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991.
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Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular that it admits operations parameterized by homology classes of classifying spaces of diffeomorphism groups of surfaces. Here we present a radical extension of this result, giving a new construction in which diffeomorphisms are replaced with homotopy equivalences, and surfaces with boundary are replaced with arbitrary spaces homotopy equivalent to finite graphs. The result is a novel kind of field theory which is related to both the diffeomorphism groups of surfaces and the automorphism groups of free groups with boundaries. Our work shows that the algebraic structures in string topology of classifying spaces can be brought into line with, and in fact far exceed, those available in string topology of manifolds. For simplicity, we restrict to the characteristic 2 case. The generalization to arbitrary characteristic will be addressed in a subsequent paper. 相似文献
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Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new. 相似文献
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999.
Gerhard Hiermann Richard F. Hartl Jakob Puchinger Thibaut Vidal 《European Journal of Operational Research》2019,272(1):235-248
We introduce an electric vehicle routing problem combining conventional, plug-in hybrid, and electric vehicles. Electric vehicles are constrained in their service range by their battery capacity, and may require time-consuming recharging operations at some specific locations. Plug-in hybrid vehicles have two engines, an internal combustion engine and an electric engine using a built-in rechargeable battery. These vehicles can avoid visits to recharging stations by switching to fossil fuel. However, this flexibility comes at the price of a generally higher consumption rate and utility cost.To solve this complex problem variant, we design a sophisticated metaheuristic which combines a genetic algorithm with local and large neighborhood search. All route evaluations, within the approach, are based on a layered optimization algorithm which combines labeling techniques and greedy evaluation policies to insert recharging stations visits in a fixed trip and select the fuel types. The metaheuristic is finally hybridized with an integer programming solver, over a set partitioning formulation, so as to recombine high-quality routes from the search history into better solutions. Extensive experimental analyses are conducted, highlighting the good performance of the algorithm and the contribution of each of its main components. Finally, we investigate the impact of fuel and energy cost on fleet composition decisions. Our experiments show that a careful use of a mixed fleet can significantly reduce operational costs in a large variety of price scenarios, in comparison with the use of a fleet composed of a single vehicle class. 相似文献
1000.
Optimal rectangle packing 总被引:1,自引:0,他引:1
Richard E. Korf Michael D. Moffitt Martha E. Pollack 《Annals of Operations Research》2010,179(1):261-295
We consider the NP-complete problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles.
We present two different constraint-satisfaction formulations of this problem. The first searches a space of absolute placements
of rectangles in the enclosing rectangle, while the other searches a space of relative placements between pairs of rectangles.
Both approaches dramatically outperform previous approaches to optimal rectangle packing. For problems where the rectangle
dimensions have low precision, such as small integers, absolute placement is generally more efficient, whereas for rectangles
with high-precision dimensions, relative placement will be more effective. In two sets of experiments, we find both the smallest
rectangles and squares that can contain the set of squares of size 1×1, 2×2,…,N×N, for N up to 27. In addition, we solve an open problem dating to 1966, concerning packing the set of consecutive squares up to 24×24
in a square of size 70×70. Finally, we find the smallest enclosing rectangles that can contain a set of unoriented rectangles
of size 1×2, 2×3, 3×4,…,N×(N+1), for N up to 25. 相似文献