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The structure uncertainty optimization problem is usually treated as double-loop optimization process, which is computation-intensive. In this paper, an efficient interval uncertainty optimization approach based on Quasi-sparse response surface (QSRS) is proposed for structure uncertainty optimization. In which, 1) with l_1 norm and l_2 norm penalty method, a few appropriate basis functions are selected form a large number of basis functions to construct QSRS accurately and only a few sampling points is required, 2) as the orthogonal chebyshev polynomials is employed as QSRS basis functions, the local uncertainty can be evaluated by the combination of QSRS and interval arithmetic. Hence, the inner optimization process is eliminated. One mathematical problem and one engineering problem are used to validate the efficiency of the proposed approach. The results show that only 25% sampling points is needed than recently published approach., Comment: l_1 norm and l_2 norm penalty, Uncertainty optimization, Quasi-sparse response surface, Interval uncertainty

The radiation symmetry and laser-plasma instabilities (LPIs) inside the conventional cylindrical hohlraum configuration are the two daunting challenges on the approach to ignition in indirectly driven inertial confinement fusion. Recently, near-vacuum cylindrical hohlraum (NVCH), octahedral spherical hohlraum (SH) and novel three-axis cylindrical hohlraum (TACH) were proposed to mitigate these issues. While the coupling efficiency might still be a critical risk. In this paper, an advanced three-axis elliptical hohlraum (TAEH) is proposed to make a compromise among these hohlraum performance. Preliminary simulations indicate that the TAEH (with a case-to-capsule ratio, CCR=2.8) could provide excellent radiation symmetry during the thorough laser pulse of the high-foot drive, comparable to the ones inside the SH (CCR=5.1) and TACH (CCR=2.2). The filling time of plasma affecting the LPIs is between those of SH and TACH, and about 1.5 times of that in the ignition hohlraum Rev5-CH of NIC and close to the one inside the NVCH (CCR=3.4). In particular, the coupling efficiency is about 22%, 29% and 17% higher than the one inside the NVCH, SH and TACH, respectively. It would be envisioned that the proposed hohlraum configuration merits consideration as an alternative route to indirect-drive ignition, complementary to the traditional cylindrical hohlraum and the proposed recently novel hohlraums.

Carpi (1993) and Lepisto (1994) proved independently that smooth words are cube-free for the alphabet {1, 2}, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. In this paper, we first establish the derivative formula of the concatenation of two smooth words and power derivative formula of smooth words over arbitrary 2-letter alphabets. Then by making use of power derivative formula, for arbitrary 2-letter alphabet {a, b} with a, b being positive integers and a