Sentence examples for multiplying from from inspiring English sources

After multiplying from the right and from the left by Γ and Γ ∗, it is not difficult to see that (2.17) yields the following [17]: A − 1 ≤ m + M m M I − A m M. (2.18).

Multiplying from the right and from the left by V ∗ A and AV respectively, we have V ∗ A 2 V ≥ ( V ∗ A V ) 2 for A > 0. From the well-known Löwner-Heinz inequality, we have ( V ∗ A 2 V ) 1 / 2 ≥ V ∗ A V and the following inequality (see in [16]): ( V ∗ A 2 V ) 1 / 2 ≤ m + M 2 m M V ∗ A V. For z ∈ [ m, M ], m > 0, the convexity of ( z − 1 + z / m M ) implies that z − 1 ≤ m + M m M − z m M. (2.16).

Nothing in my imagination of the world's possibilities the hands that built it, the lives it contained could help me account for Shanghai's over-awing presence, its high-rises multiplying from the soil into a miasma of soot and acidic rain.

Whatever the motivation, these early documented collecting practices sank slowly and deeply into human double-spiral DNA, which has been inherited for thousands of years and has kept the collecting bug alive and well and multiplying from one generation to the next.

The zero serves as a placeholder and reminder that you are now multiplying from the 'tens' value place.

A final category is fan e-mail, gratifyingly multiplied from the traditional fan letter.

Finally, books began to multiply, from which the only conclusion to be drawn was that an underground publishing and printing company had been set up.

It provided support and affordable space to Boulder County dance groups, which multiplied from three in 1990 to at least 25 today.

For example, with its original dust jacket, the value of a first-edition "The Great Gatsby" can multiply from two thousand five hundred dollars to more than two hundred thousand.

As their pesticide-resistant descendants began to multiply from Manhattan to Moscow, though, changing everything from leases to liability laws, the hunt for a solution was on.

Not only has my gas bill grown astronomically because of the chauffeuring, but my waist size has also multiplied from walking less and eating more.