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991.
992.
For a positive integer k, let k?+?k denote the poset consisting of two disjoint k-element chains, with all points of one chain incomparable with all points of the other. Bosek, Krawczyk and Szczypka showed that for each k?≥?1, there exists a constant c k so that First Fit will use at most $c_kw^2$ chains in partitioning a poset P of width at most w, provided the poset excludes k?+?k as a subposet. This result played a key role in the recent proof by Bosek and Krawczyk that O(w 16logw ) chains are sufficient to partition on-line a poset of width w into chains. This result was the first improvement in Kierstead’s exponential bound: (5 w ???1)/4 in nearly 30 years. Subsequently, Joret and Milans improved the Bosek–Krawczyk–Szczypka bound for the performance of First Fit to 8(k???1)2 w, which in turn yields the modest improvement to O(w 14logw ) for the general on-line chain partitioning result. In this paper, we show that this class of posets admits a notion of on-line dimension. Specifically, we show that when k and w are positive integers, there exists an integer t?=?t(k,w) and an on-line algorithm that will construct an on-line realizer of size t for any poset P having width at most w, provided that the poset excludes k?+?k as a subposet. 相似文献
993.
Maxime Crochemore Lucian Ilie Costas S. Iliopoulos Marcin Kubica Wojciech Rytter Tomasz Waleń 《European Journal of Combinatorics》2013
The Longest Previous Factor array gives, for each position i in a string y, the length of the longest factor (substring) of y that occurs both at i and to the left of i in y. The Longest Previous Factor array is central in many text compression techniques as well as in the most efficient algorithms for detecting motifs and repetitions occurring in a text. Computing the Longest Previous Factor array requires usually the Suffix Array and the Longest Common Prefix array. We give the first time–space optimal algorithm that computes the Longest Previous Factor array, given the Suffix Array and the Longest Common Prefix array. We also give the first linear-time algorithm that computes the permutation that applied to the Longest Common Prefix array produces the Longest Previous Factor array. 相似文献
994.
Let W 1,??,W n be independent random subsets of [m]={1,??,m}. Assuming that each W i is uniformly distributed in the class of d-subsets of?[m] we study the uniform random intersection graph G s (n,m,d) on the vertex set {W 1,??W n }, defined by the adjacency relation: W i ??W j whenever |W i ??W j |?Rs. For even?n we show that as n,m???? the edge density threshold for the property that G s (n,m,d) contains a perfect matching is asymptotically the same as that for G s (n,m,d) being connected. 相似文献
995.
Experimental and modeling study on the pyrolysis and oxidation of n-decane and n-dodecane 总被引:1,自引:0,他引:1
High pressure n-decane and n-dodecane shock tube experiments were conducted to assist in the development of a Jet A surrogate kinetic model. Jet A is a kerosene based jet fuel composed of hundreds of hydrocarbons consisting of paraffins, olefins, aromatics and naphthenes. In the formulation of the surrogate mixture, n-decane or n-dodecane represent the normal paraffin class of hydrocarbons present in aviation fuels like Jet A. The experimental work on both n-alkanes was performed in a heated high pressure single pulse shock tube. The mole fractions of the stable species were determined using gas chromatography and mass spectroscopy. Experimental data on both n-decane and n-dodecane oxidation and pyrolysis were obtained for temperatures from 867 to 1739 K, pressures from 19 to 74 atm, reaction times from 1.15 to 3.47 ms, and equivalence ratios from 0.46 to 2.05, and ∞. Both n-decane and n-dodecane oxidation showed that the fuel decays through thermally driven oxygen free decomposition at the conditions studied. This observation prompted an experimental and modeling study of n-decane and n-dodecane pyrolysis using a recently submitted revised n-decane/iso-octane/toluene surrogate model. The surrogate model was extended to n-dodecane in order to facilitate the study of the species and the 1-olefin species quantified during the pyrolysis of n-dodecane and n-decane were revised with additional reactions and reaction rate constants modified with rate constants taken from literature. When compared against a recently published generalized n-alkane model and the original and revised surrogate models, the revised (based on our experimental work) and extended surrogate model showed improvements in predicting 1-olefin species profiles from pyrolytic and oxidative n-decane and n-dodecane experiments. The revised and extended model when compared to the published generalized n-alkane and surrogate models also showed improvements in predicting species profiles from flow reactor n-decane oxidation experiments, but similarly predicted n-decane and n-dodecane ignition delay times. 相似文献
996.
GIAO calculations of the 1H NMR chemical shifts for ethanol at the SCF and DFT levels of theory are presented. The importance of molecular geometry and basis set is discussed. Vibrational correction to the hydroxyl proton chemical shift is also considered in calculations for the monomer of ethanol. The final theoretical results for the monomer obtained at the optimized DFT/B3LYP/6-311G(d,p) geometry with the 6-311G++ (d,p) basis set for NMR are in very good agreement with gas phase experimental data. For the liquid phase ethanol the hydrogen bonding effects are taken into account by performing calculations on various clusters of ethanol. It is shown that inaccuracy due to molecular geometry and basis set in the monomer of ethanol is magnified significantly in calculations for its clusters. In this context the structure of liquid ethanol as predicted recently by quantum cluster equilibrium (QCE) theory is discussed. 相似文献
997.
The one-dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the results have to be stated with recursive relations, because in general the equation is of Heun type. The inverse problem of finding integrable rational potentials based on the properties of the singular points is also presented; in particular, a general class of integrable potentials leading to the Whittaker equation is found. 相似文献
998.
Tomasz Luks 《Potential Analysis》2013,39(1):29-67
We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for α?∈?(1,2). We describe the corresponding Hardy spaces and prove the Fatou theorem for α-harmonic functions. We also give explicit formulas for the Martin kernel of the complement of the sphere and for the harmonic measure, Green function and Martin kernel of the complement of the hyperplane for the symmetric α-stable Lévy processes. Some extensions for the relativistic α-stable processes are discussed. 相似文献
999.
Marcin Kapitaniak Krzysztof Czolczynski Przemysław Perlikowski Andrzej Stefanski Tomasz Kapitaniak 《Physics Reports》2014
Coupled systems that contain rotating elements are typical in physical, biological and engineering applications and for years have been the subject of intensive studies. One problem of scientific interest, which among others occurs in such systems is the phenomenon of synchronization of different rotating parts. Despite different initial conditions, after a sufficiently long transient, the rotating parts move in the same way — complete synchronization, or a permanent constant shift is established between their displacements, i.e., the angles of rotation — phase synchronization. Synchronization occurs due to dependence of the periods of rotating elements motion and the displacement of the base on which these elements are mounted. 相似文献
1000.
Krzysztof Bogdan Tomasz Komorowski 《NoDEA : Nonlinear Differential Equations and Applications》2014,21(4):541-566
We study the principal Dirichlet eigenvalue of the operator \({L_A=\Delta^{\alpha/2}+Ab(x)\cdot\nabla}\) , on a bounded C 1,1 regular domain D. Here \({\alpha\in(1,2)}\) , \({\Delta^{\alpha/2}}\) is the fractional Laplacian, \({A\in\mathbb{R}}\) , and b is a bounded d-dimensional divergence-free vector field in the Sobolev space W 1,2d/(d+α)(D). We prove that the eigenvalue remains bounded, as A→ + ∞, if and only if b has non-trivial first integrals in the domain of the quadratic form of \({\Delta^{\alpha/2}}\) for the Dirichlet condition. 相似文献