High-Yielding Enantioselective Synthesis of the Macrolactam Aglycon of Sch 38516 from Two Units of (2R)-2-Ethyl-4-penten-1-ol

The same precursor —namely, (2R)-2-ethyl-4-penten-1-ol—was used to obtain fragments C9–C13 and C1–C8 of 1 , the aglycon of Sch 38516 (which is active against Candida sp.) and fluvirucin B₁ (which is active against influenza A virus). The key steps of the synthesis were the aldol-like reaction between the two fragments and the macrolactamization of a 13-azidotridecanoic acid derivative (see scheme). MOM=methoxymethyl, Py=2-pyridyl.     

Determination of organic acids and inorganic anions in wine by isotachophoresis on a planar chip

Isotachophoretic (ITP) separation and determination of a group of 13 organic and inorganic acids, currently present in wines, on a poly(methyl methacrylate) chip provided with on-column conductivity detection was a subject of a detailed study performed in this work. Experiments with the ITP electrolyte systems proposed to the separation of anionic constituents present in wine revealed that their separation at a low pH (2.9) provides the best results in terms of the resolution. Using a 94 mm long separation channel of the chip, the acids could be resolved within 10-15 min also in instances when their concentrations corresponded to those at which they typically occur in wines. A procedure suitable to the ITP determination of organic acids responsible for some important organoleptic characteristics of wines (tartaric, lactic, malic and citric acids) was developed. Concentrations of 2-10 mg/l of these acids represented their limits of quantitation for a 0.9 microl volume sample loop on the chip. A maximum sample load on the chip, under the preferred separating conditions, was set by the resolution of malate and citrate. A complete resolution of these constituents in wine samples was reached when their molar concentration ratio was 20:1 or less. ITP analyses of a large series of model and wine samples on the chip showed that qualitative indices [RSH (relative step height) values] of the acids, based on the response of the conductivity detector, reproduced with RSD better than 2% while reproducibilities of the determination of the acids of our interest characterized RSD values better than 3.5%.     

Some remarks on Saint-Venant's principle

We consider a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.     

On the decay of solutions in nonsimple elastic solids with memory

The decay of solutions in nonsimple elasticity with memory is addressed, analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations. In particular, a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup, but is not strong enough to entail exponential stability. The latter occurs for a dissipation mechanism of the second order, that is, the same order as the one of the leading operator.     

Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.     

On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions

In this note we investigate the spatial behavior of several nonlinear parabolic equations with nonlinear boundary conditions. Under suitable conditions on the nonlinear terms we prove that the solutions either cease to exist for a finite value of the spatial variable or else they decay algebraically. The main tool used is the weighted energy method. Our results can be applied to several situations concerning heat conduction. Received: April 4, 2004; revised: September 20, 2004     

On the Caginalp phase‐field systems with two temperatures and the Maxwell–Cattaneo law

Our aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase‐field systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain well‐posedness results and study the dissipativity of the associated solution operators. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability in porous media problem saturated by multiple immiscible fluids

This paper concerns a continuum theory of porous media saturated by multiple immiscible fluids. The case of a porous media saturated by two immiscible fluid proposes some new mathematical difficulties. We study the exponential stability of the one-dimensional problem when the nonwetting fluid is trapped in the wetting fluid and the exponential stability of the anti-plane shear deformations when the two fluids saturate the elastic media.     

On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

This paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.