Radon–Nikodým indexes and measures of weak noncompactness

The aim of this paper is to present a quantitative version of the Radon–Nikodým property and some other results related to it. This approach gives an extra insight to the classical results. We introduce two indexes: an index of representability of measures and an index of dentability. We review classic results in order to obtain relationships between these and other indexes.     

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20].     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

A topological characterization of the Sierpiński triangle

We present a topological characterization of the Sierpiński triangle. This answers question 58 from the Problem book of the Open Problem Seminar held at Charles University. In fact we give a characterization of the Apollonian gasket first. Consequently we show that any subcontinuum of the Apollonian gasket, whose boundary consists of three points, is homeomorphic to the Sierpiński triangle.     

On the γ-filtration of oriented cohomology of complete spin-flags

We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the γ-filtration. Moreover, if the formal group law determined by the oriented cohomology theory is congruent to the additive formal group law modulo 2, then at degree 2 and 3, we show that the γ-filtration of complete spin-flags is torsion free.     

Interactions with herring sperm DNA and biological studies of sparfloxacin drug‐based copper(II) compounds

Copper(II) complexes of the type [Cu(SPF)(Lⁿ)Cl] (where SPF is sparfloxacin and Lⁿ = substituted terpyridines) were synthesized and found to have a distorted octahedral geometry. Superoxide dismutase‐like activity of the complexes was measured using a nitroblue tetrazolium/reduced nicotinamide adenine dinucleotide/phenazine methosulfate system and expressed in terms of the concentration of complex which terminates the formation of formazan by 50% (IC₅₀ value), which was found to range from 0.572 to 1.522 µm . Interactions of the complexes with herring sperm DNA were studied by absorption titration, viscosity measurement and gel electrophoresis under physiological conditions. The antimicrobial efficiency of the complexes was tested against five different microorganisms and showed good biological activity. All the complexes showed good cytotoxic activity, with LC₅₀ values ranging from 4.01 to 9.64 µg ml^?1. Copyright © 2012 John Wiley & Sons, Ltd.     

Ricci flatness of certain compact pseudo-Kähler solvmanifolds

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider Ricci curvature tensor of certain compact pseudo-Kähler solvmanifolds.     

NaBH4/DOWEX(R)50WX4: A Convenient Reducing System for Fast and Efficient Reduction of Carbonyl Compounds to Their Corresponding Alcohols

The reduction of a variety of carbonyl compounds was efficiently carried out with NaBH₄/DOWEX(R)50WX4 system. The reactions were performed to give the corresponding alcohols derivatives in perfect yields in THF at room temperature. Reduction of acyloins and a‐diketones by this reducing system produced efficiently the corresponding vicinal diols. Also, the reduction of aldehydes over ketones has been accomplished successfully by this system. Regioselectivity of this system was also investigated with exclusive 1,2‐reduction of conjugated carbonyl compounds to their corresponding allylic alcohols in high to excellent yields.     

Maximum Order of Triangle‐Free Graphs with a Given Rank

The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.