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81.
A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented. 相似文献
82.
Molar excess mixing enthalpies h
E
, Gibbs free energies g
E
and hence entropies s
E
have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C
16
. The h
E
and g
E
are negative while Ts
E
are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h
E
and Ts
E
, counterbalanced in the case of Ts
E
by the positive combinatiorial Ts
E
for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h
E
and Ts
E
are now strongly positive, while those of g
E
are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C
16
molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h
E
and Ts
E
are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C
16
segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature. 相似文献
83.
We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research. 相似文献
84.
Basilis Gidas 《Journal of statistical physics》1985,39(1-2):73-131
We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t
0) ast+, with a computable constantC andt
0 the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly. 相似文献
85.
本文在两次标准加入法[1]的基础上,提出了三组份同时测定的三次标准加入法,并应用于钼、钨和钛的流动注射同时测定。测定条件:[水杨基荧光酮(SAF)]=1.25 ×10-4mol/L,[溴化+六烷基三甲基铵(CTMAB)」=2.5×10-3mol/L,pH1.35,25℃,采样、进样时间分别为10s和18s,进样频率128次/h。为消除组份间协同作用引起的吸光度加合性的偏离,定义了三组份协同系数。将其引入三组份同时测定方法,补偿了吸光度对线性的偏离。补偿后钼、钨和钛的测定范围分别为0.05~0.35,0.25~1.00,0.025~0.30mg/L。测定了钢样及模拟样品中钼、钨和钛含量,结果较好。 相似文献
86.
The semiconductive properties of a series of pyrenyl polyenes of the type R-(CH=CH)n-R, are studied as a function of the adsorption of different amount of a vapour. With regard to the compensation temperature
(T
0) the compounds are divided into two groups. For compounds which have odd number of double bonds,T
0 is infinite and in compounds having even number double bonds,T
0 is finite.T
0 for II2 is higher while that of II4 is lower than the experimental temperature. DifferentT
0 for the compounds having odd or even number of double bonds suggests a physical basis for the compensation rule, which we
believe, is related to the molecular and crystalline structure of the compounds 相似文献
87.
Helmut Viernstein Petra Weiss-Greiler Peter Wolschann 《Journal of inclusion phenomena and macrocyclic chemistry》2002,44(1-4):235-240
The solubility enhancement of triflumizole by complexation with -cyclodextrin and with dimethyl--cyclodextrin is compared with respect to the different physico-chemical properties of the host molecules. Although the inclusion reaction constants are rather similar for both complexation reactions, a completely different temperature dependence of the host-guest interaction is observed, which indicates a change of the reaction mechanisms. Moreover, the influence of ethanol as cosolvent is studied. 相似文献
88.
The results of a kinetic investigation of the non-isothermal degradation and the isothermal degradation of the residual deformation
under constant deflection for polychloroprene rubber are presented. A relationship was derived between the degree of non-isothermal
conversion and the value of the investigated mechanical property.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
89.
R. I. Damper Y. Marchand J.-D. S. Marsters A. I. Bazin 《Journal of Sol-Gel Science and Technology》1997,8(2):147-160
A common requirement in speech technology is to align two different symbolic representations of the same linguistic ‘message’.
For instance, we often need to align letters of words listed in a dictionary with the corresponding phonemes specifying their
pronunciation. As dictionaries become ever bigger, manual alignment becomes less and less tenable yet automatic alignment
is a hard problem for a language like English. In this paper, we describe the use of a form of the expectation-maximization
(EM) algorithm to learn alignments of English text and phonemes, starting from a variety of initializations. We use the British
English Example Pronunciation (BEEP) dictionary of almost 200,000 words in this work. The quality of alignment is difficult
to determine quantitatively since no ‘gold standard’ correct alignment exists. We evaluate the success of our algorithm indirectly
from the performance of a pronunciation by analogy system using the aligned dictionary data as a knowledge base for inferring
pronunciations. We find excellent performance—the best so far reported in the literature. There is very little dependence
on the start point for alignment, indicating that the EM search space is strongly convex. Since the aligned BEEP dictionary
is a potentially valuable resource, it is made freely available for research use. 相似文献
90.
The paper compares the numerical performances of the LDL decomposition of the BFGS variable-metric algorithm, the Dennis-Mei dogleg algorithm on the BFGS update, and Davidon's projections with the BFGS update with the straight BFGS update on a number of standard test problems. Numerical results indicate that the standard BFGS algorithm is superior to all of the more complex strategies.This research was supported by the National Science Foundation under Research Grant No. MCS77-07327. 相似文献