Damping of light in a weakly resonant inhomogeneous medium

On the basis of an expression obtained earlier for the permittivity in the form of a series in powers of the atomic polarizability, the mechanism of damping of light caused by the processes of reemission between two atoms is considered. It is shown that, on an increase in the polarizability, as a consequence of the light frequency approaching the resonance frequency, this mechanism leads to a sharp increase in the extinction coefficient. This effect is caused by the collective behavior of the atoms and is not connected with the natural absorption near the resonance.     

Intracellular injection of phospholipids directly alters exocytosis and the fraction of chemical release in chromaffin cells as measured by nano-electrochemistry

Using a nano-injection method, we introduced phospholipids having different intrinsic geometries into single secretory cells and used single cell amperometry (SCA) and intracellular vesicle impact electrochemical cytometry (IVIEC) with nanotip electrodes to monitor the effects of intracellular incubation on the exocytosis process and vesicular storage. Combining tools, this work provides new information to understand the impact of intracellular membrane lipid engineering on exocytotic release, vesicular content and fraction of chemical release. We also assessed the effect of membrane lipid alteration on catecholamine storage of isolated vesicles by implementing another amperometric technique, vesicle impact electrochemical cytometry (VIEC), outside the cell. Exocytosis analysis reveals that the intracellular nano-injection of phosphatidylcholine and lysophosphatidylcholine decreases the number of released catecholamines, whereas phosphatidylethanolamine shows the opposite effect. These observations support the emerging hypothesis that lipid curvature results in membrane remodeling through secretory pathways, and also provide new evidence for a critical role of the lipid localization in modulating the release process. Interestingly, the IVIEC data imply that total vesicular content is also affected by in situ supplementation of the cells with some lipids, while, the corresponding VIEC results show that the neurotransmitter content in isolated vesicles is not affected by altering the vesicle membrane lipids. This suggests that the intervention of phospholipids inside the cell has its effect on the cellular machinery for vesicle release rather than vesicle structure, and leads to the somewhat surprising conclusion that modulating release has a direct effect on vesicle structure, which is likely due to the vesicles opening and closing again during exocytosis. These findings could lead to a novel regulatory mechanism for the exocytotic or synaptic strength based on lipid heterogeneity across the cell membrane.

Amperometry and intracellular vesicle impact electrochemical cytometry with nanotip electrodes were used to monitor the effects on exocytosis and vesicular storage after nano-injection of phospholipids with different geometries into secretory cells.     

A novel four-component reaction of diethylamine, an aromatic aldehyde and an alkyl isocyanide with dialkyl acetylenedicarboxylates in the presence of silica gel: an efficient route for the regio- and stereoselective synthesis of sterically congested alkenes

The 1:1 intermediate generated by the addition of an isocyanide to a dialkyl acetylenedicarboxylate is trapped by the iminium ion intermediate that forms from the reaction between an aromatic aldehyde and diethylamine. The reactions were completed in the presence of silica gel powder. The product dialkyl 2-[(alkylamino)carbonyl]-3-[(Z)-1-(diethylamino)-1-arylmethylidene]succinates, were produced in acceptable yields. The reactions are completely regio- and stereoselective.     

Mixed benzohydroxamato-acetylacetonato metal complexes: spectral,thermal and photochemical behaviour

Summary Bis(acetylacetonato)VO^II,–Co^II,–Ni^II,–Cu^II,–Zn^II, –UO ₂ ^II and tris(acetylacetonato)Fe^III react with benzohydroxamic acid to yield the corresponding mixed ligand complexes as a result of displacement of one acetylacetone molecule. Intermolecular association may be the reason for six-coordination geometry around the metal ions. A t.g.a. study of the complexes shows, in most cases, initial loss of alcohol and water molecules associated with the complexes; subsequent decomposition steps are characterised by very sharp weight loss. The photochemical stability of the complexes has been studied. Intraligand excitation causes a decomposition in the case of Fe^III and VO^II-complexes but no detectable effect for Co^II, Ni^II, Cu^II, Zn^II, or UO ₂ ^II -complexes.     

A note on the essential pseudospectra and application

In this research article, we work with the notion of essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra.     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

Determination of maximum particle size in magnetic fluids

Higher-order moments of particle size distribution functions are determined for magnetic fluids from analysis of initial segments of magnetization curves. It is shown that the higher-order moments calculated using approximation of real particle size distributions by the Γ distribution are strongly overestimated. Agreement between the measured and calculated moments can be radically improved by truncating maximum particle size X_max. A relation between X_max and the parameters of the Γ distribution is proposed taking into account the degree of polydispersity of a magnetic fluid. Namely, the ratio between the maximum and most probable particle diameters is equal to the ratio between the mean-square magnetic moment of a particle and its squared average magnetic moment.     

Three-vortex motion with zero total circulation: Addendum

Summary Beginning with general remarks on vortex systems with zero net circulation, the three-vortex problem is considered and solved explicitly in the following special cases: 1. The distance between two vortices is small compared to the distance to the third, with two subcases: the neighboring vortices (i) have the same sign, (ii) have opposite signs. 2. The impulse of the system is small compared to the product of a typical vortex strength and the biggest distance found (at any time) between vortices. Formulas and rules for the construction of the orbits in case 2 are given; they include the circular paths that are found for zero impulse.These special cases are typical for the orbits in the different regions found between the separatrices of the Hamiltonian. Transitional paths are discussed in the case where the vortex circulations have the ratio 11–2. In this case, it is shown (by inspection) that the Hamiltonian is a harmonic function.Actually, the Hamiltonian is a harmonic function whenever the sum of the three circulations is zero, as shown in an Addendum by Prof. Hassan Aref. This is an essential result for the full understanding of the problem under consideration.

---

Zusammenfassung Anschliessend zu einigen allgemeinen Bemerkungen über Wirbelsysteme mit verschwindender totaler Zirkulation wird der Fall von drei Wirbeln betrachtet. Explizite Lösungen werden in den folgenden Fällen gegeben: 1. Der Abstand zwischen zwei Wirbeln ist klein im Vergleich zum Abstand vom dritten Wirbel; es gibt zwei Kategorien: die benachbarten Wirbel haben (i) gleiche oder (ii) ungleiche Vorzeichen. 2. Der ImpulsI des Systems ist klein im Vergleich zum Produkt einer typischen Wirbelstärke und dem allzeitigen grössten Abstand zwischen Wirbeln. Im Fall 2 werden Formeln und Instruktionen zur Konstruktion von Wirbelbahnen gegeben, einschliesslich der Kreisbahnen die im FallI=0 auftreten.Dies Spezialfälle sind typisch für die Bahnen in den verschiedenen (durch Separatrizen abgegrenzten) Regionen der Hamilton-Funktion. Bahnen in den Übergangsfällen werden diskutiert für Wirbelstärken die im Verhältnis 11–2 stehen. Für diese Verhältnisse findet man auch (durch Inspektion) dass die Hamilton-Funktion harmonisch ist.In Wirklichkeit sind aber alle Hamilton-Funktionen für drei Wirbel mit verschwindender totaler Zirkulation harmonisch. Dies wird von Prof. Hassan Aref im Addendum gezeigt. Dieses bemerkenswerte Ergebnis ist wesentlich für das volle Verständnis des behandelten Problemes.