If we assume that N mol molecules are independently photoactivated uniformly in time between 0 and t F, then the probability density function of the time lag, Δt i, between the two successive i th and (i + 1) th photoactivation events is given by the well known order statistics of the uniform distribution: (1) p (Δ t i ) = N m o l (1 − Δ t i / t F ) N m o l.
The formation of vertical systems with large aspect ratios is well known for systems ordered passively in the μm-range.
The interatomic and intermolecular co-operative effects which modify the free-atom coherent scattering process are well known for highly ordered structures such as crystalline materials but are important for amorphous solids and liquids where short-range ordering occurs.
On the other hand, it is well known that highly ordered pore structures in alumina can be achieved via a two-step process [19, 20].
While realizability conditions are well known, least order solutions, which require as few integrators as possible, pose a difficult problem.
Because the properties of the beam have to be well known in order to compare the results of the experiment and the simulation on an absolute basis, the benchmark experiment was performed using the research electron accelerator of the Physikalisch-Technische Bundesanstalt (PTB), whose beam was accurately characterized in advance.
In this work, these two techniques are presented, and comparison are carried out using the well known First Order Reliability Method (FORM), Direct Monte Carlo Simulation and Monte Carlo Simulation with Adaptive Importance Sampling technique with approximated and exact limit state functions.
Don't you need to honor someone well known in order to attract a crowd?
For example if both and are zero mean Gaussian distributed, with variances and then the MAP filter becomes the very well known zero-order Wiener filter [10].
Most recently, Alam and Imdad [23, 24] established a new relation-theoretic version of the Banach contraction principle employing general binary relation which in turn generalizes several well known relevant order-theoretic fixed point theorems.
Vitreous physical characteristics need to be well known in order to recognize its active role in ocular physiology, as shown in Table 2 [ 6].
