Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Closed formula for the relative entropy of entanglement in all dimensions

The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed formula for all the entangled state for which this state is a CSS. Quite amazing, our formula holds for multipartite states in all dimensions. In addition we show that if an entangled state is full rank, then its CSS is unique. For the bipartite case of two qubits our formula reduce to the one given in Phys. Rev. A 78, 032310 (2008).Comment: 8 pages, 1 figure, significantly revised; theorem 1 is now providing necessary and sufficient conditions to determine if a state is CS

Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered spectral projector, and some geometric hypothesis on the local behaviour of the eigenvalues at the crossings

Design and control of spin gates in two quantum dots arrays

We study the spin-spin interaction between quantum dots coupled through a two dimensional electron gas with spin-orbit interaction. We show that the interplay between transverse electron focusing and spin-orbit coupling allows to dynamically change the symmetry of the effective spin-spin Hamiltonian. That is, the interaction can be changed from Ising-like to Heisenberg-like and vice versa. The sign and magnitude of the coupling constant can also be tuned.Comment: 4 pages, 3 figure

First Principles Study of the Electronic and Vibrational Properties of LiNbO2

In the layered transition metal oxide LiNbO$_2$ the Nb$^{3+}$ ($4d^2$) ion is trigonal-prismatically coordinated with O ions, with the resulting crystal field leading to a single band system for low energy properties. A tight-binding representation shows that intraplanar second neighbor hopping $t_2 = 100$ meV dominates the first neighbor interaction ($t_1 = 64$ meV). The first and third neighbor couplings are strongly modified by oxygen displacements of the symmetric Raman-active vibrational mode, and electron-phonon coupling to this motion may provide the coupling mechanism for superconductivity in Li-deficient samples (where $T_c = 5$ K). We calculate all zone-center phonon modes, identify infrared (IR) and Raman active modes, and report LO-TO splitting of the IR modes. The Born effective charges for the metal ions are found to have considerable anisotropy reflecting the degree to which the ions participate in interlayer coupling and covalent bonding. Insight into the microscopic origin of the valence band density, composed of Nb $d_{z^2}$ states with some mixing of O $2p$ states, is obtained from examining Wannier functions for these bands.Comment: 12 pages, 7 figures; Updated with reviewer comments; Updated reference

Avaliação de cultivares de mandioca em Altamira - Pará.

bitstream/item/64570/1/Altamira-PA8.pd

Curious Variables Experiment (CURVE). CCD photometry of active dwarf nova DI UMa

We report an analysis of photometric behaviour of DI UMa, an extremely active dwarf nova. The observational campaign (completed in 2007) covers five superoutbursts and four normal outbursts. We examined principal parameters of the system to understand peculiarities of DI UMa, and other active cataclysmic variables. Based on precise photometric measurements, temporal light curve behaviour, O-C analysis, and power spectrum analysis, we investigated physical parameters of the system. We found that the period of the supercycle now equals 31.45 +/-0.3 days. Observations during superoutbursts infer that the period of superhumps equals P_sh = 0.055318(11) days (79.66 +/- 0.02 min). During quiescence, the light curve reveals a modulation of period P_orb = 0.054579(6) days (78.59 +/- 0.01 min), which we interpret as the orbital period of the binary system. The values obtained allowed us to determine a fractional period excess of 1.35% +/- 0.02%, which is surprisingly small compared to the usual value for dwarf novae (2%-5%). A detailed O-C analysis was performed for two superoutbursts with the most comprehensive coverage. In both cases, we detected an increase in the superhump period with a mean rate of dot_P/P_sh = 4.4(1.0)*10^{-5}. Based on these measurements, we confirm that DI UMa is probably a period bouncer, an old system that reached its period minimum a long time ago, has a secondary that became a degenerate brown dwarf, the entire system evolving now toward longer periods. DI UMa is an extremely interesting object because we know only one more active ER UMa star with similar characteristics (IX Dra).Comment: Accepted for publication in Astronomy & Astrophysic

Mandioca: resultados preliminares de pesquisa na Transamazônica - PA.

bitstream/item/66788/1/Altamira-Doc3.pd