Composition of Permutation Representations of Triangle Groups

A triangle group is denoted by $\Delta(p,q,r)$ and has finite presentation $$\Delta(p,q,r)=\langle x,y | x^p=y^q=(xy)^r=1 \rangle .$$ We examine a method for composition of permutation representations of a triangle group $\Delta(p,q,r)$ that was used in Everitt's proof of Higman's 1968 conjecture that every Fuchsian group has amongst its homomorphic images all but finitely many alternating groups. We see that some of these compositions must give imprimitive representations, and in particular situations, where the representations being composed are all equivalent copies of an alternating group in the same degree, we can give a complete description of the structure of the composition of the representations. This article contains the main results of the author's PhD thesis

Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing

We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We point out that quantum states exhibiting time-invariant entanglement must live in both decoherence free subspace and in the subspaces orthogonal to it. The previous studies on this feature for two qubits can be recovered from our studies as a special case. We also study the nonlocality of quantum states under collective dephasing. We find that although genuine entanglement of quantum states may not change, however their nonlocality changes. We discuss the possibility of finite time end of genuine nonlocality.Comment: 7 pages, 3 figure

Boon or bane- role of FDI in the economic growth of Pakistan

We study the effects of FDI inflows on the Pakistani economy over the period 1961-2005 using the Johansen co-integration technique and the Vector Error Correction Model. We determine that FDI does have a positive effect on the economy, particularly in the short term. Foreign investment is found to have a less important role than domestic investment. However, FDI impacts negatively on human capital. We can thus say that FDI has neither been an absolute boon nor a downright bane for Pakistan. On étudie l'impacte des IDE sur l'économie Pakistanaise pendant la période 1961-2005 en utilisant la technique de cointégration de Johansen et le VECM. On trouve que les IDE ont un effet positif sur l'économie particulièrement à court terme. Les investissements étrangers ont un rôle moins important que celui des investissements domestiques. En revanche, l'impacte sur le capital humain est négatif. Par conséquent, on peut conclure que les IDE ont été ni bénéfiques, ni néfastes.Foreign direct investment; Economic growth; Pakistan; Human capital; Domestic investment.

Explaining Income Inequalities in Developing Countries: the Role of Human Capital

Explaining Income Inequalities in Developing Countries: the Role of Human Capital