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21.
We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n
–1/2). On the other hand, Esseen(3) has shown that this rate is o(n
–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.(9) Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n
–1/2). 相似文献
22.
Matthew M. Malwitz Paul D. Butler Lionel Porcar Drew P. Angelette Gudrun Schmidt 《Journal of polymer science. Part A, Polymer chemistry》2004,42(17):3102-3112
The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay [montmorillonite, i.e., Cloisite NA+ (CNA)] was investigated with rheology and small-angle neutron scattering (SANS). The steady-state viscosity and SANS were used to measure the shear-induced orientation and relaxation of the polymer and clay platelets. Anisotropic scattering patterns developed at much lower shear rates than in pure clay solutions. The scattering anisotropy saturated at low shear rates, and the CNA clay platelets aligned with the flow, with the surface normal parallel to the gradient direction. The cessation of shear led to partial and slow randomization of the CNA platelets, whereas extremely fast relaxation was observed for laponite (LRD) platelets. These PEO–CNA networklike solutions were compared with previously reported PEO–LRD networks, and the differences and similarities, with respect to the shear orientation, relaxation, and polymer–clay interactions, were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3102–3112, 2004 相似文献
23.
The traditional use of LIBOR futures prices to obtain surrogates for the Eurodollar forward rates is proved to yield a systematic bias in the pricing of Eurodollar swaps when one assumes that the yield curve is well described by the Heath-Jarrow-Morton model. The resulting theoretical inequality is consistent with the empirical observations of Burghardt and Hoskins (1995), and it provide a theoretical basis for price anomalies that are suggested by more recent empirical data. 相似文献
24.
Rajesh H. Somani Igors Sics Benjamin S. Hsiao 《Journal of polymer science. Part A, Polymer chemistry》2006,44(24):3553-3570
Combined in situ rheo-SAXS (small-angle X-ray scattering) and -WAXD (wide-angle X-ray diffraction) studies using couette flow geometry were carried out to probe thermal stabilty of shear-induced oriented precursor structure in isotactic polypropylene (iPP) at around its normal melting point (162 °C). Although SAXS results corroborated the emerging consensus about the formation of “long-living” metastable mesomorphic precursor structures in sheared iPP melts, these are the first quantitative measures of the limiting temperature at which no oriented structures survive. At the applied shear, rate = 60 s−1 and duration ts = 5 s, the oriented iPP structures survived a temperature of 185 °C for 1 h after shear, while no stable structures were detected at and above 195 °C. Following Keller's concepts of chain orientation in flow, it is proposed that the chains with highly oriented high molecular weight fraction are primarily responsible for their stability at high temperatures. Furthermore, the effects of flow condition, specifically the shear temperature, on the distributions of oriented and unoriented crystals were determined from rheo-WAXD results. As expected, at a constant flow intensity (i.e., rate = 30 s−1 and duration, ts = 5 s), the oriented crystal fraction decreased with the increase in temperature above 155 °C, below which the oriented fraction decreased with the decrease in temperature. As a result, a crystallinty “phase” diagram, i.e., temperature versus crystal fraction ratio, exhibited a peculiar “hourglass” shape, similar to that found in many two-phase polymer–polymer blends. This can be explained by the competition between the oriented and unoriented crystals in the available crystallizable species. Below the shear temperature (155 °C), the unoriented crystals crystallized so rapidly that they overwhelmed the crystallization of the oriented crystals, thus depleting a major portion of the crystallizable species and increasing their contribution in the final total crystalline phase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3553–3570, 2006 相似文献
25.
26.
Three series of pressure‐sensitive adhesives were prepared with constant glass‐transition temperature, using emulsion polymerization. The monomers chosen were butyl acrylate, 2‐ethylhexyl acrylate (EHA), methyl methacrylate (MMA), and acrylic acid (AA). Within each polymer series, the proportion of AA monomer was held constant for each polymer preparation but acrylic ester monomer levels were varied. Adhesion performance was assessed by measurement of loop tack, static shear resistance, and through the construction of peel master‐curves. Peel master‐curves were generated through peel tests conducted over a range of temperatures and peel rates and through application of the time–temperature superposition principle. Bulk effects dominated by polymer zero shear viscosity change as AA and EHA levels were varied were attributed to the observed effect on static shear resistance and the horizontal displacements of peel master‐curves. Static shear resistance was found to strongly correlate with log(aC), a parameter introduced to horizontally shift peel master‐curves to form a superposed, “super master‐curve”. An interfacial interaction was proposed to account for deviations observed when loop tack was correlated with log(aC). Surface rearrangements via hydrogen bonding with the test substrate were suggested as responsible for the interfacial interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1237–1252, 2006 相似文献
27.
Suzdalev I. P. Buravtsev V. N. Maksimov Yu. V. Zharov A. A. Imshennik V. K. Novichikhin S. V. Matveev V. V. 《Russian Chemical Bulletin》2003,52(9):1950-1958
Magnetic phase transitions of the first and second order were revealed by Mössbauer spectroscopy in nanosystems of - and -ferric oxides and metallic europium subjected to shear stress (240°) under high pressure (20 kbar). For - and -ferric oxide nanoclusters, the Curie (Neel) points decreased to 300 K, whereas for nanostructured europium the Neel point increased from 90 to 100 K. The thermodynamic model of magnetic phase transitions predicting a change in the character of magnetic phase transitions and a decrease (increase) in the critical Neel (Curie) points in nanoclusters was developed. The type of magnetic phase transitions and the change in the critical points were caused by defects in nanoclusters, whose maximum concentration was observed for the clusters with the 20—50 nm size range. 相似文献
28.
E. P. Honig 《Rheologica Acta》1987,26(1):2-6
Equations are derived for the coaxial cylinder system in the combined oscillatory and steady-state shear mode. The limitations of the use of the various equations are presented. If the usual linear equations are used, the main limitation, in the case of oscillatory shear only, is that the frequency of measurement should be below 0.016 |
*|/(r
2
–r
1
)2. Here |
*| is the modulus of the complex viscosity, is the density of the liquid andr
1
andr
2
are the radii of the cylinders. Furthermore it is shown that there is a small error in the numerical factor of the usually applied equations. The calculations are set up in such a way that extension to higher harmonics follows in a natural way. An experimental example illustrates the use of the derived equations. 相似文献
29.
K. Osaki T. Inoue T. Uematsu Y. Yamashita 《Journal of Polymer Science.Polymer Physics》2002,40(10):1038-1045
Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τRZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τL > τRZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ1) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ2)?1/2, where γ is the magnitude of shear. Contributions to η and Ψ1 from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τst = τ + (τRZ ? τ)/(1 + 0.35τRZ γ˙) instead of τRZ. Here, γ˙ is the rate of shear, and τ is the τRZ value at the infinite dilution limit. η and Ψ1 at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002 相似文献
30.
Momentum transfer was investigated in an unbaffled agitated vessel of inner diameter 0.3 m equipped with different off-centred
impellers. The distribution of the shear rate on the tank wall as a function of the impeller type and Reynolds number was
studied in the turbulent regime of the Newtonian liquid flow. The dependences of the averaged dimensionless shear rate, friction
coefficient, and dissipated energy on the Reynolds number and eccentricity ratio were approximated using four-parameter equations.
Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May
2006. 相似文献