The diameter of paired-domination vertex critical graphs

In this paper we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γ _pr(G), is the minimum cardinality of a paired-dominating set of G. The graph G is paired-domination vertex critical if for every vertex v of G that is not adjacent to a vertex of degree one, γ _pr(G − v) < γ _pr(G). We characterize the connected graphs with minimum degree one that are paired-domination vertex critical and we obtain sharp bounds on their maximum diameter. We provide an example which shows that the maximum diameter of a paired-domination vertex critical graph is at least 3/2 (γ _pr(G) − 2). For γ _pr(G) ⩽ 8, we show that this lower bound is precisely the maximum diameter of a paired-domination vertex critical graph. The first author was supported in part by the South African National Research Foundation and the University of KwaZulu-Natal, the second author was supported by the Natural Sciences and Engineering Research Council of Canada.     

A two-compartment model interacting with dynamic drugs

By combining the total cell evolution curve and a two-compartment model interacting with dynamic anti-cancer agents, the evolution of subpopulations has been analytically obtained and investigated in this work.     

Effect of geometry on magnetization distortion in closed-circuit magnetic measurements

The effect of specimen geometry on magnetization distortion in closed-circuit measurements is reported in this letter. The degree of the distortion increases as the ratio of length to diameter (L/D) of specimen decreases, and the distortion can reduce the magnetization values as much as 42% when the applied magnetic field is 24 kOe and the L/D is 0.28. The type of magnetic material also affects the distortion. Although the phenomenon seems to be similar to the “image effect” that occurs in open-circuit measurements, reports of this effect in closed-circuit measurements have not been found in the literature. Further research effort, including 3D computer modeling, for understanding this magnetic phenomenon is underway and will be reported later.     

Self-Organization of Magnetic Nanoparticles and Inclusion of Hydrogen by Borohydride Reduction

 Different structures of the interglobular space or voids between self-organized nanoparticles lead to differences in the measurable magnetic properties of single-domain particle chains of similar composition, grain size, and amorphous structure of the single globules. The volumes and radii of nanoparticles obtained by application of a magnetic field (3 to 15 nm) are larger than those determined without application of a magnetic field during the borohydride reduction process. Two types of hydrogen containing nanotubes with diameters of up to 2 (small-size containers) and 5 nm (large-size containers) are produced using as a driving force the domain wall formation energy between ferromagnetic nanoparticles with quantum size effected dimensions prepared by this reduction method at room temperature and ambient atmosphere. Nanoscale hydrogen containers can be used instead of MeH nanoparticle electrodes as perfect energy charge transfer media of high efficiency (close to 100%) using Li ion electrolytes. No influence on the electrode temperature and no participation of OH⁻ and H₂O in the main charge/discharge transfer reactions were observed.     

Optimization of nisin production by Lactococcus lactis

Applied Biochemistry and Biotechnology - The production of nisin by batch culture of Lactococcus lactis ATCC 11454 in MRS broth (pH 6.5), as treated in 30 assays, that were set up by a fractional...     

Combining atom‐transfer radical polymerization and ring‐opening polymerization through bifunctional initiators derived from hydroxy benzyl alcohol—Preparation and characterization of initiators,macroinitiators, and block copolymers

A simple, one‐step procedure has been developed for the preparation of bifunctional initiators capable of polymerizing monomers suitable for atom‐transfer radical polymerization (ATRP) and ring‐opening polymerization (ROP). These bifunctional initiators were employed for making narrow disperse poly(styrene) macroinitiators, which were subsequently used for the ROP of various lactides to yield poly(styrene‐block‐lactide) copolymers. Thermogravimetric analysis (TGA) of these block copolymers are interesting in that it shows a two‐step degradation curve with the first step corresponding to the degradation of poly(lactide) segment and the second step associated with the poly(styrene) segment of the block copolymer. This nature of the block copolymer makes it possible to estimate the block copolymer content by TGA in addition to the ¹H NMR spectroscopic analysis. Thus, this study for the first time highlights the possibility of making porous materials by thermal means which are otherwise obtained by base hydrolysis. The bifunctional initiators were prepared by the esterification of 3‐hydroxy, 4‐hydroxy, and 3,5‐dihydroxy benzyl alcohols with α‐bromoisobutyryl bromide and 2‐bromobutyryl bromide. A mixture of products was obtained, which were purified by column chromatography. The esterified benzyl alcohols were employed in the polymerization of styrene under copper (Cu)‐catalyzed ATRP conditions to yield macroinitiators with low polydispersity. These macroinitiators were subsequently used in the ROP of L ‐, DL ‐, and mixture of lactides. The formation of block copolymers was confirmed by gel permeation chromatography (GPC), spectroscopic and thermal characterizations. The molecular weight of the block copolymers was always higher than the macroinitiator, and the GPC chromatogram was symmetrical indicating the uniform initiation of ROP by the macroinitiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 102–116, 2008     

Some criteria for the applicability of synthetic standards for laser spectral analysis of refractories

Summary The applicability of a series of synthetic standards for laser local analysis of refractories has been determined on the basis of 4 criteria: homogeneity, equality of the form and size of the craters formed by the laser beam, densities and plasma clouds. The validity of these criteria has been checked by comparison of the results received by electrone microprobe area scanning and by shooting the same places with a laser beam and reading the results with the help of synthetic standards.

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Kriterien zur Anwendbarkeit synthetischer Standards für die Laser-Spektralanalyse von feuerfesten Materialien

Zusammenfassung Die Anwendbarkeit von synthetischen Standards für die Laser-Lokalanalyse von feuerfesten Materialien wurde auf Grund von 4 Kriterien beurteilt: Homogenität, Gleichheit von Form und Größe der vom Laserstrahl verursachten Krater, Dichten und Plasmawolken. Die Gültigkeit dieser Kriterien wurde durch Vergleich der erhaltenen Ergebnisse mit den mit Hilfe der Elektronenmikrosonde erzielten Resultaten geprüft.

     

Comparative analysis of Reaction-Diffusion Manifold based reduced models for Head-On- and Side-Wall-Quenching flames

In this study, multi-dimensional molecular transport phenomena during Flame-Wall-Interactions (FWI) and their effects on model reduction strategies are investigated. In order to access the problem, the standard configurations of a two-dimensional Side-Wall Quenching (SWQ) flame and a one-dimensional Head-On Quenching (HOQ) flame are used and compared. In the case of the SWQ configuration it is shown that the gradients of the species scatter significantly both in the physical space and in the state space. Moreover, the gradient vector of the specific enthalpy describing energy losses towards the wall is not aligned with the gradient vectors of the species, which can be considered as a typical case while a flame in application might approach to the wall at any arbitrary transversal direction. This observation motivates to take the gradients’ scattering and multi-dimensional transport phenomena into account during model reduction to describe reliably the quenching process.The Reaction-Diffusion Manifold (REDIM) method is applied in this work. The method allows to take into account multi-dimensional transport in a very generic way. In order to generate the REDIM, gradient estimates are approximated by using a Singular-Value Decomposition (SVD) of SWQ detailed gradients fields. Two-dimensional REDIMs for both cases are constructed and compared to each other. Different transport (diffusion) models are implemented to compare quantitatively the manifolds with HOQ and SOQ gradients estimates. The comparison shows that the differences between reduced models with varying transport models is significantly larger than the differences for varying configurations (multidimensional gradient estimates). This justifies the use of a relatively simple REDIM for more complicated geometries and configurations. This simplifies the treatment and model reduction procedure significantly for such complicated transient phenomena.