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Recent Advances in Pure & Applied Recent Advances in Pure & Applied Recent Advances in Pure & Applied Recent Advances in Pure & Applied
Mathematics Mathematics Mathematics
Mathematics (RAPAM) (RAPAM) (RAPAM) (RAPAM) Dt. 10/07/2020 & 11/07/2020 Dt. 10/07/2020 & 11/07/2020 Dt. 10/07/2020 & 11/07/2020 Dt. 10/07/2020 & 11/07/2020
Organized By Organized By Organized By Organized By
Department of Mathematics Department of Mathematics Department of Mathematics Department of Mathematics
Narajole Raj College
Narajole Raj College Narajole Raj College
Narajole Raj College
CONTENTS
Authors Title of Presentation Page No
Abhijit Mandal &
Ashoke Das
On the Concircular Curvature Tensor of LP Sasakian Manifolds Admitting Zamkovoy
Connection
05
Amit Soft Semi-Open and Soft Semi-Closed Sets 06
Anil Kumari & Dr.
Manjeet Jakhar Galois Theory: Numerical Approach for the Fundamental Theorem
07
Dr. Bhairab Borgohain Effects of Variable Viscosity and Thermal Conductivity of a Micropolar Fluid with Suction
and Blowing in Presence of Magnetic Field
08
Debozani Borgohain MHD Flow of Chemically Reactive Micropolar Nanofluid near the Stagnation Point in the
Pesence of Thermal Radiation
09
Deepak Kumar &
Anoop Mann
Numerical Applications of Elzaki Transform in Wave Equation Solution
10
Gitika Dureja Mathematics in Nature: Golden Ratio 11
Dr. Mamoni Dhar Intuitionistic Fuzzy Soft Matrices in Medical Diagnosis
12
M. Sindhu & S.
Chandra Kumar
Odd Vertex Out-Magic Total Labeling of Some Digraphs
13
Pralay Poria & Dr.
Ajoy Kumar Maiti
A Contractive Mapping Genetic Algorithm (CMGA) Approach to Solve Cloudy Fuzzy Economic Production Quantity Model with
Demand Dependent Production Rate
14
Shilpa Patra Huber’s Theorem and Some Results in Bispaces 15
Dr. S. Karunakar
Reddy &
Dr. B. Shanker Goud
Suction/Injection Effects on a Stretching Surface of the Stagnation Point Flow through Porous
Medium in the Presence of Heat Generation
16
NARAJOLE RAJ COLLEGE
(NAAC Accredited ‘B’ Grade Govt. Aided College)
NARAJOLE: PASCHIM MEDINIPUR: WEST BENGAL: Pin-721211
Phone and Fax: +91- 9933881131: E-mail: [email protected] Website: http://www.narajolerajcollege.ac.in
Dated: 08.07.2020
It gives me immense pleasure to know that the Department of Mathematics of Narajole Raj College is going to organize a two day National webinar on "Recent Advances in Pure and Applied Mathematics" on July 10th and 11th 2020 under the guidance of IQAC, Narajole Raj College.
Mathematics can help people to better understand and describe the world around them. So it is the Universal Language. It rises above words. In fact it is quite possible that Mathe- matics will be the common link between ourselves and any aliens we may one day meet!
In this scenario, I congratulate the Convenors and the members of the organizing commit- tee for arranging this academic venture that focus on recent advances in pure and applied mathematics and making it a grand success. I rely on that this Webinar will illuminate the academic activity among the participants.
Dr. Anupam Parua, Principal, Narajole Raj College, Paschim Medinipur,
Message
NARAJOLE RAJ COLLEGE
(NAAC Accredited ‘B’ Grade Govt. Aided College)
NARAJOLE: PASCHIM MEDINIPUR: WEST BENGAL: Pin-721211
Phone and Fax: +91- 9933881131: E-mail: [email protected] Website: http://www.narajolerajcollege.ac.in
Dated: 07.07.2020
I am immensely happy to know that the Department of Mathematics, Narajole Raj College is going to organize a Two -day National Webinar on "Recent Advances in Pure and Ap- plied Mathematics (RAPAM)" on July 10th and 11th, 2020.
Mathematics is an integral part of our day to day life. The great mathematician, Py- thagoras, believed that mathematics held the key to beauty and philosophy. Mathemat- ics is the foundation of engineering, computer science, software design, economics, sta- tistical analysis, and many number of professions.
On behalf of IQAC, Narajole Raj College, I extend my warm greetings to all those who are associated with this academic conference and wish the Webinar all success.
Dr. Nilanjana Bhattacharyya Coordinator, IQAC
Narajole Raj College
Message
On the Concircular Curvature Tensor of LP Sasakian Manifolds Admitting Zamkovoy Connection
Abhijit Mandal
Assistant Professor, Raiganj Surendranath Mahavidyalaya, Raiganj , Uttar Dinajpur, West Bengal - 733134
Email: [email protected] Ashoke Das
Associate Professor, Raiganj University, Raiganj , Uttar Dinajpur, West Bengal -733134
Email: [email protected]
Abstract
The object of the paper is to study the properties of Lorentzian Para-Sasakian (briefly LP Sasakian) manifolds with respect to Zamkovoy canonical connection. We also study the Concircular curvature tensor and Concircularly flat, ξ-Concircularly flat, quasi φ- Concircularly flat, φ-Concircularly flat LP Sasakian manifolds admitting Zamkovoy ca- nonical connection. Moreover we discuss Ricci soliton on LP Sasakian manifolds with respect to Zamkovoy canonical connection
.
Soft Semi-Open and Soft Semi-Closed Sets
Amit
Assistant Professor, Department of Mathematics, I.B(PG) College , Panipat, Haryana
Email: [email protected]
Abstract
Molodstov (1999), introduced soft set theory as a new Mathematical approach for solving problems having uncertainties. In a continuation, in this paper, we introduced the notion of soft semi open sets and soft semi closed sets in soft topological spaces. Moreover, the terms soft semi interior, soft semi exterior, soft semi closure, soft semi open neighbour- hood in the soft topological space are also defined. Also, various properties and character- istics related to above terms are discussed. The addition of this topic in literature will defi- nitely strengthen the theoretical base for further applications of soft topology in decision analysis and information system.
Key-words: Soft sets, Soft topological space, soft semi open sets, soft semi closed sets, soft semi interior, soft semi exterior, soft semi neighbourhood.
Galois Theory: Numerical Approach for the Fundamental Theorem
Anil Kumari
Research Scholar, NIILM University, Kaithal, Haryana Email: [email protected]
Dr. Manjeet Jakhar
Associate Professor
,
NIILM University, Kaithal, Haryana Email: [email protected]Abstract
We give a short and self-contained proof of the Fundamental Theorem of Galois Theory (FTGT) for finite degree extensions. We derive the FTGT (for finite degree extensions) from two statements, denoted (a) and (b). These two statements, and the way they are proved here, go back at least to Emil Artin (precise references are given below). The argument is essentially taken from Emil Artin's Notre Dame Lectures [A]. More precisely, statement (a) below is im- plicitly contained in the proof Theorem 10 page 31 of [A], in which the uniqueness up to iso- morphism of the splitting field of a polynomial is verified. Artin's proof shows in fact that, when the roots of the polynomial are distinct, the number of automorphisms of the splitting extension coincides with the degree of the extension. Statement (b) below is proved as Theo- rem 14 page 42 of [A]. The proof given here (using Artin's argument) was written with Keith Conrad's help.
Effects of Variable Viscosity and Thermal Conductivity of a Micropolar Fluid with Suction and Blowing in Presence of
Magnetic Field
Bhairab Borgohain
Assistant Professor, Department of Mathematics, Tinsukia College, Tinsukia , Assam-786125
Email : [email protected]
Abstract
A numerical investigation has been carried out to determine the flow and heat transfer of a rotating micropolar fluid subject to suction and blowing considering the sheet with pre- scribed wall temperature. The fluid viscosity and thermal conductivity are assumed to vary with temperature. The micropolar model due to Eringen is used to describe the working fluid. The partial differentia equations governing the motion, angular momentum and en- ergy are reduced to ordinary differential equations using similarity transformations and then solved numerically using Runge-Kutta shooting technique. The results are presented graphically for velocity distribution, temperature distribution and micropolar distributions for various value of non-dimensional parameters. It is found that the effects of the parame- ters representing variable property of viscosity and thermal conductivity are significant.
Key-words:Micropolar fluid, Variable viscosity, Variable thermal conductivity, Stretching surface.
MHD Flow of Chemically Reactive Micropolar Nanofluid near the Stagnation Point in the Presence of Thermal Radiation
Debozani Borgohain
Assistant Professor, Department of Mathematics, Dibrugarh University, Dibrugarh, Assam- 786004
Email: [email protected]
Abstract
The present study investigates numerically the impacts of chemical reaction and thermal radiation on MHD flow of micropolar fluid past a shrinking sheet near the stagnation point under solutal and thermal convective conditions in the presence of nanoparticles. A system of ordinary differential equations is formed from the nonlinear partial differential equations governing the fluid flow using similarity transformations. These equations are then pro- grammed in MATLAB and using its solver bvp4c numerical results are obtained. The re- sults for velocity, temperature, concentration, Nusselt number and Sherwood number are shown in graphs for various values of the material parameters. It is observed that the ther- mal boundary layer of the micropolar nanofluid is enhanced by the upsurge in thermal ra- diation whereas the nanoparticle volume fraction reduces with the chemical reaction. The rates of heat transfer and mass transfer due to the fluid flow are favoured by the thermal radiation and nanofluid parameters. This present study can have its applications in heat transfer processes, in heat exchangers as well as cooling systems and also in biomedical ap- plications such as cancer therapy, nanocryosurgery, nuclear plants etc.
Numerical Applications of Elzaki Transform in Wave Equation Solution
Deepak Kumar
Assistant professor, Department of Mathematics, Geeta Degree College, Shera, Panipat, Haryana
Email: [email protected] Anoop Mann
Assistant professor, Department of Mathematics, K.U.K.
Abstract
The topic of the paper is to deal with the numerical aspects of new Integral transform viz,. El- zaki Transform was applied to solve 1-dimensional wave equation to obtained the exact solu- tions. This method is a very powerful and efficient tool for solving 1-dimensional wave equa- tion. The applicability of this new method is explained by elaborating a few examples.
Key-words: 1-dimensional wave equation, Neumann boundary conditions, Elzaki Trans- form.
Mathematics in Nature: Golden Ratio
Gitika Dureja
Assistant Professor, Department of Mathematics, I.B. (PG) College, Panipat, Haryana
Email: [email protected]
Abstract
Natural and artificial designs always contain certain elements that provide the aesthetic attributes of the individual structure or item. These design elements exhibit a pattern in the things that are aesthetically pleasing. The most famous of these patterns is the Golden Ratio that is also known as the Golden mean, Divine Section, Divine Proportion . It was first used in architecture in 2650 BC in the building of the Great Pyramids of Giza. The Golden ratio is a mathematical representation of proportionality that occurs in nature and in the arts and science. It is an irrational number (1.618) that emanates from the Fibonacci sequence. Two numbers are said to be in golden ratio if the ratio of the sum of the numbers (say a + b) di- vided by the larger number (a) is equal to the result of the large number divided by the smaller number (a/b).It is a number often encountered when taking ratio of distances in sim- ple geometric figures such as pentagon, pentagram, decagon and dodecahedron. The Golden Ratio is observed in nature, in art, in science and also in human body. The Golden Ratio is also observed in branches of trees, in snail shells, human face, in woman womb, in water waves and also in tail of a lizard. The purpose of this paper is to observe these natural aes- thetics of Golden Ratio.
Key-words : Golden Mean, Divine section, Fibonacci sequence.
Intuitionistic Fuzzy Soft Matrices in Medical Diagnosis
Mamoni Dhar
Assistant Professor, Department of Mathematics, Science College, Kokrajhar, Assam
Email:[email protected]
Abstract
In this article, the main focus is to find a new method for constructing a decision matrix us- ing intutionistic fuzzy soft matrices. In order to reach our goal addition, subtraction and complementation of intuitionistic fuzzy soft matrices are taken into consideration.
Key-words: Fuzzy sets, fuzzy matrix, intuitionistic fuzzy soft matrix.
Odd Vertex Out-Magic Total Labeling of Some Digraphs
M. Sindhu
Research Scholar, Department of Mathematics, Scott Christian College(Autonomous), Nagercoil-629003, Tamil Nadu
Email: [email protected] S. Chandra Kumar
Associate Professor, Department of Mathematics, Scott Christian College(Autonomous), Nagercoil-629003, Tamil Nadu
Email: [email protected]
Abstract
Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a
bijection with the property that for every ,
, for some constant . Such labeling is called Odd vertex out- magic total labeling if .In this paper, we examine some graphs which admits Odd Vertex out-magic total labeling.
A Contractive Mapping Genetic Algorithm(CMGA) Approach to Solve Cloudy Fuzzy Economic Production Quantity Model with
Demand Dependent Production Rate
Mr. Pralay Poria
Assistant Professor, Department of Mathematics, Sabang Sajanikanta Mahavidyalaya, Lutunia, Paschim Medinipur, West Bengal - 721166
Email: [email protected] Dr. Ajoy Kumar Maiti
Assistant Professor, Department of Mathematics, Raja Narendra Lal Khan Women’s College(Autonomous), Gope Palace,
Paschim Medinipur, West Bengal - 721102 Email: [email protected]
Abstract
The aim of the article is to develop classical economic production quantity model of an item produced with fixed set up cost and without shortages has been considered in fuzzy environment where demand rate of an item is fuzzy number and production rate is de- mand dependent. In general, fuzziness of any parameter remains fixed over time but in practice, fuzziness of parameter begins to reduce as time progress because of gathering experience and knowledge. The model is solved in crisp, general fuzzy and cloudy fuzzy environment using Yager’s index method, extension of Yager’s ranking index method and De and Beg’s ranking index method and comparison are made for all cases. Here, the average cost function is minimized using Contractive Mapping Genetic Algorithm (CMGA) to find decision for the decision maker (DM). The model is illustrated with some numerical examples and some sensitivity analyses have been done to justify the notion.
Key-words: EPQ, Yager’s, De and Beg’s ranking index method, cloudy fuzzy number, CMGA.
Huber’s Theorem and Some Results in Bispaces
Shilpa Patra
Assistant Professor, Department of Mathematics, Narajole Raj College, Narajole, Paschim Medinipur, West Bengal -721211
Email: [email protected]
Abstract
Topological spaces have been generalized in many directions. One such generalization is a σ-space or simply a space introduced by A. D. Alexandroff where only countable unions of open sets are taken to be open. Let P and Q be two topologies on a nonempty set X.
Then (X, P, Q) is called a bitopological space. A good account of bitopological spaces can be found in J. C. Kelly’s paper. Later on, several topological properties were studied in more general structure of bitopological spaces. In 1963, N. Levine had introduced the con- cept of semi open sets in a topological space and obtained some of its important proper- ties. Afterwards, Lahiri and Das studied how far the properties of semi open sets as intro- duced by Levine in a topological space are affected in the space of Alexandroff. Moreover, they generalized the notion of bitopological spaces to bispaces by using the concept of space. In 1954, A. Huber has proved the well-known Huber’s Theorem. The main purpose of our work is to generalize Huber’s theorem in the setting of bispaces and to discuss ana- lytic properties of the limit map of a sequence of continuous maps over bispaces.
Suction/Injection Effects on a Stretching Surface of the Stagnation Point Flow through Porous Medium in the Presence of Heat
Generation
Dr. S. Karunakar Reddy
Assistant Professor, Department of Mathematics, JNTUH CEH, Kukatpally, Hyderabad, Telengana
Email: [email protected] Dr. B. Shanker Goud
Assistant Professor, Department of Mathematics, JNTUH CEH, Kukatpally, Hyderabad, Telengana
Abstract
An investigation is made to steady of laminar flow of viscous fluid on stretching surface with the impact of the heat generation through porous medium in the presence of the suc- tion and injection. With the help of the similarity transformation the governing partial dif- ferential equations are transformed to nonlinear ordinary differential equations. The resul- tant equations are solved numerically by the MATLAB inbuilt solver bvp4c. The profiles of the velocity and temperature are discussed through graphs and the non-dimensional pa- rameter the wall shear stress and heat transfer coefficient are presented in the tabular form.
Key-words: Stagnation point, Heat generation, Suction, Injection, Porous medium.
