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521.
We consider the generalized shift operator associated with the Laplace-Bessel differential operator $$ \Delta _B = \sum\limits_{i = 1}^n {\frac{{\partial ^2 }} {{\partial x_j^2 }}} + \sum\limits_{i = 1}^k {\frac{{\gamma _i }} {{x_i }}\frac{\partial } {{\partial x_i }}} $$ , and study the modified B-Riesz potential ? α, β generated by the generalized shift operator acting in the B-Morrey space in the limiting case. We prove that the operator ? α, β, 0 < α < n + |γ|, is bounded from the B-Morrey space L (n+|γ|?λ)/α,λ,γ (? k,+ n ) to the B-BMO space BMO γ (? k,+ n ).  相似文献   
522.
In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium‐like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree‐Fock Roothaan (HFR). The results are in a good agreement with literature results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011  相似文献   
523.
The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011  相似文献   
524.
The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B‐spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.  相似文献   
525.
In this paper we describe a novel methodology for grafting polymers via radical photopolymerization initiated on gold surfaces by aryl layers from diazonium salt precursors. The parent 4-(dimethylamino)benzenediazonium salt was electroreduced on a gold surface to provide 4-(dimethylamino)phenyl (DMA) hydrogen donor layers; free benzophenone in solution was used as a photosensitizer to strip hydrogen from the grafted DMA. This system permitted efficient surface initiation of photopolymerization of 2-hydroxyethyl methacrylate. The resulting poly(2-hydroxyethyl methacrylate) (PHEMA) grafts were found to be very adherent to the surface as they resist total failure after being soaked in the well-known paint stripper methyl ethyl ketone. The PHEMA grafts were reacted with 1,1'-carbonyldiimidazole to yield carbamate groups that are able to react readily with amino groups from proteins. The final surface consisted of protein-functionalized PHEMA grafts where bovine serum albumin (BSA) protein is specifically linked to the grafts by covalent bonds. We used X-ray photoelectron spectroscopy to monitor the chemical changes at the gold surface all along the process from the neat gold to the end-protein-functionalized polymer grafts: the PHEMA graft thickness ranged from 7 to 27 nm, and the activation by 1,1'-carbonyldiimidazole reached 37% of the OH groups, which was sufficient for 90% surface coverage of the grafts by BSA. This work conclusively provides a new approach for bridging reactive and functional polymers to surfaces via aryl diazonium salts in a simple, fast, and efficient approach of importance in biomedical and other applications.  相似文献   
526.
The tran-bis(ethylenediamine)bis(saccharinato)Zinc(II), [Zn(sac)2(en)2] (ZSED), (en: ethylenediamine and sac: saccharinate) complex has been synthesized and its crystal structure has been determined by X-ray diffraction analysis. The compound crystallizes in space group P21/c. The Zn(II) ion is hexa-coordinated by four nitrogens of two bidentate en ligands composing the basal plane and two nitrogen atoms from the monodentate two sac ligands (N-bonded) occuping the axial sites, adopting an elongated octahedral sphere. Both en and sac ligands occupy the trans positions of the coordination octahedron. The Zn(II) ion in title compound sits on a inversion centre and is octahedrally coordinated two bidentate en (ethylenediamine) and two sac (saccharinate) (N-bonded) ligands. The magnetic environments of Cu2+ doped [Zn(sac)2(en)2] complex have been identified by electron paramagnetic resonance (EPR) technique. Cu2+ doped ZSED single crystals have been studied at room temperature in three mutually perpendicular planes. The calculated results of the Cu2+ doped ZSED indicate that Cu2+ ion contains two magnetically inequivalent Cu2+ sites in distinct orientations occupying substitutional positions in the host lattice and show very high angular dependence.  相似文献   
527.
It is known that the semigroup Sing n of all singular self-maps of X n  = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987 Gomes , G. M. S. , Howie , J. M. ( 1987 ). On the rank of certain finite semigroups of transformations . Math. Proc. Cambridge Phil. Soc. 101 : 395303 .[Crossref], [Web of Science ®] [Google Scholar].) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005 Ay?k , G. , Ay?k , H. , Howie , J. M. ( 2005 ). On factorisations and generators in transformation semigroups . Semigroup Forum 70 : 225237 .[Crossref], [Web of Science ®] [Google Scholar]). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2.  相似文献   
528.
An involution or anti-involution is a self-inverse linear mapping. Involutions and anti-involutions of real quaternions were studied by Ell and Sangwine [15]. In this paper we present involutions and antiinvolutions of biquaternions (complexified quaternions) and split quaternions. In addition, while only quaternion conjugate can be defined for a real quaternion and split quaternion, also complex conjugate can be defined for a biquaternion. Therefore, complex conjugate of a biquaternion is used in some transformations beside quaternion conjugate in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion, biquaternion and split quaternion involutions and anti-involutions are given.  相似文献   
529.
Spherical spline quaternion interpolation has been done on sphere in Euclidean space using quaternions. In this paper, we have done the spline split quaternion interpolation on hyperbolic sphere in Minkowski space using split quaternions and metric Lorentz. This interpolation curve is called spherical spline split quaternion interpolation in Minkowski space (MSquad).  相似文献   
530.
ABSTRACT

The adsorption of Cr(VI) from aqueous solutions onto raw and acid-activated clays—namely, Re?adiye region clay (R, raw Re?adiye region clay; R-H2SO4, acid-activated with H2SO4 Re?adiye region clay; R-HCl, acid-activated with HCl Re?adiye region clay) and Hanç?l? region clay (H, raw Hanç?l? region clay; H-H2SO4, acid-activated with H2SO4 Hanç?l? region clay; H-HCl, acid-activated with HCl Hanç?l? region clay)—was studied in a batch system. For optimization of the Cr(VI) adsorption on raw clays and acid-activated clays, the effect of pH, temperature, initial Cr(VI) concentration, time, and adsorbent dosage were investigated. X-ray diffraction analyses of raw and acid-activated clays were used to determine the effects of acid-activating on the layer structure of the clays. The surface characterizations of clays and modified clays were performed by using FT-IR spectroscopy. The Langmuir and Freundlich adsorption models were employed to describe the equilibrium isotherms, and thus the isotherm constants were determined. The data obtained from our investigations were well described by the Langmuir model. The adsorption capacity of the adsorbents Re?adiye and Hanç?l? clays were found to be 0.0269, 0.0144, and 0.0170 mmol/g for H, H-HCl, and H-H2SO4 and 0.0356, 0.0276, and 0.0422 mmol/g for R, R-HCl, and R-H2SO4, respectively. The results show that the adsorption was strongly dependent on pH of the medium, initial Cr(VI) concentration and temperature. The removal of Cr(VI) reached saturation in about 120 min, and the adsorption process of Cr(VI) was observed as exothermic. A maximum removal of 73% was noted at 1.0 × 10?4 M concentration of Cr(VI) in solution for H-HCl. Furthermore the enhancement of removal of Cr(VI) was observed from pH 3 to 4. The results are discussed to highlight the influence of acid activation on Cr(VI) adsorption characteristics of the clays.  相似文献   
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