Any desired diffraction pattern can be produced in the Fourier plane by the specification of a corresponding input-plane transparency. Complex-valued transmittance is generally required, but in practice phase-only transmittance is used. Many design procedures use numerically intensive, constrained optimization. We instead introduce a noniterative procedure that directly translates the desired b...

We develop a risk-efficient sequential procedure for estimating the parameter θ of the uniform density on (0,θ). We give explicit expressions for the distribution of the stopping time and derive its expectation and variance. We also tabulate the values of the expected stopping time and its standard deviation for some selected values of the parameter. Asymptotic properties such as efficiency and...

An analysis of the uncertainty in measuring the root-mean-square, rms or Rq, value of a periodic waveform which results from the use of a finite record length is presented. Even though the results of the analysis are somewhat as expected, i.e., that the uncertainty is inversely proportional to the number of periods in the record, the explicit relationship between the magnitude of the uncertaint...

Non-stationary random formation of stable nuclei from a small metastable system is considered. Distribution of waiting times to observe the first nucleus is examined, and it is shown that the steady-state nucleation rate is given by inverse of the standard deviation, which is independent of the post-critical size n where the nucleus is detected. The mean time, on the other hand, is n-sensitive ...

In addition to statistical significance, it is important to evaluate the magnitude of differences in health-related quality of life over time. Interest in establishing the minimal difference that is clinically important or the minimally important difference has burgeoned over the last few years. This review summarizes some of the leading approaches to estimating the minimally important differen...

Studies of bimanual coordination have typically estimated the stability of coordination patterns through the use of the circular standard deviation of relative phase. The interpretation of this statistic depends upon the assumption of a von Mises distribution. The present study tested this assumption by examining the distributional properties of relative phase in three bimanual coordination pat...

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distributi...