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21.
22.
KONG Dexing 《数学年刊A辑(中文版)》2000,21(4):413-440
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow” decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data. 相似文献
23.
This paper investigates the relations between theorems of the alternative and the minimum norm duality theorem. A typical theorem of the alternative is associated with two systems of linear inequalities and/or equalities, a primal system and a dual one, asserting that either the primal system has a solution, or the dual system has a solution, but never both. On the other hand, the minimum norm duality theorem says that the minimum distance from a given point z to a convex set
is equal to the maximum of the distances from z to the hyperplanes separating z and
. We consider the theorems of Farkas, Gale, Gordan, and Motzkin, as well as new theorems that characterize the optimality conditions of discrete l
1-approximation problems and multifacility location problems. It is shown that, with proper choices of
, each of these theorems can be recast as a pair of dual problems: a primal steepest descent problem that resembles the original primal system, and a dual least–norm problem that resembles the original dual system. The norm that defines the least-norm problem is the dual norm with respect to that which defines the steepest descent problem. Moreover, let y solve the least norm problem and let r denote the corresponding residual vector. If r=0, which means that z
, then y solves the dual system. Otherwise, when r0 and z
, any dual vector of r solves both the steepest descent problem and the primal system. In other words, let x solve the steepest descent problem; then, r and x are aligned. These results hold for any norm on
. If the norm is smooth and strictly convex, then there are explicit rules for retrieving x from r and vice versa. 相似文献
24.
生物声纳的高灵敏度和高可靠性一直是仿生设计所追求的目标, 然而至今仍没有一个令人信服的物理模型能很好得解释生物声纳优越性能的原因, 其主要是缺乏对动物听觉系统神经信息编码的认识. 本文从蝙蝠听觉神经系统的生理结构出发, 用圆映射和符号动力学方法讨论了蝙蝠听觉神经系统在复杂环境中处理多普勒信号的一种可能性方案, 并通过计算机仿真证明了其合理性. 针对蝙蝠神经系统的不稳定性, 用符号动力学的方法分析神经系统信息处理的机理具有良好的鲁棒性和高灵敏度. 这种新的信号处理方法的研究, 为生物声纳信号的处理过程的进一步认识提供了一种新的解释. 相似文献
25.
饮用水激光拉曼光谱的比较与分析 总被引:1,自引:1,他引:1
为了对我国目前饮用水的质量进行有效检测,对市面上几种常用品牌的饮用水以及实验室提供的蒸馏水等样品做了测量和计算。运用激光拉曼光谱的分析方法,测量了它们的激光拉曼光谱。同时,通过测量计算了样品在对称伸缩振动处拉曼谱的退偏度。结果表明,在水样品的对称伸缩振动处,其拉曼谱的相对强度大小和退偏度的大小有着相同的规律。对结果进行比较和分析后得出了如下结论:可以从拉曼光谱特征峰相对强度的大小和同一特征峰下退偏度的大小两方面来判断饮用水中矿物质含量的相对多少。为鉴定饮用水的质量提供了新的有效途径。 相似文献
26.
近年来, 硅烯(单层硅)由于其独特的结构和电子性质以及在量子霍尔效应等领域的潜在应用而成为理论和实验研究的一个热点. 借助于四带次近邻紧束缚模型, 详细计算和研究了硅烯中受电场调制的体能隙和电子能级. 结果表明: 硅烯原胞中的两个子格处于不同的平面上, 可以通过外电场区分和控制这两个子格, 这将破坏在纯石墨烯中无法被破坏的K-K'对称性, 并消除由这一对称性导致的电子能级的二重简并; 外加电场还会引起硅烯中次近邻格点之间的Rashba自旋轨道耦合, 这一作用会在不同狄拉克点有选择地消除电子能级在部分电场点的简并, 相邻能级从交叉状态变为反交叉状态; 电子能级中除一些孤立的交叉点外, 每个能级都具有确定的自旋取向, 石墨烯中电子能级的四重简并在硅烯中被完全消除, 从而导致填充因子ν=0, ±1, ±2, ±3,…的量子霍尔平台. 相似文献
27.
We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html. 相似文献
28.
Ionut Ciocan-Fontanine 《Transactions of the American Mathematical Society》1999,351(7):2695-2729
We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263-277). We also give a geometric proof of the quantum Monk formula.
29.
The known CEPA variants CEPA (v) withv = 0,1,2,3 and two new ones withv = 4, 5 are compared both formally and for various numerical examples with CP-MET. The main conclusions are: 1. In those situations
where both CP-MET and the CEPA variants are justified (i.e. for “good” closed shell states) the correlation energies obtained
with the 7 different schemes differ very little (by something like ±2%), with CEPA (1) closest to CP-MET (difference usually
a fraction of 1%) and CEPA (4) nearly as close; this is rather insensitive to whether one uses canonical or localized orbitals.
Even CEPA (3) is not too far from CP-MET, which confirms an earlier suggestion of Kelly. 2. In those cases where one of the
7 schemes fails (e.g. due to near degeneracy as in covalent molecules at large internuclear distances) the other 6 usually
fail as well, though CEPA (0) is then somewhat poorer than the other schemes. Then no longer CEPA (1) but rather CEPA (3)
is closest to CP-MET and then all schemes converge much better in a localized representation. 3. CEPA (2) usually leads to
best agreement with experiment since it simulates to some extent triple substitutions. In none of the studied examples does
CP-MET show a significant superiority as compared to the other schemes. Possible improvements to extend the domain of applicability
of these methods are discussed. 相似文献
30.
D. Blume Chris H. Greene 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(1):83-86
We analyze various microscopic calculations of vibrational frequencies for 4HeN clusters, N = 3-728. The lowest breathing frequency with total angular momentum J = 0 varies smoothly as a function of N, with a maximum around N = 50-120.
Received 11 July 2001 相似文献