Recurrence determinism and Li–Yorke chaos for interval maps

Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a recurrence, following states of the trajectory will be recurrences. In this paper, we study recurrence determinism of interval dynamical systems. We show that recurrence determinism distinguishes three main types of ω-limit sets of zero entropy maps: finite, solenoidal without non-separable points, and solenoidal with non-separable points. As a corollary, we obtain characterizations of strongly non-chaotic and Li–Yorke (non-)chaotic interval maps via recurrence determinism. For strongly non-chaotic maps, recurrence determinism is always equal to one. Li–Yorke non-chaotic interval maps are those for which recurrence determinism is always positive. Finally, Li–Yorke chaos implies the existence of a Cantor set of points with zero determinism.     

Multiplicity and stability in a sequence of two nonadiabatic nonisothermal CSTR

An analysis of mass and enthalpy balances describing dynamic behavior of two homogeneous CSTR with recirculation is performed. Methods of investigation of regions of existence of multiple steady states and stability are described. Effect of recirculation ratio, Damköhler number, cooling parameter and cooling temperature on the exit temperature is followed. The dependence of the exit temperature on the residence time is analyzed and it is shown that bizarre situations may occur (deformated “mushrooms”, two isolas, etc.). Plots are given to show the influence of system parameters on the reactor behavior.     

Calculation of countercurrent separation processes—III. Computation of two interlinked columns.

The relaxation procedure is used for solution of two interlinked distillation columns. Both approaches-sequential iterative method and the block relaxation technique are compared. A new algorithm making use of simultaneous solution of all equations is proposed.     

Genesis of “Solitary Cations” Induced by Atomic Hydrogen

Substitution of constituent atoms and/or changes of crystal structure are routinely used to tailor the fundamental properties of a semiconductor. Here, it is shown that such a tailoring can also be realized thanks to a novel hydrogen effect. Four hydrogen atoms can screen the effect the crystal potential has on a constituent cation, thus generating a solitary cation: an effectively isolated impurity, so chemically different from the unscreened constituent cations that it strongly perturbs the electronic properties of the material by increasing its fundamental band‐gap energy. Such a hydrogen‐induced screening effect is removed by thermal treatments, thus permitting reversible modifications of both the “crystal chemistry” and material's properties. This phenomenon, observed in InN and other topical nitrides, should permit the development of a new class of materials as well as the fabrication of photonic devices and optical integrated circuits with distinct, tailor‐made regions emitting or absorbing light, all integrated onto a monolithic semiconductor structure.     

Mechanism Controlling High-Temperature Degradation of Sunflower Oil Triacylglycerols in the Absence of Oxygen

The aim of the present study is to describe the mechanism controlling heat-induced formation of sunflower oil triacylglycerol and fatty acid methyl ester oligomers. The unique combination of high-performance size-exclusion chromatography with hyphenated electrospray ionization mass spectrometry (MS), atmospheric pressure chemical ionization-MS, and high-temperature gas chromatography-MS techniques allows differentiating between radical coupling species and Diels–Alder cycloadducts. Targeted analysis of thermally degraded sunflower oils confirms the exact structures of various acyclic oligomers accompanied by less-abundant products of pericyclic transformations. A series of model experiments simulate the impact of dienophile nature on the course of Diels–Alder reactions. Thus, α-tocopherylquinone, δ-tocopherylquinone, and methyl-(E)-11-oxoundec-9-enoate are synthesized as naturally occurring dienophiles bearing electron-withdrawing groups. The geometry of poor dienophiles does not affect concerted cyclization, while the structure of electron deficient dienophiles can overcome low reactivity. Practical Application: In the absence of oxygen, heat-induced degradation of polyunsaturated triacylglycerols proceed predominantly via a radical pathway, whereas concerted reactions represent minor mechanisms. Sunflower oil triacylglycerol molecules in the system without propagation stage can be effectively protected by natural and/or synthetic antioxidants. Application of chelates is also recommended. However, antioxidant-derived quinones, such as α-tocopherylquinone, can enter the Diels–Alder reaction even more easily than dienophiles without electron-withdrawing groups. Unsaturated core aldehydes possess the same reactivity. Examination of the mechanism controlling high-temperature degradation of triacylglycerols is especially important for processing engineers in edible oil refineries and food technologists. New perspective may help them to minimize undesirable changes in polyunsaturated species.     

Microwave photochemistry V: Low‐pressure batch and continuous‐flow microwave photoreactors with quartz mercury electrodeless discharge lamps. Photohydrolysis of mono‐chloroacetic acid

BACKGROUND: Low‐pressure batch and continuous‐flow microwave photoreactors were equipped with microwave powered quartz mercury electrodeless discharge lamps (Hg‐EDLs). Photohydrolysis of aqueous mono‐chloroacetic acid (MCAA) into hydroxyacetic acid and HCl was chosen as the model reaction to evaluate these photoreactors. The effects of operational parameters on the MCAA photolysis through a UV/MW process were investigated. RESULTS: Studies were carried out at relatively high MCAA concentration (0.1 mol L^?1). The photoreaction course was monitored by the pH change in the solution. The MCAA conversion was optimized as a result of a trade‐off between the thermal dependence of the photochemical quantum yield (which increases with increasing temperature) and the thermal dependence of the EDL light intensity of 254 nm line (which increases with decreasing temperature). The microwave photoreactors made it possible to study the temperature dependence of MCAA photohydrolysis. CONCLUSION: It was found that operational parameters (i.e. reaction temperature, quantum yield) had important effects on photoefficiency. Photohydrolysis of MCAA in the microwave photoreactors can be enhanced by the UV/MW system. The results of conversions (in 120 min) for the particular photoreactor set‐ups show that the best reaction conditions for MCAA photolysis were obtained in the low‐pressure batch microwave photoreactor (the conversion was 46% at 80 °C). Copyright © 2009 Society of Chemical Industry     

Lasioglossins: Three Novel Antimicrobial Peptides from the Venom of the Eusocial Bee Lasioglossum laticeps (Hymenoptera: Halictidae)

Three novel structurally related pentadecapeptides, named lasioglossins, were isolated from the venom of the eusocial bee Lasioglossum laticeps. Their primary sequences were established as H‐Val‐Asn‐Trp‐Lys‐Lys‐Val‐Leu‐Gly‐Lys‐Ile‐Ile‐Lys‐Val‐Ala‐Lys‐NH₂ (LL‐I), H‐Val‐Asn‐Trp‐Lys‐Lys‐Ile‐Leu‐Gly‐Lys‐Ile‐Ile‐Lys‐Val‐Ala‐Lys‐NH₂ (LL‐II) and H‐Val‐Asn‐Trp‐Lys‐Lys‐Ile‐Leu‐Gly‐Lys‐Ile‐Ile‐Lys‐Val‐Val‐Lys‐NH₂ (LL‐III). These lasioglossins exhibited potent antimicrobial activity against both Gram‐positive and Gram‐negative bacteria, low haemolytic and mast cell degranulation activity, and a potency to kill various cancer cells in vitro. The lasioglossin CD spectra were measured in the presence of trifluoroethanol and sodium dodecyl sulfate solution and indicated a high degree of α‐helical conformation. NMR spectroscopy, which was carried out in trifluoroethanol/water confirmed a curved α‐helical conformation with a concave hydrophobic and convex hydrophilic side. To understand the role of this bend on biological activity, we studied lasioglossin analogues in which the Gly in the centre of the molecule was replaced by other amino acid residues (Ala, Lys, Pro). The importance of the N‐terminal part of the molecule to the antimicrobial activity was revealed through truncation of five residues from both the N and C termini of the LL‐III peptide. C‐terminal deamidation of LL‐III resulted in a drop in antimicrobial activity, but esterification of the C terminus had no effect. Molecular modelling of LL‐III and the observed NOE contacts indicated the possible formation of a bifurcated H‐bond between hydrogen from the Lys15 CONH peptide bond and one H of the C‐terminal CONH₂ to the Ile11 oxygen atom. Such interactions cannot form with C‐terminal esterification.     

Isogeometric analysis in option pricing

ABSTRACT

Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper, we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochastic volatility models, we develop a methodology for solving corresponding pricing partial integro-differential equations numerically by isogeometric analysis tools and show that a very small number of space discretization steps can be used to obtain sufficiently accurate results. Presented solution by finite element method is especially useful for practitioners dealing with derivatives where closed-form solution is not available.     

Comparison of Age-dependent Quantitative Changes in the Male Labial Gland Secretion of <Emphasis Type="Italic">Bombus Terrestris</Emphasis> and <Emphasis Type="Italic">Bombus Lucorum</Emphasis>

Age-related changes of antennal-active components of male labial gland extracts were studied in two closely related bumblebee species, Bombus terrestris and B. lucorum. In B. terrestris, compounds eliciting electroantennogram (EAG) responses of virgin queens were ethyl dodecanoate, 2,3-dihydrofarnesal, 2,3-dihydrofarnesol, hexadecan-1-ol, octadeca-9,12,15-trien-1-ol, and geranylcitronellol. Compounds that elicited EAG responses from queens of B. lucorum were ethyl dodecanoate, ethyl tetradec-7-enoate, ethyl tetradec-9-enoate, ethyl hexadec-9-enoate, hexadecan-1-ol, hexadec-7-enal, octadeca-9,12-dien-1-ol, octadeca-9,12,15-trien-1-ol, and octadecan-1-ol. Quantities of these compounds in the labial glands changed significantly over the lifetime of the respective males of the two species. In both species, concentrations of the respective compounds reached their maximum within seven days after eclosion. Subsequently, a rapid decrease in the amount of EAG-active compounds occurred in B. terrestris, whereas in B. lucorum the amount of active compounds stayed approximately constant or decreased at a slow rate. Microscopy showed that in B. terrestris secretory cells of the labial glands undergo apoptosis from the fifth to the tenth day of life, whilst in B. lucorum labial gland cells remain unchanged throughout the life of the males.     

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.