Comparing predator–prey models with hidden and explicit resources

In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction.     

Linking numbers in local quantum field theory

Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge-invariant) vector potentials, integrated about spacelike separated, spatial loops, are elements of the center of the algebra of all local fields. Moreover, these commutators are proportional to the linking numbers of the underlying loops. If the commutators are different from zero, the underlying two-forms are not exact (i.e. there do not exist local vector potentials for them). The theory then necessarily contains massless particles. A prominent example of this kind, due to J.E. Roberts, is given by the free electromagnetic field and its Hodge dual. Further examples with more complex mass spectrum are presented in this article.

     

High-performance liquid chromatographic/tandem mass spectrometric identification of the phototransformation products of tebuconazole on titanium dioxide

Tebuconazole is a widely used fungicide. The formation of by-products on irradiated titanium dioxide as a photocatalyst was evaluated. Several species derived from tebuconazole degradation were identified and characterized by HPLC/MS(n). A pattern of reactions accounting for the observed intermediates is proposed. Different parallel pathways are operating (and through these pathways the transformation of the molecule proceeds), leading to a wide range of intermediate compounds. All these molecules are more hydrophylic than tebuconazole. The main steps involved are (1) the hydroxylation of the molecule with the formation of three species having [M + H](+) 324; the hydroxylation occurs on the C-1 carbon and on the aromatic ring in the two ortho-positions; (2) the cleavage of a C--C bond with the release of the tert-butyl moiety and the formation of a species having m/z 250; analogously to step 1, also on this species a further hydroxylation reaction occurs; (3) through the loss of the triazole moiety with the formation of a structure with m/z 257.     

A simple mathematical model for seasonal planktonic blooms

We show how the inclusion of the defense strategy by different species can alter the prediction of simple models. One of the defense strategy by the phytoplankton population against their grazer is the release of toxic chemicals. In turn the zooplankton population reduces there predation rate over toxin producing phytoplankton (TPP) to protect themselves from those toxic chemicals. Thus, when the level of toxicity is high, the grazing pressure is low and when the level of toxicity is low or when the toxin is absent, the grazing pressure is high. Here we have considered a TPP–zooplankton system where the rate of toxin liberation and the predation rate vary with zooplankton abundance. We observe that our proposed model has the potential to show different dynamical behaviour that are similar to that seen in real‐world situations. Further, we consider three different functional forms for the distribution of the toxins and compare them using latin hypercube sampling technique and found that the functional forms seem to have no effect in determining the final outcome of the system. Copyright © 2009 John Wiley & Sons, Ltd.     

Attempted Oxidative Deamination of N-Deacetylcolchicinoids with 3,5-Di(tert-butyl)-1,2-benzoquinone: Synthesis of 2H-1,4-Benzoxazine-Type Adducts

In an attempt to use 3,5-di(tert-butyl)-1,2-benzoquinone for the oxidative deamination of N-deacetylcolchicine ( 4 ) and N-deacetylthiocolchicine (=N-deacetyl-10-demethoxy-10-(methylthio)colchicine; 5 ) to give the corresponding ketones 2 and 3 , the 2H-1,4-benzoxazine-type adducts 8 / 9 and 11 / 12 , respectively, were formed instead, showing a new and unexpected behavior of Corey's reagent. The adducts were separated and spectroscopically characterized, and a plausible scheme of formation is reported.     

Minimal volume invariants,topological sphere theorems and biorthogonal curvature on 4‐manifolds

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4‐manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.     

Modeling the depletion of dissolved oxygen in a water body located near a city

Water bodies located nearby cities are much prone to pollution, especially in the developing countries, where effluents treatment facilities are generally lacking. The main reason for this phenomenon is the increasing population in the cities, and the large number of industries located near them. This leads to generation of huge amounts of domestic and industrial sewage that is discharged into the water bodies, increasing their organic pollutant load and resulting in the depletion of dissolved oxygen. In this paper, we propose a mathematical model for this situation, focusing especially on the resulting quality of the water, determined by the level of dissolved oxygen. The model also accounts for resources needed for the population survival and for the industrial operations. In addition, we describe also the decomposition of organic pollutants by bacteria in the aquatic medium. Feasibility conditions and stability criteria of the system's equilibria are determined analytically. The results show that human population and industries are relevant influential factors responsible for the increase in organic pollutants and the decrease in dissolved oxygen in the water body, in the sense that they may exert a destabilizing effect on the system. The numerical simulations confirm the analytical results. Copyright © 2016 John Wiley & Sons, Ltd.