Convex Optimization Techniques For Geometric Covering Problems

Convex Optimization Techniques for Geometric Covering Problems PDF
Author: Jan Hendrik Rolfes
Publisher: BoD – Books on Demand
ISBN: 375434675X
Size: 47.18 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : de
Pages : 126
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The present thesis is a commencement of a generalization of covering results in specific settings, such as the Euclidean space or the sphere, to arbitrary compact metric spaces. In particular we consider coverings of compact metric spaces $(X,d)$ by balls of radius $r$. We are interested in the minimum number of such balls needed to cover $X$, denoted by $\Ncal(X,r)$. For finite $X$ this problem coincides with an instance of the combinatorial \textsc{set cover} problem, which is $\mathrm{NP}$-complete. We illustrate approximation techniques based on the moment method of Lasserre for finite graphs and generalize these techniques to compact metric spaces $X$ to obtain upper and lower bounds for $\Ncal(X,r)$. \\ The upper bounds in this thesis follow from the application of a greedy algorithm on the space $X$. Its approximation quality is obtained by a generalization of the analysis of Chv\'atal's algorithm for the weighted case of \textsc{set cover}. We apply this greedy algorithm to the spherical case $X=S^n$ and retrieve the best non-asymptotic bound of B\"or\"oczky and Wintsche. Additionally, the algorithm can be used to determine coverings of Euclidean space with arbitrary measurable objects having non-empty interior. The quality of these coverings slightly improves a bound of Nasz\'odi. \\ For the lower bounds we develop a sequence of bounds $\Ncal^t(X,r)$ that converge after finitely (say $\alpha\in\N$) many steps: $$\Ncal^1(X,r)\leq \ldots \leq \Ncal^\alpha(X,r)=\Ncal(X,r).$$ The drawback of this sequence is that the bounds $\Ncal^t(X,r)$ are increasingly difficult to compute, since they are the objective values of infinite-dimensional conic programs whose number of constraints and dimension of underlying cones grow accordingly to $t$. We show that these programs satisfy strong duality and derive a finite dimensional semidefinite program to approximate $\Ncal^2(S^2,r)$ to arbitrary precision. Our results rely in part on the moment methods developed by de Laat and Vallentin for the packing problem on topological packing graphs. However, in the covering problem we have to deal with two types of constraints instead of one type as in packing problems and consequently additional work is required.

A Learner S Chinese English Dictionary Covering The Entire Vocabulary For All The Six Levels Of The Chinese Language Proficiency Exam

A Learner   s Chinese English Dictionary  Covering the Entire Vocabulary for all the Six Levels of the Chinese Language Proficiency Exam PDF
Author: Muhammad Wolfgang G. A. Schmidt
Publisher: disserta Verlag
ISBN: 3959353367
Size: 17.53 MB
Format: PDF, Mobi
Category : Reference
Languages : de
Pages : 384
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The focus of this small and concise Chinese-English Dictionary with around 5000 word entries is on the vocabulary of the six levels of the Chinese Language Proficiency Exam (HSK, Hàny Shuipíng Kaoshì) in Mainland China and has been compiled especially for this purpose with those in mind preparing for any of the six levels of this exam. Chinese character entries both in simplified and traditional character versions. Its unique feature is the listing of the English meaning definitions of all composite word parts of a Chinese word entry under the same main entry in this alphabetically arranged dictionary according to the conventions of the Hanyu Pinyin transcription system. This will save the user time to look up English meaning definitions elsewhere under a different Hanyu Pinyin letter heading and at the same provides the user a better insight into the different shades of word meaning of an entire Chinese word entry. The English meaning definitions given for each Chinese word entry are comprehensive, and unlike many other word lists for the six levels of the HSK, are not mere brief word glosses only. Two Chinese character indices (for both simplified and traditional character variants allow the user to locate an unknown word or character in the dictionary.

Covering Codes

Covering Codes PDF
Author: G. Cohen
Publisher: Elsevier
ISBN: 9780080530079
Size: 45.11 MB
Format: PDF, ePub, Mobi
Category : Computers
Languages : en
Pages : 541
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The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer. A number of unsolved problems suitable for research projects are also discussed.

A New Type Of Single Valued Neutrosophic Covering Rough Set Model

A New Type of Single Valued Neutrosophic Covering Rough Set Model PDF
Author: Jingqian Wang
Publisher: Infinite Study
ISBN:
Size: 32.33 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 23
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Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation.

The Covering

The Covering PDF
Author: Hank Hanegraaff
Publisher: Thomas Nelson
ISBN: 1418514829
Size: 33.80 MB
Format: PDF, Kindle
Category : Religion
Languages : en
Pages : 132
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In a world where evil seems to lurk around every corner and our thoughts turn to worry about our safety and security, the armor of God is our Father's protection in the fight against evils of our temporary home. Best-selling author Hank Hanegraaff describes God's protective covering over his children by dissecting Paul's words in Ephesians 6: 10-18 commanding us to put on the armor of God and "take our stand against the devil's schemes." Hanegraaff moves through the passage, phrase by phrase, defining God's armor, explaining what it means to embrace God's covering, and the practical ways God delivers us from evil.

The Covering Property Axiom Cpa

The Covering Property Axiom  CPA PDF
Author: Krzysztof Ciesielski
Publisher: Cambridge University Press
ISBN: 9781139454742
Size: 69.33 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages :
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Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book.

The Foot And Its Covering With Dr Campers Work On The Best Form Of Shoe

The Foot and its Covering with Dr  Campers Work  On the Best Form of Shoe  PDF
Author: J. Dowie
Publisher: Read Books Ltd
ISBN: 1473344603
Size: 15.82 MB
Format: PDF, Kindle
Category : Medical
Languages : en
Pages : 244
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The Foot and its Covering is a vintage handbook on foot care, with a special focus on the importance of good-quality and well-fitted shoes. Essentially, it is a guidebook with hints for those who wear and those who make shoes and boots, with directions on picking and wearing shoes for health, performance, and function. It describes various causes of foot deformities and common ailments, providing advice on how these can be minimised or avoided. Highly recommended for those with an interest in historical shoe manufacturing. Contents include: “Introduction”, “The Foot”, “External Anatomy of the Foot”, “Physical Well-being of the Foot”, “Inquiry into the Nature of the Covering of the Foot, Etc.”, “Measurement—Stocking and Last”, “The Bones of the Foot”, “Upon Walking”, “Shoes and Boots”, “Of the Best Shape of a Shoe”, “Of the Inconveniences Occasioned by Ill-made Shoes, and their Remedies”, etc. Many vintage books such as this are becoming increasingly scarce and expensive. We are republishing this volume now in an affordable, modern, high-quality addition complete with a specially commissioned new introduction on the history of shoemaking.

Floor Covering Weekly

Floor Covering Weekly PDF
Author:
Publisher:
ISBN:
Size: 30.55 MB
Format: PDF, Kindle
Category : Floor coverings
Languages : en
Pages :
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Field Guide To Covering Local News

Field Guide to Covering Local News PDF
Author: Fred Bayles
Publisher: CQ Press
ISBN: 1608710017
Size: 23.54 MB
Format: PDF, ePub, Mobi
Category : Language Arts & Disciplines
Languages : en
Pages : 270
View: 109

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In a time of upheaval for journalism, local news is flourishing. People want to know about the chemical spill on the highway, the kidnapping trial in district court, the cuts in the school budget. News organizations have a constant need for both professional and citizen journalists who can report those stories accurately and interestingly. In the latest installment of the Field Guide series, Fred Bayles takes you step-by-step through the process of identifying and covering the events and issues that matter most to your community.

Covering Catastrophe

Covering Catastrophe PDF
Author: Allison Gilbert
Publisher: Bonus Books, Inc.
ISBN: 9781566251808
Size: 72.98 MB
Format: PDF, Docs
Category : History
Languages : en
Pages : 303
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Covering Catastrophe tells what it was like for TV and radio journalists to report the most terrifying story of their lives-and our time.

Life

LIFE PDF
Author:
Publisher:
ISBN:
Size: 75.88 MB
Format: PDF, Mobi
Category :
Languages : en
Pages : 136
View: 488

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LIFE Magazine is the treasured photographic magazine that chronicled the 20th Century. It now lives on at LIFE.com, the largest, most amazing collection of professional photography on the internet. Users can browse, search and view photos of today’s people and events. They have free access to share, print and post images for personal use.