Plane curves of minimal degree with prescribed singularities

We prove that there exists a>0 such that for any integer d>2 and any topological types S_1,...,S_n of plane curve singularities, satisfying $\mu(S_1)+...+\mu(S_n) \leq ad^2$, there exists a reduced irreducible plane curve of degree d with exactly n singular points of types S_1,...,S_n, respectively. This estimate is optimal with respect to the exponent of d. In particular, we prove that for any topological type S there exists an irreducible polynomial of degree $d \leq 14\sqrt{\mu(S)}$ having a singular point of type S.Comment: 33 pages, LaTeX 2e, corrected some typos, simplified proofs of Lemmas 3.1, 4.

The choice of the intravenous fluid influences the tolerance of acute normovolemic anemia in anesthetized domestic pigs

The correction of hypovolemia with acellular fluids results in acute normovolemic anemia. Whether the choice of the infusion fluid has an impact on the maintenance of oxygen (O2) supply during acute normovolemic anemia has not been investigated so far. Methods: Thirty-six anesthetized and mechanically ventilated pigs were hemodiluted to their physiological limit of anemia tolerance, reflected by the individual critical hemoglobin concentration (Hbcrit). Hbcrit was defined as the Hb-concentration corresponding with the onset of supply-dependency of total body O2-consumption (VO2). The hemodilution protocol was randomly performed with either Tetrastarch (6% HES 130/0.4, TS-group, n=9), Gelatin (3.5% urea-crosslinked polygeline, GEL-group, n=9), Hetastarch (6% HES 450/0.7, HS-group, n=9) or Ringer's solution (RS-group, n=9). The primary endpoint was the dimension of Hbcrit, secondary endpoints were parameters of central hemodynamics, O2-transport and tissue oxygenation. Results: In each animal, normovolemia was maintained throughout the protocol. Hbcrit was met at 3.7+/-0.6 g/dl (RS), 3.0+/-0.6 g/dl (HS P<0.05 vs. RS), 2.7+/-0.6 g/dl (GEL, P<0.05 vs. RS) and 2.1+/-0.4 g/dl (TS, P<0.05 vs. GEL, HS and RS). Hemodilution with RS resulted in a significant increase of extravascular lung water index (EVLWI) and a decrease of arterial oxygen partial pressure (paO2), O2-extraction ratio was increased, when animals of the TS-, GEL- and HS-groups met their individual Hbcrit. Conclusions: The choice of the intravenous (i.v) fluid has an impact on the tolerance of acute normovolemic anemia induced by acellular volume replacement. Third-generation Tetrastarch preparations (e.g., HES 130/0.4) appear most advantageous regarding maintenance of tissue oxygenation during progressive anemia. The underlying mechanism includes a lower degree of extravasation and favourable effects on microcirculatory function

On the theory of Gordan-Noether on homogeneous forms with zero Hessian (Improved version)

We give a detailed proof for Gordan-Noether's results in "Ueber die algebraischen Formen, deren Hesse'sche Determinante identisch verschwindet" published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a similar direction as the present paper, but did not provide a proof for every result. In our paper, every result is proved. Furthermore, our paper is independent of Lossen's paper and includes a considerable number of new observations. An earlier version of this paper has been printed in Proceedings of the School of Science of Tokai University, Vol.49, Mar. 2014. In this version, a serious error has been corrected and some new results have been added

Letter to Kathleen Cheape regarding award of a Lucile Elliott Scholarship, June 6, 1966

A letter from Jean Lossen to Kathleen Cheape declining the Lucile Elliott Scholarship awarded to her

Letter to Kathleen Cheape regarding award of a Lucile Elliott Scholarship, June 10, 1966

A letter from Jean Lossen to Kathleen Cheape notifying Cheape that Lossen received a scholarship check despite declining the award

Letter to Pearl Von Allmen regarding award of a Lucile Elliott Scholarship, June 13, 1966

A letter from Jean Lossen to Pearl Von Allmen returning the scholarship check sent to Lossen