Invariant measures of Markov operators associated to iterated function systems consisting of φ-max-contractions with probabilities

We prove that the Markov operator associated to an iterated function system consisting of $\phi$-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system.     

Manipulation of Transmembrane Transport by Synthetic K+ Ionophore Depsipeptides and Its Implications in Glucose-Stimulated Insulin Secretion in β-Cells

The cyclic depsipeptide cereulide toxin it is a very well-known potassium electrogenic ionophore particularly sensitive to pancreatic beta cells. The mechanistic details of its specific activity are unknown. Here, we describe a series of synthetic substituted cereulide potassium ionophores that cause impressive selective activation of glucose-induced insulin secretion in a constitutive manner in rat insulinoma INS1E cells. Our study demonstrates that the different electroneutral K⁺ transport mechanism exhibited by the anionic mutant depsipeptides when compared with classical electrogenic cereulides can have an important impact of pharmacological value on glucose-stimulated insulin secretion.     

RuII Multinuclear Metallosupramolecular Rack‐Type Architectures of Polytopic Hydrazone‐Based Ligands: Synthesis,Structural Features,Absorption Spectra,Redox Behavior,and Near‐Infrared Luminescence

A novel class of polytopic hydrazone‐based ligands was synthesized. They gave heteroleptic Ru^II polynuclear rack‐like complexes of formula [Ru_nterpy_n(bridging molecular strand)]²ⁿ⁺ (terpy=2,2′:6′,2′′‐terpyridine). The new rack‐like systems can be viewed as being made of two identical or roughly identical peripheral subunits separated by several similar metal‐containing spacer subunits. The presence of pyrazine or pyrimidine units within the molecular multitopic strands introduces additional chemical diversity: whereas a pyrimidine unit leads to appended orthogonal subunits that are on the same side with regard to the main molecular strand, a pyrazine unit leads to orthogonal subunits that lie on different sides. Mixing pyrazine and pyrimidine units within the same (bridging) molecular strand also allows peculiar and topographically controlled geometries to be obtained. Redox studies provided evidence that each species undergoes reversible redox processes at mild potentials, which can be assigned to specific subunits of the multicomponent arrays. Non‐negligible electronic coupling takes place among the various subunits, and some electron delocalization extending over the overall bridging molecular strand takes place. In particular, oxidation data suggest that the systems can behave as p‐type “molecular wires” and reduction data indicate that n‐type electron conduction can occur within the multimetallic framework. All the multinuclear racks exhibit ³MLCT emission, both at 77 K in rigid matrix and at 298 K in fluid solution, which takes place in the near‐infrared region (emission maxima in the 1000–1100 nm region), and is quite structured. Rigidity of the molecular structures and delocalization within the large bridging ligands are proposed to contribute to the occurrence of the rather uncommon MLCT infrared emission, which is potentially interesting for optical communication devices.     

Lewis Acids as Mild and Effective Catalysts for the Synthesis of 3,5‐Bis[(hetero)arylidene]piperidin‐4‐ones

The aldol‐crotonic condensation reactions of N‐alkyl‐ and NH‐piperidin‐4‐one derivatives with (hetero)aromatic aldehydes promoted by Lewis acids or bases were examined. This comparative study has revealed three effective catalytic systems based on Lewis acids, i.e., LiClO₄ and MgBr₂ (in the presence of tertiary amine), and BF₃⋅Et₂O, for the synthesis of N‐alkyl‐substituted 3,5‐bis(heteroarylidene)piperidin‐4‐ones, including those bearing acid‐ or base‐labile groups both in the (hetero)aromatic groups and in the alkyl substituent at the N‐atom. The highest reaction rate was observed for LiClO₄‐mediated synthesis. Both MgBr₂‐ and LiClO₄‐mediated syntheses were inefficient in the case of NH‐piperidin‐4‐one, while BF₃⋅Et₂O provided the final compounds in high yields. This catalyst is especially advantageous as it allows simultaneous condensation and deprotection in the case of O‐protected piperidin‐4‐one.     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

An investment model with switching costs and the option to abandon

We develop a complete analysis of a general entry–exit–scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project’s output commodity. We assume that the investment project can operate in two modes, an “open” one and a “closed” one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project’s management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project’s management is to maximise the expected discounted payoff resulting from the project’s management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.     

Integration of individual TiO2 nanotube on the chip: Nanodevice for hydrogen sensing

Titania (TiO₂) exists in several phases possessing different physical properties. In view of this fact, we report on three types of hydrogen sensors based on individual TiO₂ nanotubes (NTs) with three different structures consisting of amorphous, anatase or anatase/rutile mixed phases. Different phases of the NTs were produced by controlling the temperature of post‐anodization thermal treatment. Integration of individual TiO₂ nanotubes on the chip was performed by employing metal deposition function in the focused ion beam (FIB/SEM) instrument. Gas response was studied for devices made from an as‐grown individual nanotube with an amorphous structure, as well as from thermally annealed individual nanotubes exhibiting anatase crystalline phase or anatase/rutile heterogeneous structure. Based on electrical measurements using two Pt complex contacts deposited on a single TiO₂ nanotube, we show that an individual NT with an anatase/rutile crystal structure annealed at 650 °C has a higher gas response to hydrogen at room temperature than samples annealed at 450 °C and as‐grown. The obtained results demonstrate that the structural properties of the TiO₂ NTs make them a viable new gas sensing nanomaterial at room temperature. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)