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61.
Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schr?dinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers. 相似文献
62.
In this paper, we identify q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions with a specialization of the Macdonald polynomials. This provides a representation of q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions in terms of the Demazure characters of affine Lie algebra
[^(\mathfrakgl)]l+1{\widehat{\mathfrak{gl}}_{\ell+1}}. We also define a system of dual Hamiltonians for q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Toda chains and give a new integral representation for the q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions. Finally, we represent the q-deformed
\mathfrakgll+1{\mathfrak{gl}_{\ell+1}}-Whittaker function as a matrix element of a quantum torus algebra. 相似文献
63.
We propose a general scheme of constructing braided differential algebras via algebras of “quantum exponentiated vector fields” and those of “quantum functions”. We treat a reflection equation algebra as a quantum analog of the algebra of vector fields. The role of a quantum function algebra is played by a general quantum matrix algebra. As an example we mention the so-called RTT algebra of quantized functions on the linear matrix group GL(m). In this case our construction essentially coincides with the quantum differential algebra introduced by S. Woronowicz. If the role of a quantum function algebra is played by another copy of the reflection equation algebra we get two different braided differential algebras. One of them is defined via a quantum analog of (co)adjoint vector fields, the other algebra is defined via a quantum analog of right-invariant vector fields. We show that the former algebra can be identified with a subalgebra of the latter one. Also, we show that “quantum adjoint vector fields” can be restricted to the so-called “braided orbits” which are counterparts of generic GL(m)-orbits in gl∗(m). Such braided orbits endowed with these restricted vector fields constitute a new class of braided differential algebras. 相似文献
64.
65.
66.
Dimitri Leemans 《Journal of Geometry》2010,97(1-2):83-97
We classify the rank two BCDL 2003-geometries of O’Nan and show that the maximal rank of a BCDL 2003-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985). 相似文献
67.
Convective instability in the cross-field system of thermonuclear reactors can be overridden by poloidal drifts. While in crossed fields, a long-time, large-scale turbulent regime, in which the eddies of some particular size are destined to persist longer than usual, would come into being. Perhaps, we may keep such vortexes using them as tools for maintaining the stability of still an illusory construct of plasma fusion. 相似文献
68.
We study the existence of radially symmetric solitary waves for a system of a nonlinear Klein–Gordon equation coupled with Maxwell's equation in presence of a positive mass. The nonlinear potential appearing in the system is assumed to be positive and with more than quadratical growth at infinity. 相似文献
69.
Dr. Jelena D. Nikolić Dr. Sebastian Wouters Dr. Julia Romanova Dr. Akihiro Shimizu Prof. Dr. Benoît Champagne Prof. Dr. Thomas Junkers Prof. Dr. Dirk Vanderzande Prof. Dr. Dimitri Van Neck Prof. Dr. Michel Waroquier Prof. Dr. Veronique Van Speybroeck Prof. Dr. Saron Catak 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(52):19176-19185
Despite various studies on the polymerization of poly(p‐phenylene vinylene) (PPV) through different precursor routes, detailed mechanistic knowledge on the individual reaction steps and intermediates is still incomplete. The present study aims to gain more insight into the radical polymerization of PPV through the Gilch route. The initial steps of the polymerization involve the formation of a p‐quinodimethane intermediate, which spontaneously self‐initiates through a dimerization process leading to the formation of diradical species; chain propagation ensues on both sides of the diradical or chain termination occurs by the formation of side products, such as [2.2]paracyclophanes. Furthermore, different p‐quinodimethane systems were assessed with respect to the size of their aromatic core as well as the presence of heteroatoms in/on the conjugated system. The nature of the aromatic core and the specific substituents alter the electronic structure of the p‐quinodimethane monomers, affecting the mechanism of polymerization. The diradical character of the monomers has been investigated with several advanced methodologies, such as spin‐projected UHF, CASSCF, CASPT2, and DMRG calculations. It was shown that larger aromatic cores led to a higher diradical character in the monomers, which in turn is proposed to cause rapid initiation. 相似文献
70.
Vanfleteren D Ghillemijn D Van Neck D Bultinck P Waroquier M Ayers PW 《Journal of computational chemistry》2011,32(16):3485-3496
For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree-Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren et al., J Chem Phys 2010, 132, 164111). Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. As the Hartree-Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads to a corresponding partitioning of the Hartree-Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions. 相似文献