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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.
The swelling properties of Al-pillared clays, obtained from five different smectites, were studied using X-ray diffraction. These clays, the dioctahedral beidellite and montmorillonite and the trioctahedral saponite, hectorite and laponite differ in source of isomorphic substitution and represent a series of decreasing basicity along the siloxane plane. An Al oxyhydroxy cation was inserted between the layers to form the respective pillared clays and these clays were heated incrementally to 600°C. The XRD peaks at each stage of heating were recorded as well as the same samples subsequently wetted. Basal spacings of each clay at each stage of dehydration d rehydration indicated that the swelling of tetrahedrally substituted saponite and beidellite was indeed restricted, compared with the other three clays. This was attributed to greater basicity of the oxygen plane of beidellite and saponite due to tetrahedral substitution of Si by Al, resulting in an increase in the strength of hydrogen bonds between either water or the interlayer polyhydroxy cation and the clay.The data from the XRD analyses helped in addition, to clarify the thermal transformations of the Keggin ion itself. According to the changes in thed-spacings of the pillared clays it was concluded that the Keggin ion lost its structural water at 200°C and dehydroxylated in a range beginning at 350°C. Between 500 to 600°C this polymer cation, which is thought to form the Al2O3 oxide, did not rehydrate.Dedicated to Prof. Menachem Steinberg on the occasion of his 65th birthdayThe authors wish to thank Laporte Industries, Inc., U.K. for the laponite sample. 相似文献
9.
Lahav M Kharitonov AB Willner I 《Chemistry (Weinheim an der Bergstrasse, Germany)》2001,7(18):3992-3997
(R)- or (S)-2-Methylferrocene carboxylic acids, (R)-1 or (S)-1, (R)- or (S)-2-phenylbutanoic acid, (R)-2 or (S)-2, and (R)- or (S)-2-propanoic acid, (R)-3 or (S)-3, can be imprinted in thin TiO2 films on the gate surface of ion-sensitive field-effect transistor (ISFET) devices. The imprinting is performed by hydrolyzing the respective carboxylate TiIV butoxide complex on the gate surface, followed by washing off the acid from the resulting TiO2 film. The imprinted sites reveal chiroselectivity only towards the sensing of the imprinted enantiomer. The chiral recognition sites reveal not only chiroselectivity but also chirospecificity and, for example, the (R)-2-imprinted film is active in the sensing of (R)-2, but insensitive towards the sensing of (R)2-phenylpropanoic acid, (R)-3, which exhibits a similar chirality. Similarly, the (R)-3-imprinted film is inactive in the analysis of (R)-2. The chiroselectivity and chirospecificity of the resulting imprinted films are attributed to the need to align and fit the respective substrates in precise molecular contours generated in the cross-linked TiO2 films upon the imprinting process. 相似文献
10.
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