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This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies.
New and elegant proofs of classical results and makes difficult results accessible.
Professor Rogers has written this economical and logical exposition of the theory of packing and covering at a time when the simplest general results are known and future progress seems likely to depend on detailed and complicated technical developments. The book treats mainly problems in n-dimensional space, where n is larger than 3. The approach is quantative and many estimates for packing and covering densities are obtained. The introduction gives a historical outline of the subject, stating results without proof, and the succeeding chapters contain a systematic account of the general results and their derivation. Some of the results have immediate applications in the theory of numbers, in analysis and in other branches of mathematics, while the quantative approach may well prove to be of increasing importance for further developments.
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This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
In this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. This book introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings./a
This book provides a comprehensive overview of the most important and frequently considered optimization problems concerning cutting and packing. Based on appropriate modeling approaches for the problems considered, it offers an introduction to the related solution methods. It also addresses aspects like performance results for heuristic algorithms and bounds of the optimal value, as well as the packability of a given set of objects within a predefined container. The problems discussed arise in a wide variety of different fields of application and research, and as such, the fundamental knowledge presented in this book make it a valuable resource for students, practitioners, and researchers who are interested in dealing with such tasks.
It’s time to pack perfect. Every trip, every time. Your journey starts here. When you travel, the journey is just as important as the destination—and packing is the first step. In How to Pack, Hitha Palepu, a former consultant who has traveled more than 500,000 cumulative miles around the world, shows that what and how you pack are who you are. Confidence and comfort inspire success upon arrival, whether you’re exploring a new city, hoping to nail a job interview, or relaxing on a beach. In How to Pack, you’ll learn about: · Power Pieces vs. Fantasy Pieces: How clothing earns its place in your suitcase · The Accessory Math Secret: The precise formula for all you need to finish off your outfits · Folding versus Rolling: What’s right for which items · Globetrotter Gorgeous: Editing your beauty routine while still looking great · The Packing Timeline: How to avoid “I’m forgetting something” syndrome · Pack Perfect Lists: Samples and blanks for any kind of trip