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Optimizing the profit from a complex cascade of hydroelectric stations with reci...
Korobeinikov, Andrei; Kovacec, Alexander; McGuinness, Mark; Pascoal, Marta; Pereira, Ana; Vilela, SóniaIn modern reversible hydroelectric power stations it is possible to reverse the turbine and pump water up from a downstream reservoir to an upstream one. This allows the use of the same volume of water repeatedly and was specifically developed for hydro-electric stations operating with insufficient water supply. Pumping water upstream is usually done at times of low demand for electricity, to build up reserves in ...
Optimizing the profit from a complex cascade of hydroelectric stations with rec...
Korobeinikov, Andrei; Kovacec, Alexander; McGuinness, Mark; Pascoal, Marta; Pereira, Ana I.; Vilela, SoniaIn modern reversible hydroelectric power stations it is possible to reverse the turbine and pump water up from a downstream reservoir to an upstream one. This allows the use of the same volume of water repeatedly and was speci cally developed for hydro-electric stations operating with in- su cient water supply. Pumping water upstream is usually done at times of low demand for electricity, to build up reserves i...
Diagonal minus tail forms and Lasserre's sufficient conditions for sums of squares
Fidalgo, Carla; Kovačec, AlexanderUsing our recent results on diagonal minus tail forms, we give an easily tested sufficient condition for a polynomial f(x) = P i2I fixi in IR[x] = IR[x1, . . . , xn], to be a sum of squares of polynomials (sos). We show that the class of polynomials passing this test is wider than the class passing Lasserre’s recent conditions. Another sufficient condition for f to be sos, like Lasserre’s piecewise linear in th...
Positive semidefinite diagonal minus tail forms are sums of squares
Fidalgo, Carla; Kovačec, AlexanderBy a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, ..., xn) = F(x) = D(x) − T(x), where the diagonal part D(x) is a sum of terms of the form bix2d i with all bi ≥ 0 and the tail T(x) a sum of terms ai1i2...inxi1 1 ...xin n with ai1i2...in > 0 and at least two i ≥ 1. We show that an arbitrary change of the signs of the tail terms of a positive semidefinite diagonal ...
On the corners of certain determinantal ranges
Kovačec, Alexander; Bebiano, Natália; Providência, João daLet A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define [Delta](A)=det(AoQ):Q[set membership, variant]SO(n), where o denotes the Hadamard product of matrices. For a permutation [sigma] on 1,...,n, define It is shown that if the equation z[sigma]=det(AoQ) has in SO(n) only the obvious solutions (Q=([epsilon]i[delta][sigma]i,j), [epsilon]i=±1 such that [epsi...
The Hankel Pencil Conjecture
Kovačec, Alexander; Gouveia, Maria CelesteThe Toeplitz pencil conjecture stated in [SS1] and [SS2] is equivalent to a conjecture for n £ n Hankel pencils of the form Hn(x) = (ci+j¡n+1); where c0 = x is an indeterminate, cl = 0 for l < 0; and cl 2 C¤ = Cn f0g; for l ¸ 1: In this paper it is shown to be implied by another conjecture, we call root conjecture. This latter claims for a certain pair (mnn;mn¡1;n) of submaximal minors of certain special Hn(x) ...
Convex hull calculations: a Matlab implementation and correctness proofs for th...
Kovacec, Alexander; Ribeiro, BernardeteThis paper provides full Matlab -code and informal correctness proofs for the lexicographic reverse search algorithm for convex hull calculations. The implementation was tested on a 1993 486-PC for various small and some larger, partially highly degenerate combinatorial polytopes, one of which (a certain 13- dimensional 24 vertex polyhedron) occurs naturally in the study of a well known problem posed by Profess...
The Marcus-de Oliveira conjecture, bilinear forms, and cones
Kovačec, AlexanderThe well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determinant det (X + Y) of the sum of normaln × n matricesX,Y to a certain region in the complex plane. Even the subconjecture obtained by specializing it ton = 4,X Hermitian andY normal is still open. We view the subconjecture as a special case of an assertion concerning a certain family of bilinear forms ofR16 ×C16 and give a...
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