Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page

Attachment, Forgiveness, and Generativity in Midlife

Current literature suggests secure attachment and forgiveness are positively correlated. However, to date, the relationship of adult attachment, forgiveness, and generativity has not been explored. In this current study, middle-aged adults, ages 45-80 from the George Fox University Alumni were surveyed to explore attachment (anxious and avoidant), generativity, and forgiveness. Since generativity is a prosocial trait, synonymous with altruism, suggesting one’s selfless service and concern for the well-being for others, it is predicted that generativity will have a positive relationship with forgiveness, and secure attachment. Further, multiple regression statistics were used to explore which of the independent variables (anxious attachment, avoidant attachment, and generativity) has the greatest effect on the dependent variable of trait forgiveness. Results indicated that there was a medium positive relationship between forgiveness and secure attachment, between generativity and secure attachment, and between forgiveness and generativity. Multiple regression found that each of the independent variables (anxious attachment, avoidant attachment, and generativity) were significant predictors of forgiveness with anxious attachment being the strongest predictor of forgiveness

Rotation of the solar convection zone from helioseismology

Helioseismology has provided very detailed inferences about rotation of the solar interior. Within the convection zone the rotation rate roughly shares the latitudinal variation seen in the surface differential rotation. The transition to the nearly uniformly rotating radiative interior takes place in a narrow tachocline, which is likely important to the operation of the solar magnetic cycle.The convection-zone rotation displays zonal flows, regions of slightly more rapid and slow rotation, extending over much of the depth of the convection zone and converging towards the equator as the solar cycle progresses. In addition, there is some evidence for a quasi-periodic variation in rotation, with a period of around 1.3 yr, at the equator near the bottom of the convection zone.Comment: 12 pages, 8 figures. To appear in Proc. IAU Symposium 239: Convection in Astrophysics,eds F. Kupka, I. W. Roxburgh & K. L. Chan, Cambridge University Pres

Higher Weak Derivatives and Reflexive Algebras of Operators

Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function is n-times differentiable. We give several characterizations of this property, among which one is original. The results are used to show, that for a von Neumann algebra M on H, the sub-algebra of n-times weakly D-differentiable operators has a representation as a reflexive algebra of operators on a bigger Hilbert space.Comment: This version acknowledges results from the litterature, which the first edition was unaware of. The result on the existence of a representation with a reflexive image is ne

Proving Montessori: Identity and Dilemmas in a Montessori Teacher’s Lived Experience

This phenomenological case study was conducted to better understand the experience of a Montessori teacher in a leadership role. A veteran Montessori teacher, newly hired by an established Montessori preschool, was interviewed over the course of her first year in the position. A critical discourse analysis revealed multiple social identities that contributed to her desire, and ability, to be what she felt was an authentic Montessori educator. While some of these discourses and social identities aligned, some did not, creating ideational dilemmas that affected her work, relationships, and personal identity. The findings suggest that current Montessori discourse excludes important characteristics of the teacher-lived experience. Acknowledging and discussing the social challenges Montessori teachers face is a necessary addition to teacher preparation, teacher support systems, and Montessori leadership decisions

Comment: Fisher Lecture: Dimension Reduction in Regression

Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]Comment: Published at http://dx.doi.org/10.1214/088342307000000041 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Finite von Neumann algebra factors with property Gamma

Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property gamma have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of some larger C*-algebra then there exists a projection of norm one from the larger onto the smaller algebra. A new proof of the fact that the second continuous Hochschild cohomology group of such an algebra with coefficients in the algebra vanishes, is also included.Comment: 12 page