Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Most of the organizations publish micro data for a variety of purposes including demographic and public health research. To protect the anonymity of the entities, data holders often remove or encrypt explicit identifiers. But, released information often contains quasi identifiers, which leak valuable information. Samarati and Sweeney introduced the concept of k-anonymity to handle this problem ...

In this paper we consider planar L-shaped embeddings of trees in point sets, that is, planar drawings where the vertices are mapped to a subset of the given points and where every edge consists of two axis-aligned line segments. We investigate the minimum number m, such that any n vertex tree with maximum degree 4 admits a planar L-shaped embedding in any point set of size m. First we give an u...

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

techniqlle of1eastabsolllt~id~viationsa..l) is investigated in twQ-way tables. The.• characterization.ofthe(oftennon-unique)LlSOllltions~tintwo-\Vay tables given by Kemperman (1984) and the graph inSiegel (1983) are exploited to prove several results. When all cells have an odd number of replicates, unique non-degenerate Ll solutions are possible only when the factor with fewer levels has an od...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

Competitive Searching in Polygons Beyond Generalised Streets p. 32 Finding a Shortest Pair of Paths on the Plane with Obstacles and Crossing Areas p. 42 Logspace Verifiers, NC, and NP p. 52 Structure in Average Case Complexity p. 62 Some Geometric Lower Bounds p. 72 The I/O-Complexity of Ordered Binary-Decision Diagram Manipulation p. 82 Two Arc Disjoint Paths in Eulerian Diagraphs p. 92 Findin...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

 Rosemary (Rosmarinus officinalis L.) is an important medicinal plant that contained a wide range of secondary metabolites such as rosmarinic acid. In this study, essential oil content and composition and rosmarinc acid were determined at three phenological stages (before flowering, full flowering and fruit set stages). Hydro distillation method was used for essential oil extraction and GC and ...