Green functions of the spectral ball and symmetrized polydisk

The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic (non-derogatory) matrix. When the pole is derogatory, the inequality is always strict, and the difference between the two functions depends on the order of nilpotence of the strictly upper triangular blocks that appear in the Jordan decomposition of the pole. In particular, the Green function of the spectral ball is not symmetric in its arguments. Additionally, some estimates are given for invariant functions in the symmetrized polydisc, e.g. (infinitesimal versions of) the Carath\'eodory distance and the Green function, that show that they are distinct in dimension greater or equal to $3$.Comment: 12 page

Shareholder Litigation in Mergers and Acquisitions

Using hand-collected data, we examine the targeting of shareholder class action lawsuits in merger & acquisition (M & A) transactions, and the associations of these lawsuits with offer completion rates and takeover premia. We find that M & A offers subject to shareholder lawsuits are completed at a significantly lower rate than offers not subject to litigation, after controlling for selection bias, different judicial standards, major offer characteristics, M & A financial and legal advisor reputations as well as industry and year fixed effects. M & A offers subject to shareholder lawsuits have significantly higher takeover premia in completed deals, after controlling for the same factors. Economically, the expected rise in takeover premia more than offsets the fall in the probability of deal completion, resulting in a positive expected gain to target shareholders. However, in general, target stock price reactions to bid announcements do not appear to fully anticipate the positive expected gain from potential litigation. We find that during a merger wave characterized by friendly single-bidder offers, shareholder litigation substitutes for the presence of a rival bidder by policing low-ball bids and forcing offer price improvement by the bidder

'Hole-digging' in ensembles of tunneling Molecular Magnets

The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a 'hole' to appear in the distribution of internal fields in the system. The form of this hole, and its time evolution, are studied using Monte Carlo simulations. It is shown that the line-shape of the tunneling hole in a weakly polarised sample must have a Lorentzian lineshape- the short-time half-width $\xi_o$ in all experiments done so far should be $\sim E_0$, the half-width of the nuclear spin multiplet. After a time $\tau_o$, the single molecule tunneling relaxation time, the hole width begins to increase rapidly. In initially polarised samples the disintegration of resonant tunneling surfaces is found to be very fast.Comment: 4 pages, 5 figure

Defect Formation in EBM Parts Built in Horizontal Orientation

EBM built parts in a horizontal orientation, particularly with bottom curved surfaces, are prone to variations in dimensional accuracy and defect formation. These defects likely occur due to the nature of the supports utilized and the build strategy. To understand the effect of support structures and scan direction on these defects, a series of cylindrical parts were built using different diameters, support structures and scan strategies. The as-built samples were mechanically tested and sample cross sections were analyzed. Pore formation and balling effects were observed in the lower section of some samples. The study looks at the effects of supports, geometry and scan strategy on the minimization of these defects and improving the dimensional accuracy of horizontally built samples.Mechanical Engineerin

Environment News Broadcast in Malaysia: An Analysis of Prime -Time News Coverage In Local Television Channels.

This paper examines the representation of environmental news and analyses how the environment is being covered in local Malaysian television channels in their prime-time news broadcast

Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1)xU(1) transition,the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a "numerical flowgram" method for high precision studies of the runaway effect, weakly I-order transitions, and polycritical points. We prove that the easy-plane DCP action is the field theory of a weakly I-order phase transition between the valence bond solid and the easy-plane antiferromagnet (or superfluid, in particle language) for any value of the weak coupling strength. Our analysis also solves the long standing problem of what is the ultimate fate of the runaway flow to strong coupling in the theory of scalar electrodynamics in three dimensions with U(1)xU(1) symmetry of quartic interactionsComment: 25 pages, 18 figures, Mottness and quantum criticality conference (to appear in Annals of physics

Coherence Window in the dynamics of Quantum Nanomagnets

Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow field region in which both phonon and nuclear spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the $Fe$-8 nanomolecule, for $Ni$ particles, and for $Ho$ ions in $LiHo_xY_{1-z}F_4$. The reduction in the decoherence, compared to low field rates, can exceed 6 orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.Comment: 5 LaTeX pages, 3 figure

Effect of local Coulomb interactions on the electronic structure and exchange interactions in Mn12 magnetic molecules

We have studied the effect of local Coulomb interactions on the electronic structure of the molecular magnet Mn12-acetate within the LDA+U approach. The account of the on-site repulsion results in a finite energy gap and an integer value of the molecule's magnetic moment, both quantities being in a good agreement with the experimental results. The resulting magnetic moments and charge states of non-equivalent manganese ions agree very well with experiments. The calculated values of the intramolecular exchange parameters depend on the molecule's spin configuration, differing by 25-30% between the ferrimagnetic ground state and the completely ferromagnetic configurations. The values of the ground-state exchange coupling parameters are in reasonable agreement with the recent data on the magnetization jumps in megagauss magnetic fields. Simple estimates show that the obtained exchange parameters can be applied, at least qualitatively, to the description of the spin excitations in Mn12-acetate.Comment: RevTeX, LaTeX2e, 4 EPS figure

Dislocation-induced spin tunneling in Mn-12 acetate

Comprehensive theory of quantum spin relaxation in Mn-12 acetate crystals is developed, that takes into account imperfections of the crystal structure and is based upon the generalization of the Landau-Zener effect for incoherent tunneling from excited energy levels. It is shown that linear dislocations at plausible concentrations provide the transverse anisotropy which is the main source of tunneling in Mn-12. Local rotations of the easy axis due to dislocations result in a transverse magnetic field generated by the field applied along the c-axis of the crystal, which explains the presence of odd tunneling resonances. Long-range deformations due to dislocations produce a broad distribution of tunnel splittings. The theory predicts that at subkelvin temperatures the relaxation curves for different tunneling resonances can be scaled onto a single master curve. The magnetic relaxation in the thermally activated regime follows the stretched-exponential law with the exponent depending on the field, temperature, and concentration of defects.Comment: 17 pages, 14 figures, 1 table, submitted to PR

Feedback Effect on Landau-Zener-Stueckelberg Transitions in Magnetic Systems

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intra-molecular couplings.Comment: 4 pages, 3 Postscript figures; paper reorganized, conclusions modifie