iosr-Jm   Volume-18 ~ Issue-4 ~ Jul. – Aug. 2022

Abstract : In this paper a coupled cervical cancer model incorporating diffusion and diagnosis was formulated. Two transmission subsystems werecoupled in which the transmission rate at the population was expressedas a function of the viral load, while the within-host infection rates weremodelled as functions of the number of infectives. The basic reproduction number,𝑅0𝐶of the coupled model was found to be a maximum ofthe two reproduction numbers ......

Key Word: Coupledmodel,Diagnosis,HumanpapillomaVirus,Reproduction Number, Stability Analysis

[1]. AttiaS.,EggerM.,Mu¨llerM.,ZwahlenM.,LowN.2009.Sex- ual transmission of HIV according to viral load and antiretroviral ther-apy:systematic review and metaanalysis. AIDS 23(11):1397-1404 DOI10.1097/QAD.0b013e32832b7dca.
[2]. CarrJack(1981), Applications of Centre Manifold Theory, AppliedMathematicalSciences,Vol.35,Springer-Verlag,NewYork.
[3]. CliffordG.M.,Smith,J.S.,Plummer,M.,Munoz,N.,andFranceschi,S.(2003).Humanpapillomavirustypesininvasivecervicalcancerworldwide:ameta-analysis.Britishjournalofcancer,88(1),63-73.
[4]. Diekmann, O., Heesterbeek, J., Metz J.A. (1990). On the definition and the computation of the basic reproduction ratio in models forinfectious diseases in heterogenious populations. Journal of MathematicalBiology.167,67-78.
[5]. FengZ.,Velasco-HernandezJ.,Tapia-SantosB.and LeiteA.C.

Abstract: In this paper, we perform sensitivity analysis on a mathematical model which describes the evolution of users of mathematics instructional materials over time. We use ODE23 and ODE45 sensitivity analyses to select the important parameters. Our results indicate that the total number of potential users in the learning population is the dominant most sensitive parameter.

Keywords: Sensitivity Analysis, Mathematics Instructional Materials, ODE23, ODE45, Parameters Potential Users, Learning Population

[1]. Bass, F.M. (1969). A new product growth model for consumer durables.Management Science, 15, 215-227.
[2]. Dickerson, M.D. and Gentry, J.W. (1983).Characteristics of adopters and non-adopters of home computers.Journal of Consumer Research, 10, 225-235.
[3]. Ekaka-a, E.N. (2010).Computational and mathematical modelling of plant species interactions in a harsh climate [PhD Thesis]. The University of Liverpool and The University of Chester, United Kingdom.
[4]. Gatignon, H.A., Jehoshua, E. and Robertson, T.S. (1989).Modelling multinational diffusion patterns: An efficient methodology.Management Science, 8(3), 231-247.
[5]. Mahajan, V., Muller, E. and Srivastava, R.K. (1990).Determination of adopter categories by using innovation diffusion models.Journal of Marketing Research, 27(1), 37-50..

Abstract: In this paper, we generalized an arithmetic operation of 4th multiple polygonal fuzzy numbers with its membership function. We proposed a generalized technique for basic fundamental arithmetic operations of 4th multiple polygonal fuzzy numbers by using arithmetic interval of alpha- cut.

Key Word: 4th multiple polygonal fuzzy numbers, Arithmetic interval, α-cut, Membership function

[1]. Sahaya Sudha A, Gokilamani R, An Arithmetic Operation on Hexadecagonal Fuzzy Number. International Journal of Fuzzy Logic System. 2017; 7(1): 7-26
[2]. Amutha B, Uthra G, Defuzzification of Symmetric Octagonal Intuitionistic Fuzzy Number. Advances and Applications in Mathematical Sciences. 2021; 20(9): 1719-1728
[3]. Raju V, Jayagopal R, A new Operation on Icosikaiteteragonal fuzzy number. Journal of Combinatorial Mathematics and Combinatorial Computing. 2020; 112: 127-136
[4]. L.A. Zadeh, Fuzzy sets, Information and Control, Vol.8. No3 (1965), pp 338-353.
[5]. Rezvani S, Multiplication Operation on Trapezoidal Fuzzy Numbers. Journal of Physical Sciences. 2011; 15: 17-26

Abstract: We introduce more basic axioms with which we are able to prove some "axioms" of Propositional Logic. We use the symbols from my other article: "Introduction to Logical Structures". Logical Structures (SrL) are graphs with doubly labelled vertices with edges carrying symbols. The proofs are very mechanical and does not require ingenuity to construct. It is easy to see that in order to transform information, it has to be chopped up. Just look at a kid playing with blocks with letters on them: he has to break up the word into letters to assemble another word. Within SrL we take as our "atoms" propositions with chopped up relations attached to them. We call the results: (incomplete) ".......

Key Word: Structural Logic, Knowledge, Structured Information Highlights: The proof statements. Declaration: I have nothing to declare

[1]. W. F. Esterhuyse, Introduction to Logical Structures, Scribd. 2012.
[2]. S. K. Langer, An Introduction to Symbolic Logic, Dover Publications, 2011
[3]. T. Button, Level Theory, Part 1: Axiomatizing the Bare Idea of a Cumulative Hierarchy of Sets. The Bulletin of Symbolic Logic. Cambridge. 2021. DOI: 10.1017/bsl.2021.13.
[4]. F. P. Schuler. The Geometric Anatomy of Theoretical Physics. Internet. 2015
[5]. H.O. van Rooyen. Relation Nets in Learning and Teaching: A Knowledge Representation Approach. Academia. Internet. Undated.

Abstract: AgraphGiscalledapendantedgeextensiongraphofagraphHif G is obtained from Hby adjoining a new pendant edge with eachvertexofHanddenotependantedgeextensiongraphofagraphH byHʘK1. Inthispaper,Ihaveproved.

Key Word: Graphlabeling,Gracefulgraph,Evenandoddgracefulgraph,Cyclewithparallelchords.

[1]. J. Ayel and O. Favaron, Helms are graceful, Progress in Graph Theory(Waterloo,Ont,1982),AcademicPress,Toronto,Ont.(1984),89–92.
[2]. C. Delorme, K.M. Koh, M. Maheo, Teo H. Thuillier, Cycles with a chordaregraceful,J.GraphTheory,4(1980),409–415
[3]. A.ElumalaiandG.Sethuraman,Gracefulnessofacyclewithparallel
[4]. Pk-chords,AustralasianJ.Combin.,32(2005),205–211.
[5]. A. Elumalai and G. Sethuraman, Gracefulness of a cycle with parallelchordsandparallelPk-chordsofdifferentlengths,ArsComb.,104(2012),143–148.

Abstract: ....

[1]. A.Taylor and W.Mann, Advanced Calculus. 3rd ed., Wiley, NYC, 1983.
[2]. M. Lewinter and J. Meyer, Elementary Number Theory with Programming,Wiley, NYC, 2015..

Abstract: A nontrivial graph G of order 𝑛 is paintable if its vertex set can be labeled with the natural numbers {1, 2, …, n such that for eachi = 1, 2, …, n – 1, the edge (i)(i + 1)∉ E(G). If anyvalid assignment of the vertex labels can be accomplished randomly,that is, at each stage of the process, one randomly selects any "available" vertex), the graph is called randomly paintable. We present several theorems and pose open questions.....

Key Word: paintable, randomly paintable, traceable, randomly traceable, complement, tree

[1]. F.Buckley, M.Lewinter, A Friendly Introduction to Graph Theory. Prentice-Hall, 2003.
[2]. M.Gargano, M.Lewinter and J.Malerba, Paintable graphs. Cong. Num. 148(2001), 169-175.
[3]. M.Gargano, M.Lewinter and J.Malerba, Paintable Graphs II: Trees and Product Graphs. Cong. Num. 166(2004) 215-222.

Abstract: Finite transitive permutation groups of large degree possess socle section isomorphic to a particular given primitive groups. It was observed that groups of large degree had minimum base. Further indication showed that such groups are the symmetric and the alternating groups, except for the two Mathieu groups which are 5-transitive. The concept of socle form the basis in the determination of the degree of homogeneity of these groups.

[1]. Audu,M. S., & Momoh, S.U (1990): On transitive Permutation groups. Abacus,19,( 2). 17-23.
[2]. Cameron,P.J. (1981). Finite permutation groups and finite simple groups; London Math. Soc: DOI 101112.
[3]. Cameron, P.J. (1999). Permutation groups. Math .Soc, Cambridge University Press.
[4]. Cameron,P.J. (2000). Aspect of infinite permutation groups: School of Mathematical Sciences, Queen Mary, University of London.
[5]. Cameron, P.J. (2000). t-orbit homogenous permutations. London Math Soc. Subject Classification 20B10.