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31.
A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels
In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X+ = {c∈L1: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X+. The proof is based on weak L1 compactness methods applied to suitably chosen approximating equations. 相似文献
32.
The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on ?n by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back-projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered back-projection algorithm. The results extend and refine work of Tretiak and Metz17. 相似文献
33.
Donald I. Cartwright 《Annali di Matematica Pura ed Applicata》1988,151(1):1-15
Summary We consider the random walk (Xn) associated with a probability p on a free product of discrete groups. Knowledge of the resolvent (or Green's function) of p yields theorems about the asymptotic behaviour of the n-step transition probabilities p*n(x)=P(Xn= x¦ X0=e) as n. Woess [15], Cartwright and Soardi [3] and others have shown that under quite general conditions there is behaviour of the type p*n(x)Cx– n n– 3/2. Here we show on the other hand that if G is a free product of m copies ofZ
r and if (Xn) is the « average » of the classical nearest neighbour random walk on each of the factorsZ
r, then while it satisfies an « n–3/2 — law » for r small relative to m, it switches to an n– r/2 -law for large r. Using the same techniques, we give examples of irreducible probabilities (of infinite support) on the free groupZ
*m which satisfyn
– for
. 相似文献
34.
35.
A well-known relativistic action at a distance interaction of two unequal masses is altered so as to yield purely Newtonian radial forces with fixed particle rest masses in the system center-of-momentum inertial frame. Although particle masses experience no kinematic mass increase in this frame, speeds are naturally restricted to less than the speed of light. We derive a relation between the center-of-momentum frame total Newtonian energy and the composite rest mass. In a new proper time quantum formalism, we obtain an L2(R4 R4, C) Hilbert space by varying individual particle rest masses. We propose the use of density operators, recognizing that the auxiliary proper time parameter is not an observable. The quantum formalism is applied to our altered version of the relativistic harmonic oscillator. Our generalized coherent states yield four-dimensional wave packets which follow the correct classical world lines. Appendices contain reviews of classical Hamiltonian reparametrization (incorporating our notion of manifest covariance), and a comparison of this work with the literature. 相似文献
36.
37.
Donald R. Schreiber James Huebner Seyed Rahmani Frank J. Millero 《Journal of solution chemistry》1993,22(3):201-210
Enthalpies of mixing (m
H) aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting m
H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl2 and CuCl2 were in agreement with earlier isomolal results by other workers. 相似文献
38.
One unit of S(IV) (SO2 or SHO3?) is oxidized per 2 units of [NiIII(cyclam)] species to obtain sulfate. Kinetic analyses have been done by varying the acidities (0.013 ? [H+] ? 1.0 M) and halide concentrations (0.000 ? [X?] ? 0.012 M; X=Cl and Br) at constant ionic strength (μ = 1.0 M). The rate law that incorporates the [X?] and [H+] dependence is ?d[NiIII]T/dt=2k[NiIII]T[S(IV)]T where 2k={ka[H+] + kbK + kK′X[H+] [X?] + kK′XK[X?]} {[H+] + K}?1 {1 + K′X[X?]}?1, here ka=87 ± 7 M?1 s?1, kb=(2.5 ± 0.5)×103 M?1 s?1 and pK = 1.8 ± 0.2. Rate constants ka and kb are attributed to the reactions of [NiIII(cyclam) (H2O)2]3+ with SO2 and SHO3?, respectively. Monohalo species apparent equilibrium constants K′Cl=(1600 ± 400) M?1 and K′Br=(190 ± 20) M?1 and rate constants k=80 ± 8 M?1 s?1 and k = 140 ± 15 M?1 s?1 are ascribed to the protonated pathway, involving the [NiIII(cyclam) (H2O)X]2+ and SO2(aq) reaction pairs. The other two rate constants of k=(5 ± 1)×103 M?1 s?1 and k=(3.1 ± 0.5)×104 M?1 s?1, refer to the deprotonated pathway and are assigned to the [NiIII(cyclam) (H2O)X]2+ /SHO3? redox couple. A deuterium H2O / D2O isotope effect of 2.1–2.8 can be attributed partially to an equilibrium isotope effect at low acidity though a small kinetic isotope (2.5 ± 0.5) effect is evident for the dihydrogen sulfito pathway, ka. The kinetic isotope effect and the absence of sulfite radical scavenging effects are explained by a mechanism entailing migration of a hydride from sulfur to the NiIII center to produce a NiIII—H species, which rapidly comproportionates, and S(VI). © 1993 John Wiley & Sons, Inc. 相似文献
39.
Kickham JE Guérin F Stewart JC Stephan DW 《Angewandte Chemie (International ed. in English)》2000,39(18):3263-3266
40.
An expert system for classifying and identifying low-resolution mass spectra of toxic and related compounds was developed with an expert shell program. The shell system used was an inexpensive, rule-building software package with an implementation of the ID3 algorithm. Seventy-eight target compounds were used to establish classes previously found by SIMCA class modeling. The six classes included nonhalobenzenes; chlorobenzenes; bromoalkanes and bromoalkenes; mono- and di-chloroalkanes and the analogous alkenes; tri-, tetra- and penta-chloroalkanes and the analogous alkenes; and unknowns. Identification modules for the target compounds were forward-chained to the classification modules. An expert system based on binary-encoded mass spectra, with 17 masses selected on the basis of information content, gave 97 and 86% classification accuracy for training and test spectra, respectively. Identification accuracy was 77 and 80%, respectively. An expert system was also developed which was based on ternary encoding of the mass spectra of 108 training compounds using 25 masses. Ternary encoding has many of the advantages of binary encoding, without the disadvantages. This latter system was tested with the spectra of thirty compounds found in field samples or potential air pollutants. The classification accuracy for training and test spectra was 99 and 97%, respectively. The identification accuracy was 96 and 93%, respectively. With proper precautions, the rule-building expert system can be very effective in spectral classification and identification problems. 相似文献