Sentence examples for and the second argument from inspiring English sources

where is the Heaviside function (implementing the indicator function) and the second argument of indicates the time-discretized version of the spike train.

The constructive empiricist can be understood as giving two arguments for this claim; the first argument will be presented here, and the second argument will be presented in the next subsection.

The solution of the optimization follows by setting the first and the second argument in (7) to equality for all i with 1 ≤ i ≤ N: θ i * σ i C ( γ i R ) = 1 - ∑ j = 1 N θ j * ⋅ a (9).

Predicates have a fixed finite arity in FOL, and nothing precludes binding at once a variable in the first argument of one predicate and in the second argument of another predicate.

Consequently, on the epistemic approach to fallacies taken by Biro and Siegel, the second argument, despite the fact that it is valid, is non-serious, it begs the question, and it is a fallacy.

Since is a coercive continuous bilinear form, is convex and continuous in the second argument, and for given the mapping is convex and lower semicontinuous in, it follows that for each is weakly upper semicontinuous in the second argument and the set is convex for each That is, the conditions (b) and (c) of Lemma 2.4 hold.

Clearly, F is g.h.c. in the first argument and l.s.c. in the second argument.

They are linear in the first argument and antilinear in the second argument.

Assume that F K × K K → 2 Y is C-strongly pseudomonotone, g.h.c. in the first argument, C-convex and l.s.c. in the second argument.

Let and be mappings such that is Lipschitz continuous with constant, is -strongly monotone with respect to in the first argument with constant, -relaxed cocoercive with respect to and Lipschitz continuous in the second argument with constants and, respectively, is -relaxed Lipschitz with constant, and and are -hemicontinuous with respect to and in.

(i) is -cocoercive with respect to the first argument of with constant ; (ii) is Lipschitz continuous with constant ; (iii) is Lipschitz continuous and -strongly monotone in the second argument with respect to with constant and, respectively.