The equation is analysed with respect to the following consequences. I group theoretical structure of studied. invariant under a number continous transformations: inhomogeneous Lorentzgroup, transformations PAULI, GÜRSEY and TOUSCHEK, scale transformation [ϰ→η x or ψ → η⅔ψ(ϰη, l η)]. PAULI-GÜRSEY used for interpretation isospin; γ 5 -transformation TOUSCHEK establishes quantum N , leads IN, which both are connected baryonic leptonic number. strangeness s=l -l Q suggested be discrete groups...

The polaron Hamiltonian would be easily soluble were it not for the quartic term appearing therein. It is proposed to substitute a quadratic having roughly same properties, and in such way that ground-state energy of new rigorously lower bound true energy. With very small amount work one can obtain as continuous function $\ensuremath{\alpha}$ all values $\ensuremath{\alpha}$. result agrees fairly well with results obtained by other methods. Using equivalent also an analytic expression...

We study the two-dimensional generalized magnetohydrodynamics system with dissipation and diffusion in terms of fractional Laplacians. In particular, case where term has power β=1, contrast to previous result α⩾12, we show that α>13 suffices order for solution pair velocity magnetic fields remain smooth all time.

We study the two-dimensional magneto-micropolar fluid system. Making use of structure system, we show that with zero angular viscosity solution triple remains smooth for all time.

Predation has led to the evolution of defensive armor in prey species. The dense and long hairs caterpillars (i.e., lepidopteran larvae) are generally believed play an important role as a physical defence against predators. However, few studies have been undertaken investigate how protect from predator's weapons. To determine importance caterpillar armor, we observed adults Calosoma maximowiczi (Carabidae) attacking 5 species with different hairiness under laboratory conditions. Carabids...

Polymer-supported, palladium-catalyzed cyclization reactions effectively synthesized indolecarboxylates. Palladium-catalyzed carbon-carbon bond-forming of immobilized enaminoesters followed by transesterification yielded indole 2- or 3-carboxylates with various functional groups on the benzene ring. Indolecarboxylates were efficiently cyclized via an intramolecular amination reaction N-substituted dehydrohalophenylalanines, and N-acetyl-dehydroalanines converted into indolecarboxylates...

In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) PDE model. First, local well-posedness result relying on theory cooperative dynamics systems is obtained. Via priori estimates making use special structure system and continuation argument, show that fact globally well-posed. Secondly, analyze asymptotic stability...

Plants employ various defensive tactics against herbivores but are rarely considered to use rapid movements resist predation. However, the aboveground parts of plants often forcefully moved by wind and rain. This passive movement has been overlooked as an anti-herbivore trait. The leaves many plant species, such aspens, Indian sacred fig, bamboos, palms, tremble even in a slight breeze. Leaves that easily gentle winds can sometimes strong may have other benefits well. In present study, it is...

We study the global stability issue of reaction-convection-diffusion cholera epidemic PDE model and show that basic reproduction number serves as a threshold parameter predicts whether will persist or become globally extinct. Specifically, when is beneath one, we disease-free-equilibrium attractive. On other hand, exceeds if infectious hosts concentration bacteria in contaminated water are not initially identically zero, prove uniform persistence result there exists at least one positive...

We study the two-dimensional Navier--Stokes equations forced by random noise with a diffusive term generalized via fractional Laplacian that has positive exponent strictly less than one. Because intermittent jets are inherently three-dimensional, we instead adapt theory of form stationary flows to stochastic approach presented Hofmanová, Zhu, and Zhu [Non-Uniqueness in Law Stochastic 3D Equations, arXiv:1912.11841 [math.PR]] prove its nonuniqueness law.

Rh(II)-catalyzed N-H insertion reaction of immobilized alpha-diazophosphonoacetate with 2-haloanilines followed by Horner-Emmons gave enaminoesters, which were efficiently cyclized to indoles via intramolecular palladium catalyzed on a polymer support.

We follow the approach of [13] to study N-dimensional generalized MHD system with fractional Laplacians as dissipative and diffusive terms in various anisotropic spaces. In particular, we obtain small initial data results Sobolev space type norms for which, depending on power Laplacians, may decrease regularity index many directions zero or even negative, expense increasing rest. Similar Besov spaces are also obtained.

Abstract. 1. Most lepidopteran larvae use all of their legs (thoracic and abdominal prolegs) when walking on solid substrates. When caterpillars involuntarily or intentionally drop from the tree canopy, they can regain original position by climbing silk lifelines spun out head spinnerets. However, taxonomic distribution this behaviour in Lepidoptera is unknown. 2. Here, lifeline‐climbing reported 13 species belonging to different taxa (five superfamilies six families: Zygaenidae, Drepanidae,...