Sentence examples for the unique probability from inspiring English sources

We construct a fusion frame {W, w} such that its dual fusion frame {W, v} is the unique probability optimal dual frames in some cases.

We specify certain moments (means, variances, see Table  4) and determine the unique probability distribution, which fulfils these constraints and has maximum entropy.

Our methodology is also free from exon length bias and works better in a large range of situations, as well as being easy to use because the MA approach provides a unique probability: the EPFE values.

A basic theorem says that there is a suitable σ-field containing all the intervals and a unique probability defined on this σ-field for which the probability of an interval is its length.

By the known Schwartz theorem (see, e.g., [11], Theorem 5) condition (4.9) is necessary and sufficient for the existence of a unique probability Radon measure μ on (U_{tau}(infty)) such that (overleftarrow{mu}(Omega)=(mucirctau^{-1})(Omega)) for all Borel sets (Omegasubsetvarprojlim U j)).

To counterbalance the effect of discrepancy between codon position and nucleotide diversity, a GTR model (which allows for the variation of base frequencies and unique probability for each of the six possible substitution classes) was selected in agreement with ModelTest 3.6 [ 13] for the Maximum Likelihood analyses.

The precise characterization of the RES output by means of a unique probability distribution is a challenging task.

The new algorithms are also advantageous when it is difficult to identify a unique probability density function (pdf) to represent the uncertainty in the system parameters and several pdfs need to be considered to assess the impact of the choice of the pdf on the predicted asymptotic system behaviour.

James Joyce (1999), for instance, thinks that Jeffrey's theory gets things exactly right in this regard, since one should not expect that reasonable conditions imposed on a person's preferences would suffice to determine a unique probability function representing the person's beliefs.

If the external force is the gradient of a convex potential, it has been proved that the process converges towards the unique invariant probability as the time goes to infinity.

The Ehrenfests (1912) paper was the first to recognize these questions, and to provide a partial answer: Assuming a certain hypothesis of Boltzmann's, which they dubbed the ergodic hypothesis, they pointed out that for an isolated system the micro-canonical distribution is the unique stationary probability distribution.