We discuss a new approach for the construction of the secondlevel Neumann-Neumann coarse space. Our method is based on an inexpensive and parallel analysis of the lower part spectrum of each subdomain stiffness matrix. We show that the method is flexible enough to converge fast on nonstandard decompositions and various types of finite elements used in structural analysis packages.

OBJECTIVES Our prospective study aimed to elucidate the effect of long-term experience of nonstandard employment status on the incidence of depression in elderly population using the Korean Longitudinal Study of Ageing (KLoSA) study. METHODS This study used the first- to fourth-wave cohorts of KLoSA. After the exclusion of the unemployed and participants who experienced a change in employment...

Mixed logic-systems contain both standard and nonstandard coordinate values. In this paper, it is shown that each of the specifically defined mixed logic-systems generates an internal nonstandard conse-

Mixed logic-systems contain both standard and nonstandard coordinate values. In this paper, it is shown that each of the specifically defined mixed logic-systems generates an internal nonstandard conse-

This paper reports recent progress in applying nonstandard analysis to additive number theory, especially to problems involving upper Banach density. 1 Prologue In this paper we use N for the set of all natural numbers. For any two integers a and b, a; b] denotes the interval of all integers x between a and b (a 6 x 6 b). If S is an internal set, jSj denotes the internal cardinality of S. The l...

The rst chapter presents Bayesian con rmation theory. We then construct in nitesimal numbers and use them to represent the probability of unrefuted hypotheses of standard probability zero. Popper's views on the nature of hypotheses, of probability and con rmation are criticised. It is shown that Popper conates total con rmation with weight of evidence. It is argued that Popper's corroboration c...