Estimation of the standard deviation by order statistics: the range, the average range, and some quasi ranges

Thesis (M.A.)--Boston UniversitySome rapid approximate methods of estimating the standard deviation from samples of moderate size (20 < n < 100) are presented. The emphasis is placed on solutions of problems commonly encountered in statistical quality control, especially in the electronics industry. Factors and efficiency values are given for the use of these estimators on normally distributed data. Statistical and practical engineering and administrative criteria are suggested for testing whether particular estimators are desirable in the usual industrial situation. The estimates discussed in this paper are all order statistics, i.e. statistics which are a function of only a small number of observations selected from the whole sample. These observations are selected because of the position they occupy among the other observations when all sample observations are arranged in order of magnitude. The first estimator discussed, for instance, is the range. The range of a sample is merely the numerical difference between the largest member of the sample and the smallest member of the sample. The standard deviation of the distribution from which the sample was drawn may be estimated by dividing the range by a suitable constant. The constant is a function of the sample size and of the shape of the distribution. Factors are given for sample sizes up to ten, for the normal distribution only. [TRUNCATED

A detector of small harmonic displacements based on two coupled microwave cavities

The design and test of a detector of small harmonic displacements is presented. The detector is based on the principle of the parametric conversion of power between the resonant modes of two superconducting coupled microwave cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso and Radicati, who, in 1978, suggested that superconducting coupled cavities could be used as sensitive detectors of gravitational waves, and on the work of Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind. They showed that an harmonic modulation of the cavity length l produced an energy transfer between two modes of the cavity, provided that the frequency of the modulation was equal to the frequency difference of the two modes. They achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}. We repeated the Reece, Reiner and Melissinos experiment, and with an improved experimental configuration and better cavity quality, increased the sensitivity to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device are discussed and the experimental technique is explained in detail. Possible future developments, aiming at gravitational waves detection, are also outlined.Comment: 28 pages, 12 eps figures, ReVteX. \tightenlines command added to reduce number of pages. The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://link.aip.org/link/?rs

Temporal Network Analysis of Small Group Discourse

The analysis of school-age children engaged in engineering projects has proceeded by examining the conversations that take place among those children. The analysis of classroom discourse often considers a conversational turn to be the unit of analysis. In this study, small-group conversations among students engaged in a robotics project are analyzed by forming a dynamic network with the students as nodes and the utterances of each turn as edges. The data collected for this project contained more than 1000 turns for each group, with each group consisting of 4 students (and the occasional inclusion of a teacher or other interloper). The conversational turns were coded according to their content to form edges that vary qualitatively, with the content codes taken from prior literature on small group discourse during engineering design projects, resulting in approximately 10 possible codes for each edge. Analyzed as a time sequence of networks, clusters across turns were created that allow for a larger unit of analysis than is usually used. These larger units of analysis are more fruitfully connected to the stages of engineering design. Furthermore, the patterns uncovered allow for hypotheses to be made about the dynamics of transition between these stages, and also allow for these hypotheses to be compared to expert consideration of the group’s stage at various times. Although limited by noise and inter-group variation, the larger units allowed for greater insight into group processes during the engineering design cycle

Pickering emulsions stabilized by hydrophilic nanoparticles: in situ surface modification by oil

We propose a novel route for the stabilization of oil-in-water Pickering emulsions using inherently hydrophilic nanoparticles. In the case of dialkyl adipate oils, in situ hydrophobisation of the particles by dissolved oil molecules in the aqueous phase enables stable emulsions to be formed. Emulsion stability is enhanced upon decreasing the chain length of the oil due to its increased solubility in the precursor aqueous phase. The oil thus acts like a surfactant in this respect in which hydrogen bonds form between the carbonyl group of the ester oil and the hydroxyl group on particle surfaces. The particles chosen include both fumed and precipitated anionic silica and cationic zirconia. Complementary experiments including relevant oil–water–solid contact angles and infra-red analysis of dried particles after contact with oil support the proposed mechanism

Oil Dispersants and Human Health Effects

The explosion and subsequent blowout of the Deepwater Horizon (DWH) offshore drilling rig on April 20, 2010, led to the largest accidental offshore oil spill since the advent of the petroleum industry, dwarfed only by the deliberate release of crude oil by Iraqi forces during the Persian Gulf War. Over the time until the well was capped on July 15, approximately 200 million gallons of oil spilled into the Gulf of Mexico from the ocean floor beneath the well site located approximately 50 miles off the coast of Louisiana. For perspective, this amount is nearly 20 times the amount of oil discharged during the Exxon Valdez incident in Alaska. As a result, massive mitigation efforts took place during and after the flow of oil which entailed mechanical recovery, controlled burning, and chemical dispersion. As a result unprecedented application of oil dispersant agents was employed by BP during this time until their use was curtailed by the EPA on May 26, 2010. Overall, about 17 - 20% of the crude oil was mechanically recovered and 6 – 8% burned. For the oil remaining in the environment, about 40% (of original input) was evaporated, dissolved, or dispersed into small droplets by natural processes. Initially, it was estimated that only 16.5 million gallons of oil

Ultra-stable self-foaming oils

This paper is concerned with the foaming of a range of fats in the absence of added foaming agent/emulsifier. By controlling the temperature on warming from the solid or cooling from the melt, crystals of high melting triglycerides form in a continuous phase of low melting triglycerides. Such crystal dispersions in oil can be aerated to produce whipped oils of high foamability and extremely high stability. The foams do not exhibit drainage and bubbles neither coarsen nor coalesce as they become coated with solid crystals. The majority of the findings relate to coconut oil but the same phenomenon occurs in shea butter, cocoa butter and palm kernel stearin. For each fat, there exists an optimum temperature for foaming at which the solid fat content reaches up to around 30%. We demonstrate that the oil foams are temperature-responsive and foam collapse can be controllably triggered by warming the foam to around the melting point of the crystals. Our hypothesis is given credence in the case of the pure system of tristearin crystals in liquid tricaprylin

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest

Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

Ytterbium- and chromium-doped fibre laser: from chaotic self-pulsing to passive Q-switching

A spontaneously chaotic, self-pulsing ytterbium-doped fibre laser is partially stabilized into the passively Q-switched mode of operation using a chromium-doped saturable absorber fibre. This original all-fibre laser produces sustained and stable trains of smooth pulses at high repetition rate.Comment: 1 page abstract; at 20th International laser physics workshop, Sarajevo : Bosnia And Herzegovina (2011