005101   KUSUM, SINGH T P (B.M.N Univ, Rohtak, Haryana, Email: kusumsansanwal123@gmail.com) : Performance measure of 2-stage fuzzy scheduling with single transport agent using robust ranking technique. Aryabhatta J Math Inform 2019, 11(2), 185-92.

Scheduling problems are concerned in searching an optimal or near optimal sequence in which a number of tasks can be performed subject to the number of constraints. In most of these problems, the performance measures are a function of the order or sequence of jobs. Though a number of heuristic techniques have been developed to solve the scheduling problems, yet many of these are often not practical in dynamic real world scenario due to complex constraints & unexpected disruptions. This paper put forward an algorithm to find the performance measure for fuzzy scheduling in which the transport agent returns on first machine after delivering the task on second machine. The processing time has been considered with triangular fuzzy parameters. The basic idea is to convert the fuzzy processing time in the crisp value by applying Robust Ranking technique. Robust ranking index is easier to apply and helpful tool in fuzzy decision making environment. The algorithm is based on a theorem which has been verified. Numerical illustration is also given to justify the study.

11 ref

005104   SINGH A P (Mathematics Dep, Jubail Industrial Coll, Jubail, Saudi Arabia, Email: arungeit@yahoo.co.in) : Mathematical model on stationary information system in a distributed service network. Aryabhatta J Math Inform 2019, 11(2), 181-4.

In Distributed Service Network, the main concern of the user is mostly focused on the immediate response time of a call for service. The user evaluates the efficiency of a service network in terms of how long he or she has been waiting until a service unit arrives at the scene of a call. Short-term policies such as dispatching, repositioning or routing depend critically on the information available and the communications system operated by the dispatcher at the moment a service request arises. Thus, information has great value in distributed service network. In this paper the mathematical model is proposed for the expected response time under stationary information system.

13 ref

005098   KALANOV T Z (Yozuvchilar Pisatelskaya, Tashkent, Uzbekistan, Email: tzk_uz@yahoo.com) : Definition of derivative function: Logical error in mathematics. Aryabhatta J Math Inform 2019, 11(2), 173-80.

The critical analysis of the foundations of the differential calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that differential calculus is fictitious mathematical theory because the concept of the limiting process is the starting point for definition of the derivative function. The passage to the limit "zero" in the definition of the derivative function signifies that the variable quantity takes the only essential value "zero". This fact leads to the following errors. The definition of the derivative function is based on the violation of the necessary and sufficient condition for the validity of the relationship between the increment of the function argument and the increment of the function because the increment of the function is divided by the zero increment of the argument in the case of the limiting process.  The definition of the derivative function is based on the contradiction which is that the increment of the argument is both zero and not zero in the same relationship. This contradiction represents a violation of the formal-logical law of identity and of the formal-logical law of the lack of contradiction.The definition of the differential of function is based on two contradictory (mutually exclusive) features: the differential of the argument is not zero while the increment of the argument in the definition of the derivative function is zero. 

16 ref

003843   CHAKRABARTY D (Statistics Dep, Handique Girls' Coll, Guwahati- 781 001, Assam, Email: dhritikesh.c@rediffmail.com) : A general method of defining average of function of a set of values. Arya Bhatta J Math Inform 2019, 11(2), 269-82.

A general method has been derived, in this study, for defining the average of a function of a set (or a list) of values which can describe/yield most of the definitions/formulations of average. This paper is based on the derivation of this general method of defining average along with the derivations of various definitions/formulations of average from the method obtained.

31 ref

003848   GOWRI R, RAJAYAL A K R (Mathematics Dep, Government Coll for Women, Kumbakonam, Email: gowrigck@rediffmail.com) : Supra semi alpha open sets in supra bitopological spaces. Arya Bhatta J Math Inform 2019, 11(2), 263-8.

In this paper, we define and study the notion of S_(τ_ij )-Sα-open and closed sets in supra bitopological spaces. Also, we analysed the properties of these sets.

11 ref

003870   SREEDHAR C (NBKR Institute of Science & Technology, Vidyanagar- 524 413, Email: csreedhar.nainu@gmail.co) : Extension of linear 2-functionals in complex 2-normed linear space. Arya Bhatta J Math Inform 2019, 11(2), 259-62.

In this paper we extended the theorem of Das in more general way over the field of K where K is the field R of real numbers or field C of complex numbers using norm technique of Hahn Banach theorem in normed linear spaces.

4 ref

003868   SINGH T P, YADAV H K (Baba Mast Nath Univ, Rohtak, Email: hrkyadav12@gmail.com) : Fuzzy inventory model with weibull distributed deterioration along variable demand and time varying holding cost. Arya Bhatta J Math Inform 2019, 11(2), 249-58.

The present paper investigates a fuzzy continuous inventory model for deteriorating items with variable demand. The deteriorating rate follows weibull distribution. In real world situation it has been observed that the cycle time of every supply chain system is uncertain hence, it has described with triangular fuzzy parameters. The Yager's formula and signed distance method is applied to de-fuzzify the cost function. A numerical illustration has been proposed to validate the model. The sensitivity analysis has been carried out to explore the effect of minor changes in parameters with the optimal solution associated to different parameters.

4 tables, 19 ref

003846   DEVI M, GUPTA V K, KUMAR V (Registrar Baba Mastnath Univ, Rohtak, Haryana, Email: ghalyan.manju@gmail.com) : Determination of MTSF and availability of a three unit standby stochastic system by using base state. Arya Bhatta J Math Inform 2019, 11(2), 237-48.

To evaluate easily and quickly, the key parameters of a stochastic system for its profit/cost analysis, has always remained the need of the hour. While using the Regenerative Point Technique, many state equations are to be written and solved recursively after taking Laplace/Stieltjes transforms of the state equations and then applying the concepts of limits, it takes a lot of time. Also while using Regenerative Point Graphical Technique (RPGT), introduced by Gupta [4], the presence of many circuits make the calculations lengthy. To overcome this difficulty, Gupta et al [3] introduced a new concept of 'base state' for doing reliability analysis to find the key parameters of the system (under steady state conditions) by using modified formulae of RPGT. In the present paper, the path analysis of a three unit stand-by stochastic system, in which initially, two units are in operative mode and a similar unit in cold stand-by mode, has been done to determine the 'base state' of the system, which is further used to determine the MTSF and Availability of the system using modified RPGT (under steady state conditions).

11 tables, 9 ref

003871   TOMAR S, HOODA N (Mathematics Dep, DCR Univ of Science & Technology, Sonepat, Haryana, Email: s_saroha30@yahoo.com) : Non-archimedean stability of system of AQ reciprocal functional equations. Arya Bhatta J Math Inform 2019, 11(2), 227-36.

In this paper, we will prove generalised Hyers-Ulam-Rassias stability of a system of additive and quadratic reciprocal functional equations in non- Archimedean normed spaces.

11 ref

003852   KAUR A R, ARORA B S, JHA C P C (Operational Research Dep, Delhi Univ, Delhi, Email: rrdk_07@yahoo.com) : Optimal component selection for embedded systems with mandatory redundancy in critical modules based on reuse-build-buy decision. Arya Bhatta J Math Inform 2019, 11(2), 213-26.

Embedded systems are developed in the form of modular, distributed components connected in serial or parallel. The modularized software components are a result of CBSD, wherein the components can be either obtained as COTS components, developed in-house or re-used after modification. This decision is based upon a number of internal and external factors and is known as Reuse-Build-Buy Decision. Software industries are majorly involved in reusing the components in order to save development& testing time and associated cost. Reusability of components depends upon several parameters such as cost and time for modifications & testing, reliability etc. In life-critical embedded systems, rendering the system to run in the external, uncontrolled environment will be unwise. It becomes obligatory to identify the critical modules and incorporate fault tolerance, which further implies additional cost. In this paper, RB/1/1 fault tolerant architecture has been implemented on embedded systems with mandatory redundancy for critical modules to make the system more reliable. The aim of the paper is to select hardware and software components for the modular system to maximize the overall reliability and minimizing the overall cost and SLOC with a constraint of mandatory redundancy for critical modules under RB/1/1 architecture incorporating Reuse-build-or-buy decision.

5 tables, 27 ref

003864   RENU, BHATIA P (Mathematics Dep, Baba Mastnath Univ, Rohtak, Haryana, Email: renushiv85@gmail.com) : Reliability analysis of die casting machine system having two types repair facility with condition of rest. Arya Bhatta J Math Inform 2019, 11(2), 205-12.

We are taking two high pressure die casting machines case, initially the primary unit is working while the second unit is at cold standby, non priority is standby mode the unit cannot fail in standby mode. All the state possibilities for the system have been discussed. in up states and down states. On failure of the primary unit, standby and secondary unit is operative and failed unit is put under repair immediately. The secondary unit may be working to certain time called maximum allowable operative time. The maximum allowable operative time is over the second unit is put under rest if the primary unit is in progress. In this mode two types of repair facility is considered one ordinary repairman and other expert repairman. The expert repairman is only need based when the ordinary repairman fails to repair the failed primary unit .Secondary unit is always repaired by ordinary repairman. The Failure time of primary as well as secondary unit are exponentially distributed but with different parameters. The repair time distribution of primary unit is arbitrary for both expert repairman and ordinary repairman with different probability distributions. The repair time of standby unit follows exponential distribution .The distribution of rest time, maximum allowable operative time and patience time of ordinary repairman are also assumed to follow exponential distribution distributions with different parameters. Using mean time to system failure, steady state, availabilities, expected no of visit of the system,, system behavior & profit function have been discussed in all possible cases.

4 illus, 9 ref

003851   JANAKI G, SARANYA C (PG & Research Mathematics Dep, Cauvery Coll for Women, Trichy-18, Email: janakikarun@rediffmail.com) : Correlation between pyramidal numbers. Arya Bhatta J Math Inform 2019, 11(2), 197-204.

A pyramidal number is a figurate number that represents to a pyramid with a polygonal base and a given number of triangular sides. In this paper, we have made an attempt to obtain various interesting relations among pyramidal numbers and other special numbers.

12 ref

003854   KUMAR A, PRUTHI M (Mathematics Dep, Indira Gandhi Univ, Meerpur-Rewari, Haryana, Email: ajay61286@gmail.com) : Applications of eulerian graph for mathematical and real situation. Arya Bhatta J Math Inform 2019, 11(2), 193-6.

Graph Theory is an important topic of discrete mathematics and computer science having applications in modeling a variety of real life situations in many disciplines. This article is intended for the attention of young researchers and provides an introductory discussion of some well known application problems in which role of eulerian graph and eulerian circuit is significant. In this paper, we have made an attempt to use the eulerian graph to solve the mathematical and real life situations.

10 ref

003856   KUSUM, SINGH T P (Maths Dep, B.M.N. Univ, Asthal Bohar, Rohtak, Email: kusumsansanwal123@gmail.com,) : Performance measure of 2 - stage fuzzy scheduling with single transport agent using robust ranking technique. Arya Bhatta J Math Inform 2019, 11(2), 185-92.

Scheduling problems are concerned in searching an optimal or near optimal sequence in which a number of tasks can be performed subject to the number of constraints. In most of these problems, the performance measures are a function of the order or sequence of jobs. Though a number of heuristic techniques have been developed to solve the scheduling problems, yet many of these are often not practical in dynamic real world scenario due to complex constraints & unexpected disruptions. This paper put forward an algorithm to find the performance measure for fuzzy scheduling in which the transport agent returns on first machine after delivering the task on second machine. The processing time has been considered with triangular fuzzy parameters. The basic idea is to convert the fuzzy processing time in the crisp value by applying Robust Ranking technique. Robust ranking index is easier to apply and helpful tool in fuzzy decision making environment. The algorithm is based on a theorem which has been verified. Numerical illustration is also given to justify the study. 

11 ref

003867   SINGH A P (Mathematics Dep, Jubail Industrial Coll, Jubail, Saudi Arabia, Email: arungeit@yahoo.co.in) : Mathematical model on stationary information system in a distributed service network. Arya Bhatta J Math Inform 2019, 11(2), 181-4.

In Distributed Service Network, the main concern of the user is mostly focused on the immediate response time of a call for service. The user evaluates the efficiency of a service network in terms of how long he or she has been waiting until a service unit arrives at the scene of a call. Short-term policies such as dispatching, repositioning or routing depend critically on the information available and the communications system operated by the dispatcher at the moment a service request arises. Thus, information has great value in distributed service network. In this paper the mathematical model is proposed for the expected response time under stationary information system.

13 ref

003859   MISHRA P, PANDEY C M, SINGH U, KESHRI A, SABARETNAM M (Biostatistics and Health Informatics Dep, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, Email: mishrapk79@gmail.com) : Selection of appropriate statistical methods for data analysis. Ann Card Anaesth 2019, 22(3), 297-301.

In biostatistics, for each of the specific situation, statistical methods are available for analysis and interpretation of the data. To select the appropriate statistical method, one need to know the assumption and conditions of the statistical methods, so that proper statistical method can be selected for data analysis. Two main statistical methods are used in data analysis: descriptive statistics, which summarizes data using indexes such as mean and median and another is inferential statistics, which draw conclusions from data using statistical tests such as student’s t‑test. Selection of appropriate statistical method depends on the following three things. Type and distribution of the data used, and Nature of the observations (paired/unpaired). All type of statistical methods that are used to compare the means are called parametric while statistical methods used to compare other than means (ex‑median/mean ranks/proportions) are called nonparametric methods. In the present article, we have discussed the parametric and non‑parametric methods, their assumptions, and how to select appropriate statistical methods for analysis and interpretation of the biomedical data.

3 tables, 14 ref

003862   PONALAGUSAMY R, MANCHI R (Mathematics Dep, National Institute of Technology, Tiruchirappalli- 620 015, Email: rpalagu@nitt.edu) : A four-layered model for flow of non-Newtonian fluid in an artery with mild stenosis. Sadhana 2019, 44(7), 158.

The present article deals with a four-layered mathematical model for blood flow through an artery with mild stenosis. The four-layered model comprises a cell-rich core of suspension of all the erythrocytes described as a non-Newtonian (Jeffrey) fluid, a peripheral zone of cell-free plasma (Newtonian fluid) and the stenosed artery with porous wall consisting of a thin transition (Brinkman) layer followed by Darcy region. Analytical expressions have been obtained for velocity profiles in all the four regions, total volumetric flow rate, wall shear stress and flow impedance. MATLAB software is employed to compute numerical values of the pressure gradient. The influences of different parameters such as variable core fluid viscosity, hematocrit, thickness of the plasma layer, Brinkman and Darcy layer thickness, Darcy number, Jeffrey fluid parameter, and size and shape parameters of stenosis on the physiologically vital flow characteristics, specifically velocity profile, volume flow rate, wall shear stress and flow impedance, have been examined. It is observed that the wall shear stress and resistive impedance decrease with the increase of plasma layer thickness, Jeffrey fluid parameter, Darcy number and Darcy slip parameter, and increase with the rise of hematocrit. The results in the case of variable core viscosity and constant core viscosity are compared to investigate the impact of variable core viscosity in managing the flow of blood.

20 illus, 1 table, 40 ref

003860   NAWAZ A, SINGH S, SARAVANAN P (Indian Institute of Technology, Jharkhand- 826 004, Email: saravananpichiah@iitism.ac.in) : Black carbon aerosols from the coal seam of Eastern India: A real-time analysis with statistical validation. J Earth Syst Sci 2019, 128(5), 128.

Underground coal seam fire is one of the serious problems caused by coal mining activities. Hence, the present study is focused on investigating the potential emission of black carbon (BC) and its dispersion from the fire-affected area located in the Jharia coal field, Dhanbad district of the Jharkhand state of India. The real-time BC concentration measurements in the active fire area and the adjacent neighbouring urban area were studied and reported. Results showed an average concentration of BC was 12.54 μg m⁻³ in the fumes/smokes emitting from the surface cracks and vents at the fire-affected zone. The continuous probability distribution functions, i.e., lognormal, gamma and Weibull, were used to fit the BC data individually, and among these lognormal fits, the best were for the medium-range values. Furthermore, the robustness of the obtained BC concentration was also explained by these models. All fitness was in good agreement, in the studied area, with the coefficient of regression ranging between 0.84 and 0.96. Both the experimental and predicted results clearly indicated the contribution of the BC that discharged from the coal seam fire as a source of particulate pollutant. Spatial modelling was also performed to validate the experimental consistency of BC concentration while the model was in good agreement with the underground coal fire zone as compared to the rest.

10 illus, 5 tables, 48 ref

003842   BHAVYASHREE S, BHATTACHARYYA B (Agricultural Statistics Dep, Bidhan Chandra Krishi Viswavidyalaya, Nadia, West Bengal, Email: bhavyashree5591@gmail.com) : An information theory approach for active monsoon period of coastal zone of Karnataka. J Crop Weed 2019, 15(2), 52-7.

A study of monthly rainfall for active monsoon period from June to September was carried out for the period of 1980-2013 (34 years) for coastal zone of Karnataka i.e, Dakshina Kannada and Udapi districts. In semi-arid tropics the weather conditions have a tendency to cluster together to a certain extent which means that the occurrence of rainfall on a particular day depends on the weather conditions of the previous day Markov chain is one of the best tool for describing the meteorological persistence among the tools which are available. The studies of uncertainty about the nature of day’s rainfall are rarely available. Every probability distribution has some uncertainty associated with it. The concept of Information theory approach (entropy) is introduced here to provide a quantitative measure of this uncertainty, and to test the stochastic Markovian dependence. The redundancy of state of occurrences is ranging from 35 to 46 per cent. A test equivalent to the likelihood ratio test has shown better result against, the Markov dependence on the same observations. Using likelihood ratio test, Markovain dependence is best fitted during the study period.

6 tables, 5 ref

003849   GROVER G, VINIT P K (Statistics Dep, Delhi Univ, Delhi, Email: parmeet.vinit@gmail.com) : Actuarial modelling for patients with Acute Lymphoblastic Leukaemia (ALL) based on CNS1 status. J Commun Dis 2019, 53(3), 23-32.

Worldwide, Acute Lymphoblastic Leukaemia (ALL) is the most frequent cancer in children. One of the major clinical challenges is adequate diagnosis and treatment of Central Nervous System (CNS) involvement in this disease. CNS relapse has been a barrier to the successful treatment of ALL for many years. Recent studies have shown encouraging results in the survival of these patients for a long time. However, their long-term survival depends upon the cost of therapy toxicity and financial distress. The primitive aim of the paper is to propose a yearly insurance plan to assist these patients financially during the diagnosis period.Based on the CNS status 110 patients are categorised to estimate their long-term survival. Survival times of CNS1 status and for all the patients cumulatively are estimated by Kaplan-Meier and Cox-PH model in presence of the prognostic factors. The survival estimates are used to estimate the premium cost. The premium cost is estimated using a deterministic model which is advantageous for the patient and serviceable for the insurance provider. Both the methods Kaplan-Meier and Cox-PH gave higher survival estimates for ALL patients cumulatively as compared to CNS1. Survival estimate from Cox-PH is 0.998 and 0.997 of first year of follow-up for patients taken cumulatively and in CNS1 respectively. For the fifth year the survival estimates are 0.802 and 0.783 respectively. The estimated premium cost for a 100 rupees of sum insured is rupees 4.7 for the first year and rupees 26.69 for the fifth year for patients taken cumulatively. Same for CNS1, it is rupees 6.24 and 29.42.Cox-PH model for estimating the survival is recommended since it includes the prognostic factors. The insurance plan suggests to opt for the premium as early as possibly since it costs less and increases later.

6 illus, 7 tables, 15 ref

003857   MALHOTRA K C, VASULU T S (Indian Statistical Institute, Kolkata-700 108) : Development of typological classification and its relationship to microdifferentiation in ethnic India. J Biosci 2019, 44(3), 64.

The history of the racial classification of the people of India can be looked at in three temporal phases: (1) at the national level, the initial studies of racial classification attempted along with the Census of India; (2) at the regional level, studies by anthropologists and statisticians following systematic sampling and statistical procedures were conducted after the initial national-level studies and (3) population-specific studies in different regions across the country including micro-evolutionary studies of individual populations followed the regional studies. Initially the racial classification was part of the Census survey conducted by British anthropologists in some parts of the country among castes and tribes and was based on a few physical traits. This was followed by a systematic anthropometric survey in particulars regions (e.g., UP, Bengal, etc.) by anthropologists and statisticians. This was followed by population specific micro-evolutionary studies across different regions by numerous anthropologists investigating the role of selection, drift, migration and admixture and other population structure variables among endogamous castes and tribes.

4 illus, 2 tables, 63 ref

003850   HOODA E, VERMA U (Mathematics and Statistics Dep, CCS Haryana Agricultural Univ, Hisar- 125 004, Email: ektahooda@gmail.com) : Unobserved components model for forecasting sugarcane yield in Haryana. J Appl Nat Sci 2019, 11(3), 661-5.

Unlike classical regression analysis, the state space models have time-dependent parameters and provide a flexible class of dynamic and structural time series models. The unobserved component model (UCM) is a special type of state space models widely used to analyze and forecast time series. The present investigation has been carried out to study the trend of sugarcane (gur) yield in five districts (Ambala, Karnal, Panipat, Yamunanagar and Kurukshetra) of Haryana state using the unobserved component models with level, trend and irregular components. For this purpose, the time series data on sugarcane yield from 1966-67 to 2016-17 of Ambala and Karnal, 1971-72 to 2016-17 of Kurukshetra and 1980-81 to 2016-17 of Panipat and Yamunanagar districts have been used. For all the districts, the irregular component was found to be highly significant (p=0.01) while both level and trend component variances were observed non-significant. Significance analysis of the individual component(s) has also been performed for possible dropping of the level and trend components by setting their variances equal to zero. The state space models may be effectively used pertaining to Indian agriculture data, as it takes into account the time dependency of the underlying parameters which may further enhance the predictive accuracy of the most popularly used ARIMA models with parameter constancy. Moreover, the unobserved component model is capable of handling both stationary as well as non-stationary time series and thus found more suitable for sugarcane yield modeling which is a trended yield (i.e. non-stationary in nature).

5 tables, 12 ref

003863   PRAKASH A, GOYAL M, GUPTA S (Mathematics Dep, National Institute of Technology, Kurukshetra 136 119, Email: amitmath@nitkkr.ac.in) : Numerical simulation of space-fractional Helmholtz equation arising in seismic wave propagation, imaging and inversion. Pramana – J Phys 2019, 93(2), 28.

In this paper, a reliable numerical scheme, the q-fractional homotopy analysis transform method (qFHATM), is proposed to examine the Helmholtz equation of fractional order arising in seismic wave propagation, imaging and inversion. Sufficient conditions for its convergence and error estimates are established. The q-FHATM provides a solution in a rapidly convergent series. Results for different fractional values of space derivatives are compared with the existing methods and discussed with the help of figures. A proper selection of parameters yields approximations identical to the exact solution. Parameter h¯ offers an expedient way of controlling the region of convergence of the solution. Test examples are provided to illustrate the accuracy and competency of the proposed scheme. The outcomes divulge that our scheme is attractive, user-friendly, reliable and highly effective.

18 illus, 28 ref

003861   OSMAN M S (Mathematics Dep, Cairo Univ, Giza, Egypt, Email: mofatzi@sci.cu.edu.eg) : New analytical study of water waves described by coupled fractional variant Boussinesq equation in fluid dynamics. Pramana – J Phys 2019, 93(2), 26.

The main objective of this paper is to introduce an analytical study for the water wave solutions of coupled fractional variant Boussinesq equation, which is modelled to investigate the waves in fluid dynamics. Wave transformation in fractional form is applied to convert the original fractional-order nonlinear partial differential equation into another nonlinear ordinary differential equation. The strategy here is to use the unified method to obtain a variety of exact solutions. The unified method works well and reveals distinct exact solutions which are classified into two different types, namely polynomial function and rational function solutions. The results are also depicted graphically for different values of fractional parameter. These findings are highly encouraging and have significant importance for some special physical phenomena in fluid dynamics.

6 illus, 31 ref

003841   BHALEKAR S (Mathematics Dep, Shivaji Univ, Vidyanagar, Kolhapur 416 004, Email: sbb_maths@unishivaji.ac.in) : Analysing the stability of a delay differential equation involving two delays. Pramana – J Phys 2019, 93(2), 24.

Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation D^αx(t) = g(x(t − τ₁), x(t − τ₂)) involving two delays, viz. τ₁ ≥ 0 and τ₂ ≥ 0. We use stability conditions to propose the critical values of delays. Using examples, we show that the chaotic oscillations are observed in the unstable region only. We also propose a numerical scheme to solve such equations.

15 illus, 33 ref

003869   SOUS A J (Al-Quds Open Univ, Nablus, Palestine, Email: asous@qou.edu) : Asymptotic iteration method applied to new confining potentials. Pramana – J Phys 2019, 93(2), 22.

This work intends to evaluate the energy spectrum of a particle influenced by the new type of confined interactions introduced in our previous work [Assi and Sous, Eur. Phys. J. Plus 133(5), 175 (2018); Assi et al, Mod. Phys. Lett. 33(32), 1850128 (2018)]. We have used the asymptotic iteration method (AIM) to carry out numerical computations and our results agree to a high degree of accuracy with those obtained by other researchers using different methods as shown in the tables.

5 tables, 31 ref

003855   KUMAR S, KOUR B (Mathematics and Statistics Dep, Central Univ of Punjab, Bathinda 151 001, Email: baljindervirk172@gmail.com) : Symmetry analysis of some nonlinear generalised systems of space–time fractional partial differential equations with time-dependent variable coefficients. Pramana – J Phys 2019, 93(2), 21.

In this paper, the Lie group analysis method is applied to carry out the Lie point symmetries of some space–time fractional systems including coupled Burgers equations, Ito’s system, coupled Korteweg–de-Vries (KdV) equations, Hirota–Satsuma coupled KdV equations and coupled nonlinear Hirota equations with timedependent variable coefficients with the Riemann–Liouville derivative. Symmetry reductions are constructed using Lie symmetries of the systems. To the best of our knowledge, nobody has so far derived the invariants of space–time nonlinear fractional partial differential equations with time-dependent coefficients.

48 ref

003844   CHAKRABORTY P, PORIA S (Applied Mathematics Dep, Calcutta Univ, Kolkata - 700 009, Email: priya.chakraborty18@gmail.com) : Extreme multistable synchronisation in coupled dynamical systems. Pramana – J Phys 2019, 93(2), 19.

A rule for designing extreme multistable synchronised systems by coupling two identical dynamical systems has been proposed in this paper. The basic idea behind the proposed scheme is the existence of chaos in the coupled system in the presence of initial condition-dependent constants of motion. A new conjecture has been introduced according to which an extreme multistable synchronised system can be designed if all states of one system will synchronise with the corresponding states of the other system (of the two coupled systems) and the basin of the synchronised state depends on the difference between the initial conditions of the corresponding states of the individual systems. The proposed scheme has been illustrated with the help of coupled Rössler systems, coupled Hénon maps and coupled logistic maps. Moreover, the existence of flip bifurcation with the variation of initial conditions has been shown analytically as well as numerically in the case of coupled Hénon maps. Numerical results are reported to show the proficiency of the proposed scheme to design extreme multistable synchronisation behaviour. This work establishes a theoretical foundation for constructing extreme multistable synchronised continuous as well as discrete dynamical systems.

10 illus, 39 ref

003847   EL-GANAINI S, ZAYED E M E (Mathematics Dep, Damanhour Univ, Bahira 22514, Egypt, Email: shoukryelganaini@yahoo.com) : Comment on “New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel (G /G)-expansion method”. Pramana – J Phys 2019, 93(1), 13.

This comment deals with the new auxiliary equation method (Khater method) introduced by Mostafa M A Khater, Aly R Seadawy and Dianchen Lu in Pramana – J. Phys. 90, 59 (2018). By simple calculation, it is shown that this method is wrong. The exact solutions obtained in this paper are also wrong. In this comment, the errors in the above paper are pointed out and modified. The right method (amended Khater method) has been introduced.

23 ref

003865   SEADAWY A R, LU D, IQBAL M (Jiangsu Univ, Jiangsu, People’s Republic of China, Email: dclu@ujs.edu.cn) : Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves. Pramana – J Phys 2019, 93(1), 10.

We investigated the new exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, auxiliary equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs. We used the Mathematica program to show these solutions in two and three dimensions graphically.

18 illus, 39 ref

003853   KHASARE S B, KHASARE S S (Physics Dep, Science Coll, Nagpur - 440 012, Email: shailendra.khasare@yahoo.com) : Statistical distribution of adsorption of quantum particles. Pramana – J Phys 2019, 93(1), 7.

There is a need to compute and work out the theoretical relationship between the single fermion cell and single fermion particle and the single boson cell and more than one boson particle in the assumed processes for developing the theory of adsorption, simply by maximising the entropy of the system for both types of particles. In this work, the reduction of the general expression of adsorption to the special case of the Langmuir adsorption isotherm and closely related family of curves or types of adsorption isotherms in dimensionless form have been derived using statistical mechanics for an adsorbate. The classification of the laboratory data, for adsorption distribution concept, power of generalised method in terms of nonlinear parameter least square fits by selecting different sets of derived functional form one by one is demonstrated.

1 illus, 2 tables, 12 ref

003845   CHENG L, ZHANG Y, MA W-X (Jinhua Polytechnic, Zhejiang, China, Email: jhchengli@126.com) : Pfaffians of B-type Kadomtsev–Petviashvili equation and complexitons to a class of nonlinear partial differential equations in (3+1) dimensions. Pramana – J Phys 2019, 93(1), 4.

The aim of this paper is to investigate a class of generalised Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations, which include many important nonlinear evolution equations as its special cases. By applying the fundamental Pfaffian identity, a general Pfaffian formulation is established and all the involved generating functions for Pfaffian entries need to satisfy a system of combined linear partial differential equations. The illustrative examples of the presented Pfaffian solutions are given for the (3+1)-dimensional generalised KP, Jimbo–Miwa and BKP equations. Moreover, we use the linear superposition principle to generate exponential travelling wave solutions and mixed resonant solutions of the considered equations.

6 illus, 44 ref

003866   SHAHRIARI M, MANAFIAN J (Applied Mathematics Dep, Tabriz Univ, Tabriz, Iran, Email: j_manafianheris@tabrizu.ac.ir) : Analytical behaviour of lump solution and interaction phenomenon to the Kadomtsev–Petviashvili-like equation. Pramana – J Phys 2019, 93(1), 3.

In this paper, we use the generalised Hirota bilinear method (GHBM). With the help of symbolic calculations and applying the used method, we solve the Kadomtsev–Petviashvili (KP)-like equation with p = 3 to obtain some new lump, periodic kink-wave and solitary wave solutions. All solutions have been verified with their corresponding equations with the aid of the Maple package program.

6 illus, 56 ref

002591   PANDE B, JOSHI S, PANDE S (Physics Dep, Kumaun Univ, Nainital, Uttarakhand, Email: pande.seema@yahoo.com) : Statistical study of variability in rainfall and analysis of etreme rainfall events for hill stations of Uttarakhand. J Mountain Res 2019, 14(1), 55-8.

Statistical analysis of rainfall pattern and its variability for 20 years (1990-2010) data is performed for two mountainous urban centres of Uttarakhand i.e. Almora (29.6⁰ N, 79.67⁰ E and altitude 1,204m asl) and Nainital (29.4⁰ N, 79.47⁰ E and altitude 2,020 m asl). Non Parametric method of Principal Component Analysis (PCA) gives the correlation between different extreme rainfall indices. It is concluded that PCA suggest 90% of the variance in composite matrix of extreme rainfall indices.

2 illus, 6 ref

002592   ROSEMARY G N (Mathematics Dep, Ignatius Ajuru Univ of Education, Port Harcourt, Nigeria) : Academic activity gap and first year student’s achievement in mathematics algebra course in Rivers state Nigeria. Int J Multidiscip Res Dev 2019, 6(5), 87-91.

This study investigated effect of academic activity gap on first year students’ achievement in Mathematics Algebra course. The study was conducted in Rivers State Nigeria. The pre test post test one group intact class non-equivalent quasiexperimental research design was employed. A sample of 105 BSc/Ed (Chemistry, Mathematics & Physics) students of the Faculty of Natural and Applied Sciences of Ignatius Ajuru University of Education were selected purposively. A validated and reliable (r = 0.73) instrument titled Mathematics Activity Gap Achievement Test (MAGAT) was used to collect the data. The experimental groups were students who engaged in extended academic programme during activity gap while the students that did not engage in extended academic programme during activity gap were grouped into control. The findings of the study revealed that the students in the experimental group (i.e. students who engaged in extended academic programme during activity gap) had a higher achievement mean score in MTH 114 (Basic Mathematics) than those in the control group (i.e. students who did not engage in extended academic programme during academic gap). The study also showed that there was a significant difference in students’ achievement mean score for the two groups and no significant difference in students’ achievement mean score by gender. It was recommended among others that those students who experienced academic gap should engage in extended academic activities to sustain their mathematical skills for higher academic pursuit in Mathematics.

5 tables, 13 ref

002594   SAADATMANDI A, GHASEMI-NASRABADY A, EFTEKHARI A (Applied Mathematics Dep, Kashan Univ, Kashan 87317-53153, Iran, Email: saadatmandi@kashanu.ac.ir) : Numerical study of singular fractional Lane–Emden type equations arising in astrophysics. J Astrophys Astr 2019, 40(3), 27.

The well-known Lane–Emden equation plays an important role in describing some phenomena in mathematical physics and astrophysics. Recently, a new type of this equation with fractional order derivative in the Caputo sense has been introduced. In this paper, two computational schemes based on collocation method with operational matrices of orthonormal Bernstein polynomials are presented to obtain numerical approximate solutions of singular Lane–Emden equations of fractional order. Four illustrative examples are implemented in order to verify the efficiency and demonstrate solution accuracy.

6 illus, 4 tables, 38 ref

002593   ROUT L, SADANANDAN R, MISHRA D (Avionics Dep, Indian Institute of Space Science and Technology, Thiruvananthapuram - 695 547, Kerala, Email: liturout1997@gmail.com) : Application of image enhancement and mixture of Gaussian approach in combustion research. Sadhana 2019, 44(5), 114.

Chemiluminescence is one of the most commonly used optical diagnostic techniques in combustion research where a line-of-sight projected information is generated from spatial fields. The exactness and uniqueness of reconstruction along with ease of implementation gives Abel inversion an edge over the other existing single-view reconstruction techniques for efficient estimation of spatial field from line-of-sight projections. Though there exist many such algorithms, the primary focus of these has been to ensure tractable inversion through a systematic regularization by imposing a smoothness constraint on discrete data points. But these techniques do not have the provision to process the input image prior to deconvolution in order to prevent accumulation of noise infiltrated during data acquisition. Another major limitation of these algorithms is to adopt the changes in characteristics of the input data points while maintaining optimal storage and time complexity. To address these issues, we have proposed a new image processing technique using standard Abel inversion for the application in combustion research. It provides a suitable model to ensure regularized inversion by imposing a smoothness constraint on acquired raw data. The new algorithm has been implemented to yield the physically significant chemiluminescence emission from hydroxyl radicals in flames from line-of-sight integrated images. The effectiveness of this algorithm is highlighted using exemplary OH chemiluminescence images captured from a standard swirl stabilized research burner.

8 illus, 23 ref

002588   GHOLAMIN P, SHEIKHANI A H R (Applied Mathematics Dep, Islamic Azad Univ, Lahijan, Iran, Email: ah_refahi@yahoo.com) : Dynamical analysis of a new three-dimensional fractional chaotic system. Pramana– J Phys 2019, 92(6), 91.

In the present paper, a new fractional chaotic system proposed by the authors is discussed. Moreover, based on the stability theory of fractional-order systems, conditions for the stability of nonlinear fractional-order systems are presented, and the existence and uniqueness of the solutions of the resulting new fractional chaotic attractor are also studied. Next, the necessary conditions for the existence of chaotic attractors in new fractional chaotic system are reported, and at the end the stability analysis of the corresponding equilibria is given. Last but not the least, the presented numerical simulations confirm the validity of our analysis.

9 illus, 50 ref

002595   SEADAWY A R, ALI A, LU D (Mathematics Dep, Beni-Suef Univ, Beni-Suef- 62511, Egypt, Email: Aly742001@yahoo.com) : Structure of system solutions of ion sound and langmuir dynamical models and their applications. Pramana– J Phys 2019, 92(6), 88.

The present study deals with the system of equations for the ion sound and Langmuir waves (SEISLWs) by employing the extended simple equation, modified F-expansion and exp(−Ψ(ξ )) expansion methods for constructing novel exact travelling wave solutions. Graphical simulations of some solutions are helpful to study the behaviour of SEISLWs. Hence, this approach is practically effective and productive to better understand the nonlinear problems in mathematics, physics and engineering.

12 illus, 34 ref

002587   BASHAN A (Mathematics Dep, Zonguldak Bulent Ecevit Univ, Zonguldak, Turkey, Email: alibashan@gmail.com) : A novel approach via mixed Crank–Nicolson scheme and differential quadrature method for numerical solutions of solitons of mKdV equation. Pramana– J Phys 2019, 92(6), 84.

The purpose of the present study is to obtain numerical solutions of the modified Korteweg–de Vries equation (mKdV) by using mixed Crank–Nicolson scheme and differential quadrature method based on quintic B-spline basis functions. In order to control the effectiveness and accuracy of the present approximation, five wellknown test problems, namely, single soliton, interaction of double solitons, interaction of triple solitons, Maxwellian initial condition and tanh initial condition, are used. Furthermore, the error norms L₂ and L_∞ are calculated for single soliton solutions to measure the efficiency and the accuracy of the present method. At the same time, the three lowest conservation quantities are calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants are calculated and presented. After all these processes, the newly obtained numerical results are compared with results of some of the published articles.

10 illus, 9 tables, 45 ref

002589   GOYAL M, PRAKASH A, GUPTA S (Mathematics Dep, GLA Univ, Mathura- 281 406, Email: manish.goyal@gla.ac.in) : Numerical simulation for time-fractional nonlinear coupled dynamical model of romantic and interpersonal relationships. Pramana– J Phys 2019, 92(5), 82.

The objective of this paper is to study the nonlinear coupled dynamical fractional model of romantic and interpersonal relationships using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). These procedures inspect the dynamics of love affairs among couples. Sufficient conditions for their convergence and error estimates are established. Obtained results are compared with the existing and recently developed methods. It is interesting to observe that these methods also work for those fractional models that do not have an exact solution. Results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes. Results divulge those schemes that are attractive, accurate, easy to use and highly effective.

8 illus, 4 tables, 21 ref

002590   KUHFITTIG P K F (Mathematics Dep, Milwaukee School of Engineering, WI 53202-3109, USA, Email: kuhfitti@msoe.edu) : Spherically symmetric wormholes of embedding class one. Pramana– J Phys 2019, 92(5), 75.

This paper generalises an earlier result by the author based on the well-established embedding theorems that connect the classical theory of relativity to higher-dimensional space–times. In particular, an n-dimensional Riemannian space is said to be of class m if m + n is the lowest dimension of the flat space in which the given space can be embedded. To study traversable wormholes, we concentrate on spacetimes that can be reduced to embedding class one by a suitable transformation. It is subsequently shown that the extra degrees of freedom from the embedding theory provide the basis for a complete wormhole solution in the sense of obtaining both the redshift and shape functions.

1 illus, 12 ref

002586   AL-KHEDHAIRI A, MATOUK A E, ASKAR S S (Mathematics Dep, Majmaah Univ, Al-Majmaah- 11952, Saudi Arabia, Email: aematouk@hotmail.com) : Computations of synchronisation conditions in some fractional-order chaotic and hyperchaotic systems. Pramana– J Phys 2019, 92(5), 72.

A novel criterion for achieving synchronisation in fractional-order chaotic and hyperchaotic systems is presented. Here, it is proved that the existence of a Lyapunov function in the integer-order differential system implies local stability of the steady state in its fractional-order counterpart. So, our criterion is based on computations of suitable linear feedback controllers of the fractional-order systems according to an appropriate choice of Lyapunov function. Furthermore, a new fractional-order hyperchaotic system is introduced here. The case of hyperchaos in the proposed system is verified by computing its greatest two Lyapunov exponents which are shown to be positive. The new synchronisation criterion is successfully applied to the fractional Liu system, the fractional Samardzija–Greller system, the fractional financial system and a novel fractional-order hyperchaotic system. Numerical results are used to verify the analytical results.

8 illus, 52 ref

001315   PHALGUNA P S, KAMAT D V, MOHAN P V A (Centre for Development of Advanced Computing, Bayappanahalli, Bangalore - 560 038, Email: anandmohanpv@live.in) : Novel RNS-to-binary converters for the three-moduli set {2m - 1, 2m, 2m + 1}. Sadhana 2019, 44(4), 99.

In this paper, Mixed Radix Conversion (MRC)-based Residue Number System (RNS)-to-binary converters for the three-moduli set {2m - 1, 2m, 2m + 1} are presented. The proposed reverse converters are evaluated and compared to reverse converters proposed earlier in literature using Chinese Remainder Theorem (CRT) and New CRT for this moduli set as well as two four-moduli sets {2ⁿ - 1, 2ⁿ , 2ⁿ + 1, 2ⁿ⁺¹ - 1} {2ⁿ - 1, 2ⁿ , 2ⁿ + 1, 2ⁿ⁺¹ + 1} regarding hardware requirement and conversion time.

7 illus, 5 tables, 28 ref

001312   DE S K, MAHATA G C (Mathematics Dep, Sidho-Kanho-Birsha Univ, Purulia - 723 104, Email: gcmahata@yahoo.in) : A comprehensive study of an economic order quantity model under fuzzy monsoon demand. Sadhana 2019, 44(4), 89.

This article deals with a classical economic order quantity (EOQ) model under monsoon type fuzzy demand rate. It is nothing but the generalization of cloudy fuzzy model. We split the EOQ model into three parts according to the real-time fuzzy components of the demand rate. To defuzzify the model we develop an algorithm and the solution is obtained with the help of a nonlinear optimization technique that requires maximum aspiration level of the fuzzy membership of the objective function. Moreover, for comparative study we take numerical results of the crisp, general fuzzy and cloudy fuzzy model also. By this study we have shown that the decision maker might have to choose the monsoon type fuzzy environment all the time to control the proposed inventory. Moreover, sensitivity analysis and graphical illustrations are made to justify the new fuzzy approach.

10 illus, 4 tables, 52 ref

001310   AGHELI B, FIROZJA M A (Mathematics Dep, Islamic Azad Univ, Qaemshahr, Iran, Email: b.agheli@yahoo.com) : Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions. Sadhana 2019, 44(4), 77.

An approach for searching an approximate solution of high-order integro-differential equations featuring fractional derivatives has been proposed in this paper. Initially, using trigonometric basic functions (TBFs), we determine the transformation functions in association to TBFs. Next, the approximate function is presented as a combination of TBFs and transform functions. The convergence of this approach is also presented. Using discrete derivatives of the solution to gain an approximate solution, we find the approximate solution, which satisfies the high-order integro-differential equations featuring fractional derivatives. An algorithm of this approach is applied for various examples, and one example is illustrated in detail.

5 illus, 5 tables, 25 ref

001313   HOSSEINI S S, MATIN R K, KHUNSIAVASH M, MOGHADAS Z (Mathematics Dep, Islamic Azad Univ, Karaj, Iran, Email: rkmatin@kiau.ac.ir) : Measurement of productivity changes for general network production systems with stochastic data. Sadhana 2019, 44(3), 72.

Performance evaluation of network production systems has been widely studied in recent Data Envelopment Analysis (DEA) literature where internal relations of sub-units are taken into consideration. Most of prior work assumes network systems to have simple series or parallel structures. Complexities of some practical production processes require development of DEA models for their effective analysis. However; input, intermediate products and/or output data are often stochastic and linked to exogenous random variables in most applications. The current study extends Malmquist Productivity Index (MPI) for investigating productivity changes of general network production units with stochastic data in a DEA framework. The proposed stochastic performance analysis models are then transformed into deterministic equivalent non-linear forms so they could be simplified to deterministic programming with quadratic constraints. Numerical examples including an application to productivity evaluation of branches of a university system are presented to illustrate the applicability of the proposed framework.

2 illus, 6 tables, 40 ref

001317   SHAHZAD M, SULTAN F, HAQ I, ALI M, KHAN W A (Mathematics Dep, Hazara Univ, Mansehra 21300, Pakistan, Email: faisal_maths@hu.edu.pk) : C-matrix and invariants in chemical kinetics: A mathematical concept. Pramana – J Phys 2019, 92(4), 64.

To treat a realistic chemical system, such as a liquid phase dehydrogenation reaction, a chemical scheme, which describes the chemical kinetics in terms of the small number of reaction progress variables is needed. Based on the matrix algebra, we analyse the key components, elements and reactions in the mechanism, C-matrix. Reduction techniques exploit the time-scale separation into fast and slow modes by computing the dimension reduced model via the elimination of fast mode subjecting them to the slow one. The two-step reversible reaction mechanism is considered for model reduction and to simplify the complexity of reaction mechanisms. They give a meaningful picture, but for maximum clarity, the phase flow of the solution trajectories near the equilibrium point is exploited. The Lyapunov function is applied for the stability analysis. To describe the physical behaviour of the reaction mechanism, graphical results are measured while refinement of the initial approximation is tabulated at the end.

6 illus, 2 tables, 30 ref

001316   RAJPUT N K, AHUJA B, RIYAL M K (Computer Science Dep, Ramanujan Coll, New Delhi - 110 019, Email: b.ahuja@ramanujan.du.ac.in) : A statistical probe into the word frequency and length distributions prevalent in the translations of Bhagavad Gita. Pramana – J Phys 2019, 92(4), 60.

A statistical study has been conducted on Bhagavad Gita. Four measures have been derived for the original text in Sanskrit and its translations in Hindi, English and French. First, word frequency distributions for the documents were modelled. Power law was observed with the longest tail in the case of Sanskrit. For other versions, the distributions well replicated the Zipf–Mandelbrot pattern. Second, the Kullback–Leibler (KL) divergence between the documents has been computed with the highest value recorded in all three translations from the Sanskrit text. Next, a Shannon entropy-based measure: vocabulary quotient has been calculated, which estimates the vocabulary richness the texts offer; the highest being in the case of Bhagavad Gita in Sanskrit. Finally, word-length distributions were obtained with the longest word length in Sanskrit. The results attribute to the inflectional nature of Sanskrit.

5 illus, 3 tables, 34 ref

001314   MANAFIAN J, LAKESTANI M (Applied Mathematics Dep, Tabriz Univ, Tabriz, Iran, Email: j_manafianheris@tabrizu.ac.ir) : Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation. Pramana – J Phys 2019, 92(3), 41.

In this paper, we use the Hirota bilinear method. With the help of symbolic calculation and applying this method, we solve the (2 + 1)-dimensional bidirectional Sawada–Kotera (bSK) equation to obtain some new lump-kink, lump-solitons, periodic kink-wave, periodic soliton and periodic wave solutions.

10 illus, 47 ref