Spectral flow and Dixmier traces

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd ${\mathcal L}^{(1,\infty)}$-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle. We explain how to derive a Wodzicki residue for pseudo-differential operators along the orbits of an ergodic \IR^n action on a compact space $X$. Finally we give a short proof an index theorem of Lesch for generalised Toeplitz operators

Orthogonal multiplexing techniques for switching in a digital local telephone exchange

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An Investigation of Parents\u27 Perceptions of the Junior-Academy Principal\u27s Role in the Lake Union Conference of Seventh-day Adventists

Problem. If he/she is to satisfy or accommodate the expectations of the various groups that interact with him/her, the principal needs to be aware of how they perceive his/her role; but no studies were found on parents\u27 perceptions of the junior-academy principal\u27s role. Therefore, the purpose of this study was to determine parents\u27 perceptions of the role of the principal in Seventh-day Adventist junior academies in the Great Lake states of Illinois, Indiana, Michigan, and Wisconsin. Method. A descriptive survey design was utilized for this study. A closed-type questionnaire developed by the researcher was submitted to a panel of eleven judges, modified, and pretested before it was sent to a stratified random sample of 434 parents whose children attended Seventh-day Adventist junior academies in the Lake Union Conference. The data collected were coded, and processed at Andrews University Computing Center. Chi-square was the statistical analysis used. Results. This study revealed the following results: (1) Parents agreed that the role of the junior-academy principal should include forty-eight of the forty-nine role responsibilities listed on the questionnaire. (2) The top three role responsibilities parents expected the junior-academy principal to perform were: (a) Promote unity among teachers; (b) Gain and maintain constituency confidence; (c) Hold personal conferences with teachers; (3) Of the seven areas of administrative responsibility identified, student personnel was ranked highest and spiritual leadership lowest. (4) There was a significant difference between parents\u27 perceptions of the junior-academy principal\u27s role in relation to eight demographic and personal variables. Conclusions. Based upon the results of the study, these conclusions were made: (1) Parents\u27 perceptions of the junior-academy principal\u27s role were similar to the expectations for that role as published in Seventh-day Adventist educational literature, and as expressed by Lake Union educational administrators. (2) There seems to be a relationship between parents\u27 perceptions of the junior-academy principal\u27s role and certain demographic and personal variables. (3) Parents regarded developing a good principal-parent relationship and a healthy principal-staff relationship as very important areas of administrative responsibility. (4) Parents regarded spiritual leadership the least important area of administrative responsibility