Physical Sciences and Mathematics Commons^™

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Yi Li

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)_μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)_μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ_**⩽μ**<μ* such that problem (∗)_{μ …}

An International Study Of Intensity In Talented Teenagers Using The Overexcitability Questionnaire (Oeq), John Fraas, Jane Piirto, Geri Cassone, Cheryl Ackerman

John W. Fraas

No abstract provided.

Weighing Evidence In Sexual Abuse Evaluations: An Introduction To Bayes's Theorem, James M. Wood

James M. Wood

This article introduces readers to Bayes' theorem, a simple mathematical formula that can illuminate general issues and assist evaluators in the field of child sexual abuse. The theorem is applied to a case study of sexual abuse allegations that arose during a custody dispute.

The Importance Of Analyzing Longitudinal Data In A Formative Evaluation Process: Applying Statistical Quality Control Techniques, John Fraas, Isadore Newman

John W. Fraas

No abstract provided.

Student's T-Test And The Glasgow Coma Scale, Joseph Lucke

Joseph Lucke

Study Objective: To explore how Student's t test, which assumes normal errors, is affected by the nonnormal distribution of Glasgow Coma Scale (GCS) scores.

Methods: A sample of 145,295 GCS scores from the Pennsylvania Trauma Systems Foundation was assumed to represent the true GCS distribution. Four Monte Carlo simulations, each based on 40,000 replications, were conducted to approximate the distribution of t values arising from samples drawn from the GCS distribution, using sample sizes of 10, 30, 60, and 100 per group.

Results: The histograms of t values derived from the GCS distribution resembled the corresponding Student t distributions for …

The Spinor Representation Of Surfaces In Space, Robert Kusner, Nick Schmitt

Robert Kusner

The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan [32], which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the canonical line bundle K = T(M). Given a conformal immersion of M into R3, the unique spin strucure on S2 pulls back via the Gauss map to a spin structure S on M, and gives rise to a pair of smooth sections (s1, s2) of S. Conversely, any pair of sections of S generates a (possibly periodic) conformal immersion …

Moduli Spaces Of Embedded Constant Mean Curvature Surfaces With Few Ends And Special Symmetry, Karsten Grosse-Brauckmann, Robert Kusner

Robert Kusner

We give necessary conditions on complete embedded cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are twodimensional varieties in the moduli spaces of general cmc surfaces. We characterize fundamental domains of our cmc surfaces by associated great circle polygons in the three-sphere.

Nonparametric Regression Using Bayesian Variable Selection, Michael Smith, Robert Kohn

Michael Stanley Smith

No abstract provided.

Finite Sample Performance Of Robust Bayesian Regression, Michael Smith, Sheather Simon, Kohn Robert

Michael Stanley Smith

No abstract provided.

Testing For Absolute Purchaing Power Parity, Douglas G. Steigerwald, Collin Crownover, John Pippenger

Douglas G. Steigerwald

Purchasing power parity (PPP) is an equilibrium condition equating the nominal exchange rate between two countries with the relative price of an identical bundle of goods in each country. Previous time-series researchers use price indicies to study PPP, so they study relative PPP. We use new data that measures price levels, so we test absolute PPP. Price levels provide a test of absolute PPP because, unlike price indicies, do not contain a base period in which the nominal exchange rate equals the price ratio by construction. We find support for absolute PPP.

Purchasing Power Parity, Unit Roots And Dynamic Structure, Douglas G. Steigerwald

Douglas G. Steigerwald

Recent studies of puchasing power parity (PPP) account for the possible presence of unit roots in nominal exchange rates and relative price indicies by applying standard unit-root tests to real exchange rates, which are ratios of nominal exchange rates and relative price indicies. These studies occasionally find evidence of PPP but, as a whole, the evidence is not definitive. Standard unit-root tests impose a restrictive dynamic structure between nominal exchange rates and relative price indicies. I specify and estimate a generalized dynamic structure. I reject the dynamic restrictions implicit in standard unit-root tests of PPP, and find stronger evidence of …