Extending O-minimal Fréchet Derivatives

Singularities of O-minimal Peano Derivatives

We give a complete characterisation of the sets in which Peano derivatives of functions, which are definable in an o-minimal expansion of a real closed field, are continuously respectively Fréchet differentiable.

Modules whose direct summands are FI-extending

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

Synthesis of Staphylococcus aureus lipoteichoic acid derivatives for determining the minimal structural requirements for cytokine induction.

For the investigation of the minimal structural requirements for cytokine induction, Staphylococcus aureus lipoteichoic acid derivatives with two, three, four, and five glycerophosphate backbone moieties, carrying each a d-alanyl residue, were needed. Based on two different glycerophosphate building blocks and 6b-O-phosphitylated gentiobiosyl diacylglycerol the desired target molecules (compoun...

Extending Partial Orders on O-minimal Structures to Deenable Total Orders

Concerning the frame of minimal prime ideals of pointfree function rings

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...