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1.
In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
We established that acetylacetone and acetone photolytically sensitize norbornene to undergo an efficient radical addition
of solvent (ranging from hexane, cyclic ethers, haloalkanes, acetone, alcohols and acetonitrile) across the double bond. In
view of its synthetic applicability, sensitized photoreactions of norbornene were reviewed and their mechanisms were compared.
Photolysis of acetylacetone in the presence of norbornene in hexane induced i) acetylacetone to cycloadd to norbornene giving
the expected 1,5-diketone, and ii) sensitization by triplet excited acetylacetone to generate reactive norbornene, which underwent
dimerization as well as the addition of a solvent molecule by radical chain processes. In other solvents, the radical chain
addition of solvent dominated the photoreaction, and superseded the cycloaddition, to give excellent to good yields of adducts
to norbornene. While the excited species of acetylacetone for the sensitization was deduced to be its spectroscopic triplet
excited state, that for the cycloaddition should involve a different one which may be a twisted triplet acetylacetone; sensitization
experiments showed that the cycloaddition did not occur from the spectroscopic triplet state. Triplet excited acetone sensitized
norbornene to undergo the same solvent addition more efficiently and cleanly than acetylacetone did. In view of various conflicts
existing in the proposed energy transfer mechanism, the sensitized norbornene reactions were rationalized with electron transfer
and a cation radical chain mechanism. 相似文献
3.
One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups. 相似文献
4.
S. -S. Chow 《Numerische Mathematik》1989,54(4):373-393
Summary In this paper we shall consider the application of the finite element method to a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient, and the derivation of error estimates for the finite element approximations. Such problems arise in many practical situations — for example, in shock-free airfoil design, seepage through coarse grained porous media, and in some glaciological problems. By making use of certain properties of the nonlinear coefficients, we shall demonstrate that the variational formulations associated with these boundary value problems are well-posed. We shall also prove that the abstract operators accompanying such problems satisfy certain continuity and monotonicity inequalities. With the aid of these inequalities and some standard results from approximation theory, we show how one may derive error estimates for the finite element approximations in the energy norm. 相似文献
5.
An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes. 相似文献
6.
The temperature dependence of the Cd hyperfine field in a trivacancy complex in Ni between 25 and300 K is reported. It was found that, unlike the Cd substitutional field in Ni which follows the temperature dependence of the magnetization, the Cd hyperfine field in a trivacancy complex is essentially temperature independent. This temperature anomaly is compared with other temperature anomaly of impurity hyperfine fields in ferromagnetic hosts. 相似文献
7.
Youssef Z. Boutros Mina B. Abd-el-Malek Nagwa A. Badran Hossam S. Hassan 《Applied Mathematical Modelling》2007
The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number Re and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted. 相似文献
8.
N. Jiten Singh Adriana C. Olleta Anupriya Kumar Mina Park Hai-Bo Yi Indrajit Bandyopadhyay Han Myoung Lee P. Tarakeshwar Kwang S. Kim 《Theoretical chemistry accounts》2006,115(2-3):127-135
In earlier studies, the interactions of isolated ionic species with various solvents were investigated using ab initio calculations.
The ionic species investigated included cations (proton, hydronium, ammonium, and metal cations) and anions (single electron,
hydroxide, and halide anions). However in the present study, we investigate the interactions of these ionic species with the
solvent in the presence of other competing ionic species. We also elaborate on how the information obtained from these extensive
studies have been employed in designing and synthesizing various kinds of novel ionophores and receptors. 相似文献
9.
10.
The extractability sequence of K(+) approximately Rb(+) > Cs(+) > Na(+) > Li(+) for the extraction with polyether foam suggests that the cation chelation mechanism might be operative. However, the same order was obtained for the extraction with 100% polypropylene oxide polyether foam which does not normally adopt a helical structure to form oxygen-rich cavities as easily or as effectively as polyethylene oxide to accommodate alkali metal ions. This result indicates that a hole-size/cation-diameter relationship may not be required for the high extraction of K(+). The extraction of alkali metal DPAs and hydroxides from methanol demonstrates the importance of the solvent effect. It indicates that the water-structure enforced ion-pairing (WSEIP) is the driving force for extraction of the ion-pairs. The extraction mechanism for ionic species can be described as an ion-pair extraction process. The overall effect of ion-pair formation in water and interaction of the extracted ions with foam appears to determine the extractability of the ions of the extractable ion-pair. 相似文献