Sentence examples for uniqueness I from inspiring English sources

Consider a symmetric bilinear form Eϕdefined on C∞c(Rd) by[formula]In this paper we study the stochastic process associated with the smallest closed markovian extension of (Eϕ, C∞c), and give a new proof of Markov uniqueness (i.e. the uniqueness of a closed markovian extension) based on purely probabilistic arguments.

These results concern both deterministic and generic uniqueness, i.e., uniqueness for a particular PARAFAC model or uniqueness with probability one in the case where the entries of the factor matrices are drawn from continuous distributions.

But note that, apart from the uniqueness (i.e. the "only if" part), the stability follows from that result and Lemma 2.

This was not solved satisfactorily by Fraenkel, but the Weyl/Skolem solution works here, too: a functional correspondence is (in effect) just any first-order 2-place predicate ϕ x, y) which satisfies the condition of uniqueness, i.e., ∀x, y, z{[ϕ x, y) ∧ ϕ x, z)] → y = z}.

The core of Ruhlin's approach to corporate giftology is not only delivering "uniqueness" (i.e., no fruit baskets, chocolate boxes, or cheap branded swag like water bottles or pens), but also communicating through actual physical things that you know your client and their family (most importantly their spouses), and understand their private, personal interests that have nothing to do with business.

In contrast to the above factors, neither IUCN listing nor taxonomic uniqueness, i.e., the variables best reflecting conservation value of the species, had effect on zoo population size.

1. Teach Your Child That Their Uniqueness Is Their Power Starting from a young age, it is important to ingrain in your child that the things that make them different from others are their greatest assets.

This kind of inversion bears a certain degree of inherent non-uniqueness, i.e., a variety of different ESPs combinations exist that can reproduce the deposit.

The fourth step involved adding equality constraints on the uniquenesses (i.e., disturbances) associated with the items across groups (Model 4).

In conclusion, the four measurement invariance models support the assumption of equal factor loadings, equal item intercepts, and equal item uniquenesses (i.e., strict measurement invariance) across method conditions in young adulthood.

However, the uniquenesses (i.e., disturbances) associated with each item were non-invariant at Time 3. In addition, the latent factor means were non-invariant at Time 2 and 3, indicating that there are significant differences across sexes at these time points on the DSS subscale scores, with girls reporting higher scores at both time point.