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81.
Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions 下载免费PDF全文
Yue Wang Günter Leugering Tatsien Li 《Mathematical Methods in the Applied Sciences》2017,40(10):3808-3820
By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
82.
In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived. 相似文献
83.
We construct analytical solutions for a system composed of a reaction–diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction–diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher–KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails whose exponents are roots of second-, third-, or fourth-order polynomials. These raise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered. 相似文献
84.
A waveguide occupies infinite strip with one or several narrows on a two-dimensional (2D) plane and is governed by the Helmholtz equation with Dirichlet boundary condition. On the waveguide continuous spectrum, which coincides with a half-axis, a scattering matrix is defined. At each point of the continuous spectrum this matrix has finite size, which changes at thresholds. The thresholds form a sequence of positive numbers increasing to infinity. Approximate calculation of the scattering matrix in a threshold vicinity requires special treatment. We discuss and compare two methods of numerical approximation to the scattering matrix near a threshold. 相似文献
85.
Adsorption of SO2 and O3 molecules on pristine boron nitride (B12N12) and Ni-decorated B12N12 nano-cages has been systemically investigated through density functional theory (DFT) methods. Adsorption energies (thermodynamics), bond distances, charge analysis, dipole moments, orbital analysis and density of states are calculated by van der Waals DFT method (MPW1PW91) functional. The adsorption energies of O3 and SO2 on pristine B12N12 are about −143.8 and −14.0 kJ mol−1, respectively. The interaction energies of O3 and SO2 with pristine B12N12 are indicative of chemisorption and physisorption, respectively. Ni-decorated B12N12 (Ni@BN) enhances adsorption of both O3 and SO2 species. The interaction energies for adsorption of SO2 are about −166 and −277 kJ mol−1 whereas the corresponding energies for O3 are −362 and −396 kJ mol−1 for configuration A and B, respectively. These observations show that functionalized B12N12 are highly sensitive toward SO2 and O3 molecules. 相似文献
86.
87.
René Schulz 《偏微分方程通讯》2017,42(5):703-730
We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set. 相似文献
88.
A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation 下载免费PDF全文
Zhengguang Liu Aijie Cheng Xiaoli Li 《Numerical Methods for Partial Differential Equations》2017,33(6):2043-2061
In this article, we study fast discontinuous Galerkin finite element methods to solve a space‐time fractional diffusion‐wave equation. We introduce a piecewise‐constant discontinuous finite element method for solving this problem and derive optimal error estimates. Importantly, a fast solution technique to accelerate Toeplitz matrix‐vector multiplications which arise from discontinuous Galerkin finite element discretization is developed. This fast solution technique is based on fast Fourier transform and it depends on the special structure of coefficient matrices. In each temporal step, it helps to reduce the computational work from required by the traditional methods to log , where is the size of the coefficient matrices (number of spatial grid points). Moreover, the applicability and accuracy of the method are verified by numerical experiments including both continuous and discontinuous examples to support our theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2043–2061, 2017 相似文献
89.
90.
采用直接数值模拟(DNS)方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论. 相似文献