting. Finally, we asymptotic symbol calculus and present expansion complex Weyl in terms operators.

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of variational cohomology to its classical is an isomorphism, provided that viewed as differential algebra, polynomials in finitely many variables. This theorem one key ingredients computation cohomology. For proof, we introduce sesquilinear Hochschild and Harrison complexes vanishing symmetric

Abstract We prove that if the Auslander–Reiten triangles generate relations for Grothendieck group of a Hom-finite Krull–Schmidt triangulated category with (co)generator, then has only finitely many isomorphism classes indecomposable objects up to translation. This gives converse theorem Butler and on groups. Our approach applications in context Frobenius categories.

For certain families of compact subsets the plane, isomorphism class algebra absolutely continuous functions on a set is completely determined by homeomorphism set. This analogous to Gelfand–Kolmogorov theorem for C(K) spaces. In this paper, we define family sets comprising finite unions convex curves and show that has ‘Gelfand–Kolmogorov’ property.

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures. In this article we explain how to normalize tight contact structures with respect to a fixed triangulation. Using t...

Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion b R, we can get a measure of how badly the Krull-Schmidt theorem can fail for a more general local ring. We assign to each finitely generated R-mo...

which is defined only when I is nilpotent and Q ⊂ A. Goodwillie showed that (1.2) is an isomorphism whenever it is defined, and that it coincides with (1.1) when I = 0. Using this and a 5-Lemma argument, he deduced that (1.1) is an isomorphism for any nilpotent I. The question of whether ch∗ and ch ′ ∗ agree for general nilpotent ideals I was left open in [4], and announced without proof in [7,...