We derive a new upper bound on the rate distortion function for arbitrary memoryless sources, which is based on the relation between mutual information and minimum mean-square error discovered by Guo et al. This upper bound is in general tighter than the well known upper bound given by the rate distortion function of a Gaussian source with an equal variance found by Shannon and becomes tight fo...

Abstract Many philosophers have raised difficulties for any attempt to proportion punishment severity crime seriousness. One reason this may be that offering a full theory of proportionality is simply too ambitious. I suggest more modest project: setting lower bound on proportionate punishment. That is, metric measure when not disproportionately severe. claim severe if it imposes costs criminal...

in this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/i/etmax). due to the time complexity function, this sequencing problem belongs to a class of np-hard ones. thus, a special design of a simulated annealing (sa) method is applied to solve such a hard problem. to comp...

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

In this paper, we considered solving approaches to flexible job shop problems. Makespan is not a good evaluation criterion with overlapping in operations assumption. Accordingly, in addition to makespan, we used total machine work loading time and critical machine work loading time as evaluation criteria. As overlapping in operations is a practical assumption in chemical, petrochemical, and gla...

It is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎Also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

In this paper, the sphere packing bound of Fano, Shannon, Gallager and Berlekamp and the zero-rate bound of Berlekamp are extended to general classical-quantum channels. The upper bound for the reliability function obtained from the sphere packing coincides at high rates, for the case of pure state channels, with a lower bound derived by Burnashev and Holevo [21]. Thus, for pure state channels,...

Upper bounds on Newton’s, Poisson’s, and energetic coefficients of normal restitution for the frictional impact of rigid pendulum against a fixed surface are derived, demonstrating that the upper bound on Newton’s coefficient is smaller than 1, while the upper bound on Poisson’s coefficient is greater than 1. The upper bound on the energetic coefficient of restitution, which is a geometric mean...

Some issues with Forney’s upper and lower bounds for the symbol error probability in systems with memory (e.g., intersymbol interference channels) have been pointed out in the literature. We expound on these issues. For the upper bound, we show that, although the most commonly cited proofs are not logically consistent, the bound is true for more general conditions. The reasoning leading to the ...