iosr-Jm   Volume-14 ~ Issue-1 ~ Jan-Feb 2018

Abstract: The article investigates the behavior of the ζ-function by numerical methods. On this basis, a proof of the Riemann hypothesis is given.

Keywords:number theory, natural numbers, ζ-function, Riemann hypothesis

[1]. Gradshtein I. S., Ryzhik I. M. Tables of integrals, sums, series and products. Moscow, Publ. house "Nauka", 1962 (in Russian).
[2]. Handbook of mathematical functions. Ed. by M. Abramowitz and I. A. Stegun. Moscow, Publ. house "Nauka", 1979 (in Russian).
[3]. Janke E., Emde F., Losch F. Special functions. Moscow, Publ. house "Nauka", 1968 (in Russian).
[4]. Romanov V.N. Investigation of the fundamental problems of number theory. Publishing house "Asterion", 2015 (in Russian).
[5]. Whittaker E. T., Watson G. N. A course of modern analysis. Moscow, Publ. house "Nauka", 1963 (in Russian).

Abstract: Cholera has long been, and continues to be a global challenge. Despite study of the disease for many decades, it continues to be a threat to human existence in the affected regions of the world. It is important to continue to try to understand the disease dynamics and how interaction with environment and human factors contribute to the epidemic behavior. War, lack of good drinking water and inadequate human faeces disposal facilities seems to be the driving force of the epidemic in the affected communities. In other to find a solution to this global challenge, we extended a mathematical model for cholera epidemic by Codeco (2000), by varying the net reproduction rate of humans and allowing for susceptibility of recovered individuals. It is proved that the disease-free equilibrium state of the extended.........

Keywords: Cholera; Transmission; disease-free equilibrium; mathematical models; eradication

[1]. Alen, A. and Matthias, K.G. (2007): Modeling the spread of epidemic cholera: An Age-structured model: University of Maryland, Baltimore County, Lecture note
[2]. Anh, D.D., Lopez, A.L and Thiem, V.D.( 2011): Use of oral cholera vaccines in an outbreak in Vietnam: a case control study. PLoS Negl Trop Dis 2011; 5: 1006.
[3]. Bailey, N. T. J. (1975): The Mathematical Theory of Infectious Diseases and its Application: second edition, Griffu, Londom.
[4]. Bertuzzo,E., Casagrandi, R., Gatto, M., Rodriguez, I. and Rinaldo, A. (2010): On spatially explicit models of cholera epidemics. J. R. Soc. Interface 7: 321-333
[5]. Bouma, M.J and Pascual, M (2001): Seasonal and inter-annual cycles of endemic cholera in Bengal 1891–1940 in relation to climate and geography. Hydrobiologia 460:147–156.

Abstract: This paper seeks to determine the static and dynamic buckling load of a nonlinear elastic model structure having cubic – quintic nonlinearity. The associated static problem is first solved by adopting phase plane analysis to obtain the exact result followed by asymptotic and perturbation approach to obtain the approximate solution of the problem. Next, the dynamic problem after words is solved by employing phase plane technique to obtain the exact solution and later, by employing asymptotic and perturbation approach to obtain the approximate solution. In all the cases considered, the dynamic buckling load 𝜆𝐷 is mathematically related to the static buckling load 𝜆𝑆. The adoption of asymptotic and perturbation procedure is made possible by the presence of small non-dimensional parameter on which asymptotic expansions are made possible

Keywords: Dynamic buckling, Nonlinear elastic foundation, Static buckling, Step load.

[1]. B. Budiansky, Dynamic buckling of elastic structures, criteria and estimates, in Dynamic Stability of structures, Pergamon, New York, 1966.
[2]. B. Budianskyand J. W. Hutchinson, Dynamic buckling of imperfection – sensitive structures, proceedings of XI International Congr.Applied Mechanics.Springer – Verlag, Berlin, 1966.
[3]. D. Danielson,Dynamic buckling loads of imperfection – sensitive structures from perturbation procedures, A. I. A. A. J., 7, 1969, 1506 – 1510.
[4]. J. C.Amazigo and A. M. Ette, On a two – small nonlinear parameter differential equation with application to dynamic buckling, J. of Nigerian Math. Soc. 6, 1987, 91 – 102.
[5]. V. S. Svalbonas and A. Kalnins, Dynamic buckling of shells: evaluation of various methods, Nuclear engineering Des. , 1997, 44 – 56..

Abstract: This paper deals with a new five- parameter generalized version of the exponentiated Gompertz model which is called beta exponentiated Gompertz distribution. Gompertz, exponentiated Gompertz,beta Gompertz, exponentiated exponentiated Gompertz, exponential, exponentiated exponential, beta exponentiated exponential, beta exponential distributions are its sub models. We investigate various properties of this model such as mean, median, mode, quantiles, mean residual lifetime, mean deviations and Rényi entropy.The cumulative, density, hazard, survival,moment generating and rth moment expressions are derived. Also, we obtain the variation of the skewness and kurtosis measures. A behavior of the curves for distribution and hazard rate function are discusse...

Keywords: Beta Exponentiated Gompertz, Log-Concave,moment generating function, Quantile function,Rényi entropy

[1]. El-Gohary, A., Alshamrani, A., and Al-Otaibi, A. N. (2013). The Generalized Gompertz Distribution. Applied Mathematical Modelling, 37(1), 13-24.

[2]. Ahmed, E. A. (2015). Estimation of some lifetime parameters of generalized Gompertz distribution under progressively type-II censored data. Applied Mathematical Modelling, 39(18), 5567-5578.

[3]. Borges, P. (2017). EM algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with long-term survivors: an application to uterine cervical cancer data. Journal of Statistical Computation and Simulation, 87(9), 1712-1722.

[4]. Martinez, E. Z., & Achcar, J. A. (2017). The defective generalized Gompertz distribution and its use in the analysis of lifetime data in presence of cure fraction, censored data and covariates. Electronic Journal of Applied Statistical Analysis, 10(2), 463-484.

[5]. Khan, M. S., King, R., & Hudson, I. L. (2017). Transmuted Generalized Gompertz distribution with application. Journal of Statistical Theory and Applications, 16(1), 65-80

Abstract: A class of survey weighting methods provides consistent estimation of regression coefficients under unequal probability sampling. The minimization of the variance of the estimated coefficients within this class is considered. A series of approximations leads to a simple modification of the usual design weights. One type of application where unequal probabilities of selection arise is in the cross-national comparative surveys. In this case, the paper suggests the use of certain kind of within-country weight. This idea is investigated in an application to the data from African Social Survey, where a robust regression model is fitted with vote in an election as a dependent variable and with various variables of political science interest included as explanatory variables. The result shows that the use of the modified weights leads to considerable reduction in standard errors compared to design weights. Since robust regression model is unbiased, consistency then it follows the cramar Rao inequality assumption that variance is less in the estimated coefficients thus its most efficiency in measuring weights for within country data..

Keywords:Effeciency, variance, weighted averages, robust regression model.

[1]. Kish, L. (1994). Multipopulation Survey designs; five types with seven shared aspect.
[2]. DuMouchel,W.HandDuncan,G.J.(1983).Usingsamplesurveyweightsin multiple regression analysis of stratifiedsamples.
[3]. Pfeffermann, D. and Sverchkov, M. (1999). Parametric and Semiparametric estimationofregressionmodelsfittedtosurveydata.
[4]. Godambe,V.P.andThompson,M.E.(2009)EstimatingfunctionsandSurvey Sampling.InD.PfeffermannandC.R.Rao(Eds)SampleSurveys.
[5]. Fuller,W,A.(2009)SamplingStatistics,Wiley,Hoboken

Abstract: This paper deals with the application of linear-quadratic optimal control (LQOC) system through an optimization principle formulated in term of a cost criterion and supported by an optimal control system that minimizes the cost criterion. In a linear control theory, if the cost criterion is quadratic and the optimization is over an infinite horizon, then the result of such optimal control is a linear feedback with many properties and satisfies closed loop stability the result which is intimately connected to the system in order to certify the stability properties of control theory..

Keywords: Optimization, infinite, linear, stability, cost criterion

[1]. Oduro FT., A.Y. Aidoo, K.B. Gyamfi, J. and Ackora-Prah, (2013) Solvability of the Inverse Eigenvalue Problem for Dense Symmetric Matrices‟ Advances in Pure Mathematics, Vol. 3, pp 14- 19,
[2]. K.B. Gyamfi, J. Oduro FT., A.Y. Aidoo and Ackora-Prah, (2013
[3]. Oladejo N.K,, Oduro F.T and Amponsah S.K aAn inverse eigenvalue problem for optimal Linear-Quadratic control problem. International Journal of Mathematical Achieve 5(4), (2014) 306-314
[4]. Oladejo N.K, Amponsah S.K and Oduro F.T . Exact solution of an inverse eigen value problem on a certain Hamiltonian symmetric matrices. International Journal of Emerging Technology and Advanced Engineering. Vol. 5 Issue 10 (2015) Pg 293-297
[5]. Miranda J.O.A.O .Optimal Linear Quadratic Control. Control system, Robotics and Automation. Vol.VIII INESC.JD/IST,R.Alves,Redol 9.1000-029.Lisboa, Portuga

Abstract: In this study, data were obtained from 684 subjects male and female inclusive, on the spread of five different types of bacteria infectious diseases which are Staphylococcus,Pseudomonas, Klebsiella pneumonia, Escherichia Coli and Proteus. The data were collected according to their age range which are10–20yrs,21–40yrs, 41–60yrs, 61–80yrs and 80yrs and above. Results from the correlational analysis carried out on this data set indicate thatKlebsiella pneumonia and Escherichia Coli has an almost perfect positive relationship with correlation coefficient of 0.976 followed by Staphylococcus and Pseudomonas, Staphylococcus and Klebsiella pneumonia, Staphylococcus and Escherichia Coli which has a substantial positive correlation with correlation coefficient of 0.799, 0.701 and 0.702 respectively...............

[1]. Emanuele Del Fava,ZivShkedy, NielHensm,MarcAertsm, Barbara Suligoi, Laura Canoni, Fernando Vallejo (2011): Joint Modeling of HCV and HIV Co-Infection AmongInjecting Drug User In Italy And Spain Using Individual Cross-Sectional Data.
[2]. Statistical Communication of Infectious Diseases. Vol.3 (1).
[3]. Ira M. LonginiJr, James S. Koopman, Michael Haber, George A. Cotsonis (1988): StatisticalInference of Infectious Diseases: Risk-Specific Household and CommunityTransmission Parameters.American Journal of Epidemiology.Vol.128(4) 845-859.
[4]. Landis J.R. and Koch G.G. (1977): The measurement of observer agreement for categorical data.
[5]. Biometrics. 33:159-174

Abstract: Homogeneous and non-homogeneousBirth and Death Processes (BDPs) have a great importance for many fields of applied probability.For example,Non-homogeneous(See [3],[4]and[5]) versions of the Birth and Death Processes (NHBDPs) have an important role in queuing theory.  In this paper we consider Non-Homogeneous............

Keywords: Problems modeling, Birth and death rates, Kolmogorov differential equations, Reduction of the matrix, Recurrent Sequences of Order 2 and Identification of the law.

[1]. M.Eloussati, A.Arbai and M.Benslimane,Birth and Death Processes with Finished Number of States,International Journal of Mathematics and Statistics Invention (IJMSI),12 August 2017.

[2]. M.Eloussati, A.Arbai, Birth and Death Processes_General case,International Journal of Mathematics and Statistics Invention (IJMSI),12 October 2017.
[3]. A.Zeifman, S.Leorato, E. Orsingher, Ya. Satin, G.Shilova,Some universal limits for nonhomogeneous birth and death processes, Springer, 16 August 2005.

[4]. Jan van den Broek, Hans Heesterbeek,Nonhomogeneous birth and death models for epidemic outbreak data,Biostatistics, Volume 8, Issue 2, 1 April 2007, Pages 453–467.Published: 06 September 2006.

[5]. A.I. Zeifman, Vologda State Pedagogical Institute, Vologda, S.Orlova, Russia,Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes,Stochastic Processes and their Applications 59 (1995) 157-173

Abstract: This study was carried out to determine important factors that contribute to drug trafficking in Nigeria. The study employed principal component analysis (PCA) as a variable reduction tool in this study. Using all the variables in the model may violate the principle of parsimony; therefore, it was necessary to keep the model as simple as possible. The latent root criterion was employed in variable selection under the PCA approach. The panel data model was also used to fit the relationship between drug trafficking and related factors. The data for this study was collected from Annual Statistical Bulletin/Socio-Economic data, National Bureau of Statistics and National Drug Law Enforcement Agency. It comprises of drug trafficking data from 2000 to 2011. Average Household Size...........

Keywords: Drug trafficking, panel data analysis, unemployment rate.

[1]. Havoscope (2010). Drug Trafficking, http://www.havoscope.com/black-market/drug trafficking/drug-trafficking-by-countries/-
[2]. Federal Bureau of Investigation (2010). Organised Crime: African Criminal Enterprises, http://www.fbi.global-secruity-report/html.
[3]. NIDA (2009). Principles of Drug Addiction Treatment.A research based guide, 2nd edition. NationalInstitutes of Health U.S. Department of Health andHuman Services.
[4]. NDLEA (2001). Hard Drug Trafficking Curtail Measures, http://en.wikipedia.org/wiki/Nigerian Organized crime-ndlea.html
[5]. NDCMP (2015).National Drug Control Master Plan 2015-2019

Abstract: This paper described the comparison of Euclidean and non- Euclidean geometry. Geometry was extreme important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, mainly divided in two parts: 1. Euclidean geometry 2. Non- Euclidean geometry Also non –Euclidean geometry is divided into two sub parts.  Hyperbolic geometry  Spherical geometry The intention of this article is to compare Euclidean and non –Euclidean geometry.

Keywords: Euclidean geometry, hyperbolic geometry, non –Euclidean geometry, spherical geometry.

[1]. http://www.differencebetweenand.com/difference-between-euclidean-and-non-euclidean-geometry.html
[2]. https://answers.yahoo.com/question/index?qid=20081101174004AApqpFh
[3]. http://www.upscale.utoronto.ca/GeneralInterest/Harrison/GenRel/Geometry.htmlhttp://www.cs....

Abstract: We show the norm attaining quadraicallyhyponormal weighted shift is subnormal . Also , We show that there is a Banach space X such that the set of norm attaining operators from Xto any infinite dimensional space 𝐿1 𝜇 is not de nse ..

[1] Jerry Johnson and John Wolfe, Norm attaining operators, Studia Math. 65 (1979), no. 1, 7–19.
[2] M. D. Acosta, Denseness of norm attaining mappings, Rev. R. Acad. Cien. Serie A. Mat. 100 (2006), 9-30.
[3] Acosta, M.D. (1999). Norm attaining operators into 𝐿1(𝜇), Function Spaces, Contemporary Math.,232, 1–11.
[4] Aguirre, F.J. (1998). Norm attaining operators into strictly convex Banach spaces. J. Math. Anal. Appl.,222, 431–437.
[5] R.E. Curto, Quadratic ally hypo normal weighted shifts, Integral Equations Operator Theory, 13 (1990), 49-66....

Abstract: It has been theorised that only capital expenditure targeted at infrastructural development bring about economic growth and this has brought about the doubt as to whether recurrent expenditure translates to economic growth in any form, and if yes, what aspects of the recurrent expenditure mediate upon economic growth using crude oil price as Nigeria's major source of income. This study seeks to determine the variables of recurrent expenditure that act as mediators to economic growth in Nigeria; to compute the indirect effect of recurrent expenditure on economic growth in Nigeria; to test for the significance of indirect effect using the Sobels test. From the results, rrecurrent expenditure...........

Keywords: Recurrent expenditure, crude oil prices, economic growth mediation

[1]. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182
[2]. Cohen, J.; Cohen, P.; West, S. G. & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Erlbaum
[3]. Fairchild, A. J & MacKinnon, D. P. (2009). A general model for testing mediation and moderation effects. Prevention Science, 10, 87-99.
[4]. Frazier, P. A., Tix, A. P., & Barron, K. E. (2004). Testing moderator and mediator effects in counseling psychology research. Journal of Counseling Psychology, 51, 115-134.
[5]. Iheanacho, E (2016). The Contribution of Government Expenditure on Economic Growth of Nigeria Disaggregated Approach. International Journal of Economics and Management Sciences, 5(5)....

Abstract: This paper described the comparison of Euclidean and non- Euclidean geometry. Geometry was extreme important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, mainly divided in two parts: 1. Euclidean geometry 2. Non- Euclidean geometry Also non –Euclidean geometry is divided into two sub parts.  Hyperbolic geometry  Spherical geometry The intention of this article is to compare Euclidean and non –Euclidean geometry.

Keywords: Euclidean geometry, hyperbolic geometry, non –Euclidean geometry, spherical geometry.

[1]. http://www.differencebetweenand.com/difference-between-euclidean-and-non-euclidean-geometry.html
[2]. https://answers.yahoo.com/question/index?qid=20081101174004AApqpFh
[3]. http://www.upscale.utoronto.ca/GeneralInterest/Harrison/GenRel/Geometry.htmlhttp://www......