Exponentials of Bounded Normal Operators

The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free hypothesis. It is also a continuation of a recent work by the corresponding author.Comment: 07 page

The Impact of Liberalizing International Trade of Banking Services in Morocco

The purpose of this paper is to assess welfare effects of regulating the banking sector in Morocco along the European Union lines. The agreement between the EU and Morocco, signed in February 1996 and came into force in March 2000, provides for the gradual establishment of an industrial free-trade zone by 2012 and progressive liberalization of trade in agriculture. The agreement between Morocco and the EU foresees, in addition to that, to start negotiations for a free trade area in services. The agreement contains, however, no binding commitments. But Morocco is expected to deepen further its relationships with Europe within the framework of the Neighboring Policy. The relevance of the issue of banking services’ liberalization goes beyond Morocco’s agreement with the EU. On the one hand, Morocco’s free trade agreement with the US encompasses services, more specifically financial services, in addition to manufactured goods, agricultural products, intellectual property rights, and government procurement. This agreement is expected to come into force in 2006. On the other hand, under GATS, Morocco is projected to increase its commitments and opens up further its banking sector to foreign competition. The last commitments made by Morocco in Uruguay Round were mainly under commercial presence (mode 3) as compared to cross border supply (mode 1) and consumption abroad (mode 2). Except lending to finance investment in Morocco or commercial transactions with Morocco allowed under the mode 1, no commitment has been made in other items (Achy 2002). Hence, there is a real need to understand opportunities and challenges of liberalizing banking services on the Moroccan economy.Banking services, liberalization, Welfare effects, Morocco

Some Constacyclic Codes over Finite Chain Rings

For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the $\alpha +p \beta$-constacyclic codes of length $p^s$ over the Galois ring $GR(p^e,r)$