Some Inequalities Involving the Constante, and an Application to Carleman's Inequality

AbstractSome inequalities involving the constanteare considered. A strengthened Carleman's inequality is proved

On a New Generalization of Hardy–Hilbert's Inequality and Its Applications

AbstractThis paper deals with a generalization of the Hardy–Hilbert inequality with best constant factor which involves the β function. As an application, we obtain a new equivalent form of the Hardy–Hilbert inequality

Asymptotic stability of solutions of the generalized Burgers equation

AbstractThis paper is concerned with the existence and stability analysis of the generalized Burgers equation. For the cylindrical case, the bounded solutions are found to be asymptotically stable to the similarity solution. For the super cylindrical case, the asymptotic limit of the generalized Burgers equation is an error function solution of the linearized Burgers equation. It is shown that this result generalizes the result of Scott [5]

Recent developments on the Stieltjes transform of generalized functions

This paper is concerned with recent developments on the Stieltjes transform of generalized functions. Sections 1 and 2 give a very brief introduction to the subject and the Stieltjes transform of ordinary functions with an emphasis to the inversion theorems. The Stieltjes transform of generalized functions is described in section 3 with a special attention to the inversion theorems of this transform. Sections 4 and 5 deal with the adjoint and kernel methods used for the development of the Stieltjes transform of generalized functions. The real and complex inversion theorems are discussed in sections 6 and 7. The Poisson transform of generalized functions, the iteration of the Laplace transform and the iterated Stieltjes transfrom are included in sections 8, 9 and 10. The Stieltjes transforms of different orders and the fractional order integration and further generalizations of the Stieltjes transform are discussed in sections 11 and 12. Sections 13, 14 and 15 are devoted to Abelian theorems, initial-value and final-value results. Some applications of the Stieltjes transforms are discussed in section 16. The final section deals with some open questions and unsolved problems. Many important and recent references are listed at the end

S. N. Bose (1894-1974) and the Bose quantum statistics a centennial tribute

This centennial tribute commemorates Bose the Man and Bose the Scientist. A survey of S.N. Bose's life and career is presented in some detail. His major scientific contributions including the discovery of Bose statistics and the novel derivation of the Planck black body radiation formula are described

On generation and propagation of tsunamis in a shallow running ocean

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically as t−12 for the two dimensional case and as t−1 for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper

On Hilbert's type operator norm inequalities on Herz spaces

In this paper some necessary and sufficient conditions are given for the Hilbert’s type operators to be bounded on the Herz spaces. The corresponding new operator norm inequalities are obtained