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81.
Norman O. Smith 《Journal of solution chemistry》1994,23(4):521-539
A method of finding the activity coefficients of salts, anhydrous or hydrated, in binary solid solutions, described in an earlier paper as it applies to continuous series, has been applied to discontinuous series. The salts must differ with respect to only one ion. The method requires isothermal distribution data for equilibria between liquid (aqueous) and solid solutions in the ternary system consisting of the two salts and water. The following salt pairs were used for illustration: K(I/Br) at 0, 15, 25, 35, and 50°C., (NH4/K)SCN at 0, 30, 60, and 90°C., (K/Tl)C103 at 10°C., and (NH4/K)SO3NH2, (NH4/K)Br, (Mg/Co)SO4-7H2O, and (Mn/Cu) SO4.n H2O-all at 25°C. Two kinds of behavior were noted and treated differently: systems in which the two series have the same, and those in which they have different crystal lattices. For two salts, A and B, which have the same lattice, and whose rational activity coefficients, f
A
and f
B
, can be described by 2-suffix Margules equations (regular solutions), lnf
A
=Bsx
B
2
and lnf
B
=Bsx
A
2
to be partially miscible, Bs>2, but this requirement does not apply if the lattices are different. In each series, distribution constants for the equilibria were also determined. Where possible, the calculated activities of the salts or the Gibbs excess energies of the solid solutions were compared with values reported by others who determined them by other methods. All the salt pairs studied show slight or strong positive deviations from ideality. 相似文献
82.
The ratio of endo-CHO:exo-CHO in the Diels-Alder addition of a trans-αβ-unsaturated aldehyde to cyclopentadiene can be changed from 1:2 to 8:1, depending on temperature and BF3-catalysis. 相似文献
83.
The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6-311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion-stretch elements. The angle changes are accounted for with torsion-bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion-torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol. 相似文献
84.
An ultra-thin layer of polypyrrole can be coated on non-conducting substrates, e.g., acrylic, by dip coating into a colloidal suspension of polypyrrole. This thin coating reversibly combines with low concentrations of ammonia or hydrazine with a concomitant reversible increase in resistance; 0.1 μg cm?3 of ammonia can readily be detected with a 1 cm2 area of sensor. 相似文献
85.
A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region of the plane. Using the calculus of variations the shortest path between two points which does not intersect is determined. If is unconstrained distance, we denote the shortes distance along a feasible path by . The constrained Weber problem is, then: given points and positive weights wj, j = 1,2,…,n, find a point such that is a minimum.An algorithm is formulated for the solution of this problem when is Euclidean distance and is a single circular region. Numerical results are presented. 相似文献
86.
Norman W. Bazley 《manuscripta mathematica》1976,18(4):353-369
We consider an equation of the form Au+N(u)=u in a Hilbert space and assume that the nonlinearity N is reproducing relative to a known sequence of vectors. Under this assumption the Rayleigh-Ritz-Galerkin approximations lead to a simple class of nonlinear algebraic eigenvalue problems.In a general variational case we show that Lusternik-Schnirelmann critical values of Rayleigh-Ritz-Galerkin problems provide upper bounds to those of the original problem. Lower bounds are constructed in the case N(u)=B*(Bu)3.The author would like to thank the European Research Office for their assistance in this research. 相似文献
87.
88.
The kinetic features of the copolymerization of styrene and methyl methacrylate in the presence of ethylaluminum sesquichloride in toluene do not unequivocally distinguish between first- and second-order reactions. The reaction does not attain steady-state conditions. The course of the reaction is apparently influenced by many factors including the dissociation of the polymerizable complex into unreactive monomeric species and physical phenomena such as diffusion and dilution effects as well as matrix formation. The use of azobisisobutyronitrile as an initiator indicates apparent bimolecu-lar termination but the kinetic curves show deviation from linearity. 相似文献
89.
90.
Norman Biggs 《BSHM Bulletin: Journal of the British Society for the History of Mathematics》2018,33(3):166-178
In the twentieth century the theory of games was transformed. It began as an amusing pastime, and ended as a major branch of mathematical research and a key paradigm of economic theory. Here it will be argued that the transformation was the result of the work of mathematicians, such as Ernst Zermelo, John von Neumann and Dénes K?nig, who also contributed to two other areas of mathematics that were emerging at the same time: the theory of sets and the theory of graphs. 相似文献