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On neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi-infinite or finite plane-parallel medium. A general LL-space formulation, where 1 ≤ p < ∞, is adopted. The analysis concerns a vector-valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener-Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.  相似文献   
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A promising possibility for the quantitative analysis of X-ray absorption near edge structure (XANES) spectra of nanosized electrode materials is demonstrated. We used a 2D map representation technique, which utilizes the values of the first derivatives of the absorbance with respect to the inserted Li(+) content plotted over the two-dimensional space defined by the inserted Li(+) content (mole) versus photon energy (eV) as a single map. The technique was applied to XANES spectra of the Li(y)CoO system in the first Li(+) insertion reaction for determining the structural and electronic variations associated with the change in Li(+) content. The obtained show that the intensities of two peaks at 7725 and 7711 eV increased with the Li(+) content and the difference of intensity change of these two peaks carried out for successive couples of spectra yielded the largest changes at 1.05 and 1.98 mol of Li content. This approach for quantitative analysis of XANES without using conventional simulation techniques enable us to interpret X-ray absorption spectroscopy (XAS) as a quantitative analytical technique with greater confidence.  相似文献   
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π-Conjugated organic semiconductors are promising materials for surface-enhanced Raman scattering (SERS)-active substrates based on the tunability of electronic structures and molecular orbitals. Herein, we investigate the effect of the temperature-mediated resonance-structure transitions of poly(3,4-ethylenedioxythiophene) (PEDOT) in poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT : PSS) films on the interactions between substrate and probe molecules, thereby affecting the SERS activity. Absorption spectroscopy and density functional theory calculations show that this effect occurs mainly due to delocalization of the electron distribution in molecular orbitals, effectively promoting the charge transfer between the semiconductor and probe molecules. In this work, we investigate for the first time the effect of electron delocalization in molecular orbitals on SERS activity, which will provide new design ideas for the development of highly sensitive SERS substrates.  相似文献   
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The two-dimensional (2D) infrared correlation spectra obtained from the reaction time- and concentration-dependent IR spectra elucidates the reaction of CO2 and NH3 in an aqueous solution for CO2 absorption. In the synchronous 2D correlation spectra, the interrelation of the proton with carbamate and bicarbonate indicates that the pH level affected the formation reactions of the two products. Furthermore, the interrelation of carbamate with bicarbonate confirmed the conversion of carbamate into bicarbonate with the release of protons (or the decrease of the pH). From the experimental results including the asynchronous 2D correlation spectra, the reaction of the CO2 and aqueous ammonia proceeded through the following steps: formation of carbamate, formation of bicarbonate, release of protons, and conversion of carbamate into bicarbonate. The analysis of the formation of carbamate and bicarbonate by 2D infrared correlation spectroscopy provides useful information on the reaction mechanism of CO2 and NH3 in aqueous solutions.  相似文献   
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We have examined both self-assembly and confinement effect in room-temperature ionic liquid (RTIL)-aluminum hydroxide hybrids (RAHs) to attain a fundamental understanding of special phenomena in nanoscale spaces as well as to design functional nanomaterials for practical applications. Phase-controlled one-dimensional (1D) RAHs were synthesized through a simple ionothermal process. The RAHs were hierarchically transformed in terms of the molecular structures, morphologies, and phases of the materials during the ionothermal process with respect to the concentration of RTIL. In addition to the hierarchical transformation, the RTIL/aluminum hydroxide nanohybrids revealed unexpected physical behaviors, including thermal transition variation of the RTIL in confined environments and a phase transition from nanosolid to nanoliquid affected by changes of the melting points. More importantly, intermolecular interaction induced-self-assembly and confinement effect of RTILs inside an integrated hybrid system, which have not been clearly explained to date, were analyzed by 2D infrared correlation spectroscopy (2D IR COS); dynamic behaviors of RTILs, i.e., sequentially spatial reorientation and kinetically conformational changes, were attributed to the interactions between RTILs and aluminum hydroxides. 2D IR COS offers a new way to interpret highly complex, veiled systems such as the formation mechanism of nanoparticles, biomineralization, self/supramolecular assembly, and nanoconfinement.  相似文献   
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A universal methodology to efficiently improve the photocatalyst performance of semiconductors was developed by employing exfoliated RuO2 two‐dimensional nanosheets as a conducting hybridization matrix. The hybridization with a RuO2 nanosheet is easily achieved by crystal growth or electrostatically derived anchoring of semiconductor nanocrystals on the RuO2 nanosheet. An enhanced chemical interaction of inorganic semiconductor with hydrophilic RuO2 nanosheet is fairly effective in optimizing their photocatalytic activity and photostability by the enhancement of charge separation and charge mobility. The RuO2‐containing nanohybrids show much better photocatalyst functionalities than do the graphene‐containing ones. The present study clearly demonstrates that hydrophilic RuO2 nanosheets are superior hybridization matrices, over the widely used hydrophobic graphene nanosheets, for exploring new efficient hybrid‐type photocatalysts.  相似文献   
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We describe a family of polynomials discovered via a particular recursion relation, which have connections to Chebyshev polynomials of the first and the second kind, and the polynomial version of Pell's equation. Many of their properties are listed in Section 3. We show that these families of polynomials in the variable t satisfy certain second-order linear differential equations that may be of interest to mathematicians in conformal field theory and number theory. We also prove that these families of polynomials in the setting of Date–Jimbo–Kashiwara–Miwa algebras when multiplied by a suitable power of t are orthogonal with respect to explicitly described kernels. Particular cases lead to new identities of elliptic integrals (see Section 5).  相似文献   
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