Lemma 2.2. It suffices to find disjoint L,R ∈ V such that they are (1) Large in Ω(n), or more formally stated, |L||R| ≥ α(n). (2) ∆-separated for ∆ = Ω( 1 logn) Let us define what ∆-separated means so that we can formalize this notion of “farness”. Recall that a distance from a vertex i to a set S is defined as d(i, S) = minj∈S d(i, j) (distance to the closest point in the set) and a distance f...

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

Twenty-nine soft tissue masses were studied with magnetic resonance imaging (MRI) which proved to be useful in the preoperative evaluation of these lesions. Other imaging modalities employed had significant limitations. Plain films were of little value because of the intrinsically low contrast of soft tissues. Angiography was not necessary unless MRI suggested a vascular lesion or proximity to ...

The generalization of binary operation in the classical algebra to fuzzy is an important development field algebra. paper proposes a new vector spaces over field, which called M-hazy field. Some fundamental properties spaces, and subspaces are studied, some results also proved. Furthermore, linear transformation studied their Finally, it shown that M-fuzzifying convex induced by subspace space.

This paper presents a fuzzy queuing location model for congested system. In a queuing system there are different criteria that are not constant such as service rate, service rate demand, queue length, the occupancy probability of a service center and Probability of joining the queue line. In this paper with fuzzifying all of these variables, will try to reach an accurate real problem. Finally w...

Cost and operation of inventory depends a great deal on what happens to demand when the system is out of stock. In real inventory systems, it is more reasonable to assume that part of the excess demand is backordered and the rest is lost. However, the amount of backorders (or lost sales) often incurs disturbance due to various uncertainties. To incorporate this reality, this article attempts to...

Giant cell tumours of the spine above the sacrum are rare, and may pose diagnostic and treatment difficulties. A patient with thoracic vertebral giant cell tumour in which soft tissue extension and proximity to the spine complicated management is described. Magnetic resonance imaging is the imaging modality of choice for determining the extent of disease, assisting preoperative management, and ...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

Percutaneous electrical nerve stimulation (PENS) and percutaneous neuromodulation therapy (PNT) are therapies that combine the features of electroacupuncture and transcutaneous electrical nerve stimulation (TENS). PENS is performed with a few needle electrodes while PNT uses very fine needle-like electrode arrays that are placed in close proximity to the painful area to stimulate peripheral sen...