iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: We look at a brief historical survey of controllability problems of time optimal control theory. We next look at nonlinear variation of parameters to investigate controllability of basically nonlinear systems whereby we establish nonlinear differential games of pursuit results.

Keywords: Optimal Control, Controllability, Games of Pursuit

[1]. Hermes, H. and Lasalle, J. P., Functional Analysis and Time Optimal Control (Academic Press, 1969)
[2]. Lasalle, J. P., The Time Optimal Control Problems, Annals of Mathematics, Vol. 45, 120-124, 1966
[3]. Lee, E. B. and Markus, L., Foundations of Optimal Control Theory (John Wiley and Sons, 18-29, 1967)
[4]. Chukwu, E. N., Finite time controllability of nonlinear control processes, Siam J. Control, Vol. 13, No 4, 807-816, 1975
[5]. Hajek, O., Duality for differential games and optimal control,Maths systems Theory, Vol. 8,No 1,1-7,1974

Abstract: The effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet was examined. The governing partial differential equation are nondimensionalised and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable  and using RungeKutta Gill method with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. It was found that the local heat transfer rate at the surface decreases with increasing values of the magnetic and radiation parameters.
Keywords: Boundary layer, heat transfer, MHD, radiation, stretching sheet.

[1] E. Magyari, and B. Keller, Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J.
Phys. D: Appl. Phys. 32: 1999, 577-585.
[2] E. Magyari, M.E.Ali and B. Keller B, Heat and mass transfer characteristics of the self similar boundary layer flows induced by
continuous surface stretched with rapidly decreasing velocities. Heat Mass Transfer 38: 2001, 65-74.
[3] M. Ali, and F. Al-Yousef , Laminar mixed convection boundary layers induced by a linearly stretching permeable surface. Int J
Heat Mass Transfer 45: 2002,4241-4250.
[4] M.K. Partha, P.V.S.N. Murthy, and G.P. Rajasekhar, Effect of viscous dissipation on the mixed convection heat transfer from an
exponentially stretching surface. Heat Mass Transfer 41: 2005, 360-366.
[5] M. Sajid, and T. Hayat, Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int.
Comm. Heat Mass Transfer 35: 2008, 347-356

Abstract: In this paper, we propose and analyse a mathematical model to study the dynamics of an inshore-offshore fishery with taxation as a control instrument. The inshore area is considered as a breeding place having a fixed carrying capacity where fishing is strictly prohibited. Fishing is permitted only in the offshore area after imposing a tax per unit harvested biomass by the regulatory agency in order to control over exploitation. The steady states of the system are determined. The local and global stability of the interior equilibrium are discussed. Taking tax as a control variable, the optimal harvesting policy is formulated and solved by using Pontryagin's maximum principle [1]. The results are illustrated with the help of numerical example.

Keywords: Dynamic reaction, Inshore-offshore, Local and Global Stability, Optimal Harvesting, Pontryagin's maximum principle, Steady states

[1] Pontryagin L.S., Boltyanskii V.S., Gamkrelidze R.V. and Mishchenko E.F., The Mathematical Theory of Optimal Process ( Wiley-Interscience, New York, 1962).
[2] Sutinen, J.G. and Andersen, P., The economics of fisheries law enforcement, Land Economics, 61(4), 1985, 387-397.
[3] Anderson, L.G. and Lee, D.R., Optimal governing instrument, operation level and enforcement in natural resource regulation: the case of the fishery, American Journal of Agricultural Economics, 68, 1986, 678-690.
[4] Kellog R.L., Easley J.E. Jr. and Johnson T., Optimal timing of harvest for the North Carolina Bay Scallop Fishery, American Journal of Agricultural Economics, 71(1), 1988, 50-62.
[5] Clark C.W. Mathematical Bioeconomics: The Optimal Management of Renewable Resources ( John Wiley and Sons, New York, 1976).

Abstract: In this paper, we proved a common fixed point theorem for occasionally converse commuting (OCC) self-maps without continuity of maps for non-complete complex-valued metric space.
Keywords: Converse commuting maps, occasionally converse commuting maps, fixed point and complexvalued metric space

[1] A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex-valued metric spaces, Numerical Functional Analysis
and Optimization, 32 (3) (2011), 243-253.
[2] Z. Lii, On common fixed point theorem for converse commuting self maps on metric spaces, Acta Anal. Funct. Appl., 4(3) (2002) ,
226-228.
[3] Q. Liu and X. Hu, some new common fixed point theorems for converse commuting multivalued maps in symmetric spaces with
applications, Nonlinear Analysis Forum, 10(1) (2005), 97-107.
[4] R. Chugh, Sumitra and M. Alamgir Khan, Common fixed point theorems for converse commuting maps in fuzzy metric spaces, Int.
Math. Forum, 37(6) (2011), 1183-1190.
[5] H.K. Pathak and R.K. Verma, Integral type contractive condition for converse commuting mappings, Int. J. Math. Anal., 3(24)
(2009), 1183-1190.
[6] H.K. Pathak and R.K. Verma, Common fixed point theorems for occasionally converse commuting mappings in symmetric spaces,
Kathmandu Univ. J. Sci., Eng. and Tech., 3(1) (2011), 56-62.

Abstract: This paper describes a new method of construction of triangular design. Consequently, a new series
of truly self dual triangular design is obtained.

[1]. Bose, R.C. and Shimamoto, T. (1952). Classification and Analysis of partially balanced incomplete block designs with two
associate classes. J. Am. State. Assn. 47, pp.151-184.
[2]. Clatworthy, W.H. (1973). Tables of two-associate class partially balanced designs,
[3]. Raghavarao, D. (1988). Construction and Combinational problems in Design of Experiments. Dover, New York.

Abstract: I here propose an odds ratio based on false rates as a measure of the strength of association between state of nature or condition in a population and test results in diagnostic screening tests. The method provides an estimate for the proposed odds ratio that depends only on the estimated sensitivity and specificity of the test in the event that the prevalence rate is not known. The proposed method unlike the traditional odds ratio provides estimates of not only the proposed false rates based odds ratio-type measure of association, but also alternative sample estimates of its associated standard deviation and test statistic for significance that intrinsically and structurally partials out, that is, does not include in its formulation the number of subjects in the sample known or believed to actually have the condition in nature but test negative or actually do not have the condition in nature but test positive to the condition in the screening test. The proposed method given that the prevalence rate of the condition in the population is known, provides sample estimates of the false positive rate, false negative rate and their odds as well as the proportion of the population expected to test positive to the condition in the screening test which are additional useful information to guide policy formulation and implementation over and above the traditional odds ratio method. Modified estimates of the standard deviation and test statistic for the proposed measure that adjust for the fact that some sample observations in a screening test are not known and cannot therefore validly be used in traditional odds ratio estimation method are provided. The proposed method which is shown to provide more information and to be at least as efficient as the traditional odds ratio method is illustrated with some sample data.

Key words: chi-square test of independence, false negative rate, false positive rate, odds ratio, specificity, sensitivity.

[1]. Akobeng AK (2007).Understanding diagnostic tests 2: likelihood ratios, pre- and post-test probabilities and their use in clinical practice. Acta Paediatr 96(4):487-91.
[2]. Agresti, A (2007). Introduction to Categorical Data Analysis. John Wiley and Sons. Inc., Publications. New York.
[3]. Altman DG (1996). Statistics with Confidence. BMJ Publishing Group. 28-33.
[4]. Altman DG., Bland JM (1994). Diagnostic Tests I: Sensitivity and specificity. BMJ, 308(6943):1552. London.
[5]. Fleiss JL (1973). Statistical Method for Rates and Proportions. John Wiley, New York.

Abstract: Alpha–skew–Logistic distribution is introduced following the same methodology as those of Alpha– skew–normal distribution (Elal-Olivero, 2010) and Alpha–skew–Laplace distributions (Harandi and Alamatsaz, 2013). Cumulative distribution function (cdf), moment generating function (mgf), moments, skewness and kurtosis of the new distribution is studied. Some related distributions are also investigated. Parameter estimation by method of moment and maximum likelihood are discussed. Closeness of the proposed distribution with alpha-skew-normal distribution is studied. The suitability of the proposed distribution is tested by conducting data fitting experiment and comparing the values of log likelihood, AIC, BIC. Likelihood ratio test is used for discriminating between Alpha–skew–Logistic and logistic distributions. Mathematics Subject Classification: 60E05; 62E15; 62H10
Keywords: Alpha-Skew normal distribution; Multimodal distribution; Alpha-skew normal; Alpha-skew Laplace; Kullback Leibler (KL) distance.

[1] Azzalini, A. (1985) A class of distributions which includes the normal ones. Scand. J. Stat. 12: 171 - 178.
[2] Balakrishnan, N. (1992) Handbook of Logistic Distribution. Marcel Dekker. New York.

[3] Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical Information Theoretic Approach. 2nd edn. Springer.New York.
[4] Chakraborty, S., Hazarika, P. J. (2011) A survey of the theoretical developments in univariate skew normal distributions. Assam Statist. Rev. 25(1): 41 - 63.

[5] Chakraborty, S. Hazarika, P. J., Ali, M. M. (2012) A new skew logistic distribution and its properties. Pak. J. Statist. 28(4): 513 -524.

[6] Chakraborty, S. Hazarika, P. J., Ali, M. M. (2014a) A multimodal skewed extension of normal distribution: its properties and applications. Statistics-A Journal of Theoretical and Applied Statistics, http://dx.doi.org/10.1080/ 02331888.2014.908880.

Abstract: Waiting on a queue is not usually interesting, but reduction in this waiting time usually requires planning and extra investments. The increasing population and health-need due to adverse environmental conditions have led to escalating waiting times and congestion in hospitals especially in the Emergency and Accident Departments (EAD). It is universally acknowledged that a hospital should treat its patients, especially those in need of critical care, in timely manner. Incidentally, this is not achieved in practice particularly in government owned health institutions because of high demand and limited resources in these hospitals. To enhance the level of admittance to care, optimal beds required in hospital is needed and this can be achieved by adequate knowledge of patient flow. In this paper, we show that queue theory can accurately model the flow of in-patient in hospital; we determine the optimal bed count and its performance measure.

Keywords: M/M/C queue, Poisson arrival, Exponential distribution, In-patient

[1]. Adeleke. R. A, Ogunwale O. D, Halid O. Y (2009) Application of Queueing Theory to Waiting Time of Out-patients in Hospitals. Pacific Journal of Science and Technology Vol. 10(2) 270-274
[2]. Arun Kumar and John Mo (2010) Models for Bed Occupancy Management of a Hospital in Singapore. Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh.
[3]. DeBruin A.M, A.C van Rossun MC Visser, GM Koole(2006) Modeling the emergency cardiac in-patient flow: an application of queuing theory. Health Care Management Science Vol. 10, No 2, pp 125-137
[4]. Green L. V (2002) How many Hospital Beds? Decision, Risk and Operation. Working Paper Series
[5]. Green LV, Soares J, Giglio JF, Green RA (2006) Using queueing theory to increase the effectiveness of emergency department provider staffing. Academic Emergency Medicine 13(1):61-68