We present some problems related to right(or bi-)invariant metrics d on the symmetric group of permutations S,. Characterizations and constructions of bi-invariant extremal (in the corresponding convex cone) metrics are given, esp. for n 6 5 . We also consider special subspaces of the metric space (S,,, d ) : unit balls, sets with prescribed distances (L-cliques), "hamiltonian" sets. Here we gi...

The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity cones of hyperbolic polynomials of degree d in n variables contains (n/d) pairwise distant cones in the Hausdorff metric, and therefore that any semidefinite representation of such polynomials must have dimension at lea...

In this paper, we define a new cone ball-metric and get fixed points and common fixed points for the Meir-Keeler type functions in cone ball-metric spaces. Department of Applied Mathematics, National Hsinchu University, of Education, Taiwan. E-mail address: [email protected] E-mail address: [email protected] Date: Received: 2 November 2011; Accepted: 26 May 2012. ∗ Corresponding ...

The object of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Using this concept we establish a unique common fixed point theorem for four self maps satisfying a generalized contractive condition in a cone metric space which generalizes and synthesizes the results of L. G. Huang and X. Zhang [3]( J. Math. Anal. ...

PURPOSE It has not been clarified whether early age-related macular degeneration (AMD) is associated with cone photoreceptor distribution. We used adaptive optics fundus camera to examine cone photoreceptors in the macular area of aged patients and quantitatively analyzed its relationship between the presence of early AMD and cone distribution. METHODS Sixty cases aged 50 or older were studie...

We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of DancšHegedüs-Medvegyev’s principle and the existence theorem related with Ekeland’s variational principle, Caristi’s common fixed point theorem for multivalued maps, Takahashi’s nonconvex minimization theore...

It was shown that quantum metric fluctuations smear out the singularities of Green’s functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, i.e. indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2, 3]. In...

The aim of this paper is to establish a unique common fixed point theorem for six self maps satisfying a generalized contractive condition in a cone metric space. The intent of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Our results generalize, extend and unify several well-known comparable results in the li...

Let X be a metric space, {xi}i∈N a sequence of points in X (thought of as a sequence of centers), and {di}i∈N a sequence of scaling factors such that di → ∞, and an ultrafilter ω. I’m not going to get into the details of ultrafilters here, but the main property of an ultrafilter is that it lets you define the ultralimit limω ai of any bounded sequence ai. Ultralimits use the axiom of choice to ...

The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed. 1. The Dirac equation and its current. Let M be a space-time manifold. It is a four-dimensional orientable manifold equipped with a pseudo-EuclideanMinkowski-t...