Synthesis and antitumor evaluation of novel sulfonylcycloureas derived from nitrogen mustard

A new series of sulfonylcycloureas derivatives have been synthesized and evaluated in vitro for their antitumor activity against four cancer cell lines (A431, Jurkat, U266, and K562). These compounds were prepared by the condensation of several sulfonamides (2a–m) with ethyl bis(2-chloroethyl)carbamate (1a). The relative cytotoxicity of these new derivatives in comparison to chlorambucil is reported.     

Optimal control of a two-dimensional contact problem

We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result.     

Essential oil composition of aerial parts from Algerian Anacyclus monanthos subsp. cyrtolepidioides (Pomel) Humphries

The chemical composition of the essential oil from the aerial parts of Anacyclus monanthos subsp. cyrtolepidioides (Pomel) Humphries (Asteraceae) growing in a semi-arid region of Algeria was investigated for the first time. The essential oil was obtained by hydrodistillation and fully characterized by gas chromatography-mass spectrometry (GC-MS). A total of 97 compounds were identified. The essential oil was found to be rich in trans-chrysanthenyl acetate (9.8 ± 2.0%), (E)-β-farnesene (7.4 ± 1.5%), germacrene D (6.9 ± 1.3%) and myristicin (4.8 ± 0.8%).     

A Carleman estimate for the two dimensional heat equation with mixed boundary conditions

It is well known that in a regular domain, the solutions of the Laplace equation with mixed boundary conditions can present a singular part. In this work, we prove a Carleman estimate for the two dimensional domain heat equation in presence of these singularities.