Normalized Frobenius condition number of the orthogonal projections of the identity

[EN]This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A ? Rn×n, S being an arbitrary subspace of Rn×n). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S ? Rn×n, a new index bF (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed...

Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

[EN]We analyze the best approximation

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u (*)/u (*R) , where u (*) is the friction velocity and u (*R) is the friction velocity from the uniform building height case, is expressed well as an algebraic function of lambda and sigma (h) /h (m) , where lambda is the frontal area index, sigma (h) is the standard deviation of the building height, and h (m) is the mean building height. The simulations also resulted in a simple algebraic relation for z (0)/z (0R) as a function of lambda and sigma (h) /h (m) , where z (0) is the aerodynamic roughness length and z (0R) is z (0) found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.

The Centrality of Urban Economies to the Study of Competitiveness

In recent decades the role of cities and of urban areas in the enhancement of competitiveness has become steadily more important and central to policy formation. The study of urban competitiveness is of interest, first, because it allows us to more fully understand to bases for policy and, second, because it allows us to evaluate the performance of a number of cities so as to determine what policies lead to success and what factors lead to failure or to steady decline. This research should be of interest to scholars as well as to urban practitioners.

On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Institutionalizing Intensive Family Preservation Services: A Strategy for Creating Staffing Standards Based on Projections of At-Risk Children from Referral Sources

In spite of new legislation and much public and professional interest, intensive family preservation service (IFPS) remains in a vulnerable position as compared to other child welfare services. This article details a method to project ideal IFPS caseloads as a function of children who are at-risk for placement by various referral sources. Using this approach, resource allocation for IFPS can be more nearly on equal ground with the traditional child welfare functions and help IFPS to assume its needed place as a core service in the child welfare continuum.

The strength of badenya ties: siblings and social security in old age – the case of urban Burkina Faso

In urban Burkina Faso, siblings play a decisive role in local social security. Badenya, the unity of children of the same mother, compensates in particular for the economic failure of an eldest son no longer in a position to fulfill his familial duties. Although the institution of badenya is strengthened as it increasingly comes into play to help a family avoid social marginalization, it is also overburdened, which makes its future uncertain. This article enhances the anthropological understanding of kinship by focusing on sibling relationships. Findings are based on interviews conducted between 2007 and 2010 with two generations in households in Bobo-Dioulasso and on participant-observation over the course of more than a dozen research stays since 1989.