In this survey article we revisit Hilbert’s 19th problem concerning the regularity of minimizers variational integrals. We first discuss classical theory (that is, statement and resolution in all dimensions). then recent results degenerate convex functionals. Finally, some open problems. Exercises are included for benefit researchers who entering subject.

The Th-inducing POK (Th-POK, also known as ZBTB7B or cKrox) transcription factor is a key regulator of lineage commitment of immature T cell precursors. It is yet unclear the physiological functions of Th-POK besides helper T cell differentiation. Here we show that Th-POK is restrictedly expressed in the luminal epithelial cells in the mammary glands that is upregulated at late pregnancy and la...

The present state of QFT is analysed from a new viewpoint whose mathematical basis is the modular theory of von Neumann algebras. Its physical consequences suggest new ways of dealing with interactions, symmetries, Hawking-Unruh thermal properties and possibly also extensions of the scheme of renormalized perturbation theory. Interactions are incorporated by using the fact that the S-matrix is ...