iosr-Jm   Volume-13 ~ Issue-1 ~ Jan-Feb 2017

Abstract: The Transportation Problem is the special class of Linear Programming Problem. It arises when the situation in which a commodity is shipped from sources to destinations. The main object is to determine the amounts shipped from each sources to each destinations which minimize the total shipping cost while satisfying both supply criteria and demand requirements. In this paper, we are giving the idea about to finding the Initial Basic Feasible solution as well as the optimal solution or near to the optimal solution of a Transportation problem using the method known as............

Keywords: Transportation problem,Initial basic feasible solution, degeneratesolution, Optimality.

[1]. Bazaraa M.S., Jarvis J.J., Sherali H.D., 1990. Linear Programming and Network Flows, John Weily, Second Edition, New York.
[2]. Lai Y.J., Hwang C.L., 1992. Mathematical Programming Methods and Applications, Springer, Berlin.
[3]. Swarup K., Gupta P.K., Mohan M., 2006. Operations Research, Sultan Chand and Sons, New Delhi.
[4]. Charnes, Cooper (1954). The Stepping-Stone method for explain linear programming. Calculation in transportation problems. Management Science 1(1)49-69
[5]. Dantzing G.B (1963).Linear Programming and Extensions, New Jersey: Princeton University Press.

Abstract: The uniform distribution appears due to natural random events or to the application of methods for transforming samples from any other distribution to samples with uniformly distributed values in the interval (0,1). Thus, in order to test whether a samplecomes from a given distribution, one can test whether its transformed sample is distributed according to the uniform distribution or not. Several test procedures are developed to test the goodness of fit for uniformity. In this paper, we want to study the performance of eleven different tests for uniformity by considering different sample sizes as well as different alternatives. The results so obtained are displayed in various tables and graphs. Finally, conclusions are made on the basis of the results.

Keywords: Goodness of fit, level, Monte Carlo technique, power and uniform distribution.

[1]. Anderson, T.W. and Darling, D.A.(1954): A test of goodness-of-fit, Jour. Amer. Stat. Assoc., 49, 765-769.
[2]. Esteban, M.D., Marhuenda, Y., Morales, D. and Sanchez, A. (2006): New Goodness-of-Fit Tests based on Sample Ouantiles,
Operations Research Centre, Miguel Hernandez University of Elche, Elche, Spain, 631-642.
[3]. Kolmogorov, A.N. (1933): Sulla Determinazione Empirica Di una Legge di Distribuziane, Giornale Dell' Instituta Degli Attuari, 4,
83-91.
[4]. Kuiper, N.H. (1960): Tests concerning random points on a circle, Proc. Koninkl. Neder. Akad. Van. Wetenschappen, Series A, 63,
38-47.
[5]. Lemeshko, Yu.B., Blinov, Yu.P. and Lemeshko, S.B. (2016): Goodness of Fit Tests for Uniformity of Probability Distribution Law,
Optoelectronics, Instrumentation and Data Processing, 52 (2), 128-140.

Abstract: It is true that when infections occur there might not be recovery. In this case either infections will occur or will do not occur. When measures are put in place to reduce the rate of infection, there might be a tendency for this rate to have an effect on the growth of the infection. When this rate is not checked the whole population might get infected with time. In this work we use the birth-death process to describe a simple but classical infection processes, recovery processes, infection and recovery processes and finally, infection and recovery with immigration processes. For each of these processes explicit formulas are derived for their probability distributions and moment generating functions...........

Keywords: Generating Functions, Kolmogorov Differential Equations, Markov Property, Method of Characteristics

[1]. N. T. J. Bailey, The Elements of Stochastic Processes with Applications to the Natural Sciences., New York: John Wiley & Sons, 1990.
[2]. W. Feller, An Introduction to Probability Theory and Its Applications., vol. 1, 3, Ed., New York.: John Wiley & Sons, 1968.
[3]. S. M. Ross, A First Course in Probability, Upper Saddle River, N. J.: Pearson Prentice Hall, 2006.
[4]. R. V. Hogg and A. T. Craig, Introduction to Mathematical Statistics, 5, Ed., Upper Saddle River, N. J.: Prentice Hall, 1995.
[5]. H. Cram´er, Mathematical Methods of Statistics, Princeton, N. J.: Princeton Univ. Press, 1945..

Abstract: This research is aimed at developing the students' worksheet to determine the quality of validity and practicality aspects based on expert's assessment of materials, expert's design, media specialists, an individual assessment of students' testing, a small group assessment of students trial, and a field trials assessment of students.This study is adapted from the development of ADDIE model which consists of 5 stages: 1) Analysis, 2) design, 3) Development, 4) Implementation, and 5) evaluation. The results showed that the quality of students' worksheet of mathematics on materials of factorization in algebra-based on Contextual Teaching and Learning basically on the assessment of: 1)............

Keywords: Development, students' worksheet, CTL, ADDIE

[1]. Amri, Sofan. and Iif Khoiru Ahmadi. 2010. Construction Learning Development: Its Effect Mechanism and Practice Curriculum. Jakarta: Performance Library.
[2]. BSNP. 2006. Content Standard for Primary and Secondary Education Unit: Competence Standard and Basic Competence SMP / MTs. Jakarta: BSNP
[3]. MONE. 2008. Teaching Material Development Guide. Jakarta: Ministry of
[4]. Education. DRIs, J. and Tasari. 2011. Mathematical Volume 2 for SMP and MTs Class VIII. Jakarta: Ministry of Education.
[5]. Elaine B. Johnson. Contectual 2009. Teaching and Learning: Making TeachingLearning exciting and Meaningful. Bandung: Kaifa.

Abstract: For a radix of 10, I will show that there is no number with a multiplicative persistence ≥ 12 . Résumé : Je démontre qu'en base 10, il n'existe aucun nombre dont la persistance multiplicative est supérieure ou égale à 12.

Keywords: Persistance, persistance multiplicative

[1]. http://mathworld.wolfram.com/MultiplicativePersistence.html
[2]. Guy, Richard K. (2004). Unsolved problems in number theory (3rd ed.). Springer-Verlag. pp. 398–399. ISBN 978-0-387-20860-2.
Zbl 1058.11001.
[3]. Meimaris, Antonios (2015). On the additive persistence of a number in base p. Preprint.
[4]. https://en.wikipedia.org/wiki/Persistence_of_a_number
[5]. Jean-Paul Delahaye http://www.lifl.fr/~jdelahay/pls/2013/237.pdf

Abstract: Weibull distribution has many applications in engineering and plays an important role in reliability. Estimation of the location, scale and shape parameters of this distribution for both censored and non censored samples were considered by several authors. In this paper we compare Graphical oriented methods, "trial and error" approach, the approach of Jiang/Murthy and Maximum likelihood method developed by Bain & Engelhard for sample sets containing uncensored and censored sample. Importance of each method is discussed.

Keywords: Weibull distribution, Trial and error, Estimators and Maximum likelihood.

[1]. Weibull W, A statistical distribution functions with wide applicability, J. Appl. Mech. 18, 1951, 292-297.
[2]. Lawless, J.F. (1982): Statistical Models and Methods for Lifetime Data. Wiley, New York.
[3]. Rinne, H. (2009), The Weibull Distribution The Hand book. Chapman & Hall. New York.
[4]. Jiang, R. / Murthy, D.N.P., Comment on a general linear–regression analysis applied to the three–parameter Weibull distribution; IEEE Transactions on Reliability 46, 1997,389–393.
[5]. Bartkute. V and Sakalauskas. L, The method of three-parameter Weibull distribution estimation, Acta ET Commentationes Universitatis TArtuensis De Mathematica,12, 2008, 65-78.

Abstract: In the present paper, the two dimensional Fourier-Mellin Transform (2DFMT) in the range of [0,0,0,0] to [∞,∞ 1/a, 1/b]is defined by using two dimensional Fourier-Laplace transform (2DFLT). Then, we have obtained the solution of 2DFMT of some function in the above defined range.

Keywords: Fourier Transform, Mellin Transform, Two Dimensional Fourier-Mellin Transform (2DFMT), Integral Transform.

[1]. J. Zhu: Applications of Fourier Transform to Smile Modeling Theory and Implementation Series: Springer Finance, 2nd ed. 2010, XV, 330 p. 7 illus.
[2]. Shubing Wang: Applications of Fourier Transform to Imaging Analysis, shubing@stat.wisc.edu, May 23, 2007.
[3]. Elif Sertel: Identification of Earthquake Induced Damage Areas Using Fourier Transform and SPOT HRVIR Pan Images, Sensors 2009, 9, 1471-1484; doi:10.3390/s90301471.
[4]. Daniel Dziembowski, "On Mellin transform application to solution of fractional differential equations", Scientific Research of the Institute of Mathematics and Computer Science.
[5]. S. S. Appadoo, A. Thavaneswaran and S.Mandal, "Mellin's transform and application to some time series models", Hindawi Publishing Corporation, ISRN Applied Mathematics Volume 2014, Article ID 976023, 12 pages.

Abstract: In this paper we define the k-Fibonacci Hankel matrices and then we study the different norms of
these matrices. Next we find the relation between the Euclidean norm, the column norm and the spectral norm
of these special matrices. Finally, we study the 4x4 skew symmetric k-Fibonacci matrices and find an interesting
formula for a sum of the k-Fibonacci numbers.

Keywords: k-Fibonacci and k-Lucas numbers; Skew symmetric and Hankel matrices; Matrix Norms.

[1]. S. Falcon, On the sequences of products of two k-Fibonacci numbers, American Review of Mathematics and Statistics, Vol 2(1)
(2014), 111 – 120.
[2]. S. Falcon, On the k-Lucas numbers, Int. J. Contemp. Math. Sciences, Vol. 6(21) (2011), 1039 – 1050.
[3]. S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos, Solit. &Fract. 32(5) (2007) 1615 – 24.
[4]. S. Falcon, A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solit. &Fract. 33(1) (2007) 38 – 49.
[5]. Simon Foucart, http://www.math.drexel.edu/~foucart/TeachingFiles/F12/M504Lect6.pdf

Abstract: In this paper a generalized class of regression type estimators using the auxiliary information on population mean and population variance is proposed under stratified random sampling. In order to improve the performance of the proposed class of estimator, the Jack-knifed versions are also proposed. A comparative study of the proposed estimator is made with that of separate ratio estimator, separate product estimator, separate linear regression estimator and the usual stratified sample mean. It is shown that the estimators through proposed allocation always give more efficient estimators in the sense of having smaller mean square error than those obtained through Neyman Allocation.

Keywords: Auxiliary information, ratio type Estimator, Bias, Mean Square Error.

[1]. Jack – knife technique of Gray and Schucany and Sukhatme et al.
[2]. W.G.Cochran, Sampling Techniques, third ed. John Wiley &sons, New York, 1977.
[3]. R.S.Jessen, Statistical Survey Techniques, John Wiley &sons, New York, 1978.
[4]. D.Singh, F.S.Chaudhary, Theory and Analysis of sample Survey Design, New Age Publication, New Delhi, India 1986.
[5]. S.K.Srivastava, An estimator using auxiliary information in sample surveys, Calcutta Statistical Association Bulletin 16(1967) 121-
132.

Abstract: In the previous studies a hypothesis was developed from the results by using trivariate Weibull model that the increase in leptin concentrations during the second half of the menstrual cycle may be related to changes in the steroidal milieu during the pre ovulatory period and the luteal phase. The present study was undertaken to test this hypothesis further by examining the effect of treatment with oestradiol and progesterone on leptine concentrations in normal pre menopausal women. The trivariate Weibull model is used for finding survival functions and log-likelihood functions for corresponding values of oestradiol, LH and Leptin for both untreated and treated with oestradiol and oestradiol plus progesterone respectively

Keywords: Trivariate Weibull, LH, Leptin, oestradiol and progesterone

[1]. Constantine, G.M., Savits, T.H., (1996). A multivariate Faa Di Bruno Formula with Applications. American Mathematical Society, Vol 358, pp 503-520.
[2]. Crowder, M., (1989). A Multivariate Distribuition with Weibull Connections. Journal of the Royal Statistical Society, Series B, Vol 51, pp 3-107.
[3]. Frees, E. W., Valdez, E. A., (1998).Understanding Relationships using Copulas. North American Actuarial Journal Vol 2, pp 1-25.
[4]. Li, C.L., (1997). A Model for Informative Censoring. Ph.D. Dissertation: The University Alabama at Birmingham.
[5]. L u, J-C., Bhattacharya, G., (1990). Some New Constructionsof Bivariate Weibull Models. Annals of the Institute of Statistical Mathematics, Vol 42, pp 543-559.

Abstract: Image classification is very significant for many vision of computer and it has acquired significant solicitude from industry and research over last years. We, explore an algorithm via the approximation of Fuzzy -Rough- K-means (FRKM), to bring to light data reliance, data decreasing, estimated of the classification (partition) of the set, and induction of rule from databases of the image. Rough theory provide a successful approach of carrying on precariousness and furthermore applied for image classification feature similarity dimensionality reduction and style categorization............

Keywords: Rough theory; fuzzy theory; K-means; Image classifications; Uncertain Images; RGB images

[1]. ANTONIE, Maria-Luiza; ZAIANE, Osmar R.; COMAN, Alexandru.Application of data mining techniques for medical image classification.In: Proceedings of the Second International Conference on Multimedia Data Mining.Springer-Verlag, 2001. P. 94-101.
[2]. ZHANG, Xiao-Ping; DESAI, Mita D. Wavelet based automatic thresholding for image segmentation. In: Image Processing, 1997. Proceedings., International Conference on. IEEE, 1997. p. 224-227.
[3]. BOTTIGLI, Ubaldo; GOLOSIO, Bruno. Feature extraction from mammographic images using fast marching methods. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2002, 487.1: 209-215.
[4]. SHARMA, Mona; SINGH, Sameer. Evaluation of texture methods for image analysis. In: Intelligent Information Systems Conference, The Seventh Australian and New Zealand 2001. IEEE, 2001. P. 117-121.
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