We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line ` such that ` intersects at most O( √ (m+ n) logn) disks and each of the halfplanes determined by ` contains at most 2n/3 unit disks from the set, where m is the number of intersecting pairs of disks. We also show that an axis-parallel li...

By analyzing the granted patents distribution of the energy-saving and environmental protection industry in China from 2008 to 2013, the conclusion can be reached: firstly, technological innovations of the energy-saving industry are focused on the environmentally air-conditioning and heat pump technical field, and technological innovations of the resources recycling industry is mainly concentra...

Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter–antimatter symmetry and some new ways to understand the baryo–genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the ...

A long-running issue in scorecard construction in retail banking is how to handle dramatically unbalanced class sizes. This is important because, in many applications, the class sizes are very different. We describe the impact ignoring such imbalance can have and review the various strategies which have been proposed for tackling it, embedding them in a common theoretical framework. We then des...

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.

distance-balanced graphs are introduced as graphs in which every edge uv has the followingproperty: the number of vertices closer to u than to v is equal to the number of vertices closerto v than to u. basic properties of these graphs are obtained. in this paper, we study theconditions under which some graph operations produce a distance-balanced graph.

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is ti...

This paper shows that under some circumstances the so called BCU method may not be able to find the true CUEP for a specific fault-on trajectory of a power system. The reasons to that malfunction are analysed, and a methodology than can improve the capability of the BCU method to successfully find the CUEP is presented. Finally, several applications of the proposed method to power electrical sy...

Playing games against people with a different skill level can be boring or frustrating, which decreases fun. A solution is to introduce specific rules that balance a game. In this paper we describe a study in which we used an electronic board game with tangible interaction to investigate whether balancing a game indeed increases fun experienced. We also investigate whether balancing skill level...