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61.
We consider random‐turn positional games, introduced by Peres, Schramm, Sheffield, and Wilson in 2007. A p‐random‐turn positional game is a two‐player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p ). We analyze the random‐turn version of several classical Maker–Breaker games such as the game Box (introduced by Chvátal and Erd?s in 1987), the Hamilton cycle game and the k‐vertex‐connectivity game (both played on the edge set of ). For each of these games we provide each of the players with a (randomized) efficient strategy that typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players. 相似文献
62.
An analytical method was developed to detect the three sulfonamides para-toluenesulfonamide (p-TSA), ortho-toluenesulfonamide (o-TSA) and benzenesulfonamide (BSA) in environmental water samples at concentrations down to 0.02 microg/L using liquid chromatography coupled to tandem mass spectrometry (HPLC-MS/MS). Wastewater, surface water, groundwater and drinking water samples from Berlin (Germany) were analysed for all three compounds which appear to be ubiquitously present in the aquatic environment. p-TSA was found in high concentrations in the wastewater (<0.02-50.8 microg/L) and in groundwater below a former sewage farm (<0.02-41 microg/L), and in lower concentrations in the surface water (<0.02 to 1.15 microg/L) and drinking water (<0.02-0.27 microg/L). o-TSA and BSA were detected in considerably lower concentrations. The study makes clear that p-TSA should be monitored because of its comparatively high concentration in Berlin's drinking water. 相似文献
63.
A convenient approach to compute kinetic isotope effects (KIEs) in condensed phase chemical reactions is via path integrals (PIs). Usually, the primitive approximation is used in PI simulations, although such quantum simulations are computationally demanding. The efficiency of PI simulations may be greatly improved, if higher-order Trotter factorizations of the density matrix operator are used. In this study, we use a higher-order PI method, in conjunction with mass-perturbation, to compute heavy-atom KIE in the decarboxylation of orotic acid in explicit sulfolane solvent. The results are in good agreement with experiment and show that the mass-perturbation higher-order Trotter factorization provides a practical approach for computing condensed phase heavy-atom KIE. 相似文献
64.
Let satisfy and suppose a k‐uniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets of sizes , the number of edges intersecting is (asymptotically) the number one would expect to find in a random k‐uniform hypergraph. Can we then infer that H is quasi‐random? We show that the answer is negative if and only if . This resolves an open problem raised in 1991 by Chung and Graham [J AMS 4 (1991), 151–196]. While hypergraphs satisfying the property corresponding to are not necessarily quasi‐random, we manage to find a characterization of the hypergraphs satisfying this property. Somewhat surprisingly, it turns out that (essentially) there is a unique non quasi‐random hypergraph satisfying this property. The proofs combine probabilistic and algebraic arguments with results from the theory of association schemes. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
65.
Sonny Ben‐Shimon Asaf Ferber Dan Hefetz Michael Krivelevich 《Random Structures and Algorithms》2012,41(1):23-46
We study Maker‐Breaker games played on the edge set of a random graph. Specifically, we analyze the moment a typical random graph process first becomes a Maker's win in a game in which Maker's goal is to build a graph which admits some monotone increasing property \begin{align*}\mathcal{P}\end{align*}. We focus on three natural target properties for Maker's graph, namely being k ‐vertex‐connected, admitting a perfect matching, and being Hamiltonian. We prove the following optimal hitting time results: with high probability Maker wins the k ‐vertex connectivity game exactly at the time the random graph process first reaches minimum degree 2k; with high probability Maker wins the perfect matching game exactly at the time the random graph process first reaches minimum degree 2; with high probability Maker wins the Hamiltonicity game exactly at the time the random graph process first reaches minimum degree 4. The latter two statements settle conjectures of Stojakovi? and Szabó. We also prove generalizations of the latter two results; these generalizations partially strengthen some known results in the theory of random graphs. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 相似文献
66.
Asaf Hadari 《Advances in Mathematics》2011,226(4):3282
We extend the definition of algebraic entropy to endomorphisms of affine varieties. We then calculate the algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a pseudo-Anosov mapping class. Our calculations are compatible with all known calculations of the topological entropy of this action. 相似文献
67.
We consider basic problems of non-preemptive scheduling on uniformly related machines. For a given schedule, defined by a partition of the jobs into m subsets corresponding to the m machines, \(C_i\) denotes the completion time of machine i. Our goal is to find a schedule that minimizes or maximizes \(\sum _{i=1}^m C_i^p\) for a fixed value of p such that \(0 . For \(p>1\) the minimization problem is equivalent to the well-known problem of minimizing the \(\ell _p\) norm of the vector of the completion times of the machines, and for \(0 , the maximization problem is of interest. Our main result is an efficient polynomial time approximation scheme (EPTAS) for each one of these problems. Our schemes use a non-standard application of the so-called shifting technique. We focus on the work (total size of jobs) assigned to each machine and introduce intervals of work that are forbidden. These intervals are defined so that the resulting effect on the goal function is sufficiently small. This allows the partition of the problem into sub-problems (with subsets of machines and jobs) whose solutions are combined into the final solution using dynamic programming. Our results are the first EPTAS’s for this natural class of load balancing problems. 相似文献
68.
Arnab Bhattacharyya Elena Grigorescu Asaf Shapira 《Random Structures and Algorithms》2015,46(2):232-260
In the study of property testing, a particularly important role has been played by linear invariant properties, i.e., properties of Boolean functions on the hypercube which are closed under linear transformations of the domain. Examples of such properties include linearity, Reed‐Muller codes, and Fourier sparsity. In this work, we describe a framework that can lead to a unified analysis of the testability of all linear‐invariant properties, drawing on techniques from additive combinatorics and from graph theory. Our main contributions here are the following:
69.
The Alexander-Orbach conjecture holds in high dimensions 总被引:1,自引:0,他引:1
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established,
namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral
dimension
ds=\frac43d_{s}=\frac{4}{3}
, that is, p
t
(x,x)=t
−2/3+o(1). This establishes a conjecture of Alexander and Orbach (J. Phys. Lett. (Paris) 43:625–631, 1982). En route we calculate the one-arm exponent with respect to the intrinsic distance. 相似文献
70.