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61.
Diemar A. Plattner Andreas Brunner Max Dobler Hans-Martin Müller Walter Petter Peter Zbinden Dieter Seebach 《Helvetica chimica acta》1993,76(5):2004-2033
Cyclic Oligomers of (R)-3-Hydroxybutanoic Acid: Preparation and Structural Aspects The oligolides containing three to ten (R)-3-hydroxybutanoate (3-HB) units (12-through 40-membered rings 1–8 ) are prepared from the hydroxy acid itself, its methyl ester, its lactone (‘monolide’), or its polymer (poly(3-HB), mol. wt. ca. 106 Dalton) under three sets of conditions: (i) treatment of 3-HB ( 10 ) with 2,6-dichlorobenzoyl chloride/pyridine and macrolactonization under high dilution in toluene with 4-(dimethylamino)pyridine (Fig. 3); (ii) heating a solution (benzene, xylene) of the β-lactone 12 or of the methyl ester 13 from 3-HB with the tetraoxadistanna compound 11 as trans-esterification catalyst (Fig. 4); (iii) heating a mixture of poly(3-HB) and toluene-sulfonic acid in toluene/1,2-dichloroethane for prolonged periods of time at ca. 100° (Fig. 6). In all three cases, mixtures of oligolides are formed with the triolide 1 being the prevailing component (up to 50% yield) at higher temperatures and with longer reaction times (thermodynamic control, Figs. 3–6). Starting from rac-β-lactone rac- 12 , a separable 3:1 to 3:2 mixture of the l,u- and the l,l-triolide diasteroisomers rac- 14 and rac- 1 , respectively, is obtained. An alternative method for the synthesis of the octolide 6 is also described: starting from the appropriate esters 15 and 17 and the benzyl ether 16 of 3-HB, linear dimer, tetramer, and octamer derivatives 18–23 are prepared, and the octamer 23 with free OH and CO2H group is cyclized (→ 6 ) under typical macrolactonization conditions (see Scheme). This ‘exponential fragment coupling protocol’ can be used to make higher linear oligomers as well. The oligolides 1–8 are isolated in pure form by vacuum distillation, chromatography, and crystallization, an important analytical tool for determining the composition of mixtures being 13C-NMR spectroscopy (each oligolide has a unique and characteristic chemical shift of the carbonyl C-atom, with the triolide 1 at lowest, the decolide 8 at highest field). The previously published X-ray crystal structures of triolide 1 , pentolide 3 , and hexolide 4 (two forms), as well as those of the l,u-triolide rac- 14 , of tetrolide ent- 2 , of heptolide 5 , and of two modifications of octolide 6 described herein for the first time are compared with each other (Figs. 7–10 and 12–15, Tables 2 and 5–7) and with recently modelled structures (Tables 3 and 4, Fig. 11). The preferred dihedral angles τ1 to τ4 found along the backbone of the nine oligolide structures (the hexamer and the larger ones all have folded rings!) are mapped and statistically evaluated (Fig. 16, Tables 5–7). Due to the occurrence of two conformational minima of the dihedral angle O? CO? CH2? CH (τ3 = + 151 or ?43°), it is possible to locate two types of building blocks for helices in the structures at hand: a right-handed 31 and a left-handed 21 helix; both have a ca. 6 Å pitch, but very different shapes and dispositions of the carbonyl groups (Fig. 17). The 21 helix thus constructed from the oligolide single-crystal data is essentially superimposable with the helix derived for the crystalline domains of poly(3-HB) from stretched-fiber X-ray diffraction studies. The absence of the unfavorable (E)-type arrangements around the OC? OR bond (‘cis-ester’) from all the structures of (3-HB) oligomers known so far suggests that the model proposed for a poly(3-HB)-containing ion channel (Fig. 2) must be modified. 相似文献
62.
63.
64.
Andreas Maurer 《Letters in Mathematical Physics》1990,20(1):55-63
The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP
Nmodel for d3. 相似文献
65.
Cross ratios constitute an important tool in classical projective geometry. Using the theory of Tutte groups as discussed in [6] it will be shown in this note that the concept of cross ratios extends naturally to combinatorial geometries or matroids. From a thorough study of these cross ratios which, among other observations, includes a new matroid theoretic version and proof of the Pappos theorem, it will be deduced that for any projective space M=
n
(K) of dimension n2 of M over some skewfield K the inner Tutte group is isomorphic to the commutator factor group K
*/[K
*, K
*] of K
*K{0}. This shows not only that in case M=
n
(K) our matroidal cross ratios are nothing but the classical ones. It can also be used to correlate orientations of the matroid M=
n
(K) with the orderings of K. And it implies that Dieudonné's (non-commutative) determinants which, by Dieudonné's definition, take their values in K
*/[K
*, K
*] as well, can be viewed as a special case of a determinant construction which works for just every combinatorial geometry.Research supported by the DFG (Deutsche Forschungsgemeinschaft). 相似文献
66.
Andreas Blass 《Archive for Mathematical Logic》1990,30(1):1-11
We prove several theorems about the cardinal
associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size
are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by
sets are below all non-feeble filters. If
then
and
. (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from
by Laflamme are shown to be equivalent to
. 相似文献
67.
Andreas Floer 《Communications in Mathematical Physics》1988,118(2):215-240
To an oriented closed 3-dimensional manifoldM withH
1(M, )=0, we assign a 8-graded homology groupI
*(M) whose Euler characteristic is twice Casson's invariant. The definition uses a construction on the space of instantons onM×. 相似文献
68.
It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed. 相似文献
69.
Sun S Szakal C Winograd N Wucher A 《Journal of the American Society for Mass Spectrometry》2005,16(10):1677-1686
The ion bombardment-induced release of particles from a metal surface is investigated using energetic fullerene cluster ions as projectiles. The total sputter yield as well as partial yields of neutral and charged monomers and clusters leaving the surface are measured and compared with corresponding data obtained with atomic projectile ions of similar impact kinetic energy. It is found that all yields are enhanced by about one order of magnitude under bombardment with the C60+ cluster projectiles compared with Ga+ ions. In contrast, the electronic excitation processes determining the secondary ion formation probability are unaffected. The kinetic energy spectra of sputtered particles exhibit characteristic differences which reflect the largely different nature of the sputtering process for both types of projectiles. In particular, it is found that under C60+ impact (1) the energy spectrum of sputtered atoms peaks at significantly lower kinetic energies than for Ga+ bombardment and (2) the velocity spectra of monomers and dimers are virtually identical, a finding which is in pronounced contrast to all published data obtained for atomic projectiles. The experimental findings are in reasonable agreement with recent molecular dynamics simulations. 相似文献
70.
Seubert A 《Analytical and bioanalytical chemistry》1996,354(7-8):788-796
The well-established technique of on-line coupling ion chromatography and atomic spectrometry for ultra trace analysis in high purity molybdenum and tungsten is extended to include the silicides MoSi(x) and WSi(x). An additionally included matrix elimination step allows an almost interference-free trace analysis in the silicide matrices. Reproducibility and accuracy of the on-line method were checked by comparison with several other methods, such as isotope dilution, radiochemical neutron activation analysis, direct determination by atomic absorption analysis and not at least with glow discharge mass spectrometry. The results show the high potential of the on-line method for reaching detection limits in the pg g(-1) range, but they show also remaining problems with contamination and system calibration. 相似文献