A bus oriented network where there is a charge for the amount of divisible load processed on each processor is investigated. A cost optimal processor sequencing result is found which involves assigning load to processors in nondecreasing order of the cost per load characteristic of each processor. More generally, one can trade cost against solution time. Algorithms are presented to minimize com...

Let [a, b] denote the integers between a and b inclusive and, for a finite subset X ⊆ Z, let diam (X) = max(X) − min(X). We write X <p Y provided max(X) < min(Y ). For a positive integer m, let f(m,m,m; 2) be the least integer N such that any 2-coloring ∆ : [1, N ] → {0, 1} has three monochromatic m-sets B1, B2, B3 ⊆ [1, N ] (not necessarily of the same color) with B1 <p B2 <p B3 and diam (B1) ...

One proves the existence and uniqueness of a generalized (mild) solution for nonlinear Fokker–Planck equation (FPE) u t ? ? ( ? ) + div D x b = 0 , ? ? R d ? 2 ? in where L 1 C is nondecreasing function, bounded, ? ; with strictly increasing, if not constant. Moreover, ? semigroup contractions which leaves invariant set probability density functions . If ? r | ? ? 3 then m > extends to initial ...

Grinberg defined Nyldon words as those which cannot be factorized into a sequence of lexicographically nondecreasing smaller words. He was inspired by Lyndon words, the same way except with "nondecreasing" replaced "nonincreasing." Charlier, Philibert, and Stipulanti proved that, like any word has unique factorization They also show that form right Lazard set, equivalently, Hall set. In this pa...

We consider the boundary value problem −∆pu = λ f (u) in Ω satisfying u = 0 on ∂Ω, where u= 0 on ∂Ω, λ > 0 is a parameter, Ω is a bounded domain in Rn with C2 boundary ∂Ω, and ∆pu := div(|∇u|p−2∇u) for p > 1. Here, f : [0,r] → R is a C1 nondecreasing function for some r > 0 satisfying f (0) < 0 (semipositone). We establish a range of λ for which the above problem has a positive solution when f ...

The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient λq(s), s ∈ [s0,∞) is investigated, where λ ∈ R and q(s) is a nondecreasing step function tending to ∞ as s → ∞. Let S denote the set of those λ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that S is an additive group. Four examples are given with S = {0}, S =...

We show that the emptiness problem for two-way nondeterministic finite automata augmented with one reversal-bounded counter (i.e., the counter alternates between nondecreasing and nonincreasing modes a fixed number of times) operating on bounded languages (i.e., subsets of w 1 : : : w k for some nonnull words w1; : : : ; wk) is decidable, settling an open problem in [11, 12]. The proof is a rat...