27,483 research outputs found
Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation
Hydro-thermal coordination is the problem of determining the optimal economic
dispatch of hydro and thermal power plants over time. The physics of
hydroelectricity generation is commonly simplified in the literature to account
for its fundamentally nonlinear nature. Advances in convex relaxation theory
have allowed the advent of Shor's semidefinite programming (SDP) relaxations of
quadratic models of the problem. This paper shows how a recently published SDP
relaxation is only exact if a very strict condition regarding turbine
efficiency is observed, failing otherwise. It further proposes the use of a set
of convex envelopes as a strategy to successfully obtain a stricter lower bound
of the optimal solution. This strategy is combined with a standard iterative
convex-concave procedure to recover a stationary point of the original
non-convex problem.Comment: Submitted to IEEE PES General Meeting 201
Dimension minimization of a quantum automaton
A new model of a Quantum Automaton (QA), working with qubits is proposed. The
quantum states of the automaton can be pure or mixed and are represented by
density operators. This is the appropriated approach to deal with measurements
and dechorence. The linearity of a QA and of the partial trace super-operator,
combined with the properties of invariant subspaces under unitary
transformations, are used to minimize the dimension of the automaton and,
consequently, the number of its working qubits. The results here developed are
valid wether the state set of the QA is finite or not. There are two main
results in this paper: 1) We show that the dimension reduction is possible
whenever the unitary transformations, associated to each letter of the input
alphabet, obey a set of conditions. 2) We develop an algorithm to find out the
equivalent minimal QA and prove that its complexity is polynomial in its
dimension and in the size of the input alphabet.Comment: 26 page
High-field Electron Spin Resonance of Cu_{1-x}Zn_{x}GeO_{3}
High-Field Electron Spin Resonance measurements were made on powder samples
of Cu_{1-x}Zn_{x}GeO_{3} (x=0.00, 0.01, 0.02, 0.03 and 0.05) at different
frequencies (95, 110, 190, 220, 330 and 440 GHz) at low temperatures. The
spectra of the doped samples show resonances whose positions are dependent on
Zn concentration, frequency and temperature. The analysis of intensity
variation of these lines with temperature allows us to identify them as
originating in transitions within states situated inside the Spin Peierls gap.
A qualitative explanation of the details of the spectra is possible if we
assume that these states in the gap are associated with "loose" spins created
near the Zn impurities, as recently theoreticaly predicted. A new phenomenon of
quenching of the ESR signal across the Dimerized to Incommensurate
phase-boundary is observed.Comment: 4 pages, 5 ps figures in the text, submitted to Phys. Rev. Let
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