Kernel-based interpolation at approximate Fekete points

Numerical Algorithms - We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal...     

Right preconditioned MINRES for singular systems†

We consider solving large sparse symmetric singular linear systems. We first introduce an algorithm for right preconditioned minimum residual (MINRES) and prove that its iterates converge to the preconditioner weighted least squares solution without breakdown for an arbitrary right‐hand‐side vector and an arbitrary initial vector even if the linear system is singular and inconsistent. For the special case when the system is consistent, we prove that the iterates converge to a min‐norm solution with respect to the preconditioner if the initial vector is in the range space of the right preconditioned coefficient matrix. Furthermore, we propose a right preconditioned MINRES using symmetric successive over‐relaxation (SSOR) with Eisenstat's trick. Some numerical experiments on semidefinite systems in electromagnetic analysis and so forth indicate that the method is efficient and robust. Finally, we show that the residual norm can be further reduced by restarting the iterations.     

Inclusion of aliphatic alcohols in pockets of (S)-threonyl-(S)-phenylglycine using grinding method

Inclusion compounds of a dipeptide, (S)-threonyl-(S)-phenylglycine (Thr-Phg), with several aliphatic alcohols were easily prepared by grinding them in a mortar. Thr-Phg molecules arranged in antiparallel to construct a sheet, and guest alcohols were accommodated in a chiral pocket between the sheets. 3-Butyn-2-ol and 2-butanol were included with moderate enantioselectivity, 57% ee (R) and 49% ee (R), respectively. The role of the hydroxy group of Thr-Phg is not only to construct the unique pocket but also to capture guest alcohols by hydrogen bonding.     

Recent development for enantioselective synthesis of aromatic compounds from alkynes via metallacyclopentadienes

Metallacyclopentadiene, which is recognized as a metallo‐heterocycle, is an important intermediate for the formation of aromatic derivatives. In this short review, we summarized the recent advance on construction of axial, central, planar, and helical chirality by transition‐metal‐catalyzed aromatic compounds formation via metallacyclopentadienes. J. Heterocyclic Chem., (2011).     

Novel Flavonoids in Dragon's Blood of Daemonorops draco

The three novel methylene bis[flavonoids] 1 – 3 , the novel 2‐flavene 4 , the new naturally occurring flavan 5 , and the new retro‐dihydrochalcone 6 were isolated from dragon's blood of Daemonorops draco, together with seven known compounds. The structures were elucidated by extensive 1D‐ and 2D‐NMR spectroscopic analysis.     

Trace inequalities for products of matrices

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.     

Synthesis and lectin-binding activity of luminescent silica particles peripherally functionalized with lactose

A novel O-protected lactose (Galβ1→4Glcβ1-) derivative bearing trimethoxysilyl group at the aglycon was developed as a silane coupling agent. Reaction of the coupling agent with tris(2,2′-bipyridine)ruthenium (II) dichloride (Rubpy) doped silica particle gave a Rubpy-doped silica particle peripherally functionalized with O-protected lactose derivative. De-O-protection of the particle with aqueous ammonia provided lactose-coating Rubpy-doped silica particles, combining luminophor encapsulated in silica matrix and carbohydrate having lectin-recognition ability. Specific adhesion of fluorescein isothiocyanate-labeled peanut agglutinin (FITC-PNA) to the lactose-coating Rubpy-doped silica particles was confirmed by fluorescence microscopic analysis.     

Topological Self-similarity on the Random Binary-Tree Model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.