We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of unique maximal completions. The condition is verified in several situations of interest. This leads to existence and uniqueness of maximal spacelike conformal bou...

We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of unique maximal completions. The condition is verified in several situations of interest. This leads to existence and uniqueness of maximal spacelike conformal bou...

In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.

Censored data, whether univariate or bivariate, and whether right{, left{ or interval cen-sored, can be represented by its intersection graph. Paying special attention to the bivariate case, we show how the maximal clique structure of such an intersection graph is related to the support of the nonparametric maximum likelihood estimate (NPMLE) of the cumulative distribution function (CDF) for su...

In this paper, we study the uniqueness problem of a two-phase elliptic free boundary problem arising from the phase transition problem subject to given boundary data. We show that in general the comparison principle between the suband super-solutions does not hold, and there is no uniqueness of either a viscosity solution or a minimizer of this free boundary problem by constructing counter-exam...

The Dantzig selector (Candès and Tao, 2007) is a popular ℓ1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to parallelism and, when satisfied, ensures the uniqueness of Dantzig selector estimators. The condition holds with probability 1, if the predictors are drawn from a co...

In this paper, we examine people s appraisals of unusual objects and their intuitions about whether others will like those objects. Prior work suggests uniqueness motives (e.g., Need for Uniqueness) affect appraisals, but the effect of these motives on projection of appraisals to others is unclear. Contrary to some prior work, we argue that uniqueness motives do not govern projection of apprais...

In this paper we introduce the uniqueness and completeness problems of array comprehensions. An array comprehension has the uniqueness property if it de nes each array element at most once. Uniqueness is a necessary condition for correctness in single assignment languages such as Haskell, Id, and Sisal. The uniqueness problem can be stated as a data dependence problem, which in itself can be re...

In this paper we provide an example of a modified antiferromagnetic Potts model which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs. This example runs counter to the notion that the regular tree has the slowest decay of correlation amongst d-regular graphs. Sokal [7] conjectured that uniqueness in the hard-core model on the d-regular tree im...

Mutual exclusion is directly related to a host of selections at both system and component levels; is responsible for diversification; and gives rise to uniqueness. Mutual exclusion is also evident in modelling and flood forecasting, be it in models, software tools, data, modelling practices, flood forecasting and warning issues, and management systems. The emerging picture is that (i) diversity...