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Computational
Mathematics deals with areas where the disciplines of Mathematics
and Computer Science meet. The IUP Journal
of Computational Mathematics is a new academic adventure
that offers a wide variety of research papers on pioneering
concepts, theories and models in these areas, such as computational
methods in linear algebra, non-linear dynamical systems, fuzzy
logic, neural nets and genetic algorithms, computational complexity,
as well as the application of computational techniques in
science and engineering, and the mathematical theory underlying
numerical methods, by eminent scientists, academicians and
researchers, to provide the latest information and knowledge
in the afore-mentioned areas, which are continuously growing
in depth and variety.
It
is well-known that water is the most essential element of
life. Further, it is the most critical natural resource for
human development, economic growth, and sustainability of
the ecosystem and environment. In the first paper, "An
Integrated Fuzzy Approach to Assess Water Resources' Potential
in a Watershed", the author, Ajit Pratap Singh, highlights
the importance of water, particularly for the desert state
of Rajasthan, in India, which is facing water problems due
to meager rainfall, adverse climatological conditions, and
reduced per capita water availability with the increase in
population. The paper makes an attempt to develop an integrated
fuzzy assessment model to evaluate the status of water resources
development in a watershed by analyzing different factors
important for river basin planning and management. A case
study of a watershed falling within the Banas river basin
in the Chittorgarh district of Rajasthan was used for evaluating
the status of water resources development in different sub-regions
(tehsils) of the district. The study concludes that
there is an immediate need to develop a system to preserve,
conserve and utilize water in an efficient manner through
recycling and utilization of the technological advancements,
and through efforts aimed at generating high social consciousness
among the people, with active coordination and involvement
of water-managers and water-users alike.
In
computational mathematics, numerical methods play a very important
role. The second paper, "Application of Rothe's Method
to Abstract Quasi-Linear Implicit Integrodifferential Equations
in Reflexive Banach Space", the author, Reeta S Dubey,
establishes the existence, uniqueness and continuous dependence
on initial data, of the strong solution of abstract quasi-linear
implicit integrodifferential equation in real reflexive Banach
space X, whose dual is uniformly convex by using Rothe's method
- also known as the method of lines or the method of semi-discretization
in time.
In
computer science, knowledge-based expert system is a powerful
method to solve real-world problems. This method for substation
planning is reported in the third paper, "Selecting the
Exact Location of a Substation Using Knowledge-Based Expert
Systems", by S Ghosh and H O Bansal. The exact location
for the substation is identified from the given number of
locations for the substation. The load points are connected
to the substation in optimum route using knowledge-based expert
system to avoid obstruction between any two given load points,
which also reduces the overall feeder length. The effectiveness
of the proposed method is demonstrated using an example.
The
fourth paper, "Some Aspects of a Class of Quasi-Binomial
Distributions of Order k", by Rupak Gupta and
Kishore K Das, derives a class of Quasi-Binomial Distributions
(QBDs) of order k by assuming Abel's generalization
of the binomial formula. Further, a class of GPD of order
k is also defined as a limiting case of QBDs of order
k.
Genetic
algorithms essentially form a class of non-linear search processes
occurring in the study of mathematical optimization problems
and exhibit remarkable analogy with Darwinian evolution, in
that the key issue in both these processes is a fitness-dependent
mode of selection of strategies or traits for evolutionary
propagation of the target population. Replicator equations
describe the dynamics of evolutionary game theory. The fifth
paper, "A Genetic Algorithm for the Replicator Dynamics
of a Single-Species Population", by Anmiv Prabhu, Puneet
Dhakan and Sudeepto Bhattacharya, applies numerical simulation,
using a genetic algorithm for the replicator dynamics of a
single-species population problem. It is observed that the
agents with higher fitness tend to accumulate with the iterates,
showing an oscillatory pattern without settling to any fitness
sink.
Finally,
in the paper, "Performance Analysis of Soft Handoff Algorithm
in CDMA Systems Using Fuzzy Logic", by Alok Aggarwal,
Rajendra Prasad, Mohan Lal and Sunita Devi, the powerful concept
of Fuzzy logic is used. Soft Handoff (SHO) is generally used
in cellular CDMA systems. One possible method for improving
the performance of conventional SHO is to adapt the SHO thresholds.
The paper analyzes the performance of SHO algorithm in CDMA
systems using fuzzy logic, and proposes a new procedure, which
is compared with IS-95A and IS-95B SHOs. The results of the
analysis show that the proposed algorithm performs better
in terms of outage probability, blocking probability and the
Eb/I0 ratio, when
compared with IS-95A and IS-95B SHO algorithms.
To
understand and describe change is the central theme in natural
sciences, and calculus was developed as a powerful tool for
this purpose. As Bertrand Russell wrote, "The Calculus
required continuity, and continuity was supposed to require
the infinitely little; but nobody could discover what the
infinitely little might be". Nevertheless, researches
and studies to discover that `infinitely little' continue.
This new journal is one such attempt in that direction.
-
S K Ghosh
Consulting
Editor
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