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891.
    
With the ubiquity of large‐scale computing resources has come significant attention to practical details of fast algorithms for the numerical solution of partial differential equations. Included in this group are the class of multigrid and algebraic multigrid algorithms that are effective solvers for many of the large matrix problems arising from the discretization of elliptic operators. Algebraic multigrid (AMG) is especially effective for many problems with discontinuous coefficients, discretized on unstructured grids, or over complex geometries. While much effort has been invested in improving the practical performance of AMG, little theoretical understanding of this performance has emerged. This paper presents a two‐level convergence theory for a reduction‐based variant of AMG, called AMGr, which is particularly appropriate for linear systems that have M‐matrix‐like properties. For situations where less is known about the problem matrix, an adaptive version of AMGr that automatically determines the form of the reduction needed by the AMGr process is proposed. The adaptive cycle is shown, in both theory and practice, to yield an effective AMGr algorithm. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   
892.
    
A bisection of a graph is a balanced bipartite spanning sub‐graph. Bollobás and Scott conjectured that every graph G has a bisection H such that degH(v) ≥ ?degG(v)/2? for all vertices v. We prove a degree sequence version of this conjecture: given a graphic sequence π, we show that π has a realization G containing a bisection H where degH(v) ≥ ?(degG(v) ? 1)/2? for all vertices v. This bound is very close to best possible. We use this result to provide evidence for a conjecture of Brualdi (Colloq. Int. CNRS, vol. 260, CNRS, Paris) and Busch et al. (2011), that if π and π ? k are graphic sequences, then π has a realization containing k edge‐disjoint 1‐factors. We show that if the minimum entry δ in π is at least n/2 + 2, then π has a realization containing edge‐disjoint 1‐factors. We also give a construction showing the limits of our approach in proving this conjecture. © 2011 Wiley Periodicals, Inc. J Graph Theory  相似文献   
893.
Tetraethoxysilane (TEOS), water and aluminum sec-butoxide (Al(OBus)3) are combined in several stages of prehydrolysis technique, and reaction intermediates at each stage were examined by means of both liquid and solid nuclear magnetic resonance of 13C, 29Si, 17O, and 27Al nuclei. The spectra indicate that when Al(OBus)3 is added to a prehydrolyzed TEOS solution an aluminosilicate precursor is formed in which the aluminum is tetrahedrally coordinated by four silicate ligands. When further water is added, gelation is accompanied by the expansion of aluminum coordination; the spectra indicate that this occurs by the nucleophilic attack of silanol groups. At water contents for which gels of low transparency result, this coordination expansion is accompanied by the formation of new siloxane linkages, but at water contents so high that opaque gels result, the coordination expansion proceeds much more quickly and no new siloxane linkages are observed.  相似文献   
894.
895.
896.
Transition state analogues of PNP, the Immucillins and DADMe-Immucillins, were designed to match transition state features of bovine and human PNPs, respectively. A third generation of inhibitors has been designed that contain an acyclic iminoalcohol to replace the cyclic mimic of the ribooxacarbenium ion at the transition states of PNPs. The best third generation inhibitor is equivalent to the best inhibitors found in the previous transition state analogues.  相似文献   
897.
Recent advancements in DNA sequencing by end-labeled free-solution electrophoresis (ELFSE) show the promise of this novel technique which overcomes the need for a gel by using a label (or drag-tag) to render the free solution mobility of the DNA size-dependent. It is the attachment of an uncharged drag-tag molecule of a set size to various lengths of DNA in the sample that selectively slows down smaller DNA chains which have less force to pull the drag-tag than larger DNA. So far, only globally random coil conformations have been associated with ELFSE, i.e., the DNA and the label together form a single, undeformed hydrodynamic unit. This paper investigates the conditions under which the DNA and label will segregate into two hydrodynamically distinct units, based on a theoretical approach developed for the electrophoresis of polyampholytes. Optimal experimental conditions tailored to the available label sizes and voltages are predicted along with insight into ideal label architecture.  相似文献   
898.
A perturbed angular correlation (PAC) experiment that measures dynamic damping also needs information about the fundamental quadrupole frequency to relate the damping as a function of temperature to the EFG fluctuation rate. When the experiment is unable to access slow electric field gradient (EFG) fluctuations that show the fundamental quadrupole frequency directly, one needs additional information to determine the hyperfine field parameters and thereby the connection between observed damping and EFG fluctuation rates. One way to solve this problem is to estimate the hyperfine parameters from the fluctuation rate for maximum damping (i.e. at the relaxation peak) or from the rate of maximum damping. This work relates both the maximum damping rate and the fluctuation rate at the relaxation peak to EFG magnitudes (or quadrupole frequencies) for five dynamic N-state symmetric models of fluctuating EFGs.  相似文献   
899.
N,N'-Disubstituted naphthalenediimides (NDIs), planar, electron-deficient building blocks, play an important role in materials and biological sciences. Naphthalene core substituents control the HOMO and LUMO energies, whereas the N-alkyl or aryl substituents affect the solubility, aggregation, and packing propensity in condensed phases. N,N'-Dihydroxynaphthalenediimide (DHNDI) allows expanding the chemical diversity by O-alkylation, acylation, or sulfonylation; these derivatives also allow fine-tuning of the HOMO/LUMO levels. The synthesis, UV-vis, electrochemical, solid state, and computational prediction of the properties of such derivatives are presented.  相似文献   
900.
Over a range of hydration, unsaturated diacylglycerol/phosphatidylcholine mixtures adopt an inverse micellar cubic phase, of crystallographic space group Fd3m. In this study hydrated DOPC:DOG mixtures with a molar ratio close to 1 : 2 were examined as a function of hydrostatic pressure, using synchrotron X-ray diffraction. The small-angle diffraction pattern at atmospheric pressure was used to calculate 2-D sections through the electron density map. Pressure initially has very little effect on the structure of the Fd3m cubic phase, in contrast to its effect on hydrated inverse bicontinuous cubic phases. At close to 2 kbar, a sharp transition occurs from the Fd3m phase to a pair of coexisting phases, an inverse hexagonal H(II) phase plus an (ordered) lamellar phase. Upon increasing the pressure to 3 kbar, a further sharp transition occurs from the H(II) phase to a (fluid) lamellar phase, in coexistence with the ordered lamellar phase. These transitions are fully reversible, but show hysteresis. Remarkably, the lattice parameter of the Fd3m phase is practically independent of pressure. These results show that these two lipids are miscible at low pressure, adopting a single lyotropic phase (Fd3m); they then become immiscible above a critical pressure, phase separating into DOPC-rich and DOG-rich phases.  相似文献   
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