1Department of Physics, Meghnad Saha Institute of Technology, Nazirabad,
P.O. Uchepota, Anandapur, Kolkata-700150, India
2Department of Basic Science and Humanities,
Institute of Engineering & Management, D1, Management House Salt Lake,
Sector V Kolkata -700091, India
3Department of Applied Physics, University College of Science and Technology,
92 APC Road, Kolkata-700009, India
4University of Engineering Management, University Area, Plot, Street Number 03, Action Area
III, B/5, Newtown, Kolkata, West Bengal 700160
Page Number: 374-438
In this paper we study the Electron Energy Spectra (EES) in quantum wells (QWs) of heavily doped (HD)
non-linear optical, III-V, II-VI, IV-VI and stressed Kane type compounds by formulating HDEES in each
case respectively considering all the specialties of the energy band constants of the said materials . It is
noted that the complex EES in many cases in HDS, instead of real one, occurs from the existence of the
essential poles in the corresponding EES in the absence of band tails. The EES in QWs is Quantized 2D
closed surfaces. As a collateral study we have also investigated the effective mass (EM), Density-of-states
(DOS) function and the electron statistics in this context for the purpose of comprehensive understanding.
The EM exists in the forbidden zone, which is impossible without the effect of band tailing. In the absence
of band tails, the EM in the band gap of semiconductors is infinity. Besides, depending on the type of
unperturbed carrier energy spectrum, the new forbidden zone will appear within the normal energy band
gap for HDS. Under certain limiting conditions all the results for all the models get simplified the wellknown
results of an isotropic parabolic energy bands which exhibit the mathematical compatibility of our
present generalized analysis.
Keywords:Electron Energy Spectra, Heavy Doping, Quantum Wells, Effective Mass, Density-of-States
Function (DOS)
Department of Mathematics
National Institute of Technology Manipur,Langol, Imphal-795004, Manipur, India
Email:[email protected]
Page Number: 439-450
If f(z) = nΣ v=0 c vzv is a polynomial of degree n which does not vanish in
|z|=1, then for 0|z|= (ρ) |ƒ(z)|<= n (ρ+t)n-1 ‾ (t+r) n
{1-t(t-ρ(n|c0|-t|c1)|)n ‾ (t2+ ρ2)n|c0|+ 2t2ρc1(ρ- r ‾ t+ρ)(t+r ‾ t+ρ)n-1} max|z|-r|ƒ(z)|
In this paper, we prove an interesting inequality, which not only extends the above result to Lq
version as a particular case, but also gives some interesting known results as corollaries.
Keywords: Polynomial,Lq Inequalities, Maximum Modulus.
1,2 Department of Computer Science Engineering
Institute of Engineering & Management
EP Block, Sector V, Salt Lake, Kolkata-700091. India
3,5Department of Electronic and Communication Engineering
Institute of Engineering & Management
EP Block, Sector V, Salt Lake, Kolkata-700091. India
4Department of Mechanical Engineering
Institute of Engineering & Management
EP Block, Sector V, Salt Lake, Kolkata-700091. India
Corresponding Author Email: [email protected]
Page Number: 451-455
There have been several fascinating applications of Number Theory in key cryptography. Key cryptography
enables many technologies we take for granted, such as the ability to make secure online transactions. The
purpose of this survey paper is to highlight certain important such applications. Prime numbers constitute
an interesting and challenging area of research in number theory. Diophantine equations form the central
part of number theory. An equation requiring integral solutions is called a Diophantine equation. In the
first part of this paper, some major contribution in number theory using prime number theorem is discussed
and some of the problems which still remains unsolved are covered. In the second part some of the
theorems and functions are also discussed such as Diophantine Equation, Goldbach conjecture,Fermats
Theorem, Riemann zeta function and his hypothesis that still remain unproved to this day . The Chinese
hypothesis is a special case of Fermat’s little theorem. As proved later in the west, the Chinese hypothesis
is only half right . From the data of this study we conclude that number theory is used in computer network
and applications in cryptography.We came to know about the purpose of Diophantine equation , Squarefree
natural number,Zeta function,Fermat’s theorem and Chinese hypothesis which is a special case for
Fermat’s theorem.
Keywords: Chinese hypothesis, Diophentine equation, Fermat’s theorem, Goldbach conjecture, squarefree
natural number.
In this paper, making use of concept splitting the limits of summation identities and Bailey’s lemma, an
attempt has been to establish the transformations involving Bailey’s lemma and Truncated Basic
Hypergeometric Series.
Keywords: Bailey’s lemma, q-series, Basic Hypergeometric functions, Truncated Basic Hypergeometric
functions.
1Department of Physics,
Dharsa Mihirlal Khan Institution [H.S], G.I.P Colony, Howrah-711112, India.
Kalpana Chawla Centre for Space and Nano Sciences (KCCSNS), Kolkata700010, India
Email: [email protected]
2Department of Physics,
Sister Nivedita University, DG 1/2, Action Area 1, Newtown Kolkata-700156, India
Page Number: 462-483
A modified gravity theory with f (R) = R2 coupled to a dark energy lagrangian L = −V (φ)F
(X) , X = ∇μφ∇μφ, gives plausible cosmological scenarios when the modified Friedman
equations are solved subject to the scaling relation X( dF )2= Ca(t)−6. This relation is already
known to be valid, for constant potential V (φ), when L is coupled to Einstein gravity. φ is the
k-essence scalar field and a(t) is the scale factor. The various scenarios are: (1) Radiation
dominated Ricci flat universe with deceleration parameter Q = 1. The solution for φ is an
inflaton field for small times. (2) Q is always negative and we have accelerated expansion of
the universe right from the beginning of time and φ is an inflaton for small times. (3)The
deceleration parameter Q = −5, i.e., we have an accelerated expansion of the universe. φ is
an inflaton for small times. (4)A generalisation to f (R) = Rn shows that whenever n > 1.780
or n < −0.280 , Q will be negative and we will have accelerated expansion of the universe.
At small times φ is again an inflaton.The results remind us of other physical phenomena where
existence of scaling relations signal some sort of universality for theories with different
microscopic lagrangians. Here this is seen in the case of Einstein gravity and modified gravity
theories.
Keywords:Lagrangian, Hubble parameter, pressure, dark energy, ac- celeration.
1Department of Mathematics,
Springdale high school, Kalyani, India
Email: [email protected]
2 Department of Mathematics,
Regent Education and Research Foundation, Kolkata
Email: [email protected]
Page Number: 484-495
According to modern view uncertainty is considered essential to science and technology, it is not only the
unavoidable plague but also it has impact a great utility. Generally, fuzzy sets are used to analyse fuzzy
system reliability. To analyse the fuzzy system reliability, the reliability of each component of the system
is considered as a Triangular intuitionistic Type 2 fuzzy number (TIT2FN). At first, TIT2FN and their
arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system and
a parallel system following TIT2FN have been described. Here, an imprecise reliability model of an electric
network model of a dark room is taken. To compute the imprecise reliability of the above said system, the
reliability of each component of the systems is represented by TIT2FN. A corresponding numerical example
is presented.
Keywords:Triangular intuitionistic Type 2 fuzzy number (TIT2FN), System reliability, Parallel system,
Series system.
Department of Basic Science and Humanities,
Institute of Engineering & Management,
D1 Management House Salt Lake, Sector-V, Kolkata-700091, India
Page Number: 496-501
Over centuries mathematicians have generated a wealth of rigorous and high level mathematics that is the
armoury of pure mathematicians. But there is an interesting segment of mathematics that can justifiably be
consigned to a different realm, which is the world of recreational mathematics. In this paper we will visit a
few interesting areas of this fascinating domain.
Keywords: Rigorous, armoury, realm, recreational.
Department of Mathematics/Statistics,
Ignatius Ajuru University of Education, Port Harcourt, Nigeria
Corresponding Author: [email protected]
Page Number: 502-523
In this paper, I considered the comparison of numerical methods in predicting the biodiversity gain due to
the variation of α1 and α2 together on biodiversity scenario. However, when the model parameter values
α1 and α2 are increase, the normal agricultural variable also changes. By comparing the patterns of growth
in these two interacting normal agricultural data, we have finite instance of biodiversity due to the
application of four numerical methods such as ODE45, ODE23, ODE23tb and ODE15s. We have found
the numerical prediction upon using these four numerical methods which are similar and robust, hence we
have considered ODE45 numerical simulation to be computationally more efficient than the other three
methods. The novel result we have obtained in this study have not been seen elsewhere. Keywords: ODE45, ODE23, ODE23tb, ODE15s, Normal Agriculture
1,2,3Institute of Engineering & Management
Salt Lake Electronics Complex, Kolkata-700091. India
Email: [email protected]
Page Number: 524-530
This study seeks to analyze conceptual, innovative, marketing and quantitative aspects of Bitcoin (BTC)
and how these are reflected in the volatility of its return. After describing basic concepts of digital currencies
and BTC, an electronic currency created in 2009, we contextualize BTC as a financial innovation. A purely
peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to
another without going through a financial institution .We propose a solution to the double-spending problem
using a peer-to-peer network. The longest chain not only serves as proof of the sequence of events
witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power
is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and
outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort
basis, and nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as
proof of what happened while they were gone In my contribution I want to analyses this currency-system
from a sociocy bernetic point of view .After presenting the basic mechanisms of Bitcoin money creation,
the value regulation etc. We want to focus the basic processes of self-organization in this high-complex
social system.
Keywords:Bitcoin, Innovation.
4Student of Hemsheela Model School
Durgapur, Paschim Bardhaman, West Bengal, India
Email: [email protected]
5Professor & Head, Department of Computer Science
The University of Burdwan, Burdwan, West Bengal, India
Email: [email protected]
Page Number: 531-542
In India, the Management Aptitude Test (MAT) score is taken as the primary indicator of a student’s ability
to be enrolled in the management courses. It has been observed in many cases during the group discussion
and personal interview phases for MBA course admission, that candidate with poor MAT scores do well
than those with higher scores. Hence, in that context, this research was carried out in order to assess the
validity of MAT scores in predicting future success and also to measure the nature and strength of
association between MAT scores and academic achievements. We also look at the correlation between
students’ academic performance in their higher-secondary & under-graduate levels, and their MAT scores.
Keywords: Management Aptitude Test (MAT) score, academic achievement, management courses
