Pulses propagating in a non-linear dispersive (glass) fibre can be described by the non-linear Schrdinger equation il the pulse is longer than a picosecond; for shorter pulses, this equation must be extended. In this paper we systematically derive this extended equation using the method of mult...
For interest’s sake, this ODE has a physical interpretation as a driven damped harmonic oscillator; yp represents the steady state, and c1y1 + c2y2 is the transient. 2.5.4 Equation with variable coefficients A linear ODE of order n with variable coefficients has the general form pn(x)y...
For a simple compressible substance composed of a single component (the applicable model for nearly all pure fluids), the specification of two independent thermodynamic properties completely determines the state of the system. We can write relations such as the thermal and caloric equations of state:...
416) stated that “This test should be performed for one pair of constructs at a time, rather than as a simultaneous test of all pairs of interest. The reason for this is that a non-significant value for one pair of constructs can be obfuscated by being tested with several pairs that ...
In this study, we apply the extended simple equation approach and the improved F-expansion method to obtain the wave solutions for Eq. (1). The strength of the entire optical framework is determined by the TOD parameter and well-known effects, which also serve as conditional constraints. ...
We begin with the proof of (a). Sinceuis a mild solution, a simple calculation yields the equality \begin{aligned} J(t+h) - J(t) = \int _t^{t+h} K(s) \,\textrm{d}s \end{aligned} for allt \in Iandh \in \mathbb {R}witht+h \in I. This formula and the integrability...
alternative remedial strategies when these assumptions are seriously violated / these topics are the focus of the present chapter overview of normal theory estimation / effects and detection of nonnormality / remedies for multivariate nonnormality (PsycINFO Database Record (c) 2012 APA, all rights ...
Beam propagation management is a topic of considerable interest in the field of optics. Here, we put forward a simple scheme for the realization of propagation management of light beams by introducing a double-barrier potential into the FSE. Transmission, partial transmission/reflection, and total ...
The interest of these studies is not purely speculative. Indeed one of the most popular numerical codes for the Boltzmann equation, the Bird scheme, is based on this particle approximation (see [88] and also [29] for a general discussion and references quoted therein). We finally mention an...
For the purposes of proper estimation and inference, a very important question concerns the sampling mechanism. In the absence of explicit information to the contrary, estimation methods such as maximum likelihood assume that data are generated according tosimple random sampling. Perhaps more often than...