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• Open Access   Article

  Malaria Transmission Dynamics Incorporating Asymptomatic Human Compartment

  Joseph Caleb Shaorga

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.1-10, Jun-2022

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  Abstract
  This research work presents a six-dimensional system of ordinary differential equations that captures dynamics of malaria incorporating asymptomatic human compartment. The model was analyzed for the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The next generation matrix technique is employed to obtain an explicit formula for the reproduction number a threshold parameter for the model. The model result show that the DFE is asymptotically stable when reproduction number is less than one and unstable otherwise. The existence of a unique endemic equilibrium point when reproduction number is greater than one is also determined. The numerical simulations were performed to confirm analytic results that shows increased proportion of recovered humans when both asymptomatic and infected humans are given equal consideration for treatment.

  Key-Words / Index Term
  Malaria, Susceptible, Infected, Asymptomatic, Local stability, Antibody, Basic Reproduction Number, Incidence rate, Force of Infection, and Saturated Incidence Rate

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  Citation
  Joseph Caleb Shaorga, "Malaria Transmission Dynamics Incorporating Asymptomatic Human Compartment," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.1-10, 2022

• Open Access   Article

  Various AntimagicLabeled Graphs from Graph Theory for Cryptography Applications

  Dharmendra Kumar Gurjar, Auparajita Krishnaa

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.11-18, Jun-2022

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  Abstract
  Cryptography is a field essentially concerned with sending the original message in a hidden way from the first partyto the second party such that the unwanted third party cannot understand it. For this purpose, various mathematical concepts, especially from Graph Theory have been introduced in the field of Cryptography for the purpose of safer transfer of data. Hiding of the original plain-text message is called encryption resulting in a cipher-text and deciphering the cipher-text to get back the original plain-text is called decryption. Using labeled graphs is an emerging area for cryptographic applications. Antimagic labeling is a type of graph labeling scheme and in this paper, various antimagic labeled graphs have been used for different encryption techniques for an enhanced security in data transfer.

  Key-Words / Index Term
  Antimagiclabeling, Centreless Wheel-2, Degree Matrix, Double Wheel, Helm,Laplacian Matrix, Path, Web, XOR operation.

  References
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  Citation
  Dharmendra Kumar Gurjar, Auparajita Krishnaa, "Various AntimagicLabeled Graphs from Graph Theory for Cryptography Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.11-18, 2022

• Open Access   Article

  The Alternative from Regression Curve Estimation using Mixed Fourier Series and Epanechnikov Kernel (MFs-EK) Model

  A.T.R. Dani, L. Ni’matuzzahroh, U.S. Nuraini, N.Y. Adrianingsih

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.19-25, Jun-2022

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  Abstract
  Nonparametric regression approach is generally used to avoid assumption of certain regression curve shape. Nonparametric regression has several estimators include Fourier Series (FS) and Kernel estimator. The Fourier Series estimator can adapt effectively to character of the data and kernel estimator is one of best convergence speed. In this study, the research proposed the alternative model in estimating the shape of the nonparametric regression curve using Mixed Fourier Series and Epanechnikov Kernel (MFs-EK) model. The alternative model has obtained a parameter estimate using Maximum Likelihood Estimation (MLE). Last, this study describes the estimator properties of the MFs-EK model. The proposed can be used for further analysis in nonparametric regression field.

  Key-Words / Index Term
  Fouries Series Estimator, Kernel Estimator, Mixed Estimator, Nonparametric Regression

  References
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  [29] Rahmat Hidayat, I Nyoman Budiantara, Bambang Widjanarko Otok, Vita Ratnasari, “Kernel-Spline Estimation of Additive Nonparametric Regression Model,” IOP Conference Series: Materials Science and Engineering, vol. 546, no. 5, 2019
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  Citation
  A.T.R. Dani, L. Ni’matuzzahroh, U.S. Nuraini, N.Y. Adrianingsih, "The Alternative from Regression Curve Estimation using Mixed Fourier Series and Epanechnikov Kernel (MFs-EK) Model," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.19-25, 2022

• Open Access   Article

  Putting Forward a Theorem Based On the Lobachesky Integration Formula

  Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.26-30, Jun-2022

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  Abstract
  with the help of this paper a new formula related to integration is proposed, there are various integral formulas which helps us in solving different types of problems, some of them also helps in giving generalization to some well-known results as Lobachesky Integration Formula helps us in providing, , etc. from the time of Dirichlet, Dirichlet’s Integral are equally popular among mathematicians, Undergraduates, Graduates, Professors and others having knowledge of definite Integration so, everyone who knows definite integration can understand properly. The main formula is not too difficult for proving by anyone, from the point of view of the author but the problem that suddenly strikes in the mind of the author is not that possible to everyone. but he didn’t answer the problem and was also not able to find any clue regarding it, one day he got Lobachesky Integration Formula and answer that problem which was not answered by him at that time.

  Key-Words / Index Term
  Improper Integral, Definite Integral, Convergent and Divergent Integrals, Maz Identity, Integration by Parts, Dirichlet Integral etc.

  References
  [1] A.R Vasishtha “Text Book Integral Calculus BSc. Mathematics-1, part-B”.Krishna Publication p. I-60, 2021
  [2] A.R Vasishtha and others“Text Book Integral Calculus BSc. Mathematics-1, part-B.” Krishna Publication p. I-68. 2021
  [3] G.H.Hardy “The Integral from 0 to infinite sin^2x/x^2”. The Mathematical Gazette, Vol. 5, No. 80 pp. 98–103 , 1909.
  [4] Dixon. A. C “Prove that The Integral from 0 to infinite sin^2x/x^2” The Mathematical Gazette, Vol. 6, No. 96 pp. 223–224 (January 1912),.
  [5] Hassan Jolany “An extension of Lobachevsky formula” Elemente der Mathematik, European Mathematical Society, Vol. 73 issue 3, pp.89 - 94, 2018.

  Citation
  Toyesh Prakash Sharma, "Putting Forward a Theorem Based On the Lobachesky Integration Formula," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.26-30, 2022

• Open Access   Article

  Ikuemuya’s Formula III: An Alternative Formula to the Law of Cosines for The Computation of Magnitude of Resultant Vector

  O.E. Ikuemuya

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.31-34, Jun-2022

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  Abstract
  This paper presents a simple formula for the use in Mathematics, Physics and Engineering in solving geometry related problems. It is a simple alternative formula to the law of cosines for use in the computation of magnitude of resultant vector in geometry. The formula is named the Ikuemuya’s formula III. It is simple and less cumbersome than the usual law of cosines and it does not involve the finding of squares and square roots of numbers when used in the computation of magnitude of resultant vectors as common with the law of cosines, it only makes use of basic arithmetic operation like addition, subtraction and multiplication, and the magnitude of the resultant vector can be computed quite easily.

  Key-Words / Index Term
  Alternative formula, Average constant factor, Ikuemuya’s formula III, Law of cosines, Magnitude of resultant vector, Non-perfect squares.

  References
  [1] CK-12 flexbook, “Resultant as magnitude and direction”, chap. 5, 2016
  [2] Lawrence S. Leff, Barron’s Educational series, pp.326, 2005.
  [3] Kevin K. Ferland, “Extending two classic proofs of the Pythagorean theorem to the law of cosines”, JSTOR, published by Taylor&Francis, Ltd. Vol 90, No 3 pp.182-186, 2017.
  [4] Fl01000126.schoolwires.net, “Additional Topic in Trigonometry”, chapter 6, section 2, pp.657
  [5] Jarno Mielikainen, “A novel full-search vector quantization algorithm based on the law of cosines”, IEEE signal processing letters 9 (6), 175-176, 2002.
  [6] RB Kershner, “The law of sines and law of cosines for polygons”, mathematics magazines 44 (3), 150-153, 1971.
  [7] M. W Anyakoha, New school Physics for senior secondary schools, pp. 113, 2010 edition.
  [8] O.E Ikuemuya, “Accessible formulas for computing the magnitude of Resultant vector in 2 and 3-Dimensions”, International journal of scientific Research in mathematical and statistical sciences, Vol 9, issue 1, pp. 7-13, 2022.

  Citation
  O.E. Ikuemuya, "Ikuemuya’s Formula III: An Alternative Formula to the Law of Cosines for The Computation of Magnitude of Resultant Vector," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.31-34, 2022

• Open Access   Article

  (k, d) Graceful Labelling of Some New Families of Graphs Derived from Cyclic Firecrackers

  Dedas Mishra, Gobind Mohanty, Subarna Bhattacharjee

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.35-42, Jun-2022

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  Abstract
  A graph H containing t edges is said to possess a (k,d) graceful labelling if there exist positive integers k and d and an injection f? V (H)?{0,1,..,k +(t-1)d} so that the mapping g? E(G) ?{k+sd,s =0,1,2,…t-1} defined by g(x,y) = |f(x) - f(y)|, for any (x,y) ?E(G), is surjective. A cyclic firecracker is a graph which is denoted as C_n? K_(m_i,1,1),i = 1,2,...,n, m_i ?0 is a graph consisting of one cycle C_n and each vertex of C_n is attached to the center of some star. Here we identify a family of (k,d) graceful graphs derived from cyclic firecrackers.

  Key-Words / Index Term
  (k, d)-graceful Labeling, firecracker, cyclic firecrackers.

  References
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  Citation
  Dedas Mishra, Gobind Mohanty, Subarna Bhattacharjee, "(k, d) Graceful Labelling of Some New Families of Graphs Derived from Cyclic Firecrackers," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.35-42, 2022

• Open Access   Article

  Application of GARCH Model for Accuracy Measures of Some Components of the Nigeria Economy

  L. Nkpordee, I.M. Ogolo

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.43-60, Jun-2022

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  Abstract
  The use of the GARCH model for accuracy measures of some components of the Nigerian economy was investigated in this study. Its goal was to create a GARCH model that could be used to forecast the Nigerian economy. The statistical database website of the Central Bank of Nigeria (CBN) was used to gather data for this study (www.cbn.gov.ng). Monthly capital formation, gross domestic product, labor force, savings accumulation, and capital market are among the variables from (2001-2021). The parameters that make up the GARCH model and the model selection criteria were obtained using the Gretl 19c and Minitab 16 programs (AIC, BIC, LHC, HQC, R2, R2-Adjusted, SSE and MSE). The GARCH model with the biggest effects on the Nigerian economy based on actual data is GARCH(1,1) from savings accumulations (SA), because all of its parameters are significant at 5% and 10%, and all of its model selection criteria are smaller and better than the other four GARCH models. This means that the impact of savings accumulations on the Nigerian economy is greater than the impact of other components. It was suggested that policymakers, investors, financial analysts, and economists investigate appropriate measures to improve saving accumulation stability because it has a greater impact on the Nigerian economy than other aspects considered in this study.

  Key-Words / Index Term
  Accuracy Measures; Nigeria Economy; GARCH Model; Heteroscedasticity; Time Series Analysis

  References
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  [13] A. Abduikareem, K.A . Abdulhakeem, “Analyzing oil price – macroeconomic volatility in Nigeria,”. CBN Journal of Applied Statistics, Vol.1, Issue.a, pp.15-31, 2016.
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  Citation
  L. Nkpordee, I.M. Ogolo, "Application of GARCH Model for Accuracy Measures of Some Components of the Nigeria Economy," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.43-60, 2022

• Open Access   Article

  Diverse Exponential Type Estimators for Estimating Population Means in Simple Random Sampling

  Sangeeta Malik, Megha

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.3 , pp.61-65, Jun-2022

  Abstract

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  Abstract
  Small area estimation techniques are used for estimating the population means to give good estimates in agriculture field like estimates of crop yield. This article advises fresh exponential type estimators for small area to appraise the mean of the finite population expending information on single auxiliary variable. The bias and mean square error of these estimators have been obtained. These estimators are compared for their precision with usual mean per unit, ratio estimator, product estimator and some of other existing estimators and are found to be more efficient in many practical situations. Further, it is shown that these estimators reduce to regression estimator. Numerical results of the efficiency of the proposed estimators as percent relative efficiencies (PRE) are displayed to confirm the cases of superiority of the proposed estimators with exciting estimators.

  Key-Words / Index Term
  Small area, Estimators, Mean Square Error, PRE

  References
  [1] Singh G, Singh RK, Kaur P. “Estimating Ratio of Proportions Using Auxiliary Information”. Biometrical J. 28: 637–643, 1986.
  [2] Naik VD, Gupta PC. “A note on estimation of mean with known population proportion of an auxiliary character”. Journal Indian Soc Ag
  [3] Bahl, S. and Tuteja, R.K. “Ratio and product type exponential estimators”. Information and Optimization Sciences, 12(1), 159-163, 1991.
  [4] Singh, R. and N.S. Mangat. “Elements of Survey Sampling”, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  [5] Singh H.P., and Vishwakarma G.K. “Modified exponential ratio and product estimators for finite population mean in two phase sampling”, Austrian Journal of Statistics 36(3):217–225, 2007.
  [6] Singh, R., Kumar, M., Singh, R.D., and Chaudhary, M.K.(2008). “Exponential Ratio Type Estimators in Stratified Random Sampling”, Presented in International Symposium On Optimisation and Statistics (I.S.O.S), A.M.U., Aligarh, India, 29-31 Dec2008.
  [7] Singh, R., Kumar, M., Chaudhary, M.K., Kadilar, C. “Improved Exponential Estimator in Stratified Random Sampling”, Pak. J. Stat. Oper. Res. 5(2), pp 67- 82, 2009.
  [8] H. P. Singh , R. Tailor, and N. K. Jatwa, “Modified ratio and product estimators for population mean in systematic sampling,” Journal of Modern Applied Statistical Methods, vol. 10, no. 2, pp. 424–435, 2011.
  [9] Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables, Italian Journal of Pure and Applied Math, 28, 103-110, 2011.
  [10] Kumar, Mukesh et al. “Exponential Ratio Method of Estimation in the Presence of Measurement Errors”. Int. J. Agri. Statist. Sci, 7(2): 457–461, 2011.
  [11] Shabbir, J. and Gupta, S. (2011). On Estimating finite population mean in simple and stratified random sampling, Commun. Stat. Theory and Methods 40: 199-212, 2011
  [12] Solanki RS, Singh HP. Improved estimation of population mean using population proportion of an auxiliary character. Chil J Stat. 2013; 4: 3–17
  [13] Malik S, Singh R. An improved estimator using two auxiliary attributes. Appl Math Comput. 2013; 219: 10983–10986.
  [14] Tailor Rajesh, Mishra Asha, “An Exponential Strategy for Estimation of Population Mean in Systematic Sampling” Vol.5 , Issue.3 , pp.73-78, Jun-2018
  [15] Onyango R., Oduor B., Odundo F., “Enhanced Estimation of Population Mean in Presence of Errors on a Survey Variable in Stratified Two Phase Sampling”, International Journal of Scientific Research in Mathematical and Statistical Sciences Volume-9, Issue-1, pp.32-39, February 2022.
  [16] Megha, Sangeeta Malik, (2022). Generalized Composite Regression with Ratio and Product Estimators in Double Sampling. International Journal of Scientific Research in Mathematical and Statistical Sciences, 9(2), 31-35, 2022.

  Citation
  Sangeeta Malik, Megha, "Diverse Exponential Type Estimators for Estimating Population Means in Simple Random Sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.3, pp.61-65, 2022