028733   MEHMOOD R, RANA S (Mathematics Dep, HITEC Univ, Taxila Cantt, Pakistan, Email: srhtc2016@hotmail.com) : Thermal transport of rate-type fluid impinging obliquely over a heated sheet. Pramana - J Phys 2018, 91(5), 71.

The main objective of this study is to examine the two-dimensional (2D) oblique Oldroyd-B flow on a stretching heated sheet. The flow governing problem is converted into nonlinear ordinary differential equations through proper scaling transformations. The prevailing set of equations is solved computationally with a tolerance level of 10⁻⁵. The velocity and temperature of a fluid model under consideration are portrayed to discuss the influence of all associated parameters on momentum and thermal characteristics. Heat flux at the wall has been computed numerically and analysed in a physical manner. The results obtained depict a reversed flow region for non-positive values of shear flow components once a free parameter is varied. It is noticed that heat transfer at the wall drops due to a rise in Deborah number β1 as well as Biot number Bi.

15 illus, 45 ref

028740   TARIQ K U, SEADAWY A R, ALAMRI S Z (Mathematics Dep, Taibah Univ, Saudi Arabia, Email: Aly742001@yahoo.com) : Computational soliton solutions to (3 + 1)-dimensional generalised Kadomtsev-Petviashvili and (2 + 1)-dimensional Gardner-Kadomtsev-Petviashvili models and their applications. Pramana - J Phys 2018, 91(5), 68.

In this paper, the auxiliary equation method is successfully applied to compute analytical solutions for (3+1)-dimensional generalised Kadomtsev–Petviashvili and (2+1)-dimensional Gardner–Kadomtsev–Petviashvili equations, by introducing simple transformations. These results hold numerous travelling wave solutions that are of key importance which provide a powerful mathematical tool for solving nonlinear wave equations in recent era of applied science and engineering. The method can also be extended to other nonlinear evolution models arising in contemporary physics.

7 illus, 56 ref

028726   HASSAN S Z, ABDELRAHMAN M A E (Imam Abdulrahman Bin Faisal Univ, Saudi Arabia, Email: szhassan@iau.edu.sa) : Solitary wave solutions for some nonlinear time-fractional partial differential equations. Pramana - J Phys 2018, 91(5), 67.

In this work, we have considered the Riccati–Bernoulli sub-ODE method for obtaining the exact solutions of nonlinear fractional-order differential equations. The fractional derivatives are described in Jumarie’s modified Riemann–Liouville sense. The space–time fractional modified equal width (mEW) equation and timefractional generalised Hirota–Satsuma coupled Korteweg–de Vries (KdV) equations are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations (ODEs), which were obtained from the nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

4 illus, 25 ref

028729   KHAN W A, ALSHOMRANI A S, ALZAHRANI A K, KHAN M, IRFAN M (Mathematics and Statistics Dep, Hazara Univ, Mansehra 21300, Pakistan, Email: waqar_qau85@yahoo.com) : Impact of autocatalysis chemical reaction on nonlinear radiative heat transfer of unsteady three-dimensional Eyring-Powell magneto-nanofluid flow. Pramana - J Phys 2018, 91(5), 63.

The pursuit of superior working liquids for heat/mass transfer mechanisms in engineering is on the rise, not only to maximise revenue but also to accommodate heat dissipation or chemical separation under extreme conditions. The addition of a small amount of nanoparticle, i.e. a product called nanofluid, has been initiated over the last decade. In this paper, we present a comprehensive study of unsteady three-dimensional (3D) flow of the Eyring– Powell nanofluid under convective and nanoparticles mass flux conditions. The effects of constructive/destructive chemical reactions and nonlinear thermal radiation are also considered in the Eyring–Powell nanofluid model. Additionally, suitable transformations are utilised to obtain coupled ordinary differential equations (ODEs) from the system of partial differential equations (PDEs) and the numerical solution of the system of the coupled ODEs is obtained by means of the bvp4c scheme. The obtained numerical data are plotted for the temperature and concentration profiles of nanofluids for various and converging values of physical parameters. Our findings demonstrate that the temperature of the Eyring–Powell nanofluid fall-off by changing the heat sink parameter. Furthermore, it is perceived from the sketches that the concentration of Eyring–Powell magneto-nanofluid decays at higher values of chemical reaction parameter.

9 illus, 1 table, 45 ref

028723   AZHAR E, IQBAL Z, IJAZ S, MARAJ E N (Mathematics Dep, HITEC Univ, Taxila 44700, Pakistan, Email: ehtsham@uaar.edu.pk) : Numerical approach for stagnation point flow of Sutterby fluid impinging to Cattaneo-Christov heat flux model. Pramana - J Phys 2018, 91(5), 61.

The present study examines the stagnation point flow of a non-Newtonian fluid along with the Cattaneo– Christov heat flux model. The coupled system is simplified using suitable similar solutions and solved numerically by incorporating the shooting method with the Runge–Kutta of order five. The motivation is to analyse the heat transfer using an amended form of Fourier law of heat conduction known as the Cattaneo–Christov heat flux model. The influences of significant parameters are taken into the account. The computed results of velocity and temperature profiles are displayed by means of graphs. The notable findings are as follows. The viscous and thermal boundary layer exhibits opposite trends for Reynolds number, Deborah number and power-law index. The shear stress at the wall displays reverse patterns for shear thinning and shear thickening fluids. The Prandtl number contributes to increasing the Nusselt number while the Deborah number of heat flux plays the role of reducing it.

18 illus, 28 ref

028731   KUMAR M, REDDY G J, DALIR N (Mathematics Dep, Central Karnataka Univ, Kalaburagi - 585 367, Email: gjr@cuk.ac.in) : Transient entropy analysis of the magnetohydrodynamics flow of a Jeffrey fluid past an isothermal vertical flat plate. Pramana - J Phys 2018, 91(5), 60.

This study presents the analysis of entropy generation concept for unsteady magnetohydrodynamics Jeffrey fluid flow over a semi-infinite vertical flat plate. This physical problem is constituted by transient coupled highly nonlinear equations and is evaluated numerically by using an implicit scheme. The average values of wall shear stress and Nusselt number, entropy generation number and Jeffrey fluid-flow variables are analysed for distinct values of physical parameters at both transient and steady states. The results show that the time needed for achieving a steady state pertaining to the temperature and velocity gets augmented with the increased values of Jeffrey fluid parameter. The results also specify that the entropy generation number increases with the increasing values of Jeffrey fluid parameter, group parameter and Grashof number while the opposite trend is seen for the magnetic parameter.

9 illus, 2 tables, 51 ref

028730   KUMAR H, NAIK P A, PARDASANI K R (Mathematics Dep, Islamic Science & Technology Univ, Jammu and Kashmir - 192122, Email: naik.parvaiz@yahoo.com) : Finite element model to study calcium distribution in T lymphocyte involving buffers and ryanodine receptors. Proc Natl Acad Sci India A 2018, 88(4), 585–90.

In this paper an attempt has been made to develop a mathematical model to study intracellular calcium distribution in T lymphocyte for a one dimensional unsteady state case. The model incorporates the parameters like diffusion coefficient, ryanodine receptors (RyRs), source influx and buffers. The boundary conditions have been framed using biophysical conditions of the problem. The finite element method has been employed to obtain the solution of the proposed mathematical model. The numerical results are used to study relationship between concentration and position with respect to source influx, buffers and ryanodine receptors (RyRs).

6 illus, 1 table, 30 ref

028721   AKIZ H F (Bozok Univ, Turkey, Email: hfulya@gmail.com) : Covering morphisms of local topological group-groupoids. Proc Natl Acad Sci India A 2018, 88(4), 603–6.

Let L be a local topological group whose underlying space has a universal cover. Then the fundamental groupoid $\mathrm{\pi }$₁(L) becomes a local topological group-groupoid. In this paper, we prove that the slice category LTGpCov/L of covering moprphisms p : L $\to$ L of local topological groups in which eL has also a universal cover and the category LTGpGdCov/$\mathrm{\pi }$₁(L) of covering morphisms q : G $\to$ $\mathrm{\pi }$₁(L) of local topological group-groupoids based on $\mathrm{\pi }$₁(L) are equivalent.

11 ref

028741   YANG H, XIANG C (Chongqing Univ, Chongqing 400044, China, Email: cqyanghua1@126.com) : Approaches to multiple attribute decision making based on the hesitant fuzzy uncertain linguistic information and their applications to teaching quality evaluation in higher education. Proc Natl Acad Sci India A 2018, 88(4), 577–83.

In this paper, we investigate the multiple attribute decision making problems based on the power aggregation operators with hesitant fuzzy uncertain linguistic information. Then, we have developed some power aggregation operators for aggregating hesitant fuzzy uncertain linguistic information: hesitant fuzzy uncertain linguistic power weighted average operator and hesitant fuzzy uncertain linguistic power weighted geometric operator. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the teaching quality in higher education is given to verify the developed approach and to demonstrate its practicality and effectiveness.

5 tables, 38 ref

028737   SRIVASTAVA S K, SINGH U (Mathematics Dep, Maharaja Agrasen Institute of Technology, Delhi - 110086, Email: shaileshiitr2010@gmail.com) : On T-strong convergence of numerical sequences and fourier series. Proc Natl Acad Sci India A 2018, 88(4), 571–6.

In this paper, we generalize the notion of K strong convergence of numerical sequences defined by Moricz (Acta Math Hung 54(3–4):319–327, 1989) to T-strong convergence, using a lower triangular matrix T = (a_n,k) with nondecreasing monotone rows of positive numbers tending to $\infty$ i.e., a_n,k$\le$a_n,k+1$\forall$n and lim_{k$\to$$\infty$} a_n,k =$\infty$$\forall$n. We also establish a relationship between ordinary convergence and T-strong convergence. We further show that this concept can also be applied to the strong convergence of Fourier series under C-metric and L_p-metric.

9 ref

028724   CHEN K, FU Q (Chongqing Univ, Chongqing 400030, China, Email: freedomman_1983@163.com) : Research on the comprehensive evaluation in business strategy's performance with normal distribution interval number. Proc Natl Acad Sci India A 2018, 88(4), 565–70.

In this paper, we use the Choquet integral to propose the normal distribution interval number Choquet ordered averaging operator. The operator not only considers the importance of the elements, but also can reflect the correlations among the elements. It is worth pointing out that most of the existing normal distribution interval numbers averaging operators are special cases of our operator. Finally an illustrative example for comprehensive evaluation in business strategy’s performance based on circular economy with normal distribution interval number is given to use the operator in the range of uncertain multiattribute decision-making. The results show that the method proposed in this paper is feasible.

1 table, 26 ref

028734   PAL A (Mathematics & Statistics Dep, I.I.T, Kanpur-208 016) : Analysis of different phenotypic characters of Mesta (Hibiscus sabdariffa L.) to observe the effect of various varieties of the plant. Plant Arch 2018, 18(2), 1451-4.

“Mesta” is a potentially profitable crop which is not in surplus in today’s world but proves to be a useful raw material for industrialization and domestic uses. The purpose of this research programme is to study the effect of different varieties of Mesta ( Hibiscus sabdariffa L.) in the presence of different phenotypic characters like Plant height (cm), No. of branches plant^-1, No. of leaves plant^-1, No. of nodes plant^-1 and Basal diameter (cm) plant^-1. Randomised Complete Block Design (RCBD) layout is considered to carry out this interdependence. To fulfil the objective of this work, the measurements of various plants were taken for the preparation of various data discrimination and specifications to achieve a goal through ANOVA Table which signifies the interdependence of various parts of the plant.

1 illus, 5 tables, 9 ref

027504   KUMAR R S (National Institute of Technology Agartala, Agartala - 799 046, Email: ravikhushi412@yahoo.co.in) : Modelling a type-2 fuzzy inventory system considering items with imperfect quality and shortage backlogging. Sadhana 2018, 43(10), 163.

In this paper, an inventory model considering items with imperfect quality is developed in fuzzy environment, wherein shortages are allowed and are backlogged. In order to detect the items with imperfect quality, all items are screened before they are sent for consumption, and all imperfect quality items are sold at discounted price, called salvage value. In view of the fact that demand may not be predicted precisely, because it depends upon many uncertain and perturbing market activities, it is assumed to be a type-2 fuzzy variable. Quantity of imperfect quality items in the received lot may not be predicted precisely; hence percentage of imperfect quality items is also considered as a type-2 fuzzy variable. In this regard, this study developed a defuzzification method of type-2 fuzzy variable pertaining to interval approximation. The mathematical model is analysed to find closed form formulae of order quantity and backlogging quantity. Finally, the proposed methodology and model are testified on numerical examples, and sensitivity of decision variables is examined and discussed to underline the managerial insights as well as to establish the robustness of the mathematical model.

3 illus, 6 tables, 37 ref

027509   NADUVINAMANI N B, SIDDANGOUDA A, PATIL S, SHRIDEVI S (Mathematics Dep, Gulbarga Univ, Kalaburagi - 585 106, Email: naduvinamaninb@yahoo.co.in) : Effect of couple stresses on static and dynamic characteristics of MHD wide tapered land slider bearing. Sadhana 2018, 43(10), 162.

This paper presents an analytical study on the effect of couple stress on static and dynamic characteristics of wide tapered land slider bearing in the presence of applied magnetic field. A non-dimensional modified Reynolds equation is derived for the bearing under consideration. Closed-form expressions for the steady fluid film pressure, steady load carrying capacity and dynamic characteristics, viz., dynamic stiffness and dynamic damping coefficients are obtained. Numerical computations of the results revealed that magnetohydrodynamics tapered land slider bearing lubricated with couple stress fluid provides higher steady load carrying capacity, dynamic stiffness coefficient and dynamic damping coefficient as compared with the corresponding Newtonian case. It is observed that the presence of applied magnetic field characterized by the Hartmann number in the couple stress lubrication of tapered land slider bearing provides the improved static and dynamic characteristics as compared with the non-magnetic case.

8 illus, 5 tables, 18 ref

027503   KUMAR P, PANDA G, GUPTA U C (Mathematics Dep, Indian Institute of Technology, Kharagpur, Email: geetanjali@maths.iitkgp.ernet.in) : Stochastic programming technique for portfolio optimization with minimax risk and bounded parameters. Sadhana 2018, 43(9), 149.

In this paper a portfolio optimization problem with bounded parameters is proposed taking into consideration the minimax risk measure, in which liquidity of the stocks is allied with selection of the portfolio. Interval uncertainty of the model is dealt with through a fusion between interval and random variable. As a result of this, the interval inequalities are converted to chance constraints. A solution methodology is developed using this concept to obtain an efficient portfolio. The theoretical developments are illustrated on a large data set taken from National Stock Exchange, India.

4 illus, 5 tables, 39 ref

027512   SHARMA R P, IBRAHIM S M, JAIN M, MISHRA S R (Mathematics Dep, JECRC Univ, Jaipur - 303 905, Email: ramprakash0808@gmail.com) : Chemical reaction effect on MHD rotating fluid over a vertical plate with variable thermal conductivity: A numerical study. Indian J Pure Appl Phys 2018, 56(9), 732-40.

In this article, we have considered the simultaneous influence of chemical reaction and heat source on magnetohydrodynamic assorted convective heat and mass transfer flow past a vertical plate in a rotating system. The effects of applied magnetic field have also been taken into consideration while the induced magnetic field has not been reviewed due to very minor magnetic Reynolds number. The governing nonlinear partial differential equations for the flow, energy and species have been changed into highly nonlinear coupled system of ordinary differential equations by the help of similarity transformations and which are then solved numerically by applying fourth order Runge-Kutta technique associated along with shooting technique. The impacts of different variables on the velocity, temperature, concentration, skin friction and rate of heat and mass transfer distribution in the system have been shown graphically and explained in detail. In this paper we differentiate the results with already published works and good concurrence has been acquired to ensure the validity of the study.

13 illus, 2 tables, 22 ref

027513   WANG G, CAO X, CAI X, SUN D, CAI Q, LAN W (People's Liberation Army, Beijing 100080, China, Email: 13693135873@139.com) : A new high precision data assimilation method for the barotropic primitive equation. Indian J Geo-Mar Sci 2018, 47(09), 1794-1802.

To overcome a lot of shortcomings of gradient computations in the variational data assimilation by the adjoint method, such as low accuracy, difficult implementation and great complexity et al. a new data assimilation method based on dual-number theory is proposed. The new data assimilation method can avoid the complicated reverse integration of the tangent-linear/adjoint model. It only need a forward integration in dual-number space to obtain the cost function and the corresponding gradient vector. The numerical experiment is implemented for the barotropic primitive equation. The results show that the new method can reconstruct the initial conditions of the baroscopic primitive equation conveniently and accurately and has a strong anti-noise characteristic.

11 illus, 1 table, 26 ref

027506   LOGANATHAN P, DHIVYA M (Mathematics Dep, Anna Univ, Chennai -600 025, Email: logu@annauniv.edu) : Numerical investigation on viscous dissipating and chemically reacting fluid over an impulsively started vertical cylinder. Indian J Pure Appl Phys 2018, 56(7), 551-60.

The present analysis deals with the numerical investigation of an unsteady laminar free convective flow of a viscous, incompressible, dissipative, electrically conducting, optically thin and chemically reacting fluid past a moving semi-infinite vertical cylinder embedded in a porous medium. The problem has been governed by a system of coupled nonlinear boundary layer equations with appropriate initial and boundary conditions. These governing equations have been reduced to a non-dimensional form and have been solved numerically using Crank-Nicholson implicit finite difference method, which is unconditionally stable and convergent. The influence of physical parameters such as Prandtl number, Schmidt number, Eckert number, Grashof number for heat transfer, Grashof number for mass transfer, permeability parameter, magnetic parameter, radiation parameter and chemical reaction parameter on velocity profiles, temperature profiles, concentration profiles, local skin-friction coefficient, mean skin-friction coefficient, local Nusselt number, mean Nusselt number, local Sherwood number  and mean Sherwood number have been shown graphically. An increase in the value of Eckert number increases the velocity and temperature. Also, the rate of heat transfer and mass transfer gets enhanced for decreasing values of the Eckert number.

4 illus, 30 ref

027510   SABARINATH A, ANILKUMAR A K (Applied Mathematics Div, Vikram Sarabhai Space Centre, Thiruvananthapuram- 695 022, Email: a_sabarinath@yahoo.co.in) : Sunspot cycle prediction using multivariate regression and binary mixture of Laplace distribution model. J Earth Syst Sci 2018, 127(6), 84.

Prediction of sunspot cycle is a vital activity in space mission planning and various engineering decision making. In the present study, the sunspot cycle prediction has been carried out by a hybrid model which employs multivariate regression technique and the binary mixture of Laplace distribution (BMLD) function. The Expectation Maximization (EM) algorithm is being applied to the multivariate regression analysis to obtain a robust prediction of the sunspot cycle. Sunspot cycle 24 has been predicted using this technique. Multivariate regression model has been derived based on the available cycles 1 to 23. This model could predict cycle 24 as an average of previous cycles. Prediction from this model has been refined to capture the cycle characteristics such as bimodal peak at the high solar activity period by incorporating a predicted peak sunspot number from the BMLD model. This revised prediction has shown more accuracy in forecasting the major discrete features of sunspot cycle like maximum amplitude, the Gnevyshev gap, time duration from peak to peak amplitude, and the epoch of peak amplitude. This refined prediction shows that cycle 24 will be having a peak amplitude of 78 with an uncertainty of ± 25. Moreover, the present forecast says that, cycle 24 will be having double peak with a strong second peak compared to the first peak. This hypothesis is found to be true with the realized data of cycle 24. Further, this techniques have been validated by predicting sunspot cycles 22 and 23. A preliminary level prediction of sunspot cycle 25 also been carried out using the technique presented here. Present study predicts that, cycle 25 also will be a modest cycle like the present cycle 24, and the peak amplitude may vary in a band of 75–95.

13 illus, 6 tables, 37 ref

027508   MUHAMMAD S B, SAAD R (Sains Malaysia Univ, Pulau Pinang, Malaysia, Email: rosli28260@gmail.com) : Linear regression models for estimating true subsurface resistivity from apparent resistivity data. J Earth Syst Sci 2018, 127(5), 64.

Simple linear regression (SLR) models for rapid estimation of true subsurface resistivity from apparent resistivity measurements are developed and assessed in this study. The objective is to minimize the processing time and computer memory required to carry out inversion with conventional algorithms. The arrays considered are Wenner, Wenner–Schlumberger and dipole–dipole. The parameters investigated are apparent resistivity (ρa) and true resistivity (ρt) as independent and dependent variables, respectively. For the fact that subsurface resistivity is nonlinear, the datasets were first transformed into logarithmic scale to satisfy the basic regression assumptions. Three models, one each for the three array types, are thus developed based on simple linear relationships between the dependent and independent variables. The generated SLR coefficients were used to estimate ρt for different ρa datasets for validation. Accuracy of the models was assessed using coefficient of determination (R²), F-test, standard error (SE) and weighted mean absolute percentage error (wMAPE). The model calibration R² and F-value are obtained as 0.75 and 2286, 0.63 and 1097, and 0.47 and 446 for the Wenner, Wenner–Schlumberger and dipole– dipole array models, respectively. The SE for calibration and validation are obtained as 0.12 and 0.13, 0.16 and 0.25, and 0.21 and 0.24 for the Wenner, Wenner–Schlumberger and dipole–dipole array models, respectively. Similarly, the wMAPE for calibration and validation are estimated as 3.27 and 3.49 %, 3.88 and 5.72 %, and 5.35 and 6.07 % for the three array models, respectively. When compared with standard constraint least-squares (SCLS) inversion and Incomplete Gauss–Newton (IGN) algorithms, the SLR models were found to reduce about 80–96.5 % of the processing time and memory space required to carry out the inversion with the SCLS algorithm. It is concluded that the SLR models can rapidly estimate ρt for the various arrays accurately.

5 illus, 2 tables, 30 ref

027505   LIU Y, CHEN S, WEI L, GUAN B (Northeast Petroleum Univ, Daqing, China, Email: csqing2590@163.com) : Exact solutions to complex Ginzburg-Landau equation. Pramana- J Phys 2018, 91(2), 29.

In this paper, the trial equation method and the complete discrimination system for polynomial method are applied to retrieve the exact travelling wave solutions of complex Ginzburg–Landau equation. Both the Kerr and power laws of nonlinearity are considered. All the possible exact travelling wave solutions consisting of the rational function-type solutions, solitary wave solutions, triangle function-type periodic solutions and Jacobian elliptic functions solutions are obtained, and some of them are new solutions. In addition, concrete examples are presented to ensure the existence of obtained solutions. Moreover, four types of representative solutions are depicted to present the nature of the obtained solutions.

4 illus, 48 ref

027511   SHAKEEL M, MOHYUD-DIN S T, IQBAL M A (HITEC Univ, Taxila, Pakistan, Email: syedtauseefs@hotmail.com) : Modified extended exp-function method for a system of nonlinear partial differential equations defined by seismic sea waves. Pramana- J Phys 2018, 91(2), 28.

Nonlinear partial differential equations are the main area of focus for researchers and scientists doing research in applied mathematics. Finding solutions of these nonlinear partial differential equations had gained considerable importance over the last few decades. In this work, an analytical technique named extended expfunction method is introduced for finding archetype exact solutions of innovative nonlinear coupled Konno–Oono equation. Different types of travelling wave solutions, i.e. complex hyperbolic function and complex trigonometric function solutions, with numerous capricious parameters are revealed. Subsequently, by using Maple 16, we plot 2D and 3D surfaces of analytical solutions obtained in this article. The depiction of the technique is straight, useful and can be applied to other nonlinear systems of partial differential equations.

6 illus, 16 ref

027498   BANERJEE S (Mathematics Dep, Jadavpur Univ, Kolkata- 700 032, Email: banerjee.sumita.jumath@gmail.com) : Strange quark star with Tolman IV background. Pramana- J Phys 2018, 91(2), 27.

In the present article, we have studied the behaviour of static, spherically symmetric, anisotropic stellar models within the framework of MIT Bag model in the Tolman IV background. Different physical properties like energy conditions, stability, compactness factor and surface red-shift are investigated through graphical plots and mathematical calculations. The interior solutions found are non-singular in nature, i.e., regular at the centre. The interior spherically symmetric solutions have been matched to an exterior Schwarzschild geometry.

14 illus, 35 ref

027497   ABDULLAH, SEADAWY A R, WANG J (Mathematics Dep, Taibah Univ, Al-Madinah Al-Munawarah, Saudi Arabia, Email: Aly742001@yahoo.com) : Modified KdV-Zakharov-Kuznetsov dynamical equation in a homogeneous magnetised electron-positron-ion plasma and its dispersive solitary wave solutions. Pramana- J Phys 2018, 91(2), 26.

Propagation of three-dimensional nonlinear ion-acoustic solitary waves and shocks in a homogeneous magnetised electron–positron–ion plasma is analysed. Modified extended mapping method is introduced to find ion-acoustic solitary wave solutions of the three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation. As a result, solitary wave solutions (which represent electrostatic field potential), electric fields, magnetic fields and quantum statistical pressures are obtained with the aid of Mathematica. These new exact solitary wave solutions are obtained in different forms such as periodic, kink and antikink, dark soliton, bright soliton, bright and dark solitary wave etc. The results are expressed in the forms of hyperbolic, trigonometric, exponential and rational functions. The electrostatic field potential and electric and magnetic fields are shown graphically. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical and physical problems.

7 illus, 39 ref

027500   KHAN A, BUDHRAJA M, IBRAHEEM A (Mathematics Dep, Delhi Univ, Delhi- 110 007, Email: ayshaibraheem74@gmail.com) : Combination-combination synchronisation of time-delay chaotic systems for unknown parameters with uncertainties and external disturbances. Pramana- J Phys 2018, 91(2), 20.

In this article, an adaptive control method is proposed to study the combination–combination synchronisation phenomenon of four non-identical time-delayed chaotic systems for fully unknown parameters with parametric uncertainties and external disturbances. Based on the Lyapunov–Krasovskii functional theory, an appropriate adaptive controller is constructed so that a globally and asymptotically stable synchronisation state can be established between the master and the slave systems. Unknown parameters are identified by designing suitable parameter update laws. To elaborate the presented scheme, double-delay Rossler and time-delay Chen systems are considered as the master systems and time-delay Shimizu–Morioka and time-delay modified Lorenz systems are considered as the slave systems. Numerical simulations are presented to justify the theoretical analysis.

8 illus, 33 ref

027499   CAI N, DENG C-L, WU Q-X (Northwest Univ for Nationalities, Lanzhou, China, Email: dengchunlin_ray@163.com) : On non-consensus motions of dynamical linear multiagent systems. Pramana- J Phys 2018, 91(2), 16.

The non-consensus problems of high-order linear time-invariant dynamical homogeneous multiagent systems are studied. Based on the conditions of consensus achievement, the mechanisms that lead to nonconsensus motions are analysed. Besides, a comprehensive classification of diverse types of non-consensus phases corresponding to different conditions is conducted, which is jointly depending on the self-dynamics of the agents, the interactive protocol and the graph topology. A series of numerical examples are explained to illustrate the theoretical analysis.

8 illus, 33 ref

027502   KHAN M, IRFAN M, KHAN W A, AYAZ M (Mathematics Dep, Quaid-i-Azam Univ, Islamabad- 44000, Pakistan, Email: mirfan@math.qau.edu.pk) : Aspects of improved heat conduction relation and chemical processes in 3D Carreau fluid flow. Pramana- J Phys 2018, 91(1), 14.

This article communicates the numerical consideration of 3D Carreau liquid flow under the impact of chemical responses over a stretched surface. Moreover, the heat transfer exploration is carried out with a view to improve the heat flux relation. This phenomenon is established upon the theory of Cattaneo–Christov heat flux relation that contributes by the thermal relaxation. On exploitation of an appropriate transformation a system of nonlinear ODEs is attained and then elucidated numerically by means of bvp4c scheme. The descriptions of temperature and concentration fields equivalent to the frequent somatic parameters are graphically scrutinised. Our analysis carries that the concentration of the Carreau liquid displays similar tendency and decline as the heterogeneous–homogeneous reaction parameters (k₂, k₁) augment. Furthermore, it is notable that for shear thinning (n < 1) liquid, the influence of local Weissenberg numbers (We₁, We₂) are absolutely conflicting compared with the instance of shear thickening (n > 1) liquid. Additionally, validation of numerical results is done via benchmarking with previously stated limiting cases with two different schemes namely, homotopy analysis method (HAM) and bvp4c scheme. These comparisons initiate a superb correspondence with these outcomes.

10 illus, 4 tables, 47 ref

027501   KHAN M, AHMAD L, AYAZ M (Mathematics Dep, Quaid-i-Azam Univ, Islamabad- 44000, Pakistan, Email: latifahmad@math.qau.edu.pk) : Numerical simulation of unsteady 3D magneto-Sisko fluid flow with nonlinear thermal radiation and homogeneous-heterogeneous chemical reactions. Pramana- J Phys 2018, 91(1), 13.

The chemically reactive unsteady 3D Sisko fluid flow over a bidirectional stretched surface in the presence of nonlinear thermal radiation and magnetic field is considered. The numerical scrutiny of the transformed nonlinear ODEs is performed with the help of a numerical technique known as bvp4c. The mechanism of heat and mass transfer by the applications of chemical reaction and radiation is presented using temperature and concentration graphs. A remarkable enhancing results are estimated in the presence of nonlinear thermal radiation parameter R_d and temperature ratio parameter θ_w for the temperature field. Another significant decreasing outcomes are found while plotting the concentration profile with variation of homogeneous and heterogeneous parameters (k₁, k₂). Computational results of the local skin friction and local Nusselt number are tabulated under the influence of physical parameters which governs the flow. Decrease in skin friction with varying values of λ is observed. On the other hand, the impact of R_d and θ_w on the tabular values of local Nusselt number is found in increasing order. All the graphical results and tabular values are illustrated while testing both cases of power-law fluids including pseudoplastic (0 < n < 1) and dilatant (n > 1) behaviours. A comparison of the bvp4c and shooting technique with RK-45 Fehlberg is presented which shows excellent agreement. Additionally, the present results are compared with the results in the existing literature and both are found to be in very good correlation.

8 illus, 6 tables, 29 ref

027507   MAO Y (Mathematics Dep, Northeast Petroleum Univ, Daqing- 163 318, Email: yuanyuan_teresa@126.com) : Exact solutions to (2+1)-dimensional Chaffee-Infante equation. Pramana- J Phys 2018, 91(1), 9.

In this paper, the canonical-like transformation method and trial equation method are applied to (2+1)- dimensional Chaffee–Infante equation, and some exact solutions are obtained. In particular, a new solution in terms of elliptic functions is given.

30 ref

026263   SHETTAR B M, HIREMATH P S, BUJURKE N M (Mathematics Dep, Karnatak Univ, Dharwad- 580 003, Email: bujurke@yahoo.com) : A novel numerical scheme for the analysis of effects of surface roughness on EHL line contact with couple stress fluid as lubricant. Sadhana 2018, 43(8), 122.

In this article, a Jacobian-free Newton Multigrid (JFNMG) method is used for obtaining the solution of isothermal, steady and compressible elastohydrodynamic lubrication (EHL) line contact problem with surface roughness. The lubricant is a couple stress fluid. A finite difference scheme is used for the solution of EHL equations. The proposed JFNMG method, for the solution of resulting nonlinear system of algebraic equations, comprises nonlinear Newton iterations on the outer loop and linear multigrid iterations on the inner loop. It overcomes the limitations of conventional schemes for the investigation of the problems covering wide range of physical parameters of interest. For increasing values of couple stress parameter, there is an increase in minimum film thickness and considerable decrease (in height as well as spread) of pressure spike. Also, the sensitivity of height and spread of pressure spike as a function of load, couple stress parameter and other parameters are investigated.

7 illus, 1 table, 51 ref

026262   NAVALAGI G, MEGALAMANI S B (Mathematics Dep, KIT Tiptur, Karnataka) : g*γ -closed sets in topological spaces. Int J Mgmt Soc Sci 2018, 6(6), 151-60.

In this paper, we introduce and study a new class of generalized closed sets, namely, g *$\mathrm{\gamma }$ -closed sets in topology. Also, we characterize some basic properties of these sets.Mathematics subject classification(2010); 54A05, 54C08, 54D10.

15 ref

026261   JOSEPH S, MUSTAFA M, ABDELAZEEZD Y, SUFYANAND A, ADMIN M (Mathematics Dep, Upper Nile Univ, South Sudan) : Reproducing groups on analytic features for the metaplectic representation. Asian J Sci Technol 2018, 9(05), 8134-55.

We introduce the notation of admissible subgroup H of G=R^(^1+ε)⋊Sp(1+ε,R) relative to the (extended) metapletic representation μ_e via the wigner distribution. Under mild additional assumptions, it is shown to be equivalent to the fact that the identity ∑_jf_j =∫_H ∑_j 〈f_j,μ_e (h_j ) ϕ_j 〉 μ_e (h_j)ϕ_jdh_j holds (weakly) for all f_j∈L² (R^(1+ε)). They used this equivalence to exhibit classes of admissible subgroups of Sp(2,R) by E. Cordero, F. Damai, K. Nowak, and A. Tabacco [20]. We also eastablish some connections with wavelet theory, i.e., with curvelet and contourlet frames.

20 ref

026260   AKIN L (Business Administration Dep, Mardin Artuklu Univ, Mardin, Turkey) : On two weight criterions for the hardy littlewood maximal operator in BFS. Asian J Sci Technol 2018, 9(05), 8085-9.

Our aim of this paper is to prove two-weight criterions for the Hardy-Littlewood maximal operator from weighted Lebesgue  into Banach function  (BFS). We used boundedness of geometric mean operator and sufficient condition on the weights for boundedness of certain sublinear operator from weighted Lebesgue into weighted Musielak-Orlicz 

15 ref

026259   BEKERE A M, FIRDI M D, KEJELA S B (Mathematics Dep, Jimma Univ, Jimma, Ethiopia) : Analysis of a Poiseuille flow of an incompressible fluid between concentric circular cylinders. Asian J Sci Technol 2018, 9(05), 8048-57.

This paper presents analytical solutions of a Poiseulle flow of incompressible fluid between two fixed upright concentric circular cylinders subject to slip boundary conditions by considering three different cases. In each case steady state velocity and volume flow rate distribution in the field are determined by applying slip boundary conditions. By utilizing MATLAB the obtained results are visualized in figure.The effect of slip length and a radius of a gap between the cylinders on steady state velocity and volume flow rate distribution of the fluid are discussed. It is found that, velocity profile and volume flow rate distribution of the fluid are affected by a radius of a gap between the cylinders and slip length. The result also indicates that, fluid velocity of distribution decreases when the distance between the two cylinder increases in the vertical fluid motion and maximum velocity distribution occurs at the centerline of parallel flow.

7 illus, 13 ref

026258   MUYUMBA P K, CHITENG B K, JUMBE J K, ELAGO F, BWAYA K, KIMENYEMBO KASONGO M F (Physics Dep, Copperbelt Univ, Kitwe, Zambia) : On the 4-clifford algebra in abstract differential geometry. Asian J Sci Technol 2018, 9(05), 8036-47.

In this research paper, differential triads over a topological space are defined as objects of the Cartesian product category Alg x_x F^d x_x DMod over the same fixed topological space X. From differential triads sheaves (A_ix , ∂_ix ,Ω_ix) and (A_ix , ∂_ix ,Ω_ix) we defined morphisms of differential triads using a differential morphism ∂^ij : H^ij_A → H^ij_Ω , where H^ij_A = Hom_{Alg x} (A_ix, A_ix) and H^ij_Ω = Hom_{DMod x} (Ω_i, Ω_j). From the quadratic forms, we determined quadratic differential triads and Clifford differential triads.

25 ref

025039   MANDAVA R K, VUNDAVILLI P R (School of Mechanical Sciences, Bhubaneswar- 751013, Email: rm19@iitbbs.ac.in) : Implementation of modified chaotic invasive weed optimization algorithm for optimizing the PID controller of the biped robot. Sadhana 2018, 43(5), 66.

The present research work involves the implementation of Modified Chaotic Invasive Weed Optimization (MCIWO) algorithm for optimizing the gains of torque based proportional integral and derivative (PID) controller used to control the motors of the biped robot while walking on flat surface. While designing the controller, the dynamics of the biped robot has been derived using the well-known Lagrange-Euler (L-E) formulation. Subsequently, manual tuning procedure is employed to find the ranges of the gains of PID controller used in the developed algorithm. Once it is optimized, the effectiveness of the proposed algorithm is then compared with the Differential Evolution (DE) algorithm, in terms of variation of error, torque required, zero moment point (ZMP) and dynamic balance margin (DBM) of the biped robot. It has been observed that the MCIWO algorithm tuned PID controller is found to perform better than DE tuned controller. Further, the optimal gait obtained through the developed algorithm is validated by executing it on the real robot. It has been observed that the robot has successfully negotiated the flat terrain with the gaits obtained by the optimal PID controller.

14 illus, 5 tables, 45 ref

025038   GUPTA A K, KUMAR D, SAMUAL P (Motilal Nehru National Institute of Technology, Allahabad - 211004, Email: akhileshgupta08@gmail.com) : A meta-heuristic cuckoo search and eigen permutation approach for model order reduction. Sadhana 2018, 43(5), 65.

In this paper, a new model order reduction technique is presented by combining the benefits of the meta-heuristic cuckoo search optimization and Eigen permutation methods for order reduction of higher order continuous-time systems. In the proposed approach, the numerator and the denominator polynomials of reduced order model are determined by Cuckoo search and Eigen permutation approaches, respectively. The proposed approach preserves the stability of the original system into the lower order model as the Eigen permutation retains the dominant pole with simultaneous cluster formation of the remaining real and complex poles. The effectiveness of the proposed method is validated by single-input single-output and multiple-inputs multipleoutputs numerical examples.

8 illus, 8 tables, 52 ref

025037   GHOSH U, BANERJEE J, SARKAR S, DAS S (Mathematics Dep, Calcutta Univ, Kolkata- 700 009, Email: uttam_math@yahoo.co.in) : Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter. Pramana J Phys 2018, 90(6), 0074.

Klein–Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein–Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein– Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein–Gordon equation, we can overcome the problem. The fractional Klein–Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

4 illus, 19 ref

025036   BHAT M A, KHAN A (Mathematics Dep, Jamia Millia Islamia, New Delhi- 110 025, Email: mzfar012@gmail.com) : Multiswitching combination synchronisation of non-identical fractional-order chaotic systems. Pramana J Phys 2018, 90(6), 0073.

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-orderchaoticsystems,suitablecontrollershavebeendesigned.Theoreticalanalysisandnumericalresults are presented to demonstrate the validity and feasibility of the applied method.

4 illus, 39 ref

025035   BONKILE M P, AWASTHI A, LAKSHMI C, MUKUNDAN V, V S ASWIN (Mathematics Dep, National Institute of Technology, Kozhikode - 673 601, Email: aawasthi@nitc.ac.in) : A systematic literature review of Burgers` equation with recent advances. Pramana J Phys 2018, 90(6), 0069.

Even if numerical simulation of the Burgers’ equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers’ equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective–diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers’ equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers’ equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers’ equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers’ equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary/partial differential equations.

6 illus, 210 ref

025034   KHAN A, TYAGI A (Mathematics Dep, Jamia Millia Islamia, New Delhi - 110 025, Email: artityagi28@gmail.com) : Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems. Pramana J Phys 2018, 90(5), 0067.

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

15 illus, 63 ref

025033   Z IQBAL, MEHMOOD Z, AHMAD B (Mathematics Dep, HITEC Univ, Pakistan, Email: bilalahmadgondal@yahoo.com) : Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy. Pramana J Phys 2018, 90(5), 0064.

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD- generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.

19 illus, 2 tables, 22 ref

025032   KHATER M M A, SEADAWY A Y R, LU D (Mathematics Dep, Taibah Univ, Saudi Arabia, Email: Aly742001@yahoo.com) : New optical soliton solutions for nonlinear complex fractional schrödinger equation via new auxiliary equation method and novel (GJ/ G)-expansion method. Pramana J Phys 2018, 90(5), 0059.

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrödinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrödinger equation to nonlinear complex fractional nonlinear Schrödinger equation. We apply new auxiliary equation method and novel GJ/G -expansion method on nonlinear complex fractional Schrödinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.

49 ref

025031   RAJOTIA D (Mathematics Dep, Rajasthan Univ, Jaipur - 302 004, Email: rajotia.dinesh@gmail.com) : Effects of radiation on unsteady three-dimensional boundary layer flow and heat transfer over a permeable axisymmetric shrinking sheet with suction. Indian J Pure Appl Phys 2018, 56(6), 475-82.

In the present analysis, we have investigated the effects of thermal radiation on an unsteady three-dimensional boundary layer flow of an incompressible viscous fluid and heat transfer due to a permeable axisymmetric shrinking sheet with suction and power-law variation in wall temperature. The similarity transformations have been used to convert the governing partial differential equations into non-linear ordinary differential equations and then solved numerically by shooting technique. The conditions of the existence, non-existence and duality of the similarity solution have been explored by the investigation where the solution depends not only on suction parameter but on unsteadiness parameter also. Further, it has been emerged that the range of the suction parameter S, where the similarity solution exists, is increased with the increase of unsteadiness parameter A. Also, the graphs of velocity profile, temperature profile, skin-friction coefficient and rate of heat transfer at the sheet have been drawn with various values of the parameters and then discussed these characteristic features in detail.

13 illus, 1 table, 30 ref

025040   CHEN L, WANG Y, ZHOU Y (Mathematics Dep, Harbin Institute of Technology, Harbin-150 001, People’s Republic of China, Email: chenlili_02_06@163.com) : Association analysis of multiple traits by an approach of combining P values. J Genet 2018, 97(1), 79-85.

Increasing evidence shows that one variant can affect multiple traits, which is a widespread phenomenon in complex diseases. Joint analysis of multiple traits can increase statistical power of association analysis and uncover the underlying genetic mechanism. Although there are many statistical methods to analyse multiple traits, most of these methods are usually suitable for detecting common variants associated with multiple traits. However, because of low minor allele frequency of rare variant, these methods are not optimal for rare variant association analysis. In this paper, we extend an adaptive combination of P values method (termed ADA) for single trait to test association between multiple traits and rare variants in the given region. For a given region, we use reverse regression model to test each rare variant associated with multiple traits and obtain the P value of single-variant test. Further, we take the weighted combination of these P values as the test statistic. Extensive simulation studies show that our approach is more powerful than several other comparison methods in most cases and is robust to the inclusion of a high proportion of neutral variants and the different directions of effects of causal variants.

5 illus, 1 table, 37 ref

025029   KAMOH NM, ABADA A, COMFORT S M (Mathematics/Statistics Dep, Bingham Univ, Nigeria) : A block procedure with continuous coefficients for the direct solution of general second order initial value problems of (ODEs) using shifted Legendre polynomials as basis function. Int J Multidiscip Res Dev 2018, 5(4), 236-41.

This paper presents a self starting block method for the direct solution of general second order initial value problems of ordinary differential equations. The method was developed via interpolation and collocation of the shifted Legendre polynomial as basis function. A continuous linear multistep method was generated and was evaluated at some desired points to give the discrete block method. The block method was investigated and was found to be consistent, zero stable and convergent. The method was applied on some nonlinear as well as linear ordinary differential equations problems and the performance was relatively better than those constructed by ^[1], ^[12] and ^[15] respectively.

3 tables, 20 ref

025028   CHOUDHARY R (Pt. Ravishankar Shukla Univ, Chhattisgarh) : Application of "dependent t-test" by using SPSS for conducting physical education researches. Int J Multidiscip Res Dev 2018, 5(3), 149-52.

In the field of physical education, quantitative and qualitative researches are conducted. To analyze data parametric and non-parametric statistics are used. Parametric statistics are used in case of interval and ratio scale. Dependent t-test is parametric statistics used to compare two different observations of the same group. The assumption of normality is required to apply dependent t-test. If assumption of normality is not fulfilled, option of parallel non-parametric statistics is available.

5 illus, 1 table, 7 ref

025027   IKRAM Z J W, IRAWAN E B, DWIYANA, QOHAR A, AZIS N (Mathematics Education Dep, State Univ of Malang, Malang, Indonesia) : Development of pythagoras puzzle media to enhance understanding pythagoras theorem concept. Int J Multidiscip Res Dev 2018, 5(3), 106-9.

The purpose of this study is to produce a valid and practical learning media in learning mathematics, especially in the material of Pythagoras theorem, to evaluate the product of the development result to be revised and test the product of the development result to know its practicality in the learning. The type of this research is Research and Development with the model used consist of several stages: initial research, development stage, and assessment phase. The result obtained is the value of validity or media feasibility obtained by analyzing the media validation sheet of 2 validators. The value of the feasibility of the Pythagoras puzzle media is 3 which means Pythagorean puzzle media is valid and feasible to use. The value of media practicability is obtained by analyzing student questionnaire. The value of practical obtained is 2.6 which means Pythagorean puzzle media is quite practical and need some revisions.

2 illus, 2 tables, 7 ref

025026   RASYID A A, ANSYARI K, SINAR T S (Linguistics Dep, Sumatera Utara Univ, Indonesia) : Error analysis of arabic numeral usage by Indonesian learners: Contrastive studies. Int J Multidiscip Res Dev 2018, 5(3), 19-23.

Arabic numeralia (or al-'adad) is a numerical construction that has an impact on the depth of understanding to Arabic numeral contexts adjacent to the Indonesian system. Therefore, the depth is used as the target of research in order to find and analyze the errors Indonesian learners make in forming the constructions. From the counter-analysis and error analysis, there are implications of numerals to Indonesian learners. Qualitative methods are used and focused on the use of data in the form of words, phrases, sentences, drawings, or charts and quantitative methods is focused on data expressed in terms of numbers, both nominal and interval data. From the operation of the theories and methods it is found that there are errors in the numerical control of Arabic by Indonesian learners. Quantitatively, the errors are closely related to the correlation of the linguistic domain of the learners and the depth of numerical knowledge of Indonesian and Arabic languages to numerical learning in Indonesia.

12 ref

025023   ASHMA , GOEL R, KHAN M (Mathematics and Statistics Dep, Chaudhary Charan Singh Haryana Agricultural Univ, Hisar, Email: mkhanstat@gmail.com) : Newspapers reading frequency and readership pattern towards Swachh Bharat mission. Clim Chang Environ Sustain 2018, 6(1), 72-8.

Print media is the oldest communicating tool still being used in all the life stages. The importance of print media especially newspaper can be accounted from the fact that millions of people across the country depend on the information that appears in the newspapers. Newspapers are a source of information from last many years. However, with the dissemination of television news channels, readers’ choice of getting news and information has now changed. This creation of new media has expended the horizons for news and information gatherers; therefore, the focus of this study is on newspapers reading frequency and readership pattern of respondents towards Swachh Bharat Mission among Hisar city of Haryana state. The study also identifies language preferences and time spent on reading newspapers. A sample of 100 urban respondents was interviewed randomly from two wards (50 from each ward) of the Hisar city. The results of readership behaviour signifies that majority of the respondents were having the print as well as electronic media possession, listen/watched programmes related to Swachh Bharat Mission, got new information from friends, aware about national newspapers in both Hindi and English languages, read newspapers regularly and spent 15–30 min per day in reading newspapers. Most of the respondents read newspapers for improving their knowledge and preferred Dainik Bhaskar newspaper. About one-fourth of the respondents preferred political section in the newspapers. Majority of the respondents read news related to Swachh Bharat Mission followed by campaigns.

9 tables, 22 ref