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991.
A classic result asserts that many geometric structures can be constructed optimally by successively inserting their constituent
parts in random order. These randomized incremental constructions (RICs) still work with imperfect randomness: the dynamic
operations need only be “locally” random. Much attention has been given recently to inputs generated by Markov sources. These
are particularly interesting to study in the framework of RICs, because Markov chains provide highly nonlocal randomness,
which incapacitates virtually all known RIC technology.
We generalize Mulmuley’s theory of Θ-series and prove that Markov incremental constructions with bounded spectral gap are optimal within polylog factors for trapezoidal
maps, segment intersections, and convex hulls in any fixed dimension. The main contribution of this work is threefold: (i)
extending the theory of abstract configuration spaces to the Markov setting; (ii) proving Clarkson–Shor-type bounds for this
new model; (iii) applying the results to classical geometric problems. We hope that this work will pioneer a new approach
to randomized analysis in computational geometry.
This work was supported in part by NSF grants CCR-0306283, CCF-0634958. 相似文献
992.
993.
Jin Yan 《Operations Research Letters》2008,36(1):57-60
For the bi-criteria scheduling problem of minimizing the sum of completion times and the sum of weighted completion times, min-sum of weighted completion times, we prove that there exists no constant β>1 such that (1+1/γ,β)-approximate schedules can be found for any γ>0. This result confirms a recently published conjecture. 相似文献
994.
We study a semi-discretisation scheme for stochastic optimal control problems whose dynamics are given by controlled stochastic
delay (or functional) differential equations with bounded memory. Performance is measured in terms of expected costs. By discretising
time in two steps, we construct a sequence of approximating finite-dimensional Markovian optimal control problems in discrete
time. The corresponding value functions converge to the value function of the original problem, and we derive an upper bound
on the discretisation error or, equivalently, a worst-case estimate for the rate of convergence. 相似文献
995.
SU Jun-Chen 《理论物理通讯》2002,38(4):433-446
The interaction kernel in the Bethe-Salpeter (B-S) equation for quark-antiquark bound states is derived from B-S equations satisfied by the
quark-antiquark four-point Green's function. The latter equations are
established based on the equations of motion obeyed by the quark and
antiquark propagators, the four-point Green's function and some other kinds
of Green's functions, which follow directly from the QCD generating
functional. The derived B-S kernel is given by a closed and explicit expression which contains only a few types of Green's functions. This expression is not only convenient for perturbative calculations, but also applicable for nonperturbative investigations. Since the kernel contains all the interactions taking place in the quark-antiquark bound states, it actually appears to be the most suitable starting point of studying the QCD nonperturbative effect and quark confinement. 相似文献
996.
Da-yongCai Yu-rongChen 《计算数学(英文版)》2004,22(1):61-68
In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number C2n^m is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods. 相似文献
997.
998.
Experiments with a new selection criterion in a fast interval optimization algorithm 总被引:3,自引:0,他引:3
Usually, interval global optimization algorithms use local search methods to obtain a good upper (lower) bound of the solution. These local methods are based on point evaluations. This paper investigates a new local search method based on interval analysis information and on a new selection criterion to direct the search. When this new method is used alone, the guarantee to obtain a global solution is lost. To maintain this guarantee, the new local search method can be incorporated to a standard interval GO algorithm, not only to find a good upper bound of the solution, but also to simultaneously carry out part of the work of the interval B&B algorithm. Moreover, the new method permits improvement of the guaranteed upper bound of the solution with the memory requirements established by the user. Thus, the user can avoid the possible memory problems arising in interval GO algorithms, mainly when derivative information is not used. The chance of reaching the global solution with this algorithm may depend on the established memory limitations. The algorithm has been evaluated numerically using a wide set of test functions which includes easy and hard problems. The numerical results show that it is possible to obtain accurate solutions for all the easy functions and also for the investigated hard problems. 相似文献
999.
O. Kullie D. Kolb 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,17(2):167-173
A two-dimensional, fully numerical approach to the four-component first-order Dirac-differential-equation utilizing the Finite-Element-Method
(FEM) is employed for H
2
+
and Th
2
179 +
. Using elliptic-hyperbolic coordinates and further one-dimensional singular transformations, scaling transformations and
extrapolation techniques (geometrical over iteration steps and logarithmic over grid points) we achieve for the molecules
H
2
+
and Th
2
179 +
relative accuracies better than 10-12 for 1(1/2)
g energies.
Received 16 February 2001 and Received in final form 12 July 2001 相似文献
1000.
S.A.S. Ahmed B.C. Borah D. Sharma 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,17(1):5-11
A transformation method has been applied to the exactly solvable Hulthen problem to generate a hierarchy of exactly solved
quantum systems in any chosen dimension. The generated quantum systems are, in general, energy-dependent with a single normalized
eigenfunction, as the Hulthen potential is a non-powerlaw potential. A method has been devised to convert a subset of the
generated quantum systems with energy-dependent potentials to a single normal system with an energy-independent potential
that behaves like a potential qualitatively similar to the Poschl-Teller potential. A second-order application of the transformation
method on the Hulthen system produces another Sturmian quantum system and a different method is given to regroup them into
a normal quantum system which resembles the Morse potential. Existence of normalizable eigenfunctions for these systems are
found to be dependent on the local and asymptotic behaviour of the transformation function.
Received 30 August 2000 and Received in final form 16 March 2001 相似文献