iosr-Jm   Volume-17 ~ Issue-1 ~ Jan. – Feb. 2021

Abstract: The paper analyzes the representation of even number as a sum of two odd summands. To describe even numbers and their representations, arithmetic progressions of a special kind are used, which allow us to divide
(split) the set of even numbers into classes, in each of which the representation depends on a small number of generators. On this basis the proof of Goldbach's binary conjecture is given. The connection of this conjecture
with other problems of number theory is considered..

Keywords and phrases: number theory, prime numbers, Goldbach's binary conjecture. Classification code: 11A41 – Primes; 11D85 – Representation problems

[1]. Deshouillers J.–M., Riele H.J.J.te., Sauoter Y. New experimental results concerning the Goldbach conjecture. Amsterdam: Stichting math. centrum, 1998.
[2]. Granville A., Lune J. van de., Riele H.J.J.te. Checking the Goldbach conjecture on a vector computer. Amsterdam: Stichting math. centrum, 1988.
[3]. Jutila M. On the least Golbach's number in an arithmetical progression with a prime difference. Turku, 1968.
[4]. Romanov V.N. Method for solving the Goldbach binary problem. IOSR Journal of Mathematics, V. 16, Issue 3 (Ser. II), 2020, pp. 13 – 18.
[5]. Romanov V.N. Study of fundamental problems of number theory. Saint-Petersburg, Publishing house "Asterion", 2015 (in Russian).

Abstract: Fundamental Analysis combines economic, industry and company analysis to obtain stock's fair value called underlying value. Technical Analysis is the observation of trading opportunities on the basis of market activity. In this work, we use two fundamental parameters, Earnings Per Share and Price-to-Earnings Ratio to identify profitable stock. Commodity Channel Index (CCI) and Double Exponential Moving Average (DEMA) are used to examine the buying and selling opportunities and to identify the trend strength. We try to develop Elliott wave formation through Commodity Channel Index and introduce the concept of combining the two strategies using a live example from the NSE.

Keywords and phrases: Elliott Wave theory, Commodity Channel Index, Double Exponential Moving Average

[1]. Vaghela V.&Gor, R. (2020) Market Direction by combining Elliott Wave Theory with Sentiment Indicator. Alochnachakra, Vol 9(6), 5794-5797.
[2]. Panchal M.&Gor, R. (2020) Numeric form of Technical Analysis based on Mean Reversion. Alochnachakra, Vol 9(6), 5789-5793.
[3]. Singh, A., &Gor, R. (2020) Relevancy of pricing European put option based on Gumbel distribution in actual market. Alochanachakra. Vol 9(6), 4339-4342.
[4]. Maitah, M., Prochazka, P., Cermak, M., &Šrédl, K. (2016). Commodity channel index: Evaluation of trading rule of agricultural commodities. International Journal of Economics and Financial Issues, 6(1), 176-178.
[5]. Naved, M., & Srivastava, P. (2015). Profitability of Oscillators used in Technical Analysis for Financial Market. Advances in Economics and Business Management (AEBM) Print ISSN, 2394-1545..

Abstract: The objective of this study was to evaluate the financial performance of renewable energy vehicle enterprises. First, we chose fourteen critical financial indicators reflecting profitability, growth capacity, operational capacity, and solvency from the financial statements of fifteen renewable energy vehicle companies in 2019. Next, we performed a factor analysis to construct a financial performance evaluation system using IBM SPSS Statistic 26. Finally, we analyzed the three extracted factors and the factors scores for each observation to study the companies' financial performance..

Keywords: Financial Performance; Factor Analysis; Evaluation System; Renewable Energy Vehicle Companies.

[1]. Bosilj. Vukšić, Vesna, and Mojca Indihar‐Štemberger. "The impact of business process orientation on financial and non‐financial performance." Business Process Management Journal (2008).
[2]. Richard A. Johnson, Dean W. Wichern.Applied Multivariate Statistical Analysis[M]. Prentice Hall: NJ, USA,2007.
[3]. SINA NET FINANCE, "Stock SINA FINANCE," Dec. 12, 2020. [Online]. Available: https://finance.sina.com.cn/stock/.
[4]. Ritchie, William J., and Robert W. Kolodinsky. "Nonprofit organization financial performance measurement: An evaluation of new and existing financial performance measures." Nonprofit Management and Leadership 13.4 (2003): 367-381.
[5]. Dumitrescu, Luigi, Mihai Ţichindelean, and Simona Vinerean. "Using factor analysis in relationship marketing." Procedia Economics and Finance 6 (2013): 466-475.

Abstract: An unification of the circular and hyperbolic functions is proposed. The q-analysis is performed to obtain q-extension of more general function. The general function produces circular and hyperbolic functions as
different states of the unified function. q- De Moivre formula and q- Euler formula for unified function are proposed..

Keywords: q-extension, unification of trigonometric functions, q- De Moivre formula, q- Euler formula for unified function PACS: 02.90.+p, 05.90.+m, 01.90.+g

[1]. Gauss, C. F. (1813). Disquisitiones generales circa seriem infinitam ... , Comm. soc. reg. sci. Gott. rec., Vol. II; reprinted in Werke 3 (1876), 123-162
[2]. Heine, E. (1846). Uber die Reihe ... , J. reine angew. Math. 32, 210-212.
[3]. Tsallis C 1994 Quimica Nova 17 468–71
[4]. E. P. Borges 1998 J. Phys. A. Math. Gen. 31 5281-5288
[5]. José M. Amigó , Sámuel G. Balogh and Sergio Hernández Entropy 2018, 20, 813

Abstract: A three-parameter univariate distribution is presented named Logistic Weibull distribution along with its relevant properties like cumulative distribution function, probability density function, survival and hazard rate
function. Parameter estimation methods like maximum likelihood estimation (MLE) are discussed and applied for the estimation of purposed parameter distribution. With the help of a real dataset, the distribution's
goodness-of-fit has been evaluated in comparison to other existing distributions.......

Key Word: Estimation method, Goodness-of-fit ,Logistic distribution, , MLE ,Weibull distribution

[1]. Chaudhary, A.K. & Kumar, V. (2020). Logistic Inverse Exponential Distribution with Properties and Applications. International Journal of Mathematics Trends and Technology (IJMTT), 66(10), 151-162.
[2]. Chaudhary, A.K. & Kumar, V. (2020).A Study on Properties and Applications of Logistic Modified Exponential Distribution. International Journal of Latest Trends in Engineering and Technology (IJLTET), 17(5).
[3]. Chaudhary, A.K. & Kumar, V. (2020). The Logistic NHE Distribution with Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(12), 591-603.
[4]. Chaudhary,A.K.& Kumar, V.(2020). A Study on Properties and Goodness-of- Fit of The Logistic Inverse Weibull Distribution. Global Journal of Pure and Applied Mathematics(GJPAM),16(6),871-889.
[5]. Gupta, R. D., & Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137(11), 3537-3547.

Abstract: Mohand transforms are very useful integral transforms for solving many advanced problems of engineering and sciences like heat conduction problems, vibrating beams problems, population growth and decay problems, electric circuit problems etc. In this article,we present a reliable combination of homotopy perturbation method and Mohandtransform (MHPM) to solve Burger's equations ,the nonlinear terms in the equations can be handled by using of homotopy perturbation method(HPM). The results show that the new method is more effective and convenient to use and high accuracy of it is evident...

Keywords: Mohand Transform, Homotopy Perturbation method, Burgers equation, Nonlinear Partial differential equation

[1]. J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Nonlin. Mech. 35 (2008), 37-43.
[2]. Bateman, Some recent researches on the motion of fluids, Mon. Wea. Rev., 43 (1915), 163-170.
[3]. Burger, J. M., Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion, Trans. Roy. Neth. Acad. Sci., 17 (1939), 1-53.
[4]. M. M. Mahgoub, The New Integral Transform "Mohand Transform " , Advances in Theoretical and Applied Mathematics , Vol.12, No.2, 2017,pp. 113-120.
[5]. Mahgoub, M.A.M., The new integral transform "Mahgoub Transform", Advances in Theoretical and Applied Mathematics, 11(4), 391-398, 2016.

Abstract: This study revealed that ischemia and hypoxia are the forms of stress present in soft tissue cells that can lead to cellular injury. The study also explained that cellular injuries exhibit viscoelastic properties in the body of the living organisms as cells are damaged. The analytic solution showed that the magnitude of ischemia and hypoxia that led to cellular injury was 270 kN and the time taken for the dead cells to escalate was three months and one week. The solution showed that the environmental factor that affected the cellular injury that led to escalation of dead cells to cellular injury was temperature given as  between 0 0 80  100 c. The model result also showcased that the amplitude of the hypoxia...........

Keywords: Cellular Injury, Stress, Ischemia, Hypoxia, Apotosis, Necrosis, Cell death.

[1]. Ahn, J.and Ambrosone, C. B. (2006). Oxidative Stress and Breast Cancer in Oxidative Stress, Disease and Cancer, 897-931.
[2]. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. & Watson, J. D. (1994). Molecular biology of the cell. New York: Garland.
[3]. Amadi –ikpa, K.A. and Okonkwo, C.A. (2018). Cellular Signalling and Carcinogenosis. Monograph.
[4]. Aminetzach, Yael T.; Macpherson, J. Michael; Petrov, Dmitri A. (2005). "Pesticide Resistance via Transposition-Mediated Adaptive Gene Truncation in Drosophila". Science (Washington, D.C.: American Association for the Advancement of Science) 309 (5735):764–767. Bibcode:2005Sci...309..764A. doi:10.1126/science.1112699. ISSN 0036-8075. PMID 16051794.
[5]. Blokhina, O. and Fagerstedt, K (2006): Oxidative Stress, Disease and Cancer: Oxidative Stress and Antioxidant Defenses in Plants. pp151-199.

Abstract: The aim of this paper is to find a formula for a topology J on X such that any extremal topology on is an ideal extension to for some ideal on . Characterizations related to such ideals are also discussed

Keywords: Extremal topology, filter, ultrafilter, ideal, ideal extension

[1]. John L. Kelley, General Topology, Springer- Verlag 1955.
[2]. Kherie M. Mera and Mabruk A. Sola, Extremal Topology, Damascus University Journal for basic science, vol.21, No1, 2005.
[3]. Sola, M. A. and Najm M. S, On Extremal Topology, The Libyan Journal of Sicience,19B,39-42, 2016.
[4]. Vaidyanathaswamy, R., Set Topology, Chelsea Publishing Company, 1946.

Abstract: Based on the current situation of environmental pollution in the Changbai Mountain Area, the maximum safe level of plastic in the Changbai Mountain Area is estimated with the help of environmental Kuznets curve, and suggestions are made to reduce the plastic pollution in the Changbai Mountain Area to make it reach the safe level

Keywords: plastic pollution；environmental Kuznets curve; ternary linear regression.

[1]. Xu Dongyu, Ma Yunchi. Environmental pollution in the tourism development of Changbai Mountain[J]. Cooperative Economy and Technology,2017,(09):38-39.
[2]. Huang LIA, Zhang RUI, Chen QH. The current situation of resource development and ecological environmental protection in Changbai Mountain area[J]. Environment and Development,2019,31(11):183-184.
[3]. WU Bing,LIU Yanjun,LI He. Exploring the idea of ecological protection and restoration of mountains, forests, fields, lakes and grasses in Changbai Mountains, Jilin Province[J]. Environment and Development,2019,31(09):207-208+210.
[4]. Meng Fansheng, Chen Jinlan. An analysis of the problems of ecological environment and protection measures in Changbai Mountain area [J]. Jilin Forestry Science and Technology,2004,(06):32-34.
[5]. Chen ZK, Cen Q. The application of mathematical simulation modeling in the empirical study of ecological environment--Zhoushan as an example[J]. Technology Economics and Management Research,2012,(01):27-30.