Further evidence for conjectures in block theory

Beautiful conjectures in graph theory

Some conjectures looking for a NCG theory

It is pointed out that ambiguities in the regularization of actions with second derivatives seem to happen with the same multiplicity that the standard model of elementary particles

Three conjectures in extremal spectral graph theory

We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of P2 and Pn−2 is the unique graph of maximum spectral radius over all planar graphs. This was conjectured by Boots and Royle in 1991 and independently by Cao and Vince in 1993. Similarly, we prove a conjecture of Cvetković and Rowlinson from 1...

Domains and Two Conjectures in Dimension Theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively , in the context of (locally) essential domains.

Deregulation of Stemness-Related Genes in Endometriotic Mesenchymal Stem Cells: Further Evidence for Self-Renewal/Differentiation Imbalance

Background: Any irregularities in self-renewal/differentiation balance in endometriotic MSCs can change their fate and function, resulting in endometriosis development. This study aimed to evaluate the expression of OCT4 transcripts (OCT4A, OCT4B, and OCT4B1), SOX2, and NANOG in endometriotic MSCs to show their aberrant expression and to support self-renewal/differentiation imbalance in these c...