Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

La cooperación triangular: los donantes tradicionales ante la cooperación Sur-Sur

La cooperación triangular constituye una modalidad novedosa con relevantes potencialidades para el sistema internacional de ayuda y para la cooperación española. Además de constituirse como un instrumento mediante el que impulsar la cooperación Sur-Sur, de creciente interés en la nueva arquitectura de la ayuda, le otorga a la cooperación española claras oportunidades para dar contenido práctico a la agenda con los países de renta media y, específicamente, con América Latina. Conocedora de estas implicaciones, España inició su andadura en esta modalidad de ayuda en 2005, con una actividad centrada en los países latinoamericanos. Sin embargo, no existen estudios que analicen estas intervenciones y sus implicaciones. Esto es lo que motivó un estudio promovido por la Fundación Carolina sobre dos experiencias concretas de cooperación triangular. El presente artículo presenta las principales enseñanzas extraídas de ese análisis sobre el terreno, al tiempo que recoge algunas orientaciones que puedan ser de utilidad para la práctica futura en este ámbito.

Simulación de procesos químicos (curso 2011-2012)

Apuntes en formato html que incluyen los siguientes temas de la parte de simulación en la asignatura «simulación y optimización de procesos químicos» TEMA 1. Introducción 1.1 Introducción. 1.2 Desarrollo histórico de la simulación de procesos. Relación entre simulación optimización y síntesis de procesos. 1.3 Tipos de simuladores: Modular secuencial. Modular simultáneo. Basada en ecuaciones. TEMA 2. Simulación Modular Secuencial 2.1 Descomposición de diagramas de flujo (flowsheeting) 2.2 Métodos basados en las matrices booleanas Localización de redes cíclicas máximas. Algoritmo de Sargent y Westerberg. Algoritmo de Tarjan. 2.3 Selección de las corrientes de corte: 2.3.1 Caso general planteamiento como un "set-covering problem" (algoritmo de Pho y Lapidus) 2.3.2 Número mínimo de corrientes de corte (algoritmo de Barkley y Motard) 2.3.3 Conjunto de corrientes de corte no redundante (Algoritmo de Upadhye y Grens) TEMA 3. Simulación Modular Simultánea 3.1 Efecto de las estrategias tipo cuasi Newton sobre la convergencia de los diagramas de flujo. TEMA 4. Simulación Basada en Ecuaciones 4.1 Introducción. Métodos de factorización de matrices dispersas. Métodos a priori y métodos locales. 4.2 Métodos locales: Criterio de Markowitz. 4.3 Métodos a priori: 4.3.1 Triangularización por bloques: a. Base de salida admisible (transversal completo). b. Aplicación de los algoritmos de Sargent y Tarjan a matrices dispersas. c. Reordenación. 4.3.2 Transformación en matriz triangular bordeada. 4.4 Fase numerica. Algoritmo RANKI 4.5 Comparación entre los diferentes sistemas de simulación. Ventajas e Inconvenientes. TEMA 5. Grados de libertad y variables de diseño de un diagrama de flujo 5.1 Teorema de Duhem y regla de las fases 5.2 Grados de libertad de un equipo 5.3 Grados de libertad de un diagrama de flujo 5.4 Elección de las variables de diseño.

A public key cryptosystem based on block upper triangular matrices

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while maintaining the key size. We also propose a key exchange protocol that guarantees that both parties share a secret element of this group and a digital signature scheme that provides data authenticity and integrity.

The Triangular Relationship between Fundamental Rights, Democracy and the Rule of Law in the EU: Towards an EU Copenhagen Mechanism. CEPS Paperbacks. November 2013

This study examines the protection of fundamental rights, democracy and rule of law in the European Union, and the challenges that arise in reflecting on ways to strengthen EU competences in these contested terrains. It provides a ‘state of play’ and critical account of EU-level policy and legal mechanisms assessing the relationship between rule of law, democracy and fundamental rights in the member states of the Union. The cross-cutting challenges affecting their uses, effective implementation and practical operability constitute a central point of the analysis. The study argues that the relationship between rule of law, democracy and fundamental rights is co-constitutive. Any future rule of law-related policy discussion in the EU should start from an understanding of the triangular relationship between these dimensions from the perspective of ‘democratic rule of law with fundamental rights’, i.e. the legally based rule of a democratic state that delivers fundamental rights. The three criteria are inherently and indivisibly interconnected, and interdependent on each of the others, and they cannot be separated without inflicting profound damage to the whole and changing its essential shape and configuration.

Triangular Geopolitics in Europe’s Eastern Neighbourhood. CEPS Commentary, 2 December 2014

Over the last few months, Russia has employed a number of economic and security measures to derail the Deep and Comprehensive Free Trade Agreement (DCFTA) between the EU and Ukraine. Russia’s opposition to the Agreement was based on the argument that it would damage its economy and weaken its trade ties with Ukraine. Russia’s actions ultimately led to war in Ukraine, but did not succeed in reversing Ukraine’s EU integration policies; instead there are now trilateral negotiations between the EU, Ukraine and Russia on mere technical trade aspects of the DCFTA. The Kremlin is using similar rhetoric and, to some extent, similar coercive measures against the DCFTAs with Moldova and Georgia. But the small scale of Moldovan and Georgian trade with Russia is not a legitimate reason for the EU to replicate the Ukraine ‘trialogue’ on the DCFTAs in these countries. Instead, Moldova’s heavy dependence on Russia’s energy and the former’s transit role for the EU offers a greater possibility to set up trilateral negotiations, similar to the recently finalised gas trialogue between the EU, Ukraine and Russia.

Solving triangular systems on a parallel computer /

Includes bibliographical references.

The triangular society. Leaves from the life of a Portland family.

Mode of access: Internet.

Linearized theory of conical supersonic flow with application to triangular wings /

Loose-leaf.

The history of Crowland Abbey, digested from the materials collected by Mr. Gough, and published ... 1783 and 1797; including an abstract of the observations of Mr. Essex, respecting the ancient and present state of the abbey, and the origin and use of the triangular bridge ...

"Appendix: Concerning the history of the building of our more ancient abbey churches, and the rise and progress of the pointed or English architecture; digested from the essays published by J. Taylor, on the architecture of the middle ages, by ... T. Warton, J. Bentham, and J. Milner, and Captain Grose ..." (p. [143]-182) has special half-title.

Proceedings of the M [three dots in triangular formation̈ W [three dots in triangular formation̈ Grand lodge of Free and accepted masons of the state of California at its annual communication

Mode of access: Internet.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Growth mechanism of truncated triangular GaAs nanowires

During the growth of GaAs nanowires on the {111}B GaAs substrate, truncated triangular GaAs nanowires were commonly observed in the bottom region of nanowires. Through detailed structural analysis by electron microscopy, we have determined the growth mechanism of truncated triangular GaAs nanowires.