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51.
Pierre Lalonde 《Journal of Combinatorial Theory, Series A》2006,113(6):980-994
We define a bijection that transforms an alternating sign matrix A with one −1 into a pair (N,E) where N is a (so called) neutral alternating sign matrix (with one −1) and E is an integer. The bijection preserves the classical parameters of Mills, Robbins and Rumsey as well as three new parameters (including E). It translates vertical reflection of A into vertical reflection of N. A hidden symmetry allows the interchange of E with one of the remaining two new parameters. A second bijection transforms (N,E) into a configuration of lattice paths called “mixed configuration.” 相似文献
52.
Luke Pebody 《Journal of Combinatorial Theory, Series A》2006,113(3):551-555
Answering a question of Körner and Simonyi, this paper gives a strongly consecutive repeat-free code of maximal size in [b]n. 相似文献
53.
Simon R. Blackburn 《Journal of Combinatorial Theory, Series A》2006,113(7):1572-1581
The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. There is no set of 2n−2+1 permutations having this property. 相似文献
54.
M. Sun 《Applied Mathematics and Optimization》1996,34(3):267-277
We focus on numerically solving a typical type of Hamilton-Jacobi-Bellman (HJB) equations arising from a class of optimal controls with a standard multidimensional diffusion model. Solving such an equation results in the value function and an optimal feedback control law. The Bellman's curse of dimensionality seems to be the main obstacle to applicability of most numerical algorithms for solving HJB. We decompose HJB into a number of lower-dimensional problems, and discuss how the usual alternating direction method can be extended for solving HJB. We present some convergence results, as well as preliminary experimental outcomes.This research was funded in part by an RGC grant from the University of Alabama. 相似文献
55.
Marcel Herzog 《Journal of Combinatorial Theory, Series A》2008,115(7):1235-1245
Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99]. 相似文献
56.
This paper reports the validation of the results obtained by combining near infrared spectroscopy and multivariate curve resolution-alternating least squares (MCR-ALS) and using high performance liquid chromatography as a reference method, for the model reaction of phenylglycidylether (PGE) and aniline. The results are obtained as concentration profiles over the reaction time. The trueness of the proposed method has been evaluated in terms of lack of bias. The joint test for the intercept and the slope showed that there were no significant differences between the profiles calculated spectroscopically and the ones obtained experimentally by means of the chromatographic reference method at an overall level of confidence of 5%. The uncertainty of the results was estimated by using information derived from the process of assessment of trueness. Such operational aspects as the cost and availability of instrumentation and the length and cost of the analysis were evaluated. The method proposed is a good way of monitoring the reactions of epoxy resins, and it adequately shows how the species concentration varies over time. 相似文献
57.
A second-order accurate numerical method for the two-dimensional fractional diffusion equation 总被引:1,自引:0,他引:1
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method. 相似文献
58.
Omar Ramadan 《International Journal of Infrared and Millimeter Waves》2007,28(1):113-119
Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented
for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating
the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the
PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations
are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited
electromagnetic applications. 相似文献
59.
60.
Izaskun Garrido Barry Lee Gunnar E. Fladmark Magne S. Espedal. 《Mathematics of Computation》2006,75(255):1403-1428
Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.