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981.
982.
Benoît Perthame 《Applications of Mathematics》2004,49(6):539-564
Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on bacteria like Escherichia coli or amoeba like Dictyostelium discoïdeum exhibiting pointwise concentrations.For human endothelial cells, several experiments show the formation of networks that can be interpreted as the initiation of angiogenesis. To recover such patterns a hydrodynamical model seems better adapted.The two systems can be unified by a kinetic approach that was proposed for Escherichia coli, based on more precise experiments showing a movement by jump and tumble. This nonlinear kinetic model is interesting by itself and the existence theory is not complete. It is also interesting from a scaling point of view; in a diffusion limit one recovers the Keller-Segel model and in a hydrodynamical limit one recovers the model proposed for human endothelial cells.We also mention the mathematical interest of analyzing another degenerate parabolic system (exhibiting different properties) proposed to describe the angiogenesis phenomena i.e. the formation of capillary blood vessels. 相似文献
983.
Youri Davydov Ricardas Zitikis 《Proceedings of the American Mathematical Society》2004,132(4):1203-1210
We consider weak convergence of empirical measures generated by stationary random process perturbed by deterministic noise . We assume that the noise has asymptotic distribution. In particular, we demonstrate that if the process is ergodic, or satisfies some mixing assumptions, then the influence of deterministic noise on is the same as it would be if were stochastic. Such results are of importance when investigating fluctuations and convex rearrangements of stochastic processes.
984.
Jerzy Kakol Stephen A. Saxon Aaron R. Todd 《Proceedings of the American Mathematical Society》2004,132(6):1703-1712
Let be a completely regular Hausdorff space, and let be the space of continuous real-valued functions on endowed with the compact-open topology. We find various equivalent conditions for to be a -space, resolving an old question of Jarchow and consolidating work by Jarchow, Mazon, McCoy and Todd. Included are analytic characterizations of pseudocompactness and an example that shows that, for , Grothendieck's -spaces do not coincide with Jarchow's -spaces. Any such example necessarily answers a thirty-year-old question on weak barrelledness properties for , our original motivation.
985.
Dan Popovici 《Proceedings of the American Mathematical Society》2004,132(8):2303-2314
We obtain a Wold-type decomposition theorem for an arbitrary pair of commuting isometries on a Hilbert space. More precisely, can be uniquely decomposed into the orthogonal sum between a bi-unitary, a shift-unitary, a unitary-shift and a weak bi-shift part, that is, a part that can be characterized by the condition that and are shifts. Moreover, contains bi-shift and modified bi-shift maximal parts.
986.
Partial regularity for the stochastic Navier-Stokes equations 总被引:2,自引:0,他引:2
Franco Flandoli Marco Romito 《Transactions of the American Mathematical Society》2002,354(6):2207-2241
The effects of random forces on the emergence of singularities in the Navier-Stokes equations are investigated. In spite of the presence of white noise, the paths of a martingale suitable weak solution have a set of singular points of one-dimensional Hausdorff measure zero. Furthermore statistically stationary solutions with finite mean dissipation rate are analysed. For these stationary solutions it is proved that at any time the set of singular points is empty. The same result holds true for every martingale solution starting from -a.e. initial condition , where is the law at time zero of a stationary solution. Finally, the previous result is non-trivial when the noise is sufficiently non-degenerate, since for any stationary solution, the measure is supported on the whole space of initial conditions.
987.
V. Kh. Sabirov 《Chemistry of Natural Compounds》2001,37(4):381-387
The x-ray crystal structure of thiamine bromide hydrate was studied. The crystals are monoclinic, a = 12.348, b = 24.852, c = 11.682 ,= 113.67°, Z = 4, space group P2
1
/c. The crystal structure is constructed of two crystallographically independent thiamine cations, bromide anions, and water molecules. The thiamine cations have the F-conformation. The structure contains intermolecular short contacts involving S and N atoms of the thiazole ring. 相似文献
988.
An analog of the finite-dimensional theorem about the upper semicontinuity of the geometric difference of continuous multivalued maps for separable Banach spaces is obtained. Sufficient conditions for the continuity of the geometric difference of multivalued maps in finite-dimensional spaces without the nonempty interior condition are obtained. Examples that demonstrate the unimprovability of these results are given. 相似文献
989.
A spatially nonhomogeneous random walk t on the grid =m X n is considered. Let t
0 be a random walk homogeneous in time and space, and let t be obtained from it by changing transition probabilities on the set A= X n, || < , so that the walk remains homogeneous only with respect to the subgroup n of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for t. 相似文献
990.
E. Mezzetti A. Chiodoni R. Gerbaldo G. Ghigo L. Gozzelino B. Minetti C. Camerlingo C. Giannini 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(3):357-362
This paper reports on the striking correlation between nanosize mosaic domain walls in YBCO films and 1D rows of parallel
Josephson junctions, determining the J
c
vs.B curves. From X-ray data analysis, it results that the average “hidden" domain wall, faceted at a nanometric scale, is almost
mimicking the Josephson Junction (JJ) 1D array. The assumption that the JJs and the domain-wall arrays are coincident, enables
to find out the particular scaling field, making the J
c
vs.B curves independent of temperature. This scaling field can be interpreted in terms of the Josephson nature of the transport
current across these particular patterns in the intermediate temperature range. By means of our model it is also possible
to calculate two asymptotic behaviors of the pinning force as a function of field, for low and high fields, respectively.
These behaviors are punctually repeated by the experimental results in the same asymptotic limit, so that two corresponding
vortex regimes are clearly pointed out. All results can be interpreted by concluding that in the intermediate temperature
range, the strong pinning observed in high quality YBCO films is due to the Josephson Junctions average patterns. These patterns
are the counterpart related to the transport mechanisms of “hidden" structural nano-domains.
Received 16 October 2000 and Received in final form 28 November 2000 相似文献