Heat and mass transfer effects on unsteady MHD free convection flow along a horizontal porous plate in presence of heat source and periodic free stream velocity
ATUL KUMAR SINGH, AKHILESH KUMAR, N. P. SINGH and AJAY KUMAR SINGH*
Abstract : In this paper hydromagnetic free convection and mass transfer flow along a horizontal porous plate is studied in the presence of heat source and taking into account the periodic free stream velocity. Following perturbation technique, solutions for liquid velocity, temperature and concentration fields are obtained. In addition expression for skin-friction, heat transfer and mass transfer are also derived. The results obtained have been numerically discussed with the help of graphs and tables.

Two Sex model for Horizontal Transmission of STD in a constant homogeneous mixing population
Umar Malllam Abdulkarim
Abstract :In this paper, we examined the two sex model of Hsieh⁴ and Kimbir et al.,⁵, and extended these models to study transmission dynamics of socially transmitted disease,( STD ) in a proportional mixing population with vital dynamics, and no disease induced death. Our major focus is to reduce the cost of disease intervention towards eradication of curable STD, like gonorrhea and others, which is better achieved through preventive measure rather than treatment, a concept that is cheaper and affordable, in developing economies like ours. We have proposed a variant of the Kimbir et al.,⁵ model of prevention of HIV / AIDS in a varying population to study the transmission dynamics of STD. Stability of the equilibriums states are discussed via the reproductive ratio of the infection and the Routh - Hurwitz conditions on the model parameters. Threshold conditions for eradication and persistent of the disease are derived and interpretation are discussed.
Key words: Equilibrium states, reproductive ratio, Epidemics threshold, STD, stability.

Optimal reserve inventory between two machines under scbz property of interarrival times between breakdowns
S. Srinivasan*, A. Sulaiman** and R. Sathiyamoorthi***
Abstract : A system in which there are two machines in series is considered. The output of the first machine M₁ is the input for the second machine M₂. When machine M₁ undergoes breakdown, the repair time of the same is taken to be a random variable. The machine M₂ will be forced to be idle if there is no supply from M₁. A reserve inventory between M₁ and M₂ is suggested so as to avoid the idle time of M₂. So the determination of optimal reserve inventory between M₁ and M₂ has been attempted by several authors, taking the different associated costs. In this paper the optimal size of reserve inventory is derived under the assumption that the random variable which denotes interarrival times between successive breakdowns of M1 satisfies the so called "Setting the Clock Back to Zero" (SCBZ) property.
Key words : Series system, Optimal reserve, SCBZ Property.

Unsteady hydromagnetic flow of viscous fluid in inclined rectangular channel with free surface
AJAY KUMAR SINGH*, P. P. SINGH and N. P. SINGH
Abstract : In the present paper laminar flow of an incompressible conducting, viscous fluid in an inclined rectangular channel with free surface exposed to the atmosphere is studied under the influence of uniform magnetic field. The bottom of the rectangular channel moves in its own plane with a velocity which decreases exponentially with time. The uniform magnetic field acts normal to the flow. The velocity field of the fluid to obtain using finite Fourier sine transform and Laplace transform. The results of some earlier authors have been deduced as particular cases of this study.

Effect of Vaccination and Population Area Size on the Transmission Dynamics of Bird- Flu Epidemics in a Proportionate Mixing Population
Umar M. A.
Abstract : We have examined the effect of vaccination, and population area size on the transmission dynamics of bird flu epidemics in a poultry farm, using two class of models, an age -structured epidemic model and a homogeneous epidemics model in which the transmission rate in the case of homogeneous model, is assumed not age-depended, while it is assumed age-dependent in the age-structured model. The per capital contact rate and the vital rates are assumed not age depended. It is observed in both cases, that the area size occupied by the population influences the rate of transmission of the virus. Wild birds, which are normally on free range, are observed to be responsible for the spread of the virus to poultry farms; however the transmission rate may be less than in poultry birds, due to their free range nature. This is not investigated this work. This is assumed to has helped to control the concentration of the wild birds population density in a particular location, where they are found, and less per capital contact rate. Thus, the disease spread is minimal. Threshold parameters for both models are examined to determine the stability of the non -trivial steady states.

MHD Free Convection Flow of a Viscous Fluid with Heat Source in Rotating System
AJAY KUMAR SINGH*, Y. K. SHARMA, M. K. YADAV and N. P. SINGH
Abstract : Free convection effects in unsteady flow of an incompressible, electrically conducting, viscous liquid in a porous medium past an infinite isothermal, porous vertical plate with constant suction velocity in the presence of a heat source and transverse uniform magnetic field in a rotating system is studied. It is observed that an increase in heat source parameter or rotation parameter decreases primary velocity but increases secondary velocity. The effects of magnetic parameter or Grashof number on these velocities are noted in reverse order.

A cryptographic model with intrusion detection capability
Abayomi Joshua Jegede* and Salami Hamza Onoruoiza**
Abstract :The goal of this study is to develop a hybrid security model which combines the strengths of encryption with the capabilities of intrusion detection. The research conducts an exploratory study of the subject of encryption and intrusion detection. The model proposed here is a program model which is implemented as a totally decentralized distributed application consisting of three main systems (or modules): the encryption system, decryption system and intrusion detection system). These subsystems work together to achieve the overall objectives of the hybrid cryptosystem. The system flowchart is used to illustrate how each of the program module functions as well as their interactions in an overall system. Visual Basic is used as the language of implementation because it is highly interactive and has extensive support for modularity. The strength of this model is in its flexibility which provides the means for the security administrator to change the cryptographic keys as frequently as necessary.
Key words : Cryptography, plaintext, ciphertext, encryption, decryption, key, intrusion detection.

Trie-like Structure for Implementation of Porter Stemming Algorithm
K. Thammi Reddy¹, M. Shashi² and L. Prathap Reddy³
Abstract : Modern information retrieval is focused on the extraction of key terms from documents to aid in the accessing and navigation of web pages and electronic information. These key terms are used to represent a document in the search space. Relevance of a document for a query is determined in terms of presence or absence of common key terms. The obvious solution is to test for absolute matching of the key terms present in the query and the terms in the documents. However, the key terms may have many morphological variants that share similar semantic interpretations and it may be beneficial for the information retrieval system to consider these terms equivalent. The process of Stemming transforms morphological variants of a word into the root by removing the suffix and re-coding the remaining, if required. The transformation required for stemming a specific word will be decided based on the suffix of the word. Hence it is appropriate to accommodate all possible suffices/ending list in a structure that supports efficient matching of suffices with the ending of a word to be stemmed. We devised a Trie-like data structure for accommodating the ending list and appropriately suggesting the transformation procedures. We have implemented the most widely used stemmer algorithm known as Porter stemmer using the Trie-like structure and proved its efficiency compared to the standard implementation of Porter stemmer available for public on www. This paper presents the details of implementation and comparative analysis.
Key words : Intelligent information retrieval, Stemming, Trie structure, Text mining.

Effect of Magnetic Field on Blood Flow through Capillary
Rekha Bali and Shraddhya Dubey
Abstract : In this paper we have presented a model to asses the applicability of applied magnetic field on blood flow through a capillary surrounded by a tissue. Tissue has been described by mixture of two interacting continua-A linear elastic solid and a viscous fluid. In order to account a red blood cells clustering. Viscosity of blood is taken as radial co-ordinate dependent. We have solved the equations with the help of boundary and matching conditions. Effect of magnetic field on wall shearing stress and velocity in capillary has been find out and discussed.
Key words : Magnetic field, Blood Flow, Capillary, Biphasic Model.

Estimation of Expected Time to Cross the Antigenic Diversity Threshold of HIV Infected
R. Kannan, K.A. Venkatachalam, R. Sathiyamoorthi and *G. Malarvizhi
Abstract : In the study of HIV infection and its consequences the seroconversion of the infected is a vital event. The estimation of the expected time to cross the antigenic diversity threshold of the HIV infected over the time interval (0,t] is an important aspect which helps medical intervention. The interarrival times between successive sexual contacts of a non-infected with an infected is important factor that determines the expected time to seroconversion of the infected. Sathiyamoorthi and Kannan⁶ have obtained the expected time to seroconversion and its variance when interarrival times are i.i.d random variables and also the case where they are correlated, assuming the threshold distribution as exponential. In this paper it is assumed that the intercontact times between successive contacts are correlated random variables and the threshold distribution is gamma which does not satisfy the LMP property. Shock model with correlated intercontact time has been studied by Sathiyamoorthi⁵. In developing this model the results of Gurland² has been used. The mean time to cross the antigenic diversity threshold and its variance are derived and numerical illustrations are provided.
Key words: Human Immuno-deficiency Virus, Antigenic diversity threshold, intercontact times, Seroconversion, Acquired Immuno Deficiency Syndrome.

Quality attributes of web based applications
Sanjay Tyagi and Ashok Kumar
Abstract : In the recent years, web applications have become prevalent around the world. The number of web applications has increased immensely. Many companies have developed or integrated their mission critical applications using web technologies to provide online access to anyone at any time. As more business relies on web applications & the applications becomes more complex, there is a growing concern about their quality & reliability. Thus, it becomes crucial to identify all the quality attributes of the web applications, which are to be tested to ensure that applications are reliable & meet their design specifications. In this paper, an attempt has been made to identify the attributes that affect the quality of web-based applications.
Key words : Efficiency, maintainability, software quality attributes, reliability, scalability, usability, web applications.

Optimal inventory management for deteriorating items with trended demand and shortages under inflation
Sudhir K. Sahu¹, Gobinda C. Panda² and Dipana J. Mohanty³
Abstract : A lot-size inventory model for deteriorating items is derived with linearly increasing demand by allowing complete backlogging .The effects of inflation and time value of money are studied on the model. It is assume that the units in inventory determine over time at a constant rate. The inventory policy is discussed over the finite planning horizon with one re-order points. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out with the help of a numerical example.
Key words: Inventory, inflation, deterioration, shortage, demand.

Morphisms of state machine
S. Jaya Bharathi¹ and K. Angaleeswari²
Abstract : In this paper we define a new transition preserving morphisms of state machines through state function ; = This correspondence concerns the relationship between the transition preserving morphisms of state machine and the graph equivalent and hence the state machine through state function and the state machine through graph can be extended for n-machines through graph equivalent. The homomorphism of n-machines using composite function is also shown.
Key words : State machines, State function, homomorphism, isomorphism, graph.

A nonlinear impulsive differential system
R. Rangarajan¹ and Hamood A.K. Alhaddad²
Abstract : In the present paper, we investigate the existence and uniqueness of periodic solution of a nonlinear impulsive first order differential system by innovatively applying the method of periodic successive approximations of Samoilenko. A.M.^6,7.
2000 AMS Classification Number: - 45J05, 34K05, 45L05, 47G20.
Key words : Impulsive Differential System, Periodic Solutions, Successive Approximations.

The Quantum and Atomic of Banach algebras and axiom of choice on the lattice of all varieties of Banach algebras
M. H. FAROUGHI and *G. KHALILZADEH
Abstract : A variety of Banach algebras is a non-empty class of Banach algebras in which there exists such a family of laws that all of its members satisfy all the laws. We define the cores of varieties and prove that each variety has a unique core. We will introduce the Quantum and Atomic of Banach algebras and the Quantum of Banach algebras shows its degree of elevation, moreover, it shows the physical structure of that Banach algebras. Finally we will introduce the axiom of choice and Hausdorff maximality principle on the lattice of all varieties.

Modelling of aerosol mass-size distributions at semi-arid environment based on markov model & pareto analysis
K. Sreenivasa Rao¹ T.V. Ramakrishna Rao* R. Rama Krishna Reddy* and K. Sudhakar Babu¹
Abstract : The measurements of total concentration and mass-size distribution of near-surface aerosols noted using a ten-channel Quartz Crystal Micro balance (QCM). QCM is operated at hourly intervals for 4-5 days in every month and the data for the years 2000 & 2001 at dry subhumid and semi-arid zone, Anantapur (14.62°N;77.65°E) is considered. The data is generally used to study the response of aerosol characteristics to regional mesoscale and synoptic processes. In this paper, we attempt to introduce dynamic stochasticity through Markov model and employ a well-known technique of ABC - Analysis generally known as Pareto Analysis to aerosol mass size distribution data and predict future state probabilities of aerosol mass size distribution through steady state. To our knowledge, this is the first time that such a methodology is developed synthesizing techniques in the theories of Operations Research and Stochastic Processes to probe into the random phenomenon of aerosol mass-size distributions. The theoretical results are well supported by empirical work on the aerosol mass sizes.

Analysis of a network queue modelcomprised of biserial and parallel channel linked with a common sever
DEEPAK GUPTA, T.P. SINGH* and RAJENDER KUMAR**
Abstract : This paper is an attempt to steady the steady state analysis of a complex network of queues in which a common channel is linked in series with each of two systems, one containing two bi-serial channels and other two parallel series channels. The arrival and service pattern both follow Poisson law. The generating function technique, laws of calculus and statistical tools have been used to find the various queue characteristics. The model finds its application in decision making in the process industries, in banking system, in networking and many administrative setups and business service. A numerical example is also given to clarify the the model.
Key words : Steady state behaviour, Poission stream, Biserial channels, Mean queue size, variance etc.

A Study of an Integral Transform and Fractional Integral Operator involving Generalized Mellin-Barnes Type Contour Integral
KANTESH GUPTA and VANDANA AGRAWAL
Abstract : In the present paper, we first define an integral transform whose kernel is generalized Mellin Barnes type contour integral which is popularly known in the literature as -function. Further, we define a fractional integral operator of general arguments and having -function as its kernel. Next, we establish an interesting theorem involving the image of our earlier defined integral transform in the fractional integral operator of our study. Then, we establish three new corollaries of our main theorem involving functions that are of interest by themselves. The importance of the present study lies in the fact that all our findings are unified and general in nature. Several new results can be obtained from our main theorem and corollaries as their special cases. We give here exact reference to two known results.
Key words : Modified -transform, function Mathematics Subject Classification. 44A20, 33C60, 2633

The effect of alertness on the time to cross the antigenic diversity threshold in hiv infection
R. Jaisankar¹ and R. Sathiyamoorthi²
Abstract : Antigenic diversity plays an important role in the breakdown of the immune system of the HIV infected Study on the Antigenic diversity threshold has been carried out by Nowak and May¹ and Stilianakis². In this paper an attempt is made for estimating the time to cross the antigenic diversily threshold (CADT) when the preventive strategy is adopted by the individuals to avoid the infection and to elongate the time to CADT. Numerical illustrations are also provided using simulation technique to substantiate the results.

C-path homotopy in metric spaces
KIRAN SHRIVASTAVA and ARTI MISHRA
Abstract : In this paper we extend the concept of path homotopy in metric spaces to c-path homotopy in metric spaces. Several parallel results as compared with those for path homotopy are obtained.
SUBJECT CLASSIFICATION: (2000) : 55-01, 54-01.
Key words : c-paths, c-path homotopy, reverse c-path, constant c-path.

On partial quasi-bilateral generating functions involving Laguerre and Gegenbauer polynomials
A. DAS*
Abstract : In this article, we have obtained a generalization of a known result on quasi-bilateral generating relation involving Laguerre and Gegenbauer polynomials from the existence of partial quasi-bilateral generating relation of the polynomials under consideration. Some particular results of interest are also discussed here.

Planning and Selection of Field Operations through Decision Support System
P.K. Butey and Karan Singh*
Abstract  : The power and machinery is the single largest cost component constituting about 60% of the total investment cost on mechanized farm. Thus, the profit of a farm depends, to a great extent, on the appropriate mechanization and planning of the farm. The main constraint in the planning of farm mechanization has been due to the complexity of available machinery systems and their diversity with respect to type, size, number and operational characteristics. The complexity and importance of agricultural operations management has also increased as agriculture have adapted capital-intensive production systems stimulating the development of more formal planning and monitoring techniques. Planning being adapted include decision support systems aimed at achieving better production control. Specifically, this project addresses operational planning or scheduling of field operations. The planning procedure involves the allocation of time and resources to activities considering inherent uncertainty and risks. The method used is applied decision analysis together with the principles of Bayesian networks.

Some new identites of the Rogers-Ramanujan type-I
P. Rajkhowa and Shaikh Fokor Uddin Ali Ahmed*
Abstract  : In this paper, we derive some new identities of the Rogers - Ramanujan type related to modulo 17,19,51 and 57 using multiple summations.
Historical development : The following two identities, for |q|<l, namely

and 

are the celebrated Rogers- Ramanujan identities. These two identities have motivated extensive research over the past 100 years. These identities were first discovered and proved by L.J. Rogers in 1894. In 1913, Srinivasa Ramanujan, unaware of Rogers' work, obtained the results independently. In 1917, I.J. Schur of Germany, again discovered these identities independently.
In the ensuing decades, Ramanujan, Rogeres, G.N. Watson, W.N. Bailey, L.J. Slater and others discovered several other identities of different moduli. More recently the work of G.E. Andrews needs special mention. A. Verma and V.K. Jain have done some good work.
There are two aspects of these identities : the analytical aspect and the combinatorial aspect. In these paper we study only the analytical aspect.
Key words : Basic Hypergeometric series; q-analogue of Saalschutz
Theorem; Jacobi's Triple product identity.

Datamining for DNA microarray data analysis and visualization
R.R. SHELKE^*1 and V.M. DESHMUKH²
Abstract : In recent years, advances in molecular genetics technologies such as DNA microarrays allow for the first time to obtain a "global" view of the cell. Researchers can now routinely investigate the biological molecular state of a cell measuring the simultaneous expression of tens of thousands of genes using DNA microarrays. In the present work, the datamining for such a DNA microarray data has been focused in greater details. To fulfill this need datamining technique has been developed based on the analysis of literature profiles generated by extracting the frequencies of certain terms from thousands of abstracts stored in the Medline literature database. The 'cell slide images' have been processed to calculate different gene values in the particular slide which in turn maintain the database for cluster analysis and visualization which helps to compare database of DNA sample images for disease diagnosis . The diseases taken into consideration in the present work are cancer, hepatatis and diabetis.
Key words : Datamining, DNA, Clustering and Visualisation.

Flow in a rotating porous annulus of variable permeability due to suction and injection
K. Jayarami Reddy¹, G. Venkata Ramana Reddy² and N. BhaskaR Reddy³
Abstract : We consider a highly porous material occupying the annular region between two coaxial infinitely long cylinders. A viscous incompressible fluid fills the porous medium and is initially in a state of rigid rotation together with the medium. The porous annulus is partly of constant permeability (up to some radius) and the rest is of variable permeability, in such a way that the permeability is a continuous function of radius in the entire annulus. The flow has been disturbed by imposing suction/ injection at the outer/ inner cylindrical boundary respectively. The rate of injection at the inner cylinder is equal to the rate of suction at the outer cylinder. The Brinkman's law has been used to represent the motion in the porous medium. We consider the steady flow corresponding to this problem. An exact analytical solution is obtained in terms of Bessel functions. The manner in which the steady boundary layer gets modified by the presence of a variable permeability has been examined. It has been established that by a careful choice of variable permeability of the medium, the flow can be regulated so as to make the velocity nearly constant in the entire channel except in the boundary layer on the source and the sink. The results are compared with the already existing theories in the case of constant permeability.
Key words : Source-sink flows, Permeability, Brinkmans's law, Ekman layer.

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