The radii of the planetary and satellite orbits are in approximate agreement with geometric progressions. The question of whether the observed patterns have some physical basis or are due to chance may be addressed using a Monte Carlo approach. We find that the estimated probability of chance occurrence depends sensitively on the restrictions imposed on the population of orbits. We argue that i...

We derive a rigorous estimate of the size of islands (in both phase space and parameter space) appearing in smooth Hamiltonian approximations of scattering billiards. The derivation includes the construction of a local return map near singular periodic orbits for an arbitrary scattering billiard and for the general smooth billiard potentials. Thus, universality classes for the local behavior ar...

Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mecha...

Fractional factorial split-plot designs are widely used when it is impractical to perform fractional experiments in a completely random order. When there too many subplots per whole plot, or few plots, with replicated settings of the plot factors preferred. However, such an important study undeveloped literature. This paper considers WP from viewpoint clear effects. We investigate sufficient an...

In some experiments, the levels of factors are difficult to change; then fractional factorial split-plot (FFSP) designs suitable for selection. an FFSP design, divided into two classes—the whole plot (WP) and subplot (SP) factors. selection WP can affect that SP factors, which attracts much attention Paying more a new optimality criterion selecting such is proposed. The robustness proposed meth...

Low probability of intercept radar signals, which are often problematic to detect and characterize, have as their goal ‘to see and not be seen’. Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques for the purpose of analyzing these low probability of intercept radar signals. This paper presents the novel appr...