Dynamic Generalized Assignment Problems with Stochastic Demands and Multiple Agent--Task Relationships

The assignment problem is a well-known operations research model. Its various extensions have been applied to the design of distributed computer systems, job assignment in telecommunication networks, and solving diverse location, truck routing and job shop scheduling problems.This paper focuses on a dynamic generalization of the assignment problem where each task consists of a number of units to be performed by an agent or by a limited number of agents at a time. Demands for the task units are stochastic. Costs are incurred when an agent performs a task or a group of tasks and when there is a surplus or shortage of the task units with respect to their demands. We prove that this stochastic, continuous-time generalized assignment problem is strongly NP-hard, and reduce it to a number of classical, deterministic assignment problems stated at discrete time points. On this basis, a pseudo-polynomial time combinatorial algorithm is derived to approximate the solution, which converges to the global optimum as the distance between the consecutive time points decreases. Lower bound and complexity estimates for solving the problem and its special cases are found.     

On the boundary limits of monotone Sobolev functions in variable exponent Orlicz spaces

Our aim in this note is to deal with boundary limits of monotone Sobolev functions with ▽u∈ Lp(·)logLq(·)(B) for the unit ball BRn. Here p(·) and q(·) are variable exponents satisfyingthe log-Hlder and the log log-Hlder conditions, respectively.     

Topological aspects of excitons in artificial structure

The exciton properties of thin nanotube structures are investigated theoretically. Anisotropic size dependencies have been found in the exciton binding energy, the kinetic energy for the relative motions of an electron and a hole, and the wavefunction. These anisotropies arise from the different boundary conditions in the tube-length and circumferential directions, namely, the topological features of nanotubes. We also found that it is possible to change the topology of exciton wavefunctions by varying the tube-length and the tube-radius. These findings suggest that the optical properties of nanotubes such as oscillator strength or nonlinear susceptibilities can be controlled by tuning the structural parameters, thus yielding a novel guiding principle for designing optical functional materials.     

Direct Estimation of the Surface Location of Immobilized Functional Groups for Concerted Catalysis Using a Probe Molecule

The location of active sites during concerted catalysis by a metal complex and tertiary amine on a SiO₂ surface is discussed based on the interaction between the functionalized SiO₂ surface and a probe molecule, p‐formyl phenylboronic acid. The interactions of the probe molecule with the surface functionalities, diamine ligand, and tertiary amine, were analyzed by FT‐IR and solid‐state ¹³C and ¹¹B MAS NMR. For the catalyst exhibiting high 1,4‐addition activity, the diamine ligand and tertiary amine base exist in closer proximity than in the catalyst with low activity.     

Regioselective protection of sugars catalyzed by dimethyltin dichloride

The first catalytic process for protection of hydroxyl groups in sugars has been developed. Highly regioselective protection was accomplished along with high chemical yield. The regioselectivity of the benzoylation was realized as an intrinsic character of sugars based on a stereorelationship among their hydroxyl groups. Furthermore, complete protection of alpha-methyl glucoside and beta-methyl xyloside was accomplished.     

Preparation and characterization of poly(l-phenylalanine) chiral stationary phases with varying peptide length

Three new chiral stationary phases with different lengths of l-phenylalanine peptide were prepared by solid-phase synthesis with tert-butoxycarbonyl (Boc)-l-phenylalanine on silica. The effect of phenylalanine peptide length on enantioselectivity was studied. The best separation of R/S-warfarin was achieved by the chiral stationary phase with intermediate peptide length. These stationary phases were found to exist mainly in alpha-helical conformation by using FT-IR spectra. The end-capping reagents for the N-terminus of the peptide were also evaluated.     

Trapping of a dopaquinone intermediate in the TPQ cofactor biogenesis in a copper-containing amine oxidase from Arthrobacter globiformis

The biogenesis of the topaquinone (TPQ) cofactor of copper amine oxidase (CAO) is self-catalyzed and requires copper and molecular oxygen. A dopaquinone intermediate has been proposed to undergo 1,4-addition of a copper-associated water molecule to form the reduced form of TPQ (TPQ(red)), followed by facile oxidation by O(2) to yield the mature TPQ (TPQ(ox)). In this study, we have incorporated a lysine residue in the active site of Arthrobacter globiformis CAO (AGAO) by site-directed mutagenesis to produce D298K-AGAO. The X-ray crystal structure of D298K-AGAO at 1.7-A resolution revealed that a covalent linkage formed between the epsilon-amino side chain of Lys298 and the C2 position of a dopaquinone derived from Tyr382, a precursor to TPQ(ox). We assigned the species as an iminoquinone tautomer (LTI) of lysine tyrosylquinone (LTQ), the organic cofactor of lysyl oxidase (LOX). The time course of the formation of LTI at pH 6.8 was followed by UV/vis and resonance Raman spectroscopies. In the early phase of the reaction, an LTQ-like intermediate was observed. This intermediate then slowly converted to LTI in an isosbestic manner. Not only is the presence of a dopaquinone intermediate in the TPQ biogenesis confirmed, but it also provides strong support for the proposed intermediacy of a dopaquinone in the biogenesis of LTQ in LOX. Further, this study indicates that the dopaquinone intermediate in AGAO is mobile and can swing from the copper site into the active-site wedge to react with Lys298.     

Scheduling of corrugated paper production

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.     

Conformational changes during apoplastocyanin folding observed by photocleavable modification and transient grating

A new method to investigate the initial protein folding dynamics is developed based on a pulsed laser light triggering method and a unique transient grating method. The side chain of the cysteine residue of apoplastocyanin (apoPC) was site-specifically modified with a 4,5-dimethoxy-2-nitrobenzyl derivative, where the CD and 2D NMR spectra showed that the modified apoPC was unfolded. The substituent was cleaved with a rate of about 400 ns by photoirradiation, which was monitored by the disappearance of the absorption band at 355 nm and the increase in the transient grating signal. After a sufficient time from the photocleavage reaction, the CD and NMR spectra showed that the native beta-sheet structure was recovered. Protein folding dynamics was monitored in the time domain with the transient grating method from a viewpoint of the molecular volume change and the diffusion coefficient, both of which reflect the global structural change, including the protein-water interaction. The observed volume decrease of apoPC with a time scale of 270 micros is ascribed to the initial hydrophobic collapse. The increase in the diffusion coefficient (23 ms) is considered to indicate a change from an intermolecular to an intramolecular hydrogen bonding network. The initial folding process of apoPC is discussed based on these observations.