We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg arbitrary order in the dimensional regulator $d=4-2\epsilon$ space-time dimensions. A pure basis of Integrals is constructed for pentagon family leg, satisfying a single-variable canonical differential equation Simplified Differential Equations approach. The relevant boundar...

We study the moduli spaces of polygons in R and R, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gelfand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson arise as a reduction of the Gelfand-Cetlin system on the Grassmannian, and with these determine the pentagon and hexagon spaces up to equivariant symplectomorphism....

We study real solutions of a class of Painlevé VI equations. To each such solution we associate a geometric object, a one-parametric family of circular pentagons. We describe an algorithm which permits to compute the numbers of zeros, poles, 1-points and fixed points of the solution on the interval (1,+∞) and their mutual position. The monodromy of the associated linear equation and parameters ...

The terrorist attacks of September 11, 2001 on the World Trade Center and the Pentagon have rekindled public debate about National Identification Schemes (NIDS) in the US, Canada, and other countries. While much of the debate has focused on the tradeoffs between security protection and the potential loss of privacy and other civil liberties, this paper examines the prior question of whether a N...

Work supported by an Alfred P. Sloan Doctoral Dissertation Fellowship. We consider the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon’s diagonals, recovering unpublished results of Conway and proving new ones. We generalize this to a ‘‘pentagram map’’ on convex polygons of more than five sides, showing that iterated images of any initial polygon converge exp...

This study aims to analyze the effect of fraud pentagon on fraudulent financial statements with audit committee as moderating variable. The population this was property, real estate, and construction companies listed Indonesia Stock Exchange during 2016-2018. sampling technique used purposive obtained 52 156 units analysis. data were analyzed using logistic regression analysis by IBM SPSS Ver.2...