On the Fourth order Schr\"odinger equation in four dimensions: dispersive estimates and zero energy resonances

We study the fourth order Schr\"odinger operator $H=(-\Delta)^2+V$ for a decaying potential $V$ in four dimensions. In particular, we show that the $t^{-1}$ decay rate holds in the $L^1\to L^\infty$ setting if zero energy is regular. Furthermore, if the threshold energies are regular then a faster decay rate of $t^{-1}(\log t)^{-2}$ is attained for large $t$, at the cost of logarithmic spatial weights. Zero is not regular for the free equation, hence the free evolution does not satisfy this bound due to the presence of a resonance at the zero energy. We provide a full classification of the different types of zero energy resonances and study the effect of each type on the time decay in the dispersive bounds.Comment: Revised according to referee suggestions. To appear in J. Differential Equation

The Headscarf Controversy in Turkey

This article is based on a monographic field study, which was conducted in October 2007. In addition, the results of other studies on the headscarf issue conducted at different times between 2003 and 2007 have also been used to follow the development over the course of time. The study found that the headscarf prohibition has no strong social basis. As it would be a mistake to see the headscarf prohibition as an element of the secularism project, defining an ideology on the basis of the headscarf, an important religious symbol in Turkey, presents a risk to the progress of democracy, and only serves to increase political polarization. Formulating public policies on the basis of the headscarf prohibition will only help destroy social peace. Social engineering projects which aim to change or destroy political, religious and ethnic positions of citizens are not permitted in Western-type contemporary democracies. There is no headscarf problem in Turkey in a sociological sense, the real problem lies in the totalitarian/authoritarian approach which stems from groundless fears and/or ideological choices of the social elite or economic power centers.Headscarf, hijab, Islamic fundamentalism

Dispersive estimates for massive Dirac operators in dimension two

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the $t^{-1}$ decay rate holds in the $L^1\to L^\infty$ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular that a faster decay rate of $t^{-1}(\log t)^{-2}$ is attained for large $t$, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.Comment: 40 page

Coupled THM modelling of engineered barriers for the final disposal of spent nuclear fuel isolation

This paper describes the thermohydromechanical (THM) simulation of engineered barrier systems (EBS) for the final disposal of nuclear spent fuel in Finland. The bentonite barriers were simulated with the Barcelona Basic Model and the model was calibrated from laboratory tests. The evolution of gap closure and the presence of a fracture intersecting the disposal were analysed. The simulations were performed in 2D axisymmetrical geometries. Full 3D simulations were carried out in order to check the effect of the third dimension. The time required for the barriers to reach full saturation, the maximum temperature, deformations and displacements at the buffer–backfill interface and the homogenization of components both locally and globally are the main interests. The effect of rock fracture and the hydraulic conductivity of the rock are subjected to 2D sensitivity analyses.Peer ReviewedPostprint (published version

The effects of tourism on the incomes of municipality Didim Municipality sample

Turizm faaliyetlerinden elde edilen gelirlerin ülke ekonomileri açsından ne kadar önemli oldugunu son çeyrek yüzyılda ortaya çıkmıstır.Turizm faaliyetlerinin, sagladıgı döviz girisi ile makro düzeyde basta ödemeler bilançosu üzerinde yarattıgı dengeye getirici etki olmak üzere, mikro düzeyde yerel ekonomilerde yarattıgı gelir etkisi, bölgede yasayan tüm ekonomik birimlerin toplam gelirlerini artırmaktadır. Didim yerelindeki tüm özel ve tüzel ekonomik birimler, turizmin büyük oranda dönemsel gelir etkisinden paylarına düseni almakta ve toplam gelirlerini artırmaktadırlar. Turizmin dönemsel gelir etkisi, bir yerel yönetim kurulusu olan Didim Belediyesi'nin önemli gelir kaynaklarındandır. Bu baglamda, çalısma turizmin belediye gelirleri üzerinde yarattıgı etkiyi Didim Belediyesi özelinde konu almıstır.Buna baglı olarak Didim Belediyesi'nin dönemsel turizm hareketlerinden, gelirleri baglamında nasıl etkilendigini ortaya koymayı amaçlamıstır. Çalısmada turizmin genel çerçevesi ve yarattıgı gelir etkisi açıklanmıs ve yerel yönetimler baglamında belediyelerin genel çerçevesi ve gelirleri tanımlanarak, Didim Belediyesinin gelir kaynaklarına turizmin etkileri gösterilmistir. Çalısmada tümdengelim yöntemi uygulanmıs ve literatür taraması yapılarak, statistiksel veriler kullanılmıstır. It has come out in the last quarter century how important the incomes obtained from tourism activities are from the point of view of the countries? economies. The balancing effect that tourism activities created chiefly on payment balance in the macro level and the income effect they created on the local economies in the micro level have increased the overall incomes of all the economical units living in the region. All the private and judicial economical units in Didim region mostly get their share from periodical income effect of tourism and increase their overall incomes. Periodical income effect of tourism is one of the most important sources of income for Didim Municipality, which is a local institution of administration. In this sense, Didim Municipality has taken the effect that tourism created on the incomes of the municipality into private consideration. Depending on this, it is intended to reveal how Didim Municipality is affected by periodical tourism activities in the context of incomes. In the study, the general framework of tourism and the income effect that it created are explained and the effects of tourism on the incomes of Didim Municipality are shown by defining the general frame and incomes of municipalities in the sense of local administrations. In the study, deduction method is applied, literature review is made and statistical data is used

Permanences Against Cultural Amnesia: Reconstructing the Urban Narrative of the Rum Community of Fener, Istanbul

In this article I reconstruct the place narrative of the Rum community (Greeks of Turkey) in Fener, Istanbul through unrest, displacement, and gentrification, and how the urban fabric, everyday life, and encounters transformed through different phases of urban change. Fener was a neighbourhood where cultural groups coexisted with mutual respect. This environment started to deteriorate when societal unrest towards non-Muslims resulted in a city-wide assault in 1955 and a subsequent displacement of many non-Muslims from the neighbourhood. The neighbourhood decayed and later became an attractive spot for gentrifiers because of its multicultural history. This implicated a massive physical change after an unimplemented regeneration project leading to gentrification. I theorize this narrative mainly based on Whitehead’s “permanences,” the stabilities in the physical and non-physical presence of Rums in Fener and Bhabha’s “in-between temporalities” as complements of permanences, defining space-time envelopes that signify both adjustment and resilience, but also amnesia as a result of urban unrest through social and physical change. The Rum urban narrative provides a complex story of challenged community identity; therefore, it necessitates the use of several qualitative research methods: interviews with older residents, historical investigation with documentation, and personal observation. The study results show that the Rum community’s daily practices and placeworlds were lost; however, the community remembers permanences better than in-between temporalities. Linking fragmented narratives by reconstructing them fights cultural amnesia and leads to a better connection with place and past contexts