Physical Sciences and Mathematics Commons^™

Statistical Pronouncements Iv, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.

The Quartzite Problem Revisited, Jeffrey L. Howard

Environmental Science and Geology Faculty Research Publications

A review of past terminology and previous petrological studies suggests that quartzite should be classified descriptively as both a sedimentary and a metamorphic rock. Quartzite is identified in the field as a quartz‐rich rock (exclusive of chert and vein quartz) that is exceptionally hard and, when broken by a rock hammer, fractures irregularly through both grains and cement (where present) to form an irregular or conchoidal fracture surface. Quartzite is differentiated from quartzose sandstone (arenite), which is softer and fractures around individual grains, and from chert and vein quartz by a bright vitreous luster. Quartzite is classified further on the …

Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If u_α(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that lim_α→0αu_α(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.

Discrete Approximations Of Differential Inclusions In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study discrete approximations of continuous-time evolution systems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "broken lines." This result allows us to establish the value and strong solution convergences of discrete approximations of the Bolza problem for constrained infinite-dimensional differential/evolution inclusions under natural assumptions on the initial data.

Differentials In The Homological Homotopy Fixed Point Spectral Sequence, Robert R. Bruner, John Rognes

Mathematics Faculty Research Publications

We analyze in homological terms the homotopy fixed point spectrum of a T–equivariant commutative S–algebra R. There is a homological homotopy fixed point spectral sequence with E^2_(s,t) = H^(−s)_(gp) (��;H_t(R;��_p)), converging conditionally to the continuous homology H^c_(s+t)(R^(h��);��_p) of the homotopy fixed point spectrum. We show that there are Dyer–Lashof operations β^ϵQ^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E^(2r)–term of the spectral sequence there are 2r other classes in the E^(2r)–term (obtained mostly by Dyer–Lashof operations …

Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich

Mathematics Research Reports

We extend the definition of the limiting Frechet subdifferential and the limiting Frechet normal cone from Asplund spaces to Asplund generated spaces. Then we prove a sum rule, a mean value theorem, and other statements for this concept.

Interaction Of Sea Ice Sediments And Surface Sea Water In The Arctic Ocean: Evidence From Excess 210Pb, M. Baskaran

Environmental Science and Geology Faculty Research Publications

We measured the activities of ²¹⁰Pb, ²²⁶Ra, ²³⁸U and ¹³⁷Cs in a suite of ice-rafted sediments (IRS) from the Arctic Ocean in an attempt to assess the interaction of sea ice sediments and surface water. The concentrations of these nuclides were compared to those of the benthic sediments in the coastal and shelf regions of the Arctic Ocean, which are believed to be the major source region for the IRS. The concentration factors (CF = activity of a nuclide in IRS/average activity in benthic sediments) are ∼1 and 4-92 for ¹³⁷Cs and ²¹⁰Pb, respectively. …

Abelson’S Paradox And The Michelson-Morley Experiment, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

Teaching Random Assignment: Do You Believe It Works?, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Textbook authors admonish students to check on the comparability of two randomly assigned groups by conducting statistical tests on pretest means to determine if randomization worked. A Monte Carlo study was conducted on a sample of n = 2 per group, where each participant’s personality profile was represented by 7,500 randomly selected and assigned scores. Independent samples t tests were conducted and the results demonstrated that random assignment was successful in equating the two groups on 7,467 variables. The students’ focus is redirected from the ability of random assignment to create comparable groups to the testing of the claims of …

Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen

Mathematics Research Reports

We develop various (exact) calculus rules for Frechet lower and upper subgradients of extended-realvalued functions in general Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.

X-Ray Variability During The Quiescent State Of The Neutron Star X-Ray Transient In The Globular Cluster Ngc 6440, Edward M. Cackett, Rudy Wijnands, Craig O. Heinke, Peter D. Edmonds, Walter H. G. Lewin, David Pooley, Jonathan E. Grindlay, Peter G. Jonker, Jon M. Miller

Physics and Astronomy Faculty Research Publications

The globular cluster NGC 6440 is known to harbor a bright neutron star X-ray transient. We observed the globular cluster with Chandra on two occasions when the bright transient was in its quiescent state, in 2000 July and 2003 June (both observations were made nearly 2 yr after the end of their preceding outbursts). The quiescent spectrum during the first observation is well represented by a two-component model (a neutron star atmosphere model plus a power-law component that dominates at energies above 2 keV). During the second observation (which was roughly of equal duration to the first observation) we found …

Comparison Of Two-Dimensional And Three-Dimensional Simulations Of Dense Nonaqueous Phase Liquids (Dnapls): Migration And Entrapment Of A Nonuniform Permeability Field, John A. Christ, Lawrence D. Lemke, Linda M. Abriola

Environmental Science and Geology Faculty Research Publications

The influence of reduced dimensionality (two-dimensional (2-D) versus 3-D) on predictions of dense nonaqueous phase liquid (DNAPL) infiltration and entrapment in statistically homogeneous, nonuniform permeability fields was investigated using the University of Texas Chemical Compositional Simulator (UTCHEM), a 3-D numerical multiphase simulator. Hysteretic capillary pressure–saturation and relative permeability relationships implemented in UTCHEM were benchmarked against those of another lab-tested simulator, the Michigan-Vertical and Lateral Organic Redistribution (M-VALOR). Simulation of a tetrachloroethene spill in 16 field-scale aquifer realizations generated DNAPL saturation distributions with approximately equivalent distribution metrics in two and three dimensions, with 2-D simulations generally resulting in slightly higher maximum …

Gap Labeling, Claude Schochet

Mathematics Faculty Research Publications

This joint review covers:

Moulay-Tahar Benameur and Hervé Oyono-Oyono, Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). (English summary) Operator algebras and mathematical physics, (Constanţa, 2001), 11-22, Theta, Bucharest, 2003.

Jerome Kaminker and Ian Putnam, A proof of the gap labeling conjecture, Michigan Mathematical Journal 51(3) (2003), 537-546.

Jean Bellisard, Riccardo Benedetti and Jean-Marc Gambaudo, Spaces of tilings, finite telescopic approximations, and gap-labeling, Communications in Mathematical Physics 261(1) (2006), 1-41.

The gap labeling theorem was originally conjectured by Bellissard [in From number theory to physics (Les Houches, 1989), 538-630, Springer, Berlin, 1992; MR1221111 (94e:46120)]. …

Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi

Mathematics Faculty Research Publications

In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.