ON THE IMPULSIVE BEVERTON–HOLT EQUATION AND EXTINCTION CONDITIONS IN POPULATION DYNAMICS

Abstract This paper is devoted to investigate extinction and nonextinction conditions of the extended Beverton–Holt equation (BHE) for dynamics of populations in Ecology when potential discontinuities at sampling points are included in the model. The proposed model is described by means of four sequences of parameters. Two of them are the intrinsic growth rate and the carrying capacity sequences which are included in the basic BHE model. The other two ones, namely, the harvesting (i.e., the hunting or fishing quota) and the internal consumption (which can include positive and negative migrations in the considered population habitat) sequences are included to parameterize the model discontinuities. Such discontinuities are related to impulses in the corresponding continuous‐time logistic equation. The obtained results establish how the harvesting quota and/or the internal consumption has to be fixed to guarantee the population nonextinction or, eventually, its extinction. Finally, some controllability results related to the search of a carrying capacity sequence such that the solution of the proposed impulsive BHE tracks a reference one are obtained.     

CaF2：xYb3+, yEr3+纳米颗粒的合成及其上转换发光性质

采用水热合成法制备了CaF₂：xYb³⁺,yEr³⁺（x=0.1~0.8,y=0.01~0.08）纳米颗粒,利用X射线粉末衍射仪、透射电子显微镜和F-4600荧光分光光度计表征了样品的物相和形貌尺寸,并探究了Yb³⁺和Er³⁺掺杂浓度对样品的上转换发光性质的影响。结果表明,所合成的样品为立方相,球形颗粒,平均直径为 12 nm,敏化剂Yb³⁺的最佳掺杂摩尔分数为20%,而激活剂Er³⁺的最佳掺杂摩尔分数为6%。此时,绿光与红光的强度之比最大。     

Preparation and characterization of poly(butylene terephthalate)/poly(ethylene terephthalate) copolymers via solid‐state and melt polymerization

To increase the T_g in combination with a retained crystallization rate, bis(2‐hydroxyethyl)terephthalate (BHET) was incorporated into poly(butylene terephthalate) (PBT) via solid‐state copolymerization (SSP). The incorporated BHET fraction depends on the miscibility of BHET in the amorphous phase of PBT prior to SSP. DSC measurements showed that BHET is only partially miscible. During SSP, the miscible BHET fraction reacts via transesterification reactions with the mobile amorphous PBT segments. The immiscible BHET fraction reacts by self‐condensation, resulting in the formation of poly(ethylene terephthalate) (PET) homopolymer. ¹H‐NMR sequence distribution analysis showed that self‐condensation of BHET proceeded faster than the transesterification with PBT. SAXS measurements showed an increase in the long period with increasing fraction BHET present in the mixtures used for SSP followed by a decrease due to the formation of small PET crystals. DSC confirmed the presence of separate PET crystals. Furthermore, the incorporation of BHET via SSP resulted in PBT‐PET copolymers with an increased T_g compared to PBT. However, these copolymers showed a poorer crystallization behavior. The modified copolymer chain segments are apparently fully miscible with the unmodified PBT chains in the molten state. Consequently, the crystal growth process is retarded resulting in a decreased crystallization rate and crystallinity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 882–899, 2007.     

Modelling the velocity of air through beds of cereal grains

The quality of cereal grains in storage will deteriorate toan unacceptable level if they are not kept dry and cool. Tomodel the drying and cooling process, an accurate knowledgeof the airflow distribution is required. In this paper, theequations used to model the air velocity are analysed. To study the flow of air through a typical drying system forstored grain, a two-dimensional rectangular bin is considered,with a single source of air on the bin floor. Two paths ofstudyare undertaken: the first is a linear analysis for low velocities,and following on from this is a nonlinear approach for largervelocities. The linear analysis is used to study a bin witha semi-infinite height, and the drying pattern is studied inthis bin using the air traverse time. Then bins with a finiteheight are analysed: it is shown that, for tall enough bins,the semi-infinite solution is accurate enough. A perturbationanalysis is used to study the semi-infinite bin when the airvelocity is too large for the linear analysis to be accu rate.It is shown that the effect of the nonlinearity is to move theair away from the high-velocity regions towards the areas oflower velocity.     

On a Moving Boundary Problem Aristing in Fluidized Bed Combustion

We consider a model describing the combustion of a coal particlein a fluidized bed, in which attrition plays a dominant role.The model consists of (1) a quasi-linear elliptic equation forthe oxygen concentration, supplemented by boundary conditionson the moving surface representing the burning particle interface,(2) an evolution equation for the carbon consumption, and (3)an equation governing the motion of the interface in terms ofa specified function of the carbon consumption at the interface.We prove a global existence and uniqueness result, togetherwith a priori bounds for the solution; the existence of travellingwaves will also be established.     

ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

Commutators with idempotent values on multilinear polynomials in prime rings

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x ₁, . . . , x _n ) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that

$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$

for all r ₁, . . . , r _n ∈ρ. Then either [f(x ₁,…,x _n ),x _n+1]x _n+2 is an identity for ρ or d(ρ)ρ = 0.

     

La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体的溶剂热合成及白色上转换发光性质

采用溶剂热方法制备了La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体,并利用粉末X射线衍射仪、透射电子显微镜和X射线能谱仪表征了其组成、结构和形貌,用荧光分光光度计测量了样品的室温上转换发射光谱,结果表明,样品具有红、绿和蓝色3个发射带,其辐射跃迁分别归属于Tm3+的1G4→3H6(蓝色)和1G4→3...     

High-resolution FTIR spectrum of vinyl chloride: rovibrational analysis of the v 10 and v 11 fundamental bands

The Fourier transform gas-phase infrared spectra of the v ₁₀ and v ₁₁ bands of natural CH₂=CHCl have been measured with a resolution of 0.005 cm^?1 in the frequency range 820–1010 cm^?1. These vibrations of symmetry species A″ give rise to c-type bands and the transitions observed are characterized by δK _a = ±1 and δK _c = 0, ±2. Both J and K structures have been resolved in different subbranches and about 1800 (J ≤ 64, K _a ≤ 13) and 2800 (J ≤ 72, K _a ≤ 14) transitions for the v ₁₀ and v ₁₁ fundamentals, respectively, have been identified for the ³⁵Cl isotopomer. Combined analysis of the assigned data with the available ground state constants allowed the determination of the band origins, rotational and centrifugal distortion parameters for the v ₁₀ = 1 and v ₁₁ = 1 excited states of CH₂=CH³⁵Cl isotopic species. The molecular constants obtained account for slight perturbations in the v ₁₀ vibrational level.