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Nonstandard And Standard Compactifications Of Ordered Topological Spaces, Sergio Salbany, Todor D. Todorov
Nonstandard And Standard Compactifications Of Ordered Topological Spaces, Sergio Salbany, Todor D. Todorov
Mathematics
We construct the Nachbin ordered compactification and the ordered realcompactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of monotone continuous functions are completely described. We give also a characterization of the class of completely regular ordered spaces which are closed subspaces of products of copies of the ordered real line, answering a question of T.H. Choe and Y.H. Hong. The methods used are topological (standard) and nonstandard.
Giant Sequoia Insect, Disease, And Ecosystem Interactions, Douglas D. Piirto
Giant Sequoia Insect, Disease, And Ecosystem Interactions, Douglas D. Piirto
Natural Resources Management and Environmental Sciences
Individual trees of giant sequoia (Sequoia gigantea [Lindl.] Decne.) have demonstrated a capacity to attain both a long life and very large size. It is not uncommon to find old-growth giant sequoia trees in their native range that are 1,500 years old and over 15 feet in diameter at breast height. The ability of individual giant sequoia trees to survive over such long periods of time has often been attributed to the species high resistance to disease, insect, and fire damage. Such a statement, however, is a gross oversimplification, given broader ecosystem and temporal interactions. For example, why isn't …
On The Game Of Googol, Theodore P. Hill, Ulrich Krengel
On The Game Of Googol, Theodore P. Hill, Ulrich Krengel
Research Scholars in Residence
In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson — building on ideas of Stewart — showed that, in a game theoretic sense, there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). We extend this to the case where the number of items is unknown with a known upper bound. Corollary 3 extends one of the main results in [HK] to all randomized stopping times. We also include a modified, somewhat more formal argument for Ferguson's …
The Three-Line Magnetic Hyperfine Spectrum Of 57Fe, Norman A. Blum, Richard B. Frankel
The Three-Line Magnetic Hyperfine Spectrum Of 57Fe, Norman A. Blum, Richard B. Frankel
Physics
Longitudinal magnetization of a 57Co in iron metal foil source and an iron metal foil absorber in a uniform external magnetic field results in a simple three-line magnetic hyperfine absorption spectrum. Measurement of the spectral splitting as a function of applied magnetic field yields the 57Fe excited-and ground-state g-factors.
Pointwise Kernels Of Schwartz Distributions, Todor D. Todorov
Pointwise Kernels Of Schwartz Distributions, Todor D. Todorov
Mathematics
We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.
A P-Adic Cohomological Method For The Weierstrass Family And Its Zeta Invariants, Goro Kato
A P-Adic Cohomological Method For The Weierstrass Family And Its Zeta Invariants, Goro Kato
Mathematics
After a survey of the Weierstrass family and cohomology, we compute the lifted homology of the Weierstrass family with compact supports so that explicit formulae for the zeta function of each fibre of the Weierstrass family may be obtained. The (co-)homology theory that we use is found in [L1], [L2] and [L3]. Therefore, this article can be regarded as an application of Lubkin's p-adic theory of cohomologies to an algebraic family called the Weierstrass scheme over the ring (Z/pZ)[g2,g3). The cohomological background for the computation will be rather carefully exploited.
A Binary Tree Decomposition Space Of Permutation Statistics, Don Rawlings
A Binary Tree Decomposition Space Of Permutation Statistics, Don Rawlings
Mathematics
Based on the binary tree decomposition of a permutation, a natural vector space of permutation statistics is defined. Besides containing many well known permutation statistics, this space provides the general context for an archetypal recurrence relationship that contains most of the classic combinatorial sequences and some of their known generalizations.
Riemannian Geometry Of Orbifolds, Joseph Ernest Borzellino
Riemannian Geometry Of Orbifolds, Joseph Ernest Borzellino
Mathematics
We investigate generalizations of many theorems of Riemannian geometry to Riemannian orbifolds. Basic definitions and many examples are given. It is shown that Riemannian orbifolds inherit a natural stratified length space structure. A version of Toponogov's triangle comparison theorem for Riemannian orbifolds is proven. A structure theorem for minimizing curves shows that such curves cannot pass through the singular set. A generalization of the Bishop relative volume comparison theorem is presented. The maximal diameter theorem of Cheng is generalized. A finiteness result and convergence result is proven for good Riemannian orbifolds, and the existence of a closed geodesic is shown …
One-Sided Refinements Of The Strong Law Of Large Numbers And The Glivenko-Cantelli Theorem, David Gilat, Theodore P. Hill
One-Sided Refinements Of The Strong Law Of Large Numbers And The Glivenko-Cantelli Theorem, David Gilat, Theodore P. Hill
Research Scholars in Residence
A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly almost-sure convergence property of the classical empirical distribution function, but also has the property that all its quantiles converge almost surely. …
A Survey Of Prophet Inequalities In Optimal Stopping Theory, Theodore P. Hill, Robert P. Kertz
A Survey Of Prophet Inequalities In Optimal Stopping Theory, Theodore P. Hill, Robert P. Kertz
Research Scholars in Residence
This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems, including extensions and variations, descriptions and examples of the main proof techniques, and a list of a number of basic open problems.