For n=2m\geqslant 4, let \Omega\in \mathbb{R}^{n} be a bounded smooth domain and N\subset \mathbb{R}^{L} a compact smooth Riemannian manifold without boundary. Suppose that \left \{ uk \right \}\in W^{m,2}\left ( \Omega ,N \right ) is a sequence of weak solutions in the critical dimension to the perturbed m-polyharmonic maps \frac{{\text{d}}}{{{\text{dt}}}}\left| {_{t = 0}{E_m}({\text{II}}(u + t\xi )) = 0} \right with Ωk → 0 in W^{m,2}\left( \Omega ,N \right )* and {u_k} \rightharpoonup u weakly in W^{m,2}\left( \Omega ,N \right ). Then u is an m-polyharmonic map. In particular, the space of m-polyharmonic maps is sequentially compact for the weak- W^{m,2} topology., Shenzhou Zheng., and Obsahuje seznam literatury
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold "a harmonic manifold is locally symmetric" and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting., Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa., and Obsahuje bibliografii
The perturbed Laplacian matrix of a graph G is defined as DL = D−A, where D is any diagonal matrix and A is a weighted adjacency matrix of G. We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use the notion of Perron component for the perturbed Laplacian matrix of a graph and show how its second smallest eigenvalue can be characterized using this definition., Israel Rocha, Vilmar Trevisan., and Obsahuje seznam literatury
A key to genera of South American Deltocephalini Dallas, 1870 based on adult males is presented. Two new genera, each based on a single new species from Argentina are described and illustrated: Corrientesia gen. n. based on type species C. ochrescens sp. n. and Salnogia gen. n. based on type species S. fletcheri sp. n. A new species of Graminella DeLong, 1936, G. schrocki sp. n. from Argentina is also described and illustrated. Graminella stelliger (Berg, 1884) equals Fusanus acristylus Cheng, 1980, syn. n. A new combination, Limpica pallida (Linnavuori & DeLong, 1979) comb. n., transferred from Reventazonia Linnavuori, 1959, is also proposed. Quaziptus Kramer, 1965, is returned from Paralimnini Distant, 1908 to Deltocephalini Dallas, 1870., Yani Duan, Christopher H. Dietrich., and Obsahuje bibliografii
Short-winged (brachypterous) and long-winged (macropterous) adult females of Pyrrhocoris apterus (L.) originating from a Mediterranean population (Israel) were analyzed for their adipokinetic responses. The adipokinetic response, expressed as an increase of haemolymph lipids after injection of adipokinetic hormone from Locusta migratoria (Lom-AKH-I), was assessed in relation to age and dose of the hormone. We demonstrate in this study that the adipokinetic responses induced by bug's corpora cardiaca extract and Lom-AKH-I were dose-dependent for both brachypterous and macropterous females. Significant differences between the morphs were recorded for doses >= 0.25 corpora cardiaca equivalent (P < 0.01) and doses >= 0.25 pmol Lom-AKH-I (P < 0.05). The haemolymph lipid elevations induced in both morphs by 2 pmols Lom-AKH-I are comparable with that induced by crude extract of one pair of the bug's own corpora cardiaca. The age-dependent test showed much higher adipokinetic responses (P < 0.01) in macropterous females (>= 5 days old) than in the brachypterous females of the same age, when treated with 2 pmols Lom-AKH-I. Starting from day 7, the concentration of haemolymph lipids was also considerably higher (2.5-5 times) in macropterous females than in the brachypterous ones. The obtained data indicate that difference in mobilization of lipids between brachypterous and macropterous females is a geographically independent feature and represents a true wing morph characteristic of P. apterus., Dalibor Kodrík, Radomír Socha, and Lit