We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal. As an application, we prove that the following two hold in L: (1) For every infinite regular cardinal λ, there exists a special λ-Aronszajn tree whose projection is almost Souslin; (2) For ev...

In the present study, a general probabilistic design framework is developed for cyclic fatigue life prediction of metallic hardware using methods that address uncertainty in experimental data and computational model. The methodology involves (i) utilization of fatigue tests data conducted on coupons of Ti6Al4V material (ii) continuum damage mechanics based material constitutive models to simula...

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatmen...

In mathematics, a metric space is a set where a distance (called a metric) is defined between elements of the set. In this paper, we introduce the concept of a metric space in the framework of reservoir modelling and reservoir uncertainty. The distance between two models is a single measure that can be easily understood by the reservoir team, and can be tailored to the application of interest. ...

Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra Uq[ ̂ sl(2|1)] are constructed for arbitrary level k = α, where α 6= 0,−1 is a complex parameter appearing in the 4-dimensional evaluation representations. They are intertwiners among the level-α highest weight Fock-Wakimoto modules. Screen currents which commute with the action of Uq[...

We seek error models for simulations that model chaotic flow. Stable statistics for the solution and for the error are obtained after suitable averaging procedures. 2006 Elsevier Inc. All rights reserved.

We present an approach for assessing the uncertainties in simulation code outputs in which one focuses on the physics submodels incorporated into the code. Through a Bayesian analysis of a hierarchy of experiments that explore various aspects of the physics submodels, one can infer the sources of uncertainty, and quantify them. As an example of this approach, we describe an effort to describe t...

The Principal Principle (PP) says that, for any proposition A, given any admissible evidence and the proposition that the chance of A is x%, one’s conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994a) has ...

The Principal Principle (PP) says that, for any proposition A , given any admissible evidence and the proposition that the chance of A is x%, one’s conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994) has ...