a) Language L1 can be shown to be non-regular using the pumping lemma. Assume for contradiction that L1 is regular and let p be the corresponding pumping length. Choose w to be the word 01101. Because w is an element of L1 and has length more than p, the pumping lemma guarantees that w can be split into three parts, w = xyz, where |xy| ≤ p and for any i ≥ 0, we have xyz ∈ L1. In order to obtain...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

With the advent of XML as a standard for data representation and exchange on the Internet, storing and querying XML data becomes more and more important. Several XML query languages have been proposed, and the common feature of the languages is the use of regular path expressions to query XML data. This poses a new challenge concerning indexing and searching XML data, because conventional appro...

Phenotypic traits of lichens can be greatly modified by environmental factors. Granulose thalli on soil and podetia, densely covered with granules, referring to common and widespread lichen Cladonia cervicornis subsp. verticillata were found near zinc smelter. The granules are stratified, filled with fungal medulla and heavily encrusted with calcium oxalate weddellite crystals, not observed on ...

We present a new algorithm for efficient learning of regular languages from examples and queries. A reliable teacher who knows the unknown regular grammar G (or is able to determine if certain strings are accepted by the grammar) will guide the learner in achieving the goal of inferring an equivalent grammar $\mbox{G}^{*}$. The teacher provides the learner with a structurally complete set of po...

A kernel-trace description of right congruences on an inverse semigroup is developed. It is shown that the trace mapping is a complete nhomomorphism but not a V-homomorphism. However, the trace classes are intervals in the complete lattice of right congruences. In contrast, each kernel class has a maximum element, namely the principal right congruence on the kernel, but in general there is no m...

In this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order we introduced in [ETNA, Vol.37, pp.189–201, 2010]. Among all the mixed finite element spaces having optimal order of convergence on quadrilateral grids, this space has the smallest unknowns. However, the scalar variable is only suboptimal in general; thus we have employed a post-processin...

This paper proposes a mortar finite element method for solving the two-dimensional second-order elliptic problem with jumps in coefficients across the interface between two subregions. Non-matching finite element grids are allowed on the interface, so independent triangulations can be used in different subregions. Explicitly realizable mortar conditions are introduced to couple the individual d...

The purpose of this paper is to propose a proof for the PoincaréFriedrichs inequality for piecewise H1 functions on anisotropic meshes. By verifying suitable assumptions involved in the newly proposed proof, we show that the Poincaré-Friedrichs inequality for piecewise H1 functions holds independently of the aspect ratio which characterizes the shape-regular condition in finite element analysis...