iosr-Jm   Volume-13 ~ Issue-4 ~ Jul-Aug 2017

Abstract: This paper contains the reviews and descriptions of fundamental results concerning the solutions of some popular linear continuous-time control models with constant coefficients. Different types of stability results are discussed. Fundamental definitions on controllability for finite-dimensional systems are recalled and necessary and sufficient conditions for different types of controllability were given. The paper was concluded, by remarks and comments concerning possible extensions..

Keywords: Distributed parameter systems, controllability, linear system, stability.

[1]. Chen C.T. Introduction to Linear system Theory. Holt, Rinehart and Winston Inc. New York, 1970.
[2]. Kaczorek .T. Linear Control Systems. Research studies Press and John Wiley. New York, 1993
[3]. Klamka .J. System Characteristics: Stability, Controllability, Observability. Control Systems, Robotics and Automation – vol V11
[4]. Lee E.B. and Markus .L. Foundations of Optimal Control Theory. John Wiley and Sons, Inc. New York. London 1967.
[5]. Cao Y, et all Stability Analysis of Linear – time delay systems subject to input saturation. IEE Transaction on Circuits and Systems. 49, PP233 – 240 (2002).

Abstract: Control system is said to be observable if it contains or is coupled to enough information which enables us to determine precisely the relationship between the input and the resulting output variables at any given finite time. Here, we develop certain necessary and sufficient conditions which assure that the following linear control system with input............

Keywords: Characteristic polynomial, controllability, observability

[1]. Hautus M.L.J. Controllability and observability conditions of Linear autonomous systems. Nedrl. Akad, Wetensch, Proc. Ser. A72 (1969) PP 443-448.
[2]. Chukwu E.N. On the null-controllability of non-linear delay systems with restrained controls. J.Math Anal. Appl.78 (1980) pp283-299.
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Abstract: Linear programming plays an important role in our lives, it impact is marked as one of the most important scientific advancement since the nineteenth century. Simplex method is one of the most popular and most important methods of finding the solution to the LP problems. The simplex method in general tends to run in time linear to the number of constraints of the problem but in certain worst cases it tends to run in polynomial time algorithm. This become difficult to the researcher in the first time of its appearance and also shows poor performance in some problems (i.e. Klee and Minty problem)...........

Keywords: Linear programming, Simplex method, Interior point method

[1]. D.S. Hira. and P.K. Gupta. Operations research, Seventh revised Edition 2014. ISBN: 81-219-0281-9
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[4]. E.R. Barnes, A Variation on Karmarkar's Algorithm for Solving Linear Programming problems, Mathematical Programming 36, 1986, p. 174-182
[5]. G.B. Dantzig, linear programming and extension. 1968. Princeton, N. J. Princeton Univ. Press, 1963. ISBN: 0-691-08000-3.

Abstract: Key exchange protocols are a fundamental aspect of information security. A clear understanding of these protocols is required for security practitioners who wish to apply such protocols in SSH, TLS, or similar secure communications protocols. This paper provides a generalized overview of the most widely used key exchange protocols as well as an analysis of any weaknesses in such protocols

Keywords: Diffie-Hellman, MQV, Key exchange, ElGamal

[1] Diffie, W.; Hellman, M. "New directions in cryptography", IEEE Transactions on Information Theory. 22 (6): 644–654, November 1976. doi:10.1109/TIT.1976.1055638.
[2] Steiner, Michael, Gene Tsudik, and Michael Waidner. "Diffie-Hellman key distribution extended to group communication." Proceedings of the 3rd ACM conference on Computer and communications security. ACM, 1996.
[3] Boneh, Dan. "The decision diffie-hellman problem." Algorithmic number theory (1998): 48-63.
[4] Bresson, Emmanuel, et al. "Provably authenticated group Diffie-Hellman key exchange." Proceedings of the 8th ACM conference on Computer and Communications Security. ACM, 2001.
[5] Boyko, V., MacKenzie, P., & Patel, S. (2000). Provably secure password-authenticated key exchange using Diffie-Hellman. In Advances in Cryptology—Eurocrypt 2000 (pp. 156-171). Springer Berlin/Heidelberg.

Abstract: This study addresses the dynamic behaviour of a chemical oscillator. Of particular interest is the study of the associated Hopf bifurcations. Centre manifold theory and normal form theory are employed in this work to analyse the bifurcation and the stability of the Brusselator. Analysis reveals that there is Hopf bifurcation for the oscillator and the equilibrium loses stability and bifurcates into periodic solutions with limit cycles associated with the Brusselator that are always stable.

Keywords: Birfucation, stability, normal, periodic

[1]. G. Nicolis , ii. Prigogine (1977) Self-organizations in Non-equilibrium Systems New York: Wiley-Interscience.
[2]. J.Tyson (1972). Some Further Studies of Non-linear Oscillations in Chemical Systems. Journal of Chemical Physics, 58, 3919-
3930.
[3]. P. Yu and A.B. Gumel (2001), Bifurcation and Stability Analysis for a Coupled Brusselator Model. Journal of Sound and Vibration
244(5), 795-820
[4]. R. Lefever and G. Nicolis (1971). Chemical Instabilities and Sustained Oscillations. Journal of Theoretical Biology, 30,267- 284
[5]. S.wiggins (1990) Introduction to Applied Non-linear Dynamical Systems and Chaos. First Edition Springer-Verlag
[6]. Stephen. K. Scott (1993) Chemical chaos. First Edition Clarendon Press,Oxford.
[7]. Yuri A. Kuznetsov (1998) Elements of Applied Bifurcation Theory, Second Edition, Springer-Verlag, New York.

Abstract: The scope of Operations Research (OR) has changed essentially over the most recent quite a few years. Beginning from Re-order Point (ROP) to Enterprise Resources Planning (ERP) and Supply Chain Management (SCM), OR has experienced far in wording of scope and techniques being utilized. JIT reasoning, lean generation, and coordinated assembling have essentially changed the ways how we plan and investigate the operations. As of late, OR and coordination's fields get nearer, since there is no real way to isolate those capacities any more drawn out from the operational Research process point of view. Conventional OR's focus is going to move from a component of the association to the supply chain, beginning from providers of providers to clients of clients.

Keywords: Scope, Opportunity, Challenges, Operations Research, Supply Chain Management, techniques, function, organization, customers, information, developments, training, leadership, satisfaction, service, technological solutions.

[1]. Mistry N, Tolania M, Osrinb D. Drug-resistant tuberculosis in Mumbai, India: An agenda for operations research. Operations Research for Health Care. Volume 1, Issues 2–3, June–September 2012, Pages 45–53.
[2]. Zachariah R, Harries AD, Ishikawa N, Rieder HL, Bissell K, Laserson K, Massaquoi M, Van Herp M, & Reid T (2009). Operational research in low-income countries: what, why, and how? The Lancet infectious diseases, 9 (11), 711-7.

[3]. Royston G. Meeting global health challenges through operational research and management science. Bulletin of the World Health Organization 2011; 89:683-688.
[4]. Malhotra S, Zodpey S. Operations Research in Public Health. Indian Journal of Public Health. 2010; 54(3): 145-50
[5]. Gillett, Billy E. 2007. Introduction to Operations Research. New Delhi: Tata McGraw-Hill.

Abstract: In this paper...........

Keywords: .........

[1] C. Boonpok, Biminimal Structure Spaces, International Mathematical Forum, 15(5)(2010), 703-707.
[2] T. Fukutake, On generalized closed sets in bitopological spaces, Bull. Fukuoka Univ. Ed. Part III, (35)(1986), 19-28.
[3] R.Gowri, S.Vembu, Soft minimal and soft biminimal spaces, Int Jr. of Mathematical Science and Appl., Vol. 5, no.2, (2015), 447-455.
[4] R.Gowri, S.Vembu, Soft g-closed Sets in Soft Biminimal Spaces, International Journal of Mathematics And its Applications, (5)(2017), 361-366.
[5] B.M Ittanagi, Soft Bitopological Spaces, International Journal of Computer Applications, (107)(7)(2014).
[6] J.C Kelly, Bitopological Spaces, Proc. London Math. Soc., (13)(1963), 71-81. 9.

Abstract: In this paper we introduce the concept of quasi 𝒢-topological simple group. Also some basic properties, theorems and examples of a quasi 𝒢-topological simple groups are investigated. Moreover we studied the important result, If the mapping between two quasi 𝒢-topological simple groups is 𝒢-continous at the identity element, then 𝑓 is 𝒢-continous.

Keywords: Quasi topological group, 𝒢-open set, 𝒢-continous, Quasi 𝒢-topological simple gr oup..

[1]. A.V.Arhangel'skii, M.Tkachenko, Topological Groups and Related Structures, At- lantis press/world Scientific, Amsterdampairs, 2008.
[2]. C.Selvi, R.Selvi, On Generalized Topological Simple Groups, Ijirset Vol.6, Issue 7, July (2017).
[3]. Muard Hussain, Moiz Ud Din Khan, Cenap Ozel, On generalized topological groups, Filomat 27:4(2013),567-575
[4]. Dylan spivak, Introduction to topological groups, Math(4301).
[5]. J. R. Munkres, Topology, a first course, Prentice-Hall, Inc., Englewood cliffs, N.J.,1975.

Abstract: In this current work, we compute the general solution and determine the Hyers-Ulam stability for a new form of Viginti duo functional equation in Multi-Banach Spaces by using xed point technique.

Keywords: Hyers-Ulam stability, Multi-Banach Spaces, Vigintic duo Functional Equations, Fixed Point Method.

[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64-66.
[2] M. Arunkumar, A. Bodaghi, J. M. Rassias and E. Sathiya, The general solution and approximations of a decic type functional equation in various normed spaces, J. Chungcheong Math. Soc., 29 (2) (2016).
[3] P. Gavruta,A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184, no. 3 (1994) 431{436.
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[5] Dales, H.G and Moslehian, Stability of mappings on multi-normed spaces, Glasgow Mathematical Journal, 49 (2007), 321-332.

Abstract: In this paper, we studied the dynamics of typhoid fever model; we tested for theexistence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the disease free equilibrium (DFE) and the endemic equilibrium (EE) for the system of the equation. The local stability of the disease free equilibrium was obtained. The next generation approach is used to determine the basic reproductive number R0. We proved that the disease free equilibrium is globally asymptotically stable when R0 <1 and the disease will always die out.

Keywords: Basic reproduction number, equilibrium states, existence and uniqueness of solution, mathematical model, typhoid fever;

[1]. Lauria D. T., Maskery B, Poulos C., and Whittington D., An optimization model for reducing typhoid cases in developing countries
without increasing public spending, Vaccine, JVAC-8805 (2009). http://dx.doi.org/10.1016/j.vaccine.2008.12.032
[2]. World Health Organisation(WHO/V and B/03.07),2003. Background document: The diagnosis, treatment and prevention of typhoid
fever.www.who.int/vaccines-document/
[3]. Adetunde, I. A, 2008. Mathematical models for the dynamics of typhoid fever in kassena-nankana district of upper east region of
Ghana. J. Modern Math Stat., 2: 45-49
[4]. Joshua and Etukudo Mathematical model of the spread of Typhoid fever, World Journal of Applied Science and Technology Vol.
3. No. 2(2011). 10-12
[5]. Kalajdzievska, D. and LI, M. Y, "Modeling the effects of carriers on transmission dynamics of infectious disease", Math. Biosci.
Eng., 8(3):711-722, 2011, http://dx.doi.org/10.39 34/mbe.2011.8.711

Abstract: In this paper we investigate several decomposition formulas associated with hypergeometric functions A H in three variables. Many operator identities involving these pairs of symbolic operators are first
constructed for this purpose. By means of these operator identities, as many as 5 decomposition formulas are then found, which express the aforementioned triple hypergeometric functions in terms of such simpler functions as the products of the Gauss and Appell hypergeometric functions.

Keywords: Decomposition formulas; hypergeometric functions; Multiple hypergeometric functions; Gauss hypergeometric function; Appell's hypergeometric functions

[1]. J.L. Burchnall, T.W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940) 249–270.
[2]. J.L. Burchnall, T.W. Chaundy, Expansions of Appell's double hypergeometric functions. II, Quart. J. Math. Oxford Ser. 12 (1941) 112–128.
[3]. T.W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942) 159–171.
[4]. T.W. Chaundy, On Appell's Fourth Hypergeometric Functions. The Quart. J. Mathematical oxford (2) 17 (1966) pp.81-85.
[5]. H. Exton, On Srivastava's symmetrical triple hypergeometric function B H , J. Indian Acad. Math. 25 (2003) 17–22.

Abstract: To analyze single data set-based benchmark experiments using R. Exploratory and inferential methods are used to compare the distributions and to finally set up mathematical (order) relations between the algorithms. I reviewed the theoretical framework of the current work for inference problems in benchmark experiments. Benchmarking UCI and Grasshopper domains presented two domain-based benchmark experiments. A large number of regression diagnostic tests showing the problems and solution of diagnostics and procedures and Outlier diagnostics and procedures have been proposed in the econometrics literature. MATLAB and Gauss code for implementing these methods can be found on many sources

Keywords: Benchmarking, R, Grasshopper and UCI domain, Regression, Matlab, Outlier diagnostics.

[1]. Gilks, W.R., S. Richardson and D.J. Spiegelhalter. 1996. Markov Chain Monte Carlo in Practice, (London: Chapman & Hall).
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Abstract: This article discusses the mathematical model of SEIRS-SEI type malaria disease. Modification of the model is done by giving the treatment in humans, in the form of vaccines and anti-malarial drugstreatment. In this model, the human population is divided into four classes, namely susceptible human, exposed human, infected human, and recovered human. The mosquito population is divided into three classes, namely susceptible mosquito, exposed mosquito and infected mosquito. Furthermore, the analysis of the model to show..........

Keywords: Epidemic Model, Malaria, SEIRS-SEI model, Treatment, Vaccines

[1] Laarabi, H., Labriji, E.H., Rachik, M., and Kaddar, A., Optimal Control of an Epidemic Model with A Saturated Incidence Rate, Modelling and Control, .17(4),2012, 448-459.
[2] Putri, R.G., Jaharuddin, and Bakhtiar, T., SIRS-SI Model of Malaria Disease with Application of Vaccines, Anti-Malarial Drugs, and Spraying, IOSR Journal of Mathematics (IOSR-JM), Vol.10, Issue V Ver. II, 2014.
[3] Chitnis, N., Chussing, J.M., and Hyman, J.M., 2006, Bifurcation Analysis of A Mathematical Model for Malaria Transmission, Siam J. Appl. Math. 67( 1), 2006, 24–45
[4] Bloland, P.B., and Williams, H.A.,Malaria Control During Mass Population Movements and Natural Disasters,(Washington, The National Academies Press, 2002)
[5] Schwartz, L., Brown, G.V., Genton, B., and Moorthy, V.S., A Reiew of Malaria Vaccine Clinical Projects Based on the WHO Rainbow Table. Malaria Journal, 11(11), 2012

Abstract: In this paper we establish Common fixed point theorem for six mappings in Menger spaces by using implicit relation under the notion of sub compatibility and sub sequentially continuity.

Keywords: Menger space, Compatibility, Sub compatibility, Reciprocal continuity, Sub sequentially continuity, Common fixed point.

[1] Ali J., Imdad M. and Bahaguna D., Common fixed point theorems in Menger spaces with common property (E.A.) Comput. Math. Appl. 60(12) (2010), 3152-3159.
[2] Ali J., Imdad M., Mihet D. and Tanveer M. Common fixed points of strict contractions in Menger spaces, Acta Math. Hungar. 132(4) (2011), 367-386.
[3] BouhadjeraH.,andDjoudi A., Common fixed point theorems for subcompatible D-maps of integral type. General Math. 18(4) (2010), 163-174.
[4] BouhadjeraH.,andGodet-Thobie C., Common fixed theorems for pairs of subcompatible maps, arXiv:0906.3159v 1[math. FA] 17 June (2009) [Old version].
[5] BouhadjeraH.,andGodet-Thobie C., Common fixed theorems for pairs of subcompatible maps, arXiv:0906.3159v 2[math. FA] 23 May (2011) [New version].