Sentence examples for standard existence from inspiring English sources

According to the standard existence theory for ordinary differential equations there exists a continuous solution of this system, on some interval.

(1.4) Actually, standard existence and uniqueness results follows from a similar process in Theorem 1.1 in [21].

There is a fairly standard existence monist and nihilist reply to arguments in the vicinity of 1 3, which involves attempts to paraphrase claims of commonsense.

end{aligned} end{aligned} (13) Since the square root function is not Lipschitz continuous near 0, we cannot apply standard existence theorems to obtain a solution to (13) with the full multiplicative noise term.

The study of problem (1) requires some care because, even if pairs of constant lower and upper solutions can easily be exhibited, the presence of the curvature term rules out in general the possibility of applying the standard existence results, due to the possible occurrence of derivative blow-up phenomena (see, e.g., [5]).

Proof By the standard existence theorem for ODEs, it follows that system (3.3) possesses a local solution ( u ˜ ( t ), v ( t ), ψ ˜ ( t ) ) ∈ C ( 0, T ; E ), where [ 0, T max ) is the maximal interval of existence of the solution of (3.3). Now, we prove that this local solution is a global solution.

Perhaps if Common Core supporters want to silence their critics, they should start by informing more citizens about the Standards' existence.

The reasons for the first loss were multiple, and fairly standard (the existence of other religions, evolution, the problem of evil); the effect was, let's say, devastating.

Motivated by these considerations, Maddy set out to inquire into the standards of existence implicit in mathematical practice, and into the implicit ontological commitments of mathematics that follow from these standards (Maddy 1990).

A US renewable energy company has become the first in the world to win a Cradle-to-Cradle (C2C) silver certificate for its solar panels – one of the strictest sustainability standards in existence.

In the book, Wilkins condemns "the radical abolitionists of New England" and writes that "most southerners strove to treat their slaves with respect and provide them with a sufficiency of goods for a comfortable, though — by modern standards — spare existence".