125,227 research outputs found
Integral closure of Noetherian rings
No full textAfter giving a proposition which reduces the problem of computing the integral closure of a general noetherian ring to the three problems: Compute a universal denominator d (element in the conductor). Compute radical of the ideal generated by d. Compute ideal quotients. We show that for the common case of affine domains, i.e. domains which are finitely generated over fields, of characteristic zero, we can use an effective localization in order to perform most of the computation in one dimensional rings where it can be done with linear algebra
Formica dolosa Trager, MacGown & Trager, 2007, stat. nov.
No full textFormica dolosa Buren, 1944 stat. nov. Figures 1, 4 e, 5 e, 6 e Formica pallidefulva subsp. schaufussi var. meridionalis Wheeler, W. M. 1904: 370 [Unavailable name.] Formica pallidefulva subsp. schaufussi var. dolosa Wheeler, W. M. 1912: 90 [Unnecessary replacement name for meridionalis; also unavailable.] Formica pallidefulva subsp. schaufussi: Wheeler, W. M. 1913 b: 552 (in part) [Misidentification.] Formica pallidefulva subsp. schaufussi var. dolosa: Wheeler, W. M. 1913 b: 554 Formica (Neoformica) schaufussi subsp. dolosa Buren, 1944: 309. [First available use of dolosa.] Syntype workers, Bull Creek, Travis Co., Texas (W. M. Wheeler) (MCZ) [Examined. Three workers on one pin, labeled true types of dolosa by S. Cover, and two gynes on one pin labeled syntypes by S. Cover] Formica pallidefulva subsp. schaufussi: Emery, 1893: 654 [Misidentification.] Formica schaufussi: Creighton, 1950: 551 [Misidentification.] Formica schaufussi subsp. dolosa: Creighton, 1950: 551 Formica schaufussi: Robson & Traniello, 1998: (in part) [Vouchers examined.] NOTE: We have selected a specimen in the Mayr collection (NMW) labeled Nord Amerika / Schaufuss as lectotype of Formica schaufussi Mayr, as this corresponds to the locality and collector information in Mayr s (1866) description. This sample clearly belongs to the much less pilose Formica pallidefulva. Thus, the name Formica schaufussi Mayr falls to the synonymy of Formica pallidefulva, below. DIAGNOSIS Worker The largest, most pilose, most densely pubescent and least shiny of reddishyellow members of the pallidefulva group (F. archboldi is duller, but always much darker and averages smaller). Weakly bicolored; head, mesosoma and legs light coppery red (south) to yellowish or reddish brown (north); gaster a little darker than head and mesosoma. Dorsal sclerites of mesosoma with abundant erect pilosity (Fig. 6 e); erect macrochaetae on gaster abundant and long (longest macrochaetae 0.16 - 0.30 mm), straight to slightly curved. Mesosoma, especially propodeal dorsum, pubescent; gaster dulled by long, dense, pale grayish, appressed microchaetae (Fig. 4 e). Gaster with small shallow foveolae in some samples, these nearly lacking in others. The propodeal crest is nearly always rounded in F. dolosa. The larger workers of this species are the largest eastern US Formica, matched within the genus only by the allopatric and otherwise quite different F. ravida Creighton. Queen Color, gastral pubescence, abundant pilosity and lack of shininess like the workers, with the usual differences in size. Sculpture a little more accented with notable fine tessellation of entire head, mesosoma and gastral dorsum; wings, when present, clear brownish to dark smoky gray. Three mesoscutal spots present as in F. incerta, but these pale and diffuse. Male Pubescence dense and pilosity abundant; surface sculpture punctate; head and gaster dark brown, mesosoma reddish brown to dark reddish brown with legs the same color; wings dark smoky gray. Larger than the nearly similar F. incerta, in which the mesosoma is normally about the same color as the head and gaster. DISTINGUISHING FEATURES The propodeal crest of F. dolosa is nearly always rounded in profile, and is typically sharp or even carinulate in the other species. This large, hairy, densely pubescent and faintly bicolored ant is most likely to be confused with F. biophilica. Compared to F. biophilica, F. dolosa has conspicuous appressed pubescence on the mesosoma, has more abundant, but slightly shorter gastral pilosity (longest macrochaetae up to 0.30 mm), has longer, denser pubescence on the gaster (compare Fig. 4 b and 4 e), and averages larger and heavier-bodied. The number of macrochaetae on the pronotum usually exceeds that on the propodeum of F. dolosa, (46 of 54 specimens) whereas the number on the propodeum more often exceeds that on the pronotum of F. biophilica (20 of 32 specimens). F. dolosa usually has relatively smaller eyes compared to F. biophilica (Table 1). In the field, F. dolosa occupies the drier end of the habitat spectrum, the two overlapping mainly in pine-oak woodlands of the Southeastern U. S., and in dry-mesic prairies further north. In the Northeastern U. S., larger, more pilose workers of F. incerta are often misidentified as F. dolosa, but F. dolosa averages larger and more pilose, has mesosomal pubescence and denser gastral pubescence, has longer scapes and legs; is generally lighter, more yellowish or reddish in color, and is more strictly associated with highly drained soils. ETYMOLOGY This name comes from the Latin adjective dolosus, meaning cunning or sly. Perhaps Wheeler was referring to the fleetness of its escape when alarmed, as this species is very shy and an excellent escape artist. RANGE AND HABITAT Widely distributed from New England across the Great Lakes region, west to Wisconsin and Iowa and south to northern Florida, the Gulf Coast states and Texas. Records of this ant in Colorado by Gregg are all misidentified F. incerta (L. Rericha, personal communication). F. dolosa is decidedly most abundant on acid-soil sites. These include a variety of droughty or well-drained habitats such as barrens, glades, prairies or open oak or pine woodlands on silicaceous or loessic soils. Though reported (as schaufussi) from plowed fields and pastures in the Northeast, F. dolosa is not usually common in such communities. J. Trager found F. dolosa in calcareous glades in Alabama and Missouri, but it is not abundant in these sites. In stark contrast to F. incerta and F. biophilica, F. dolosa does not nest in mesic habitats or in moist, fertile soils. SPECIMENS EXAMINED ALABAMA: Lawrence; ARKANSAS: Logan; FLORIDA: Alachua; Bay; Columbia; Escambia; Gilchrist; Jackson; Jefferson; Lake; Leon; Liberty; Okaloosa; Santa Rosa; Suwannee; Walton; GEORGIA: Clarke; Lumpkin; ILLINOIS: Mason; MARYLAND: Allegany; Dorchester; MASSACHUSETTS: Plymouth; Worchester MISSISSIPPI: Chickasaw; Choctaw; Lafayette; Lee; Lowndes; Noxubee; Oktibbeha; Pontotoc; Scott; Tishomingo; Winston; MISSOURI: Franklin; Johnson; Lincoln; Washington; NEW JERSEY: Ocean; NEW YORK: Nassau; Suffolk; NORTH CAROLINA: Nash OHIO: Adams; SOUTH CAROLINA: Aiken; Barnwell; McCormick; Oconee; TEXAS: Travis; WISCONSIN: Adams; Crawford; Dane; Grant; Iowa; Marshall; Sauk; Walworth; Waukesha. NATURAL HISTORY Nests may be hidden beneath a rock or piece of wood, but most nest entrances are at the base of a grass clump or other herbaceous plant. Some open onto bare ground, the entrance surrounded by a crater of excavated soil adorned with plant fragments, charcoal bits or fine gravel. J. MacGown collected F. dolosa in nests at the bases of large trees on relatively drier and more open ridges in mixed forests in northern Mississippi, and from an infrequently mowed area under loblolly pines near his house in Oktibbeha Co. Mississippi. The nest at the latter site was a low mound about 45 cm across and about 15 cm high at the midpoint. Part of the mound was inhabited by Camponotus castaneus Latreille. In the East and Gulf Coast United States, F. dolosa is host to the slavemaker Polyergus lucidus longicornis M. R. Smith. J. Trager's collection contains samples of this slavemaker with F. dolosa slaves from Massachusetts, New York, New Jersey, South Carolina and Mississippi. In Missouri, F. dolosa is occasionally among the many hosts of F. pergandei, but we have only observed them in combination with other host species (see Natural History of F. biophilica for a case in point). In Florida, J. Trager observed F. dolosa and F. archboldi competing for domination of colonies of Toumeyella scales on long-leaf pine grass-stage seedlings. Occasionally, fights would arise in which the larger F. dolosa threw or chased F. archboldi workers to the ground. Winged sexuals were collected in nests in mid-June in Florida and Georgia, and one male was found in a nest in western Missouri in August. Both worker and sexual pupae are always enclosed in a cocoon.Published as part of Trager, J. C., MacGown, J. A. & Trager, M. D., 2007, Revision of the Nearctic endemic Formica pallidefulva group., pp. 610-636 in Memoirs of the American Entomological Institute 80 on pages 619-62
Square-free Algorithms in Positive Characteristic
No full textWe study the problem of the computation of the square-free decomposition for polynomials over fields of positive characteristic. For fields which are explicitly finitely generated over perfect fields, we show how the classical algorithm for characteristic zero can be generalized using multiple derivations. For more general fields of positive characteristic one must make an additional constructive hypothesis in order for the problem to be decidable. We show that Seidenberg's Condition P gives a necessary and sufficient condition on the field K for computing a complete square free decomposition of polynomials with coefficients in any finite algebraic extension of K
Formica biophilica Trager, MacGown & Trager, 2007, new species
No full text<p>Formica biophilica James C. Trager new species</p> <p>Figures 4 b, 5 b, 6 b</p> <p>Formica pallidefulva: Creighton, 1950, in part [Misidentification]</p> <p>Formica schaufussi subsp. dolosa: Creighton, 1950, in part [Misidentification]</p> <p>TYPE DATA</p> <p>HL 1.43; HW 1.15; EL 0.42; SL 1.70; WL 2.34; PnW 0.95; PnM 6; PpM 14; TM 30</p> <p>Type specimen label: ALABAMA, Chilton Co., Interstate- 65 rest area 3 mi. E of Thorsby. 1 - X- 1983. M. B., J. R., B. R. DuBois. (JCT). Holotype and three paratypes on two pins. The holotype and one paratype will be deposited at MCZ and the other two specimens will be added to the excellent material of this species collected in Alabama and elsewhere by W. S. Creighton, now housed at LACM.</p> <p>DIAGNOSIS</p> <p>Worker Gracile, shiny, and the brightest yellow member of the group. Head, mesosoma and legs light reddish- to pale brownish yellow; head and mesosoma not at all or only a little lighter than gaster. Dorsal sclerites of mesosoma and especially the gaster with long, usually curved, erect macrochaetae. Number of macrochaetae on propodeum usually exceeds the number on the pronotum (20 of 32 specimens examined). Sheen of gaster readily visible through pubescence composed of pale, slender, grayish hairs of medium density (Fig. 4 b). Erect macrochaetae on gaster long, commonly 0.25 - 0.30 mm, tapering to a point and curved (Fig. 6 b).</p> <p>Queen Color, gastral pubescence and shininess like the workers, with the usual differences in size; with faint tessellation of upper portion of head, pronotum, sides of mesothorax, propodeum and gastral dorsum; wings, when present, clear to light brownish.</p> <p>Male Pubescence and pilosity abundant; mesosomal dorsum dull-punctate; head and gaster very dark brown, appearing black; mesosoma dusky yellowish brown, legs reddish brown; wings clear to light brownish. A little brighter in color, especially mesosoma, less pilose, pilosity also finer, and less pubescent than dolosa.</p> <p>DISTINGUISHING FEATURES</p> <p>F. biophilica and F. incerta are sympatric in the southern part of the latter's range. In the field, F. biophilica appears more brightly and uniformly reddish-yellow in color, and (if several workers of a colony are present) weakly polymorphic, whereas F. incerta is more brownish yellow, smaller overall, and usually (though not invariably) more monomorphic within colonies. Metrically, F. biophilica is more slender, has a proportionally longer mesosoma and narrower head than F. incerta (compare SI, TWI and CI values, Table 1). F. biophilica usually has more macrochaetae on the propodeum than on the pronotum (20 of 32 specimens), whereas F. incerta usually has more macrochaetae on the pronotum than on the propodeum (22 of 31 specimens).</p> <p>F. biophilica is also somewhat more brightly and uniformly colored, shinier and overall less hairy, and has a sharper petiolar crest in profile than F. dolosa. The F. biophilica specimens examined in this study also had a significantly higher CTI and OI (were more slender and had relatively larger eyes) than F. dolosa (Table 1). In the South, the less pilose minor workers and nanitics of F. biophilica are difficult to differentiate from F. pallidefulva. Often a rather squarer propodeal profile and more uniform bright reddish yellow color indicate F. biophilica. Additionally, on average the TWI of F. pallidefulva is larger than that of F. biophilica (Table 1). Ecologically, specimens from fens, bogs, swamps and fresh or salt marshes are most likely to be F. biophilica. In the northern part of the range of F. biophilica, its bright color will always distinguish it from the at least partially brown F. incerta and F. pallidefulva.</p> <p>ETYMOLOGY</p> <p>The name biophilica is given in allusion to E. O. Wilson's popularly inspirational coining biophilia, meaning the love of other species as a part of human nature. Specimens from Alabama, Dr. Wilson's home state, were chosen as the type series to further honor his contributions to myrmecology, conservation and behavioral biology.</p> <p>RANGE AND HABITAT</p> <p>Found in mesic to hydric open habitats, including fields, prairies, lawns, fens, bogs, marshes and open woodlands, from the Carolinas to Missouri, south to northern Florida and central Texas. Northward, its occurrence is more sporadic, especially in formerly glaciated regions, where F. biophilica shifts to drier (thus warmer) loess and sandy grassland locations. It reaches central Illinois in the Illinois River outwash sand prairies and reaches southeastern New York in the sandy plains along the East Coast and on Long Island. The habitat overlaps that of F. incerta in unglaciated prairies and eastern meadows, and overlaps that of F. dolosa in southern pine woodland and savanna. F. biophilica is absent from the most xeric and infertile sites occupied by F. dolosa. In the Ozarks and other southern U. S. hills, F. biophilica occurs in groundwater fens, bogs, marshes and flatwoods. This is the only southern Formica that occurs in these wetland habitats, where it nests in the elevated hummocks of organic matter formed by grass or sedge tussocks. It is less common than F. pallidefulva in human habitats, but occasionally shows up in lawns, parks and campuses, especially in parts of the South where fire ants are less abundant.</p> <p>SPECIMENS EXAMINED</p> <p>ARKANSAS: Logan; ALABAMA: Butler; Chilton; DeKalb; Lawrence; Mobile; Morgan; St. Clair; Tuscaloosa; DELAWARE: Sussex; DISTRICT OF COLUMBIA: Washington; FLORIDA: Alachua; Columbia; Gadsden; Okaloosa; Polk; Walton; GEORGIA: Clarke; Habersham; Lumpkin; Rabun; ILLINOIS: Mason; LOUISIANA: Natchitoches; Tammany; Washington; MISSISSIPPI: Alcorn; Bolivar; Chickasaw; Lafayette; Lee; Monroe; Oktibbeha; Panola; Pontotoc; Tippah; MISSOURI: Franklin; Lincoln; Reynolds; Washington; NEW YORK: Rockland; SOUTH CAROLINA: Pickens; TENNESSEE: Davidson; Monroe; Sevier; TEXAS: Cass; Collin; Potter.</p> <p>NATURAL HISTORY</p> <p>Nests of F. biophilica have simple, cryptic openings in wetlands, grasslands or less often, in open woodlands. The entrance is usually hidden amongst grass or sedges. In springtime, colonies of F. biophilica may build a 10 - 25 cm diameter mound of soil and plant fragments nestled against a grass or sedge clump, this collapsing in disuse during the hot, dry weather of summer. In fens, bogs and wet meadows, when ground at the base is permanently or seasonally saturated, F. biophilica nests in the upper parts of graminoid tussocks. One colony under a strip of bark in unmowed grass in eastern Missouri contained four larvae of myrmecophilous staphylinid beetles, probably Xenodusa cava LeConte (but not collected for determination).</p> <p>This species has been found as host to the slavemaker Polyergus lucidus s. l. in Washington, D. C., northern Georgia and east-central Missouri. The variety of this slavemaker parasitizing F. biophilica has longer scapes and is somewhat less shiny and slightly more pubescent than typical P. lucidus lucidus Mayr, which parasitizes F. incerta. F. biophilica occurs among the many hosts of F. pergandei in the prairies of Missouri, but has only been observed in combination with other host species. At one site, a F. pergandei nest contained a melange of six slave species including (in order of decreasing relative abundance) F. pallidefulva, F subsericea Say, F. biophilica, F. dolosa, F. incerta and F. obscuriventris Mayr, certainly the most species-rich, naturally occurring ant colony on record!</p> <p>Sexuals have been collected in nests in Missouri, Texas and Georgia in mid-June to early July, but no flight or colony-founding activity has been recorded. There is one example of a queen-male bilateral gynandromorph in a Missouri collection. The worker pupae are always enclosed in a pale tan cocoon, and the sexuals in a larger, darker cocoon.</p>Published as part of <i>Trager, J. C., MacGown, J. A. & Trager, M. D., 2007, Revision of the Nearctic endemic Formica pallidefulva group., pp. 610-636 in Memoirs of the American Entomological Institute 80</i> on pages 617-61
Polyergus ruber Trager, 2013, new species
No full textPolyergus ruber new species Figures 39, 40, 41 Polyergus lucidus longicornis: Vargo and Gibbs 1987 (misidentification). Holotype worker: USA, GEORGIA Clark Co. Athens. 165 Doe Run. [CAS, CASENT0281055] Paratypes: 4 workers, 3 gynes, 3 males: Same data as holotype [MCZ, CAS]. Holotype measurements HL 1.90, HW 1.80, SL 1.79, ½ VeM 9, ½ PnM 3, WL 2.86, GL 2.60, HFL 2.44, CI 95, SI 99, HFI 136, FSI 136, LI 4.76, TL 7.36. Paratype measurements (N= 5) [MCZ, CAS, FSCA] HL 1.60–1.90 (1.75), HW 1.52–1.80 (1.64), SL 1.68–1.79 (1.71), ½ VeM 3–9 (6.8), ½ PnM 1–4 (2.2), WL 2.52–2.86 (2.66), GL 2.04–2.60 (2.34), HFL 2.09–2.44 (2.26), CI 93–95 (94), SI 99–113 (105), HFI 134–146 (138), FSI 124–136 (132), LI 4.12–4.76 (4.41), TL 6.16–7.36 (6.75). Measurements (N= 26) HL 1.52–1.90 (1.65), HW 1.42–1.80 (1.64), SL 1.68–1.79 (1.71), ½ VeM 3–9 (6.8), ½ PnM 1–4 (2.2), WL 2.52–2.86 (2.66), GL 2.04–2.60 (2.34), HFL 2.09–2.44 (2.26), CI 93–95 (94), SI 99–113 (105), HFI 124–136 (132), FSI 124–136 (132), LI 4.12–4.76 (4.41), TL 6.16–7.36 (6.75). Worker description. This species is most similar to longicornis, but is shinier and has less pilosity. Head rectangular to weakly hexagonal, HL greater than HW; with conspicuous vertex pilosity consisting of (5) 8–20 erect macrosetae; scapes at least reaching, normally surpassing vertex corners, gradually thickening in distal half; pronotum with 0–6 dorsal erect setae; mesonotal profile weakly convex for most of its length; propodeal profile variable ranging from evenly rounded to a weakly obtuse, rounded angle; petiole narrow, sides convex and converging dorsad, petiolar dorsum rounded or with median portion flat, less often feebly concave; first tergite lacking pubescence; first tergite pilosity sparse, weakly flexuous or straight. Head matte to very faintly shining; mesosoma matte dorsally but shining laterally; gaster weakly shining to shiny. Discussion. This is among the three largest species of the lucidus group, almost in the same size range as longicornis, but characterized by a shinier head and mesosoma, especially the pronotum, and less abundant pilosity, especially on the vertex. Color is clear red with at most slight infuscation of the extremities. P. r u b e r appears intermediate between longicornis and lucidus in its proportions, pilosity, and shininess. The sheen and lesser vertex pilosity distinguishes ruber from the more matte longicornis (ruber ½ VeM 13) while the longer appendages distinguish it from lucidus (ruber SI> 92 + vs. lucidus <91). Etymology. With the name ruber, Latin for red or ruddy, I refer to the brighter, all-red color of this ant species, in comparison to other southeastern species, especially the somewhat similar, but dark-legged longicornis. Natural history. Polyergus ruber tracks its host, F. biophilica, in distribution, namely, a U-shaped range south from Maryland to Georgia, west to Louisiana, then north to eastern Missouri. It would be unsurprising if this ant showed up from collecting in at least southern Illinois. Polyergus ruber was studied by Vargo and Gibbs (1987, reported as lucidus longicornis) in Athens, GA. Aside from its unique host association, ruber seems much like its relatives in the lucidus group in most respects. Raids were observed from early June to mid-August, and may have continued after these observations ended, as the activity was still vigorous, so perhaps starting just a few weeks earlier and persisting perhaps a bit longer than in other species of the group. I observed parts of a raid, and a mating flight that occurred several hours before the raid, in Georgia, and two raids of these ants in Missouri, all in July, and they are much like those of the other species. At both locations, pre-raiding milling was initiated around 1700 hr. The size of raiding parties in the Georgia colonies was estimated between 500 and 1000, quite large compared to other known lucidus group species. Colonies and raiding parties were somewhat smaller in Missouri. Vargo and Gibbs observed dealate gynes near the outskirts of nests before raids in late July, and saw one of these follow a raid and enter the raided nest. Habitats of this species included a variety of upland, grassy and open woodland types, with acid soils. Distribution of studied specimens. GEORGIA Clarke Co. Athens. 165 Doe Run. Flight at noon. Raid at 1930 hr. 10 July 1986 J. C. Trager (JCT) GEORGIA Clarke Co. Athens USA UGA Riverbend Lab. 3–11 July 1986 E. Vargo, JC Trager (JCTC); LOUISIANA St. Tammany Par. Lake Ramsey WMA SC 3 - 3 Longleaf pine savanna. Pitfall trap. D Colby (multiple collections July–October 1997, LSU); MARYLAND Prince Georges Co. Berwyn [Heights] 6-25 - 1940 AB Gahas. W S Ross Coll. (FMNH); MISSISSIPPI Chickasaw Co. Tombigbee Nat’l Forest 33 o 55 ’ 39 ”N / 88 o 50 ’ 57 ”W 20-27 -June 2003 J. G. Hill (MEM); MISSOURI Lincoln Co. Cuivre River St. Pk. Sac Prairie 20 Apr. 1989 J.C. Trager (JCTC); NORTH CAROLINA Canover 1 -VIII- 32 Vanderford (NCSU); NORTH CAROLINA Burke Co. Morganton On ground 10 -VI- 1989 H. Barron (NCSU); NORTH CAROLINA Raleigh Raiding Nest 7 -VII- 1987 DL Stephan (NCSU); NORTH CAROLINA Granville Co. Oxford 1 -VII- 1977 F. Sutherland (NCSU); NORTH CAROLINA Durham Co. Durham K. Hedlund (no date) (NCSU); NORTH CAROLINA Wake Co. Cary June 10, 1984 DL Stephan (NCSU); NORTH CAROLINA Gaston Co. NE Cherryville Sept. 6, 1983 PJ Devine (NCSU).Published as part of Trager, James C., 2013, Global revision of the dulotic ant genus Polyergus (Hymenoptera: Formicidae, Formicinae, Formicini), pp. 501-548 in Zootaxa 3722 (4) on pages 528-529, DOI: 10.11646/zootaxa.3722.4.5, http://zenodo.org/record/24914
Computation of the radical of polynomial ideals over fields of arbitrary characteristic
No full textWe study the problem of the computation of the radical of an ideal of polynomials with coefficients over fields of arbitrary characteristic. We show how to use Seidenberg's condition P to solve this problem in the case of positive characteristic
Generators of the ideal of an algebraic space curve
No full textIn this paper we show that the ideal of any algebraic curve in affine 3-space
whose Jacobian matrix has rank at least 1 at every singular point of the curve can be generated by three polynomials and we give
constructive procedures to compute such generators
Computation of topological invariants for real projective surfaces with isolated singularities
No full textGiven a real algebraic surface S in RP3RP3, we propose a procedure to determine the topology of S and to compute non-trivial topological invariants for the pair (RP3,S)(RP3,S) under the hypothesis that the real singularities of S are isolated. In particular, starting from an implicit equation of the surface, we compute the number of connected components of S, their Euler characteristics and the labeled 2-adjacency graph of the surface
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