A possible mathematics for the unification of quantum mechanics and general relativity

This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time variables x,t, furnished with an additional indefinite inner product invariant under Poincar\'e transformations, and isomorphisms of these spaces that preserve the indefinite metric. The indefinite metric is responsible for breaking the symmetry between space and time variables and for selecting a family of Hilbert subspaces that are preserved under Galileo transformations. Within these subspaces the usual quantum mechanics with Schr\"odinger evolution and t as the evolution parameter is derived. Simultaneously, the Minkowski space-time is isometrically embedded into H, Poincar\'e transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincar\'e transformations. The main new result is a proof that the framework accommodates arbitrary pseudo-Riemannian space-times furnished with the action of the diffeomorphism group

Femtosecond energy transfer between chromophores in allophycocyanin trimers

Ultrafast energy-transfer processes in allophycocyanin (APC) trimers from Mastigocladus laminosus have been examined by a femtosecond absorption technique. Isotropic absorption recovery kinetics with τ=440±30 fs were observed in APC trimers at 615 nm. In APC monomers such a fast process was not observed. The anisotropy in both samples was constant and close to 0.4 during the first few picoseconds. The results are consistent with a model of the APC trimer in which the two APC chromophores have different absorption spectra with maxima about 600 and 650 nm. The transfer of energy from the 600 nm chromophore to the 650 nm chromophore occurs in 440 fs and is dominated by the Förster dipole—dipole energy-transfer mechanism

Perovskite-like catalysts for the catalytic flameless combustion of methane

Modified LaCoO3 and LaMnO3 were investigated as catalysts for low tvemperature flameless combustion of methane. Modifications were carried out by the substitution part of La for Sr2+ and Ce4+, by the addition of 0.5% of Pt or Pd and by the substitution with Ag, which have limited solubility in the perovskite structure and may exist as intraframework Ag+ and extraframework metallic silver. Catalysts were synthesized by flame pyrolysis, which lead to a significant increase of both surface area and thermal resistance in comparison with the catalysts prepared by traditional sol-gel method. Samples were mainly characterized by XRD, BET and TPR techniques. Catalytic activity for the flameless combustion of methane was investigated by means of bench scale continuous apparatus, equipped with a quadrupolar mass spectrometer. In addition the resistance of every catalysts against sulphur poisoning was tested by using tetrahydrothiophene (THT) as poisoning agent. In most cases modification of perovskites led to an activity improvement, which was much more evident in the case of silver substitution. All the FP-prepared catalysts showed full methane conversion below 600\ub0C, with CO2 and H2O as the sole detected products. Sr-substitution and addition of noble metals increased resistance to sulphur poisoning, while silver was not effective from this point of view, its main advantage being a substantial increase of the initial activity, which lead to satisfactory performance even after poisoning

Dynamics of Rotating Accretion Flows Irradiated by a Quasar

We study the axisymmetric, time-dependent hydrodynamics of rotating flows that are under the influence of supermassive black hole gravity and radiation from an accretion disk surrounding the black hole. This work is an extension of the earlier work presented by Proga, where nonrotating flows were studied. Here, we consider effects of rotation, a position-dependent radiation temperature, density at large radii, and uniform X-ray background radiation. As in the non-rotating case, the rotating flow settles into a configuration with two components (1) an equatorial inflow and (2) a bipolar inflow/outflow with the outflow leaving the system along the pole. However, with rotation the flow does not always reach a steady state. In addition, rotation reduces the outflow collimation and the outward flux of mass and kinetic energy. Moreover rotation increases the outward flux of the thermal energy and can lead to fragmentation and time-variability of the outflow. We also show that a position-dependent radiation temperature can significantly change the flow solution. In particular, the inflow in the equatorial region can be replaced by a thermally driven outflow. Generally, as it have been discussed and shown in the past, we find that self-consistently determined preheating/cooling from the quasar radiation can significantly reduce the rate at which the central BH is fed with matter. However, our results emphasize also a little appreciated feature. Namely, quasar radiation drives a non-spherical, multi-temperature and very dynamic flow. These effects become dominant for luminosities in excess of 0.01 of the Eddington luminosity.Comment: accepted for publication in Ap

On observation of position in quantum theory

Newtonian and Scroedinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a ``concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space

La-Ag-Co perovskites for the catalytic flameless combustion of methane

Ag represents an interesting dopant for the highly active LaCoO3 perovskites used for the catalytic flameless combustion (CFC) of methane, due to its ability to adsorb and activate oxygen and to the possibility of incorporation into the framework as Ag+ or Ag2+, with formation of oxygen vacancies. In the present work we compared the catalytic activity and resistance to sulphur poisoning of a series of LaCoO3, x%Ag/LaCoO3, La1-xAgxCoO3 samples (nominal composition), the latter two notations indicating post-synthesis Ag loading or direct incorporation during the synthesis, respectively. The samples were prepared by flame pyrolysis (FP) and by the sot-gel (SG) method, leading to different particle size and possibly to different incorporation degree of the dopant, quantified by Rietveld refinement of XRD patterns. Higher activity was observed, in general, with fresh catalysts synthesised by FP. The SG samples demonstrated a slightly better resistance to sulphur poisoning when considering the conversion decrease between the fresh and the poisoned samples, due to lower surface exposure. However, interesting data have been obtained with some of the Ag-doped poisoned FP samples, performing even better than the fresh SG-prepared ones. Ag addition led to a complex change of activity and resistance to poisoning. The activity of FP-prepared samples doped with a small amount of Ag (e.g. 5 mol%) was indeed lower than that of the undoped LaCoO3. By contrast, a further increase of Ag concentration led to increasing catalytic activity, mainly when big extra framework Ag particles were present. By contrast, for SG samples a low Ag amount was beneficial for activity, due to an increased reducibility of Co3+

Changes in the relative copy numbers of chloroplast and mitochondrial DNA in the leaves of Vitis vinifera L. after high-temperature treatment in vitro

In the context of global warming, studying the consequences of increased temperature on agricultural crops becomes important for predicting the shortand long-term impacts on productivity. The effects of elevated temperature on grapevine plants lead to increased yield losses in viticulture. Micropropagated grapevine plants of the ‘Chardonnay’ variety were grown in vitro on MS medium and subjected to heat treatment at 45°C for 120 minutes. The control group of plants was not exposed to heat treatment. The levels of relative copy numbers of chloroplast and mitochondrial DNA were determined in leaf tissues of all plant groups using the RT-PCR method 30 days after heat treatment. In the group of plants subjected to heat treatment, statistically significant (p>0.05) reductions in the relative copy numbers of mitochondrial and chloroplast DNA were observed compared to the control group, with a decrease of over 30%. The copy number of chloroplast DNA exceeded that of mitochondrial DNA by more than 20 times in both the experimental and control groups. Heat treatment of micropropagated grapevine plants in vitro resulted in a closer correlation (r=+0.86) in the regulation of activity between these organelles, alongside the decrease in relative copy numbers of both mitochondrial and chloroplast DNA. This study demonstrates the promising use of relative copy numbers of chloroplast and mitochondrial DNA in plant leaves to investigate their potential physiological response to adverse environmental factors