iosr-Jm   Volume-15 ~ Issue-2 ~ March-April 2019

Abstract: A model for the transmission dynamics of HIV/TB co-infection with controls in a HIV endemic area was formulated using differential equations. The effect of post-exposure prophylaxis was recognized and considered. The parameters responsible for the diseases spread were analyzedin other to find the most sensitive of them all. The effective basic reproduction number, 0 R of the systems was obtained and shown that the disease will spread only if R0 1 and would die off with time if 1. 0 R  Numerical Simulations carried out using MATLAB on the model showed the dynamics of the infection in each class and also the impact of the variations of the control parameter values in the various classes.

Key Word: HIV endemic area, post-exposure prophylaxis, basic reproduction number.

[1]. AIDS gov. (2015). https://www.aids/hiv-aids-basics/hiv-aids 101/how-to-get-hiv-aids.
[2]. AIDS gov. (2015). Post-exposure prophylaxis. https:/www.aids.gov/hiv-aids-basics/prevention/reduce-your-risk/post-exposure.
[3]. Avert (2017). Information on AIDS: HIV and AIDS in Nigeria. https://www.avert.org>sub-sahara-africa.
[4]. BosenaTebeje, ChevnetHailu (2010): Assesment of HIV Post Prophylaxis use Among Health Workers of Government Health
Institutions in Jimma zone, Oromiya Region Southwest Ethiopia.
[5]. Crampin A.C., Kasimba S., Mwaungulu N.J, Dacombe R., Floyd S., Glynn J.R., Fine P.E.M. (2011). Married to M. Tuberculosis:
Risk of infection and disease in spouses of smear positive TB Patients. Trop. Med. Int. Health.16 (7): 811-818.

Abstract: In this paper, we present the implementation of interior-point methods for *()Pκ-linear complementarity problem based on a kernel function. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed kernel-based interior-point methods.

Keywords: Linear complementarity problems, interior-point methods, kernel function

[1]. Cottle, R.W., Pang, J.-S., Stone R.E.: The Linear Complementarity Problem. Academic Press, Boston, MA (1992)
[2]. Darvay, Z.: New interior-point algorithms in linear programming. Adv. Model Optim., 5(1), 51-92 (2003)
[3]. Fathi, Y.: Computational complexity of LCPs associated with positive definite matrices. Math. Program., 17(1), 335-344 (1979)
[4]. El Ghami, M., Wang, G.Q.: Interior-point methods for *()Pκ-linear complementarity problem based on generalized trigonometric barrier function. Int. J. Appl. Math., 30(1): 11-33, 2017.
[5]. Kojima, M., Megiddo, N., Noma, T., Yoshise, A.: A Unified Approach to Interior Point Algorithms for Linear Complementarity problems. Lecture Notes in Computer Science 538, Springer-Verlag, New York (1991)

Abstract: In this paper we discuss about the mixed summation-integral type operators having Baskakov basis functionin summation and Szasz-Mirakyan basis function in integration. We have central moments and some other basic results for these operators, and obtain the rate of point-wise convergence, a Voronovskaya type asymptotic formula and error estimate in simultaneous approximation.

Keywords: Baskakov operators; Szasz Mirakyan operators; Simultaneous approximation; Asymptotic formula; Error estimate;.Rate of convergence

[1]. Gupta V., "A note on modified Szasz operators," Bull Inst. Math. Academia, Sinica 21(3) (1993), 275-278.
[2]. Gupta V. and Agrawal P.N., "Rate of convergence for certain BaskakovDurrmeyer type operators," Ann. Of Oradea Univ., Fasc. Math. 14 (2007), 33-39.
[3]. Gupta V. and Gupta M.K., "Rate of convergence for certain families of summation integral type operators," J. Math. Anal. Appl. 296 (2004), 608-618.
[4]. Gupta V., Gupta M.K. and Vasishtha V., "Simultaneous approximation by summation integral type operators," J. Nonlin. Funct. Anal. Appl. 8 (2003), 399-412.
[5]. Srivastava H.M. and Gupta V., "A certain family of summation integral type operators," Math. Comput. Modeling. 37(2003), 1307-1315.

Abstract: A circulant graph𝐶𝑛(𝑅) is said to have the Cayley Isomorphism (CI) property if whenever 𝐶𝑛(𝑆)is isomorphic to𝐶𝑛(𝑅), there is some a∈𝑍𝑛∗for which S = aR.In this paper, we prove that 𝐶27𝑛(𝑅), 𝐶27𝑛(𝑆)and 𝐶27𝑛(𝑇)are isomorphic circulant graphs without CI-property whereR = {1, 9n-1, 9n+1, 3𝑝1, 3𝑝2, . . . , 3𝑝𝑘−2}, S = {3n+1, 6n-1, 12n+1, 3𝑝1, 3𝑝2, . . . , 3𝑝𝑘−2},T = {3n-1, 6n+1,12n-1, 3𝑝1, 3𝑝2, . . . ,3𝑝𝑘−2},k ≥ 3, gcd(𝑝1, 𝑝2,..., 𝑝𝑘−2) = 1 and 𝑛,𝑝1,𝑝2,...,𝑝𝑘−2ℕand also obtain new abelian groups from these isomorphic circulant graphs.

Keywords: Adam's isomorphism or Type-1 isomorphism, Type-2 isomorphism, Cayley Isomorphism (CI) property, symmetric equidistance condition, Type-1 group on 𝐶𝑛(𝑅),Type-2 group on𝐶𝑛(𝑅) w.r.t. 𝑚

[1] A. Adam, Research problem 2–10,J. Combinatorial Theory,3 (1967), 393.
[2] B. Alspach, J. Morris and V. Vilfred, Self-complementary circulant graphs, Ars Com., 53 (1999), 187-191.
[3] P.J. Davis, Circulant Matrices, Wiley, New York, 1979.
[4] B. Elspas and J. Turner, Graphs with circulant adjacency matrices, J. Combinatorial Theory,9 (1970), 297-307.
[5] F. Harary, Graph Theory,Addison-Wesley, Reading, MA, 1969.

Abstract: In this paper, we will discuss alternative fuzzy algebra to solve dual fully fuzzy linear system (DFFLS) of the form 𝐴 ⨂𝑥 ⨁𝑐 =𝐵 ⨂𝑥 ⨁𝑑 where coefficient matrix𝐴 and𝐵 are 𝑛𝑥𝑛 fuzzy matrix, 𝑐 and𝑑 fuzzy vector, and 𝑥 is unknown fuzzy vector, using ST Decomposition method. Finally, numerical example are given to illustrate our method.

Keywords: Dual fully fuzzy linear system, fully fuzzy linear system, fuzzy number, ST decomposition method Trapezoidal fuzzy number

[1]. L. A. Zadeh, Fuzzy sets, Information and Control, 8, 1965, 338-353.
[2]. S. J. H. Ghonchehand M. Paripour, Numerical solving of general fuzzy linear system by huang's method, Int. J. Comput. Math. Sci., 2(11),2008,810-812.
[3]. S. Molouzadeh, P. Darabi, and H. Khanandi, The pseudo inverse matrices to solve general fully fuzzy linear system, Journal of Soft Computing and Applications, 2013, 2013, 1-11.
[4]. V. Vijayalakshmiand R. Sattanathan,ST decomposition method for solving fully fuzzy linear system using gauss jordan for trapezoidal fuzzy matrices, International Mathematical Forum, 6(45), 2011, 2245-2254.
[5]. A. Kumar, Neetu, and A. Bansal, Anew method to solve fully fuzzy linear system with trapezoidal fuzzy numbers, Canadian Journal on Science and Engineering Mathematics, 1(3),2010, 45-57.

Abstract: In this paper we investigate parity combination cordial labelling for some graph obtained by duplication of graph elements on path, cycle and star graph..

Keywords: Graph labelling, parity combination cordial labelling, parity combination cordial graph, duplication.

[1]. D.M.Burton, elementary number theory, Tata McGraw Hill Edition, New Delhi, (2010).
[2]. J.A.Gallian, a dynamic survey of graph labelling,the elementary journal of combinatriocs(2018), #DS6
[3]. I. Cahit, Cordial Graph: A Weaker Version of Graceful and Harmonious Graph, Ars Combin.,23, (1987), 201-207
[4]. F. Harary, Graph Theory, Narosa Publishing House, New Delhi (2001).
[5]. S. M. Hegde and Sudhakar Shetty, Combinatorial Labeling of Graphs, Applied Mathematics E-Notes, 6(2006), 251-258

Abstract: In this paper we introduce the concepts of contra 𝛼 generalized continuous mappings and contra 𝛼 generalized irresolute mappings in neutrosophic topological spaces. We also discuss various properties and relations between the newly introduced continuous mappings and the other existing contra continuous mappings in neutrosophic topological spaces. Mathematics Subject Classification (2010): 54A40, 03E72.

Keywords: Neutrosophic topology, neutrosophic contra 𝛼 generalized continuous mapping, neutrosophic contra 𝛼 generalized irresolute mapping.

[1]. Atanassov, k., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986, 87-96.
[2]. Chang, C., Fuzzy topological spaces, J.Math.Anal.Appl., 1968, 182-190.
[3]. Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 1997, 81-89.
[4]. Dhavaseelan, R., and Jafari, S., "Generalized Neutrosophic closed sets", New trends in neutrosophic theory and its applications, 2017, Volume II.
[5]. Dhavaseelan.R, Jafari.S, Ozel.C and Al-Shumrani.M.A, Generalized Neutrosophic Contra –Continuity, New trends in neutrosophic theory and applications, 2017, volume II.

Abstract: AproofisgiventhatifAandBareoperatorsonacomplex........

Keywords: Numericalrange,λ-

Abstract: Consumable water distribution is a key service which is provided by any country. There are master plans working on this and from that proper piping systems are required for long term town and city projects to reduce maintenance, repairs and to continue the constructions cost effectively. Whole piping network consists of transmission region and distribution region to carry sufficient quantity of water from pumping station to the tower and from tower to the service areas. There is a special procedure to lay pipes called as concept of underground pipelines installation............

Keywords: bends, distribution region, head loss, safety factor, thrust blocks

[1]. AWWA Principles and Practices of Water Supply Operations,Introduction to Water Distribution, Vol. (3).
[2]. Soilhttps://www.researchgate.net/publication/227557214_Soil_Definition_Function_and_Utilization_of_Soil (accessed Jan 16, 2019).
[3]. Geotechnical Training Manual No 7 Pipe Bedding and Backfill United States Department of the Interior Bureau of Reclamation Technical https://www.coursehero.com/file/31440926/pipebedpdf/ (accessed Jan 16, 2019).

[4]. https://www.scribd.com/document/320979765/CIVL354-Notes-1-Soil-Compaction (accessed Jan 16, 2019).
[5]. Silva DPHHPN, Lanel GHJ, Perera MTM. Integer Quadratic Programming (IQP) Model for Cut Order. International Organization of Scientific Research-Journal of Mathematics (IOSR-JM) [Internet]. 2017;13(2):76-80.