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The reason is that, in this case, ({e^{2kipi}/sqrt{pi } }) is not an orthonormal basis because there exists a weight cosα in (2.13).
Given a concept space (mathfrak {C}), there exists a weight matrix W i satisfying forall u,v mathrm{d}(boldsymbol{v_{u}},boldsymbol{v_{v}}) = |boldsymbol{W_{i}}cdot boldsymbol{v_{u}}^{mathrm{T}},boldsymbol{{W_{i}}cdot boldsymbol{v_{v}}^{mathrm{T}}|_{2} if rank(A)=rank(B =N.
Supported solutions are then defined as those solutions for which there exists a weight vector, with strictly positive weights, such that they are optimal for the associated single-objective projected problem.
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There exists a maximum weight matching in which all the added edges form reverse complementary pairs.
Proposition 2 There exists a maximum weight matching in which all the added edges form reverse complementary pairs.
Suppose there exists a clique of weight C* in G. Then a vertex u, whose participation in any possible clique in G reduces the weight of that clique below C*, is incompatible with the optimal alignment and can be safely eliminated (similar to [ 36]).
In this paper we shall prove that there exists a class of weights, slightly larger than Ap, with the following property: If an operator T Lp0,1 u)→Lp0,∞ u) is bounded, for some p0>1 and every u in this class then, for every u∈A1,.
A metric d defined over the leaf-set L (t ) of a tree t is t -additive (or additive w.r.t t ), if there exists a positive edge-weighting function w : E (T ) → R +, such that for each i, j ∈ L (t ), D (i, j ) = ∑ e ∈ pat h T (i, j ) w (e ).
Therefore, the recommendation (class I, level of evidence A) exists for a weight reduction of overweight or obese individuals who have not undergone any cardiovascular event.
There exists a considerable literature in which weight scaled by height (body mass index, BMI) is used as a proxy for socially defined physical attractiveness.
Although there exists a wide range of gestational weight gain guidelines by different countries throughout the world, almost half of the countries had similar IOM guidelines [ 7].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com