In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a given bounded set. We formulate the problem in the classical framework of Hilbert spaces and prove unique solvability using standard techniques like the Fredholm alternative.

During the past 25 yr, several different dallisgrass (Paspalum dilatatum Poir.) biotypes have been discovered, but little is known regarding their cytology and reproductive behavior. This study was undertaken to determine the cytology, method of reproduction, and fertility of three biotypes and the forage yield and quality of two of them. Two biotypes, Torres and Uruguaiana, were introduced from southern Brazil and the third, Uruguayan, was collected in Uruguay. All three are hexaploids with 2n = 6x = 60. The Torres biotype was meiotically irregular, with a mean chromosome association of 58.74 univalents and 0.63 bivalents per cell. Two accessions of the Uruguaiana biotype were studied; they had a mean meiotic chromosome association of 9.62 univalents, 25.17 bivalents, and 0.01 quadrivalents. Eleven accessions of the Uruguayan biotype were studied; their mean chromosome associations were 1.26 univalents, 29.28 bivalents, and 0.04 quadrivalents. It was proposed that the lack of chromosome pairing in the Torres biotype is genetically controlled. The genomic formulas of the Uruguaiana and Uruguayan biotypes are proposed to be AABBC1C2 and AABBCC, respectively. An examination of megasporogenesis and embryo sac development revealed that all three biotypes reproduce by apomixis, with apospory followed by pseudogamy. One Uruguayan accession was a facultative apomict with a small degree of sexuality. The forage yield potential and forage quality were determined for the Torres and Uruguayan biotypes, as well as for common dallisgrass. Torres produced less forage than the other two. Common dallisgrass produced less forage than the mean of the Uruguayan accessions in most environments. In vitro dry matter disappearance (IVDMD) differences among accessions were relatively small. Common dallisgrass did not differ in IVDMD from any of the Uruguayan accessions.

Novel genotypes of the subtropical grass Eragrostis curvula for the study of apomixis (diplospory) S. Cardone · P. Polci · JP. Selva · M. Mecchia · S. Pessino · P. Hermann · V. Cambi · P. Voigt · G. Spangenberg · V. Echenique Abstract The aim of this work was to obtain a series of genetically related lines of Eragrostis curvula with different ploidy levels and reproductive modes, which can be used for the discovery of genes associated to diplospory. E. curvula is a widely cultivated forage grass native to Southern Africa that reproduces naturally by obligate diplosporous apomixis (asexual reproduction by seeds) of the Antennaria type. In vitro culture of immature inflorescences of the apomictic cultivar Tanganyika led to the regeneration of a diploid S. Cardone Facultad de Agronomía, (FAUBA) P. Polci · JP. Selva · V. Echenique ( ) CERZOS (Euphytica (2006) 151:263-272 ESTs expressed sequence tags MDH malate dehydrogenases MMC megaspores mother cell PRX peroxidases RAPDs random amplified polymorphic DNAs.

Apomixis has been reported in eastern gamagrass [Tripsacum dactyloides (L.) L.I, but considerable uncertainty exists concerning the mechanism of apomixis involved. Because of this and the recent interest in improving the grass by breeding, this study was undertaken to characterize apomixis in eastern gamagrass. Megasporogenesis and embryo sac development were observed in ovules of eight eastern gamagrass genotypes: five diploid pistillate plants (2n = 2x = 36), two triploid (2n = 3x = 54) accessions, and one tetraploid (2n = 4x = 72) accession. The triploid and tetraploid accessions were apomictic. In these three, the megaspore mother cell enlarged; but rather than undergoing meiosis, the cell remained meiotically inactive. The only apparent changes were continued cell elongation and vacuolation. Eventually, the nucleus of the elongated megaspore mother cell divided mitotically and subsequently produced an 8‐nucleate embryo sac, which appeared similar to a Polygonum type sac. The embryo developed parthenogenetically. Pollination or fertilization was necessary for endosperm development, which indicates pseudogamy. The diploid plants reproduced by normal sexual means. After the first mitotic division, there was no difference in the appearance between the apomictic and sexual embryo sacs. These findings confirm that the apomictic mechanism in eastern gamagrass is diplospory of the Antennaria type followed by pseudogamy.

Warm-season perennial bunchgrasses frequently are used for hay and grazing in central Texas. We compared 6 alternative grasses with 2 more commonly grown species ['Ermelo' weeping lovegrass, (Eragrostis curvula (Schrad.) Nees var. curvula Nees) and 'Selection-75' kleingrass (Panicum coloratum L.] on 2 soils during 2 years. Grasses were transplanted into field plots at Stephenville and Temple, Tex. 1993 and harvested 3 times in 1994 and 1995. Weeping lovegrass and 'WW-B.Dahl' old world bluestem [Bothriochloa bladhii (Retz) S.T. Blake] were the highest yielding (P < 0.05) grasses and averaged 9,350 and 7,630 kg dry matter ha -1 in 1994 and 1995, respectively. 'Irene' tufted digitgrass (Digitaria eriantha Stued.) and kleingrass produced similar (P > 0.05) yields (6,560 and 6,340 kg dry matter ha -1 ). Experimental line 409-704 buffelgrass [Cenchrus ciliaris L. syn. Pennisetum ciliare (L.) Link], 'Carostan' flaccidgrass (Pennisetum flaccidum Greisb.), 'Palar' Wilman lovegrass (Eragrostis superba Peyr.), and P.I. 269961 Oriental pennisetum (Pennisetum orientale Rich) yielded less than 3,000 kg dry matter ha -1 at Stephenville and were invaded by weeds. Tillers per plant generally explained most of the yield differences as plant density was held constant. Ermelo lovegrass and WW-B.Dahl old world bluestem produced 2 to 3 times more tillers plant -1 than other grasses. Concentrations of neutral detergent fiber were higher (P < 0.05) in digitgrass and the lovegrasses than in other grasses (39 vs 36% of dry matter). These data indicate that WW-B.Dahl old world bluestem and Irene tufted digitgrass should be useful in forage-livestock systems in central Texas.