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951.
Empirical model potentials are found to be very useful for generating most competitive minima of large water clusters, whereas correlated (e.g. second order-Møller–Plesset perturbation (MP2) theory or higher) calculations are necessary for predicting their accurate energetics and vibrational features. The present study reports the structures and energetics of (H2O)32 clusters at MP2 level using aug-cc-pvDZ basis set, starting with low-lying structures generated from model potentials. Such high-end and accurate calculations are made feasible by the cost-effective fragment-based molecular tailoring approach (MTA) in conjunction with the grafting procedure. The latter is found to yield electronic energies with a sub-millihartree accuracy with reference to their full calculation counterparts. The vibrational spectra of nine low-lying (H2O)32 isomers are obtained from the corresponding MTA-based Hessian matrix. All these low-lying isomers show almost similar spectral features, which are in fair agreement with the experiment. The experimental spectrum of (H2O)32 is thus better understood from the vibrational features of this set of very closely spaced isomers. The present case study of (H2O)32 clearly demonstrates the efficacy in obtaining accurate structures, energetics and spectra at correlated level of theory by combining model potential-based structures with fragmentation methods. 相似文献
952.
In this paper, we study the following modified Kirchhoff‐type equations of the form: where a > 0, b ≥ 0, and . Under appropriate assumptions on V (x) and h(x,u), some existence results for positive solutions, negative solutions, and sequence of high energy solutions are obtained via a perturbation method. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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955.
Numerical approximations to the solution of a singularly perturbed elliptic convection–diffusion problem in two space dimensions are generated using a monotone finite difference operator on a tensor product of piecewise‐uniform Shishkin meshes. The bilinear interpolants of these numerical approximations are parameter‐uniformly convergent to the solution of the continuous problem, in the pointwise maximum norm. In this article, discrete approximations to the first derivatives of the solution are shown to be globally first‐order (up to logarithmic factors) uniformly convergent, when the errors are scaled within the analytical layers of the continuous problem. Numerical results are presented to illustrate the theoretical error bounds established in an appropriated weighted C1–norm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 225–252, 2015 相似文献
956.
Alberto Seeger 《Numerical Functional Analysis & Optimization》2013,34(1-2):247-260
Let K(x) be an s-by-r rectangular matrix depending on a parameter x ε E and denote by g(x) the sum of its m largest singular values (1 ≤ m ≤ Min{s,r}). If K(x) depends affinely on x, then g is a nondifferentiable convex function. In this paper we consider first the affine case and give some formulas for the conjugate, subdifferential, and ε-subdifferential of g. These formulas are then used to obtain perturbation bounds for g(x). We study next the nonaffine case and discuss some questions related with the regularity, generalized subdifferentiability, and directional differentiability of g. 相似文献
957.
This paper considers the updating problem of the hyperbolic matrix factorizations. The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided. Then, some differential inequalities and first order perturbation expansions for the updated hyperbolic factors are derived. These results generalize the corresponding ones for the updating problem of the classical QR factorization obtained by Jiguang SUN. 相似文献
958.
The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures. 相似文献
959.
We investigate the perturbations of charged scalar field in 5-dimensional Gauss–Bonnet AdS black hole backgrounds. From the perturbation behaviors we obtain the objective picture on how the high curvature influences the spacetime perturbation and the condensation of the scalar hair. The high curvature effects can also be read from the linear response function such as the susceptibility and the correlation length, when the system approaches the critical point. We find that the Gauss–Bonnet term does not affect the critical exponents of the system and they still take the mean-field values. 相似文献
960.
Issarachai Ngamroo 《Physica C: Superconductivity and its Applications》2010,470(22):1986-1993
It is well known that the superconducting magnetic energy storage (SMES) is able to quickly exchange active and reactive power with the power system. The SMES is expected to be the smart storage device for power system stabilization. Although the stabilizing effect of SMES is significant, the SMES is quite costly. Particularly, the superconducting magnetic coil size which is the essence of the SMES, must be carefully selected. On the other hand, various generation and load changes, unpredictable network structure, etc., cause system uncertainties. The power controller of SMES which is designed without considering such uncertainties, may not tolerate and loses stabilizing effect. To overcome these problems, this paper proposes the new design of robust SMES controller taking coil size and system uncertainties into account. The structure of the active and reactive power controllers is the 1st-order lead-lag compensator. No need for the exact mathematical representation, system uncertainties are modeled by the inverse input multiplicative perturbation. Without the difficulty of the trade-off of damping performance and robustness, the optimization problem of control parameters is formulated. The particle swarm optimization is used for solving the optimal parameters at each coil size automatically. Based on the normalized integral square error index and the consideration of coil current constraint, the robust SMES with the smallest coil size which still provides the satisfactory stabilizing effect, can be achieved. Simulation studies in the two-area four-machine interconnected power system show the superior robustness of the proposed robust SMES with the smallest coil size under various operating conditions over the non-robust SMES with large coil size. 相似文献