Sentence examples for the regular problem from inspiring English sources

Then we use perturbation results for linear operators to solve the regular problem.

In this paper we are primarily interested in the regular problem that arise as direct consequences of the general theory developed previously, and we consider to put in perspective those models of initial value problems which can be formulated as nonlinear differential equations of variational inequalities.

In [2], Cid et al. applied the substitution (u = x^{mu}), (mu=frac{1}{b+1} ), and then transformed the singular periodic boundary value problem (3) to the regular problem textstylebegin{cases} x"(t)+ax'(t)+s(t)x^{beta}-r(t)x^{alpha}=0, quad tin [0, T], x 0)=x(T),quadquad x'(0)=x'(T), end{cases} (4) where (r(t)=frac{e(t)}{mu}), (s(t)=frac{c}{mu}), (alpha =1-2mu), (beta=1-mu).

Readers are invited to submit solutions to the regular problems, and two columns later (not every issue of TR contains a "Puzzle Corner" column), one submitted solution is printed for each regular problem.

To that, Benedict replies that courts have eviscerated states' power to block Indian casinos, adding: "All the regular problems of casino development are compounded by sovereignty.

Section 2 is devoted to the auxiliary regular problem (1.12), (1.2).

Further, we shall remark that although the minimal operator is densely defined in the case that (a = -infty) and (b = +infty), the minimal operators of the induce regular problems that will be used to approximate the singular one are not densely defined, and so their self-adjoint extensions have to be characterized by the theory of subspaces.

Though the program was currently non-operational in Assam and Jammu, the discussions have clearly revealed that due to the involvement of multiple agents in these states, delays in the supply of foodgrain to the schools was a regular problem.

end{cases} (2.2) The following results are crucial in discussing regular problem for the linear case (for a proof see [1]).

Traffic jams on the M4 are a regular problem for businesses and commuters.

The fact is, says Gerald Knaus, the head of the European Stability Initiative think-tank, that today, Croatia is dealing with the same, regular problems as its Central European neighbours - such as an ageing population and economic problems "and that in itself is a success".