Conformational polymorphs of 22‐cyano‐N‐methyl‐5‐phenylpent‐2‐en‐4‐ynamide

Although the two polymorphic modifications, (I) and (II), of the title compound, C₁₃H₁₀N₂O, crystallize in the same space group (P2₁/c), their asymmetric units have Z′ values of 1 and 2, respectively. These are conformational polymorphs, since the mol­ecules in phases (I) and (II) adopt different rotations of the phenyl ring with respect the central 2‐cyano­carboxy­amino­prop‐2‐enyl fragment. Calculations of crystal packing using Cerius² [Molecular Simulations (1999). 9685 Scranton Road, San Diego, CA 92121, USA] have shown that (I) is more stable than (II), by 1.3 kcal mol^?1 for the crystallographically determined structures and by 1.56 kcal mol^?1 for the optimized structures (1 kcal mol^?1 = 4.184 kJ mol^?1). This difference is mainly attributed to the different strengths of the hydrogen bonding in the two forms.     

A benchmark solution for 2D Stokes flow over cavity

Two-dimensional Stokes flow in a half plane with coupled cavity having the form of semi-ellipse is considered. The exact solution for the boundary problem is obtained. The solution can be a benchmark for numerical approaches. An example of the benchmarking is given.     

Pointwise estimates for solutions to the porous medium equation with measure as a forcing term

For porous media equations with a Radon measure on the right-hand side, we derive pointwise estimates for solutions via the Riesz potentials.