The penalized Fischer-Burmeister SOC complementarity function

In this paper, we study the properties of the penalized Fischer-Burmeister (FB) second-order cone (SOC) complementarity function. We show that the function possesses similar desirable properties of the FB SOC complementarity function for local convergence; for example, with the function the second-order cone complementarity problem (SOCCP) can be reformulated as a (strongly) semismooth system of equations, and the corresponding nonsmooth Newton method has local quadratic convergence without strict complementarity of solutions. In addition, the penalized FB merit function has bounded level sets under a rather weak condition which can be satisfied by strictly feasible monotone SOCCPs or SOCCPs with the Cartesian R ₀₁-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations.     

Mann-Whitney test for associated sequences

Let {X ₁, ...,X _m } and {Y ₁, ...,Y _n } be two samples independent of each other, but the random variables within each sample are stationary associated with one dimensional marginal distribution functionsF andG, respectively. We study the properties of the classical Wilcoxon-Mann-Whitney statistic for testing for stochastic dominance in the above set up.     

Biosynthesis of (+)-,(-)- and (±)-tetrahydropalmatines

Specific incorporation of didehydroreticuline and reticuline into (±)- (+)-, and (-)-tetrahydropalmatines in Cocculus laurifolius and of (R)- and (S)-reticulines into (R)- and (S)-tetrahydropalmatines respectively has been demonstrated. Feeding of[l-³H, 4'-methoxy-¹⁴C]reticuline suggested that reticuline was not converted in the plants into didehydroreticuline and racemisation of optically active forms of tetrahydropalmatine did not take place via dehydrotetrahydropalmatine     

Biosynthesis of tetrahydropalmatine and palmatine

The incorporation of (±)-norlaudanosoline, norprotosinomenine, nororientaline, norlaudanidine, reticuline and laudanosine into tetrahydropalmatine and palmatine has been studied, and specific utilization of reticuline demonstrated. Feeding of (±)-[N-methyl-¹⁴C] reticuline showed that C atom 8 of tetrahydropalmatine and palmatine are formed by oxidative cyclisation of the N-Me group of reticuline. Parallel experiments with (R)-; and (S)-, reticulines demonstrated specific incorporation of (R)- isomer into these bases. Feeding experiments also revealed that the plants can convert tetrahydropalmatine into palmatine with high efficiency.     

Optimal ship navigation with safety distance and realistic turn constraints

We consider the optimal ship navigation problem wherein the goal is to find the shortest path between two given coordinates in the presence of obstacles subject to safety distance and turn-radius constraints. These obstacles can be debris, rock formations, small islands, ice blocks, other ships, or even an entire coastline. We present a graph-theoretic solution on an appropriately-weighted directed graph representation of the navigation area obtained via 8-adjacency integer lattice discretization and utilization of the A^∗ algorithm. We explicitly account for the following three conditions as part of the turn-radius constraints: (1) the ship’s left and right turn radii are different, (2) ship’s speed reduces while turning, and (3) the ship needs to navigate a certain minimum number of lattice edges along a straight line before making any turns. The last constraint ensures that the navigation area can be discretized at any desired resolution. Once the optimal (discrete) path is determined, we smoothen it to emulate the actual navigation of the ship. We illustrate our methodology on an ice navigation example involving a 100,000 DWT merchant ship and present a proof-of-concept by simulating the ship’s path in a full-mission ship handling simulator.     

Stereocalpin A, a bioactive cyclic depsipeptide from the Antarctic lichen Stereocaulon alpinum

A new cyclic depsipeptide stereocalpin A (1) has been isolated from the MeOH extract of the Antarctic lichen Stereocaulon alpinum by various chromatographic methods. The structure of stereocalpin A (1) was mainly determined by analysis of the NMR spectroscopic data and by chemical methods. Stereocalpin A (1) is a unique cyclic peptide incorporating an unprecedented 5-hydroxy-2,4-dimethyl-3-oxo-octanoic acid in the structure. Stereocalpin A (1) shows moderate cytotoxicity against three human solid tumor cell lines.