An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Reproductive behavior and health in consanguineous marriages

In many regions of Asia and Africa, consanguineous marriages currently account for approximately 20 to 50% of all unions, and preliminary observations indicate that migrants from these areas continue to contract marriages with close relatives when resident in North America and Western Europe. Consanguinity is associated with increased gross fertility, due at least in part to younger maternal age at first livebirth. Morbidity and mortality also may be elevated, resulting in comparable numbers of surviving offspring in consanguineous and nonconsanguineous families. With advances in medicine and public health, genetic disorders will account for an increased proportion of disease worldwide. Predictably, this burden will fall more heavily on countries and communities in which consanguinity is strongly favored, as the result of the expression of deleterious recessive genes. However, studies conducted in such populations indicate that the adverse effects associated with inbreeding are experienced by a minority of families.

Roofed polyquinanes: synthesis and electronic structure

Starting from readily available norbornenobenzoquinone 7 and employing a photothermal metathesis reaction as the main strategy, novel "roofed" polyquinane bisenones 3 and 13 have been synthesized. Among these, the former is potentially serviceable for further elaboration to dodecahedrane 1. Catalytic hydrogenation of 3 provided the dione 12, which fully inscribes the circumference of dodecahedrane sphere. The "roofed" C-16-bisenone 3 has been successfully annulated to C19-bisenone 24 and C19-trisenone 26 by employing the Greene methodology and Pauson-Khand reaction, respectively. The molecular structures of 3 and 13 were computed using molecular mechanics and semiempirical MO methods. The nonbonded distances between the double bonds vary strongly with the method employed. The interactions between the pi-MO's were, therefore, probed by means of photoelectron (PE) spectroscopy. Comparison with the PE spectra of a series of model systems with increasing complexity enabled an unambiguous assignment of the observed peaks. The symmetric and antisymmetric combinations of the pi-MO's of the enone moieties of 3 and 13 show large splittings, characteristic of propano-bridged systems in which through-space and through-bond effects act in concert.

Dependence of giant magnetoresistance on oxygen stoichiometry and magnetization in polycrystalline La0.67Ba0.33MnOz

We have studied resistivity, magnetization, and magnetoresistance in polycrystalline La0.67Ba0.33MnOz by reducing the oxygen stoichiometry from z=2.99 to 2.80. As the oxygen content decreases, the resistivity of La0.67Ba0.33 MnOz increases and the magnetic transition temperature shifts to lower temperature. A large magnetoresistance effect was observed over a wide temperature range for all samples except the insulating z=2.80 sample. The similarity between our results on oxygen-deficient polycrystalline La0.67 Ba0.33MnOz and films previously reported to have a very large intrinsic magnetoresistance is discussed. At low temperature the magnetoresistance was observed to be strongly dependent on the magnetization. A possible mechanism for this effect is discussed.

Electronic conduction in LaNiO3-delta: the dependence on the oxygen stoichiometry delta

We report a systematic study of the electronic transport properties of the metallic perovskite oxide LaNiO3-delta as a function of the oxygen stoichiometry delta (delta less than or equal to 0.14). The electrical resistivity, magnetoresistance, susceptibility, Hall effect and thermopower have been studied, All of the transport coefficients are dependent on the value of delta. The resistivity increases almost exponentially as delta increases. We relate this increase in rho to the creation of Ni2+ with square-planar coordination. We find that there is a distinct T-1.5-contribution to the resistivity over the whole temperature range. The thermopower is negative, as expected for systems with electrons as the carrier, but the Hall coefficient is positive. We have given a qualitative and quantitative explanation for the different quantities observed and their systematic variation with the stoichiometry delta.

Magnetoresistance of the metallic perovskite oxide LaNiO3-delta

We report a study of the magnetoresistance (MR) of the metallic perovskite oxide LaNiO3-delta as a function of the oxygen stoichiometry delta (delta less than or equal to 0.14), magnetic field (H less than or equal to 6 T) and temperature (1.5 K less than or equal to T less than or equal to 25 K). We find a strong dependence of the nature of the MR on the oxygen stoichiometry. The MR at low temperatures changes from positive to negative as the sample becomes more oxygen deficient (i.e. delta increases). Some of the samples, which are more resistive, show resistivity minima at T-min approximate to 20 K. We find that in these samples the MR is positive for T > T-min and negative for T < T-min. We conclude that in the absence of strong magnetic interaction, the negative MR in these oxides can arise from weak-localization effects.

Spin-orbital ordering and mesoscopic phase separation in the double perovskite Ca2FeReO6

Neutron powder diffraction measurements on Ca2FeReO6 reveal that this double perovskite orders ferrimagnetically and shows anomalous lattice parameter behavior below T-C=521 K. Below similar to300 K and similar to160 K we observe that the high-T monoclinic crystal structure separates into two and three monoclinic phases, respectively. A magnetic field suppresses the additional phases at low T in favor of the highest-T phase. These manifestations of the orbital degree of freedom of Re 5d electrons indicate that these electrons are strongly correlated and the title compound is a Mott insulator, with competing spin-orbitally ordered states.

Synthesis and structure of La14V6CuO36.5: a transparent Cu(I) vanadate containing [OCuO](3-) sticks

The title compound, La14V6CuO36.5, was prepared from a stoichiometric mixture of La2O3,V2O5, and CuO at 1050-1080 degreesC. The compound forms transparent, pale green crystals and was characterized by wavelength dispersive spectroscopy and single crystal X-ray diffraction. The structure contains isolated VO43- tetrahedra and [OCuO](3-) sticks dispersed in a lanthanum oxide network. Films of La14V6CuO36.5 were grown on R-plane sapphire by using pulsed laser deposition. Rutherford backscattering spectroscopic and X-ray diffraction analyses of the films showed oriented growth of the title phase, a similar to5 eV optical band gap and n-type conductivity. The compound is an example of a transparent copper(I) oxide.

Novel ABO(3) oxides related to perovskite and YAlO3 structure types in the La-B-V-O (B = Ni, Cu) systems

The synthesis, structure and magnetic properties of mixed-metal oxides of ABO(3) composition in the La-B-V-O (B = Ni, Cu) systems are described in the present paper. While the B = Ni oxides adopt GdFeO3-like perovskite structure containing disordered nickel and vanadium at the octahedral B site, La3Cu2VO9 crystallizes in a YAlO3-type structure. A detailed investigation of the superstructure of nominal La3Cu2VO9 by WDS analysis and Rietveld refinement of powder XRD data reveal that the likely composition of the phase is La13Cu9V4O38.5, where the Cu and V atoms are ordered in a root13a(h) (a(h) = hexagonal a parameter of YAlO3-like subcell) superstructure. Magnetic susceptibility data support the proposed superstructure consisting of triangular Cu-3 clusters. At low temperatures, the magnetic moment corresponds to S = 1/2 per Cu-3 cluster, while at high temperatures the behavior is Curie-Weiss like, showing S = 1/2 per copper. The present work reveals the contrasting behavior of La-Cu-V-O and La-Ni-V-O systems: while a unique line-phase related to YAlO3 structure is formed around La3Cu2VO9 Composition in the copper system, a continuous series of perovskite-GdFeO3 solid solutions, LaNi1-xVxO3 for 0 less than or equal to x less than or equal to 1/3 seems to be obtained in the nickel system, where the oxidation state of nickel varies from 3+ to 2+.

Properties of the Ferrimagnetic Double-Perovskites A2FeReO6 (A=Ba and Ca)

We have synthesized ceramics of A2FeReO6 double-perovskites A2FeReO6 (A=Ba, Ca). Structural characterizations indicate a cubic structure with a=8.0854(1) Å for Ba2FeReO6 and a distorted monoclinic symmetry with a=5.396(1) Å, b=5.522(1) Å, c=7.688(2) Å and β=90.4° for Ca2FeReO6. The barium compound is metallic from 5K to 385K, i.e. no metal-insulator transition has been seen up to 385K, and the calcium compound is semiconducting from 5K to 385K. Magnetization measurements show a ferrimagnetic behavior for both materials, with Tc =315 K for Ba2FeReO6 and above 385K for Ca2FeReO6. At 5K we observed, only for Ba2FeReO6, a negative magnetoresistance of 10% in a magnetic field of 5T. Electrical, magnetic and thermal properties are discussed and compared to those of the analogous compounds Sr2Fe(Mo,Re)O6 recently studied.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of ``how much'' information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on ``what'' is coded by primary afferents. Amongst the kinematic variables tested-position, velocity, and acceleration-primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.