Simultaneous two-dimensional Space and Time Measurement of Ultrashort Optical Pulses based on Spatial-Spectral Interferometry.

2001 ◽  
pp. 138-140
Author(s):  
Takasumi Tanabe ◽  
Nobutastu Takei ◽  
Hiroshi Tanabe ◽  
Fumihiko Kannari
Keyword(s):  
Dimensional Space ◽  
Time Measurement ◽  
Two Dimensional ◽  
Optical Pulses ◽  
Spectral Interferometry ◽  
Ultrashort Optical Pulses ◽  
Space And Time

scholarly journals On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equatio

2017 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Wave Equation ◽  
Fundamental Solution ◽  
Open Problem ◽  
Special Functions ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Diffusion Wave ◽  
Space And Time ◽  
Mellin Convolution

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Impact ionization probabilities as functions of two-dimensional space and time

2001 ◽  
Vol 89 (5) ◽  
pp. 2742-2751 ◽  
Author(s):  
S. A. Plimmer ◽  
J. P. R. David ◽  
B. Jacob ◽  
G. J. Rees
Keyword(s):  
Impact Ionization ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Space And Time
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