(1) Let F , F1, F2 be finite sequences of elements of R and given r1, r2. If F1 = 〈r1〉 F or F1 = F a 〈r1〉 and if F2 = 〈r2〉 F or F2 = F a 〈r2〉, then ∑(F1−F2) = r1− r2. (2) Let F1, F2 be finite sequences of elements of R. If lenF1 = lenF2, then len(F1 +F2) = lenF1 and len(F1−F2) = lenF1 and ∑(F1 +F2) = ∑F1 +∑F2 and ∑(F1−F2) = ∑F1−∑F2. (3) Let F1, F2 be finite sequences of elements of R. If lenF1 ...

The hypothesis that the intracranial EEG has local structure and short-term non-stationarity is tested with a little-studied measure of non-linear phase coupling, the bicoherence in human subdural and deep temporal lobe probe data from 11 subjects during sleeping, waking and seizure states. This measure of cooperativity estimates the proportion of energy in every possible pair of frequency comp...

Theoretical approaches to magnitude-frequency analysis (MFA) of sediment transport in channels couple continuous flow probability density functions (PDFs) with power law flow-sediment transport relations (rating curves) to produce closed-form equations relating MFA metrics such as the effective discharge, Qeff, and fraction of sediment transported by discharges greater than Qeff, f1, to statist...

Starpoint combiners are most often used for simpler combining applications. In theory an infinite number of frequencies can be starpointed, however in application it is generally limited to a maximum of five or six channels with the bulk of the combiners of this type being two and three channel. The luxury of an inexpensive system with fairly conservative size considerations is one of the highl...

Both comparative category rating (CCR) and degradation category rating (DCR) methods [20] have been heavily employed in the subjective evaluations of media systems. The resulting metrics, comparative mean-opinion-score (CMOS) and degradation mean-opinion-score (DMOS), can be used to describe the system subjective quality. However, the subjective metrics may work unsuccessfully when the variance...

In this paper F1 denotes a non empty finite topology space and A, B, C denote subsets of F1. Let us consider F1. One can check that ∅(F1) is connected. We now state two propositions: (1) For all subsets A, B of F1 holds (A ∪ B) b = A ∪ B. (2) (∅(F1)) b = ∅. Let us consider F1. Observe that (∅(F1)) b is empty. Next we state the proposition (3) Let A be a subset of F1. Suppose that for all subset...

The entrance-channel mass-asymmetry dependence of the compound nucleus formation time in light heavyion reactions has been investigated within the framework of semiclassical dissipative collision models. The model calculations have been applied successfully to the formation of the Ar compound nucleus as populated via the Be1 Si, B1 Al, C1 Mg, and F1 F entrance channels. The shape evolution of s...