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1.
There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.
2.
The reaction of KCN with Al(CH3)3 to form K[Al(CH3)3CN] is greatly facilitated by the presence of an aromatic solvent: for p-xylene a solid complex, K[Al(CH3)3CN]·C6H4(CH3)2, has been isolated. The crystal structure of potassium cyanotrimethylaluminate has been determined from three-dimensional X-ray data measured by counter methods. K[Al(CH3)3CN] crystallizes in the monoclinic space group C2/c with cell dimensions a = 19.902(7), b = 9.211(4), c = 9.615(4) Å, β = 107.74(5)°, and pcalcd. = 1.09 g cm?1 for Z = 8. Least squares refinement gave a conventional weighted R factor of 4.9% for 807 independent reflections. The monomeric [Al(CH3)3CN]? units possess no crystallographic symmetry, and the packing in the unit cell is such that the nitrogen atoms on three such units approach the potassium atom to within 3.11 Å. The average aluminum-methyl carbon bond distance is 1.971 (7) Å, while the aluminum-cyano carbon distance is 2.047 (7) Å. This significant lengthening is attributed to partial electron deficiency in the aluminum-cyano carbon bond. 相似文献
3.
Summary
Existence and unicity for the solution of the one-dimensional two-phase Stefan problem with energy specification
in the liquid phase is established via potential theoretic arguments employing the Schauder fixed point theorem and a contracting map.This work was supported in part by NSF Grant MCS-7801687.This work was carried out at UT-Austin while on sabbatical from the University of Adelaide. 相似文献
4.
Ann M. Schmiedekamp Anthony Ginnetti Brian Piccione Kevin Cannon M. Dominic Ryan 《International journal of quantum chemistry》2007,107(6):1415-1429
Octahedral, six‐coordinate Co2+ can exist in two spin states: S = 3/2 and S = 1/2. The difference in energy between high spin (S = 3/2) and low spin (S = 1/2) is dependent on both the ligand mix and coordination stereochemistry. B3LYP calculations on combinations of neutral imidazole, NH3, and H2O ligands show that low‐spin isomers are stabilized by axial H2O ligands and in structures that also include trans pairs of equatorial NH3 and protonated imidazole ligands, spin crossover structures are predicted from spin state energy differences. Occupied Co d orbitals from the DFT calculations provide a means of estimating effective ligand strength for homoleptic and mixed ligand combinations. These calculations suggest that in a labile biological system, a spin crossover environment can be created. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 相似文献
5.
6.
John T. Cannon 《Communications in Mathematical Physics》1974,35(3):215-233
Nelson's free Markoff field on ? l+1 is a natural generalization of the Ornstein-Uhlenbeck process on ?1, mapping a class of distributions φ(x,t) on ? l ×?1 to mean zero Gaussian random variables φ with covariance given by the inner product \(\left( {\left( {m^2 - \Delta - \frac{{\partial ^2 }}{{\partial t^2 }}} \right)^{ - 1} \cdot , \cdot } \right)_2 \) . The random variables φ can be considered functions φ〈q〉=∝ φ(x,t)q(x,t)d x dt on a space of functionsq(x,t). In the O.U. case,l=0, the classical Wiener theorem asserts that the underlying measure space can be taken as the space of continuous pathst →q(t). We find analogues of this, in the casesl>0, which assert that the underlying measure space of the random variables φ which have support in a bounded region of ? l+1 can be taken as a space of continuous pathst →q(·,t) taking values in certain Soboleff spaces. 相似文献
7.
C.J. Cannon 《Journal of Quantitative Spectroscopy & Radiative Transfer》1973,13(10):1011-1021
The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated. 相似文献
8.
Whereas the rates of propene polymerisation catalysed by zirconocene ion pairs are strongly anion-dependent, hexene polymerisations are not; the findings demonstrate the existence of very different kinetic regimes for two closely related reactions. 相似文献
9.
10.
This paper considers the time dependent stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries: The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments. 相似文献