Monochromatic k-edge-connection colorings of graphs

A path in an edge-colored graph $G$ is called monochromatic if any two edges on the path have the same color. For $k\ge 2$, an edge-colored graph $G$ is said to be monochromatic $k$-edge-connected if every two distinct vertices of $G$ are connected by at least $k$ edge-disjoint monochromatic paths, and $G$ is said to be uniformly monochromatic $k$-edge-connected if every two distinct vertices are connected by at least $k$ edge-disjoint monochromatic paths such that all edges of these $k$ paths are colored with a same color. We use $m{c}_k\left(G\right)$ and $um{c}_k\left(G\right)$ to denote the maximum number of colors that ensures $G$ to be monochromatic $k$-edge-connected and, respectively, $G$ to be uniformly monochromatic $k$-edge-connected. In this paper, we first conjecture that for any $k$-edge-connected graph $G$, $m{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+\lfloor \frac{k}{2}\rfloor$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$. We verify the conjecture for $k=2$. We also prove the conjecture for $G=K_{k+1}$ and $G=K_{k,n}$ with $n\ge k\ge 3$. When $G$ is a minimal $k$-edge-connected graph, we give an upper bound of $m{c}_k\left(G\right)$, i.e., $m{c}_k\left(G\right)\le k-1$. For the uniformly monochromatic $k$-edge-connectivity, we prove that for all $k$, $um{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+1$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$.     

Development and validation of a reversed‐phase HPLC method for CYP1A2 phenotyping by use of a caffeine metabolite ratio in saliva

CYP1A2 is important for metabolizing various clinically used drugs. Phenotyping of CYP1A2 may prove helpful for drug individualization therapy. Several HPLC methods have been developed for quantification of caffeine metabolites in plasma and urine. Aim of the present study was to develop a valid and simple HPLC method for evaluating CYP1A2 activity during exposure in xenobiotics by the use of human saliva. Caffeine and paraxanthine were isolated from saliva by liquid‐liquid extraction (chlorophorm/isopropanol 85/15v/v). Extracts were analyzed by reversed‐phase HPLC on a C₁₈ column with mobile phase 0.1% acetic acid/methanol/acetonitrile (80/20/2 v/v) and detected at 273nm. Caffeine and paraxanthine elution times were <13min with no interferences from impurities or caffeine metabolites. Detector response was linear (0.10–8.00µg/ml, R²>0.99), recovery was >93% and bias <4.47%. Intra‐ and inter‐day precision was <5.14% (n=6). The limit of quantitation was 0.10µg/ml and the limit of detection was 0.018±0.002µg/mL for paraxanthine and 0.032±0.002µg/ml for caffeine. Paraxanthine/caffeine ratio of 34 healthy volunteers was significantly higher in smokers (p<0.001). Saliva paraxanthine/caffeine ratios and urine metabolite ratios were highly correlated (r=0.85, p<0.001). The method can be used for the monitoring of CYP1A2 activity in clinical practice and in studies relevant to exposure to environmental and pharmacological xenobiotics. Copyright © 2015 John Wiley & Sons, Ltd.     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

The deformation and fracture of balloons

Inflation of balloons provides a straightforward way of achieving large biaxial deformations. Previous studies have shown that when a balloon bursts, crack propagation occurs at very high speed – much higher than would be expected from the low strain modulus and elastic wave velocity of the rubber. The present paper is concerned with studies of the deformation and fracture of cylindrical balloons. On inflation, the deformations of such a balloon pass through an unstable region but subsequently increase monotonically with pressure. In this relatively high pressure region, the ratio of the longitudinal and circumferential extension ratios is broadly in accord with expectations from high-strain elasticity theory when the ratio of the corresponding stresses is taken into account. On bursting, crack speeds up to around 300 m/s in this region. It is shown that these speeds are in accord with large increase in incremental moduli for the highly-strained rubber. Marked changes in crack tip profile observed at very high crack speeds are consistent with control of the rate of growth by inertia rather than by the viscoelastic properties of the rubber (as is believed to be the case at lower speeds). Consistent with this, various elastomers having different glass transition temperatures show similar crack growth behaviour in the very high speed region.     

Probabilism,entropies and strictly proper scoring rules

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism.An agent's evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent's evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

Design and development of a two‐dimensional system based on hydrophilic and reversed‐phase liquid chromatography with on‐line sample treatment for the simultaneous separation of excreted xenobiotics and endogenous metabolites in urine

In the present work we describe a two‐dimensional liquid chromatographic system (2D‐LC) with detection by mass spectrometry (MS) for the simultaneous separation of endogenous metabolites of clinical interest and excreted xenobiotics deriving from exposure to toxic compounds. The 2D‐LC system involves two orthogonal chromatographic modes, hydrophilic interaction liquid chromatography (HILIC) to separate polar endogenous metabolites and reversed‐phase (RP) chromatography to separate excreted xenobiotics of low and intermediate polarity. Additionally, the present proposal has the novelty of incorporating an on‐line sample treatment based on the use of restricted access materials (RAMs), which permits the direct injection of urine samples into the system. The work is focused on the instrumental coupling, studying all possible options and attempting to circumvent the problems of solvent incompatibility between the RAM device and the two chromatographic columns, HILIC and RP. The instrumental configuration developed, RAM‐HILIC‐RPLC‐MS/MS, allows the simultaneous assessment of urinary metabolites of clinical interest and excreted compounds derived from exposure to toxic agents with minimal sample manipulation. Thus, it may be of interest in areas such as occupational and environmental toxicology in order to explore the possible relationship between the two types of compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

Thermally induced solid-state transformation of cimetidine. A multi-spectroscopic/chemometrics determination of the kinetics of the process and structural elucidation of one of the products as a stable N3-enamino tautomer

Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics.