The fungus Rhizopus microsporus …? ; shown in the micrograph on the cover picture, harbors the endosymbiotic bacteria Burkholderia rhizoxinica that produces the antimitotic polyketide macrolide rhizoxin (see structure). In their Communication on page 5001 ff. , C. Hertweck and co‐workers show that the enzyme rhizoxin polyketide synthase is uniquely capable of introducing a β branch (highlighted by the magnifying glass) by a Michael‐type addition of a malonyl unit to an acryloyl intermediate.
The question whether or not the sum of two maximal monotone operators is maximal monotone under Rockafellar’s constraint qualification—that
is, whether or not “the sum theorem” is true—is the most famous open problem in Monotone Operator Theory. In his 2008 monograph
“From Hahn-Banach to Monotonicity”, Stephen Simons asked whether or not the sum theorem holds for the special case of a maximal monotone linear operator and
a normal cone operator of a closed convex set provided that the interior of the set makes a nonempty intersection with the
domain of the linear operator. In this note, we provide an affirmative answer to Simons’ question. In fact, we show that the
sum theorem is true for a maximal monotone linear relation and a normal cone operator. The proof relies on Rockafellar’s formula for the Fenchel conjugate of the sum as well as some
results featuring the Fitzpatrick function.
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A new conjugate gradient method is proposed in this paper. For any （inexact） line search, our scheme satifies the sufficient descent property. The method is proved to be globally convergent if the restricted Wolfe-Powell line search is used. Preliminary numerical result shows that it is efficient. 相似文献
Efficient and general conditions for the formation of stereodefined trisubstituted alkenes by using the rhodium‐catalyzed reaction of unactivated Baylis–Hillman adducts with either organoboronic acids or potassium trifluoro(organo)borates are reported (see scheme).
