1,3Department of Mathematics, Federal University of Lafia P.M.B 146 Lafia
2Department of Mathematics, Federal University of Technology, Owerri
Page Number: 257-261
This paper considers the semigroup of partial transformation Pn and investigated the elements of collapse
given by c ( Α ) =| C ( Α) |=| ∪ tΑ-1 ≥ 2| . Consequently, the formular for the total number of collapsible
elements for | t Α -1 |= 2 and | tΑ-1|= 3 in P n is presented.
Keywords: Collapse, idempotent, Nilpotent, Partial transformation semigroup.
1Department of Basic Science and Humanities,Institute of Engineering & Management (IEM), Kolkata
Page Number: 262-271
We have reviewed the proof [1] of a conjecture posted in the Online Encyclopedia of Integer Sequences
(OEIS)[2] , which states that there are exactly five positive integers that can be represented in more than one
way as the sum of non-negative integral powers of 2 and 3. The case for both powers being positive follows
from a theorem of Bennett. We have also devised alternative logics to the elementary methods applied in
the original paper “On duplicate representations as 2 x +3 y for nonnegative integers x and y” [1] to prove the
case where zero exponents are allowed. Besides, we have included a nominal program towards the end, that
verifies the statement of the conjecture.
Keywords: Online Encyclopedia of Integer Sequences (OEIS), exactly five positive integers, non-negative
powers of 2 and 3, Bennett theorem and zero exponents.
1Department of Computer Application, C.R.T.I.Tinkonia, Goods shed Road, Burdwan, India
2Department of Computer Science, The University of Burdwan,
Burdwan, India
3Department of Computer Science, M.U.C. Women’s College,
B.C. Road, Burdwan, India
4Department of Computer Science & Electronics, R.K.M. Vidyamandira,
Belur Math,Belur,India
Page Number: 272-299
At present market, with the help of science, the information technology has developed rapidly as well
as the information security as an important part of information technology is also strongly affecting
people's work and life. When the development of science and technology brings convenience to
characters, it also exposes many security issues. In recent years, information security incidents such as
information leakage, SQL injection vulnerabilities, network penetration, and hacking attacks have
triggered irreparable losses to enterprises, society, and individuals. In our paper, a symmetric key
encryption with fuzzy based session key has been proposed for satisfying the key issues like security;
increase the strength of symmetric key. Here the session key is generated using fuzzy logic. Now the
encryption is done by using this session key and symmetric key. Here a new authentication scheme is
developed to generate cipher text. Different types of experiments to test the robustness of keys and
encryption technique and comparative study with existing standard techniques have been done with
satisfactory results. This paper has taken steps to develop an attack capability for use within a cyber
challenge environment. The principles discussed within this paper aim to be applicable to all challenges
against mathematical cryptanalysis and cryptographic protocol in general and also it is used to cover
threat modeling, construction of cyber security test beds and take footsteps against offensive cyber
operations.
Keywords: Symmetric key, Session key, Fuzzy logic, Encryption, Decryption, Cryptanalysis.
1,2,3Department of Basic Science and Humanities
Institute of Engineering & Management
Salt Lake Management Building, Kolkata-700091. India
Page Number: 300-310
In this paper we have tried to study the geometry of tetrahedron as a member of polyhedron family and
hence calculate the face angles on each face of a tetrahedron with help of “C” Programming. We will also
be looking into the applications of tetrahedron structure in chemistry in the structure of various molecules,
in aviation it is used as a Wind Sock which serves as a reference to pilots indicating the direction of the
wind as well as Geology where the ‘Tetrahedral Hypothesis” was used to explain the formation of earth.
Keywords: Euclidean Geometry, Riemannian Geometry, Tetrahedron, Dihedral Angle, Face Angle,
Circumsphere.
1CSE (2ndYear),Institute Of Engineering & Management, Kolkata
2CSE (2ndYear),Institute Of Engineering & Management, Kolkata
3EEE (2ndYear),Institute Of Engineering & Management, Kolkata
Page Number: 311-320
When we talk about new technologies and the advancement in the field of Computer Science, the first
thing that comes to our mind is Artificial Intelligence and Machine Learning. Artificial Intelligence has
seen resurgence in the 21 st century because of its ability to mimic functions done by human intelligence
like “problem solving” and “learning”. It is slowly becoming the area of interest of the new generation
because of its modern capabilities which even human intelligence struggle to perform like competing
at highest level in strategic game systems, intelligent routing, operating cars autonomously and
simulations. Artificial Intelligence may look easy but there are several tools involved in making it
successful. One of the main tool is “Statistical Methods”. Linear algebra and Partial Differential
Equations have become the base of this field. The objective of our paper is to throw light on how
Statistical Methods and Mathematical optimization provide the base for the working of Supervised
Learning. Over years, algorithms inspired by Partial Differential Equations (PDE) and Linear Algebra
have had an immense impact on many processing and autonomously performed tasks that involve
speech, image and video data. Image processing tasks and intelligent routing done using PDE models
has lead to ground-breaking contributions. The reinterpretation of many modern machine capabilities
like artificial neural networks through PDE lens has been creating multiple celebrated approaches that
benefit a vast area. In this paper, we have established some working of these methods in different sub-
fields of Artificial Intelligence. Guided by well-established theories we demonstrate new insights and
algorithms for Supervised Learning and demonstrate the competitiveness of different numerical
experiments used in the sub-fields. Not only will we see the wide application of Artificial intelligence
but also its ability to slowly replace human works leading to unemployment which are part of its
limitation. This research will provide wider insights into the multiple mathematical processes which
acts as roots to make the field of Computer Science interesting and successful.
Keywords: Computer Science, Artificial Intelligence, Partial Differentiation, Linear Algebra.
1Department of Mathematics,Chukwuemeka Odumegwu Ojukwu University,Anambra State, Nigeria.
2 Department of Environmental Health Science,University of Eswatini, P.O. Box 369, Mbabane,Eswatini, Swaziland.
3Department of Mathematics,Chukwuemeka Odumegwu Ojukwu University,Anambra State, Nigeria.
Page Number: 321-334
For n ∈ N a positive integer, let f n (x) = ∑ nj=0 a n−j x n−j ; a n ≠ 0; n < 5 be a general polynomial
equation of degree less than five in one variable. Before now, we are unaware of any known unified
method for solving f n (x) = 0 (n < 5) in radical until Kulkarni did so in 2006. However, it is quite
ironical and contradicting to observe (one among many other issues) that the method introduced
by Kulkarni fails if n = 1 (since n = 1 satisfies n < 5) which is the case of general polynomial
equation of degree one. It is the purpose of this paper to address this issue and many more with an
approach that is quite simple and novel.
Keywords: Quartic equation, Cubic equation, resolvent equation. Auxiliary function, seeking solution .
1Department of Electronis and Communication Engineering
Bankura Unnayani Institute Of Engineering, Bankura, West Bengal, India ,
2Vidyasagar University,Midnapur, West Bengal ,India,
3National Institute of Technology, Durgapur,WestBengal,India,
Page Number: 335-343
Fifth generation systems are required to fulfill the objectives like compatibility, flexibility, high speed data
rate and low cost. Universal Mobile Telecommunication System (UMTS) use WCDMA as the air interface
for 4th generation mobile system. The performance of wireless communication system is often limited by
the radio channel models. In urban areas, channel is modeled as Rayleigh fading channel. This channel
causes multipath channels and other problems resulting degraded performance. Hence, channel estimation
before receiver helps to receive the transmitted signal using rake receiver. Rake receiver is a conventional
receiver for DS-CDMA system. In this, channel is estimated adaptively using LMS algorithm and
performance of this algorithm is studied for various multipath channels and step sizes. Moreover, the
channel introduces Inter Symbol Interference (ISI) and channel equalizers are used to compensate for the
ISI. In this work, BER vs. SNR performance of Zero Forcing Equalizer (ZFE), Minimum Mean Square
Error (MMSE) and MMSE- Decision Feedback Equalizer (MMSE-DFE) in WCDMA downlink system are
compared with conventional rake receiver for various spread factors in Rayleigh multipath fading channel
with Additive White Gaussian Noise.
Keywords: WCDMA, UMTS, DS-CDMA, LMS, ZFE.
1Department of Computer Science & Engineering Institute of Engineering & Management, Kolkata-700091
2Department of Mechanical Engineering Institute of Engineering & Management, Kolkata-700091
3Department of Information Technology Institute of Engineering & Management, Kolkata-700091
Page Number: 344-353
In the information era, a huge amount of terabytes is generated from our day to day lives. This mainly
comes from our modern information system and advanced digital technologies such as internet of this and
cloud computing.Since the datas are huge the analysis of these datas require a large amount of efforts at
multiple levels and for multiple purposes. Therefore to cope up with this big data analysis is a current area
of research. Due to rapid growth of such data solutions need to be studied and found. The ones taking the
decisions also called as decision makers need to have a detailed insights about the data they are handling
otherwise how can they come up with correct and best decions,which can only be provided using data
analytics. As a result this article provides a platform or rather a solution or we can also call it a brief
analysation of big data challenges open research issues and also some of the different methods and tools
which can be used for data analytics. It also opens a new horizon for the researchers to come up with the
solution. Keywords: Data analytics, Big Data analytics, Quantum computing, Tools for big data analytics, IOT,
Cloud Computing, Apache Hadoop.
It is plausible that language is processed by the innate spinal sign reflex mechanism. Human speech sound
contains logical properties of phoneme and mora, which interact with in-brain antigen/antibody molecular
structures and networking memories in the postnatally developed logical circuits optimized for signals of
syllables, a character set (long lasting syllables) and electronic form (interactive and ubiquitous syllables).
For grammatical decoding, sound localization function at the brainstem auditory nuclei is converted to
process sound vectors of grammatical syllables. For axiomatic scientific concepts, sign reflex logic of “If
A then B” must be upgraded by mathematical group logic to be acquired by learning, so that the results of
interdisciplinary conceptual operations should become meaningful and productive. As electronic data is
interactive, we can discover as many relevant linguistic information as possible with keyword search on the
internet within a few seconds. As a result, we obtain multi-disciplinary and voluminous linguistic
information but with uncertain reliability. To inherit collective human intelligence and correct any errors in
linguistic information of the past, regenerative reading might be appropriate for individual ontogenesis to
repeat intellectual and conceptual phylogeny. Errors cannot be corrected by the original authors
posthumously but only by those who are alive now and equipped with error correction techniques for
linguistic information.
Keywords: digital evolution, dichotomy & dualism, group logic, spinal sign reflex, collective human
intelligence, forward error corrections (FEC), Homo sapiens
Dept. of Basic Science and Humanities, I.E.M, Kolkata, India
Page Number: 363-373
This paper deals with concise study on the applications of data-structure and algorithms associated with
field of computer science. It has huge significance in the proper functioning of operating system and
improvement of the throughput by resource utilization. There is an amount of essential complexity in
the operations related to the data and files present in computer system. No brute-force approaches can
minimize and manifest it so easily by adopting to the non-harmonized methodology of the storage and
management, but it can be placed so that it doesn't get in the way and it's also easy to understand. The
best such place is a data structure. Data structures have many applications in the area of system
development, data base design, software coding and computer-networks. In this paper, we have
presented a succinct explanation about the efficiency and application of algorithms upon different
domains followed by a survey of different areas. Keywords: algorithm, brute-force, computer-networks, data-structures, operating system
