1950 the 18-year old Edward Nelson posed the problem of finding χ (see its history in [S]). A number of relevant results were obtained under additional restrictions on monochromatic sets. K. Falconer, for example, showed [F] that χ is at least 5 if monochromatic sets are Lebesgue measurable. Amazingly though, the problem has withstood all assaults in general case, leaving us with embarrassingly...

The aim of this paper is to explore the relationship between wages, human capital and investment in financial assets with risky returns at the individual level. To explore this relationship from an international perspective, we analyse individual level data from the British Household Panel Survey, the German Socio-Economic Panel and the U.S. Panel Study of Income Dynamics. Our findings suggest ...

This paper reports a set of experiments motivated by the observation that the design of group decision processes is crucial to the success of electronic meeting room usage. Decision processes can be designed with more emphasis either on exchanging meanings (discussing issues) or exchanging artefacts (generating and structuring topics). Our problem is that, given a particular case to be discusse...

Given a rational point on a curve in a rational isogeny class, a natural question concerns the field of definition of its pre-images. The multiplication by m endomorphism is a powerful and much-used tool. The pre-images for this map are found by factorizing a monic polynomial of degree m. For m = 2, Everest and King gave examples where the existence of a quadratic factor coincided with the exis...

In this paper we investigate colorings of sets avoiding similarly colored subsets. If S is an arbitrary colored set and T is a "xed family of bijections of S to itself, then two subsets A; B ⊆ S are said to be colored similarly with respect to T, if there exists a transformation t ∈T mapping A onto B, and preserving a coloring of A. This general setting covers some well-known topics such as non...

Let X be a convex curve in the plane (say, the unit circle), and let S be a family of planar convex bodies, such that every two of them meet at a point of X. Then S has a transversal N ⊂ R of size at most 1.75 · 10. Suppose instead that S only satisfies the following “(p, 2)-condition”: Among every p elements of S there are two that meet at a common point of X. Then S has a transversal of size ...

STUDY QUESTION How well does the recently developed UK model predicting the success rate of IVF treatment (the 2011 Nelson model) perform in comparison with a UK model developed in the early 1990s (the Templeton model)? SUMMARY ANSWER Both models showed similar performance, after correction for the increasing success rate over time of IVF. WHAT IS KNOWN ALREADY For counselling couples under...

How to join PubMed Commons J Urol. 2005 Jun;173(6):1848-9. Eliminating the current Bell curve to improve the results of radical prostatectomy. Nelson JB. Comment on The effect of hospital volume on cancer control after radical prostatectomy. [J Urol. 2005] Variations among high volume surgeons in the rate of complications after radical prostatectomy: further evidence that technique matters. [J ...

Nelson algebras were first studied by Rasiowa and BiałynickiBirula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted – which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstr...