New thermoplastic poly(carbonate-urethane)s based on chain extenders with sulfur atoms

New thermoplastic segmented polyurethanes were obtained by a one-step melt polyaddition using 40, 50 and 60 mol% poly(hexane-1,6-diyl carbonate) diol of \(\bar{M}_{n} = 860\) g mol^?1, 1,1′-methanediylbis(4-isocyanatobenzene) and 2,2′-[sulfanediylbis(benzene-1,4-diyloxy)]diethanol, 2,2′-[oxybis(benzene-1,4-diylsulfanediyl)]diethanol or 2,2′-[sulfanediylbis(benzene-1,4-diylsulfanediyl)]diethanol as a chain extender. FTIR, atomic force microscopy, differential scanning calorimetry and thermogravimetry were used to examine the polyurethanes’ structure and thermal properties. Moreover, their Shore A/D hardness, tensile, adhesive and optical attributes were determined. They were transparent high-molar-mass materials showing good tensile strength (up to 51.9 MPa). The polyurethanes exhibited improved adhesion to copper taking into consideration that of conventional ones, and middle or high refractive index values (1.57–1.60), and both these parameters increased with an increase of the content of sulfur atoms in the polyurethane chain. The newly obtained polyurethanes can be considered as materials for numerous medical and optical appliances.     

Effect of the platinum surface on the potential of nitrate-selective electrodes without internal solution

The effects of oxidation or reduction of the platinum contact used in nitrate-selective electrodes without internal reference solutions were studied by using voltammetric curves. A correlation was found between the state of the platinum surface and the standard potential of the ion-selective electrode under potentiometric conditions.     

Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability

We prove a fixed point theorem for nonlinear operators, acting on some function spaces (of set-valued maps), which satisfy suitable inclusions. We also show some applications of it in the Ulam type stability.     

On typically real functions which are generated by a fixed typically real function

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ.     

Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary

In this paper we consider the problem

(P)     

Zur Kenntnis der Reaktionsfähigkeit des Thiomorpholins und alkylsubstituierter Thiomorpholine, 4. Mitt.

Thiomorpholine as well as alkyl substituted thiomorpholines and their Sdioxides, respectively, are transformed into the corresponding N-Aminothiomorpholines by nitrosation (1–5) followed by the reduction with zinc in acetic acid/acetic acid anhydride under simultaneous formation of the corresponding N-acetyl derivates, and hydrolysis by hydrochloric acid (6–9). Examples of this method are described. 4-Aminothiomorpholines and their Sdioxides react with aldehydes or ketones to give azomethines (10–31). Acylation with mono-and dicarbonic acid chlorides leads to the N-acyl derivatives32–44.Mannich condensation is also possible. By oxidation with yellow mercury oxide tetracenes are formed (46–47).

Teil der DissertationM. Schmitz, Techn. Hochschule Aachen, 1975.     

Alien limit cycles near a Hamiltonian 2-saddle cycle

It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Classification of rotational special Weingarten surfaces of minimal type in {\mathbb{S}^2 \times \mathbb{R}} and {\mathbb{H}^2 \times \mathbb{R}}

In this paper we classify the complete rotational special Weingarten surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ ; i.e. rotational surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ whose mean curvature H and extrinsic curvature K _e satisfy H = f(H ² ? K _e ), for some function ${f \in \mathcal{C}^1([0,+\infty))}$ such that f(0) = 0 and 4x(f′(x))² < 1 for any x ≥ 0. Furthermore we show the existence of non-complete examples of such surfaces.     

The properties of functional inclusions and Hyers–Ulam stability

We prove that a set-valued function satisfying some functional inclusions admits, in appropriate conditions, a unique selection satisfying the corresponding functional equation. As a consequence we obtain the result on the Hyers–Ulam stability of that functional equation.     

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a TI scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.