Cyclotomic polynomials product forms and continued fractions

2010 ◽  
pp. 704-725
Author(s):  
Jörg Arndt
TAPPI Journal ◽  
2018 ◽  
Vol 17 (09) ◽  
pp. 507-515 ◽  
Author(s):  
David Skuse ◽  
Mark Windebank ◽  
Tafadzwa Motsi ◽  
Guillaume Tellier

When pulp and minerals are co-processed in aqueous suspension, the mineral acts as a grinding aid, facilitating the cost-effective production of fibrils. Furthermore, this processing allows the utilization of robust industrial milling equipment. There are 40000 dry metric tons of mineral/microfbrillated (MFC) cellulose composite production capacity in operation across three continents. These mineral/MFC products have been cleared by the FDA for use as a dry and wet strength agent in coated and uncoated food contact paper and paperboard applications. We have previously reported that use of these mineral/MFC composite materials in fiber-based applications allows generally improved wet and dry mechanical properties with concomitant opportunities for cost savings, property improvements, or grade developments and that the materials can be prepared using a range of fibers and minerals. Here, we: (1) report the development of new products that offer improved performance, (2) compare the performance of these new materials with that of a range of other nanocellulosic material types, (3) illustrate the performance of these new materials in reinforcement (paper and board) and viscosification applications, and (4) discuss product form requirements for different applications.


Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.


Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 840
Author(s):  
Maxim Sølund Kirsebom

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.


1981 ◽  
Vol 88 (10) ◽  
pp. 753-753
Author(s):  
Katherine E. McLain ◽  
Hugh M. Edgar

1979 ◽  
Vol 89 ◽  
pp. 95-101
Author(s):  
S. Mikkola

A continued fraction was derived for the summation of the asymptotic expansion of astronomical refraction. Using simple approximations for the last denominator of the fraction, accurate formulae, useful down to the horizon, were obtained. The method is not restricted to any model of the atmosphere and can thus be used in calculations based on actual aerological measurements.


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