Invariant Manifolds For Weak Solutions To Stochastic Equations 2000

Let Z(M) be the 3-manifold invariant of Le, Murakami and Ohtsuki. We give a direct computational proof that the degree 1 part of Z(M) satisfies Z 1 (M) = (\Gamma1) b 1 (M) 2 M , where b 1 (M) denotes the first Betti number of M and where M denotes the Lescop generalization of the Casson-Walker invariant of M . Moreover, if b 1 (M) = 2, we show that Z(M) is determined by M . Research supported in part by the CNRS. This and related preprints can be obtained by accessing the WEB at http://www.math.sciences.univ-nantes.fr/preprints/ 1 Introduction ...

. If V is a closed translation-invariant rotation-invariant subspace of continuous functions on R 2 with the usual topology which contains nonpolynomial functions, then V contains a subspace of Helmholtz functions. In addition, a converse theorem is given showing when V is precisely a space of Helmholtz functions. We conclude with applications to a mean value theorem for the Helmholtz equation. 2 1 Introduction In 1929, the Roumanian mathematician Dimitrie Pompeiu formulated the following problem [11, 12]: Characterize the bounded measureable s...

In this paper, we derive an explicit group-invariant formula for the Euler-Lagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex that is based on a general moving frame construction and is of independent interest.

Abstract This paper reviews the moving frame approach to the construction of the invariant variational bicomplex. Applications include explicit formulae for the Euler-Lagrange equations of an invariant variational problem, and for the equations governing the evolution of differential invariants under invariant submanifold flows.

JO ~AO FARIA MARTINS AND TIMOTHY PORTER Abstract. We give an interpretation of Yetter's Invariant of manifolds M in terms ofthe homotopy type of the function space TOP( M, B(G)), where G is a crossed moduleand B(G) is its classifying space. From this formulation, there follows that Yetter'sinvariant depends only on the homotopy type of M, and the weak homotopy type of thecrossed module G. We use this interpretation to define a twisting of Yetter's Invariant by cohomology classes of crossed modules, defined as cohomology classes of their classif...

www.math.umn.edu/~olver

Abstract. We give an interpretation of Yetter?s Invariant of manifolds M in terms of the homotopy type of the function space TOP(M, B(G)), where G is a crossed module and B(G) is its classifying space. From this formulation, there follows that Yetter?s invariant depends only on the homotopy type of M, and the weak homotopy type of the crossed module G. We use this interpretation to define a twisting of Yetter?s Invariant by cohomology classes of crossed modules, defined as cohomology classes of their classifying spaces, in the form of a state s...

Abstract This paper proposes a new rotation-invariant and scale-invariant representation for texture image retrieval based on steerable pyramid decomposition. By calculating the mean and standard deviation of decomposed image subbands, the texture feature vectors are extracted. To obtain rotation or scale invariance, the feature elements are aligned by considering either the dominant orientation or dominant scale of the input textures. Experiments were conducted on the Brodatz database aiming to compare our approach to the conventional steerab...

. This is the first part of a series of three papers. The whole series aims to develop the tools for the study of all almost Hermitian symmetric structures in a unified way. In particular, methods for the construction of invariant operators, their classification and the study of their properties will be worked out. In this paper we present the invariant differentiation with respect to a Cartan connection and we expand the differentials in the terms of the underlying linear connections belonging to the structures in question. Then we discuss the...

Abstract This paper proposes a new rotation-invariant and scale-invariant representation for texture image retrieval based on steerable pyramid decomposition. By calculating the mean and standard deviation of decomposed image subbands, the texture feature vectors are extracted. To obtain rotation or scale invariance, the feature elements are aligned by considering either the dominant orientation or dominant scale of the input textures. Experiments were conducted on the Brodatz database aiming to compare our approach to the conventional steerab...

In statistics, an invariant estimator is a criterion that ca...

In differential equations, the Laplace invariant of any of c...

In optics the Lagrange invariant is a measure of the light p...

In mathematics, Seiberg–Witten invariants are invariants o...

In mathematics, in particular in algebraic topology, the Hop...

In mathematics, the Kervaire invariant, named for Michel Ker...