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.

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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.

     

Plasma Oxidation of Polypropylene Fibers for Concrete Reinforcement

Russian Journal of Applied Chemistry - In this project, the fibers were applied to increase the tensile strength of the concrete and produce fiber reinforced concrete (FRC). Polypropylene (PP) is...     

Evolution of Holographic Entropy Quantities for Composite Quantum Systems

Theoretical and Mathematical Physics - We consider entanglement entropy quantities for a three-part system, namely, the tripartite information, total correlation, and so-called secrecy monotone. A...     

On the temperature dependence of the surface energy of actinide crystal faces

The temperature coefficient of the surface energy has been calculated and the influence of the temperature on the anisotropy of the surface energy has been demonstrated for crystal faces of the polymorphic phases of actinides.     

Electrochemical reactions of chalcogenbiscyclanones and the products of their S-, O-, and N-heterocyclization

In this work, the routes of the redox reactions of chalcogenbiscyclanones and the products of their S-, O-, N-heterocyclization in organic solvents were analyzed and validated. The influence of the nature of the heteroatoms and substituents on the redox activity of S- and Se-containing biscyclanones, benzannelated thianthrenes, oxathianthrenes, and diazepine was established based on electrochemical studies, ESR spectroscopy data, and the results of quantum chemical calculations