On modified Lemke algorithm for solving quadratic programming problems
AKPAN, S. S.¹, NDUKA, E. C.² and Udo, M. E.³
Abstract : It is very clear from many literature that the traditional methods for solving any quadratic programming problem including that of Lemke is basically tableau transformation were a new tableau is generated from the immediate preceding one by series of elementary tableau transformation where the entering variable is the minimum value chosen from the minimum ratio test criterion. This we noticed tend to worsen the problem of round off error especially in this modern age were information are easily assessed through computer.

In this paper we modify Lemke algorithm by introducing the matrix algebra approach instead of the usual tableau transformation to control the accuracy of the inverse of the Hessian matrix. This we observe actually check the problem of the round off error.

On Application of random number generator to the production of recharge pin code
¹Akpan, Stephen S., ¹*Williams, Edem E., ¹Ugbe, Thomas A.,
Abstract : The Pin Code printed on the GSM recharge card is a mean of recharging or updating users account. This code can be of variable length made up of digits. There are many methods of arrangement of these numbers depending on the network employed; each GSM operator has a unique relationship established among successive pin codes in relation to their serial number. In this paper it is established that the Pseudo Random number generator can be used to generate a GSM Pin Code such as the fourteen digit GLO Pin Code without repetition, beginning with the smallest two digit 10 and incremented by 1 after each group of numbers till the highest digit 99 is obtained, provided an initial control variable is established for the network.
Key words : Random Numbers, Pin Code, Generator, Pseudo, Repetition, Prediction.

Application of matlab^® symbolic maths with variable precision arithmetic (vpa) to compute some high order Gauss-radau-kronrod quadrature formulas
H.T. Rathod¹, R.D. Sathish² and S.V. Hiremath³
Abstract : Extended Gauss Radau quadrature rules of the type, first conceived and computed by Kronrod are investigated. We have developed an efficient algorithm for this case which we believe is not considered so far in the literature. We have further proposed and investigated the existence of the generalized form of Gauss - Radau - Kronrod quadrature rules such that the new abscissas are real, lie in the interval of integration, ie [-1,1] and the associated weight coefficients are all positive. Some sample output of the MATLAB programs for these extended quadrature rules are displayed with 32-digit accuracy. We have also appended MATLAB codes which fully use the symbolic maths variables for ready reference, verification and development of software for future applications
Key words : Gauss Radau quadrature, Legendre polynomials, Kronrod quadrature rules, extended Gauss Radau Kronrod quadrature rule.

On two component mixture of bimodal distributions
K. SRINIVASA RAO* Y.M.V.N.S. KUMAR* B.V.S. NARAYANA* G.V.S. RAJKUMAR**
Abstract : In this paper, we introduce a two component mixture of bimodal distribution given by K.S. Rao et al. (1988). The various distributional properties of this distribution are derived. The extreme order Statistics of this distributions are also obtained, this distribution much useful the approximating the random phenomena involved in several datasets arising at places like biological experiments, Chemical experiments, inventory control, reliability and lab testing etc. where the population under studies is heterogeneous .Some of the inferential aspects of this distributions is also study.
Key words : mixture of distributions, distribution function, bimodality, order statistics.

Unsteady free convection flow in porous medium past a horizontal porous plate in presence of heat source, periodic free stream velocity and temperature
N.P. SINGH*, AJAY KUMAR SINGH^$ ATUL KUMAR SINGH^# and P.K. SHARMA^#
Abstract : In this paper free convection flow along a horizontal porous plate is studied in the presence of heat source and taking into account the periodic free stream velocity and temperature. Following perturbation technique, solutions for liquid velocity and temperature fields are obtained. Expressions for skin-friction and heat transfer are also derived. The results obtained are discussed for different values of the parameters entered into the equations governing the flow. It is observed that the velocity decreases with increase in permeability parameter while the temperature decreases with increase in Prandtl number or absorption type heat source.

An Algorithmic Graphical approach for Ground level logistics management of Jatropha seed distribution
*S.P. Srinivasan **P. Malliga and ***K. Thiagarajan
Abstract : Oil from Jatropha and pongamia seeds gives more yields in the production of biodiesel. This bio energy replaces petro-diesel and deserves specific attention. However the collection, distribution of oilseeds is highly complicated task.The existing system of supply chain models have used the following different algorithms namely, Markov chain process, Integer Programming, Benders decomposition etc., The above mentioned algorithms are giving positive values for using respective systems. The proposed model recommends the optimal distribution centers of Jatropha seed through optimized unilateral graphical approach with possible and necessary constraints. (Whichever applicable, and wherever needed). The process consists of four different levels of module. The paper focused on the initial level of process. To optimize the appropriate solution of distribution method in a graphical approach algorithmically. The resultant solution obtained may go ahead to the next level of the module in the supply chain with network.
Key words : Biodiesel, Unilateral graph, bilateral graph, supply chain, Jatropha seed, JPS -Algorith

mK_2,3 is vertex prime
Selvam Avadayappan and R. Sinthu
Abstract : A graph G(V, E) is said to have a vertex prime labeling if its edges can be labeled with distinct integers from {1,2,3,..., |E|} such that for each vertex of degree at least 2, the greatest common divisor of the labels on its incident edges is 1. A graph that admits a vertex prime labeling is called a vertex prime graph. In this paper, we prove that mK_2,3 is a vertex prime graph, where m is any positive integer.
Key words : labeling of graphs, vertex prime labeling of graphs.
Subject Classification Code: 05C (Primary)

Computational study of hydromagnetic effects on the viscous incompressible dissipative fluid past an infinite verticle plate
Ram Naresh Singh, Hariom Singh Tomar and D.S. Sharma
Abstract : In this paper we study a problem of the unsteady free convection flow of a viscous incompressible dissipative fluid under the influence of transverse magnetic field. We consider that the fluid past an infinite vertical plate. Here we applied finite difference technique to find out the numerical solution of the problem. We obtained various values of the parameters e_r (Eckert number), P_r (Prandtal number), skin friction (t) and M (Hartmann number), the results have been shown graphically.
Key words : Viscous Incompressible Dissipative Fluid, Eckert number, Prandtal number, Hartmann number, Skin friction.

A Real-Time IKBS for Students Results Computation
Moses E. Ekpenyong
Abstract : Real-time processing of students' results has always been the desire of every University academic system. This paper reports on a recent breakthrough in this direction. It develops an Intelligent Knowledge Based System (IKBS) that makes all computational, monitoring and tracking details of students' results processing a snap and also transparent to the users. The IKBS is programmed with Microsoft Excel; an excellent functional processing software, and is currently implemented in the University of Uyo, Nigeria for the processing of students results. The paper could also serve as the IKBS reference manual.
Key words : Cell Referencing, Functional Programming, Intelligent Systems, Knowledge Engineering, RDE.

A Model of Fluid Filtration and Reabsorption in a Capillary - Tissue Exchange System
Rashi Bhardwaj and P. N. Tandon* (F.N.A.Sc.)
Abstract : A simple model of capillary-tissue fluid exchange system is developed with particular emphasis on the permeability properties of the blood vessel based on Starling's law. Inertia effects have been neglected in comparison to viscous effects because of low Reynolds number blood flow in capillary. Capillary blood vessel is approximated by circular cylindrical tube with permeable wall. Introducing three layered model for blood with central core region, flow region with Casson fluid surrounded by a peripheral layer of viscous fluid so as to represent a cell free region near the wall and a thickly concentrated plug region due to the cell migration towards the central line. If the net flow of suspending medium filtered is zero then the total amount of plasma entering from capillary into the tissue and re-absorbing back into the capillary are equal. If it is positive, the fluid in excess into the tissue leaks into the lymphatic vessel to join back with main arterial blood flow and removal of separated waste products through veins and spleen. Thus, Lymphatic flow plays an important role in protecting the tissue from edema and dehydration.

An EOQ Model with Ramp type Demand Rate, Weibull Deterioration Rate and Constant Production without Shortage
S.K. SAHOO¹, C. K.SAHOO¹ and A. KALAM²
Abstract : In this paper present inventory constant production system for Weibull deteriorating items has been developed with demand rate as a ramp type function of time. The finite production rate is proportional to the demand rate and deterioration rate. The constant production cost of inversely proportional to the demand rate. The model without shortage case in inventory solved here. Sensitivity of the decision variables to changes in the parameter values is examine and affect of these changes on the optimal policy are discussed and numerical examples presented to illustrate the model developed.
Key words: Ramp type demand; Weibull deterioration; unit production cost; without shortage; Demand.

A model of base stock system for patient customers with lead time distribution undergoing a parametric change
S. Sachithanantham¹, V. Ganesan², and R. Sathiyamoorthi³
Abstract : Base Stock system for patient customers in inventory control is a special type of problem which introduces the fact that the shortages do not result in the loss of profit due to the fact that immediately a demand for the product is reported; an order is placed for supply. This is in addition to the inventory on hand called the ground level inventory. Hence the socalled base stock denoted as B is equal to the total of the inventory on ground and the inventory on orders placed. In this paper the optimal value of B is obtained using the fact that the lead time is a random variable and it satisfies the so called Setting the Clock Back to Zero (SCBZ) property which amounts to the change in the parameter of the lead time distribution after a change point.
Key words : Base stock, Patient Customers SCBZ property, Change point, lead time.

Optimal reserve of semifinished product in between two machines in series
J. GEETHA*, SULAIMAN** and R. SATHIYAMOORTHI***
Abstract : When two machines M₁ and M₂ are in series the output of M₁ which is the semi finished product is the input for M₂. If M₁ goes to the down state the supply or input to M₂ is stopped and M₂ goes to the down state. The idle time cost of M₂ is high and prohibitive. Hence a reserve of semi finished product in between M₁ and M₂ is suggested. In this paper the optimal reserve size is determined under the assumption the interarrival times between breakdowns of M₁ is a random variable which undergoes a parametric change after a truncation point which is also a random variable. Numerical illustration is also provided.
Key words : System in Series, Optimal Reserve, Change of parameter.

Study of Statistical Technique Using Neural Network
Sudhir Kumar Sahu and Pragnyaban Mishra*
Abstract : Neural networks have received a great deal of attention over the last few years. They are being used in the area of prediction and classification, areas where regression models and other related statistical techniques have traditionally been used. There has been much publicity about the ability of artificial neural networks to learn and generalize. In fact, the most commonly used artificial neural networks, called multilayer perceptrons, are nothing more than nonlinear regression and discriminant models that can be implemented with standard statistical software. This paper explains what neural networks are, translates neural network terminology into statistical terminology, and shows the relationships between neural networks and statistical models such as generalized linear models, maximum redundancy analysis, projection pursuit, and cluster analysis. Neural networks and statistics are not competing methodologies for data analysis. There is considerable overlap between the two fields. Neural networks include several models such as MLPs that are useful for statistical applications. Statistical methodology is directly applicable to neural networks in a variety of ways, including estimation criteria, optimization algorithms, confidence intervals, diagnostics, and graphical methods. Better communication between the fields of statistics and neural networks would benefit both.

Newton Raphson Approach to Determine The Power of Transformation
Wan Muhamad Amir W Ahmad¹, Nyi Nyi Naing², Tengku Mohd Ariff Raja Hussein³ and Mustafa Mamat⁴
Abstract : The formal method for the transformation depends on the values of l. For instances, if the values of l is equal to 2, it shows that the square transformation is needed. In this study, we calculated the optimal values of l based on the Newton Raphson procedure using modified normal probability distribution.
Key words: Newton Raphson Algorithm and modified of Normal Probability Distribution.

An approximation method for the analysis of GI/G/1 queues
Sandeep Dixit
Abstract : We study in this paper an approximation method for the calculation of various performance measures of a GI/G/1 queue. We analyze the idle-period distribution as the starting point. The result is then taken as input to many known results to get other performance measure. We show that the distribution of the GI/G/1 idle period satisfies a nonlinear integral equation. This equation directly leads to an accurate approximation solution of the idle-period distribution of the GI/G/1 queue where the interarrival times have a generalized hyperexponential distribution (GH).

Weak-compatibility and fixed point theorems in fuzzy metric space
*R. S. Chandel and **K. K. Kumbhare
Abstract : B. Singh and S. Jain⁹ prove the existence of unique common fixed point of two weakly compatible pair of maps satisfying an expansive condition. This note examines the same expansive condition for existence of unique common fixed point of five self-maps and relaxing the condition of completeness. and introduced new condition.
Key words: Fuzzy metric space, Weak-compatibility, Complete metric space.
Mathematics Subject Classification : 47H10, 54H25

An Exponential Production-Inventory Problem with Exponential Demand, Time Dependent Deterioration Rate with Shortages
D. SAMAL¹, A. KALAM², S.K. SAHU³, M. MISHRA⁴
Abstract : In this paper present inventory system for time dependent deteriorating items has been developed with exponential demand rate and exponential production. The finite production rate is proportional to the demand rate and deterioration rate. The model with shortage case in inventory solved here. Sensitivity of the decision variable to changes in the parameter values is examine and affect of this changes on the optimal policy are discussed and numerical examples presented to illustrate the model developed.
Key Words: Exponential demand, Deterioration, Production, Shortage.

On the circular chromatic number of deleted vertex subgraphs
R. Ganapathy Raman¹ and R. Sattanathan²
Abstract : An alternative approach to the existence of a vertex n Î V(G) such that c(G - n) ³ c(G) - 1 is presented. If such a vertex exists for a planar graph, we show that there must also be one of minimum degree.
Key words : Chromatic numbers star chromatic number.

Unsteady MHD flow with heat and mass transfer through porous medium past an oscillating porous horizontal plate in slip flow regime
N. P. Singh*, Usha Singh** and P. P. Singh**
Abstract : In the present paper an analysis of velocity, temperature, concentration, skin-friction, heat transfer and mass transfer of the fully developed flow of a viscous incompressible fluid of small electrical conductivity is studied analytically. The flow is considered in porous medium past an oscillating, infinite porous horizontal plate in slip flow regime under the influence of transverse magnetic field of uniform strength. Exact solutions for velocity, temperature and concentration field are obtained. The expressions for skin-friction, heat and mass transfer rate are also derived. The results obtained are numerically presented through graphs or tabular form followed by discussion.

Bayesian Analysis In Ridge Regression
¹Muhammad Iqbal Al-Banna Bin Ismail, ²Zulhanif and ³Ismail Bin Mohd.
Abstract : Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates and significance tests for each predictor involved may be underestimated. However many case in the econometric models reported with few observations multicollinearity which could be misleading inferences based on regression models. Ridge estimators are often used to alleviate the problem of multicollinearity. Ridge regression, based on adding a smally quantity k, to the diagonal of a correlation matrix of highly collinear independent variables, can reduce the error variance of estimators, but at the expense of introducing bias. Because bias is a monotonic increasing function of k, the problem of the appropriate amount of k to introduce as the ridge analysis increment has yet to be resolved This paper proposes alternative method for estimate regression coefficients used Bayesian method via Gibss sampling. Key words : Bayesian Analysis, Multicollinearity, Ridge Regression, Gibss Sampling.

A note on unsteady flow of maxwell visco-elastic fluid through a rectilinear pipe
Hariom Singh Tomar*, Ram Naresh Singh and D.S. Sharma
Abstract : In this paper we study unsteady flow of Maxwell visco-elastic fluid through a rectilinear pipe having its cross-section is a loop has been discussed in this analysis. Expressions for velocity variations have been obtained. A few particular cases of results with pressure gradient as any function of time, i.e. flow under an impulsive pressure gradient, flow under constant pressure gradient and flow under harmonically oscillating pressure gradient, have also been discussed. Use of Laplace transformations has been made to solve the differential equations. The effects of elastic parameter on the flow when the pressure gradient is any function of time have represented by graphs.
Key word : Unsteady flow, Maxwell visco-elastic fluid, Rectilinear pipe.

Gracefulness of Central Graphs
R. Sattanathan¹ and S.Manikandan²
Abstract : Given a graph G consisting of vertices and edges, a vertex labeling of G is an assignment f of labels to the vertices of G that produces for each edge xy a label depending on the vertex labels f (x) and f (y). A vertex labeling f is called a graceful labeling of a graph G with q edges if f is an injection from the vertices of G to the set {0,1,2,...q} such that when each edge xy is assigned the label |f (x)-f (y)| the resulting edge labels are distinct. A graph G is called graceful if there exists a graceful labeling of G (see figure 1). In this Paper we give some results on Central graphs (The Central Graph C(G) of a graph G is obtained by subdividing each edge of G exactly once and joining all the non-adjacent vertices of G (see figure 2)) and gracefulness of Central graphs of Cycles being investigated.
Key words : Graceful Labeling, Central Graphs.

Bugging and Debugging of Software Metrics for an Artificial Immune Recognition System
S. CHITRA¹, K. THIAGARAJAN² and M. RAJARAM³
Abstract : Software is an integral part of many critical and non-critical applications, and virtually any industry is dependent on computers for their basic functioning. Techniques to measure and ensure reliability of hardware have seen rapid advances, leaving Software as the bottleneck in achieving overall system reliability. Hence there rises a situation for the developers to develop high quality software. Having that in mind it is necessary to provide the reliability of the software to the developers before it is shipped. This can be achieved based on immune system. The immune system that is otherwise known as 'second brain' for its abilities to recognize new intruders and remember past occurrences. Simulating the immune system or translating immune system mechanisms into software learning is an interesting topic on its own. This will produce high quality, reliable results over a wide variety of problems compared to a range of other approaches, without the need of expert fine-tuning.
Index Terms : Artificial Recognition Balls, Artificial Immune Recognition System, Operating systems, software reliability growth models, Software Failure Rate.

Public key cryptography-implementation using R-2R ladder network
^aDavinder Singh, ^bRavinder Rathee and ^cManoj Duhan
Abstract : Cryptography is the art of achieving security by encoding messages to keep the information non-readable. Cryptography actually is a mathematical scrambling and unscrambling of data to achieve, Confidentiality (Readable only to sender and receiver); Integrity (not modified by any one to integrity of message); Non repudiation (sender can't refuse the claim of not sending); and Entity authentication. While sending or receiving the data, special keys are used to encrypt/decrypt data to verify the original contents. This key makes the process of cryptography secure. Public key systems use two keys such that one key, the public key, can be used to encrypt some text that can then only be decrypted using the securely-held private key. There are two approaches for the generation of encryption/decryption keys i.e. software and hardware. The purpose of this paper is to generate encryption key using hardware technique. To design electronics circuit basic concept is derived from the Knapsack problem. Then R-2R ladder network is used for the implementation of Knapsack algorithm. The electronics circuit design is evaluated using (ORCAD-Pcpise) software and analyzed practically on electronics bread board as well. The circuit implementation aim is achieved through many intermediate steps which are followed as firstly terminology and transformation are defined foe public key cryptography, then the knapsack problem is discussed and after that knapsack algorithm (greedy algorithm) is achieved using the electronics circuits. Some modification also has been discussed to make circuit more practical and more secure.

Graphs whose sum of independent domination number and chromatic number equals to 2n-6 for any n>3
G. MAHADEVAN¹, A. SELVAM AVADAYAPPAN² and M. AMRA PARVEEN³
Abstract : A subset S of V is called a dominating set in G, if every vertex in V- S is adjacent to at least one vertex in S. A Dominating set is said to be independent dominating set if the induced subgraph < V > is independent. The minimum cardinality taken over all, such independent dominating sets is called the independent domination number and is denoted by g_i(G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number c(G). It was already proved that g_i(G) + c(G) £ 2n-1 and corresponding extremal graphs were characterized of order up to 2n-5. In this paper we characterize the class of graphs for which g_i(G)+c(G) = 2n-6 for any n > 3.
Key words : Independent domination number, Chromatic number
AMS Subject Classification: 05C (Primary).

Region of interest image coding using cut plane segmentation method for medical image compression
R. Tamilselvi¹, K. Sarukesi², K. Thiagarajan³ and S. Jayabarathi⁴
Abstract : In this Paper an algorithm for Cut plane Segmentation method for ROI coding is proposed. Various results for Segmentation, Slicing, Searching and then ROI cut in the image are observed.
Key words: ROI (Region of Interest), Cut - Plane Method, Searching Algorithm.

Multilayer Feedforward Neural Network Model and Box-Jenkins Model for Seasonal Load Forecasting
*Norizan Mohamed, **Maizah Hura Ahmad, **Zuhaimy Ismail and **Khairil Anuar Arshad
Abstract : Artificial neural networks (ANNs) have been extensively studied and have been used as time series forecasting method. When neural network is compared to seasonal ARIMA (SARIMA) model, SARIMA model outperforms neural networks model when seasonality in a series exist. This paper aims to investigate the effectiveness of preprocessing data in neural networks model. In this study, the trend is absent and only seasonality exists, hence we only applied deseasonalization as preprocessing data. The forecasting performances among these three models, i.e., the SARIMA model, the neural network model with raw data and the neural network models with preprocessing data are compared. Comparing the performances using the root mean squared error (RMSE), the mean absolute error (MAE) and mean absolute percentage error (MAPE), we find that neural networks with preprocessing data are able to capture seasonality but SARIMA still outperforms both two neural network models.
Key words: Load Forecasting; Deseasonalization; Seasonal Autoregressive Integrated Moving Average; Artificial Neural Networks; Multilayer Feed-forward Neural Network;

Analysis of the feeding system of a Commercial Mill two associate components and with no provision for shutdown repair
*V. K. Pathak and **B.L. Dewangan
Abstract : This paper deals with the performance evaluation of a Commercial mill system involving two essential components viz. one main unit and two associate units. Associate units depend upon main unit for functioning. Only one repairman is used for repairing the failed components of all the units. Taking exponential failure rates and arbitrary, repair rates, various system effectiveness measures such as transition probabilities, mean time to system failure, availability, busy period of repairman are calculated. At last, profit analysis is done on the basis of above measures.

Behaviour Analysis of Feeding System in Sugar Industry
Satyavati* and T.P. Singh**
Abstract : The present paper discusses the operational behaviour of feeding system (i.e. the main functionary part) of the sugar plant. The system consist of three subsystems (having a number of units with different configurations) i.e. the crushing system, bagasse carrying system and the steam generation system. The units of crushing and bagasse system are in series while the units of Boilers and steam generation system are in parallel. Taking constant failure or general repair rates for each subsystem, the steady state availability are evaluated. Availability tables for various failure and repair rates with graphs are given followed by a parameter.
Key words : Operational behaviour, feeding system, availability- analysis etc.

Evolution and Comparison of Machine learning Classifiers with impact Result
Anil Rajput*, Ramesh Prasad Aharwal** and Amit Dutta***
Abstract : Machine learning classifiers are mostly used for prediction of system behavior ,Evolution and comparison of different machine learning classifiers used in Data Mining practical in health datasets, how to select the most suited data mining algorithm for a medical application. In this paper we used three medical datasets for our experiment. Experiment performed on WEKA 3.5.7 software which is a newest version of WEKA software.
Key words : Classification, Data Mining, WEKA, J48, Naïve Bays.

Reliability analysis for two-unit system with ccs failures and human errors
G.Y. SAGAR, S.M. VERMA and Y.R. REDDY
Abstract : The present paper deals with the reliability analysis of two-unit identical system, which is affected by common cause shock (CCS) failures and human errors along with individual failures. The influence of CCS failures in addition to human errors is emphasized in the reliability analysis of a system. Expressions for system reliability and mean time between failures (MTBF) are developed when the system is affected by CCS failures as well as human errors. Also, these reliability indices are compared in the presence of CCS failures as well as human errors with that of the situation when CCS failures are affecting the system. Reliability Plots are shown and Numerical illustration of MTBF results is also presented to support the model.
Key words : Reliability-Mean time Between Failurs (MTBF)-Common Cause Shock Failures-Human Errors.

Harmonic Univalent Functions with Fixed Point and Negative Coefficients
K. K. Dixit and Saurabh Porwal
Abstract : Let and denote the class of functions , where , , , and , that map the unit disc onto starlike and convex domains respectively satisfying . In this paper, sharp coefficient estimates, distortion properties for functions in and have been obtained. This leads to extreme points.

Dynamical systems for metric spaces
Bharathi K. and Shabbir A.
Abstract : The present paper is an extension work of the Barnsley¹ and Devaney³. We introduce Poincare and Shift maps, furthermore we establish and proved some theorems for topological sensitivity and global stability.
Key words: Global stability, Metric spaces, Poincare map, AMS mathematical subject classification 45 B10.

Convergence of orthonormal wavelets
R.C. Meghwal
Abstract : The aim of this paper is to study the convergence of mother wavelet specially shanon's wavelet when bounded variation is impose on it.
Key words : Wavelets, mother Wavelets, Father Wavelets, ortho normal Wavelets, Shanon Wavelets, convergence and bounded variation. Before starting the paper first we give some basic definitions, notations, results and main results which will be used in the paper.

Analysis of a Predator-Prey Model with Intraspecies Coexistence
M.H. Rahmani Doust, R. Rangarajan and M. N. Modoodi*
Abstract : This paper deals with Lotka-Volterra predator-prey equations of two species. Moreover, we make assumption that, there exists coexistence within each species separately. The methods which can be used in this context are vector field, linearization and Lyapanov's second. For each equilibrium point, stable and unstable manifolds will be determined.
2000 AMS Classification Number: 34D20, 37C10, 92D40, 93B18
Key words : Lotka-Volterra Model, Predator-Prey Equations, Intraspecies Coexistence

On K^l (E, 1) summability of fourier series
V.N. Tripathi and Sonia Pal
Department of Mathematics S.B.P.G. College Baragaon, Varanasi, U.P. (India)
Abstract : The Present paper deals with a theorem on K^l (E, 1) Summability of fourier series under general conditions.

Love wave scattering due to a surface impedance in the surface of a vertical discontinuous surface layer
S. Mudgal
Abstract : The scattering of Love waves due to a surface impedance in the surface of a vertical discontinuous surface layer is studied in the present paper. The solution of the problem is obtained when the width of the vertical disconti-nuity is very small. The reflected, transmitted and scattered waves are obtained by using the method of Fourier transformation and Wiener-Hopf technique. The numerical computations are carried out for the amplitude of the scattered waves versus wave number. There is a sharp fall of the amplitude with slight increase in the wave number.
Key words : Love waves, Fourier analysis, scattering, amplitude, wave number.

An Efficient Step Size For BFGS
Azfi Zaidi Mohammad Sofi¹, Mustafa Mamat², Ismail Mohd³ and Yosza Dasril⁴
Abstract : In this paper we introduced what we are calling a combination of step size of Broyden-Fletcher-Goldfarb-Shanno (CSS-BFGS) to solve unconstrained optimization problem. Analytically, we have proved that the algorithm is superlinearly convergence. The numerical result of CSS-BFGS was shown at the end of this paper. The result shown that in term of iteration number n_i and function evaluation n_f, our alternative step size is more effective than the original BFGS algorithm.
Key words : exact line search, step size, BFGS, differebtiable, superlinearly convergence.

A result on superstability
Kiran Shrivastava
Abstract : In this paper it is shown that a binary function on a normed linear space that satisfies a condition which implies approximate associativity, is superstable.
Key words : Normed space, associativity, superstability.
SUBJECT CLASSIFICATION: 1991 Mathematics 39B72, 39B22.

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