We consider a problem to schedule a set of jobs on a singlemachine under the constraint that the maximum job completion timedoes not exceed a given limit. Before a job is released for processing, itmust undergo some preprocessing treatment which consumes resources.Itis assumed that the release time of a job is a positive strictly decreasingcontinuous function of the amou...

Many papers and books on fractional differential equations have appeared recently. Most of them are devoted to the solvability of the linear fractional equation in terms of a special function see, e.g., 1, 2 and to problems of analyticity in the complex domain 3 . Moreover, Delbosco and Rodino 4 considered the existence of a solution for the nonlinear fractional differential equation D 0 u f t,...

A notion of asymptotic Hamming distance suitable for the study of algorithmic randomness is developed. As an application of this notion, it is shown that there is no fixed procedure that computes a Mises-WaldChurch stochastic set from a complex set. Here a set is complex if its prefixes have Kolmogorov complexity bounded below by an unbounded, nondecreasing computable function.

It is known that if a predictable nondecreasing process generates a bounded potential, then its final value satisfies the Garsia inequality. We prove the converse, that is, a random variable satisfying the Garsia inequality generates a bounded potential. We also propose some useful relations between the Garsia inequality and the Cramer conditions, and different ways how to construct a potential.

We present a new comparison principle by introducing a notion of upper quasi-monotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle.

Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the Riemann–Stieltjes integral with a convex integrand and monotone nondecreasing integrator. Results are deduced for the special case of weighted Riemann integrals. Mathematics subject classification (2000): Primary 26D15, Secondary 26D10..

We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.

We study subsets of [1, x] on which the Euler φ-function is monotone (nondecreasing or nonincreasing). For example, we show that for any > 0, every such subset has size < x, once x > x0( ). This confirms a conjecture of the second author.

An example is presented to show that the worst case complexity of Bertsekas small label rst strategy for the shortest path problem is exponential It becomes polynomial if when scanning a node i its successors j i are examined in the nondecreasing order of dij the distance between i and j

Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.