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71.
This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc. 相似文献
72.
基于Aguado等人拟合的APW势能面(PES), 运用准经典轨线(QCT)方法, 对反应Li+HF(ν=0, j=0)→LiF+H的动力学性质进行了计算. 主要研究了不同碰撞能条件下的反应截面、转动取向、产物散射角分布和竞争反应模式等. 结果表明, 该反应存在直接提取型和间接插入型两种反应模式, 在低能量下反应以间接插入反应模式为主, 能量大于200 meV时则以直接提取反应为主. 相似文献
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74.
M.S. Child 《Contemporary Physics》2013,54(3):212-221
Monodromy (or once round) is a classical property of integrable dynamical systems in two or more degrees of freedom, which imposes a characteristic pattern on the quantum mechanical eigenvalue distribution. This article explains the connection by showing how the presence of an isolated critical point of the Hamiltonian leads to a classical action function that is multi-valued with respect to energy and angular momentum. Consequently, by the Bohr correspondence principle between actions and quantum numbers, there can be no uniquely defined global system of quantum numbers. Implications for the interpretation of highly excited molecular spectra are brought out by reference to quasi-linear molecules, which transfer one degree of freedom from rotational to vibrational motion during the excitation process. Emphasis is placed on the simplest examples, while a brief resumé of the wide scope of the quantum monodromy phenomenon is given in the final section. 相似文献
75.
Nonlinear two-point boundary-value problems (TPBVP) can be reduced to the iterative solution of a sequence of linear problems by means of quasilinearization techniques. Therefore, the efficient solution of linear problems is the key to the efficient solution of nonlinear problems.Among the techniques available for solving linear two-point boundary-value problems, the method of particular solutions (MPS) is particularly attractive in that it employs only one differential system, the original nonhomogeneous system, albeit with different initial conditions. This feature of MPS makes it ideally suitable for implementation on parallel computers in that the following requirements are met: the computational effort is subdivided into separate tasks (particular solutions) assigned to the different processors; the tasks have nearly the same size; there is little intercommunication between the tasks.For the TPBVP, the speedup achievable is ofO(n), wheren is the dimension of the state vector, hence relatively modest for the differential systems of interest in trajectory optimization and guidance. This being the case, we transform the TPBVP into a multi-point boundary-value problem (MPBVP) involvingm time subintervals, withm–1 continuity conditions imposed at the interface of contiguous subintervals. For the MPBVP, the speedup achievable is ofO(mn), hence substantially higher than that achievable for the TPBVP. It reduces toO(m) if the parallelism is implemented only in the time domain and not in the state domain.A drawback of the multi-point approach is that it requires the solution of a large linear algebraic system for the constants of the particular solutions. This drawback can be offset by exploiting the particular nature of the interface conditions: if the vector of constants for the first subinterval is known, the vector of constants for the subsequent subintervals can be obtained with linear transformations. Using decomposition techniques together with the discrete version of MPS, the size of the linear algebraic system for the multi-point case becomes the same as that for the two-point case.Numerical tests on the Intel iPSC/860 computer show that substantial speedup can be achieved via parallel algorithms vis-a-vis sequential algorithms. Therefore, the present technique has considerable interest for real-time trajectory optimization and guidance.Dedicated to the Memory of Professor Jan M. SkowronskiThis paper, based on Refs. 1–3, is a much condensed version of the material contained in these references.The technical assistance of the Research Center on Parallel Computation of Rice University, Houston, Texas is gratefully acknowledged. 相似文献
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77.
利用准经典轨线理论 ,在BW 2和G3两个势能面上 ,研究了Cl +HD反应的动力学 .计算结果表明 ,产物的转动取向对势能面及反应体系的质量因子非常敏感 .在BW 2势能面上 ,计算的两个产物的转动取向强于在G3势能面上计算的结果 ,而无论是在BW 2势能面上还是在G3势能面上 ,DCl产物的取向都强于HCl产物的取向 .计算结果还表明 ,在不同的势能面上反应物的转动激发对反应的影响有着显著的不同 .在BW 2势能面上 ,反应物的初始转动激发有利于Cl+HD反应的进行 ;而在G3势能面上 ,反应物的初始转动激发消弱了反应的反应性 相似文献
78.
我们在无限维空间中研究微分包含的生存W—单调轨道的存在性.基于Zorn引理,我们给出了一个逼近方法,在较弱的条件下得到了一个存在性定理,其特殊情形则包含了已有的生存定理和微分方程理论中的若干结果作为应用,我们首先研究了微分包含生存解的整体存在性,得到了整体生存理.然后我们研究了微分包含解的稳定性,得到一些新的结果. 相似文献
79.
该文研究微分包含单调轨道的存在性.基于一个新的逼近方法,作者证明了无限维空间中的一个存在性,其特殊情形包含了已有的若于生存定理. 相似文献
80.
Shuxiang Yu 《中国科学A辑(英文版)》1997,40(6):572-577
Using the notion of an isolating block, some existence criteria of trajectories connecting two critical pints of planar dynaniiral
systems are given.
Project supported by the National Natural Science Foundation of China. 相似文献