We give a short, operator-theoretic proof of the asymptotic independence of the minimal and maximal eigenvalue of the n× n Gaussian Unitary Ensemble in the large matrix limit n→ ∞. This is done by representing the joint probability distribution of those extreme eigenvalues as the Fredholm determinant of an operator matrix that asymptotically becomes diagonal. The method is amenable to explicitl...

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

the main purpose of this paper is to detemine the fine spectrum of the generalized difference operator delta_{uv} over the sequence space c0. these results are more general than the fine spectrum of the generalized difference operator delta_{uv} of srivastava and kumar.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh's theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

BACKGROUND Many factors have been found to affect the difficulty of colonoscope insertion, such as age, gender, body mass index (BMI), history of abdominal surgery and operator etc. However, a scoring system may be more useful to predict the difficulty during colonoscopy. METHODS The individual and procedure-related data of 616 patients undergoing colonoscopy were prospectively collected from...

Detection for cough in mice has never yielded clearly audible sounds, so there is still a great deal of debates as to whether mice can cough in response to tussive stimuli. Here we introduce an approach for detection of mouse cough based on sound monitoring and airflow signals. 40 Female BALB/c mice were pretreated with normal saline, codeine, capasazepine or desensitized with capsaicin. Single...

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

A nonvariational generation of a min-max principle by A. Lazer is made. And it is used to prove a new existence results for a nonconservative systems of ordinary differential equations with resonance.

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.