The Dynamics of Two Massive Planets on Inclined Orbits

The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems.Comment: 25 pages, 15 figures, 2 tables, accepted for publication in Icaru

Characterizations of Δ-Volterra lattice: a symmetric orthogonal polynomials interpretation

In this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x2)1−tμ(x)(1+x2)1−tμ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry

Los tipos de abogados según el test MBTI

Este artículo se basa en la transcripción traducida del Artículo de Larry Richard y losdocumentos complementarios estudiados por el suscrito. Lo hemos hecho con el fin de efectuar los análisis pertinentes de las posibles consecuencias, que se derivan de los resultados del Test Myers-Briggs Type Indicator, o MBTI, cuando se aplica dicho Test a los Abogados.Asimismo como influyen en las Organizaciones forenses los principios, teorías y técnicas que estudia nuestra materia opcional "Gestión Empresarial".</p

Los tipos de abogados según el test MBTI

<p>Este artículo se basa en la transcripción traducida del Artículo de Larry Richard y los<br />documentos complementarios estudiados por el suscrito. Lo hemos hecho con el fin de efectuar los análisis pertinentes de las posibles consecuencias, que se derivan de los resultados del Test Myers-Briggs Type Indicator, o MBTI, cuando se aplica dicho Test a los Abogados.<br />Asimismo como influyen en las Organizaciones forenses los principios, teorías y técnicas que estudia nuestra materia opcional "Gestión Empresarial".</p

Styles of international mediation in peace processes between states and terrorist organizations

As a conflict management strategy, mediation has offered a way to abate or resolve conflicts, and it is a solid alternative to escalating hostilities. Most academic works analyze mediation by studying the mediators' roles and behavior, and such study is facilitated by the use of categories or typologies. This thesis seeks to identify an additional method known as the styles of mediation. Because international mediation has been used in terrorism conflicts, this thesis explores the styles of international mediation that have been employed in peace processes between states and terrorist organizations, and uses the Israeli-Palestinian, Northern Ireland, and Sri Lankan peace processes as case studies. Two specific styles of mediation are suggested: personalistic mediation and institutionalized mediation, both strongly linked to the frameworks under which the mediation is exercised. Personalistic mediation is a framework of mediation that develops and establishes itself as the mediation unfolds, largely due to the mediators' own work and determination. Institutionalized mediation takes place when an institution created in a peace process adopts a mediation strategy and exercises it under its institutional umbrella. The proposed styles may not only help analysts define frameworks in future mediations, but also compare mediation, and in some cases even predict--to an extent--patterns and results of mediation.http://archive.org/details/stylesofinternat1094549432Civilian, UruguayApproved for public release; distribution is unlimited