Stochastic partial differential equations for some measure-valued diffusions

Summary We consider two classes of measure-valued diffusion processes; measure-valued branching diffusions and Fleming-Viot diffusion models. When the basic space is R ¹, and the drift operator is a fractional Laplacian of order 1<α≦2, we derive stochastic partial differential equations based on a space-time white noise for these two processes. The former is the expected one by Dawson, but the latter is a new type of stochastic partial differential equation.     

Double Shrinkage Estimators in the GMANOVA Model

In the GMANOVA model or equivalent growth curve model, shrinkage effects on the MLE (maximum likelihood estimator) are considered under an invariant risk matrix. We first study the fundamental structure of the problem through which we decompose the estimation problem into some conditional problems and then demonstrate some classes of double shrinkage minimax estimators which uniformly dominate the MLE in the matrix risk.     

On the degree and separability of nonconvexity and applications to optimization problems

We study qualitative indications for d.c. representations of closed sets in and functions on Hilbert spaces. The first indication is an index of nonconvexity which can be regarded as a measure for the degree of nonconvexity. We show that a closed set is weakly closed if this indication is finite. Using this result we can prove the solvability of nonconvex minimization problems. By duality a minimization problem on a feasible set in which this indication is low, can be reduced to a quasi-concave minimization over a convex set in a low-dimensional space. The second indication is the separability which can be incorporated in solving dual problems. Both the index of nonconvexity and the separability can be characteristics to “good” d.c. representations. For practical computation we present a notion of clouds which enables us to obtain a good d.c. representation for a class of nonconvex sets. Using a generalized Caratheodory’s theorem we present various applications of clouds.     

Investigation for the cyclization efficiency of linear tetrapeptides: Synthesis of tentoxin B and dihydrotentoxin

Investigation of the cyclization efficiency of N-methyl linear tetrapeptides using a molecular modeling study and chemical synthesis is described. The linear peptide with two N-methyl groups, MeAla-Leu-MePhe-Gly, forms γ-turn like conformation with the amine at N-terminus and the carbonyl at C-terminus in closer proximity to give the desired cyclic tetrapeptide, dihydrotentoxin. In addition, synthesis of tentoxin B by the combination of Fmoc solid-phase peptide synthesis and cyclization in solution phase has been reported. An unusual amino acid, an L-N-methyl-β-hydroxyphenylalanine derivative, which was assembled on solid support, was prepared from ethyl cinnamate. Cyclic tetrapeptide formation and cleavage of benzyl ether were optimized with DIPCI/HOBt/DIPEA and Et₃SiH/Pd(OH)₂, respectively.     

Dual approach to minimization on the set of pareto-optimal solutions

LetX ^* be the set of Pareto-optimal solutions of a multicriteria programming problem. We are interested in finding a vectorxX ^* which minimizes another criterion. SinceX ^* is a nonconvex set, our problem is that of minimization over a nonconvex set. By exploiting the fact that the number of criteria is often very small compared with the number of variables, we use a dual approach to obtain a practical algorithm. We report preliminary numerical results on problems with up to 100 variables and 5 criteria.The authors express their special thanks to Professor H. P. Benson and the referees for many valuable comments and suggestions and for pointing out valuable references. They also thank Dr. Y. Ishizuka for the references of Theorem 2.2.     

Transition metal complexes coordinated by an NAD(P)H model compound and their enhanced hydride-donating abilities in the presence of a base

The ruthenium(II) and rhenium(I) complexes containing an NAD(P)H model compound, 1-benzyl-1,4-dihydronicotinamide (BNAH), as ligand, [Ru(tpy)(bpy)(BNAH)]2+ (1 a) and [Re(bpy)(CO)3(BNAH)]+ (1 b), were quantitatively produced by the reaction of the corresponding metal hydrido complexes with BNA(+) (1-benzylnicotinamidium cation). In the presence of base with pK(a) = 8.9, 1 a and 1 b have much greater reducing power than "free" BNAH. The oxidation potentials of 1 a in the absence and the presence of triethylamine were 0.55 V and -0.04 V, respectively, versus Ag/AgNO(3), whereas that of "free" BNAH was 0.30 V. Spectroscopic results clearly showed that the base extracts a proton from the carbamoyl group on 1 a and 1 b to give the deprotonated BNAH coordinating to the transition-metal complexes [Ru(tpy)(bpy)(BNAH-H+)]+ (3 a) and [Re(bpy)(CO)3(BNAH-H+)] (3 b); this deprotonation underlies the enhancement in reducing ability. The deprotonated forms 3 a and 3 b can efficiently reduce other NAD(P) models to give the corresponding 1,4-dihydro form, resulting in the deprotonated BNA+ being coordinated to the metal complexes [Ru(tpy)(bpy)(BNA(+)-H+)]2+ (2 a) and [Re(bpy)(CO)3(BNA+-H+)]+ (2 b); "free" BNAH and the protonated adducts 1 a and 1 b cannot act in this way. X-ray crystallography was performed on the PF6- salt of 2 a, and showed that the deprotonated nitrogen atom on the carbamoyl group coordinates to the ruthenium(II) metal center with a bond length of 2.086(3) Angstroms. Infrared spectral data suggested that the deprotonated carbamoyl group on the reduced forms 3 a and 3 b is converted to the imido group, and that the oxygen atom coordinates to the metal center.