Distance geometry

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  • In the early 20th century, Hermann Minkowski (1864-1909) proposed an idea about a new metric, one of many metrics of non-Euclidean geometry that he developed called Taxicab geometry. The purpose of this paper is to design activities so that students can construct the concept of distance and realise practical applications of Taxicab geometry.

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  • Chemistry plays a key role in conquering diseases, solving energy problems, addressing environmental problems, providing the discoveries that lead to new industries, and developing new materials and technologies for national defense and homeland security. However, the field is currently facing a crucial time of change and is struggling to position itself to meet the needs of the future as it expands beyond its traditional core toward areas related to biology, materials science, and nanotechnology....

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  • Although much of its discovery process is descriptive and qualitative, chemistry is fundamentally a quantitative science. It serves a wide range of human needs, activities, and concerns. The mathematical sciences provide the language for quantitative science, and this language is growing in many directions as computational science in general continues its rapid expansion. A timely opportunity now exists to strengthen and increase the beneficial impacts of chemistry by enhancing the interaction between chemistry and the mathematical sciences.

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  • Abstract. The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of Rs , find a point such that the sum of the distances from that point to n given nonempty closed convex subsets of...

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  • In this book it is proposed to enlist the reasoning faculty from the very first: to let one problem grow out of another and to be dependent on the foregoing, as in geometry, and so to explain each thing we do that there shall be no doubt in the mind as to the correctness of the proceeding. The student will thus gain the power of finding out any new problem for himself, and will therefore acquire a true knowledge of perspective.

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  • An image is a two dimensional projection of a three dimensional scene. Hence a degeneration is introduced since no information is retained on the distance of a given point in the space. In order to extract information on the three dimensional contents of a scene from a single image it is necessary to exploit some a priori knowledge either on the features of the scene, i.e. presence/absence of architectural lines, objects sizes, or on the general behaviour of shades, textures, etc.

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  • http://www.nap.edu/catalog/4886.html We ship printed books within 1 business day; personal PDFs are available immediately. Mathematical Challenges from Theoretical/Computational Chemistry Committee on Mathematical Challenges from Computational Chemistry, National Research Council ISBN: 0-309-56064-0, 144 pages, 8.5 x 11, (1995) This PDF is available from the National Academies Press at: http://www.nap.edu/catalog/4886.

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  • Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: An Introduction to Relativity 8.

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  • The solution structure ofNereis diversicolorsarcoplasmic calcium-binding protein (NSCP) in the calcium-bound form was determined by NMR spec-troscopy, distance geometry and simulated annealing. Based on 1859 NOE restraints and 262 angular restraints, 17 structures were generated with a rmsd of 0.87 A ˚ from the mean structure. The solution structure, which is highly similar to the structure obtained by X-ray crystallography, includes two open EF-hand domains, which are in close contact through their hydrophobic surfaces....

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  • Geometry and Trigonometry Geometry and Trigonometry Although many people find geometry and trigonometry intimidating, the small investment required to understand a few basic principles in these disciplines can pay large dividends. For example, what if you needed to find the distance between two points, or rotate one object around another? These small tasks are needed more often than you may think, and are easier to accomplish than you may realize. Movement Along an Angle Earlier we discussed velocity as a vector quantity because it combined magnitude and direction.

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  • Lines and angles Triangles Isosceles and equilateral triangles Rectangles, squares, and parallelograms Circles Advanced circle problems Polygons Cubes and other rectangular solids Cylinders Coordinate signs and the four quadrants Defining a line on the coordinate plane Graphing a line on the coordinate plane Midpoint and distance formulas Coordinate geometry Summing it up In this chapter, you’ll review the fundamentals involving plane geometry, starting with the following: • • • • • • Relationships among angles formed by intersecting lines Characteristics of any triangle Cha...

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  • CHAPTER 8 GEARED SYSTEMS AND VARIABLE-SPEED MECHANISMS GEARS AND GEARING Gear tooth terminology Gears are versatile mechanical components capable of performing many different kinds of power transmission or motion control. Examples of these are • • • • Changing rotational speed. Changing rotational direction. Changing the angular orientation of rotational motion. Multiplication or division of torque or magnitude of rotation. • Converting rotational to linear motion and its reverse. • Offsetting or changing the location of rotating motion.

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  • In real life, we can tell where objects are by measuring distance between them. As for placing them, moving them, and keeping track of where they are nature has developed a pretty good system. On the computer though, we have to somehow keep track of objects in a 3D scene. Mathematicians have developed the coordinate system. You have probably learned in geometry about the X and the Y axis. Well, these two axis define a coordinate plane, that is, a two dimentional world. However, to work in three dimentions, we need one more axis, the Z axis....

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