189 research outputs found
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
- …