iosr-Jm   Volume-11 ~ Issue-1 ~ Jan-Feb 2015

Abstract: One of the classical problems in mathematics is the Discrete Logarithm Problem (DLP).The difficulty and complexity for solving DLP is used in most of the cryptosystems. In this paper we design a public key system based on the ring of polynomials over the field 𝐹𝑝 is developed. The security of the system is based on the difficulty of finding discrete logarithms over the function field 𝐹𝑝𝑛 with suitable prime p and sufficiently large n. The presented system has all features of ordinary public key cryptosystem. Keywords: Discrete logarithm problem, Function Field, Polynomials over finite fields, Primitive polynomial, Public key cryptosystem..

[1]. Lilly P.L, Saju M.I., A method of designing a public-key cryptosystem based on discrete logarithm problem, IRJPA-4(11), 2014, 628-630.
[2]. Diffie W., Helman M.E., New Directions in Cryptography, IEEE Transactions on information theory, Vol. IT-22, Nov.1976, 644-654.
[3]. Digital Signature Standard, Federal Information Processing Standards Publication 186, May 1994.
[4]. Odlyzko A., Discrete logarithms: The past and the Future; Designs, Codes and Cryptography, (2000), 129-145.
[5]. McCurley K., The discrete logarithm problem, Proceedings of Symposia in Applies Mathematica, Vol.42, 1990, 49-74.

Abstract: In this work, we study a two grid finite element methods for solving coupled partial differential equations of Time-Harmonic Maxwell's equations. A brief survey of finite element methods for Maxwell's equation and related fundamentals, such as Sobolev spaces, elliptic regularity results, finite element methods for Second order problems and its algorithms were reviewed. The method is based on discretization using continuous 1 H -conforming elements for decoupling systems of partial differential equations. With this method, the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid.

Keywords: Time-Harmonic Maxwell's equation, finite element methods, two-grid scheme, fine and coarser grids.

1]. J. Xu and A. Zhou, Local and parallel finite element algorithms based on two-grid discretizations, Math. Comp. 69 (2000), 881-909.
[2]. M. Marion and J. Xu, Error estimates on a new nonlinear Galerkin method based on two-grid finite elements, SIAM J. Numer. Anal.,
32, 4(1995), 1170-1184.
[3]. J. Xu, A novel two-grid method for semilinear equations, SIAM J. Sci. Comput., 15, 1(1994), 231-237.
[4]. P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterderm, 1978.
[5]. R. P. Fedorenko, A relaxation method for elliptic difference equations, USSR Computational Math Phys...1(5) 1092-1096,(1961).
[6]. M. Marion and J. Xu, Error estimates on a new nonlinear Galerkin method based on two grid finite elements, SIAM J. Numer. Anal.,
32,4(1995), 1170-1184.

Abstract: Bipolar affective disorder is a mental illness classified as mood disorder. Many people with bipolar disorder still go about their normal day-to-day schedule of duties. This is quite dangerous for the civil society. As the severity increases, affected persons become more erratic, more violent and often make poor judgments.In this paper, factors other than the traditional, genetic, environmental and neurochemical have been investigated among one hundred and nine teaching and non-teaching staff of a university. These are sex, age, occupation and body mass index (BMI). Using the Modified Logistic Ridge estimator, sex, age and body mass index have been found to contribute significantly to bipolar disorder. Both the standard error test and the odd ratios were used to determine the significance or otherwise of the factors. Men are more predisposed, older people (≥40𝑦𝑒𝑎𝑟𝑠) are more predisposed and Body mass index is positively correlated to bipolar disorder. The model can be used to determine the probability of involvement in each of the eight sub populations. Intervention should focus on men, people aged 40 and above and people with a higher body mass index.

Keywords: Bipolar Disorder, Collinearity,Logistic Estimator,Logistic Ridge Estimator, Modified Logistic Ridge Estimator, Odd ratios.

1]. American Psychiatric Association (2001). Diagnostic and Statistical Manual of Mental Disorders (4thed.).Washington, DC: TeRevision (DSM-IV-TR).
[2]. Benazzi, F. (2004).Inter-episode mood liability in mood disorders: residual symptom or natural course of illness? Psychiatry ClinNeurosci.58(5):480-6.
[3]. Brook, A.R et al (2006). Incurring Greater Health care Costs; Risk Stratification of Employees with Bipolar Disorder.Journal of Clinical Psychiatry, Vol.8 (1).
[4]. Der, G.&Everitt, S. (2009).A Handbook of Analysis usingSAS (3rd edition).Boca Raton: CRC Press,Champion and Hall.
[5]. Gnust, R.F (1984).Toward a Balanced Assessment of Collinearity Diagnostics. American Statistician.Vol.38, p. 79-82.
[6]. Huxley NA, Parikh SV, Baldessarini RJ.(2000) Effectiveness of psychosocial treatments in bipolar disorder: state of the evidence. Harv Rev sychiatry.8(3):126–140.

Abstract: In the present paper we propose to find solutions to transportation problems by non linear programming methods of Operations Research. No civilization can grow without development of better transportation facilities. Actually time and cost play an important role in its proper development. It may be realized that gradually the means of transportation improved and with the passage of time several methods were developed to minimize transportation cost and time. Here below, we have chosen to minimize the transportation cost.

Keywords: Innovations ,Transportation, Linear Programming, Non-linear Programming.

[1]. Nonlinear and Dynamic Programming;S.D.Sharma, Kedar Nath Ram Nath & company, Meerut, India.
[2]. An Algorithm for Quadratic Programming; M.Frank,P.Wolfe, Naval Research Logistics Quaterly, No.3,1956.p.95-110.
[3]. The Simplex method for Quadratic Programming;P.Wolfe, Econometrica, No.27,1959,p.382-398.
[4]. Non-linear Programming ,Theory and 'Algorithms ,Mokhtar S. Bazaraa ,Sherali,C.M. Shetty, Wiley Interscience,A John Wiley & Sons,Inc.,Publicatrion.

Abstract: In this paper we want to highlight the properties of digital root and some result based on digital root. There are many interesting properties of digital root. We can also study nature of factors of a given number based on Vedic square and then we can implement this concept for an algorithm to find out a number is prime or not.
Keywords: Digital Roots, factors, Integral roots, partition, Vedic square, Primality test.

[1]. A. Gray, "Digital Roots and Reciprocals of Primes," The Mathematical Gazette, vol. vol. 84, no. no. 499, p. p. 86, Mar 2000.
[2]. T. Ghannam, "The Mystery of Numbers: Revealed Through Their Digital Root," p. p. 68–73R, 2012.

Abstract: The aim of this paper is to study the existence and uniqueness of solution of abstract Volterra integral equations of the second kind in complete locally convex topological space. An example illustrating the obtained result is given.
Keywords: Abstract Volterra integral equations, locally integrable solution

[1]. Abdou M.A., Badr A.A., El-Kojok M.M., On the solution of a mixed nonlinear integral equation, Appl. Math. Comput. 217 (2011) 5466–5475.
[2]. Agarwal R.P., Banas J., Dhage B.C., Sarkate S.D., Attractivity results for a nonlinear functional integral equation, Georgian Math. J. 18 (2011) 1–19.
[3]. Agarwal R.P., O'Regan D., Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001.
[4]. Arfken G., H. Weber, Mathematical Methods for Physicists, Harcourt/Academic Press, 2000.
[5]. Bainov D.D., Myskis A.D., Zahariev A.I, On an abstract analog of the Belmann-Gronwall inequality, Publication of the Research Institute for Mathematical science, Kyoto University, vol. 20, no. 5, 1984

Abstract: The notion of GQN-Maps is introduced and some results regarding these maps are obtained.

Keywords: Quasi-nonexpansive maps, GQN-maps, convex set, fixed point set, continuous maps, retract, retraction mapping, locally weakly compact, conditional fixed point property. AMS subject classification codes: 47H10, 54H25

[1]. Browder, F.E. andPetryshyn, W.V.: The Solutions Of Iterations Of Nonlinear Functional Analysis Of Banach Spaces, Bull. Amer. Math. Soc. 72 (1966), 571 – 575.
[2]. Bruck R. E.: Nonexpansive Retracts of Banachspaces, Bull. Amer. Math. Soc. 76 (1970), 384 – 386.
[3]. Bruck, R. E.: Properties of Fixed Points of Nonexpansive Mappings InBanach Spaces, Trans. Amer. Math. Soc., Vol. 179 (1973), 251 – 262.
[4]. Bruck,R.E.: A Common Fixed Point Theorem For A Commuting Family of Nonexpansivemaps, Pac. J. Math., Vol. 53, No.1, 1974, 59 – 71.
[5]. Chidume, C.E.: Quasi-Nonexpansive Mappings AndUniform Asymptotic Regularity, Kobe J. Math. 3 (1986), No.1,29 – 35.

Abstract:This paper seeks numerical solutions to a stiff initial value problem using a modified extended backward differentiation formula. Some implicit schemes were developed based on the linear multi-step method. Stiff initial value problems are solved using the various stages of the derived modified extended backward differentiation formula, the result obtained at different stages are compared with Euler implicit method and Simpson's implicit method. The results obtained are considered in determining which of the methods is more accurate and efficient in providing solutions to stiff initial value problems when compared with the exact solution.
Keywords: Stiff initial value problems, Modified extended backward differentiation formula, Euler implicit method, Simpson's implicit method and Linear multistep method.

[1]. T.J. Abdulla, J.R. Cash, An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems.
Computers and Mathematics with Application 42(2001) 121-129
[2]. J. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, New York, 1987.
[3]. J. Butcher, J.R. Cash, M.T. Diamantakis, DESI methods for stiff initial value problems, ACM Trans. Math. Software 22 (1996)
401-422.
[4]. J.R. Cash, Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs
and DAEs, Journal of Computational and Applied Mathematics 125 (2000) 117-130.
[5]. J.R. Cash, S. Considine, An MEBDF code for stiff initial value problems, ACM Trans. Math. Software 18 (1992) 142-160.
[6]. J.R. Cash, An extension of Olver's method for the numerical solution of linear recurrence relations, Math. Comp. 32 (1978) 497-
510.

Abstract:In this paper we proposed bootstrap algorithm for the estimation of parameters of the non-linear regression analysis by cooperating the Gauss- Newton method. We used bootstrapping to provide estimates of exponential regression coefficients. The computational difficulties that would have encountered in using the proposed method have been resolved by developing a computer program in R which was used to implement the algorithm. From the result obtained the bootstrap algorithm yielded a better reduced error sum of squares SS than the analytical method. With these results, we have a greater confidence in the result obtained.
Keywords: bootstrap, algorithm, exponential, regression, parameters, non-linear, Gauss-Newton.

[1]. Casella, G., 2003, Introduction to the Silver Anniversary of the Bootstrap, Statistical Science, Vol.18, No.2, pp. 133-134.
[2]. Efron, B., (1979). Bootstrap Methods: Another look at the Jackknife. The Annuals of Statistics, 7, 1-26.
[3]. Efron, B., 2003, Second Thought on Bootstrapping, Statistical Science, Vol. 18, No. 2, 135-140.
[4]. Efron, B. and Tibshirani, R.J., 1998, An Introduction to the Bootstrap, Library of Congress Cataloging in Publication Data, CRC
Press, Boca Raton, Florida, 60-82.
[5]. Freedman, . A., 1981, Bootstrapping Regression Models, Annals of Statistical Statistics, Vol. 9, 2, 158-167.

Abstract: The public transportation industry is facing significant problems in all size cities in India. This study is concerned of assessment of public transport demand for Gwalior Division and identifies the major factors for poor ridership with estimation of the probable shift of personal vehicle users to public transport due to the increase in its level of service also identifies ways to account for qualitative factors in the public transport project evaluation by adjusting travel time values to reflect comfort and convenience. For this Data Envelopment Analysis is used, it is a non-parametric method of efficiency measurement.

[1]. Report of the Sub-Group On State Road Transport Undertakings formed under the Working Group on Road Transport Constituted by Planning Commission. Twelfth Five Year Plan (2012 – 2017).
[2]. Mitran G.,Ilie S.: 'Air pollution from road traffic by transport modeling.'Ph.D Scientific Report No1University of Pitesti.Romania (2011)
[3]. Review of the Performance of State Road Transport Undertakings(2010-11)
[4]. Mintesnot Gebeyehu and Shin-ei :Diagnostic Evaluation of Public Transportation Mode choice in Addis Ababa(Journal of Urban Transportation) Takano Hokkaido University, Sapporo, Japan. (2010)
[5]. Ashim Ratna Bajracharya: The Impact of model shift on the transport ecological foot print; A case study of the proposed BRT in Ahmedabad.(2008)

Abstract: Bangladesh is conventionally a radiant cultural country. Wedding ceremony is playing a vital role to its cultural norm and heritage. But the marriage issue creates depression among the young men and women. This article depicts a mathematical model with simulated result to visualize the trend and nature of the depression of Bangladeshi young women, who are in peer pressure to get married. There are some significant causes for creating depression, such as economic solvency, education, dynasty, beauty, media role (Print, electronic) etc. The model has been developed on the basis of media role (Print, electronic) to the beauty of the women, which affect the depression level of a woman who is about to be married. To recognize which women are more affected by these issues, the women are classified into two groups as extremely susceptible group and low susceptible group. These groups are defined by four non-linear differential equations on the basis of the impact of their corresponding treatment and depression. And the result shows that the role of media (Print, electronic) on beautification of the women has very negligible impact to their depression to get married.

Keywords: Depression, pressure, Equilibrium, Bifurcation

[1]. Ariela Frieder, MD; Anne L. Dunlop, MD, MPH; Larry Culpepper, MD, MPH; Peter S. Bernstein, MD, MPH. The clinical content of preconception care: women with psychiatric conditions: American Journal of Obstetrics & Gynecology Supplement to DECEMBER 2008, doi: 10.1016/j.ajog.2008.09.001.
Books:
[2]. S. Nolen-Hoeksema, Abnormal Psychology, Second Edition. (New York, USA: McGraw-Hill, 2001.)
Journal Papers:
[3]. S. E. Agras, W.S. and D. Spangler, "Exposure to media-portrayed images adversely affects vulnerable girls: a longitudinal experiment,"
Journal of Social and Clinical Psychology, vol. 20, no. 3,pp. 324–340, 2001.
[4]. W. J. Van den Driessche, P., "Reproduction numbers and sub threshold endemic equilibria for compartmental models of disease
transmission," Mathematical BioSciences, vol. 180, pp. 29–48,2002.

Abstract:This study is aimed at studying the effects of small perturbations in the coriolis () and the centrifugal (΄) forces, the triaxiality (1, 2) of the bigger primary and the radiation (q) pressure force of the smaller primary on the stability of libration point in the Restricted Three-Body Problem(RTBP) in particular to study the effect of perturbations in the coriolis and the centrifugal forces on the of the libration points in the restricted three body problem when the bigger primary is a triaxial rigid body and the smaller primary a source of radiation. The equations of motion of the restricted problem under influence of the perturbations in the coriolis and the centrifugal forces, triaxiality and radiation were established. These equations of motion are found to be affected by the aforesaid parameters. They generalize the classical equations of motion of restricted problem and those obtained by others. Five libration points were obtained three collinear points (𝐿1, 𝐿2, 𝐿3) and two triangular points (𝐿4, 𝐿5). The libration points were found to be affected by the small perturbation for the range 0 ≤  < c. The critical mass value c is affected by all the aforesaid parameters in the coriolis and centrifugal forces, the triaxial nature of the bigger primary and the radiation pressure force of the smaller primary. This generalizes the equation of orbits of the classical restricted three body problem and those obtained by others.
Keywords: Classical mechanics, Motion, Perturbations, Coriolis, Triaxial, Triangular,Syndoic.

[1]. AbdulRaheem, A. and Singh, J. (2006). Combined effects of Perturbations Radiation and Oblations on the Stability of
Equilibrium Point in the Restricted Three-Body problem. Ast. J, 131: 1880-1885.
[2]. Bhatnagar, K.B and Hallan, P.P. (1979). Effect of Perturbation Potential on the Stability of Equilibrium Points in the Restricted
Problem Celestial Mechanics and Dynamics Astronomy 20,95-103
[3]. Chernikov, V.A. (1970). The photo-gravitational Restricted Three-Body Problem, Astr. 2, 47:217-223 (Russian) Translated as
Soviet Astr. A J. 14(1): 176-181
[4]. Choudhry, R.K and Kumar,V. (1986). Existence of Libration Points in the Generalised Photo-gravitational Restricted Problem of
Three Bodies. Bulletin of Astronomical Society, India. 14:79-90.
[5]. Duboshin, G.N. (1968) Celestial Mechanics Nauka, Moscow.
[6]. Finlay, F. (1958).Celential Mechaics Pergamon Press. California

Abstract:The embedding and NP-complete problems in the context of various graph labeling schemes were remained in the focus of many researchers. Here we have explored embedding and NP-Complete problems for some variants of cordial labeling.
Keywords: Graph labeling, equitable labeling, embedding of graphs, NP-complete problems. Mathematics Subject Classification (2010): 05C78, 05C60.

[1] J. A. Gallian, A Dynamic Survey of Graph Labeling, The electronic journal of combinatorics, 17, 2014, #DS6.
[2] I. Cahit, Cordial Graphs: A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23, 1987, 201 - 207.
[3] S. K. Vaidya and C. M. Barasara, Edge Product Cordial Labeling of Graphs, Journal of Mathematical and Computational Science,
2(5), 2012, 1436 - 1450.
[4] G. Chartrand and L. Lesniak, Graphs and Digraphs 4/e (Chapman & Hall/CRC Press, 2005).
[5] S. K. Vaidya and C. M. Barasara, Total edge product cordial labeling of graphs, Malaya Journal of Matematik, 3(1), 2013, 55 - 63.
[6] R. Ponraj, S. Sathish Narayanan and R. Kala, Difference Cordial Labeling of Graphs, Global Journal of Mathematical Sciences:
Theory and Practical, 5(3), 2013, 185 - 196.

Abstract:In last years, the rain in Albaha is differ from year to year, this leads to the standard that the rain falls in this city. In this study we try to find a mathematical model represent this observations. Then we try to contact the plain of this study; the problem, goals, the methodology in analysis also the concepts that related to Markov-Chain that applied in the study. Markov-Chain helps for obtaining the model that represent rainy, dry days for the years (1431-1434) for AlBaha (Rain falls). Lastly we test the model by obtaining the matrix for rainy and dry days. by comparing the case in each day and the previous by four days.
Keywords: Markov Chains - Rainy Days - Dry Days - Stochastic Process- Rain falls.

[1]. Baigorria G, Jones J (2010). GiST, A stochastic model for generating spatially and temporally correlated daily rainfall data. J Clim, 23, 5990–6008.
[2]. Baily T. (1967) "The Elam ails of stochastic process with application to the national sciences" John Wiley and Sons.

[3]. Cappe O (2005). Inference in hidden Markov models. Springer, New York

[4]. Danuso F. (2002). Climak: a stochastic model for weather data generation. Italy, J. Agron. 6(1):57-71.

[5]. Deni, S. M. and Jemain, A. A. (2009). Fitting the distribution of dry and wet spells with alternative probability models. Met. and Atmosph. Physics ,104, 13-27.
[6]. Edword P.C. Kao (1997) " An Introduction to stochastic processes".