On the extremal values of the second largest Q-eigenvalue

We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue.     

Hypersurfaces in the Lorentz-Minkowski space satisfying Lkψ?=?Aψ?+?b

We study hypersurfaces in the Lorentz-Minkowski space \mathbbLⁿ⁺¹{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L _k ψ = Aψ + b, where L _k is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1, A ? \mathbbR^(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and b ? \mathbbLⁿ⁺¹{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces \mathbbSⁿ₁(r){\mathbb{S}^n_1(r)} or \mathbbHⁿ(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders \mathbbS^m₁(r)×\mathbbR^n-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}}, \mathbbH^m(-r)×\mathbbR^n-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or \mathbbL^m×\mathbbS^n-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006).     

Evaluation of ent-kaurenoic acid derivatives for their anticariogenic activity

Ent-kaur-16(17)-en-19-oic acid (kaurenoic acid, KA) is a tetracyclic diterpene prototype for natural anticaries agents. Six KA derivatives were prepared and their antimicrobial activity against the main microorganisms involved in the caries process evaluated. The sodium salt of KA (KA-Na) was the most active, displaying very promising MIC values for most pathogens. Time-kill assays against the primary causative agent of caries (Streptococcus mutans) indicated that KA and KA-Na only inhibited growth in the first 12 h, suggesting a bacteriostatic effect. After this period (12-24 h), their bactericidal effect was clearly noted. KA and KA-Na showed no synergy when combined with the gold standard anticariogenic (chlorhexidine dihydrochloride, CHD) in the checkerboard assays against S. mutans.     

Fractional Navier-Stokes equations and a Hölder-type inequality in a sum of singular spaces

In this paper we study the local well-posedness of the fractional Navier-Stokes system with initial data belonging to a sum of two pseudomeasure-type spaces denoted by PM^a,b:=PM^a+PM^b. The proof requires showing a Hölder-type inequality in PM^a,b, as well as establishing estimates of the semigroup generated by the fractional power of Laplacian (−Δ)^γ on these spaces.     

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge.     

X‐ray analog pixel array detector for single synchrotron bunch time‐resolved imaging

Dynamic X‐ray studies can reach temporal resolutions limited by only the X‐ray pulse duration if the detector is fast enough to segregate synchrotron pulses. An analog integrating pixel array detector with in‐pixel storage and temporal resolution of around 150 ns, sufficient to isolate pulses, is presented. Analog integration minimizes count‐rate limitations and in‐pixel storage captures successive pulses. Fundamental tests of noise and linearity as well as high‐speed laser measurements are shown. The detector resolved individual bunch trains at the Cornell High Energy Synchrotron Source at levels of up to 3.7 × 10³ X‐rays per pixel per train. When applied to turn‐by‐turn X‐ray beam characterization, single‐shot intensity measurements were made with a repeatability of 0.4% and horizontal oscillations of the positron cloud were detected.     

Self‐Assembled Submonolayer of β‐Cyclodextrins on Gold Electrode for the Selective Determination of 4‐Aminobiphenyl

The formation of an inclusion complex between 4‐aminobiphenyl (4‐AB) and β‐cyclodextrin molecules (β‐CD), allows the use of thiolated β‐CDs as chemi‐adsorbed material on a Au electrode as a self‐assembled submonolayer for the selective square wave voltammetric determination of 4‐AB. The submonolayer was characterized by reductive desorption and an association constant of 1.2×10⁴ L/mol was obtained. The optimization of variables yielded a linear dependence of ip/4‐AB concentration in the range of 10^?5 to 10^?4 mol/L. The selectivity of the method was evaluated in the presence of other aromatic amines obtaining better results with the modified electrode. This methodology was applied to the voltammetric determination of 4‐AB in wastewater samples.     

Differentiation of Protonated Aromatic Regioisomers Related to Lignin by Reactions with Trimethylborate in a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

Several lignin model compounds were examined to test whether gas-phase ion–molecule reactions of trimethylborate (TMB) in a FTICR can be used to differentiate the ortho-, meta-, and para-isomers of protonated aromatic compounds, such as those formed during degradation of lignin. All three regioisomers could be differentiated for methoxyphenols and hydroxyphenols. However, only the differentiation of the ortho-isomer from the meta- and para-isomers was possible for hydroxyacetophenones and hydroxybenzoic acids. Consideration of the previously reported proton affinities at all basic sites in the isomeric hydroxyphenols, and the calculated proton affinities at all basic sites in the three methoxyphenol isomers, revealed that the proton affinities of the analytes relative to that of TMB play an important role in determining whether and how they react with TMB. The loss of two methanol molecules (instead of one) from the adducts formed with TMB either during ion–molecule reactions, or during sustained-off resonance irradiated collision-activated dissociation of the ion–molecule reaction products, revealed the presence of two functionalities in almost all the isomers. This finding supports earlier results suggesting that TMB can be used to count the functionalities in unknown oxygen-containing analytes.     

Comparison of Functional Group Selective Ion–Molecule Reactions of Trimethyl Borate in Different Ion Trap Mass Spectrometers

We report here a comparison of the use of diagnostic ion–molecule reactions for the identification of oxygen-containing functional groups in Fourier-transform ion cyclotron resonance (FTICR) and linear quadrupole ion trap (LQIT) mass spectrometers. The ultimate goal of this research is to be able to identify functionalities in previously unknown analytes by using many different types of mass spectrometers. Previous work has focused on the reactions of various boron reagents with protonated oxygen-containing analytes in FTICR mass spectrometers. By using a LQIT modified to allow the introduction of neutral reagents into the helium buffer gas, this methodology has been successfully implemented to this type of an ion trap instrument. The products obtained from the reactions of trimethyl borate (TMB) with various protonated analytes are compared for the two instruments. Finally, the ability to integrate these reactions into LC-MS experiments on the LQIT is demonstrated.