Geodesic Ricci solitons on unit tangent sphere bundles

In the paper, (Abbassi and Kowalski, Ann Glob Anal Geom, 38: 11–20, 2010) the authors study Einstein Riemannian $g$ natural metrics on unit tangent sphere bundles. In this study, we equip the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$ with an arbitrary Riemannian $g$ natural metric $\tilde{G}$ and we show that if the geodesic flow $\tilde{\xi }$ is the potential vector field of a Ricci soliton $(\tilde{G},\tilde{\xi },\lambda )$ on $T_1M,$ then $(T_1M,\tilde{G})$ is Einstein. Moreover, we show that the Reeb vector field of a contact metric manifold is an infinitesimal harmonic transformation if and only if it is Killing. Thus, we consider a natural contact metric structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi }, \tilde{\xi })$ over $T_1 M$ and we show that the geodesic flow $\tilde{\xi }$ is an infinitesimal harmonic transformation if and only if the structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi },\tilde{\xi })$ is Sasaki $\eta $ -Einstein. Consequently, we get that $(\tilde{G},\tilde{\xi }, \lambda )$ is a Ricci soliton if and only if the structure $(\tilde{G}, \tilde{\eta }, \tilde{\varphi }, \tilde{\xi })$ is Sasaki-Einstein with $\lambda = 2(n-1) >0.$ This last result gives new examples of Sasaki–Einstein structures.     

Almost contact metric manifolds whose Reeb vector field is a harmonic section

We investigate almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section. We first consider an arbitrary Riemannian manifold and characterize the harmonicity of a unit vector field ??, when ??? is symmetric, in terms of Ricci curvature. Then, we show that for the class of locally conformal almost cosymplectic manifolds whose Reeb vector field ?? is geodesic, ?? is a harmonic section if and only if it is an eigenvector of the Ricci operator. Moreover, we build a large class of locally conformal almost cosymplectic manifolds whose Reeb vector field is a harmonic section. Finally, we exhibit several classes of almost contact metric manifolds where the associated almost contact metric structures ?? are harmonic sections, in the sense of Vergara-Diaz and Wood?[25], and in some cases they are also harmonic maps.     

A boundary value approach to the numerical solution of initial value problems by multistep methos †

A boundary value appraoch to the numerical solution of initial value problems by means of linear multistep methods is presented. This theory is based on the study of linear difference equations when their general solution is computed by imposing boundary conditions. All the main stability and convergence properties of the obtained methods are investigated abd compared to those of the classical multistep methods. Then, as an example, new itegration formulas, called extended trapezoidal rules, are derived. For any order they have the same stability properties (in the sense of the definitions given in this paper) of the trapezoidal rule, which is the first method in this class. Some numerical examples are presented to confirm the theoretical expectations and to allow us to trust a future code based on boundary value methods.     

Analysis and Optimal Boundary Control of a Nonstandard System of Phase Field Equations

We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.     

Fit-for-purpose in veterinary drug residue analysis: development and validation of an LC-MS/MS method for the screening of thirty illicit drugs in bovine urine

A selective and sensitive method for screening 31 analytes (nine corticosteroids, eight β‐agonists, seven anabolic steroids, six promazines and zeranol) in bovine urine was validated according to 2002/657/EC guidelines. Upon optimization of sample treatment conditions, the extraction was performed by diethylether at pH 9, after deconjugation. Extraction yields (R%) proved higher than 70% for 19 analytes, 50<R%<70 for 5 analytes, lower than 50% but reproducible for the remaining six analytes. The analyses were carried out using HPLC‐ESI‐MS/MS. The method sensitivity proved high enough to largely exceed the CCβ requirements of the Italian residue detection plan, ranging from 1 to 3 ng/mL (20 ng/mL for promazines). The present method allowed the simultaneous analysis of most drugs for which the European legislation prescribes official controls. Its practical applicability was verified on 494 real samples as an alternative to the traditional screening protocols based on multiple immunometric analysis, demonstrating high efficiency and comprehensive investigation capacity, allowing epidemiological assessment of the current trends in cattle breeding drug abuse. Among non‐compliant results, nine borderline cases of growth‐promoters illegal treatments, making use of long‐term low‐dosage administrations and typically yielding urine residues below the cut‐off value for immunochemical methods, were detected by using the present LC‐MS/MS method.     

Extendable cohomologies for complex analytic varieties

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern–Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho–Sad type index theorem for holomorphic foliations of singular complex varieties.     

Micellization behavior of [C16-12-C16], 2Br gemini surfactant in binary aqueous-solvent mixtures

The micellization behavior of bis cationic gemini surfactant, N,N′-dihexadecyl-N,N,N′,N′-tetramethyl-1,12-dodecanediammonium dibromide [C₁₆H₃₃N⁺(CH₃)₂-(CH₂)₁₂-N⁺(CH₃)₂C₁₆H₃₃, 2Br⁻] has been studied in binary aqueous mixtures of dimethyl sulfoxide, methanol, 1,4-dioxane, glycerol and ethylene glycol by conductivity and surface tension measurements at 300 K. The critical micellar concentration, degree of micelle ionization (α), surface excess concentration (Г_max), minimum surface area per molecule of surfactant (A_min), Gibbs free energy of micellization (ΔG_m°), the surface pressure at cmc (π_cmc), and the Gibbs energy of adsorption (ΔG_ad°) of the gemini surfactant have also been determined. The cmc, α, A_min increases where as (ΔG_m°), Г_max, and π_cmc decreases with increasing volume percentage of the solvents in the solvent–water binary mixture. The interfacial properties of the gemini surfactant, solute–solute, solvent–solute interactions and the effectiveness of a surface-active molecule in binary solvent systems have been discussed.     

Effects of Long-Term Storage on Radical Scavenging Properties and Phenolic Content of Kombucha from Black Tea

Kombucha is a fermented beverage. Its consumption has significantly increased during the last decades due to its perceived beneficial effects. For this reason, it has become a highly commercialized drink that is produced industrially. However, kombucha is still also a homemade beverage, and the parameters which, besides its organoleptic characteristics, define the duration of its potential beneficial properties over time, are poorly known. Therefore, this study aimed to determine the effect of 9-month storage at 4 °C with 30-day sampling on the pH, total phenolic, and flavonoid contents, free radical scavenging properties of kombucha fermented from black tea. Our results highlighted that, after four months, the phenolic content decreased significantly from the initial value of 234.1 ± 1.4 µg GAE mL⁻¹ to 202.9 ± 2.1 µg GAE mL⁻¹, as well its antioxidant capacity tested by two in vitro models, DPPH, and ABTS assays. Concomitantly, the pH value increased from 2.82 to 3.16. The novel findings of this pilot study revealed that kombucha from sugared black tea can be stored at refrigerator temperature for four months. After this period the antioxidant properties of kombucha are no longer retained.     

Renormalization Group and Asymptotic Spin-Charge Separation for Chiral Luttinger Liquids

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d=1 nonsolvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems.