Sentence examples for a dual form from inspiring English sources

Others count differently – they may have a plural form meaning "of unexpected number" or a dual form.

This may in turn be formulated in a dual form.

This statement is a dual form of Corollary 2.

Also, Corollary 23 is a dual form of Corollary 7.

We notice that Lemma 3 is a dual form of Lemma 2.

Here, is a dual form of -Busemann-Petty centroid inequality (1.2).

The final result is a dual phase steel formed by ferrite and martensite, having a stochastic geometric structure.

Hebrew has a morphological dual form for nouns that naturally occur in pairs, and for units of measurement and time this contrasts with the plural (יום 'day' יומים 'two days' ימים 'days'days

The q kernels correspond to q feature mappings Ψ k : χ → H k, k = 1, …, q and l is some convex loss function and the primal problem is then: when the optimization is coupled with hinge loss, the problem has a simple dual form (Kloft et al., 2011): max α   α T e − 1 2 | | (α T G (K i ∼ ) α ) k = 1 q | | p *, where all the variables are all as defined before but p * = p p − 1.

The stochastic approach is based on the representation of a sequence of alarms under the dual form of a homogeneous Markov chain and its corresponding superposition of Poisson processes.

Dual form means a transdermal patch plus one of the other products such as gum, lozenge, nasal spray, mouth spray or inhalator.