Kindly read my article in Binoy Majumber issue of Kabitirtha

National Workshop

Two-Day

National Workshop

On

Activity Based Teaching & Learning: Innovative

Teacher Education Initiatives

                                                                             

27^th & 28^th March, 2017

Organized by

Department of Education

Vinaya-Bhavana

(Institute of Education)

VISVA-BHARATI
Santiniketan

            www.visva-bharati.ac.in

Two-day National Workshop

Dr. Narayan Ch Ghosh

Former Professor in Mathematics

Respected Sir,

            It is a matter of great pleasure to inform you that Department of Education, Vinaya Bhavana, Visva-Bharati, Santiniketan is going to organize Two-day National Workshop on “Activity Based Teaching and Learning: Innovative Teacher Education Initiatives” for B.Ed. trainees of the Department, from 27^th to 28^th March, 2017 in the Department of Education, Vinaya Bhavana, Visva-Bharati, Santiniketan.

We are inviting you as a Chief Guest for Inaugural Session of the Two-day National Workshop. Kindly make it convenient to please come and oblige us for the same.

For the detailed information, workshop brochure is attached here in this mail. 

We hope that you will take out some time from your busy schedule to be here at Vinaya Bhavana with us. Kindly give your consent in written or via E-mail to attend the workshop.

Thanking you in positive anticipation.

-- 

Thanks & Regards

Dr. Sarita Anand

(Workshop Convener)

             &

Assistant Professor,
Department of Education,
Vinaya-Bhavana,
Visva-Bharati-A Central University & An Institution of National Importance,
Santiniketan, Bolpur,
Dist-Birbhum, West Bengal-731235, India
e-mail- sarita.anand@visva-bharati.ac.in
Mob.- +91-9333044901(W.B.), +91-9335067036(U.P.)

Attachments 

LABORATORY   BASED   MATHEMATICS   TEACHING

Narayan Ch Ghosh

E.K.T.P. Phase IV, No. C-34/4, Kolkata-700107

Email : ghosnarayan@gmail.com, Mobile : 91 9433870760, 9804223949,

ABSTRACT

Mathematical Concepts started to build in the early stage of mankind and it has been developed, refined continuously with the change of society. Mathematics of Folk life, body of traditional mathematic, originally transmitted orally and even now almost same procedure are continuing. Folk mathematics may be regarded as an undercurrent to the mainstream of mathematics; it nourishes the mainstream, and at the same time, is nurtured by it. Being extremely practical in nature it serves the daily need of the people of every walk of life. Common people with elementary education can apply it at ease to the solution of various problems arising out of everyday life, seek recreation in it, and are encouraged to devise new problems or puzzles orally, whether those are significant or trifling. But in the present developed society, people are using mathematics multifarious ways mathematics learning is associated with fears, tears, trauma and even conscious people used say, learning of mathematics is a tuff job. For folk people nature is their laboratory. Commensuration with nature based laboratory here author tried to build an idea for Laboratory based mathematics teaching in the present globalised thinking of education.

ASPECTS OF LOITSIANSKY’S TYPE OF INVARIANT

ASPECTS OF LOITSIANSKY’S TYPE OF INVARIANT

*,1Ghosh, N. C., 2Pijush Basak and 3Abhijit Bhattacharya

1S.N. Bose Institute for Mathematics & Mathematical Sciences

2Narula Institute of Technology

3B.P. Poddar Institute of Management & Technology

                                                                    ABSTRACT

Turbulence is seen as one of the last outstanding unsolved problems in classical physics. In the last century, great minds viz, Heisenberg, von Weizs"acker, Kolmogorov, Prandtl and G.I. Taylor had worked on it. Einstein put his last postdoc Bob Kraichnan on the subject of Turbulence. Despite the fact that isotropic turbulence constitutes the simplest type of turbulent flow, it is still not possible to render the problem analytically traceable without introducing the two point double and triple longitudinal velocity correlations to admit self-similarity solution with respect to a single length-scale, which has served as a useful hypothesis since its inception by von Karman and Howarth (1938). Rapid development of experimental and numerical techniques in this area and the growth of computing power created a lot of activities on turbulence research. Here authors have elaborated a debated concept Loitsiansky’s type of invariant associated with turbulent study from analytical point.

Copyright©2016 Ghosh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.
INTRODUCTION

Homogeneous isotropic turbulence is a kind of idealization for real turbulent motion, under the assumption that the motion is governed by a statistical law invariant for arbitrary translation (homogeneity), rotation or reflection (isotropy) of the coordinate system. This idealization was first introduced by Taylor (1935) and used to reduce the formidable complexity of statistical expression of turbulence and thus made the subject feasible for theoretical treatment. Up to now, a large amount of theoretical work has been devoted to this rather restricted kind of turbulence. However, turbulence observed either in nature or in laboratory has much more complicated structure.

Although remarkable progress has been achieved so far in discovering various characteristics of turbulence, our understanding of the fundamental mechanism of turbulence is still partial and unsatisfactory. The assumption of similarity and self-preservation, which permits an analytical determination of the energy decay in isotropic turbulence, has played an important role in the development of turbulence theory for more than half a century. In the traditional approach to search for similarity solutions for turbulence, the existence

of a single length and velocity scale has been assumed, and then the conditions for the appearance of such solutions have been examined. Excellent contributions had been made to this direction by von Karman and Howarth (1938), who firstly deduced the basic equation and presented a particular set of its solutions for the final decaying turbulence. Later on, two Russian scholars, Loitsiansky (1939) and Millionshtchikov (1941), separately obtained the solutions for the Karman-Howarth equation after the term related to the effect of the

triple velocity correlation has been neglected (Ghosh and Ghosh, 1982; Ghosh, 2001). Their work was an extension of the “small Reynolds number” solution first given by von Karman and Howarth. Dryden gave a comprehensive review on this subject (Dryden, 1943). Detailed research on the

solutions of the Karman-Howarth equation was conducted by Sedov, who showed that one could use the separability constraint to obtain the analytical solution of the Karman-Howarth equation (Sedov, 1944). Sedov’s solution could be expressed in terms of the confluent hypergeometric function. Batchelor (1948) readdressed this problem under the assumption that the Loitsiansky integral is a dynamic invariant, which was a widely accepted assumption, but was later found to be invalid. Batchelor concluded that the only complete self-preserving solution which was intrinsically consistent existed at low turbulence Reynolds number, for which the turbulent kinetic energy is accordant with the final period of turbulent decay. Batchelor also found a self-preserving solution to the Karman-Howarth equation in the limit of infinite Reynolds number, for which the Loitsiansky integral is an invariant. Objections were later raised against using the Loitsiansky integral as a dynamic invariant. In fact, at high Reynolds number this integral can be proved to be a weak function of time Proudman and Reid (1954) and Batchelor and Proudman (1956). Saffman proposed an alternative dynamic invariant which yielded another powerlaw decay in the limit of infinite Reynolds number (Hinze,1975). While the results of Batchelor and Saffman formally constitute complete self-preserving solutions to the inviscid

Karman-Howarth equation, it must be kept in mind that they only exhibit partial self-preservation with respect to the full viscous equation. Later on, George (1992) revived this issue concerning the existence of complete self-preserving solutions in isotropic turbulence. In an interesting paper he claimed to find a complete self-preserving solution, valid for all Reynolds numbers. George’s analysis was based on the dynamic equation for the energy spectrum rather than on the Karman-Howarth equation. Strictly speaking, the solution presented by George was an alternative self-preserving solution to the equations of Karman-Howarth and Batchelor since George relaxed the constraint that the triple longitudinal velocity correlation is self-similar in the classical sense. Speziale and Bernard (1992) reexamined this issue from a basic theoretical

and computational standpoint. Several interesting conclusions have been drawn from their analysis. From the development of turbulence theory, it is known that the research on decaying homogeneous isotropic turbulence is one of the most important and extensively explored topics. Despite all the efforts, a general theory describing the decay of turbulence based on the first principles has not yet been developed (Skrbek and Stalp,2000). It seems that the theory of self-preservation in homogeneous turbulence has lots of interesting features which have not yet been fully understood and are worth of further study (Speziale and Bernard, 1992). This paper offers a short, but interesting feature of Loitsiansky invariant unified investigation of isotropic turbulence, based on the exact solutions of the Karman-Howarth equation. The statistical procedures of random fluctuation in a turbulent flow has been investigated by Taylor (1935), Robertson (Robertson, 1940) and many others. Karman and Howarth (1938) proposed the equation of translation for a second order velocity correlation of a homogeneous isotropic flow field. The equation constituting the relation of second order velocity correlation with the third order velocity correlation in collaboration with

viscous damping denoted by Laplacian of second order velocity correlations.
*Corresponding author: Ghosh, N. C.
S.N. Bose Institute for Mathematics & Mathematical Sciences
ISSN: 0976-3376 Asian Journal of Science and Technology
Vol. 07, Issue, 11, pp.3857-3861, November, 2016

ASPECTS OF FLOWS OF THE RIVERS MENTIONED IN THE INDIAN EPIC RAMAYANA

Professor N.C. Ghosh

S.N. Bose Institute of Mathematics & Mathematical Sciences

E.K.T.P. Phase –IV, No. C-34/4

Kolkata - 700107

Dr. Prolay Mondal

Dept. of Geography, Raigunj University

Raigunj, Uttar Dinajpur, W.B.

Ranjan Kumar Das

Assistant Teacher, Bamshore High School

Bamshore, Burdwan

A B S T R A C T

India is rich with voluminous and quality treasure trove of literature, art, music, sculpture and other various forms of culture and fine arts which can be traced back to the very beginning of the early period of civilisation. Out of well known two Indian Epics, Ramayana has always been considered as a marvelous one and considered as the first written literature; though for years it was in varbal form- commonly known in Sruti style. Over the centuries it was developed by several authors during its Sruti style and thereafter in written form. Therefore social aspects, culture, geography, mathematical idea of daily life seen in different parts of Indian subcontinent were been incorporated in different Ramayanas. Many works were been done to explore various aspects viz. philosophy, spirituality, politics, economics, sociology, culture, literature, language, poetry and others elaborated in Ramayanas. But interestingly geography, mainly rivers flows, were never been a popular subject of analysis of the Epic Ramayana; though different rivers are been referred several times in this Epic. Though flows of water and its impacts have been discussed in different occasions are been noted in different chapters in almost all the Ramayanas perhaps due to shortcomings of knowledge in fluid mechanics  these aspects have been ignored in all the discussions. Here an attempt has been taken to study rivers mentioned in the Ramayana and tries to coordinate their relevance on different socio-cultural aspects of life of the people it was used flows. The paper also will try to sketch the account of the rivers from their source to mouth along with their different fluvial properties like shift in the river course, the extension of the flood plain etc. and its end points. The growth of habitation in connection with the major rivers, mentioned in Ramayana has also been considered as important aspects of study in this analysis. The study is totally backed by the literature-based qualitative approach. The major finding of this study supports the view that the rivers as mentioned in Ramayana by Kritibas Ojha in 15th century played a crucial role in the then socio-cultural and other various facets of human life of wide region of eastern India. These rivers have undergone changes in present times which is equally significant so for as the human life of present India is concerned.

TATA has no big project  in West Bengal. In connection with Joyti Basu's continuous effort TATA lastly had decided their long destination in W.B. They had tried to built RATANPUR at Singur like JAMSHEDPUR. But situation compelled them to leave the Idea. I visited Sanand. A remote area is going to be big industrial hub there. Will TATA come back in West Bengal ? I believe history repeats itself, but in higher form. Is there situation has changed for better option.