3,867 research outputs found

    Irreducible compositions and the first return to the origin of a random walk

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    Let n=b1+...+bk=b1++bkn = b_1 + ... + b_k = b_1' + \cdot + b_k' be a pair of compositions of nn into kk positive parts. We say this pair is {\em irreducible} if there is no positive j<kj < k for which b1+...bj=b1+...bjb_1 + ... b_j = b_1' + ... b_j'. The probability that a random pair of compositions of nn is irreducible is shown to be asymptotic to 8/n8/n. This problem leads to a problem in probability theory. Two players move along a game board by rolling a die, and we ask when the two players will first coincide. A natural extension is to show that the probability of a first return to the origin at time nn for any mean-zero variance VV random walk is asymptotic to V/(2π)n3/2\sqrt{V/(2 \pi)} n^{-3/2}. We prove this via two methods, one analytic and one probabilistic

    A Comparative Study of Customer Perceptions Regarding Green Restaurant Practices: Fast Food vs. Upscale Casual

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    The current exploratory study was designed to determine the impact that green restaurant practices may have on intention to visit a restaurant and willingness to pay more because of those green practices. The study analyzed a convenience sample of 260 surveys from customers in fast food restaurants and 501 surveys from customers in upscale casual restaurants in the Midwestern United States (U.S.) in order to determine if there were differences in the perception of guests regarding these types of restaurants and their green practices. The findings showed that upscale casual restaurant customers believed they are knowledgeable at a higher level than the fast food restaurant customers about green restaurant practices, have a higher mean rating on the importance of environmental record and recycling in restaurants, and believed that restaurants should use local products when they can. In both groups of customers, there was a positive relationship between green practices utilized at home and customers’ willingness to pay more for green restaurant practices as well as their intention to visit the restaurant using green practices. Management implications are discussed

    Sand Impact Tests of a Half-Scale Crew Module Boilerplate Test Article

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    Although the Orion Multi-Purpose Crew Vehicle (MPCV) is being designed primarily for water landings, a further investigation of launch abort scenarios reveals the possibility of an onshore landing at Kennedy Space Center (KSC). To gather data for correlation against simulations of beach landing impacts, a series of sand impact tests were conducted at NASA Langley Research Center (LaRC). Both vertical drop tests and swing tests with combined vertical and horizontal velocity were performed onto beds of common construction-grade sand using a geometrically scaled crew module boilerplate test article. The tests were simulated using the explicit, nonlinear, transient dynamic finite element code LS-DYNA. The material models for the sand utilized in the simulations were based on tests of sand specimens. Although the LSDYNA models provided reasonable predictions for peak accelerations, they were not always able to track the response through the duration of the impact. Further improvements to the material model used for the sand were identified based on results from the sand specimen tests

    Leadership Training In An MBA Program Using Peer-led Team Learning

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    Leadership training is an important part of any MBA program, but is often difficult to provide in an effective way. Over the last three years, we implemented a program of Peer-Led Team Learning in two core courses of our MBA curriculum, which we believe provides a good solution. The program combines leadership training with practical hands-on application of the ideas taught, and provides for an effective feedback loop. Response to the program has been overwhelmingly positive. The program and benefits for learning leadership are discussed in this paper

    Synthesis and characterization of redox active cyrhetrene–triazole click products

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    We report the synthesis and characterization of two new cyclopentadienyl tricarbonyl rhenium(I) (cyrhetrene) complexes modified with a 1,4-disubstituted 1,2,3-triazole moiety. The two compounds, (η5-[4-phenyltriazol-1-yl]cyclopentadienyl) tricarbonyl rhenium(I), and (η5-[4-(4-aminophenyl)triazol-1-yl]cyclopentadienyl) tricarbonyl rhenium(I), were structurally characterized using 1H and 13C NMR, ATR-IR spectroscopy, UV–vis spectroscopy, mass spectrometry and X-ray crystallography where appropriate. The electrochemical behaviour of these two cyrhetrene–triazole complexes was explored using cyclic voltammetry, whereupon we observed that irreversible oxidation of the pendant 4-substituted-triazole moiety occurs before any electron transfer at the metal centre. This redox behaviour is in stark contrast to that of the analogous manganese(I) cymantrene–triazole derivatives, recently reported by our group

    Discriminative Topological Features Reveal Biological Network Mechanisms

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    Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how well it reproduces a few key features of the real-world data, such as degree distributions, mean geodesic lengths, and clustering coefficients. Often pairs of models can reproduce these features with indistinguishable fidelity despite being generated by vastly different mechanisms. In such cases, these few target features are insufficient to distinguish which of the different models best describes real world networks of interest; moreover, it is not clear a priori that any of the presently-existing algorithms for network generation offers a predictive description of the networks inspiring them. To derive discriminative classifiers, we construct a mapping from the set of all graphs to a high-dimensional (in principle infinite-dimensional) ``word space.'' This map defines an input space for classification schemes which allow us for the first time to state unambiguously which models are most descriptive of the networks they purport to describe. Our training sets include networks generated from 17 models either drawn from the literature or introduced in this work, source code for which is freely available. We anticipate that this new approach to network analysis will be of broad impact to a number of communities.Comment: supplemental website: http://www.columbia.edu/itc/applied/wiggins/netclass
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