The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Van't Hoff analysis in chiral chromatography

The present review discusses the theory and application of van't Hoff analysis in chiral chromatography, with main focus on liquid chromatography. The topics considered include the physical meaning of van't Hoff equation's parameters, interpretation of thermodynamic data in terms of retention and enantioseparation mechanisms, abnormal behavior of van't Hoff plots, and best practices to avoid biased results.