In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset subject to forbidden r+ s configurations, where r+s = 4. Generalizing previous work on weak discrepancy in [5, 12, 13], the notion of fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [7] as the minimum nonnegative k for which there exists a function f : V → R ...

The Fudenberg and Maskin folk theorem for discounted repeated games assumes that the set of feasible payoffs is full dimensional . We obtain the same conclusion using a weaker condition. This condition is that no pair of players has equivalent von Neumann-Morgenstern utilities over outcomes. We term this condition NEU ("non-equivalent utilities"). The condition is weak, easily interpreted, and ...

We deene a property of substructures of models of arithmetic, that of being length-initial , and show that sharply bounded formulae are absolute between a model and its length-initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length-initial submodels of some given model.

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy: • first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional measurements can improve the accuracy of the result of this series of measurements; • second, we can...

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators Re(λ) 1/2C(λ+A)−1, Re(λ) > 0 on the complex right half plane and weak Lebesgue L2,∞–admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the ’Weiss conjecture’ within the scale of Lorentz spaces L...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫

Reliability and validity are crucial issues in research. Reliability is concerned with lowered quality of data due to random errors in measurement. Validity is concerned with whether variables measure what they purport to measure or are biased by other systemic factors, excluding random errors. Strength of correlation is limited by reliability. Given the problems in measuring reliability and va...

In the preceding chapters, the effects of lensing were so strong as to leave an unmistakable imprint on a specific source, allowing a detailed treatment. However, only the densest regions of the universe are able to provide such a spectacular lensing effect. To study more representative regions of the universe, we must examine large numbers of sources statistically. This is the domain of weak l...