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利用杨辉三角形对称性推导高阶运动微分方程   总被引:1,自引:0,他引:1       下载免费PDF全文
施勇  马善钧 《物理学报》2006,55(10):4991-4994
利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系,发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程,并讨论了理想约束系统下的高阶运动微分方程. 关键词: 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束  相似文献   
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对覆盖广义Rough集中的隶属关系、隶属函数进行了定义,并利用隶属函数定义了集合的Rough包含与Rough相等,得到一些与Pawlak的Rough集不同的性质。  相似文献   
4.
陈五立  石俊  黄亦斌 《大学物理》2006,25(6):31-32,53
通过例证说明,通解法对于偏微分方程而言,其适用范围要比通常认为的大.并表明,只要适当变通,行波法就可用于有界情况.  相似文献   
5.
In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.  相似文献   
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The first MCM-41-supported bidentate phosphine palladium(0) complex has been prepared. This complex is a highly efficient catalyst for Sonogashira reaction and can be reused at least 10 times without any decrease in activity.  相似文献   
7.
In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|α|?u|p?2?u) + λ 1/|x|β |?u|p?2?u · x = |x|γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|α|?u|p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? RN(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.  相似文献   
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The electrochemical and in-situ surface-enhanced Raman spectroscopy (SERS) techniques were used to investigate the electrooxidation behavior of methanol in acidic, neutral and alkaline media at a Pt-Ru nanoparticle modified glassy carbon (Pt-Ru/GC) electrode. The results showed that methanol could be dissociated spontaneously at the Pt-Ru/GC electrode to produce a strongly adsorbed intermediate, CO. It was found that CO could be oxidized more easily in the alkaline medium than in the acidic and neutral media. The peak potential of methanol oxidation was shifted from 0.663 and 0.708 V in the acidic and neutral media to -0.030 V in the alkaline medium, which is due to that the adsorption strength of CO on the Pt surface in the alkaline medium is weaker than that in the acidic and neutral media. The final product of the methanol oxidation is CO2. However, in the alkaline medium, CO2 produced would form CO3^2- and HCO3^- resulting in the decrease in the alkaline concentration and then in the decrease in the performance of DMFC. Therefore, the performance of the alkaline DMFC is not Stable.  相似文献   
9.
采用透射电镜(TEM)和选区电子衍射(SAED)技术, 分别表征了Pt-CNTs/GC电极的表面形貌和所负载铂纳米原子簇的结构. 以CO和CH3OH为探针分子, 用循环伏安和计时电流等常规电化学方法检测了CO和CH3OH在Pt-CNTs/GC电极上的氧化行为. 研究结果表明, CO在Pt-CNTs/GC电极上有3个氧化电流峰(Ⅰ, Ⅱ, Ⅲ), 其中峰Ⅰ为CO桥式吸附的氧化峰, 而峰Ⅱ和Ⅲ则分别为CO线形吸附在碳纳米管负载的不同粒径的Pt纳米原子簇以及Pt原子薄膜上所分裂的氧化峰; CH3OH在Pt-CNTs/GC电极上也能自发解离吸附强吸附中间体CO; Pt-CNTs/GC电极对CH3OH的氧化峰电流不总是随CNTs上载铂量的增加而增大, 表明在制备直接甲醇燃料电池阳极时, 应选择合适的载铂量.  相似文献   
10.
We construct silver–gold alloy nanoparticles (Ag–AuNPs) as the basis of a reagentless, sensitive and simple mercury sensor. Ag–AuNPs were electrodeposited directly on transparent indium tin oxide film coated glass. Hg(II) ions in aqueous solution could be reduced by Ag atoms existing in Ag–AuNPs; the deposition/amalgamation of Hg on the nanoparticles resulted in a blue shift of the localized surface plasmon resonance peak. Therefore, Hg2 + can be detected quantitatively by using a spectrophotometer. The sensor response is linear in the range from 0.05 to 500 ppb of Hg(II) concentration. No sample separation or preconcentration is required for detection of ultralow levels of mercury in water samples. The results shown herein have potential applications in the development of a new optical sensor for the detection of low concentrations of mercury.  相似文献   
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