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• Independent random variables with independent sum and difference
• Characterization of probability distributions through the independence of linear forms
• Characterization of probability distributions through the symmetry of the conditional distribution of one linear form given another
• Characterization theorems on the field of p-adic numbers
• Miscellaneous characterization theorems

"It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups" -- Provided by publisher

This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples and corrected exercises. The book presents the notions of Poincaré's recurrence, of ergodicity, of mixing. It enlights also existing links between dynamical systems and Markov chains. The final objective of this book is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems: a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method based on decorrelation estimates

• Getting started
• A diversity of birds
• How to identify birds
• Understanding birds
• Field craft
• Birding at home
• Go farther

"Targeted to beginners and beyond, National Geographic's fun, inspiring guide to the art, craft, and science of bird-watching combines practical know-how and expert knowledge. Browsable and bursting with helpful illustrations and photographs, Birding Basics offers new ideas for when, where, and how to get to know the birds in your world. Not a field guide but a primer in best practices, authored by birding expert Noah Strycker, this breezy book features easy-to-follow advice on what to look and listen for, how to use field guides and birding apps, the best equipment to start with, and ways to engage with other birders around the world. Filled with fun facts and seasoned advice, this useful book will help you attract birds to your backyard, master bird identification, name a bird by its song, and witness the magic of migration. Sidebars feature fun facts, identification tips, and easy projects for exploring the world on the wing. For everyone who loves watching the birds, whether out the window or on the trail, this colorful, easy-to-use guide to better birding has everything you need"-- Provided by publisher

• I. Foundations. Evolution, science, and molecular biology ; DNA : the repository of biological information ; Chemical basis of information molecules ; Protein structure ; Protein function
• II. Nucleic acid structure and methods. DNA and RNA structure ; Studying genes ; Genomes, transcriptomes, and proteomes ; Topology : functional deformations of DNA ; Nucleosomes, chromatin, and chromosome structure
• III. Information transfer. DNA replication ; DNA mutation and repair ; Recombinational DNA repair and homologous recombination ; Site-specific recombination and transposition ; Transcription : DNA-dependent synthesis of RNA ; RNA processing ; The genetic code ; Protein synthesis
• IV. Regulation. Regulating the flow of information ; The regulation of gene expression in bacteria ; The transcriptional regulation of gene expression in eukaryotes ; The posttranscriptional regulation of gene expression in eukaryotes
• Model organisms appendix
• Glossary
• Solution to problems

Written and illustrated with unsurpassed clarity, "Molecular Biology: Principles and Practice" introduces fundamental concepts while exposing students to how science is done. The authors convey the sense of joy and excitement that comes from scientific discovery, highlighting the work of researchers who have shaped and who continue to shape the field today.See what's in the LaunchPad"

• Precambrian. Hadean; Archaean; Proterozoic; Ediacaran
• Palaeozoic. Cambrian; Ordovician; Silurian; Devonian; Carboniferous; Permian
• Mesozoic. Triassic; Jurassic; Cretaceous
• Cenozoic. Palaeogene; Neogene; Quaternary

"It is difficult to conceive of the vast scale of the history of life on Earth, from the very first living organisms sparking into life in hydrothermal deep-sea vents to the dizzying diversity of life today. The evolution of life is a sweeping epic of a tale, with twists and turns, surprising heroes and unlikely survivors. The Earth beautifully distils this complex story into a meaningful scale. In taking a closer look at 47 carefully selected organisms over fifteen periods in our planetary history, this book tells the whole story of life on Earth, and the interconnectedness that unites us through our ecosystems and planetary history. Prepare to be confounded by the ingenuity of evolutionary biologies, humbled by our own brief part in this epic history, and disquieted by our disproportionate impact on the world we call home"--Amazon