iosr-Jm   Volume-19 ~ Issue-3 ~ May – June 2023

Abstract : We present a Variable-scale methods (VSM) with finite-difference methods (FDM) for modelling 2-D acoustic.......

Keywords: Finite-difference methods, Seismograms, seismic wave propagation, variable scale methods

[1]. Alford, R. M., Kelly, K. R., and Boore, D. M., (1974), Accuracy of finite-difference modelling of the acoustic wave equation:
Geophysics, v. 39, no. 6, p. 834-842
[2]. Alterman, Z. S., and Karal, F. C., (1968), Propagation of elastic waves in layered media by finite-difference methods: Bull. Seism.
Soc. Am., v. 58, no. 1, p. 367-398
[3]. Boore, D. M., (1972), Finite-difference methods for seismic wave propagation in heterogeneous materials: in Computational
Physics, v. 11,B. a. Bolt (editor), Academic Press, New York.
[4]. Chen, K., (1984), Numerical modelling of elastic wave propagation in anisotropic inhomogeneous media: a finite element approach
(ext. abst): Soc. Expl. Geophysics. 54th Intern. Mtg., p. 631-632..

Abstract :Our main aim here is to a necessary and sufficient Absorbing Boundary Conditions for the Wave equation in Orthogonal Coordinates. Absorbing Boundary Conditions are obtained for Cartesian Coordinates and Cylindircal Coordinates . We present Cartesian and Cylindrical results for the one medium and two media. These two seismograms show acceptaple results.

Key words : Absorbing Boundary Conditions, Orthogonal Coordinates, Cauchy equation, Seismogram

[1]. Clayton, R. W., and Engquist, B., (1977), Absorbing boundary conditions for acoustic and elastic wave equations: Bull. Seism. Soc.
America, v. 67, no. 6, p. 1529-1540.
[2]. Demir İ., (1998), Seismic wave modelling using finite difference methods: Ph.D. Thesis, University of Glamorgan.
[3]. Emerman S. H., and Stephen R. A., (1983), Comment on absorbing boundary conditions for acoustic and elastic wave equations:
Bull. Seism. Soc. America. v. 72, p. 661-665.
[4]. Fuyuki M., and Matsumato Y., (1980), Finite Difference analysis of Rayleigh wave scattering at a trench: Bull. Seism. Soc.
America. v. 70, p. 2051-2069.
[5]. Higdon R. L., (1991), Absorbing boundary conditions for elastic waves: Geophysics, v. 56, p. 231-241.

Abstract : The authors have studied a new class of arithmetic Cayley graphs, namely, the nilpotent...

Keywords: Nilpotent Cayley Graph, Eccentricity, Radius, Diameter, Girth, Circumference

[1]. Apostol, T. M., Introduction to Analytic Number Theory, Springer International Student Edition (1989).
[2]. Beck, I., Colouring of commutative rings, J. Algebra 116, 208-206 (1998).
[3]. Berrizbeitia, P., and Giudici, R.E., Counting pure k-cycles in sequences of Cayley graphs, Discrete Math., 149, 11-18(1996).
[4]. Berrizbeitia, P., and Giudici, R.E., On cycles in the sequence of unitary Cayley graphs. Reporte Techico No.01-95, Universidad Simon Bolivar, Dpt.de Mathematics Caracas, Venezula (1997).
[5]. Bondy, J.A., and Murty, U.S.R, Graph Theory with Applications, Macmillan, London (1976).

Abstract : Let (G=(V,E) be a simple undirected graph. An independent set is a subset 𝑆 of 𝑉(𝐺) such that no two vertices in 𝑆 are adjacent. A maximal independent set is an independent set that is not a proper subset of any other independent set. A graph is said to be unicyclic if it contains exactly one cycle. A graph 𝐺 with vertex set 𝑉(𝐺) is called a quasi-unicyclic graph, if there exists a vertex......

Keywords: independent set; maximal independent sets; unicyclic graphs; quasi-unicyclic graphs.

[1]. X. Geng, S. Li, and S.K. Simic, On the spectral radius of quasi-k-cyclic graphs, Linear Algebra Appl. 433 (2010) 1561-1572.
[2]. Z. Jin, X. Li, Graphs with the second largest number of maximal independent sets, Discrete Math. 308 (2008) 5864-5870.
[3]. M. J. Jou, The number of maximal independent sets in graphs, Master Thesis, Department of Mathematics, National Central University, Taiwan, (1991).
[4]. M. J. Jou and G. J. Chang, Maximal independent sets in graphs with at most one cycle, Dicrete Appl. Math. 79 (1997) 67-73.
[5]. M. J. Jou and G. J. Chang, Survey on conunting maximal independent sets, in: Proceedings of the Second Asian Mathematical Conference, S. Tangmance and E. Schulz eds., World Scientific, Singapore, (1995) 265-275

Abstract : An analysis has been carried out to study a problem of the heat generation/absorption and thermal radiation effects on Heat and Mass transfer in Hydromagnetic Williamson nanofluids flow over an exponentially stretching sheet in porous medium. Using appropriate similarity transformations, the governing nonlinear partial differential equations are transformed into non-linear ordinary differential equations. The transformed non-linear ordinary differential equations are then solved numerically by in built bvp4c solver package in MATLAB. The velocity profile, temperature profile and concentration profile are discussed and the influence parameters like Brownian motion parameter, Thermophoresis parameter, Thermal radiation parameter, Prandtl number, Heat source/sink parameter, Williamson parameter, Porosity parameter, Hartmann number and Lewis number are depicted graphically.

Keywords: Nanofluids, Williamson fluid, Hydromagnetic, Heat generation/absorption, Thermal Radiation, Exponentially stretching sheet

[1]. Sakiadis, B.C. (1961). Boundary layer behaviour on continuous solid flat surfaces American Institute of Chemical Engineers Journal, 7, 26-28. [2]. Tsou, F.K., Sparrow, E.M., Goldstein, R.J. (1967). Flow and heat transfer in the boundary layer on a continuous moving surface., 10(2), 219–235.
[3]. Erickson, L.E., Fan, L.T., Fox, V.G. (1966). Heat and mass transfer in the laminar boundary layer flow of a moving flat surface with constant surface velocity and temperature focusing on the effects of suction/injection Ind. Eng. Chem. Fundam., 5, 19-2.
[4]. Khan, M.R., (2020). Numerical analysis of oblique stagnation point flow of nanofluid over a curved stretching/shrinking surface, Phys. Scripta, 95 (10), 105704.
[5]. Li, X., Khan, A.U., Khan, M.R., Nadeem, S. & Khan, S.U. (2019). Oblique stagnation point flow of nanofluids over stretching/shrinking sheet with Cattaneo–Christov heat flux model: existence of dual solution, Symmetry, 11 (9), 1070.

Abstract : In this paper, a new fuzzy linear programming model is proposed to find fuzzy critical path and fuzzy completion time of a fuzzy project. All the activities in the project network are represented by trapezoidal Intuitionistic fuzzy numbers(TFI). A new representation of trapezoidal Intuitionistic fuzzy number is introduced to reduce the constraints in the fuzzy linear programming model. Further, an example is illustrated which shows the advantages of using the proposed representation over the existing representation of trapezoidal Intuitionistic fuzzy number and will present with great clarity the proposed technique and illustrate its application for fuzzy critical path of the project network problems.

Keywords: Trapezoidal Intuitionistic fuzzy number(TFI), Fuzzy linear Programming,Centroid, Ranking function, Fuzzy critical path .

[1]. Afzali A, Rafsanjani MK, Saeid AB.(2016). A fuzzy multi-objective linear programming model based on interval-valued
intuitionistic fuzzy sets for supplier selection.
International Journal of Fuzzy Systems. 18(5),864-874.
[2]. Angelov, P., (1997). Optimization in an intuitionistic fuzzy environment, Fuzzy Sets and Systems,86,299-306.
[3]. Atanassov.K.T.,( 1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems,20,87-96.
[4]. Cherian, L. and Kuriakose, A.S., (2009). Intuitionistic fuzzy optimization for linear programming problems, The Journal of Fuzzy
Mathematics, 17,139-144.
[5]. Deng-Feng-Li, (2008).A note on "Using intuitionistic fuzzy sets for fault – tree analysis on printed circuit board assembly", Micro
Electronics Reliability, 2008, 48, 1741..

Abstract : This paper presents some facts about Pell and Modified Pell numbers. Pell numbers can be changed to Modified Pell numbers and Vice Versa using matrices. The identities satisfied by Pell and Modified Pell numbers with proofs are also discussed in this paper.

Keywords: Recurrence relation, Pell numbers, Modified Pell numbers, Binet formula. .

[1]. A.F.Horadam, Applications of modified Pell numbers to representations, Ulam Quart. , Vol.3, pp. 34-53, 1994.
[2]. N. Bicknell, A primer on the Pell sequence and related sequence, Fibonacci Quart., Vol.13, No.4, pp. 345-349, 1975.
[3]. Ahmet Dasdemir , On the Pell, Pell-Lucas and Modified Pell numbers by matrix method, Appled Mathematical Sciences, Vol.5, No.64, pp.3173-3181, 2011

Abstract : In this paper, we apply spgωα open sets to present and study a new class of functions called spgωα continuous functions and spgωα irresolute functions in topological spaces . Some characterizations and several properties are obtained.

Keyw ords : spgωα closed sets, spgωα continuous functions, spgωα irresolute maps

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7, (2014), 7 19.

Abstract : The current age is characterized by the pursuit of speed. As a result, artificial intelligence is widely applied. If a company receives a large number of order requests, we can utilize algorithms to calculate the optimal completion of orders obtained the maximum profit.

Keywords: scheduling, artificial intelligence (AI)..

[1]. Susan A. Slotnick, Order acceptance and scheduling: A taxonomy and review, European Journal of Operational Research, Vol. 212 (2011), 1-11.
[2]. Mehdi Fazeli-Kebria, Ghasem Moslehi, Naser Mollaverdi and Mohammad Reisi-Nafchi, Customer's order acceptance and scheduling to maximise total profit, International Journal of Operational Research, Vol. 34, No. 2 (2019), 301-320.
[3]. Mohammad Yavari, Service level and profit maximisation in order acceptance and scheduling problem with weighted tardiness, International Journal of Industrial and Systems Engineering, Vol. 43, No. 3.(2023), 331-362.

Abstract : Background: Turbulent natural convection in an enclosure plays a big part in heat transmission and the building environment. Sophisticated buildings around the world are outfitted with costly heaters and coolers to maintain comfortable temperatures for human existence, manufacturing, and sophisticated farming methods, a scenario that many people cannot afford. Over a time, researchers have consistently developed a number of numerical study models to simulate the natural turbulent flow in these rectangular enclosures to solve complex problems associated with turbulent flows. In spite of several experimental studies and model simulations on the structure of natural turbulence convection, the fundamental mechanism in turbulent phenomena is still incomplete..........

Keywords: Vorticity vector formulation,Vorticity, Stream function, Vector potential, Reynold stress

[1]. G. V. Kuznetsov and M. A. Sheremet, "Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls.," International Journal of Heat and Mass Transfer, pp. 163-177, 2010.
[2]. P. Sompong and S. Witayangkurn, "Natural convention in a trapezoidal enclosure with wavy top surface.," Journal of Applied Mathematics, 2013.
[3]. R. Mayoyo, K. J. Sigey and M. J. Okwoyo, "An investigation of bouyancy driven natural convection in cylindrical enclosure.," 2015.
[4]. Z. Altaç and N. Ug˘urlubilek, Assessment of turbulence models in natural convection from two and three dimensional rectangular enclosures., International Journal of Thermal Sciences, 2016.
[5]. K. O. Awuor and M. G. Gicheru, "Numerical simulation of natural convection in rectangular enclosures.," 2017.