Sentence examples for a singular version of from inspiring English sources

In Section 3, we establish a singular version of Moser-Trudinger inequality with the exact growth condition on hyperbolic space (Theorem 1).

This paper is concerned with a singular version of Moser-Trudinger inequality with the exact growth condition on hyperbolic space (mathbb{H}^{n}).

In this paper, we prove a singular version of Moser-Trudinger inequality with the exact growth condition in the n-dimension hyperbolic space (mathbb{H}^{n}).

In this section, we shall establish a singular version of Moser-Trudinger inequality with the exact growth condition on hyperbolic space.

In this paper, we are concerned with a singular version of the Moser-Trudinger inequality with the exact growth condition in the n-dimension hyperbolic space (mathbb{H}^{n}).

end{aligned} Using the well-known singular version of Gronwall inequality [12], we can deduce that there exists a constant (overline{M}_{2}>0) such that (psi(t)leqoverline{M}_{2}).

What was ignored then was this singular version of supply and demand: Long-standing literary and commercial fiction voices are maturing, and many of them have reached a plateau economically and critically.

The singular version of the Moser-Trudinger inequality on the Heisenberg group was also proved by Lam, Lu and Tang in [12].

Motivated by the above results, we consider the singular version of the Moser-Trudinger inequality with the exact growth condition on hyperbolic space.

This dictionary is focused on definitions, and so contains only singular versions of nouns, even though their plural versions are perfectly acceptable as Scrabble words; for example, if you type the word "WORDPLAY," it will be found, but the word "WORDPLAYS" will not be found, even though it is in the official North American Scrabble list, called TWL.

In her first-person-singular version of "The Lady Is a Tramp," she hesitated a split second before applying to herself the word "tramp" — lightly.