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1.
The Laplacian and Dirac operators on critical planar graphs 总被引:6,自引:0,他引:6
R. Kenyon 《Inventiones Mathematicae》2002,150(2):409-439
On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and Dirac
operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain
explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate
the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron. In the associated
dimer and spanning tree models, for which the determinants of the Dirac operator and the Laplacian respectively play the role
of the partition function, this allows us to compute the entropy and correlations in terms of the local geometry. In addition,
we define a continuous family of special discrete holomorphic functions which, via convolutions, gives a general process for
constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs.
Oblatum 6-III-2002 & 12-VI-2002?Published online: 6 August 2002 相似文献
2.
Evans-Nguyen KM Schoenfisch MH 《Langmuir : the ACS journal of surfaces and colloids》2005,21(5):1691-1694
Fibrin proliferation from both human fibrinogen solutions and platelet-poor plasma was studied quantitatively as a function of substrate surface properties. A quartz crystal microbalance was used to monitor both protein adsorption and fibrin proliferation in real time at hydrophobic, hydrophilic, positively charged, and negatively charged surfaces. Scanning electron microscopy was used to characterize the morphology of the polymerized fibrin layers. The observed changes in mass indicate that fibrinogen adsorption occurs rapidly and mediates subsequent fibrin proliferation. Notably, substrate surface properties significantly affect the ability of adsorbed fibrinogen to promote fibrin proliferation. 相似文献
3.
Richard Kenyon 《Inventiones Mathematicae》1992,107(1):637-651
Summary Aperturbation of a tiling of a region inR
n
is a set of isometries, one applied to each tile, so that the images of the tiles tile the same region.We show that a locally finite tiling of an open region inR
2 with tiles which are closures of their interiors isrigid in the following sense: any sufficiently small perturbation of the tiling must have only earthquake-type discontinuities, that is, the discontinuity set consists of straight lines and arcs of circles, and the perturbation near such a curve shifts points along the direction of that curve.We give an example to show that this type of rigidity does not hold inR
n
, forn>2.Using rigidity in the plane we show that any tiling problem with a finite number of tile shapes (which are topological disks) is equivalent to a polygonal tiling problem, i.e. there is a set of polygonal shapes with equivalent tiling combinatorics.Oblatum 19-III-1991 相似文献
4.
A combination and modification of two existing methods, which involves balancing static and dynamic pressure differences between points along the surface and conserving mass through cross sections below the surface in the reference frame moving with the phase velocity, is applied to surface gravity waves of arbitrary amplitude in water of finite depth. For a given still water depth and wave height the method determines in closed form the phase velocity, wavelength, and wave profile of the stable wave. The main assumption is that the horizontal component of the fluid velocity be independent of depth. The motion is not assumed to be irrotational. The wavelength of the stable wave is found to be about 3.6 times the still water depth for infinitesimal amplitude, and at finite amplitude the wavelength decreases as the amplitude increases. Therefore, shallow water waves are concluded to be unstable even at infinitesimal amplitude, for which the assumption is accurate. Previously it has been argued that only at finite amplitude will shallow water waves change form as they propagate. The wave profile is found to be sinusoidal for infinitesimal amplitude and to be asymmetric at finite amplitude, the crests being higher and narrower and the troughs shallower and broader. These results are consistent with well-known theoretical work and laboratory measurements. 相似文献
5.
6.
Richard Kenyon 《Israel Journal of Mathematics》1997,97(1):221-238
LetS⊂ℝ2 be the Cantor set consisting of points (x,y) which have an expansion in negative powers of 3 using digits {(0,0), (1,0), (0,1)}. We show that the projection ofS in any irrational direction has Lebesgue measure 0. The projection in a rational directionp/q has Hausdorff dimension less than 1 unlessp+q ≡ 0 mod 3, in which case the projection has nonempty interior and measure 1/q. We compute bounds on the dimension of the projection for certain sequences of rational directions, and exhibit a residual
set of directions for which the projection has dimension 1.
This work was partially completed while the author was at the Institut Fourier, Grenoble, France. 相似文献
7.
M.J. Corden J.D. Dowell D. Eastwood J. Garvey R.J. Homer M. Jobes I.R. Kenyon T. McMahon R.J. Vallance P.M. Watkins J.A. Wilson J. Gago M. Jung P. Sonderegger D. Treille P.L. Woodworth V. Eckardt J. Fent K.C.T.O. Sumorok 《Physics letters. [Part B]》1977,68(1):96-100
Measurements have been made of relative production cross sections of the by π±, K±, p and p? at 39.5 GeV/c incident on copper. production rates from π?, K? and p? are similar. The relative particle/anti-particle production cross sections for x>0 are , σ(K+)/σ(K?)=(0.85±0.5) and . The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation. 相似文献
8.
Charles W. Koch Dolan H. Eargle George L. Kenyon 《Journal of mass spectrometry : JMS》1977,12(10):624-627
Electron impact induced fragmentations and rearrangements of 1-phenyl-2,2,3-trimethylphosphetane 1-oxide, 1-phenylphospholane 1-oxide and 1-phenylphosphorinane 1-oxide were investigated. A process common to all of these phosphine oxides was electron impact induced formation of new carbon-carbon bonds involving the phenyl rings. Evidence for such rearrangements included observation of hydrocarbon fragment ions containing seven or more carbons. 相似文献
9.
10.