After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first...After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.展开更多
Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposi...Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.展开更多
Accounting scandals are becoming perpetual in nature.They range from the ancient Mesopotamia,to the South Sea Bubble of 1720,to the famous Enron of 2001,down to Parmalat,Tesco,and Toshiba of today.The series of accoun...Accounting scandals are becoming perpetual in nature.They range from the ancient Mesopotamia,to the South Sea Bubble of 1720,to the famous Enron of 2001,down to Parmalat,Tesco,and Toshiba of today.The series of accounting scandals that have occurred in the last two decades calls for a greater concern by the accounting profession.The accounting scandals that have occurred in this 21st century alone have shown that there is a need to look beyond corporate governance in the fight against financial deception.In this paper,we argue that even in the face of the Sarbanes-Oxley Act(SOA)of 2002 and other regulations around the world that are targeted towards effective corporate governance,accounting scandals have never ceased to occur.Most of the legislations that have been passed in recent times were targeted at corporate governance,forgetting the crucial role that audit plays within the agency relationship.And whenever there is any revelation of fraudulent financial reporting,investors do not ask who are the directors,but the first question they ask is who are the auditors?Hence,there is a need to improve audit quality by approaching it from a forensic accounting perspective in order to reduce the incidence of financial statement frauds in this era of information revolution,thus restoring investors’confidence back in the financial reporting process and corporate governance.In this paper,we propose a forensic accounting paradigm as a viable option for reducing accounting scandals,since this will compliment corporate governance systems.展开更多
An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained...An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained.In the disorder phase v=0.369(±0.044),y_(T)=1/ν=2.71(±0.32),in the order phase ν=0.393(±0.048),y_(T)=2.54(±0.31).They approximate to the prediction of the scaling theory.展开更多
文摘After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.
文摘Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.
文摘Accounting scandals are becoming perpetual in nature.They range from the ancient Mesopotamia,to the South Sea Bubble of 1720,to the famous Enron of 2001,down to Parmalat,Tesco,and Toshiba of today.The series of accounting scandals that have occurred in the last two decades calls for a greater concern by the accounting profession.The accounting scandals that have occurred in this 21st century alone have shown that there is a need to look beyond corporate governance in the fight against financial deception.In this paper,we argue that even in the face of the Sarbanes-Oxley Act(SOA)of 2002 and other regulations around the world that are targeted towards effective corporate governance,accounting scandals have never ceased to occur.Most of the legislations that have been passed in recent times were targeted at corporate governance,forgetting the crucial role that audit plays within the agency relationship.And whenever there is any revelation of fraudulent financial reporting,investors do not ask who are the directors,but the first question they ask is who are the auditors?Hence,there is a need to improve audit quality by approaching it from a forensic accounting perspective in order to reduce the incidence of financial statement frauds in this era of information revolution,thus restoring investors’confidence back in the financial reporting process and corporate governance.In this paper,we propose a forensic accounting paradigm as a viable option for reducing accounting scandals,since this will compliment corporate governance systems.
基金Supported by Funds of Institute of Theoretical Physics,Academia Sinica.
文摘An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained.In the disorder phase v=0.369(±0.044),y_(T)=1/ν=2.71(±0.32),in the order phase ν=0.393(±0.048),y_(T)=2.54(±0.31).They approximate to the prediction of the scaling theory.
