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11.
Clemens Markett 《Constructive Approximation》1989,5(1):383-404
One of the most far-reaching qualities of an orthogonal system is the presence of an explicit product formula. It can be utilized to establish a convolution structure and hence is essential for the harmonic analysis of the corresponding orthogonal expansion. As yet a convolution structure for Fourier-Bessel series is unknown, maybe in view of the unpractical nature of the corresponding expanding functions called Fourier-Bessel functions. It is shown in this paper that for the half-integral values of the parameter
,n=0, 1, 2,, the Fourier-Bessel functions possess a product formula, the kernel of which splits up into two different parts. While the first part is still the well-known kernel of Sonine's product formula of Bessel functions, the second part is new and reflects the boundary constraints of the Fourier-Bessel differential equation. It is given, essentially, as a finite sum over triple products of Bessel polynomials. The representation is explicit up to coefficients which are calculated here for the first two nontrivial cases
and
. As a consequence, a positive convolution structure is established for
. The method of proof is based on solving a hyperbolic initial boundary value problem.Communicated by Tom H. Koornwinder. 相似文献
12.
13.
Arif Ahmet Baaran hsan ali Clemens Anklin Sansei Nishibe Otto Sticher 《Helvetica chimica acta》1988,71(6):1483-1490
A new phenlypropanoid glycoside has been isolated from the methanolic extract of the aerial parts of Stachys lavandulifolia (Lamiaceae), lavandulifolioside (1) . On the basis of chemical and spectral data the structure of the new compound 1 has been elucidated as β-(3,4-dihydroxyphenyl)ethyl O-α-L -arabinopyranosyl-(1→2)-α-L -rhamnopyranosyl-(1→3)-4-O-caffeoyl-β-D -glucopyranoside. 相似文献
14.
Grosnick D Wright SC Bolton RD Cooper MD Frank JS Hallin AL Heusi PA Hoffman CM Hogan GE Mariam FG Matis HS Mischke RE Piilonen LE Sandberg VD Sanders GH Sennhauser U Werbeck R Williams RA Wilson SL Hofstadter R Hughes EB Ritter MW Highland VL McDonough J 《Physical review letters》1986,57(26):3241-3244
15.
16.
Clemens?Uanschou Roswitha?Frieht Fritz?PittnerEmail author 《Monatshefte für Chemie / Chemical Monthly》2005,136(8):1365-1381
Summary. In contrast to eukaryotic cells certain eubacterial strains have acquired the ability to utilize L-carnitine (R-(–)-3-hydroxy-4-(trimethylamino)butyrate) as sole source of energy, carbon and nitrogen. The first step of the L-carnitine degradation to glycine betaine is catalysed by L-carnitine dehydrogenase (L-CDH, EC 1.1.1.108) and results in the formation of the dehydrocarnitine. During the oxidation of L-carnitine a simultaneous conversion of the cofactor NAD+ to NADH takes place. This catabolic reaction has always been of keen interest, because it can be exploited for spectroscopic L-carnitine determination in biological fluids – a quantification method, which is developed in our lab – as well as L-carnitine production.Based on a cloned L-CDH sequence an expedition through the currently available prokaryotic genomic sequence space began to mine relevant information about bacterial L-carnitine metabolism hidden in the enormous amount of data stored in public sequence databases. Thus by means of homology-based and context-based protein function prediction is revealed that L-CDH exists in certain eubacterial genomes either as a protein of approximately 35 kDa or as a homologous fusion protein of approximately 54 kDa with an additional putative domain, which is predicted to possess a thioesterase activity. These two variants of the enzyme are found on one hand in the genome sequence of bacterial species, which were previously reported to decompose L-carnitine, and on the other hand in gram-positive bacteria, which were not known to express L-CDH. Furthermore we could not only discover that L-CDH is located in a conserved genetic entity, which genes are very likely involved in this L-carnitine catabolic pathway, but also pinpoint the exact genomic sequence position of several other enzymes, which play an essential role in the bacterial metabolism of L-carnitine precursors. 相似文献
17.
Germer A Mügge C Peter MG Rottmann A Kleinpeter E 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(9):1964-1973
The solution-state conformations of N,N',N"-triacetyl chitotriose (1) and other potential chitinase inhibitors 2-4 were studied using a combination of NMR spectroscopy (NOESY) and molecular mechanics calculations. Determination solely of the global energy minimum conformation was found to be insufficient for an agreement with the NMR results. An appropriate consistency between the NMR experimental data and theoretical calculations was only reached by assessing the structures as population-weighted average conformers based on Boltzmann distributions derived from the calculated relative energies. Analogies, but also particular differences, between the synthetic compounds 2-4 and the naturally-occurring N,N',N"-triacetyl chitotriose were found. Furthermore, the conformation of compounds 1 and 2 when bound to hevamine was also studied using transferred NOESY experiments and the binding process was found to impart a level of conformational restriction on the ligands. The preferred conformation as determined for 1 in the bound state to hevamine belonged to one of the conformational families found for the compound when free in solution, although full characterisation of the bound-state conformations was impeded due to severe signal overlap. Saturation transfer difference NMR experiments were also employed to analyse the binding epitopes of the bound compounds. We thus determined that it is mainly the acetyl amido groups of the trisaccharide and the heterocyclic moiety which are in close contact with hevamine. 相似文献
18.
Clemens C. Freyhardt Michael Wiebcke Jürgen Felsche Günter Engelhardt 《Journal of inclusion phenomena and macrocyclic chemistry》1994,18(2):161-175
Single-crystal X-ray structure analyses of N(nPr)4[B5O6(OH)4][B(OH)3]2,1, and N(nBu)4 [B5O6(OH)4][B(OH)3]2,2, reveal that these materials are novel clathrates, the isotypic host structures of which are three-dimensional assemblies of hydrogen-bonded [B5O6(OH)4]– ionsand B(OH)3 molecules. The assembly of only the pentaborate anions is a distorted (i.e., along [102] elongated) fourconnected diamond-related network. The N(nPr)
4
+
and N(nBu)
4
+
ions are trapped within the complex three-dimensional channel systems of the host frameworks. Both1 and2 crystallize monoclinically with space groupP21/c andZ=4. The cell constants are:1:a=13.592(5),b=12.082(2),c=17.355(6) Å, =106.60(2)° (298K);2:a=13.874(3),b=12.585(1),c=17.588(4) Å, =107.04(1)° (238 K). The results obtained by both11B and13C MAS NMR spectroscopy are discussed. Thermogravimetric studies under a flowing inert-gas atmosphere suggest that water, stemming from polycondensation of the hydrous borate species, is released from the clathrates at ca. 443 K (1) and 398 K (2) before the decomposition of the organic cations starts at ca. 603 K (1) and 603 K (2).Author for correspondence.
Supplementary Data relating to this article are deposited with the British Library as supplementary publication No. SUP 82172 (82 pages). 相似文献
19.
Mixtures of BCl3 and H2S are irradiated with 10.55 μm radiation (P(16) line of the 001–100 band of CO2) from a TEA laser. After several hours of irradiation it is found that the maximum 10B to 11B ratio of recovered gaseous boron containing material (primarily unreacted BCl3) is 0.413 ± 0.004. The corresponding ratio of the BCl3 starting material is 0.242 ± 0.002. The 10B concentration has therefore been increased from 19.5% to 29.2%. Further, by irradiating similar mixtures with 10.18 μm radiation (R(30) line of the same CO2 vibrational band) this ratio changes to 0.169 ± 0.002, the 10B concentration being lowered to 14.4%. All experiments are performed in a small static system and chemical procedures for recovering milligram quantities of BCl3 selectively enriched in either isotope are described. 相似文献
20.
The mixed‐valent oxotantalate Eu1.83Ta15O32 was prepared from a compressed mixture of Ta2O5 and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, RF = 0.027 for I > 2σ (I). The structure is isotypic to Ba2Nb15O32. The salient feature is a [Ta(+8/3)6O12iO6a] cluster consisting of an octahedral Ta6 core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)3O13] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu1.83Ta15O32 is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a Mmol/(NAμB) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μB for free Eu (2+) ions with 4f7 configuration in 8S7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers. 相似文献