The Private-Public Law Divide in International Dispute Resolution

Heß, Burkhard

doi:10.1163/9789004384903

Cited by 5 publications

(5 citation statements)

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“…They satisfy (2) for any values of p and q. These trivial solutions yield an undefined value 0/0 for the probability in (1). While these are not admissible as solutions to the problem (since there are not two balls to draw), they will prove useful in obtaining admissible solutions and in proving some results.…”

Section: Trivial Solutionsmentioning

confidence: 99%

“…In (1), the factor of 2 in the numerator always divides the denominator, so we have p ≤ xy and q ≤ 1 2 (x + y)(x + y − 1). (Cancellation of common factors may reduce p and q further.)…”

Section: General Solutionmentioning

confidence: 99%

“…This problem, for the special case of 50-50 odds, appeared in the Varsity Math puzzle feature of the National Museum of Mathematics in New York City [4]. The author of that puzzle is Dick Hess of the museum staff [1]. Here we solve the problem for arbitrary odds.…”

Section: Introductionmentioning

confidence: 99%

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Solution of an Odds Inversion Problem

Moniot

2021

The American Mathematical Monthly

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From a bag containing red and blue balls, two are removed at random. The chances are 50-50 that they will differ in color. What were the possible numbers of balls initially in the bag?" This problem appeared in the National Museum of Mathematics' Varsity Math puzzle, week 117. It is quite easy to solve, but what if we generalize to arbitrary odds? In this article, we characterize the solutions of the general case. We show that for most odds values that are at most 50-50, there is an infinite number of solutions, while for a certain well-defined class of odds below 50-50 and for any odds greater than 50-50, the number of solutions is zero or finite. We also explore some other interesting and surprising properties of this problem.

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Section: Trivial Solutionsmentioning

confidence: 99%

Section: General Solutionmentioning

confidence: 99%

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Solution of an Odds Inversion Problem

Moniot

2021

The American Mathematical Monthly

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“…Ref [8] does not give the temperature of the HPGe crystals when the study was performed but the liquid-nitrogen-cooled MINIBALL and AGATA crystals typically vary between temperatures of 95 K and 100 K under normal conditions [14]. The temperature of the SAGe crystal in this study was 113 K, a value which was chosen in manufacture to optimise energy resolution.…”

Section: Investigating Parameters Of the Simulationmentioning

confidence: 99%

Characterisation of a small electrode HPGe detector

Unsworth

Boston

et al. 2019

Nuclear Instruments and Methods in Physics Research Section A:

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Small electrode HPGe detectors in an inverted coaxial geometry are increasingly in use in applications where both high efficiency and excellent energy resolution are required. The unusual electric field configuration of these detectors results in extremely long charge collection times compared to planar and coaxial devices. In this work we have characterised such a detector using gamma-ray coincidence measurements and optimised an electric field simulation to reproduce the positional variation of detector response. We show that, alongside accurate crystal geometry and applied electric potential, a temperature correction is crucial to correctly determining appropriate charge carrier mobility parameters. This work will help to guide the future development of HPGE detectors for applications including radioactive waste assay, radio-isotope dating, and fundamental nuclear physics.

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“…This application was suggested by Kathryn Hess. In an upcoming paper on configuration spaces of products with Ben Knudsen [HK18], they are using these model structures on modules over simplicial operads. Finally, in Section 8, we show that, if A is left-or right-proper, then so are the injective and projective model structures on a category of enriched diagrams D → A, again under assumptions on the hom-objects of D. This time, these assumptions imply that injective fibrations are in particular pointwise fibrations, and that projective cofibrations are in particular pointwise cofibrations respectively.…”

Section: Introductionmentioning

confidence: 99%