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Full-Text Articles in Physical Sciences and Mathematics
Large Sets Of Zero Analytic Capacity, John Garnett, Stan T. Yoshinobu
Large Sets Of Zero Analytic Capacity, John Garnett, Stan T. Yoshinobu
Mathematics
We prove that certain Cantor sets with non-sigma-finite one-dimensional Hausdorff measure have zero analytic capacity.
Sequential Searches: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials Revisited, Don Rawlings
Sequential Searches: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials Revisited, Don Rawlings
Mathematics
No abstract provided.
Whose Limit Is It Anyway?, Joseph E. Borzellino
Whose Limit Is It Anyway?, Joseph E. Borzellino
Mathematics
In a tongue-in-cheek manner, we investigate the notion of limit. We illustrate some of its shortcomings and show that addressing these shortcomings can often lead to unexpected consequences.
A Sequential Search Distribution: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials, Travis Herbranson, Don Rawlings
A Sequential Search Distribution: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials, Travis Herbranson, Don Rawlings
Mathematics
The distribution for the number of searches needed to find k of n lost objects is expressed in terms of a refinement of the q-Eulerian polynomials, for which formulae are developed involving homogeneous symmetric polynomials. In the case when k = n and the find probability remains constant, relatively simple and efficient formulas are obtained. From our main theorem, we further (1) deduce the inverse absorption distribution and (2) determine the expected number of times the survivor pulls the trigger in an n-player game of Russian roulette.
Back To Classics: Teaching Limits Through Infinitesimals, Todor D. Todorov
Back To Classics: Teaching Limits Through Infinitesimals, Todor D. Todorov
Mathematics
The usual ϵ, δ-definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires a “candidate L” for the limit value. Thus, we have to start our first calculus course with “guessing” instead of “calculating”. In this paper we criticize the method of using calculators for the purpose of selecting candidates for L. We suggest an alternative: a working formula for calculating the limit value L of a real function in terms of infinitesimals. Our formula, if considered as a definition of limit, is equivalent to the usual ϵ, δ-definition but does not involve …
Extreme-Value Moment Goodness-Of-Fit Tests, Theodore P. Hill, Victor Perez-Abreu
Extreme-Value Moment Goodness-Of-Fit Tests, Theodore P. Hill, Victor Perez-Abreu
Research Scholars in Residence
A general goodness-of-fit test for scale-parameter families of distributions is introduced, which is based on quotients of expected sample minima. The test is independent of the mean of the distribution, and, in applications to testing for exponentiality of data, compares favorably to other goodness-of-fit tests for exponentiality based on the empirical distribution function, regression methods and correlation statistics. The new minimal-moment method uses ratios of easily-calculated, unbiased, strongly consistent U-statistics, and the general technique can be used to test many standard composite null hypotheses such as exponentiality, normality or uniformity (as well as simple null hypotheses).