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41.
The molecule crystallizes in a ketohydrazone tautomeric form. The tautomeric form is stabilized by a strong intramolecular hydrogen bond of 2.709(2) Å binding the 3-oxo to the nearest nitrogen atom in the azine chain. The compound crystallizes in the monoclinic space group P2l/c witha=7.0470(4),b=11.3090(9),c=16.2250(4) Å, =90.310(3)°, V=1293.0(1) Å3, Z=4,Dx=1.3576 g cm–3 and (Cu-K)=7.03 cm–1. The molecule is nearly planar not regarding the methyl group; the small deviations from planarity are indicative of intramolecular interactions between the phenylazo group and indandione group. Some of the bond lengths and angles found in the molecule are distorted due to resonance, -electron delocalization and strain. The relation between these chemical effects and structural results are discussed. 相似文献
42.
Joachim Wagner 《Journal of Applied Crystallography》2012,45(3):513-516
The scattering function for polydisperse core–shell particles with Schulz–Flory size distributions of both the core radius and the shell thickness is analytically calculated. The results of the analytical solution are compared with the results of a numerical integration over both size distributions, as well as with available analytical solutions for homogeneous spheres. The CPU time required for the calculation of the scattering function can be reduced by several orders of magnitude compared with numerical integration. This is of tremendous importance in nonlinear curve fitting requiring repeated calculation of the theoretical function in an iterative process. 相似文献
43.
The singular stress, electric fields and magnetic fields in a rectangular piezoelectromagnetic body containing a center Griffith crack under longitudinal shear are obtained. Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problems of the crack, which is assumed to be impermeable, to dual integral equations. The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind. Expressions for stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived. Also obtained are the field intensity factors and the energy release rates. Numerical results obtained show that the geometry of the rectangular body have significant influence on the field intensity factors and the energy release rates. 相似文献
44.
A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
45.
The problem of two‐dimensional tracer advection on the sphere is extremely important in modeling of geophysical fluids and has been tackled using a variety of approaches. A class of popular approaches for tracer advection include ‘incremental remap’ or cell‐integrated semi‐Lagrangian‐type schemes. These schemes achieve high‐order accuracy without the need for multistage integration in time, are capable of large time steps, and tend to be more efficient than other high‐order transport schemes when applied to a large number of tracers over a single velocity field. In this paper, the simplified flux‐form implementation of the Conservative Semi‐LAgrangian Multi‐tracer scheme (CSLAM) is reformulated using quadratic curves to approximate the upstream flux volumes and Gaussian quadrature for integrating the edge flux. The high‐order treatment of edge fluxes is motivated because of poor accuracy of the CSLAM scheme in the presence of strong nonlinear shear, such as one might observe in the midlatitudes near an atmospheric jet. Without the quadratic treatment of upstream edges, we observe at most second‐order accuracy under convergence of grid resolution, which is returned to third‐order accuracy under the improved treatment. A shallow‐water barotropic instability also reveals clear evidence of grid imprinting without the quadratic correction. Consequently, these tests reveal a problem that might arise in tracer transport near nonlinearly sheared regions of the real atmosphere, particularly near cubed‐sphere panel edges. Although CSLAM is used as the foundation for this analysis, the conclusions of this paper are applicable to the general class of incremental remap schemes. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
46.
In this paper, the local radial point interpolation meshless method (LRPIM) is used for the analysis of two‐dimensional potential flows, based on a local‐weighted residual method with the Heaviside step function as the weighting function over a local subdomain. Trial functions are constructed using radial basis functions. The present method is a truly meshless method based only on a number of randomly located nodes. Integration over the subdomains requires only a simple integration cell to obtain the solution. No element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. The novelty of the paper is the use of a local Heaviside weight function in the LRPIM, which does not need local domain integration and integrations only on the boundary of the local domains are needed. Effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated. The behavior of shape parameters of multiquadrics has been systematically studied. Two numerical tests in groundwater and fluid flows are presented and compared with closed‐form solutions and finite element method. The results show that the use of a local Heaviside weight function in the LRPIM is highly accurate and possesses no numerical difficulties. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
47.
K. Bhattacharyya T. Hayat A. Alsaedi 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2014,94(6):522-528
In this investigation, the steady boundary layer flow of Casson fluid over a porous stretching/shrinking sheet is studied. The governing equations are transformed using similarity transformations and then solved analytically. In both stretching and shrinking sheet cases, the closed form exact solutions are obtained. The solution is always unique for stretching sheet case. On the other hand, in shrinking sheet case, the solution may exist or may not and if exists it may be unique or may be of dual nature; these all depend on the value of Casson parameter and wall mass transfer parameter. Also, the analysis reveals that for steady flow of Casson fluid stronger mass suction is needed. 相似文献
48.
Tal Ben‐Nun Avi Ginsburg Pablo Szkely Uri Raviv 《Journal of Applied Crystallography》2010,43(6):1522-1531
X+ is a user‐friendly multi‐core accelerated program that fully analyses solution X‐ray scattering radially integrated images. This software is particularly useful for analysing supramolecular self‐assemblies, often found in biology, and for reconstructing the scattering signal in its entirety. The program enables various ways of subtracting background noise. The user selects a geometric model and defines as many layers of that shape as needed. The thickness and electron density of each layer are the fitting parameters. An initial guess is input by the user and the program calculates the form‐factor parameters that best fit the data. The polydispersity of one size parameter at a time can be taken into account. The program can then address the assembly of those shapes into different lattice symmetries. This is accounted for by fitting the parameters of the structure factor, using various peak line shapes. The models of the program and selected features are presented. Among them are the model‐fitting procedure, which includes both absolute and relative constraints, data smoothing, signal decomposition for separation of form and structure factors, goodness‐of‐fit verification procedures, error estimation, and automatic feature recognition in the data, such as correlation peaks and baseline. The program's intuitive graphical user interface runs on Windows PCs. Using X+, the exact structure of a microtubule in a crowded environment, and the structure, domain size, and elastic and interaction parameters of lipid bilayers, were obtained. 相似文献
49.
Herein, a general method to calculate the scattering functions of polyhedra, including both regular and semi‐regular polyhedra, is presented. These calculations may be achieved by breaking a polyhedron into sets of congruent pieces, thereby reducing computation time by taking advantage of Fourier transforms and inversion symmetry. Each piece belonging to a set or subunit can be generated by either rotation or translation. Further, general strategies to compute truncated, concave and stellated polyhedra are provided. Using this method, the asymptotic behaviors of the polyhedral scattering functions are compared with that of a sphere. It is shown that, for a regular polyhedron, the form factor oscillation at high q is correlated with the face‐to‐face distance. In addition, polydispersity affects the Porod constant. The ideas presented herein will be important for the characterization of nanomaterials using small‐angle scattering. 相似文献
50.
Kenneth A. Rubinson Christopher Stanley Susan Krueger 《Journal of Applied Crystallography》2008,41(2):456-465
Small‐angle neutron scattering (SANS) provides a unique method to probe soft matter in the 10–100 nm length scale in solutions. In order to determine the shape and size of biological macromolecular structures correctly with SANS, a background‐subtracted, undistorted scattering curve must be measured, and the required accuracy and precision is especially needed at the short‐length‐scale limit. A true scattering curve is also needed to discern whether intermolecular interactions are present, which also are probed in the SANS experiment. This article shows how to detect intermolecular interactions so that subsequent structure modeling can be performed using only data that do not contain such contributions. It is also shown how control of many factors can lead to an accurate baseline, or background, correction for scattering from proteins, especially to account for proton incoherent scattering. Failure to make this background correction properly from proteins, polymers, nucleic acids and lipids can result in incorrect values for the calculated shapes and sizes of the molecules as well as the derived magnitudes of the intermolecular interactions. 相似文献