iosr-Jm   Volume-8 ~ Issue-2

Abstract: An examination of breastfeeding and postpartum amenorrhea survey was carried out on 196 rural Mada women in central Nigeria. It was realized that, age, educational background and religious belief does not affect the duration of postpartum amenorrhea (PPA). The survival function of subjects decreases as the duration of breastfeeding without resuming menses increases, while, the hazard function increases as the duration of breastfeeding without return menses increases. Also, the duration of PPA varies from one woman to another. The study also shows that the association between breastfeeding and PPA does not necessarily indicate that duration of breastfeeding affect the duration of PPA, but could be that the two are control by some physiological effect of hormones.

Keywords: Amenorrhea, Breastfeeding, Fertility, Hazard, Postpartum, Survival.

[1] R.G. Potter, M.L. New, J.B. Wyon, and J.E Gordon, Application of Field Studies to Research on the Physiology of Human
Reproduction: Lactation and its Effects on Birth Interval in Eleven Punjab Villages, India. Journal of chronic diseases 18: 1965,
1125-1140.
[2] R.E Jones, A Hazard Model Analysis of Breastfeeding Variables and Maternal Age on Return to Menses Postpartum in Rural
Indonesian Women. Human Biology. 60: 1988, 853-871.
[3] United Nations (1991), Maternal and Child Care Development. Recommendation of Innocent Declaration on Breastfeeding
Promotion (1990). United Nations: New York.
[4] B. Figueiredo, C.C. Dias, R. Nunes-Coasta,, S. Brandao & C. Canario, Breastfeeding and Postpartum Amenorrhea Depression: State of the Art Review. Journal of Pediatric. 13: 2013, S0021-7557.

[5] A.P. Makinde, Socio-Cultural Factors Affecting Fertility in Sub-Sahara Africa. Workshop on Prospects for Fertility Decline in High Fertility Countries. Population Division, Department of Economic and Social Affair. United Nation Secretariat. New York, 2001.

[6] A.G. Pinto, Longitudinal Analysis of the Risk of Resumption of Menses in Guatemalan. CDE Working Paper Centre for Demography and Ecology, University of Wisconsin- Madison. NO. 94: 1995, 23.

[7] J.P. Habicht, J. Davanzo, W.P. Butz, and L. Meyers, The Contraceptive Role of Breastfeeding. Population Study. 39: 1985, 213.

[8] K.B.S. Bonyata, Breastfeeding and Fertility. International Board Certificated Lactation Consultant (IBCLC), 2011.

[9] A.S.McNeilly, Lactation Control of Reproduction. Reproduction Fertility Development.13, 2001,583.

[10] M.M. Rahman, The Effect of Breastfeeding on Amenorrhea Attrition Rates in Rural Bangladesh. Journal of Biosocial Science 20: 2009, 32-35. [11] M.M. Rahman,

Abstract: A volume flexible inventory model is developed. This model is developed for deteriorating item by assuming that the deterioration rate is depend on a parameter and time. The production rate is variable, production cost become a function of production rate, unit cost depending upon material cost, labour cost and tool cost. The demand rate is increasing exponentially shortages are allowed. Cost minimization technique used to find out optimal values for different inventory variables.

Key words: volume flexibility, deterioration

[1]. Alder, . G. L and R. Nanda, (1974) The effects of learning on optimal lot size determination- single product case, AIIE Trans. 6, 14-20.
[2]. Axster, S. and S. E. Elmaghraby, (1981) A note on EMQ under learning and forgetting,AIIE Trans. 13 ,86-90.

[3]. Baker, R. C. and Urban, T. L., (1988) A deterministic inventory system with an inventory-level-dependent demand rate, Opl.Res. Soc.39, 823-831.

[4]. Balkhi, Z. T. and Benkherouf, L. (1996 b)On the optimal replenishment schedule for an inventoy system with deteriorating items and time varying demand and production rates.Computers & Industrial Engineering, 30 ; 823-829.

[5]. Bhunia,A.K.and Maiti,M. (1997) Deterministic inventory models for variable production. Jour of Opi. Res. Soc., 48 : 221-224.

[6]. Bose, S., Goswami, A and Chaudhuri, K.S. (1995) An EOQ model for deteriorating items with linear time dependent demand rate and shortages unde inflation and time discounting.Jour Of Opl, Res. Soc., 46 : 507-728.

[7]. Chang, H. J. and Dye, C. Y. (1999)An EOQ model for deteriorating items with time varying demand and partial backlogging.Jour, of Opl. Res. Soc., 50 : 1176-1182.
[8]. Cheng, T. C. (1991) An economic order quantity model with demand dependent unit production cost and imperfect production processes, IIE Trans.23, 23-28.

[9]. Covert, R. P. and Philip, G. C. (1973) An EOQ model for items with weilbull distribution deterioration. A1TE Trans, 5 (4) : 323-329.

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Abstract: EEG (Electroencephalograph) is a technique for identifying neurological disorders. EEG signal is very weak and has very strong background noise; the average EEG signal is only about 50V , the biggest 100V. The presence of physiological artifacts such as eye blinks, eyeball movement, muscular movement and cardiac pulses in EEG recordings obscure the underlying processes and makes analysis problematic. EEG is used for diagnosis of Epilepsy. It takes doctors a lot of time for diagnosis. So we have developed a tool for detection of Epilepsy. In this paper we propose a technique of detecting epilepsy disorder using Wavelet transform and Wavelet packet transform through MATLAB. Then we compare with Wavelet transformation and Wavelet packet transformation. This paper also provides a technique of detecting epileptic disorder with great accuracy.

Keywords: EEG Signal, Epileptic Disorder, Wavelet, Wavelet Packet.

[1] Aboufadel, Edward, et al. Discovering Wavelets, New York: John Wiley & Sons, 1999.

[2] A. Akansu and Y. Liu. On signal decomposition techniques. Opt. Eng., 30:912-920, 1991.

[3] Mintaze Kerem Günel. Management of Epilepsy Research, Results and Treatment, Janeza Trdine 9, 51000 Rijeka, Croatia, 2011.

[4] A.H.Siddiqi, H.K odal Sevindir, Z.Aslan. Spectral Analysis of EEG Signal by using Wavelet and Harmonic Transforms, Birkhauser, 1999.

[5] CS. Burrus, R.A. Gopinath, and H. Guo. Introduction to Wavelets and Wavelet Packet Transforms.

[6] A.R Calderbank, 1. Daubechies, W. Sweldens, and B.-L. Yeo.). Wavelet transforms that map integers to integers. Appl. Contp.Hurin. Anal., 1998.

[7] Saeid Sanei and J.A. Chambers. EEG Signal Processing, Centre of Digital Signal Processing Cardiff University, UK, 2008.

[8] Charles K. Chui. An introduction to wavelets, Academic Press, 1999.

[9] O. Christensen and K.L. Christensen. Approximation Theory, From Taylor polynomials to wavelets, Birkhäuser, Boston, 2004.

[10] E.W. Cheney. Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Abstract: This paper consist inverse thermoelastic problem of heat conduction with the application of partially distributed heat supply and internal heat generation. In this paper unknown temperature, displacement stress functions are determined by using finite Marchi-Zgrablich transform and Fourier cosine transform. The results are obtained in the form of Bessel's function and infinite series. Keywords: Inverse thermoelastic problem, Stress function, Thermoelastic displacement

[1] Khobragade N.W. and Lamba N.K.: "Thermal Stresses of a Thin Annular Disc Due to Partially Distributed Heat Supply", Int. J Latest Trend Math Vol-1 No. 1 October 2011

[2] Marchi E and Zgrablich G: Heat conduction in Hollow cylinder with radiation Proc. Edingburgh Math. Soc. V1.14 Part 2(1964), pp159-164.

[3] N.M.Ozisik: Boundary value problem of heat conduction, International text book co. Scranton, Pennsylvania, (1968) pp. 481-492.

[4] Nowacki, W.: "The state of stress in a thick circular plate due to a temperature field", Bull. Acad. Polon. Sci. ser., Tech., Vol. IV, No.5, 1957.

[5] Roychoudhary S. K.: "A note on the quasi-static thermal stresses in a thin circular plate due to transient temperature applied along the circumferences of a circle over the upper face", Bull. Acad. Polon. Sci. ser., Tech. No. 1, pp.20-21, 1972.
[6] Wankhede P.C: "On the Quasi-static thermal stresses in a circular plate," Indian J.pur and Appl. Math. 13(11), pp. 1273-1277, 1982.

Abstract: The paper is devoted to the stability of a class of quasi-linear parabolic distributed parameter system (DPS). By using the linear matrix inequality (LMI) and Lyapunov functional methods, a sufficient condition is derived to ensure the uniformly stability of quasi-linear parabolic DPS. The numerical simulations are presented.

Keywords: Quasi-linear distributed parameter system, Lyapunov functional, linear matrix inequality

[1] A. Bensoussan, G.D. Prato, M.C. Delfour, S.K. Mitter, Representation and Control of Infinite Dimensional Systems, Vol. I (Birkh•auser, Boston, 1992).
[2] R.F. Curtain, H. Zwart, An Introduction to Infinite- Dimensional Linear System Theory (Springer, New York, 1995)
[3] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, (Springer, New York, 1983)
[4] Henriquez H. R., Stabilization of hereditary distribution parameter control systems, Systems & Control Letters 44, 2001, 35–43.
[5] Wang L. S., Xu D. Y., Asymptotic behavior of a class of reaction-diffusion equations with delays, Journal of Mathematical Analysis and Applications 281, 2003, 439–453.
[6] D. Hinrichsen, A.J. Pritchard, Robust stability of linear evolution operators on Banach spaces, SIAM J. Control Optim., 32,1994,1503-1541.
[7] Linshan Wang, Yangfan Wang, LMI-based Approach of Global Exponential Robust Stability for a Class of Uncertain Distributed Parameter Control Systems with Time-varying Delays, Journal of Vibration and Control,15(8) , 2009, 1173-1185.
[8] Luo, Y. P. and Deng, F. Q., LMI-based approach of robust control for uncertain distributed parameter control systems with time-delay, Control Theory & Applications,23 ,2006, 318–324.
[9] A. Pisano, E. Usai, Output-feedback control of an underwater vehicle prototype by higher-order sliding modes, Automatica,40,2004,1525-1531.
[10] C. C. Hua, X.-P. Guan, G.-R. Duan, Variable structure adaptive fuzzy control for a class of nonlinear time-delay systems, Fuzzy Sets and Systems,148, 2004,453-468.

Abstract: In this paper a new dogleg method for solving the trust region subproblem where convergence is based on constructing two paths is presented. The condition on the paths is incorporated into an algorithm to determine the optimum point of a smooth function. Numerical experiments with some classical problems showed that the new dogleg method is robust and efficient.

Keywords: Trust region, Trust region subproblem, Dogleg paths, Convergence

[1]. Y.H. Dai and D.C. Xu, A new family of trust region algorithm for unconstrained optimization, J. Computational. Mathematics 21, 2003, 221-228
[2]. E.M. Gertz, A quasi-Newton trust-region method. Mathematical Programming Ser. A, 100, 2004, 447 – 470
[3]. J.E. Dennis(JR), M. El-Alem and M.C. Maciel, A global convergence theory for general trust-region based algorithms for equality constrained optimization, SIAM Journal on Optimization, 7(1), 1997, 177 - 207.
[4]. Shultz G.A., Schnabel R.B. and R.H. Byrd, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence, SIAM J. Number. Analy. 22, 1985, 47 – 67.
[5]. Ph.L. Toint, Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space, IMA J. Numer. Analy., 8 , 1986, 231 – 252.
[6]. N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint, Sensitivity of trust-region algorithm to their parameters 4 OR 3 (2005) 227 – 241.
[7]. J.H. Fu and W.Y. Sun, Nonmonotone adaptive trust-region method for unconstrained optimization problems. Applied Mathematics and Computation 163, 2005, 489 – 504.
[8]. Y.H. Dai and D.C. Xu, A new family of trust region algorithm for unconstrained optimization, J. Computational. Mathematics 21, 2003, 221-228
[9]. N.I.M. Gould, D. Orban, and Ph.L. Toint, Numerical methods for large-scale nonlinear optimization, Acta Number, 14, 2005, 299 – 361.
[10]. J.E. Dennis (JR) and Schnabel R.B, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Inc., Englewood Cliffs, New Jersy, 1983.

Abstract: The concept of locally dually flat Finsler metrics are originated from information geometry. As we know, 𝛼,𝛽 -metrics defined by a Riemannian metric 𝛼 and 1-form 𝛽 form an important class of Finsler metrics. In this paper, we study and characterize Locally dually flat Matsumoto metric 𝐹=𝛼2/𝛼− 𝛽 with isotropic S-curvature which is not Riemannian.
Key words: Matsumoto metric, locally dually flat, locally minkowskian, isotropic S-curvature. AMS Subject Classification (2010): 53C60, 53B40

[1] S.I. Amari and H.Nagaoka , Methods of information geometry-Oxford University Press , AMS Translation of Math. Monographs, 191, (2000).

[2] S. Bacso, X. Cheng and Z. Shen, Curvature Properties of (𝛼,𝛽)--metrics, Adv. Stud. Pure Math. Soc., Japan (2007). [3] Cheng,X., Shen. Z and Zhou, On a class of Locally dually flat Finsler metrics. J.Math., 21(11), 1-13(2005). [4] X. Cheng and Tian.Y, Locally dually flat Finsler metrics with special curvature properties., J.Diff.Geom.Appl. 2011.

[5] X. Cheng and Z. Shen, A Class of Finsler metrics with isotropic S-curvature, Israel J. Math., 169(2009), 317-340.

[6] S.K.Narasimhamurthy, Latha Kumari G.N and C.S.Bagewadi, Projectively flat kropina metric with 𝐾=0. J. Applied Mathematical Sciences., 5(2011), 585-593.

[7] S.K.Narasimhamurthy and D.M.Vasantha, Projective change between Randers metric and Special (𝛼,𝛽)-metrics sJ. Informatics and Mathematical Sciences , (2012).

[8] Z. Shen, Riemann-Finsler geometry with applications to information geometry, J. Chin. Ann.Math., 27B(1)(2006), 73-94.

[9] Z. Shen, Volume Comparison and its applications in Riemann-Finsler Geometry, J. Adv. in Math.,128 (1997), 306-328.

[10] Xia,Q., On locally dually flat (𝛼,𝛽)-metrics J. Differential geometry and applications, 29(2), (2011),233-243.

Abstract: The present paper deals with the determination of displacement and thermal stresses in a thick 𝑀≠0 circular plate under steady temperature field. Arbitrary heat flux is applied at the upper surface of a thick 𝑀≠0 circular plate, whereas lower surface at zero temperature and the fixed circular edge is thermally insulated. Here we compute the effects of Michell function on the thickness of circular plate with internal heat generation. The governing heat conduction equation has been solved by the method of integral transform technique. The results are obtained in a series form in terms of Bessel's functions. The results for temperature change, displacement and stresses have been computed numerically and illustrated graphically.

Keywords: Thick plate 𝑀≠0 , thin plate 𝑀=0 , thermal stresses, steady state.

[1] W. Nowacki, The state of stresses in a thick circular disk due to temperature field, Bull. Acad. Polon. Sci., Ser. Sci. Techn., 5, 227, (1957) .

[2] Roy Choudhary S. K., A note of quasi static stress in a thin circular plate due to transient temperature applied along the circumference of a circle over the upper face, Bull Acad. Polon Sci, Ser, Scl, Tech., 20-21, (1972).

[3] J. N. Sharma, P. K. Sharma and R. L. Sharma, Behavior of thermoelastic thick plate under lateral loads, Journal of Thermal Stresses, 27, 171-191, (2004).
[4] V. S. Gogulwar and K. C. Deshmukh, Thermal stresses in a thin circular plate with heat sources, Journal of Indian Academy of Mathematics, 27, (1), (2005).

[5] V. S. Kulkarni and K. C. Deshmukh, Quasi-static thermal stresses in steady state thick circular plate, Journal of Brazilian Society of Mechanical Sciences and Engineering, XXX, (2) 175, (2008).

[6] K.C. Deshmukh, S. D. Warbhe and V.S. Kulkarni, Non-homogeneous steady state heat conduction problem in a thin circular plate and thermal stresses, Int. J. Thermophysics, 30, 1688-1696, (2009).

[7] K. C. Deshmukh, Y. I. Quazi, S. D. Warbhe and V. S Kulkarni, Thermal stresses induced by a point heat source in acircular plate by quasi static approach, Theoretical and Applied Mechanics Letters 1, 031007, ( 2011).

[8] Naotake Noda, Richard B Hetnarski and Yoshinobu Tanigawa , Thermal stresses 2 nd edn., 259-261, Taylor and Francis New York, (2003).

[9] M. N. Ozisik, Boundary value problems of heat conduction International Text Book Company, Scranton, Pennsylvania, (1968).

Abstract: In an automobile system repairs and replacements is a task which requires careful and detailed monitoring. To estimate the expected time to reach the breakdown point(Total failure state) and variance of a system due to the successive occurrence of small reparable break downs in (0,t] by using the applications of Order statistics, and assuming that the threshold follows gamma distribution. The effects of increasing in the length of inter arrival times between small reparable break downs on the values of mean and variance has been found. The analytical results are substantiated with numerical illustrations.

Key words: Breakdown point, Gamma distribution, Order statistics.

[1] Esary .J.D, Marshall, A.W and Prochan.F (1973)"shock Models and wear processes", Ann. of pro., Vol.12: pp-18-28

[2] Esary, J.D., Marshall, A.W. and Proschan F. (1973). Shock models and wear processes. "Ann. Probability", 1(4), 627-649.

[ 3] Ramanarayanan.R (1976), "cumulative damage process and alertness of the worker", IEEE transaction on reliability, R25 (4): pp-281-83.

[4] Abhijit Dasgupta and Michael percht (1991) "Material Failure Mechanisms and Damage", IEEE Transaction on Reliability, 40(5): pp-531-36.

[5] Gupta, R. D. and Kundu D. (1999). Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41, 173 - 188.

[6] Ganeshan.M.S, Chitra kala rani.T (2002) "stochastic model for the cumulative effects of industrial accidents". A journal on stochastic process and its Applications, vol.5 (1); pp-53-57

[7] Ji Hwan cha,JieMi(2011) "On a stochastic survival model for a system under randomly variable environment" Methodology and computing in applied probability vol 13 (3); pp 549-561.

Abstract: In the present analysis, we study the two-dimensional, steady, free convection and mass transfer flow past a continuously moving semi infinite vertical porous plate in a porous medium in the presence of thermal radiation, chemical reaction, Dufour and Soret effects. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are then solved numerically using finite difference method. The non-dimensional velocity, temperature and concentration profiles are displayed graphically for various interesting parameters entering into the problem and discussed in detail.

Key words: Free convection, vertical plate, porous medium, steady flow, Dufour and Soret effects, thermal radiation.

[1]. D.A. Nield, A. Bejan, Convection in Porous Media (third ed., Springer, New York, 2006). [2]. D.B. Ingham, I. Pop (Eds.), Transport Phenomena in Porous Media (Vol. III, Elsevier, Oxford, 2005).

[3]. K. Vafai (Ed.), Handbook of Porous Media (second ed., Taylor & Francis, New York, 2005).

[4]. P. Vadasz, Emerging Topics in Heat and Mass Transfer in Porous Media (Springer, NewYork, 2008).

[5]. Anghel M., Takhar H.S. and Pop I., Dufour and Soret effects on free convection boundary- layer over a vertical surface embedded in a porous medium, Studia Universitatis Babes-Bolyai Mathematica, XLV, 2000, 11-21.

[6]. Postelnicu A., Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects, Int. J. Heat Mass Transfer, 47, 2004, 1467-1472.

[7]. nuar Ishak, MHD Boundary layer flow due to an exponentially stretching sheet with radiation effect, Sains Malaysiana, 40(4), 2011, 391-395.

[8]. P. Bala Anki Reddy and N. Bhaskar Reddy , Thermal radiation effects on hydro-magnetic flow due to an exponentially stretching sheet, Int. J. Appl. Math. Comput., 3(4), 2011, 300-306.

[9]. V. Singh and Shweta Agarwal, Heat transfer in a second grade fluid over an exponentially stretching sheet through porous medium with thermal radiation and elastic deformation under the effect of magnetic field, Int. J. of Appl. Math and Mech., 8(4), 2012, 41-63.

[10]. Makinde, O.D., A. Ogulu, The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, 195(12), 2008, 1575-1584.

Abstract: In this paper, we present necessary and sufficient condition that a function 𝑓 𝑥 = 𝑎𝑛∞𝑛=1𝑐𝑜𝑠𝑛𝑥, where the coefficient 𝑎𝑛 (n = 1,2,3,……) are quasi-monotone to be of class 𝐿(𝜙,𝜓). Finally we discussed the applications of the Fourier series

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Abstract: In this paper we have generalised the theorem of Sulaiman which gives some unknown results and known result.s..

Keywords: Absolute summability, increasing sequence, Hölder inequality Minkowski inequality and infinite series.

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[2] Bari, N.K.; Best approximation and differential properties of two conjugate functions, T. Mat. Obs. 5, 1956.
[3] Bor, H.; A new application of quasi power-increasing sequences II, Bor fixed point theory and application, 2013.
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[6] Sulaiman, W.T.; On some generalization of absolute Cesaro summability factors, J. of classical Analysis Vol. 1, 2012.