322,913 research outputs found
New Upper Bounds for Mathieu-Type Series
No full textThe Mathieu’s series S(r) was considered firstly by É.L. Mathieu in 1890;
its alternating variant Š(r) has been recently introduced by Pogány et al. [Some families of Mathieu a-series and
alternating Mathieu a-series, 2006]
where various bounds have been established for S, Š. In this note we obtain
new upper bounds over S(r), Š(r) with the help of Hardy–Hilbert double integral
inequality
Integral Representation of a Series Which One Includes the Mathieu A-Series
No full textAbstractIntegral expression is deduced for the series S(r,μ,ν,a)=∑n=1∞2F1ν−μ+12,ν−μ2+1;ν+1;−r2a(n)2a(n)ν−μ+1(a(n)2+r2)μ−1/2, where r>0, μ>1/2, ν+1<μ and a:0<a(1)<a(2)<⋯<a(n)↑∞, and 2F1 is the Gauß hypergeometric function. The result precizes the integral expression for the generalized Qi type Mathieu a-series S(r,p,a)=∑n=0∞a(n)(a(n)2+r2)−p−1 given in [J. Inequal. Pure Appl. Math. 4 (2003), (4.5)] generalizing some other results by Cerone and Lenard, Tomovski and Qi as well. Bounding inequalities are given for S(r,μ,ν,a) using the derived integral expression
Torsion units in integral group ring of the Mathieu simple group M22
No full textAbstractWe investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group M22. We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.</jats:p
Mathieu Griffonet : à ses confrères les écrivains de mauvaises brochures, en défense de la bonne cause des représentans
No full textMathieu GriffonetAnalyse de Rivoire: Contre les négatifs ; suivi d'un "Dialogue entre l'auteur et l'imprimeur"
Léopold L. Foulem : Abstractions très singulières
No full textIn his essay on Foulem’s ceramic pieces, Mathieu identifies the elements that make them closer to sculptures than functional objects. The artist pushes back the limits of ceramics by creating unique objects resting on disproportionately large bases and devoid of all functionality. The author also explores the subject of abstraction, which happens to be the title of the series, as well as how form and surface interplay. Texts in French and English. 4 bibl. ref
Peperomia robusta G. Mathieu 2020, sp. nov.
No full textPeperomia robusta G. Mathieu, sp. nov. (Fig. 2, 3). Holotypus: MADAGASCAR. Reg. Alaotra-Mangoro [Prov. Toamasina]: Zahamena NP, NW border, 7 km SE of Antanandavao, along trail to camp 1 (1300 m N of campsite), 17°29'41"S 48°43'59"E, 1300 m, 26.IX.2001, Mathieu 446 (BR [BR000000916063]!; iso-: B [B100001403]!, G [G00341878]!, MO-5662979!, TAN!). Peperomia robusta G. Mathieu differs by the pilose indument from P. portulacoides (Lam.) A. Dietr., an essentially glabrous species, and from P. pedunculata C. DC., of which the indument is characterized by short erect trichomes. Perennial terrestrial herb, occasionally epiphytic, up to 40(–50) cm tall. Stem simple or 1–3 branched, erect or basally decumbent, terete, up to 8 mm diam. at the base, internodes 4–8 cm, pilose, dark red. Leaves opposite or 3–4-verticilate; petiole 8–10 mm long, pilose, red; lamina coriaceous to succulent, broad obovate, sometimes elliptic, 3–7 × 2–4 cm, smallest at the base of the stem, length/width ratio ca 1.6, apex rounded, base obtuse to acute or cuneate, 3-nerved, often only central nerve distinct, slightly impressed adaxially, both sides loosely pilose (usually more dense abaxially or at the nerves) or glabrescent, rather dark dull green adaxially, pale green abaxially, margin entire, ciliate, more dense in the apical half. Inflorescence 1 terminal spadix or 2–3(–4) together; peduncle 1 –2 cm long, basally pilose; rachis 5– 10 cm long, glabrous, loosely to moderately densely flowered, floral bracts orbicular or slightly elliptic. Fruit globose, ca. 0.5 mm diam., subbasally attached, entirely covered with sticky papillae, individual papilla longer than wide, style wide conical, horseshoe shaped ridge around subapical stigma, highest adaxially, open abaxially, conical pseudopedicellate when mature. Etymology. – The specific epithet refers to the general habit of the plant. It is one of the largest Peperomia species of Madagascar. Distribution and habitat. – The new species is endemic to North-East Madagascar from the National Park of Zahamena to the Loky-Manambato Protected Area (Daraina) where it occurs in medium altitude moist evergreen forests at an elevation of 700–1400 m. Because of its distribution and the number of currently known collections it is not considered as a rare species. Conservation status. – Peperomia robusta is known from 15 locations, all but two are encompassed in the protected area network (Anjanaharibe Sud, COMATSA Nord, Corridor Ankeniheny Zahamena, Loky Manambato, Manongarivo, Marojejy, Masoala and Zahamena). With an Extent of Occurrence (EOO) of c. 59,000 km ², an Area of Occupancy (AOO) of 60 km ² and no current threats, P. robusta is assigned a status of “Least Concern” [LC] using the IUCN Red List Categories and Criteria (IUCN, 2012). Notes. – Peperomia robusta resembles P. portulacoides, which is essentially glabrous. However, varieties of the latter species with indument have been published: P. portulacoides var. pilosa Baker from the Seychelles and P. portulacoides var. hirtella Wawra from Sri Lanka. Var. pilosa shows a short, erect indument. Its synonimization with P. tomentosa (Vahl) A. Dietr. (FRIEDMANN, 2011: 78) is questionable. Peperomia tomentosa not only exhibits a villous indument but is also distinct in its (sub)sessile leaves. Var. hirtella shows much smaller leaves (1–1.5 cm long). It is only known from its type collection and probably belongs to P. heyneana Miq. Peperomia robusta has to be distinguished from P. pedunculata, known from La Réunion, which does show an indument, characterized however by short erect trichomes. Moreover, the leaves of that species are smaller, 2–4(–5) cm long, elliptic, and usually show an obtuse apex. At last, there is some resemblance in general habit with P. mantadiana G. Mathieu. That is a glabrous species showing elliptic-lanceolate leaves. Peperomia robusta is considered as belonging to Peperomia subg. Micropiper, as it is the case with P. portulacoides and P. pedunculata (FRENZKE et al., 2015). Paratypi. – MADAGASCAR. Reg. Alaotra-Mangoro [Prov. Toamasina]: Mount Ankaroka, [17 °48'S 48°32'E], 1200 –1400 m, X.1937, Humbert 17511 (P); Zahamena AP, massif de l’Andrangovalo, [17°40'S 48°45'E], 1200–1300 m, X.1937, Humbert 17755 (P); ibid. loco, entre les rivière Sahatavy et Sivora, 17 °36'34"S 48°47 '10"E, 709 m, 2.X.2001, Ratovoson 547 (MO). Reg. Analanjirofo [Prov. Toamasina]: Masoala NP, N ridge of Ambohitsitondroinan’Mahalevona, 25°26'16"S 49°57'22"E, 1190 m, 23.II.2003, Lowry 6126 (MO, P). Reg. Atsinanana [Prov. Toamasina]: Rahobevava massif, [17°59'59"S 48°46'57"E], 1250 m, 12.III.1951, Cours 4330 (P, TAN). Reg DIANA [Prov. Antsiranana]: Manongarivo, 14°02'S 48°18'E, 1050 m, 15.XI.1994, Gautier 2555 (BR, G, TAN). Reg SAVA [Prov. Antsiranana]: Marojejy massif, NE side, [14°25'S 49°43'E], 800–1200 m, 25.I.–25.II.1949, Humbert 23165 (BR, P); ibid. loco, W side, 1000–1200 m, 9.XI.–2.XII.1939, Humbert 31394 (P); vallée inférieure de l’Androranga, Mt Anjenabe, [14°17'S 49°46'E], 1100–1130 m, 3–7.XII.1950, Humbert 24161bis (P); Marojejy PA, along E trail to summit, 14°26'20"S 49°44'50"E, 1150 m, 25.X.2001, Mathieu 485 (BR, MO, P, TAN); Distr. Vohemar, forêt de Binara, Daraina, 13°16'38"S 49°35'21"E, 1012 m, 20.XI.2005, Nusbaumer 1639 (BR, G, K, MO, TEF); Distr. Andapa, forêt de Betaolana, 11 km NW of Ambodiangezoka (camp 2), 14°36'22"S 49°25'30"E, 1200 m, 22.X.1999, Rakotomalaza 2025 (G); Marojejy, 14°29'S 49°38'E, 1300–1500 m, 21–22.I.1994, Rasoavimbahoaka 17 (MO, TAN); Andranomilolo, forêt située env. 13 km à l’W d’Andranopositra, 14°19'21"S 49°17'46"E, 1380 m, 7.XI.2006, Ravelonarivo 1955 (BR, MO, P, TAN).Published as part of Mathieu, Guido, 2020, Endemic Peperomia (Piperaceae) novelties from eastern Madagascar, pp. 75-82 in Candollea 75 (1) on page 78, DOI: 10.15553/c2020v751a7, http://zenodo.org/record/572481
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