Tatra mountains mathematical publications, Oct 31, 2023
The direct calculation of the generalized operator entropy proves to be difficult due to the appe... more The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our work, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illustrating the theoretical result are discussed.
In the present paper and as an application of Roth's theorem concerning the rational approximatio... more In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational terms are transcendental numbers. We recall that all the infinite series that we are going to treat are Liouville numbers. At the end this article, we establish an approximation measure of these numbers.
In this paper, we investigate commutativity of ring R with involution * which admits a derivation... more In this paper, we investigate commutativity of ring R with involution * which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not super uous.
International Journal of Open Problems in Computer Science and Mathematics, Nov 1, 2017
In this paper we establish some commutativity criteria for a ring with involution (R, *) in which... more In this paper we establish some commutativity criteria for a ring with involution (R, *) in which derivations satisfy certain algebraic identities. Some related results characterizing commutativity of prime rings have been discussed. Furthermore, we provide examples to show that the conditions imposed in the hypotheses of our results are necessary.
The aim of this paper is to provide some results and applications of continued fractions with mat... more The aim of this paper is to provide some results and applications of continued fractions with matrix arguments. First, we recall some properties of matrix functions with real coefficients. Afterwards, we give a continued fraction expansion of the symmetric operator entropy.
Comptes rendus de l'Académie des sciences. Série 1, Mathématique, 1993
Le but de cette these est d'etudier des conditions suffisantes que doivent verifier des fract... more Le but de cette these est d'etudier des conditions suffisantes que doivent verifier des fractions continues a convergence rapide pour que celles-ci soient irrationnelles, transcendantes ou algebriquement independantes. Ensuite, on calcule leur mesure d'irrationalite, d'approximation et d'independance algebrique. Soit a=a#0;a#1,a#2,. . . La fraction continue de quotients partiels a#0,a#1,a#2,. . . , de meme b=b#0;b#1,b#2,. . . . On montre que si si a#n>b#n>a#n##1#7 pour tout n suffisamment grand, alors a,b,aa,ab et a/b sont transcendants. Et s'il existe r>1 et une suite de reels l#n qui tend vers + tel que r##1a#n>b#n>a#n#-#1#l#n##1 pour tout n1 alors a et b sont algebriquement independants. Ce resultat reste valable dans le cas p-adique. On montre aussi qu'il se generalise au cas de plusieurs fractions continues. Nous donnons aussi quelques proprietes du developpement de nombres irrationnels en fraction continue optimale, ainsi que quelques relations entre les developpements en fraction continue reguliere et optimale
In the present paper, we give sufficient conditions on the elements of the continued fractions A ... more In the present paper, we give sufficient conditions on the elements of the continued fractions A and B that will assure us that the continued fraction A B is a transcendental number. With the same condition, we establish a transcendental measure of A B. where (a i > 0, b i > 0 are integers for any i ≥ 1).
In the present paper, we give sufficient conditions on the elements of the continued fractions A ... more In the present paper, we give sufficient conditions on the elements of the continued fractions A and B that will assure us that the continued fraction A B is a transcendental number. With the same condition, we establish a transcendental measure of A B. where (a i > 0, b i > 0 are integers for any i ≥ 1).
International Journal of Computational and Applied Mathematics & Computer Science, Dec 29, 2022
In the present paper, we prove the algebraic independence of a finite number of real continued fr... more In the present paper, we prove the algebraic independence of a finite number of real continued fractions which have partial quotients that increase rapidly. Then, we give an algebraic independence measure of these continued fractions.
In the present paper, we give sufficient conditions on the elements of the continued fractions $A... more In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
The direct calculation of the Generalized operator entropy proves difficult by the appearance of ... more The direct calculation of the Generalized operator entropy proves difficult by the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our paper, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illutrating the theoretical result are discussed.
... January 2006 41 *Address for correspondence: Salah Salhi Université Moulay Ismail, Faculté de... more ... January 2006 41 *Address for correspondence: Salah Salhi Université Moulay Ismail, Faculté des Sciences et Techniques Département de Mathématiques, Groupe d'Algèbre et Applications BP 509-Boutalamine, Errachidia, Morocco e-mail: [email protected] ...
Journal of Mathematical and Computational Science, 2021
In this work, we introduce the concept of *-K-operator frames in Hilbert pro-C *-modules, which i... more In this work, we introduce the concept of *-K-operator frames in Hilbert pro-C *-modules, which is a generalization of K-operator frame. We present the analysis operator, the synthesis operator and the frame operator. We also give some properties and we study the tensor product of *-K-operator frame for Hilbert pro-C *-modules.
We recall that means arise in various contexts and contribute to solving many scientific problems... more We recall that means arise in various contexts and contribute to solving many scientific problems. The aim of the present paper is to give a continued fraction expansion of the Heinz operator mean for two positive definite matrices. We note that the direct calculation of the Heinz operator mean proves difficult by the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation. We use the matrix continued fraction algorithm. At the end of our paper, we deduce a continued fraction representation of the symmetric operator entropy.
The aim of this paper is to give some properties and results of continued fractions with matrix a... more The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued fraction expansion of the Gauss hypergeometric function. At the end, some numerical examples illustrating the theoretical results are discussed.
In this article we investigate some commutativity criteria for a ring with involution {(R,\ast} )... more In this article we investigate some commutativity criteria for a ring with involution {(R,\ast} ) in which generalized derivations satisfy certain algebraic identities. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
Tatra mountains mathematical publications, Oct 31, 2023
The direct calculation of the generalized operator entropy proves to be difficult due to the appe... more The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our work, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illustrating the theoretical result are discussed.
In the present paper and as an application of Roth's theorem concerning the rational approximatio... more In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational terms are transcendental numbers. We recall that all the infinite series that we are going to treat are Liouville numbers. At the end this article, we establish an approximation measure of these numbers.
In this paper, we investigate commutativity of ring R with involution * which admits a derivation... more In this paper, we investigate commutativity of ring R with involution * which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not super uous.
International Journal of Open Problems in Computer Science and Mathematics, Nov 1, 2017
In this paper we establish some commutativity criteria for a ring with involution (R, *) in which... more In this paper we establish some commutativity criteria for a ring with involution (R, *) in which derivations satisfy certain algebraic identities. Some related results characterizing commutativity of prime rings have been discussed. Furthermore, we provide examples to show that the conditions imposed in the hypotheses of our results are necessary.
The aim of this paper is to provide some results and applications of continued fractions with mat... more The aim of this paper is to provide some results and applications of continued fractions with matrix arguments. First, we recall some properties of matrix functions with real coefficients. Afterwards, we give a continued fraction expansion of the symmetric operator entropy.
Comptes rendus de l'Académie des sciences. Série 1, Mathématique, 1993
Le but de cette these est d'etudier des conditions suffisantes que doivent verifier des fract... more Le but de cette these est d'etudier des conditions suffisantes que doivent verifier des fractions continues a convergence rapide pour que celles-ci soient irrationnelles, transcendantes ou algebriquement independantes. Ensuite, on calcule leur mesure d'irrationalite, d'approximation et d'independance algebrique. Soit a=a#0;a#1,a#2,. . . La fraction continue de quotients partiels a#0,a#1,a#2,. . . , de meme b=b#0;b#1,b#2,. . . . On montre que si si a#n>b#n>a#n##1#7 pour tout n suffisamment grand, alors a,b,aa,ab et a/b sont transcendants. Et s'il existe r>1 et une suite de reels l#n qui tend vers + tel que r##1a#n>b#n>a#n#-#1#l#n##1 pour tout n1 alors a et b sont algebriquement independants. Ce resultat reste valable dans le cas p-adique. On montre aussi qu'il se generalise au cas de plusieurs fractions continues. Nous donnons aussi quelques proprietes du developpement de nombres irrationnels en fraction continue optimale, ainsi que quelques relations entre les developpements en fraction continue reguliere et optimale
In the present paper, we give sufficient conditions on the elements of the continued fractions A ... more In the present paper, we give sufficient conditions on the elements of the continued fractions A and B that will assure us that the continued fraction A B is a transcendental number. With the same condition, we establish a transcendental measure of A B. where (a i > 0, b i > 0 are integers for any i ≥ 1).
In the present paper, we give sufficient conditions on the elements of the continued fractions A ... more In the present paper, we give sufficient conditions on the elements of the continued fractions A and B that will assure us that the continued fraction A B is a transcendental number. With the same condition, we establish a transcendental measure of A B. where (a i > 0, b i > 0 are integers for any i ≥ 1).
International Journal of Computational and Applied Mathematics & Computer Science, Dec 29, 2022
In the present paper, we prove the algebraic independence of a finite number of real continued fr... more In the present paper, we prove the algebraic independence of a finite number of real continued fractions which have partial quotients that increase rapidly. Then, we give an algebraic independence measure of these continued fractions.
In the present paper, we give sufficient conditions on the elements of the continued fractions $A... more In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
The direct calculation of the Generalized operator entropy proves difficult by the appearance of ... more The direct calculation of the Generalized operator entropy proves difficult by the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our paper, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illutrating the theoretical result are discussed.
... January 2006 41 *Address for correspondence: Salah Salhi Université Moulay Ismail, Faculté de... more ... January 2006 41 *Address for correspondence: Salah Salhi Université Moulay Ismail, Faculté des Sciences et Techniques Département de Mathématiques, Groupe d'Algèbre et Applications BP 509-Boutalamine, Errachidia, Morocco e-mail: [email protected] ...
Journal of Mathematical and Computational Science, 2021
In this work, we introduce the concept of *-K-operator frames in Hilbert pro-C *-modules, which i... more In this work, we introduce the concept of *-K-operator frames in Hilbert pro-C *-modules, which is a generalization of K-operator frame. We present the analysis operator, the synthesis operator and the frame operator. We also give some properties and we study the tensor product of *-K-operator frame for Hilbert pro-C *-modules.
We recall that means arise in various contexts and contribute to solving many scientific problems... more We recall that means arise in various contexts and contribute to solving many scientific problems. The aim of the present paper is to give a continued fraction expansion of the Heinz operator mean for two positive definite matrices. We note that the direct calculation of the Heinz operator mean proves difficult by the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation. We use the matrix continued fraction algorithm. At the end of our paper, we deduce a continued fraction representation of the symmetric operator entropy.
The aim of this paper is to give some properties and results of continued fractions with matrix a... more The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued fraction expansion of the Gauss hypergeometric function. At the end, some numerical examples illustrating the theoretical results are discussed.
In this article we investigate some commutativity criteria for a ring with involution {(R,\ast} )... more In this article we investigate some commutativity criteria for a ring with involution {(R,\ast} ) in which generalized derivations satisfy certain algebraic identities. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
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