On isomorphisms of some Köthe function <Emphasis Type="Italic">F</Emphasis>-spaces

We prove that if Köthe F-spaces X and Y on finite atomless measure spaces (Ω _X ; Σ _X , µ _X ) and (Ω _Y ; Σ _Y ; µ _Y ), respectively, with absolute continuous norms are isomorphic and have the property

$\mathop {\lim }\limits_{\mu (A) \to 0} \left\| {\mu (A)^{ - 1} 1_A } \right\| = 0$

(for µ = µ _X and µ = µ _Y , respectively) then the measure spaces (Ω _X ; Σ _X ; µ _X ) and (Ω _Y ; Σ _Y ; µ _Y ) are isomorphic, up to some positive multiples. This theorem extends a result of A. Plichko and M. Popov concerning isomorphic classification of L _p (µ)-spaces for 0 < p < 1. We also provide a new class of F-spaces having no nonzero separable quotient space.

     

On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view.     

*-Representations of Twisted Generalized Weyl Constructions

We study bounded and unbounded *-representations of Twisted Generalized Weyl Algebras and algebras similar to them for different choices of involutions.     

Contracting with asymmetric demand information in supply chains

We solve a buyback contract design problem for a supplier who is working with a retailer who possesses private information about the demand distribution. We model the retailer’s private information as a space of either discrete or continuous demand states so that only the retailer knows its demand state and the demand for the product is stochastically increasing in the state. We focus on contracts that are viable in practice, where the buyback price being strictly less than the wholesale price, which is itself strictly less than the retail price. We derive the optimal (for the supplier) buyback contract that allows for arbitrary allocation of profits to the retailer (subject to the retailer’s reservation profit requirements) and show that in the limit this contract leads to the first-best solution with the supplier keeping the entire channel’s profit (after the retailer’s reservation profit).     

Steric control of the excited-state intramolecular proton transfer in 3-hydroxyquinolones: steady-state and time-resolved fluorescence study

3-Hydroxyquinolones (3HQs), similarly to their 3-hydroxychromone analogs, undergo excited state intramolecular proton transfer (ESIPT) resulting in dual emission. In the ground state, 2-phenyl-3HQ derivatives are not flat due to a steric hindrance between the 2-phenyl group and the 3-OH group that participates in the ESIPT reaction. To study the effect of this steric hindrance on the ESIPT reaction, a number of 3HQ derivatives have been synthesized and characterized in different organic solvents by steady-state and time-resolved fluorescence techniques. According to our results, 2-phenyl-3HQ derivatives undergo much faster ESIPT (by nearly 1 order of magnitude) than their 2-methyl-3HQ analogs. Moreover, 1-methyl-2-phenyl-3HQ having a strongly twisted 2-phenyl group undergoes a two- to three-fold slower ESIPT compared to 2-phenyl-3HQ. These results suggest that the flatter conformation of 2-phenyl-3HQ, which allows a close proximity of the 2-phenyl and 3-OH groups, favors a fast ESIPT reaction. The absorption and fluorescence spectra of the 3HQ derivatives additionally confirm that the steric rather than the electronic effect of the 2-phenyl group is responsible for the faster ESIPT reaction. Based on the spectroscopic studies and quantum chemical calculations, we suggest that the 2-phenyl group decreases the rotational freedom of its proximal 3-OH group in the more planar conformation of 2-phenyl-3HQ. As a result, the conformations of 3HQ, where the 3-OH group orients to form an intramolecular H-bond with the 4-carbonyl group, are favored over those with a disrupted intramolecular H-bond. Therefore, the 2-phenyl group sterically favors the intramolecular H-bond and thus accelerates the ESIPT reaction. This conclusion provides a new understanding of the ESIPT process in 3-hydroxyquinolones and related systems and suggests new possibilities for the design of ESIPT based molecular sensors and switchers.     

Close-packed monolayers of charged Janus-type nanoparticles at the air-water interface

Two DNA-block copolymers, poly(caprolactone)-DNA and poly(methyl metacrylate)-DNA, were synthesized by conjugation of a short single strand of DNA (12 or 22 mer) to a single reactive group at one end of the synthetic polymer. These polymers self-assemble in water, without the need of any cosolvent, forming micelle-like aggregates that were imaged by TEM. The solution behavior of the bioconjugated polymers was investigated by surface tension measurements. In the direction of dilution, the surface tension was measured using a down-scaled Wilhelmy plate method. To proceed in the reverse direction (concentration), we measured the surface tension of a sessile drop during its evaporation. This latter method was firstly validated using ionic and non-ionic surfactants, including polymeric surfactants. It was then applied to investigate the unimer to micelles transition of the DNA-block copolymers. In all cases, a reversible transition was observed demonstrating the existence of a critical micellar concentration, close to 0.01 mmol L⁻¹ for all the conjugates. The CMC was only slightly influenced by the length of the hydrophilic DNA block.     

Formation of Pyrogenic Silica: Spectroscopic and Quantum Chemical Insight

This article describes the genesis of amorphous silica under high-heat conditions from SiO₂ molecules through protoparticles, primary particles, and aggregates to agglomerates using vibrational spectra and quantum chemical simulations data. The impact of small molecules (water, HCl, CO₂) is also discussed. The article also explains the nature of the pyrogenic silica amorphism.