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.     

Ultrafast MRI of the fetus: an increasingly important tool in prenatal diagnosis of congenital anomalies

Objective

To demonstrate the additional utility of ultrafast magnetic resonance imaging (MRI) of the fetus in the evaluation of sonographically detected or equivocal fetal congenital anomalies.

Material and Methods

Twenty five pregnant women with ultrasound detected fetal congenital anomalies underwent ultrafast fetal MRI.

Results

MRI findings altered the diagnosis of two cases of giant arachnoid cyst and sizable interhemispheric cyst associated with agenesis of the corpus callosum. MRI added additional findings of occult spinal diastematomyelia in two out of four cases of Chiari/meningocele malformation. MRI revealed impaired sulcation and unilateral cleft palate in suspected case of Walker-Warburg syndrome. In the remaining 18 cases MRI confirmed the diagnosis of Meckel–Gruber syndrome in three cases, hydronephrosis in six cases, cerebral ventriculomegaly in five cases, isolated omphalocele in three cases and findings suggestive of aneuploidy in the last case.

Conclusion

Ultrasound is the screening method of choice for evaluation of the fetus. Ultrafast MRI is a complementary adjunctive modality with excellent tissue contrast that can image the fetus in multiple planes and add information in sonographically detected or equivocal congenital anomalies that may be significant to establish definitive accurate diagnosis and hence adequate management and counseling.     

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.     

On the Simplicity of the Lie Algebra of a Leavitt Path Algebra

For a field F and a row-finite directed graph Γ, let L(Γ) be the associated Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra [L(Γ), L(Γ)] to be simple.     

Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects

The potential application of SWCNTs as mass nanosensors is examined for a wide range of boundary conditions. The SWCNT is modeled via nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The added nano-objects are considered as rigid solids, which are attached to the SWCNT. The mass weight and rotary inertial effects of such nanoparticles are appropriately incorporated into the nonlocal equations of motion of each model. The discrete governing equation pertinent to each model is obtained using an effective meshless technique. The key factor in design of a mass nanosensor is to determine the amount of frequency shift due to the added nanoparticles. Through an inclusive parametric study, the roles of slenderness ratio of the SWCNT, small-scale parameter, mass weight, number of the attached nanoparticles, and the boundary conditions of the SWCNT on the frequency shift ratio of the first flexural vibration mode of the SWCNT as a mass sensor are also discussed.