iosr-Jm   Volume-12 ~ Issue-1 ~ Jan-Feb 2016

Abstract: This paper introduces pre generalisedregular weakly continuous maps , pgrω–irresolute maps, strongly pgrω–continuous maps , perfectly pgrω–continuous maps and studies some of their properties.

Keywords: pgrω–closed sets, pgrω–open sets, pgrω–continuous maps, pgrω-irresolute maps, strongly pgrω-continuous maps, perfectly pgrω–continuous maps.

[1] N .Levine, Semi-open sets and semi-continuity in topological spaces,70(1963), 36- 41.

[2]. S. P.Arya and T.M. Nour , Chatcterizationsof s-normal spaces, Indian J. Pure Appl, Math 21(1990), 717-719

[3]. Y. Gnanambal, and Balchandran, On generalized pre regular continuous maps in topological spaces, Indian J. Pure. Appl. Math., June 1999

[4]. S. S. Benchalli, P. G. PatilSomenew Continuous Maps in Topological Spaces, journal of advanced topics in topology, VOL. NO. -2 (2010)

[5] R.S. Wali and Prabhavati S. Mandalgeri, On α regular ω-closed sets inTopological spaces, Int. J. of Math Archive 5(10), 2014, 68-76.

Abstract: The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a reference model. By using the solution of the Lyapunov equation, the convergence of the tracking error to the origin, is proved. The proposed approach employs linear controllers rather than nonlinear ones. Therefore, the designing method is simple for use and the resulting controller is easy to implement. An application of the proposed approach for a class of perturbed systems is also considered. Finally, numerical examples are given to demonstrate the validity of the results.

Keywords: robust tracking, model following, discrete-time systems, linear systems, disturbances, Lyapunov equation, linear controller

[1]. Hopp, T. H., & Schmitendorf, W. E. (1990). Design of a linear controller for robust tracking and model following. Journal of dynamic systems, measurement, and control, 112(4), 552-558.
[2]. Oucheriah, S. (1999). Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers. Automatic Control, IEEE Transactions on, 44(7), 1473-1477.
[3]. Lawrence, D. A., & Rugh, W. J. (1995). Gain scheduling dynamic linear controllers for a nonlinear plant. Automatica, 31(3), 381-390.
[4]. Ni, M., & Li, G. (2006). A direct approach to the design of robust tracking controllers for uncertain delay systems. Asian Journal of Control, 8(4), 412.
[5]. Ni, M. L., Er, M. J., Leithead, W. E., & Leith, D. J. (2001). New approach to the design of robust tracking and model following controllers for uncertain delay systems. IEE Proceedings-Control Theory and Applications, 148(6), 472-477.
[6]. Basher, A. H., Mukundan, R., & O'CONNOR, D. A. (1986). Memoryless feedback control in uncertain dynamic delay systems. International Journal of Systems Science, 17(3), 409-415..

Abstract:This paper analyses a dynamic system which is reviewed at equidistant points of time and at each review, the system is classified into one possible number of states and subsequently a decision has to be made. The economic consequences of the decisions taken at the review times are reflected in costs. These properties of Markov decision process are employed to study the maintenance condition of deteriorating equipment. Consequently, the optimal cost of transition from a bad condition to a good condition and the long-run fraction of time that the equipment is in bad condition were obtained. The result could be used to study the status of
equipment used in various organizations to determine their efficiency and productivity.
Keywords: Markov decision process, optimal cost, long-run fraction of time, decision epochs, maintenance, deterioration.

[1]. Abubakar, U.Y, Reju, S.A. and Awojoyogbe, B.O. (2007).Markov Decision Model and the application to the cost of treatment of
Leprosy disease.Leonardo journal of sciences 11,69-78.
[2]. Abubakar, U.Y. (2011). Markov Decision Model for Human Health with Policy Iteration.Journal of science, Technology,
Mathematics and Education (JOSTMED), 7(2)..
[3]. Bakker, J.D., H.J. van der Graaf, and J.M. van Noortwijk (1999).Model of Lifetime-Extending Maintenance. In M.C. Forde, editor,
Proceedings of the 8thInternational Conference on Structural Faults and Repair, London, UnitedKingdom, 1999. Edinburgh:
Engineering Technics Press.
[4]. Barlow, R.E., and F. Proschan (1965).Mathematical Theory of Reliability. New York: John Wiley and Sons.
[5]. Das, P.C. (1999). Prioritization of bridge maintenance needs, Case Studies in Optimal Design and Maintenance Planning of Civil
Infrastructure Systems, D.M. Frangopol, editor, ASCE, Reston, Virginia, 26-44.
[6]. Derman, C. (1970).Finite State Markovian Decision Processes. New York: Academic Press
[7]. Dekker, R. (1996). Applications of maintenance optimization models: a review and analysis. Reliability Engineering and System
Safety, 51:229-240.

Abstract: In this paper we develop a dissolve oxygen temperature decay mathematical model for water pollution in Damoder River at Dhanbad region. Equations for dissolved oxygen (Do) and biological oxygen demand (BOD) have been derived and solved analytically. The solution can be used to determine BOD and DO for suitable value of the parameters

Keywords: Dissolved Oxygen, Biological Oxygen Demand, Water pollution, Damoder River

[1]. Streeter, HW and EB Phelps (1925): A study of the pollution and natural purification of the ohio river, U.S. Public Health Bulletin, 146 (1925).
[2]. Dobbins R. A.,:Atmospheric motion and air pollution, John Wiley & Sons, New York (1979).
[3]. Dobbins, W.E. and Belle D. A. : Difference modeling of stream pollution & J. San. Eng. Div. Proc. ASCE 94 SAS; 995 (1968).
[4]. Graves, G.W., G.B. Halfield and: mathematical Programming for regional water Whinston A quality management water Res. 8(12) (1925)
[5]. Graves, G.W., D.E.: Application of a large scale non linear Programming problem to pollution control, AFIPS, 39 conference proceeding ,2007

Abstract: A modified separation of variables (Eigenfunction-Expansions) suggested by Ivan [1] was investigated for unsteady Couette flow of a second grade fluid in a layer of porous medium. We find that it produces the correct solution shown to agree identically with the Laplace Transform obtained for a class of unsteady flows of generalized second grade fluid for the same problem.

Keywords: second grade fluid, Eigenfunction expansions, unsteady flow, Laplace transform

[1]. Christov,I .C., On a difficulty in the formulation of initial and boundary Conditions Mechanics Research Communications 51 (2013)86-92
[2]. T. HAYAT, MASOOD KHAN, M. AYUB, A. M. SIDDIQUI, The unsteady Couette flow of a second grade fluid in a layer of porous medium. Warszawa (2005)57, 5, pp. 405–416,
[3]. Duhamel, J.M.C., 1833. Sur la methode generale relative au mouvement de la chaleur dans les corps solides plonges dans des milieux dont la temperature varie avec le temps. Journal de Ecole Royale Polytechnique 22 (14), 20–77
[4]. Bagely RL. A theoretical basis for the application of fractional calculus to visco ellasticity . J of Rheology 1983, 27(3) 201-210(2013)86-92.
[5]. K. Vafai and C. L. Tien, Boundary and inertia effects on flow and heat transfer in porous meida, Int. J. Heat Mass Transf., 24, 195, 1981.
[6]. P. M. Jordan, P. Puri, Exact solutions for the unsteady plane Couette flow of a dipolarfluid, Proc. Roy. Soc. Lond. Ser. A, 458, 1245, 2002.
[7]. Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids, 2nd ed. Clarendon Press Oxford

Abstract: It should be noted that a Borel measure may not be determined by its values on compact 𝐺𝛿 sets. But if some of the conditions are imposed on a Borel measure so that it can be determined by its values on compact 𝐺𝛿 sets. The answer to this question is Regularity. We can discus as in this paper by proving the result that a Borel measure is determined by its values on compact 𝐺𝛿 sets and further that every Baire measure has a unique extension to a regular Borel measure.

[1]. G. Choquet. Lectures on Analysis Volume II: Representation Theory, volume 2 of Mathematics Lecture Note Series. W.A. Benjamin, Inc, London, 1969.
[2]. M. Ghasemi, S. Kuhlmann, and M. Marshall. Application of Jacobi's representation theorem to locally multiplicatively convex topological real algebras.J. Funct. Anal., 266(2): 1041 1049,2014
[3]. William Arveson. Notes on measure and integration in locally compact spaces. University of California,USA. (1996)
[4]. Halmos, P. R., Measure Theory, Van Nostrand, Princeton, 1950.
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[6]. P. Mattila, "Geometry of sets and measures in euclidean spaces". Cambridge Studies in Advanced Mathematics, 44. Cambridge University Press, Cambridge, 1995

Abstract:In this paper, for a marketing organization consisting of two grades which is subject to depletion of manpower(wastages) due to policy decisions with high or low attrition rate, an important system characteristic namely the variance of time to recruitment is obtained for three mathematical models using a suitable policy of recruitment when(i) wastages form an order statistics and (ii) threshold for each grade has two components, and (iii) the inter-policy decisions form an ordinay renewal process, order statistics and geometric process. The system characteristics are analyzed by numerical illustration and the findings are reported.
Keywords: Order statistics, Ordinary renewal process, Policy of recruitment, Threshold with two components, Two types of policy decisions with high or low attrition rate, Variance of time to recruitment.

[1]. D.J.Bartholomew, Statistical Models for Social Processes, John Wiley and Sons,New York, 1973.
[2]. D.J. Barthlowmew and A.F.Forbes, Statistical Techniques for Manpower Planning, 1stEdition, John Wiley and Sons, New York, 1979.
[3]. R.Sathiyamoorthi and R.Elangovan, Shock model approach to determine the expected time for recruitment, Journal of Decision and Mathematika Sciences,3(1-3),1998, 67-78, .
[4]. Vijayasankar,N., Elangovan.R., and Sathiyamoorthi.R., Determination of expected time to recruitment when backup resource of manpower exits, Ultra Scientist, 25(1) B, 2013,61-68.

Abstract:A ring R is called (left) Artinian if it is Artinian as a left module over itself. In this paper, we have discussed about the prime ring, semi-prime ring and their connection to quotient ring. Mainly, we focused on" A right quotient ring which is a semi-simple Artinian ring if and only if the ring is a semi-prime ring, has a finite rank and has a maximum condition on right annihilators".
Keywords: Quotient ring, Prime ring, prime field, Artinian ring, Annihilator, Char(R).

[1]. C Musili Introduction to Rings and Modules University of Hyderabad Narosa Publishing House, 1990.
[2]. E. R. Gentile, "On rings with one-sided field of quotients", Proc. Amer. Math. Soc.,11(1960), 380-384.
[3]. A. W. Goldie, "The structure of prime rings under ascending chain conditions", Proc. London Math. Soc., 8 (1958), 589-608.
[4]. A. W. Goldie, "Semi-prime rings with maximum condition", Proc. London Math. Soc., 10(1960), 201-220.
[5]. R. E. Johson. "Representations of prime rings", Trans. Amer. Math. Soc., 74 (1953), 351-357.
[6]. R. E. Johson. "Semi-prime rings", Trans. Amer. Math. Soc., 76 (1954), 375-388.

Abstract: This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.
Keywords: LSD, Trapezoidal Fuzzy Numbers, Alpha Cut, Membership Function, Ranking Function, Total Integral Value, Graded Mean Integration Representation.

[1]. S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl. Math. Comput., 156 (2004) 381-386.
[2]. S. Abbasbandy, M. Amirfakhrian, The nearest approximation of a fuzzy quantity in parametric form, Appl. Math. Comput., 172
(2006) 624-632.
[3]. S. Abbasbandy, M. Amirfakhrian, The nearest trapezoidal form of generalized left right fuzzy number, Internat. J. Approx.
Reason., 43 (2006) 166-178.
[4]. S. Abbasbandy, T. Hajjari, Weighted trapezoidal approximation-preserving cores of a fuzzy number, Computers and Mathematics
with Applications, 59 (2010) 3066-3077.
[5]. E. Baloui Jamkhaneh and A. Nadi Ghara, Testing statistical hypotheses for compare means with vague data, International
Mathematical Forum, 5 (2010) 615-620.
[6]. S. Bodjanova, Median value and median interval of a fuzzy number, Inform. Sci. 172 (2005) 73-89.

Abstract:Inventory decisions in supply chain are crucial for its success. Making these decisions in inventory systems with multiple items is a challenging task for managers. These decisions become more important for the items with expiration date. Quadratic rate of deterioration is taken in this article. Most approaches in the literature for optimizing decisions in such an environment consider only a single item inventory. This paper presents a multi item inventory model to optimize the unit time profit of inventory management for the products having an expiration date after which the product can not be sold. As on one side the shortage costs are significant, on the other side, to maintain appropriate inventory levels for such type of products and avoid shortages is a very problematic job. This article offers an approach for optimization and thus has business significance.

[1]. Ben-Daya M, Raouf A. On the constrained multi-item single period inventory problem. International Journal of Production
Management. 1993; 13(11):104–112.Indian J Vol 7 (4) | April 2014 | www.indjst.org ournal of Science and Technology 471.
[2]. Bhattacharya DK. Production, manufacturing and logisticson multi-item inventory. Eur J Oper Res. 2005; 162(3):786–91.
[3]. Lenard JD, Roy B. Multi-item inventory control: A multicriteria view. Eur J Oper Res. 1995; 87(3):685–92.
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Production Management. 1982; 20(5):657–67.
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243.
[7]. Goswami A, Chaudhuri KS. An economic order quantity model for items with two levels of storage for a linear trend in demand.
Journal of Operation Research Society. 1992;43(2):157–67.

Abstract:The effects of radiation and hall current on MHD free convection three dimensional flow in a vertical channel filled with a porous medium has been studied. We consider an incompressible viscous and electrically conducting incompressible viscous fluid in a parallel plate channel bounded by a loosely packed porous medium. The fluid is driven by a uniform pressure gradient parallel to the channel plates and the entire flow field is subjected to a uniform inclined magnetic field of strength Ho inclined at an angle of inclination  with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically and the temperature difference of the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, temperature field, rate
of heat transfer in terms of their amplitude and phase angles are shown graphically.

[1]. Crammer, K. R. and Pai, S. I. "Magneto Fluid Dynamics for Engineers and Applied Physicists," McGraw-Hill Book Co. New York,
1973.
[2]. Ferraro, V. C. A. and Plumpton, C. "An Introduction to Magneto Fluid Mechanics," Clarendons Press, Oxford, 1966.
[3]. Shercliff, J. A. "A Text Book of Magneto Hydrodynamics," Pergamon Press Ltd. New York, 1965.
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(ZAMP), 15, 1964, 400-407.
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University SCIENCE A, 7(3), 2006, 340-346..

Abstract:Closed-form analytic expression for displacement and stresses at any point in a homogenous
monoclinic half-space are developed. The fault is of infinite length in the strike direction and is of finite width
located at an arbitrary point of a homogenous, monoclinic, perfectly elastic half-space. Deformation of
monoclinic half-space with free boundary caused by a long inclined strike-slip fault is studied analytically and
numerically.
Keywords: Inclined Strike-slip Fault, Monoclinic, Free Boundary, Finite Width

[1]. Kumar,A., Singh, S.J., Singh, J., Static Deformation of Two Welded Monoclinic Elastic Half-Spaces due
to a Long Inclined Strike-slip Fault, Proc. Indian Acad. Sci., 111, 2002, 125-131.
[2]. Maruyama, T., On Two-Dimensional Elastic Dislocations in a Infinite and Semi-infinite Medium, Bull.
Earthq. Res. Inst. Vol. 44, 1966, 811-871
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Fault, Proc. Indian Acad. Sci. , Vol. 59, 1993, 455-464
[4]. Sahrawat, R.K., Godara, Y. and Singh, M., Deformation of a Uniform Half-space with Rigid Boundary
Caused by a Long Inclined Strike-slip Fault of Finite Width, IOSR Journal of Mathematics, 10, 2014,
100-108
[5]. Singh, S.J. and Garg N.R., On the Representation of Two-Dimensional Sesmic Sources, Acta Geophys.
Pol., Vol. 34, 1986, 1-12

Abstract: Traffic congestion is a phenomenon of increased disruption of the traffic movement. In India, with increasing vehicles on the road, traffic congestion is quickly increasing. Much has been written about the queueing theory technique and its powerful application. This paper is an attempt to analyze the contribution and application of queueing theory in the field of traffic congestion. For this Bhagwanpur Golambar intersection of Muzaffarpur city (located in India) is chosen. The paper summarizes a range of queueing theory results in the following areas: waiting time, utilization analysis and system design. The traffic congestion follows a repeatable pattern during the day, and the locals accept it as a daily routine. Keywords: queueing theory, system design, traffic congestion, utilization analysis, waiting time.

[1]. G.F.Newell, Approximation methods for queues with application to the fixed-cycle traffic light, SIAM Review 7(4), 1965, 223-240.
[2]. R. Adeleke,O.D.Ogunwale, O.Y. Halid, Application of Queueing Theory to Waiting Time of Out-Patients in Hospitals, Pacific Journal of Science and Technology, 10(2),2009, 270-274.
[3]. Namdeo V. Kalyankar, Network Traffic Management, Journal of Computing, Vol.2, 2009, 191-194.
[4]. V., Nico, Woensel T.V. and A. Verbruggen, A Queueing Based Traffic Flow Model, Trans. Res., Vol.5, 2000, 121-135.
[5]. H.A. TAHA, Operation research: an introduction (Fourth Edition, Macmillan Publishing: New York, 1987).
[6]. R.A. Adeleke,C. Adebiyi, O. Akinyemi, Application of Queueing theory to Omega Bank PLC, Ado- Ekiti, Nigeria, 1, 2006,122-129.

Abstract:This paperextending to n-ary block of Soundarpandian (1980a), a partially balanced n-ary Block (PBNB)
design discussed.
Keywords: A-,D- and E- Optimal N- ary designs.

1. ABDELBASIT, K.M and PLACKETT, R.L., (1983). Experimental design for binary data. J.Am. Statist. Assoc. 78, 90-98.
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