Stationary disks and Green functions in almost complex domains

Using generalized Riemann maps, normal forms for almost complex domains (D, J) with singular foliations by stationary disks are defined. Such normal forms are used to construct counterexamples and to determine intrinsic conditions, under which the stationary disks are extremal disks for the Kobayashi metric or determine solutions to almost complex Monge-Ampere equation.Comment: 25 page

Regularity of Kobayashi metric

We review some recent results on existence and regularity of Monge-Amp\`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity. A main consequence of our results is the fact that the Kobayashi pseudo-metric k on an appropriare open subset of each of the above domains is actually a smooth Finsler metric. The class of domains to which our result apply is very large. It includes for instance all smoothly bounded strongly pseudoconvex complete circular domains and all their sufficiently small deformations.Comment: 14 pages, 8 figures - The previously announced main result had a gap. In this new version the corrected statement is given. To appear on the volume "Geometric Complex Analysis - Proceedings of KSCV 12 Symposium

Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically non-linear Cosserat type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our non-linear approach. Plane wave solutions are briefly discussed within this model.Comment: 22 pages, 1 figure; v2 updated versio

Monge-Ampere foliations with singularities at the boundary of strongly convex domains

Let D subset of C-N be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampere type equation in D with a simple pole at the boundary. Using the Lempert foliation of D in extremal discs, we construct a solution u whose level sets are boundaries of horospheres. Among other things, we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution

Inverted Haavelmo Effects in a General Equilibrium Analysis of the Impact of Implementing the Scottish Variable Rate of Income Tax.

The Scottish Parliament has the authority to make a balanced-budget expansion or contraction in public expenditure, funded by corresponding local changes in the basic rate of income tax of up to 3p in the pound. This fiscal adjustment is known as the Scottish Variable Rate of income tax, though it has never, as yet, been used. In this paper we attempt to identify the impact on aggregate economic activity in Scotland of implementing these devolved fiscal powers. This is achieved through theoretical analysis and simulation using a Computable General Equilibrium (CGE) model for Scotland. This analysis generalises the conventional Keynesian model so that negative balanced-budget multipliers values are possible, reflecting a regional “inverted Haavelmo effect”. Key parameters determining the aggregate economic impact are the extent to which the Scottish Government create local amenities valuable to the Scottish population and the extent to which this is incorporated into local wage bargaining.Fiscal federalism, devolution, regional wage bargaining and migration, Scotland, regional computable general equilibrium analysis.

The pluricomplex Poisson kernel for strongly convex domains

Let D be a bounded strongly convex domain in the complex space of dimension n. For a fixed point p epsilon partial derivative D, we consider the solution of a homogeneous complex Monge-Ampere equation with a simple pole at p. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of D with pole at p. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of D, uniqueness in terms of the associated foliation and boundary behaviors. Finally, using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

Risk of cancer after assisted reproduction: a review of the available evidences and guidance to fertility counselors

Infertile women requiring ovarian stimulation and assisted reproduction techniques (ART) are faced with difficult issues. The fear that using hormones could increase their risk of cancer is the most significant. One of the main challenges for assessing cancer risk after ART is the difficulty to separate it from the underlying condition of infertility per se. The delay or the inability to achieve a pregnancy is an important risk factor for breast, endometrial and ovarian cancer. We analyzed the current literature on the topic

Scottish Fiscal Choices Post-Referendum : Powers, Purpose and Potential Impact

The Referendum on Scottish independence held on the 18th September, 2014, resulted in a significant majority vote (55% as against 45%) in favour of “no”. Accordingly, Scotland will remain a member of the U.K. for the foreseeable future.1 However, further changes in the Scottish fiscal system are inevitable. Firstly, some tax changes are already in the pipeline (for April 2015 and 2016) as a consequence of the provisions of the Scotland Act 2012. Secondly, all of the UK leaders of the main unionist parties committed, in the latter stages of the referendum campaign, to transferring significant additional powers to the Scottish Parliament in the event of a majority no vote.2 Lord Smith of Kelvin Chairs a Commission charged with rapidly generating a proposal for a new devolution settlement for Scotlan