On a Morse conjecture for analytic flows on compact surfaces

The aim of this paper is to prove a Morse conjecture; in particular it is shown that a topologically transitive analytic flow on a compact surface is metrically transitive. We also build smooth topologically transitive flows on surfaces which are not metrically transitive.     

Efficient algorithms on distributive lattices

We present several efficient algorithms on distributive lattices. They are based on a compact representation of the lattice, called the ideal tree. This allows us to exploit regularities in the structure of distributive lattices. The algorithms include a linear-time algorithm to reconstruct the covering graph of a distributive lattice from its ideal tree, a linear-time incremental algorithm for building the ideal lattice of a poset and a new incremental algorithm for listing the ideals of a poset in a combinatorial Gray code manner (in an code.)     

Fixed point theorems with respect to a contractive condition of integral type

We derive some fixed point theorems for mappings satisfying a contractive condition of integral type.     

Structure of foliations of codimension greater than one

We study the structure of a foliation of high codimension which admits a transverse foliation. We introduce four families of open saturated sets. These open sets have a simple characterization and allow us to establish a structure theorem as in codimension 1.     

The Hydrothermal Synthesis of Petalite Mineral Phases and their Morphological Changing by Increasing of Temperature

In this investigation the Petalite minerals were synthesized hydrothermally at different temperatures from a glass with the composition Li₂CO₃:Al₂O₃: SiO₂ and the relation 1: 1: 8. On that occasion the following mineral phases arised:

• at low temperatures (410°C) α-petalite (unit cell å = 11.737 Å/b̊ = 5.17 Å/c̊ = 7.63 Å, space group P₂/a);
• At 490 °C α-petalite was splitted to quartz and an orthorhombic β₁-petalite (unit cell å = 18.24 Å/c̊ = 10.54 Å/c̊ = 10.57 Å, space group P_mC_n). β₁-petalite could be observated until 1000 °C.
• at 560 °C tetragonal β₂-petalite (unit cell å = 7.50 Å/c̊ = 9.07 Å, space group P 4₃2₁2) in parallel with β₁-petalite;
• Behind 750 °C β₂-petalite was not observed.
• Behind 900 °C a pseudohexagonal mineral phase developed from β₁-petalite. May be it is possible to indicate this phase as hexagonal (unit cell å = 5.217 Å/c̊ = 5.464 Å, space group P 6₂22 or P 6₄22). The author suggests to denote this phase as β₃-petalite.

     

The Hydrothermal Effect on Crystal Development and Electrical Conductivity of Li2CO3

Lithiumcarbonat was treated hydrothermally in the range of temperature from 80 °C to 600 °C. The Li₂CO₃-crystals of the starting material were monoclinic with the unit cell a = 8.39 Å, b = 5.00 Å, c = 6.21 Å, β = 114.5° and the space group C2/c (Zemann). During the increase of temperature the habit of the Li₂CO₃-crystals changed in the ranges of higher temperatures that they could be described as pseudocubic. In parallel with this development the electrical conductivity of the crystals also changed.     

Aggregation phenomena in polyelectrolyte multilayers made from polyelectrolytes bearing bulky functional,hydrophobic fragments

The functionalization of polyelectrolyte multilayers often implies the use of bulky functional fragments, attached to a standard polyelectrolyte matrix. Despite of the high density of non-charged, often hydrophobic substituents, regular film growth by sequential adsorption proceeds easily when an appropriate polyelectrolyte counter ion is chosen. However, the functional fragments may cluster or aggregate. This complication is particularly evident when using chromophores and fluorophores as bulky pendant groups. Attention has to be paid to this phenomenon for the design of functional polyelectrolyte films, as aggregation may modify crucially the properties. The use of charged spacer groups does not necessarily suppress the aggregation of functional side groups. Still, clustering and aggregation depend on the detailed system employed, and are not obligatory. In the case of cationic poly(acrylamide)s labeled with naphthalene and pyrene fluorophores, for instance, the polymers form intramolecular hydrophobic associates in solution, as indicated by strong excimer formation. But the polymers can undergo a conformational rearrangement upon adsorption so that they are decoiled in the adsorbed films. Analogous observations are made for polyanions bearing mesogenic biphenyls fragments. In contrast, polycations functionalized with the dye coumarin 343 show little aggregation in solution, but a marked aggregation in the ESA films.     

The Morphology of Some Hydrothermally Synthesized Li-Minerals: A-Zeolite, α-Eucryptite, β-Spodumene and β-Eucryptite

The hydrothermal treatment of glass with the composition 2 LiF, Al₂O₃, 3 SiO₂ at 1 kbar in the range of 150 °C to 850 °C gave rise to the formation of A-zeolite with orthorhombic unit cell with å = 10.31 Å/b̊ = 8.18 Å/c̊ = 5.0 Å (space group Pna2₁), α-eucryptite, trigonal, å = 13.4 Å/bº = 13.4/Å/cº = 9.0 Å (space group R 3 ), β-spodumene, pseudocubic/tetragonal, å = 7.53 Å/b̊ = 7.53 Å/c̊ = 9.15 Å (space group P4₃2₁2), β-eucryptite, monoclinic, å = 7.75 Å/b̊ = 5.2 Å/c̊ = 11.16 Å (space group P6₂22). The morphology and development of the mineral phases depend on the temperature of formation.