Let T be a unit equilateral triangle, and T1, . . . , Tn be n equilateral triangles that cover T and satisfy the following two conditions: (i) Ti has side length ti (0 < ti < 1); (ii) Ti is placed with each side parallel to a side of T . We prove a conjecture of Zhang and Fan asserting that any covering that meets the above two conditions (i) and (ii) satisfies ∑n i=1 ti ≥ 2. We also show that ...

Evidence-based treatments and preventive interventions in the child and family area have not met with widespread adoption by practitioners. Despite the high prevalence of child behavioral and emotional problems, many parents and families in need are not receiving or participating in services, and when they do, the most efficacious interventions are not what is usually provided. Simultaneously a...

Cellular manufacturing (CM) is one of the most important subfields in the design of manufacturing systems and as a recently emerged field of study and practice, virtual cellular manufacturing (VCM) inherits the importance from CM. One type of VCM problems is VCM with alternative processing routes from which the route for processing each part should be selected. In this research, a bi-objective ...

This paper describes an instant formation method of uniform-sized proteoliposomes for membrane protein assays using fluorescence microscopy. The applied electrospray technique was the same as our previous works [1], although here we directly sprayed proteovesicles (<1 μm size) dispersed in “an aqueous buffer” and micropatterned them on a substrate; technical problems/conditions of the electrosp...

We present a multi-objective evolutionary algorithm to exploit a medium-sized fuzzy outranking relation to derive a partial order of classes of alternatives (we call it RP-NSGA-II). To measure the performance of RP-NSGA-II, we present an empirical study over a set of simulated multi-criteria ranking problems. The result of this study shows that RP-NSGA-II can effectively exploit a medium-sized ...

In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small and medium-sized real-l...

One effective way to make a large-capacity mobile communication system is to use a microcellular system. One way to do this is to place the base station antennas lower than the surrounding buildings. This result in what is called a street microcellular system. We previously presented basic simulation results evaluating the performance of a different-sized cell combination algorithm (DCC) design...

Article history: Received 15 April 2014 Received in revised form 29 September 2014 Accepted 28 October 2014 Available online 4 November 2014

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...