96 research outputs found
Entomobrya erratica Brown 1932
No full textE. erratica Brown, 1932 – Entomobrya erratica Brown, 1932: 336 AK Christiansen & Bellinger 1980, 1998; Skidmore 1995; Babenko & Fjellberg 2006 NT Rusek 1994; Skidmore 1995 NU Brown 1932; Davis 1936; Mills & Richards 1953; Christiansen & Bellinger 1980, 1998; Danks 1981 as kincaidi; Babenko 1993 as comparata; Babenko & Fjellberg 2006 QC Skidmore 1995 Remarks: Christiansen (1958) was the first author to consider this species as a probable synonym of E. kincaidi, and for a long time this remained the dominant opinion; later it was proved incorrect and E. erratica was upheld. Skidmore’s record (1995) of this arctic species for QC may be erroneous because it is probably based on Christiansen’s description (1958, p. 484) of original locality of erratica as “Quebec: Hudson Strait (Akpatok Island)”. Akpatok Island is now part of NU. General distribution: Nearctic and Eastern Palaearctic (Wrangel Island).Published as part of Babenko, Anatoly, Stebaeva, Sophya & Turnbull, Matthew S., 2019, An updated checklist of Canadian and Alaskan Collembola, pp. 1-125 in Zootaxa 4592 (1) on page 88, DOI: 10.11646/zootaxa.4592.1.1, http://zenodo.org/record/265692
Pseudachorutes aleksandrae Babenko & Kuznetsova & Nakamori & Shveenkova 2021, sp. nov.
No full textPseudachorutes aleksandrae Babenko sp. nov. Figs 1–14, Table 1 Type material. Russia: holotype, female (preadult), Republic of Sakha (Yakutia), Suntar-Khayata Mt. Range, upper reaches of Kyubyume River, vicinity of «Vostochnaya» weather station, 63°14.45’N 139°37.88’E, herbaceous meadow on terrace, 2100 m alt., 15 July 2002. O. Makarova leg. [MSPU collection]. Paratypes, 4 males, 5 females and 3 juveniles from the same sample [MSPU collection]. Other material. 9 specimens, Russia, Magadan Province, Bolshoi Annachag Mt. Range, upper reaches of Kolyma River, vicinity of former «Aborigen» field station [~ 61°56’N 149°40’E], 25 July 1979. V. Behan-Pelletier leg.; 9 males, 16 females and 9 juveniles, same region, but upper reaches of Ola River, ~ 120 km northward from Magadan [~ 60°39’N 151°16’E], alt. 980–1150 m, August 2011. O. Makarova & A. Babenko leg. Diagnosis. Medium sized species. PAO rather large, elliptic. Buccal cone blunt, labrum with 4/2334 setae, labium with 12 ordinary setae and without seta L or labial organites. Dorsal chaetotaxy rich with variable number of setae on Th. I, 3–4 setae in front of setae p3–p4 on Th. II–III and not especially long sensilla. Mucro with lateral lamella almost reaching tip. Each anal valve with three hr-setae. Description. Length (without antennae) 1.0– 1.8 mm, holotype ̅̅ 1.2 mm. Colour grey-blue, rather dark. Tegument granulation coarse and uniform. Antennae slightly shorter than head, Ant. III–IV fused dorsally, ventral separation well marked. Ant. IV with trilobed apical vesicle, external ms, subapical or and seta i present; sensilla (S1–S4, S7–S8) on dorsal side of Ant. IV clearly differentiated (Fig. 2), ventral side with few sensilliform setae of various shape (Fig. 3). Antennal organ of Ant. III typical, inner sensilla small, sgv about as long as sgd, ventral ms and usually 18 common setae present. Ant. I–II with 7 and 12 setae, respectively. Head with 8+8 subequal ocelli. PAO rather large, usually elliptic, consisting of 10–14 vesicles, its long axis to ocellus B ratio as 2.2–3.0: 1 (Figs 11–12). Buccal cone short and blunt (Fig. 8). Maxilla styliform with tiny apical teeth (Fig. 9), lamellae not clearly seen. Mandible delicate, with two thin teeth and one additional small denticle subapically (Fig. 10). Distal edge of labrum rounded, number of labral setae as follows: 4/2334. Main part of labium with four proximal ordinary setae, seta L and labial organites absent; basomedian (submentum) and basolateral (mentum) parts of labium with usual set of four setae each, i.e. 4+4 (Fig. 7). Perilabial area with 5+5 setae. Chaetotaxy rather variable, most typical pattern of dorsal chaetotaxy presented on Fig. 1, but asymmetrical abnormalities frequent especially on interocular part (area frontalis) of head (Figs 1, 4) and in lateral parts of terga, sensilla only 1.2–1.5 times longer than ordinary setae (Figs 5–6), their number as usual: 22/11111. Main characteristics: Th. I with 3+3, 3+4 or 4+4 setae, only Th. II with a2-setae and ms, dorso-external group on both Th. II–III with 3–4 setae (a3–a4, m3–m4) in front of p3–p4, m3 on Th. II often absent, on Th. III absent only occasionally. Abd. I–III with 2–3 setae (a3, m3–m4) in front of p3–p4. Abd. V without p2 as usual. Thoracic sterna without setae. Ventral tube with 4+4 setae, no seta on sternum of Abd. I, Abd. II with 3–4+3–4 ventral setae, Abd. III with 6–9 such setae. Tenaculum with 3+3 teeth as usual. Furca not especially long. Manubrium with 8–10+8–10 setae on main part, 4–5 setae on each basolateral lobe and 2 basal setae in line (Fig. 13). Dorsal side of dens with six setae and uniform coarse granulation, hyaline field on its ventral side about as large as mucro length. Mucro with upturned tip and broad lateral lamella almost reaching tip (Fig. 13). Each anal valve both in mature specimens and juveniles with three hr-setae (Fig. 14). Legs I–III with most usual number of setae: 1, 2, 2(3) setae on upper subcoxae, 0, 2, 2 setae on lower subcoxae, 3, 6(7), 7–8 setae on coxae, 6, 6, 6 on trochanters, 13, 12, 11 setae on femora and 19, 19, 18 setae on tibiotarsi. Unguis with clear tooth in mid part of inner edge, lateral teeth absent. Variation. Typically, the number of setae on Th. I is a stable feature in the genus, often used to separate closely related species. Surprisingly, this is not typical of P. aleksandrae sp. nov.: all type specimens from Yakutia always have only 3+3 setae on Th. I, while individuals with 4+4 setae clearly prevail in the Magadan Province. In addition, the dorsal sensilla in the latter are somewhat longer compared to ordinary setae. Etymology. The new species is named after the youngest granddaughter of the author as a gift for her five-year anniversary. Affinities. Among the two dozen species of the genus Pseudachorutes described on material from Japan, China, South and North Korea or found in these regions, only six, namely P. shiragamiensis and P. hitakamiensis (Japan), P. andrei Weiner & Najt, 1985 and P. dalensi Weiner & Najt, 1985 (N Korea), P. cheni Shi, Jiang & Pan, 2008 and P. wandae Gao, Yin & Palacios-Vargas, 2008 (China), have four proximal setae on labium like P. aleksandrae sp. nov. All of them can be more or less easily distinguished from the latter species. Both Japanese species mentioned above, P. shiragamiensis and P. hitakamiensis, have a different type of dorsal chaetotaxy with only two setae in front of p3–p4 on Th. II–III and only one seta in front of p3–p4 on Abd. I–III (so called parvulus - type). Apart from this, the former has a contrasting colour with white Th. II–III and Abd. VI, four teeth on mandibles and elongated buccal cone. The latter is characterized by small PAO with only 6–7 lobes, by the presence of two labral setae (vs 4 in P. aleksandrae sp. nov.) and only two hr-setae on each anal valve. Pseudachorutes dalensi from North Korea is unique in the above set due to several clavate setae on each tibiotarsi. Pseudachorutes andrei, described from the same region and apparently widespread in the eastern Palaearctic (see remarks to this species redescription below), may be easily distinguished because of much longer dorsal sensilla compared to ordinary setae (3.5–4.0: 1 vs 1.0–1.5: 1 in P. aleksandrae sp. nov.), rounded PAO with more (17–24) vesicles and only two tiny hr-setae on each anal valve. The Chinese species mentioned above, i.e. P. cheni and P. wandae, in addition to the similar shape of the labium, are also quite comparable with P. aleksandrae sp. nov. in their dorsal chaetotaxy (disregarding the presence of 2+2 sensilla on Abd. I–III in P. cheni, postulated in the original description, which, in our opinion, needs confirmation) although with much longer sensilla compared to ordinary setae (3–4: 1 in P. cheni and 5.5–7.5: 1 in P. wandae vs 1.0–1.5: 1 in P. aleksandrae sp. nov.). Apart from this, P. cheni has less number of labral setae (4/352 vs 4/ 2334 in P. aleksandrae sp. nov.), and mucro « without outer and inner lamellae », whereas P. wandae is characterized by the presence of spiniform seta L on labium. There are also two poorly described Japanese species, P. japonicus Kinoshita, 1916 and P. infuscata Yosii, 1954, whose buccal cone shape is unknown. The former can be distinguished due to a small rounded PAO with few vesicles, mandibles with five teeth and low lateral lamellae on mucro. The latter was described as a form of P. parvulus and considered now on www. collembola.org as its junior synonym. This opinion, as well as the presence of true P. parvulus in the eastern Palaearctic, probably needs modern confirmation, since several similar species have been described in the region since then (see, also description of P. cf. hitakamiensis below). Four species with the same type of labium are described in the present paper. Among them only P. concinnus sp. nov. is characterized by a blunt buccal cone without setae L similar to that in P. aleksandrae sp. nov. Additionally, these two species also have similar chaetotaxy but can be easily distinguished because of different number of prelabral setae (4 in P. aleksandrae sp. nov. vs 2 in P. concinnus sp. nov.) and hr-setae on anal valves (3 in P. aleksandrae sp. nov. vs 2 in P. concinnus sp. nov.) as well as due to distinctly differentiated setae on the head and clavate seta A1 on each tibiotarsus in P. concinnus sp. nov. In the western parts of the Palaearctic, the presence of all four proximal setae on the labium, i.e. A, B, C, D according to Massoud (1967), is clearly a predominant feature for the genus. For example, only one out of ten known congeners from Ukraine has not four, but three such setae (Kaprus’ & Weiner 2009). Four species of this fauna are also deprived of both seta L and labial organites, and only one of them, P. scythicus Kaprus’ & Weiner, 2009, has the same number of labral and prelabral setae as P. aleksandrae sp. nov. but differ in the shape and size of PAO and the number of hr-setae on anal valves. Distribution. The new species is known from three remote areas of northeastern Siberia.Published as part of Babenko, Anatoly, Kuznetsova, Natalia, Nakamori, Taizo & Shveenkova, Yulia, 2021, A review of Pseudachorutes Tullberg, 1871 (Collembola, Neanuridae) from the East Asia, with description of six new species, pp. 351-391 in Zootaxa 4938 (4) on pages 352-356, DOI: 10.11646/zootaxa.4938.4.1, http://zenodo.org/record/457480
On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
No full textThe question of adaptive approximation by splines has been studied for a number of years by various authors. The results obtained have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others.
In this dissertation we investigate some questions of adaptive approximation by various classes of splines (linear, multilinear, biquadratic) with free knots. In particular, we will study the asymptotic behavior of the optimal error of weighted approximation in different norms by interpolating splines from these classes. The proofs lead to the construction of asymptotically optimal simplicial or box partitions of the domain for interpolation by linear and multilinear splines, respectively.
In addition, applications to quadrature formulas are considered
On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
No full textExact asymptotics of the uniform error of interpolation by multilinear splines
No full textAbstractThe question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this paper we will investigate the questions regarding adaptive approximation of C2 functions with arbitrary but fixed throughout the domain signature by multilinear splines. In particular, we will study the asymptotic behavior of the optimal error of the weighted uniform approximation by interpolating and quasi-interpolating multilinear splines
Optimal Recovery of Integral Operators and its Applications
No full textIn this paper we present the solution to a problem of recovering a rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE’s
Stechkin\u27s Problem for Differential Operators and Functionals of First and Second Orders
No full textIn this paper, we present the solution to Stechkin’s problem for differential operators and functionals of first and second orders on the class of functions that are defined on a finite interval and have bounded third derivative. Two related problems are discussed: (1) finding sharp constants in the Landau–Kolmogorov inequalities, and (2) optimal recovery of an operator with the help of a set of linear operators (or arbitrary single-valued mappings) on elements of some set that are given with an error
Stechkin\u27s problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applications
No full textIn this paper we solve the problem of approximating functionals (ϕ(A)x, f) (where ϕ(A) is some function of self-adjoint operator A) on the class of elements of a Hilbert space that is defined with the help of another function ψ(A) of the operator A. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate |(ϕ(A)x, f)| with the help of kψ(A)xk and kxk. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H¨ormander theorem on comparison of operators in the case when operators are acting in a Hilbert space and are functions of a self-adjoint operator. As another application we obtain Taikov-type inequalities for functions of the operator 1 i d dt in the spaces L2(R) and L2(T), as well as for integrals with respect to spectral measures, defined with the help of classical orthogonal polynomials
Inequalities for the norms of finite difference operators of multiply monotone sequences
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