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     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

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.     

Revised Robertson's test theory of special relativity: Space-time structure and dynamics

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant Robertson's subfamilies. It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory.Part of this work was done at the Department of Physics, Utah State University, Logan, Utah 84322.     

Spectroscopic characterization of mineral crystals produced by the bacterium Azospirillum brasilense

The results of spectroscopic structural and trace elemental analyses of mineral crystals produced by the soil nitrogen-fixing bacterium Azospirillum brasilense cultivated in a synthetic medium are presented and discussed. The mineral formed is shown to have a structure close to struvite (MgNH(4)PO(4) x 6H(2)O; ASTM file No. 15-762) with some differences which may be attributed to the presence of isomorphic admixtures of other cations (struvite is known to have a variety of forms). AAS/AES and ion chromatography analyses for a number of biologically important microelements and their role in the formation of the crystal structure, as well as some questions related to biomineralization are also discussed.     

Synthesis of mixed metal decaosmium carbido clusters: The X-ray structures of the monoanions [Os10C(CO)24Cu(NCMe)]− and [Os10C(CO)24AuPPh3]−

The high nuclearity mixed metal cluster monoanions [Os₁₀C(CO)₂₄Cu(NCMe)]^? (I) and [Os₁₀C(CO)₂₄AuPPh₃]^? (II) have been obtained by reaction of the carbido-dianion [Os₁₀C(CO)₂₄]^2? (III) with one equivalent of [Cu(NCMe)₄] [BF₄] and Ph₃PAuCl, respectively, in CH₂Cl₂. X-ray analysis of the [PPh₃Me]⁺ salts of I and II show that the Cu and Au ligands have added to capping tetrahedra of the dianion III in μ₃- and μ₂-bridging positions, respectively.     

Directional operators and radial functions on the plane

LetEçS ¹ be a set with Minkowski dimensiond(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions ofE. The main result of this paper shows that these operators are bounded onL _rad ^p (R²) forp>1+d(E) and unbounded whenp<1+d(E). We also give some end-point results.