Circular Chromatic Indices of Regular Graphs

The circular chromatic index of a graph G, written , is the minimum r permitting a function such that whenever e and are adjacent. It is known that for any , there is a 3‐regular simple graph G with . This article proves the following results: Assume is an odd integer. For any , there is an n‐regular simple graph G with . For any , there is an n‐regular multigraph G with .     

Genetic-algorithm-based simulation optimization considering a single stochastic constraint

In this paper, we consider the discrete optimization via simulation problem with a single stochastic constraint. We present two genetic-algorithm-based algorithms that adopt different sampling rules and searching mechanisms, and thus deliver different statistical guarantees. The first algorithm offers global convergence as the simulation effort goes to infinity. However, the algorithm’s finite-time efficiency may be sacrificed to maintain this theoretically appealing property. We therefore propose the second heuristic algorithm that can take advantage of the desirable mechanics of genetic algorithm, and might be better able to find near-optimal solutions in a reasonable amount of time. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing ones.     

Approximately global optimization for assortment problems using piecewise linearization techniques

Recently, Li and Chang proposed an approximate model for assortment problems. Although their model is quite promising to find approximately global solution, too many 0–1 variables are required in their solution process. This paper proposes another way for solving the same problem. The proposed method uses iteratively a technique of piecewise linearization of the quadratic objective function. Numerical examples demonstrate that the proposed method is computationally more efficient than the Li and Chang method.     

In situ preparation of high relaxivity iron oxide nanoparticles by coating with chitosan: A potential MRI contrast agent useful for cell tracking

Iron oxide nanocrystals are of considerable interest in nanoscience and nanotechnology because of their nanoscale dimensions, nontoxic nature, and superior magnetic properties. Colloidal solutions of magnetic nanoparticles (ferrofluids) with a high magnetite content are highly desirable for most molecular imaging applications. In this paper, we present a method for in situ coating of superparamagnetic iron oxide (SPIO) with chitosan in order to increase the content of magnetite. Iron chloride salts (Fe³⁺ and Fe²⁺) were directly coprecipitated inside a porous matrix of chitosan by Co-60 γ-ray irradiation in an aqueous solution of acetic acid. Following sonication, iron oxide nanoparticles were formed inside the chitosan matrix at a pH value of 9.5 and a temperature of 50 °C. The [Fe³⁺]:[Fe²⁺]:[NH₄OH] molar ratio was 1.6:1:15.8. The final ferrofluid was formed with a pH adjustment to approximately 2.0/3.0, alongside with the addition of mannitol and lactic acid. We subsequently characterized the particle size, the zeta potential, the iron concentration, the magnetic contrast, and the cellular uptake of our ferrofluid. Results showed a z-average diameter of 87.2 nm, a polydispersity index (PDI) of 0.251, a zeta potential of 47.9 mV, and an iron concentration of 10.4 mg Fe/mL. The MRI parameters included an R1 value of 22.0 mM⁻¹ s⁻¹, an R2 value of 202.6 mM⁻¹ s⁻¹, and a R2/R1 ratio of 9.2. An uptake of the ferrofluid by mouse macrophages was observed. Altogether, our data show that Co-60 γ-ray radiation on solid chitosan may improve chitosan coating of iron oxide nanoparticles and tackle its aqueous solubility at pH 7. Additionally, our methodology allowed to obtain a ferrofluid with a higher content of magnetite and a fairly unimodal distribution of monodisperse clusters. Finally, MRI and cell experiments demonstrated the potential usefulness of this product as a potential MRI contrast agent that might be used for cell tracking.     

Hard nanocomposite comprising stereoregular syndiotactic polypropylene with chemically bonded gold nanoparticles

An effective method to synthesize directly a hard composite material containing uniformly dispersed nanogold particles chemically bonded with a stereospecific, crystalline polymer matrix has been developed. Syndiotactic polypropylene was synthesized and functionalized to have a hydroxyl terminal group (sPP_OH) via a metallocene catalysis with a selective chain transfer. Next, sPP_OH was activated to react with ethylene sulfide forming the thiol‐terminated polymer, sPP_SH. sPP_SH was then chemically bonded to gold nanoparticles (AuNPs) formed in situ via a reduction of HAuCl₄. The bonding between thiol and AuNP stabilized the AuNPs and led to the formation of sPP_AuNPs composite containing uniformly‐dispersed AuNPs of a 19–40 nm size without noticeable aggregation. Furthermore, the chemical bonding of AuNPs has afforded sPP_AuNPs a thermal degradation temperature (T_D) 49.4 °C higher than the pristine sPP or sPP_OH and 25.7 °C higher than sPP_SH without any adverse effect on the crystalline temperature and melting temperature. In addition, the characteristic UV‐Vis absorption wavelength of sPP_AuNPs remains the same at various temperatures, thus indicating the independence of optical property on temperature as well as the good thermal stability of the sPP_AuNPs composite. ¹H NMR, ¹³C NMR, FESEM, STEM, XPS, TGA and DSC were used to investigate the molecular structure, morphology and thermal properties of the resulting sPP_AuNPs nanocomposite. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

An Improved Fuzzy Modeling Method for a Class of Multi-Input Non-affine Nonlinear Systems

In this paper, an improved fuzzy modeling method is developed for a class of non-affine nonlinear systems. The idea comes from the concepts of the optimization tools and the Takagi–Sugeno fuzzy modeling technique. Specifically, this method is suitable especially for non-affine nonlinear systems. Two benchmark single-input and one multi-input non-affine nonlinear systems are illustrated to show that the proposed modeling scheme is superior to existing modeling methods.     

A reusable CuSO4 · 5H2O/cationic 2,2′‐bipyridyl system catalyzed homocoupling of terminal alkynes in water

A reusable CuSO₄ · 5H₂O/cationic 2,2′‐bipyridyl system catalyzed the homocoupling reaction of terminal alkynes in water using I₂ as the additive in the presence or absence of tetrabutylammonium bromide, giving the 1,3‐diynes in good to high yields. After reaction, the residual aqueous solution could be reused several times. Copyright © 2011 John Wiley & Sons, Ltd.     

A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the viscosity theory introduced by Crandall and Lions. However, we need to pay special attention both analytically and numerically to prevent the zero level curve from overturning so that it can be interpreted as the graph of a function. We demonstrate our Lax-Friedrichs type numerical methods for computing the L-solution using its original level set formulation. In addition, we couple our numerical methods with a singular diffusive term which is essential to computing solutions to a more general class of HJ equations that includes conservation laws. With this singular viscosity, our numerical methods do not require the divergence structure of equations and do apply to more general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using weighted ENO local Lax-Friedrichs methods as developed recently by Jiang and Peng. We verify that our numerical solutions approximate the proper viscosity solutions obtained by the second author in a recent Hokkaido University preprint. Finally, since the solution of scalar conservation law equations can be constructed using existing numerical techniques, we use it to verify that our numerical solution approximates the entropy solution.

     

On generalized geometric programming problems with non-positive variables

Generalized geometric programming (GGP) problems occur frequently in engineering design and management. Some exponential-based decomposition methods have been developed for solving global optimization of GGP problems. However, the use of logarithmic/exponential transformations restricts these methods to handle the problems with strictly positive variables. This paper proposes a technique for treating non-positive variables with integer powers in GGP problems. By means of variable transformation, the GGP problem with non-positive variables can be equivalently solved with another one having positive variables. In addition, we present some computationally efficient convexification rules for signomial terms to enhance the efficiency of the optimization approach. Numerical examples are presented to demonstrate the usefulness of the proposed method in GGP problems with non-positive variables.