Stability of Quadratic Projection Methods

In this paper we discuss the stability of an alternative pollution-free procedure for computing spectra. The main difference with the Galerkin method lies in the fact that it gives rise to a weak approximate problem which is quadratic in the spectral parameter, instead of linear. Previous accounts on this new procedure can be found in Levitin and Shargorodsky (2002) [math.SP/0212087] and Boulton (2006) [math.SP/0503126].Comment: 19 pages, 4 figures. In this updated version we have made a small number of minor correction

Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator

A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined. The strategy relies on computing the second order spectrum relative to subspaces of continuous piecewise linear functions. For smooth perturbations of the angular Kerr-Newman Dirac operator, explicit rates of convergence due to regularity of the eigenfunctions are established. Existing benchmarks are validated and sharpened by several orders of magnitude in the unperturbed setting.Comment: 27 pages, 2 figures, 5 tables. Some errors fixe

Arguments towards the construction of a matrix model groundstate

We discuss the existence and uniqueness of wavefunctions for inhomogenoeus boundary value problems associated to x^2y^2-type matrix model on a bounded domain of R^2. Both properties involve a combination of the Cauchy-Kovalewski Theorem and a explicit calculations.Comment: 3 pages, Latex Proceedings for the XIX Simposio Chileno de Fisica, SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chil

The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition

The spectrum of the bosonic sector of the D=11 supermembrane with central charges is shown to be discrete and with finite multiplicities, hence containing a mass gap. The result extends to the exact theory our previous proof of the similar property for the SU(N) regularised model and strongly suggest discreteness of the spectrum for the complete Hamiltonian of the supermembrane with central charges. This theory is a quantum equivalent to a symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the space-like sector is a Riemann surface of positive genus. In this context, it is argued how the theory in 4D exhibits confinement in the N=1 supermembrane with central charges phase and how the theory enters in the quark-gluon plasma phase through the spontaneous breaking of the centre. This phase is interpreted in terms of the compactified supermembrane without central charges.Comment: 33 pages, Latex. In this new version, several changes have been made and various typos were correcte

On the groundstate of octonionic matrix models in a ball

In this work we examine the existence and uniqueness of the groundstate of a SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and uniqueness argument of the groundstate wavefunction follows from the Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which is drafted in some detail.Comment: Latex, 6 page

Massless ground state for a compact SU(2) matrix model in 4D

We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU(2) matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to analyze the quantum spectral properties of this class of supersymmetric matrix models subject to constraints which can be generalized for arbitrary number of colors.Comment: 12 pages, Latex. Somme clarifications. Minor changes. Version to appear at NP

The ground state of the D=11 supermembrane and matrix models on compact regions

We establish a general framework for the analysis of boundary value problems of matrix models at zero energy on compact regions. We derive existence and uniqueness of ground state wavefunctions for the mass operator of the $D=11$ regularized supermembrane theory, that is the $\mathcal{N}=16$ supersymmetric $SU(N)$ matrix model, on balls of finite radius. Our results rely on the structure of the associated Dirichlet form and a factorization in terms of the supersymmetric charges. They also rely on the polynomial structure of the potential and various other supersymmetric properties of the system.Comment: Latex, 26 pages. We have added some comments at the introduction in order to make it easier for the reader. Results of the paper unchange

On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding

The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.Comment: 11 pages, LaTe

Does authentic self-esteem buffer the negative effects of bullying victimization on social anxiety and classroom concentration? Evidence from a short-term longitudinal study with early adolescents

Background Bullying victimization is a risk factor for social anxiety and disrupted classroom concentration among young people. Self-esteem has been implicated as a protective factor, but extant literature is sparse. Aims Aim of present study was to test if a new measure of authentic self-esteem can buffer the negative effects of bullying victimization on social anxiety and disrupted classroom concentration concurrently and across time. Sample A short-term longitudinal questionnaire design was employed with 836 12- and 13-year-olds. Methods Peer nominations of bullying victimization and self-reports of authentic self-esteem were collected during winter term, and self-reports of social anxiety and disrupted classroom concentration were solicited then and also 5 months later. Results Hierarchical multiple regression models indicated that authentic self-esteem moderated the association between bullying victimization and (i) social anxiety both concurrently and longitudinally and (ii) disrupted classroom concentration longitudinally. The Johnson-Neyman technique identified where on its scale authentic self-esteem had its buffering effects, and these were found to be at relatively low or moderate levels. Conclusions Even moderate levels of authentic self-esteem can mitigate the association between being bullied and (i) social anxiety and (ii) disrupted classroom concentration. Efforts to monitor and where necessary enhance the authentic self-esteem of young people are warranted

Parenting about challenges and adolescents' social anxiety, disrupted classroom concentration and resilience knowledge: the mediating role of authentic self-esteem

A large theoretical and empirical literature indicates that parenting practices affect young people’s well-being and resilience, but there is much still to learn about psychological mechanisms, especially beyond infancy/early childhood. A recent model of authentic self-esteem argues that it arises out of experiences of challenge situations shared with parents and that it can subsequently act as a protective factor that supports well-being and resilience among young people. The aim of the current study is to test: (i) if parenting about challenges can predict three indices of adolescents’ well-being, namely their (a) social anxiety, (b) disrupted classroom concentration, and (c) ability to spontaneously generate resilient strategies, and more substantially (ii) if authentic self-esteem can mediate those associations if found. Adolescents (N = 836) completed a questionnaire that measured all of the study variables via self-report with the exception that unprompted open questions were used to gauge their ability to spontaneously generate resilient strategies. Parental discussions of challenges did significantly predict all three well-being indices, and authentic self-esteem was found to mediate all of these relationships. These results support the view that parenting about challenges is a practice that supports well-being and resilience in adolescents. It appears to do so through promoting the development of authentic self-esteem, a capacity to evaluate the self in a positive manner in the context of challenges. The theoretical and practical significance of these findings are discussed