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81.
82.
M. Vaičiulis 《Lithuanian Mathematical Journal》2009,49(2):222-233
In this paper, we introduce an increment ratio statistic (IR
N,m
) based estimator for estimation of the tail index of a heavy-tailed distribution. For i.i.d. observations depending on the
zone of attraction of an α-stable law (0 < α < 2), the IR
N,m
statistic converges to a decreasing function L(α) as both the sample size N and bandwidth parameter m tend to infinity. We obtain a rate of decay of the bias EIR
N,m
−L(α) and mean square error E(IR
N,m
−L(α))2. A central limit theorem (IR
N,m
−EIR
N,m
)⟹ (0,σ2(α)) is also obtained. Monte Carlo simulations show that our tail index estimator has quite good empirical mean square error
and, unlike the Hill estimator, is not so sensitive to a change of bandwidth parameter m.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-25/08. 相似文献
83.
The performance of the so-called superconvergent quantum perturbation theory (Wenhua Hal et al2000 Phys. Rev. A 61 052105) is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z (in atomic units). Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems. 相似文献
84.
Yevgeni S. Mamasakhlisov Ali Naji Rudolf Podgornik 《Journal of statistical physics》2008,133(4):659-681
Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge
disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous
solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely
quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible
thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical
mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it
is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus
a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder
induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the
disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening,
leads to a global attractive instability in the system. 相似文献
85.
Peter Giesl 《Journal of Mathematical Analysis and Applications》2007,335(1):461-479
We consider the general nonlinear differential equation with x∈R2 and develop a method to determine the basin of attraction of a periodic orbit. Borg's criterion provides a method to prove existence, uniqueness and exponential stability of a periodic orbit and to determine a subset of its basin of attraction. In order to use the criterion one has to find a function W∈C1(R2,R) such that LW(x)=W′(x)+L(x) is negative for all x∈K, where K is a positively invariant set. Here, L(x) is a given function and W′(x) denotes the orbital derivative of W. In this paper we prove the existence and smoothness of a function W such that LW(x)=−μ‖f(x)‖. We approximate the function W, which satisfies the linear partial differential equation W′(x)=〈∇W(x),f(x)〉=−μ‖f(x)‖−L(x), using radial basis functions and obtain an approximation w such that Lw(x)<0. Using radial basis functions again, we determine a positively invariant set K so that we can apply Borg's criterion. As an example we apply the method to the Van-der-Pol equation. 相似文献
86.
Bai Xiaoming; Yang Xiao-Song; Li Huimin 《IMA Journal of Mathematical Control and Information》2007,24(4):483-491
87.
提出了一种新型高效太阳能聚光镜, 这种聚光镜用一组特定系数, a2, a4, a6, a8, a10, a12, a14, a16 与 C的高次柱面内壁的一部分作为反射镜. 利用高次柱面方程和光反射定律, 推导出了在高次柱面内壁上太阳反射光束的方向矢量与高次柱面系数C, a2,a4, a6, a8, a10, a12, a14, a16的关系, 通过优化设计这些系数, 可以使入射到高次柱面内壁上的太阳光束反射后全部聚焦在一条与柱面母线平行的宽度很窄的线段上, 形成线聚光. 这组特定系数用粒子群优化算法求得, 并经计算机模拟证明其聚焦效果. 用这组特定系数的高次柱面作为聚光镜, 其对光的压缩比可达148倍, 其线性光斑可作为一种强光源或高温光源. 高次柱面反射镜可由金属或玻璃直接磨制而成, 也可由高次柱面骨架和铺设在骨架上的镀铝聚酯薄膜构成.
关键词:
太阳能聚光镜
高次柱面
多项式系数优化
线性聚焦 相似文献
88.
89.
本文讨论了周期结构复合材料特征值的多尺度计算,提出了高阶多尺度Rayleigh商校正算法,并给出了收敛性分析. 最后,通过大量数值实验结果表明,新算法是有效且必要的. 相似文献
90.
Weak pullback attractors are defined for non-autonomous difference inclusions and their existence and upper semi continuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for (at least) a single trajectory rather than all trajectories at each starting point. The concept is thus useful, in particular, for discrete time control systems. 相似文献