The aim of this paper is to prove that the Dedekind zeta function for a number field has a meromorphic continuation to the complex plane, obtaining the analytic class number formula with it, and to present some of the applications of these results. In particular, It will be shown its use in proving Dirichlet’s prime number theorem and in calculating the class number of quadratic fields. The pro...

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

Whaley’s Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 3 . It is also shown that that every finite modular lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 2 , and every finite distribut...

OBJECTIVES To investigate the relationship between accumulated health-related problems (deficits), which define a frailty index in older adults, and mortality in population-based and clinical/institutional-based samples. DESIGN Cross-sectional and cohort studies. SETTING Seven population-based and four clinical/institutional surveys in four developed countries. PARTICIPANTS Thirty-six tho...

i ntroduction: the aim of this study was to evaluate the clinical and histological status of the pulp in sound human premolars after direct pulp capping (dpc) with four different dpc methods/materials. methods and materials: this study was conducted on eight volunteers who had to extract four first premolars due to orthodontic treatment. subsequent to tooth isolation, standardized class i occlu...

this study shows the usefulness of artificial neural network (ann) in maintenance planning and man-agement. an ann model based on the multi-layer perceptron having three hidden layers and four processing elements per layer was built to predict the expected downtime resulting from a breakdown or a maintenance activity. the model achieved an accuracy of over 70% in predicting the expected downtime.