190,376 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
Fig. 2. – Peperomia robusta G. Mathieu. A in Endemic Peperomia (Piperaceae) novelties from eastern Madagascar
No full textFig. 2. – Peperomia robusta G. Mathieu. A. General habit; B. Detail of node; C. Fruit (lateral view). [A, B: Mathieu 446, BR; C: Mathieu 485, BR] [Drawing: G. Mathieu]Published as part of Mathieu, Guido, 2020, Endemic Peperomia (Piperaceae) novelties from eastern Madagascar, pp. 75-82 in Candollea 75 (1) on page 79, DOI: 10.15553/c2020v751a7, http://zenodo.org/record/572481
C. Mollier, Une Apocalypse taoïste du Ve siècle. Le livre des incantations divines des grottes abyssales (Rémi Mathieu)
No full textMathieu Rémi. C. Mollier, Une Apocalypse taoïste du Ve siècle. Le livre des incantations divines des grottes abyssales (Rémi Mathieu). In: L'Homme, 1992, tome 32 n°121. Anthropologie du proche. pp. 219-220
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
Fig. 1. – Peperomia irrasa G. Mathieu. A in Endemic Peperomia (Piperaceae) novelties from eastern Madagascar
No full textFig. 1. – Peperomia irrasa G. Mathieu. A. General habit; B. Detail of node; C. Detail of leaf apex. [Humbert 24638, BR, P] [Drawing: G. Mathieu]Published as part of Mathieu, Guido, 2020, Endemic Peperomia (Piperaceae) novelties from eastern Madagascar, pp. 75-82 in Candollea 75 (1) on page 77, DOI: 10.15553/c2020v751a7, http://zenodo.org/record/572481
Fig. 3. – Peperomia robusta G. Mathieu. A in Endemic Peperomia (Piperaceae) novelties from eastern Madagascar
No full textFig. 3. – Peperomia robusta G. Mathieu. A. General habit; B. Apical part of flowering stem; C. Infrutescence. [Nusbaumer 1639] [Photos: L. Nusbaumer]Published as part of Mathieu, Guido, 2020, Endemic Peperomia (Piperaceae) novelties from eastern Madagascar, pp. 75-82 in Candollea 75 (1) on page 80, DOI: 10.15553/c2020v751a7, http://zenodo.org/record/572481
Mathieu Gilbert — Peut-on loger les Français ?
No full textC. P. Mathieu Gilbert — Peut-on loger les Français ?. In: Population, 21ᵉ année, n°6, 1966. p. 1242
Mathieu Gilbert — Peut-on loger les Français ?
No full textC. P. Mathieu Gilbert — Peut-on loger les Français ?. In: Population, 21ᵉ année, n°6, 1966. p. 1242
Peperomia variilimba G. Mathieu 2020, sp. nov.
No full textPeperomia variilimba G. Mathieu, sp. nov. (Fig. 4, 5). Holotypus: MADAGASCAR. Reg. Alaotra-Mangoro [Prov. Toamasina]: Zahamena, 17°30'01"S 48°44'00"E, 1250 m, 26.IX.2001, Mathieu 447 (BR [BR000000916064, BR000000916124]!; iso-: B [B100001404]!, BM!, G [G00341879]!, K!, MO-5662978!, P [P00547548]!, TAN!). Peperomia variilimba G. Mathieu differs from P. villilimba C. DC. in the alternate leaf position. Perennial herb, epiphytic on mossy trunks. Stem slender, creeping, scandent or pendent, flowering branches apically erect, simple or moderately branched, rooting from the nodes, pilose, internodes 1 – 4 cm. Leaves alternate, exceptionally subopposite; petiole pilose, up to 11 mm long; lamina thin to succulent, orbicular, elliptic, obovate or oblanceolate, 0.9–3.0 × 0.9–1.9 cm, length-width ratio 1–2.7, pilose, usually more densely around petiole insertion, sometimes glabrescent, apex rounded or obtuse, exceptionally retuse, the very tip sometimes slightly emarginate, base rounded, obtuse or acute, margin entirely ciliate. Inflorescence a solitary (sometimes two) terminal spadix; peduncle pilose, ca 1.5 cm long, somewhat widening near the rachis; rachis 3–7 cm long, glabrous; floral bract orbicular to elliptic, centrally peltate, ovary ellipsoid. Fruit globose, ca 0.5 mm diam., partially sunken in rachis, pericarp entirely covered with sticky papillae, individual papilla as long as wide, style flat conical, stigma apical, pseudopedicellate when mature. Etymology. – The specific epithet refers to the quite variable leaves, as well in shape as in succulence and indument density. Distribution and habitat. – The new species is endemic to the medium altitude moist evergreen forests at an elevation range from 900 to 2300 m. Peperomia variilimba is known from the Tsaratanana massif in the North-East to Analamazaotra in the Centre East. It is apparently common. Conservation status. – Peperomia variilimba is known from eleven locations, all of which are encompassed in the protected area network (Analamazaotra, Anjanaharibe-Sud, COMASTA Nord, Mantadia, Torotorofotsy, Tsaratanana and Zahamena). With an Extent of Occurrence (EOO) of c. 21,000 km ², an Area of Occupancy (AOO) of 36 km ² and no current threats, P. variilimba is assigned a status of “Least Concern” [LC] using the IUCN Red List Categories and Criteria (IUCN, 2012). Notes. – In its general habit P. variilimba resembles P. villilimba. However, the latter species is characterized by an opposite leaf position. The taxonomic concept of P. villilimba has been rather confusing for almost a century due to an inaccurate description of its leaf position in the protologue. The holotype of P. villilimba (Baron 2606, P) was considered by Casimir de Candolle as exhibiting alternate leaves (CANDOLLE, 1911: 48). The specimen concerned is showing only 6 leaves, which were pressed and mounted with considerable superposition. After remounting (straightening of the 2 superposed spadices and turning the specimen so that its former back is in front now) the opposite leaf position became evident. This position is also obvious in the isotype at K, apparently never seen by Candolle. In P. villilimba there is a marked length difference between the indument of the leaf surfaces (long) and of the margin (short). That difference is lacking in P. variilimba. The general habit of P. variilimba also resembles P. rotundilimba C. DC., which shows an opposite (or 3-verticillate) leaf position. P. variilimba ] is considered as belonging to subgenus Micropiper, as it is the case with P. villilimba (FRENZKE et al., 2015). Paratypi. – MADAGASCAR. Reg. Boeny [Prov. Mahajanga]: Distr. Andapa, Anjanaharibe-Sud RS, around camp 2, 14°44'52"S 49°27'58"E, 1350 m, 18.X.2001, Mathieu 468 (BR, G, MO, P, TAN). Reg DIANA [Prov. Antsiranana]: Tsaratanana massif, trail from Mangindrano up South ridge of the Maromokotro peak, 1800–2000 m, 8.V.1974, Gentry 11579 (MO, P); ibid. loco, 2000–2300 m, XI–XII.1937, Humbert 18352 (P); mountains N of Mangindrano, Ambatohafo valley, [14°12'00"S 49°06'30"E], 1200–1400 m, 19.I.–12.II.1951, Humbert 25363 (P); Tsaratanana massif, 2000 m, I.1923, Perrier de la Bâthie 15351 (P); SAVA, Andapa, Doany, Andranomilolo, 10 km NW of Andranopositra, 14°18'34"S 49°19'05"E, 1128 m, 16.XI.2006, Rakotovao 3411 (BR [2 sheets]); ibid. loco, 13 km W of Andranopositra, 14°19'23"S 49°17'54"E, 1462 m, 10.XI.2006, Ravelonarivo 2001 (BR). Reg. Alaotra- Mangoro [Prov. Toamasina]: Zahamena PA, Andrangovalo massif, [17°40'S 48°45'E], 1200–1400 m, X.1937, Humbert & Cours 17802bis (P); Mantadia NP, PK 10, 18°49'48"S 48°25'58"E, 950 m, 17.IX.2001, Mathieu 431 (BR, TAN); Analamazaotra RS, 18°56'45"S 48°25'10"E, 900 m, 18.IX.2001, Mathieu 438 (BM, BR, MO, P, TAN); Ambatovy, 18°50'13"S 48°18'59"E, 1186 m, 5.V.2008, Rakotondrafara 737 (MO, TAN).Published as part of Mathieu, Guido, 2020, Endemic Peperomia (Piperaceae) novelties from eastern Madagascar, pp. 75-82 in Candollea 75 (1) on pages 78-82, DOI: 10.15553/c2020v751a7, http://zenodo.org/record/572481
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