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Discrete Groups and Geometry

This volume contains a selection of refereed papers presented in honour of A.M. Macbeath, one of the leading researchers in the area of discrete groups. The subject has been of much current interest of late as it involves the interaction of a number of diverse topics such as group theory, hyperbolic geometry, and complex analysis.

This volume contains a selection of refereed papers presented in honour of A.M. Macbeath, one of the leading researchers in the area of discrete groups.

Interactions Between Compressed Sensing Random Matrices and High Dimensional Geometry

"This book is based on a series of post-doctoral level lectures given at Université Paris-Est Marne-la-Vallée in November 2009 ..."--Abstract.

"This book is based on a series of post-doctoral level lectures given at Université Paris-Est Marne-la-Vallée in November 2009 ..."--Abstract.

Famous Problems of Geometry and How to Solve Them

Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.

Euler was unable to give a solution, and even to this day there is no complete
solution for this problem. One of the most famous of unsolved problems, which
can be stated in terms of elementary concepts, is known as Fermat's Last
Theorem.

Mode Locking of an Active Multipass Geometry

Ultrashort laser pulses in the microjoule regime are of prime importance for manyapplications. Previous record pulse energiesobtained directly from an oscillator in ambient atmosphere were below 2 Î1⁄4J. This thesis describes a newly developed thin-disk laser oscillator with an increasedround-trip gain by employing a self-imaging active multipass geometry. The generationof high energy subpicosecond pulses with a pulse energy of up to 25.9 Î1⁄4J at apulse duration of 928 fs, while operated in ambient atmosphere, could be demonstrated.Stable single-pulse operation has been obtained with an average outputpower in excess of 76W at a repetition rate of 2.93MHz. Self starting passive modelockingwas accomplished using a semiconductor saturable absorber mirror (SESAM)with a modulation depth of 3.5%. The laser was operated at output-coupling rates ofup to 78%.

However, especially for an AMC laser, this approach is only applicable within
certain limits: as is shown in Chap. 4, the stability width of an AMC, in terms of
dioptric power of the TD, strongly decreases with increasing spot size on the TD.

CliffsQuickReview Geometry

CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. From planes, points, and postulates to squares, spheres, and slopes — and everything in between — CliffsQuickReview Geometry can help you make sense of it all. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. Begin with a review of fundamental ideas such as theorems, angles, and intersecting lines. In no time, you'll be ready to work on other concepts such as Triangles and polygons: Classifying and identifying; features and properties; the Triangle Inequality Theorem; the Midpoint Theorem; and more Perimeter and area: Parallelograms, trapezoids, regular polygons, circles Similarity: Ratio and proportion; properties of proportions; similar triangles Right triangles Circles: Central angles and arcs; inscribed angles; chords, secants, tangents; arc length, sectors Geometric solids and coordinate geometry CliffsQuickReview Geometry acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. Here are just a few ways you can search for topics: Use the free Pocket Guide full of essential information Get a glimpse of what you’ll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center Use the glossary to find key terms fast. With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.

This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. Begin with a review of fundamental ideas such as theorems, angles, and intersecting lines.