Sentence examples for many solutions and from inspiring English sources

Elemental germanium can be electrodeposited from many solutions and melts of its compounds.

Diophantine equations fall into three classes: those with no solutions, those with only finitely many solutions, and those with infinitely many solutions.

Applied to the simplest Diophantine equation, ax + by = c, where a, b, and c are nonzero integers, these methods show that the equation has either no solutions or infinitely many, according to whether the greatest common divisor (GCD) of a and b divides c: if not, there are no solutions; if it does, there are infinitely many solutions, and they form a one-parameter family of solutions.

However, with many solutions, and especially MAC addresses, privacy concerns remain.

However, many solutions and "new" polyethylenes have been suggested in order to address this issue.

Many solutions and standards diverge from each other, while others are characterized as scientific proposals aiming at solving the problem.

We show that the problem (1.5) has countably many solutions if and satisfy some suitable conditions.

In this section we present that problem (1.5) has countably many solutions if and satisfy some suitable conditions.

During the same time I had seen many solutions proposed and implemented, most of which seriously failed to address the needs of the customers.

"There are many solutions to problems and I'm man enough and big enough to know we're not in a good position at the moment," he said.

They proved that IBVP (1.4) has at least one solution and infinitely many solutions by using variational method and critical point theorem.