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111.
V. Jeyakumar 《Mathematical Programming》2006,106(1):81-92
The strong conical hull intersection property (CHIP) is a geometric property of a collection of finitely many closed convex
intersecting sets. This basic property, which was introduced by Deutsch et al. in 1997, is one of the central ingredients
in the study of constrained interpolation and best approximation. In this paper we establish that the strong CHIP of intersecting
sets of constraints is the key characterizing property for optimality and strong duality of convex programming problems. We
first show that a sharpened strong CHIP is necessary and sufficient for a complete Lagrange multiplier characterization of
optimality for the convex programming model problem
where C is a closed convex subset of a Banach space X, S is a closed convex cone which does not necessarily have non-empty interior, Y is a Banach space,
is a continuous convex function and g:X→Y is a continuous S-convex function. We also show that the strong CHIP completely characterizes the strong duality for partially finite convex
programs, where Y is finite dimensional and g(x)=−Ax+b and S is a polyhedral convex cone. Global sufficient conditions which are strictly weaker than the Slater type conditions are given
for the strong CHIP and for the sharpened strong CHIP.
The author is grateful to the referees for their constructive comments and valuable suggestions which have contributed to
the final preparation of the paper. 相似文献
112.
Thomas Krainer 《Mathematische Nachrichten》2010,283(12):1680-1695
We show the completeness of the system of generalized eigenfunctions of closed extensions of elliptic cone operators under suitable conditions on the symbols (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
113.
114.
We study a special dual form of a convex minimization problem in a Hilbert space, which is formally suggested by Fenchel dualityand is useful for the Dykstra algorithm. For this special duality problem, we prove that strong duality holds if and only if the collection of underlying constraint sets {C
1,...,C
m} has the strong conical hull intersection property. That is,
where D° denotes the dual cone of D. In general, we can establish weak duality for a convex minimization problem in a Hilbert space by perturbing the constraint sets so that the perturbed sets have the strong conical hull intersection property. This generalizes a result of Gaffke and Mathar. 相似文献
115.
Bert-Wolfgang Schulze Boris Sternin Victor Shatalov 《Annals of Global Analysis and Geometry》1998,16(2):141-172
The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah–Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point. 相似文献
116.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in
p
,
n
, respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in
n
. The function c:
p+n
is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in
n
. Computational experiments show that the resulting algorithms work well for problems with smalln. 相似文献
117.
《Chemphyschem》2003,4(5):445-456
The dissociation dynamics of trans‐azomethane upon excitation to the S1(n,π*) state with a total energy of 93 kcal mol?1 is investigated using femtosecond‐resolved mass spectrometry in a molecular beam. The transient signal shows an opposite pump–probe excitation feature for the UV (307 nm) and the visible (615 nm) pulses at the perpendicular polarization in comparison with the signal obtained at the parallel polarization: The one‐photon symmetry‐forbidden process excited by the UV pulse is dominant at the perpendicular polarization, whereas the two‐photon symmetry‐allowed process initiated by the visible pulse prevails at the parallel polarization. At the perpendicular polarization, we found that the two C? N bonds of the molecule break in a stepwise manner, that is, the first C? N bond breaks in ≈70 fs followed by the second one in ≈100 fs, with the intermediate characterized. At the parallel polarization, the first C? N bond cleavage was found to occur in 100 fs with the intensity of the symmetry‐allowed transition being one order of magnitude greater than the intensity of the symmetry‐forbidden transition at the perpendicular polarization. Theoretical calculations using time‐dependent density functional theory (TDDFT) and the complete active space self‐consistent field (CASSCF) method have been carried out to characterize the potential energy surface for the ground state, the low‐lying excited states, and the cationic ground state at various levels of theory. Combining the experimental and theoretical results, we identified the elementary steps in the mechanism: The initial driving force of the ultrafast bond‐breaking process of trans‐azomethane (at the perpendicular polarization) is due to the CNNC torsional motion initiated by the vibronic coupling through an intensity‐borrowing mechanism for the symmetry‐forbidden n–π* transition. Following this torsional motion and the associated molecular symmetry breaking, an S0/S1 conical intersection (CI) can be reached at a torsional angle of 93.1° (predicted at the CASSCF(8,7)/cc‐pVDZ level of theory). Funneling through the S0/S1 CI could activate the asymmetric C? N stretching motion, which is the key motion for the consecutive C? N bond breakages on the femtosecond time scale. 相似文献
118.
Michael Baer Alexander M. Mebel Gert D. Billing 《International journal of quantum chemistry》2002,90(6):1577-1585
The idea to derive the nonadiabatic coupling terms by solving the Curl equations (Avery, J.; Baer, M.; Billing, G. D. Mol Phys 2002, 100, 1011) is extended to a three‐state system where the first and second states form one conical intersection, i.e., τ12 and the second and the third states form another conical intersection, i.e., τ23. Whereas the two‐state Curl equations form a set of linear differential equations, the extension to a three‐state system not only increases the number of equations but also leads to nonlinear terms. In the present study, we developed a perturbative scheme, which guarantees convergence if the overlap between the two interacting conical intersections is not too strong. Among other things, we also revealed that the nonadiabatic coupling term between the first and third states, i.e., τ13 (such interactions do not originate from conical intersection) is formed due to the interaction between τ12 and τ23. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 相似文献
119.
《Chemphyschem》2003,4(1):61-66
A new theoretical formulation is given for the reaction rate and path for the important reaction class of aromatic radical anion dissociation in solution [Ar? X]?.→Ar.+X?, and is illustrated for the case of the cyanochlorobenzene radical anion [CN? Φ? Cl]?. in dimethylformamide. Among the theory's novel features is the inclusion of the conical intersection aspect of this ground electronic state problem, which is key in allowing the reaction to occur and which has a significant impact on the reaction barrier height. Reasonable agreement with the experimental rate is found. 相似文献
120.
This study has been conducted to compare two different numerical models for the evaluation of the performance characteristics of a diffuser‐nozzle based piezoelectric micropump. Here, the transient displacements of the membrane and the flow characteristics in the piezoelectric micropump have been closely investigated with the FSI model and the prescribed deformation model for two different frequencies. It has been found that the behaviour of the membrane computed with the FSI model is not in accordance with that with the prescribed deformation model, and that the net flow rate with the FSI model is larger than that with the prescribed deformation model. Therefore, the choice of numerical model is very important in conducting numerical analysis for piezoelectric micropumps. The results of this study can be utilized as basic data for the design and analysis of piezoelectric micropumps. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献