KHADER M M, SAAD K M

**000420** KHADER M M, SAAD K M (Mathematics Dep, Najran Univ, Najran, Saudi Arabia) : **Numerical studies of the fractional korteweg-de vries, korteweg-de vries-burgers’ and burgers’ equations.** Proc Natl Acad Sci India Sect A Phys Sci 2021, 91(1), 67-77.

In this paper, we present an accurate numerical method to compute the approximate solutions of the Korteweg–de Vries, Korteweg–de Vries–Burger’s and Burger’s equations with Liouville–Caputo fractional space derivatives, respectively. We implement the spectral collocation method based on the shifted Chebyshev polynomials. The method reduces each model to a set of ODEs which is solved by using the finite difference method. The results obtained by the proposed method are compared with exact solutions, the *q*-homotopy analysis transform method and the variational iteration method. The efficiency and the accuracy of the results were ascertained by comparing the approximate solution with the exact solution in the case of classical models and evaluating the residual error function in the case of fractional models.

32 ref

KUMAR M, VARSHNEY P

**000419** KUMAR M, VARSHNEY P (Mathematics Dep, Motilal Nehru National Institute of Technology, Allahabad- 211004, Uttar Pradesh) : **Numerical simulation of van der pol equation using multiple scales modified lindstedt–poincare method.** Proc Natl Acad Sci India Sect A Phys Sci 2021, 91(1), 55-65.

In this paper, an efficient perturbation algorithm combining the method of Multiple Scales and Modified Lindstedt–Poincare Techniques is proposed to solve the equation of Van der Pol oscillator with very strong nonlinearity. This algorithm combines the advantages of both methods. Solution of Van der Pol equation by the Multiple Scales Modified Lindstedt–Poincare (MSMLP) method is compared with the Multiple Scales method and numerical solution using MATLAB 7.8. The convergence criterion for the solution by Multiple Scales and MSMLP methods is discussed and shown that Multiple Scales method fails the convergence criterion for large values of small parameter, while MSMLP method satisfies the convergence criterion for both small and large values. Numerical simulation has been performed in MATLAB 7.8 for different values of small parameter to prove the efficiency and accuracy of the proposed method.

26 ref

PAVITHRA P, SUBBIAH M

**000418** PAVITHRA P, SUBBIAH M (Mathematics Dep, Pondicherry Univ, Puducherry- 605 014) : **Note on instability regions in the circular rayleigh problem of hydrodynamic stability.** Proc Natl Acad Sci India Sect A Phys Sci 2021, 91(1), 49-54.

Batchelor and Gill’s semicircular bound on the range of the complex wave velocity of an arbitrary unstable mode in the stability problem of inviscid incompressible homogeneous axial flows with respect to axisymmetric disturbances is further reduced. *Significance* In the circular Rayleigh problem of hydrodynamic stability, we have obtained a parabolic instability region. The significance of this result is that it depends on the discriminant Ψ(r)Ψ(r) which plays a vital role in deciding whether a basic axial flow is stable or not to axisymmetric disturbances. However, our parabolic instability region is an unbounded one unlike the semicircular instability region of Batchelor and Gill, which has the weakness that it does not depend on Ψ(r)Ψ(r). So we have demonstrated that our parabola intersects the semicircle of Batchelor and Gill for two classes of basic flows, and consequently the semicircular instability region of Batchelor and Gill is further reduced. Moreover, we have stated the stability problem consisting of a second-order ODE and associated boundary conditions in three different but related variables. The significance of this is that further analytical results can be obtained for this problem, and some of these are presented in our subsequent paper.

12 ref

GAUR K, GUPTA R

**000631** GAUR K, GUPTA R (Statistics Dep, SKN Agriculture Univ, Jobner, Rajasthan) : **Hypertension epidemiology in India in the global context.** RUHS J Health Sci 2021, 6(1), 6-13.

Hypertension has emerged as the most important cause of death and disability in India as well globally. According to Global Burden of Diseases study, in the year 2017, it led to 1.54 million deaths in India and 10.4 million deaths globally. It also led to 38.1 million disability adjusted life years lost in India and 220.0 million globally. The global burden of hypertension has increased from 594 million patients in 1975 to 1.13 billion in 2015. In the past decades, hypertension burden has shifted from high- and uppermiddle income countries to lower-middle income and lowincome countries in South Asia and Africa. Hypertension prevalence in South Asian countries ranges from 20-25 %. Representative Indian studies have reported hypertension in 25.3 % adults, more in men (27.4 %) compared to women (20.0 %) which translates to 200 million hypertensives in the country. Hypertension awareness, treatment, and control rates are low and less than half of patients with hypertension are on treatment and 10 % controlled to target. Policy level and health-system level interventions to prevent and manage hypertension and clinical interventions focused on treatment to targets and adherence to lifestyle and drug therapies is crucial to reduce hypertension related cardiovascular disease burden.

2 illus, 2 tables, 38 ref

AYYAPPAN G, DEEPA T

**000417** AYYAPPAN G, DEEPA T (Mathematics Dep, Pondicherry Engineering Coll, Pillaichavady- 605 014, Puducherry) : **Analysis of an admission control m ^{[x]}/g(a,b)/1m[x]/g(a,b)/1 queue with multiple vacation, restricted re-service, closedown and setup times.** Proc Natl Acad Sci India 2021, 91(1), 35-47.

The objective of this paper is to analyze an M[X]/G(a,b)/1M[X]/G(a,b)/1 queueing model with admission control, multiple vacation, restricted re-service, setup and closedown times. At the moment of service completion, the leaving batch of customers may request for re-service with probability ηη and it is not compulsory to accept the request. The server accepts the request with probability ζζ and restricts it with probability 1−ζ1−ζ. All the batches of customers are not allowed all the time into the system. On completion of a service or re-service, if the queue length is ωω, where ω<aω<a, then the server resumes closedown work. After that, the server leaves for a vacation of random length. When the server returns from a vacation if the queue length is still less than *a*, he leaves for another vacation and so on until he finds at least *a* customers in the queue. If the queue length is at least *a*, then the server commences setup work before starting the service. Using supplementary variable technique, the steady-state probability generating function of the system size at an arbitrary time is obtained. The performance measures and cost model are also derived. Numerical illustrations are presented to visualize the effect of system parameters.

22 ref

TRIPATHY B C, SEN M, NATH S

**000416** TRIPATHY B C, SEN M, NATH S (Mathematics Dep, Tripura Univ, Agartala- 799 022, Tripura) : **On generalized difference ideal convergence in generalized probabilistic N-normed spaces.** Proc Natl Acad Sci India 2021, 91(1), 29-34.

In this article, we introduce the concept of Δm−IΔm−I-convergent and Δm−IΔm−I Cauchy sequences in generalized probabilistic *n*-normed spaces and establish some results relating to this concept. We also study Δm−I∗Δm−I∗ convergence in the same space. *Statement* Probabilistic norm generalizes and unifies different notions of norm, represented by a distance function, rather than a positive real number. Ideal convergence unifies many notions of convergence of sequences. In this article, we have introduced the notion of generalized difference ideal convergent sequences in probabilistic *n*-normed space, which generalizes and unifies many existing notions. Hence, the results of this article have been established in general setting.

25 ref

SHAIKH A Y, GORE S V, KATORE S D

**000401** SHAIKH A Y, GORE S V, KATORE S D (Mathematics Dep, Indira Gandhi Mahavidyalaya, Ralegaon- 445 402, Email: swapnilgore411@gmail.com) : **Cosmic acceleration and stability of cosmological models in extended teleparallel gravity.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02048-y.

In this paper, we study the model of f (T ) gravity in the presence of dark matter and modified holographic Ricci dark energy (MHRDE) in locally rotationally symmetric (LRS) Bianchi type-I space–time. To achieve a physically realistic solution of the field equations, we have considered volumetric power and exponential expansion laws. We plot the corresponding cosmological parameters for dark energy components in terms of redshift; thereafter we investigate the accelerated expansion of the Universe. The physical and geometrical parameters of the models are also discussed in detail. The Statefinder diagnostic pair and jerk parameter are analysed to characterise completely different phases of the Universe.

16 illus, 67 ref

SHAIKH A Y, SHAIKH A S, WANKHADE K S

**000398** SHAIKH A Y, SHAIKH A S, WANKHADE K S (Mathematics Dep, Indira Gandhi Mahavidyalaya, Ralegaon- 445 402, Email: shaikh_2324ay@yahoo.com) : **Transist dark energy and thermodynamical aspects of the cosmological model in teleparallel gravity.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02047-z.

In this article, the perfect fluid is introduced for plane symmetric space–time in the framework of teleparallel gravity using hybrid expansion law (HEL). The behaviour of accelerating Universe is discussed by considering the depiction model of f (T ) gravity, i.e. f (T ) = T η. The geometrical and physical parameters of the model are studied. An effective equation of state (EoS) has been investigated in the cosmological evolution with perfect fluid. The basic equations of thermodynamics have been deduced and the thermodynamical aspects of the model have been discussed. Thermodynamic temperature and entropy density of the model are also obtained. The statefinder parameters and jerk parameter analysis are discussed for our obtained model to distinguish our model from other dark energy models.

17 illus, 95 ref

BALA P, KAUR A, KAUR K

**000397** BALA P, KAUR A, KAUR K (Mathematics Dep, Punjab Agricultural Univ, Ludhiana- 141 004, Email: pravi2506@gmail.com) : **Arbitrary amplitude electron-acoustic solitons and double layers with Cairns–Tsallis-distributed hot electrons.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02060-2.

In the present research paper, propagation attributes of nonlinear electron-acoustic (EA) waves have been investigated in an unmagnetised plasma system consisting of cool fluid electrons and hot electrons observing the hybrid Cairns–Tsallis distribution. Sagdeev pseudopotential method has been used to explore the occurrence of large-amplitude solitons and double layers, focussing on how their characteristics depend upon different parameters. The analysis is further extended to examine the dynamics of large- and small-amplitude double layers. It is revealed that the present plasma system supports the existence of negative potential solitons and double layers in certain region of parameter space. The numerical results show that the Cairns–Tsallis-distributed hot electrons may affect the spatial profiles of EA waves and double layers. The present investigation may be relevant to the observation from Viking satellite in the dayside auroral zone.

6 illus, 56 ref

HUSSAIN Z, ZEESAHAN R, SHAHZAD M, ALI M, SULTAN F, ANTER A M, ZHANG H, KHAN N

**000390** HUSSAIN Z, ZEESAHAN R, SHAHZAD M, ALI M, SULTAN F, ANTER A M, ZHANG H, KHAN N (Mathematics Dep, COMSATS Univ Islamabad, Mansehra- 220 60, Pakistan, Email: faisal_maths@hu.edu.pk) : **An optimised stability model for the magnetohydrodynamic fluid.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02043-3.

Magnetohydrodynamics (MHD) is a very challenging problem which affects the stability of Poiseuille flow. Therefore, in this work we investigate the instability of an electrically conductive fluid between two parallel plates under the influence of a transverse magnetic field. We apply the Chebyshev collocation method to solve the generalised Orr–Summerfield equations to determine wave number, growth rates and spatial modes of the eigenmodes. To get the neutral curves of MHD instability, the QZ method is used. It is observed that the magnetic field has a stabilising effect on the flow and the stability increases as we increase the Hartmann number and for various wave numbers, magnetic field put down the growth of perturbation. It is concluded that effect of perturbations is little in span-wise direction for different Hartmann numbers that increase the critical values of Reynolds numbers.

7 illus, 1 table, 26 ref

SALEEM M, TUFAIL M N, CHAUDHRY Q A

**000389** SALEEM M, TUFAIL M N, CHAUDHRY Q A (Mathematics Dep, Management and Technology Univ, Sialkot- 51310, Pakistan, Email: musharafa.saleem@skt.umt.edu.pk) : **Unsteady MHD Casson fluid flow with heat transfer passed over a porous rigid plate with stagnation point flow: Two-parameter Lie scaling approach.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02054-0.

This study examined the steady flow of Casson fluid over a rigid porous plate in an infinite region with magnetohydrodynamic (MHD), thermal radiation and heat source-sink effects. Under the influence of stagnation point flow and thermal transport, the physical model is strengthened. The model consists of nonlinear partial differential equations (PDEs), which are controlled after applying approximation of the boundary layer (BL). The significance of this flow model here is that these PDEs have been turned into ordinary differential equations (ODEs) by means of two-parameter Lie scaling transformations. These ODEs are rectified using the MATLAB bvp4c technique. Convergence analysis of these ODEs demonstrate the consistency of the model. Dimensionless parameters are: Casson fluid parameter β, Hartmann number Mt , Darcy ratio K, thermal radiation t and heat source-sink parameter Qt . These parameters are analysed using graphs for fluid flow, temperature and physical quantities. These quantities are analysed using graphs and a table. All the prominent parameters increased the flow of fluid, but thermal transport was decreased for different parameters.

13 illus, 1 table, 40 ref

NAYAK B, MISHRA S R

**000388** NAYAK B, MISHRA S R (Mathematics Dep, Siksha ‘O’ Anusandhan Deemed to be Univ, Bhubaneswar- 751 030, Email: satyaranjan_mshr@yahoo.co.in) : **Squeezing flow analysis of CuO–water and CuO–kerosene-based nanofluids: A comparative study.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02053-1.

Heating and cooling are two important procedures in manufacturing as well as transportation industries. Rather than the conventional fluids, solutions of fluids with metal nanoparticles have higher thermal conductivity for effective cooling. Therefore, present paper is a comparative study of squeezing flow analysis of copper oxide–water and oil (kerosene)-based nanofluid between two parallel plates. Magnetohydrodynamic flow of kerosene-based nanofluid along with the dissipative heat energy may enhance the thermal properties of the fluid. Assuming selfsimilar variables, the governing equations get transformed into non-dimensional forms and approximate analytical techniques such as variation parameter method is employed for these transformed equations. With the well posed physical parameters, the computation is carried out using the mathematical package MATHEMATICA and displayed via graphs and numerical results are shown in tabular form. Favourable cases in comparison with earlier studies are also studied wherever possible. However, when the plates are away from each other, it is seen that the kerosene-based nanofluid velocity overrides the water-based nanofluid whereas the impact is reversed in the case of squeezing.

11 illus, 2 tables, 26 ref

IQBAL A, NAEEM I

**000387** IQBAL A, NAEEM I (Mathematics Dep, Lahore Univ of Management Sciences, Lahore Cantt- 54792, Pakistan, Email: imran.naeem@lums.edu.pk) : **Generalised conservation laws, reductions and exact solutions of the K(m, n) equations via double reduction theory.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02071-z.

In this article, we present the general form of conservation laws for the nonlinear Rosenau–Hyman compacton K(m, n) equations using multiplier’s approach. General formulas for some new conservation laws are established for the K(m, n) equations. We describe three different cases where Lie symmetries are associated with these generalised conservation laws. The double reduction theory is utilised to construct some new reductions and exact solutions for different values of m and n.

3 tables, 29 ref

KUMAR S, KUMAR D, KHARBANDA H

**000384** KUMAR S, KUMAR D, KHARBANDA H (Mathematics Dep, Delhi Univ, Delhi- 110 007, Email: sachinambariya@gmail.com) : **Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the (2 + 1)-dimensional KP-BBM equation.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02057-x.

In the present article, our main aim is to construct abundant exact solutions for the (2+1)-dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM) equation by using two powerful techniques, the Lie symmetry method and the generalised exponential rational function (GERF) method with the help of symbolic computations via Mathematica. Firstly, we have derived infinitesimals, geometric vector fields, commutation relations and optimal system. Therefore, the KP-BBM equation is reduced into several nonlinear ODEs under two stages of symmetry reductions. Furthermore, abundant solutions are obtained in different shapes of single solitons, solitary wave solutions, quasiperiodic wave solitons, elastic multisolitons, dark solitons and bright solitons, which are more relevant, meaningful and useful to describe physical phenomena due to the existence of free parameters and constants. All these generated exact soliton solutions are new and completely different from the previous findings. Moreover, the dynamical behaviour of the obtained exact closed-form solutions is analysed graphically by their 3D, 2D-wave profiles and the corresponding density plots by using the mathematical software, which will be comprehensively used to explain complex physical phenomena in the fields of nonlinear physics, plasma physics, optical physics, mathematical physics, nonlinear dynamics, etc.

8 illus, 2 tables, 26 ref

JHANGEER A, REZAZADEH H, SEADAWY A

**000377** JHANGEER A, REZAZADEH H, SEADAWY A (Mathematics Dep, Namal Institute, Mianwali- 42250, Pakistan, Email: adil.jhangeer@gmail.com) : **A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02067-9.

In this paper, a diverse range of travelling wave structures of perturbed Fokas–Lenells model (p-FLM) is obtained by using the extended (G /G2)-expansion technique. The existence of the obtained solutions is guaranteed by reporting constraint conditions. Then, the governing model is converted into the planer dynamical system with the help of Gallelian transformation. Every possible form of phase portraits is plotted for pertinent parameters, viz. k, β, d1, d2, d3. We also used the Runge–Kutta fourth-order technique to extract the nonlinear periodic solutions of the considered problem and outcomes are presented graphically. Furthermore, quasiperiodic and chaotic behaviour of p-FLM is analysed for different values of parameters after deploying an external periodic force. Quasiperiodic– chaotic nature is observed for selected values of parameters k, β, d1, d2, d3 by keeping the force and frequency of the perturbed dynamical system fixed. The sensitive analysis is employed on some initial value problems (IVPs). It is seen that de-sensitisation is present in the perturbed dynamical system while for the same values of parameters, the unperturbed dynamical system has a nonlinear periodic solution.

12 illus, 22 ref

SINGH S, SAKTHIVEL R, INC M, YUSUF A, MURUGESAN K

**000375** SINGH S, SAKTHIVEL R, INC M, YUSUF A, MURUGESAN K (Mathematics Dep, National Institute of Technology, Tiruchirappalli- 620 015, Email: krsakthivel@yahoo.com) : **Computing wave solutions and conservation laws of conformable time-fractional Gardner and Benjamin–Ono equations.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-020-02070-0.

This paper presents travelling wave solutions for the nonlinear time-fractional Gardner and Benjamin– Ono equations via the exp(−(ε))-expansion approach. Specifically, both the models are studied in the sense of conformable fractional derivative. The obtained travelling wave solutions are structured in rational, trigonometric (periodic solutions) and hyperbolic functions. Further, the investigation of symmetry analysis and nonlinear selfadjointness for the governing equations are discussed. The exact derived solutions could be very significant in elaborating physical aspects of real-world phenomena. We have 2D and 3D illustrations for free choices of the physical parameter to understand the physical explanation of the problems. Moreover, the underlying equations with conformable derivative have been investigated using the new conservation theorem.

4 illus, 54 ref

KUMAR S, RANI S

**000369** KUMAR S, RANI S (Mathematics Dep, Delhi Univ, Delhi- 110 007, Email: sachinambariya@gmail.com) : **Lie symmetry analysis, group-invariant solutions and dynamics of solitons to the (2 + 1)-dimensional Bogoyavlenskii–Schieff equation.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-021-02082-4.

In the present work, abundant group-invariant solutions of (2 + 1)-dimensional Bogoyavlenskii– Schieff equation have been investigated using Lie symmetry analysis. The Lie infinitesimal generators, all the geometric vector fields, their commutative and adjoint relations are provided by utilising the Lie symmetry method. The Lie symmetry method depends on the invariance criteria of Lie groups, which results in the reduction of independent variables by one. A repeated process of Lie symmetry reductions, using the double, triple and septuple combinations between the considered vectors, converts the Bogoyavlenskii–Schieff (BS) equation into nonlinear ordinary differential equations (ODEs) which furnish numerous explicit exact solutions with the help of computerised symbolic computation. The obtained group-invariant solutions are entirely new and distinct from the earlier established findings. As far as possible, a comparison of our reported results with the previous findings is given. The dynamical behaviour of solutions is discussed both analytically as well as graphically via their evolutionary wave profiles by considering suitable choices of arbitrary constants and functions. To ensure rich physical structures, the exact closed-form solutions are supplemented via numerical simulation, which produce some bright solitons, doubly solitons, parabolic waves, U-shaped solitons and asymptotic nature.

8 illus, 2 tables, 29 ref

BALA P, GILL T S

**000363** BALA P, GILL T S (Mathematics Dep, Punjab Agricultural Univ, Ludhiana- 141 004, Email: pravi2506@gmail.com) : **Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons.** Pramana- J Phys 2021, 95(1), 10.1007/s12043-021-02080-6.

In the present investigation, authors have studied the linear mode structure of electron-acoustic waves, their modulational instability and rogue wave profiles in four-component plasma system consisting of stationary ions, cold electron fluid, Tsallis-distributed hot electrons and an electron beam. By applying standard perturbation method to the fluid equations, the dispersion relation is obtained that depends on various parameters such as beam density, beam velocity, beam temperature and non-extensivity q. Based on the phase velocities, two electron-acoustic (EA) modes known as slow and fast, have been extracted as real modes for which a detailed analysis is presented. Further, the basic set of equations is reduced to nonlinear Schrödinger equation (NLSE), where the nonlinearity and dispersion coefficients compete and significantly affect the stability characteristics of EA waves. For both the modes, a comprehensive study of modulational instability and rogue wave profile has been carried out by taking into consideration the effect of non-extensivity and beam velocity. The obtained results have been compared with other research works. The present investigation may be relevant to the observation from Viking satellite in the day-side auroral zone.

10 illus, 89 ref

SRINIVAS N, VIJAYASEKHAR J

**000191** SRINIVAS N, VIJAYASEKHAR J (Mathematics Dep, GITAM Deemed to be Univ, Hyderabad, Email: vijayjaliparthi@gmail.com) : **Vibrational frequencies of dichlorine monoxide: A Mathematical Model.** Orient J Chem 2021, 37(1), 240-2.

We have determined stretching vibrational frequencies of a triatomic molecule, i.e. Dichlorine monoxide (Cl2 O) upto third overtone by Lie algebraic method. Fundamental vibrational wavenumbers calculated by Lie algebraic model are compared with available experimental values.

1 table, 12 ref

JOSE K P, RESHMI P S

**000161** JOSE K P, RESHMI P S (PG Research Mathematics Dep, St. Peter’s Coll, Kolenchery- 682 311, Kerala) : **A production inventory model with deteriorating items and retrial demands.** Opsearch 2021, 58(1), 71-82.

This paper considers a single server perishable inventory system in which customers arrive in a homogeneous Poisson stream. The system has a production unit which produces a single item in an exponentially distributed time interval. At the time of arrival, a customer leads to service if the server is available with a positive level of inventory. Otherwise, the customer goes to a waiting place(orbit) of infinite capacity with pre-determined probability or exits the system with complementary probability. Each customer in the orbit tries to access the server in an exponentially distributed time interval. After every unsuccessful retrial, the customer returns to the orbit with a pre-allotted probability or is lost forever with complementary probability. An algorithmic solution to the problem is obtained using Matrix Analytic Method. The mean number of customer loss before and after entering the system, the rate of successful retrials among overall retrials and some other performance measures of the system are derived. The impacts of system parameters on different measures are numerically studied. A suitable cost function is constructed and the optimum control policy is numerically obtained.

20 ref

BALAJI S, THIRU V S

**000032** BALAJI S, THIRU V S (Mathematics Dep, SASTRA Deemed Univ, Thanjavur- 613 401) : **Strong chromatic index of generalized polygon snake graphs.** Natl Acad Sci Lett 2021, 44(2), 151-4.

A strong edge-coloring of a graph *G* is a proper edge-coloring such that every color class induces a matching. In this paper, we discuss the strong chromatic index of a cycle on *k* vertices and use the result to calculate the strong chromatic index of (*m,n*)*k*-gon snake graphs which generalize the families of graphs referred to as the (*m,n*) triangle snake graphs and (*m,n*) quadrilateral snake graphs.

10 ref

JAIN R, ACHARYA M, KANSAL S

**000031** JAIN R, ACHARYA M, KANSAL S (Mathematics Dep, Government Coll Patharia, Patharia- 470 666, M.P) : **Characterization of line-cut signed graphs.** Natl Acad Sci Lett 2021, 44(2), 147-50.

A *signed graph* S=(Su,σ)S=(Su,σ) consists of an underlying graph SuSu and a function σ:E(Su)⟶{+,−}σ:E(Su)⟶{+,−}. For a graph *G*, its lict graph written as Lc(G)Lc(G) is the intersection graph Ω(E(G)∪C(G))Ω(E(G)∪C(G)). For a signed graph *S*, its *line-cut* *signed graph* (in short called lict signed graph) is denoted by Lc(S)Lc(S) has underlying graph Lc(Su)Lc(Su) and two vertices *u* and *v* joint by negative edge if *u* and *v* both are negative adjacent edges of *S* or *u* is a negative edge incident to a cut-vertex *v* of negative degree odd in *S* and by positive edge otherwise, here *C*(*S*) is the set of cut-vertices of *S*. In this paper, we establish structural characterization of lict signed graphs Lc(S)Lc(S).

15 ref

SINGH A

**000030** SINGH A (Mathematics and Statistics Dep, Banasthali Vidhyapith, Banasthali- 304 022) : **Some characterizations of wavelet transform.** Natl Acad Sci Lett 2021, 44(2), 143-5.

In this paper, by using the theory of wavelet convolution associated with Fourier convolution, operational properties are discussed on wavelet transform of Sω(R),Dω(R)Sω(R),Dω(R) and McMc spaces. Further, Calderón’s formula is investigated for WM,aWM,a space.

7 ref

MEENU, KUMAR V, SUSHMA

**045035** MEENU, KUMAR V, SUSHMA (Mathematics Dep, Baba Mastnath Univ, Rohtak, Email: meenulohchab3333@gmail.com) : **FIxed point theorem for -weak contraction mappings.** J Comp & Math Sci 2020, 11(9), 61-71.

In this paper, we present some common fixed point theorem for generalized -weak contraction mappings. Also, we discuss the existence and uniqueness of common fixed points for single valued mappings satisfying the notion of weak compatibility in a complete metric space.

30 ref

LAHUTA L B, RYBINSKI W, BOCIANOWSKI J, NOWOSAD K, BORNER A

**046484** LAHUTA L B, RYBINSKI W, BOCIANOWSKI J, NOWOSAD K, BORNER A (Mathematical and Statistical Methods Dep, Poznan Univ of Life Sciences, Poland, Email: jan.bocianowski@up.poznan.pl) : **Raffinose family oligosaccharides in seeds of common vetch (Vicia sativa L. ssp. sativa).** Legum Res 2020, 43(4), 512-7.

The composition and content of low-molecular weight soluble carbohydrates in seeds of 66 accessions of common vetch (Vicia sativa L. ssp. sativa) stored in the Polish and German gene banks, originating from Europe, Asia, Middle East and North Africa, were analyzed using a gas chromatography method. Genotypes showed differences in the composition of carbohydrates depending on the origin of seeds. Common features of accessions were: i) the predominance of raffinose family oligosaccharides (RFOs) in soluble carbohydrates, and ii) verbascose as the main oligosaccharide in RFOs. Several accessions with lowered RFOs content were identified. They may be suitable for breeding focused on diminishing RFOs, as antinutritional compounds in seeds.

2 illus, 3 tables, 27 ref

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