this paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. an upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. the theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads n...

Job-Shop Scheduling (JSS) problems are among the more difficult to solve in the class of N P -complete problems. The only successful approach has been Branch-and-Bound based algorithms, but such algorithms depend heavily on good bound functions. Much work has been done to identify such functions for the JSS problem, but with limited success. Even with recent methods, it is still not possible to...

During the past few decades, a number of methods for selection of input-output pairings for decentralized control have been proposed. Most of these available methods require evaluation of every alternative in order to find the optimal pairings. As the number of alternatives grows rapidly with problem size, pairing selection through an exhaustive search can be computationally forbidding for larg...

The following full text is a preprint version which may differ from the publisher's version. Abstract: We study the critical probability p c (M) in two-dimensional M-adic fractal percolation. To find lower bounds, we compare fractal perco-lation with site percolation. Fundamentally new is the construction of an computable increasing sequence that converges to p c (M). We prove that p c (2) > 0....

Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster convergence of restarting APG method relies on the potentially unknown constant in QGC to appropriately restart APG, which restricts its app...

1 Basic inequality For any real numbers ρ d satisfying ρ 1 = 1, and for any natural number m, we have d|m µ(d) d|m ρ d 2 = e|m λ e , λ e = [d 1 ,d 2 ]=e ρ d 1 ρ d 2. Our goal is to optimize the choice of (ρ d) d1. Let m = (n, P (z)), multiply by a n and sum over n using (g): say. Minimizing XG + R is quite difficult. However, if we restrict the support of ρ to d √ D, it is relatively easy to mi...

In this paper, we extend reduced-basis output bound methods developed earlier for elliptic problems, to problems described by parametrized parabolic partial differential equations. The essential new ingredient and the novelty of this paper consist in the presence of time in the formulation and solution of the problem. First, without assuming a time discretization, a reduced-basis procedure is p...

When artifical neural networks (ANN) are used in the prediction problems, it is usually desirable that some form of confidence bound is placed on the predicted value. Methods to estimate the confidence bound are available. However, these methods are valid under certain assumptions, which are rarely satisfied in practice. The behavior of the estimated confidence bound are not well understood whe...