Singularities of Functions on the Martinet Plane, Constrained Hamiltonian Systems and Singular Lagrangians

We consider here the analytic classification of pairs $(\omega,f)$ where $\omega$ is a germ of a 2-form on the plane and $f$ is a quasihomogeneous function germ with isolated singularities. We consider only the case where $\omega$ is singular, i.e. it vanishes non-degenerately along a smooth line $H(\omega)$ (Martinet case) and the function $f$ is such that the pair $(f,H(\omega))$ defines an isolated boundary singularity. In analogy with the ordinary case (for symplectic forms on the plane) we show that the moduli in the classification problem are analytic functions of 1-variable and that their number is exactly equal to the Milnor number of the corresponding boundary singularity. Moreover we derive a normal form for the pair $(\omega,f)$ involving exactly these functional invariants. Finally we give an application of the results in the theory of constrained Hamiltonian systems, related to the motion of charged particles in the quantisation limit in an electromagnetic field, which in turn leads to a list of normal forms of generic singular Lagrangians (of first order in the velocities) on the plane

Gauss-Manin Connections for Boundary Singularities and Isochore Deformations

We study here the relative cohomology and the Gauss-Manin connections associated to an isolated singularity of a function on a manifold with boundary, i.e. with a fixed hyperplane section. We prove several relative analogs of classical theorems obtained mainly by E. Brieskorn and B. Malgrange, concerning the properties of the Gauss-Manin connection as well as its relations with the Picard-Lefschetz monodromy and the asymptotics of integrals of holomorphic forms along the vanishing cycles. Finally, we give an application in isochore deformation theory, i.e. the deformation theory of boundary singularities with respect to a volume form. In particular we prove the relative analog of J. Vey's isochore Morse lemma, J. -P. Fran\c{c}oise's generalisation on the local normal forms of volume forms with respect to the boundary singularity-preserving diffeomorphisms, as well as M. D. Garay's theorem on the isochore version of Mather's versal unfolding theorem

A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface

In this note we give a positive answer to a question asked by Y. Colin de Verdi\`ere concerning the converse of the following theorem, due to A. N. Varchenko: two germs of volume forms are equivalent with respect to diffeomorphisms preserving a germ of an isolated hypersurface singularity, if their difference is the differential of a form whose restriction on the smooth part of the hypersurface is exact

New Paradigms in Mitigating Unplanned Events Caused by Human Error

PresentationStatistics from several industry and government sources indicate that the OSHA PSM process safety incident frequency has dropped dramatically. However, the improvement trend seems to have plateaued. It has also been noted that operator error was identified as either the primary or secondary root cause in over 80% of these events. Much has been accomplished by employing computer systems, behavioral policies, and compliance actions in various stages of implementation. However, the desired results are not being achieved. The asymptote in performance could be due to uncoordinated technology implementation and policy enforcement which are not synergistic in achieving the overall goal. It is hypothesized that the next paradigm in process safety and human productivity will require an integrated approach to man-machine-method solutions. Failure to follow established standard operating procedures continues to be the single most repeated cause for human failure. Academic research points the finger at the cognitive decision- making disconnect between executing the written procedure manually and the level of automation applied to the process. It is proposed that computer augmentation of written procedures, mobile-enabled with real-time links to a process control system, is a missing capability which could error-proof manually executed tasks. Pilot attempts using this technique have been deployed but have been limited to proprietary, custom solutions. This paper will explore advances in platform-neutral computer technology, including breakthroughs such as augmented reality, which could provide cost-effective alternatives to the traditional hardwired approach of deterministic automation solutions to reduce human factor errors

Economic Geography and Regional Growth: An Empirical Evidence From Greece

There is a huge literature regarding the main determinants and sources of economic growth. Most of the recent work emphasizes on the role of knowledge, and innovation activities typically produced by a specific sector of the economy, and furthermore in the role of entrepreneurship and analysing the implications and the importance for economic growth. Moreover, the socio-economic and public policies aimi to distinguish the determining factors of growth, in order to enhance the regional cohesion and the convergence process. Much of the recent work on regional growth can be viewed as refining the basic economic insights of economic geography. There are two principal theories of why growth rates are differ, the first is the theory of comparative advantage and the second is the theory of increasing returns to scale. This paper attempts to examine the main sources of regional growth through an inter-and intra sectoral analysis. In particular, the paper attempts to investigate through an empirical inter-comparison study using statistical-data from several Greek regions, the determinant sectoral factors and the implications to growth process. We also employ the empirical non-parametric analysis. We find support for the existence of economic geography effects in several manufacturing sectors and moreover we find that these effects are economically very significant.

Peripheral Regions in Duress: Counter-Social Capital Impediments of Local Development in Rural Greek Areas

Unlike most enthusiastic narratives of various success stories in recent North European regional economic development led by innovation, localized learning, social capital and institutional embeddedness, this paper deals with a set of major stresses and problems of local economic development in peripheral, less favoured, regions. By drawing upon concrete research experience of regional development projects we try to shed light upon the processes of spatio-economic change and the management of local production in connection with prevailing cultural attitudes/values in less developed Greek rural areas. attidudes/values constituting a kind of localized “counter-social capital†deposit that impedes any likely innovative local development initiatives. The paper argues that the major problems facing these areas are not only or solely associated with the effects of market economy restructuring and the operation of macroeconomic and macropolitical forces at the regional and local level, but, also with inadequate management of human skills, lack of productive mentality and negative cultural values and attitudes. The policy relevance of our analysis calls for the elaboration of alternative development strategies aimed rather at enchancing local social capital potentialities than at improving hard infrastructures and providing financial incentives to local firms.