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We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length. Examples of these universally optimal codes include Hamming, Golay, and Reed-Solomon codes, among many others, and this helps to explain...
This paper presents a probabilistic numerical approach for stability analysis of soil and rock slopes. The slope is divided into a family of inclined slices, and according to the upper bound theorem in plasticity theory, a work-energy balance equation is constructed for each soil/rock slice. Geotechnical parameters such as the cohesion, the friction angle and the pore pressure ratio etc. are modelled...
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