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991.
992.
M. Soledad Aronna J. Frédéric Bonnans Pierre Martinon 《Journal of Optimization Theory and Applications》2013,158(2):419-459
In this article, we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss–Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent, if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system), we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated with the perturbed problem. We present numerical tests that validate our method. 相似文献
993.
Pierre Antoine Grillet 《代数通讯》2013,41(2):558-573
A construction is given for semigroups S such that S 3 has just two elements. 相似文献
994.
Pierre Carpentier Guy Cohen Anes Dallagi 《Computational Optimization and Applications》2013,56(3):635-674
When dealing with numerical solution of stochastic optimal control problems, stochastic dynamic programming is the natural framework. In order to try to overcome the so-called curse of dimensionality, the stochastic programming school promoted another approach based on scenario trees which can be seen as the combination of Monte Carlo sampling ideas on the one hand, and of a heuristic technique to handle causality (or nonanticipativeness) constraints on the other hand. However, if one considers that the solution of a stochastic optimal control problem is a feedback law which relates control to state variables, the numerical resolution of the optimization problem over a scenario tree should be completed by a feedback synthesis stage in which, at each time step of the scenario tree, control values at nodes are plotted against corresponding state values to provide a first discrete shape of this feedback law from which a continuous function can be finally inferred. From this point of view, the scenario tree approach faces an important difficulty: at the first time stages (close to the tree root), there are a few nodes (or Monte-Carlo particles), and therefore a relatively scarce amount of information to guess a feedback law, but this information is generally of a good quality (that is, viewed as a set of control value estimates for some particular state values, it has a small variance because the future of those nodes is rich enough); on the contrary, at the final time stages (near the tree leaves), the number of nodes increases but the variance gets large because the future of each node gets poor (and sometimes even deterministic). After this dilemma has been confirmed by numerical experiments, we have tried to derive new variational approaches. First of all, two different formulations of the essential constraint of nonanticipativeness are considered: one is called algebraic and the other one is called functional. Next, in both settings, we obtain optimality conditions for the corresponding optimal control problem. For the numerical resolution of those optimality conditions, an adaptive mesh discretization method is used in the state space in order to provide information for feedback synthesis. This mesh is naturally derived from a bunch of sample noise trajectories which need not to be put into the form of a tree prior to numerical resolution. In particular, an important consequence of this discrepancy with the scenario tree approach is that the same number of nodes (or points) are available from the beginning to the end of the time horizon. And this will be obtained without sacrifying the quality of the results (that is, the variance of the estimates). Results of experiments with a hydro-electric dam production management problem will be presented and will demonstrate the claimed improvements. A more realistic problem will also be presented in order to demonstrate the effectiveness of the method for high dimensional problems. 相似文献
995.
Time-reversal symmetry relation for nonequilibrium flows ruled by the fluctuating Boltzmann equation
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and velocity in the one-particle phase space. The symmetry relation concerns the fluctuating particle and energy currents of the gas flowing between reservoirs or thermalizing surfaces at given particle densities or temperatures. 相似文献
996.
Pierre Bayard Antonio J. Di Scala Osvaldo Osuna Castro Gabriel Ruiz-Hernández 《Geometriae Dedicata》2013,162(1):153-176
We study surfaces in ${\mathbb{R}^4}$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of ${\mathbb{R}^2}$ . We classify all surfaces with one principal angle equal to 0 and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in ${\mathbb{R}^4}$ with respect to a plane. They turn out to be extrinsic products. We characterize which surfaces with constant principal angles are compositions in the sense of Dajczer-Do Carmo. Finally, we classify surfaces with constant principal angles contained in a sphere and those with parallel mean curvature vector field. 相似文献
997.
In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation. 相似文献
998.
Dr. Wasim Abuillan Dr. Mariam Veschgini Salomé Mielke Dr. Akihisa Yamamoto Xianhe Liu Dr. Oleg Konovalov Prof. Dr. Marie Pierre Krafft Prof. Dr. Motomu Tanaka 《Chemphyschem》2019,20(6):898-904
The structure and lateral correlation of fluorocarbon-hydrocarbon tetrablock di(F10Hm) domains at the air/water interface have been determined by quantitative analysis of grazing incidence small-angle X-ray scattering (GISAXS) data. The measured GISAXS signals can be well represented by the full calculation of the form and structure factors. The form factor suggests that di(F10Hm) domains take a hemiellipsoid shape. Both major and minor axes of the hemiellipsoids monotonically increased in response to the elongation of the hydrocarbon blocks, which can be explained by the concominant increase in van der Waals interaction. The structure factor calculated from the GISAXS signals suggests that the domains take an orthorhombic lattice. Remarkably, the lateral correlation can reach over a distance that is more than 14 times longer than the distance to the nearest neighbors. Our data suggest that quantitative GISAXS enables the optimal design of mesoscopic self-assemblies at the air/water interface by fine-tuning of the structures of molecular building blocks. 相似文献
999.
Ultraviolet and infrared conical emissions were observed during the filamentation in air of powerful femtosecond laser pulses produced by a portable terawatt laser system. The broadband spectrum was measured from 200 nm up to 14 microm and covered the complete optical transmission window of the atmosphere. The angularly resolved spectrum showed some X-wave structure across the frequency range analyzed. However, we demonstrated that the strong conical emission observed in the mid- and far-infrared is mainly owing to the four-wave mixing between the pump pulse and its blueshifted conical emission. 相似文献
1000.
In this paper, the magnetic and transport properties of the Ti
x
Nb1 − x
CoSn solid solution compounds with half Heusler cubic MgAgAs-type structure have been studied. This work shows the onset of
ferromagnetism associated with a semiconductor to metal transition. The transition occurs directly from ferromagnetic metal
to semiconducting state as it is the case in the TiCo
x
Ni1 − x
Sn series studied previously. A weak quantity of Ti in NbCoSn is suffcient to allow the appearance of ferromagnetic order
and metallic state. The variations of the Curie temperature as a function of saturation and effective paramagnetic moments
are related to the itinerant ferromagnetism model. A comparison is made with the TiCoSn
x
Sb1 − x
series (also studied previously), where the transition from TiCoSn ferromagnetic metal to non-magnetic semiconductor TiCoSb
occurs through an intermediate metallic Pauli-like state.
相似文献