Array algorithms for H^2 and H^∞ estimation

Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms

An algebraic characterization of complete inner product spaces

We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a multiplicative property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj

On complex strictly convex spaces. III

Si danno alcuni risultati su una geometria di spazi di Banach connessione con alcuni problemi ad essa relativi.We give some results related to a geometry of Banach spaces connection with some related problems

Follow-up of 100 dogs with acute diarrhoea in a primary care practice.

This study aimed to examine the aetiology of acute diarrhoea and the relapse rate in 100 client-owned dogs presented to a first-opinion clinic. History, physical examination, faecal testing and owner questionnaire data were collected at initial presentation (T0) and at either the time of relapse or at a recheck performed within 3 months. All dogs received treatment according to their clinical signs. Of 96 dogs that completed the study, 37 (38.5%) relapsed during the study period, 21 (21.9%) relapsed within 3 months, and 16 others (16.6%) at 3 months to 1 year after initial examination. Dogs that had undergone a change in housing location within 1 month prior to presentation and dogs <1 year old were significantly more likely to have positive parasitological analyses (P=0.02 and P=0.001, respectively). Pica was a risk factor for relapse (P=0.0002)