A multivalued version of Sharkovskiĭ’s theorem holds with at most two exceptions

A multivalued version of Sharkovskiĭ’s theorem is formulated for M-maps on linear continua and, more generally, for triangular M-maps on a Cartesian product of linear continua. This improves the main result of [AP1] in the sense that our multivalued analogue holds with at most two exceptions. A further specification requires some additional restrictions. For instance, 3- orbits of m-maps imply the existence of k-orbits for all k ? \mathbbNk \in {\mathbb{N}} , except possibly for k ?k \in {4, 6}. It is also shown that, on every connected linearly ordered topological space, an M-map with orbits of all periods can always be constructed. This demonstrates that Baldwin’s classification of linear continua in terms of admissible periods [Ba] is useless for multivalued maps.     

An engine breaking the ΩEP-property

We present a construction which shows that some special continua do not have the nonwandering-eventually-periodic property. The construction applies e.g. to the topologist's sin curve and to the harmonic fan.     

Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

Wind tunnel simulation of air pollution dispersion in a street canyon

Physical simulation was used to study pollution dispersion in a street canyon. The street canyon model was designed to study the effect of measuring flow and concentration fields. A method of C02-laser photoacoustic spectrometry was applied for detection of trace concentration of gas pollution. The advantage of this method is its high sensitivity and broad dynamic range, permitting monitoring of concentrations from trace to saturation values. Application of this method enabled us to propose a simple model based on line permeation pollutant source, developed on the principle of concentration standards, to ensure high precision and homogeneity of the concentration flow. Spatial measurement of the concentration distribution inside the street canyon was performed on the model with reference velocity of 1.5 m/s.     

Dependence of the S-matrix on the choice of field variables in the effective Lagrangian

The dependence of the on-shellS-matrix on the change of the Lagrangian induced by a nonlinear substitutionF() is investigated by means of a graphical analysis. A cancellation mechanism is found and used to show that the tree approximation of theS-matrix is independent of such a substitution and that the Jacobian of the substitution has to be introduced in order to cancel a new class of singular one-loop graphs and to recover the primaryS-matrix at the one-loop level.