scholarly journals Units, for good measure

Physics Today ◽  
2020 ◽  
Vol 73 (9) ◽  
pp. 12-12 ◽  
Author(s):  
Michael Albrow
Keyword(s):  
2014 ◽  
Vol 9 (12) ◽  
pp. 959-960 ◽  
Author(s):  
Giovanni Longo
Keyword(s):  

Author(s):  
C. E. Soteros ◽  
D. W. Sumners ◽  
S. G. Whittington

AbstractIn this paper we are concerned with questions about the knottedness of a closed curve of given length embedded in Z3. What is the probability that such a randomly chosen embedding is knotted? What is the probability that the embedding contains a particular knot? What is the expected complexity of the knot? To what extent can these questions also be answered for a graph of a given homeomorphism type?We use a pattern theorem due to Kesten 12 to prove that almost all embeddings in Z3 of a sufficiently long closed curve contain any given knot. We introduce the idea of a good measure of knot complexity. This is a function F which maps the set of equivalence classes of embeddings into 0, ). The F measure of the unknot is zero, and, generally speaking, the more complex the prime knot decomposition of a given knot type, the greater its F measure. We prove that the average value of F diverges to infinity as the length (n) of the embedding goes to infinity, at least linearly in n. One example of a good measure of knot complexity is crossing number.Finally we consider similar questions for embeddings of graphs. We show that for a fixed homeomorphism type, as the number of edges n goes to infinity, almost all embeddings are knotted if the homeomorphism type does not contain a cut edge. We prove a weaker result in the case that the homeomorphism type contains at least one cut edge and at least one cycle.


2008 ◽  
Vol 18 ◽  
pp. S520-S521
Author(s):  
S. Loeber ◽  
S. Vollstaedt-Klein ◽  
C. von der Goltz ◽  
K. Mann ◽  
F. Kiefer

Author(s):  
I. S. E. Carmichael ◽  
W. S. MacKenzie

SummaryThe lattice parameters of twenty calcium-bearing anorthoclases and potassium-bearing acid plagioclases have been determined by powder methods. The 201̄ spacing of the homogenized anorthoclases gives a good measure of the Or content irrespective of the amount of calcium present ; this spacing combined with α* (010): (001) may be used to determine the ternary composition of homogeneous feldspars more potassic than approximately Or15. The lattice parameters of feldspars less potassic than Or15 cannot be used for the determination of their ternary composition.


1994 ◽  
Vol 14 (4) ◽  
pp. 345-359 ◽  
Author(s):  
Alvin E. Winder ◽  
Ted T. L. Chen ◽  
William C. Mfuko

This study addresses the question: has the opening of their markets to American tobacco products in Japan, South Korea, and Taiwan led to an increase in smoking behavior among women and youth? The data on smoking rates for women and youth is presented. This data was obtained for each country before markets were opened to the importation of American tobacco products through the agency of non-governmental organizations in these countries. Comparison data was obtained from similar Asian countries whose markets were not opened. The data from Japan, South Korea, and Taiwan show a sizeable increase in smoking rates for women and youth. The authors believe, based upon anecdotal data, that importation of tobacco products combined with aggressive marketing and advertising by American firms is, in a good measure, responsible for the reported increase.


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