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A Panorama of Statistics

A Panorama of Statistics: Perspectives, Puzzles and Paradoxes in Statistics Eric Sowey, School of Economics, The University of New South Wales, Sydney, Australia Peter Petocz, Department of Statistics, Macquarie University, Sydney, Australia This book is a stimulating panoramic tour – quite different from a textbook journey – of the world of statistics in both its theory and practice, for teachers, students and practitioners. At each...

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Brownian Brownian Motion-I

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work the authors study a 2D version of this model, where the molecule is a heavy disk of mass M 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by conv...

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Locally Toric Manifolds and Singular Bohr-Sommerfeld Leaves

A real polarization modelled on fibres of the moment map. The author computes the results directly and obtains a theorem similar to Sniatycki's, which gives the quantization in terms of counting Bohr-Sommerfeld leaves. However, the count does not include the Bohr-Sommerfeld leaves which are singular. Thus the quantization obtained is different from the quantization obtained using a Kohler polarization.

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Zeta Functions for Two-Dimensional Shifts of Finite Type

This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $\zeta^{0}(s)$, which generalizes the Artin-Mazur zeta function, was given by Lind for $\mathbb{Z}^{2}$-action $\phi$. In this paper, the $n$th-order zeta function $\zeta_{n}$ of $\phi$ on $\mathbb{Z}_{n\times \infty}$, $n\geq 1$, is studied first. The trace operator $\mathbf{T}_{n}$, which is the transition matrix for...

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Connes-Chern Character for Manifolds With Boundary and Eta Cochains

The authors express the Connes-Chern of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off parameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression invol...

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Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three

The authors of this title study the sample path regularity of the solution of a stochastic wave equation in spatial dimension d 3. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. Further, the authors obtain joi...

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Topological Classification of Families of Diffeomorphisms Without Small Divisors

The author gives a complete topological classification for germs of one-parameter families of one-dimensional complex analytic diffeomorphisms without small divisors. In the non-trivial cases the topological invariants are given by some functions attached to the fixed points set plus the analytic class of the element of the family corresponding to the special parameter. The proof is based on the structure of the limits of orbits when...

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How the Brain Learns Mathematics, 2 edition

To reach all your math students, use your brain—and theirs, too! This updated bestseller takes readers to the next level with new brain-friendly strategies backed by the latest research and even more ways to seamlessly incorporate what you learn about your students’ developing minds into your math classroom. Discover the cognitive mechanisms for learning math, explore factors that contribute to learning difficulties, and follow a fou...

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College Algebra and Trigonometry, 6th edition

For courses in college algebra and trigonometry . Steadfast Support for your Evolving Course The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. With this latest edition, the authors respond to the challenges of new student expectations and new classroo...