50,625 research outputs found
Paraxizicus brevicercus Gorochov & Kang 2005
No full text1. Paraxizicus brevicercus Gorochov & Kang, 2005 Paraxizicus brevicercus Gorochov, Liu & Kang, 2005: 71 -72; Mao & Shi, 2007: 64. Material examined. None. Distribution. CHINA (Hubei). MAP 1. Distribution of the genus Paraxizic u s from China.Published as part of Shi, Fu-Ming, Bian, Xun & Chang, Yan-Lin, 2011, Notes on the genus Paraxizicus Gorochov & Kang, 2007 (Orthoptera: Tettigoniidae: Meconematinae) from China, pp. 37-45 in Zootaxa 2896 on page 38, DOI: 10.5281/zenodo.20669
Retract rational fields
No full textAbstractLet k be an infinite field. The notion of retract k-rationality was introduced by Saltman in the study of Noetherʼs problem and other rationality problems. We will investigate the retract rationality of a field in this paper. Theorem 1: Let k⊂K⊂L be fields. If K is retract k-rational and L is retract K-rational, then L is retract k-rational. Theorem 2: For any finite group G containing an abelian normal subgroup H such that G/H is a cyclic group, for any complex representation G→GL(V), the fixed field C(V)G is retract C-rational. Theorem 3: If G is a finite group, then all the Sylow subgroups of G are cyclic if and only if Cα(M)G is retract C-rational for all G-lattices M, for all short exact sequences α:0→C×→Mα→M→0. Because the unramified Brauer group of a retract C-rational field is trivial, Theorems 2 and 3 generalize previous results of Bogomolov and Barge respectively (see Theorems 5.9 and 6.1)
Noether's problem for p-groups with a cyclic subgroup of index p2
No full textAbstractLet K be any field and G be a finite group. Let G act on the rational function field K(xg:g∈G) by K-automorphisms defined by g⋅xh=xgh for any g,h∈G. Noether's problem asks whether the fixed field K(G)=K(xg:g∈G)G is rational (=purely transcendental) over K. We will prove that if G is a non-abelian p-group of order pn (n⩾3) containing a cyclic subgroup of index p2 and K is any field containing a primitive pn−2-th root of unity, then K(G) is rational over K. As a corollary, if G is a non-abelian p-group of order p3 and K is a field containing a primitive p-th root of unity, then K(G) is rational
Xizicus (Eoxizicus) hainani Gorochov & Kang 2005
No full textXizicus (Eoxizicus) hainani Gorochov & Kang, 2005 Specimens examined. 2 ♂, Bawangling, Changjiang, Hainan, 30–31 May 2014, collected by Jiao Jiao. Distribution. Hainan (Bawangling, Jianfengling).Published as part of Jiao, Jiao, Chang, Yan-Lin & Shi, Fu-Ming, 2014, Notes on a collection of the tribe Meconematini (Orthoptera: Tettigoniidae) from Hainan, China, pp. 548-556 in Zootaxa 3869 (5) on page 552, DOI: 10.11646/zootaxa.3869.5.4, http://zenodo.org/record/22908
Paraxizicus Gorochov & Kang 2005
No full textGenus Paraxizicus Gorochov & Kang, 2005 Paraxizicus Gorochov, Liu & Kang, 2005: 71; Mao & Shi, 2007: 63 –68. Type species: Paraxizicus brevicercus Gorochov & Kang, 2005. Generic diagnosis. Body medium size. Head hypognathous; fastigium verticis conical, dorsally furrowed; eyes protruding anteriorly; apical segment of maxillary palpi almost as long as subapical one, apex enlarged. Pronotum with obviously posterior transverse sulcus, humeral sinus indistinct. Thoracic auditory spiracle completely free. Tegmina long, surpassing apices of postfemora. Hind wings a little longer than tegmina. Male tenth abdominal tergite with posterior process or without, sclerotized part of tenth tergite separated from epiproct by wide membranous area; epiproct rather small, simple, semimembranous, directed more or less downwards; cerci simple or complex, with one process on baso-ventral part or without; subgenital plate almost trapezoid or rectangle; genitalia membranous. Ovipositor long or short, comparatively curved dorsad, ventral valvulae with hooked apices. Female subgenital plate small or comparatively large; cerci conical, straight or faintly curved.Published as part of Shi, Fu-Ming, Bian, Xun & Chang, Yan-Lin, 2011, Notes on the genus Paraxizicus Gorochov & Kang, 2007 (Orthoptera: Tettigoniidae: Meconematinae) from China, pp. 37-45 in Zootaxa 2896 on page 37, DOI: 10.5281/zenodo.20669
Bezout's Theorem and ideals of terminal forms
No full textAbstractLet k be any field, k[X1,…,Xn] be the polynomial ring of n variables over k. For any f=f0+f1+⋯+fr∈k[X1,…,Xn] where each fi is a homogeneous polynomial of degree i and fr≠0, define tm(f)=fr. If I is an ideal in k[X1,…,Xn], define tm(I) to be 〈tm(f):f∈I⧹{0}〉, the ideal generated by the terminal forms tm(f). Using Bezout's Theorem and Macaulay's Theorem, we will establish the following. If f,g∈k[X1,X2] satisfying that gcd{f,g}=gcd{tm(f),tm(g)}=1 and I=〈f,g〉, then tm(I)=〈tm(f),tm(g)〉. Actually the above result is equivalent to Bezout's Theorem, which sheds another perspective of Bezout's Theorem. These results are valid in k[X1,…,Xn] also
Sinochlora trispinosa Shi & Chang 2004
No full text8. Sinochlora trispinosa Shi & Chang, 2004 (Figs. 15 –16, 39, 45, 48; Map 1) Sinochlora trispinosa Shi & Chang 2004, Oriental Insects, 38: 338; Liu & Kang 2007, J. Nat. Hist., 41 (21): 1337. Sinochlora retrolateralis Liu & Kang 2007, J. Nat. Hist., 41 (21): 1337 (Syn. nov.). Material examined. Holotype: male, Jiuwanshan, Guangxi, 25 Aug. 2001. Paratypes: 1 male, Dadongshan, Lian, Guangdong, 3 Sep. 1994, coll. Hong Peng, 1 female, same locality, 12 Sep. 1994, coll. Xu-Sheng Zhang. Other specimens, 2 males, Jiuwanshan, Guangxi, 1–2 Aug. 2006, 2 males, Fangxiang, Leishan, Guizhou, 18 Sep. 2005, coll. Fu-Ming Shi; 3 males, Mujiao, Tongdao, Hunan, 26 Jul. 2004, coll. Jian-Feng Wang. Discussion. The species is slightly similar to S. aequalis Liu & Kang, 2007, S. mesominora Liu & Kang, 2007 and S. szechwanensis Tinkham, 1945, but differs from them in: epiproct with three stout apical spines, the central spine swollen at base and strongly recurved, much longer than lateral ones. Distribution. China (Fujian, Hunan, Guangdong, Guangxi, Guizhou).Published as part of Wang, Gang, Lu, Rong-Sheng & Shi, Fu-Ming, 2012, Remarks on the genus Sinochlora Tinkham (Orthoptera: Tettigoniidae, Phaneropterinae), pp. 1-16 in Zootaxa 3526 on page 5, DOI: 10.5281/zenodo.28273
Sinochlora stylosa Shi & Chang 2004
No full text5. Sinochlora stylosa Shi & Chang, 2004 (Figs. 13 –14, 21, 38, 44, 46 –47, 67; Map 2) Sinochlora stylosa Shi & Chang 2004, Oriental Insects, 38: 336; Liu & Kang 2007, J. Nat. Hist., 41 (21): 1322. Material examined. Holotype: male, Libo, Guizhou, 23 Aug. 2000, coll. Fu-Ming Shi. Paratypes: 2 males and 2 females, Libo, Guizhou, 19–24 Aug. 2000, coll. Fu-Ming Shi. Other specimens, 5 males, Libo, Guizhou, 17–24 Aug. 2000, coll. Fu-Ming Shi; 1 male, Libo, Guizhou, 2 Oct. 2008, coll. Zai-Hua Yang. Supplementary description. Male stridulatory file with about 44 teeth regularly arranged. Female subgenital plate with apical lobes obtuse-angled at apex (Fig. 67). Discussion. The species is similar to S. sinensis Tinkham, 1945 and S. trapezialis Liu & Kang, 2007, but differs from them in: male epiproct with a stout apical spine, female subgenital plate with apical lobes obtuseangled at apex and the notch relatively shallow. Distribution. China (Guizhou).Published as part of Wang, Gang, Lu, Rong-Sheng & Shi, Fu-Ming, 2012, Remarks on the genus Sinochlora Tinkham (Orthoptera: Tettigoniidae, Phaneropterinae), pp. 1-16 in Zootaxa 3526 on pages 3-5, DOI: 10.5281/zenodo.28273
- …
