Sentence examples for certain solutions of from inspiring English sources

The observation that certain solutions of ruthenium complexes can absorb atmospheric nitrogen has led to hope that one day a simpler and better method of nitrogen fixation may be found.

We give an explicit integral formula for certain solutions of the equation D=0.

Continuing former experiments with microelectrolysis of certain solutions of metallic salts we could confirm the assumption that production of dendrites were caused by electric forces.

Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.

On the other hand, it was noted in [13], for example, that certain solutions of the GNEP (the normalized Nash equilibria, to be defined later) can be found by solving a suitable standard VI associated to the GNEP.

For the periodic solution case, i.e., (Qequiv I_{n}), as shown in [15], one can transform the problem into one of finding certain solutions of the Cauchy problem by introducing a homotopy parameter (lambdain[0,1]).

then exponentially for and where is a certain solution of a logistic equation.

By using a fluctuation lemma, Li and Chen [4] obtained sufficient conditions which ensure the second species will be driven to extinction while the first one will stabilize at a certain solution of a logistic equation.

From the proof of Theorem 3 it follows that if x is a q-periodic solution of (1), then x has the following form x(n)=(c_{1}, c_{2}, dots, c_{q},c_{1}, c_{2}, dots, c_{q}, dots), where ((c_{1}, c_{2}, dots, c_{q})) is a certain solution of system (18).

Now, certain solutions c of the integer coefficient knapsack are no solutions of the real-valued coefficient knapsack and vice versa.

for certain solutions z of ( S λ ).