iosr-Jm   Volume-12 ~ Issue-6 ~ Nov-Dec 2016

Abstract: In the background of pointfree topology, if L is a locale, the Vietoris locale V (L) corresponding to L has been constructed using the spectrum of L. If L is a spatial, subfit locale, then V (L) is also a subfit locale. Also if L is second countable locale, then V(L) is second countable and hence seperable.

Keywords: Vietoris locale, second countable, Subfit, Seperable.

[1]. Jorge Picardo, Ales Pultr ,Frames and Locales –Topology without points(springer Basel AG 2012)
[2]. Peter.T.Johnstone, Stone Spaces(Cambridge University Press,1982)
[3]. Steven Vickers, Topology via logic(Cambridge Tracts in Theoretical Computer Science, Cambridge University Press1989)
Journal Papers
[4]. B.Banaschewski,C.J.Mulvey,Stone cech Compacti_cation of locales-II,Journal of pure and applied Algebra 33(1984) 107-122,North Holland
[5]. J.Isbell,First steps in descriptive theory of locales,Trans.Am.Math.Soc.327(1991)353371..

Abstract: It is believed that pi (π) is a transcendental number. In author's opinion, it is not the fact. The paper aims at showing that pi (π) is an algebraic number with exact value 17-8√3. The derivation of this value is supported by several geometrical constructions, arithmetic calculations and use of some simple algebraic formulae.

[1]. Exact area of equilateral triangle formula = (√3 † 4) × side², Area of circumscribed hexagon = (2√3) r², Area of circumscribed dodecagon = 12(2 - √3) r²
[2]. Basic Algebra & Geometry concept, History of pi (π) Complete thesis of my research titled as ""Exact value of pi ‟‟ has being published in following journals:
[3]. IOSR(international organization scientific research) journal of mathematics in May-June 2012.
[4]. IJERA (international journal of Engineering research and applications) in July-August 2013.

Abstract: The design of a modern movie theatre is very complicated and it should be done very methodically keeping in mind the innumerable number of details that it should be attended to. A certain degree of price discrimination can be seen at movie theatres. There is a different and varied price not only for when but also for where one sits in a movie theatre. This is to say that one is charged more for the same movie and the same experience based on from where he or she sits. As by norm, the seats in front are charged lesser than the seats at the back. The comfort of viewing, i.e. physical comfort is the best at the back, and worst in the front, but the last few 'expensive' rows may not be the most 'ideal' place to watch the movie from. In this paper includes the design of an ideal movie theatre such that one can have the best possible angle of vision using STAADD PRO ANALYSIS and LSM

Keywords: Movie theatre, Beams, Purlins , Footing, STAADD PRO ANALYSIS , LSM.

[1]. NATIONAL BUILDING CODE
[2]. IS 800-1984, code of practise for general construction in steel.
[3]. IS 456-2000, code of practise for plain & reinforced concrete.
[4]. "Theory of structures" by S.Ramamrutham.
[5]. "Strength of materials & Theory of structures" by B C Punmia.

Abstract: The existence and uniqueness solution of a nonlinear partial differential equation (NPDE)of fractional order are discussed and proved in a Banach space ℋ due to Picard's method depending on the properties we expect a solution to possess. Moreover, some properties concerning the stability of solutions are obtained.A systemof nonlinear Volterra integral equations of the second kind (SNVIEs) is obtained. The modified Toeplitz matrix method (MTMM) is used, as a numerical method, to obtain a nonlinear systemof algebraic equations (NAS). Also, many important theorems related to the existence and uniqueness solution of the algebraic system are derived. Finally,numerical results are obtained and the error is calculated.

Keywords: nonlinear partial differential equation of fractional order,semigroup, system of nonlinear Volterra
integral equations of the second kind,modified Toeplitz matrix method, nonlinear algebraic system

[1]. S.Chandrasekhar and G.Münch , The theory of fluctuation in brightness of the Milky-Way, Astrophy.J.125, 94-123.
[2]. M.C.Mackey and Rudnicki, Global stability in a delayed partial differential equation describing cellular replication,
J.Math.Biol,33(1994), 89-109.
[3]. J.A.J.Metz and O.Diekmann, The " Dynamic of Physiologically Structured Populations" Springer lecture Notes in Biomathematics,
Vol.68, Springer-Verlag, New York,1986.
[4]. M.M.EL-Borai, Some probability densities and fundamental solutions of fractional evolution equation, Chaos, Solitons & Fractals
14(2002), 433-440 .
[5]. M.M.El-Borai, Semigroups and some nonlinear fractional differential equations, J.Appl.Math. Comput. 149 (2004), 823-831 ..

Abstract: A numerical algorithm from Maximum Likelihood (ML) and Improved Analytical (IA) was developed. This was used to estimate the parameters of the two-parameter Weibull distribution, namely scale and shape parameters. Since the Maximum Likelihood Estimators of the Weibull distribution do not have closed form solutions, the profile likelihood of the two-parameter Weibull distribution was considered for the purpose.Real life data were used in the study and data were also simulated for the distribution with sample sizes (10, 100, 1000 and 10000) and numerical approach was adopted to obtained the estimate of the distribution. The standard errors were computed and a 5% wald-confidence interval was constructed for the estimates of the distribution. The results of this study show that the profile likelihood constructed by the combination of MLE and Newton Raphson's method provides an efficient means of estimating parameters from intractable probability distribution model (two-parameter Weibull distribution) in both simulation and real life data.

Keywords: Two-parameter Weibull Model, Profile Likelihood, Maximum Likelihood Estimation,Newton Raphson Method

[1] Atkinson, A. C.,Pericchi, L. R.,& Smith, R. L. (1991). Grouped likelihood for the shifted power transformation. Journal of the Royal Statistical Society: Series B, 53: 473- 482.

[2] Beaumont, M. A., Zhang, W., & Balding, D. J.(2002). Approximate Bayesian computation in population genetics.Genetics, 2 (162), 2025-2035.

[3] Cheng, R. C. H. & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B, 45: 394-403.

[4] Cheng, R. C. H. & Traylor, L. (1995). Non-regular maximum likelihood problems. Journal of the Royal Statistical Society: Series B, 57: 3-44.

[5] Cox, D. R. & Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities., Biometrika, 2( 91), 729-737.

Abstract: We have tested the convergence of a newly definedpolynomialon the interval [0,1+𝑟𝑛 ] for Lebesgue integral in𝐿1norm as �)𝑛+𝑟−1andsothe results of Bernstein has been extended in the given inte

rval .

Keywords: Bernstein Polynomials, Convergence, Bernstein typePolynomial,𝐿1 norm,Lebesgueintegrable function

[1]. A. Habib, "On the degree of approximation of functions by certain new Bernstein typePolynomials," Indian J. pure Math., vol. 7, pp. 882-888, 1981.
[2]. Anwar Habib , " On Bernstein Polynomials" IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 1 Ver. V (Jan - Feb. 2015), PP 26-34 www.iosrjournals.org
[3]. Anwar Habib and Saleh Shehri : "On the Convergence of Generalized Polynomials", Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 9,Number 2 (2013),pp. 133-136
[4]. A Habib , S Umar and H H Khan , " On the Degree of Approximation by Bernstein type Operators"Communications , de la Fac. Des Sc. De L'Univ. d'Ankara, Tom 33 Annee 1984 pp.121-136
[5]. E. Cheney and A. Sharma, "On a generalization of Bernstein polynomials," Rev. Mat. Univ. Parma, vol. 2, pp. 77-84, 1964.

Abstract:In this paper, we introduce a new class of open sets called δ-α-open sets together with its corresponding operators δ-α-interior and δ-α -closure. This class of sets is strictly contained in the class of δ-α preopen and δ-α semiopen sets. We also study some of the fundamental properties of this set.

Keywords: open set, closed set, δ-αopen, δ-α closed, δ-α open, δ-α close

[1]. N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl., 2 (1968), 103-118.
[2]. O Njastad. On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961–970.
[3]. T. Noiri, Remarks on   semiopen sets and   preopen sets, Demonstratio Math., 36, 4 (2003), 1007-1020.
[4]. U. S. Chakraborty,   b -open sets and   b -continuity, Acta Universitatis Apulensis, 35 (2013), 17-28.
[5]. N. Levine, Semi-open sets and semi-continuity in topological space, Amer. Math. Monthly, 70 (1963) ,36-41.

Abstract: It is known that N(0,1) has wide range of real life applications, whereas, Cauchy distribution is used mainly for theoretical studies with rare applications. Normal distribution has many interesting properties and its moment based kurtosis is treated as standard to compare kurtosis of other distribution. On the contrary moments for Cauchy distribution does not exists and hence its moment based kurtosis is undefined. This paper proposes a probability density (f) based new measure of kurtosis (Kf) and is further applied to compare kurtosis of N(0,1) with C(0,1), and N(0, 1) with C(0, λ)

Keywords: Probability density, Distribution Function, Kurtosis, Newton Raphson method

[1]. Kelvin P. Balanda and H.L. MacGillivray. "Kurtosis: A Critical Review". The American Statistician 42:2, May 1988, Pp 111-119.
[2]. Lawrence T. DeCarlo. "On the meaning and use of kurtosis", Psychological methods, 2 : 3, 1997, Pp 292-307.
[3]. David C. Blest. "A new measure of kurtosis adjusted for skewness", Aust. N. Z. J. Stat. 45:2, 2003, Pp 175-179.
[4]. Rosco J.F., Arthur Pewsey and Jones M.C., "On Blest‟s measure of kurtosis adjusted for skewness", preprint submitted to Computational Statistics and Data Analysis, 2011.

Abstract: We propose an architecture of a conjecture concerning the Riemann Hypothesis in the form of an 'alternative' to the Pólya strategy: we construct a Hamiltonian Polya H ˆ whose spectrum coincides exactly with that of the Harmonic Oscillator Hamiltonian osc H ˆ if and only if the Riemann Hypothesis holds true. In other words, we formulate the Riemann Hypothesis by means of a non-ommutative structure on the real axis, i.e. that of he Harmonic Oscillator, by an equation of the type Polya osc osc Hˆ (Hˆ ) = Hˆ : the Harmonic Oscillator operator, if viewed as an argument of Polya H ˆ , reproduces itself. 1991 Mathematics Subject Classification. 11M26.

Keywords: and phrases: Riemann Hypothesis, Riemann Zeta function, Hilbert-Pólya conjecture, Harmonic Oscillator, classical and quantum mechanics, thermodynamic limit

[1]. E. C. Titchmarsh and E. R. Heath-Brown: The theory of the Riemann Zeta-function, Clarendon Press, Oxford 1988.
[2]. Hilbert-Pólyaconjecture:http://en.wikipedia.org/wiki/Hilbert-Pólya_conjecture.Seealso
http://www.dtc.umn.edu/odlyzko/polya/index.html.
[3]. M. V. Berry and G. P. Keating: H = x  p and the Riemann zeros, in Supersymmetry and Trace Formulae: Chaos and Disorder,
Plenum, New York 1999, 355–367.
[4]. M. V. Berry and G. P. Keating: The Riemann zeros and eigenvalue asymptotics, SIAMS Review41:2 (1999), 236–266.
[5]. A. Connes: Trace formula in noncommutative geometry and the zeros of the Riemann Zeta function, Selecta Mathematica, New
Series 5:1 (1999), 29–106.

Abstract: In this paper, motivated by the works of Jenkins [11], Leung [12] and Panigrahi and Murugusundaramoorthy [16] we defined a subclass of p - valent analytic functions using a generalized differential operator and compute coefficient differences. We also point out, as particular cases, the results obtained earlier by various authors. Keywords and phrases: Multivalent functions, p-valent starlike functions, p-valent convex functions, oeplitz determinant, Hankel determinant, Differential operator

Keywords: Multivalent functions, p-valent starlike functions, p-valent convex functions, Toeplitz determinant, Hankel determinant, Differential operator

[1]. F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 27(2004), 1429-1436.
[2]. M. Darus and R. W. Ibrahim, Generalization of differential operator, J. Math. Stat., 4(2008), 138-144.
[3]. M. Darus and R. W. Ibrahim, New classes containing generalization of differential operator, Appl. Math. Sci., 3(2009), 2507-2515.
[4]. P. L. Duren, Univalent Functions. Grundlehren der Mathematischen Wissenschaften Fundamental Principles of Mathematical
Sciences]}, 259. Springer- Verlag, New York, 1983.
[5]. G. M. Golusin, On distortion theorems and coefficients of univalent functions, Rec. Math. [Mat. Sbornik] N.S., 19(1946). 183-202..

Abstract: WIn this paper, we establish some common fixed point theorems for two pairs of weakly compatible mappings in fuzzy metric spaces using the (CLRST) property. Our results extend, generalize and improve several results of metric spaces to fuzzy metric spaces.

Keywords: metric space, t-norm, weakly compatible mappings, (CLRST) property, (E. A) property, fixed point.

[1]. Aamri M. and Moutawakil D. E., "Some new common fixed point theorems under strict contractive conditions", Journal of Mathematical Analysis and Applications, vol. 270, no.1, ( 2002) pp. 181–188,.
[2]. Ali J., Imdad M. and Bahuguna D., "Common fixed point theorems in Menger spaces with common property (E.A)", Comput. Math. Appl., 60(12) (2010) 3152-3159.
[3]. Fang J.X.,"On fixed point theorems in fuzzy metric spaces", Fuzzy sets and systems, 46(1992), 107-113
[4]. Gregus Jr. M., "A fixed point theorem in Banach space", Bull. Un. Math. Ital. 17-A (5) (1980) 193-198.
[5]. George A., Veeramani P., "On some results in Fuzzy Metric Spaces", Fuzzy Sets and System, 64 (1994), 395-399.

Abstract: In this paper we have to study on the problem of 'Corruption' in different ways by using mathematical modelling. The problem of corruption is everywhere, so we will try to find the formula for how to measure corruption in the society? So, in this connection we have found the formula that is Mathematical corruption model for measuring corruption in the society of the country. Therefore we have taken some illustrations for measuring the corruption in the society.

Keywords: mathematical thinking, corruption mentality, modelling, applied

[1]. Matti Heilio (2009); Mathematics for Society, Industry and Innovation, Journal of Mathematical Modelling and Application, Vol.1, No.1, 77-88
[2]. Michael Gr. Voskoglou (2009); Transition Across Levels In The Process Of Learning: A Fuzzy Model, Journal of Mathematical Modelling and Application, Vol.1, No.1, 37-44

[3]. Michael Gr. Voskoglou, G. T. E. I. P. Greece (2010), A stochastic model for case-based Reasoning, Journal of Mathematical Modelling and Application, Vol.1, No.3, 33-39.
[4]. Patricia Camarena Gallardo, N. P. I. Mexico (2009); Mathematical Modelling and Knowledge Transference, Journal of Mathematical Modelling and Application, Vol.1, No.1, 18-36
[5]. Rui Gomes Neves, Vítor Duarte Teodoro (2010); Enhancing Science and Mathematics Education with Computational Modelling, Journal of Mathematical Modelling and Application, Vol.1, No.2, 2-15

Abstract: The theoretical study of the effect of Corticosterone release scores was determined. Formulae of fuzzy two parameter Weibull distribution, fuzzy Survival and fuzzy hazard rate function and its α-cut sets were presented. Using fuzzy survival and hazard rate model based on two parameter Weibull distributions, we showed that in the test termination, if the fuzzy Survival value increases then the fuzzy hazard rate value decreases in the lower α-cuts and if the fuzzy Survival value decreases then the fuzzy hazard rate value
increases in the upper α-cuts.

Keywords: Fuzzy Survival model, Fuzzy Hazard Model, Corticosterone, Weibull distribution

[1] Beuving G Vooder gma. Daily rhythm of corticosterone is laying hens influence of egg laying. J Reprod Fert , 51, 1977, 169-173.

[2] Birrenkott GP Wiggins M E, Determination of dexamethasone and corticosterone half lives in male broilers. Poilt Sci , 63, 1984, 1064-1068.

[3] Chen, C.H., Mon, L., Fuzzy System reliability analysis by interval of confidence, Fuzzy sets and systems, 56, 1993, 29-36.

[4] Chen. S. M., New method for fuzzy system reliability analysis, Cybernetics and systems, 27, 385-401.

[5] I.A.Downing, W.L.Bryden., Determination of corticosterone concentrations in egg albumen: A non-invasive indicator of stress in laying hens, Physiology & Behavior, 95, 2008, 381-387..

Abstract: The magnetic field of many astrophysical bodies is generated in the flow of electrically conducting fluidconfirmed in a spherical shell, the flow is normally a threshold process, the dynamo requires motions of sufficientstrength to overcome the innate magnetic diffusion. With presence of an ambient field, the requirement ofstrength of motion is not needed, and the magnetic field could be generated even for relatively weak flowswe compute the non-axisymmetric magnetic field with imposed stationary and oscillatory external ambientmagnetic field similar to Darah and Sarson 2007 which studied the axisymmetric magnetic field.............

Keywords: Mean-field dynamo; non-axisymmetric; nonlinear; ambient field.

[1]. Barenghi C.F. 1993, Geophys. Astrophys. FluidDynamos, 71, 163–185
[2]. Bigazzi A. Ruzmaikin A. 2004, The AstrophysicalJournal, 604, 944–959.
[3]. Brandenburg A., Krause F, Moss, D., &Tuominen I.1989a, A&A, 213, 411
[4]. Darah A. A., & Sarson G. R. 2007, Astron. Nach.,328, 25–35.
[5]. Frean D. R. 2004, The Geodynamo, appears in Dormy,E. (ed), athematical Aspects of Natural Dynamos,EDPScinces, Les Ulis

Abstract: A new class of probability distribution namely Weighted Marshall-Olkin Bivariate Exponential Distribution is considered in this paper. The distribution of concomitant of order statistics and joint distribution of two concomitant of order statistics has been obtained. Further explicit expression for single moment of concomitant of order statistics is obtained. Explicit expression for moment generating function of concomitant of order statistics has been obtained also.

Keywords: Concomitant, Weighted Marshall-Olkin bivariate exponential distribution, moments, order statistics.

[1]. Aleem, M. (2006): Concomitant of Order Statistics from Bivariate Inverse Rayleigh Distribution. Pak. j. stat. oper. res., 2, 45-48.
[2]. Balasubramanian, K. and Beg, M.I. (1998): Concomitant of Order Statistics in Gumbel's Bivariate Exponential distribution. Sankhya Ser.- B, 60, 399-406.
[3]. Begum, Anjuman A. and Khan, A.H. (2000): Concomitant of order statistics from Marshall and Olkin's bivariate Weibull distribution. Calcutta Statist. Assoc. Bull., 50 (197-198), 65-70.
[4]. Begum, Anjuman A. (2003): Concomitant of order statistics from bivariate Pareto II distribution. Int. j. stat. sci.,2, 27-35.
[5]. Chacko, M. and Thomas, P.Y. (2011): Estimation of Parameter of MorgensternType Bivariate Exponential Distribution Using Concomitant of Order Statistics. Stat. Methodol., 8, 363-376.

Abstract: It is observed that fuzzy graph is defined in different way in available literature .different approaches like fuzzy line graph, linear fuzzy graph and product fuzzy graphs were introduced with their properties. AMS Subject Classification: 05C72

Keywords: Fuzzy graph, Linear fuzzy graph, fuzzy line graph, product Fuzzy Graphs

[1]. A. Nagoor Gani and J. Malarvizhi " Isomorphism on Fuzzy Graphs" International Journal of Computational and Mathematical Sciences 2:4 2008.
[2]. A. Nagoor Gani and S. R. Latha; " On Irregular fuzzy graphs" Applied Mathematical Sciences,vol. 6, 2012, No. 11, 517-523.
[3]. A. Nagoor Gani and K. Radha, "On Regular Fuzzy Graphs" Journal of Physical Sciences, Vol. 12, 33-40 (2010).
[4]. A. Rosenfeld and fuzzy graphs. In Fuzzy Sets and their applications to Congnitive and Dicision processes. Zadeh L. A., Fu K. S.Shimura M., Eds. Acdemic Press. New York (1975) 77-95.
[5]. Harary,F.1972, Graph theory, Addison-Wesley,Reading,MA,3rd Printing.

Abstract: Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: Every even integer greater than 2 can be expressed as sum of two primes Proof:We can prove above conjecture with the help of mathematical induction Let P(n) be the statement that "every even integer greater than 2 can be expressed as sum of two primes " i.e. every number of form 2n, n≥2 can be expressed as sum of two primes We have,

,,,,,,,,.

Abstract: This research is a class action (Classroom Action Research) which aims to improve student's understanding in learning mathematics of class VIII SMP Negeri 5 Watampone through contextual approach. The subjects are students of class VIII semester of academic year 2011/2012 which are 42 students. Cycle I and Cycle II respectively was implemented during 4 times meetings. The instrument of data collection is a test of student's learning outcomes performed each end of the cycle and observation. Data are analyzed by using quantitative analysis and qualitative analysis. The results showed that: (1) the first cycle, the average score of student's learning outcomes is 60.24 of the highest possible score of 100, standard deviation of 13.49 and in middle category, (2) in the second Cycle,

Keywords: Contextual Approach, Student's Learning Outcomes

[1] Rahma, Sitti. Meningkatkan Pemahaman Pembelajaran Matematika kelas IIC SMP Negeri 21 Makassar pada Pokok Bahasan Lingkaran Melalui Pendekatan Kontekstual. Bachelor Thesis. Makassar: Faculty of Mathematics and Natural Science, 2005.
[2] Marpaung, Y. Perubahan Paradigma Pembelajaran Matematika di Sekolah. Paper presented in National Seminar of Mathematics Education in University of Sanata Dharma, Yogyakarta, Indonesia. 2003.
[3] National Council of Teachers of Mathematics, Principles and Standards for School Mathematics. Reston, Va: NCTM. 2000.
[4] Departemen Pendidikan Nasional. Pendekatan Kontekstual (Contextual Teaching and Learning). Jakarta: Dirjen Pendidikan Dasar dan Menengah. 2003.
[5] Upu, H. Problem Posing dan problem Solving dalam Pembelajaran Matematika. Makassar: Pusaka Ramadan.This heading is not assigned a number. 2003

Abstract: The properties of rank of a finite semigroup were presented by Howie in [1], and this properties is more general in algebraic system such as semigroup, or indeed even a group. We use this concept (properties) to compute the upper rank and the intermediate rank of direct product of a distinct monoid and the quotient group.

Keywords: Monoid, Independent set, Quotient group and Cyclic group.

[1]. J. M. HOWIE AND M. I. MARQUES RIBEIRO, Rank properties in finite semigroups, commun. Algebra 27(1999), 5333-5347.
[2]. E. MARCZEWSKI, Independence in abstract algebras: results and problems, Colloq. Math. 14 (1966), 169-188.
[3]. J. M. HOWIE, Fundamentals of semigroup theory (Oxford University Press, 1995).
[4]. U. I. ASIBONG-IBE, Element of group theory I, African Heritage Research Publication, Lagos, Nigeria ,(1998).
[5]. A. M. CEGARRA AND M. PETRICH, The Rank of Commutative Semigroup, Mathematica Bohemica, 134 (2009) , No. 3, 301-
318.
[6]. A. M. CEGARRA AND M. PETRICH, The Rank of Commutative Cancellative Semigroup, Acta Math. Hungar, 107, (1-2)
(2005),71-75.,.