Host–Guest Chemistry of a Bis‐Calix[4]pyrrole Derivative Containing a trans/cis‐Switchable Azobenzene Unit with Several Aliphatic Bis‐Carboxylates

The azobenzene unit used as a photochemically and thermally switchable linker in the assembly of a bis‐calix[4]pyrrole receptor provides a means to modulate the binding of bis‐carboxylates of significant biological importance in cancer research. Conversely, the complexation of different bis‐anionic guests has significant kinetic effects on both the photochemical and thermal trans/cis isomerization of the azobenzene unit.     

Area-Minimizing Currents mod 2Q: Linear Regularity Theory

We establish a theory of Q -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents mod(p) when p = 2Q , and to establish a first general partial regularity theorem for every p in any dimension and codimension . © 2020 Wiley Periodicals LLC.     

On Admissibility Criteria for Weak Solutions of the Euler Equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper, we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct, in more than one space dimension, we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique.     

New spline spaces with generalized tension properties

The paper describes a new space of variable degree polynomials. This space is isomorphic to ℙ₆, possesses a Bernstein like basis and has generalized tension properties in the sense that, for limit values of the degrees, its functions approximate quadratic polynomials. The corresponding space of C ³, variable degree splines is also studied. This spline space can be profitably used in the construction of shape preserving curves or surfaces. AMS subject classification (2000)  65D07, 65D17, 65D10     

Über die Reduktion von Sulfaten

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