Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.     

Elastic scattering and total reaction cross section for the He + Al system

The elastic scattering of the radioactive halo nucleus ⁶He on ²⁷Al target was measured at four energies close to the Coulomb barrier using the RIBRAS (Radioactive Ion Beams in Brazil) facility. The São Paulo Potential (SPP) was used and its diffuseness and imaginary strength were adjusted to fit the elastic scattering angular distributions. Reaction cross-sections were extracted from the optical model fits. The reduced reaction cross-sections of ⁶He on ²⁷Al are similar to those for stable, weakly bound projectiles as ^6,7Li, ⁹Be and larger than stable, tightly bound projectile as ¹⁶O on ²⁷Al.     

Nonsequential double ionization with few-cycle laser pulses

We investigate differential electron momentum distributions in nonsequential double ionization with linearly polarized, few-cycle pulses, using a classical model based on a laser-assisted inelastic (e(-),2e(-)) rescattering mechanism. These yields, as functions of the momentum components parallel to the laser polarization, are highly asymmetric and strongly influenced by the phase difference between the pulse envelope and its carrier oscillation, radically changing their sign around a critical phase. This behavior provides a powerful tool for absolute-phase measurements.     

The chlorate-iodine clock reaction

A clock reaction produced by mixing chlorate and iodine solutions in perchloric acid media is reported. This is the first example of a clock reaction using chlorate as a reagent. Increasing chlorate and acid concentration reduces the induction period. Changing the initial iodine concentration does not affect the length of the induction period. The discovery of this clock reaction opens the possibility that a new family of oscillation reactions can be built using chlorate as reagent.     

Rigidity of critical circle mappings II

We prove that any two real-analytic critical circle maps with cubic critical point and the same irrational rotation number of bounded type are conjugate for some .

     

Persistence,Permanence and Global Stability for an n-Dimensional Nicholson System

For a Nicholson’s blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.     

Coating of polyamide 12 by sol–gel methodology

The combination of sol–gel methodology with rapid prototyping (RP) produces functionalized 3D structures with potential applications in various fields. However, this combination has been little explored. In this paper, we used the sol–gel method to deposit vanadium isopropoxide onto polyamide (PA12) constructed by RP and pretreated with acetic acid, to obtain a functionalized substrate with new thermal, physical, and chemical properties. Vanadium isopropoxide (one, five, or ten layers) was deposited onto the PA12 piece by dip-coating. We characterized the coated PA12 by thermal analyses, X-ray diffraction, and infrared spectroscopy, which revealed that V=O and Si–O–Si groups exist on the PA12 surface. PA12 coating with vanadium isopropoxide enhanced the decomposition temperature. Differential scanning calorimetry revealed increased fusion and decomposition enthalpy as a function of the PA12 coating. Therefore, deposition of vanadium isopropoxide onto PA12 pretreated with acetic acid improves the thermal stability of PA12 prepared by RP.     

Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities

The paper addresses the occurrence of possible restrictions on the flows defined by scalar retarded functional differential equations (FDEs), locally around certain simple singularities, compared with the possible flows of ordinary differential equations (ODEs) with the same singularities. It is found that for the Hopf and the Bogdanov-Takens singularities, there are no restrictions on the local flows defined by scalar FDEs, even when the nonlinearities depend on just one delayed value of the solutions. On the other hand, for the singularity associated with a zero and a conjugated pair of pure imaginary numbers as simple eigenvalues, it is shown that there occur restrictions on the flows defined by scalar FDEs with nonlinearities involving just one delay, as well as two delays satisfying a certain resonance condition. These restrictions are of geometric significance, since they amount to the impossibility of observing the homoclinic orbits that occur in arbitrarily small neighborhoods of the singularity for ODEs. Versal unfolfings for the considered singularities by FDEs and the possible restrictions on the associated flows are also studied.     

Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ ₀〉 = cos α | 10〉 + sin α | 01〉 and | ? ₀〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C _ij × C _ik × C _il , where C _mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C _ij × C _kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.     

Determination of the inclusion complex constant between oleuropein and cyclodextrins by complexation theory

Oleuropein (OLE) is a major phenolic compound of olive leaf (Olea europaea) and has many therapeutic properties associated with olive leaf extracts. This work concerns the determination of the inclusion complex constant between OLE and cyclodextrins (CDs), based on the competition of two guests for the CD cavity, one being a dye and the other OLE. The dye used was methylorange (MO) and pH 3 was selected, since MO molar absorptivity at 500 nm is at maximum in this condition. A solution of MO, OLE, and α-CD or β-CD, with citrate buffer was used for determining the absorbance values. From these data and by appropriate mathematical modeling, the equilibrium constant for the formation of OLE:CD complexes were obtained: for OLE:α-CD K = 1,352.4 L mol^?1 (R ² = 0.9975) and for OLE:β-CD K = 1,827.9 L mol^?1 (R ² = 0.9991). The results show that OLE has a greater affinity for β-CD than for α-CD and given the relatively high constants, OLE:CD complexes have potential for giving longer shelf lives for OLE medicinal and food additive preparations.