We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

In the subspace sketch problem one is given an $n \times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in arbitrary way build a small space data structure $Q_p$, so that for any $x \in \mathbb{R}^d$, probability at least 2/3, has $Q_p(x) = (1 \pm \varepsilon) \|Ax\|_p$, where $p \geq 0$ randomness over construction of $Q_p$. The central question is, how many bits a...

262 Word count: 4,729 Text + 4 Tables + 7 Figures = 7,479 Submission Date: August 1 st , 2007 Revised version submitted Date: November 15 th , 2007 Paper submitted for Presentation and Publication in the TRANSPORTATION RESEARCH RECORD, JOURNAL OF TRANSPORTATION RESEARCH BOARD AFTER BEING PRESENTED TRANSPORTATION RESEARCH BOARD’S 87 TH ANNUAL MEETING, WASHINGTON, D.C., 2008

This paper provides a model-free approach based on the Multi-Resolution Simultaneous Perturbation Stochastic Approximation (MR-SPSA) for maximizing power production of wind farms. The main advantage is that the method based on MR-SPSA can achieve fast controller tuning without any plant model by exploiting the information of the wind farm configuration such as turbines location and wind directi...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...