Fixed-point theorem in classes of function with values in a dq-metric space

We prove a fixed point result for nonlinear operators, acting on some classes of functions with values in a dq-metric space, and show some applications of it. The result has been motivated by some issues arising in Ulam stability. We use a restricted form of a contraction condition.     

Boron doped carbon nanotubes via ceramic catalysts

A facile metal catalyst free route to synthesize boron doped (0.6%–1.0%) carbon nanotubes via ceramic nanowires in which the formation of the nanowires (probably serving as templates), the carbon nanotubes and their doping all occur unanimously in the reaction, is presented.

     

8,11-Dioxa-(3,4-benzo)-(4.3.3)propellan

The synthesis of the title compound derived from the tetralin system is reported. On the basis of PMR and MS spectra the possibility of the formation of an isomeric bispirane is discussed.

     

Dendrites and light mappings

It is shown that a metric continuum is a dendrite if and only if for every compact space (continuum) and for every light confluent mapping such that there is a copy of in for which the restriction is a homeomorphism. As a corollary it follows that only dendrites have the lifting property with respect to light confluent mappings. Other classes of mappings are also discussed. This is a continuation of a previous study by the authors (2000), where open mappings were considered.

     

Uncountable intersections of open sets under CPA

We prove that the Covering Property Axiom CPA , which holds in the iterated perfect set model, implies the following facts.

• If is an intersection of -many open sets of a Polish space and has cardinality continuum, then contains a perfect set.

• There exists a subset of the Cantor set which is an intersection of -many open sets but is not a union of -many closed sets.

The example from the second fact refutes a conjecture of Brendle, Larson, and Todorcevic.

     

Decision-making in a fuzzy environment with fuzzy termination time

The multistage control of a deterministic and stochastic system in a fuzzy environment is considered. The fuzzy environment is meant as fuzzy constraints imposed on subsequent controls and a fuzzy goal to be attained. The fuzzy decision is assumed to be the intersection of fuzzy constraints and a fuzzy goal. The problem is to find a maximizing decision. The termination time is given as a specified fuzzy set in the space of control stages. For solving the problem, the dynamic programming is applied.     

Dense Relations Are Determined by Their Endomorphism Monoids

We introduce the class of dense relations on a set X and prove that for any finitary or infinitary dense relation on X, the relational system (X,) is determined up to semi-isomorphism by the monoid End(X,) of endomorphisms of (X,). In the case of binary relations, a semi-isomorphism is an isomorphism or an anti-isomorphism.     

Hemolysis of Erythrocytes and Erythrocyte Membrane Fluidity Changes by New Lysosomotropic Compounds

This work contains the results of studies on the influence of newly synthesized lysosomotropic substances (lysosomotropes) on human erythrocytes. Six homologous series of the compounds differing in the alkyl chain length and counterions were studied. They were found to hemolyse erythrocytes and to change their osmotic resistance. The observed hemolytic effects were dependent both on the compounds structure (polar head dimension and alkyl chain length of compound) and its form (the kind of the counterion). In parallel, the influence of lysosomotropes on fluidity of the erythrocyte membrane was studied. Three different fluorescent probes were used; 1,6-diphenyl-1,3,5-hexatriene (DPH), 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene, p-toluenesulfonate (TMA-DPH) and 6-dodecanoyl-2-dimethylaminonaphthalene (laurdan). Their anisotropy (DPH and TMA-DPH) or general polarization (laurdan) values after incorporation into ghost erythrocyte membranes were measured. The results obtained show that fluidity changes accompanied the effects observed in hemolytic experiments both quantitatively and qualitatively.