let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

We study the geometric structure of the spectral factors of a given spectral density Φ. We show that these factors can be associated to a set of invariant subspaces and we exhibit the manifold structure of this set, providing also an explicit parametrization for it, in the special case of coinciding algebraic and geometric multiplicity of the zeros of the maximum-phase spectral factor. We also ...

A filter optimization was investigated to design a set of filters for a five channel multi-spectral camera, three of which result in high colorimetric performance when used alone, and the full set having high quality spectral performance. Each candidate filter was selected from a set of 33 glass filters with three different thicknesses where filters may be combined in optical series. The effect...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

Spectral clustering is a powerful clustering method for document data set. However, spectral clustering needs to solve an eigenvalue problem of the matrix converted from the similarity matrix corresponding to the data set. Therefore, it is not practical to use spectral clustering for a large data set. To overcome this problem, we propose the method to reduce the similarity matrix size. First, u...

Background: Deep learning has revolutionized artificial intelligence and has transformed many fields. It allows processing high-dimensional data (such as signals or images) without the need for feature engineering. The aim of this research is to develop a deep learning-based system to decode motor intent from electromyogram (EMG) signals. Methods: A myoelectric system based on convolutional ne...

The aim of this study is to investigate the novel application of a ‎handheld near infra-red spectrophotometer coupled with classification methodologies as a screening approach in detection of adulterated lime juices. For this purpose, a miniaturized near infra-red spectrophotometer (Tellspec®) in the spectral range of 900–1700 nm was used. Three diffuse reflectance spectra of 31 pure...

A geometric approach to stochastic realization theory, and hence to spectral factorization problems, has been developed by Lindquist and Picci [1985,1991], Lindquist, Michaletzky and Picci [1995]. Most of this work was done abstractly. Fuhrmann and Gombani [1998] adopted an entirely Hardy space approach to this set of problems, studying the set of rectangular spectral factors of given size for ...

We present the results of exploratory data analysis for a data set that consists of crossposting information for 89,687 newsgroups over a period of 3.4 years. The data set we use is a part of Microsoft Netscan data. Our goal is to investigate the community structure of the newsgroup data set with a specific focus on spectral hierarchical clustering. We present a spectral hierarchical clustering...