Denote by W (T ), r(T ) and ‖T‖ the numerical range, the numerical radius and the spectral norm of a complex matrix T . Let (A,B) be a pair of Hermitian matrices. It is shown that if 0 ∈ W (A+ iB) then d(A,B) = inf{|μ| : μ / ∈ W (A+ iB)} is an upper bound for inf{r(E + iF ) : (A+ E) + i(B + F ) is diagonalizable by congruence}; if 0 / ∈ W (A+ iB) then the Crawford number c(A,B) = min{|μ| : μ ∈ ...

G row th o f the unicellular b lue-green alga Anacystis nidulans in m edia containing sublethal concentrations o f D C M U -typ e inhibitors o f p hotosynthetic electron transport in strong w hite light gave rise to shade type appearance in this organism , as characterized by an increased ratio o f phycocyanin to chlorophyll and reduced ratios, b oth , o f carotenoids to chlorophyll and o f tot...

R e i n e r L u c k e n b a c h u n d N i k o l a u s M ü l l e r [1] Organisch-Chemisches Institut der Universität Mainz Z . Naturforsch. 34b, 464 -480 (1979); eingegangen am 10. A u g u s t / 1 9 . Dezember 1978 R ing Opening, W o o d w a r d H o f f m a n n Rules, Allylic Cations, Dimerisation, 1,5-Hexadienes React ion of cyc lopropyl halides with sodium iodide in acetone [i.e. under typical...

Let F be a union-closed family of subsets of an m-element set A. Let n = |F| ≥ 2. For b ∈ A let w(b) denote the number of sets in F containing b minus the number of sets in F not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over ...

We show that the positive part of a result on interpolation by Bloch functions due to B. Bøe and A. Nicolau is a direct consequence of C. Sundberg’s description of the traces of BMOA functions on interpolating sequences for H∞. The Bloch space B consists of all the analytic functions f in the unit disk D of the complex plane such that ‖f‖B = sup z∈D (1− |z|)|f ′(z)| < ∞. Recall that the hyperbo...

* This investigation was supported by research grant CA-4557 from the National Cancer Institute, U.S. Public Health Service (for the Cincinnati laboratory), and USPHS grants E-1992 and C-4965 (for the Boston laboratory). 1 Huebner, R. J., W. P. Rowe, H. C. Turner, and W. T. Lane, these PROCEEDINGS, 50, 379 (1963). 2 Sabin, A. B., and M. A. Koch, these PROCEEDINGS, 50, 407 (1963). 3 Black, P. H....

J. J. Becker, G. T. Blaylock, T. Bolton, J. S. Brown, K. 0. Bunnell, T. H. Burnett, R. E. Cassell, D. Coffman, V. Cook, D. H. Coward, D. E. Dorfan, G. Dubois, A. L. Duncan, G. Eigen, K. F. Einsweiler, D. Favart, B. I. Eiscnsteiu, T. fieese, G. Gladding, C. Grab, F. Grancagnolo, A. D. Guy, R. P. Hamilton, J. Hauser, C. A. Heusch, D. G. Hitlin, L. K6pke, W. S. Lo&man, U. Mall&, C. G. Matthews, P....

T h e title is an EITHER OR question . T h e p ap e r w ill p robab ly reveal th a t the an sw er m u st be BOTH -A N D . In th is p ap er a report w ill be g iven o f th e w ork w ith the p ro jec t ‘N orw eg ian le a rn e rs ’ p rob lem s w ith E ng lish prosody . N orw eg ian -E ng lish i n t o n a t i o n T h e focus w ill b e o n h in d ran ces m et w ith , w hen chang ing from an auditive...

F. Adlkofer, S. Agulnik, D. Arndt, L. Bassi, J. S. Bedford, Μ. Α. Bender, C. G. Bingham, J. J. W. A. Boei, R. Bonomi, A. Bosi, B. G. Brown, P. R. Bryant, C. R. E. Coggins, S. P. Colyer, T. Cremer, F. Darroudi, D. Dichiara, M. Digweed, D. J. Doolittle, Μ. E. Drets, R. Drouin, S. Du Manoir, J. E. Duarte, Α . A. Edwards, H. Fender, Μ . Fenech, P. Finnon, Μ. Fiore, G. Α. Folie, Ε. L. Frome, F. Gens...