Related papers: Rough Cauchy Sequences in a Cone Metric Space
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solutions taking as initial condition a finite Radon measure, not…
Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…
We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
In this paper, we extend a fixed point theorem due to Ciric to a cone metric space.
We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of…
We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…
The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple…
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0}=1$. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special…
In this paper, the notion of convexity of picture fuzzy multisets was introduced and some of their properties were presented after studying the concept of picture fuzzy multisets.
We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
Let $(X,d)$ be a finite metric space with $|X|=n$. For a positive integer $k$ we define $A_k(X)$ to be the quotient set of all $k$-subsets of $X$ by isometry, and we denote $|A_k(X)|$ by $a_k$. The sequence $(a_1,a_2,\ldots,a_{n})$ is…
Some examples and basic properties of ultrametric spaces are briefly discussed.