Smith Normal Form of Matrices Associated with Differential Posets

We prove a conjecture of Miller and Reiner on the Smith Normal Form of the operator $DU_{n}$ associated with a differential poset under certain conditions. We do so by proving that the conjecture is equivalent to the existence of a certain decomposition of the $\mathbb{Z}[x]$-module $(\mathbb{Z}^{p_{n} }, DU_{n})$, similar to the invariant factor decomposition of $\mathbb{Q}[x]$-modules. We then use our result to verify the conjecture in certain special cases.Comment: 12 pages, 1 figur

Algebraic Representation of Social Capital Matrix

This paper proposes a mathematical model based on a Boolean algebra involving a 4×4 social capital matrix [Shah (2008)], that emerges through interaction within and across individuals, communities, institutions and state. The framework provides a coding system for the existence or otherwise of various categories of social interaction. The model illustrates that social interaction can be neatly described in a format that facilitates the interpretation of social intra- and interactions among the four types of players in generating economic activity.Social Capital (Matrix), Linear Space, Interactive Systems, Boolean Algebra

Anti Money Laundering Mechanism: An Application of Principal-Agent Model for Pakistan

In this paper anti money laundering policy of the international financial regime is analyzed in principal agent model perspective. The strategy of the principal for formal agents is deliberated for global financial stability. This strategy encompasses incentive and dis-incentive for cooperation of formal agent. Formal agent by cooperating with principal may induce dis-incentive for informal agent. All the integrating stake holders make decision on the basis of comparison of present value of marginal cost of non-cooperation and present value of returns from cooperation. As the desired objective of the principal is to minimize transaction of money through informal channels therefore it has to include informal agents and clients in the strategy. The successful anti money laundering strategy can only be evolved by the cooperation of all the stakeholders.International Financial Regime, Principal Agent model and Money Laundering

Convergence Model of Governance: A Case Study of the Local Government System of Pakistan

The future of devolution plan in Pakistan may be analysed in view of our Convergence model. This model views stability of the local Govt. system drawn on Devolution Plan 2001. It claims that as there would be more volatile and non-committed (floating) number of agents in the political market and governance system, there is more probability of divergence; i.e. the system will remain unstable. Contrary to that more is the systematic trend in political market and governance system more is the probability that the convergence in the system occurs and that in turn leads to stability of the over all system. In this ‘Convergence’ Model different types of agents have been highlighted on the basis of their political ffiliation and being in competition as ruling elite and/or their allies and non-ruling elite and/or their allies. The agents have interactive relationship horizontally and vertically with other agents i.e. either they are ally or otherwise. The composition of this structure of the agents and clients is based on the principle of bottom top pproach i.e. Union council’s members, Nazim and their political competitors, Tehsil council and Nazim, District Nazim and his allied district assembly members and their political competitors, Member provincial Assembly and their political rivals, Member National Assembly/Senator, and their political rival and the ruling political elites, Provincial Government and their political rivals, and Political elites ruling Federal Government and their political rivals.

Asset price bubbles: implications for monetary, regulatory, and international policies

Monetary policy ; Price regulation