New integrals for electric and magnetic potentials of arbitrary time-independent charge distributions moving with constant velocity are derived. In contrast to the familiar retarded potential integrals, the new integrals express the potentials in terms of the position occupied by the charge distribution at the moment t for which the potentials are being determined. Two different methods are use...

For many physical systems like vehicles, acceleration can be easily measured for the respective states. However, the outputs are usually affected by stochastic noise disturbance. The mentioned systems are often sensitive to noise and structural uncertainties. Furthermore, it is very difficult to estimate the multiple integrals of the signal, acceleration to velocity and velocity to position. In...

We prove certain L estimates (1 < p <∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain L boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals.

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain L boundedness for these oscillatory integrals under rather weak size conditions on the kernel function. Keywords—Fourier transform, oscillatory integrals, Orlicz spaces, B...

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Overlap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and coworkers, who developed a variational approach to the Sherrington-Kirkpatrick model. We propose here an iterative procedure to show that, in the so-called Boltzmann ROSt, Aizenman...