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61.
Summary. In shape optimization problems, each computation of
the cost function by the finite element method
leads to an expensive analysis. The use of the second order derivative
can help to reduce the number of analyses. Fujii ([4], [10])
was the first to study this problem. J. Simon [19] gave the second order
derivative for the Navier-Stokes
problem, and the authors describe in [8], [11], a method which gives an
intrinsic expression of the first and second order derivatives on the
boundary
of the involved domain.
In this paper we study higher order derivatives. But one can ask
the following questions:
-- are they expensive to calculate?
-- are they complicated to use?
-- are they imprecise?
-- are they useless?
\medskip\noindent
At first sight, the answer seems to be positive, but classical results of
V. Strassen [20] and J. Morgenstern [13] tell us that the higher order
derivatives are not expensive to calculate, and can be computed
automatically. The purpose of this paper is to give an answer to the third
question by proving that the higher order derivatives of a function can be
computed with the same precision as the function itself.
We prove also that the derivatives so computed are
equal to the derivatives of the discrete problem (see Diagram 1). We
call the discrete
problem the finite dimensional problem processed by the computer. This result
allows the use of automatic differentiation ([5], [6]), which works only on
discrete problems.
Furthermore, the computations of Taylor's expansions
which are proposed at the end of this paper, could be a partial answer to
the last question.
Received January 27, 1993/Revised version received July 20, 1993 相似文献
62.
Genetic diversity and haplotype structure of 21 Y‐STRs,including nine noncore loci,in South Tunisian Population: Forensic relevance 下载免费PDF全文
Faten Makki‐Rmida Arwa Kammoun Nadia Mahfoudh Adnene Ayadi Abdullah Ahmed Gibriel Bakhta Mallek Leila Maalej Zouheir Hammami Samir Maatoug Hafedh Makni Saber Masmoudi 《Electrophoresis》2015,36(23):2908-2913
Y chromosome STRs (Y‐STRs) are being used frequently in forensic laboratories. Previous studies of Y‐STR polymorphisms in different groups of the Tunisian population identified low levels of diversity and discrimination capacity (DC) using various commercial marker sets. This definitely limits the use of such systems for Y‐STRs genotyping in Tunisia. In our investigation on South Tunisia, 200 unrelated males were typed for the 12 conventional Y‐STRs included in the PowerPlex® Y System. Additional set of nine noncore Y‐STRs including DYS446, DYS456, DYS458, DYS388, DYS444, DYS445, DYS449, DYS710, and DYS464 markers were genotyped and evaluated for their potential in improving DC. Allele frequency, gene diversity, haplotype diversity (HD), and DC calculation revealed that DYS464 was the most diverse marker followed by DYS710 and DYS449 markers. The standard panel of 12 Y‐STRs (DC = 80.5%) and the nine markers were combined to obtain DC of 99%. Among the 198 different haplotypes observed, 196 haplotypes were unique (HD = 99.999). Out of the nine noncore set, six Y‐STRs (DYS458, DYS456, DYS449, DYS710, DYS444, and DYS464) had the greatest impact on enhancing DC. Our data provided putative Y‐STRs combination to be used for genetic and forensic applications. 相似文献
63.
Regioselective One‐pot Synthesis of New Unsymmetric Spiro Dihydrofurans in the Reaction of Mixed Two Different Cyclic β‐Dicarbonyl Compounds with BrCN and Aldehydes in the Presence of Et3N 下载免费PDF全文
Crossed one‐pot reaction of mixed cyclic β‐dicarbonyl with various aldehydes in the presence of cyano gen bromide and triethylamine leads to the selective and efficient formation of crossed new unsymmetri cal spiro dihydrofurans at room temperature. The products were obtained in good to excellent yields. Structure elucidation was carried out by 1H NMR, 13C NMR, FT‐IR spectroscopy, Mass analyses and X‐ray crystallography technique. A proposed mechanism was discussed for the formation of products. 相似文献
64.
This paper deals with a characterization of a multivariate stable process using an independence property with a positive random variable. Moreover, we establish a characterization of a multivariate Lévy process based on the notion of cut in a natural exponential family. This allows us to draw some related properties. More precisely, we give the probability density function of this process and the law of the mixture of the Lévy process governed by the convolution semigroup with respect to an exponential random variable. These results are confidentially connected with the univariate case given by [G. Letac and V. Seshadri, Exponential stopping and drifted stable processes, Stat. Probab. Lett., 72:137–143, 2005]. 相似文献
65.
Katritzky AR Abo-Dya NE Abdelmajeid A Tala SR Amine MS El-Feky SA 《Organic & biomolecular chemistry》2011,9(2):596-599
The transprotection of N-Fmoc-cysteine containing di- and tripeptides possessing a free SH group to produce the corresponding S-Fm-cysteine di- and tripeptides bearing a free amino group is accomplished efficiently with DBU in dry THF. The N-Fmoc to S-Fm transformation mechanism is discussed. S-Fm-Cysteine di- and tripeptides readily form amide bonds on coupling with N-(Pg-α-aminoacyl)benzotriazoles and N-(Pg-α-dipeptidoyl)benzotriazoles to give larger peptides. 相似文献
66.
67.
A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value f (V(G)) = ?u ? V(G) f (u){f (V(G)) = \sum_{u\in V(G)} f (u)}. The Roman domination number, γ
R
(G), of G is the minimum weight of a Roman dominating function on G. The Roman bondage number b
R
(G) of a graph G with maximum degree at least two is the minimum cardinality of all sets E¢ í E(G){E^{\prime} \subseteq E(G)} for which γ
R
(G − E′) > γ
R
(G). In this paper we present different bounds on the Roman bondage number of planar graphs. 相似文献
68.
Behzad Ramin Salehi Rad Mohammad Reza Nematollahi Nader 《Methodology and Computing in Applied Probability》2019,21(4):1045-1056
Methodology and Computing in Applied Probability - We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their... 相似文献
69.
Ch. Zgheib E. Nassar M. Hamad R. Nader P. Masri J. Pezoldt G. Ferro 《Superlattices and Microstructures》2006,40(4-6):638
The effect of the germanium coverage prior to the epitaxial growth of 5 μm thick 3C-SiC on Si(100) substrates were evaluated with Atomic Force Microscopy and μ-Raman spectroscopy. The 3C-SiC layers were grown by atmospheric pressure chemical vapor deposition via a special procedure leading to layers with compressive instead of tensile stress. The Ge amount was varied from 0 up to 2 ML. The obtained results showed that the residual stress inside the layers is shifted in the compressive direction; the crystalline quality is improved with the Ge introduction but on the account of the surface roughness. These results open the route for the use of Ge-modified Si(100) as a potential substrate in order to improve the heteroepitaxial growth of 3C-SiC on silicon substrates. 相似文献
70.