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81.
We give sufficient conditions for a metric space to bilipschitz embed in L 1. In particular, if X is a length space and there is a Lipschitz map ${u: X \rightarrow \mathbb R}$ such that for every interval ${I \subset \mathbb R}$ , the connected components of u ?1(I) have diameter ${\leq {\rm const} \cdot {\rm diam}(I)}$ , then X admits a bilipschitz embedding in L 1. As a corollary, the Laakso examples, (Geom Funct Anal 10(1):111–123, 2000), bilipschitz embed in L 1, though they do not embed in any any Banach space with the Radon–Nikodym property (e.g. the space ? 1 of summable sequences). The spaces appearing the statement of the bilipschitz embedding theorem have an alternate characterization as inverse limits of systems of metric graphs satisfying certain additional conditions. This representation, which may be of independent interest, is the initial part of the proof of the bilipschitz embedding theorem. The rest of the proof uses the combinatorial structure of the inverse system of graphs and a diffusion construction, to produce the embedding in L 1. 相似文献
82.
Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online. 相似文献
83.
We present effective linear programming based computational techniques for solving nonconvex quadratic programs with box constraints (BoxQP). We first observe that known cutting planes obtained from the Boolean Quadric Polytope (BQP) are computationally effective at reducing the optimality gap of BoxQP. We next show that the Chvátal–Gomory closure of the BQP is given by the odd-cycle inequalities even when the underlying graph is not complete. By using these cutting planes in a spatial branch-and-cut framework, together with a common integrality-based preprocessing technique and a particular convex quadratic relaxation, we develop a solver that can effectively solve a well-known family of test instances. Our linear programming based solver is competitive with SDP-based state of the art solvers on small instances and sparse instances. Most of our computational techniques have been implemented in the recent version of CPLEX and have led to significant performance improvements on nonconvex quadratic programs with linear constraints. 相似文献
84.
<正>Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain. 相似文献
85.
Hanzhong Zhang Jeff Owens Enke Wang Xin-Nian Wang 《The European Physical Journal C - Particles and Fields》2009,61(4):825-828
High-p
T photon–hadron correlations are studied within the next-to-leading order (NLO) perturbative QCD parton model with modified
parton-jet fragmentation functions due to jet quenching in high-energy A+A collisions. In central A+A collisions, the away-side hadrons with large z
T=p
T
h
/p
T
γ
are controlled mainly by the surface emission of the gamma-jet events, while a small z
T region will be volume emission bias. In other words, gamma jets for a small-z
T region probe the dense matter deeper than those gamma jets for a large-z
T region, so the small-z
T gamma jets are found to be slightly more sensitive to the properties of the dense matter than the large-z
T gamma jets. 相似文献
86.
Shultz DA Fico RM Bodnar SH Kumar RK Vostrikova KE Kampf JW Boyle PD 《Journal of the American Chemical Society》2003,125(38):11761-11771
A magnetostructural correlation (conformational electron spin exchange modulation) within an isostructural series of biradical complexes is presented. X-ray crystal structures, variable-temperature electron paramagnetic resonance spectroscopy, zero-field splitting parameters, and variable-temperature magnetic susceptibility measurements were used to evaluate molecular conformation and electron spin exchange coupling in this series of molecules. Our combined results indicate that the ferromagnetic portion of the exchange couplings occurs via the cross-conjugated pi-systems, while the antiferromagnetic portion occurs through space and is equivalent to incipient bond formation. Thus, molecular conformation controls the relative amounts of ferro- and antiferromagnetic contributions to exchange coupling. In fact, the exchange parameter correlates with average semiquinone ring torsion angles via a Karplus-Conroy-type relation. Because of the natural connection between electron spin exchange coupling and electronic coupling related to electron transfer, we also correlate the exchange parameters in the biradical complexes to mixed valency in the corresponding quinone-semiquinone radical anions. Our results suggest that delocalization in the cross-conjugated, mixed-valent radical anions is proportional to the ferromagnetic contribution to the exchange coupling in the biradical oxidation states. 相似文献
87.
88.
89.
We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels. 相似文献
90.
Zhong Q Bhattacharya S Kotsopoulos S Olson J Taly V Griffiths AD Link DR Larson JW 《Lab on a chip》2011,11(13):2167-2174
Quantitative polymerase chain reactions (qPCR) based on real-time PCR constitute a powerful and sensitive method for the analysis of nucleic acids. However, in qPCR, the ability to multiplex targets using differently colored fluorescent probes is typically limited to 4-fold by the spectral overlap of the fluorophores. Furthermore, multiplexing qPCR assays requires expensive instrumentation and most often lengthy assay development cycles. Digital PCR (dPCR), which is based on the amplification of single target DNA molecules in many separate reactions, is an attractive alternative to qPCR. Here we report a novel and easy method for multiplexing dPCR in picolitre droplets within emulsions-generated and read out in microfluidic devices-that takes advantage of both the very high numbers of reactions possible within emulsions (>10(6)) as well as the high likelihood that the amplification of only a single target DNA molecule will initiate within each droplet. By varying the concentration of different fluorogenic probes of the same color, it is possible to identify the different probes on the basis of fluorescence intensity. Adding multiple colors increases the number of possible reactions geometrically, rather than linearly as with qPCR. Accurate and precise copy numbers of up to sixteen per cell were measured using a model system. A 5-plex assay for spinal muscular atrophy was demonstrated with just two fluorophores to simultaneously measure the copy number of two genes (SMN1 and SMN2) and to genotype a single nucleotide polymorphism (c.815A>G, SMN1). Results of a pilot study with SMA patients are presented. 相似文献