Abstract A family of bivariate copulas given by: for v + 2 u < v+2u\lt 2 , C ( , ) = F − 1 ∕ C\left(u,v)=F\lef...

The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each of these problems is trivially unbounded when the number of sides is even. We show that when this number is odd, the optimal solution to these three problems is identical, and arbitrarily close to a trapezoid. The paper also considers the ...

Hain’s trapezoidation algorithm is a fast, practical algorithm for the reduction of simple polygons into horizontally aligned trapezoids partitioned into a minimal collection of trapezoid sequences. An extension to this algorithm is described which allows trapezoidation of simple polygons with an arbitrary number of non-intersecting holes. The minimal computational cost per hole is a traversal ...

Given a simple graph G = (V, E) and a fixed positive integer k. In a graph G, a vertex is said to dominate itself and all of its neighbors. A set D ⊆ V is called a k-tuple dominating set if every vertex in V is dominated by at least k vertices of D. The k-tuple domination problem is to find a minimum cardinality k-tuple dominating set. This problem is NP-complete for general graphs. In this pap...

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of minimum vertex covers (or independent sets), as well as the total number of vertex covers, and reduce the time complexity from O(n) to O(n log n), where n is the...

In his 1998 paper, Ryan classified the sets of unit, proper, and plain trapezoid and parallelogram orders. We extend this classification to include unit, proper, and plain triangle orders. We prove that there are 20 combinations of these properties that give rise to distinct classes of ordered sets, and order these classes by containment. Mathematics Subject Classifications (2000) 06A06, 05C62

Using (1.1), the authors obtained estimations of error for the mid-point, trapezoid, and Simpson quadrature formulae. They also gave applications of the mentioned results in numerical integration and for special means. In this paper, we establish two perturbations of (1.1). Using the perturbations, we derive some new error bounds for the mid-point, trapezoid, and Simpson quadrature formulae. Si...

Let G be a graph. A component of G is a maximal connected subgraph in G. A vertex v is a cut vertex of G if κ(G− v) > κ(G), where κ(G) is the number of components in G. Similarly, an edge e is a bridge of G if κ(G− e) > κ(G). In this paper, we will propose new O(n) algorithms for finding cut vertices and bridges of a trapezoid graph, assuming the trapezoid diagram is given. Our algorithms can b...

This letter presents a low power CMOS pulse generator based on spectral efficiently gated oscillator for multiband impulse radio ultra-wideband (UWB) system. The pulse generator is based on an on/off switched LC oscillator with the trapezoid switching pulse. By using trapezoid pulse for on/off switching signal of the oscillator, better output spectral characteristic can be achieved without addi...