On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces

En este trabajo se estudia la perturbación de la inversa generalizada grupo en el ámbito de los operadores lineales y acotados sobre un espacio de Banach complejo. Se establecen, en primer lugar, caracterizaciones de los {1,2}-inversos generalizados de operadores perturbados que verifican una condición de no singularidad. Posteriormente se caracteriza la clase de operadores perturbados para los cuales existe el operador inverso grupo y verifican ciertas condiciones geométricas. Se prueba que los operadores perturbados tienen una determinada estructura de matriz 2 por 2 de operadores y se desarrolla una representación para la resolvente de tales matrices de operadores a partir de la cual se obtiene una representación para el operador inverso grupo. Este resultado extiende al contexto de operadores un resultado para matrices por bloques incluido en el libro [Campbell y Meyer, Generalized inverses of Linear Transformations, Dover, 1979] y nos proporciona una herramienta para el análisis de la perturbación. Otras aportaciones son la obtención de xpresiones explícitas para el operador inverso grupo el operador perturbado y su proyección espectral asociada al 0 y la obtención de cotas superiores para el error relativo de la inversa de Drazin y de los proyectores espectrales y un resultado de continuidad de la inversa grupo para operadores en espacios de Banach. Las aportaciones de este trabajo extienden o complementan resultados obtenidos previamente por autores sobre el mismo tema (Djordjevic, Koliha, Rakoèevic) Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I + A(D)(B - A) is invertible and R(B) boolean AND N(A(r)) = {0}. We show that they can be written with respect to the decomposition X = R(A(r))circle plus N(A(r)) as a matrix operator, B = (B-1 B-12 B-21 B21B1-1B12), where B-1 and B-1(2) + B12B21 are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of parallel to B-# - A(D)parallel to and parallel to BB# - A(D)A parallel to. We obtain a result on the continuity of the group inverse for operators on Banach space

Magnetic Phase Diagram of GdNi2B2C: Two-ion Magnetoelasticity and Anisotropic Exchange Couplings

Extensive magnetization and magnetostriction measurements were carried out on a single crystal of GdNi2B2C along the main tetragonal axes. Within the paramagnetic phase, the magnetic and strain susceptibilities revealed a weak anisotropy in the exchange couplings and two-ion tetragonal-preserving alpha-strain modes. Within the ordered phase, magnetization and magnetostriction revealed a relatively strong orthorhombic distortion mode and rich field-temperature phase diagrams. For H//(100) phase diagram, three field-induced transformations were observed, namely, at: Hd(T), related to the domain alignment; Hr(T), associated with reorientation of the moment towards the c-axis; and Hs(T), defining the saturation process wherein the exchange field is completely counterbalanced. On the other hand, For H//(001) phase diagram, only two field-induced transformations were observed, namely at: Hr(T) and Hs(T). For both phase diagrams, Hs(T) follows the relation Hs[1-(T/Tn)^2]^(1/2)kOe with Hs(T-->0)=128.5(5) kOe and Tn(H=0)=19.5 K. In contrast, the thermal evolution of Hr(T) along the c-axis (much simpler than along the a-axis) follows the relation Hr[1-T/Tr]^(1/3) kOe where Hr(T-->0)=33.5(5) kOe and Tr(H=0)=13.5 K. It is emphasized that the magnetoelastic interaction and the anisotropic exchange coupling are important perturbations and therefore should be explicitly considered if a complete analysis of the magnetic properties of the borocarbides is desired

Can the Consumption–Wealth Ratio Predict Housing Returns? Evidence from OECD Countries

This is the peer reviewed version of the following article: CAPORALE, G.M., SOUSA, R.M. and WOHAR, M.E., 2016. Can the consumption-wealth ratio predict housing returns? Evidence from OECD countries. Real Estate Economics, In Press. which has been published in final form at http://dx.doi.org/10.1111/1540-6229.12135. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.©2016 American Real Estate and Urban Economics Association We use a representative consumer model to analyze the relation between the transitory deviations of consumption from its common trend with aggregate wealth and labor income, cay, and the housing risk premium. The evidence based on data for 15 OECD countries shows that, if financial and housing assets are seen as complements, investors will temporarily allow consumption to rise when they expect a rise in future housing returns. By contrast, if housing assets are treated as substitutes for financial assets, consumption will be reduced

Infrastructure for Detector Research and Development towards the International Linear Collider

The EUDET-project was launched to create an infrastructure for developing and testing new and advanced detector technologies to be used at a future linear collider. The aim was to make possible experimentation and analysis of data for institutes, which otherwise could not be realized due to lack of resources. The infrastructure comprised an analysis and software network, and instrumentation infrastructures for tracking detectors as well as for calorimetry.Comment: 54 pages, 48 picture

Cointegration analysis with state space models

Abstract: This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration and polynomial cointegration are defined. Based upon these definitions the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By means of detailing the cases most relevant for empirical applications, the I(1), MFI(1) and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly mentioned.

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure

Observation of Scaling Violations in Scaled Momentum Distributions at HERA

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of $x$ and $Q^2$ using the ZEUS detector. The evolution of the scaled momentum, $x_p$, with $Q^2,$ in the range 10 to 1280 $GeV^2$, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of $Q^2$.Comment: 21 pages including 4 figures, to be published in Physics Letters B. Two references adde

Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya

Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization