IFNA and World Congresses of Nonlinear Analysts (WCNA)

V.Lakshmikantham

Florida Institute of Technology

Melbourne, FL 32901, USA

It is with the following spirit, the International Federation of Nonlinear Analysts (IFNA) was established and the First World Congress of Nonlinear Analysts (WCNA) was held during August 19-26, 1992 in Tampa Florida (USA).

As we approach the beginning of the 21st century, the evolution of our social and technological systems is becoming more complex and interconnected. Sciences, engineering and technology have triggered a multitude of nonlinear problems. The far reaching advances in communication and network industry, a new awareness in the hierarchies of our social, economic and political structures, the unabated devastation of our environment caused by a runaway technology (whose only purpose appears to be to stimulate the consumption of goods), and the predictive theories of weather, earthquakes and wealth of nations are subtly directing us towards a global civilization. It is abundantly clear that the next century will dominate crossing of cultural and traditional divisions. The time honored boundaries of different existing disciplines of the present century are tending to disappear giving way to broader global disciplines that inter-relate several traditional subject areas. Our contemporary problems of overpopulation, pollution, ozone depletion, dwindling natural resources, threat of nuclear war, terrorism, spread of new diseases, computer revolution and so forth are global problems which require that we attempt to solve them together with an emphasis on teamwork.љ No one discipline or a nation can solve these problems independently. What happens on the other side of the world can profoundly affect us where we live and it is getting crystal clear that the only solution to the present world upsurge of revolution is to build a global civilization. All this is necessitating a combined objective approach leading to global disciplines to deal with the diverse aspects of human creativity.

The increasing compartmentalization and concomitant specialization of knowledge that was the trend of the present century is undergoing subtle changes. The age of living in the increased estrangement between disciplines in the arts and sciences is slowly waning. The ideal of productively and deeply working in two or three disciplines which are not contiguous in the current geography of thought, such as math and anthropology, political science and music, chemistry and philosophy is seen as within the realm of possibility. The idea that we should, of course, continue to value academic specialization but must also work for integration of knowledge and the re-establishment of truly liberal learning as the coherent intellectual core of academic institutions, is rapidly gaining ground.

It is, therefore, clear that the attempt to understand the nonlinear world will dominate, in future years, large parts of mathematics in most areas of science, technology and various other disciplines.љ Future researchers will be able to utilize ultra high speed computers coupled with massive electronic data libraries to address complex global problems with resources that are more powerful and effective than those available today.љ Thus there is a definite need to have a forum, on a global basis, to forge "Unity in Diversity" and for bringing more cooperation and collaboration into the world community of nonlinear analysts.

The aims of IFNA and the WCNA are:

-         to promote, encourage and influence more cooperation, understanding and collaboration in the world community of nonlinear analysts from various disciplines;

-         to forge unity in diversity by bringing together a variety of disciplines that attempt to solve the nonlinear phenomena and to understand the nonlinear world;

-         to influence unification of ideas in order to shrink the boundaries of disciplines;

-         to create a sense of wholeness and participation in a common enterprise;

-         to assist interaction on a broader and deeper scale for the benefit of all disciplines;

-         to highlight recent advances, to stimulate discussions and to share ideas for future trends in research from various disciplines from mathematics to medicine.

So far there were four (4) WCNAs. The first one was in Tampa, Florida (USA) in 1992; the second WCNA was in Athens (Greece) in 1996; the third WCNA was in Sicily (Italy) in 2000; and the fourth WCNA was in Orlando (USA) in 2004. Each WCNA on average has around 1500-1600 participants from 90 countries, 150 organized sessions, 200 short communications, 150 one hour lectures and 30-40 keynote addresses. Nobel Laureates were among the participants twice.

Clearly the WCNA is a great success. It was hailed by several distinguished experts from various disciplines as a great event of historical proportion and significance.љ The excellent work done in organizing the WCNA has been praised as the heroic work in organization even when local help was not available.љ It was certainly an important contribution to the advancement of knowledge in nonlinear phenomena appearing in many different disciplines and to the international cooperation.

A remarkable aspect of all the Congresses is the broad scope of topics covered from various disciplines.љ The topics include nonlinear operators, degree theory, fixed point theory, bifurcation and critical point theory, variational methods, dynamical systems, evolution equations, various qualitative and quantitative aspects of ODE and PDE, set-valued analysis, stochastic analysis, numerical and computational aspects, control theory and optimization, nonlinear waves, fluid mechanics, structural mechanics, manufacturing systems, computer visions, environmental problems, neural networks, chaos, artificial intelligence, population dynamics, ecotoxicology, chemical and biochemical oscillations, telecommunications, wealth of nations, problems in aerospace systems, guidance and navigation, blow-up phenomena, image processing, atmospheric and climate dynamics, theory of finance and its complexity, x-ray crystallography problems, ocean acoustics, inverse scattering theory, Navier-Stokes equations, nonlinear elasticity, quasi-Newton methods, magneto-hydrodynamics, ill-posed problems, structural engineering problems, hysteresis operators, hybrid systems, biomedical applications, and cosmology.

 

 

 

V.Lakshmikantham, Dr.; the President and Founder of the International Federation of Nonlinear Analysts, as well as the Chairman of the Global Organizing Committee of the World Congress of Nonlinear Analysts. He is also Professor and Head of the Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL USA. He has over 20 research monographs and 300 research papers.