Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors

Convergence of Newton's method for a single real equation

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed

Spool for releasing and retracting flat conductor cable

Spool design and operation permit installation of up to 8 cables on single unit. Heat treating the cables while wound in a coil obtains effective recoil action

Collimated beam manifold with the number of output beams variable at a given output angle

An optical manifold is described which transforms a collimated beam, such as a laser beam, into a plurality of parallel beams having uniform intensity or having a desired intensity ratio. The manifold comprises an optical substrate coated on its rear surface with a fully reflective layer and on its front surface with a partially reflecting layer having a reflectivity gradient. An input collimated beam entering the rear surface and impinging on the front surface is reflected, multiply between the front and rear surfaces producing a plurality of parallel beams that emerge from the front surface. The intensities of the emerging beams have a relationship that depends on the reflectivity of the front surface at the points where the beams emerge. By properly selecting the reflectivity gradient, the emerging beams have uniform intensity or a desired intensity ratio

Cable insulation cut-through tester

Device accurately measures cut-through load within specified time or time when cut-through occurs at specific load. Tests are performed at ambient conditions or in an environmental chamber

Anolis roosevelti

Number of Pages: 2Integrative BiologyGeological Science

Magnitude and frequency of wind speed shears and associated downdrafts

Data are presented indicating the frequency of occurrence of wind shear and downdrafts together with information on the simultaneous occurrence of these two phenomena. High resolution wind profile measurements recorded at a 150 meter ground winds tower facility were used for the analysis. From instantaneous measurements during horizontal wind speeds of gale-force and below intensity, vertical motion at the 10, 60, and 150 m levels was approximately 60 percent downward and 40 percent upward. At the 18 level the percentages were reversed. Updraft maxima were an order of magnitude or two greater than downdrafts at all levels. Frequency of vertical motion or = 9.7 kts for a year at four levels was 338 occurrences upward and 274 downward. Approximately 90 percent of these updrafts occurred at the 18 m level almost equally during summer and winter, and 65 percent of the downdrafts were at the 150 m level during summer

Nationwide forestry applications program: Corrections to forest reflectance as a function of low Sun angle and slope

There are no author-identified significant in this report

The treatment of mixing in core helium burning models -- III. Suppressing core breathing pulses with a new constraint on overshoot

Theoretical predictions for the core helium burning phase of stellar evolution are highly sensitive to the uncertain treatment of mixing at convective boundaries. In the last few years, interest in constraining the uncertain structure of their deep interiors has been renewed by insights from asteroseismology. Recently, Spruit (2015) proposed a limit for the rate of growth of helium-burning convective cores based on the higher buoyancy of material ingested from outside the convective core. In this paper we test the implications of such a limit for stellar models with a range of initial mass and metallicity. We find that the constraint on mixing beyond the Schwarzschild boundary has a significant effect on the evolution late in core helium burning, when core breathing pulses occur and the ingestion rate of helium is fastest. Ordinarily, core breathing pulses prolong the core helium burning lifetime to such an extent that models are at odds with observations of globular cluster populations. Across a wide range of initial stellar masses ($0.83 \leq M/\text{M}_\odot \leq 5$), applying the Spruit constraint reduces the core helium burning lifetime because core breathing pulses are either avoided or their number and severity reduced. The constraint suggested by Spruit therefore helps to resolve significant discrepancies between observations and theoretical predictions. Specifically, we find improved agreement for $R_2$, the observed ratio of asymptotic giant branch to horizontal branch stars in globular clusters; the luminosity difference between these two groups; and in asteroseismology, the mixed-mode period spacing detected in red clump stars in the \textit{Kepler} field.Comment: Accepted for publication in MNRAS; 11 pages, 6 figure