Results 31 to 40 of about 265 (83)

Spacetime causality in the study of the Hankel transform

, 2006
We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the ...
Burnol, Jean-Francois
core   +1 more source

Extending Sonine kernels to arbitrary dimensions

Banach Journal of Mathematical Analysis
Abstract The theory of general fractional calculus with Sonine kernels has been well developed by Luchko in the one-dimensional case. Inspired by recent work on Mikusiński’s operational calculus for fractional partial differential operators, we construct a multi-dimensional version of the theory of Sonine kernels, solving a recognised open ...
openaire   +1 more source

Two-dimensional Time-dependent Point Interactions

, 2016
We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet time-evolution is ...
Carlone, R., Correggi, M., Figari, R.
core   +1 more source

Fundamental Solutions and Decay of Fully Non-local Problems

, 2018
In this paper, we study a fully non-local reaction-diffusion equation which is non-local both in time and space. We apply subordination principles to construct the fundamental solutions of this problem, which we use to find a representation of the mild ...
Pozo, Juan C., Vergara, Vicente
core   +1 more source

On the Rigorous Correspondence Between Operator Fractional Powers and Fractional Derivatives via the Sonine Kernel

Fractal and Fractional
Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address these challenges, we have developed a universal framework for defining the fractional calculus ...
Zelin Liu, Xiaobin Yu, Yajun Yin
openaire   +2 more sources

Biorthogonal Quantum Systems

, 2005
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual ...
Abramowitz M., Banach S., Brezinski C., Curtright T., Curtright T., Dieudonné J., Gohberg I. T., Goursat E., Kato T., Luca Mezincescu, Morse P. M., Muskhelishvili N. I., Neumann C. G., Prudnikov A. P., Rofe-Beketov F. S., Thomas Curtright, Tkachenko V. A., Vilenkin N., Watson G. N.   +18 more
core   +2 more sources

Symmetrical Sonin kernels in terms of the hypergeometric functions

, 2023
In this paper, we introduce a new class of the kernels of the integral transforms of the Laplace convolution type that we call symmetrical Sonin kernels. For a symmetrical Sonin kernel given in terms of some elementary or special functions, its associated kernel has the same form with possibly different parameter values.
openaire   +1 more source

Plasma Electronics [PDF]

, 1965
Contains reports on seventeen research projects.National Science Foundation (Grant GK-57)United States Atomic Energy Commission (Contract AT(30-1)-3285)United States Atomic Energy Commission under Contract AT(30-1 ...
Bers, Abraham, Brown, T. S., Clarke, J. F., Fessenden, T. J., Gardiol, F., Gerry, E. T., Gyftopoulos, E. P., Hoag, J. K., Kusse, B. R., Kyong, S. H., Lidsky, Lawrence M., Lieberman, M. A., Lubin, M. D., Moir, R. W., Musha, T., Robertson, E. A., Rose, D. J., Schneider, H. M., Wagner, C. E., Wilkins, D. R., Woo, J. C.   +20 more
core  

Monte Carlo simulation of nonlinear Couette flow in a dilute gas

, 2000
The Direct Simulation Monte Carlo method is applied to solve the Boltzmann equation in the steady planar Couette flow for Maxwell molecules and hard spheres.
Andrés Santos, Brey, Garzó, Garzó, José Marı́a Montanero, Kim, Makashev, Montanero, Montanero, Montanero, Montanero, Risso, Risso, Santos, Tehver, Tij, Vicente Garzó, Wadsworth   +17 more
core   +1 more source

The static and dynamic conductivity of warm dense Aluminum and Gold calculated within a density functional approach

, 2005
The static resistivity of dense Al and Au plsmas are calculated where all the needed inputs are obtained from density functional theory (DFT). This is used as input for a study of the dynamic conductivity.
D. M. Ceperley, K. Trainor, L. J. Dagens, M. W. C. Dharma-wardana, M. W. C. Dharma-wardana, R. Evans, T. E. Faber   +6 more
core   +1 more source