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It is shown that this least squares solution can be characterized by a linear matrix inequality minimization problem.
Cis keto-enol tautomers of dimethoxy curcuminoids in solution can be characterized by resonance-assisted intramolecular hydrogen bond and a low barrier potential well in the proton transfer pathway between two equivalent tautomeric forms.
Rheological measurements indicated that the Carbopol solution can be characterized by the power law (K=9, n=0.2) under the range of shear conditions (0.1 1000 s−1) expected near the impeller in the mixing tank.
It turns out that the condition for such a system without a nonzero solution can be characterized by a rank minimization problem, and thus the proposed approximation theory can be used to establish some sufficient conditions for the system to possess only zero solution.
It is clear that the solution can be characterized as u t,x)= int_{0}^{t} int_{mathbb{R}}p t-s,x-y)B(ds,dy), (1.2) here (p(t,x)=frac{1}{sqrt{4pint_{mathbb{R}}p t-s{4t}}) is the heat kernel of Lapalacian.
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For vector optimization, the optimality solutions can be characterized with the help of different geometrical concepts.
Oleinik [8] has shown that discontinuities of such admissible solutions can be characterized by the following condition: f u - f u L u - u L ≥ s ≥ f u - f u R u - u R. (2.7).
Along this fixed point branch, the two groups remain clustered; the excitatory cells also remain clustered, that is, the solution branch can be characterized by ((x_{E},x_{I1},x_{I1})).
In fact, if f is pseudomonotone on C, then for any x ∗ ∈ SOL ( C, f ), we have 〈 f ( x ), x − x ∗ 〉 ≥ 0, ∀ x ∈ C. Hence, it suffices to show that the solution set SOL ( C, f ) can be characterized as the intersection of a family of halfspaces.
These two different solutions for a fixed value of can be characterized via the roots of for.
These structures can be characterized by numerous solution techniques; the structures also can be inferred from atomic force microscopy of two-dimensional periodic arrays that the motifs form via cohesive interactions.
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CEO of Professional Science Editing for Scientists @ prosciediting.com