Algebraic Solutions of the Lam\'e Equation, Revisited

A minor error in the necessary conditions for the algebraic form of the Lam\'e equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, "On algebraic solutions of Lam\'e's differential equation", J. Differential Equations 41 (1981), 44-58.] It is shown that if the group is the octahedral group S_4, then the degree parameter of the equation may differ by +1/6 or -1/6 from an integer; this possibility was missed. The omission affects a recent result on the monodromy of the Weierstrass form of the Lam\'e equation. [See R. C. Churchill, "Two-generator subgroups of SL(2,C) and the hypergeometric, Riemann, and Lam\'e equations", J. Symbolic Computation 28 (1999), 521-545.] The Weierstrass form, which is a differential equation on an elliptic curve, may have, after all, an octahedral projective monodromy group.Comment: 20 pages, elsart document class, no figure

New Records of Native and Introduced Plants from Nebraska

Recent field work in Nebraska by staff of the University of Nebraska Herbarium has produced a number of records of previously uncollected specimens and has confirmed the presence of species collected only a few times long ago. Some of the records are of American species which are indigenous to Nebraska or which have recently spread to the state, while other records are of foreign species which are thoroughly established in the wild. Some of these are potentially serious weeds, though none have reached that stage yet. All specimens cited are deposited in the University Herbarium in Nebraska Hall, Lincoln, except that those marked with an asterisk are at the University of Nebraska at Omaha. Typha domingensis Pers. Typhaceae. Lancaster Co., Pawnee Lake, in extensive Typha marsh on west side, 18 September 1974, Kaul 2426. This extends the range north from Kansas. Potamogeton crispus L. Potamogetonaceae. Dodge Co., Fremont State Lakes, 22 June 1969, Sutherland 2383*. Morrill Co., Bridgeport State Lake, in shallow water along shore, 7 July 1974, Churchill 3848. Pawnee Co., Burchard Lake, submerged along inlet, 28 July 1973, Churchill 2039. Sherman Co., Beaver Creek State Wayside, shallow water, 31 May 1973, Churchill 777. This species is thoroughly established in the northeastern. states and in California, and it appears to be spreading rapidly in Nebraska man-made lakes. Vallisneria americana Michx. Hydrocharitaceae. Cherry Co., east end of Ballard\u27s Marsh, 9 July 1973, Churchill 1652. This is our second record for the state, the first being Kiener 27528, 21 Lake, Cherry Co., 27 August 1951. This submerged aquatic is abundant in eastern and northern states but in Nebraska, where it is at the western edge of its range, it is rare. It is an important duck food. Aegilops cylindrica Host. Poaceae. Douglas Co., Omaha, at 44th & Cass St., along tracks, 17 June 1971, Sutherland 2983. Lancaster Co., at 19th & Vine St. along tracks, Lincoln, 29 June 1972, Churchill 249. This plant was introduced from Europe and is becoming a bad weed in some states, though not in Nebraska

Relative Afterslip Moment Does Not Correlate With Aftershock Productivity:Implications for the Relationship Between Afterslip and Aftershocks

Aseismic afterslip has been proposed to drive aftershock sequences. Both afterslip moment and aftershock number broadly increase with mainshock size, but can vary beyond this scaling. We examine whether relative afterslip moment (afterslip moment/mainshock moment) correlates with several key aftershock sequence characteristics, including aftershock number and cumulative moment (both absolute and relative to mainshock size), seismicity rate change, b‐value, and Omori decay exponent. We select M w ≥ 4.5 aftershocks for 41 tectonically varied mainshocks with available afterslip models. Against expectation, relative afterslip moment does not correlate with tested aftershock characteristics or background seismicity rate. Furthermore, adding afterslip moment to mainshock moment does not improve predictions of aftershock number. Our findings place useful empirical constraints on the link between afterslip and potentially damaging M w ≥ 4.5 aftershocks and raise questions regarding the role afterslip plays in aftershock generation

The role of radiation in mesoscale flows: Physics, parameterizations, codes

The topics discussed include the following: an overview of radiation and mesoscale flows and lessons learned from the intercomparison of GCM radiative codes