Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\Phi$ and $\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\mathfrak{u}$ at the canonical form on $\Omega$. We also find the dimension of $\Omega$ in terms of the Weyl group of $\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group $U$ for the case of finite field $k$.Comment: 11 page

In situ visualization of Ni-Nb bulk metallic glasses phase transition

We report the results of the Ni-based bulk metallic glass structural evolution and crystallization behavior in situ investigation. The X-ray diffraction (XRD), transmission electron microscopy (TEM), nano-beam diffraction (NBD), differential scanning calorimetry (DSC), radial distribution function (RDF) and scanning probe microscopy/spectroscopy (STM/STS) techniques were applied to analyze the structure and electronic properties of Ni63.5Nb36.5 glasses before and after crystallization. It was proved that partial surface crystallization of Ni63.5Nb36.5 can occur at the temperature lower than for the full sample crystallization. According to our STM measurements the primary crystallization is originally starting with the Ni3Nb phase formation. It was shown that surface crystallization drastically differs from the bulk crystallization due to the possible surface reconstruction. The mechanism of Ni63.5Nb36.5 glass alloy 2D-crystallization was suggested, which corresponds to the local metastable (3x3)-Ni(111) surface phase formation. The possibility of different surface nano-structures development by the annealing of the originally glassy alloy in ultra high vacuum at the temperature lower, than the crystallization temperature was shown. The increase of mean square surface roughness parameter Rq while moving from glassy to fully crystallized state can be caused by concurrent growth of Ni3Nb and Ni6Nb7 bulk phases. The simple empirical model for the estimation of Ni63.5Nb36.5 cluster size was suggested, and the obtained values (7.64 A, 8.08 A) are in good agreement with STM measurements data (8 A-10 A)

Coulomb singularity effects in tunnelling spectroscopy of individual impurities

Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristicsComment: 7 pages, 2 figure

Energy dependence of Ti/Fe ratio in the Galactic cosmic rays measured by the ATIC-2 experiment

Titanium is a rare, secondary nucleus among Galactic cosmic rays. Using the Silicon matrix in the ATIC experiment, Titanium has been separated. The energy dependence of the Ti to Fe flux ratio in the energy region from 5 GeV per nucleon to about 500 GeV per nucleon is presented.Comment: 8 pages, 4 figures, accepted for publication in Astronomy Letter

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Nucleosynthesis in neutrino heated matter: The vp-process and the r-process

This manuscript reviews recent progress in our understanding of the nucleosynthesis of medium and heavy elements in supernovae. Recent hydrodynamical models of core-collapse supernovae show that a large amount of proton rich matter is ejected under strong neutrino fluxes. This matter constitutes the site of the vp-process where antineutrino absorption reactions catalyze the nucleosynthesis of nuclei with A > 64. Supernovae are also associated with the r-process responsible for the synthesis of the heaviest elements in nature. Fission during the r-process can play a major role in determining the final abundance patter and in explaining the almost universal features seen in metal-poor r-process-rich stars.Comment: 10 pages, 3 figures, invited talk at NIC-IX, International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX, CERN, Geneva, Switzerland, 25-30 June, 200

Possible structure in the cosmic ray electron spectrum measured by the ATIC-2 and ATIC-4 experiments

A strong excess in a form of a wide peak in the energy range of 300-800 GeV was discovered in the first measurements of the electron spectrum in the energy range from 20 GeV to 3 TeV by the balloon-borne experiment ATIC (J. Chang et al. Nature, 2008). The experimental data processing and analysis of the electron spectrum with different criteria for selection of electrons, completely independent of the results reported in (J. Chang et al. Nature, 2008) is employed in the present paper. The new independent analysis generally confirms the results of (J. Chang et al. Nature, 2008), but shows that the spectrum in the region of the excess is represented by a number of narrow peaks. The measured spectrum is compared to the spectrum of (J. Chang et al. Nature, 2008) and to the spectrum of the Fermi/LAT experiment.Comment: LaTeX2e, 10 pages, 4 figures, a paper for ECRS 2010 (Turku, Finland); http://www.astrophys-space-sci-trans.net/7/119/2011

Ensembles of probability estimation trees for customer churn prediction

Customer churn prediction is one of the most, important elements tents of a company's Customer Relationship Management, (CRM) strategy In tins study, two strategies are investigated to increase the lift. performance of ensemble classification models, i.e (1) using probability estimation trees (PETs) instead of standard decision trees as base classifiers; and (n) implementing alternative fusion rules based on lift weights lot the combination of ensemble member's outputs Experiments ale conducted lot font popular ensemble strategics on five real-life chin n data sets In general, the results demonstrate how lift performance can be substantially improved by using alternative base classifiers and fusion tides However: the effect vanes lot the (Idol cut ensemble strategies lit particular, the results indicate an increase of lift performance of (1) Bagging by implementing C4 4 base classifiets. (n) the Random Subspace Method (RSM) by using lift-weighted fusion rules, and (in) AdaBoost, by implementing both

Electromagnetic counterparts of compact object mergers powered by the radioactive decay of r-process nuclei

The most promising astrophysical sources of kHz gravitational waves (GWs) are the inspiral and merger of binary neutron star(NS)/black hole systems. Maximizing the scientific return of a GW detection will require identifying a coincident electromagnetic (EM) counterpart. One of the most likely sources of isotropic EM emission from compact object mergers is a supernova-like transient powered by the radioactive decay of heavy elements synthesized in ejecta from the merger. We present the first calculations of the optical transients from compact object mergers that self-consistently determine the radioactive heating by means of a nuclear reaction network; using this heating rate, we model the light curve with a one-dimensional Monte Carlo radiation transfer calculation. For an ejecta mass ∼10−2 M⊙ (10−3 M⊙) the resulting light-curve peaks on a time-scale ∼1 d at a V-band luminosity νLν∼ 3 × 1041 (1041) erg s−1[MV=−15(−14)]; this corresponds to an effective ‘f' parameter ∼3 × 10−6 in the Li-Paczynski toy model. We argue that these results are relatively insensitive to uncertainties in the relevant nuclear physics and to the precise early-time dynamics and ejecta composition. Since NS merger transients peak at a luminosity that is a factor of ∼103 higher than a typical nova, we propose naming these events ‘kilo-novae'. Because of the rapid evolution and low luminosity of NS merger transients, EM counterpart searches triggered by GW detections will require close collaboration between the GW and astronomical communities. NS merger transients may also be detectable following a short-duration gamma-ray burst or ‘blindly' with present or upcoming optical transient surveys. Because the emission produced by NS merger ejecta is powered by the formation of rare r-process elements, current optical transient surveys can directly constrain the unknown origin of the heaviest elements in the Univers

Zeno and anti-Zeno effects for photon polarization dephasing

We discuss a simple, experimentally feasible scheme, which elucidates the principles of controlling ("engineering") the reservoir spectrum and the spectral broadening incurred by repeated measurements. This control can yield either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of the quasi-exponential decay of the observed state by means of frequent measurements. In the discussed scheme, a photon is bouncing back and forth between two perfect mirrors, each time passing a polarization rotator. The horizontal and vertical polarizations can be viewed as analogs of an excited and a ground state of a two level system (TLS). A polarization beam splitter and an absorber for the vertically polarized photon are inserted between the mirrors, and effect measurements of the polarization. The polarization angle acquired in the electrooptic polarization rotator can fluctuate randomly, e.g., via noisy modulation. In the absence of an absorber the polarization randomization corresponds to TLS decay into an infinite-temperature reservoir. The non-Markovian nature of the decay stems from the many round-trips required for the randomization. We consider the influence of the polarization measurements by the absorber on this non-Markovian decay, and develop a theory of the Zeno and anti-Zeno effects in this system.Comment: 11 pages, 4 figure