Complete integrability and complex solitons for generalized Volterra system with branched dispersion

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

The Coxeter relations and KP map for non-commuting symbols

We give an action of the symmetric group on non-commuting indeterminates in terms of series in the corresponding Mal’cev–Newmann division ring. The action is constructed from the non-Abelian Hirota–Miwa (discrete KP) system. The corresponding companion map, which gives generators of the action, is discussed in the generic case, and the corresponding explicit formulas have been found in the periodic reduction. We discuss also briefly connection of the companion to the KP map with context-free languages.

Effects of a latency period between pre-stimulation and teat cup attachment and periodic vacuum reduction on milking characteristics and teat condition in dairy cows

The goal of the present study was to examine the suitability of a short pre-stimulation (P) for 15 s followed by a latency period (L) of 30 s before cluster attachment for machine milking. In addition we tested the effect of a periodic reduction of the vacuum under the teat (VR) during the massage phase from 43 kPa to 12–15 kPa on milking characteristics and teat tissue condition. The study was carried out in 9 cows in a cross-over design. Animals were milked twice daily, and each of the 4 treatment combinations was used for six subsequent milkings (P+L vs. continuous P, and standard pulsation vs. VR, respectively). Milk flow was recorded during all experimental milkings. Longitudinal ultrasound cross sections of the teat were performed by B-mode ultrasound after the last milking of each treatment at 0, 5, and 15 min after the end of milking, respectively. None of the evaluated milking characteristics (total milk yield, main milking time, peak flow rate, average milk flow) differed between treatments. Teat measures as obtained by ultrasound cross sections showed no significant difference if individual treatments were compared at the three time points individually. However, teat wall thickness (TWT) tended to be smaller in VR vs. non-VR treatments at 5 min after milking (P=0·05). In conclusion, teat preparation consisting of a short stimulation followed by a latency period represents a similarly efficient pre-stimulation as a continuous pre-stimulation. VR seems to reduce the load on the teat tissue during milking and thus reduces the development of oedema and hence a less pronounced increase of TWT while milking characteristics are similar with or without VR.

Generative reproduction efficiency and the population age structure of Rumex confertus Willd.

<i>Rumex confertus</i> is one of the alien species vigorously entering native meadow as well as ruderal communities in major river valleys. In about a hundred years the species invaded almost the whole territory of Poland. Many reports stating that Russian Dock may reach high coverage in various phytocoenoses contradict those of its low generative reproduction efficiency. In communities where it most frequently occurs, germination is hindered by the lack of empty spaces. In such conditions the population size remains stable due to vegetative reproduction. Only hay-growing meadows seem to promote the influx of new genets into population, which is likely associated with vegetation cover removal and periodic reduction of competition from other species.

Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of polarized kink solutions.

Analysis of epithelial K+ transport in Malpighian tubules ofDrosophila melanogaster: evidence for spatial and temporal heterogeneity

SUMMARYTransport of K+ by the lower, main and distal segments of the Malpighian tubules of Drosophila melanogaster was analyzed using self-referencing K+-selective microelectrodes. Transport properties of the Malpighian tubules of Drosophila melanogaster change along their length. Self-referencing ion-selective (SeRIS) microelectrode measurements (relative to the bath concentration of 20 mmoll−1) showed a 1% reduction (P&lt;0.05) of [K+] in the unstirred layer adjacent to the main segment of the Malpighian tubules, confirming secretion of K+ from the bath to the tubule lumen. Conversely, SeRIS measurements showed a 0.7% increase (P&lt;0.05) in [K+] in the unstirred layer adjacent to the lower segment of Malpighian tubules, confirming reabsorption of K+ from the luminal fluid to the bath. Measurements using SeRIS also showed that the distal segment neither secreted nor reabsorbed K+. There was pronounced spatial heterogeneity in K+ transport by the lower segment and the main segment; not all morphologically similar cells participated equally in K+ transport, nor did all main segment cells respond equally to stimulation of K+ transport by cyclic AMP. Pronounced temporal heterogeneity in K+ reabsorption by the lower Malpighian tubules was also observed. We suggest that this reflects periodic reduction in K+ reabsorption due to retention of fluid within the lower segment when the ureter contracts.