EBC‐219: A New Diterpene Skeleton,Crotinsulidane, from the Australian Rainforest Containing a Bridgehead Double Bond

EBC‐219 ( 4 ), isolated from Croton insularis (Baill), was established by spectroscopic and DFT methods as the first member of a new diterpene skeletal class, uniquely defined by the presence of a bicyclo[10.2.1] bridgehead olefin. The proposed biogenetic pathway to 4 from the co‐isolated natural products EBC‐131 ( 1 ), EBC‐180 ( 2 ) and EBC‐181 ( 3 ) is highly likely. EBC‐180 ( 2 ) and EBC‐181 ( 3 ) showed moderate to strong cytotoxic activity against various cancer cell lines.     

Mortar method for matching grids in a mixed scheme as applied to the biharmonic equation

Nitsche’s mortar method for matching grids in the Hermann-Miyoshi mixed scheme for the biharmonic equation is considered. A two-parameter mortar problem is constructed and analyzed. Existence and uniqueness theorems are proved under certain constraints on the parameters. The norm of the difference between the solutions to the mortar and original problems is estimated. The convergence rates are the same as in the Hermann-Miyoshi scheme on matching grids.     

The Nitsche mortar method for matching grids in a mixed finite element method

It is well-known that nonmatching grids are often used in finite element methods. Usually, grids are being matched along lines or surfaces that divide a domain into subdomains. Such lines or surfaces are called interfaces. The interface matching means the satisfaction of some continuity conditions when crossing the interface. The direct matching procedures fall into three groups: Methods that use Lagrange multipliers, mortar methods based on the Nitsche technique, and penalty methods.     

Isolation and confirmation of the proposed cleistanthol biogentic link from Croton insularis

The proposed cleistanthol biosynthetic intermediate en route to spruceanol, and other related family members, was isolated for the first time from Croton insularis, confirming the Jacobs-Reynolds hypothesis. Anticancer evaluation of the new isolates and their aerial oxidation products is also reported.