Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

On the sense preserving mappings in the Helm topology in the plane

∗Research supported by the grant No. GAUK 186/96 of Charles University.

On Projective Plane of Order 13 with a Frobenius Group of Order 39 as a Collineation Group

One of the most outstanding problems in combinatorial mathematics and geometry is the problem of existence of finite projective planes whose order is not a prime power.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Self-Avoiding Walks in the Plane

Румен Руменов Данговски, Калина Христова Петрова - Разглеждаме броя на несамопресичащите се разходки с фиксирана дължина върху целочислената решетка. Завършваме анализа върху случая за лента, с дължина едно. Чрез комбинаторни аргументи получаваме точна формула за броя на разходките върху лента, ограничена отляво и отдясно. Формулата я изследваме и асимптотично.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Inventory investment and sectoral characteristics in some OECD countries

This paper discusses the effects of sectoral structure on the long run macroeconomic inventory behaviour of national economies. Data on 15 OECD countries are included in the analysis, which is based on correlation and cluster analysis methodologies. The study is part of a long-term research project exploring factors influencing the inventory behaviour of national economies. First, we introduce some basic characteristics of macroeconomic inventory formation in the 15 OECD countries. We argue that our previous results on the existence of specific characteristic features of macroeconomic inventory investment are justified, hence it makes sense to study the factors influencing these features. We then examine the contribution of various sectors to the production of in the countries involved and the relationship between sectoral structure and inventory intensity (annual inventory change/Gross Value Added). We find that the high share of agriculture and manufacturing increases inventory intensity, that the increasing share of services has a negative effect and that the role of construction and trade is not obvious. The relatively low stability of the statistical results warns us to be cautious with our judgements. Further, case-by-case analysis would be required to obtain more solid results.

A Consumption-Based Approach to Carbon Emission Accounting – Sectoral Differences and Environmental Benefits

In recent years there has been growing concern about the emission trade balances of countries. This is due to the fact that countries with an open economy are active players in international trade. Trade is not only a major factor in forging a country’s economic structure, but contributes to the movement of embodied emissions beyond country borders. This issue is especially relevant from the carbon accounting policy and domestic production perspective, as it is known that the production-based principle is employed in the Kyoto agreement. The research described herein was designed to reveal the interdependence of countries on international trade and the corresponding embodied emissions both on national and on sectoral level and to illustrate the significance of the consumption-based emission accounting. It is presented here to what extent a consumption-based accounting would change the present system based on production-based accounting and allocation. The relationship of CO2 emission embodied in exports and embodied in imports is analysed here. International trade can blur the responsibility for the ecological effects of production and consumption and it can lengthen the link between consumption and its consequences. Input-output models are used in the methodology as they provide an appropriate framework for climate change accounting. The analysis comprises an international comparative study of four European countries (Germany, the United Kingdom, the Netherlands, and Hungary) with extended trading activities and carbon emissions. Moving from a production-based approach in climate policy to a consumption-based principle and allocation approach would help to increase the efficiency of emission reductions and would force countries to rethink their trading activities in order to decrease the environmental load of production activities. The results of this study show that it is important to distinguish between the two emission accounting approaches, both on the global and the local level.