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1.
We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω0, where ω0 is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small. 相似文献
2.
Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX
W ⊂A
Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove
that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite
type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations,
we obtain all sofic systems.
The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716. 相似文献
3.
We obtain various results involving the centroid branches of randomly chosen trees from simply generated families. 相似文献
4.
5.
6.
Suppose one is given two related generating functionsa(x) = a
n
x
n
andb(x) = b
n
x
n
, often it is of interest to determine the limiting behaviour of the quantitiesa
n
/b
n
We survey some earlier results of this nature and give some new ones 相似文献
7.
8.
David Liptak William H. Ilsley Milton D. Glick John P. Oliver 《Journal of organometallic chemistry》1980,191(2):339-345
The structure of di-ortho-tolylmercury has been determined by single crystal X-ray methods from counter data. The compound crystallizes in the monoclinic space group C2/c with unit cell dimensions a 10.970(2), b 10.448(3), c 11.409(3) Å; β 115.48(2)°, V 1180.5(5) Å3, ?calc 2.158 g/cm3 and Z = 4. The structure was solved with conventional heavy atom techniques. The crystal consists of individual molecular units with the mercury atom located on the crystallographic 2-fold axis of symmetry. The CHgC fragment is nearly linear with an angle of 178.0(4)°. The methyl groups lie on the same side of the molecule and the rings are twisted with respect to one another by 58.9°. The HgC bond distance is 2.09(1) Å. 相似文献
9.
The outer-distance of a nodeu in a rooted treeT
n
is the height of the subtree determined byu and all nodesv such thatu is on the path joiningv and the root ofT. We show that the expected outer-distance of nodes of treesT
n
in certain families is asymptotic toB logn where the constantB depends on . 相似文献
10.
Eugene R. Corey Joyce Y. Corey Milton D. Glick 《Journal of organometallic chemistry》1977,129(1):17-25
The structures of 5-methyl-5-phenyl-5H-dibenzo[b,f] silepin (I) and 5-methyl- 5-phenyl-1O,11-dihydro-5H-dibenzo [b,f] silepin (II) have been determined from three-dimensional X-ray data collected by counter methods. I crystallizes in the orthorhombic space group Pnam with a 7.596(3), b 18.102(5) and c 12.190(2) Å; observed and calculated densities (Z = 4) are 1.17 and 1.18 g cm?3, respectively. II crystallizes in the monoclinic space group with a 11.115(3), b 7.920(3), c 20.765(5) Å and β 111.71(2)°; observed and calculated densities (Z = 4) are 1.17 g cm?3. Anisotropic refinement of nonhydrogen atoms, with hydrogen atoms included at fixed ideal locations, gave conventional R-factors of 4.5% (I) and 5.0% (II). Compound I exhibits the boat conformation for the tricyclic framework and is located on a crystallographically required mirror plane. Com- pound II has the expected folded boat conformation. The torsion angle about the 10,11-bond is 0.0° for I, a crystallographic symmetry requirement, and 89.9° for II. Mean SiC bond distances are 1.863 Å(I) and 1.875 Å(II). The dihedral angles between the planar benzo groups are 129.7° (I) and 137.2° (II); introduc- tion of unsaturation at the 10,11-position decreases the dihedral angle in the tri- cyclic system, i.e., the tricyclic system is more bent. 相似文献