001311   AHMED H F, BAHGAT M S M, ZAKI M (Mathematics Dep, El-Minia Univ, El-Minia, Egypt, Email: msmbahgat66@hotmail.com) : Analytical approaches to space- and time-fractional coupled Burgers’ equations. Pramana – J Phys 2019, 92(3), 38.

We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplacevariational iteration method (LVIM) and the reduced differential transform method (RDTM). The solutions are obtained as rapidly convergent series with simply calculable terms. Numerical studies of the application of these approaches for a number of sample problems are given and are illustrated graphically. With these methods, it is possible to investigate the nature of solutions when the fractional derivative parameters are changed. The numerical results reveal the effectiveness and the correctness of the proposed methods.

11 illus, 4 tables, 40 ref

001309   ADEM A R, YILDIRIM Y, YASAR E (Mathematics Dep, Uludag Univ, Bursa, Turkey, Email: emrullah.yasar@gmail.com) : Complexiton solutions and soliton solutions: (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Pramana – J Phys 2019, 92(3), 36.

In this work, we derive the complexiton solutions for Date–Jimbo–Kashiwara–Miwa (DJKM) equation using the extended transformed rational function algorithm that relies on the Hirota bilinear form of the considered equation. Additional solutions such as complex-valued solutions also fall out of this integration scheme. Multisoliton-type solutions, in other words one-soliton, two-soliton and three-soliton solutions, which comprise both wave frequencies and generic phase shifts are presented through the medium of the multiple exp-function methodology which falls out as a result of generalisation of Hirota’s perturbation technique.

7 illus, 25 ref

000091   PAUL G C, RASHEDUNNABI A H M, HAQUE M D (Mathematics Dep, Rajshahi Univ, Rajshahi 6205, Bangladesh, Email: pcgour2001@yahoo.com) : Testing efficiency of the generalised G'/G -expansion method for solving nonlinear evolution equations. Pramana – J Phys 2019, 92(2), 25.

In this investigation, we employ the generalised (G'/G)-expansion method to test its efficiency in extracting travelling wave solutions of nonlinear evolution equations (NLEEs). As test cases, the modified Kuramoto–Sivashinsky (mK-S) and the modified Burgers–Korteweg–de Vries (mB-KdV) equations are considered because of their importance in soliton theory. The general solutions are obtained in hyperbolic, trigonometric and rational function forms for both the equations. Taking specific parametric values in the corresponding general solutions, some new exact travelling waves in trigonometric and hyperbolic forms and only in hyperbolic form are obtained for the mK-S and mB-KdV equations, respectively. The obtained results are checked to see whether the criticism made by Parkes (Comput. Fluids 42, 108 (2011)), that the so-called ‘new’ solutions derived by the (G'/G)-expansion method are often erroneous and are merely disguised versions of previously known solutions, is justified also for the generalised (G'/G)-expansion method. The solutions were checked with Maple by putting them back into their corresponding equations. With specific values of parameters, some of our obtained solutions satisfied directly and some solutions never satisfied the considered NLEEs. Among the satisfactory solutions, some are found to be in disguised versions of some results obtained in this study.

11 illus, 46 ref

000068   ADEM A R, YILDIRIM Y, YASAR E (Mathematics Dep, Uludag Univ, 16059 Bursa, Turkey, Email: emrullah.yasar@gmail.com) : Soliton solutions to the non-local Boussinesq equation by multiple exp-function scheme and extended Kudryashov’s approach. Pramana – J Phys 2019, 92(2), 24.

In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark– singular soliton-type solutions of nlBq by the extended Kudryashov’s algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.

7 illus, 31 ref

000078   GUO X, LIU J, ZHANG Y, WANG Q (Shandong Univ of Science and Technology, Tai’an, 271019, Shandong, People’s Republic of China, Email: guoxiurong007@163.com) : New exact solutions for the (3 + 1)-dimensional potential-YTSF equation by symbolic calculation. Pramana – J Phys 2019, 92(2), 23.

In this paper, we employ the improved homoclinic test technique and the extended homoclinic test technique. With the help of the symbolic calculation and applying the improved methods, we solve the (3 + 1)- dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation to obtain some new periodic kink-wave, periodic soliton and periodic wave solutions.

4 illus, 38 ref

000087   MOATIMID G M, EL-DIB Y O, ZEKRY M H (Mathematics and Computer Science Dep, Beni-Suef Univ, Beni-Suef, Egypt, Email: marwa.zekry@science.bsu.edu.eg) : Instability analysis of a streaming electrified cylindrical sheet through porous media. Pramana – J Phys 2019, 92(2), 22.

The current study deals with the influence of a uniform electric field on a cylindrical streaming sheet. This paper investigates a few representatives of porous media. These media are considered to be uniform, homogeneous and isotropic. The analysis is based on viscous potential theory, which assumes that the viscous forces affect only the interface between the fluids. The mathematical treatment is based on the normal modes analysis. For convenience, cylindrical coordinates are used. The boundary-value problem yields coupled second-order and damped differential equations with complex coefficients. These equations are combined with a single equation under the concepts of the symmetric and antisymmetric deformations. The Routh–Hurwitz criterion is adopted to govern the stability of the system. Several special cases are recovered upon appropriate data choices. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through some sets of figures. These parameters are the Darcy’s coefficients, basic velocities, dielectric constants, viscosity and thickness of the inner cylinder. We have found that the thickness of the inner cylinder plays a dual role on the stability picture. Also, the Darcy’s coefficient and dielectric constants have stabilising influence and the dynamic viscosity has a destabilising effect.

15 illus, 21 ref

000101   SULTAN F, KHAN W A, ALI M, SHAHZAD M, IRFAN M, KHAN M (Mathematics and Statistics Dep, Hazara Univ, Mansehra 21300, Pakistan, Email: Faisal.Sultan@Ugent.be) : Theoretical aspects of thermophoresis and Brownian motion for three-dimensional flow of the cross fluid with activation energy. Pramana – J Phys 2019, 92(2), 21.

The current review proclaims the forced convective flow and heat–mass transfer characteristics of cross nanofluid past a bidirectional stretched surface. The most significant aim of the current review is to incorporate the features of Buongiorno relation, activation energy, nonlinear thermal radiation and heat sink–source for a three-dimensional flow of the cross fluid. Appropriate transformations are employed to transform the modelled partial differential equations (PDEs) of momentum, temperature and concentration into coupled nonlinear ordinary differential equations (ODEs). The governing boundary value problem is numerically integrated with the help of bvp4c scheme. The obtained numerical data are plotted for the temperature and concentration profiles of nanofluid for various converging values of physical parameters. The dependence of increasing thermophysical parameters on temperature and concentration profiles of the cross nanofluid is graphically demonstrated. Furthermore, detailed study reveals that the concentration of the cross nanofluid decreases for increasing values of Brownian motion parameter. It is also perceived from the sketches that the concentration of the cross nanofluid decreases for higher values of chemical reaction parameter. The validity of the achieved numerical outcomes is ensured by making a comparison with the existing work as special cases.

9 illus, 2 tables, 41 ref

000092   PRAKASH A, GOYAL M, GUPTA S (Mathematics Dep, National Institute of Technology, Kurukshetra - 136 119, Email: amitmath0185@gmail.com) : A reliable algorithm for fractional bloch model arising in magnetic resonance imaging. Pramana – J Phys 2019, 92(2), 18.

Magnetic resonance imaging (MRI) is used in physics, chemistry, engineering and medicine to study complex materials. In this paper, numerical solution of fractional Bloch equations in MRI is obtained using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). Sufficient conditions for the convergence of FVIM and its error estimate are established. The obtained results are compared with the existing as well as recently developed methods and with the exact solution. The obtained numerical results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using the Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes.

6 illus, 1 table, 42 ref

000083   KHAN M, IRFAN M, KHAN W A (Mathematics Dep, Quaid-i-Azam Univ, Islamabad 44000, Pakistan, Email: mirfan@math.qau.edu.pk) : Heat transfer enhancement for Maxwell nanofluid flow subject to convective heat transport. Pramana – J Phys 2019, 92(2), 17.

Nanoliquids possess remarkable features that have fascinated numerous researchers because of their utilisation in nanoscience and nanotechnology. A mathematical relation for the two-dimensional flow of Maxwell nanoliquid over a stretching cylinder is established. Buongiorno’s relation is considered here to visualise the impact of Brownian moment and thermophoresis mechanisms on Maxwell liquid. The convective heat transport is deliberated for heat transfer mechanisms. Transformation procedure yields nonlinear differential system which is then computed through the homotopic approach. The results obtained are studied in detail in relation to somatic parameters. It is notable that the velocity of Maxwell liquid shows conflicting behaviour for curvature parameter α and Deborah number β. Moreover, the liquid temperature increases for increased values of Brownian motion N_b and thermophoresis parameter N_t. Additionally, the authentication of numerical consequences is prepared via benchmarking with formerly identified restrictive circumstances and we initiate a splendid communication with these results.

9 illus, 4 tables, 43 ref

000084   KHAN W A, ALI M, SULTAN F, SHAHZAD M, KHAN M, IRFAN M (Mathematics and Statistics Dep, Hazara Univ, Mansehra 21300, Pakistan, Email: waqar_qau85@yahoo.com) : Numerical interpretation of autocatalysis chemical reaction for nonlinear radiative 3D flow of cross magnetofluid. Pramana – J Phys 2019, 92(2), 16.

A simple relation of chemical processes for three-dimensional flow of a cross magnetofluid over bidirectional stretched surface is constructed. The impact of convective heat transport in the manifestation of non-linear thermal radiation and features of heat source–sink are also considered for heat transfer mechanism. Furthermore, in this research paper, the innovative relation between heterogeneous and homogeneous responses with equivalent diffusivities for reactant and autocatalysis is exploited. Apposite alterations are guaranteed to obtain ordinary differential equations (ODEs) with high nonlinearity. Numerically, the bvp4c technique is exploited to the interpret the structure of ODEs. Portrayals of temperature and concentration for cross liquid equivalent to abundant somatic parameters are presented graphically as well as in tabular form. Our results reveal that the temperature of the cross fluid decreases with fluctuation in the heat sink parameter. Furthermore, it is perceived from the figures that the concentration of the cross fluid reduces for higher values of chemical reaction parameters.

10 illus, 2 tables, 38 ref

000086   MAHMOOD T, IQBAL Z, SHAHZAD A (Mathematics Dep, HITEC Univ, Taxila 44700, Pakistan, Email: 12-phd-mt-005@hitecuni.edu.pk) : A numerical investigation of time-dependent MHD axisymmetric transport of Sisko fluid towards elongating porous disk. Pramana – J Phys 2019, 92(2), 14.

In this paper, we examined the unsteady boundary layer flow and heat transfer of a Sisko fluid model over an axisymmetric stretching porous disk in the presence of uniform magnetic field. Mathematical modelling is performed in cylindrical polar coordinates. By means of suitable transformations, the governing time-dependent partial differential equations are reduced to nonlinear coupled ordinary differential equations. Shooting method with Runge–Kutta of order 5 is employed to compute non-dimensional velocity and temperature. The effects of pertinent parameters are portrayed through graphs. The skin friction coefficient and Nusselt number are tabulated to study the behaviours at the stretching surface.

12 illus, 2 tables, 21 ref

000075   EL-DIB Y O (Mathematics Dep, Ain Shams Univ, Heliopolis 11341, Egypt, Email: yusryeldib52@hotmail.com) : Periodic solution of the cubic nonlinear Klein–Gordon equation and the stability criteria via the He-multiple-scales method. Pramana – J Phys 2019, 92(1), 7.

The current work demonstrated a new technique to improve the accuracy and computational efficiency of the nonlinear partial differential equation based on the homotopy perturbation method (HPM). In this proposal, two different homotopy perturbation expansions, the outer expansion and the inner one, are introduced based on two different homotopy parameters. The multiple-scale homotopy technique (He-multiple-scalas method) is applied as an outer perturbation for the nonlinear Klein–Gordon equation. A highly accurate periodic temporal solution has been derived from three orders of perturbation. The amplitude equation, which is imposed as a uniform condition, is of the fourth-order cubic–quintic nonlinear Schrödinger equation. The standard HPM with another homotopy parameter has been used as an inner perturbation to obtain a spatial solution of the nonlinear Schrödinger equation. The cubic– quintic Landau equation is obtained in the inner perturbation technique. Finally, the approximate solution is derived from the temporal and spatial solutions. Further, two different tools are used to obtain the same stability conditions. One of them is a new tool based on the HPM, by constructing the nonlinear frequency. The method adopted here is important and powerful for solving partial differential nonlinear oscillator systems arising in nonlinear science and engineering.

45 ref

000099   SINGH M, GUPTA R K (Punjabi Univ, Talwandi Sabo - 151 302, Email: manjitcsir@gmail.com) : Group classification, conservation laws and Painlevé analysis for Klein–Gordon–Zakharov equations in (3+1)-dimension. Pramana – J Phys 2019, 92(1), 1.

In this paper, we study Klein–Gordon–Zakharov equations which describe the propagation of strong turbulence of the Langmuir wave in a high-frequency plasma. Using the symbolic manipulation tool Maple, the classifications of symmetry algebra are carried out, and the construction of several local non-trivial conservation laws based on a direct method of Anco and Bluman is illustrated. Starting with determination of symmetry algebra, the one- and two-dimensional optimal systems are constructed, and optimality is also established using various invariant functions of full adjoint action. Apart from classification and construction of several conservation laws, the Painlevé analysis is also performed in a symbolic manner which describes the non-integrability of equations.

3 tables, 40 ref

000100   SINGH M, VATS S (Shri Ram Swaroop Memorial Univ, Lucknow - 225 003) : Mathematically designed bioprocess for release of value added products with pharmaceutical applications from wastes generated from spices industries. Int J Pharm Sci & Res 2019, 10(1), 130-8.

A mathematical model optimizing bio-physico-chemical pre-treatment of steam exploded Piper nigrum, and Syzygium aromaticum lignocellulosic biomass waste was developed. The model was developed using, RSM, involving central composite face-centered design (CCD) with six parameters, three levels and 40 runs, at 95 % confidence level. Six parameters optimized were quantity of each enzyme (a) Cellulase (ml); (b) Xylanase (ml) for enzymatic actions at 50 ºC; (c) Incubation time of 2-15 days for which substrate were dipped in various solvent systems; (d) Volume of solvent systems used; (e) Time of incubation at given steam pressure for steam explosion; and (f) Steam pressure 10-15 Psi. Cellulase and xylanase enzymes used were with activity (3.563 IU/mL), (33.32 IU/mL) respectively. ANOVA was applied for validation of the predicted model at 95 % of confidence level. The Base 10 log transformation was selected from the comparative study, and the model predicted 13.79 µmoles/mL, the release of polyphenols at 2 days of incubation of substrate with 10 ml of the solvent system, under 15.0 psi steam explosion pressure for 15 min, with the treatment of 1.00 ml of cellulose. The released polyphenols were tested against human pathogenic microbes (Staphylococcus aureus, Escherichia coli, Pseudomonas aeruginosa, and Micrococcus) and found to possess strong antimicrobial properties.

1 illus, 7 tables, 27 ref

000089   PAL T K, DATTA D (Radiological Physics and Advisory Div, Bhabha Atomic Research Centre (BARC), Mumbai - 400 085, Email: ddatta@barc.gov.in) : Development of possibilistic statistics and its application to quantify uncertainty of subsurface solute transport model. Sadhana 2019, 44(2), 44.

Imprecise information on any system is addressed by possibility theory wherein the system is modeled as a fuzzy set. Alpha level representation of a fuzzy set in the form of an interval defines the possibility theory. Uncertainty of any model in this context is quantified as mean value ± standard deviation of a possibilistic (imprecise) parameter. This paper presents the possibilistic statistical techniques to estimate the mean and standard deviation of a possibilistic parameter of subsurface solute transport model. The solute transport model parameters, such as groundwater velocity, solute dispersion coefficient, etc., are sparse and imprecise in nature. Such parameters are characterized by the possibility distribution. In this paper, analytical expression of solute transport model is used to estimate the mean value and standard deviation of possibilistic spatial and temporal concentration of solute.

7 illus, 4 tables, 19 ref

000071   BASHA H, REDDY G J, NARAYANAN N S V (Mathematics Dep, Central Univ of Karnataka, Kalaburagi - 585 367, Email: gjr@cuk.ac.in) : A numerical study of natural convection properties of supercritical water (H₂O) using Redlich–Kwong equation of state. Sadhana 2019, 44(2), 37.

In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient ($\mathrm{\beta }$) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate $\mathrm{\beta }$ values. The calculated values of $\mathrm{\beta }$ based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for H₂O in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.

16 illus, 8 tables, 41 ref

000076   FATHI-VAJARGAH B, HASSANZADEH Z (Applied Mathematics Dep, Guilan Univ, P.O. Box 41335-19141, Rasht, Iran, Email: hassanzadeh.83@gmail.com) : Improvements on the hybrid Monte Carlo algorithms for matrix computations. Sadhana 2019, 44(1), 1.

In this paper, we present some improvements on the Markov chain Monte Carlo and hybrid Markov chain Monte Carlo algorithms for matrix computations. We discuss the convergence of the Monte Carlo method using the Ulam–von Neumann approach related to selecting the transition probability matrix. Specifically, we show that if the norm of the iteration matrix T is less than 1 then the Monte Carlo Almost Optimal method is convergent. Moreover, we suggest a new technique to approximate the inverse of the strictly diagonally dominant matrix and we exert some modifications and corrections on the hybrid Monte Carlo algorithm to obtain the inverse matrix in general. Finally, numerical experiments are discussed to illustrate the efficiency of the theoretical results.

2 illus, 5 tables, 19 ref

000090   PATEL C, KUSHWAHA K S (Mathematics and Statistics Dep, Jawaharlal Nehru Krishi Vishwavidyalaya, Jabalpur, Madhya Pradesh) : Prediction of gross cropped area in Madhya Pradesh through a multiple regression approach. J Pharmacogn Phytochem 2019, 8(1), 82-8.

Indian agriculture is a land-based activity and as such water and land have been the basic elements of life support system and is an important resource for the economic life of a majority of people in the country. The pattern of land use is not uniform but it changes from place to place and time to time. The gross cropped area (Y), forest area (X₁), area not available for cultivation (X₂), area for other uncultivable land (X₃), and area of fallow land (X₄), are varying from year to year in Madhya Pradesh. The multiple Regression model may describe the pattern and projection of total cropped area based on predictor variables (x₁, x₂, x₃, x₄). In order to get evidence about the applicability of multiple regression procedure, Jarqua-Bera (J.B.) test, histogram of residuals, normal probability plot to test normality of errors, spearman’s rank correlation test for homogeneity of errors and Durbin-Watson ‘d’ statistic to test the independence of autocorrelation in error terms have been applied on secondary data of variables (y, x₁, x₂, x₃, and x₄) in M.P. state for 31 years.

4 tables, 14 ref

000081   JOHNSTEPHAN J, VINOTHKUMAR N, GAJENDRAN P, MUTHAIYAN A (Mathematics Dep, Hindustha Institute of Technology, Coimbatore, Tamilnadu, Email: johnstephan21@gmail.com) : Vertex edge domination in intuitionistic fuzzy graphs. Int J Info Computing Sci 2019, 6(2), 117-21.

Let G be an intuitionistic fuzzy graph. A vertex cover of intuitionistic fuzzy graphs is a set of vertices such that each strong edge of the intuitionistic fuzzy graph is incident to at least one vertex of the set. In this paper we introduce the concept of intuitionistic fuzzy vertex cover and obtain some interesting results on vertex cover in intuitionistic fuzzy graphs.

3 illus, 7 ref

000079   HANNAH REVATHY F, MANI N (Mathematics Dep, Sri Ramakrishna Coll of Arts & Science (Autonomous), Coimbatore - 641 006, Email: mani.n@srcas.ac.in) : A study on the impact of school bullying on students using R programming & SPSS. Int J Info Computing Sci 2019, 6(2), 111-6.

This study concentrates on the impact of school bullying on students while incorporating the statistical tools and the methods of Data Collection. It also enables the researcher to create awareness on this subject among students and others thereby eliciting the importance, need and the ways of stopping school bullying.

1 table, 5 ref

000077   GOPAL E N, MAHESWARI V, KUMAR P V (Mathematics Dep, Vels Institute of Science Technology and Advanced Studies (VISTAS), Chennai – 600 117, Email: enandhu77@gmail.com) : Special type labeling for the extended duplicate graph of quadrilateral snake graph. Int J Info Computing Sci 2019, 6(2), 59-68.

In this paper, we discuss about the Duplicate graph of Quadrilateral Snake, On Signed Product labeling, Sum Difference Cordial labeling, Sum Divisor Cordial labeling and Prime Cordial labeling are admits.

5 illus, 9 ref

000074   CHITRA V M, XAVIOR D A, ISIDO D F (Mathematics Dep, Loyola Coll, Chennai - 600 034, Email: chithu1234@yahoo.com) : On neighbourhood difference cordial labeling of graphs. Int J Info Computing Sci 2019, 6(2), 24-34.

In this paper we introduce a variation of difference cordial labeling of graphs called neighbourhood difference cordial labeling and we investigate the neighbourhood difference cordial labeling of path, cycle, complete graph, complete bipartite graph, the ladder graph, triangular ladder, diagonal ladder, the grid and the generalized Petersen graph.

10 illus, 4 ref

000088   NARASIMMAN P (Mathematics Dep, Thiruvalluvar Univ Coll of Arts and Science, Tirupattur - 635 901, Email: drpnarasimman@gmail.com) : Fuzzy stability of a quartic functional equation via two methods. Int J Info Computing Sci 2019, 6(2), 15-23.

The main purpose of this article is to institute the generalized Ulam – Hyers stability of a quartic functional equation in fuzzy normed space using two methods.

26 ref

000096   SARIDHA S, RAJARETNAM T (Mathematics Dep, Cauvery Coll For Women, Tiruchirappalli - 620 018, Email: saritha.sathish82@gmail.com) : A study on plus weighted multiset transformation semigroups. Int J Info Computing Sci 2019, 6(1), 84-98.

The objective of this paper is to introduce and study the concepts of algebraic structures on Plus Weighted Multiset Finite Automata (pwmf a). Homomorphism and concepts related to congruence relation on semigroups are analysed. Plus Weighted Multiset Transformation Semigroups(pwmts) and coverings on pwmf a are established.

17 ref

000073   CHITRA K, RAJARETNAM T (Mathematics Dep, Cauvery Coll For Women, Tiruchirappalli - 620 018, Email: chitra.mahathi86@gmail.com) : Algebraic properties of max weighted finite state mealy machines. Int J Info Computing Sci 2019, 6(1), 69-83.

The purpose of this paper is to introduce and study the concepts of weak homomorphism, homomorphism, strong homomorphism, identical states and admissible relations on Max weighted finite state mealy machine (mwfmm).

11 ref

000097   SELVAM A G M, DHINESHBABU R , JACINTHA M (Mathematics Dep, Sacred Heart Coll (Autonomous), Tirupattur - 635 601, Email: agmshc@gmail.com) : Stability of equilibria in a discrete model of prey-predator interactions with allee effect. Int J Info Computing Sci 2019, 6(1), 58-63.

This paper investigates a 2–D discrete time predator - prey interaction model in the presence of an Allee effect. The equilibrium points are obtained and their stability is analyzed. The phase portraits are presented for diverse range of parameter values. Qualitative behavior is demonstrated with the support of bifurcation diagrams. Numerical simulations are performed for interactions in the presence / absence of Allee effect and the discrete model exhibits rich dynamics.

6 illus, 10 ref

000098   SELVAM A G M, JACOB S B (Mathematics Dep, Sacred Heart Coll (Autonomous), Tirupattur, Vellore, Email: agmshc@gmail.com) : Analysis of fractional-order prey - predator model with harvesting. Int J Info Computing Sci 2019, 6(1), 52-8.

This work analyzes the dynamical behavior of harvesting in a discrete fractional order prey - predator model. Utilizing a discretization process to the fractional order model, we obtain its discrete version. Existence of fixed points is established and a detailed analysis of the stability of fixed points is carried out with the linearization process and the impact of harvesting on the ecosystem is discussed. To verify the analytical results, numerical evidence for different sets of biologically feasible parameter values is provided. Time series, phase portrait and bifurcation diagrams are plotted to study the stability of the model. Analysis of sensitivity to the initial conditions of the system is also performed.

5 illus, 7 ref

000069   ANITA (Mathematics Dep, Khalsa Coll For Women, Amritsar, Email: anitaarora@live.in) : A study of maximum entropy principle under weighted constraint. Int Rev Pure Appl Math 2019, 15(1), 121-31.

It is emphasized that the concept of weighted information has been proved to be very constructive because of its significance in goal oriented experiments. On the other hand, weighted mean has its own importance in the field of Statistics. The present communication is a step in the direction of the study of maximum entropy principle when weighted mean is prescribed. With the help of maximum entropy principle, we have made the study of optimizational problem related with generalized parametric measure of entropy.

2 illus, 2 tables, 17 ref

000072   BINWAL J, BABER A (Mathematics Dep, Mody Univ of Science and Technology, Rajasthan - 332 311, Email: baberaakanksha8@gmail.com) : A study of modeling and simulation of graph pebbling with impetus of interdisciplinary exploration. Int Rev Pure Appl Math 2019, 15(1), 113-20.

Consider a connected graph G with finite number of vertices and edges whose vertices are assigned with whole numbers represents the number of pebbles on each vertex. Pebbling step and pebbling number of a connected graph G are playing a vital role. In this paper, we discuss and give an overview of mathematical modeling and simulation of graph pebbling on undirected graphs as well as directed graphs with available literature of what arrangement of directed graphs allow for pebbling to be meaningful. We also discuss the pebbling numbers of various orientations of directed graphs such as directed wheel graphs, directed complete graphs , directed demonic graphs etc. In this continuation, we discuss the importance of demonic directed graphs with that the sharp upper bound and lower bound of the pebbling numbers of the directed graphs is the same as that of the undirected graphs. These are the impetus of interdisciplinary exploration in context of mathematical modeling and simulation for certification of graph isomorphism and decyclization of graphs. We also propose the condition for two strongly connected digraphs are having equal pebbling numbers.

1 illus, 1 table, 19 ref

000080   Jeba Presitha B, RAMYA S (Parks Coll, Tirupur, Tamil Nadu) : A study of near-rings and it's involving theorems. Int Rev Pure Appl Math 2019, 15(1), 107-11.

The purpose of the present paper is to prove some theorems for nearrings with unity. Near-ring is an algebraic structure similar to a ring but satisfying fewer axioms. Every ring is a near-ring, hence near-rings are generalized rings. Two ring axioms are missing: The commutative of addition and other distributive law. The mapping of a group into itself under pointwise addition and composition of maps. The study and research on near-rings is systematic and also it's continuous.

6 ref

000095   RAMYA S, PRESITHA B J (Mathematics Dep, PARK’S Coll, Tirupur, Tamil Nadu) : Solving an unbalanced fuzzy transportation problem using a heptagonal fuzzy numbers by robust ranking method. Int Rev Pure Appl Math 2019, 15(1), 93-105.

In this paper, we consider an unbalanced fuzzy transportation problem where cost, requirement and availability are heptagonal fuzzy numbers. We use the proposed method to solve an unbalanced fuzzy transportation problem. Fuzzy transportation problem can be converted into a crisp valued transportation problem using Robust Ranking method.

6 tables, 11 ref

000094   PRIYA P, PRIYANKA R (Mathematics Dep, St.Josep’s Coll For Women, Tirupur, Tamil Nadu) : A comparative study on optimal solution in fuzzy transportation problem using fuzzy numbers. Int Rev Pure Appl Math 2019, 15(1), 83-92.

This paper is concerned with the closed, bounded, and non empty feasible region of the transportation problem using fuzzy numbers which ensures the existence of an optimal solution to the balanced fuzzy transportation problem. The objective is minimize the transportation cost of some commodities through a complicated network when the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers. Then the fuzzyfication of the cost of the transportation problem is discussed with the help of the numerical example. Finally we compared to the transportation cost.

1 illus, 9 tables, 6 ref

000082   KALYAN K, JAMES M (Mathematics and Statistics Dep, SHUATS, Prayagraj, (U.P), Email: jamesmohit@yahoo.co.in) : Edge domination number of Sierpinski Cycle graph of order n. Int Rev Pure Appl Math 2019, 15(1), 51-81.

Edge domination in Graph is a growing area for researcher and mathematician. In graph theory, an edge dominating set for a graph G(V,E) is a subset S⊆E such that every edge not in S is adjacent to at least one edge in S. The edge domination number is the number of edges in a smallest dominating set for graph G(V,E). Generalized Sierpinski Graphs is a geometrical figure in which each part has the same patterns as the whole. They are useful in modelling structures. In this paper we have examined the edge domination number of Sierpinski Cycle graph of order n≥3.

4 tables, 19 ref

000085   KUMAR P, ARIEF M (Mathematics Dep, Govt. Degree Coll, Kathua(J&K), Email: pawan811@yahoo.in) : Sandwich composition operator on weighted hardy spaces. Int Rev Pure Appl Math 2019, 15(1), 45-50.

Let C_φ, D be the composition and differentiation operators defined by C_φf = f_0φ and Df = f respectively. In this paper, the boundedness and compactness of the Sandwich composition operator DC_φD on the weighted Hardy spaces have been characterized.

22 ref

000093   PRASAD R, VERMA S K, KUMAR S (Mathematics & Astronomy Dep, Lucknow Univ, Lucknow - 226 007, Email: rp.manpur@rediffmail.com) : On submanifolds of an almost contact manifold. Int Rev Pure Appl Math 2019, 15(1), 37-44.

The present paper deals with the study of submanifolds of an almost contact manifold. We have studied certain results for a submanifold of an almost contact manifold equipped with quarter-symmetric metric connection.

18 ref

000070   AYYAPPAN G, SOMASUNDARAM B, THAMIZHSELVI P (Mathematics Dep, Pondicherry Engineering Coll, Puducherry - 605 014, Email: ayyappanpec@hotmail.com) : Analysis of an M^[X₁], M^[X₂]/G₁, G₂/1 retrial queueing system with priority services, abandoned customers, working breakdown, repair and randomized vacation policy. Int Rev Pure Appl Math 2019, 15(1), 1-23.

The topic under study is a single server retrial queue consisting of two classes of batch arrivals with non-preemptive priority service, abandoned customers, working breakdown, repair and randomized vacation policy. Two independent compound Poisson processes are encountered where the service times are generally distributed for two classes of customers. At a breakdown instant during busy period, the system continues to provide auxiliary service for the current customer, who is in the service station. The customer who is being served could be left out by the server for certain probabilities, in case of a new arrival for a low priority service. When the system becomes empty, the server goes for vacation of random length. If there are no customers waiting at the completion epoch of vacation, the server either takes another vacation or remains idle. We use the established norm which is the corresponding steady state results for time dependent probability generating functions are obtained. Along with that, the expected waiting time for the expected number of customers in the high and low priority queues are computed. Numerical results along with the graphical presentations are shown elaborately.

4 illus, 3 tables, 19 ref

026265   PATEL R S, VERMA J K (Mathematics Dep, Govt Auto P G Coll, Satna, M. P, Email: jk.verma87@yahoo.com) : Solution of an economic model using dynamic deformation procedure. Asian J Adv Basic Sci 2018, 6(1), 69-71.

Since most of the economic problems are related to the optimization problems, therefore the techniques of the Dantzig [1] can be applied, to all such economic problems in which these problems corresponds to linear form under some constraints conditions. Many nonlinear variety of economic problems are solved by the nonlinear techniques based on the quadratic programming method under the Kuhn-Tucker [10] conditions. Scarf developed a finite algorithm based on the subdivision of the simplex into finite subsets called primitive sets, then utilizing the Lemke complementarity pivoting procedure he provided the first constructive proof to Brouwer's fixed point theorem. Scarf's work attracted many others researchers. Thereafter, many important refinement and extensions to his algorithm were developed with the help of triangulation of simplex carried by Kuhn [7], Todd [21], Eaves [2] and Merril [16] etc. However, algorithm developed by Freudenthal [5], Kuhn [7,8], Todd [21] etc. were the extension of the Scarf's algorithm to have better approximation of the fixed point of a continuous mapping from a simplex into itself. Whereas Merril [16], Eaves [2], Eaves and Saigal [3] etc. developed several algorithms for points to set mapping or semi continuous mapping. In this paper we have tried to give a dynamic manifold construction process to find the solution of different type of economic problems.

1 illus, 23 ref

026264   MISHRA P P, SHRIVASTAVA R (Mathematics Dep, Govt. P G Coll, Panna, M.P, Email: mishrapp@yahoo.com) : A study of connectivity for hyperspaces in cyclic order. Asian J Adv Basic Sci 2018, 6(1), 28-30.

An arc is a homeomorphic path, which is a continuous function in a space. In this paper, we have studied arcwise connectivity for the spaces which have closed connected subsets in a way that, these are separated by disjoined open sets.

5 ref

028725   DAYAN F, AHMAD B, ZULQARNAIN M, ALI U, AHMAD Y, ZIA T J (Mathematics Dep, Management and Technology Univ, Lahore, Pakistan, Email: fazaldayan1@gamil.com) : On some topological indices of triangular silicate and triangular oxide networks. Int J Pharm Sci Res 2018, 9(10), 4326-31.

A topological index is a numeric quantity from the structural graph of a molecule. It has become a very useful tool in the prediction of pharmacological, toxicological and physico - chemical properties of a compound. In this paper, we have computed some topological indices of triangular silicate TsL (n) and triangular oxide TOL (n) networks.

3 illus, 2 tables, 26 ref

028732   MAJUMDAR P, SAHA A K, MAJUMDAR M (Mathematics Dep, National Institute of Technology, Jirania, Tripura - 799 046,, Email: majumderpriyanka94@yahoo.com) : A mathematical approach of exploration towards extreme risk factor in cancer of optimal condition. Int J Pharm Sci Res 2018, 9(9), 3732-42.

The aim of this present investigation is to identify the most important risk factor for cancer by means of a mathematical model. The study begins with considering some types of cancer viz. breast, colorectum as well as lung and bronchus cancer as most of the cancer patients suffer from these types of cancers. Teaching-Learning-Based Optimization technique is applied to sorting out the most lethal cancer among all cancer consider in this study and it is found that lung and bronchus cancer is the most fatal. Further, we investigate the risk factor associated to lung and bronchus cancer by means of Literature, Expert and Local Hospital survey. All the risk factor has their own importance for death from cancer in medical aspects. Multi-Criteria Decision Making technique is applied to recognize the most significant risk factor among all the factors in statistical scenario. It is identified that smoking is the most concerning risk factor. The information related from the study may help to take necessary measure to control the death rate due to lung and bronchus cancer.

7 illus, 10 tables, 43 ref

029941   LANDOWSKI M (Mathematical Methods Dep, Maritime Univ of Szczecin, Waly Chrobrego 1-2, 70-500 Szczecin, Poland, Email: m.landowski@am.szczecin.pl) : A discussion on ‘‘On the solution of a class of fuzzy system of linear equations’’. Sadhana 2018, 43(12), 205.

The paper is a discussion on the results obtained by Salkuyeh in the article (Sadhana 40(2):369–377, 2015). Salkuyeh considers the solution of the fuzzy system of linear equations (FSLE) and gives numerical examples where the results of FSLE are calculated. It was shown that the results by Salkuyeh are not full solutions and do not satisfy equivalent forms of the analysed FSLE. The paper presents a multidimensional approach to finding the solution of the FSLE. On the basis of the notation of the horizontal fuzzy number, a full solution that satisfies the FSLE and its equivalent forms is obtained.

12 ref

029939   CHAUDHARY S, KANIKA K M, CHOUDHARY M K (Mathematics Dep, Malaviya National Institute of Technology, Jaipur 302 017, Email: d11.santosh@yahoo.com) : Newtonian heating and convective boundary condition on MHD stagnation point flow past a stretching sheet with viscous dissipation and Joule heating. Indian J Pure Appl Phys 2018, 56(12), 931-40.

An analysis has been presented to study the effects of viscous dissipation and Joule heating on two-dimensional steady stagnation-point flow of an incompressible viscous electrically conducting fluid over a stretching plate with Newtonian heating and convective boundary condition in the presence of uniform transverse magnetic field. Similarity variables reduce the governing boundary layer partial differential equations to a set of non-linear ordinary differential equations and solved numerically using the Galerkin finite element method. Effects of various parameters such as stretching parameter, magnetic parameter, conjugate parameter, Prandtl number and Eckert number for velocity and temperature distributions have been discussed in detail through graphical representation. Moreover, numerical results of local skin-friction coefficient and local Nusselt number for different values of controlling parameters have been shown in tabular form and analyzed. Numerical values have been validated by comparing the present results with previously published works.

13 illus, 2 tables, 44 ref

029942   RAO M V S, GANGADHAR K, VARMA P L N (Mathematics Dep, Acharya Nagarjuna Univ, Andhra Pradesh - 523 001, Email: kgangadharmaths@gmail.com) : A spectral relaxation method for three-dimensional MHD flow of nanofluid flow over an exponentially stretching sheet due to convective heating: An application to solar energy. Indian J Phys 2018, 92(12), 1577–88.

The principle aim of the present investigation is to study the boundary layer analysis of nanofluid flow over a bidirectional exponentially stretching sheet in the presence of transverse magnetic field and also in convective condition. The effects of Brownian motion and thermophoretic diffusion of nanoparticle are considered from the mathematical model. Governing partial differential equations are reduced into coupled non-linear ordinary differential equations using suitable similarity transformations, further the system of equations are solved by a new spectral relaxation method. Validation of the results is achieved by comparison with emitting case from previous studies in the literature. Also, it has been shown that the convergence rate of the spectral relaxation method is significantly improved by using the method in conjunction with the successive over relaxation method. The results reveal the existence of interesting Sparrow–Gregg-type Hills for temperature distribution pertinent to some range of parametric values. Moreover the numerical data of drag coefficient, local heat and mass transfer rates are evaluated and analyzed. Effects of local Biot number on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of local Biot number.

14 illus, 6 tables, 39 ref

029946   YOKUS A, BULUT H (Actuarial Dep, Firat Univ, 23119 Elazig, Turkey, Email: asfyokus@yahoo.com) : Numerical simulation of KdV equation by finite difference method. Indian J Phys 2018, 92(12), 1571–5.

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier–Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L₂ and L_$\infty$ norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

3 illus, 2 tables, 33 ref

029943   REDDY K V, MAKINDE O D, REDDY M G (Mathematics Dep, Lara Institute of Technology & Science, Guntur (Dist) 522 213, Email: venugopal.reddy1982@gmail.com) : Thermal analysis of MHD electro-osmotic peristaltic pumping of Casson fluid through a rotating asymmetric micro-channel. Indian J Phys 2018, 92(11), 1439–48.

In this paper, we investigate the combined effects of wall slip, viscous dissipation, and Joule heating on MHD electro-osmotic peristaltic motion of Casson fluid with heat transfer through a rotating asymmetric micro-channel. Using long wavelength and small Reynolds number assumptions, the governing equations of momentum and energy balance are obtained and tackled analytically. The effects of various embedding parameters on the stream function, velocity, temperature, skin friction, Nusselt number and trapping phenomenon are displayed graphically and discussed. It is found that Casson fluid velocity, temperature, and heat transfer rate are enhanced with a boost in electro-osmotic force.

10 illus, 31 ref

029945   WANG B Q, LONG Z W, LONG C Y, WU S R (Guizhou Univ, Guiyang 550 025, China, Email: zwlong@gzu.edu.cn) : Effects of the generalized uncertainty principle on the thermal properties of Kemmer oscillator. Indian J Phys 2018, 92(11), 1419–24.

A series of aspects of the quantum gravity predict a modification in the Heisenberg uncertainty principle to the generalized uncertainty principle (GUP). In the present work, using the momentum space representation, we study the behavior of the Kemmer oscillator in the context of the GUP. The wave function, the probability densities, and the energy spectrum are obtained analytically. Furthermore, the thermodynamic properties of the system are investigated by using the numerical method and the influence of GUP on thermodynamic functions are also discussed.

6 illus, 38 ref

029944   SINGH J, AMUDA T O (Mathematics Dep, Ahmadu Bello Univ, Zaria, Nigeria, Email: teejaymath@gmail.com) : Perturbation effects in the generalized circular restricted three-body problem. Indian J Phys 2018, 92(11), 1347–55.

We study numerically the existence and stability of a test particle around the equilibrium points in the circular restricted three-body problem, and is generalized to include the effects in both primaries, oblateness and radiation together with P–R drag, small perturbations $\mathrm{\sigma }$ and $\mathrm{\epsilon }$¹ given in the Coriolis and centrifugal forces $\mathrm{\alpha }$ and $\mathrm{\beta }$, respectively. The primaries are a neutron eclipsing binary system, which consists of bright oblate-stars possessing P–R drag. In the numerical exploration of the binary systems (Kruger 60 and Achird), we computed the radiation factors qi (i = 1, 2) and the dimensionless velocity of light c_d which is a component of the P–R drag. It is interesting to note that, the involved parameters influence the position and stability of the triangular points. It is also observed that theses points are unstable due to the presence of a positive real part of the complex roots.

2 illus, 7 tables, 29 ref

029940   KHAN M A, NAG M, PORIA S (Mathematics Dep, Ramananda Coll, Bishnupur - 722 122, Email: mdmaths@gmail.com) : Multistability in coupled different-dimensional dynamical systems. Pramana - J Phys 2018, 91(6), 89.

Multistability or coexistence of different chaotic attractors for a given set of parameters depending on the initial condition only is one of the most exciting phenomenon in dynamical systems. The schemes to design multistability systems via coupling two identical or non-identical but the same-dimensional systems have been proposed earlier. Coupled different-dimensional systems are very useful to describe the real-world physical and biological systems. In this paper, a scheme for designing a multistable system by coupling two different-dimensional dynamical systems has been proposed. Coupled Lorenz and Lorenz–Stenflo systems have been considered to illustrate the scheme. The efficiency of the scheme is shown numerically, by presenting phase diagrams, bifurcation diagrams and variation of maximum Lyapunov exponents.

6 illus, 18 ref

028722   AKTER S, DHAR S, NAHAR N, DAS L C (Mathematics Dep, Premier Chittagong Univ, Chittagong, Bangladesh, Email: tuhin1000@yahoo.com) : Ionisation of metastable 3P-state hydrogen atom by electron with exchange effects. Pramana - J Phys 2018, 91(6), 78.

In the present work, the triple-differential cross-sections (TDCSs) for the ionisation of metastable 3P-state hydrogen atoms at an incident electron energy of 250 eV with exchange effects are computed in the asymmetric coplanar geometry for various kinematic conditions. The final-state wave function of Das and Seal (Phys. Rev. A 47, 2978 (1993)) is used here. The results of the present calculation are compared with the available hydrogenic ground-state experimental data and other existing theoretical results. An analysis of the results reveals qualitative enhancement with other compared results. The implication of the present study offers an extensive scope for experimental verification in such a field of ionisation.

4 illus, 1 table, 51 ref

028727   KHAN A, BUDHRAJA M, IBRAHEEM A (Mathematics Dep, Delhi Univ, Delhi -110 007, Email: ayshaibraheem74@gmail.com) : Multiswitching compound-compound synchronisation of six chaotic systems. Pramana - J Phys 2018, 91(6), 73.

In this paper, a novel synchronisation scheme involving six chaotic systems is proposed. The proposed scheme is named as ‘compound–compound synchronisation’. Instead of using a scaling system in compound synchronisation, a compound scaling signal is applied to the proposed scheme. The phenomenon of multiswitching synchronisation and the proposed scheme are combined together. Appropriate controllers are designed by employing nonlinear control method and Lyapunov stability theory to achieve asymptotically stable synchronisation states. An example of identical Chen systems is presented to demonstrate the proposed methodology. The proposed scheme is very different and complex in comparison with the previous schemes, as this scheme is first of its kind having five drive systems and one response system. Computational results are presented to justify the theoretical analysis. Numerical results and theoretical studies converge to the same conclusions.

6 illus, 27 ref