Ordering of the Mandelbrot-like set of the exponential map

We graphically study the Mandelbrot-like set of the complex exponential family of maps E(lambda)(z)=lambdae(z), which we call the Baker-Rippon-Devaney (BRD) set. We observe that the period of every hyperbolic component can be deduced with the naked eye by using two simple rules. (c) 1998 American Institute of Physics.     

Titanocene(III)‐Catalyzed 6‐exo Versus 7‐endo Cyclizations of Epoxypolyprenes: Efficient Control and Synthesis of Versatile Terpenic Building Blocks

In this article, a complete study on the selectivity of titanocene(III) cyclization of epoxypolyprenes is presented. The requirements for the formation of six‐ or seven‐membered rings during these cyclizations are determined, taking into account the different substitution pattern in the epoxypolyprene precursor. Thus, a complete selectivity to 6‐exo or 7‐endo cyclization process has been achieved, yielding mono‐, bi‐, and even tricyclic compounds, constituting a new and efficient access to this type of derivative. Additionally, this procedure opens the possibility to prepare excellent building blocks for the synthesis of polycyclic compounds with a trisubstituted oxygenated function, which is present in several natural terpenes.     

Step‐like melting mechanisms of isothermally crystallized isotactic polypropylene

The complex melting behavior of isotactic polypropylene, after isothermal crystallization, was studied within the context of step‐like melting mechanisms which were previously proposed for high temperature polymers. The morphological characteristics of the melting process were also studied as a function of molecular weight, and close similarities were observed with respect to high temperature polymers. Positive birefringence crystals of low molecular weight samples developed double melting behavior in three steps. The first melting step was assigned to continuous melting of secondary crosshatch reversing lamellae, together with recrystallization of the remaining isothermal crystals. In the second melting step (first melting endotherm), crystals tended to lose their original coarse negative birefringence due to melting of secondary reversing branching. This effect rendered new, finer texture, but still negative birefringence crystals. In the third melting step (second melting endotherm), there was a combination of melting of two crystal populations, one consisting of the remaining fraction of reversing primary crystals, and the other consisting of nonreversing primary crystals. A crosshatch secondary branching model was therefore proposed to explain the overall results. Mixed birefringence spherulites of high molecular weight samples displayed similar, although proportional, behavior under identical crystallization and melting conditions corroborating the proposed melting mechanism. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2188–2200, 2008     

Mixed threefold and fourfold carbon coordination in compressed CO2

Carbon dioxide (CO2) has been recently reported to possess an amorphous form, named "carbonia," structurally similar to other group-IV oxide glasses. By combining ab initio constant pressure molecular dynamics, density-functional perturbation theory, and experimental IR spectra, we show that carbonia, and possibly also phase VI, is not SiO2-like, and that instead it is partially tetrahedral containing also a sizable amount of carbon in threefold coordination, but no sixfold octahedral coordination. Enthalpic considerations suggest that carbonia is a metastable intermediate state of the transformation of molecular CO2 into fully tetrahedral phases.     

Unexpected dimeric products from the amidomethylation of pentasubstituted benzenes

An isomeric series of unexpected diarylmethane products with flexible substituents, isolated from amidomethylation reactions of p-dimethoxybenzene derivatives, was analyzed by X-ray crystallography to reveal novel solid-state structures, two of which have identical elemental cell parameters.     

Excitation energy partition in deeply inelastic collisions between40Ar and Ag at 27 MeV per nucleon

The dynamics of the two partners produced in dissipative collisions has been experimentally studied for the system⁴⁰Ar + Ag at 27 MeV per nucleon. Primary masses of the fragments can then be calculated; the excitation energy partition between the two fragments is derived from the number of particles evaporated by each fragment. We found that this division evolves from equipartition to a repartition close to thermal equilibrium in the excitation energy range 300–350 MeV or interaction times 5-10×l0^?22 s.     

2-[(trifluoroacetyl)amino]benzoquinone and the hydrochloride and perchlorate salts of 2-aminohydroquinone

Hydrogen bonding parameters for the title materials are reported. 2-[(trifluoroacetyl)amino]benzoquinone crystallizes in the monoclinic space group P2 ₁/c, with a = 18.195(4), b = 5.110(1), c = 9.635(2), = 104.22(3)°, V = 868.4(3) ų, and Z = 4. This compound exhibits two weak intramolecular hydrogen bonds. The first is between a hydrogen atom of the quinone ring and the carbonyl oxygen of the trifluoroacetamide group; it has a distance of 2.24 Å and a C—HsO angle of 122°. The second is between the hydrogen atom of the trifluoroacetamide group and a quinone carbonyl group; it has a distance of 2.26 Å and a N—HsO angle of 107°. 2-Aminohydroquinone hydrochloride crystallizes in the orthorhombic space group Pca2₁, with a = 16.220(3), b = 5.211(1), c = 8.719(2), V = 737.0(2) ų, and Z = 4. 2-Aminohydroquinone perchlorate crystallizes in the orthorhombic space group P2₁2₁2₁, with a = 7.110(1), b = 7.139(1), c = 18.043(4), V = 915.8(3) ų, and Z = 4. All active hydrogens of the two salts exhibit intermolecular hydrogen bonds that serve to organize a three-dimensional framework for each case.