Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

Solid-phase extraction applied to the determination of ochratoxin A in wines by reversed-phase high-performance liquid chromatography

A reversed-phase high-performance liquid chromatographic method is described for the analysis of Ochratoxin A at low microg l(-1) levels in samples of artificially contaminated wines. The method involves solid-phase extraction of samples using octadecylsilane cartridges and an additional preconcentration step prior to chromatography with isocratic elution and fluorimetric detection. The method was evaluated for accuracy and precision with relative standard deviations lower than 10%. Recoveries of ochratoxin A added to commercial wines over the range 0.1-3.0 microg l(-1) were higher than 80% in the assays. The performance of the octadecylsilane cartridge method tested compared very favourably with results of other published studies of ochratoxin A which use immunoaffinity columns or solvent extraction techniques.     

The origin of the bistability in the thiazyl radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA): A first principles bottom-up investigation of the magnetic properties of its high temperature polymorph

A first principles bottom-up study is performed on the high temperature polymorph of the thiazyl radical 1,3,5-trithia-2,4,6-triazapentalenyl, TTTA, a purely organic molecule-based magnet that shows thermal bistability, with the aim of getting a quantitative understanding at the molecular level the mechanism of thermal bistability and the factors that control the existence of a hysteresis loop. Experimental studies on crystals of TTTA have shown that it is a thermally bistable material that exhibits a broad hysteresis loop encompassing room temperature (the high temperature phase is paramagnetic, while the low temperature phase is magnetically silent). Both structures present 1D π-stacks and the changes in the magnetic properties up to now have been solely attributed to changes within these stacks, which in the high temperature phase are composed of evenly-spaced radicals and in the low temperature phase the radicals are separated by alternately long and short spacings. Our study shows that the magnetic topology of the high temperature polymorph is clearly 3D with important interactions between the stacks, however a 1D magnetic model gives a qualitative reproduction of the macroscopic magnetic properties. This suggests that a proper investigation into the origin of the bistability of this material requires consideration of the inter-stack interactions as well as looking at the difference in packing within the stacks.     

Dissipative operators and additive perturbations in locally convex spaces

Let be a densely defined operator on a Banach space X. Characterizations of when generates a C₀‐semigroup on X are known. The famous result of Lumer and Phillips states that it is so if and only if is dissipative and is dense in X for some . There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kamińska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non–normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented.     

Uniform saturation in linear inequality systems

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of the value and the optimal set under the elimination of the given constraint, phenomena which can be seen as weaker forms of excess information in linear optimization problems. We say that an inequality of a given linear inequality system is uniformly saturated when it is saturated for any solvable linear optimization problem posed on its solution set. This paper characterizes the uniform saturated inequalities and other related classes of inequalities. This work was supported by the MCYT of Spain and FEDER of UE, Grant BFM2002-04114-C02-01.     

Synthesis, structure, and magnetic behavior of bis(2-amino-5-fluoropyridinium) tetrachlorocuprate(II)

Reaction of CuCl2 with 2-amino-5-fluoropyridine and HCl in aqueous solution yields bis(2-amino-5-fluoropyridinium) tetrachlorocuprate(II), (5FAP)2CuCl4, (1). The complex crystallizes in the monoclinic space group P21/c with cell dimensions a = 6.926(7) A, b = 21.73(2) A, c = 10.911(10) A, beta = 100.19(2) degrees , V = 1616(3) A3, and R1 = 0.0424 based on 2640 independent reflections. The crystal packing shows that each tetrachlorocuprate ion has four nearest-neighbor Cu(II) ions through three types of Cu-Cl...Cl-Cu potential magnetic interactions: one short Cl...Cl distance (d1 = 3.657 A) and two longer Cl...Cl distances (d2 = 4.073 A) that form a layered distorted honeycomb structure. The third nearest neighbor (d3 = 4.239 A) links these layers into a three-dimensional structure. Both powder and single-crystal magnetic susceptibility measurements on 1, over the temperature range of 1.8-325 K, show significant antiferromagnetic interactions. Attempts to analyze the data using a variety of models showed a best fit to the strong-rung ladder model, with 2Jrung = -17.170(14) and 2Jrail = -5.94(5) K [-11.92(1) and -4.13(3) cm(-1), respectively] for the powder, although a comparable result is obtained using an alternate chain model. However, neither of these two models is compatible with a layered distorted honeycomb crystal packing structure. A first-principles bottom-up theoretical study using the 165 K crystallographic data reproduces the macroscopic properties and reveals that at low temperature the crystal has a 3D magnetic topology (all three magnetic pathways are significant) and a singlet ground state.     

Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Graphene-based nano-patch antenna for terahertz radiation

The scattering of terahertz radiation on a graphene-based nano-patch antenna is numerically analyzed. The extinction cross section of the nano-antenna supported by silicon and silicon dioxide substrates of different thickness are calculated. Scattering resonances in the terahertz band are identified as Fabry–Perot resonances of surface plasmon polaritons supported by the graphene film. A strong tunability of the antenna resonances via electrostatic bias is numerically demonstrated, opening perspectives to design tunable graphene-based nano-antennas. These antennas are envisaged to enable wireless communications at the nanoscale.     

Improvement of random coefficient differential models of growth of anaerobic photosynthetic bacteria by combining Bayesian inference and gPC

The time evolution of microorganisms, such as bacteria, is of great interest in biology. In the article by D. Stanescu et al. [Electronic Transactions on Numerical Analysis, 34, 44–58 (2009)], a logistic model was proposed to model the growth of anaerobic photosynthetic bacteria. In the laboratory experiment, actual data for two species of bacteria were considered: Rhodobacter capsulatus and Chlorobium vibrioforme. In this paper, we suggest a new nonlinear model by assuming that the population growth rate is not proportional to the size of the bacteria population, but to the number of interactions between the microorganisms, and by taking into account the beginning of the death phase in the kinetic curve. Stanescu et al. evaluated the effect of randomness into the model coefficients by using generalized polynomial chaos (gPC) expansions, by setting arbitrary distributions without taking into account the likelihood of the data. By contrast, we utilize a Bayesian inverse approach for parameter estimation to obtain reliable posterior distributions for the random input coefficients in both the logistic and our new model. Since our new model does not possess an explicit solution, we use gPC expansions to construct the Bayesian model and to accelerate the Markov chain Monte Carlo algorithm for the Bayesian inference.     

Global regularity in ultradifferentiable classes

We study ω-regularity of the solutions of certain operators that are globally C ^∞-hypoelliptic in the N-dimensional torus. We also apply these results to prove the global ω-regularity for some classes of sublaplacians. In this way, we extend previous work in the setting of analytic and Gevrey classes. Different examples on local and global ω-hypoellipticity are also given.