iosr-Jm   Volume-5 ~ Issue-5

Abstract: Acceptance sampling is concerned with inspection and decision making regarding products ,one of the oldest aspects of quality assurance. The most effective of acceptance sampling is not to "inspect quality into the product" but rather as an audit tool to ensure that the output of a process conforms to requirements. Acceptance sampling is most likely to be useful in few of these cases i) when testing is destructive ii) when the cost of 100% inspection is extremely high iii)when there are potentially serious product liability risks and the vendor's process is satisfactory, a program for continuously monitoring the product is necessary. The Characteristics of "Selection of one plan suspension system with special type of double sampling originally developed by K.K.Suresh and V.Sangeetha are reconsidered in this paper from computational point of view.In this paper spread-sheet –excel work sheet and algorithm are used to calculate the probability of accepting a lot given the proportion non-conforming under one plan suspension system with special type of double sampling (STDS) plan as reference plan.

Keywords: OP, STDS, RQL, EXCEL WORKSHEET, ARL

[1] Cone.A.F and Dodge H.F (1962): A Cumulative results plan for small Inspection , Sandia Corporation Repring, SCR-678, ALBUQUERQUE,NM.

[2] Glouba.A (1953) :Designing single sampling inspection plans when the sample size is fixed Journal of American Statistical Association,vol48,pp278-288

[3] Lily Christina. A (1995): Contributions to the study of Design and analysis of suspension system and some other sampling plans, Ph..D Thesis , Department of Statistics, Bharathiyar University ,coimbatore-46,India.

[4] Soundararajan, v (1981):Sampling Inspection plans when the sample size is fixed ,Journal of Madras University, Section B vol44,pp91-99.

[5] Suresh K.K and Jayalakshmi .S(2007): Designing of switching system with special type double sampling plans specified quality levels, Impact Journal of Science and Technology,vol1,No1-2,pp441-49

[6] Suresh K.K and Kaviyarasu.V(2008): Certain results and tables relating Qss-1 with conditional RGS plan, IAPQR Transaction,vol.1No1-2pp61-70.

[7] Suresh K.K. and Saminathan .R(2007): Selection of Multiple repetitive group sampling plan involving Maximum Allowable percent Defective and Maximum Allowable Average Outgoing Quality, International Journal of Statistics and Management system,Vol.2No1-2pp22-30.

[8] Vijayaraghavan.R(1989)On Designing Multiple deferred state sampling (Mds-1(0,2)) plans involving minimum sum of risks ,Journal of Applied statistics,vol16,No1,pp87-88

[9] Troxell.J.R(1972) : An investigation of Suspension system for small inspection, Ph. D Thesis, Rutgers University, New Jersey.

[10. Troxell,J.R(1980): Suspension system for small inspection,Technometrics,Vol.22 No.14,pp517-533.

Abstract: In this paper, I have invented the formulae of the height of the triangle. My findings are based on pythagoras theorem.

1 Geometry concepts & pythagoras theorem.

Abstract: We are proposing a modified form of the Milne's Predictor-Corrector formula for solving ordinary differential equation of first order and first degree. Here we are approximating the value of the dependent variable under five initial conditions (where Milne takes four initial conditions) and then improving this value (closer to the exact value) by proper substitution in the formulae. This process is an iterative way to obtain the values and the process continuing until we get a proper level of accuracy.

Keywords: ODE, Milne's modified Predictor-Corrector, quantitative comparison, accuracy

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Abstract: We are familiar with the geometric definition of Real roots of a Quadratic function as the x-intercept of the Quadratic functions graph; however such a geometric definition is not given for the Complex roots of a Quadratic function. This paper geometrically defines complex numbers as solution of Quadratic Equations. In-order to achieve this a new coordinate space is defined where given a quadratic function with complex solution we can geometrically plot complex solutions to it, in this new coordinate frame. Thus the solution to any Quadratic equation with complex solutions can be derived geometrically. Also this coordinate frame will define the entire Complex Plane as a Solution Space of Quadratic functions with complex roots.

Wikipedia Articles: Complex numbers Wikipedia

Complex plane Wikipedia Articles: Quadratic function Wikipedia Articles:

Quadratic equation

Paul Dawkins: Calculus I (Link: http://tutorial.math.lamar.edu/)

Abstract: In this paper, we obtain some results on fixed points for expansion mappings in D-metric and Tri D-metric spaces, introduced by Dhage [1] .Our results includes several fixed point results in ordinary metric spaces as special cases on the line of Maia [5]. KEYWORDS AND PHRASES: Fixed point, D-metric spaces, Expansion maps, etc. SUBJECT CLASSIFICATION: Primary 47H10, Secondary 54H25.

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[4] A comparison of two contraction principles, Math. Sci. Res., Hot-Line, 3 (8), (1999), 49-53. MAIA, M.G.

[5] Un osscravazions sulle contrazoni metriche, Rend. Sem. Math. Padova, 40 (1968), 139-143. RHOADES, B.E.

[6] A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., (1976), 257-290. ROSENHOLTZ;

[7] Local expansion derivatives and fixed points, Fund. Math., 91 (1976), 1-4. WONG, S.Z., LI., B.Y., GAO, Z.M., ISEKI, K.;

[8] Some fixed point theorems on expansion mappings, Math. Japonica 29, 4(1984), 631-636.

Abstract: The aim of this paper to introduced a semi extremely disconnected space on Topological space in fuzzy sitting , Several properties and characterizations of such space are discussed.

Key words :- fuzzy semi extremely disconnected space , fuzzy semi hyper connected space , Generalized fuzzy semi extremely disconnected space.

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[5] Pao-Ming, P. and Ying-Ming, L. Fuzzy Topology .I. Neighborhood Structure of a Fuzzy Point and Moore-Smith Convergence, J. Math. Anal. Appl.,ol.76, pp.571-599, (1980).

[6] N. Bourbaki, General Topology , Part I, Addison Wesley, Reading, Mass. 1996.

[7] Ratna Dev Sarma , Extermally Disconnected in Fuzzy Topological Space, MATEMATIQKI VESNIK , 46 (1994), 17 - 23.

[8] M. Caldas, G. Navalagi, and R. Saraf, On fuzzy weakly semiopen functions, Proyec ciones 21 (2002), 51 - 63.

[9] Z. Petri_cevi_c, On S-Closed and Extermally Disconnected fuzzy topological space, MATEMATIQKI VESNIK, 50 (1998), 37 – 45.

[10] G. Balasubramanian and V. Chandrasekar , Fuzzy 𝛼 - Connected and Fuzzy 𝛼 - Disconnected in Fuzzy Topological Space , MATEMATIQKI VESNIK , 56 (2004), 47 – 56 .

Abstract: In this paper, we study a vaccination model for tuberculosis (TB) dynamics at the population level. We prove that the solution to the model is positive and bounded. The basic reproduction number is determined. We show that the disease-free equilibrium (DFE) is globally asymptotically stable if and the existence of at least one endemic equilibrium of the model. Numerical simulations of the model is also carried out to show the efficacy of the vaccine. Numerical experiments suggest that a strategy of continuous vaccination would result in a more stable DFE for disease elimination.

Keywords: mathematical model; epidemiology; infectious disease; basic reproduction number; equilibrium; stability; vaccine; uniform persistence

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[5] Centers for Disease Control and Prevention(CDC), Reported tuberculosis in the United States, Morbidity and Mortality Weekly Report, Recommendations and Reports, 50, 13 – 18 (2001).

[6] Colijn,C., Cohen,T.,Murray,M., Mathematical models of tuberculosis: accomplishments and future challenges, Proc. Natl. Acad. Sci. USA 103(11), 1-28(2006).

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[8] Dye,C., Williams,B.G., Criteria for the control of drug-resistant tuberculosis, Proc. Natl. Acad. Sci. USA 97(14), 8180-8185 (2000). [9] Fine,P., Lloyd,S., Stanford,J., Nkhosa,P., Kusanga,A., Chaguluka,S., Warndorff,D., Jenkins,P., Yates,M., Ponnighauss,J., Environmental Mycobacteria in Northern Malawi: implications for the epidemiology of tuberculosis and leprosy, Epidemiol Infect, 126(3), 379-387 (2001). [

10] Gao,D., Ruan,S., An SIS patch model with variable transmission coefficients, Mathematical Biosciences 232,, 110-115(2011).

Abstract: Model validity is the stability and reasonableness of the regression coefficients, the plausibility and usability of the regression function and ability to generalize inference drawn from the regression analysis. Model validation is an important step in the modeling process and helps in assessing the reliability of models before they can be used in decision making. This research work therefore seeks to study regression model validation process use in data splitting techniques. We review regression model validation by comparing predictive index accuracy of data splitting techniques. Various validation statistic such as the mean square error (MSE) and R2 were used as criteria for selecting the best model and the best selection procedure for each data set. The data splitting techniques provides the most precise estimate of R2 which reduce the risk over fitted models than in data splitting techniques.

Keywords: Data splitting technique, coefficient of determination, piecewise regression and validation.

[1] Agrawal R.C., Agrawal D.P.: Need and Ways of Collaboration between Institute and Industry, Proceedings of Technical Education in 21st Century (ICTE-21), Department of Manpower Planning, Government of Madhya Pradesh, Bhopal, 1998, 207-210.
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Abstract: Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. Strategies for controlling the spread of any infectious disease include a rapid reduction in both the infected populations (if a cure is available) as well as a rapid reduction in the susceptible class if a vaccine is available. For diseases like malaria where a vaccine has recently been developed, it therefore makes it possible to reduce the susceptible class through vaccination. In this study, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium which is locally asymptotically stable, if o R  1, where o R is a parameter which depends on the given model parameters. The analytical solution clearly shows that, with a proper combination of treatment and vaccination, malaria can be eradicated from the community.

Keywords: disease-free equilibrium points, Infectious disease, malaria, reproduction number, stability

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