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Summary Motivated by different mean value properties, the functional equationsf(x) – f(y)/x–y=[(x, y)], (i)xf(y) – yf(x)/x–y=[(x, y)] (ii) (x y) are completely solved when, are arithmetic, geometric or harmonic means andx, y elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).) 相似文献
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Marcel Erné 《Algebra Universalis》1988,25(1):290-321
By a result of Pigozzi and Kogalovskii, every algebraic latticeL having a completely join —irreducible top element can be represented as the lattice L() of equational theories extending some fixed theory . Conversely, strengthening a recent result due to Lampe, we show that such a representationL=L() forcesL to satisfy the following condition: if the top element ofL is the join of a nonempty subsetB ofL then there are elementsb..., B such thata=(... (((b1 a) b2) a) ... bn) a for alla L. In presence of modularity, this equation reduces to the identitya=(a b1) ... (a bn). Motivated by these facts, we study several weak forms of distributive laws in arbitrary lattices and related types of prime elements. The main tool for applications to universal algebra is a generalized version of Lampe's Zipper Lemma.Presented by Ralph Freese. 相似文献
125.
Dénes Petz 《Communications in Mathematical Physics》1988,114(2):345-349
We prove that for the relative entropy of faithful normal states ? and ω on the von Neumann algebraM the formula $$S(\varphi ,\omega ) = \sup \{ \omega (h) - \log \varphi ^h (I):h = h^* \in M\}$$ holds. 相似文献
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L. Käubler W. Enghardt H. Prade P. Carlé L. O. Norlin K. -G. Rensfelt U. Rosengård 《Zeitschrift für Physik A Hadrons and Nuclei》1988,329(2):143-150
Using the reaction138Ba(α,2n)140Ce the magnetic moment of the 10 1 + isomer atE x =3714.7 keV in theN=82 nucleus140Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ N . Measuredg-factors in140Ce are compared to calculations within the shell model with configuration mixing. For the 10 1 + isomer in140Ce the four proton configuration π(1g 7 2/2 ,2d 5 2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d 3/2,π3s 1 2 or π1h 11 2 shells and admixtures of neutron excitations to the wave function of the 10 1 + state could be excluded. The strongE1γ-branch of the deexcitation of the 10 1 + isomer in140Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f 7/2 andπ1h 9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei140Ce,141Pr and145Eu may be understood. 相似文献
127.
The reaction between thiocarbamate herbicides and 2,6-dichlorobenzoquinone-N-chloroimine or 2,6-dibromobenzoquinone-N-chloroimine is suitable for the detection of these herbicides on thin-layer plates with high sensitivity. The reactions were followed by infrared, nuclear magnetic resonance and mass spectrometry. We have established the formation of 2,6-dichlorobenzoquinone-S-alkyl sulphenylimines. In the case of the bromo-derivative, halogen exchange and substitution on the quinone ring took place simultaneously leading to the formation of mixed halogenated 2,6-dihalo- and, in addition, 2,3,6-trihalobenzoquinone-S-alkyl sulphenylimines. The final product of the detection reaction, i.e. 2,6-dichlorobenzoquinone-S-alkyl sulphenylimine was reacted with 2,6-dibromobenzoquinone-N-chloroimine where 2,6-dichloro-3-bromobenzoquinone-S-alkyl sulphenylimine formed as a consequence of the looser bromine-carbon linkage on the 2 and 6 positions of the quinone ring. 相似文献
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