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221.
    
In this paper, we consider the first order Hardy inequalities usingsimple equalities. This basic setting not only permits to derive quickly manywell-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edgeLaplacian, or the Grushin type operator.  相似文献   
222.
    
This paper deals with an integral of non-convolution type involving Meijer's G-function in the kernel, which depends on variables, one of which is a parameter. L2-properties and relation with the Kontorovich-Lebedev transform are given  相似文献   
223.
袁歆懿  陈菊  田强 《力学学报》2024,58(8):2351-2363

多刚体系统动力学的指标-1微分代数方程组仅包含加速度级别约束方程, 未考虑位移和速度约束方程. 数值积分过程中位移和速度约束违约逐渐增加, 导致计算结果精度下降, 需引入约束稳定方法减小约束违约. 首先根据Hamilton变分原理, 建立了SE(3)描述的多刚体系统动力学模型. 其次给出4种约束稳定方法在SE(3)上形式: Baumgarte方法、罚函数方法、增广拉格朗日方法和约束违约增强稳定方法. 相较于传统多刚体系统动力学建模, 基于SE(3)的动力学建模可描述转动对平动的耦合效应, 能更精确地模拟系统的动力学行为, 可提升约束稳定方法的性能. 在SE(3)框架下, 将4种约束稳定方法与RKMK (Runge-Kutta Munthe-Kass)数值方法结合, 对含位移约束和速度约束的动力学方程进行求解. 最后通过两个动力学算例: 含球铰的空间双球摆算例以及含圆柱铰的曲柄滑块机构算例, 分别给出了4种约束稳定方法在SE(3)上对动力学系统的位移和速度约束违约的修正对比结果, 并分析了系统能量的变化图. 结果表明: SE(3)框架下, 4种约束稳定方法结合RKMK算法均表现出良好的保结构和保能量性质, 其中SE(3)上增广拉格朗日方法所得位移和速度约束违约较小, 总能量保持情况更好; SE(3)上Baumgarte方法能更好地平衡系统计算效率和精度.

  相似文献   
224.
We establish the energy equality for Leray–Hopf weak solutions of the 3D incompressible inhomogeneous Navier–Stokes equations in Lorentz–Besov spaces. This result may be regarded as an extension of that by Cheskidov and Luo (2020).  相似文献   
225.
    
In this paper we investigate an optimal investment problem under short-selling and portfolio insurance constraints faced by a defined contribution pension fund manager who is loss averse. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the S-shaped utility, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.  相似文献   
226.
227.
    
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints – we recall the mathematical construction in the context of so called implicit Lagrangian systems. We explain how they can be used to produce new numerical methods, that we call Dirac integrators. On a test example of a simple pendulum in a gravity field we compare the Dirac integrators with classical explicit and implicit methods, we pay special attention to conservation of constrains. Then, on a more advanced example of the Ziegler‐type system we show that the choice of numerical methods can indeed affect the conclusions of qualitative analysis of the dynamics of mechanical systems. We also tell why we think that Dirac integrators are appropriate for this kind of systems by explaining the relation with the notions of geometric degree of non‐conservativity and kinematic structural stability.  相似文献   
228.
    
In this paper, we present a direct B‐spline spectral collocation method to approximate the solutions of fractional optimal control problems with inequality constraints. We use the location of the maximum of B‐spline functions as collocation points, which leads to sparse and nonsingular matrix B whose entries are the values of B‐spline functions at the collocation points. In this method, both the control and Caputo fractional derivative of the state are approximated by B‐spline functions. The fractional integral of these functions is computed by the Cox‐de Boor recursion formula. The convergence of the method is investigated. Several numerical examples are considered to indicate the efficiency of the method.  相似文献   
229.
    
The UV finiteness found in calculations of the 4‐point amplitude in supergravity at loop order has not been explained, which motivates our study of the relevant superspace invariants and on‐shell superamplitudes for both and . The local 4‐point superinvariants for are expected to have nonlinear completions whose 6‐point amplitudes have non‐vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For , we find at that local 6‐point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4‐point counterterm and thus gives a plausible explanation of the observed finiteness. However, at we construct a local 6‐point superinvariant with non‐vanishing SSL's, so the SSL argument does not explain the observed UV finiteness. For supergravity there are no 6‐point invariants at either or 4, so the SSL argument predicts UV finiteness.  相似文献   
230.
    
We constrain cosmological parameters using only Hubble parameter data and quantify the impact of future Hubble parameter measurements on parameter estimation for the most typical dark energy models. We first constrain cosmological parameters using 52 current Hubble parameter data including the Hubble constant measurement from the Hubble Space Telescope. Then we simulate the baryon acoustic oscillation signals from WFIRST (Wide-Field Infrared Survey Telescope) covering the redshift range of z ∈[0.5,2] and the redshift drift data from E-ELT (European Extremely Large Telescope) in the redshift range of z ∈[2,5]. It is shown that solely using the current Hubble parameter data could give fairly good constraints on cosmological parameters. Compared to the current Hubble parameter data, with the WFIRST observation the H(z) constraints on dark energy would be improved slightly, while with the E-ELT observation the H(z) constraints on dark energy is enormously improved.  相似文献   
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