LOGANATHAN P, DEEPA K

**039156** LOGANATHAN P, DEEPA K (Mathematics Dep, Anna Univ, Chennai- 600 025, Email: logu@annauniv.edu) : **Heat and mass transfer analysis of Casson fluid flow on a permeable riga-plate.** Indian J Pure Appl Phys 2020, 58(02), 79-86.

Numerical analysis has been carried out for a Casson fluid flow on a riga-plate with temperature dependent thermal conductivity. The physical model which governs the transport properties is solved numerically. This investigation emphasizes the consequence of variable thermal conductivity and electrically conducting magnetic field on the fluid flow. Rate of heat transfer is elevated, while the flow exposed to constructive case of variable thermal conductivity. The flow speed is enhanced for the improved values of modified Hartmann number. Correlation of the results with the similarity solutions declares the accuracy.

11 illus, 33 ref

CHAUDHARY S, CHAUDHARY S, CHAUDHARY M K

**039155** CHAUDHARY S, CHAUDHARY S, CHAUDHARY M K (Mathematics Dep, Malaviya National Institute of Technology, Jaipur- 302 017, Email: d11.santosh@yahoo.com) : **Numerical investigation of unsteady MHD flow and radiation heat transfer past a stretching surface in porous media with viscous dissipation and heat generation/absorption.** Indian J Pure Appl Phys 2020, 58(02), 71-8.

Viscous dissipation and radiation effects on unsteady flow of laminar incompressible viscous electrically conducting fluid through stretching surface in a porous media with magnetic field and heat generation/absorption have been investigated. Taking suitable similarity variables, the governing boundary layer equations are converted into a set of ordinary differential equations and solved numerically by Runge-Kutta fourth order method along with shooting technique. The effects of the various physical dimensionless parameters such as unsteadiness parameter, permeability parameter, magnetic parameter, radiation parameter, Prandtl number, heat generation/absorption parameters and Eckert number for velocity and temperature distributions have been analyzed in detail through graphical representations. Further skin friction coefficient and Nusselt number at the surface are numerated and compared with previous researchers.

11 illus, 2 tables, 23 ref

PATEL R S, VERMA J K

**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

MISHRA P P, SHRIVASTAVA R

**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

DAYAN F, AHMAD B, ZULQARNAIN M, ALI U, AHMAD Y, ZIA T J

**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

MAJUMDAR P, SAHA A K, MAJUMDAR M

**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

LANDOWSKI M

**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

CHAUDHARY S, KANIKA K M, CHOUDHARY M K

**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

RAO M V S, GANGADHAR K, VARMA P L N

**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

YOKUS A, BULUT H

**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 L_{2} 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

REDDY K V, MAKINDE O D, REDDY M G

**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

WANG B Q, LONG Z W, LONG C Y, WU S R

**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

SINGH J, AMUDA T O

**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

KHAN M A, NAG M, PORIA S

**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

AKTER S, DHAR S, NAHAR N, DAS L C

**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

KHAN A, BUDHRAJA M, IBRAHEEM A

**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

MEHMOOD R, RANA S

**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

TARIQ K U, SEADAWY A R, ALAMRI S Z

**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

HASSAN S Z, ABDELRAHMAN M A E

**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

KHAN W A, ALSHOMRANI A S, ALZAHRANI A K, KHAN M, IRFAN M

**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

AZHAR E, IQBAL Z, IJAZ S, MARAJ E N

**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

KUMAR M, REDDY G J, DALIR N

**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

KUMAR H, NAIK P A, PARDASANI K R

**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

AKIZ H F

**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

YANG H, XIANG C

**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

SRIVASTAVA S K, SINGH U

**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

CHEN K, FU Q

**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

PAL A

**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

KUMAR R S

**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

NADUVINAMANI N B, SIDDANGOUDA A, PATIL S, SHRIDEVI S

**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

KUMAR P, PANDA G, GUPTA U C

**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

SHARMA R P, IBRAHIM S M, JAIN M, MISHRA S R

**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

WANG G, CAO X, CAI X, SUN D, CAI Q, LAN W

**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

LOGANATHAN P, DHIVYA M

**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

SABARINATH A, ANILKUMAR A K

**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

MUHAMMAD S B, SAAD R

**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 (R^{2}), F-test, standard error (SE) and weighted mean absolute percentage error (wMAPE). The model calibration R^{2} 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

LIU Y, CHEN S, WEI L, GUAN B

**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

SHAKEEL M, MOHYUD-DIN S T, IQBAL M A

**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

BANERJEE S

**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

ABDULLAH, SEADAWY A R, WANG J

**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

KHAN A, BUDHRAJA M, IBRAHEEM A

**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

CAI N, DENG C-L, WU Q-X

**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

KHAN M, IRFAN M, KHAN W A, AYAZ M

**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 (k_{2}, k_{1}) augment. Furthermore, it is notable that for shear thinning (n < 1) liquid, the influence of local Weissenberg numbers (We_{1}, We_{2}) 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

KHAN M, AHMAD L, AYAZ M

**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 (k_{1}, k_{2}). 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

MAO Y

**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

SHETTAR B M, HIREMATH P S, BUJURKE N M

**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

NAVALAGI G, MEGALAMANI S B

**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

JOSEPH S, MUSTAFA M, ABDELAZEEZD Y, SUFYANAND A, ADMIN M

**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 ∑_{j}f_{j} =∫_{H }∑_{j }〈f_{j},μ_{e} (h_{j} ) ϕ_{j} 〉 μ_{e} (h_{j})ϕ_{j}dh_{j} holds (weakly) for all f_{j}∈L^{2} (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

AKIN L

**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

BEKERE A M, FIRDI M D, KEJELA S B

**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