To verify the periodic boundary condition (PBC) treatment which was implemented in a TRI-angle elements induced numerical analyzer (TRIAINA), the pressure tube creep problem is chosen and examined with three cases of ...
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To verify the periodic boundary condition (PBC) treatment which was implemented in a TRI-angle elements induced numerical analyzer (TRIAINA), the pressure tube creep problem is chosen and examined with three cases of normal, 2.5% creep, and 5.0% creep on the aspects of the multiplication factor and relative pin power. The McCARD code is used for the homogenized group constants generation. It is shown that the differences are nearly negligible for the pressure tube creep problem.
Subsets of \mathbb{F}_2^n\mathbb{F}_2^n that are \varepsilon\varepsilon-biased, meaning that the parity of any set of bits is even or odd with probability \varepsilon\varepsilon close to 1/21/2, are powerful tools for...
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Subsets of \mathbb{F}_2^n that are \varepsilon-biased, meaning that the parity of any set of bits is even or odd with probability \varepsilon close to 1/2, are powerful tools for derandomization. A simple randomized construction shows that such sets exist of size O(n/\varepsilon^2), and known deterministic constructions achieve sets of size O(n/\varepsilon^3), O(n^2/\varepsilon^2), and O((n/\varepsilon^2)^{5/4}). Rather than derandomizing these sets completely in exchange for making them larger, we attempt a partial derandomization while keeping them small, constructing sets of size O(n/\varepsilon^2) with as few random bits as possible. Equivalently, we construct small ensembles of error-correcting codes, most of which meet the Gilbert--Varshamov bound. The naive randomized construction requires O(n^2/\varepsilon^2) random bits. We give two constructions. The first uses Nisan's space-bounded pseudorandom generator to partly derandomize the classic Wozencraft ensemble of error-correcting codes and requires O(n \log (1/\varepsilon))
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