In this paper, we consider the time-frequency localization of the generator of a principal shift-invariant space on the real line which has additional shift-invariance. We prove that if a principal shift-invariant space on the real line is translation-invariant then any of its orthonormal (or Riesz) generators is non-integrable. However, for any n ≥ 2, there exist principal shiftinvariant space...

The ethical, social and political dimensions of legislative regulations of issues concerning the citizens’ health are generally recognized to be of increasing significance in modern deliberative democracies. However, nanotechnologies in health have raised extra difficulties in deliberative democracies’ procedural justice arrangements. Could a deliberative model of democracy based on substantive...

In this note, we argue that the axiomatic requirement of range to the measure of aggregated total uncertainty (ATU) in Dempster-Shafer theory is not reasonable.

We construct an algebra of generalized functions endowed with a canoni­ cal embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution. We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring ...

Suppose that "uncertainty" about labor market conditions has increased. Does this change induce an unemployed worker to search longer, or shorter? This paper shows that the answer is drastically different depending on whether an increase in "uncertainty" is an increase in risk or that in true uncertainty in the sense of Frank Knight. We show in a general framework that, while an increase in ris...

In this paper, the existence and uniqueness of the solution of random impulsive neutral functional differential equation is investigated under sufficient condition. The results are obtained by using the Contraction principle.

| This paper contains a simple but powerful statement and proof of the Energy-Time uncertainty principle.

Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertaintly intelligently, we need to be able to represent it and reason about it. In this book, Joseph Halpern examines formal...