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91.
A method to design lasers that emit an arbitrary beam profile is studied. In these lasers, output-coupling is performed by a diffraction grating that imposes a phase and amplitude distribution onto the diffracted light. A solid-state laser emitting beams with a two-dimensional Airy intensity profile is demonstrated both theoretically and experimentally. In this case, the diffraction grating adds a transverse cubic phase to the diffracted light. An Airy beam is obtained by performing optical Fourier transform of the out-coupled light. The laser beam profile and power characteristics are shown to agree with theory. 相似文献
92.
93.
Zeev Smilansky 《Israel Journal of Mathematics》1990,71(1):29-32
We describe a shelling of the octahedron inE
3 which cannot be realized in the conventional geometric way. 相似文献
94.
Zeev Zeitlin 《European Journal of Operational Research》1981,8(2):152-158
This paper is concerned with the problem of optimal integer allocation having a doubly concave objective function. The problem is studied with application to some model of optimal reliability. To derive the optimality conditions, we introduce the notion of integer local equilibrium, considering three of its variations. We also investigate some additional conditions under which this equilibrium is the optimal solution.An appropriate solution algorithm is presented. 相似文献
95.
The kinetics of hydrogen abstraction from cyclohexene by CCl3 radicals were studied in CCl4 solution as a function of cyclohexene concentration and temperature in the range of 26–140°C. The CCl3 radicals were produced both by radiolysis of CCl4 and by photolysis of CCl3Br. The rate constant for the reaction was found to be given by the equation where θ = 2.303 RT kcal/mol. This activation energy leads to C? H bond strength for the allylic hydrogen of 85 ± 1 kcal/mol, which means a resonance stabilization energy of 11 ± 1.5 kcal/mol for the C-C6H11 radical. 相似文献
96.
97.
This aim of this note is to present a probabilistic approach to an algebraic problem in image reconstruction. The role of probability theory is to identify the relevant variables that characterize the solutions, and to provide alternative variational methods of reconstruction. 相似文献
98.
99.
Mohammad T. Hajiaghayi Guy Kortsarz Vahab S. Mirrokni Zeev Nutov 《Mathematical Programming》2007,110(1):195-208
Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the
graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider
four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover problem (MPb-EC) where the goal is to find a min-power subgraph so that the degree of every node v is at least some given integer b(v), the Min-Power k-node Connected Spanning Subgraph problem (MPk-CSS), Min-Power k-edge Connected Spanning Subgraph problem (MPk-CSS), and finally the Min-Power k-Edge-Disjoint Paths problem in directed graphs (MPk-EDP). We give an O(log4
n)-approximation algorithm for MPb-EC. This gives an O(log4
n)-approximation algorithm for MPk-CSS for most values of k, improving the best previously known O(k)-approximation guarantee. In contrast, we obtain an approximation algorithm for ECSS, and for its variant in directed graphs (i.e., MPk-EDP), we establish the following inapproximability threshold: MPk-EDP cannot be approximated within O(2log1-ε
n) for any fixed ε > 0, unless NP-hard problems can be solved in quasi-polynomial time.
This paper was done when V. S. Mirrokni was at Computer Science and Artificial Intelligence Laboratory, MIT. 相似文献
100.
Zeev Nutov 《Discrete Applied Mathematics》2007,155(2):82-91
Let G be a simple digraph. The dicycle packing number of G, denoted νc(G), is the maximum size of a set of arc-disjoint directed cycles in G. Let G be a digraph with a nonnegative arc-weight function w. A function ψ from the set C of directed cycles in G to R+ is a fractional dicycle packing of G if ∑e∈C∈Cψ(C)?w(e) for each e∈E(G). The fractional dicycle packing number, denoted , is the maximum value of ∑C∈Cψ(C) taken over all fractional dicycle packings ψ. In case w≡1 we denote the latter parameter by .Our main result is that where n=|V(G)|. Our proof is algorithmic and generates a set of arc-disjoint directed cycles whose size is at least νc(G)-o(n2) in randomized polynomial time. Since computing νc(G) is an NP-Hard problem, and since almost all digraphs have νc(G)=Θ(n2) our result is a FPTAS for computing νc(G) for almost all digraphs.The result uses as its main lemma a much more general result. Let F be any fixed family of oriented graphs. For an oriented graph G, let νF(G) denote the maximum number of arc-disjoint copies of elements of F that can be found in G, and let denote the fractional relaxation. Then, . This lemma uses the recently discovered directed regularity lemma as its main tool.It is well known that can be computed in polynomial time by considering the dual problem. We present a polynomial algorithm that finds an optimal fractional dicycle packing. Our algorithm consists of a solution to a simple linear program and some minor modifications, and avoids using the ellipsoid method. In fact, the algorithm shows that a maximum fractional dicycle packing with at most O(n2) dicycles receiving nonzero weight can be found in polynomial time. 相似文献