Optimal shapes of compact strings
نویسندگان
چکیده
منابع مشابه
ON OPTIMAL NOZZLE SHAPES OF GAS-DYNAMIC LASERS
Pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. The exact shape is obtained for the uncoupled approximation of Anderson's bimodal model. In this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; otherwise...
متن کاملOPTIMAL NOZZLE SHAPES OF CO2-N2-H2O GASDYNAMIC LASERS
In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...
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We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuri...
متن کاملCompact q-Gram Profiling of Compressed Strings
We consider the problem of computing the q-gram profile of a string T of size N compressed by a context-free grammar with n production rules. We present an algorithm that runs in O(N ↵) expected time and uses O(n+kT,q) space, where N ↵ qn is the exact number of characters decompressed by the algorithm and kT,q N ↵ is the number of distinct q-grams in T . This simultaneously matches the curr...
متن کاملUnited Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS OPTIMAL SHAPES OF COMPACT STRINGS
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines [1, 2, 3, 4, 5]. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved [1, 2] that the answer for infinite systems is a face-centred-cubic lattice. This simply stated...
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ژورنال
عنوان ژورنال: Nature
سال: 2000
ISSN: 0028-0836,1476-4687
DOI: 10.1038/35018538