Entanglement Thresholds for Random Induced States

For a random quantum state on obtained by partial tracing a random pure state on , we consider the question whether it is typically separable or typically entangled. For this problem, we show the existence of a sharp threshold of order roughly . More precisely, for any and for d large enough, such a random state is entangled with very large probability when , and separable with very large probability when . One consequence of this result is as follows: for a system of N identical particles in a random pure state, there is a threshold such that two subsystems of k particles each typically share entanglement if k > k₀, and typically do not share entanglement if k < k₀. Our methods also work for multipartite systems and for “unbalanced” systems such as , . The arguments rely on random matrices, classical convexity, high‐dimensional probability, and geometry of Banach spaces; some of the auxiliary results may be of reference value. © 2013 Wiley Periodicals, Inc.     

The shark teeth is a topological IFS-attractor

We show that the space called the shark teeth is a topological IFS-attractor, that is, for every open cover of $X = \bigcup\nolimits_{i = 1}^n {f_i (X)}$ , its image under every suitable large composition from the family of continuous functions {f ₁, ..., f _n } lies in some set from the cover. In particular, there exists a space that is not homeomorphic to any IFS-attractor but is a topological IFS-attractor.     

An adeno-associated viral vector transduces the rat hypothalamus and amygdala more efficient than a lentiviral vector

Background  

This study compared the transduction efficiencies of an adeno-associated viral (AAV) vector, which was pseudotyped with an AAV1 capsid and encoded the green fluorescent protein (GFP), with a lentiviral (LV) vector, which was pseudotyped with a VSV-G envelop and encoded the discosoma red fluorescent protein (dsRed), to investigate which viral vector transduced the lateral hypothalamus or the amygdala more efficiently. The LV-dsRed and AAV1-GFP vector were mixed and injected into the lateral hypothalamus or into the amygdala of adult rats. The titers that were injected were 1 × 10⁸ or 1 × 10⁹ genomic copies of AAV1-GFP and 1 × 10⁵ transducing units of LV-dsRed.     

A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps

We give a lower estimate of the Hausdorff dimension for attractors which can be obtained by an overlapping construction.     

Dimension of measures invariant with respect to the Wa?ewska partial differential equation

We study asymptotic properties of a nonlinear first-order partial differential equation which describes the reproduction of blood cells. This equation under conditions proposed by Wa?ewska generates a semigroup of transformations with highly chaotic behaviour of trajectories. We show that this semigroup has invariant measures with arbitrary large dimension.     

The Knaster problem and the geometry of high-dimensional cubes

We study questions of the following type: Given positive semi-definite matrix $\text{G}$, does there exist a sequence of vectors in $\text{R}{}^{\mathrm{n}}$ whose Grammian equals to $\text{G}$ and which has some specified additional properties (typically related to the sup norm)? In particular, we show that the answer to the 1947 Knaster problem about real functions on spheres is negative for sufficiently large dimensions. To cite this article: B.S. Kashin, S.J. Szarek, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Carbon dioxide conversion to valuable chemical products over composite catalytic systems

This paper reports an experimental study on catalytic conversion of carbon dioxide to methanol,ethanol and acetic acid.Catalysts having different catalytic functions were synthesized and combined in different ways to enhance the selectivity to desired products.The combined catalyst system possessed the following functions:methanol synthesis,Fischer-Tropsch synthesis,water-gas-shift and hydrogenation.Results showed that the methods of integrating these catalytic functions played an important role in achieving the desired product selectivity.We speculate that if methanol synthesis sites were located adjacent to the C-C chain growth sites,the formation rate of C₂ oxygenates would be enhanced.The advantage of using a high temperature methanol catalyst PdZnAl in the combined catalyst system was demonstrated.In the presence of PdZnAl catalyst,the combined catalyst system was stable at 380°C.It was observed that,at high temperature,kinetics favored oxygenate formation.The results implied that the process can be intensified by operating at high temperature using Pd-based methanol synthesis catalyst.Steam reforming of the byproduct organics was demonstrated as a means to provide supplemental hydrogen.Preliminary process design,simulation,and economic analysis of the proposed CO₂ conversion process were carried out.Economic analysis indicates how ethanol production cost was affected by the price of CO₂ and hydrogen.     

Search for disoriented chiral condensate in 158<Emphasis Type="Italic">A</Emphasis> GeV Pb+Pb collisions in WA98 experiment

The current status of the search for localized domains of disoriented chiral condensates (DCC) in Pb+Pb collisions at 158A GeV/c are presented. A new method based on the discrete wavelet transformation (DWT) technique along with an analysis of correlation between charged and neutral particles has been used for the search of localized DCC domains. We show that both the methods indicate the presence of non-statistical fluctuations in data.     

A laser extraction/combustion technique for in situ delta(13)C analysis of organic and inorganic materials

A CO(2) laser extraction system is described for in situ delta(13)C analysis of organic and inorganic materials. Carbonaceous compounds volatilized by the laser are quantitatively converted to CO(2) gas by a combustion furnace mounted after the sample chamber. Gases produced by the laser and combustion processes are swept by helium carrier gas and separated by a packed gas chromatography column prior to their introduction to an isotope ratio monitoring mass spectrometer. A sample of lentil bean was analyzed at a spatial resolution of 200 μm and yielded delta(13)C values with precision of +/- 0.3 per thousand. The accuracy of delta(13)C measurements was better than +/- 0.5 per thousand from NBS 22 (mineral oil), USGS 24 (graphite), and IAEA CO-1 (calcium carbonate). Copyright 1999 John Wiley & Sons, Ltd.