Volume-7 , Issue-4 , Aug 2020, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Statistical Analysis of the Costs of OPEC Crude Oil

  V. Swapna, Kanthala Sampath Kumar, V.V. Hara Gopal

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.1-9, Aug-2020

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  In this study, Seasonal Na?ve, ETS (Error, Trend, Seasonal), Neural Networks (NN), and ARIMA methods are applied for forecasting the Time series data and out of these NN is found to be the most efficient method. The present study employs measures, ME, RMSE, MAE, MASE and ACF1 to evaluate the performance of the model. These are used to compare the performance of the proposed technique and that of ARIMA and other methods. The study adopts the data of the costs of crude oil from the Organization of the Petroleum Exporting Countries (OPEC). Linear and non-Linear methods of forecasting the prices of crude oil among the OPEC are discussed, and their advantages and disadvantages are also illustrated for improving the performance and prediction. The revealing results of the proposed i.e. NN method outperforms the others in forecasting accurate results

  Key-Words / Index Term
  Time Series, Crude Oil Price, Neural Networks (NN), Auto Regressive (AR), Moving Average (MA), Stationary, Linear Model, non-Linear Model

  References
  [1] Ashok K. Nag and Amit Mitra (2002): ?Forecasting Daily Foreign Exchange Rates Using Genetically Optimized Neural Networks?, Journal of Forecasting, 21, 501-511.
  [2] Al-Amri, S. S., Kalyankar, N. V., & Khamitkar, S. D. (2010). Image segmentation by using edge detection. International journal on computer science and engineering, 2(3), 804-807.
  [3] Agrawal, M., & Mishra, P. (2012). A comparative survey on symmetric key encryption techniques. International Journal on Computer Science and Engineering, 4(5), 877.
  
  [4] Box, G.E.P. and G.M. Jenkins (1970): ?Time series analysis: Forecasting and control?, San Francisco: Holden-Day.
  [5] C.M. Kuan and T.Liu, ?Forecasting exchange rates using feedforward and recurrent neural networks,? J. Appl. Econometrics, vol. 10, 1995, pp. 347?364.
  [6] Honlun Yip, Hongqin Fan, Yathung Chiang (2014): "Predicting the maintenance cost of construction equipment: Comparison between general regression neural network and Box?Jenkins time series models", Automation in Construction, Vol.38, Pages. 30?38.
  [7] Makridakis, S., S.C. Wheelwright, and R.J. Hyndman (1998): ?Forecasting: Methods and Applications?, New York: John Wiley & Sons.
  [8] Nikolaos Kourentzes, Forecasting time series with neural networks in R (https://kourentzes.com/forecasting/2017/02/10/forecasting-time-series-withneural-networks-in-r/)
  [9] Rani, S. J., & Haragopal, V. V. Forecasting Exchange Rates using Neural Neworks.
  [10] Rob J Hyndman (https://robjhyndman.com/hyndsight/)
  [11] Ruslana Dalinina, Introduction to Forecasting with ARIMA in R
  (https://blogs.oracle.com/datascience/introduction-to-forecasting-with-arima-in-r)

  Citation
  V. Swapna, Kanthala Sampath Kumar, V.V. Hara Gopal, "Statistical Analysis of the Costs of OPEC Crude Oil," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.1-9, 2020

• Open Access   Article

  Sum Construction of Automorphic Symmetric Balanced Incomplete Block Designs

  C.W. Otulo, Z.M. Muga, N.B. Okelo, J.O. Nyakinda

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.10-13, Aug-2020

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  In this study Sum construction method of automorphic symmetric balanced incomplete block designs has been presented in details. Efficiency of a test design used in the Sum construction of automorphic symmetric balanced incomplete block designs has been determined alongside its existence. The process involved the application of sum construction to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design used in the sum construction method has been found to be existing with an efficiency of 77.78%. The sum constructed automorphic symmetric balanced incomplete block designs provide more information per block than the parent designs

  Key-Words / Index Term
  Symmetric Balanced Incomplete Block Design (SBIBD), Automorphism and Automorphic Symmetric Balanced Incomplete Block Design(AUSBIBD)

  References
  [1] J. P. Alabi, ?Construction of Balanced Incomplete Block Design of Lattice Series I and II.? International Journal of Innovative and Scientific and Engineering, Vol 16, No. 4 pp.10-22, 2018.
  [2] G. Allan, ?Some Open (And Some Closed) Questions On Symmetric BIBDs and PBIBD`s." Annals of the New York Academy of Sciences, New York, 1979.
  [3] B. Chan, A. Eccleston, ?On construction of complete and Partial Nearest Neighbor Balanced designs,? Australasian J. combinatorics Vol 8, No. 3, pp.39-50, 2017.
  [4] R. Fisher, ?An Introduction to Balanced Incomplete Block Designs,? Combinatorial Designs, London; 1939.
  [5] A. C. Kelechi, ?Symmetric and Unsymmetric Balanced Incomplete Block Designs: A Comparative Analysis,? International Journal of Statistics and Applications, Vol. 2, No. 4, pp.33-39, 2012.
  [6] C. S. Kumarland, ?Efficiency of Nearest Neighbor Balanced Block Designs for Second Order Correlated Error,? Journal of mathematics, Vol. 13. No. 1, pp.62-71, 2017.
  [7] W. C. Otulo, S. Ojunga, E. Otumba, ?Screening New strains of sugarcane using Augmented Block Design,? Mathematical theory and Modelling, Vol. 5, No. 5, pp.153-161, 2019.
  [8] E. T. Parker, ?Remarks on Balanced Incomplete Block Designs,? Proceedings of American Mathematical society, Vol. 14, No. 5, pp. 729-730, 2016.
  [9] S. Parvathy, S. Bury, ?Final Report on Theory of Block Designs,? Indian Institute of Science Education and Research Journal, Vol. 4 No. 3, pp.12-37, 2017.
  [10] A. Rajarathinam, S. Mahalakshmi, K. Ghosh, ?Construction of Efficiency Balanced Block Designs with Repeated Blocks,? Int. J. Mathematical Statistics, Vol. 5, No. 3, pp. 43-46, 2016.
  [11] K. Sinha, A. Das, A. Dey, ?Kageyama S. An Efficient Balanced Treatment Incomplete Block Designs," Australasian J. combinatorics, Vol. 8, No. 2, pp.32-36, 2016.

  Citation
  C.W. Otulo, Z.M. Muga, N.B. Okelo, J.O. Nyakinda, "Sum Construction of Automorphic Symmetric Balanced Incomplete Block Designs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.10-13, 2020

• Open Access   Article

  A Hybrid Homotopy Perturbation Method with Natural Transform to Solve Partial Differential equations

  Bachir N. Kharrat, George A. Toma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.14-19, Aug-2020

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  Abstract
  In this paper, we present a new combination between the natural transform and the homotopy perturbation method. This hybrid technique allows to obtain numerical and analytical solutions for initial value problems represented by non - linear partial differential equations of a various normal orders. This presented method depends on applying the natural transform to solve the non - linear partial differential equation, then we construct the Homotopy on the transformed equation that including the initial conditions, after that we apply the inverse transform of the natural transform to find the solution of the equation. Obviously that the solution of the equation depends on the initial conditions. To show the power and accuracy of our method we present three initial value problems where we obtained exact or approximate solutions with high accuracy. This work also showed that this proposed hybrid method is suitable scheme for solving non - linear partial differential equations

  Key-Words / Index Term
  Approximate solution, Exact solution, Homotopy perturbation method, Initial value problems, Natural Transform, Non-linear partial differential equations

  References
  [1] J. H. He, ?A coupling method of a homotopy technique and a perturbation technique for non-linear problems,? International Journal of Non-Linear Mechanic, Vol. 35, No. 1, pp. 37-43, 2000.
  [2] J. H. He, ?Homotopy perturbation technique,? Computer Methods in Applied Mechanics and Engineering, vol. 178, pp. 257-262, 1999.
  [3] J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities,? Applied Mathematics and Computation, vol. 151, no. 1, pp. 287?292, 2004.
  [4] J. H. He, ?Homotopy perturbation method: A new nonlinear analytical technique,? Applied Mathematics Computation, vol. 135 (1), pp. 73-79, 2003.
  [5] J. H. He, ?Application of homotopy perturbation method to nonlinear wave Equations,? Chaos Solitons Fractals, vol. 26 (3), pp. 695-700, 2005.
  [6] B. N. Kharrat, G. A.Toma, ?Development of Homotopy Perturbation Method for Solving Nonlinear Algebraic Equations,? International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 7 (2), pp. 47-50, 2020.
  [7] M. A. Tahmina, A. M. Mansur, ?Homotopy Perturbation Method for Solving Highly Nonlinear Reaction-Diffusion-Convection Problem,? , American Journal of Mathematics and Statistics Vol. 9 (3). pp. 136-141, 2019.
  [8] S. Iqbal, A. Javed, ?Application of optimal homotopy asymptotic method for the analytic solution of singular Lane?Emden type equation,? Applied Mathematics And Computation, Elsevier, 2011.
  [9] A. Yildirim, D. Agirseven, ?The Homotopy Perturbation Method for Solving Singular Initial Value Problems,? International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10 (2). 235, 2009.
  [10] J. H. He, ?Application of homotopy perturbation method to nonlinear wave Equations,? Chaos Solitons Fractals, Vol. 26 (3), pp. 695-700, 2005.
  [11] M. A. Tahmina, M. S. A. Moinuddin, A. M. Mansur, ?Semi-Analytical Approach to Solve Non-linear Differential Equations and Their Graphical Representations,? International Journal of Applied Mathematics & Statistical Sciences, Vol. 3, Issue 1, pp. 35-56, 2014.
  [12] M. Ghoreishi, M. B. Ismail, ?The Homotopy Perturbation Method (HPM) for Nonlinear Parabolic Equation with Nonlocal Boundary Conditions,? Applied Mathematical Sciences, Vol. 5 (3), pp. 113 ? 123, 2011.
  [13] S. H. Javeed, D. Baleanu, A. Waheed, M. Khan, H. Affan, ?Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations,? MDPI - Mathematics, Vol. 7, 40, 2019.
  [14] H. Z. Khan, A. W. Khan, ?N-transform properties and applications,? NUST Journal of Engineering Sciences, Vol. 1, pp. 127-133, 2008.
  [15] M. B. F. Belgacem, R. Silambarasan, ?Theory of natural transform,? Mathematics in Engineering Science and Aerospace, Vol. 3, No. 1, pp. 105-135, 2012.
  [16] G. A. Toma, ?A Hybrid Semi-Analytical Method with Natural Transform for Solving Integro ? Differential Equations,? International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 7, Issue. 3, pp.1?7,2020.
  [17] M. N. L. Tawfiqa, K. A. Jabberb, ?Solve the groundwater model equation using fourier transforms method,? International Journal of Applied Mathematics and Mechanics, vol. 5, No. 1, pp.75?80,2017.
  [18] D. A. Polyanin, M. V. Alexander, ?Handbook of Mathematics for Engineers and Scientists,? CRC Press, 2006.
  [19] F. Bulnes, ?Mathematical electrodynamics: groups, cohomology classes, unitary representations, orbits and integral transforms in electro-physics,? American Journal of Electromagnetics and Applications, Vol. 3, No. 6, pp. 43?52, 2015.
  [20] D. Bolukbas, A. Arifergin, ?A radon transform interpretation of the physical optics integral,? Microwave and Optical Technology Letters, Vol. 44, No. 3, pp. 284?288, 2005.
  [21] E. W. Higgins, D. C. Munson, ?A hankel transform approach to tomographic image reconstruction,? IEEE Transactions on Medical Imaging ,Vol. 7, No. 1, pp. 59?72, 1988.
  [22] B. F. Belgacem, A. A. Karaballi, ?Sumudu transform fundamental properties,? Journal of Applied Mathematics and Stochastic Analysis, 2006.
  [23] C. Yang, M. A. Wazwaz, Q. Zhou, W. Liu, ?Transformation of soliton states for a (2+1) dimensional fourth-order nonlinear schrdinger equation in the Heisenberg ferromagnetic spin chain,? Laser Physics, Vol. 29, No. 3, 2019.
  [24] X. Liu, H. Triki, Q. Zhou, ?Generation and control of multiple solitons under the influence of parameters,? Nonlinear Dynamics, Vol. 95, No. 1, pp. 143?150, 2019.
  [25] L. W. Yang, Q. Zhou, D. Mihalache, B. A. Malomed, ?One soliton shaping and two-soliton interaction in the fifth-order variable-coefficient nonlinear schrdinger equation,? Nonlinear Dynamics, Vol. 95, No. 1, pp. 369?380, 2019.
  [26] A. Entesar, O. , W. Al-Hayani, "Hybridization of Genetic Algorithm with Homotopy Analysis Method for Solving Fractional Partial Differential Equations ", Eurasian Journal of Science & Engineering, 2019.
  [27] N. Panagant, S. Bureerat, "Solving Partial Differential Equations Using a New Differential Evolution Algorithm", Mathematical Problems in Engineering, 2014.
  [28] J. Biazar a, H. Ghazvini , "Convergence of the homotopy perturbation method for partial differential equations". Nonlinear Analysis: Real World Applications, Elsevier, 2009.
  [29] L. F. Spevaka and O. A. Nefedova , "Solving a Two- Dimensional Nonlinear Heat Conduction Equation with Nonzero Boundary Conditions by the Boundary Element Method", AIP Conference Proceedings , 2017.
  [30] Ming Li , C.S. Chen , A. Karageorghis, " The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions ", Computers and Mathematics with Applications, Elsevier, 2013.
  [31] S. Afshar, B. Soltanalizadeh ," Solution Of The Two- Dimensional Second-Order Diffusion Equation With Nonlocal Boundary Condition", International Journal of Pure and Applied Mathematics, 2014.
  [32] M. S. Rawashdeh, Ha. Al-Jammal, "New approximate solutions to fractional nonlinear systems of partial differential equations using the FNDM", Advances in Difference Equations, Springer, 2016.
  [33] A. Cheniguel, " Numerical Simulation of Two-Dimensional Diffusion Equation with Non Local Boundary Conditions", International Mathematical Forum, 2012.
  [34] M. Tahmina Akter, M. A. Chowdhury, "Homotopy Perturbation Method for Solving Highly Nonlinear Reaction-Diffusion-Convection Problem", American Journal of Mathematics and Statistics, 2019.
  [35] E. E. Eladdad and E. A. Tarif ," On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations", Advances in Mathematical Physics, 2019.
  [36] C. Jesuraj, A. Rajkumar, "A New Modified Sumudu Transform Called Raj Transform to Solve Differential Equations and Problems in Engineering and Science", International Journal on Emerging Technologies, 2020.
  [37] B. N. Kharrat and G. Toma, " A New Hybrid Sumudu Transform With Homotopy Perturbation Method For Solving Boundary Value Problems", Middle-East Journal of Scientific Research, 28 (2): 142-149, 2020.
  [38] B. N. Kharrat and G. Toma, "Development of Homotopy Perturbation Method for Solving Nonlinear Algebraic Equations", International Journal of Scientific Research in Mathematical and Statistical Sciences. V 7, Issue 2, pp. 47-50, 2020.

  Citation
  Bachir N. Kharrat, George A. Toma, "A Hybrid Homotopy Perturbation Method with Natural Transform to Solve Partial Differential equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.14-19, 2020

• Open Access   Article

  Estimating the Epidemic Size of COVID-19 in SAARC Countries Using Classical SIR Model

  Riaz Mahmud, Sofi Mahmud Parvez

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.20-25, Aug-2020

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  Abstract
  The Coronavirus disease 2019 (COVID-19) is an infectious disease that evolved from Wuhan, China. It is now expanded in almost all over the world and became pandemic by the time. In this study, we have used the classical SIR (Susceptible, Infected, and Recover) model to estimate dynamics of the infection of COVID-19 in eight different countries (India, Pakistan, Bangladesh, Afghanistan, Nepal, the Maldives, Sri-Lanka, and Bhutan) of South Asian Association for Regional Co-operation (SAARC). The maximum and minimum basic reproduction number R0 (2.71 and 1.10) of coronavirus among the SAARC countries are estimated for Bhutan and Pakistan, respectively. In this article, we tried to estimate the epidemic infection size for each SAARC country and compare them using the SIR model`s statistical parameters. The estimation may not be valid if the significant variation of data occurs in the coming days

  Key-Words / Index Term
  COVID-19, Pandemic, Classical SIR model, SAARC

  References
  [1] Joseph T Wu., Kathy Leung, Gabriel M. Leung, "Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a
  modelling study," The Lancet, Vol. 395, Issue. 10225, pp. 689-697, 2020.
  [2] Isaac I. Bogoch, Alexander Watts, Andrea Thomas-Bachli, Carmen Huber, Moritz UG Kraemer, and Kamran Khan, "Pneumonia of Unknown Etiology in Wuhan, China: Potential for International Spread Via Commercial Air Travel," Journal of Travel Medicine, Vol. 27, Issue. 2, pp. 1-3, 2020.
  [3] Coronavirus disease 2019 (COVID-19) Situation Report ? 38, World Health Organization, 27-02-2020.
  [4] WHO Timeline - COVID-19, World Health Organization (WHO), 27-04-2020.
  [5] Samrat Kumar Dey, Md. Mahbubur Rahman, Kabid Hassan Shibly, Umme Raihan Siddiqi, Arpita Howlader, ?Epidemic Trend Analysis of SARS-CoV-2 in SAARC Countries Using Modified SIR (M-SIR) Predictive Model?, medRxiv, 2020.
  [6] GUERRERO FLORES, DANNY JOEL, ?Spread of Covid-19: a Study Case of Honduras, Forecasting with Logistic Model and SIR Model (Version FIRST DRAFT),? Zenodo, 2020.
  [7] Fred Brauer, Carlos Castillo-Chavez, ?Mathematical Models in Population Biology and Epidemiology,? Springer, New York, NY, pp. 345-409, 2012.
  [8] Batista, Milan, ?Estimation of the final size of the COVID-19 epidemic,? MedRxiv, 2020.
  [9] M. Batista (2020). ?fitVirusCOVID19?, MATLAB Central File Exchange, Retrieved May 12, 2020.

  Citation
  Riaz Mahmud, Sofi Mahmud Parvez, "Estimating the Epidemic Size of COVID-19 in SAARC Countries Using Classical SIR Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.20-25, 2020

• Open Access   Article

  Some New Classes of k-distance Trees with Alpha Labeling

  Dedas Mishra, Sushant Kumar Rout, Subarna Bhattacharjee

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.26-34, Aug-2020

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  Abstract
  By a k- distance tree we mean a tree T which possesses a path H with the condition that each vertex of T is at a distance at most k from H. By a graceful labelling of a tree T we mean a bijection f of the vertices of T, i.e V(T) into the set {0,1,2,...,|V(T)|} with the condition that the set of the labels of the edges constitutes the set {1,2,3,...,|V(T)|- 1}, where the label of each edge (a,b) in T is defined by |f(a) ? f(b)|. An a - labelling of a tree T is a graceful labelling f of T if there exists an integer r > 0 for which we have either f(a) < r ≤ f(b) or f(b) < r ≤ f(a) for each edge (a,b) of T. In this paper we use techniques to associate two or more graceful trees and construct a generalized class of trees, namely k ? distance trees that possess a - labelling

  Key-Words / Index Term
  graceful labeling, a - labeling, k-distance trees

  References
  [1] A. Rosa, ?On certain valuations of the vertices of a graph, Theory of Graphs? In the Proceedings of International Symposium, Rome, Gordon and Breach, N. Y. and Dunod Paris, pp. 349-355, 1966.
  [2] Saad I. El. Zanati, Carles Vanden Eynden, ?On Rosa Type Labeling and Cyclic Decompositions?, Mathematica Slovaca, Vol. 59, pp 1 ? 18, 2009.
  [3] P. Panigrahi and D.Mishra, ?Larger Graceful and Interlaced Lobster Obtained by Joining Smaller Ones?, South East Asian Bulletin of Mathematics, Vol. 33, pp. 509-525, 2009.
  [4] G. Sethuraman and P. Ragukumar, ?Every tree is a subtree of graceful tree, graceful graph and alpha-labeled graph?, To appear in Ars Combinatoria.
  [5] W. C. Chen, H. I. Lu, and Y. N. Lu, ?Operations of Interlaced Trees and Graceful Trees?, South East Asian Bulletin of Mathematics, Vol. 4, pp. 337 ? 348, 1997.
  [6] J.A. Gallian, ?A dynamic survey of graph labeling?, Electronic Journal of Combinatorics, DS6, 22nd edition, December 15, 2019.
  [7] D. Mishra, A. C. Panda, and R. B. Dash, ?A Class n- distance Graceful Trees?, Studies In Mathematical Sciences, Vol-3, No-2, pp. 21 ? 27, 2011.
  [8] A. C. Panda, D. Mishra, and R. B. Dash, ?Some New Classes Of Graceful Trees?, International Journal of Mathematical Sciences And Engineering Applications, Vol-7 No. 3, pp. 1 ? 21, 2013.
  [9] D. Mishra, ?Graceful Lobsters Obtained by Component Moving and Joining Techniques?, Ph.D. thesis, Indian Institute of Technology, Kharagpur, India, 2006.
  [10] A. C. Panda, ?Some New Classes of Graceful Trees Obtained By Component Moving Transformations?, Ph.D. thesis, Utkal University, Vani Vihar, Bhubaneswar, India, 2014.
  [11] P. Hrnciar and A. Havier, ?All Trees of Diameter Five Are Graceful?, Discrete Mathematics, Vol.233, pp. 133-1502001.
  [12] D. Mishra, S. K. Rout, P. C. Nayak, ?Some New Graceful Generalized Classes of Diameter Six Trees?, Electronic Journal of Graph Theory and Applications, Vol. 5, No. 1, pp. 94?111, 2017.
  [13] J.JebaJesintha, R. Jayaglory, G. Bhabita, Odd Graceful Labelling of the Union of Cycle and Lobsters, International Journal of Computer Sciences and Engineering, Vol.-7, Special Issue, 5,pp. 59-63, 2019.

  Citation
  Dedas Mishra, Sushant Kumar Rout, Subarna Bhattacharjee, "Some New Classes of k-distance Trees with Alpha Labeling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.26-34, 2020

• Open Access   Article

  Comparison of Macroeconomic Behavior in Some ASIAN Countries (1991 ? 2017)

  E. Zakchona, P. Sihombing

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.35-45, Aug-2020

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  Abstract
  This research aims to analyse the comparison of macroeconomic of some Asian countries in long period. The sample population was limited by four Asian countries which its gross domestic product depreciated significantly during financial crisis of Asia and global, such as Indonesia, Malaysia, Singapore, and South Korea. The research data is formed by Vector Auto Regression (VAR) model and empirical result is executed by granger causality model on E-views 11 programme to gauge the relationship between gross domestic product, exchange rate, inflation rate, foreign direct investment, net export, government expenditures, unemployment rate, and savings. The results showed that gross domestic product impacted foreign direct investment and savings in Indonesia. Then, gross domestic product of South Korea is part of savings and consumption index, and its growth has effect to inflation rate. Next, number of gross domestic product impacts on inflation rate in Singapore. In contrast, gross domestic product of Malaysia is not represented by independent variables. Overall, these macroeconomic variables do not explain gross domestic product growth significantly in Indonesia, Malaysia, Singapore, and South Korea

  Key-Words / Index Term
  gross domestic product, exchange rate, inflation rate, consumption index, foreign direct investment, net export, government expenditure, unemployment rate, savings

  References
  [1] A. Pohan, ?Picture of Indonesia?s Monetary Policies?, ?Potret Kebijakan Moneter Indonesia?, Raja Grafindo Persada Publisher, Jakarta, pp.1-336, 2008.
  [2] A. Pohan, ?Framework of monetary policy and its implementation in Indonesia?, ?Kerangka kebijakan moneter dan implementasinya?, Raja Grafindo Persada Publisher, Jakarta, pp.1-332, 2008.
  [3] C. Wheelan, ?Naked economics: undressing the dismall science?, Norton Paperback Publisher, New York, pp. 149-167, 2002.
  [4] Krugman, ?International economy: theory and policies?, ?Ekonomi internasional: teori dan kebijakannya?, Raja Grafindo Persada Publisher, Jakarta, pp.8-9, 1994
  [5] M. Kuncoro, ?Theory, problem, and its policy: economic development?, ?Teori, masalah, dan kebijakan: ekonomi pembangunan?, Erlangga Publisher, Jakarta, pp.1-400, 2010.
  [6] M. Nanga, ?Macroeconomics: theory, problem, and its policy?, ?Makroekonomi: teori, masalah, dan kebijakannya?, Raja Grafindo Persada Publisher, Jakarta, pp.1-554, 2001.
  [7] M.D. Ariefianto, ?Econometrics: essential and application of E-views?, ?Ekonometrika: esensi dan pengaplikasian E-views?, Erlangga Publication, Yogyakarta, pp.1-255, 2012.
  [8] M.F. Qudratullah, ?Analysis of applied regression: theory, case, and its application by SPSS?, ?Analisis regresi terapan: teori, contoh kasus dan aplikasi dengan SPSS?, Andi Publisher, Yogyakarta, pp.179, 2013.
  [9] M.L. Jhingan, ?Economic development and its planning?, ?Ekonomi pembangunan dan implementasinya?, Raja Grafindo Persada Publication, Jakarta pp.3-67, 2008.
  [10] M.P. Todaro, ?Economic development in the third world?, ?Ekonomi pembangunan di dunia ketiga?, Erlangga Publisher, Jakarta, pp.-, 1997.
  [11] N.G. Mankiw, ?Macroeconomics theory?, ?Teori makroekonomi?, Erlangga Publisher, Jakarta, pp.-, 2003.
  [12] N.G. Mankiw, ?Macroeconomics?, ?Makroekonomi?, Gelora Aksara Pratama Publisher, Jakarta, pp.260, 2006.
  [13] N.G. Mankiw, ?Macroeconomics?, ?Makroekonomi?, Erlangga Publisher, Jakarta, pp.-, 2007.
  [14] R. Dornbursch, et al. ?Macroeconomics?, ?Makroekonomi?, Media Global Edukasi Publication, Jakarta, pp.-, 2004.
  [15] S. Sagir, ?Capital section of Indonesia?s economy?, ?Kapita selekta ekonomi Indonesia?, Prenada Media Group Publisher, Jakarta, pp.-, 2009.
  [16] S. Sukirno, ?Microeconomic: introduction of microeconomic theory?, ?Mikroekonomi: pengantar teori mikroekonomi?, Raja Grafindo Persada Publisher, Jakarta, pp.417-418, 1994.
  [17] The World Bank, ?Best investment for people?, ?Investasi terbaik untuk masyarakat?, Salemba Empat Publisher, Jakarta, pp.-, 2005.
  [18] A. Septian, Mawardi, M.A.K. Rizki, ?The effect of inflation rate and unemployment rate to Indonesia?s economic growth?, ?Pengaruh inflasi dan tingkat pengangguran terhadap pertumbuhan ekonomi di Indonesia?, i-economic, Vol.2, Issue.1, pp., 2016.
  [19] A. Z. Baharumsyah, S. Rashid, ?Exports, imports and economic growth in malaysia: empirical evidence based on multivariate time series?, Asian Economic Journal, Vol.13, Issue.4, pp.389-406, 2002.
  [20] B. Rao, ?East Asian economies: trends in saving and investment?, Economic and Political Weekly, Vol.36, Issue.13, pp.1123-1133, 2001.
  [21] B.S. Cheng, T.W. Lai, ?Government expenditures and economic growth in South Korea: a VAR approach?, Journal of Economic Development, Vol.22, Issue.1, pp.11-24, 1997.
  [22] D. Ernita, S. Amar, E. Syofyan, ?Analysis of economic growth, investment, and consumption in Indonesia?, ?Analisis pertumbuhan ekonomi, investasi, dan konsumsi di Indonesia?, Jurnal Kajian Ekonomi, Vol.1, Issue.2, pp.176-193, 2013.
  [23] D. Owusu, E.Y. Cobbold, ?Singapore?s economic growth: FDI??, International Journal of Multidisciplinary Research and Development, Vol.7, Issue.1, pp.124-127, 2019.
  [24] G.S. Field, ?The Employment problem in Korea?, Journal of The Korean Economy, Vol.1, Issue.2, pp.207-227, 2000.
  [25] H.M. Irpan, R.M. Saad, N. Ibrahim, ?Investigating relationship between unemployment rate and GDP growth in Malaysia?, Economic, Vol.1, Issue.3, pp.4057-4064, 2012.
  [26] H. Syamsuyar, Ikhsan, ?The effect of exchange rate to Indonesia?s economic growth?, ?Dampak sistem nilai tukar terhadap pertumbuhan ekonomi Indonesia?, Jurnal Ilmiah Mahasiswa Ekonomi Pembangunan, Vol.2, Issue.3, pp.414-422. 2017.
  [27] I. Suhendra, D.A. Irawati, ?The effect of savings, government expenditure, and private investment to gross domestic product of Indonesia?, ?Pengaruh tabungan, pengeluaran pemerintah, dan investasi swasta terhadap produk domestik bruto di Indonesia?, Jurnal Ilmu Ekonomi, Vol.6, Issue.2, pp.115-273, 2016.
  [28] J. Ha, J.W. Lee, L. Sumulong, ?ADBI working paper series rebalancing growth in the Republic of Korea?, Asian Development Bank Paper Series, Issue. 224, pp.1-28, 2010.
  [29] K. Mansur, M. Mamalakis, S. idris, ?Savings, investment & FDI contribution to Malaysian economic growth in the globalization era?, International Business and Economic Research Journal, Vol.2, Issue.8, pp.1-14, 2003.
  [30] M. A. Abdullah, Rusdarti, ?The impact of government expenditure on economic growth in Indonesia, Malaysia and Singapore?, Journal of Economic Education, Vol.6, Issue.1, pp. 11-18, 2017.
  [31] M. Kholis, ?The effect of foreign direct investment to Indonesia?s economic growth?, ?Dampak foreign direct investment terhadap pertumbuhan ekonomi Indonesia?, Jurnal Organisasi dan Manajemen, Vol.8, Issue.2, pp.111-120, 2012.
  [32] M. Kogid, R. Asid, J. Lily, D. Mulok, N. Loganathan, ?The effect of exchange rates on economic growth: empirical testing on nominal versus real?, The IUP Journal of Financial Economic, Vol.10, Issue.1, pp.8-17, 2012.
  [33] M. Naseri, N. Zada, ?The Effect of inflation on economic growth; evidence from Malaysia?, International Centre for Education in Islamic Finance, Vol.5, Issue.7, pp.1-14, 2013.
  [34] M.S. Shaari, T.H. Hong, S.N. Sukheri, ?Foreign direct investment and economic growth: evidence from Malaysia?, Vol.5, Issue.10, pp.100-106, 2012.
  [35] R. Maulina, J.F. Salim, R. Juliansyah, ?The effect of inflation rate and unemployment rate to economic growth?, ?Pengaruh tingkat inflasi dan pengangguran terhadap pertumbuhan ekonomi?, Jurnal Ekonomi, Vol.4, Issue., pp.46-54, 2018
  [36] S. Koojaroenprasit, ?The impact of foreign direct investment on economic growth: a case study of South Korea?, International Journal of Business and Social Science, Vol.3, Issue.21, pp.8-19, 2012.
  [37] W. Oh, K. Lee, ?Energy consumption and economic growth in Korea: testing the causality relation?, Journal of Policy Modelling, Vol.26, Issue.8-9, pp.973-981, 2004.
  [38] T. Abeysinghe, T.L. Yeok, ?Exchange rate appreciation and export competitiveness: the case of Singapore?, Applied Economic, Vol.30, Issue.1, pp.51-55, 2010.
  [39] W. Zang, M. Baimbridge, ?Exports, imports and economic growth in South Korea and Japan: a tale of two economies?, Applied Economics, Vol.44, Issue.3, pp.1-12, 2012.
  [40] A. Hasnul, ?The effect of government expenditure on economic growth: the case of Malaysia?, Munich Personal RePec Archive, No. 71254, pp.1-15, 2016.
  [41] C. Hanck, et.al. ?Introduction to econometrics with R?, Essen Publication, Germany, 2019.
  [42] J.W. Lee, ?The Republic of Korea?s economic growth and catch-up: implications for the People?s Republic of China?, ADBI Working Paper Series, Vol. Issue.571, pp.3-33, 2016.
  [43] Population.sg, ?Singapore`s unemployment rate: How low can we go??, Jobs & Economy,

  Citation
  E. Zakchona, P. Sihombing, "Comparison of Macroeconomic Behavior in Some ASIAN Countries (1991 ? 2017)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.35-45, 2020

• Open Access   Article

  Connectedness and Compactness via Ideal

  Rohit Gaur, Anjali Srivastava

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.4 , pp.46-49, Aug-2020

  Abstract

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  References

  Citation

  Abstract
  In this article, we introduce and study α-I-connectedness. Also we extend the concept of compact spaces into a new type of spaces; we call it α-I-compact spaces. And we introduce the notion α-I-separated sets and study some of their basic properties.

  Key-Words / Index Term
  α-I-connectedness, α-I-compactness, α-I-separated sets

  References
  [1]. R. Engelking, ?General Topology?, Second Edition, Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin, 1989.
  [2]. M. E. Abd El-Monsef, A. E. Radwan, and A. I. Nasir, Some generalized forms of connectedness in ideal topological space, Archives Des Sciences, Vol. 66 Issue. 3, pp. 334?342, 2013.
  [3] M. E. Abd El-Monsefa, A. A. Nasefb, A. E. Radwanc and R. B. Esmaeeld, On α-open sets with respect to an ideal, Journal of Advanced Studies in Topology, Vol. 5, Issue. 3, pp. 1-9, 2014.
  [4] Anjali Srivastava and Rohit Gaur, About new sets and topologies in ideal topological spaces, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 7, Issue. 1, pp. 107-110, 2020.

  Citation
  Rohit Gaur, Anjali Srivastava, "Connectedness and Compactness via Ideal," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.4, pp.46-49, 2020