Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005     

Predicted rate enhancements of dephosphorylation in functional oximate comicelles

The rate enhancements of dephosphorylation of p-nitrophenyldiphenyl phosphate by comicelles of cetyltrimethylammonium bromide with a functional cosurfactant are due wholly to increased concentration of the nucleophile in the micelle.     

Using the generalized maximum covering location model to control a project’s progress

Project control consists of monitoring a project’s progress at so called control points, finding possible deviations from the baseline schedule and if necessary, making adjustments to the deviated schedule subject to the available control budget, the adjusting strategies and also other technical and environmental possibilities in order to bring the schedule back on the right track. In this study, we adapt for the first time the generalized maximum covering location model to determine the adjusting strategies such that the maximum control coverage is achieved, i.e. under the given constraints, a schedule that is globally as close to the baseline schedule as possible is obtained. Numerical examples are given to illustrate the intricacies of the proposed method and also to demonstrate its applicability.

     

Iron‐Mediated Cleavage of C?C Bonds in Vicinal Tricarbonyl Compounds in Water

Drei von einer Sorte : Vicinale Tricarbonyl‐Verbindungen gehen Eisen(III)‐vermittelte C‐C‐Spaltungen ein (siehe Schema). Die Ergebnisse sind relevant für den Aminosäurenachweis durch Ninhydrin und für den Vitamin‐C‐Stoffwechsel.

     

Operator maps of Jensen-type

Let \(\mathbb {B}_J({\mathcal {H}})\) denote the set of self-adjoint operators acting on a Hilbert space \(\mathcal {H}\) with spectra contained in an open interval J. A map \(\Phi :\mathbb {B}_J({\mathcal {H}})\rightarrow {{\mathbb {B}}}({\mathcal {H}})_\text {sa} \) is said to be of Jensen-type if

$$\begin{aligned} \Phi (C^*AC+D^*BD)\le C^*\Phi (A)C+D^*\Phi (B)D \end{aligned}$$

for all \( A, B \in \mathbb {B}_J({\mathcal {H}})\) and bounded linear operators C, D acting on \( \mathcal {H} \) with \( C^*C+D^*D=I\), where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form \(\Phi (A)=f(A)\) for some operator convex function f defined in J.

     

Hilbert $$C^*$$-modules as a subcategory of operator systems and injectivity

In this paper, we study a category whose objects are Hilbert \(C^*\)-modules and whose morphisms are completely semi-\(\phi \)-maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi-\(\phi \)-maps on Hilbert \(C^*\)-modules, leading to an analog of the Arveson’s extension theorem for completely semi-\(\phi \)-maps (in contrast with \(\phi \)-maps). This theorem together with previous results suggest that the completely semi-\(\phi \)-maps are proper generalizations of the completely positive maps.     

Study of Salinity and pH Effects on Gelation Time of a Polymer Gel Using Central Composite Design Method

Experiments were conducted to investigate the main effects of salinity (NaCl) concentrations and pH factors and their interactions on the gelation time response of a polymer gel used in a water shutoff system in oil field reservoirs. Central composite design (CCD) was used to design experiments and a mathematical model building. The main advantage of CCD was to generate the quadratic mathematical model for the gelation time as functions of salinity and pH factors. Tests were limited and optimized by CCD points including low star (axial), low factorial, central, high factorial, and high star points. The evaluation of the data and the developed model were performed through the examination of graphical trend of residuals and a numerical approach. Analysis of variance (ANOVA) was used to estimate the amount of data variations from the model predictions. It was found that the model was significant at the 99% confidence against test data. The results showed that the gelation time was dependent more on pH than salinity. For low pH, the gelation time increased with increasing of the salinity, while for a high pH (>4) the relationship was inversed. The research shows that CCD can effectively be applied for the modeling of gelation time and finding an optimum condition to achieve maximum or minimum gelation time for different salinity and pH factors.     

A Genetically Encoded,Phage‐Displayed Cyclic‐Peptide Library

Superior to linear peptides in biological activities, cyclic peptides are considered to have great potential as therapeutic agents. To identify cyclic‐peptide ligands for therapeutic targets, phage‐displayed peptide libraries in which cyclization is achieved by the covalent conjugation of cysteines have been widely used. To resolve drawbacks related to cysteine conjugation, we have invented a phage‐display technique in which its displayed peptides are cyclized through a proximity‐driven Michael addition reaction between a cysteine and an amber‐codon‐encoded N^?‐acryloyl‐lysine (AcrK). Using a randomized 6‐mer library in which peptides were cyclized at two ends through a cysteine–AcrK linker, we demonstrated the successful selection of potent ligands for TEV protease and HDAC8. All selected cyclic peptide ligands showed 4‐ to 6‐fold stronger affinity to their protein targets than their linear counterparts. We believe this approach will find broad applications in drug discovery.     

Add/drop filter using in-plane slanted gratings in azo polymers

We have fabricated in-plane slanted gratings on azo-functionalized polymeric films using a fast, direct-writing method. By properly adjusting the resonance, these gratings can be used as 90 degrees integrated reflectors and add/drop filters in the plane of the film. We have produced an attenuation of 14.8 dB at 1560.2 nm with a FWHM of 6.47 nm. Also, a signal of 1548 nm wavelength was added to the output from a different direction. Any light shifted from the resonance will pass through the filter undisturbed.     

Binding,and thermodynamics of <Emphasis Type="Italic">β</Emphasis>-cyclodextrin inclusion complexes with some coumarin laser dyes and coumarin-based enzyme substrates: a simulation study

This paper addresses modelling the nature of interactions between β-CD and some coumarins including recently reported novel sulphur analogues to form inclusion complexes of appealing medicinal, photochemical and photophysical properties. The binding energy and the total stabilization energy (E^ONIOM) are used to confirm the most favorable inclusion complex structure. Thermodynamic parameters reveal exothermic inclusion reaction in gas phase. Thermal stability of fluorescent enzyme substrate of coumarin nucleus increases in the order: gas?<?cyclohexane?<?water, indicating better stability in water. Furthermore, molecular characteristics such as optimized geometries, MO’s and electrostatic potential energy map surfaces and energies are reported and correlated with some reactivity indices. Our results validated the experimentally available data reported in the literature. Inclusion complexes of β-CD with coumarins should result in improving its laser efficiency in environmentally benign aqueous medium.