A (left) quotient of a language L by a word w is the language wL = {x | wx ∈ L}. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state complexity of L, which is the number of states in a minimal deterministic finite automaton accepting L. An atom of L is an equivalence class of the relation in which two words are equivalent if for each quotien...

Let L be a set of regular languages of A∗. An L-polynomial is a finite union of products of the form L0a1L1 · · · anLn, where each ai is a letter of A and each Li is a language of L. We give an explicit formula for computing the intersection of two L-polynomials. Contrary to Arfi’s formula (1991) for the same purpose, our formula does not use complementation and only requires union, intersectio...

This study was carried out to analyze the variations of Benzene, Toluene, and para- Xylene (BTp-X) present in the urban air of Delhi. These pollutants can enter into the human body through various pathways like inhalation, oral and dermal exposure posing adverse effects on human health. Keeping in view of the above facts, six different locations of Delhi were selected for the study during summe...

The x-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel x shapes in the plane. A subfamily of these graphs are {x, |,−}-contact graphs which are the contact graphs of axis parallel x, |, and − shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are x-intersection gra...

1 Stable 2-Pairs and (X; Y)-Intersection Graphs 2 Abstract Given two xed graphs X and Y , the (X; Y)-intersection graph of a graph G is a graph where 1. each vertex corresponds to a distinct induced subgraph in G that is iso-morphic to Y , and 2. two vertices are adjacent ii the intersection of their corresponding sub-graphs contains an induced subgraph isomorphic to X. This notion generalizes ...

In this paper, we investigate the problem of Boolean operation on circular-arc polygons. We present a concise and efficient method, in which the concept of related edges is introduced. Given two circular-arc polygons with M and N edges, respectively, the proposed method only takes O((l+k)∗ log l+M +N) time, where k is the number of intersection points, l is the number of related edges. The prop...

A closed Teichmüller geodesic in the moduli space Mg of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that for any L > 0 there exist R > ǫ > 0, independent of g, so that the L-short geodesics in Mg all lie in the intersection of the ǫ-thick part and the R-thin part. We also estimate the number of L-short geodesics in Mg, bounding this from above and below b...

The intersection between 3D objects plays a prominent role in spatial reasoning, geometric modeling and computer vision. Detection of possible intersection between objects can be based on the objects’ triangulated boundaries, leading to computing triangle-triangle intersection. Traditionally there are separate algorithms for cross intersection and coplanar intersection. There is no single algor...

Many geometric optimization problems in CAD/CAM can be reduced to a maximal intersection problem on the sphere: given a set of N simple spherical polygons on the unit sphere and a real number constant L # 2p; find an arc of length L on the unit sphere that intersects as many spherical polygons as possible. Past results can only solve this maximization problem for two very restricted special cas...

Functional Dependencies (or simply FDs) are by far the most common integrity constraint in the real world. When relations are incomplete and thus contain null values the problem of whether satisfaction is additive arises. Additivity is the property of the equivalence of the satisfaction of a set of functional dependencies (FDs), F, with the individual satisfaction of each member of F in an inco...