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排序方式: 共有683条查询结果,搜索用时 265 毫秒
51.
The Poisson induction and coinduction procedures are used to construct Banach Lie–Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie–Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail. 相似文献
52.
The Wiener-Hopf factorization of 2×2 matrix functions and its close relation to scalar Riemann-Hilbert problems on Riemann surfaces is investigated. A family of function classes denoted C(Q1,Q2) is defined. To each class C(Q1,Q2) a Riemann surface Σ is associated, so that the factorization of the elements of C(Q1,Q2) is reduced to solving a scalar Riemann-Hilbert problem on Σ. For the solution of this problem, a notion of Σ-factorization is introduced and a factorization theorem is presented. An example of the factorization of a function belonging to the group of exponentials of rational functions is studied. This example may be seen as typical of applications of the results of this paper to finite-dimensional integrable systems. 相似文献
53.
Kaori Kobayashi Takanori Matsui Shozo Tsunekawa 《Journal of Molecular Spectroscopy》2011,269(2):242-247
The trans-ethyl methyl ether molecule has three low-lying torsional modes, that is, two inequivalent methyl internal rotations and an asymmetric skeletal torsion. The internal rotations of the CCH3 and OCH3 methyl rotors and the skeletal torsion correspond to the vibrational modes, ν28, ν29 and ν30 respectively. In this study, the microwave absorption spectrum in the ν28 = 1 CCH3 torsional state was analyzed for the first time. Nine hundred fifty seven lines up to J = 48 and K = 4 were assigned, and the rotational, centrifugal distortion and internal rotational tunneling parameters were determined with the use of a tunneling matrix formalism. By combining the present results on the ν28 = 1 torsional state with those for the ν30 = 1 skeletal torsional state and the ν29 = 1 OCH3 torsional state, torsional couplings are estimated in order to understand quantitatively the inverted A/E sequence patterns observed for those three excited torsional states. 相似文献
54.
Merlet D Béguin L Courtieu J Giraud N 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2011,209(2):315-322
The application of the G-SERFph pulse sequence is presented on enantiomeric mixtures dissolved in a chiral liquid crystal. It aims at editing, within one single 2D spectrum, every proton coupling which is experienced by a given proton site in the molecule, and leads to real phased T-edited spectroscopy (T=J+2D). This NMR experiment is based on the combination of homonuclear semi-selective refocusing techniques with a spatial frequency encoding of the sample. This approach, which consists in handling selectively each coupling in separate cross sections of the sample, is applied to the visualization of enantiomers dissolved in a chiral liquid crystalline phase. Advantages and limits of this methodology are widely discussed. 相似文献
55.
Jonatan Lenells 《Physica D: Nonlinear Phenomena》2011,240(6):512-525
We consider initial-boundary value problems for the derivative nonlinear Schrödinger (DNLS) equation on the half-line x>0. In a previous work, we showed that the solution q(x,t) can be expressed in terms of the solution of a Riemann-Hilbert problem with jump condition specified by the initial and boundary values of q(x,t). However, for a well-posed problem, only part of the boundary values can be prescribed; the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In general, an effective solution of the problem therefore requires solving the global relation. Here, we present the solution of the global relation in terms of the solution of a system of nonlinear integral equations. This also provides a construction of the Dirichlet-to-Neumann map for the DNLS equation on the half-line. 相似文献
56.
57.
The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda hierarchy. A deep connection with the singular sector of the hodograph equations of the 1-layer Benney (classical long wave equation) hierarchy is stablished. This property is a consequence of the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler-Poisson-Darboux equations. 相似文献
58.
Considered herein is a modified periodic Camassa–Holm equation with cubic nonlinearity which is called the modified μ-Camassa–Holm equation. The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure. Local well-posedness of the initial-value problem to the modified μ-Camassa–Holm equation in the Besov space is established. Existence of peaked traveling-wave solutions and formation of singularities of solutions for the equation are then investigated. It is shown that the equation admits a single peaked soliton and multi-peakon solutions with a similar character of the μ-Camassa–Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and several wave-breaking mechanisms for solutions with certain initial profiles are described in detail. 相似文献
59.
60.
Evaluating the accuracy of theoretical one‐bond 13C─13C scalar couplings and their ability to predict structure in a natural product 下载免费PDF全文
Jacob Powell Domenic Valenti Harley Bobnar Erika Drain Blaine Elliott Sydney Frank Tyler McCullough Sean Moore Andrew Kettring Robbie Iuliucci James K. Harper 《Magnetic resonance in chemistry : MRC》2017,55(11):979-989
This study explores the feasibility of using a combination of experimental and theoretical 1‐bond 13C─13C scalar couplings (1JCC) to establish structure in organic compounds, including unknowns. Historically, nJCC and nJCH studies have emphasized 2 and 3‐bond couplings, yet 1JCC couplings exhibit significantly larger variations. Moreover, recent improvements in experimental measurement and data processing methods have made 1JCC data more available. Herein, an approach is evaluated in which a collection of theoretical structures is created from a partial nuclear magnetic resonance structural characterization. Computed 1JCC values are compared to experimental data to identify candidates giving the best agreement. This process requires knowledge of the error in theoretical methods, thus the B3LYP, B3PW91, and PBE0 functionals are evaluated by comparing to 27 experimental values from INADEQUATE. Respective errors of ±1.2, ±3.8, and ±2.3 Hz are observed. An initial test of this methodology involves the natural product 5‐methylmellein. In this case, only a single candidate matches experimental data with high statistical confidence. This analysis establishes the intramolecular hydrogen‐bonding arrangement, ring heteroatom identity, and conformation at one position. This approach is then extended to hydroheptelidic acid, a natural product not fully characterized in prior studies. The experimental/theoretical approach proposed herein identifies a single best‐fit structure from among 26 candidates and establishes, for the first time, 1 configuration and 3 conformations to complete the characterization. These results suggest that accurate and complete structural characterizations of many moderately sized organic structures (<800 Da) may be possible using only 1JCC data. 相似文献