Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Bis(5‐hydroxy‐2‐hydroxy­methyl‐4‐pyrone‐κ2O4,O5)bis(2‐hydroxy­methyl‐5‐oxido‐4‐pyrone‐κ2O4,O5)­calcium(II) tetrahydrate

In the title compound, [Ca(C₆H₅O₄)₂(C₆H₆O₄)₂]·4H₂O, which is a kojic acid–Ca²⁺ complex, the Ca atom is on a twofold axis and is octacoordinated by O atoms from four pyrone ligand mol­ecules. The hydroxyl and ketone O atoms of each ligand form a five‐membered chelate ring with the Ca atom. The crystal structure is stabilized by partial stacking and O—H?O hydrogen bonds.     

Magnetic microcapsules for targeted delivery of anticancer drugs

To achieve targeted distribution of anticancer drugs with sustained activity, ferromagnetic ethylcellulose microcapsules containing an anticancer drug, mitomycin C (FM-MMC-mc), were prepared by a method based on phase separation principles. Two prototypes of FM-MMC-mc were made: one with the drug as the core and zinc ferrite on its capsular surface (outer type); the other with both the drug and zinc ferrite as the core (inner type). Both preparations provided a sustained-release property and a sensitive response to conventional magnetic force, although certain differences in the release rate of drug, magnetic responsiveness, and particle size were found between the two dosage forms. Animal studies showed that the magnetic microcapsules could be magnetically controlled in the artery and urinary bladder. VX2 tumors in the rabbit hind limb and urinary bladder were successfully treated with magnetic control of FM-MMC-mc. Pharmacokinetic study revealed that the targeting of the microcapsules markedly enhanced the drug absorption into the surrounding tissues for a prolonged period of time. The results indicate the feasibility and effectiveness of the magnetic microcapsules as a targeted drug delivery system.     

Optimality criterion for a class of nonlinear integer programs

Graver's optimality conditions based on Hilbert bases apply to an integer program with linear equations and a linear objective function. We generalize this result to include a fairly large class of nonlinear objective functions. Our extension provides in particular a link between the superadditivity of the difference-objective function and the Hilbert bases of conic subpartitions of .     

Infrared vibrational autodetachment spectroscopy of microsolvated benzonitrile radical anions

Vibrational spectra of microsolvated benzonitrile radical anions (C6H5CN- -S; S = H2O and CH3OH) were measured by probing the electron detachment efficiency in the 3 microm region, representing resonance bands of autodetachment via OH stretching vibrations of the solvent molecules. The hydrogen-bonded OH band for both the cluster anions exhibited a large shift to the lower energy side with approximately 300 cm-1 compared to those for the corresponding neutral clusters. The solvent molecules are bound collinearly to the edge of the CN group of the benzonitrile anion in the cluster structures optimized with the density functional theory, in which the simulated vibrational energies are in good agreement with the observed band positions. Natural population analyses were performed for a qualitative implication in changes of solvent orientation upon electron attachment. Asymmetric band shapes depending on the vibrational modes are discussed with respect to dynamics of the autodetachment process from a theoretical aspect incorporated with density functional calculations.     

Superquadratic convergence of DLASQ for computing matrix singular values

DLASQ is a routine in LAPACK for computing the singular values of a real upper bidiagonal matrix with high accuracy. The basic algorithm, the so-called dqds algorithm, was first presented by Fernando-Parlett, and implemented as the DLASQ routine by Parlett-Marques. DLASQ is now recognized as one of the most efficient routines for computing singular values. In this paper, we prove the asymptotic superquadratic convergence of DLASQ in exact arithmetic.     

Continuous relaxation for discrete DC programming

Discrete DC programming with convex extensible functions is studied. A natural approach for this problem is a continuous relaxation that extends the problem to a continuous domain and applies the algorithm in continuous DC programming. By employing a special form of continuous relaxation, which is named “lin-vex extension,” the produced optimal solution of the extended continuous relaxation coincides with the solution of the original discrete problem. The proposed method is demonstrated for the degree-concentrated spanning tree problem, the unfair flow problem, and the correlated knapsack problem.     

Grafting of hyperbranched poly(amidoamine) onto carbon black surfaces using dendrimer synthesis methodology

To modify carbon black surface, the surface grafting of hyperbranched poly(amidoamine) onto the surface by using dendrimer synthesis methodology was investigated. Carbon black having amino groups (initiator sites) was prepared by the reduction of surface nitro groups introduced by nitration of aromatic rings. It was found that hyperbranched poly(amidoamine) was propagated from carbon black surface by repeating two processes: (1) Michael addition of methyl acrylate (MA) to surface amino groups and (2) amidation of the resulting esters with ethylenediamine: the percentage of poly(amidoamine) grafting reached to 96.2% after 10th‐generation. The grafting of hyperbranched poly(amidoamine) onto polystyrene‐bead as a model compound of carbon black was also achieved by the above procedures. However, the theoretical propagation of poly(amidoamine) dendrimer was not achieved, because of steric hindrance of grafted polymer. Hyperbranched poly(amidoamine)‐grafted carbon black gave a stable dispersion in a good solvent for poly(amidoamine). Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical indefinite integration by double exponential sinc method

We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with integrand function evaluations is

for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary sinc method. Computational results show the accordance of the actual convergence rates with the theoretical estimate.