The chords’ problem is a variant of an old problem of computational geometry: given a set of points of , one can easily build the multiset of the distances between the points of the set but the converse construction is known for a longtime as difficult. The problem that we are going to investigate is also a converse construction with the difference that it no more the one of the distances multi...

H. Edelsbrunner1, A. Ivanov2 and R. Karasev3 Institute of Science and Technology Austria, Yaroslavl State University Moscow State University, Yaroslavl State University Moscow Institute of Physics and Technology, Yaroslavl State University e-mail: [email protected], [email protected], [email protected] получена 22 ноября 2006 Ключевые слова: Discrete and Computational Geometry, Computation...

Many problems concerning the theory and technology of rhythm, melody, and voice-leading are fundamentally geometric in nature. It is therefore not surprising that the field of computational geometry can contribute greatly to these problems. The interaction between computational geometry and music yields new insights into the theories of rhythm, melody, and voice-leading, as well as new problems...

The Shatters relation and the VC dimension have been investigated since the early seventies. These concepts have found numerous applications in statistics, combinatorics, learning theory and computational geometry. Shattering extremal systems are set-systems with a very rich structure and many different characterizations. The goal of this thesis is to elaborate on the structure of these systems.

The maximum segment density problem is this: Given a sequence of pairs (ai, wi), i = 1, 2, . . . , n, with wi > 0, and another pair of numbers L ≤ U , we have to find a subsequence ai, ai+1, . . . , aj whose density (ai + ai+1 + . . .+ aj)/(wi +wi+1 + . . .+wj) is maximum under the constraint that L ≤ wi + wi+1 + . . . + wj ≤ U . A principal motivation for studying this problem is its applicati...

Conformal geometry has deep roots in pure mathematics. It is the intersection of complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed....

the methamphetamine has been studied theoretically at the mp2 [1]/6-31g[2] level in gas phase.methamphetamine has been investigated via nmr, frequencies calculation and nbo analysis. thestructure of methamphetamine was designed primarily using of chem. bio draw and it geometry hasbeen optimized at the mp2/6-31g computational level. the present work consists the study of themethamphetamine repor...

It has long been an open problem whether or not there exists a partial geometry with parameters (s, t, α) = (4, 27, 2). Such a partial geometry, which we call a McLaughlin geometry, would have the McLaughlin graph as point graph. In this note we use tools from computational group theory and computational graph theory to show that a McLaughlin geometry cannot have certain automorphisms, nor can ...