The reaction of 2,4,6-tris(trimethylsiloxy)-1,3,5-triazine with chlorocarbenium ions: a new access to 1-oxa-3-azabutatrienium and 2-azaallenium salts

Chlorocarbenium salts - of the Vilsmeier-Arnold type react with the silylated isocyanuric acid to give 1-oxa-3-azabutatrienium salts under mild conditions. From reactions of diarylchloromethenium salts - with and ketones or tertiary carboxamides high yields of 2-azaallenium salts were obtained. A few chloro substituted 2-azaallenium salts were prepared from and carbonyl compounds. The mechanisms of the new reactions are discussed.     

Phenylsulfonyl-methylenation of aldonolactones

The low temperature addition of dilithiomethylphenyl sulfone to 2,3-O-isopropylidene-D-erythronolactone, and to 5-O-(tert-butyldimethylsilyl)-2,3-O-isopropylidene-D-ribofuranolactone gives the lactols 2 and 3a , respectively. Dehydration of lactol 2 in the presence of boron trifluoride etherate produces tetrahydrofuranylidene sulfones 5 and 6 in good yields. The reaction of lactol 3a under the same reaction conditions proceeds with formation of the 1′,5′-anhydro derivative 7 via competing intramolecular substitution.     

Ruthenium‐Catalyzed Cascade Annulation of Indole with Propargyl Alcohols

Cascade transformations forming multiple bonds and one‐pot procedures provide rapid access to natural‐product‐like scaffolds from simple precursors. These atom‐economic processes are valuable tools in organic synthesis and drug discovery. Herein, we report on ruthenium‐catalyzed cascade annulations of indole with readily available propargyl alcohols. These provide rapid access to diverse carbazoles, cyclohepta[b]indoles, and further fused polycycles with high selectivity. A bifunctional ruthenium complex featuring a redox‐coupled cyclopentadienone ligand acts as a common catalyst for the different cascade processes.     

Isoperimetric constants of manifolds with small handles

Mathematische Zeitschrift -     

Asymptotic expansions,L-values and a new quantum modular form

In 2010, Zagier introduced the notion of a quantum modular form. One of his first examples was the “strange” function F(q) of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan’s mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of F(q).     

Isomorphisms of integral alternative loop rings

This paper first settles the “isomorphism problem” for alternative loop rings; namely, it is shown that a Moufang loop whose integral loop ring is alternative is determined up to isomorphism by that loop ring. Secondly, it is shown that every normalized automorphism of an alternative loop ringZ L is the product of an inner automorphism ofQ L and an authomorphism ofL.     

Maximal Unstable Dissipative Interval to Preserve Multi-scroll Attractors via Multi-saturated Functions

In this paper, we present families of piecewise linear systems which are controlled by a continuous piecewise monoparametric control function for the generation of monoparametric families of multi-scroll attractors. Thus, the maximum range of values that the parameter set can take in order to preserve the useful dynamics for generating of multi-scroll attractors is found and it will be called maximal robust dynamics interval. This class of dynamical systems is the result of combining two or more unstable “one-spiral” trajectories. We give necessary and sufficient conditions in order to preserve multi-scroll attractors in terms of a parameter, i.e., a family of multi-scroll attractors is generated by means of a family of switching systems with multiple monoparametric companion matrices. Lastly, we provide an example to show how the developed theory works.     

Are covering (enveloping) morphisms minimal?

We prove that for certain classes of modules such that direct sums of -covers ( -envelopes) are -covers ( -envelopes), -covering ( -enveloping) homomorphisms are always right (left) minimal. As a particular case we see that over noetherian rings, essential monomorphisms are left minimal. The same type of results are given when direct products of -covers are -covers. Finally we prove that over commutative noetherian rings, any direct product of flat covers of modules of finite length is a flat cover.