Differential evolution is a method for numerical optimization when there is no clear knowledge of the gradient of the problem to be optimized. This method was suggested by Storn R and Price K, and generally works on multidimensional real valued functions, which are not continuous or differentiable. Optimization problem is considered as a black box which provides a measure of quality when the gradient is unknown. Logarithmic spirals are found abundantly in nature in the form of gastropods such as nautilus, cowie, grove snail, Thatcher shell, etc. It was also found that the rank-size pattern of the cities of USA approximately follows a logarithmic spiral. The usual procedure of curve fitting fails in fitting a spiral to the empirical data. It is more complex to fit a spiral to the data which is not measured from the origin. In the paper, “Fitting an Origin-Displaced Logarithmic Spiral to Empirical Data by Differential Evolution Method of Global Optimization”, the author, S K Mishra, has used differential evolution method of global optimization to fit a logarithmic spiral to empirical data measured with displaced origin. He has used the Box’s algorithm with repeated trials using numerical data.

Hydromagnetic flows in rotating systems continuously encourage research in the areas of engineering, science and applied mathematics. These flows are necessary for controlling the rocket propulsion, crystal growth technology, and also magnetohydrodynamic (MHD) energy generators. MHD is experiencing a great improvement and differentiation. Studies have been conducted on the MHD heat and mass transfer in a flow of viscous incompressible fluid past an infinite vertical plate, and have been solved analytically assuming that the oscillatory suction is normal to the plate. Several analytical and numerical solutions are reported for different geometrical configurations. In the paper, “Effects of Injection/Suction on an Oscillatory Hydromagnetic Flow Through Porous Medium in a Rotating Porous Channel”, the authors, Vimal Kumar, S S Yadav and Rajeev Jha, have considered that the porous channel with constant injection/suction, rotates on an axis perpendicular to the plates of the channel. They have also considered the application of a magnetic field of uniform strength perpendicular to the plates.

A compact space is the one where one takes an infinite number of steps in the space and gets arbitrarily close to some other point of the space. The main reason for considering the spaces is that they are similar to finite sets in certain ways.

In other words, most of the results which are shown for finite sets are extended to compact spaces with minimal changes. There are many important properties generalized by compactness, such as closed and bounded intervals on the real line. The extreme value theorem generalizes to compact spaces. Thus, there are many important theorems in the class of compact spaces. In the paper, “On Nearly Compact Spaces With Respect to an Ideal”, the authors, R Alagar and R Thenmozhy, have considered various definitions of compact space and discussed various theorems based on compact spaces. They have introduced the concept of nearly compact spaces with respect to an ideal and have also discussed some of their properties.

A magic square, as the name indicates, is a square of order n in which n2 distinct integers are arranged in such a way that the sum of n numbers in all rows, all columns and both diagonals add up to the same constant. These magic squares are applied in astrology to cast horoscopes. In the paper, “Magic Square Construction Algorithms and Their Applications”, the authors, Krishnappa H K, N K Srinath and Ramakanth Kumar P, have proposed some algorithms for the construction of magic squares under various categories, such as when n is odd or even.

Neural network is a powerful general purpose tool readily available for prediction, classification and clustering. Its applications are spread over a wide range of industries, from predicting time series in the financial sector to diagnosing medical conditions, from recognizing numbers written on cheques, to predicting the failure rates of engines. It has its origin in the functioning of the neurons focusing on the anatomy of the brain; this model inspired the field of artificial intelligence in solving the problems outside the sphere of neurobiology. The applications of Artificial Neural Networks (ANNs) in various other fields, especially in the area of finance and stock markets have attracted the researchers in the early 1990s and later became one of most important techniques in the prediction of stock index returns. In the paper, “Do ANNs Successfully Predict Stock Returns? Testing its Application in Indian Stock Market”, the authors, Renu Vashisth and Abhijeet Chandra, have discussed the architecture and learning of ANNs, and how they can be used in predicting the daily returns of the Nifty index. They have discussed the ability of neural network models in handling complicated data and producing good results.

-- Sashikala Banoor
Consulting Editor