Competitive exclusion and coexistence in a Leslie–Gower competition model with Allee effects

The classical competitive exclusion principle states that two populations competing for a limited resource cannot coexist, one of the populations will drive the other to extinction. We prove in this work that when one population is subject to Allee effects, then for certain parameter regimes both competing populations may either coexist or one population may drive the other to extinction depending on initial conditions.     

L 2-\overline{\partial}-Cohomology groups of some singular complex spaces

Let X be a pure n-dimensional (where n≥2) complex analytic subset in ? ^N with an isolated singularity at 0. In this paper we express the L ²-(0,q)- $\overline{\partial}$ -cohomology groups for all q with 1≤q≤n of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L ²-(0,q)- $\overline{\partial}$ -cohomology groups of the smooth points of X, in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities.     

A discrete two-stage population model: continuous versus seasonal reproduction

A discrete two-stage model which describes the dynamics of a population where juveniles and adults compete for different resources is developed. A motivating example is the green tree frog (Hyla cinerea) where tadpoles and adult frogs feed on separate resources. First, continuous breeding is assumed and the asymptotic behavior of the resulting autonomous model is fully analyzed. It is shown that the unique interior equilibrium is globally asymptotically stable when the inherent net reproductive number is greater than one. However, when the inherent net reproductive number is less than one, the population becomes extinct. Then a seasonal breeding described by a periodic birth rate with period 2 is assumed. It is proved that for this nonautonomous model a period two solution is globally asymptotically stable when the inherent net reproductive number is greater than one and when the inherent net reproductive number is less than one the population becomes extinct. Finally, the advantage (in terms of maximizing the number of juveniles and adults in the population over a fixed time period) of having a seasonal breeding is studied by comparing the average of the juvenile and adult numbers of the periodic solution for the nonautonomous model to the equilibrium solution of the autonomous model. Our results indicate that for high birth rates the equilibrium of the autonomous model is higher than the average of the two cycle solution. Therefore, all other factors being equal, seasonal breeding appears to be deleterious to populations with high birth rates. However, for low birth rates seasonal breeding can be beneficial. It is also shown that for a range of birth rates the nonautnomous model is persistent while the solution to the autonomous model goes to extinction.     

Transient Analysis for State-Dependent Queues with Catastrophes

Abstract

Queueing systems with catastrophes and state-dependent arrival and service rates are considered. For two types of queueing systems namely, queues with discouraged arrivals and infinite server queue, explicit expressions for the transient probabilities of system size are obtained by using continued fractions technique. Some system performance measures and steady-state probabilities are studied. The effect of system parameters on system size probabilities are also illustrated numerically. It is observed that the steady-state probabilities differ when catastrophes are present, while they are identical in the absence of catastrophes.     

Sequence‐Defined Introduction of Hydrophobic Motifs and Effects in Lectin Binding of Precision Glycomacromolecules

This study investigates the influence of an increasingly hydrophobic backbone of multivalent glycomimetics based on sequence‐defined oligo(amidoamines) on their resulting affinity toward bacterial lectins. Glycomacromolecules are obtained by stepwise assembly of tailor‐made building blocks on solid support, using both hydrophobic aliphatic and aromatic building blocks to enable a gradual change in hydrophobicity of the backbone. Their binding behavior toward model lectin Concanavalin A (ConA) is evaluated using isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) showing higher affinities for glycomacromolecules with higher content of hydrophobic and aromatic moieties in the backbone. Finally, glycomacromolecules are tested in a bacterial adhesion inhibition study against Escherichia coli where more hydrophobic backbones yield higher inhibitory potentials most likely due to additional secondary interactions with hydrophobic regions of the protein receptor as well as a change in conformation exposing carbohydrate ligands for increased binding. Overall, the results highlight the influence and thereby importance of the polymer backbone itself on the resulting properties of polymeric biomimetics.     

Synthesis of 7a-substituted Hajos-Wiechert ketone analogues

A general and efficient route to 2-substituted 1,3-cyclopentadiones 3 has been developed. This operationally simple, two-step procedure is amenable to multigram scale preparations of these useful synthetic intermediates. These compounds are then transformed to previously unknown, higher analogues of the Hajos-Parrish-Eder-Sauer-Wiechert ketone (enone 1, R = Me) following an enantioselective Robinson annulation.     

Fiber Integrated Metal-Organic Frameworks as Functional Components in Smart Textiles

Owing to high modularity and synthetic tunability, metal–organic frameworks (MOFs) on textiles are poised to contribute to the development of state-of-the-art wearable systems with multifunctional performance. While these composite materials have demonstrated promising functions in sensing, filtration, detoxification, and biomedicine, their applicability in multifunctional systems is only beginning to materialize. This review highlights the multifunctionality and versatility of MOF-integrated textile systems. It summarizes the operational goals of MOF@textile composites, encompassing sensing, filtration, detoxification, drug delivery, UV protection, and photocatalysis. Building upon these recent advances, this review concludes with an outlook on emerging opportunities for the diverse applications of MOF@textile systems in the realm of smart wearables.     

Physical insights from a penetration depth model of optically pumped NMR

A model of optically pumped NMR (OPNMR) behavior in GaAs that connects the photon energy dependence of the OPNMR signal intensity for (69)Ga with different polarizations of light has been developed. Inputs to this model include experimental conditions--external magnetic field (B(0)), temperature (T), and optical pumping parameters (tau(L), laser helicity)--as well as parameters that arise from sample-specific characteristics--electron spin lifetime (T(1e)), electron lifetime (tau(e)), electron-nuclear correlation time (tau(c)), and sample thickness (z). These various inputs affect the profile of the OPNMR signal intensity as a function of photon energy (E) in a predictable manner. Therefore, the profile can serve as a composite fingerprint by which individual parameters can be inferred when not known. Characteristics of the profile include the photon energy for maximum OPNMR signal intensity and the intensity ratio between sigma(+) and sigma(-) light.     

Optically pumped nuclear magnetic resonance of semiconductors

Optically pumped NMR (OPNMR) of direct gap and indirect gap semiconductors has been an area of active research interest, motivated by both basic science and technological perspectives. Proposals to enhance and to spatially localize nuclear polarization have stimulated interest in this area. Recent progress in OPNMR has focused on exploring the experimental parameter space in order to elucidate details of the underlying photophysics of optical pumping phenomena. The focus of this review is on recent studies of bulk samples of GaAs and InP, namely, the photon energy dependence, the magnetic field dependence, and the phase dependence of OPNMR resonances. Models for the development of nuclear polarization are discussed.