A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

7,7′‐Diamino‐2,2′‐diindolylmethane: A Building Block for Highly Efficient and Selective Anion Receptors—Studies in Solution and in the Solid State

The easy‐to‐make 7,7′‐diamino‐2,2′‐diindolylmethane was used as a building block for the construction of anion receptors operating by hydrogen bonds. Its various bisamide and bisurea derivatives were designed and synthesised as acyclic as well as macrocyclic molecules, then their structural and anion binding properties were studied in solution and in the solid state. The bisamide receptors demonstrate high affinity towards oxoanions in highly polar and partially aqueous solutions (DMSO with up to 25 % H₂O) with significant selectivity for dihydrogen phosphate. Remarkably, the bisurea‐based molecules are able to bind anionic guests even in pure methanol and show selectivity toward tetrahedral oxoanions, that is, hydrogen sulphate and dihydrogen phosphate. X‐ray analysis revealed that both classes of molecules adopt a similar conformation in the solid state: a bent sheet shape with a binding pocket equipped with hydrogen‐bond donors (four for the amides and six for the bisureas), whose orientation is particularly tailored for oxoanions. The results of ROESY NMR experiments are in agreement with the findings for the solid state and confirmed that both bisamides and bisureas can easily adapt the conformation with convergent hydrogen‐bond donors, which is highly suitable for anion binding.     

Photopolymerized polypyrrole microvessels

We report on the preparation of water-filled polymer microvessels through the photopolymerization of pyrrole in a water/chloroform emulsion. The resulting structures were characterized by complementary spectroscopic and microscopic techniques, including Raman spectroscopy, XPS, SEM, and TEM. The encapsulation of fluorescent, magnetic, and ionic species within the microvessels has been demonstrated. Confocal microscopy and fluorescence anisotropy measurements revealed that the encapsulated chromophore (Rhodamine 6G) resides within voids in the capsules; however, strong interaction of the dye with polypyrrole results in a measurable decrease in its rotational dynamics. Microvessels loaded with ferrofluid exhibit magnetic properties, and their structures can be directed with an external magnetic field. TEM measurements allowed imaging of individual nanoparticles entrapped within the vessels. The application of Cu(2+)-loaded microvessels as a transducer layer in all-solid-state ion-selective electrodes was also demonstrated.     

Synthesis and optoelectronic properties of hexahydroxylated 10-O-R-substituted anthracenes via a new modification of the Friedel-Crafts reaction using O-protected ortho-acetal diarylmethanols

A new modification of the Friedel-Crafts type intramolecular cyclization involving O-protected ortho-acetal diarylmethanols as a new type of reactant, was carried out for the first time in a medium containing a large amount of water at room temperature and enabled synthesis of a series of electron-rich, hexahydroxylated 10-O-R-substituted anthracenes, where R is an alkyl (Me, nBu, n-C(16)H(33)) or arylalkyl group (CH(2)Ph, CH(2)-2-Napht, CH(2)C(6)H(4)CH(2)OAr) and also evaluation of their electronic and optoelectronic properties in solution, crystal, and solid thin film. In this transformation, a central 10-O-R-substituted benzene ring was formed, fused to rings originating from two independent aromatic aldehydes. The reaction proceeded via two identified mechanisms involving acetal and/or free aldehyde groups. The acid sensitive acetal and dibenzyl alkoxy functions have never been used together in the intramolecular Friedel-Crafts type cyclization. The new compounds revealed deep blue fluorescence and quantum yields in solution around 0.3. The electrical properties investigated for thin films obtained by vacuum deposition on glass were 10-O-R-substituent dependent and showed much faster transient current decay in the case of the 10-O-CH(2)Ph derivative than for the material with a 10-O-Me substituent (the lifetime of charge carriers was 25 times shorter in this case). The AFM images of thin films, Stokes shifts, and X-ray analysis of π-stacking interactions in crystals of the new materials have been also obtained.     

Dual-polarization interferometry for quantification of small molecules using aptamers

An interferometry-based method was developed for detection of a small molecule, argininamide. The quantification of argininamide was demonstrated using aptamers immobilized on silicone oxynitride sensor surface via avidin–biotin binding. The aptamers formed a thin film over avidin layer corresponding to a thickness of 1.2 nm, consistent with a molecular positioning of multipoint attachment to the surface. The binding of argininamide did not cause any significant changes in the thickness of the aptamer film, suggesting that the specific binding did not affect the overall conformation of the aptamer molecules after adaptive rearrangement of aptamer molecules. However, the binding results in clearly detectable changes in mass calculated from multiple parameters determined by mass deposition and structural changes. The limit of detection of the developed sensor was determined to be 5 μM. The sensor can monitor real-time changes in argininamide concentrations with high reliability and sensitivity. The model system demonstrated that a combined measurement considering structural and mass changes through interferometry-based techniques can overcome one of the major problems associated with real-time monitoring of small mass analytes.     

Factor maps and invariant distributional chaos

The main aim of this article is to show that maps with the specification property have invariant distributionally scrambled sets and that this kind of scrambled set can be transferred from factor to extension under finite-to-one factor maps. This solves some open questions in the literature of the topic.     

Pointwise products of some Banach function spaces and factorization

The well-known factorization theorem of Lozanovski? may be written in the form L¹≡E⊙E^′$L^1\equiv E\odot E^{\prime }$, where ⊙ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize F through E  , i.e., when F≡E⊙M(E,F)$F\equiv E\odot M(E,F)$, where M(E,F)$M(E,F)$ is the space of pointwise multipliers from E to F  . Properties of M(E,F)$M(E,F)$ were investigated in our earlier paper [41] and here we collect and prove some properties of the construction E⊙F$E\odot F$. The formulas for pointwise product of Calderón–Lozanovski? _Eφ$E_{\phi }$-spaces, Lorentz spaces and Marcinkiewicz spaces are proved. These results are then used to prove factorization theorems for such spaces. Finally, it is proved in Theorem 11 that under some natural assumptions, a rearrangement invariant Banach function space may be factorized through a Marcinkiewicz space.     

Generalized <Emphasis Type="Italic">n</Emphasis>-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range

Let n ≥ 2 and let Ω ? ? ⁿ be an open set. We prove the boundedness of weak solutions to the problem

$$u \in W_0^1 L^\Phi \left( \Omega \right) and - div\left( {\Phi '\left( {\left| {\nabla u} \right|} \right)\frac{{\nabla u}}{{\left| {\nabla u} \right|}}} \right) + V\left( x \right)\Phi '\left( {\left| u \right|} \right)\frac{u}{{\left| u \right|}} = f\left( {x,u} \right) + \mu h\left( x \right) in \Omega ,$$

where ? is a Young function such that the space W ₀ ¹ L ^Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L ^Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω = ? ⁿ .

     

Recent results on iteration theory: iteration groups and semigroups in the real case

In this survey paper we present some recent results in the iteration theory. Mainly, we focus on the problems concerning real iteration groups (flows) and semigroups (semiflows) such as existence, regularity and embeddability. We also discuss some issues associated to the problem of embedddability, i.e. iterative roots and approximate iterability. The topics of this paper are: (1) measurable iteration semigroups; (2) embedding of diffeomorphisms in regular iteration semigroups in \({{\mathbb{R}}^n}\) space; (3) iteration groups of fixed point free homeomorphisms on the plane; (4) embedding of interval homeomorphisms with two fixed points in a regular iteration group; (5) commuting functions and embeddability; (6) iterative roots; (7) the structure of iteration groups on an interval; (8) iteration groups of homeomorphisms of the circle; (9) approximately iterable functions; (10) set-valued iteration semigroups; (11) iterations of mean-type mappings; (12) Hayers–Ulam stability of the translation equation. Most of the results presented here was obtained by the means of functional equations. We indicate the relations between the iteration theory and functional equations.