Fundamental Flaws in Feller's Classical Derivation of Benford's Law

Feller's classic text 'An Introduction to Probability Theory and its Applications' contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition ("large spread") for a random variable $X$ to be approximately Benford distributed, that is, for $\log_{10}X$ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstrate that large spread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of "spread" or measure of dispersionComment: 7 page

Retail Innovation - The never-ending road to success? A critical analysis of pitfalls and opportunities

This paper outlines the current and continuous changes occurring in the retail and social environment that necessitate the constant evolution of retail formats. Over recent years experiential retail formats have appeared in recognition of the increasing need to ‘entertain’ shoppers and satisfy their ‘leisure’ needs. A number of ‘best practice’ examples of such retail innovation have been presented. While such experiential innovations appear to be the ‘holy grail’ of modern retailing, they often require considerable investments of both capital and management time. This paper has used an autoethnographic approach to reflect upon the constraints and costs involved in the design, construction and operation of such a retail enterprise to provide a unique and holistic assessment of the benefits and challenges experiential innovation holds in developing new retail formats and initiatives. The findings from this research highlight a number of previously unreported pitfalls that are likely to be encountered, financially, operationally and symbolically. It is recommended that retailers continue to explore experiential innovations, but that they proceed with caution

Testing the Origin of Cosmological Magnetic Fields through the Large-Scale Structure Consistency Relations

We study the symmetries of the post-recombination cosmological magnetohydrodynamical equations which describe the evolution of dark matter, baryons and magnetic fields in a self-consistent way. This is done both at the level of fluid equations and of Vlasov-Poisson-Maxwell equations in phase space. We discuss some consistency relations for the soft limit of the (n + 1)-correlator functions involving magnetic fields and matter overdensities. In particular, we stress that any violation of such consistency relations at equal-time would point towards an inflationary origin of the magnetic field.Comment: 23 page

Towards a renewal of the propeller in aeronautics

The reasons for reconsidering the propeller for aircraft propulsion, the areas of application, and necessary developments are considered. Rising fuel costs and an increasing theoretical and experimental data base for turboprop engines have demonstrated that significant cost savings can be realized by the use of propellers. Propellers are well-suited to powering aircraft traveling at speeds up to Mach 0.65. Work is progressing on the development of a 150 seat aircraft which has a cruise speed of Mach 0.8, powered by a turboprop attached to an engine of 15,000 shp. Aeroelasticity analyses ae necessary in order to characterize the behavior of thin profile propfan blades, particularly to predict the oscillations through the entire functional range. High-power reducers must be developed, and the level of cabin noise must be controlled to less than 90 dB. Commercial applications are predicted for turboprops in specific instances

Top Spin and Experimental Tests

We examine pair mass dependence near threshold as a means to measure the spin of the top quark in hadron collisions, and we discuss the possibility that a top squark signal could be hidden among the top events.Comment: 9 pages, RevTeX, 3 figures. Contribution to the Thinkshop on Top-Quark Physics for the Tevatron Run II, Fermilab, October 16 - 18, 199

General Issues in the Evolution of Fermion Masses and Mixings

General issues in the renormalization group evolution of fermion masses and mixings is discussed. An effective fixed point in the top quark Yukawa coupling can strongly constrain its value at the electroweak scale. Predictions following from Yukawa coupling unification are affected by threshold corrections at the grand unified scale. The Landau pole translates into an upper limit on the strong gauge coupling $\alpha _3(M_Z)$. Given the hierarchy in the fermion sector, the evolution of the Cabbibo-Kobayashi-Maskawa matrix can be expressed in terms of a single scaling parameter $S$. Using this scaling factor and analogous scaling factors for the quark and lepton masses, we outline a systematic strategy that readily yields electroweak predictions for any GUT scale texture.}Comment: (Talk given at the SUSY93 Conference MSB), 9 pages + 3 PS figures not included (available on request), MAD/PH/75