The rationale and methodology for retrieval based on the relative locations of documents within a geometric information space are introduced. Results from category A routing and filtering experiments in TREC-5 are discussed. The techniques used are related to the vector space model, latent semantic indexing, and other methods that rely on statistical qualities of texts to assess document relate...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

1 Introduction In a highly original, but not yet sufficiently appreciated contribution entitled " Six theorems about metric spaces " [32], John Isbell presented and discussed the following intriguing observations: from X into X with α • α = Id X and with d(α (x), α (y)) ≤ d (x , y) for all x , y ∈ X. (ii) Every metric space (X, d) can be embedded isometrically into an injec-tive metric space (ˆ...

Teramoto et al. [TAKD06] defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from S, a bounded subset of R. We generalize this definition of measure over all metric spaces by appealing to covering and packing radius. The definition of gap ratio needs only a metric unlike discrepancy, a widely used uniformity measure, that depends on the notion o...

The Poisson kernels and relations between them for a massive scalar field in a unit ball B with Hua’s metric and conformal flat metric are obtained by describing the B as a submanifold of an (n+1)-dimensional embedding space. Global geometric properties of the AdS space are discussed. We show that the (n+1)-dimensional AdS space AdSn+1 is isomorphic to RP 1 ×Bn and boundary of the AdS is isomor...

Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. ...

A high-speed multiprocessor architecture for brain-like analyzing information represented in analytic, graphand table forms of associative relations to search, recognize and make a decision in n-dimensional vector discrete space is offered. Vector-logical process models of actual applications, where the quality of solution is estimated by the proposed integral non-arithmetical metric of the int...

in this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. we investigate some properties of this metric, and finally presentan application. we think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.