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Gallin Peter Prof. Dr. 《ZDM》2003,35(3):110-119
In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17th century.  相似文献   
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A spiro orthoester with an exomethylene group (exoSOE) was radically copolymerized with acrylonitrile or vinyl acetate at several feed ratios to obtain the corresponding copolymers having spiro orthoester moieties in the side chain. The obtained copolymers could be crosslinked via the double ring‐opening polymerization of the spiro orthoester moieties in their side chain by a treatment with BF3OEt2. The volume changes upon the crosslinking of the copolymers were evaluated by density measurements with a micromeritics gas pycnometer. The copolymers experienced less than 1% volume expansion instead of volume shrinkage during typical cationic crosslinking, regardless of the copolymer compositions. Negligible shrinkage was observed during the thermal cationic crosslinking of a film cast from a nitrobenzene solution of the copolymers containing a benzylthiophenium salt as a thermally latent cationic initiator. The constantly low volume changes during the crosslinking of the copolymers from exoSOE probably depended on the almost zero volume change during the cationic polymerizations of spiro orthoester derivatives. This indicates that exoSOE is an effective monomer for crosslinkable polymers without volume changes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3666–3673, 2006  相似文献   
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Natural human hair was modified by the graft polymerization of propylene sulfide in an aqueous medium. The amount of the polymer grafted onto the reduced hair was 0.15–0.19 g on 1.0 g of hair. The grafted polymer was isolated by the hydrolysis of the hair in the polymer‐grafted hair under basic conditions and was confirmed to be poly(propylene sulfide) by 1H NMR, 13C NMR, and Fourier transform infrared spectra. The number‐average molecular weights of the isolated polymers from the grafted products were 10,000–12,000. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3778–3786, 2006  相似文献   
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Spiro orthocarbonate (SOC) monomers having either an exomethylene group {3,3‐dimethyl‐9‐methylene‐1,5,7,11‐tetraoxaspiro[5.5]undecane (ExoSOC)} or an allyl group {9‐allyl‐3,3‐dimethyl‐1,5,7,11‐tetraoxaspiro[5.5]undecane (AllylSOC)} were radically copolymerized with vinyl monomers at several feed ratios to obtain the corresponding copolymers having SOC moieties in the side chain. The obtained copolymers were crosslinked via the double ring‐opening polymerization of the SOC moieties by a treatment with boron trifluoride etherate. The volume changes during the crosslinking of the copolymers were evaluated by density measurements with a gas pycnometer. As the SOC moiety composition increased, the volume shrinkage during the crosslinking was suppressed, and that finally changed into volume expansion. The volume changes during the crosslinking of the copolymers from AllylSOC were slightly larger than those of the copolymers from ExoSOC. The higher volume expansions in the crosslinking of AllylSOC‐based copolymers were ascribable to the lower steric hindrance around the SOC moieties. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 7040–7053, 2006  相似文献   
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Tristimulus colorimetry using a digital still camera (DSC) as a colorimeter has been developed. A photograph of a sample and standard solutions was taken simultaneously with the DSC, and it was transferred to a PC. On the PC, the colors of the sample and of the standard solutions were analyzed and L* (brightness), a* (red-green component), and b* (yellow-blue component) values were determined with laboratory-made software. A dedicated light-box containing white-color LEDs as light source was made of white acrylic to make constant exposure at each photograph. Various settings of the DSC, such as exposure mode, white balance, and so on, that affect analytical figures, were studied with determination of iron with 1,10-phenanthroline. This method was successfully applied to the determinations of iron in a river water sample and of residual chlorine in tap water samples with N,N-diethylphenylenediamine (DPD).  相似文献   
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The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.  相似文献   
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Summary The electrocapillary properties of polyacrylic acid have been studied by two methods. Exploratory measurements have been made of the effect of the polymer on the differential capacity of a mercury drop in 0.1 m sodium perchlorate. They showed that the polymer was strongly adsorbed over a wide range of potentials but that it did not appear to form a monolayer. The surface excess of polymer obtained from drop weight data showed a maximum at very low concentrations and then a decline at higher concentrations. The bulk of the work was carried out by making surface tension measurements, using a sessile mercury drop, in solutions of a fraction of polyacrylic acid (mol. wt. 7.02×104) in potassium chloride at 0.01, 0.1, 0.2, and 0.5 m at 25°C.The data have been used to evaluate the surface excesses of the polymer and of the inorganic ions. The distribution of K+ and Cl in the electrical double layer and the contact adsorption of Cl on the mercury were very little affected by the presence of the polymer. The surface excess of polymer was always found to be greatest at low concentrations, to decrease steeply at first as the concentration was increased and then to decrease more slowly at higher concentrations.Possible explanations of this behaviour are discussed and it is concluded that the rapid decrease is a consequence of molecular weight dispersion and the stronger adsorption of high molecular weight polymer. The slow decrease in surface excess at higher concentrations may be a result of configurational changes of the polymer molecules.Surface pressure data show that, despite this decrease in the surface excess, the surface coverage reaches a high level at very low polymer concentrations and then continues to increase slowly as the concentration of polymer is increased. This apparent contradiction is due to changes in configuration of the adsorbed polymer molecules. At higher bulk concentrations the chain configurations are more compact and each adsorbed molecule makes more contacts with and so occupies a greater area of the mercury surface than at low concentrations.The conclusion is reached that the surface excess of polymer is mostly contained in a layer probably more than 1000 Å thick. It consists of a concentrated and entangled mass of polymer chains. Relatively few of these chains are in contact with the mercury at any istant. The concentration in this surface layer decreases steadily with increasing distance from the mercury surface and it merges without discontinuity into the bulk solution.With 10 figures in 22 details  相似文献   
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