Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

AbstractGiven an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined byΔ(T)=|T|1/2U|T|1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e. Δ0(T)=T and Δn(T)=Δ(Δn−1(T)), n∈N. We prove that the sequence {Δn(T)}n∈N converges for every r×rdiagonalizable matrix T. We show that the limit Δ∞(⋅) is a map of class C∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r×r matrices with r different eigenvalues

Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

Given an r × r complex matrix T ,ifT = U|T | is the polar decomposition of T , then, the Aluthge transform is defined by Δ(T)=|T |1/2U|T |1/2. Let Δn(T ) denote the n-times iterated Aluthge transform of T ,i.e.Δ0 (T ) = T and Δn(T ) = Δ(Δn-1(T )), n ∈ N. We prove that the sequence {Δn(T )}n∈N converges for every r × r diagonalizable matrix T .We show that the limit Δ∞(·) is a map of class C ∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.Facultad de Ciencias Exacta

The iterated Aluthge transforms of a matrix converge

Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|1/2U|T|1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e., Δ0(T)=T and Δn(T)=Δ(Δn-1(T)), nεN. We prove that the sequence {Δn(T)}nεN converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.Facultad de Ciencias Exacta

VICISITUDES DE LA REFORMA EDUCATIVA DE 1870 EN EL ESTADO DE CUNDINAMARCA: EL PAPEL DE DÁMASO ZAPATA

Hace cien años murió Dámaso Zapata, y su sentencia aún resuena con notableactualidad: “La generalidad de los políticos no ha comprendido lo que es laescuela, ni de cuanto es ella capaz”, dijo luego de su retiro de la Dirección deInstrucción Pública del Estado de Cundinamarca, después de ocho años deservicio a la causa instruccionista

A novel effect. Changes in the electrochemical response of polycrystalline platinum promoted by very fast potential perturbations

It is well established that the voltammogram of polycrystalline platinum in acid electrolyte in the potential range corresponding to the stability of bulk water depends on the electrode history including the type of perturbation applied to the electrode and on the electrolyte composition.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

A novel effect. Changes in the electrochemical response of polycrystalline platinum promoted by very fast potential perturbations

It is well established that the voltammogram of polycrystalline platinum in acid electrolyte in the potential range corresponding to the stability of bulk water depends on the electrode history including the type of perturbation applied to the electrode and on the electrolyte composition.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

Two-level interacting boson models beyond the mean field

The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.Comment: 14 pages, 13 figure

Resistencia a la fatiga térmica de la fundición vermicular

La Fundición Vermicular (FV) se caracteriza por su elevada resistencia a la fatiga térmica. Esta propiedad permite su uso para confeccionar piezas sometidas a condiciones de trabajo de ciclado térmico. En la microestructura de la FV es común la presencia de grafito nodular, lo que puede afectar las propiedades físicas de la fundición. En este contexto, la resistencia a la fatiga térmica de la FV con variados porcentajes de nódulos fue evaluada mediante ensayos de reciclado térmico entre 70 y 600ºC. Los resultados indicaron que, para una cantidad aceptable de 20% de nódulos, el número de ciclos a la primera fisura fue de 350, mientras que para porcentajes de 60 y 80% de nódulos el número de ciclos disminuyó considerablemente a 95 y 80, respectivamente.Vermicular cast iron (VCI) is characterized by its high resistance to thermal fatigue. This property allows manufacture components subjected to thermal shocks. In the microstructure of VCI is common the presence of nodular graphite, which can affects the physical properties of the material. In this context, the thermal fatigue resistance of the VCI with varying percentages of nodules was evaluated by thermal cycling tests between 70 and 600°C. The results indicated that for an acceptable amount of 20% graphite nodules, the number of cycles at the first crack was 350, while for percentages of 60 and 80% of nodules the number of cycles considerably decreased to 95 and 80, respectively

Analysis of electronic structure and X-ray absorption and emission spectra in MgO within the FP-LAPW method

In this work we calculated MgO ab initio X-ray Absorption and Emission spectra using the Full Potential Linearized Augmented Plane Wave method within the Density Functional Theory formalism. The X-ray Absorption and Emission spectra for the K and L2;3 edges of Mg and O atoms were calculated including a core hole in order to study the electronic structure of valence and conduction bands of the system. Both kinds of spectra were compared with experimental data obtaining a very good agreement and the improvement in the spectra due to the use of Tran Blaha modified Becke-Johnson (TB-mBJ)potential is manifested. This potential describes better the insulator properties, produces a band gap that is in good agreement with the experimental value and improves the intensities and the structure of the spectra. Was interesting to find the presenceof Mg d states below the Fermi energy in the equilibrium volume of MgO. The XANES experiments were better reproduced by introducing the full core hole in the calculationsusing TB-mBJ potential while for XES the best agreement was obtained without core hole. The Bader?s topological method was employed to analyse the ionic behaviour. Using the electronic charges obtained with the Bader?s Method and the equilibrium lattice parameter, we obtained the value of the Lattice Energy and we compared it with the value obtained by the Born-Haber cycle showing a good agreement. The charge density for MgO was plotted, and a maximally localized Wannier function for O is shown.Fil: Grad, Gabriela Beatriz. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Grupo de Espectroscopia Atomica y Nuclear; ArgentinaFil: González, Enrique. R.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Grupo de Espectroscopia Atomica y Nuclear; ArgentinaFil: Torres Díaz, Jorge. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Grupo de Espectroscopia Atomica y Nuclear; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Bonzi, Edgardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Grupo de Espectroscopia Atomica y Nuclear; Argentin