Sentence examples for increasing types from inspiring English sources

With the growth of biofilms, increasing types of microorganisms compete for limited resources (e.g., nitrogen, oxygen, and phosphate), forcing L. rubarum to reinforce its competitiveness and self-protection.

So we use X which is of degree increasing type.

If X x,y):=5x 3 y 2+12x y 2+7x y+6x+5, then X is of degree increasing type.

The condition on Λ (step 1 above) means that X is of degree increasing type.

Let (X in mathbb {Z}[underline {x}]) be a polynomial of degree increasing type.

In this paper we have not studied the hardness of solving diophantine equations of degree increasing type.

Because (tilde {m}) is of degree increasing type, we have (sum underline {k}^{prime } - sum underline {i} geq 1).

So we may assume that solving the diopantine equations of degree increasing type is hard in general.

A polynomial (X in mathbb {Z}[underline {x}]) is of degree increasing type if (sigma |_{Lambda _{X}}) is injective.

We give a method to construct a public key X of degree increasing type with (X underline {a}/d) = 0).

Another key idea is to use a polynomial, as the public key, of degree increasing type to recover the plaintext.