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1.
Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc and Street in 1970. Many ad hoc solutions to this remarkable shortcoming have been found, but a general theory of compositionality was missing until Petri?, in 2003, introduced the concept of g-dinatural transformations, that is, dinatural transformations together with an appropriate graph: he showed how acyclicity of the composite graph of two arbitrary dinatural transformations is a sufficient and essentially necessary condition for the composite transformation to be in turn dinatural. Here we propose an alternative, semantic rather than syntactic, proof of Petri?'s theorem, which the authors independently rediscovered with no knowledge of its prior existence; we then use it to define a generalised functor category, whose objects are functors of mixed variance in many variables, and whose morphisms are transformations that happen to be dinatural only in some of their variables.We also define a notion of horizontal composition for dinatural transformations, extending the well-known version for natural transformations, and prove it is associative and unitary. Horizontal composition embodies substitution of functors into transformations and vice-versa, and is intuitively reflected from the string-diagram point of view by substitution of graphs into graphs.This work represents the first, fundamental steps towards a substitution calculus for dinatural transformations as sought originally by Kelly, with the intention then to apply it to describe coherence problems abstractly. There are still fundamental difficulties that are yet to be overcome in order to achieve such a calculus, and these will be the subject of future work; however, our contribution places us well in track on the path traced by Kelly towards a calculus of substitution for dinatural transformations.  相似文献   
2.
We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in Girolami (2014), can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.  相似文献   
3.
A ring-down interferometer (RDI) based on a modified Mach–Zehnder structure by incorporating a pair of mirrors with very high reflectivity into each of its two arms, respectively is proposed in this paper. Launching a coherent light pulse into the interferometer, in each arm, pulse ring-down occurs between its two mirrors and outputs a chain of pulses. The two chains of pulses from the two arms combine and interfere pulse by pulse at the detector and the difference of the light phase between the two arms will be enlarged linearly in proportion to the times of ring-down.  相似文献   
4.
The use of an achromatic interferometer is explored as a means of doing in-plane ESPI measurements using a laser diode as the light source. This interferometer type, which uses a diffraction grating in place of the conventional beamsplitter, has two features that make it suitable for making ESPI measurements over extended areas, even when using a low-coherence laser diode source. First, the parallelogram optical geometry of the interferometer causes all rays passing through to have the same optical path lengths. Second, the interferometer is achromatic, whereby the piezo-actuated mirror that steps the illumination light does so by the same phase angle, independent of wavelength. This latter feature accommodates the spectral impurity of a laser diode source. A periodic variation of fringe visibility is observed in experiments, where narrow ranges of high visibility occur at regular spatial intervals. This behavior derives from the clustered discrete spectral character of laser diode light output. A method to “tune” the interferometer by slightly rotating the diffraction grating is described so as to achieve consistent high fringe visibility throughout the measured images.  相似文献   
5.
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switchings between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering nearly periodic regimes that appear close to the cycling chaos due to imperfections or to instability. Using numerical simulations of coupled Lorenz, Roessler, and logistic map models, we show that the coherence is high in the case of imperfection (so that asymptotically the cycling chaos is very regular), while it is low close to instability of the cycling chaos.  相似文献   
6.
In 4F system, compressed sensing is usually implemented by using phase modulation in Fourier domain. In this paper, we present a type of 4F system based on intensity modulation in Fourier domain as the measurement system for compressed sensing. The feasibility of this system is demonstrated. At the point of coherence, the two modulation methods are compared and superiority of intensity modulation in Fourier domain was verified. Simulations are presented and the conclusion we presented is validated. Finally, we analyze the results.  相似文献   
7.
This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.  相似文献   
8.
Starting from the axiomatic definition of finitely maxitive T-conditional possibility (where T is a continuous triangular norm), the paper aims at a comprehensive and self-contained treatment of coherence and extension of a possibilistic assessment defined on an arbitrary set of conditional events. Coherence (or consistence with a T-conditional possibility) is characterized either in terms of existence of a linearly ordered class of finitely maxitive possibility measures (T-nested class) agreeing with the assessment, or in terms of solvability of a finite sequence of nonlinear systems for every finite subfamily of conditional events. Coherence reveals to be a necessary and sufficient condition for the extendibility of an assessment to any superset of conditional events and, in the case of T equal to the minimum or a strict t-norm, the set of coherent values for the possibility of a new conditional event can be computed solving two optimization problems over a finite sequence of nonlinear systems for every finite subfamily of conditional events.  相似文献   
9.
We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system–environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our proposed measure captures the back-flow of information from the environment to the system and compatible with well known distinguishability criteria of non-Markovianity.  相似文献   
10.
王骏  杨蓉  郑娇  赵建林 《光子学报》2016,(4):138-144
提出了利用数字全息干涉术可视化观测液相扩散过程.实验中,采用马赫-曾德干涉仪光路记录乙醇与水之间两相扩散过程的多幅数字全息图;再通过数值再现不同扩散状态的波前相位分布,获得液体中的摩尔浓度分布;最后,根据菲克定律获得两相流扩散系数.结果表明:利用数字全息干涉术可实现对液相扩散传质过程的快速、实时及高精度测量;该方法还具有可实现远程监控、拥有大量微观数据的优点;此外,采用文中全息干涉光路结合波分与角分复用技术可实现多相流扩散系数的测量,为获得溶液中非线性变化特征参量提供了有效技术手段.  相似文献   
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