KANDU D

**042879** KANDU D (Mathematics Dep, MMMUT Gorakhpur, U P) : **A case study of mortality in rural population of Gorakhpur, U.P..** Indian J Sci Res 2020, 10(2), 77-9.

In this paper, an attempt has been made to evaluate the mortality rates among rural population through CDR, IDR, ASDR and distribution of deaths by cause of death from the data obtained on survey of 300 sample households of particularly Gorakhpur district, situated in north-eastern part of Uttar Pradesh.

2 illus, 3 tables, 8 ref

BARI M N, MALIK M A

**042864** BARI M N, MALIK M A (Mathematics Dep, The Punjab Univ, Lahore - 54590, Pakistan, Email: drnadeembari@gmail.com) : **Primitive representations and the modular group.** Indian J Sci Technol 2020, 13(25), 2547–57.

Primitive representations are useful to explore the modular group action on real quadratic field. By using primitive representations structure of G-orbit are obtained. Finding: Conditions on n and a, b, c are determined when α ^{G} = (− α) ^{G} , α^{ G} = (− − α) ^{G} , α ^{G} = (−α) ^{G} , α ^{G} = (− α) ^{G} = (− − α) ^{G} = (−α) ^{G} and α ^{G} ̸= (− α) ^{G} ̸= (− − α) ^{G} ̸= (−α)^{ G} , where α = ^{a+ √ n} _{c }with b = a ^{2−n}_{ c} is real quadratic irrational number. We also find some elements of modular group PSL(2,Z) that moves α to − α , α to − − α and α to −α. By using these conditions, we can construct the structure of the G-orbit. These results are verified by suitable examples.

6 illus, 9 ref

MALIK M A , JAVED M A

**042834** MALIK M A , JAVED M A (Mathematics Dep, The Punjab Univ, Lahore, Pakistan, Email: aamirmath@live.com) : **On circuit structure of PSL (2, Z)-orbits of length eight.** Indian J Sci Technol 2020, 13(22), 2220–8.

Modular group or PSL(2,Z) is a well-known group of the non-singular square matrices of order two by two with unit determinant. An Action of this group on real quadratic fields is represented by coset diagrams consisting of closed paths known as circuits. For a particular value of n , one or more than one circuits combine to form an orbit. The length of a circuit identifies all the circuits of an orbit. The main objective of this study is to explore all the circuits of length eight and their corresponding orbits. Some circuit equivalent properties, the group theoretical approach, along with the statistical methodology, is adopted to classify the orbits containing circuits of length eight. We also use already discovered results related to circuits of lengths two, four, and six to formulate the basis for our new results of length eight. We have discovered all the equivalence classes for the circuits of length eight, which are twenty-one in number. For a particular reduced number α, circuits of length eight can have all four; α,−α, its algebraic conjugateα¯ and − α¯ , either in one circuit or (α) ^{G} = (−α) ^{G} with (−α) ^{G} = (−α¯) ^{G} or (α) ^{G} = (α¯) ^{G} with (−α) ^{G} = (−α) ^{G} or (α) ^{G} = (−α) ^{G} with (−α) ^{G} = (α) ^{G} , depending upon the equivalent class of the circuit. Moreover, we have introduced reduced positions and G-midway and discovered that for any reduced numbers α_{i} starting from α_{1} , reduced positions have a recurring pattern α_{2},−α_{3},−α_{4},α_{5}, and so on. PSL(2, Z) orbits are entirely classified and drawn, along with the cyclically equivalent circuits of length eight.

3 illus, 2 tables, 16 ref

SELVAKUMAR V, SATPATHI D K, KUMAR P T V P , HARAGOPAL V V

**042819** SELVAKUMAR V, SATPATHI D K, KUMAR P T V P , HARAGOPAL V V (Mathematics Dep, Bhavan's Vivekananda Coll of Science and Commerce, Hyderabad, Email: p20170106@hyderabad.bitspilani.ac.in) : **Modeling and prediction of third-party claim using a Machine learning approach.** Indian J Sci Technol 2020, 13(21), 2071–9.

The main objective of this research paper is to build an appropriate mathematical model that helps in forecasting overall claim amount based on the chosen characteristics of the data. In the field of actuarial research, forecasting the third-party claim amount for Motor vehicles is a challenging task, and only limited empirical research studies are done in predicting the claim. In this context, the annual time series historical claim data were collected for a period of 34 years to examine the predictive performance of the linear regression model, exponential smoothing model, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and hybrid ARIMA-ANN models to predict third party claim amount of motor insurance data in India. The data are analyzed, and the empirical evidence from the study shows that the ANN model improved the accuracy prediction when compared to Linear Regression, Exponential smoothing model, ARIMA and a hybrid model with respect to the performance criteria such as root mean squared error (RMSE) and mean absolute percentage error (MAPE). Therefore, the ANN model is more potent in forecasting TP claim amounts by considering the adequacy, suitability, and accuracy of the data modeling. This data analytics approach would help motor insurance companies in India to have an idea about the expected future claim amounts. Also, this modeling approach will help the Motor Insurance companies of India to provide a better customer-centric forecasting model, which ensures better claims settlement and management.

5 illus, 3 tables, 21 ref

KHANTWAL D, GAIROLA U C

**044801** KHANTWAL D, GAIROLA U C (Mathematics Dep, Graphic Era Hill Univ, Dehradun, Uttarakhand, Email: ucgairola@rediffmail.com) : **A note on the paper “On completeness in metric spaces and fixed point theorems".** J Mountain Res 2020, 15, 127-30.

In the present note, we show that the assumption of continuity used in the fixed point theorem of Gregori et al. (Results Math. 73 (2018), no. 4, Art. 142, 13) can be relaxed to some weaker version of continuity. More precisely, we prove a fixed point theorem for orbitally continuous and k-continuous mappings in weak G-complete metric space and provide an appropriate example to show that our result is not only valid for continuous mappings but also for some discontinuous mappings. Moreover, we apply our main result to establish a common fixed point theorem for two self-mappings.

10 ref

JAVED M A, MALIK M A

**042754** JAVED M A, MALIK M A ( Mathematics Dep, GC Univ, Katchery Road, 54000, Lahore, Pakistan, Email: aamirmath@live.com) : **Properties of circuits in coset diagrams by modular group.** Indian J Sci Technol 2020, 13(14), 1458–69.

Graham Higman gave the idea of coset diagrams for the action of modular group PSL(2,Z) on real quadratic irrationals. These special types of graphical figures are composed of closed paths known as Circuits. These circuits can be classified into certain types of even length with respect to the number of inside\outside triangles. This study is to discuss different properties of reduced numbers in coset diagrams of the type (p,q). In this study, we have investigated different properties of type (p, q) using reduced quadratic irrationals and continued fractions. We have categorized reduced numbers in accordance with their position in the real line. Distance between two ambiguous numbers and reduced numbers is introduced in this article which will help the reader to understand the structural significance of reduced numbers in a circuit. We have explored different conditions under which certain reduced numbers have the same circuit. Moreover, continued fractions have been used to assist the foundation laid by modular group action and different general results have been derived in this context. : It was possible to define new notions of equivalent, cyclically equivalent and similar circuits using partitions of n and discuss various properties of reduced numbers included in coset diagrams of circuits with length up to four. This study helps us in classifying PSL (2, Z)-orbits of Q( √ m)\Q = ∪ k∈N Q ^{∗} ( √ k ^{2}m), where Q^{ ∗ }( √ n) = { a+ √ n c : ( a, a ^{2}−n c , c ) = 1}.

3 illus, 4 tables, 10 ref

CHAUHAN I S, CHAUHAN T S

**042750** CHAUHAN I S, CHAUHAN T S (Mathematics Dep, Bareilly Coll, Bareilly (U.P.), Email: indiwarsingh.chauhan@gmail.com) : **D-homothetic deformation of an η-Einstein Para-Sasakian manifold.** Indian J Sci Technol 2020, 13(13), 1435–9.

The main purpose of this paper is to study the theory of Dhomothetic deformation of an η-Einstein Para-Sasakian manifold. A deformation technique is employed to solve the resulting problem. We provide its application in the general theory of relativity. Section 2 deals with recurrent and symmetric Para-Sasakian Manifolds. In section 3 we have defined and studied projectively symmetric Para-Sasakian manifold. The notion of ϕ-holomorphic sectional curvature in an η-Einstein Para-Sasakian manifold has been delineated in the section 4. In this very section, we shall study the relevant commutation formulae which give rise to the required curvature tensor. The obtained results were compared with the previous works^{(1--3)} in this field and were found to be in good agreement. The study concludes the following results: 1. If n-dimensional Para-Sasakian manifold is to be recurrent projective symmetric then the recurrent projective curvature tensor vanishes identically. 2. If n-dimensional Para-Sasakian manifold is to be projective semi-symmetric then the semi-recurrent projective curvature tensor vanishes identically. 3. If n-dimensional Para-Sasakian manifold is to be projective scalar-symmetric then the scalar projective curvature vanishes identically. 4. If D-homothetic deformation of η-Einstein Para-Sasakian manifold is constant ϕ-holomorphic sectional curvature then we shall obtain the value of scalar fields.

6 ref

PRAKASH K A, KRISHNARANI S D

**042685** PRAKASH K A, KRISHNARANI S D (Statistics Dep, Farook Coll (Autonomous) (Affiliated to Univ of Calicut), Kozhikode - 673 632, Kerala, Email: krishnaranisd@ gmail.com ) : **A study of the impact of recent floods on the micro, small, and medium business enterprises of Kerala.** Indian J Sci Technol 2020, 13(6), 686 – 95.

To study the impact of Kerala floods of 2018 in the Micro, Small, and Medium Business Enterprises of Kerala. The study was conducted with the primary data obtained from the ground response of the entrepreneurs by the method of questionnaire. A comprehensive study was undertaken utilizing the competence of advanced statistical tools and software that provided clear insights on the socio-economic aftermaths of the calamity. The customer arrival has declined in the flood affected urban areas while rural localities remained same. Purchasing capacity of customers decelerated in the rural localities whereas in urban localities approximate to normal. The expenditure incurred for the entrepreneurs as the result of the devastation was enormously hiked at the same time the employment generation experienced a significant dip in the sector. The overall function of the sector is slowly approaching the normalcy. The rural localities suffered extremely from the disruption of transportation due to extensive damages on roads and highways whereas urban localities have relieved from the disruption of movement of goods. It was found that insurance coverage has not helped them to recover from the losses incurred due to flood. The enterprises functioning in ecologically sensitive areas were the worst affected by the flood. The distribution of income was found to have significant divergence among the urban and rural localities. Mandating the inclusion of insurance policy reforms with specific consideration for employment generation and enhancement of rural economy is necessary. Strict implementation of environmental norms should be constituted.

5 illus, 3 tables, 4 ref

ALI L, ASLAM M, KHAN Y A

**042667** ALI L, ASLAM M, KHAN Y A (Mathematics Dep, Government Coll Univ, Lahore, Pakistan, Email: rehmani_lhr@yahoo. com) : **On Jordan Ideals of Inverse Semirings with Involution.** Indian J Sci Technol 2020, 13(4), 430 – 8.

The main objective of this article is to introduce *-Jordan ideals of a certain class of semirings called MA-semirings with involution and to investigate some conditions for which the above said ideals contained in the center. We use the Jacobian identities and 2-torsion freeness of MA semirings. In this connection, we establish some important results of ring theory for the class of MA-semirings. The commutative property is helpful to study the theory of semirings with ease therefore we find some conditions to impose commutativity in semirings, which are indeed novel idea in the field of semirings. Furthermore, these conditions are used in a most generalized way that these conditions bring the *-Jordan ideals to the center, therefore, it would be the corollary of result that semiring is commutative.

14 ref

ALKHAWALDEH M A, KHASAWNEH M A S

**042665** ALKHAWALDEH M A, KHASAWNEH M A S (Special Education Dep, King Khalid Univ, Saudi Arabia, Email: malkhawaldeh@kku.edu.sa ) : **The impact of using an infographic-based training program on improving visual motor memory among EFL students.** Indian J Sci Technol 2020, 13(4), 405 – 16.

This study aimed at investigating the impact of an infographic-based training program on improving the visual motor memory among EFL students. The study used a semi-experimental approach and the program was applied on 60 EFL students enrolled in the schools of the Directorate of Education in Asir region, Saudi Arabia. The students were divided into two groups: an experimental and control groups. The researcher applied the training program on students after training the teachers on how to better utilize all the elements of the training program effectively. The results showed statistically significant differences in the post-test of visual motor memory skills between the experimental and control groups, which were in favor of the experimental group. The results also revealed that there were no statistically significant differences in the visual motor memory posttest due to the variables of gender and interaction between group and gender. The study concluded that using infographics enhanced the participants’ visual motor memory skills in learning English as a second language regardless of their gender, which indicates the appropriateness of the training program for such students. The study recommended this training program to be used by EFL teachers and EFL curricula designers to consider integrating infographics in the design of these courses.

4 tables, 18 ref

SUNOJ B S, MATHEW VARKEY T K

**042655** SUNOJ B S, MATHEW VARKEY T K (Mathematics Dep, Government Polytechnic Coll, Attingal, Kerala, Indiax, Email: spalazhi@yahoo. com) : **Linear incidence edge prime labeling – more results on path related di graphs.** Indian J Sci Technol 2020, 13(2), 141 – 8.

Our aim is to find new families of di graphs that admit linear incidence edge prime labeling. Here the vertices are assigned with 0,1,…,m−1 and edges with 2g(v) + g(u), where u is the initial vertex and v is the terminal vertex and g is the vertex labeling function. The graph is prime when the greatest common incidence number of vertices with in degree greater than one is one. Here we prove that di graph of corona product of Pn with K2, strong shadow graph of path P_{n}, strong splitting graph of path P_{n}, square graph of path P_{n}, tortoise graph of path P_{n}, graph obtained by joining the corresponding internal vertices of two copies of path P_{n}, strong Z graph of path P_{n} admit linear incidence edge prime labeling. One can generalize these results and find some structural properties. These results may be applied to the transportation problem, chemical graph theory and decision analysis.

6 illus, 6 ref

SIDE S, PRATAMA M I, BADWI N, SANUSI W

**042649** SIDE S, PRATAMA M I, BADWI N, SANUSI W ( Mathematics Dep, Negeri Makassar Univ, Parangtambung, Makassar, Indonesia, Email: syafruddin@unm. ac.id ) : **Analysis and simulation of siri model for dengue fever transmission.** Indian J Sci Technol 2020, 13(3), 340 – 51.

The aim of this study is to obtain SIRI model for dengue fever (DHF) transmission, conduct analysis, and simulation of SIRI model in disease-free and endemic and also to predict the number of DHF cases. Dengue fever is caused by a virus carried by the Aedes aegypti and Aedes albopictus mosquitoes, the SIRI model is a modification of the SIR model. Analysis of the SIRI model use the Lyapunov function method, then the data used in the simulation are assuming to show two possible dengue status are disease free and endemic status. The simulation also using the number of dengue case in Makassar city for showing the status of dengue fever transmission in Makassar city. Simulation models using Maple software are to predict the number of dengue cases in the following months. The results of this study are the SIRI model of the transmission of dengue fever with variables that have recovered can be re-infected with dengue fever, analysis of the SIRI model of dengue transmission provides information that the equation system in the SIRI model which is asymptotically stable, it means that dengue cases always exist at a certain time and certain region. The simulation results of the SIRI model in this study illustrate the number of dengue cases in the following months. While the first simulation found the basic reproduction number is R0 = 0.0366 ≤ 1 this means that dengue transmission is at an alarming stage, but the second simulation finds the basic reproduction number R0 = 31.2733 > 1, this means that, a person infected with dengue causes eight individuals will be infected with dengue fever, so that it is in the endemic stage, and the last simulation using data of the number of dengue case in Makassar city found = 1, that means, Makassar city is a free disease case for dengue fever transmission. SIRI model for DHF transmission is a mathematical health application. Model analysis guarantees existence, disease-free or endemic status, while simulation results can be used as a reference in DHF prevention.

4 illus, 4 tables, 17 ref

JOHARI A, OKTAFIANI D W, DEWI R S

**044634** JOHARI A, OKTAFIANI D W, DEWI R S (Mathematical and Natural Science Education Dep, Jambi Univ, Jambi, Indonesia, Email: johari_asni@yahoo.com) : **The presence of ladybug beetle (Coleoptera: Coccinellidae) as a predator on agriculture in Jambi region.** J Ent Res 2020, 44(1), 45-50.

The results showed that 13 types of ladybugs beetles were present in several agriculture cultivation in the Jambi region, namely; Epilachna sp. Verania discolor Fabricius, Verania lineata Thunberg, Coelophora reninplagiata Mulsant, Coelophora 9 muculata Thunberg, Coccinella arcuata Fabricius, Chilomenes sexmaculata Fabricius, Heteroneda reticulata Fabricius, Harmonia (Callineda), Micromedicata, Microticata. There were 3405 individuals of ladybugs beetles, with the most common species was the Epilachna sp. and the fewest species found were Heteroneda reticulata. Diversity indices at each station were station I (2.20), II (1.89), III (1.78), IV (2.17), and station V (2.05). The highest diversity index of ladybugs beetles species is at station I and the lowest diversity index is at station III. The diversity of ladybugs beetles in all stations shows the criteria of moderate diversity. Dominance index at station I (0.11), II (0.20), III (0.20), IV (0.13), and V (0.16). The highest dominance index at station II and III has the same dominance index value, and the lowest dominance index at station I. All stations have the same criteria, which indicates that no species dominate. For the evenness index at station I (0.95), II (0.76), III (0.81), IV (0.87), and V (0.85). Highest evenness index was at station I, and low evenness index was at station II. All stations indicate that the evenness index has moderate evenness criteria that indicates a stable community.

3 illus, 2 tables, 17 ref

KEFENE M Z, MAKINDE O D, ENYADEN L G

**042554** KEFENE M Z, MAKINDE O D, ENYADEN L G (Applied Mathematics Dep, Adama Science and Technology Univ, Adama, Ethiopia, Email: mesfink2005@gmail.com) : **MHD variable viscosity mixed convection of nanofluid in a microchannel with permeable walls.** Indian J Pure Appl Phys 2020, 58(12), 892-908.

In this study, we examine the combined effects of buoyancy forces, pressure gradient, thermophoresis, Brownian motion, variable viscosity of nanofluid flow in a microchannel with suction and injection in the presence of uniform magnetic field imposed in cross-wise direction. It is assumed that the dynamic viscosity of the nanofluid is related with temperature exponentially and that the vertical parallel-plates temperature is held asymmetrically. Applying similarity transformation, the governing system of partial differential equations (PDEs) are transformed into a set of non-dimensional nonlinear partial differential equations whose solutions are obtained numerically by semi-discretization centered finite difference method along with Runge-Kutta Fehlberg integration technique scheme. Qualitative description of graphical results depicting the effect of thermophysical parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt number and Sherwood number are presented.

24 illus, 43 ref

DAS U J, DORJEE S

**042532** DAS U J, DORJEE S ( Mathematics Dep, Gauhati Univ, Guwahati-781 014, Assam, Email: utpaljyotidas@yahoo.co.in) : **Unsteady MHD oscillatory visco-elastic fluid flow through an inclined channel in presence of chemical reaction with soret and dufour effects.** Indian J Pure Appl Phys 2020, 58(9), 691-7.

The purpose of present paper is to analyze the Soret and Dufour effects on an unsteady magneto hydrodynamic oscillatory flow of radiative, visco-elastic fluid through an inclined channel filled with saturated porous medium with non-uniform wall temperature in presence of first-order chemical reaction. The governing dimensionless momentum equation coupled with the energy and mass diffusion equations are solved analytically. The expressions for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are obtained and are analyzed graphically for various values of the dimensionless flow parameters.

26 illus, 18 ref

CHAUDHARY S, CHOUDHARY M K, CHAUDHARY S

**042517** CHAUDHARY S, CHOUDHARY M K, CHAUDHARY S (Mathematics Dep, Malaviya National Institute of Technology, Jaipur - 302 017, Email: d11.santosh@yahoo.com) : **Finite element scheme for MHD forced convection flow near stagnation point and heat transfer by Newtonian heating, constant wall temperature and constant heat flux.** Indian J Pure Appl Phys 2020, 58(7), 538-47.

Two dimensional, steady, forced convection magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid in a forward stagnation region of an infinite solid surface with Newtonian heating, constant wall temperature and constant heat flux has been investigated. Governing partial differential equations for the exploration have been formulated and converted to nonlinear ordinary differential equations by inserting convenient variables. An efficient finite element scheme along to Gauss elimination method has been introduced to find the numerical solutions of the resultant equations. Variation in velocity and temperature distributions against the pertinent parameters like magnetic parameter, Prandtl number and Eckert number have been displayed graphically while skin-friction coefficient and Nusselt number have been discussed quantitatively. A comparison of the computational results has been found in excellent agreement with open literature for limiting cases.

11 illus, 2 tables, 41 ref

SAINI C K, GUPTA A

**044524** SAINI C K, GUPTA A (Mathematics and Statistics Dep, Jawaharlal Nehru Krishi Vishwa Vidyalaya, Jabalpur- 482 004, Madhya Pradesh, Email: schetan761@gmail.com) : **Fitting statistical model on some agricultural dynamic variables to analyse growth of Barley (Hordeum vulgare) production and productivity in Jaipur district of Rajasthan.** J Crop Weed 2020, 16(1), 78-81.

In this paper, we study stochastic models to analysis production and productivity of barley in Jaipur district of Rajasthan. There we took two dynamic variables or factors on which stochastic model has been fitted. The factor is as following Barley production (000 tones) and productivity (kg ha-1). The stochastic models which used for fitting purpose as following: Linear, Quadratic, Compound, Cubic and Power,there we used three criteria to comparison among model namely (i) Adjusted R^{2} , (ii) Residual mean squares error (RMSE) and (iii) coefficient of determination (R^{2} ). The model which shows the highest R^{2} and least RMSE,it would be best for a specific factor. The results indicated that the cubic, compound and power are the most suitable model to study barley production and productivity in Jaipur district of Rajasthan

2 illus, 2 tables, 7 ref

KULLI V R, CHALUVARAJU B, KUMARA M

**044469** KULLI V R, CHALUVARAJU B, KUMARA M (Mathematics Dep, Gulbarga Univ, Gulbarga- 585 106, Email: vrkulli@gmail.com) : **Inverse total restrained domination in graphs.** J Comp & Math Sci 2020, 11(3), 6-11.

Let D be a minimum total restrained dominating set of a graph G = (V, E). If V – D contains a total restrained dominating set D' of G, then D' is called an inverse total restrained dominating set with respect to D. The inverse total restrained domination number tr –1 (G) of a graph G is the minimum cardinality of an inverse total restrained dominating set of G. In this paper, we initiate a study of this parameter and establish some results on this new parameter. Also we obtain a NordhausGaddum type result.

1 illus, 18 ref

PONRAJ A P, SHERIF M Z

**044468** PONRAJ A P, SHERIF M Z (Meenakshi Academy of Higher Education and Research, Chennai) : **Remarks on pre−H−open set.** J Comp & Math Sci 2020, 11(2), 1-5.

In this paper we define pre−H^{∗}−open set and study the properties between pre− H −open set and pre− H^{∗}−open set in generalized topological space with Hereditary class.

5 ref

PAL A, DAS A, THAKURIA J

**044463** PAL A, DAS A, THAKURIA J (Statistics Dep, Acharya Prafulla Chandra Coll, Kolkata, West Bengal, Email: arabinda@apccollege.ac.in) : **Electrocardiographic changes in chronic obstructive pulmonary disease - An observational study from North-East of India.** J Commun Dis 2020, 52(1), 32-7.

Chronic obstructive pulmonary disease has got significant cardiovascular morbidity and mortality. The adverse cardiac effect can be picked up early by Electrocardiography (ECG) and echocardiography. Here, in this study, we tried to find out the different ECG changes in COPD and its correlation with disease duration, severity and other factors. We conducted a cross-sectional observational study in the Assam Medical College, Dibrugarh for a span of one year where 234 spirometrically confirmed COPD patients had undergone ECG. Most of the patients belonged to GOLD stage III (40 %) and P-pulmonale was the most common ECG abnormality (63.3 %). Other ECG findings were right axis deviation, right ventricular hypertrophy, incomplete right bundle branch block, S1Q3T3, S1Q3 pattern and Atrial Fibrillation (AF), having an increasing trend of abnormalities with the severity of GOLD stage. Increased incidence of AF is due to severity and longer duration of the disease. AF and right axis deviation occur more in smokers. Low voltage ECG is a nonspecific finding. The ECG changes were well correlated with disease severity and duration.

5 tables, 25 ref

SHARMA A, RAVI V, SEHGAL V K, GROVER G

**044461** SHARMA A, RAVI V, SEHGAL V K, GROVER G (Statistics Dep, Delhi Univ, Delhi, Email: anuragsharma532@gmail.com) : **Comparing the performance of different high dimensional variable selection techniques on the low dimensional HIV/AIDS data set.** J Commun Dis 2020, 52(1), 14-21.

Heavy censoring and high dimensionality have caused a great deal of difficulties for fitting and selection of model. This paper focuses on the performance of these four variable reduction techniques proposed by Khan and Shaw (2013) to select the variables to estimate the survival time of low dimensional HIV/ AIDS patients’ data. The techniques used are adaptive elastic net, weighted elastic net, adaptive elastic net with censoring constraints and weighted elastic net with censoring constraints. The performance of these approaches is compared among themselves along with the full model (model with all the predictors). It is observed that Adaptive Elastic Net with Censoring Constraints performed best among all the methods. Moreover, these four techniques can also be used for future prediction of survival time under AFT model.

4 tables, 32 ref

PRIETO G, ANDRADE A G, MARTÍNEZ D M

**040336** PRIETO G, ANDRADE A G, MARTÍNEZ D M (Autónoma de Baja California Univ, Mexicali, México, Email: aandrade@uabc.edu.mx) : **Numerical analysis of histogram-based estimation techniques for entropy-based spectrum sensing.** IETE Tech Rev 2020, 37(1), 91–7.

Due to its robustness to noise uncertainty, Entropy-Based Spectrum Detection (EnBD) has been proposed to sense primary transmissions in cognitive radio networks. Based on the histogram method, the number of bins must be optimal to accurately estimate the entropy of the samples received. In this work, the performance of the EnBD with respect to several rules for determining the number of bins in the histogram is evaluated. And, it is demonstrated that detection performance is different for each of the aforementioned rules due to the probability distribution of the primary signal.

5 illus, 3 tables, 21 ref

DEVANSHU A, SINGH M, KUMAR N

**040327** DEVANSHU A, SINGH M, KUMAR N (Electrical Engineering Dep, Delhi Technological Univ, Delhi - 110 042, Email: ambrish.devanshu@gmail.com) : **Sliding mode control of induction motor drive based on feedback linearization.** IETE J Res 2020, 66(2), 256–69.

In this paper, sliding mode control theory is demonstrated to design and control the rotor speed and rotor flux of the feedback linearized induction motor (IM) drive. Dynamic equations of the IM in stationary reference frame are linearized using feedback linearization control technique. Direct differentiation method is being used for the linearization of dynamic model of IM. First, rotor speed and flux are decoupled through proportional-integral (PI) regulator and the resultant controlled variables are fed to the feedback linearization controller. To improve the dynamic performance of the motor, sliding mode flux and speed controllers are proposed. The model has been simulated using MATLAB/Simulink and validated experimentally using dSpace1104 controller board, inverter, and IM in the laboratory. Results clearly indicate the effectiveness of the proposed controller over PI controllers at different operating conditions such as load disturbance and speed reversal is analysed and compared in real time.

8 illus, 3 tables, 33 ref

BASHA G W, WOYA A A, TEKILE A K

**039752** BASHA G W, WOYA A A, TEKILE A K (Statistics Dep, Bahir Dar Univ, Amhara, Ethiopia, Email: garewa2010@gmail.com) : **Prevalence and risk factors of active trachoma among primary school children of Amhara Region, Northwest Ethiopia.** Indian J Ophthalmol 2020, 68(5), 750-4.

Trachoma is the leading infectious cause of blindness in the world. It is caused by conjunctival infection with the bacterium Chlamydia trachomatis. The objective of this study was to determine the prevalence and risk factors of active trachoma among primary school children in Amhara region, Ethiopia. A cross‑sectional study was conducted from April to May 2018. Data on socio demographic and health characteristics of a child were collected using a structured questionnaire and eye examination for this study. Bivariate and multiple logistic regression statistical analyses were used to determine the prevalence and risk factors of active trachoma among primary school children living in Amhara region,Northwest Ethiopia. The prevalence of active trachoma among primary school children living in Amhara region was 10.3 % in this study. The results of multiple logistic regression analysis revealed that children who wash their face at least two times per day (AOR = 0.37, 95 % CI: 0.14–0.97), children with noflies on their face (AOR = 0.12, 95 % CI: 0.10–0.30) had significantly lower risk of being infected by trachoma and children of households who spend 30 min to 1 h to fetch water (AOR = 10.02, 95 % CI: 1.10–93.53) had significantly higher risk of being infected by trachoma in the study area. The result of this study showed that risk factors: frequency of face washing per day, presence of flies on child’s face during interview, and time required to fetch water for the household were found to be significantly associated with trachoma. Therefore, the study recommends that any concerned bodies directed at prevention and control of trachoma among primary school children living in Amhara region should give special attention to these factors. Implementing the World Health Organization (WHO) endorsed SAFE (Surgery, Antibiotics, Facial cleanliness, Environmental improvement) strategy was recommended for the effective prevention and control of trachoma in the study area since the prevalence of active trachoma, 10.3 % was higher than the WHO recommended thresholds (>10 % prevalence).

2 tables, 18 ref

BHUYAN M, CHUTIA C

**039674** BHUYAN M, CHUTIA C (Mathematics Dep, DCB Girls’ Coll, Jorhat, Assam, Email: moloyabhuyan@yahoo.com) : **Existence of smooth epimorphism from fuchsian group to the group of automorphisms of compact riemann surface to the point group of carbon tetrachloride.** Ultra Scient phys Sci-Sect A 2020, 32(3), 13-21.

A finite group G acts as a group of automorphisms on a compact Riemann surface S of genus g if and only if there exist a Fuchsian group G and an epimorphism ɸ: G ® G such that kerɸ = K is a surface group of genus g. And then ɸ is named as smooth homomorphism. The objective of this paper is to establish aset of necessary and sufficient conditions for the existence of smooth epimorphism from a Fuchsian group G to the finite group of symmetries of Carbon Tetra chloride molecule, whose abstract group representation is {a,b|a^{4}= b^{3}=(ab)^{2}}.

1 table, 18 ref

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

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

MUYUMBA P K, CHITENG B K, JUMBE J K, ELAGO F, BWAYA K, KIMENYEMBO KASONGO M F

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

In this research paper, differential triads over a topological space are defined as objects of the Cartesian product category Alg x_{x }F^{d }x_{x} DMod over the same fixed topological space X. From differential triads sheaves (A_{ix} , ∂_{ix },Ω_{ix}) and (A_{ix} , ∂_{ix },Ω_{ix}) we defined morphisms of differential triads using a differential morphism ∂^{ij }: H^{ij}_{A} → H^{ij}_{Ω} , where H^{ij}_{A }= Hom_{Alg x} (A_{ix}, A_{ix}) and H^{ij}_{Ω }= Hom_{DMod x} (Ω_{i}, Ω_{j}). From the quadratic forms, we determined quadratic differential triads and Clifford differential triads.

25 ref

MANDAVA R K, VUNDAVILLI P R

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

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

14 illus, 5 tables, 45 ref

GUPTA A K, KUMAR D, SAMUAL P

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

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

8 illus, 8 tables, 52 ref

GHOSH U, BANERJEE J, SARKAR S, DAS S

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

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

4 illus, 19 ref

BHAT M A, KHAN A

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

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

4 illus, 39 ref

BONKILE M P, AWASTHI A, LAKSHMI C, MUKUNDAN V, V S ASWIN

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

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

6 illus, 210 ref

KHAN A, TYAGI A

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

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

15 illus, 63 ref

Z IQBAL, MEHMOOD Z, AHMAD B

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

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

19 illus, 2 tables, 22 ref

KHATER M M A, SEADAWY A Y R, LU D

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

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

49 ref

RAJOTIA D

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

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

13 illus, 1 table, 30 ref

CHEN L, WANG Y, ZHOU Y

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

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

5 illus, 1 table, 37 ref

KAMOH NM, ABADA A, COMFORT S M

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

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

3 tables, 20 ref

CHOUDHARY R

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

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

5 illus, 1 table, 7 ref

IKRAM Z J W, IRAWAN E B, DWIYANA, QOHAR A, AZIS N

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

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

2 illus, 2 tables, 7 ref

RASYID A A, ANSYARI K, SINAR T S

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

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

12 ref

ASHMA , GOEL R, KHAN M

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

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

9 tables, 22 ref