Analisi della funzione ventricolare nel Diabete mellito tipo 2: uno studio mediante ecocardiografia con 2D Strain.

Il diabete mellito è senza dubbio una delle patologie a maggior impatto socio-economico della nostra epoca. L'OMS riconosce che esso rappresenta una delle maggiori sfide poste dalle malattie croniche. Le conoscenze su quella che viene considerata non una malattia, ma una sindrome che raggruppa numerose condizioni morbose, eterogenee dal punto di vista eziopatogenetico, ma con il comune denominatore dell'iperglicemia, si sono enormemente accresciute

Singular Cauchy problem for the general Euler-Poisson-Darboux equation

In this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable

On an identity for the iterated weighted spherical mean and its applications

Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms.We generalize iterated spherical means to weighted ones based on generalized translation operators and consider applications to B-hyperbolic equations and transmission tomography problems. © 2016 Shishkina, E.L., Sitnik, S.M

On fractional powers of the Bessel operator on semiaxis

In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator. © 2018 Sitnik SM, Shishkina EL

General form of the Euler-Poisson-Darboux equation and application of the transmutation method

In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations. © 2017 Texas State University

ON FRACTIONAL POWERS OF BESSEL OPERATORS

In this paper we study fractional powers of the Bessel differential operator. The fractional powers are defined explicitly in the integral form without use of integral transforms in its definitions. Some general properties of the fractional powers of the Bessel differential operator are proved and some are listed. Among them are different variations of definitions, relations with the Mellin and Hankel transforms, group property, generalized Taylor formula with Bessel operators, evaluation of resolvent integral operator in terms of the Wright or generalized Mittag-LeFFer functions. At the end, some topics are indicated for further study and possible generalizations. Also the aim of the paper is to attract attention and give references to not widely known results on fractional powers of the Bessel differential operator

ON FRACTIONAL POWERS OF BESSEL OPERATORS

In this paper we study fractional powers of the Bessel differential operator. The fractional powers are defined explicitly in the integral form without use of integral transforms in its definitions. Some general properties of the fractional powers of the Bessel differential operator are proved and some are listed. Among them are different variations of definitions, relations with the Mellin and Hankel transforms, group property, generalized Taylor formula with Bessel operators, evaluation of resolvent integral operator in terms of the Wright or generalized Mittag-LeFFer functions. At the end, some topics are indicated for further study and possible generalizations. Also the aim of the paper is to attract attention and give references to not widely known results on fractional powers of the Bessel differential operator

On an identity for the iterated weighted spherical mean and its applications

Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms.We generalize iterated spherical means to weighted ones based on generalized translation operators and consider applications to B-hyperbolic equations and transmission tomography problems. © 2016 Shishkina, E.L., Sitnik, S.M

On fractional powers of the Bessel operator on semiaxis

In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator. © 2018 Sitnik SM, Shishkina EL

General form of the Euler-Poisson-Darboux equation and application of the transmutation method

In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations. © 2017 Texas State University