A Ricci inequality for hypersurfaces in the sphere

Let Mⁿ be a complete Riemannian manifold immersed isometrically in the unity Euclidean sphere In [9], B. Smyth proved that if Mⁿ, n ≧ 3, has sectional curvature K and Ricci curvature Ric, with inf K > −∞, then sup Ric ≧ (n − 2) unless the universal covering of Mⁿ is homeomorphic to Rn or homeomorphic to an odd-dimensional sphere. In this paper, we improve the result of Smyth. Moreover, we obtain the classification of complete hypersurfaces of with nonnegative sectional curvature.Received: 11 November 2003     

A generalization of von Neumann's assignment problem and K. Fan optimization result

Summary In this paper we generalize the assignment problem in higher dimensions, referring at to another study by the authors. The hide-and-seek game, which is intimately related to the assignment problem, is extended, and an elegant result due to K. Fan about extrema is generalized.     

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.     

A safe harbor can protect an endangered species from its predators

The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second patch the prey grows logistically. The model is formulated in a comprehensive way so as to include specialist as well as generalist predators, as a continuum of possible behaviors. This model described by a set of three ordinary differential equation is an extension of some previous models proposed and analysed in the literature on metapopulation models. The following analysis issues will be addressed: boundedness of the solution, equilibrium feasibility and stability, and dynamic behaviour dependency of the population and environmental parameters. Three types for both equilibria and limit cycles are possible: trivial, predator-free and coexistence. Classical analysis techniques are used and also theoretical and numerical bifurcation analysis. Besides the well-known local bifurcations, also a homoclinic connection as a global bifurcation is calculated. In view of the difficulty in the analysis, only the specialist case will be analysed. The obtained results indicate that the safe harbor can protect the endangered species under certain parametric restrictions.

     

Ecoepidemic models with disease incubation and selective hunting

In this paper we consider ecoepidemic models in which the basic demographics is represented by predator-prey interactions, with the disease modeled by an SEI system. At first we consider a basic Lotka-Volterra type of interaction. Then we also introduce competition for resources among individuals of the prey population. Several variations of the model are presented, in which the prey intra-specific population pressure assumes different forms, depending on the virulence of the disease. Indeed, the latter may affect the exposed and infected individuals so much that they may not be able to compete with the sound ones for resources. A further distinguishing feature of this investigation lies in the way in which the predator actively selects the prey for hunting. For instance in some cases predators may discard the diseased ones, as less palatable, while in other situations they would instead search expressly for the infected, since these are weaker individuals and thus easier to hunt. The equilibria of the systems are analyzed, showing that in some cases bifurcations arise, contrary to what happens to similar classical Holling type I ecoepidemic models. These persistent oscillations seem to be triggered by the number of subpopulations present in the system, which is larger than those introduced in the former models, counting also the latent class. Furthermore, adding predation to an SEI epidemic model has profound effects on the stability of its equilibria. In particular, once the predators are introduced into an SEI epidemic at a stable endemic equilibrium, their presence destabilizes this equilibrium making the previous stable conditions unrecoverable.     

Optimization of DNA extraction from dental remains

Efficient DNA extraction procedures is a critical step involved in the process of successful DNA analysis of such samples. Various protocols have been devised for the genomic DNA extraction from human tissues and forensic stains, such as dental tissue that is the skeletal part that better preserves DNA over time. However DNA recovery is low and protocols require labor‐intensive and time‐consuming step prior to isolating genetic material. Herein, we describe an extremely fast procedure of DNA extraction from teeth compared to classical method. Sixteen teeth of 100‐year‐old human remains were divided into two groups of 8 teeth and we compared DNA yield, in term of quantity and quality, starting from two different sample preparation steps. Specifically, teeth of group 1 were treated with a classic technique based on several steps of pulverization and decalcification, while teeth of group 2 were processed following a new procedure to withdraw dental pulp. In the next phase, the samples of both group underwent the same procedure of extraction, quantification and DNA profile analysis. Our findings provide an alternative protocol to obtain a higher amount of good quality DNA in a fast time procedure, helpful for forensic and anthropological studies.     

Characterization of atenolol transformation products on light-activated TiO2 surface by high-performance liquid chromatography/high-resolution mass spectrometry

We have studied the photocatalytic transformation of atenolol, 4-[2-hydroxy-3-[(1-methyl)amino]propoxyl]benzeneacetamide, a cardioselective beta-blocking agent used to treat cardiac arrhythmias and hypertension, under simulated solar irradiation using titanium dioxide as photocatalyst. The investigation involved monitoring drug decomposition, identifying intermediate compounds, assessing mineralization, and evaluating toxicity. High-performance liquid chromatography (HPLC) coupled to high-resolution mass spectrometry (HRMS) via an electrospray ionization (ESI) interface was a powerful tool for the identification and measurement of the degradation products; 23 main species were identified. Intermediates were characterized through their chromatographic behavior and evolution kinetics, coupled with accurate mass information. Through the full analysis of MS and MS(n) spectra and a comparison with parent drug fragmentation pathways, the diverse isomers were characterized. Neither atenolol nor the intermediates formed exhibit acute toxicity. All intermediates are easily degraded and no compound identified could withstand 2 h irradiation. Photomineralization of the substrate in terms of carbon mineralization and nitrogen release was rapid and, within 4 h of irradiation, organic nitrogen and carbon were completely mineralized.     

Living polymerization: Rationale for uniform terminology

Polymer chemistry textbooks (e.g., B. Vollmert, Polymer Chemistry, Springer‐Verlag: New York, 1973, p 37; G. Odian, Principles of Polymerization, 3rd ed., Wiley: New York, 1991, p 8; H. G. Elias, An Introduction to Polymer Science, VCH: Weinheim, 1997, p 51) classify polymerization reactions as chain, step, and living according to the dependence of their degree of polymerization (DP ) or molecular weight (M̄) on conversion. This article discusses the rationale for uniform terminology in living polymerization. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1706–1708, 2000     

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.