Generalised Thurston-Bennequin invariants for real algebraic surface singularities

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch surface singularity. For such singularities, the value of the linking form is the Thurston-Bennequin number of the real link of the singularity. As a special case of unibranch surface singularities, the behaviour of the linking form is investigated on the Brieskorn double points x^m+y^n\pm z^2=0.Comment: 22 pages, TeX, 12 figure

Morse-Bott functions on orthogonal groups

We make a detailed study of various (quadratic and linear) Morse-Bott trace functions on the orthogonal groups $O(n)$. We describe the critical loci of the quadratic trace function Tr$(AXBX^T)$ and determine their indices via perfect fillings of tables associated with the multiplicities of the eigenvalues of $A$ and $B$. We give a simplified treatment of T. Frankel's analysis of the linear trace function on $SO(n)$, as well as a combinatorial explanation of the relationship between the mod $2$ Betti numbers of $SO(n)$ and those of the Grassmannians $\mathbb{G}(2k,n)$ obtained from this analysis. We review the basic notions of Morse-Bott cohomology in a simple case where the set of critical points has two connected components. We then use these results to give a new Morse-theoretic computation of the mod $2$ Betti numbers of $SO(n)$.Comment: 28 page

There is a unique real tight contact 3-ball

We prove that there is a unique real tight contact structure on the 3-ball with convex boundary up to isotopy through real tight contact structures. We also give a partial classification of the real tight solid tori with the real structure being antipodal map along longitudinal and the identity along meridional direction. For the proofs, we use the real versions of contact neighborhood theorems and the invariant convex surface theory in real contact manifolds

Every real 3-manifold is real contact

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with respect to the real structure. We show that every real 3-manifold can be obtained via surgery along invariant knots starting from the standard real $S^3$ and that this operation can be performed in the contact setting too. Using this result we prove that any real 3-manifold admits a real contact structure. As a corollary we show that any oriented overtwisted contact structure on an integer homology real 3-sphere can be isotoped to be real. Finally we give construction examples on $S^1\times S^2$ and lens spaces. For instance on every lens space there exists a unique real structure that acts on each Heegaard torus as hyperellipic involution. We show that any tight contact structure on any lens space is real with respect to that real structure.Comment: 26 pages, 10 figures. In the new version various mistakes were corrected, the Introduction has been improved, Proposition 1.2 and Corollary 1.5 added, the second subsection for Section 6 delete

Türkiye'de Bahçe Bitkileri Konusunda Organik Üretime Yönelik Yapılan Ar-Ge Çalışmalarının Etki Değerlemesi I Organik Bahçe Bitkileri Konusunda Yapılmış Tagem Destekli Dört Ar-Ge Çalışmasının Etki Değerlemesi

Türkiye'de organik tarım konusunda yürütülen araştırma çalışmaları iki farklı yöntem izlemiştir. Araştırma faaliyetlerinin bir kısmı araştırma enstitülerinin kendi arazisinde yürütülürken, bir kısmı ise üretici bahçelerinde yürütülmektedir. Bu projede, enstitü bahçesinde ve üretici bahçesinde yürütülen dört farklı araştırma projesinin makro ve mikro etkilerinin, bu etkilerin ortaya çıkmasında yer alan yayım kanalları ile ihtiyaç duyulan Ar-Ge çalışmaları ortaya konulmaya çalışılmıştır. Bu projelerde ele alınan türlerin organik yetiştiriciliğinin yapıldığı ve araştırmaların yürütüldüğü üretici bahçelerinin olduğu illerde (Aydın, Bursa, Konya, Manisa) çok tabakalı gayeli örnekleme ile belirlenen örnek hacmine göre üreticilerle anket yolu ile veriler toplanmıştır. Ayrıca, işleyici/ihracatçı firmalar, sözü geçen illerdeki Tarım İl Müdürlüğü Organik Tarım Timleri, organik tarım araştırmaları yapan araştırma enstitülerinden elde edilen birincil veriler ile, organik ürün fiyatları, organik tarım politikaları ve benzeri ikincil veriler araştırmada materyal olarak kullanılmıştır. Elde edilen verilerin analizinde, brüt kar, iç karlılık oranı, fayda/masraf oranı gibi ekonomik analizler kullanılmıştır

Brieskorn manifolds as contact branched covers of spheres

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.Comment: 8 pages, 1 figur

Generalised thurston- bennequin invariants for singularities of real algebraic curves and surfaces

Ph.D. - Doctoral Progra

Is per capita electricity consumption stationary? Time series evidence from OECD countries

This study examines the stationary properties of per capita electricity consumption in which the endogenously determined break points are incorporated in 23 high income OECD countries by using annual data over 1960-2005 period. We utilize Lagrange Multiplier (LM) unit root test that endogenously determines structural breaks in level and/or trend. We find that 21 country series reject the unit root null hypothesis at the 5% significance level, except for 2 country series. Thus, our empirical findings provide significant evidence that per capita electricity consumption is stationary in almost all countries considered in the study. The stationarity of per capita electricity consumption indicates that it should be possible for the series to forecast future movements in the energy consumption based on the past behaviors of the series. Important policy implications emerge from our empirical results of the unit root test with multiple structural breaks. (C) 2011 Elsevier Ltd. All rights reserved