169,913 research outputs found
Nonnegative solutions of some quasilinear elliptic inequalities and applications
No full textAbstract. Let f : R ! R be a continuous function. It is shown that
under certain assumptions on f and A: R ! R+ weak C 1 solutions of the differential inequality −div(A(|ru|)ru) > f(u) on RN are nonnegative.
Some extensions of the result in the framework of subelliptic operators on Carnot groups are considered
ENTIRE SOLUTIONS OF CERTAIN FOURTH ORDER ELLIPTIC PROBLEMS AND RELATED INEQUALITIES
No full textWe study distributional solutions of semilinear biharmonic equations of the type
∆2u+f(u)=0 onRN,
where f is a continuous function satisfying f(t)t ≥ c|t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy-Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions
Epidendrum olorteguii Damian, Hagsater & Mitidieri. A. Habit. B. Inflorescence. C. Flower. D. Dissected 2022, sp. nov.
No full textEpidendrum olorteguii Damián, Hágsater & Mitidieri, sp. nov. (Figure 1) Type:— PERU: Amazonas Department, Bongara Province, District of Yambrasbamba, Centro Poblado El Progreso, 5°42’58.06”S 77°49’43.63”O, 2200–2300 m, November 2020, Sergio Olortegui & Alexander Damián 5050 (holotype: USM! isotypes: UFV!). Similar to Epidendrum tamaense Foldats (1968: 328; Hágsater in Hágsater & Sánchez 2006: t. 891.), but flowers nearly twice as large, the flowers green to yellow or rarely ivory white, the lip cream suffused with light green at the mid-lobe (vs. olive-green with, lip marked with purple veins); lanceolate to oblong-lanceolate sepals, 3.0–4.0 cm long (vs. elliptic, 2.0 cm long); petals narrowly elliptic, acuminate (vs. narrowly obtrullate, obtuse to acute); the lip with obliquely sub-rectangular to oblong lateral lobes (vs. sub-orbicular), and the mid-lobe with a short apiculus at the apex and two revolute, obliquely triangular lobes (vs. deeply emarginate, the lobes non revolute, sub-orbicular). Description:— Herb up to 120 cm tall; terrestrial, erect, sympodial, new stems produced from middle of previous stem. Roots 5–6 mm in diameter, thick, scarce, from the base of primary stems. Stems 20–45 × 0.3–0.6 cm, simple, cane like, terete, new stem produced from sub-apical internode of previous stem, lower part covered by 3–5 tubular, imbricated, chartaceous, gray non-foliar sheaths. Leaves 2–4 aggregate towards apex apical half of stem, distichous, articulate, spreading, base embracing, blade 8.5–14.5 × 2.2–6.0 cm, lanceolate to elliptic-lanceolate in mature specimens, acute, thin, margin entire; sheaths 2.5–3.5 × 0.3–0.6 cm, tubular, infundibuliform in dry specimens. Spathe lacking. Inflorescence 17–20 cm long, apical, racemose, arching nutant, few-flowered; peduncle 7 cm long, laterally compressed, slightly ancipitose, rachis 13–15 cm long, sub-terete. Floral bracts 1.0–1.5 × 0.5–0.6 cm, shorter than the ovary, progressively shorter towards the apex of the rachis, ovate, acute, 3-veined, margins microscopically denticulate. Ovary 4 cm long, slightly arching, terete, furrowed, ventrally thickened apical third. Flowers 4–10, 2–5 flowers successive, several open at a time, resupinate, green to yellow or rarely ivory white (Léon Martínez s.n.), column darker green or dirty white, tinged purple towards apex, lip when green pale towards the disc and calli; fragrance not perceived. Sepals spreading, fleshy, free, 9-veined, margins entire, spreading; dorsal sepal 30–38 × 9–10 mm, lanceolate to oblong-lanceolate, acute, basal margins revolute, slightly carinate dorsally; lateral sepals 32–40 × 10–13 mm, lanceolate to oblong-lanceolate, oblique, acuminate, with a prominent dorsal keel. Petals 27–35 × 5–6 mm, strongly reflexed, parallel to ovary, fleshy, narrowly oblanceolate, acuminate, 3-veined, margins entire, spreading. Labellum 22–32 × 28–30 mm, fleshy, trilobed, fused to the column, base obliquely cordate; bicallose, the calli divergent, elongate, rounded, disc 3-ribbed, lateral ribs in front of calli inconspicuous, low, parallel, with a low, wide mid-rib reaching apex of labellum; lateral lobes 10–15 × 20–24 mm, prominent, convex, transversely subrectangular, basal corners narrowly rounded to obtuse, distal corner widely rounded, multi-veined, margins entire, spreading; mid-lobe 8–10 × 20–22 mm, curved in natural position, flabellate with two obliquely triangular lobes and a narrow, cuneate isthmus in the basal half, apical half truncate, with a short, thickened, narrowly triangular, reflexed, apiculus at the apex, the lobes divergent, obliquely triangular, obtuse, slightly revolute at the apex, margins entire. Column 15–16 mm long, short, thick, straight, slightly widening apically, constricted near the base; clinandrium-hood very short, margin entire; nectary deep, penetrating two-thirds the ovary, widened behind perianth, unornamented. Anther 7.9 × 6.6 mm ovoid, glandular-papillose, 4-celled. Pollinia 4, dark yellow, obovate, laterally compressed, subequal, caudicles granulose, as long as pollinia, viscarium semi-liquid, translucent. Capsule not seen. Additional specimens examined: — PERU: Amazonas; Prov. Bongara, Dtto. Yambrasbamba, Centro Poblado El Progreso, 2300 m, octubre 2017, Sergio Olortegui s.n. (USM!). Other records: PERU: Amazonas; Prov. Bongara, Distr. Yambrasbamba, El Progreso, Vivero “Mi Angelito,” colectada en el área de Nicolasa Velásquez, Marco Leon Martínez s.n., digital image, white form (AMO!). San Martín: Prov. Rioja, Distr. Pardo Miguel, Chisquilla, 2100 m, 22 June 2019, José Edquén 2092, digital images (AMO!). Etymology:—In honor of Sergio Olortegui Chamoli (1994-) an enthusiastic orchid grower in the city of Moyobamba (San Martin) and collector of the specimen that served as a holotype. Distribution and ecology:— Epidendrum olorteguii is found epiphytic in montane forests of the eastern slopes of the Andes between 2200–2300 m in altitude (Figure 3). Flowering is registered in September and October Conservation status:—Data deficient (DD). Known presently from two localities 50 km distant, on the northern border between the Departments of Amazonas and San Martín. The known population of E. olorteguii and its habitat is protected by the community of Venceremos (Yambrasbamba, Amazonas), due to its ecosystem service of providing water to the adjacent communities of Oso Perdido and El Progreso. Both are located within the Bosque Protector Alto Mayo. However, the area is under constant pressure by locals who seek new areas for logging and farming. Taxonomic Discussion:— Epidendrum olorteguii belongs to the Incomptum group. The species is recognized by its large habit, the large leaves, 8.5–14.5 × 2.2–6.0 cm, the green flowers to yellow or rarely ivory white, column darker green or dirty white, tinged purple towards apex, the lip cream suffused with light green at the mid-lobe, the lanceolate to oblong-lanceolate sepals 38–40 mm long, the petals narrowly elliptic, and the lip 22–32 × 28–30 mm, trilobed, the lateral lobes 7–10 × 12–14 mm, prominent, transversely sub-rectangular, basal corners narrowly rounded, distal corner widely rounded and the mid-lobe 15 × 16 mm, constricted at base, then transversely elliptic, sides involute; apex with a short, thickened, narrowly triangular, reflexed apiculus. It is somewhat similar to Epidendrum tamaense found from Ecuador to Venezuela, which has smaller plants, leaves 3–14 × 2.0– 4.3 cm (vs. 8.5–14.5 × 2.2–6.0 cm), green to olivegreen flowers, lip marked with purple veins (vs. green flowers to ivory white, lip light green at the mid-lobe); sepals 1.5–2.1 cm long (vs. 3.8–4.0 cm long); petals narrowly obtrullate, obtuse to acute (vs. narrowly elliptic), and the 3- lobed lip has lateral lobes sub-orbicular (vs. transversely sub-rectangular), midlobe obcuneate, deeply emarginate, with two sub-orbicular lobes (vs. transversely elliptic with a reflexed apiculus at the apex) (Hágsater 2006) (Figure 2B). Epidendrum ornis Hágsater, Edquén, E.Santiago & E.Mondragón (in Hágsater & Sánchez 2018b: 1688) is somewhat reminiscent, but the flowers are ochre-yellow, smaller; the sepals 13–15 mm long, the petals linear-oblanceolate, and the lateral lobes of the lip are obliquely dolabriform, and the mid-lobe rectangular-oblong, with the apex expanded, bilobed and emarginate, thus forming small, rounded lobes. Epidendrum incomptum Rchb. f. (see Santiago & Hágsater in Hágsater & Sánchez 2018b: pl. 844) ranging from Chiapas, Mexico to Panama, differs by its smaller flowers, sepals 12–17 mm long, and the lip trilobed, slightly convex, base cordate; ecallose, with one low, thin, smooth mid-rib running to the apex of the lip; lateral lobes divaricate, obliquely ovate, rounded, with the forward edge usually straight; mid-lobe entire, sub-quadrate, truncate, minutely apiculate. Table 1 presents a summary of the principal differences of the morphological features that distinguish E. olorteguii from morphologically similar species.Published as part of Damián, Alexander, Hágsater, Eric & Mitidieri, Nicole, 2022, A new Peruvian species of Epidendrum (Laeliinae: Orchidaceae) belonging to the Epidendrum incomptum group, pp. 99-106 in Phytotaxa 552 (1) on pages 100-104, DOI: 10.11646/phytotaxa.552.1.9, http://zenodo.org/record/667330
Entire solutions of certain fourth order elliptic problems and related inequalities
No full textWe study distributional solutions of semilinear biharmonic equations of the type
Δ2u+f(u)=0 onRN,
where f is a continuous function satisfying f (t)t ≥ c |t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy- Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions
Hardy inequalities with optimal constants and reminder terms
No full textWe show that the classical Hardy inequalities with optimal constants in the Sobolev spaces W1,p 0 and in higher-order Sobolev spaces on a bounded domain ! ! Rn can be refined by adding remainder terms which involve Lp norms. In the higher-order case further Lp norms with lower-order singular weights arise. The case 1 < p < 2 being more involved requires a different technique and is developed only in the space W1,p 0
Crossoglossa puipuiensis (Malaxideae : Orchidaceae), a New Species, and New Records of Crossoglossa from Peru
No full textCrossoglossa puipuiensis Damián & Mitidieri (Orchidaceae) is described and illustrated as a new species from Peru. It differs from C. steinii by having an orbicular (vs. ovate to ovate-elliptic) labellum bearing at its base two, erect, subquadrate to rectangular (vs. prostrate, lanceolate to ovate) calli. Crossoglossa neirynckiana and C. dalessandroi are reported as new to the Peruvian flora
Representation formulae for solutions to some classes of higher order systems and related Liouville theorems
No full textLet m>=1 be an integer and N > 2m. Let μ be a positive Radon measure on RN. We study necessary and sufficient conditions on possible distributional solutions of (−")mu = μ on RN, that guarantee the validity of the representation formula u(x) = l + c(2m) ! RN dμ(y) |x − y|N−2m a.e. on RN, where l # R and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations
A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
No full textWe study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [P.-L. Lions, SIAM Rev., 24 (1982), pp. 441–467], we partially extend results known for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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