Absence of wandering domains for some real entire functions with bounded singular sets

Let $f$ be a real entire function whose set $S(f)$ of singular values is real and bounded. We show that, if $f$ satisfies a certain function-theoretic condition (the “sector condition”), then $f$ has no wandering domains. Our result includes all maps of the form $z\mapsto \lambda \frac{\sinh (z)}{z} + a$ with $\lambda >0$ and $a\in \mathbb{R }$ . We also show the absence of wandering domains for certain non-real entire functions for which $S(f)$ is bounded and $f^n|_{S(f)}\rightarrow \infty $ uniformly. As a special case of our theorem, we give a short, elementary and non-technical proof that the Julia set of the exponential map $f(z)=e^z$ is the entire complex plane. Furthermore, we apply similar methods to extend a result of Bergweiler, concerning Baker domains of entire functions and their relation to the postsingular set, to the case of meromorphic functions.     

Modifications of the Hurwicz’s decision rule

The Hurwicz’s criterion is one of the classical decision rules applied in decision making under uncertainty as a tool enabling to find an optimal pure strategy both for interval and scenarios uncertainty. The interval uncertainty occurs when the decision maker knows the range of payoffs for each alternative and all values belonging to this interval are theoretically probable (the distribution of payoffs is continuous). The scenarios uncertainty takes place when the result of a decision depends on the state of nature that will finally occur and the number of possible states of nature is known and limited (the distribution of payoffs is discrete). In some specific cases the use of the Hurwicz’s criterion in the scenarios uncertainty may lead to quite illogical and unexpected results. Therefore, the author presents two new procedures combining the Hurwicz’s pessimism-optimism index with the Laplace’s approach and using an additional parameter allowing to set an appropriate width for the ranges of relatively good and bad payoffs related to a given decision. The author demonstrates both methods on the basis of an example concerning the choice of an investment project. The methods described may be used in each decision making process within which each alternative (decision, strategy) is characterized by only one criterion (or one synthetic measure).     

Rapid and easy quantification of elemental sulphur in aqueous samples from biological reactors: the turbidimetric method revisited

Recent developments in wastewater treatment have led to a renewed interest to obtain elemental sulphur (S°) as a by-product from bioreactors. However, practical studies are limited by the gap of adequate analytical techniques for its determination. This paper provides a statistical study and matrix effect evaluation of an adapted spectrophotometric method for routine S° analyses in aqueous samples, based on a methodology previously described by Hart (1961). Four complex matrices were tested: domestic sewage and effluent samples from three different bioreactors. Tested performance criteria included linearity, matrix effect, limit of detection and quantification and S° recovery. Results were linear (R² = 0.99994) in the studied range (5 to 100 mg S° L^?1) and no matrix effect was observed. The accuracy was based on recovery values that varied from 100% to 106%. The colloidal S° separation and extraction protocol was also considered suitable for aqueous samples, reaching more than 99.0% of S° recovery.     

RGDS‐ and SIKVAVS‐Modified Superporous Poly(2‐hydroxyethyl methacrylate) Scaffolds for Tissue Engineering Applications

Three‐dimensional hydrogel supports for mesenchymal and neural stem cells (NSCs) are promising materials for tissue engineering applications such as spinal cord repair. This study involves the preparation and characterization of superporous scaffolds based on a copolymer of 2‐hydroxyethyl and 2‐aminoethyl methacrylate (HEMA and AEMA) crosslinked with ethylene dimethacrylate. Ammonium oxalate is chosen as a suitable porogen because it consists of needle‐like crystals, allowing their parallel arrangement in the polymerization mold. The amino group of AEMA is used to immobilize RGDS and SIKVAVS peptide sequences with an N‐γ‐maleimidobutyryloxy succinimide ester linker. The amount of the peptide on the scaffold is determined using ¹²⁵I radiolabeled SIKVAVS. Both RGDS‐ and SIKVAVS‐modified poly(2‐hydroxyethyl methacrylate) scaffolds serve as supports for culturing human mesenchymal stem cells (MSCs) and human fetal NSCs. The RGDS sequence is found to be better for MSC and NSC proliferation and growth than SIKVAVS.

     

Silica hybrid nanocomposites

In this work we present experimental results about the formation, properties and structure of sol — gel silica based biocomposite containing Calcium alginate as an organic compound. Two different types of silicon precursors have been used in the synthesis: tetramethylortosilicate (TMOS) and ethyltrimethoxysilane (ETMS). The samples have been prepared at room temperature. The hybrids have been synthesized by replacing different quantitis of the inorganic precursor with alginate. The structure of the obtained hybrid materials has been studied by XRD, IR Spectroscopy, EDS, BET and AFM. The results proved that all samples are amorphous possessing a surface area from 70 to 290 m²/g. It has also been established by FT IR spectra that the hybrids containing TMOS display Van der Walls and Hydrogen bonding or electrostatic interactions between the organic and inorganic components. Strong chemical bonds between the inorganic and organic components in the samples with ETMS are present. A self-organized nanostructure has been observed by AFM. In the obtained hybrids the nanobuilding blocks average in size at about 8–14 nm for the particles.     

Chemical Characterization and Bioactivity of Commercial Essential Oils and Hydrolates Obtained from Portuguese Forest Logging and Thinning

Essential oils (EOs) and hydrolates (Hds) are natural sources of biologically active ingredients with broad applications in the cosmetic industry. In this study, nationally produced (mainland Portugal and Azores archipelago) EOs (11) and Hds (7) obtained from forest logging and thinning of Eucalyptus globulus, Pinus pinaster, Pinus pinea and Cryptomeria japonica, were chemically evaluated, and their bioactivity and sensorial properties were assessed. EOs and Hd volatiles (HdVs) were analyzed by GC-FID and GC-MS. 1,8-Cineole was dominant in E. globulus EOs and HdVs, and α- and β-pinene in P. pinaster EOs. Limonene and α-pinene led in P. pinea and C. japonica EOs, respectively. P. pinaster and C. japonica HVs were dominated by α-terpineol and terpinen-4-ol, respectively. The antioxidant activity was determined by DPPH, ORAC and ROS. C. japonica EO showed the highest antioxidant activity, whereas one of the E. globulus EOs showed the lowest. Antimicrobial activity results revealed different levels of efficacy for Eucalyptus and Pinus EOs while C. japonica EO showed no antimicrobial activity against the selected strains. The perception and applicability of emulsions with 0.5% of EOs were evaluated through an in vivo sensory study. C. japonica emulsion, which has a fresh and earthy odour, was chosen as the most pleasant fragrance (60%), followed by P. pinea emulsion (53%). In summary, some of the studied EOs and Hds showed antioxidant and antimicrobial activities and they are possible candidates to address the consumers demand for more sustainable and responsibly sourced ingredients.     

Substituent effects on the basicity of 3,7-diazabicyclo[3.3.1]nonanes

Basicity constants for a series of 3,7-diazabicyclo[3.3.1]nonane derivatives in acetonitrile with a variation over 13 orders of magnitude have been determined using a spectrophotometric titration technique. An excellent correlation between basicity and calculated proton affinities obtained at PCM-B3LYP/6-31+G(d)//B3LYP/6-31G(d) level was found. The results are discussed in terms of substituent effects and compared to (15)N NMR chemical shifts.     

Vibrational overtone spectroscopy of three-membered rings

We have recorded vapor-phase photoacoustic spectra of cyclopropane, ethylene oxide, and ethylene sulfide in the third, fourth, and fifth CH-stretching overtone regions. We have used a harmonically coupled anharmonic oscillator local mode model to facilitate analysis of the spectra. Fermi resonance between the CH-stretching and HCH-bending vibrations is essential to explain the observed wide and multistructured CH-stretching overtone bands. A number of weak combination bands can account for the remaining experimental features observed to the blue of the CH-stretching regions. We have reassigned the fundamental spectra of these three-membered rings.     

Carboxylate anions binding and sensing by a novel tetraazamacrocycle containing ferrocene as receptor

A tetraazamacrocycle containing ferrocene moieties has been synthesized and characterized. The tetraprotonated form of this compound was evaluated as a receptor (R) for anion recognition of several substrates (S), Cl(-), PF(6)(-), HSO(4)(-), H(2)PO(4)(-) and carboxylates, such as p-nitrobenzoate (p-nbz(-)), phthalate (ph(2-)), isophthalate (iph(2-)) and dipicolinate (dipic(2-)). (1)H NMR titrations in CD(3)OD indicated that this receptor is not suitable for recognizing HSO(4)(-) and H(2)PO(4)(-), but weakly binds p-nbz(-), and strongly interacts with ph(2-), dipic(2-), and iph(2-) anions forming 1 : 2 assembled species. The largest beta(2) binding constant was determined for ph(2-), followed by dipic(2-) and finally iph(2-). The effect of the anionic substrates on the electron-transfer process of the ferrocene units of R was evaluated using cyclic voltammetry (CV) and square wave voltammetry (SWV) in methanol solution and 0.1 mol dm(-3)(CH(3))(4)NCl as the supporting electrolyte. Titrations of the receptor were undertaken by addition of anion solutions in their tetrabutylammonium or tetramethylammonium forms. The protonated ligand exhibits a reversible voltammogram, which shifts cathodically in the presence of the substrates. The data revealed kinetic constraints in the formation of the receptor/substrate entity for dipic(2-), ph(2-) and iph(2-) anions, but not for p-nbz(-). In spite of the slow kinetics of assembled species formation with the ph(2-) substrate, this anion provides the largest redox-response when the supramolecular entity is formed, followed by dipic(2-), iph(2-) and finally p-nbz(-) anions. This trend is in agreement with the (1)H NMR results and the values of the binding constants. Single crystal X-ray structures of the receptor with PF(6)(-), ph(2-), iph(2-) and p-nbz(-) were carried out and showed that supermolecules with a RS(2) stoichiometry are formed with the first three anions, but RS(4) with p-nbz(-). In all cases the binding occurs outside the macrocyclic cavity via N-H...O=C hydrogen bonds for carboxylate anions and N-H...F hydrogen bonds for the PF(6)(-) anion, which is in agreement with the solution results. The macrocyclic framework adopts different conformations in order to interact with each substrate having Fe...Fe intramolecular distances ranging from 10.125(14) to 12.783(15)A.