Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.     

Inverse systems of groupoids,with applications to groupoid C⁎-algebras

We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connections to noncommutative CW-complexes and interval algebras. We prove that an inverse system of groupoids with Haar system preserving bonding maps has a limit, and that we get a corresponding direct system of groupoid $C^{?}$-algebras. An explicit construction of an inverse system of groupoids is used to approximate a σ-compact groupoid G by second countable groupoids; if G is equipped with a Haar system and 2-cocycle then so are the approximation groupoids, and the maps in the inverse system are Haar system preserving. As an application of this construction, we show how to easily extend the Maximal Equivalence Theorem of Jean Renault to σ-compact groupoids.     

Possibilistic risk aversion and coinsurance problem

The coinsurance problem is an important topic in insurance decisions. A risk-averse agent should choose a coinsurance rate maximizing the expected final wealth. In this paper, we propose a possibilistic model of coinsurance problem. A decision problem whose solution is the optimal coinsurance is formulated. Some of its properties, the calculation modality and its behavior towards the changes of risk aversion are studied.     

Synthesis and characterization of new copper(II) complex compounds with chlorhexidine. Part I

Three new copper(II) complex compounds with chlorhexidine diacetate as a ligand have been prepared and characterized by elemental and thermogravimetrical analyses, molar conductances, magnetic susceptibility measurements, infrared, electronic and EPR spectra. The complexes correspond to the formulas: [Cu₂(CHX)Cl₄]·2C₂H₅OH, [Cu₂(CHX)Br₄]·2C₂H₅OH and [Cu₂(CHX)(CH₃COO)₂] (CH₃COO)₂·2C₂H₅OH, where CHX = chlorhexidine, their composition and stereochemistry depending on the reaction conditions and the metal salt used. Chlorhexidine acts as neutral tetradentate NNNN donor, coordinating through the four imine nitrogen atoms. Investigations on antimicrobial activity in vitro show that all the complexes are active against the tested microorganisms, the complex with chloride being more active against Gram negative bacteria than chlorhexidine diacetate..      

Synthesis,characterization and antibacterial activity of some new complexes of Cu(II), Ni(II), VO(II), Mn(II) with Schiff base derived from 4-amino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one

Coordination compounds of Cu(II), VO(II), Ni(II), and Mn(II) with the Schiff base obtained through the condensation of 4-amino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one with 3-formyl-6-methyl-chromone were synthesized. The characterization of the newly formed compounds was done by ¹H NMR, UV–Vis, IR, ESR spectroscopy, elemental analysis and molar electric conductibility. The crystal structure of 1-phenyl-2,3-dimethyl-4-(N-3-formyl-6-methyl-chromone)-3-pyrazolin-5-one (HL) has been determined by X-ray diffraction studies, as well as the one of its copper(II) complex [CuL(OAc)]·CH₃OH which contains an anionic ligand and an acetate in the coordination sphere of the metal. The single crystal X-ray structure for (HL) was analyzed for its various weak H-bonding and dimeric association.     

A risk approach by credibility theory

This paper attempts to treat some topics of risk theory by means of credibility theory. We study the risk aversion of an agent faced with a situation of uncertainty represented by a discrete fuzzy variable, the relationship between stochastic dominance and credibilistic dominance, and an index of riskiness of discrete credibilistic gambles. In the framework of an optimal saving credibilistic model, the way the presence of risk modifies the level of optimal saving is studied. The main tool of our investigation is an operator defined by B. Liu and Y. K. Liu by which to a discrete fuzzy variable one associates a discrete random variable with the same expected value as the former.     

Generalized Bosbach states: Part II

We continue the investigation of generalized Bosbach states that we began in Part I, restricting our research to the commutative case and treating further aspects related to these states. Part II is concerned with similarity convergences, continuity of states and the construction of the s-completion of a commutative residuated lattice, where s is a generalized Bosbach state.     

Multigroup deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delays: A stability analysis

In this paper, we investigate the dynamics of a multigroup disease propagation model with distributed delays and nonlinear incidence rates, which accounts for the relapse of recovered individuals. The main concern is the stability of the equilibria, sufficient conditions for global stability being obtained by applying Lyapunov‐LaSalle invariance principle and using Lyapunov functionals, which are constructed using their single‐group counterparts. The situation in which the deterministic model is subject to perturbations of white noise type is also investigated from a stability viewpoint.     

Stability of periodic traveling flexural‐gravity waves in two dimensions

In this work, we solve the Euler's equations for periodic waves traveling under a sheet of ice. These waves are referred to as flexural‐gravity waves. We compare and contrast two models for the effect of the ice: a linear model and a nonlinear model. The benefit of this reformulation is that it facilitates the asymptotic analysis. We use it to derive the nonlinear Schrödinger equation that describes the modulational instability of periodic traveling waves. We compare this asymptotic result with the numerical computation of stability using the Fourier–Floquet–Hill method to show they agree qualitatively. We show that different models have different stability regimes for large values of the flexural rigidity parameter. Numerical computations are also used to analyze high‐frequency instabilities in addition to the modulational instability. In the regions examined, these are shown to be the same regardless of the model representing ice.     

Competition between green and infrared emission in Er:YLiF4 upconversion lasers

The competition between two laser transitions in Er:YLiF₄ (⁴S_3/2 → ⁴I_15/2 at 551 nm and ⁴S_3/2 → ⁴I_13/2 at 850 nm) is studied using a model based on rate equations. The laser emission is pumped by upconversion at 795 nm; for comparison, we also discuss upconversion pumping by another mechanism, at 970 nm. The conditions that favor laser emission in various regimes on these two transitions are found.