As most robust combinatorial min-max and min-max regret problems with discrete uncertainty sets are NP-hard, research in approximation algorithm and approximability bounds has been a fruitful area of recent work. A simple and well-known approximation algorithm is the midpoint method, where one takes the average over all scenarios, and solves a problem of nominal type. Despite its simplicity, th...

Variational symmetry is a property of Hamiltonian control systems. It is the basis for learning optimal control. In order to apply a continuous-time control strategy to a real plant, we need to discretize the data with respect to time. This paper investigates the variational symmetry for the discretized Hamiltonian systems. It is proved that the discretization based on the midpoint rule preserv...

Abstract In this paper, we first obtain an identity for differentiable mappings. Then, establish some new generalized inequalities convex functions involving parameters and fractional integrals. We show that these results reduce to several Simpson-, midpoint- trapezoid-type inequalities. The given in study are the generalizations of proved earlier papers.

We use the Wong–Zakai approximation as an intermediate step to derive numerical schemes for stochastic delay differential equations. By approximating the Brownian motion with its truncated spectral expansion and then using different discretizations in time, we present three schemes: a predictor-corrector scheme, a midpoint scheme, and a Milstein-like scheme. We prove that the predictor-correcto...

Algorithmic regularization uses a transformation of the equations of motion such that the leapfrog algorithm produces exact trajectories for two-body motion as well as regular results in numerical integration of the motion of strongly interacting few-body systems. That algorithm alone is not sufficiently accurate and one must use the extrapolation method for improved precision. This requires th...

The properties of Cpmk in the presence of asymmetric specification limits are discussed. It is shown that Cpmk tends to zero as the process variation increases and vice versa. Furthermore, if the process variation is small, Cpmk has its maximum near the target value but the maximum moves towards the specification midpoint as the variation increases. This is a desirable property as for large var...

The obligate methylotroph Methylophilus methylotrophus contains three distinct soluble cytochromes c. The major cytochromes, cytochrome cH (about 50% of the total) and cytochrome cL (about 42%), were similar in most respects to the cytochromes cH and cL of the facultative methylotroph Pseudomonas AM1 [O'Keeffe & Anthony (1980) Biochem. J. 192, 411-419]. Cytochrome cH had a high isoelectric poin...

Midpoint filter is quite effective in recovering the images confounded by the short-tailed (uniform) noise. It, however, performs poorly in the presence of additive long-tailed (impulse) noise and it does not preserve the edge structures of the image signals. Median smoother discards outliers (impulses) effectively, but it fails to provide adequate smoothing for images corrupted with nonimpulse...