We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

In [1] Chas and Sullivan have defined an intersection-type product on the homology of the free loop space LM of an oriented manifold M. In this paper we show how to extend this construction to a topological conformal field theory of degree d. In particular, we get operations on H∗LM which are parameterized by the homology of the moduli space of open-closed Riemann surfaces.

We study the affine orbifold laminations that were constructed in [LM]. An important question left open in [LM] is whether these laminations are always locally compact. We show that this is not the case. The counterexample we construct has the property that the regular leaf space contains (many) hyperbolic leaves that intersect the Julia set; whether this can happen is itself a question raised ...

In this paper we investigate bundles whose structure group is the loop group LU(n). These bundles are classified by maps to the loop space of the classifying space, LBU(n). Our main result is to give a necessary and sufficient criterion for there to exist a Fourier type decomposition of such a bundle ξ. This is essentially a decomposition of ξ as ζ⊗LC, where ζ is a finite dimensional subbundle ...

We verify the following three basic results on the free loop space LM . (1) We show that the set of all points, where the fundamental form on LM is nondegenerate, is an open subset. (2) The connections of a Fréchet bundle over LM can be extended to S1-central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the cu...

Abstract. While the tangent space to an equisingular family of curves can be discribed by the sections of a twisted ideal sheaf, this is no longer true if we only prescribe the multiplicity which a singular point should have. However, it is still possible to compute the dimension of the tangent space with the aid of the equimulitplicity ideal. In this note we consider families Lm = {(C, p) ∈ |L...

In [3] Chas and Sullivan defined an intersection product on the homology H∗(LM) of the space of smooth loops in a closed, oriented manifold M . In this paper we will use the homotopy theoretic realization of this product described by the first two authors in [2] to construct a second quadrant spectral sequence of algebras converging to the loop homology multiplicatively, when M is simply connec...

We consider the classic problem of computing (the length of) the longest common subsequence (LCS) between two strings A and B with lengths m and n, respectively. There are several input sensitive algorithms for this problem, such as the O(σn+min{Lm,L(n−L)}) algorithms by Rick [15] and Goeman and Clausen [5] and the O(σn + min{σd, Lm}) algorithms by Chin and Poon [4] and Rick [15]. Here L is the...