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1.
An investigation of finite-size scaling for systems with long-range interaction: The spherical model
A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr
–d –
, whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL
d–d×
d
subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities. 相似文献
2.
Georgi R. Grozev 《Numerische Mathematik》1989,56(4):331-343
Summary LetLM
N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x
i
}
1
n
,a <x
1 < ... <x
n
<b and an incidence matrixE = (e
ij
)
i=1
n
,
r-1
j=0
with
Denote byLM
N
O
the subset ofLM
N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL
p-norms inLM
N belong toLM
N
O
.The results are reformulated as comparison theorems for quadrature formulae. 相似文献
3.
The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria. 相似文献
4.
Georgi E. Chernev Bisserka I. Samuneva Petar R. Djambaski Isabel M. M. Salvado Helena V. Fernandes 《Central European Journal of Chemistry》2006,4(1):81-91
In this work we present experimental results about the formation, properties and structure of sol — gel silica based biocomposite
containing Calcium alginate as an organic compound. Two different types of silicon precursors have been used in the synthesis:
tetramethylortosilicate (TMOS) and ethyltrimethoxysilane (ETMS). The samples have been prepared at room temperature. The hybrids
have been synthesized by replacing different quantitis of the inorganic precursor with alginate. The structure of the obtained
hybrid materials has been studied by XRD, IR Spectroscopy, EDS, BET and AFM. The results proved that all samples are amorphous
possessing a surface area from 70 to 290 m2/g. It has also been established by FT IR spectra that the hybrids containing TMOS display Van der Walls and Hydrogen bonding
or electrostatic interactions between the organic and inorganic components. Strong chemical bonds between the inorganic and
organic components in the samples with ETMS are present. A self-organized nanostructure has been observed by AFM. In the obtained
hybrids the nanobuilding blocks average in size at about 8–14 nm for the particles. 相似文献
5.
6.
Krause M Popov VN Inakuma M Tagmatarchis N Shinohara H Georgi P Dunsch L Kuzmany H 《The Journal of chemical physics》2004,120(4):1873-1880
Metal-carbon cage vibrations of crystalline endohedral D2d-M2@C84 (M=Sc,Y,Dy) dimetallofullerenes were analyzed by temperature dependent Raman scattering and a dynamical force field model. Three groups of metal-carbon cage modes were found at energies of 35-200 cm(-1) and assigned to metal-cage stretching and deformation vibrations. They exhibit a textbook example for the splitting of molecular vibrations in a crystal field. Induced dipole-dipole and quadrupole-quadrupole interactions account quantitatively for the observed mode splitting. Based on the metal-cage vibrational structure it is demonstrated that D2d-Y2@C84 dimetallofullerene retains a monoclinic crystal structure up to 550 K and undergoes a transition from a disordered to an ordered orientational state at a temperature of approximately 150 K. 相似文献
7.
The mechanism of the keto-enol tautomerism of malonaldehyde was studied by ab initio methods using 6-21G** and 6-311G** basis functions at the HF level. Two separate mechanisms were examined: through-space proton transfer in the ω-shaped form and through-space proton transfer in a sickle-shaped form obtained from the ω form by rotation. The transition state structure of the ω form is non-planar, whereas that of the sickle form is planar. The sickle form is connected with a 2nd order saddle, indicating that there should exist a lower energy barrier, i.e. that the through-bond mechanism may be preferred. The calculated energy barriers of keto-enol tautomerism for the sickle form is twice as high as those for the omega form. 相似文献
8.
9.
10.
Georgi N. Babatschew 《Fresenius' Journal of Analytical Chemistry》1960,173(2):121-125
Zusammenfassung Es werden Methoden zur Bestimmung der Hauptelemente in den Mutterlaugen bei der Seesalzgewinnung beschrieben. Die Kationen und Anionen werden durch Ionenaustausch in einer Kolonne mit Wofatit KPS-200 in H-Form getrennt. Im Durchlauf werden Chlorid und Sulfat als Summe und Chlorid allein bestimmt. Sulfat wird als Differenz berechnet. Calcium, Magnesium und Eisen bestimmt man komplexometrisch. Die Summe Kalium und Natrium bestimmt man komplexometrisch als Magnesium nach lonenaustausch in einer Wofatit KPS-200-Säule in Mg2+-Form. Natrium wird als Natriumzinkuranylacetat bestimmt, und Kalium ergibt sich aus der Differenz. 相似文献