Sparked by high-profile confrontations between police and citizens in Ferguson, Missouri, and elsewhere, many commentators have criticized the excessive militarization of law enforcement. We investigate whether surplus military-grade equipment acquired by local police departments from the Pentagon has an effect on crime rates. We use temporal variations in US military expenditure and betweencou...

We propose a new version of the spatial model of voting. Platforms of five parties are evolving in a two-dimensional landscape of political issues so as to get maximal numbers of voters. For a Gaussian landscape the evolution leads to a spatially symmetric state, where the platform centers form a pentagon around the Gaussian peak. For a bimodal landscape the platforms located at different peaks...

We derived 14 types of tiling cases under a restricted condition in our previous report, which studied plane tilings with congruent convex pentagons. That condition is referred to as the category of the simplest set of node (vertex of edge-to-edge tiling) conditions when the tile is a convex pentagon with four equal-length edges. This paper shows the detailed properties of convex pentagonal til...

In binary projective spaces PG(v, 2), minimal 1-saturating sets, including sets with inner lines and complete caps, are considered. A number of constructions of the minimal 1-saturating sets are described. They give infinite families of sets with inner lines and complete caps in spaces with increasing dimension. Some constructions produce sets with an interesting symmetrical structure connected...

Fraudulent financial reporting is defined as fraud committed by the management of a company providing false picture statements, which, course, harms investors and other related parties. This research aims to analyze effect using pentagon theory. The Pentagon theory measured targets, stability, external pressure, institutional ownership, ineffective monitoring, changes in KAP, directors, number ...

At the beginning of the series of papers we present systematic approach to exhaust the convex pentagonal tiles of edge-to-edge (EE) tilings. Our procedure is to solve the problem systematically step by step by restricting the candidates to some class. The first task is to classify both of convex pentagons and pentagonal tiling patterns. The classification of the latter is based on the analysis ...

We show that the billiard in a regular polygon is weak mixing in almost every invariant surface, except in the trivial cases which give rise to lattices in the plane (triangle, square and hexagon). More generally, we study the problem of prevalence of weak mixing for the directional flow in an arbitrary non-arithmetic Veech surface, and show that the Hausdorff dimension of the set of non-weak m...

From the pentagon onwards, the area of the regular convex polygon with n sides and unit diameter is greater for each odd number n than for the next even number n + 1. Moreover, from the heptagon onwards, the difference in areas decreases when n increases. Similar properties hold for the perimeter. A new proof of a result of Reinhardt follows.