In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...

Given any ǫ > 0 and any planar region Ω bounded by a simple n-gon P we construct a (1 + ǫ)-quasiconformal map between Ω and the unit disk in time C(ǫ)n. One can take C(ǫ) = C + C log 1 ǫ log log 1 ǫ . Date: August 13, 2009. 1991 Mathematics Subject Classification. Primary: 30C35, Secondary: 30C85, 30C62 .

We propose a method for non-linear data projection that combines Generative Topographic Mapping and Coordinated PCA. We extend the Generative Topographic Mapping by using more complex nodes in the network: each node provides a linear map between the data space and the latent space. The location of a node in the data space is given by a smooth nonlinear function of its location in the latent spa...

polycyclic aromatic hydrocarbons (pahs) are a group of organic compounds made up of two or more fused benzene rings in linear, angular or cluster arrangements. the pahs are formed by incomplete combustion or high temperature pyrolytic process involving organic matter. thirty sampling sites were selected to characterize the pahs concentrations in ambient air in tehran. sixteen pahs were measured...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

A mapping $f:V^n longrightarrow W$, where $V$ is a commutative semigroup, $W$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings i...

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

The text is designed for use in a 40 lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in ...