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Research & Reviews:
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STM JOURNALS
I take the privilege to present the print version for the [Volume 1 Issue (3)] of Research & Reviews: Discrete Mathematical Structures. The intension of RRDMS is to create an atmosphere that stimulates creativeness, research and growth in the area of Discrete Mathematical Structures. The development and growth of the mankind is the consequence of brilliant Research done by eminent Scientists and Engineers in every field. RRDMS provides an outlet for Research findings and reviews in areas of Discrete Mathematical Structures found to be relevant for National and International recent developments & research initiative. The aim and scope of the Journal is to provide an academic medium and an important reference for the advancement and dissemination of Research results that support high level learning, teaching and research in the domain of Discrete Mathematical Structures. Finally, I express my sincere gratitude and thanks to our Editorial/ Reviewer board and Authors for their continued support and invaluable contributions and suggestions in the form of authoring write ups/ reviewing and providing constructive comments for the advancement of the journals. With regards to their due continuous support and co-operation, we have been able to publish quality Research/Reviews findings for our customers base. I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.
Dr. Archana Mehrotra Director STM Journals
Research & Reviews: Discrete Mathematical Structures
Contents
1. Dynamic Analysis of a Switched Boost Converter Singular System using Mehtod-Rachid Algorithm Santhosh KV, Rohit Kalyani
1
2. A Discrete Gamma Lifetime Model and ItsReliability Applications Pramendra Singh Pundir, Hare Krishna
5
3. A Hierarchical Bayes Analysis to Study the Impact of Genetic Susceptibility and Environmental Exposure Akanksha Gupta, S. K. Upadhyay
21
4. Some I-Convergent Difference Sequence Spaces Defined by a Sequence of Orlicz Functions Ayhan Esi, Mehmet Acikgoz, Ayten Esi
32
5. Characterizing the Existence of P4 Pinaki Mitra
39
Research & Reviews: Discrete Mathematical Structures ISSN: 2394-1979 (online) Volume 1, Issue 3 www.stmjournals.com
Dynamic Analysis of a Switched Boost Converter Singular System using Mehtod-Rachid Algorithm Santhosh KV, Rohit Kalyani* Department of ICE, MIT Manipal, India Abstract Electronics technology is a very dynamically evolving technology as compared to any other domains. The advent of these changes is forcing us to relook at the conventional physics, and mathematical models related to switching systems in particular or singular systems in general. Mostly we always drive system characteristics assuming a singular system to be linear. Singular systems are those the dynamics of which are governed by a mixture of algebraic and differential equations. Switched linear systems of the form đ??¸đ?‘ĽĚ‡ = đ??´đ?‘Ľ + đ??ľđ?‘˘, đ?‘Ś = đ??śđ?‘Ľ, with E singular. We study the concept of controllability and observability of switched singular systems by computing the transfer function matrix using Mehtod-Rachid algorithm.
Keywords: Singular systems, switched linear systems, Mehtod-Rachid algorithm, controllability, observability
RRDMS (2014)Š STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures ISSN: 2394-1979 (online) Volume 1, Issue 3 www.stmjournals.com
A Discrete Gamma Lifetime Model and Its Reliability Applications Pramendra Singh Pundir1*, Hare Krishna2 1
Department of Statistics, University of Allahabad, Allahabad (UP) and DST-CIMS, BHU, Varanasi (UP), India 2 Department of Statistics, CCS University, Meerut (UP), India Abstract In this paper, we have first developed discrete gamma failure (dGam) lifetime model by discretizing the well-known gamma failure distribution. Thereafter, we have given a description of the distributional properties and reliability characteristics of dGam model. The next section consists of a few theorems on dGam and provides a basis for ML and Bayes estimation procedures are carried out in next sections along with a thorough simulation study depicting the behavior of these estimators. Finally, some real life situations have been discussed where dGam provides most plausible fitting. Keywords: Gamma distribution, discrete lifetime models, reliability, failure rate
RRDMS (2014)Š STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures ISSN: 2394-1979 (online) Volume 1, Issue 3 www.stmjournals.com
A Hierarchical Bayes Analysis to Study the Impact of Genetic Susceptibility and Environmental Exposure Akanksha Gupta*, S. K. Upadhyay Department of Statistics and DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India Abstract Genetic susceptibility and environmental exposure are considered as two important causes for the development of a rare disease. The genetic susceptibility is a hereditary factor which is inherent in an individual by birth. The environmental factors, on the other hand, are caused by living habits, food habits and other environmental components. Several studies are done in the past to know which particular factor is responsible for the occurrence of rare diseases. However, there are diseases which occur due to the interaction of both these factors. The paper considers a well known multinomial-Dirichlet modelling assumption with two-stage hierarchical Bayes analysis in order to study the impact of gene and environmental factors when the data available are in the form of cases and controls. The case of missing data problem is also entertained for the completeness of the study. A numerical illustration is provided based on a real data set on ovarian cancer among Israeli women. Keywords: Case-control study, gene-environment interaction, hierarchical Bayes, missing data, Metropolis-Hastings algorithm
RRDMS (2014)Š STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures ISSN: 2394-1979 (online) Volume 1, Issue 3 www.stmjournals.com
Some I-Convergent Difference Sequence Spaces Defined by a Sequence of Orlicz Functions Ayhan Esi*, Mehmet Acikgoz, Ayten Esi Department of Mathematics, University of Adiyaman, Turkey Abstract I I In this paper, we introduce the difference sequence spaces c , , c0 , ,
mI , and m0I , using a sequence of Orlicz functions M k . We study some properties of these sequence spaces like completeness, solidness, symmetricity, convergence free and some inclusion relations. Keywords: I-convergence, asymptotic density, Orlicz function, monotone
RRDMS (2014)© STM Journals 2014. All Rights Reserved
Research & Reviews: Discrete Mathematical Structures ISSN: 2394-1979 (online) Volume 1, Issue 3 www.stmjournals.com
Characterizing the Existence of P4 Pinaki Mitra* Department of CSE, IIT Guwahati, Guwahati, India Abstract In a graph G = (V, E) P4 denotes a path of length 4 vertices <v1, v2, v3, v4> such that there is no edge between either <v1, v3> or <v2, v4>. This exists either in graph G = (V, E) or its complement or both for which both G and the complement Gc are connected. In this article we give a proof for this property.
Keywords: P4, Complement graph, star Sub-graph, induction
RRDMS (2014)Š STM Journals 2014. All Rights Reserved