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On Irrational Points in the Plane

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Advances in Pure Mathematics 2017年第4期7卷 299-305页

作者： thomas Beatty Timothy Jones Florida Gulf Coast University Fort Myers Florida USA

This paper summarizes research intended to develop a pedagogically friendly argument that establishes the fact that (x,ex ) is never a rational point in the plane. A point (x, y)∈R2 is rational if both x and y are rational. Applying a method based on Hurwitz polynomials, the research establishes simple irrationality proofs for nonzero rational powers of e and logarithms of positive rationals (excluding one).

关键词： Rational Point Irrationality Sum of Derivatives Prime Divisibility Hurwitz Polynomial

Pringsheim Convergence and the Dirichlet Function

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Advances in Pure Mathematics 2016年第6期6卷 441-445页

作者： thomas Beatty Bradley Hansen Department of Mathematics Florida Gulf Coast University Ft. Myers FL USA

Double sequences have some unexpected properties which derive from the possibility of commuting limit operations. For example, may be defined so that the iterated limits and exist and are equal for all x, and yet the Pringsheim limit does not exist. The sequence is a classic example used to show that the iterated limit of a double sequence of continuous functions may exist, but result in an everywhere discontinuous limit. We explore whether the limit of this sequence in the Pringsheim sense equals the iterated result and derive an interesting property of cosines as a byproduct.

关键词： Convergence Pointwise Limit Double Sequence Pringsheim Dirichlet Function Baire Category Theorem Cosine

On Conditional Probabilities of Factoring Quadratics

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Advances in Pure Mathematics 2020年第3期10卷 114-124页

作者： thomas Beatty Gabriela von Linden Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.

关键词： Factorization Polynomial Quadratic Integers Rational Numbers Monic Modular Arithmetic Conditional Probability

Structured Shuffles and the Josephus Problem

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Open Journal of Discrete Mathematics 2012年第4期2卷 138-141页

作者： Shaun Sullivan thomas Beatty Florida Gulf Coast University Fort Myers USA

The Australian Shuffle consists of placing a deck of cards onto a table according to this rule: put the top card on the table, the next card on the bottom of the deck, and repeat until all the cards have been placed on the table. A natural question is “Where was the very last card placed located in the original deck?” Card trick magicians have known empirically for years that the fortieth card from the top of a standard fifty-two card deck is the final card placed by this shuffle. The moniker “Australian” comes from putting every other card “Down Under”. We develop a formula for the general case of N cards, and then extend that generalization further to cases involving the discard of k cards before or after putting one on the bottom of the deck. Finally, we discuss the connection of the Australian Shuffle and its generalizations to the famous Josephus problem.

关键词： Josephus Shuffling

Generalized Series of Bernoulli Type

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Advances in Pure Mathematics 2023年第9期13卷 537-542页

作者： thomas Beatty Nicholas Bianco Nicole Legge Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

关键词： Bernoulli Series Convergence Sum Recursion Formula Zeta-Function Sine Maclaurin Series Infinite Product

Erratum to “A Review of Arctic–Subarctic Ocean Linkages: Past Changes, Mechanisms, and Future Projections”

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Ocean-Land-Atmosphere Research 2023年第1期2卷 234-236页

作者： Qiang Wang Qi Shu Shizhu Wang Agnieszka Beszczynska-Moeller Sergey Danilov Laura de Steur thomas W.N.Haine Michael Karcher Craig M.Lee Paul G.myers Igor V.Polyakov Christine Provost Øystein Skagseth Gunnar Spreen Rebecca Woodgate Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research(AWI) BremerhavenGermany First Institute of Oceanography and Key Laboratory of Marine Science and Numerical ModelingMinistry of Natural ResourcesQingdaoPeople’s Republic of China Shandong Key Laboratory of Marine Science and Numerical Modeling QingdaoPeople’s Republic of China Institute of Oceanology Polish Academy of SciencesSopotPoland. Department of Mathematics and Logistics Jacobs UniversityBremenGermany. Norwegian Polar Institute Fram CentreTromsøNorway. Earth&Planetary Sciences The Johns Hopkins UniversityBaltimoreMDUSA. Ocean Atmosphere Systems GmbH HamburgGermany. Applied Physics Laboratory University of WashingtonSeattleWAUSA. Department of Earth and Atmospheric Sciences University of AlbertaEdmontonABCanada. International Arctic Research Center and College of Natural Science and Mathematics University of Alaska FairbanksFairbanksAKUSA. Finnish Meteorological Institute HelsinkiFinland. Laboratoire LOCEAN-IPSL Sorbonne Université(UPMCUniversity Paris 6)CNRSIRDMNHNParisFrance. Institute of Marine Research and Bjerknes Centre of Climate Research BergenNorway. Institute of Environmental Physics University of BremenBremenGermany

In the Review Article"A Review of Arctic–Subarctic Ocean Linkages:Past Changes,Mechanisms,and Future Projections"[1],the x-axis in Figure 4B and y-axis in Figure 8F were skewed during picture beautification by an ***... 详细信息

关键词： Arctic arctic Figure

Review of key telepsychiatry outcomes

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World Journal of Psychiatry 2016年第2期6卷 269-282页

作者： Sam Hubley Sarah B Lynch Christopher Schneck Marshall thomas jay Shore Helen and Arthur E Johnson Depression Center Department of Family Medicine Department of Clinical Health Psychology University of Colorado Denver

AIM: To conduct a review of the telepsychiatry ***: We conducted a systematic search of the literature on telepsychiatry using the search terms, "telepsychiatry", "telemental health", "telecare", "telemedicine", "e-health", and "videoconferencing". To meet criteria for inclusion, studies had to:(1) be published in a peer-reviewed journal after the year 2000;(2) be written in English;(3) use videoconferencing technology for the provision of mental health assessment or treatment services; and(4) use an adequately-powered randomized controlled trial design in the case of treatment outcome studies. Out of 1976 studies identified by searches in Pub Med(Medline database), Ovid medline, Psych Info, Embase, and EBSCO PSYCH, 452 met inclusion criteria. Studies that met all inclusion criteria were organized into one of six categories:(1) satisfaction;(2) reliability;(3) treatment outcomes;(4) implementation outcomes;(5) cost effectiveness; and(6) and legal issues. All disagreements were resolved by reassessing study characteristics and ***: Overall, patients and providers are generally satisfied with telepsychiatry services. Providers, however, tend to express more concerns about the potentially adverse of effects of telepsychiatry on therapeutic rapport. Patients are less likely to endorse such concerns about impaired rapport with their provider. Although few studies appropriately employ non-inferiority designs, the evidence taken together suggests that telepsychiatry is comparable to face-to-face services in terms of reliability of clinical assessments and treatment outcomes. When non-inferiority designs were appropriately used, telepsychiatry performed as well as, if not better than face-to-face delivery of mental health services. Studies using both rudimentary and more sophisticated methods for evaluating cost-effectiveness indicate that telepsychiatry is not more expensive than face-to-face delivery of mental health services and that telepsy

关键词： Telepsychiatry Telemental health Videoconferencing Treatment access Implementation

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随钻声波测井新技术

国外测井技术 2007年第1期22卷 53-60页

作者： Jeff Alford Roger B.Goobie Colin M.Sayers Ed Tollefsen jay Cooke Andy Hawthorn John C.Rasmus Ron thomas 美国得克萨斯州休斯敦 Helis油气公司美国得克萨斯州休斯敦美国得克萨斯州Sugar Land PPI技术服务公司美国得克萨斯州休斯敦

在诸多钻井决策中，优选泥浆比重是最具挑战性而且也是最重要的决策之一。如今，新型随钻声波测井仪器的应用能够更好地帮助钻井工程师进行这些钻井决策。

关键词：随钻声波测井技术声波测井仪器泥浆比重决策钻井挑战性工程师

CD28 ligation increases macrophage suppression of T-cell proliferation

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Cellular & Molecular Immunology 2012年第4期9卷 341-349页

作者： Daniel Silberman Amanda Bucknum thomas Bartlett Gabriella Composto Megan Kozlowskil Amanda Walker Amy Werda Jackelyn Cua Arlene H Sharpe John E Somerville James E Riggs Department of Biology Rider University Lawrenceville NJ 08648 USA Department of Pathology Harvard Medical School Cambridge MA 02115 USA Immunosciences Bristol-Myers Squibb Princeton NJ 08543 USA

When compared to spleen or lymph node cells, resident peritoneal cavity cells respond poorly to T-cell activation in vitro. The greater proportional representation of macrophages in this cell source has been shown to actively suppress the T-cell response. Peritoneal macrophages exhibit an immature phenotype （MHC class IIlo, B7lo） that reduces their efficacy as antigen-presenting cells. Furthermore, these cells readily express inducible nitric oxide synthase （iNOS）, an enzyme that promotes T-cell tolerance by catabolism of the limiting amino acid arginine. Here, we investigate the ability of exogenous T-cell costimulation to recover the peritoneal T-cell response. We show that CD28 ligation failed to recover the peritoneal T-cell response and actually suppressed responses that had been recovered by inhibiting iNOS. As indicated by cytokine ELISpot and neutralizing monoclonal antibody （mAb） treatment, this ＇cosuppression＇ response was due to CD28 ligation increasing the number of interferon （IFN）-y-secreting cells. Our results illustrate that cellular composition and cytokine milieu influence T-cell costimulation biology.

关键词： CD28 costimulation macrophages suppression