Hubble\u27s law implies Benford\u27s law for distances to galaxies

A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances from the Earth to galaxies are a reasonably good fit to the probabilities predicted by Benford’s law, the well known logarithmic statistical distribution of significant digits. The purpose of the present article is to give a theoretical explanation, based on Hubble’s law and mathematical properties of Benford’s law, why galaxy distances might be expected to follow Benford’s law. The new galaxy-distance law derived here, which is robust with respect to change of scale and base, to additive and multiplicative computational or observational errors, and to variability of the Hubble constant in both time and space, predicts that conformity to Benford’s law will improve as more data on distances to galaxies becomes available. Conversely, with the logical derivation of this law presented here, the recent empirical observations may be viewed as independent evidence of the validity of Hubble’s law

Extreme Tail Ratios and Overrepresentation among Subpopulations with Normal Distributions

Given several different populations, the relative proportions of each in the high (or low) end of the distribution of a given characteristic are often more important than the overall average values or standard deviations. In the case of two different normally-distributed random variables, as is shown here, one of the (right) tail ratios will not only eventually be greater than 1 from some point on, but will even become infinitely large. More generally, in every finite mixture of different normal distributions, there will always be exactly one of those distributions that is not only overrepresented in the right tail of the mixture but even completely overwhelms all other subpopulations in the rightmost tails. This property (and the analogous result for the left tails), although not unique to normal distributions, is not shared by other common continuous centrally symmetric unimodal distributions, such as Laplace, nor even by other bell-shaped distributions, such as Cauchy (Lorentz) distributions

A Better Definition of the Kilogram

Fixing the value of Avogadro\u27s constant, the number of atoms in 12 grams of carbon-12, at exactly 844468863 would imply that one gram is the mass of exactly 18x140744813 carbon-12 atoms. This new definition of the gram, and thereby also the kilogram, is precise, elegant and unchanging in time, unlike the current 118-year-old artifact kilogram in Paris and the proposed experimental definitions of the kilogram using man-made silicon spheres or the watt balance apparatus

Direct laser interference patterning for photocatalytically active self-cleaning surfaces

Laser surface structuring has long proven to be a suitable tool to produce surfaces that repel both water and bacteria on actively antibacterial and inert surfaces. As a mostly undesired side effect, the laser induced surface oxidation, that occurs when producing the pattern can also have a significant effect on the behavior of the surface. For this reason, the focus of this work is to employ direct laser interference patterning to not only affect the surface topography of titanium but to simultaneously produce a precisely tailored oxide layer. Using this approach, photocatalytically active surfaces were produced. Those surfaces can produce a variety of radicals when illuminated with UV-A light which are then used to degrade organic compounds like bacteria or organic waste. With this in mind, this work aims to develop a one-step production method for self-cleaning surfaces that uses not only the lasers topographical but also its chemical surface modifications to produce photocatalytically active surfaces with high surface area

The farmers' beef club

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Inspection of commercial fertilizers

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Inspection of commercial fertilizers

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Inspection of commercial fertilizers : spring sales

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