Search

To the memory of Trevor Evans (1925–1991), the pioneer of interchange laws in universal algebra We establish a combinatorial model for the Boardman–Vogt tensor product of several absolutely free operads, that is, free symmetric operads that are also free as -modules. Our results imply that such a tensor product is always a free -module, in contrast with the results of Kock and Bremner–Madariaga on hidden commutativity for the Boardman–Vogt tensor square of the operad of non-unital associative algebras. [ABSTRACT FROM AUTHOR]

The impact of processing parameters on the microstructural and superconducting properties of yttrium-barium-copper-oxide/silver powder composites were investigated. Specifically, transport measurements and x-ray diffraction analysis were performed on samples prepared by static, dynamic and hot pressing techniques. The results showed a degradation in the critical temperature and critical current density of dynamically pressed samples.

We construct for a forgetful functor from nonsymmetric operads to weight graded associative algebras, two functorial "enveloping operads," the right inverse and the left adjoint of the forgetful functor. Those functors turn out to be related by operadic Koszul duality, and that relationship can be utilized to exhibit an example of a binary quadratic non-Koszul operad for which the Ginzburg–Kapranov functional equation holds and an example of a binary quadratic Koszul operad for which the Koszul property cannot be established using Gröbner bases. Both examples resolve standing open problems in operad theory. We also apply the enveloping operad functors to get a new proof of the Lagrange inversion formula using homotopical algebra. [ABSTRACT FROM AUTHOR]

A series of brightly luminescent new mononuclear TpPyLn(An)2(H2O) (where An− = carboxylate anion, Ln = Eu or Tb and TpPy− = tris(3-(2′-pyridyl)pyrazolyl)borate) and dinuclear (TpPyLn)2pma(MeOH)2 (Ln = Eu, Tb, pma4− = tetraanion of pyromellitic acid) complexes were prepared and characterized by X-ray crystallography. Within each series the compounds possess similar molecular structures, which differ only by the nature of the carboxylate anions. The quantum efficiencies for metal-centered emission of the complexes were up to 29(3)% for Eu3+ and 53(5)% for the Tb3+ compounds and significantly depend on the electronic structure of the additional ligand (i.e. the carboxylate). The aliphatic carboxylate compounds’ luminescence quantum yields were all similar, but different from those for the aromatic ones. The complexes with trifluoroacetate and pentafluorobenzoate unexpectedly displayed lower quantum efficiencies compared to those with the corresponding non-fluorinated analogues. Energy transfer from Tb3+ to Eu3+ occurs in a mixture of (TpPyEu)(pma)(TbTpPy)(MeOH)2, (TpPyEu)2(pma)(MeOH)2 and (TpPyTb)2(pma)(MeOH)2 but is not very efficient. The Tb3+-compounds displayed green electroluminescence, and both the Eu3+ and Tb3+ complexes exhibited bright metal-centered red (Eu3+) or green (Tb3+) triboluminescence. [ABSTRACT FROM AUTHOR]

The article discusses the annual meeting of the professional organization Irish Mathematical Society (IMS) at Trinity College Dublin in Ireland on April 15-16, 2016 which featured talks on graph inequalities, universal approximation in analysis, and rigid symmetric frameworks.