# Research

**RESEARCH ACTIVITIES**

The post graduate Department of Mathematics was upgraded as a Research Department in 1999. The Department produced the first ever Ph. D. in Mathematics from an affiliated college of the Mahatma Gandhi University. So far the department has produced 31 Ph. D. holders in Mathematics and Statistics under the supervision of 7 Research Guides. Presently one Research Guide and 2 Research Scholars are working with the Department.

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Research Guide |
Research Scholars |

Dr. Aparna Lakshmanan S.
Assistant Professor Department of Mathematics Cochin University of Science and Technology, Cochin-22, Kerala |
Ms. Ninu S. Lal |

Ms. Deepa V. G. |

** **

**Ph Ds produced from the Department**

Research Guides |
Research Scholars |
Title of the Thesis |

Dr. Sunny Kuriakose A | Dr. Mary George (2003) | Fuzzy mathematical approach to economic problems |

Dr. Mary Benedict (2006) | Algorithmic approach to some intersection graphs | |

Dr. Gigi George (2007) | Fuzzification of decision theory and allied areas | |

Dr. Binimole Punnose (2007) | A study of fuzzy topological vector spaces | |

Dr. Vijayalakshmi Menon (2008) | Fuzzy mathematics and medical diagnosis | |

Dr. Philomina M.T. (2009) | Some problems in topology and frames | |

Dr. Sobhana Devi, C. K. (2009) | Fuzziness in operation research and game theory | |

Dr. Lisy Cherian (2010) | Optimization in fuzzy environment | |

Dr. Tutu M John (2013) | A study of certain economic problems using fuzzy mathematics | |

Dr. Thavamani, J. P. (2014) | Edge product graphs | |

Dr. Annie Varghese (2014) | A study of economic equilibria using fuzzy and intuitionistic fuzzy mathematical tools | |

Dr. Shiny Jose (2015) | Some problems in intuitionistic fuzzy optimization and decision making | |

Dr. Philomena, C. F. (2015) | Study of frames in fuzzy context | |

Dr. Rogi Jacob (2016) | A study on fuzzy image processing and related areas | |

Dr. Manjusha R. (2019) | A Study on metric dimension of graphs and applications | |

Dr. Sheeja T. K. (2019) | Study of rough sets and applications to information theory | |

Dr. S. Arumugham | Dr. Karuppasamy, K (2010) | Studies in fractional graph theory |

Dr. Varughese Mathew (2012) | Studies in graph theory – Rational approach | |

Dr. Bibin K. Jose (2012) | Domination in hypergraphs | |

Dr. Nirmala Kumari, S (2016) | Studies in graph theory: Domination related problems | |

Dr. Manju Raju (2019) | Domination in graphs – Theory and applications | |

Dr. P. Ramakrishnan | Dr. Mini, P. M. (2010) | Contribution of Jainas to mathematics with special reference to Ganitasarasangraha of Mahavira |

Dr. Aparna Lakshmanan S. | Dr. Anu V. (2020) | A Study on Two Graph Parameters- Double Roman Domination Number and Homometric Number |

Dr. Jeepamol J. Pallathingal (2020) | Studies on Graph Operators | |

Dr. Jismy Varghese(2022) | A study on domination parameters in graphs | |

Dr. Seena Varghese | Leech labelling and some related concepts | |

Dr. E. S. Jeevanand (Statistics) | Dr. Mathachan Pathiyil (2008) | Some inference problems related to geometric distribution |

Dr. Cyriac Antony (2012) | Financial market analysis and investment decisions – A statistical approach | |

Dr. Dhanya, M (2016) | Estimation of reliability measures of some commonly used heavy tailed lifetime distributions | |

Dr. Thambi, K. K. & Dr. E. S. Jeevanand (Statistics) | Dr. Joseph Justin Rebello (2018) | A stochastic risk model with two sided jumps with applications in insurance |

Dr. Rajan Varughese (Statistics) | Dr. Bijamma Thomas (2015) | Software reliability growth models |

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### Ongoing Projects

Dr. Anu Nuthan Joshua is a Co- Principal Investigator of the Indo- Russian(DST-RSF) Project ‘Development and study of methods for reliability enhancement of tethered high altitude unmanned telecommunication platform’, sanctioned by DST in 2022.

### Completed Projects

**Software Reliability Data Analysis with Stress-Strength Model using the Power law distribution****“Some Problems in Graph Theory with special reference to Fuzzy Intersection Graphs”****“An Analysis of Effectiveness of Student Support Systems in Individual Performances using Fuzzy Relations”.**

**Summary of the UGC minor project**

**“Estimation of time zo test transform for Classical Pareto distribution IN some real data situation”**

**(Dr.E.S.Jeevanand, Associate Professor, Department of Mathematics.)**

The field of reliability is of recent origin. In the real world, all products and systems are unreliable in the sense that they degrade with age and ultimately fail. Since the process of deterioration leading to failure occurs in a random manner, the concept of reliability requires a probabilistic framework. With the wide spread manufacture and use of increasingly sophisticated mechanical, electrical and electronic equipment during the second half of the last century, questions of reliability became of interest. The term reliability of a product (system) denotes the probability that the product (system) will perform its intended function for a specified time period when operating under normal environmental conditions. Even though the above definition of reliability is explained with reference to the behavior or length of life of a system, it is equally applicable in the analysis of any duration variable that describes a well-defined population subject to decrement due to the operation of forces of attrition over time. It may not be out of place to point out that the methods of lifetime analysis can be applied in many areas beyond survival analysis (and reliability which is concerned with failure of industrial objects). It needs to be recognized that the data to be analyzed should be in the form of the time of occurrence of the event of interest. Such events may be from economics – time spent in the state of unemployment, from sociology – time spent out of jail until next conviction, and from other disciplines. In general, one may call this methodology as event time analysis.

### TTT-plot

The TTT-plot an empirical and scale invariant plot based on failure data, and the corresponding asymptotic curve, named the scaled TTT-Transform were introduced by Barlow and Campo (1975) and used for model identification purposes. Since then these tools have proven to be very useful in several applications in reliability. The TTT-Transform has also been found quite useful in theoretical applications such as looking for test statistics for particular purposes and to study their power. They are also been found quite useful in practical applications such as ageing properties, characterization of distributions, maintenance optimization and also in design of experiments (See Deshpande and Suresh (1990) and Bergman and Klefsjo(1998)). For more reliability application of the TTT one can refer the papers of Klefsjo and Bergman (1984), Gill (1986), Westberg and Klefsjo (1994), Csorgo and Zitikis (1998), Feng-Bin Sun and Kececloglu (1999), Kvaloslashy and Lindqvist (1998) and Raqabi and Madi(2002). The application of this transform in econometrics and its close relationship with the Lorenz curve have been studied by many authors including Chandra and Singpurwalla (1981), Klefsjo (1984), Pham and Turkkan (1994), Kochar et al. (2002), among others. The scaled total time on test (TTT) transform of *F *is defined as (Klefsjo(1984))

f(*p*) = for 0 £ *p *£ 1. (1.1)

m = and = inf{*x*: *F*(*x*)³y} for 0 £ *y *£ 1.