The Metrical Theory of Jacobi-Perron Algorithm
Author: F. Schweiger
Publisher:
Published: 2014-01-15
Total Pages: 124
ISBN-13: 9783662178140
DOWNLOAD EBOOK →Author: F. Schweiger
Publisher:
Published: 2014-01-15
Total Pages: 124
ISBN-13: 9783662178140
DOWNLOAD EBOOK →Author: F. Schweiger
Publisher: Springer
Published: 2006-11-15
Total Pages: 117
ISBN-13: 3540470107
DOWNLOAD EBOOK →Author: L. Bernstein
Publisher: Springer
Published: 1971-01-01
Total Pages: 160
ISBN-13: 9783540054979
DOWNLOAD EBOOK →Author: Steven R. Finch
Publisher: Cambridge University Press
Published: 2018-12-06
Total Pages: 783
ISBN-13: 110860403X
DOWNLOAD EBOOK →Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Author: L. Bernstein
Publisher:
Published: 2014-01-15
Total Pages: 164
ISBN-13: 9783662177259
DOWNLOAD EBOOK →Author: Leon Bernstein
Publisher: Springer Verlag
Published: 1971-01-01
Total Pages: 160
ISBN-13: 9780387054971
DOWNLOAD EBOOK →Author: N. Pytheas Fogg
Publisher: Springer
Published: 2003-10-24
Total Pages: 404
ISBN-13: 3540457143
DOWNLOAD EBOOK →A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.
Author: Fritz Schweiger
Publisher: Oxford University Press, USA
Published: 2000
Total Pages: 250
ISBN-13: 9780198506867
DOWNLOAD EBOOK →Mathematician Fritz Schweiger, whose academic affiliation is not provided, provides an introduction to a field of research that has seen remarkable progress in recent decades, concentrating on multidimensional continued fractions which can be described by fractional linear maps or equivalently by a set of (n + 1) x (n + 1) matrices. Addressing the question of periodicity, he refines the problem of convergence to the question of whether these algorithms give "good" simultaneous Diophantine approximations. He notes that these algorithms are not likely to provide such "good" approximations which satisfy the n-dimensional Dirichlet property. Also studied are the ergodic properties of these maps. Annotation copyrighted by Book News Inc., Portland, OR