Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is ExtR(G,G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more splitters, in fact we are able to prescribe the...

Ulrich G. Mueller, Nicole M. Gerardo, Duur K. Aanen, Diana L. Six, and Ted R. Schultz 1Section of Integrative Biology, University of Texas at Austin, Austin, Texas 78712; email: [email protected] 2Smithsonian Tropical Research Institute, Apartado 2072, Balboa, Republic of Panama 3Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona 85721-0088; email: nge...

the genus tortula includes about 114 species in the world and 18 species were found in iran. in the present paper, t. vahliana (schultz) mont. is reported for the first time from iran.

Following recent developments in the classification of bosonic short-range entangled phases, we examine many-body quantum systems whose ground state fractionalization obeys Lieb-Schultz-Mattis (LSM) theorem. We generalize topological such phases by LSM anomalies (arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into account, provide direct computations anomaly specific exam...

the relationship between the randic , wiener, hosoya , balaban, schultz indices, harary numbers anddistance matrix to enthalpies of formation (airf), heat capacity, (cp) , enthalpies of combustion (ah °c ),enthalpy of vaporization (ah °vap) and normal boiling points (bpk)of c2 c10 normal alkanes isrepresented