Sentence examples similar to solutions proof from inspiring English sources

"With GuardTime's solution, proof depends solely on the data itself – free from the choice of storage device, third party validation, or well kept secrets or keys".

It can be easily proved that this sub-division algorithm can detect the border of two components within one data point shift from the optimal solution (proof not shown here).

Therefore, the modified physical prototype with the round solution proofed feasibility and efficiency of this approach.

Proof of Theorem 1.2for negative solutions: The proof for negative solutions can be carried out in a similar fashion by using t n < 0, defining − 1 + u n = − 1 + t n − 1 ( θ 1 ϕ 1 + u n ⊤ ) < 0, − 1 + v n = − 1 + t n − 1 ( θ 2 ϕ 1 + v n ⊤ ) < 0, and using − | s | α 2 instead of s α 1 in applying Fatou's lemma using (H4−) and reversing the inequalities appropriately.

Then, for each λ ∈ ] 2 d 2 2 ( b − a ) ∥ α ∥ L 1 ( [ a + b 2, b ] ) G ( d ), c 2 2 ( b − a ) ∥ α ∥ L 1 ( [ a, b ] ) G ( c ) [, problem (P1) admits at least two nonnegative weak solutions. Proof Our aim is to apply Corollary 3.1. To this end, we pick c 1 = 0 and c 2 = c.

We give the global existence of solutions without proof.

As shown in Table 1, only two solutions include Proof of Data Possession protocols.

We start with the local existence of strong solutions whose proof can be found in Theorem 1.1 of [16].

The most important analytical results of this work are summarized as a theorem of existence and uniqueness of non-negative and bounded numerical solutions, whose proof relies on the non-singularity property of M-matrices, and the fact that the entries of the inverses of these matrices are positive real numbers.

At the same time, Mr. Haddon writes with such sympathy, such understanding of Christopher's interior life, that he makes all his obsessions and needs into a mirror of our own cravings for safety and order, while turning Christopher's "detective story" into a bildungsroman that's not about finding solutions and proofs but about coming to terms with the disorder and betrayals of grown-up life.

If hypotheses (H1 - H2) are hold, then for every, (3.9) ( have a unique fuzzy solution. Proof. For each and, define by (3.10).