there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

We introduce a non-interferometric single beam method for automated spectral phase characterization and adaptive pulse compression of amplified ultrashort femtosecond pulses taking advantage of third order harmonic generation in air. This new method, air-MIIPS, compensates high-order phase distortions based on multiphoton intrapulse interference phase scan (MIIPS).

We demonstrate an optical comb source that generates 550 ultra-narrow spectral lines with a spectral linewidth of 1.5-3 kHz, spanning over the C-band. The source originates from a single-mode Brillouin laser processed with phase modulation, pulse compression, and four-wave mixing. As a result, the narrow linewidth of the Brillouin laser improves the phase noise of every spectral line of the fre...

Fine spectra of various matrix operators on different sequence spaces have been examined by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r,0,s)...

Fine spectra of various matrix operators on different sequence spaces have been examined by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the lower triangular matrix   , , ...

In this paper, we determine the watermark domain that maximizes data hiding capacity. We focus on the situation in which the watermarked signal undergoes lossy compression involving quantization in a specified compression domain. A novel linear model for the process of quantization is proposed which leads to analytical results estimating the data hiding capacity for various watermarking domains...

A wide class of fast image compression algorithms are elaborated in this paper. Proposed technique di er from the known spectral algorithms so that it truncates generalized cepstrum rather than spectrum together with additional information on spectrum phase for increasing of compression rate.

We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon’s noiseless coding theorem, for a linearly quantized stochastic Gaussian signal (noise). The compression ratio decreases logarithmically with the amplitude of the frequency spectrum P (f) of the noise. Entropy ...

Compressive sensing allows signals to be efficiently captured by exploiting their inherent sparsity. Here we implement sparse sampling to capture the electronic structure and ultrafast dynamics of molecular systems using phase-resolved 2D coherent spectroscopy. Until now, 2D spectroscopy has been hampered by its reliance on array detectors that operate in limited spectral regions. Combining spa...

Cognitive Radios observe the spectral environment through spectrum estimation. In particular, reconfigurable Software Defined Radio architectures generate large amounts of sample data, which can be computationally expensive to analyse. Compression by time-shifted random preintegration prior to spectrum estimation reduces the amount of data to be processed. It is simple to implement and scalable...