Sentence examples for method we shall from inspiring English sources

By the mathematical induction method, we shall generalize Theorem 6.

By Lemma 2.2 (reduction method), we shall show the existence of the third weak solution of (1.1).

Here, by using the Liapunov function method, we shall show that the solution of problems (1.1 - 1.3 1.1 - 1.3entislly dexponentiallyelay parameter τ is sufficiently small.

In Section 4, by the Galerkin method, we shall establish the results of existence and uniqueness of a solution for problem (1.1).

By using the Liapunov function method, we shall show that the solution is exponentially decay if the delay parameter τ is sufficiently small.

Then, by constructing suitable approximate problems, and using a priori estimates and a test function method, we shall finish the proof of this existence results.

A nonlinear evolution equation known as KdV Burgers equation is derived by using reductive perturbation method, and we shall analyze that the influence of various physical parameters modifies the width and amplitude of DA shocks due to dependence of nonlinear, dispersion and dissipative terms on such parameters.

But until a large-scale conversion to these methods has occurred, we shall have little relief from a situation that, by any common-sense standards, is intolerable.

We have also briefly considered the means and methods by which we shall gain a good knowledge of the moral qualities and institutions peculiar to the various forms of government-only, however, to the extent demanded by the present occasion; a detailed account of the subject has been given in the Politics.

In this paper, following the methods of [8], we shall further provide many new convolution identities involving Bernoulli, Euler and Genocchi numbers.

It can easily be shown through the method of pgf that if T t) is Markov, then the stochastic equation method is equivalent to the method of Markov theory; as we shall see, however, the stochastic equation method is more powerful and does not need to assume Markov for T t).