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71.
We prove that the quantum double of the quasi-Hopf algebra of dimension attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] to a simple complex Lie algebra and a primitive root of unity q of order n2 is equivalent to Lusztig's small quantum group (under some conditions on n). We also give a conceptual construction of using the notion of de-equivariantization of tensor categories. 相似文献
72.
73.
Pavel Materna 《Acta Analytica》2013,28(3):295-319
To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. 相似文献
74.
We consider extensions of certain states. The states are defined on the systems of sets that are closed under the formation of the symmetric difference (concrete quantum logics). These systems can be viewed as certain set‐representable quantum logics enriched with the symmetric difference. We first show how the compactness argument allows us to extend states on Boolean algebras over such systems of sets. We then observe that the extensions are sometimes possible even for non‐Boolean situations. On the other hand, a difference‐closed system can be constructed such that even two‐valued states do not allow for extensions. Finally, we consider these questions in a σ‐complete setup and find a large class of such systems with rather interesting state properties. 相似文献
75.
Kimon Fountoulakis Jacek Gondzio Pavel Zhlobich 《Mathematical Programming Computation》2014,6(1):1-31
We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA, $\mathbf{\ell _1\_\ell _s}$ , PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an ${\mathcal {O}}(n^3)$ computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in $\mathbf{\ell _1\_\ell _s}$ and PDCO softwares. We go a few steps further. First, we use the matrix-free IPM, an approach which redesigns IPM to avoid the need to explicitly formulate (and store) the Newton equation systems. Secondly, we exploit the special features of the signal processing matrices within the matrix-free IPM. Two such features are of particular interest: an excellent conditioning of these matrices and the ability to perform inexpensive (low complexity) matrix–vector multiplications with them. Computational experience with large scale one-dimensional signals confirms that the new approach is efficient and offers an attractive alternative to other state-of-the-art solvers. 相似文献
76.
Pavel Kurasov 《Journal d'Analyse Mathématique》2009,107(1):251-286
The extension theory for semibounded symmetric operators is generalized by including operators acting in a triplet of Hilbert
spaces. We concentrate our attention on the case where the minimal operator is essentially self-adjoint in the basic Hilbert
space and construct a family of its self-adjoint extensions inside the triplet. All such extensions can be described by certain
boundary conditions, and a natural counterpart of Krein’s resolvent formula is obtained. 相似文献
77.
We describe a method for construction of jump analogues of certain one-dimensional diffusion processes satisfying solvable stochastic differential equations. The method is based on the reduction of the original stochastic differential equations to the ones with linear diffusion coefficients, which are reducible to the associated ordinary differential equations, by using the appropriate integrating factor processes. The analogues are constructed by means of adding the jump components linearly into the reduced stochastic differential equations. We illustrate the method by constructing jump analogues of several diffusion processes and expand the notion of market price of risk to the resulting non-affine jump-diffusion models. 相似文献
78.
Natalia Selivanova Aidar Gubaidullin Pavel Padnya Ivan Stoikov Yuriy Galyametdinov 《Liquid crystals》2019,46(3):415-421
Supramolecular organised materials were prepared from nonionic surfactants and the following macrocyclic ionic liquids: n-tert-butylthiacalix[4]arenes containing quaternary ammonium fragments with amino acid substituents. Tetraethylene glycol monododecyl ether and decadiethylene glycol monododecyl ether were used as nonionic surfactants. They form lamellar and hexagonal mesophases in aqueous media, respectively. Liquid crystal and structural properties of these systems were studied. Intermolecular interactions of system components leading to formation of lyomesophases were estimated. Molecular structure of thiacalixarene contributes to the formation of a hydrogen bonding with surfactants. This process, in turn, initiates formation of a denser packed hexagonal structure. 相似文献
79.
Rabindranath Lo Anna Mašínová Maximilián Lamanec Dana Nachtigallová Pavel Hobza 《Journal of computational chemistry》2023,44(3):329-333
Here, the effect of solvent on the stability of non-covalent complexes, was studied. These complexes were from previously published S22, S66, and X40 datasets, which include hydrogen-, halogen- and dispersion-bonded complexes. It was shown that the charge transfer in the complex determines whether the complex is stabilized or destabilized in solvent. 相似文献
80.
The design of catalysts for the chemical recycling of plastic waste will benefit greatly from an intimate knowledge of the interfacial polymer–catalyst interactions that determine reactant and product distributions. Here, we investigate backbone chain length, side chain length, and concentration effects on the density and conformation of polyethylene surrogates at the interface with Pt(111) and relate them to experimental product distributions resulting from carbon–carbon bond cleavage. Using replica-exchange molecular dynamics simulations, we characterize the polymer conformations at the interface by the distributions of trains, loops, and tails and their first moments. We find that the preponderance of short chains, in the range of 20 carbon atoms, lies entirely on the Pt surface, whereas longer chains exhibit much broader distributions of conformational features. Remarkably, the average length of trains is independent of the chain length but can be tuned via the polymer–surface interaction. Branching profoundly impacts the conformations of long chains at the interface as the distributions of trains become less dispersed and more structured, localized around short trains, with the immediate implication of a wider carbon product distribution upon C–C bond cleavage. The degree of localization increases with the number and size of the side chains. Long chains can adsorb from the melt onto the Pt surface even in melt mixtures containing shorter polymer chains at high concentrations. We confirm experimentally key computational findings and demonstrate that blends may provide a strategy to reduce the selectivity for undesired light gases.The design of catalysts for the chemical recycling of plastic waste will benefit greatly from an intimate knowledge of the interfacial polymer–catalyst interactions that determine reactant and product distributions. 相似文献