In one of their papers, F. Gécseg and B. Imreh gave a characterization for monotone string languages by regular expressions. It has turned out that the monotone string languages are exactly those languages that can be represented by finite unions of seminormal chain languages. In this paper a similar characterization is given for monotone DR-languages.

We prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a quest...

A crossing-free straight-line drawing of a graph is monotone if there is a monotone path between any pair of vertices with respect to some direction. We show how to construct a monotone drawing of a tree with n vertices on an O(n) × O(n) grid whose angles are close to the best possible angular resolution. Our drawings are convex, that is, if every edge to a leaf is substituted by a ray, the (un...

r down tò 2 , it is a weakly monotone increasing function. But in a monotone function, a value can only appear once (or in one continuous range). Since the function is divided into two weakly monotone regions, a xed value can appear at most twice (or in two continuous ranges). This suuces to show that there can be at most two intersections between (I r) and O r , one in each weakly monotone reg...

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory,...

In this paper, we give two explicit examples of unbounded linear maximal monotone operators. The first unbounded linear maximal monotone operator S on l is skew. We show its domain is a proper subset of the domain of its adjoint S∗, and −S∗ is not maximal monotone. This gives a negative answer to a recent question posed by Svaiter. The second unbounded linear maximal monotone operator is the in...

We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and coneto-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (...

The paper presents an economical model for double variable acceptance sampling with inspection errors. Taguchi cost function is used as acceptance cost while quality specification functions are normal with known variance. An optimization model is developed for double variables acceptance sampling scheme at the presence of inspection errors with either constant or monotone value functions. The m...

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distributio...