in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

Global geometric properties of product manifolds M = M × R2, endowed with a metric type 〈·, ·〉 = 〈·, ·〉R + 2dudv + H(x, u)du 2 (where 〈·, ·〉R is a Riemannian metric on M and H : M × R → R a function), which generalize classical plane waves, are revisited. Our study covers causality (causal ladder, inexistence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate...

Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space (X, dist). The DTW and GED measures are massively used in various fields of computer science and computational biology, consequently, the tasks of computing these measures are ...

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with metric ρ ·, · . Given > 0, does there exist a δ > 0 such that if f : G1 → G2 satisfies ρ f xy , f x f y < δ for all x, y ∈ ...

This paper presents a procedure for performing parameter optimization of ignition and growth continuum models for high explosive systems. Continuum modeling of reactive flow in high explosive systems can yield highly accurate predictions of experimental observations. However, the numerical parameter optimization that is needed to establish these predictions generally requires many evaluations o...

Abstract Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains distinguished group, known as the Lipschitz group. We show only quotient of this group remains meaningful context projective metric geometry. can be viewed point set on algebra and, under certain restrictions, leads to an algebraic description so-called kinematic map...

We consider a functional-analytic setting for querying large image databases by colour content, in which the colour distributions (histograms), describing the colour content of an image, are probability measures on the colour space C. The Kantorovich distance turns out to be among the most relevant metrics on the space of colour distributions. We study the colour histogram space equipped with a...

Dynamic Time Warping (DTW) is one of the basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequence of points in some metric space pX, distq. The DTW measure is massively used in many practical fields of computer science, and computing the DTW between two sequences is a classical problem in P. Despite extensive efforts to find mor...

We consider Support Vector Machines (SVMs) learned together with linear transformations of the feature spaces on which they are applied. Under this scenario the radius of the smallest data enclosing sphere is no longer fixed. Therefore optimizing the SVM error bound by considering both the radius and the margin has the potential to deliver a tighter error bound. In this paper we present two nov...