Sentence examples for maximum principle that from inspiring English sources

Furthermore, we know by the strong maximum principle that on for all if.

It follows from the maximum principle that ((z_0^+,y_0^+)) is a positive solution of problem (1).

If w is not always a positive solution, then it follows from the maximum principle that (wequiv0).

It follows from the strong maximum principle that (frac{partial u^{partialeta}(x)<0) and (frac{partial v^{partialeta }(x)<0) for (xinpartialOmega), therefore, there exist (M>0) and (m>0) such that m v^(x leq u^(x leq M v^(x quadtext{for }xinoverline{Omega}.

First, it follows from (1.3), (1.7), and the maximum principle that (2.1).

From (49) we infer, using the maximum principle, that z n + 1 ≫ 0 in [ 0, 1 ].

For any appropriately sized unit vectors u, v, we have from the Cauchy-Schwartz inequality and the maximum modulus principle that begin{aligned} biglvert bigllangle u,T z) v bigrrangle bigrvert ^{2} le Vert uVert biglVert T z) v bigrVert le1.

In this paper, we have presented a new xor-haplotyping method XHSD based on the maximum parsimony principle that infers the haplotype pairs for each member of a group of unrelated individuals by observing their xor-genotypes.

Hence the maximum principle implies that u 1 ≫ 0, that is, α 0 ≪ α 1, in [ 0, 1 ].

which, together with the maximum principle, means that frac{partial u(x)}{partial n}< frac{partialalpha(x)}{partial n},quad xinpartialOmega, that is, alphaprec u.

Main results of our paper are based on the maximum boundaries principle, that is, on the fact that the maximal and minimal values of the solution can be achieved only at the points or The boundaries maximum principle in the case of the zero operator was considered in the recent papers [2, 3].