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1.
It is a well-known feature of odd space-time dimensions d that there exist two inequivalent fundamental representations A and B of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in A and B. As a consequence, a parity-invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long-held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge-conjugation operations. We work explicitly in 2 + 1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions. 相似文献
2.
Abdo Y. Alfakih 《Discrete Applied Mathematics》2007,155(10):1244-1253
Let V={1,2,…,n}. A mapping p:V→Rr, where p1,…,pn are not contained in a proper hyper-plane is called an r-configuration. Let G=(V,E) be a simple connected graph on n vertices. Then an r-configuration p together with graph G, where adjacent vertices of G are constrained to stay the same distance apart, is called a bar-and-joint framework (or a framework) in Rr, and is denoted by G(p). In this paper we introduce the notion of dimensional rigidity of frameworks, and we study the problem of determining whether or not a given G(p) is dimensionally rigid. A given framework G(p) in Rr is said to be dimensionally rigid iff there does not exist a framework G(q) in Rs for s?r+1, such that ∥qi-qj∥2=∥pi-pj∥2 for all (i,j)∈E. We present necessary and sufficient conditions for G(p) to be dimensionally rigid, and we formulate the problem of checking the validity of these conditions as a semidefinite programming (SDP) problem. The case where the points p1,…,pn of the given r-configuration are in general position, is also investigated. 相似文献
3.
A quasilinearization method for a class of integro-differential equations with mixed nonlinearities 总被引:2,自引:1,他引:1
We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented. 相似文献
4.
We develop the monotone method for impulsive hybrid set integro-differential equations in all its generality. Some interesting observations are presented. 相似文献
5.
A relatively rare phenomenon, the induction of thermotropic mesophases from combinations of homologues of non-mesogenic compounds, is examined in some detail. Thus, monotropic nematic phases have been obtained from binary mixtures of 4-alkyl-N-(4-cyanophenyl)piperidines (I). Except for the hexyl homologue, the compounds I with butyl to nonyl as alkyl groups are non-mesomorphic as neat materials. From phase diagrams, the nematic clearing temperatures of the binary mixtures are found to vary linearly with composition and to increase as the molecular lengths of the components are increased. By introducing a methyl group at the 1-position of the alkyl chain, the melting points of the neat components are depressed, and the nematic clearing temperatures of the binary mixtures are lowered. Factors associated with the induction of this mesomorphism and with the 'kinetic' and thermodynamic stabilities of the monotropic nematic phases are discussed. Among these is the orientation between the rings of the core groups in I and in the more common mesogens, the trans-4-alkyl-1-(4-cyanophenyl) cyclohexanes, II. 相似文献
6.
A class of non-mesogenic molecules, which as mixtures exhibit monotropic nematic phases, is described. 相似文献
7.
3-Amino-2-methyl-4(3H)-quinazolinone has been doubly lithiated, on nitrogen and in the 2-methyl group, with n-butyllithium. The lithium reagent thus obtained reacts with a variety of electrophiles (D(2)O, benzophenone, cyclohexanone, cyclopentanone, acetophenone, benzaldehyde, tetraisopropylthiuram disulfide (TITD)) to give the corresponding 2-substituted derivatives in very good yields. Reactions of the dilithio reagent with 2 molar equiv of methyl iodide or phenyl isocyanate give disubstituted derivatives. Double lithiation of the 2-ethyl and 2-propyl analogues have been achieved using LDA, and subsequent reactions with most electophiles are then similar. In the reaction of the dianion of the 2-ethyl compound with TITD, deamination from position 3 takes place with the formation of the 2-substituted derivative. In reactions with prochiral ketones, the dianion of the 2-ethyl compound gives very high diastereoselectivity. Lithiation and subsequent reactions of 3-(methylamino) analogues take place in a similar manner, thus providing access to a range of substituted 3-(methylamino)-2-alkyl-4(3H)-quinazolinones by a general procedure. Lithiation of 3-(dimethylamino)-2-ethyl-4(3H)-quinazolinone did not take place under similar conditions. Lithiation of 3-amino-2-unsubstituted-4(3H)-quinazolinone was also unsuccessful. 相似文献
8.
The chromatographic behaviour of alkaline earth metals on iminodiacetic acid bonded silica was studied. It was found that the ionic strength of the eluent greatly affected both retention time and selectivity by controlling the extent to which either simple ion exchange or surface complexation was responsible for retention. With a 0.1 M KNO3 eluent, the retention order was Mg(II), Sr(II), Ca(II) and Ba(II), indicating a strong contribution to retention from ion exchange. However, when using a 1.5 M KNO3 eluent, Ba(II) was found to elute first, indicating complexation to be more dominant under these conditions (pH 4.2). The effect of the ionic strength of the sample was also studied and it was found that by matching the eluent cation with that of the sample matrix, efficient separations of alkaline earth metals in 1.0 M NaCl and KCl brines could be obtained without matrix system peaks. Using post-column reaction with o-cresolphthalein complexone, trace levels of Ca(II) and Mg(II) were determined in medicinal NaCl saline solution and laboratory-grade KCl. 相似文献
9.
Bashir S Derrick PJ Mutter R 《European journal of mass spectrometry (Chichester, England)》2004,10(4):487-493
The peak intensities obtained when 2,5-dihydroxybenzoic acid (DHB) was used as a 'classic' matrix were measured using substance P (SP) and betacyclodextrin (BCD) as analytes. Enhancements in peak intensities were observed going from 1:1 MeOH/H2O to dimethylforamide (DMF) as matrix solvents. Also non-covalent interactions between SP and solvent and DHB were observed suggesting close interactions between matrix, solvent and analyte in the gas-phase. Peak enhancements were previously reported with 'superDHB' (DHB and 2-hydroxy-5-methoxybenzoic acid at 10% v/v). Co-addition of structural analogues and their respective absorption coefficients were determined. It was found that other analogues used as co-matrices could give analyte peak enhancement similar to reported for sDHB with the additional benefit that some analogues could act as matrices with DHB addition. No direct correlation was observed between absorption coefficient and the ability of the molecule to act as a 'good' UV MALDI matrix. 相似文献
10.
O. Kóréh K. Torkos M. Bashir Mahara J. Borossay 《Journal of Radioanalytical and Nuclear Chemistry》1998,235(1-2):47-52
There is often a need to calculate isotopic uranium activities from total uranium mass or gamma spectrometry measurement data.
This calculation is based on a model of the relationship of the234U activity to that of235U since both are enriched together in the normal gaseous diffusion enrichment process. This paper presents equations for calculating
these activities that have been developed from several sources of data. These equations have been used for several characterization
studies and have produced very good results when compared to results from actual isotopic uranium analyses. However, because
the variability in the model causes significant uncertainty in the calculated results, alpha-spectrometry is recommended for
critical applications. 相似文献