Etude curriculaire du statut des probabilités et sstatistiques au Maroc: perspectives d'améliora... more Etude curriculaire du statut des probabilités et sstatistiques au Maroc: perspectives d'amélioration
New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure f... more New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure f... more New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
Evolution pheneomena mainly in the non autonomous case are treated and some abc's on copulas are... more Evolution pheneomena mainly in the non autonomous case are treated and some abc's on copulas are recalled in order to study deeply evolution copulas which describe dependence aspects between two or many variables.
Ce travail est dédié au défilement historique de enseignement des statistiques et probabilités ch... more Ce travail est dédié au défilement historique de enseignement des statistiques et probabilités chez nous et ailleurs. Quelques pistes d'amélioration sont proposées
Unifying nature of a research vision as we see it. Mathematical analysis, probability, finace, di... more Unifying nature of a research vision as we see it. Mathematical analysis, probability, finace, didactics and other areas of knowledge!!!!!
We give a new sufficient condition which allows to test primality of Fermat's numbers. This c... more We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary arithmetic technical tools and it will be susceptible to open gates for revolutionary statement that all Fermat's numbers are all decomposable.
The concept of boundary values of holomorphic semigroups in a general Banach space is studied. As... more The concept of boundary values of holomorphic semigroups in a general Banach space is studied. As an application, we consider the Riemann-Liouville semigroup of integration operator in the little Holder spaces $\rm{lip}_0^\alpha[0,\, 1] , \, 0<\alpha<1$ and prove that it admits a strongly continuous boundary group, which is the group of fractional integration of purely imaginary order. The corresponding result for the $L^p$-spaces ($1<p<\infty$) has been known for some time, the case $p=2$ dating back to the monograph by Hille and Phillips. In the context of $L^p$ spaces, we establish the existence of the boundary group of the Hadamard fractional integration operators using semigroup methods. In the general framework, using a suitable spectral decomposition,we give a partial treatment of the inverse problem, namely: Which $C_0$-groups are boundary values of some holomorphic semigroup of angle $\pi/2$?
Etude curriculaire du statut des probabilités et sstatistiques au Maroc: perspectives d'améliora... more Etude curriculaire du statut des probabilités et sstatistiques au Maroc: perspectives d'amélioration
New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure f... more New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure f... more New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
Evolution pheneomena mainly in the non autonomous case are treated and some abc's on copulas are... more Evolution pheneomena mainly in the non autonomous case are treated and some abc's on copulas are recalled in order to study deeply evolution copulas which describe dependence aspects between two or many variables.
Ce travail est dédié au défilement historique de enseignement des statistiques et probabilités ch... more Ce travail est dédié au défilement historique de enseignement des statistiques et probabilités chez nous et ailleurs. Quelques pistes d'amélioration sont proposées
Unifying nature of a research vision as we see it. Mathematical analysis, probability, finace, di... more Unifying nature of a research vision as we see it. Mathematical analysis, probability, finace, didactics and other areas of knowledge!!!!!
We give a new sufficient condition which allows to test primality of Fermat's numbers. This c... more We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary arithmetic technical tools and it will be susceptible to open gates for revolutionary statement that all Fermat's numbers are all decomposable.
The concept of boundary values of holomorphic semigroups in a general Banach space is studied. As... more The concept of boundary values of holomorphic semigroups in a general Banach space is studied. As an application, we consider the Riemann-Liouville semigroup of integration operator in the little Holder spaces $\rm{lip}_0^\alpha[0,\, 1] , \, 0<\alpha<1$ and prove that it admits a strongly continuous boundary group, which is the group of fractional integration of purely imaginary order. The corresponding result for the $L^p$-spaces ($1<p<\infty$) has been known for some time, the case $p=2$ dating back to the monograph by Hille and Phillips. In the context of $L^p$ spaces, we establish the existence of the boundary group of the Hadamard fractional integration operators using semigroup methods. In the general framework, using a suitable spectral decomposition,we give a partial treatment of the inverse problem, namely: Which $C_0$-groups are boundary values of some holomorphic semigroup of angle $\pi/2$?
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