025030   MOHANTY D J, KUMAR R S, GOSWAMI A (Mathematics Dep, Indian Institute of Technology, Kharagpur- 721 302, Email: dipanajyoti80@gmail.com) : Trade-credit modeling for deteriorating item inventory system with preservation technology under random planning horizon. Sadhana 2018, 43(3), 45.

This paper deals with a stochastic deteriorating item inventory model with preservation technology and trade-credit finance. The planning horizon of many seasonal or fashionable items stochastically varies to some extent. On the other side, the demand of such items increases in initial phase followed by a constant. This type of demand pattern can be modeled as ramp-type demand. Deterioration of such products is a characteristic, which can be reduced by making the investment on latest equipment and technology. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In these regards, this study examines the joint effect of preservation technology investment and trade-credit policy, wherein shortage is allowed and mixture of partial backlog and lost sales. Six cases may arise depending upon three parameters of time µ (demand increases up to µ), T (when on-hand inventory reaches to zero) and M (trade-credit period). The mathematical models are mainly categorized in two cases: (i) µ ≤  M and (ii) µ > M. The model is illustrated through numerical experiments, sensitivity analysis, and graphical representation.

7 illus, 2 tables, 36 ref

025025   WEI Z, RAJAGOPAL K, ZHANG W, KINGNI S T, AKGUL A (School of Mathematics and Physics, China University of Geosciences, Wuhan- 430074, China, Email: weizhouchao@163.com) : Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors. Pramana – J Phys 2018, 90(4), 50.

Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke–Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.

17 illus, 1 table, 40 ref

025024   CHEN Z, NING L (School of Mathematics and Information Science, Shaanxi Normal Univ, Xian, China, Email: ninglijuan@snnu.edu.cn) : Impact of depth and location of the wells on vibrational resonance in a triple-well system. Pramana – J Phys 2018, 90(4), 49.

The effect of depth and location of a triple-well potential on vibrational resonance is investigated in a quintic oscillator driven by a low-frequency force and a high-frequency force. The values of low-frequency ω and amplitude g of the high-frequency force at which vibrational resonance occurs are derived both numerically and theoretically. It is found that: as ω varies, at most one resonance takes place and the response amplitude at resonance depends on the depth and the location of the potential wells. When g is altered, the depth and location of wells can control the number of resonances, resulting in two, three and four resonances. The system parameters can be adjusted by controlling the depth and position of the wells to achieve optimum vibrational resonance. Furthermore, the changes induced by these two quantities in the tristable system are found to be richer than those induced in bistable systems.

10 illus, 35 ref

024166   ABRAR M N, HAQ R U, AWAIS M, RASHID I (Mathematics Dep, Capital Univ of Science and Technology, Islamabad- 44000, Email: nasirabrar10@gmail.com) : Entropy analysis in a cilia transport of nanofluid under the influence of magnetic field. Nucl Eng Tech 2017, 49(8), 1680- 88.

In this study, analysis is performed on entropy generation during cilia transport of water based titanium dioxide nanoparticles in the presence of viscous dissipation. Moreover, thermal heat flux is considered at the surface of a channel with ciliated walls. Mathematical formulation is constructed in the form of nonlinear partial differential equations. Making use of suitable variables, the set of partial differential equations is reduced to coupled nonlinear ordinary differential equations. Closed form exact solutions are obtained for velocity, temperature, and pressure gradient. Graphical illustrations for emerging flow parameters, such as Hartmann number (Ha), Brinkmann number (Br), radiation parameter (Rn), and flow rate, have been prepared in order to capture the physical behavior of these parameters. The main goal(i.e., the minimizing of entropy generation) of the second law of thermodynamics can be achieved by decreasing the magnitude of Br, Ha and A parameters.

9 illus, 2 tables, 36 ref

024165   KRISHNA P M, SHARMA R P, SANDEEP N (Mathematics Dep, VIT Univ, Vellore- 632 014, Email: dr.nsrh@gmail.com) : Boundary layer analysis of persistent moving horizontal needle in Blasius and Sakiadis magnetohydrodynamic radiative nanofluid flows. Nucl Eng Tech 2017, 49(8), 1654- 9.

The boundary layer of a two-dimensional forced convective flow along a persistent moving horizontal needle in an electrically conducting magnetohydrodynamic dissipative nanofluid was numerically investigated. The energy equation was constructed with Joule heating, viscous dissipation, uneven heat source/sink, and thermal radiation effects. We analyzed the boundary layer behavior of a continuously moving needle in Blasius (movingfluid) and Sakiadis (quiescentfluid) flows. We considered Cu nano-particles embedded in methanol. The reduced system of governing Partial differential equations (PDEs) was solved by employing the Rungee-Kutta-based shooting process. Computational outcomes of the rate of heat transfer and friction factors were tabulated and discussed. Velocity and temperature descriptions were examined with the assistance of graphical illustrations. Increasing the needle size did not have asignificant influence on the Blasius flow. The heat transfer rate in the Sakiadis flow was high compared with that in the Blasiusflow.

10 illus, 4 tables, 31 ref

024164   HAYAT T, KHAN M I, WAQAS M, ALSAEDI A (Mathematics Dep, Quaid-I-Azam Univ, Islamabad- 44000, Pakistan, Email: jazfmg_khan@yahoo.com) : On the performance of heat absorption/generation and thermal stratification in mixed convective flow of an Oldroyd-B fluid. Nucl Eng Tech 2017, 49(8), 1645- 53.

This investigation explores the thermally stratified stretchable flow of an Oldroyd-B material bounded by a linear stretched surface. Heat transfer characteristics are addressed through thermal stratification and heat generation/absorption. Formulation is arranged for mixed convection. Application of suitable transformations provides ordinary differential systems through partial differential systems. The homotopy concept is adopted for the solution of nonlinear differential systems. The influence of several arising variables on velocity and temperature is addressed. Besides this, the rate of heat transfer is calculated and presented in tabular form. It is noticed that velocity and Nusselt number increase when the thermal buoyancy parameter is enhanced. Moreover, temperature is found to decrease for larger values of Prandtl number and heat absorption parameter. Comparative analysis for limiting study is performed and excellent agreement is found.

9 illus, 4 tables, 48 ref

024163   QAYYUM S, HAYAT T, SHEHZAD S A, ALSAEDI A (Mathematics Dep, Quaid-I-Azam Univ, Islamabad- 44000, Email: Sajidqayyum94@gmail.com) : Effect of a chemical reaction on magnetohydrodynamic (MHD) stagnation point flow of Walters-B nanofluid with newtonian heat and mass conditions. Nucl Eng Tech 2017, 49(8), 1636- 44.

The main purpose of this article is to describe the magnetohydrodynamic stagnation pointflow of Walter-B nanofluid over a stretching sheet. The phenomena of heat and mass transfer are based on the involvement of thermal radiation and chemical reaction. Characteristics of Newtonian heating are given special attention. The Brownian motion and thermophoresis models are introduced in the temperature and concentration expressions. Appropriate variables are implemented for the transformation of partial differential frameworks into sets of ordinary differential equations. Plots for velocity, temperature, and nanoparticle concentration are displayed and analyzed for governing parameters. The skin friction co-efficient and local Nusselt and Sherwood numbers are studied using numerical values. The temperature and heat transfer rate are enhanced within the frame of the thermal conjugate parameter.

17 illus 4 tables, 40 ref

024162   MAHADEVAN G, IRAVITHUL BASIRA A, SIVAGNANAM C (Mathematics Dep, Deemed Univ, Gandhigram, Dindigul, Email: drgmaha2014@gmail.com) : Some characterization of complementary triple connected domination number of 3 ? regular graphs. J Ind Pollut Control 2017, 33(2), 1639- 44.

A graph is said to be triple connected if any three vertices lie on a path in G. A subset S of V of a nontrivial graph G is said to be complementary triple connected dominating set, if S is a dominating set and the induced sub graph is triple connected. The minimum cardinality taken over all complementary triple connected dominating sets is called the complementary triple connected domination number of G and is denoted by Υctc (G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is called chromatic number χ(G). In this paper, we investigate 3 - regular graphs for which Υctc (G)= X(G)=3.

6 ref

024161   BABU S R R C, VENKATESWARLU S, LAKSHMI K J (Mathematics Dep, JNTUA, Anantapur, Email: ravichandrababusr@gmail.com) : MHD chemically reacting and radiating nanofluid flow over a vertical cone embedded in a porous medium with variable properties. J Ultra Scient Phys Sci 2018, 30(2), 110- 20.

In this study, we examine the combined effects of thermal radiation, chemical reaction on MHD hydromagnetic boundary layer flow over a vertical cone filled with nanofluid saturated porous medium under variable properties. The governing flow, heat and mass transfer equations are transformed into ordinary differential equations using similarity variables and are solved numerically by a Galerkin Finite element method. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction. The effects of various controlling parameters on these quantities are investigated. Pertinent results are presented graphically and discussed quantitatively. The present results are compared with existing results and found to be good agreement. It is found that the temperature of the fluid remarkably enhances with the rising values of Brownian motion parameter (Nb).

19 illus, 17 ref

024160   REDDY M G, KRISHNA M V (Mathematics Dep, Rayalaseema Univ, Andhra Pradesh- 518 007, Email: veerakrishna_maths@yahoo.com) : Heat and mass transfer on unsteady MHD free convective flow through a porous medium over an infinite vertical plate with time dependent permeability and oscillatory suction. J Ultra Scient Phys Sci 2017, 29(12), 515- 29.

We considered the free convective flow over an infinite vertical porous plate under the influence of uniform transverse magnate field with time dependent permeability and oscillatory suction. The equations of the flow are solved by perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the Nusselt number and Sherwood number are also attained and their behavior computationally discussed.

5 illus, 4 tables, 37 ref

024159   JAIN S, CHOUDHARY R (Mathematics & Statistics Dep, Manipal Univ, Jaipur- 303 007, Email: shalini.jain@jaipur.manipal.edu) : Second law analysis in MHD flow and heat transfer of a rotating Casson fluid over a stretching surface. Indian J Pure Appl Phy 2018, 56(1), 53- 62.

Second law analysis in three-dimensional MHD boundary layer flow and heat transfer of a rotating Casson fluid over a stretching surface has been investigated. Such flow problems have relevance in extraction and manufacturing of rubber and polymer sheets. Solution of these problems is of great interest as they serve a practical purpose. Partial differential equations governing flow and heat transfer have been transformed into non-linear ordinary differential equations by using suitable similarity transformations. These non-linear differential equations have been solved numerically by using shooting techniques with fourth order Runge-Kutta method. Effects of Casson fluid parameter β, rotation parameter λ, Prandtl number Pr and magnetic field parameter M on velocity profile, temperature profile and skin friction number have been analyzed and depicted through graphs and tables. Entropy generation number and Bejan number have also been obtained and discussed.

18 illus, 5 tables, 37 ref

024158   CHAUDHARY S, CHAUDHARY M K (Mathematic Dep, Malaviya National Institute of Technology, Jaipur- 302 017, Email: d11.santosh@yahoo.com) : Viscous dissipation and joule heating effects on an unsteady magnetohydrodynamic flow over a linearly stretching permeable surface with uniform wall temperature. Indian J Pure Appl Phy 2017, 55(12), 864- 72.

An analysis has been presented to describe the effects of viscous dissipation and Joule heating on an unsteady laminar two-dimensional flow of a viscous incompressible electrically conducting fluid over a stretching permeable surface in the presence of a uniform transverse magnetic field. Similarity solutions for the problem have been formulated and reduced nonlinear ordinary differential equations have been solved numerically using fourth order Runge-Kutta method with shooting technique. Influences of various parameters, namely, mass transfer parameter, unsteadiness parameter, magnetic parameter, Prandtl number and Eckert number on velocity and temperature distributions have been plotted graphically while skin-friction coefficient and Nusselt number have been shown numerically. A comparison of the obtained numerical results has been made with previously published results for non-magnetic case.

9 illus, 3 tables, 47 ref

024157   JAIN S, BOHRA S (Mathematics & Statistics Dep, Manipal Univ, Jaipur- 303 007, Email: shalini.jain@jaipur.manipal.edu) : Heat and mass transfer over a three-dimensional inclined non-linear stretching sheet with convective boundary conditions. Indian J Pure Appl Phy 2017, 55(12), 847- 56.

This investigation has been made to study of heat and mass on three-dimensional boundary layer flow of an incompressible fluid due to inclined non-linear stretching sheet with convective boundary conditions. The effect of thermophoresis and chemical reaction has been taken into account. Numerical solution has been obtained for the set of non-linear coupled ordinary equations which are reduced by using similarity transformations from non-linear partial differential equations. Transforms system of equations has been solved using Runge–Kutta–Fehlberg fourth–fifth order method along with shooting technique. Effects of various parameters on velocity, temperature and concentration profiles have been obtained. These results have been presented through graphs and also our analysis explores the physical quantities of interest through the tables.

9 illus, 3 tables, 39 ref

024156   LIANG Q, WANG D (Northwestern Polytechnical Univ, Xi’an Shaanxi- 710 072, Email: liangqingwei@nwpu.edu.cn) : Influence study of Weibull distribution parameter on double stress down-step accelerated life test. Indian J Geo-Mar Sci 2018, 47(01), 46-52.

Based on the study of time and efficiency of double step-down-stress accelerated life test, the influence of the change of the shape parameters of Weibull distribution on the time and efficiency of the double step-down-stress accelerated life test is studied. Combined with Matlab software, Monte Carlo method is used. The simulation of different shape parameter of Weibull distribution is carred out. Results show that with the increase of sample size, the failure time curve of Weibull distribution stably intersects in 60 %-70 % of the sample size. When shape parameter m is relatively small, small failure sample number of double step-down-stress accelerated life test can be choosen to carry out truncation test, which will help to shorten test time. When shape parameter m is relatively large, the large failure sample number of double step-down-stress accelerated life test can be choosen to carry out truncation test. This conclusion can also be applied to all double stress accelerated life test.

4 illus, 2 tables, 21 ref

024155   ABOUELREGAL A E, ABO-DAHAB S M (Mathematics Dep, Mansoura Univ, Mansoura- 35516, Email: ahabogal@mans.edu.eg) : A two-dimensional problem of a mode-I crack in a rotating fibre-reinforced isotropic thermoelastic medium under dual-phase-lag model. Sadhana 2018, 43(1), 13.

In the present work, a general model of the equations of generalized thermoelasticity for a homogeneous isotropic elastic half-space solid whose surface is subjected to a mode-I crack problem under the effect of rotation is investigated. The normal mode analyses are used to obtain the expressions for the temperature distribution, the displacement component and thermal stresses in the context of the dual-phase-lag theory of thermoelasticity proposed by Tzou. The boundary of the crack is subjected to a prescribed stress distribution and temperature. Some particular cases are also discussed in the context of the problem. The numerical values of the temperature distribution, the displacement components and thermal stresses are also computed for a suitable material and the results are presented graphically. The effects of rotation, reinforcement and the phase lags parameters are discussed in detail in the light of earlier works.

13 illus, 46 ref

024154   DAS P, AKHTER A, SINGH M K (Applied Mathematics Dep, Indian Institute of Technology, Dhanbad-826 004, Email: pintudas62@gmail.com) : Solute transport modelling with the variable temporally dependent boundary. Sadhana 2018, 43(1), 12.

In this present study, analytical and numerical solutions are obtained for solute transport modelling in homogeneous semi-infinite porous medium. The dispersion coefficient is assumed to be initial dispersion and velocity is assumed to be temporally dependent with initial seepage velocity. Also, the concept of dispersion is directly proportional to the square of the seepage velocity used for finding the solution. Initially, the domain is not solute free. At one end of the domain, source concentration with the effect of different temporally dependent functions taken into account. The concentration gradient assumed to be zero due to no mass flux at other end of the domain. Laplace Transform Technique is used to obtain the exact solution, whereas Explicit Finite Difference method is used for approximate solution. The different types of temporally dependent velocity are used for the graphical representation of the solution. The accuracy of the solution explored by the Relative error analysis.

16 illus, 6 tables, 21 ref

024153   VIJAYASEKHAR J, RAO M V S, SREERAM V (Mathematics Dep, GITAM Univ, Hyderabad, Email: vijayjaliparthi@gmail.com) : Vibrational spectra of copper tetramesityl porphyrin using Vibron model. Oriental J Chem 2018, 34(1), 559-61.

In this paper we calculated the fundamental level vibrational spectra of Metalloporphyrin (bio molecule) copper tetramesityl porphyrin (Cu(TMP)) using Vibron model.

1 illus, 2 tables, 11 ref

024152   SHARMA V, SINGHAL A (Mathematics Dep, N.A.S. (P.G.) Coll, Uttar Pradesh- 250 002., Email: vireshsharma1@yahoo.com) : Evaluation of M.T.T.F. and variance of a k-out of N:G redundant complex system under waiting for repair. Bull Pure Appl Sci- Sect E 2018, 37E(1), 254-9.

This paper presents the investigations for the evaluation of reliability behavior of a k-out of N:G redundant complex system with r repair facilities incorporating the concept of waiting.

3 illus, 5 ref

024151   SUVARNA T, REDDY A M (Mathematics Dep, SK Univ, Andhra Pradesh- 515 003., Email: suvarna8886@gmail.com) : Reliability analysis of six unit bridge and parallel series networks with critical and non-critical human errors. Bull Pure Appl Sci- Sect E 2018, 37E(1), 245-53.

Humans play a pivotal role in the design, development and operational phases of engineering systems. Reliability evaluation of systems without taking into consideration the human element does not provide a realistic picture. Hence, there is a definite need for incorporating the occurrence of human errors in system reliability evaluation. This paper presents reliability analysis of bridge and parallel-series networks with critical and non-critical Human errors. A newly developed approach is used to perform the system reliability analysis. The approach demonstrated in this paper, which consists of six unit bridge network, is a modified version of the block diagram approach.

6 illus, 1 table, 4 ref

024150   RAMESHKUMAR A, KAVITHA G (Mathematics Dep, Srimad Andavan Arts and Science Coll, Tamilnadu-620 005, Email: andavanmathsramesh@gmail.com) : Two finite simple directed graphs. Bull Pure Appl Sci- Sect E 2018, 37E(1), 223-9.

The main result of the paper is that in practically interesting situations determining the optimal number of colors in the proposed coloring is an NP-hard problem. A possible conclusion to draw from this result is that for practical transitive tournament search algorithms we have to develop approximate greedy coloring algorithms. It is an empirical fact that coloring the nodes of a graph can be used to speed up clique search algorithms. In directed graphs transitive sub tournaments can play the role of cliques. In order to speed up algorithms to locate large transitive tournaments we propose a scheme for coloring the nodes of a directed graph.

3 illus, 2 illus, 10 ref

024149   SHARMA V, SHARMA R K, SINGHAL A (Mathematics Dep, N.A.S. (P.G.) Coll, Uttar Pradesh-250 003., Email: vireshsharma1@yahoo.com) : Reliability behaviour of a two-state stand by redundant power plant under arbitrary failure time distribution. Bull Pure Appl Sci- Sect E 2018, 37E(1), 200-7.

This paper presents the investigations for the evaluation of reliability of the power supply having been carried out with the help of Boolean function orthogonalization algorithm. The motive of the complex system is to supply from MPH to several critical consumers.

3 illus, 2 tables, 4 ref

024148   RANI M, HOODA N (Mathematics Dep, Deenbandhu Chhotu Ram Univ of Science and Technology, Haryana-131 039, Email: manjuantil7@gmail.com) : Some fixed point theorems for mappings on complete Sb?Metric space. Bull Pure Appl Sci- Sect E 2018, 37E(1), 178-83.

In this paper, we prove some common fixed point theorems in S_b-metric space using an increasing function ϕ : [0, ∞) → [0, ∞) with lim_n→∞ ϕⁿ(t) = 0 and ϕ(t) < t for each fixed > 0. Our results extend the result of Savitri & Hooda [8] of S-metric space.

10 ref

024147   SATYANARAYANA B, KUMAR Y P, PURNIMA B V (Mathematics Dep, Acharya Nagarjuna Univ, Nagarjuna Nagar- 522 510, Email: drbsn63@yahoo.co.in) : On Euler-Beta transform of I-function of two variables. Bull Pure Appl Sci- Sect E 2018, 37E(1), 171-7.

In this paper, the authors establish the Euler-Beta transform of various products involving a General Class of Polynomials, Struve’s function and I-function of two variables. Some similar formulae are also derived as special cases.

11 ref

024146   MADAN D K, GABA A, RAGHAV J S (Mathematics Dep, Ch. Bansilal Univ, Haryana-127 021, Email: dk_madaan@rediffmail.com) : Strike-Slip fault model with linear and parabolic dislocations with width-depth ratio. Bull Pure Appl Sci- Sect E 2018, 37E(1), 157-70.

This paper tackles the problem of static deformation of an orthotropic elastic layer of uniform thickness overline an orthotropic elastic half-space. This is caused by a very long vertical strikeslip fault in the layer with rigid surface and this problem is solved analytically. The effect of ratio of width and depth of the faults has been studied for parabolic and linear slip profiles by varying the horizontal dimensionless displacements and by depicting contour maps for the stresses

2 illus, 12 ref

024145   MAHTO G (S N Sinha Coll, Bihar- 805 120, Email: ganeshmahto0201@gmail.com) : Effect of radiation and oblateness on the equilibrium points in the elliptic restricted three body problem. Bull Pure Appl Sci- Sect E 2018, 37E(1), 152-6.

In this paper we have obtained the location of equilibrium points in the elliptic restricted three body problem. We suppose that the bigger primary is oblate and the smaller primary as radiating. We find the positions of triangular equilibrium points in our problem and note that the positions of triangular points are shifted away from the line joining the primaries than in the classical case. Thus the positions are affected due to introduction of eccentricity, semi-major axis, radiation and oblateness factors of both primaries.

25 ref

024144   RATH P, DASH R B, GHOSH S K (Mathematics Dep, Ravenshaw Univ, Cuttack- 753 003, Email: priyadarsinirath0@gmail.com) : Solution of fuzzy multi-objective fractional linear programming problem using fuzzy programming technique based on exponential membership function. Bull Pure Appl Sci- Sect E 2018, 37E(1), 109-16.

A method of solving multi-objective fuzzy fractional linear programming problem (MOFFLPP) is presented. All the coefficients of the fractional multi-objective functions and the constraints are taken to be fuzzy numbers. In this paper a MOFFLPP is first reduced to crisp multi-objective linear programming problem and then the crisp MOLPP is solved by Zimmerman’s technique using exponential membership functions.

17 ref

024143   JAIN D (Mathematics Dep, Deenbandhu Chhoturam Univ of Science and Technology, Haryana- 131 039., Email: deepakjain.jain6@gmail.com) : Expansive mappings in digital metric spaces. Bull Pure Appl Sci- Sect E 2018, 37E(1), 101-8.

In this paper, we prove some common fixed point theorems for expansive mappings in digital metric spaces.

4 illus, 16 ref

024142   DHUMAL M L, KIWNE S B (Mathematics Dep, Deogiri Coll, Maharashtra- 431 005, Email: mldhumal19@gmail.com) : Numerical treatment of fisher?s equation using finite difference method. Bull Pure Appl Sci- Sect E 2018, 37E(1), 94-100.

A numerical method is proposed to approximate the solutions of nonlinear Fisher reaction diffusion equation using finite difference method. Fisher’s equation describes the process of interaction between diffusion and reaction. The method is based on replacing each term in the Fisher’s equation using finite difference method. Fisher equation has many applications in science and engineering fields. In this paper we study Du-Fort Frankel finite difference method for Fisher’s equation. This method is derived from Leapfrog explicit scheme.

1 table, 15 ref

024141   RAMESHKUMAR A, STANLY L A J (Mathematics Dep, Srimad Andavan Arts & Science Coll, Tamil Nadu- 620 005., Email: andavanmathsramesh@gmail.com) : Application of magneto-Williamson model in nanofluid flow. Bull Pure Appl Sci- Sect E 2018, 37E(1), 82-93.

This paper investigates the effect of the nano particle effect on magneto hydrodynamic boundary layer over a stretching in the current of heat generation or absorption with heat and mass fluxes. The governing partial differential equations of the system are transformed into a system of ordinary differential equations and solved numerically with the effect of the non-Newtonian Williamson parameter, heat capacities ratio parameter, heat generation or absorption parameter, Schmidt number on the fluid properties as well as on the skin friction, heat and mass transfer rates are described and explained in detailed through graph.

8 illus, 16 ref

024140   AHMED N (Statistics Dep, D.H.S.K. Coll, Assam- 786 001, Email: mdnahmed@yahoo.com) : Restricted constraints in a max-flow and min-cost problem. Bull Pure Appl Sci- Sect E 2018, 37E(1), 63-81.

The present paper defines a combination of two most important and old flow problems such as maximum flow and minimum cost flow. In the first one a flow with the maximum value from source node to sink node is sought. The second one seeks a flow with the minimum total transferring costs from source nodes to demand nodes. Here an attempt is made to obtain an optimal route of a more realistic situation as to scheduling some restricted constraint, in which its transferring cost is minimized and its value is maximized. The proposed algorithm is formulated and solved by the lexicographic search approach. It is seen that the time required for the search of the optimal solution is fairly less. Also the algorithm is applied to different order matrices with number of stations = 5, 8, 10, … , 50 and in the dimensions of 6 to exhibit its effectiveness.

9 illus, 17 tables, 26 ref

024139   ASHA S, LINA S S (Mathematics Dep, Nanjil Catholic Coll of Arts and Science, Tamil Nadu-629 152, Email: selestinlina@gmail.com) : On sequential graphs. Bull Pure Appl Sci- Sect E 2018, 37E(1), 54-62.

A labeling or valuation of a graph G is an assignment f of labels to the vertices of G that indices for each edge xy a label depending on the vertex labels f(x) and f(y). In this paper we study some classes of graphs which admit sequential labeling.

5 ref

024138   DEVARAJ J, TEFFILIA M (Mathematics Dep, WCC Coll, Tamilnadu- 629 001, Email: teffiliafranklin@gmail.com) : On harmonious graphs. Bull Pure Appl Sci- Sect E 2018, 37E(1), 47-53.

Let G = (V (G), E(G)) be a graph with q edges. A function f is called harmonious labeling of graph G if f:V→{0,1,2,...,q-1} is injective and the induced function f* : E → {0,1,2,...,q} defined as f*(uv) = (f(u) + f(v))(mod q) is bijective. A graph which admits harmonious labeling is called harmonious graph. In this paper we prove that the jewel graph, triangular ladder graph, special flower graph, duplicating all the vertex of mK₁, in P₂+mK₁, T(P_n) ʘ K^c_m are harmonious graphs.

1 illus, 6 ref

024137   TIWARI J , TIWARI R (Computer Science Dep, Davi-Ahilya Univ, Madhya Pradesh- 452 009, Email: jayesh_tiwari2005@yahoo.com) : Common fixed point for compatible mappings of type (?) satisfying an implicit relation. Bull Pure Appl Sci- Sect E 2018, 37E(1), 41-6.

Here we prove a common fixed point theorem for compatible mappings of type (α) satisfying an implicit relation. We extend results of Popa [9] for five mappings.

15 ref

024136   BAPAT M V (Shri Kelkar Coll, Maharashtra- 416 630, Email: mukundbapat@yahoo.com) : Neighborhood cordial (Nhd-C) labeling - A new method of graph labeling. Bull Pure Appl Sci- Sect E 2018, 37E(1), 15-20.

We introduce a new technique of graph labeling named as Neighborhood Cordial (Nhd-C) Labeling of Graphs and show that paths, cycles, FL (Cn), S (C₃,n), pathunion Pm(C₃), Pm (C₄),K_1,m: K_1,m , TreeYn are nhd-c graphs.

3 illus, 9 ref

024135   SARPOTDAR P S, YADAV A D (Physics Dep, Parvatibai Gurupad Dhere Arts and Shri. Mahesh Janardan Bhosale Scienc, Ratnagiri- 415 703, Email: padphy@gmail.com) : Independent verification of Euler?s formula in graph theory for N identical circles. Bull Pure Appl Sci- Sect E 2018, 37E(1), 9 - 14.

This paper discusses the famous Euler’s formula in graph theory and its independent verification for the case of n identical circles forming a planar graph. A planar connected graph is generated using n circles, and an intuitive approach is taken to construct formulae for the number of vertices (v), edges (e) and faces (f), where symmetry of the pattern is used to determine the relation between v, e and f.

5 illus, 1 table, 2 ref

024134   UPADHYAYA L M (Mathematics Dep, Municipal Post Graduate Coll, Uttarakhand- 248 179, Email: lmupadhyaya@rediffmail.com) : On the degenerate laplace transform - I. Bull Pure Appl Sci- Sect E 2018, 37E(1), 1 - 8.

We make an attempt in this paper to extend the very recent work of Kim and Kim [24] on degenerate Laplace transform. Using the definition of the degenerate Laplace transform as given by Kim and Kim [24] and some of the results developed by them in this study we prove the first and second translation theorems and the change of scale property for the degenerate Laplace transform and give some illustrations highlighting the applications of these results for the degenerate Laplace transform of a function.

29 ref

023302   REZA M, PANIGRAHI S, MISHRA A K (Mathematics Dep, National Institute of Science and Technology, Berhampur- 760 007, Email: reza@nist.edu) : Stagnation point flow and heat transfer for a visco elastic fluid impinging on a quiescent fluid. Sadhna 2017, 42(11), 1979-86.

A theoretical study is made in the region near the stagnation point when a lighter incompressible viscoelastic fluids impinges orthogonally on the surface of another quiescent heavier incompressible viscous fluid. Similarity solutions of the momentum balance equations for both fluids are equalized at the interface. It is noted that an exact boundary layer solution is obtained for the lower lighter fluid. The velocity of the lower fluid is independent of lateral interface velocity but the velocity of the upper viscoelastic fluid increases with increasing lateral interface velocity. It is observed that lateral interface velocity increases with increasing viscoelastic parameter for fixed values of density and viscosity ratio of the two fluids. The convective heat transfer is investigated base on the similarity solutions for the temperature distribution of the two fluids. The interface temperature increases with increasing viscoelastic parameter of the upper viscoelastic fluid.

22 illus, 10 ref

023301   SIVASANKARAN S, ANANTHAN S S, BHUVANESWARI M, HAKEEM A K A (Mathematics Dep, King Abdulaziz Univ, Saudi Arabia- 21589, Email: sd.siva@yahoo.com) : Double-diffusive mixed convection in a lid-driven cavity with non uniform heating on sidewalls. Sadhna 2017, 42(11), 1929-41.

The effect of sinusoidal heating on double-diffusive mixed convective flow with heat and mass transfer in a lid-driven square cavity is numerically investigated. The horizontal walls of the cavity are adiabatic and impermeable. Sinusoidal boundary temperatures and concentrations are imposed along the left and right sidewalls of the cavity. The governing unsteady equations for continuity, momentum, energy and species transfer are solved using the finite-volume method. The numerical solutions are computed for various parameters such as the Richardson number, amplitude ratio, buoyancy ratio and phase deviation. The obtained results are discussed in detail under different combinations of the pertinent parameters.

7 illus, 1 table, 27 ref

023300   PRIYADHARSHINI S, PONALAGUSAMY R (Mathematics Dep, National Institute of Technology, Tiruchirappalli- 620 015, Email: priya.nit13@gmail.com) : Computational model on pulsatile flow of blood through a tapered arterial stenosis with radially variable viscosity and magnetic field. Sadhna 2017, 42(11), 1901-13.

An unsteady two-fluid model of blood flow through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been analysed in the present paper. In this article, blood in the core region is assumed to obey the law of Jeffrey fluid and plasma in the peripheral layer is assumed to be Newtonian. The values for velocity, wall shear stress, flow rate and flow resistance are numerically computed by employing finite-difference method in solving the governing equations. A comparison study between the velocity profiles obtained by the present study and the experimental data represented graphically shows that that the rheology of blood obeys the law of Jeffrey fluid rather than that of Newtonian fluid. The effects of parameters such as taper angle, radially variable viscosity, hematocrit, Jeffrey parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution and flow resistance have been investigated. The results in the case of radially variable magnetic field and constant magnetic field are compared to observe the effect of magnetic field in driving the blood flow. It is observed that increase in hematocrit increases the wall shear stress. The values of wall shear stress and flow resistance are obtained at various time instances and compared. It is pertinent to note that the magnitudes of flow resistance are higher in the case of converging tapered than non-tapered and diverging tapered artery.

12 illus, 57 ref

023299   VIDHYALAKSHMI S, GOPALAN M A, THANGAM S A (Mathematics Dep, Shrimati Indira Gandhi Coll, Tamil Nadu) : Construction of family of triples where the sum of any two members of a triple is a perfect square. Int J Multidiscipl Res Dev 2017, 4(11), 142-50.

This paper deals with the construction of families of integer triples where, in each triple, the sum of any two members is a perfect square.

6 ref

023298   MBAH G C E, ONWUAMAEGBU P C, OKOYE C (Mathematics Dep, Univ of Nigeria, Nigeria) : Mathematical model on prostate cancer growth and its control. Int J Multidiscipl Res Dev 2017, 4(11), 68-81.

In this work, we considered the general overview of the prostate cancer disease, and some of the factors influencing its growth,then presented a mathematical model describing the growth of the disease based on those factors. The model consists of a set of three ordinary differential equations, each describing the process of formation of prostate cancer. The solutions to the model equations have were obtained and ways of controlling or preventing the disease also presented. The equilibrium and stability conditions and the results of the model simulations are also discussed.

7 illus, 39 ref

023297   RANGANATHA D (Studies in Mathematics Dep, Univ of Mysore, Karnataka, Email: ddranganatha@gmail.com) : Ramanujan type congruences modulo powers of 5 and 7. Indian J Pure Appl Math 2017, 48(3), 449-65.

Let b_l(n) denote the number of l-regular partitions of n. In 2012, using the theory of modular forms, Furcy and Penniston presented several infinite families of congruences modulo 3 for some values of l. In particular, they showed that for ?, n ? 0, b₂₅ ( 3^2?+3n + 2 • 3^2?+2 – 1)? 0 (mod 3). Most recently, congruences modulo powers of 5 for c₅(n) was proved by Wang, where c_N(n) counts the number of bipartitions (?₁,?₂) of n such that each part of ?₂ is divisible by N. In this paper, we prove some interesting Ramanujan-type congruences modulo powers of 5 for b₂₅(n), B₂₅(n), c₂₅(n) and modulo powers of 7 for c₄₉(n). For example, we prove that for j ? 1, c₂₅ ( 5^2j n + 11 • 5^2j + 13/12 ) ?0 (mod 5^j+1), c₄₉ (7^2j n + 11 • 7 ^2j + 25/12 ) ?0 (mod 7 ^j+1) and b₂₅( 3^2?+3 • 5^2j?1 • n + 2 • 3^2?+2 • 5^2j?1 ? 1 ´ ?0 (mod 3 • 5^2j?1).

13 ref

023296   WU Z, ZHANG CHI, HUANG J (Mathematics Dep, Univ of Science and Technology of China, China, Email: zhfwu@mail.ustc.edu.cn) : Finite groups with given Ó-n- embedded subgroups 1. Indian J Pure Appl Math 2017, 48(3), 429-48.

Let G be a finite group and ? = {?_i|i ? I} be a partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall ?-set of G if every non-identity member of H is a Hall ?_i-subgroup of G and H contains exactly one Hall ?_i-subgroup of G for every ?_i ? ?(G). A subgroup H is said to be ?-permutable if G possesses a complete Hall ?-set H such that HA^x= A^xH for all A ? H and all x ? G. Let H be a subgroup of G. Then we say that: (1) H is ?-embedded in G if there exists a ?-permutable subgroup T of G such that HT = H^?G and H ? T ? H_?G, where H_?G is the subgroup of H generated by all those subgroups of H which are ?-permutable in G, and H^?G is the ?-permutable closure of H, that is, the intersection of all ?-permutable subgroups of G containing H. (2) H is ?-n-embedded in G if there exists a normal subgroup T of G such that HT = H^G and H ? T ? H_?G. In this paper, we study the properties of the new embedding subgroups and use them to determine the structure of finite groups.

23 ref

023295   HAJIZADEH S, NASRABADI M M (Mathematics Dep, Univ of Birjand, Iran, Email: shajizadeh@birjand.ac.ir, mnasrabadi@birjand.ac.ir) : On absolute central automorphisms of a group fixing the center element wise. Indian J Pure Appl Math 2017, 48(3), 423-7.

Let G be a finite p-group. The automorphism ? of a group G is said to be an absolute central automorphism, if for all x ? G, x^?1x^? ? L(G), where L(G) is the absolute center of G. In this paper, we obtain a necessary and sufficient condition that each absolute central automorphism of G fixes the center element-wise. 

5 ref

023294   XI W, WANG L (Applied Mathematics Dep, Northwestern Polytechnical Univ, China, Email: lgwangmath@163.com) : Bounds for the signless laplacian energy of digraphs 1. Indian J Pure Appl Math 2017, 48(3), 411-21.

Let G be a digraph with n vertices, a arcs, c₂ directed closed walks of length 2. Let q₁, q₂, . . . , q_n be the eigenvalues of the signless Laplacian matrix of G. The signless Laplacian energy of a digraph G is defined as ESL(G) = ⁿ ? _i=1 |q_i ? a/n |. In this paper, some lower and upper bounds are derived for the signless Laplacian energy of digraphs.

17 ref

023293   UBA M O, UZOCHUKWU M I, ONYIDO M A (Univ of Nigeria, Nigeria, Email: markjoe.uba@unn.edu.ng) : Algorithm for approximating solutions of hammerstein integral equations with maximal monotone operators. Indian J Pure Appl Math 2017, 48(3), 391-410.

Let X be a uniformly convex and uniformly smooth real Banach space with dual space X^?. Let F : X ? X^? and K : X^? ? X be bounded monotone mappings such that the Hammerstein equation u + KFu = 0 has a solution. An explicit iteration sequence is constructed and proved to converge strongly to a solution of this equation. 

31 ref

023292   LONE M S, KRISHNASWAMY D (Mathematics Dep, Annamalai Univ, Tamilnadu, Email: saleemlone9@gmail.com) : Representation of projectors involving minkowski inverse in minkwski space. Indian J Pure Appl Math 2017, 48(3), 369-89.

A certain class of results about the different representations of Oblique projectors is present in the literature. These results represent Oblique projectors as the functions of orthogonal projectors with given onto and along spaces. But these results are valid under the restriction that the functions of orthogonal projectors involved are invertible. In this paper we extend and generalize these results. The extension lies in making a transition from Euclidean space to Minkowski space M and the generalization is obtain by voiding the invertibility condition and use of the Minkowski inverse. Furthermore, the nobility lies in utilizing the m-projectors instead of the regular orthogonal projectors. 

29 ref

023291   AMIROV S (Mathematics Dep, Karabuk Univ, Turkey, Email: samirov@karabuk.edu.tr) : Boundary value problem for one evolution equation. Indian J Pure Appl Math 2017, 48(3), 363-7.

The characteristic property of this type of equations is the failure of the Petrovski’s “A” condition when coefficients are constant [1]. In this case, Cauchy problem is incorrect in the sense of Hadamard. Hence in this paper, the space, guaranteeing the correctness of the boundary value problem in the sense of Hadamard, is selected by adding some additional conditions to the coefficients of the equation. 

15 ref

023290   CHANDRASEKHAR K, DESHPANDE P (Mathematics Dep, Univ of Kentucky, USA, Email: ak.c@uky.edu; pdeshpande@cmi.ac.in) : Face enumerations for line arrangements in A2- torus. Indian J Pure Appl Math 2017, 48(3), 345-62.

A toric arrangement is a finite collection of codimension-1 subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let f_i denote the number of i-dimensional faces; these so-called face numbers satisfy the Euler relation ? _i(?1)ⁱ f _i = 0. However, not all tuples of natural numbers satisfying this relation arise as face numbers of some toric arrangement. In this paper we focus on toric arrangements in a 2-dimensional torus and obtain a characterization of their face numbers. In particular we show that the convex hull of these face numbers is a cone. 

6 illus,11 ref

023289   NISHIZAWA Y (General Education, Ube National Coll of Technology, Japan, Email: yusuke@ube-k.ac.jp) : Symmetric inequalities with power- exponential functions. Indian J Pure Appl Math 2017, 48(3), 335-44.

We establish symmetric inequalities with power-exponential functions and propose a conjecture. 

13 ref