A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 ...

Rubinstein, Safra and Thomson (1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social cho...

Background. Historically, most acute stroke clinical trials were neutral statistically, with trials typically dichotomising ordinal scales, such as the modified Rankin Scale. Studies published before 2007 have shown that preserving the ordinal nature of these scales increased statistical power. A systematic review of trials published since 2007 was conducted to reevaluate statistical methods us...

OBJECTIVE This study investigates isolated effects of vection and optokinetic nystagmus (OKN) on visually induced motion sickness (VIMS) provoked by rotating optokinetic drum patterns. BACKGROUND VIMS was the subject of recent standardization activities, but the effects of OKN have not been studied in the absence ofvection. METHOD Experiment 1 suppressed OKN by eye fixation and examined VIM...

‎‎in this paper‎, ‎we define fuzzy subnexuses over a nexus $n$‎. ‎define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎finally‎, ‎we show that if s is a meet‎‎closed subset of the set fsub(n), ‎of fuzzy subnexuses of a nexus n‎, ‎and‎‎h= ⋀s ϵ s, ‎then the fractions s^-1 n and h^-1 n are isomorphic as meet-semilattices‎.

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel’s constructible universe L. This characterization can be used to prove the generalized continuum...

How do ordinals measure the strength and computational power of formal theories and what information can be gleaned from this correlation? This will be the guiding question of this talk. The connection between ordinal representation systems and theories is established in ordinal analysis, a central area of proof theory. Ordinal-theoretic proof theory came into existence in 1936. Gentzen showed ...

In this paper, we propose a computationally efficient method to solve the large dimension Adaptive Subcarrier Assignment and Bit Allocation (ASABA) problem of multiuser orthogonal frequency division multiplexing system. Our algorithm consists of three Ordinal Optimization (OO) stages to find a good enough solution to the considered problem. First of all, we reformulate the considered problem to...

(A for ‘above’; B for ‘below.’) A lattice satisfying this condition is called finitely separable. It is easy to see that every countable lattice is finitely separable. We used this to show the following surprising result: the ordinal sum of two free lattices is projective if and only if one of them is finitely generated or both are countable. In this note we give a complete characterization of ...