Consider the following weighted digital sum (WDS) variant: write integer n as n = 21 + 22 + · · · + 2k with i1 > i2 > · · · > ik ≥ 0 and set WM (n) := ∑k t=1 t 2t . This type of weighted digital sum arises (when M = 1) in the analysis of bottom-up mergesort but is not “smooth” enough to permit a clean analysis. We therefore analyze its average TWM (n) := 1 n ∑ j<n WM (j). We show that TWM (n) h...

Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...

We study policies aiming to minimize the weighted sum of completion times of jobs in the context of coordination mechanisms for selfish scheduling problems. Our goal is to design local policies that achieve a good price of anarchy in the resulting equilibria for unrelated machine scheduling. In short, we present the first constant-factor-approximate coordination mechanisms for this model. First...

In this paper we obtain the bound on the average sensitivity of the weighted sum function. This confirms a conjecture of Shparlinski. We also compute the weights of the weighted sum functions and show that they are almost balanced.

In this paper we obtain the bound on the average sensitivity of the weighted sum function. This confirms a conjecture of Shparlinski. We also compute the weights of the weighted sum functions and show that they are almost balanced.

Let A(D) denote the disk algebra and uCφ be the weighted composition operator on A(D). In this paper, we characterize the compactness of sum of weighted composition operators on A(D). Furthermore, we also find the norm of sum of weighted composition operators on A(D). Mathematics Subject Classification: 47B33

We consider single facility location problems with equity measures, de0ned on networks. The models discussed are, the variance, the sum of weighted absolute deviations, the maximum weighted absolute deviation, the sum of absolute weighted di2erences, the range, and the Lorenz measure. We review the known algorithmic results and present improved algorithms for some of these models. ? 2002 Elsevi...