Measuring the similarity of two polygonal curves is a fundamental computational task. Among alternatives, the Fréchet distance is one of the most well studied similarity measures. Informally, the Fréchet distance is described as the minimum leash length required for a man on one of the curves to walk a dog on the other curve continuously from the starting to the ending points. In this paper we ...

Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet, who analyzed locally convex properties in terms of the defining double sequence of weights. We complement their results by considering a defining sequence which is the product of two single sequences. ...

As a continuation from [2], some higherorder statistical dependency aspects of chaotic spreading sequences used in communication systems are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, forms the building block of nonlinear dependence assessment of the family of spreading sequences under investigation. Explicit result...

Curve matching is a fundamental problem which occurs in many applications. In this paper, we extend the Fréchet distance to measure partial curve similarity, study its properties, and develop efficient algorithms to compute it. In particular, under the L1 or L∞ metrics, we present an algorithm to compute, in O(m2) time, the partial Fréchet distance between a segment and a polygonal curve of siz...

We study the complexity of computing the Fréchet distance (also called dog-leash distance) between two polygonal curves with a total number of n vertices. For two polygonal curves in the plane we prove an Ω(n log n) lower bound for the decision problem in the algebraic computation tree model allowing arithmetic operations and tests. Up to now only a O(n) upper bound for the decision problem was...

In this paper, we introduce a new generalization of the well-known Fréchet distance between two polygonal curves, and provide an efficient algorithm for computing it. The classical Fréchet distance between two polygonal curves corresponds to the maximum distance between two point objects that traverse the curves with arbitrary non-negative speeds. Here, we consider a problem instance in which t...

‎we say that a module $m$ is a emph{cms-module} if‎, ‎for every cofinite submodule $n$ of $m$‎, ‎there exist submodules $k$ and $k^{'}$ of $m$ such that $k$ is a supplement of $n$‎, ‎and $k$‎, ‎$k^{'}$ are mutual supplements in $m$‎. ‎in this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎in particular‎, ‎we prove tha...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking. We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time. For example, for curves in the punctured plan...