where n ≥  is an integer, τ > , σ ≥ , d > c ≥ , b > a ≥ , r, P ∈ C([t,∞), (,∞)), P ∈ C([t,∞)× [a,b], (,∞)), Q ∈ C([t,∞), (,∞)), Q ∈ C([t,∞)× [c,d], (,∞)), f ∈ C(R,R), f is a nondecreasing function with xf (x) > , x = . The motivation for the present work was the recent work of Culáková et al. [] in which the second-order neutral nonlinear differential equation of the form [ ...

In this paper we study both the nonpreemptive and preemptive versions of the popular unit-time open shop scheduling problem. For the set of feasible schedules, we construct the linear description of the convex hull of the vectors of the job completion times. Based on the properties of the resulting scheduling polyhedron, we show that the problem of constructing an optimal schedule minimizing an...

We denote by (P ) the problem given by the equation (1), the boundary condition (2) and the initial condition (3). We assume that the function c satisfies the hypothesis (Hc) c is a continuous nondecreasing function such that c ′ ∈ Lloc(R); and that the initial condition u0 and the boundary data u D satisfy the hypotheses (H0) u0 ∈ L∞(Ω) and we define U0 := ‖u0‖L∞(Ω); (HD) u D is Lipschitz cont...

Existence of solutions of differential and integral equations is subject of numerous investigations see, e.g., the monographs 1–3 or 4 . Moreover, a lot of work in this domain is devoted to the existence of solutions in certain special classes of functions e.g., positive functions or monotone functions . We merely mention here the result obtained by Caballero et al. 5 concerning the existence o...

In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation   2 | | = ( ) ( ) ( ) ( ) m div u u p x f u q x g u     are established, where 2 m  , f and g are nondecreasing and vanish at the origin. The locally H older continuous functions p and q are nonnegative. We extend results previously obtained for special cases of f a...

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 for some nonnull words ) is decidable, resolving a problem left open in [4,7]. The proof is a rather involved reduction to ...

Proof is offered that s approximately ig for all forms of selection where fitness is a nondecreasing function of a normally distributed phenotype (called fitness potential); s is selection coefficient, i is standard selection differential, and g is standard differential effect of a locus genotype.Evidence is presented that the cost of selection does not limit genic polymorphism; that truncation...

For a probability measure P on R and n∈N consider en = inf ∫ min a∈α V (‖x−a‖)dP (x) where the infimum is taken over all subsets α of R with card(α) ≤ n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n-asymptotics of en for nonsingular and for (singular) self-similar distributions P and we find the asymptotic performance of optimal quantizers using weig...

A Boolean function f : {0, 1} 7→ {0, 1} is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make Ω( d log d ) queries. This result improves upon the Ω( d log2 d ) lower bound for the same class of testers due to Chen et al. (STOC, 2017).

We show that for every nondecreasing concave function ω : [0,∞) → [0,∞) with ω(0) = 0, either every finite metric space embeds with distortion arbitrarily close to 1 into a metric space of the form (X,ω◦d) for some metric d on X, or there exists α = α(ω) > 0 and n0 = n0(ω) ∈ N such that for all n > n0, any embedding of {0, . . . , n} ⊆ R into a metric space of the form (X,ω ◦ d) incurs distorti...