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51.
A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999 相似文献
52.
Hideaki Ishikawa Kazuo Yamamoto Kazumi Fujima Misako Iwasawa 《International journal of quantum chemistry》1999,72(5):509-523
A powerful and accurate numerical three‐dimensional integration scheme was developed especially for molecular orbital calculations. A multicenter integral is decomposed into the sum of single‐center integrals using nuclear weight functions and calculated using Gaussian quadrature rules. The decomposed single‐center integrands show strong anisotropy. With a careful selection of the Gaussian quadrature rule according to the anisotropy, it is possible to obtain an accuracy of 13 digits with a small number of integration points for the overlap integrals, normalization integrals, and molecular integrals for the hydrogen molecule. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 509–523, 1999 相似文献
53.
《Journal of computational chemistry》2018,39(21):1656-1665
Here, we describe a computational approach for studying enzymes that catalyze complex multi‐step reactions and apply it to Ribulose 1,5‐bisphosphate carboxylase–oxygenase (Rubisco), the enzyme that fixes atmospheric carbon dioxide within photosynthesis. In the 5‐step carboxylase reaction, the substrate Ribulose‐1,5‐bisphosphate (RuBP) first binds Rubisco and undergoes enolization before binding the second substrate, CO2. Hydration of the RuBP.CO2 complex is followed by C C bond scission and stereospecific protonation. However, details of the roles and protonation states of active‐site residues, and sources of protons and water, remain highly speculative. Large‐scale computations on active‐site models provide a means to better understand this complex chemical mechanism. The computational protocol comprises a combination of hybrid semi‐empirical quantum mechanics and molecular mechanics within constrained molecular dynamics simulations, together with constrained gradient minimization calculations using density functional theory. Alternative pathways for hydration of the RuBP.CO2 complex and associated active‐site protonation networks and proton and water sources were investigated. The main findings from analysis of the resulting energetics advocate major revision to existing mechanisms such that: hydration takes place anti to the CO2; both hydration and C C bond scission require early protonation of CO2 in the RuBP.CO2 complex; C C bond scission and stereospecific protonation reactions are concerted and, effectively, there is only one stable intermediate, the C3‐gemdiolate complex. Our main conclusions for interpreting enzyme kinetic results are that the gemdiolate may represent the elusive Michaelis–Menten‐like complex corresponding to the empirical Km (=Kc) with turnover to product via bond scission concerted with stereospecific protonation consistent with the observed catalytic rate. © 2018 Wiley Periodicals, Inc. 相似文献
54.
Hannes H. Loeffler Christoph A. Sotriffer Rudolf H. Winger Klaus R. Liedl Bernd M. Rode 《Journal of computational chemistry》2001,22(8):846-860
The relative free energies of hydration of the dipeptides glycylalanine and alanyl‐glycine in their naturally occurring form have been calculated both for the zwitterionic and protonated species. Emphasis was laid on comparisons between the conventional cutoff method and the Particle Mesh Ewald method to account for possible differences in electrostatic contributions to the free energy. Furthermore, the convergence behavior of the total free energy and its individual contributions were examined. The results, obtained by means of the thermodynamic integration technique as implemented in the free energy module of the AMBER program suite, suggest that in aqueous solution glycylalanine is more stable than alanylglycine by 2.7 kcal/mol in the zwitterionic form and by 3.5 kcal/mol in the protonated form. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 846–860, 2001 相似文献
55.
In this paper, we extend one of Erdélyi's classical integrals for the Gauss hypergeometric functions to a special class of generalized hypergeometric functions in which certain pairs of numerator and denomiator parameters differ by positive integers. Our main results are achieved by applying the fractional integration by parts and series manipulation technique. Some special cases are also pointed out which includes a new extension of a Thomae-type transformation. 相似文献
56.
Fumio Hiroshima 《Journal of Functional Analysis》2008,254(8):2127-2185
A Feynman-Kac-type formula for a Lévy and an infinite-dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of e−tHPF generated by the Pauli-Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics is constructed. When no external potential is applied HPF turns translation-invariant and it is decomposed as a direct integral . The functional integral representation of e−tHPF(P) is also given. Although all these Hamiltonians include spin, nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions. As an application of the functional integral representations energy comparison inequalities are derived. 相似文献
57.
F.?Y.?Kuo W.?T.?M.?DunsmuirEmail author I.?H.?Sloan M.?P.?Wand R.?S.?Womersley 《Methodology and Computing in Applied Probability》2008,10(2):239-275
Highly structured generalised response models, such as generalised linear mixed models and generalised linear models for time
series regression, have become an indispensable vehicle for data analysis and inference in many areas of application. However,
their use in practice is hindered by high-dimensional intractable integrals. Quasi-Monte Carlo (QMC) is a dynamic research
area in the general problem of high-dimensional numerical integration, although its potential for statistical applications
is yet to be fully explored. We survey recent research in QMC, particularly lattice rules, and report on its application to
highly structured generalised response models. New challenges for QMC are identified and new methodologies are developed.
QMC methods are seen to provide significant improvements compared with ordinary Monte Carlo methods.
相似文献
58.
We consider a general Euler-Korteweg-Poisson system in R 3, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi. 相似文献
59.
几个含有根式的不定积分例题的另解 总被引:1,自引:0,他引:1
实例说明用第一类换元积分法或分部积分法求解几个典型不定积分,其被积函数含有根式a2-x2或x2±a2. 相似文献
60.
Mojtaba Bakherad 《Linear and Multilinear Algebra》2019,67(5):871-885
In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method. 相似文献