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Stochastic and Integral Geometry
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
The Isis-Book (Metamorphoses, Book XI)
Preliminary material /J. GWYN GRIFFITHS -- INTRODUCTION /J. GWYN GRIFFITHS -- SIGLA /J. GWYN GRIFFITHS -- TEXT AND TRANSLATION /J. GWYN GRIFFITHS -- COMMENTARY /J. GWYN GRIFFITHS -- ADDENDA /J. GWYN GRIFFITHS -- A SELECT BIBLIOGRAPHY OF WORKS CONSULTED /J. GWYN GRIFFITHS -- GENERAL INDEX /J. GWYN GRIFFITHS.
Mathematical Constants II
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.
Fabulae
This new Oxford Classical Text of Sophocles is the product of many years of close collaboration between the two editors. Most of the major difficulties of text and interpretation have been discussed in graduate seminars held in Oxford. The evidence of the manuscript tradition has been carefully assessed, and the results of one important discovery have been exploited for the first time. It has also been possible to take account of many little-known or forgotten conjectures, mostly due to critics of the nineteenth century, and some of these have been adopted or given a place in the apparatus criticus. A number of other conjectures are correctly attributed for the first time, and in a few passages the editors have ventured to offer proposals of their own.
The Isis-book
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The Global Theory of Minimal Surfaces in Flat Spaces
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
