iosr-Jm   Volume-21 ~ Issue-4 ~ Jul. – Aug. 2025

Abstract : Human beings are curious to explore new and new events in course of time flittering. Necessity is the mother of invention- the proverb illustrates gradual needs and progressive development. Each and every invention changed the level of Society yielded the new opportunities to adopt and run for a period. The adaptation of a new technology shifted the social heritage, much of the interest in culture and Mathematics focused on understanding the nature of primitive mentality. The development of number system enabled the people to remember the earlier data........

Keywords: Invention, adaptation, cognitive studies, Transformation.

[1] Carraher (Nunes), T.N., Carraher, D.W., And A. D. Schliemann, (1985) Mathematics In The Streets And In Schools. British Journal Of Developmental Psychology, 3, Pp. 21–29.
[2] Khan Farida Abdulla (2004 Living, Learning And Doing Mathematics: A Study Of Working Class Children In Delhi, Contemporary Education 3. Dialogue,2,Pp.199-277.
[3] Saxe.G.B. & Esmonde, I.(2005). Dowling, P. (1995) 'Discipline And Mathematise: The Myth Of Relevance In Education', Perspectives In Education, 16, 2. Available At
Http://Homepage.Mac.Com/Paulcdowling/Ioe/Publications/Dowling1995/Index.Html
[4] Saxe, G.B., & Esmonde, I. (2005). Studying Cognition In Flux: A Historical Treatment Of Fu In The Shifting Structure Of Oksapmin Mathematics. Mind, Culture, & Activity. Available At Http://Lmr.Berkeley.Edu/Docs/Saxe_Esmonde_Mca1234_2.Pdf. Accessed 27-01-2010.

Abstract : The present paper deals with the determination of displacement and thermal stresses in a thick circular plate with internal heat generation. Arbitrary heat flux is applied at the upper surface of a thick circular plate, whereas lower surface at zero temperature and the fixed circular edge is thermally insulated. Here we compute the effects of internal heat generation of a thick circular plate in terms of stresses along radial direction. The governing heat conduction equation has been solved by the method of integral transform technique. The results are obtained in a series form in terms of Bessel’s functions. The results for temperature change and stresses have been computed numerically and illustrated graphically.

Keywords: Internal heat generation, steady state, thermal stresses.

[1] Bhongade CM And Durge M H (2013). Effect Of Michell Function On Steady State Behavior Of Thick Circular Plate. IOSR J. Of Mathematics 8(2) 55-60.
[2] Deshmukh KC And Kulkarni VS (2008). Quasi-Static Thermal Stresses In Steady State Thick Circular Plate. Journal Of Brazilian Society Of Mechanical Sciences And Engineering XXX(2) 175.
[3] Deshmukh KC, Warbhe SD And Kulkarni VS (2009). Non-Homogeneous Steady State Heat Conduction Problem In A Thin Circular Plate And Thermal Stresses. Int. J. Thermophysics 30 1688-1696.
[4] Noda N, Hetnarski R And Tanigawa Y (2003). Thermal Stresses (Taylor And Francis, New York) 2nd Edn. 259-261.
[5] Nowacki W (1957). The State Of Stresses In A Thick Circular Disk Due To Temperature Field. Bull. Acad. Polon. Sci., Scr. Scl. Tech. 5 227.

Abstract : A sum divisor cordial labeling of a graph G with vertex set V(G) is a bijection f from......

Keywords: Sunflower graph, flower graph, jelly fish graph, crown graph, sub division of star graph, cordial graphs, Sum divisor cordial graphs

[1] A. Rosa, On Certain Valuations Of The Vertices Of A Graph, Theory Of Graphs (Rome, July 1966), Gordon And Breach, N.Y. And Paris, 1967 349-355.
[2] R. Frucht And F. Harary, On The Corona Of Two Graphs, Aequationes Math. 4(1970), 322-325.
[3] I. Beck, Coloring Of Commutative Rings, J. Algebra, 116(1), 1988 208-226.
[4] R. Varatharajan And S. Navanaeetha Krishnan And K. Nagarajan, Divisor Cordial Graphs, International J. Math. Combin 4, 15-25 (2011).
[5] S. K Vaidya And N.H Shah, Further Results On Divisor Cordial Labeling, Annals Pure Appl. Math., 4(2), Pp 150-159, (2013).

Abstract : In this work, we develop and analyze a delayed SEIRW (Susceptible–Exposed–Infectious–Recovered–Waned) compartmental model to study the transmission dynamics of influenza in Kenya. The model incorporates a discrete time delay representing the effects of behavioral response and diagnostic lags, and is extended to include a vaccinated compartment to assess the impact of immunization strategies. We derive the endemic equilibrium and investigate its local and global stability properties. Local stability analysis employs a linearization approach and characteristic equations, revealing that the endemic equilibrium remains stable for sufficiently small delays but may undergo.....

Key Words: Time delay, Hopf bifurcation, Functional, Robustness, Bounded delays, Epidemic persistence

[1] Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The Construction Of Next-Generation Matrices For Compartmental
Epidemic Models. Journal Of The Royal Society Interface, 7(47), 873–885.
[2] Hethcote, H. W. (2000). The Mathematics Of Infectious Diseases. SIAM Review, 42(4), 599–653.
[3] Kuang, Y. (1993). Delay Differential Equations With Applications In Population Dynamics. Academic Press[4]
Van Den Driessche, P., & Watmough, J. (2002). Reproduction Numbers And Sub-Threshold Endemic Equilibria For Compartmental Models Of Disease Transmission. Mathematical Biosciences, 180, 29–48.
[5] Ruan, S. (2006). Delay Differential Equations In Single Species Dynamics. In: Arino O., Hbid M.L., Dads E.A. (Eds) Delay Differential Equations And Applications, NATO Science Series II, Vol. 205. Springer..

Abstract Assume that G is a (p, q) graph. Let V(G) to {1,2,…,p} be mapped by f. Assign the label |f (u )− f(v ) | to each edge uv. It's referred to as differential cordial labeling. When f is 1 −1 and|𝑒𝑓(0)−𝑒𝑓(1)| ≤1, the number of edges labeled with 1 and those not labeled with 1 are indicated by 𝑒𝑓(1) and 𝑒𝑓(0) , respectively. A difference cordial graph is one that has a.......

Keywords And Phrases: Cordial labeling, Difference cordial labeling , Zero divisors, Zero divisor graphs

[1] F.Harary, Graph Theory, Addision Wesley ,Newdelhi(1969)
[2] Narsingh Deo, Graph Theory With Applications To Engineering & Computer Science Dover Publications, Inc. Mineola, New York (1974)
[3] I.Cahit, Cordial Graphs: A Weaker Version Of Graceful And Harmonious Graphs, Ars Combin.,23(1987)201-207
[4] Y.S.Ho.S.M.Lee, And S.C.Shee, Cordial Labeling Of Unicyclic Graphs And Generealized Petersen Graphs, Congr.Number., 68(1989) 109-122.
[5] A.Rosa,On Certain Valuations Of The Vertices Of A Graph, Theory Of Graphs(Internat. Symposium,Rome,July 1996),Gordan And Breach,N.Y And Dunod Paris (1967) 349-355.

Abstract: This article presents an analysis of various software tools for the processing and visualization of functions in polar coordinates. It highlights specialized mathematical programs and computational environments that allow for graphing polar curves, analyzing their behavior, and performing dynamic simulations. Among the main analytical advantages are the ease of graphically representing complex functions, the ability to perform precise area and length calculations, and the option of immediately exploring transformations and parameter variations. In the educational field, the use of these tools contributesthat has a.......

Keywords polar functions, analytic geometry, two-dimensional elements, academic performance, computational tools

[1] Apostol, T. M., Vélez Cantarel, F. (2019). Calculus I: Cálculo Con Funciones De Una Variable, Con Una Introducción Al Álgebra Lineal. Alemania: Reverte.
[2] Sullivan, M. (1997). Precalculo. Colombia: Prentice Hall Hispanoamericana, S.A..
[3] The Polar Function: A Single Model Analysis. (N.D.). (N.P.): Stephen John Shroyer.
[4] Crama, Y., Hammer, P. L. (2011). Boolean Functions: Theory, Algorithms, And Applications. Estados Unidos: Cambridge University Press.
[5] Kosniowski, C. (1983). Fun Mathematics On Your Microcomputer. Reino Unido: Cambridge University Press.