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1.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
2.
Danch A. Lohner K. Ungerank M. Stelzer F. 《Journal of Thermal Analysis and Calorimetry》1998,54(1):161-170
Bis [(ω-(4′-cyanobiphenyl)-4-yl)oxy-n-alkyl]norborn-5-ene-2,3-dicarboxylate was polymerised via ring opening metathesis polymerisation
(ROMP). Two disubstituted polynorbornene derivatives both of cis configuration with different length of the side-chain were
studied. Differential scanning calorimetry (DSC) was used to study the effect of thermal history on the assignment of the
glass transition event associated with the biaxial orientation of a smectic phase. Glass transition temperatures, the change
of isobaric specific heats at Tg and the enthalpies of isotropisation were calculated. The DSC traces only show the classic step-wise change in Tg in some cases, giving the evidence that the amorphous domains are constrained and highly restricted in movement due to the
morphology developed as a result of the biaxial stretching. Based on the literature data of mono- and disubstituted polynorbornene
derivatives and our calorimetric experiments, the shape of Tg dependence on number of (CH2) units is interpreted. The origin of this shape is discussed.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
Fürstner A Ackermann L Gabor B Goddard R Lehmann CW Mynott R Stelzer F Thiel OR 《Chemistry (Weinheim an der Bergstrasse, Germany)》2001,7(15):3236-3253
Exchange of one PCy3 unit of the classical Grubbs catalyst 1 by N-heterocyclic carbene (NHC) ligands leads to "second-generation" metathesis catalysts of superior reactivity and increased stability. Several complexes of this type have been prepared and fully characterized, six of them by X-ray crystallography. These include the unique chelate complexes 13 and 14 in which the NHC- and the Ru-CR entities are tethered to form a metallacycle. A particularly favorable design feature is that the reactivity of such catalysts can be easily adjusted by changing the electronic and steric properties of the NHC ligands. The catalytic activity also strongly depends on the solvent used; NMR investigations provide a tentative explanation of this effect. Applications of the "second-generation" catalysts to ring closing alkene metathesis and intramolecular enyne cycloisomerization reactions provide insights into their catalytic performance. From these comparative studies it is deduced that no single catalyst is optimal for different types of applications. The search for the most reactive catalyst for a specific transformation is facilitated by IR thermography allowing a rapid and semi-quantitative ranking among a given set of catalysts. 相似文献
4.
Benchmarking of ruthenium initiators for the ROMP of a norbornenedicarboxylic acid ester 总被引:1,自引:0,他引:1
Sandra Demel Wolfgang Schoefberger Christian Slugovc Franz Stelzer 《Journal of molecular catalysis. A, Chemical》2003,200(1-2):11-19
The kinetic study of ring-opening metathesis polymerization (ROMP) of a diester functionalised norbornene derivative, (±)-exo,endo-bicyclo[2.2.1]hept-5-ene-2,3-dicarboxylic acid diethyl ester, with a series of ruthenium benzylidene complexes revealed the applicability of these initiators for well defined polymerization reactions. Values for the rate of initiation as well as the rate of propagation of the initiators were determined and correlated to the molecular weight and polydispersity of the isolated polymers. As the only initiator providing an entry to virtually monodisperse polymers the classical “first generation Grubbs-catalyst” was identified, while N-heterocyclic carbene based initiators polymerized with a rate of propagation much higher than the rate of initiation yielding polymers with a broader molecular weight distribution. 相似文献
5.
(CO)6Fe2(PhPH)2 bildet mit PhPCl2 den phosphidoverbrückten tetranuklearen Komplex [PhPHFe2(CO)6PPh]2PPh. 31P{1H}-NMR-Spektren der Titelverbindung werden als [AB]2C-Systeme analysiert, Stereoisomere werden diskutiert. 31P-NMR Studies on PhPH(CO)6Fe2(PPh)3Fe2(CO)6PPhH ? a Tetranuclear Complex with an Unusual (PPh)3 Bridge (CO)6Fe2(PhPH)2 and PhPCl2 form [PhPHFe2(CO)6PPh]2PPh, a tetranuclear complex with phosphido bridges. 31P{1H}-NMR spectra are analysed as [AB]2C systems, stereoisomers are discussed. 相似文献
6.
Othmar Leukart Emanuel Escher Domenico Regoli Robert Schwyzer 《Helvetica chimica acta》1979,62(2):546-552
Thirteen peptides, analogues of bradykinin (BK), enkephalin, Substance P (SP) and [Sar1]-angiotensin II ([Sar1]-ATII) have been synthesized by the solid-phase method. In all these peptides the residue Phe and Tyr were substituted with the boron-containing amino-acid L -o-carboranylalanine (Car). The purity and identity of the peptides were established by TLC., cellulose-electrophoresis and amino acid analysis. 相似文献
7.
8.
Schmidt R Blaich T Elze TW Emling H Freiesleben H Grimm K Henning W Holzmann R Keller JG Klingler H Kulessa R Kratz JV Lambrecht D Lange JS Leifels Y Lubkiewicz E Moore EF Wajda E Prokopowicz W Schütter C Spies H Stelzer K Stroth J Walus W Wollersheim HJ Zinser M Zude E 《Physical review letters》1993,70(12):1767-1770
9.
10.