Sentence examples for due to uniqueness of from inspiring English sources

Due to uniqueness of minimum-norm element, we must have.

However, the structure elucidation is most challenging task mainly due to uniqueness of natural products and unexpected spectral patterns and the residual complexity frequently noticed.

To this end, consider X = ∑ j ∈ N 1 A j X j, where X j = ∑ i = 1 N λ i j X i and f ( X j ) = ∑ i = 1 N μ i j X i. Due to uniqueness of the coefficients in a conditional simplex, it holds that λ i = ∑ j ∈ N 1 A j λ i j, and due to locality of f, it follows that μ i = ∑ j ∈ N 1 A j μ i j.

Due to uniqueness of the coefficients (cf. (1.3)) in a conditional simplex, we have λ λ k + ( 1 − λ ) μ k = 1 A k for all k = 1, …, N. By means of 0 < λ < 1, it holds that λ λ k + ( 1 − λ ) μ k = 1 A k if and only if λ k = μ k = 1 A k. Since the last equality holds for all k, it follows that Y = Z = X.

Barriers to entry due to uniqueness of facility.

Our results differ from those of Kjaer et al. [ 2001]: the activation of the precuneus under subliminal conditions in our study might be due to uniqueness of the imagery effect of the word.

Among these methods, the retina provides a higher level of security for recognition due to uniqueness and the stability of the blood vessel pattern during one's life.

In spite of the limitations due to the uniqueness of the real case object of study, some specific issues dealing with spherical tanks were simultaneously addressed (sloshing, soil structure interaction, FE modeling), so providing a rational framework for the analysis of such special structures, particularly useful for practical purposes.

end{aligned} Straightforward computations show that the eigenfunction pair ((phi ^,psi^)) is a positive solution to problem (2.4) when (R_{0}^{D}=sqrt{A^). Due to the uniqueness of the principal eigenvalue of (2.4), one can obtain (2.7) immediately.

We further demonstrated that this non-uniform distribution of MMES is not due to the uniqueness of read mapping, as similar distributions were observed in both uniquely and non-uniquely matched junction reads, for both human and mouse datasets (Figure S2).

However, due to the uniqueness of electricity and the design of deregulated electricity markets this premium might be substantially higher than its optimal level.