Exponential instability in an inverse problem for the Schrodinger equation

We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrodinger operator.We show that this problem is severely ill posed. The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are optimal

Counting and characterising functions with “fast points” for differential attacks

Higher order derivatives have been introduced by Lai in a cryptographic context. A number of attacks such as differential cryptanalysis, the cube and the AIDA attack have been reformulated using higher order derivatives. Duan and Lai have introduced the notion of “fast points” of a polynomial function f as being vectors a so that computing the derivative with respect to a decreases the total degree of f by more than one. This notion is motivated by the fact that most of the attacks become more efficient if they use fast points. Duan and Lai gave a characterisation of fast points and Duan et al. gave some results regarding the number of functions with fast points in some particular cases. We firstly give an alternative characterisation of fast points and secondly give an explicit formula for the number of functions with fast points for any given degree and number of variables, thus covering all the cases left open in Duan et al. Our main tool is an invertible linear change of coordinates which transforms the higher order derivative with respect to an arbitrary set of linearly independent vectors into the higher order derivative with respect to a set of vectors in the canonical basis. Finally we discuss the cryptographic significance of our results

Global stability for the multi-channel Gel'fand-Calder\'on inverse problem in two dimensions

We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$

Constructing cultural identities : Romanian popular music

During the communist era in Romania, cultural activity was crippled by censorship. Any work of art, and especially literature and music (more accessible to the public) were examined and the officials decided what could be made available to the public. The fall of the communists brought cultural freedom and competition and it meant Romania's entrance in the context of globalization. This work examines the way in which the globalization of culture changes not only the relationships between different cultures and spaces but also between the nation state and cultural identities that are constructed and manifested on its territory. Also, it will be argued that globalization provides new grounds and custodians for the construction of cultural identities. One of these custodians is popular music, which is investigated here. The impact of globalization on local cultures, cultural identities and new strategies and processes of cultural identity construction will be analyzed through the case of four important trends in Romanian popular music