Markov partition in non-hyperbolic interval dynamics

We considerC ² unimodal mapsf such that all periodic points are hyperbolic, the critical point is non-degenerated and non-recurrent, and the Julia set does not contain intervals. We construct a Markov partition for a big part of the Julia set. Then we use it to estimate the limit capacity and Hausdorff dimension of the Julia set.Partially supported by CNPq, S.C.T.-Brazil     

Fast and efficient preparation of Baylis-Hillman-derived (E)-allylic azides and related compounds in aqueous medium

A practical access to alkyl- and aryl-substituted (E)-2-(azidomethyl)alkenoates and related azido compounds from the corresponding allylic bromides in aqueous acetone is described. An alternative method to obtain the starting bromides based on heterogeneous catalysis under mild conditions was also investigated.     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Using a Conic Formulation for Finding Steiner Minimal Trees

We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution for this latter problem using an interior-point algorithm.     

Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions

We answer a problem of Liao [S.T. Liao, Standard systems of differential equations and obstruction sets—from linearity to perturbations, in: System Researches, Proceedings Dedicated to the 85th Anniversary of Qian Xue-Sen, Zhejiang Education Press, Hangzhou, China, 1996, pp. 279-290 (in Chinese)]: A C¹ vector field or a C¹ diffeomorphism on an n-dimensional manifold has equal entropy with that of its bundle extensions. We also prove that each ergodic probability with simple Lyapunov spectrum has at most n²n! covering probabilities on each bundle extension.     

Determination of degree of conversion as a function of depth of a photo-initiated dental restoration composite—III application to commercial Prodigy Condensable™

In this third work, we evaluated the degree of conversion (DC) versus depth of dental filling composite named Prodigy Condensable™ using infrared spectroscopy. Confirming previous results, there was a gradual reduction of DC with increasing depth but the composite exhibited extreme values of DC, an upper value (45.9%) on the surface and a lower one (6.1%) at a depth of 5 mm. The composite presented the worst performance among materials studied. The composite formulation was 80% of inorganic fillers and BisfenolA/dimethacrylate (BisGMA) (18%)/triethyleneglycoldimethacrylate (TEGDMA) (2.0%) as monomers. As stated before, type/ratio/viscosity of monomers and type, amount, size and size distribution of fillers all together had an important role in the cure reaction contributing to the final performance of the composite.     

Unusual solid-state behavior in a neutral [2]catenane bearing a hydrolyzable component

A template-directed strategy to forming a bis(diimide) macrocycle through an intermediate asymmetric [2]catenane is reported. Saponification of the ester linkages within the crown ether component is much slower in the mechanically interlocked structure when compared to the free crown. The predominance of a single translational isomer leads to a dimeric structure, resulting in the generation of infinite channels within the crystal lattice. [structure: see text]     

Preparation and crystal structure ofexo-2,exo-6-dihydroxy-2,6-dimethyl-9-oxabicyclo[3.3.1]nonane

In a further exploration of the structural factors causing alicyclic diols such asexo-2,exo-6-dihydroxy-2,6-dimethylbicyclo[3.3.1]nonane (1) to adopt the helical tubuland inclusion host structure, the title compound (8) has been synthesized and its crystal structure determined. This 9-oxa analogue of (1) has a totally different structure [C₁₀H₁₈O₃; orthorhombic;P2₁2₁2;a 18.989(4),b 19.064(3),c 14.256(3) Å;Z 20; with finalR 0.065] due to involvement of the ether oxygen atom in the hydrogen bonding network. The structure of the diol (8) approximatesP¯42₁ c symmetry, and 16 of the 20 molecules per cell create a hostlike structure of this symmetry, which consists of tightly bound hydrogen bonded pillars parallel toc. The remaining guestlike molecules occupy inequivalent pseudo ¯4 sites separated byc/2 to form weakly bound columns parallel toc. Hydrogen bonds also occur between the pillars and columns. An ordered structure with sensible intermolecular contacts can be formed inP2₁2₁2₁ with thec axis doubled. A difference betweena andb axial lengths correlates with a difference in occupancies of pseudo-¯4-related sites for the guest-like component of the structure.     

Helical tubulate inclusion compounds of ferrocene and squalene

The inclusion compounds of 2,8-dimethyltricyclo[5.3.1.1^3,9]dodecane-syn-2,syn-8-diol,3, with ferrocene and with squalene have been prepared. The crystal structures of these helical tubulate compounds: (3)₃·(ferrocene)_0.75 [P3₁21,a=b=13.7480(6),c=7.0312(5) Å,Z=1,R=0.038] and (3)₃·(squalene)_0.23 [P3₁21,a=b=13.677(1),c=7.0533(9) Å,Z=1,R=0.042] are described. Supplementary Data relating to this article are deposited with the British Library as supplementary publication No. SUP 82151 (16 pages).