Sentence examples for addition the proofs of from inspiring English sources

In addition, the proofs of Theorem 2.1 and Theorem 2.2 are shorter than those of Theorem 1.3 and Theorem 1.4 because we never use Lemma 1.8, but Theorem 1.3 and Theorem 1.4 are strongly dependent on this lemma.

In addition, the proofs of our results are quite different from those of some known results since a given pair of elements in a Banach algebra may not be compared.

In addition, the proof-of-concept applications that were demonstrated in the last decade for rolled-up and template-based microjets will be discussed.

Therefore, the study design was able to provide some interesting information in addition to the proof-of-principle of the SDA method.

In addition the proof of the safety concept of the application can only be achieved via costly tests and set-ups in labs and tracks.

In addition, the proof of the discrete energy conservation is an open problem.

In addition, the proof of Theorem 2.8 is simpler than the one of Theorem 1.7 because it ignores Lemma 1.8, but Theorem 1.7 depends on this lemma utterly.

In addition, the proof of Corollary 3.2 originates from the existence of maximal elements in noncompact Hadamard manifolds, while the authors of [25] used the KKM property to prove their result.

In addition the proof of our theoretical conclusion we have done an extensive simulation for higher-order adaptive modulation such as QPSK and QAM. Figure 4 shows the scattered noisy signals from which the digital information has been reproduced.

In addition, the proof of concept for NIPD of fetal microdeletion syndromes via sequencing has recently been described [ 97].

Altogether, we have demonstrated the feasibility of the template-directed incorporation of the 3′-terminated dye-labelled nucleotides 2– 5 that can be cleaved in one step to enable the next addition, thus providing the proof-of-principle of a functional system also targeted to run in cyclic mode.