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Jaypee Institute of Information Technology, Noida
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  • Dept of Mathematics

Research thrust areas as recognized by major funding agencies

(a)  Fractals & Chaos and Mathematical Analysis

(b)  Numerical Analysis and Computational Continuum Mechanics

(c)  Statistics, Fuzzy, Information Theory and Operations Research

Fractals & Chaos and Mathematical Analysis

Fractals and chaos are new frontiers of science and important emerging interdisciplinary areas of research nowadays. Wavelets and fractals have significant contributions in the fields of image and signal processing, image compression, data compression and other various approximations.  Almost all branches of sciences and engineering are benefiting from the new insights provided by them. Many shapes found in nature which are highly rough and complex at different scales, fractal interpolation methods are popularly accepted approximation tools in such cases. Mathematical analysis provides the foundation for further development in these areas. The applications of explorations in these areas encompasses various disciplines of sciences, engineering, medicine, business, weather forecasting and several other areas of human activities.

Numerical Analysis and Computational Continuum Mechanics

The numerical solution of the problems occurring in Computational Continuum Mechanics is of great practical importance. The governing simultaneous ordinary and partial differential equations remain highly nonlinear and therefore, cannot be solved analytically. These equations can be solved numerically by using numerical methods such as finite element, finite difference, quasi-linearization, mesh free methods.

Statistics, Fuzzy, Information Theory and Operations Research

In this age of information revolution, the role of statistics, fuzzy sets, information theory and operations research is of prime importance. The statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Also the results of measurements of such data can be best described by using fuzzy numbers and fuzzy vectors. Statistical analysis methods have to be adapted for the analysis of fuzzy data. Information theory deals with the study of problems concerning information processing, information storage, information retrieval and decision-making. This includes the study of uncertainty measures and various practical and economical methods of coding information for transmission. Operations research is required to deal with wide range of problem-solving techniques applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models.

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