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21.
We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved. 相似文献
22.
Richard Arratia Bla Bollobs Gregory B. Sorkin 《Journal of Combinatorial Theory, Series B》2004,92(2):199-233
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers. 相似文献
23.
Curtis Bennett Kathy J. Dempsey Bruce E. Sagan 《Journal of Algebraic Combinatorics》1994,3(3):261-283
We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F
q. Another member is constructed so as to mirror the partial order in the subspace lattice. 相似文献
24.
Gyan Bhanot 《Journal of statistical physics》1990,60(1-2):55-75
I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL
d
lattice scales like
. I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity. 相似文献
25.
P. J. Forrester 《Journal of statistical physics》1988,51(3-4):457-479
The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q
2/k
B
T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2. 相似文献
26.
Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N
2
and N
2
+
partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species Th
, electrons Te
, and vibrational T
v
temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =Te/Th
was varied between 1 and 2 as well as the ratio
v
=T
v
/T
h
for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N
2
are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N
+
. The effects of v
and e
on thermodynamic and transport properties of N
2
are then discussed. 相似文献
27.
The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below. 相似文献
28.
According to the experiment results of X-ray diffraction and IR, the reduced partition function ratio (RPFR) and the contribution of various related vibration modes of uranium-crown ether complex (DCH18C6·H_3O)_2UO_2Cl_4 were theoreticallv calculated in detail. The equilibrium constant K_(eq) (that is, the single stage isotopic separation factor α) of exchange reaction for uranium isotopic chemical exchange system UO_2~(2+)(H_2O)_5—(DCH18C6.H_3O)_2UO_2Cl_4 is estimated to be 1.000746 at 12℃ and 1.000672 at 29℃, respectively, which are quite close to the experimental values 1.0010±0.0002 arid 1.0012±0.0004. Theoretical analysis shows that in the course of forming the complex of uranium with crown ether, the coordinated water of uranium is stripped, which performs a key action on the remarkable isotope effect for this system. 相似文献
29.
Partition coefficients P of the HNCS, HNCO and HN3 hydropseudohalic acids between a number of organic solvents and water were determined. It has been found that log P increases with pKa of the acid and with the basicity of the solvent, but the effect of pKa on P is the smaller the more basic is the solvent. The relationships have been explained in terms of hydrogen bond formation between undissociated acid and solvent molecules. H-bonding between the pseudohalic acids and organic solvents has been confirmed by IR spectra on the example of HN3 in benzene. Association constants for H-bonding between the three acids and water, benzene, dibutyl ether and tri-n-butyl phosphate were determined from partition data. It has been found that H-bonding increases with the strength of the acid, whereas the contribution to partition from non-specific interactions with water and organic solvents depends on the molecular surface area of the acid molecule. 相似文献
30.
Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility. 相似文献