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41.
定义了一类相空间中的准几率分布函数系,这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上,其中定义α=αp-i?q和α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp[i(1-α)qp]做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用,而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候,准几率分布函数就是一个类似于Husimi的分布函数fHLα(q,p);当g(λ)是一个表示椭圆的复函数时,准几率分布函数就是一个椭圆分布函数fEα(q,p);再在g(λ)为复函数的基础上附加α=0,就可得到标准序分布函数fS(q,p)、反标准序分布函数fAS(q,p)和Wigner分布函数fW(q,p),此时g(λ)表示高度为1/12π?而长度为λ的矩形窗.
关键词:
窗口Fourier变换
相空间
Wigner分布函数 相似文献
42.
Bingxin LiuYoshio Tatamitani Jun ShimadaTeruhiko Ogata 《Journal of Molecular Spectroscopy》2002,211(1):99-106
The microwave spectrum of the 35Cl and 37Cl isotopic species of 1-chloro-1,1,2-trifluoroethane (HCFC-133b) has been investigated in the frequency region 10 to 50 GHz using a Stark modulation microwave spectrometer. A pulsed jet Fourier transform microwave spectrometer was also used for the measurement of hyperfine splittings. A least-squares analysis of the observed b-type Q- and R-branch transition frequencies gave rotational and centrifugal distortion constants and components of the chlorine nuclear quadrupole coupling constant tensors in the principal axes system as follows: A=4625.161 (3) MHz, B=2004.127 (2) MHz, C=1875.813 (2) MHz, ΔJ=0.144 (9) kHz, ΔJK=1.0748 (8) kHz, ΔK=1.57 (1) kHz, δJ=0.01376 (4) kHz, δK=−0.146 (4) kHz, χaa=−57.958 (10) MHz, χbb=21.231 (11) MHz, and χcc=36.727 (11) MHz for 35ClCF2CH2F species, and A=4607.684 (6) MHz, B=1960.565 (2) MHz, C=1834.823 (2) MHz, ΔJ=0.106 (7) kHz, ΔJK=1.022 (3) kHz, ΔK=1.48 (1) kHz, δJ=0.0142 (2) kHz, δK=−0.18 (2) kHz, χaa=−46.268 (11) MHz, χbb=17.319 (13) MHz, and χcc=28.950 (13) MHz for 37ClCF2CH2F species. The structural parameters are calculated from the observed six rotational constants by assuming the partial structure of ab initio calculation. The electronic properties of the C-Cl bond are evaluated from the observed nuclear quadrupole constants of chlorine. These molecular properties are compared with those of other related molecules. 相似文献
43.
44.
Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn. 相似文献
45.
The rotational spectra of the deuterium cyanide isotopic species DCN, D13CN, DC15N, and D13C15N were recorded in the vibrational ground and first excited bending state (v2=1) up to 2 THz. The R-branch transitions from J=3←2 to J=13←12 were measured with sub-Doppler resolution. These very high resolution (∼70 kHz) and precise (±3-10 kHz) saturation dip measurements allowed for resolving the underlying hyperfine structure due to the 14N nucleus in DCN and D13CN for transitions as high as J=10←9. Additional high JR-branch (J=25←24 to J=28←27) transitions around 2 THz and direct l-type (ΔJ=0, J=19 to J=25) transitions from 66 to 118 GHz were recorded in Doppler-limited resolution. For the ground state of D13C15N, the J=1←0 transition was measured for the first time. The transition frequency accuracies for the other deuterated species were significantly improved. These new experimental data, together with the available infrared rovibrational data and previously measured direct l-type transitions, were subjected to a global least squares analysis for each isotopomer. This yielded precise sets of molecular constants for the ground and first excited vibrational states, including the nuclear quadrupole and magnetic spin-rotation coupling constants of the 14N nucleus for DCN and D13CN. The hyperfine structure due to the D, 13C, and 15N nuclei have not been resolved, but led to a broadening of the observed saturation dips. 相似文献
46.
差分吸收光谱法测量大气痕量气体浓度误差分析及改善方法 总被引:8,自引:2,他引:6
差分吸收光谱技术(DOAS)中采用线性最小二乘拟合方法,用痕量气体标准差分吸收截面对测量得到的差分吸收光谱进行拟合,得出大气中痕量气体的浓度.计算结果的准确性不仅取决于光谱的测量精度,而且受标准差分吸收截面以及仪器函数和温度等诸多因素的影响.详细地分析了计算误差的产生原因,提出了用高浓度样品池得到标准吸收截面的方法,针对光谱固有结构,以及温度对标准吸收截面的影响,改进了浓度反演算法.大量的实验表明,综合运用上述方法,即便对低浓度的样气,相对测量误差也能降低到10%以下. 相似文献
47.
Jong Chan Lee Jin Young Park So Young Yoon Yong Hun Bae Seung Jun Lee 《Tetrahedron letters》2004,45(1):191-193
A novel and direct method for the synthesis of α-halocarbonyl compounds using sequential treatment of carbonyl compounds with [hydroxy(tosyloxy)iodo]benzene followed by magnesium halides under solvent-free microwave irradiation conditions is described. 相似文献
48.
Molecular electroactive monolayers have been produced from vinylferrocene (VFC) via light-assisted surface anchoring to H-terminated n- and p-Si(1 0 0) wafers prepared via wet chemistry, in a controlled atmosphere. The resulting Si-C bound hybrids have been characterized by means of XPS and AFM. Their performance as semiconductor functionalized electrodes and their surface composition have been followed by combining electrochemical and XPS measurements on the same samples, before and after use in an electrochemical cell. White-light photoactivated anchoring at short (1 h) exposure times has resulted in a mild route, with a very limited impact on the initial quality of the silicon substrate. In fact, the functionalized Si surface results negligibly oxidized, and the C/Fe atomic ratio is close to the value expected for the pure molecular species. The VFC/Si hybrids can be described as (η5-C5H5)Fe2+(η5-C5H4)-CH2-CH2-Si species, on the basis of XPS results. Electrochemical methods have been applied in order to investigate the role played by a robust, covalent Si-C anchoring mode towards substrate-molecule electronic communication, a crucial issue for a perspective development of molecular electronics devices. The response found from cyclic voltammograms for p-Si(1 0 0) functionalized electrodes, run in the dark and under illumination, has shown that the electron transfer is not limited by the number of charge carriers, confirming the occurrence of electron transfer via the Si valence band. The hybrids have shown a noticeable electrochemical stability and reversibility under cyclic voltammetry (cv), and the trend in peak current intensity vs. the scan rate was linear. The molecule-Si bond is preserved even after thousands of voltammetric cycles, although the surface coverage, evaluated from cv and XPS, decreases in the same sequence. An increasingly larger surface concentration of Fe3+ at the expenses of Fe2+ redox centers has been found at increasing number of cv’s, experimentally associated with the growth of silicon oxide. Surface SiO− groups from deprotonated silanol termination, induced by the electrochemical treatments, are proposed as the associated counterions for the Fe3+ species. They could be responsible for the observed decrease in the electron transfer rate constant with electrode ageing. 相似文献
49.
Vincenzo Santagada Ferdinando FiorinoElisa Perissutti Beatrice SeverinoSara Terracciano Giuseppe CirinoGiuseppe Caliendo 《Tetrahedron letters》2003,44(6):1145-1148
A novel and convenient microwave-assisted dimerization of an active peptide compound using the DKPs as scaffold is described. The key reaction giving rise to the diketopiperazine scaffold is the intermolecular coupling. No epimerization was detected in the reactions used. Conventional and microwave heating of the reactions are compared. Synthesis by microwave irradiation gave the desired compounds in higher yields and in shorter reaction times than those obtained by conventional heating. 相似文献
50.
一类混合型微分差分方程的周期解 总被引:1,自引:0,他引:1
利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件. 相似文献