iosr-Jm   Volume-17 ~ Issue-3 ~ May – June 2021

Abstract: In this paper, the effect of perturbation on complete controllability of both linear and non-linear control systems were analysed. It was seen that if a linear system is completely controllable, then the perturbed system is also completely controllable provided that the sum of norm differences of the concerned matrices is as small as possible. For non-linear systems, it was seen that if the system is completely controllable,and the linearization of the perturbing function is stable at the origin, then the perturbed control system is also completely controllable.

Key words: Controllability, Complete Controllability, Linearization, Perturbation.

[1]. S.E. Aniaku: Necessary conditions for controllable systems to be observable. African ournal of Computing and ICT . Vol 7 No 3. Sept. 2014.
[2]. Stephen Barnett: Introduction to Mathematical Control Theory. Clarendon press. Oxford 1975.
[3]. Deuer J.P: Perturbation of Linear Contrl Systems. SIAM J. Control Vol 9 No. 3 (1971), pp 393 - 400.
[4]. R. Kent Nagle, Edward B. Saff: Fundamentals of Differential Equations. Second Edition.The Benjamin Cummings Pub. Com- pany. Inc. Carlifornia, 1989.
[5]. S.E Aniaku Stabilizability of systems with perturbations. Thesis Submitted to Dept. of Maths and Comp. Sc; Faculty of Sciences RSUST, Port-Harcourt 2010.

Abstract: In this paper, we have discussed the future condition of COVID-19 in Bangladesh with graphical trends by analyzing the present situation.It was an exertion to predict the final epidemic conditions by usingthe Susceptible-Infected-Recovered (SIR)model.And by applying the Homotopy perturbation method,we solved the SIR model according to the present data for Bangladesh.The results obtained can undoubtedly predict COVID-19 situations.

Key words: COVID-19,SIR model, WHO

[1]. W. H. Organization et al., "Covid-19 weekly epidemiological update, 23 february 2021," 2021.
[2]. N. C. Peeri, N. Shrestha, M. S. Rahman, R. Zaki, Z. Tan, S. Bibi, M. Baghbanzadeh, N. Aghamohammadi, W. Zhang, and U. Haque, "The sars, mers and novel coronavirus (covid-19) epidemics, the newest and biggest global health threats: what lessons have we learned?" International journal of epidemiology, vol. 49, no. 3, pp. 717–726, 2020.
[3]. M. A. Islam, S. Kundu, S. S. Alam, T. Hossan, M. A. Kamal, and R. Hassan, "Prevalence and characteristics of fever in adult and paediatric patients with coronavirus disease 2019 (covid-19): A systematic review and meta-analysis of 17515 patients," PloS one, vol. 16, no. 4, p. e0249788, 2021.
[4]. M. A. Islam, S. S. Alam, S. Kundu, T. Hossan, M. A. Kamal, and C. Cavestro, "Prevalence of headache in patients with coronavirus disease 2019 (covid-19): A systematic review and meta-analysis of 14,275 patients," Frontiers in neurology, vol. 11, 2020.
[5]. J. Saniasiaya, M. A. Islam, and B. Abdullah, "Prevalence and characteristics of taste disorders in cases of covid-19: A meta-analysis of 29,349 patients," Otolaryngology–Head and Neck Surgery, p. 0194599820981018, 2020

Abstract: This article is aimed at establishing the null - controllability of a non linear control systems in Euclidean space . Sufficient conditions for a non-linear control system to be steered to a zero target by means of Brouwer's Fixed Point Theorem were developed. Thus, by the application of Brouwer's Fixed Point Theorem, it was proved that the non linear control systems......

Key-words: Fixed Point, bounded linear operator, Controllable, admissible

[1]. Chukwu, E.N: On the null-controllability of non-linear delay systems with restrained controls. J. Math. Anal.Appl, 78 (1980) pp 283 - 299.
[2]. Onwuatu J.U: Null-controllability of non-linear infinite Neutral systems.KYBERNETIKA, Vol 29 (1993) No 4. pp 325 - 336.
[3]. Histo.K and Etsujiro.S:On a Null-controllability region of Non-linear systems. Trans. of the Society of Instrument and Control Engineers. Vol E 1, No 1 pp 1 - 5(2001).
[4]. S.E Aniaku and P.C. Jackreece: Null-controllability and Uniqueness of Optimal Trajectory For Controllable Systems.IOSR Journal of Mathematics. Vol 13 Issue 3 Ver V pp 45 - 51 (2017).
[5]. S.E Aniaku, E.C Mbah, P.U Nwokoro, C.N Obi: Null-Controllability For Linear Control Systems Using Fixed Point Theorem. Global Journal Of Pure and Applied Mathematics. Vol 14 No 3 (2018) pp 441 - 418

Abstract: The work in this article is about Group Divisible Designs (GDDs) with three groups of sizes n1, n2 and n3, where n1=3, n2=n and n3=n+1 and block size four. First, we establish necessary conditions for the existence of GDD(3,n,n + 1,4;λ1,λ2): for n1=3,n2=n and n3=n+1. Necessary conditions include an inequality......

Key words: Group divisible designs (GDDs);Balanced incomplete block designs (BIBDs); a Design

[1]. B. Billings, K. Namyalo and D.G. Sarvate, Group Divisible Designs GDD(n1 + n2,3;λ1,λ2) with equal number of blocks of two configurations, JCMCC 102, (2017), 19-44.
[2]. H.L. Fu, C.A. Rodger,Group Divisible Designs with Two Associate Classes, n = 2 or m = 2, Journal of Combinatorial Theory Series A, 83(1), (1998),
[3]. 94-117.
[4]. H.L. Fu, C.A. Rodger, and D.G. Sarvate, The existence of Group divisible designs with first and second associates having block size 3, ArsCombin., 54, (2000), 33-50
[5]. K. Namyalo, D. G. Sarvate and L. Zhang, GDD(n1,n,n + 1,4;λ1,λ2) for n1 = 1 or 2, JCMCCV ol110(2019)19 − 37,

Abstract: This paper presents analytical solutions to oscillatory flow in micro-tube and micro-annulus in the presence of second order velocity slip. The flow is set up as a result of fluctuations of pressure gradient in a sinusoidal form. The condition on which the second order slip is significant in micro-tube and micro-annulus is also established. Result shows that the critical frequency is periodic and also higher for micro-tube than micro-annulus. It is established that the more complicated second order velocity slip should be used for non-critical frequency.

Keywords: Oscillatoryflow; Micro-tube; Micro-annulus; Second order velocity slip

[1]. Schaaf, S.A., Chambre, P.L.: Flow of Rarefied Gases. Princeton University Press, Princeton (1961).
[2]. Sparrow,E. M. Lin,S.H. Laminar heat transfer in tubes under slip-flow conditions,
[3]. ASME J. Heat Transfer 84 (4), pp.363–369 1962.
[4]. Inman, R. M. Heat transfer for laminar slip flow of a rarefied gas in a parallel plate channel or a circular tube with uniform wall temperature, NASA TN, 1964, D-2213.
[5]. Ameel,T.A Barron,R.F. Wang, X. Warrington,R.O. Laminar forced convection in a

Abstract: In this work, a semi-analytical approach is employed to investigate flow formation of time dependent free convection flow in a vertical annulus. The governing momentum and energy equations governing the flow are derived and closed form expressions are obtained in Laplace domain while the Fourier approximation is used in transforming the solutions from Laplace domain to time domain. During the course of investigation of flow formation with time, nature of fluid and ratio of radiuses, it is found that these governing parameters play a major role in the attainment of steady state solution.

Keywords: Annulus; Fourier approximation; Free convection; Asymmetric heating

[1]. El-Shaarawi, M.A.I. and Sarhan, A. (1981).Developing laminar free convection in an open ended vertical annulus with a rotating inner cylinder. Journal of Heat Transfer 103: 552-558.
[2]. Joshi, H, M., (1987). Fully developed natural convection in an isothermal vertical annular duct International Communication in Heat and Mass Transfer.14: 657-664.
[3]. Lein, F.S., Chaó-Kung Cheng and Chang, Y.M.: (1985) Effect of free convection and mass transfer on the flow past an impulsively moving infinite vertical circular cylinder, International Communication in Heat and Mass Transfer.12: 127-137.
[4]. Asmaa, A. H. (2012). Numerical study of mixed convection of air in the entrance region of vertical concentric annulus. The Iraqi Jornal for mechanical and material engineering 12(4): 735- 753.
[5]. Mahmud, S. and Fraser, R. A. (2002). Irreversibility analysis of concentrically rotating annulus. International Communication in Heat and Mass Transfer. 29:697-706.

Abstract: Transaction exposure is a risk faced by the company that while dealing in the international trade, the currency rates may change before making the final settlement. The greater the time gap between the agreement and the final settlement, the higher is the risk associated with the change in the foreign exchange rates. In this paper we explain the effect of Gumbel distribution in the exchange rate error under the linear demand with additive error in newsvendor setting when the retailer or manufacturer undertakes to share the exchange rate risk..

Keywords: Transaction Exposure, Exchange Rate Error, Newsvendor Problem, Optimal Pricing and Quantity, Gumbel distribution

[1]. Arcelus. F.J., Gor R. M., Srinivasan G.,Foreign exchange transaction exposure in a newsvendor setting, European Journal of Operational Research, 227(2013) 552-557
[2]. Sanjay Patel and Ravi Gor, Exchange rate risk sharing contract model, IOSR Journal of Mathematics(IOSRJM), e-ISSN: 2278-5728, p-ISSN: 2319-765X.,Volume11,Issue 2, Version-I (Mar-Apr. 2015),PP 47-52
[3]. Goel, M., 2012. Management of transaction exposure: a comparative analysis of MNCs in India.International Journal of Service Science, Management, Engineering and Technology3, 37–54.
[4]. Eitemann, D.K., Stonehill, A.I., Moffett, M.H., 2010. Multinational Business Finance,12th ed.Prentice Hall, Boston.
[5]. Shubita, M.F., Harris, P., Malindretos, J., Bobb, L.M.,2011. Foreign exchange exposure: an overview. International Research Journal of Finance and Economics 78, 171– 177

Abstract: We consider two Equations of Matiyasevich concerningthe constant and log(π) (binary system) and two other Equations of Keiper (with the primes).
We connect the two systems of Equations and analysewith them the first Li-Keiper coefficient and two specialvalues of integrals over the Zeta function connecting outside and inside of the critical strip (on the Riemann Hypothesis),with a numerical experiment.

Key words: Constants gamma and log(π), Binary system, Primes numbers,Critical strip.

[1]. MatiyasevichY., "Yet another Representation for the Reciprocals of the Non trivial Zeros of the Riemann Zeta Function", Mat. Zametki, 97:3 (2015).
[2]. KeiperJ.B., "Power Series Expansions of Riemann'sfunction": Mathematics, Volume 58, number 198, (1992), pp. 765-773
[3]. VaccaG., "A new series for the Eulerian constant =0.577… ", Quart. J. Pure Appl. Math..41 (1909-1910), pp. 363-366.
[4]. Sondow J., "New Vacca-type rational series for Euler's constant  and its "alternating" analog ln4/", Additive number theory, Springer, New York (2010), pp. 331-340.
[5]. PattersonS.J., An introduction to the theory of the Riemann zeta-function (No. 14). Cambridge University Press. (1995).

Abstract: This paper investigated some algebraic theoretic properties of fuzzy set on.....

Key words: Fuzzy set, Algebraic Sum, Algebraic Product, Bounded Sum, Bounded Difference, Membership function

[1]. Audu M.S. (1986), Generating Sets for Transitive Permutation groups of prime-power order. The Journal of Mathematical
Association of Nigeria Abacus, 17(2), 22-26.
[2]. Aremu K.O., Ejima O, and Abdullahi M. S (2017), On the fuzzy T1 non Deranged Permutation Group of GT1 Asian Journal of
Mathematics and Computer Research, 18, 152-157.
[3]. Cayler A. (1889), The Collected Mathematical Papers of the Arthur Carley II, (1851-1860), Cambridge University Press.
[4]. Garba A. I. and Ibrahim A. A. (2009), A New Method of Constructing a Variety of Finite Group Based on Some Succession Scheme. International journal of physical Science, 2(3),77-79
[5]. Garba A. I. and Ibrahim A. A. (2010), A New Method of Constructing a Variety of Finite Group Based on some Succession Scheme. Internal Journal of Physical science, 2(3):23-26

Abstract: A symbolic model, based on a Continuous Time Markov Chain, is proposed for degrading systems analysis. Three types of degrading systems, namely completely recoverable, partially recoverable and non-recoverable ones, and two types of critical sets of states are defined in terms of this model. It is shown that for the proposed model, analytical expressions for probabilities of being in any possible state at each instant can be derived explicitly. Therefore, analytical expressions for the probability of reaching any set of target states at any instant can also be derived. The problems of computing the probability of reachability the target sets of states, if the values of the parameters are given, are solved.

Key words: degrading systems, finite time horizon, Continuous Time Markov Chains, critical sets of states, reachability of target sets of states

[1]. B. de Jonge, P. A. Scarf. A review on maintenance optimization. European Journal of Operational Research. 2020; 285 (3): 805- 824.
[2]. B. Dowdeswell, R. Sinha, S. G. MacDonell. Finding faults: A scoping study of fault diagnostics for Industrial Cyber-Physical Systems. Journal of Systems and Software. 2020; 168, Article 110638, https://doi.org/10.1016/j.jss.2020.110638
[3]. R. Cassidy, N. S. Singh, P. R. Schiratti, et al. Mathematical modelling for health systems research: a systematic review of system dynamics and agent-based models. BMC Health Services Research. 2019; 19 (845), Article 845, https://doi.org/10.1186/s12913- 019-4627-7
[4]. G. Vanagas, T. Krilavičius, K. L. Mathematical modelling and models for optimal decision-making in health care. Computational and Mathematical Methods in Medicine. 2019. Article 2945021, https://doi.org/10.1155/2019/2945021
[5]. M. A. Hossain, M. Ahmad, M. R. Islam, et al. Mathematical modelling of clinical engineering approach to evaluate the quality of patient care. Health and Technology. 2020; 10: 547–561, https://doi.org/10.1007/s12553-019-00390-9