Loblolly pine (Pinus tueda L.) occurs naturally on soils that are frequently low in fertility and water availability (Allen et al., 1990; Schultz 1997). Despite these limitations, this species maintains a high level of productivity on most sites (Schultz, 1997). Knowledge of plantation loblolly pine root system growth and physiology is needed to understand how this species is adapted to soil re...

Duplication of an atrio-ventricular valve is a rare anomaly. In most instances the double, or even triple, atrio-ventricular orifice is on the left sidethe so-called "double mitral valve" (Hartmann, 1937; Wimsatt and Lewis, 1948; Schraft and Lisa, 1950; Prior, 1953; Wigle, 1957; Pachaly and Schultz, 1962; Edwards et al., 1965). Only exceptional cases of "double tricuspid valve" have been descri...

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 generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869] for solving linear systems Ax = b is implemented as a sequence of least squares problems involving Krylov subspaces of increasing dimensions. The most usual implementation is Modified Gram-Schmidt GMRES (MGS-GMRES). Here we show that MGS-GMRES is backward stable. The re...

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...