M. Majdoub | University of Tunis El Manar (original) (raw)

Papers by M. Majdoub

Research paper thumbnail of Electrical and sensing properties of partially benzylated β-cyclodextrin: Effect of benzyl chain length

ABSTRACT Thin films of two partially benzylated β-CDs (β-cyclodextrins) were used to functionaliz... more ABSTRACT Thin films of two partially benzylated β-CDs (β-cyclodextrins) were used to functionalize ITO (indium tin oxide) and Si/SiO2 substrates which were deposited by spin coating technique, to fabricate respectively a diode device and an EIS (electrolyte–insulator–semiconductor) sensor. We have studied electrical properties of ITO/β-CDs (Bz)n=5,10/Al diodes by means of current–voltage measurement and impedance spectroscopy. The application of these new modified β-CD (Bz)n=5,10 in the field of chemical sensors has been studied. Electrochemical capacitance measurements with EIS structures were made to test and calibrate physico-chemical sensors with regards to their sensitivity and selectivity. The sensing properties of these partial benzylated β-CD films towards Pb2+ in aqueous solution for sensor application were tested.A significant effect of the average of benzylation degree on both electrical and sensing properties has been investigated.

Research paper thumbnail of A non-water-soluble modified β-cyclodextrin for sensitive electrode

Partially benzylated h-cyclodextrins (h-CDs) are deposited with no coupling agent on the silica s... more Partially benzylated h-cyclodextrins (h-CDs) are deposited with no coupling agent on the silica surface of a wafer which was used as an electrolyte -insulator -semiconductor (EIS) heterostructure to detect cations in aqueous solution. The sensitivity of the EIS devices has been tested for Ca 2+ , Cu 2+ , K + and heavy metal cations Pb 2+ and Cd 2+ . The results showed a Nernstian response towards Pb 2+ as found with h-cyclodextrins incorporated in gel membrane, with good selectivity. The benzylation of the h-cyclodextrins did not affect the complexation properties of the molecule. However, a considerable capacitive effect should be taken into account. The results were compared to a previous work where the h-CD molecules were fixed onto silica insulator surfaces obtained by means of either one of these two ways: chemically grafted to polymethyl-hydrosiloxanes (PMHS) chains, or physically entrapped in plasticized poly(vinyl chloride) (PVC).

Research paper thumbnail of Double logarithmic inequality with a sharp constant

Proceedings of the American Mathematical Society, 2006

We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log es... more We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log estimate is "almost" sharp. These estimates are applied to prove a Moser-Trudinger type inequality for solutions of a 2D wave equation.

Research paper thumbnail of Scattering for the two-dimensional NLS with exponential nonlinearity

Nonlinearity, 2012

We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödin... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below to the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

Research paper thumbnail of Charge transfer processes in polymer light-emitting diodes

Materials Science and Engineering: C, 2002

Optical characterisation of an organic soluble poly (paraphenylene vinylene) (PPV) derivative inv... more Optical characterisation of an organic soluble poly (paraphenylene vinylene) (PPV) derivative involving an alkyloxy pendant group on the phenylene ring has shown a shift of the absorption and emission towards longer wavelengths in comparison to PPV ones. The changes of the optical characteristics are ascribed to the redistribution of the k molecular orbital over the phenylene ring induced by the alkyloxy substituent. The comparison of the absorption and emission of the PPV derivative in solution or as a thin layer shows the role of the interchain interactions in condensed matter. Another example of the importance of charge transfer processes in PLED is provided by the indium tin oxide (ITO)/poly (vinyl carbazole) (PVK) hole transport layer interface. The weakening of the ITO absorption in the UV resulting from interband transitions has been interpreted by the depletion of the ITO free carriers at the contact of PVK. The shift towards longer wavelengths of the plasma frequency in the near infrared confirms the reduction of the free electron concentration in ITO, which has been estimated to 30% using the Drude free electron theory. The formation of a dipole layer at the interface can account for such charge transfers. D

Research paper thumbnail of ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

Journal of Hyperbolic Differential Equations, 2009

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exp... more We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity

Research paper thumbnail of On Uniqueness for Supercritical Nonlinear Wave and Schrodinger Equations

International Mathematics Research Notices, 2014

Research paper thumbnail of Scattering for the two-dimensional energy-critical wave equation

Duke Mathematical Journal, 2009

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Go... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the energy is below or equal to the critical value, then the solution approaches a free Klein-Gordon solution at the time infinity. An interesting feature in the critical case is that the Strichartz estimate together with Sobolev-type inequalities can not control the nonlinear term uniformly on each time interval: it crucially depends on how much the energy is concentrated. Thus we have to trace concentration of the energy along time, in order to set up favorable nonlinear estimates, and only after that we can apply Bourgain's induction argument (or any other similar one). We show the same result for the "subcritical" nonlinear Schrödinger equation.

Research paper thumbnail of Lack of compactness in the 2D critical Sobolev embedding, the general case

Comptes Rendus Mathematique, 2012

This paper is devoted to the description of the lack of compactness of the Sobolev embedding of H... more This paper is devoted to the description of the lack of compactness of the Sobolev embedding of H 1 (R 2 ) in the critical Orlicz space L(R 2 ). It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser in as in the radial setting investigated in . However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an L ∞ estimate far away from the origin and which is no longer valid in the general framework. Within the general framework of H 1 (R 2 ), the strategy we adopted to build the profile decomposition in terms of examples by Moser concentrated around cores is based on capacity arguments and relies on an extraction process of mass concentrations. The essential ingredient to extract cores consists in proving by contradiction that if the mass responsible for the lack of compactness of the Sobolev embedding in the Orlicz space is scattered, then the energy used would exceed that of the starting sequence.

Research paper thumbnail of Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity

Communications on Pure and Applied Mathematics, 2006

We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a se... more We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein-Gordon equation in two space dimension. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method.

Research paper thumbnail of ANALYSIS & PDE

Research paper thumbnail of Energy scattering for 2D critical wave equation

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Go... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the energy is below or equal to the critical value, then the solution approaches a free Klein-Gordon solution at the time infinity. The interesting feature in the critical case is that the Strichartz estimate together with Sobolev-type inequalities can not control the nonlinear term uniformly on each time interval, but with constants depending on how much the solution is concentrated. Thus we have to trace concentration of the energy along time, in order to set up favorable nonlinear estimates, and then to implement Bourgain's induction argument. We show the same result for the "subcritical" nonlinear Schrödinger equation.

Research paper thumbnail of Well- and ill-posedness issues for energy supercritical waves

Analysis & PDE, 2011

We investigate the initial value problem for some energy supercritical semilinear wave equations.... more We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. We also obtain some ill-posedness/weak ill-posedness results. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation.

Research paper thumbnail of On the lack of compactness in the 2D critical Sobolev embedding

This paper is devoted to the description of the lack of compactness of H 1 rad (R 2 ) in the Orli... more This paper is devoted to the description of the lack of compactness of H 1 rad (R 2 ) in the Orlicz space. Our result is expressed in terms of the concentrationtype examples derived by P. -L. Lions in . The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and take into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of non linear wave equation with exponential growth, where the Orlicz norm plays a decisive role.

Research paper thumbnail of Ill-posedness of -supercritical waves

Comptes Rendus Mathematique, 2007

... I 345 (2007) 133 138 http://france.elsevier.com/direct/CRASS1/ Partial Differential Equations... more ... I 345 (2007) 133 138 http://france.elsevier.com/direct/CRASS1/ Partial Differential Equations Ill-posedness of H 1 -supercritical waves Slim Ibrahim a , Mohamed Majdoub b , Nader Masmoudi ca Department of Mathematics & Statistics ... [9] C. Kenig, G. Ponce, L. Vega, On the ill ...

Research paper thumbnail of Electrical and sensing properties of partially benzylated β-cyclodextrin: Effect of benzyl chain length

ABSTRACT Thin films of two partially benzylated β-CDs (β-cyclodextrins) were used to functionaliz... more ABSTRACT Thin films of two partially benzylated β-CDs (β-cyclodextrins) were used to functionalize ITO (indium tin oxide) and Si/SiO2 substrates which were deposited by spin coating technique, to fabricate respectively a diode device and an EIS (electrolyte–insulator–semiconductor) sensor. We have studied electrical properties of ITO/β-CDs (Bz)n=5,10/Al diodes by means of current–voltage measurement and impedance spectroscopy. The application of these new modified β-CD (Bz)n=5,10 in the field of chemical sensors has been studied. Electrochemical capacitance measurements with EIS structures were made to test and calibrate physico-chemical sensors with regards to their sensitivity and selectivity. The sensing properties of these partial benzylated β-CD films towards Pb2+ in aqueous solution for sensor application were tested.A significant effect of the average of benzylation degree on both electrical and sensing properties has been investigated.

Research paper thumbnail of A non-water-soluble modified β-cyclodextrin for sensitive electrode

Partially benzylated h-cyclodextrins (h-CDs) are deposited with no coupling agent on the silica s... more Partially benzylated h-cyclodextrins (h-CDs) are deposited with no coupling agent on the silica surface of a wafer which was used as an electrolyte -insulator -semiconductor (EIS) heterostructure to detect cations in aqueous solution. The sensitivity of the EIS devices has been tested for Ca 2+ , Cu 2+ , K + and heavy metal cations Pb 2+ and Cd 2+ . The results showed a Nernstian response towards Pb 2+ as found with h-cyclodextrins incorporated in gel membrane, with good selectivity. The benzylation of the h-cyclodextrins did not affect the complexation properties of the molecule. However, a considerable capacitive effect should be taken into account. The results were compared to a previous work where the h-CD molecules were fixed onto silica insulator surfaces obtained by means of either one of these two ways: chemically grafted to polymethyl-hydrosiloxanes (PMHS) chains, or physically entrapped in plasticized poly(vinyl chloride) (PVC).

Research paper thumbnail of Double logarithmic inequality with a sharp constant

Proceedings of the American Mathematical Society, 2006

We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log es... more We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log estimate is "almost" sharp. These estimates are applied to prove a Moser-Trudinger type inequality for solutions of a 2D wave equation.

Research paper thumbnail of Scattering for the two-dimensional NLS with exponential nonlinearity

Nonlinearity, 2012

We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödin... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below to the critical value, then the solution approaches a free Schrödinger solution at the time infinity.

Research paper thumbnail of Charge transfer processes in polymer light-emitting diodes

Materials Science and Engineering: C, 2002

Optical characterisation of an organic soluble poly (paraphenylene vinylene) (PPV) derivative inv... more Optical characterisation of an organic soluble poly (paraphenylene vinylene) (PPV) derivative involving an alkyloxy pendant group on the phenylene ring has shown a shift of the absorption and emission towards longer wavelengths in comparison to PPV ones. The changes of the optical characteristics are ascribed to the redistribution of the k molecular orbital over the phenylene ring induced by the alkyloxy substituent. The comparison of the absorption and emission of the PPV derivative in solution or as a thin layer shows the role of the interchain interactions in condensed matter. Another example of the importance of charge transfer processes in PLED is provided by the indium tin oxide (ITO)/poly (vinyl carbazole) (PVK) hole transport layer interface. The weakening of the ITO absorption in the UV resulting from interband transitions has been interpreted by the depletion of the ITO free carriers at the contact of PVK. The shift towards longer wavelengths of the plasma frequency in the near infrared confirms the reduction of the free electron concentration in ITO, which has been estimated to 30% using the Drude free electron theory. The formation of a dipole layer at the interface can account for such charge transfers. D

Research paper thumbnail of ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

Journal of Hyperbolic Differential Equations, 2009

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exp... more We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity

Research paper thumbnail of On Uniqueness for Supercritical Nonlinear Wave and Schrodinger Equations

International Mathematics Research Notices, 2014

Research paper thumbnail of Scattering for the two-dimensional energy-critical wave equation

Duke Mathematical Journal, 2009

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Go... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the energy is below or equal to the critical value, then the solution approaches a free Klein-Gordon solution at the time infinity. An interesting feature in the critical case is that the Strichartz estimate together with Sobolev-type inequalities can not control the nonlinear term uniformly on each time interval: it crucially depends on how much the energy is concentrated. Thus we have to trace concentration of the energy along time, in order to set up favorable nonlinear estimates, and only after that we can apply Bourgain's induction argument (or any other similar one). We show the same result for the "subcritical" nonlinear Schrödinger equation.

Research paper thumbnail of Lack of compactness in the 2D critical Sobolev embedding, the general case

Comptes Rendus Mathematique, 2012

This paper is devoted to the description of the lack of compactness of the Sobolev embedding of H... more This paper is devoted to the description of the lack of compactness of the Sobolev embedding of H 1 (R 2 ) in the critical Orlicz space L(R 2 ). It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser in as in the radial setting investigated in . However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an L ∞ estimate far away from the origin and which is no longer valid in the general framework. Within the general framework of H 1 (R 2 ), the strategy we adopted to build the profile decomposition in terms of examples by Moser concentrated around cores is based on capacity arguments and relies on an extraction process of mass concentrations. The essential ingredient to extract cores consists in proving by contradiction that if the mass responsible for the lack of compactness of the Sobolev embedding in the Orlicz space is scattered, then the energy used would exceed that of the starting sequence.

Research paper thumbnail of Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity

Communications on Pure and Applied Mathematics, 2006

We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a se... more We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein-Gordon equation in two space dimension. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method.

Research paper thumbnail of ANALYSIS & PDE

Research paper thumbnail of Energy scattering for 2D critical wave equation

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Go... more We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the energy is below or equal to the critical value, then the solution approaches a free Klein-Gordon solution at the time infinity. The interesting feature in the critical case is that the Strichartz estimate together with Sobolev-type inequalities can not control the nonlinear term uniformly on each time interval, but with constants depending on how much the solution is concentrated. Thus we have to trace concentration of the energy along time, in order to set up favorable nonlinear estimates, and then to implement Bourgain's induction argument. We show the same result for the "subcritical" nonlinear Schrödinger equation.

Research paper thumbnail of Well- and ill-posedness issues for energy supercritical waves

Analysis & PDE, 2011

We investigate the initial value problem for some energy supercritical semilinear wave equations.... more We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. We also obtain some ill-posedness/weak ill-posedness results. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation.

Research paper thumbnail of On the lack of compactness in the 2D critical Sobolev embedding

This paper is devoted to the description of the lack of compactness of H 1 rad (R 2 ) in the Orli... more This paper is devoted to the description of the lack of compactness of H 1 rad (R 2 ) in the Orlicz space. Our result is expressed in terms of the concentrationtype examples derived by P. -L. Lions in . The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and take into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of non linear wave equation with exponential growth, where the Orlicz norm plays a decisive role.

Research paper thumbnail of Ill-posedness of -supercritical waves

Comptes Rendus Mathematique, 2007

... I 345 (2007) 133 138 http://france.elsevier.com/direct/CRASS1/ Partial Differential Equations... more ... I 345 (2007) 133 138 http://france.elsevier.com/direct/CRASS1/ Partial Differential Equations Ill-posedness of H 1 -supercritical waves Slim Ibrahim a , Mohamed Majdoub b , Nader Masmoudi ca Department of Mathematics & Statistics ... [9] C. Kenig, G. Ponce, L. Vega, On the ill ...