T paper investigates the effects of a limited consumer memory on the price competition between firms. It studies a specific aspect of memory—namely, the categorization of available price information that the consumers may need to recall for decision making. This paper analyzes competition between firms in a market with uninformed consumers who do not compare prices, informed consumers who compa...

We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.

We analyze the moment of inertia I(S), relative to the center of gravity, of finite plane lattice sets S. We classify these sets according to their roundness: a set S is rounder than a set T if I(S) < I(T). We show that roundest sets of a given size are strongly convex in the discrete sense. Moreover, we introduce the notion of quasi-discs and show that roundest sets are quasi-discs. We use wea...

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

1. The Darboux definition of the Riemann Integral Let f : [a, b]→ R be a it bounded function. Definition 1.1. A partition P of [a, b] is collection of points {x0, · · · , xn} which satisfiy a = x0 < x1 < · · · < xn = b. Denote by ∆xk the length of the interval [xk−1, xk], i.e., ∆xk = xk−xk−1. Then the mesh |P| is by definition equal to max1≤k≤n∆xk. Given a bounded function f and a partition P o...

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

SPATIOTEMPORAL MULTICAST AND PARTITIONABLE GROUP

We provide a new framework for generating multiple good quality partitions (clusterings) of a single data set. Our approach decomposes this problem into two components, generating many high-quality partitions, and then grouping these partitions to obtain k representatives. The decomposition makes the approach extremely modular and allows us to optimize various criteria that control the choice o...

In [DO03] we explored partitioning regular k-gons into “circular” convex pieces. Circularity of a polygon is measured by the aspect ratio: the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. We seek partitions with aspect ratio close to 1, ideally the optimal ratio. Although we start with regular polygons, most of the machinery developed extends to ar...

Due to dynamic and uncertain nature of many optimisation problems in real-world, the applied algorithm in this environment must be able to continuously track the changing optima over time. In this paper, we report a novel speciation-based firefly algorithm for dynamic optimisation, which improved its performance by employing prior landscape historical information. The proposed algorithm, namely...