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71.
We investigate via density functional theory (DFT) the appearance of small MgO-supported gold clusters with 8 to 20 atoms in a scanning tunneling microscope (STM) experiment. Comparison of simulations of ultrathin films on a metal support with a bulk MgO leads to similar results for the cluster properties relevant for STM. Simulated STM pictures show the delocalized states of the cluster rather than the atomic structure. This finding is due to the presence of s- derived delocalized states of the cluster near the Fermi energy. The properties of theses states can be understood from a jellium model for monovalent gold. 相似文献
72.
It is well-known that (ℤ+, |) = (ℤ+, GCD, LCM) is a lattice, where | is the usual divisibility relation and GCD and LCM stand for the greatest common divisor
and the least common multiple of positive integers.
The number $
d = \prod\nolimits_{k = 1}^r {p_k^{d^{(k)} } }
$
d = \prod\nolimits_{k = 1}^r {p_k^{d^{(k)} } }
is said to be an exponential divisor or an e-divisor of $
n = \prod\nolimits_{k = 1}^r {p_k^{n^{(k)} } }
$
n = \prod\nolimits_{k = 1}^r {p_k^{n^{(k)} } }
(n > 1), written as d |
e
n, if d
(k) for all prime divisors p
k
of n. It is easy to see that (ℤ+\{1}, |
e
is a poset under the exponential divisibility relation but not a lattice, since the greatest common exponential divisor (GCED)
and the least common exponential multiple (LCEM) do not always exist. 相似文献
73.
Timo Tossavainen Pentti Haukkanen Martti Pesonen 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1117-1130
In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare. 相似文献
74.
75.
Pentti Haukkanen 《数学研究与评论》1997,(2)
AClasofRationalArithmeticalFunctionswithCombinatorialMeaningsPentiHaukkanen(Dept.ofMath.Scis.,Univ.ofTampere,P.O.Box607,FIN-... 相似文献
76.
Chemical analysis is a multi-stage process, which starts with primary sampling and ends with evaluation of the resuts. Especially in trace analysis and microanalysis of solid materials, sampling can far outweigh all other sources of error. For estimating the reliability of complete analytical procedures, a method is needed which can be used to estimate the errors made in the primary and the secondary sampling and sample preparation steps. Based on Gy's theory of sampling, a computer program (SAMPEX) was written for the solution of practical sampling problems. The method involves the estimation of the sampling constant, C. For well-characterized materials, C can be estimated from the material properties. If the necessary material properties are difficult to estimate, C can be evaluated experimentally. The program can be used to solve the following problems: minimum sample size for a tolerated relative standard deviation of the fundamental sampling error; relative size for a tolerated for a given sample size; maximum particle size of the material for a specified standard deviation and sample size; balanced design of a multi-stage sampling and sample-reduction process; and sampling for particle size determination. 相似文献
77.
Summary LetA be a regular arithmetical convolution andk a positive integer. LetA
k
(r) = {d: d
k
A(r
k
)}, and letf A
k
g denote the convolution of arithmetical functionsf andg with respect toA
k
. A pair (f, g) of arithmetical functions is calledadmissible if(f A
k
g)(m) 0 for allm and if the functions satisfy an arithmetical functional equation which generalizes the Brauer—Rademacher identity. Necessary and sufficient conditions are found for a pair (f, g) of multiplicative functions to be admissible, and it follows that, if(f A
k
g)(m) 0 f(m) for allm, then (f, g) is admissible if and only if itsdual pair (f A
k
g, g
–1
) is admissible.Iff andg
–1
areA
k
-multiplicative (a condition stronger than being multiplicative), and(f A
k
g)(m) 0 for allm, then (f, g) is admissible, calledCohen admissible. Its dual pair is calledSubbarao admissible. If (f A
k
g)
–1
(m) 0 itsinverse pair (g
–1
, f
–1
) is also Cohen admissible.Ifg is a multiplicative function then there exists a multiplicative functionf such that the pair (f, g) is admissible if and only if for everyA
k
-primitive prime powerp
i
either (i)g(p
i
) 0 or (ii)g(p
) = 0 for allp
havingA
k
-type equal tot. There is a similar kind of characterization of the multiplicative functions which are first components of admissible pairs of multiplicative functions. IfA
k
is not the unitary convolution, then there exist multiplicative functionsg which satisfy (i) and are such that neitherg norg
–1 isA
k
-multiplicative: hence there exist admissible pairs of multiplicative functions which are neither Cohen admissible nor Subbarao admissible.An arithmetical functionf is said to be anA
k
-totient if there areA
k
-multiplicative functionsf
T
andf
V
such thatf = f
T
A
k
f
V
-1
Iff andg areA
k
-totients with(f A
k
g)(m) 0 for allm, and iff
V
= g
T
, then the pair (f, g) is admissible. The class of such admissible pairs includes many pairs which are neither Cohen admissible nor Subbarao admissible. If (f, g) is a pair in this class, and iff(m), (f A
k
g)
–1
(m), g
–1
(m),f
–1
(m) andg(m) are all nonzero for allm, then its dual, its inverse, the dual of its inverse, the inverse of its dual and the inverse of the dual of its inverse are also admissible, and in many cases these six pairs are distinct.A number of related results, and many examples, are given. 相似文献
78.
Pentti Oksman Géza Stájer Kalevi Pihlaja Mati Karelson 《Journal of the American Society for Mass Spectrometry》1994,5(2):113-119
Electron impact ionization mass spectrometry indicates that the behavior of W-unsubstituted pyrirnidin-4-ones with CH2-R type substitution at C-2 differs from homologs that are N-substituted and/or 2-aryl- or 2-methyl-substituted. A dominant intramolecular cycliza-tion was found to occur between 3ZV (in agreement with the predominance of the 3NH tautomers) and the ortho positions of the aryl moiety in compounds with a CH2-aryl substitution at C-2. Theoretical calculations with an AMI SCFR method on 2-, 6-, and 2, 6-disubstituted pyrimidin-4-ones support the mass spectrometric observations. 相似文献
79.
Pekka Juusola Pentti Minkkinen Lasse Leino Jarmo K. Laihia 《Monatshefte für Chemie / Chemical Monthly》2007,38(11):951-965
(E)- and (Z)-Urocanic acids are endogenous chemicals in the normal mammalian skin. The first and the second thermodynamic dissociation
constants (pK
a1 and pK
a2) of urocanic acid isomers were determined using UV spectrophotometry in aqueous solutions. The values with standard deviation
(pK
a1 = 3.43 ± 0.12 and pK
a2 = 5.80 ± 0.04) and (pK
a1 = 2.7 ± 0.3 and pK
a2 = 6.65 ± 0.04) were obtained to (E)- and (Z)-urocanic acids, respectively. The second dissociations were studied also by potentiometric titration in aqueous sodium chloride
solutions up to the isotonic salt concentration (0.154 mol dm−3), and the second thermodynamic dissociation constants as well as activity parameters for both isomers were determined at
temperature 25°C and for (E)-urocanic acid also at 37°C. The obtained pK
a2 values were close to those found by UV spectrophotometry. The equations for the calculation of the second stoichiometric
dissociation constants of urocanic acid isomers on molality and molarity scale in aqueous sodium chloride solutions were derived.
The obtained pK
a1 and pK
a2 values for (Z)-urocanic acid appear to be essentially lower than some previously reported values in literature. 相似文献
80.
Kalevi Pihlaja Pentti Kuosmanen Pirjo Vainiotalo 《Journal of mass spectrometry : JMS》1988,23(11):770-776
The electron-impact-induced mass spectra of 1,3-dioxolane (la), 1,3-dithiolane (2a) and 1,3-oxatbiolane (3a) and their 2-methyl (1b–3b) and 2,2-dimethyl [(CH3)2: 1c–3c or (CD3)2: 1d–3d] derivatives have been studied in detail to gain further insight into their ion structures and competing reaction pathways with low-resolution, high-resolution, metastable and collision-induced dissociation (CID) techniques. For compounds 1a–1d the most significant reaction is loss of H˙ and CH3˙ by α-cleavage and a subsequent formation of CHO+ and C2H3O+ ions. The [M ? H]+ ions from 1a and 1b give a C2H3O+ ion which does not have the acyl cation structure as shown by their CID spectra. In compounds 3a–3d the sulphur-containing ions predominate, the C2H3O+ now having the acyl cation structure. 1,3-Dithiolanes (2a–2d) exhibit the most complicated fragmentation patterns. Furthermore the [M ? H]+ ion from 2a and [M ? CH3]+ ion from 2b have different structures as well as the [M ? H]+ ion from 2b and [M ? CH3]+ ion from 2c, as shown by their CID spectra. This can be utilized to explain why 3a–3c and 2a give principally a thiiranyl cation, whereas 2b gives a mixture of this and the thioacyl cation and 2c practically only the open-chain thioacetyl cation. 相似文献