The Experts below are selected from a list of 70026 Experts worldwide ranked by ideXlab platform
Feyzi Basar - One of the best experts on this subject based on the ideXlab platform.
-
spectrum and fine spectrum of the upper triangular triple band Matrix over some sequence spaces
ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences, 2015Co-Authors: Feyzi Basar, Ali KaraisaAbstract:The fine spectra of lower triangular triple-band matrices in some sequence spaces was examined by several authors. Recently, Karakaya and Altun determined the fine spectra of upper triangular double-band matrices over the sequence spaces c0 and c, in [1]. In this paper, we determine the fine spectra of the upper triangular triple-band Matrix over the sequence spaces c0, c and l∞. Additionally, we give the approximate point spectrum, the defect spectrum and the compression spectrum of the Matrix Operator A(r, s, t) over the spaces c0, c and l∞ with some applications. These results are more general than the corresponding results obtained by Karakaya and Altun [J. Comput. Appl. Math. 234 (2010), 1387–1394].
-
on the fine spectrum of the Operator defined by the lambda Matrix over the spaces of null and convergent sequences
Abstract and Applied Analysis, 2013Co-Authors: Medine Yesilkayagil, Feyzi BasarAbstract:The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the Operator defined by the lambda Matrix over the sequence spaces and c. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the Matrix Operator on the sequence spaces and c. Finally, we present a Mercerian theorem. Since the Matrix is reduced to a regular Matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.
-
fine spectra of upper triangular triple band matrices over the sequence space
Abstract and Applied Analysis, 2013Co-Authors: Ali Karaisa, Feyzi BasarAbstract:The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Basar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The Operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the Operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the Operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the Matrix Operator over the space and we give some applications.
Ali Karaisa - One of the best experts on this subject based on the ideXlab platform.
-
spectrum and fine spectrum of the upper triangular triple band Matrix over some sequence spaces
ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences, 2015Co-Authors: Feyzi Basar, Ali KaraisaAbstract:The fine spectra of lower triangular triple-band matrices in some sequence spaces was examined by several authors. Recently, Karakaya and Altun determined the fine spectra of upper triangular double-band matrices over the sequence spaces c0 and c, in [1]. In this paper, we determine the fine spectra of the upper triangular triple-band Matrix over the sequence spaces c0, c and l∞. Additionally, we give the approximate point spectrum, the defect spectrum and the compression spectrum of the Matrix Operator A(r, s, t) over the spaces c0, c and l∞ with some applications. These results are more general than the corresponding results obtained by Karakaya and Altun [J. Comput. Appl. Math. 234 (2010), 1387–1394].
-
spectrum and fine spectrum generalized difference Operator over the sequence space l1
Mathematical Sciences Letters, 2014Co-Authors: Ali KaraisaAbstract:In this paper, we examined the fine spectrum of upper triangul ar double-band matrices over the sequence spaces `1. Also, we determined the point spectrum, the residual spectrum and the continuous spectrum of the Operator A(e;e) on `1. Further, we derived the approximate point spectrum, defect spectrum and compression spectrum of the Matrix Operator A(e;e) over the space `1.
-
fine spectra of upper triangular triple band matrices over the sequence space
Abstract and Applied Analysis, 2013Co-Authors: Ali Karaisa, Feyzi BasarAbstract:The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Basar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The Operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the Operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the Operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the Matrix Operator over the space and we give some applications.
-
fine spectra of upper triangular double band matrices over the sequence space
Discrete Dynamics in Nature and Society, 2012Co-Authors: Ali KaraisaAbstract:The Operator on sequence space on is defined , where , and and are two convergent sequences of nonzero real numbers satisfying certain conditions, where . The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the Operator defined by a double sequential band Matrix over the sequence space . Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the Matrix Operator over the space .
Bassam Bamieh - One of the best experts on this subject based on the ideXlab platform.
-
an input output approach to structured stochastic uncertainty
IEEE Transactions on Automatic Control, 2020Co-Authors: Bassam Bamieh, Maurice FiloAbstract:We consider linear time-invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is to characterize second-order properties such as mean-square stability (MSS) and performance. A purely input–output treatment of these systems is given without recourse to state-space models, and, thus, the results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for MSS in terms of the spectral radius of a linear Matrix Operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state-space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties. For cases where state-space realizations are given, linear Matrix inequality equivalents of the input-output conditions are given.
-
an input output approach to structured stochastic uncertainty in continuous time
arXiv: Systems and Control, 2018Co-Authors: Maurice Filo, Bassam BamiehAbstract:We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a purely input-output approach, i.e. without having to resort to state space realizations. This has the advantage of encompassing a wider class of models (such as infinite dimensional systems and systems with delays). The input-output approach leads to uncovering new tools such as stochastic block diagrams that have an intimate connection with the more general Stochastic Integral Equations (SIE), rather than Stochastic Differential Equations (SDE). Various stochastic interpretations are considered, such as It\=o and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a Matrix Operator that takes different forms when different stochastic interpretations are considered.
-
an input output approach to structured stochastic uncertainty
arXiv: Systems and Control, 2018Co-Authors: Bassam Bamieh, Maurice FiloAbstract:We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is to characterize second-order properties such as mean-square stability and performance. A purely input-output treatment of these systems is given without recourse to state space models, and thus the results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for mean-square stability in terms of the spectral radius of a linear Matrix Operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties. For cases where state space realizations are given, Linear Matrix Inequality (LMI) equivalents of the input-output conditions are given.
-
structured stochastic uncertainty
Allerton Conference on Communication Control and Computing, 2012Co-Authors: Bassam BamiehAbstract:We consider linear time invariant systems in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. We provide a purely input-output treatment of these systems without recourse to state space models, and thus our results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for mean square stability in terms of the spectral radius of a linear Matrix Operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties.
Jurgen Fischer - One of the best experts on this subject based on the ideXlab platform.
-
extension of radiative transfer code momo Matrix Operator model to the thermal infrared clear air validation by comparison to rttov and application to calipso iir
Journal of Quantitative Spectroscopy & Radiative Transfer, 2014Co-Authors: Cintia Carbajalhenken, Lionel Doppler, Jacques Pelon, Francois Ravetta, Jurgen FischerAbstract:Abstract 1-D radiative transfer code Matrix-Operator Model (MOMO), has been extended from [ 0.2 − 3.65 μ m ] the band to the whole [ 0.2 − 100 μ m ] spectrum. MOMO can now be used for the computation of a full range of radiation budgets (shortwave and longwave). This extension to the longwave part of the electromagnetic radiation required to consider radiative transfer processes that are features of the thermal infrared: the spectroscopy of the water vapor self- and foreign-continuum of absorption at 12 μ m and the emission of radiation by gases, aerosol, clouds and surface. MOMO׳s spectroscopy module, Coefficient of Gas Absorption (CGASA), has been developed for computation of gas extinction coefficients, considering continua and spectral line absorptions. The spectral dependences of gas emission/absorption coefficients and of Planck׳s function are treated using a k-distribution. The emission of radiation is implemented in the adding–doubling process of the Matrix Operator method using Schwarzschild׳s approach in the radiative transfer equation (a pure absorbing/emitting medium, namely without scattering). Within the layer, the Planck-function is assumed to have an exponential dependence on the optical-depth. In this paper, validation tests are presented for clear air case studies: comparisons to the analytical solution of a monochromatic Schwarzschild׳s case without scattering show an error of less than 0.07% for a realistic atmosphere with an optical depth and a blackbody temperature that decrease linearly with altitude. Comparisons to radiative transfer code RTTOV are presented for simulations of top of atmosphere brightness temperature for channels of the space-borne instrument MODIS. Results show an agreement varying from 0.1 K to less than 1 K depending on the channel. Finally MOMO results are compared to CALIPSO Infrared Imager Radiometer (IIR) measurements for clear air cases. A good agreement was found between computed and observed radiance: biases are smaller than 0.5 K and Root Mean Square Error (RMSE) varies between 0.4 K and 0.6 K depending on the channel. The extension of the code allows the utilization of MOMO as forward model for remote sensing algorithms in the full range spectrum. Another application is full range radiation budget computations (heating rates or forcings).
-
Radiative transfer solutions for coupled atmosphere ocean systems using the Matrix Operator technique
Journal of Quantitative Spectroscopy and Radiative Transfer, 2012Co-Authors: André Hollstein, Jurgen FischerAbstract:Abstract Accurate radiative transfer models are the key tools for the understanding of radiative transfer processes in the atmosphere and ocean, and for the development of remote sensing algorithms. The widely used scalar approximation of radiative transfer can lead to errors in calculated top of atmosphere radiances. We show results with errors in the order of±8% for atmosphere ocean systems with case one waters. Variations in sea water salinity and temperature can lead to variations in the signal of similar magnitude. Therefore, we enhanced our scalar radiative transfer model MOMO, which is in use at Freie Universitat Berlin, to treat these effects as accurately as possible. We describe our one-dimensional vector radiative transfer model for an atmosphere ocean system with a rough interface. We describe the Matrix Operator scheme and the bio-optical model for case one waters. We discuss some effects of neglecting polarization in radiative transfer calculations and effects of salinity changes for top of atmosphere radiances. Results are shown for the channels of the satellite instruments MERIS and OLCI from 412.5 nm to 900 nm.
-
numerical simulation of the light field in the atmosphere ocean system using the Matrix Operator method
Journal of Quantitative Spectroscopy & Radiative Transfer, 2001Co-Authors: Frank Fell, Jurgen FischerAbstract:Abstract A computer code to calculate the light field in the stratified atmosphere–ocean system is described and validated. The code is based on the Matrix-Operator method and includes multiple scattering as well as the effects at the flat or rough sea surface and the ocean ground. Special emphasis is put on the methods employed to ensure numerical accuracy and energy conservation. The code is validated by comparing model predictions with the analytical solution of the radiative transfer equation for a semi-infinite Rayleigh scattering atmosphere and by a model intercomparison for selected problems of the radiative transfer in the atmosphere–ocean system. The observed deviations from the analytical solution are smaller than 0.1% for solar and observation zenith angles
Maurice Filo - One of the best experts on this subject based on the ideXlab platform.
-
an input output approach to structured stochastic uncertainty
IEEE Transactions on Automatic Control, 2020Co-Authors: Bassam Bamieh, Maurice FiloAbstract:We consider linear time-invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is to characterize second-order properties such as mean-square stability (MSS) and performance. A purely input–output treatment of these systems is given without recourse to state-space models, and, thus, the results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for MSS in terms of the spectral radius of a linear Matrix Operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state-space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties. For cases where state-space realizations are given, linear Matrix inequality equivalents of the input-output conditions are given.
-
an input output approach to structured stochastic uncertainty in continuous time
arXiv: Systems and Control, 2018Co-Authors: Maurice Filo, Bassam BamiehAbstract:We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a purely input-output approach, i.e. without having to resort to state space realizations. This has the advantage of encompassing a wider class of models (such as infinite dimensional systems and systems with delays). The input-output approach leads to uncovering new tools such as stochastic block diagrams that have an intimate connection with the more general Stochastic Integral Equations (SIE), rather than Stochastic Differential Equations (SDE). Various stochastic interpretations are considered, such as It\=o and Stratonovich, and block diagram conversion schemes between different interpretations are devised. The MSS conditions are given in terms of the spectral radius of a Matrix Operator that takes different forms when different stochastic interpretations are considered.
-
an input output approach to structured stochastic uncertainty
arXiv: Systems and Control, 2018Co-Authors: Bassam Bamieh, Maurice FiloAbstract:We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is to characterize second-order properties such as mean-square stability and performance. A purely input-output treatment of these systems is given without recourse to state space models, and thus the results are applicable to certain classes of distributed systems. We derive necessary and sufficient conditions for mean-square stability in terms of the spectral radius of a linear Matrix Operator whose dimension is that of the number of uncertainties, rather than the dimension of any underlying state space models. Our condition is applicable to the case of correlated uncertainties, and reproduces earlier results for uncorrelated uncertainties. For cases where state space realizations are given, Linear Matrix Inequality (LMI) equivalents of the input-output conditions are given.
