We consider the scalar equation ẋ(t)+ m ∑ j=1 aj(t) ∫ h 0 x(t − s)dr j(s) = 0 (h = const > 0, ẋ = dx/dt), where r j(s) are nondecreasing functions. Besides, we do not require that aj(t) are positive for all t 0 . So the function z+ m ∑ j=1 aj(t) ∫ h

If the first lower symmetric derívate of a continuous function is nonnegative, then it is nondecreasing. If the second lower symmetric derívate of a continuous function is nonnegative, then it is convex. In this paper it is shown that if continuity is replaced by Baire one, Darboux in each of these, then the resulting statements are true.

This paper studies the global output convergence of a class of recurrent neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying inputs. We establish two sufficient conditions for global output convergence of this class of neural networks. Symmetry in the connection weight matrix is not required in the pres...

We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.

and Applied Analysis 3 Ma and Xu 15 also applied the fixed point theorem in cones to obtain some results on the existence of generalized positive solutions. It is the purpose of this paper to show some new results on the existence and multiplicity of generalized positive solutions of 1.4 , 1.8 by Dancer’s global bifurcation theorem. To wit, we get the following. Theorem 1.3. Let h : 2 → 0,∞ , f...

This paper considers the consequences of an avoidable risk of irreversible environmental catastrophe for society’s optimal long-run consumption/pollution tradeoffs. The risk is assumed to be a nondecreasing function of pollution concentration which evolves as a dynamic environmental renewal process. The main objective of the paper is to derive qualitative insights regarding the effects of such ...

Let Ω be an open subset of R where 2 ≤ n ≤ 7; the reason for restriction on n is that our work will make use of the regularity theory for area minimizing hypersurfaces. Let s ∈ L∞(Ω), let γ : [0,∞) → [0,∞) be zero at zero, nondecreasing and convex and for f ∈ L∞(Ω) let

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant , there exists a polynomial-time approximation algorithmwith an asymptotic worst-case performance ratio of no more than 1 + .

In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open ...

We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreasing sequences. Striking complex analogues are presented. The inequalities on the real domain are used to derive new integral inequalities related to those of Gauss– Pólya type.