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61.
Semion I. Kuchanov Konstantin V. Tarasevich Timur V. Zharnikov 《Journal of statistical physics》2006,122(5):875-908
The statistical theory of gelation in the simplest process of the non-random polycondensation (S. I. Kuchanov, T. V. Zharnikov,
J. Stat. Phys., 111(5/6), 1273 (2003)) has been refined as to be able to take into account the effect of a monomer configuration
on topological characteristics of the polymer network of the gel. Proceeding from the kinetic analysis of such a polycondensation,
we rigorously prove that it can be described in terms of some stochastic branching process. The parameters of the process
depend on the overall number of functional groups in the monomer as well as on the pattern of their mutual arrangement. Examples
of some model systems illustrate the effect of kinetic and configurational factors on the topology of a polymer network formed
in the course of non-random polycondensation. 相似文献
62.
Hassan Allouba Rick Durrett John Hawkes Edwin Perkins 《Journal of Theoretical Probability》1997,10(3):773-794
We use supercritical branching processes with random walk steps of geometrically decreasing size to construct random measures. Special cases of our construction give close relatives of the super-(spherically symmetric stable) processes. However, other cases can produce measures with very smooth densities in any dimension. 相似文献
63.
Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods. 相似文献
64.
本文研究Meleard-Roelly(1992,1993)和Metivier(1987)构造的带交互作用的测度值分枝过程的状态性质.我们证明在自然假设下该过程关于Lebesgue测度是绝对连续的,其密度有连续修正且满足一个随机偏微分方程. 相似文献
65.
66.
Dendronized Hyperbranched Macromolecules: Soft Matter with a Novel Type of Segmental Distribution
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Priv.‐Doz. Dr. Albena Lederer Prof. Dr. Walther Burchard Tobias Hartmann Johannes S. Haataja Dr. Nikolay Houbenov Andreas Janke Dr. Peter Friedel Dr. Ralf Schweins Dr. Peter Lindner 《Angewandte Chemie (International ed. in English)》2015,54(43):12578-12583
Dendronization of a hyperbranched polyester with different generation dendrons leads to pseudo‐dendritic structures. The hyperbranched core is modified by the divergent coupling of protected monomer units to the functional groups. Compared to dendrimers, the synthetic effort is significantly less, but the properties are very close to those of high‐generation dendrimers. The number of functional groups, molar mass, and rheology behavior even in the early generation (G1–G4) pseudo‐dendrimers strongly resembles the behavior of dendrimers in higher generations (G5–G8). Comparison of the segmental and internal structure with perfect dendrimers is performed using SANS, dynamic light scattering and viscosity analysis, microscopy and molecular dynamics simulation. The interpretation of the results reveals unique structural characteristics arising from lower segmental density of the core, which turns into a soft nano‐sphere with a smooth surface even in the first generation. 相似文献
67.
《Macromolecular theory and simulations》2017,26(6)
Monte Carlo simulations reveal long chain branching (LCB) topology based on kinetics of systems like low‐density polyethylene (ldPE). Examining the topologies computed shows the majority of branch arms to be short as compared to backbone length, while also a significant branch‐on‐branch fine structure is observed. Until now, predicting scattering function P −1(θ) from LCB has only been successful for structures like simple combs or stars. Topologies in graph theoretical form are used to predict scattering function P −1(θ) and by summating intramolecular distances, accounting for branching and excluded volume. Experimental size exclusion chromatography with multiangle light scattering can be brought in line with the predicted branching character. Branching is less than predicted due to a different fine structure in ldPE leading to stronger size contraction. 相似文献
68.
High-speed holographic microscopy is applied to take three successive photographs of fast propagating cracks in Homalite 100 or in Araldite B at the moment of bifurcation. Crack speed at bifurcation is about 540 m/s on Homalite 100, and about 450 m/s on Araldite B. From the photographs, crack speeds immediately before and after bifurcation are obtained, and it is found that discontinuous change of crack speed does not exist at the moment of bifurcation in the case of Homalite 100, but exists in the case of Araldite B. From the photographs, crack opening displacement (COD) is also measured along the cracks as a function of distance r from the crack tips. The measurement results show that the CODs are proportional to √r before bifurcation. After bifurcation, the CODs of mother cracks are proportional to √r, though the CODs of branch cracks are not always proportional to √r. The energy release rate is obtained from the measured CODs, and it is found that energy release rate is continuous at bifurcation point in both cases of Homalite 100 and Araldite B. Energy flux that shows the energy flow toward a crack tip is also obtained. 相似文献
69.
This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate
viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain
branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain
branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear
creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure
of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device.
Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison
to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples.
Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity,
whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison
to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different
time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological
results from literature on model branched polymers of different molecular topography and chemical composition.
Received: 12 July 2001 Accepted: 30 October 2001 相似文献
70.
The analytical expressions of the various structural units and the average degree of branching for the hyperbranched polymers resulted from AB2 polycondensation with substitution effect were derived by the kinetic mechanism.The reactivity difference between the B group in linear unit and that in terminal group has great effect on the molecular parameters of the products obtained.The concentration of terminal units has a maximum with the increase of the conversion of A groups(x).The higher the reactivity ratio(r) of linear B group to branched one is,the later the maximum appears and the larger it is.The degree of branching of the hyperbranched polymers obtained is controllable by adjusting the parameters of r and x,which increases with increasing both x and r. 相似文献