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SOLVABILITY OF SYLVESTER OPERATOR EQUATION WITH BOUNDED SUBNORMAL OPERATORS IN HILBERT SPACES
Bekkar, Lourabi Hariz,Mansour, Abdelouahab The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.
Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System
Medjber, Salim,Bekkar, Hacene,Menouar, Salah,Choi, Jeong Ryeol Hindawi Limited 2016 Advances in mathematical physics Vol.2016 No.-
<P>The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions) of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.</P>
SURFACES OF REVOLUTION SATISFYING △IIG = f(G + C)
Chahrazede Baba-Hamed,Mohammed Bekkar 대한수학회 2013 대한수학회보 Vol.50 No.4
In this paper, we study surfaces of revolution without par- abolic points in 3-Euclidean space R3, satisfying the condition △IIG = f(G+ C), where △II is the Laplace operator with respect to the second fundamental form, f is a smooth function on the surface and C is a con- stant vector. Our main results state that surfaces of revolution without parabolic points in R3 which satisfy the condition △IIG = fG, coincide with surfaces of revolution with non-zero constant Gaussian curvature.
SURFACES OF REVOLUTION SATISFYING Δ<sup>II</sup>G = f(G + C)
Baba-Hamed, Chahrazede,Bekkar, Mohammed Korean Mathematical Society 2013 대한수학회보 Vol.50 No.4
In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.
Fateh Merdj,Ahmed Mekki,Djamil Guettiche,Boualem Mettai,Zakaria Bekkar Djeloul Sayah,Zitouni Safidine,Abderrazak Abdi,Rachid Mahmoud,Mohamed M. Chehimi 한국고분자학회 2018 Macromolecular Research Vol.25 No.6
Air quality monitoring is of major concern as it is directly linked to public health. It requires the development of high sensitive devices with fast response towards hazardous gas and volatile compounds. Such performances depend on the nature and quality of deposition of the sensing layer. Herein, adherent polypyrroledodecylbenzene sulfonic acid (PPy–DBSA) films were deposited on a N-(3-trimethoxysilylpropyl) pyrrole modified ITO coated polyethylene teraphtalate (PET) flexible substrate by facile direct electrochemical oxidation of pyrrole in an aqueous solution of sulfonic acid. The obtained PPy-DBSA films were subjected to various characterization techniques such as, FTIR, Raman, SEM and conductivity measurements. Chemiresistive gas sensing tests have demonstrated selectivity and sensitivity of films toward ammonia vapors over the other vapors (nitrogen dioxide, carbon dioxide, hydrogen sulfide, acetone, methanol and ethanol) with higher response at 20 ppm, reasonably fast response time of 3 min and reaching detection limit of 3ppm. The response of the sensor can reasonably be related to the strong electrostatic interactions between vapor molecules and the dopant agents within PPy films. In comparison PPy- DBSA films prepared on pristine ITO/PET has exhibited lower response at 20 ppm of ammonia exposure, which highlights the role of surface modification and the contribution from the dopant agent nature for ammonia sensing. Moreover, chemiresistive response performances have been tested in the presence of humidity, under varied temperatures, and finally their behaviors were featured by an impedance spectroscopy in both presence and absence of gas. This work conclusively shows that the sensing performances are not only driven by the molecular interactions between the sensor and the analyte but also by the quality of deposition and adhesion of the former to the transducer. The latter feature can be controlled by appropriate chemical surface modification.
Fateh Merdj,Ahmed Mekki,Djamil Guettiche,Boualem Mettai,Zakaria Bekkar Djeloul Sayah,Zitouni Safidine,Abderrazak Abdi,Rachid Mahmoud,Mohamed M. Chehimi 한국고분자학회 2018 Macromolecular Research Vol.26 No.6
Air quality monitoring is of major concern as it is directly linked to public health. It requires the development of high sensitive devices with fast response towards hazardous gas and volatile compounds. Such performances depend on the nature and quality of deposition of the sensing layer. Herein, adherent polypyrroledodecylbenzene sulfonic acid (PPy–DBSA) films were deposited on a N-(3-trimethoxysilylpropyl) pyrrole modified ITO coated polyethylene teraphtalate (PET) flexible substrate by facile direct electrochemical oxidation of pyrrole in an aqueous solution of sulfonic acid. The obtained PPy-DBSA films were subjected to various characterization techniques such as, FTIR, Raman, SEM and conductivity measurements. Chemiresistive gas sensing tests have demonstrated selectivity and sensitivity of films toward ammonia vapors over the other vapors (nitrogen dioxide, carbon dioxide, hydrogen sulfide, acetone, methanol and ethanol) with higher response at 20 ppm, reasonably fast response time of 3 min and reaching detection limit of 3ppm. The response of the sensor can reasonably be related to the strong electrostatic interactions between vapor molecules and the dopant agents within PPy films. In comparison PPy- DBSA films prepared on pristine ITO/PET has exhibited lower response at 20 ppm of ammonia exposure, which highlights the role of surface modification and the contribution from the dopant agent nature for ammonia sensing. Moreover, chemiresistive response performances have been tested in the presence of humidity, under varied temperatures, and finally their behaviors were featured by an impedance spectroscopy in both presence and absence of gas. This work conclusively shows that the sensing performances are not only driven by the molecular interactions between the sensor and the analyte but also by the quality of deposition and adhesion of the former to the transducer. The latter feature can be controlled by appropriate chemical surface modification.