Sentence examples for upper bonds from inspiring English sources

To employ the method, according to lower and upper bonds of a design variable a number of layers or intervals are selected.

Our semi-supervised consensus clustering algorithm is described in Algorithm 2. Similar to [ 4], for a given n ×  d dataset of n samples and d genes, a n ×  q data subspace (q <  d) is generated by (1) q = q min + ⌊ α (q max - q min ) ⌋ α ∈ [ 0,1] is a uniform random variable, q m i n and q m a x are the lower and upper bonds of the subspace.

The first peak is a superposition of the lines corresponding to the lower bonding states, the intermediate peak is related to a superposition of the upper bonding and the lower anti-bonding states, and the last peak is due to a superposition of the upper anti-bonding states.

Additionally, one can see that energies corresponding to the bonding states are generally inferior, and there is only one crossover between the lower anti-bonding potential curve and the upper bonding one.

The separation performance of the nanoporous graphene membranes for the three gas mixtures far surpasses the upper bond of the conventional polymer membranes.

The next result is used in order to establish the fact that the sequence defined in Theorem 3.1 approximates the solution of the nonlinear Volterra integro-differential equation, as well as giving an upper bond of the error committed.

Let B be the maximal path in G and u an upper bond of B. If u is not an end point, there exists x∈G such that x≠u and (u,x ∈E(G).

To find the upper bond for the average time till all cluster members manage to send their status messages, we assume that all members wait for time Tw(d) before they send their messages.

In Section 3 we have obtained the complete moment convergence for a sequence of mean zero H-valued CNA random vectors which is coordinatewise weakly upper bonded by a random variable and the related results.

From Equations (9), (11), (12), (13) and (14), we can find the upper bond of the total average time for all cluster members to send their status messages as: T avg = T cf + [ T mf ] + 2 β R μ - 1 [ T m ] + [ T in ] + [ T cl ], (15).

This regional cause-specific mortality envelope serves as an upper bond of mortality from a certain cause and partly ensures the internal consistency among incidence, prevalence and mortality rates [ 6].