We start from a given Lorentz metric and a vector field of world lines along which observers and measure devices may move. We describe a procedure to associate one-particle Hilbert spaces and one-particle Hamiltonians to space-like hypersurfaces using a transi, tion to a Riemannian metric. With the aid of suitable boundary conditions one can confine the particle within a world tube ("box quanti...

A novel support vector machine method for classification is presented in this paper. A modified kernel function based on the similarity metric and Riemannian metric is applied to the support vector machine. In general, it is believed that the similarity of homogeneous samples is higher than that of inhomogeneous samples. Therefore, in Riemannian geometry, Riemannian metric can be used to reflec...

In this paper it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in [10]. He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-proje...

We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is the general linear group endowed with its natural rightinvariant metric, and the metric on the homogeneous space is chosen such that the quotient space is the image of a Riemannian submersion from the total space. As a result, we obtain complete geodesics that a...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...

Three types of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold are studied. The study is focused on fundamental properties and the transference of structures. 1. Introduction. In this paper, we discuss some geometric properties of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold. If the base space is an...

considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...