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81.
A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G. 相似文献
82.
Thallada Bhaskar Kazuya Murai Toshiki Matsui Mihai Adrian Brebu Md. Azhar Uddin Akinori Muto Yusaku Sakata Katsuhide Murata 《Journal of Analytical and Applied Pyrolysis》2003,70(2):369-381
The thermal degradation of acrylonitrile-butadiene-styrene copolymer (ABS-Br; 10 g) containing brominated flame retardant (Br: 9.59 wt.%) was carried out at 450 °C using a semi batch operation using two different temperature programs. The heating rate was found to affect the quality of the degradation oil and yield of products (liquid, gas and residue). Data on the effect of the temperature program on the accumulation of liquid products was presented. It was found that the majority of the bromine was concentrated in the carbon residue and while majority of the nitrogen accumulates in the liquid products irrespective of degradation mode. The use of a one step constant heating rate process (I) produced a higher liquid yield (39%), than a two step process (29%). Differences were also noted in the Br and N contained in the liquids produced by the two processes. 相似文献
83.
Mihai Tibăr 《Israel Journal of Mathematics》2007,157(1):309-322
We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general
linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles.
For one-dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy
via monodromies of nearby sections. Our standpoint allows one to find, in certain cases, the structure of the Milnor fibre
up to the homotopy type. 相似文献
84.
85.
José Seade Mihai Tibăr Alberto Verjovsky 《Bulletin of the Brazilian Mathematical Society》2005,36(2):275-283
Using a geometric approach, we determine the relations between the local Euler obstruction Euf of a holomorphic function f and several generalizations of the Milnor number for functions on singular spaces.
*This work was partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially
supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401. 相似文献
86.
Essam K. Al-Hussaini Nagi S. Abd-El-Hakim 《Annals of the Institute of Statistical Mathematics》1989,41(3):617-622
Motivated by the idea that different causes of failure of a given system could lead to different failure distributions, a mixture of two-component distributions, one of which is the two-parameter Inverse Gaussian (IG) and the other the two-parameter Weibull (W), is proposed as a failure model. The IG-W mixture model convers several types of failure rates (FR's). It is shown that depending on the parameter values, the IG-W mixture model is capable of covering six different combinations of FR's, as one of the components has an upsidedown bathtub failure rate (UBTFR) or increasing failure rate (IFR) and the other component has a decreasing failure rate (DFR), constant failure rate (CFR), or IFR. A study is made for the mixed FR based on these six combinations. 相似文献
87.
The method of neutron activation and gamma-ray spectrometry was used for studying galvanic corrosion of dental amalgam. The
behaviour of galvanic couples of zinc containing and zinc free amalgam with dissimilar electrodes from other restorative material
was investigated in various electrolytic media, in absence and presence of oxygen. Severe corrosion of amalgam takes place
when coupled with gold electrodes. 相似文献
88.
In real semialgebraic geometry it is common to represent a polynomial q which is positive on a region R as a weighted sum of squares. Serious obstructions arise when q is not strictly positive on the region R. Here we are concerned with noncommutative polynomials and obtaining a representation for them which is valid even when strict
positivity fails.
Specifically, we treat a ``symmetric' polynomial q(x, h) in noncommuting variables, {x1, . . . , } and {h1, . . . , } for which q(X,H) is positive semidefinite whenever
are tuples of selfadjoint matrices with ||Xj|| ≤ 1 but Hj unconstrained. The representation we obtain is a Gram representation in the variables h
where Pq is a symmetric matrix whose entries are noncommutative polynomials only in x and V is a ``vector' whose entries are polynomials in both x and h. We show that one can choose Pq such that the matrix Pq(X) is positive semidefinite for all ||Xj|| ≤ 1. The representation covers sum of square results ([Am. Math. (to appear); Linear Algebra Appl. 326 (2001), 193–203; Non commutative Sums of Squares, preprint]) when gx = 0. Also it allows for arbitrary degree in h, rather than degree two, in the main result of [Matrix Inequalities: A Symbolic Procedure to Determine Convexity Automatically
to appear IOET July 2003] when restricted to x-domains of the type ||Xj|| ≤ 1.
Partially supported by NSF, DARPA and Ford Motor Co.
Partially supported by NSF grant DMS-0140112
Partially supported by NSF grant DMS-0100367 相似文献
89.
This work addresses the computation of free-energy differences between protein conformations by using morphing (i.e., transformation)
of a source conformation into a target conformation. To enhance the morphing procedure, we employ permutations of atoms: we
seek to find the permutation σ that minimizes the mean-square distance traveled by the atoms. Instead of performing this combinatorial
search in the space of permutations, we show that the best permutation can be found by solving a linear assignment problem.
We demonstrate that the use of such optimal permutations significantly improves the efficiency of the free-energy computation. 相似文献
90.
In this paper we discuss the problem of verifying and computing optimal controls of systems whose dynamics is governed by
differential systems with a discontinuous right-hand side. In our work, we are motivated by optimal control of mechanical
systems with Coulomb friction, which exhibit such a right-hand side. Notwithstanding the impressive development of nonsmooth
and set-valued analysis, these systems have not been closely studied either computationally or analytically. We show that
even when the solution crosses and does not stay on the discontinuity, differentiating the results of a simulation gives gradients
that have errors of a size independent of the stepsize. This means that the strategy of “optimize the discretization” will
usually fail for problems of this kind. We approximate the discontinuous right-hand side for the differential equations or
inclusions by a smooth right-hand side. For these smoothed approximations, we show that the resulting gradients approach the
true gradients provided that the start and end points of the trajectory do not lie on the discontinuity and that Euler’s method
is used where the step size is “sufficiently small” in comparison with the smoothing parameter. Numerical results are presented
for a crude model of car racing that involves Coulomb friction and slip showing that this approach is practical and can handle
problems of moderate complexity. 相似文献