Category: Volume 33

Mathematical Modeling of Impact of Pollutants on Industries Based on Resource Biomass


1Department of Mathematics  V.S.S.D. (P.G.) College, Kanpur India


2Department of Mathematics P.P.N. (P.G.) College, Kanpur India


Depletion of resources such as forestry, minerals etc. and resource-based industries such as wood and paper etc., due to rising pollution, is one of the biggest challenges which the humankind is facing today. In this paper, a mathematical model has been designed to give an insight into the effect of pollutants on natural resources which in turn affects the growth and stability of industries dependent on such biomass. The model is analyzed using stability theory of differential equations. Five dependent variables are considered in the model and some important assumptions are made. Two equilibria are found in the equilibrium analysis and conditions of local and global stability of interior equilibrium are obtained. Numerical simulation is also done to demonstrate the analytical findings. It is found in the study that as we impose an environmental tax on the polluters, the concentration of pollutants in the environment is controlled and the stable equilibrium shifts in such a way that the densities of resource biomass and dependent industries are close to the densities which correspond to the pollution free ecosystem.

KEYWORDS: Pollutants, Resource biomass, Industry, Mathematical model, Stability analysis. 2020 Mathematics Subject Classification No.: 92D40

Inroduction Many interesting phenomena that occur in oblique shock wave reflection have been discovered in the past. The main feature herein is the existence of two possible configurations of...

Mathematical Modelling to Study Effect of Vaccination on Transmission of CORONA Virus

1*Lecturer in Mathematics Government Polytechnic, Himmatnagar-383001 (India)


Since 2019 end, whole of the world is fighting for survival against Covid-19. To overcome the pandemic,
global pharmaceutical sector started vaccine research. Early 2021, rose with a hope of vaccine discovery and
few companies across the globe have invented and started manufacturing Covid-19 vaccine. As on date
vaccination is playing a crucial role in curtaining the spread of this deadly virus caused disease. In this
paper, a Compartmental Model is developed to study the spread of Covid-19 taking two different categories
of human population into consideration. One is the vaccinated population and other is population without
vaccination. Expressions for Reproduction Number are derived for Disease Free Equilibrium (DFE) and Endemic
Equilibrium. Stability of the equilibria is also discussed.

KEYWORDS: Covid-19, Disease transmission model, Basic reproduction number, Eigen Values. Classification Codes: 34A34, 34D23, 92-10

Synthesis, Properties and Applications of Lead-Free Perovskites:A Review

1*Department of Physics, Bareilly College, Bareilly-243005 (India)
2Department of Applied Science and Humanities, Jamia Millia Islamia, New Delhi-110025 (India)


Perovskites are the materials or compounds having a structure similar to calcium titanium oxide (CaTiO3). These materials possess the basic structure of ABX3, in which A & B are the cations with +1 and +2 electron vacancy and X is an anion which may be either halogen or oxygen. Perovskites are chiefly being used in solar cells in the photo absorbing layer for solar to electrical energy conversion with relatively high efficiencies, besides their use in LEDs, photodetectors, X-ray detectors, lasers etc. The power conversion efficiency (PCE) of Perovskite solar cell (PSC) has increased from 10% in the year 2012 to 29.1% in 2020 and are promising to cross the theoretical maximum (Shockley-Queisser) limit of 33% for conventional silicon solar cells, besides having great thermal and mechanical stability values. Toxicity due to the presence of lead and associated instability of PSCs have led to the intensive research in lead-free perovskite solar cells (LF-PSCs). In this review article we have tried to explore the current status of synthesis, properties and applications of perovskites in PSCs,particularly lead-free perovskites, and will suggest future prospects in this widely attracted field of non-conventional energy generation.

KEYWORDS: Lead-free Perovskites, Power Conversion Efficiency, Charge Carrier Recombination, Electron Transport Layer, Hole Transport Layer.

The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)


The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,…,V, where vertices in Vhave pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

KEYWORDS: Coloring, ; Packing chromatic number, Circulant graph, AMS Subject Classification: 05C15, 05E30

The packing chromatic number χ(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,…,Vk ,...

Computation of Nirmala Indices of Some Chemical Networks

Department of Mathematics Gulbarga University, Gulbarga 585106 (India)
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)


Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

KEYWORDS: Nirmala index, first and second inverse Nirmala indices,, chemical networks., Mathematics Subject Classification: 05C09, 05C92, 92E10.

Development of Library Components for Floating Point Processor

Department of Electronics, M.G.P.G. College, Gorakhpur (India)
Department of Physics , M.G.P.G. College, Gorakhpur (India)
Department of Physics , M.G.P.G. College, Gorakhpur (India)


This paper deals with development of an n-bit binary to decimal conversion, decimal to n bit binary conversion and decimal to IEEE-754 conversion for floating point arithmetic logic unit (FPALU) using VHDL. Normally most of the industries now a days are using either 4-bit conversion of ALU or 8-bit conversions of ALU, so we have generalized this, thus we need not to worry about the bit size of conversion of ALU. It has solved all the problems of 4-bit, 8-bit, 16-bit conversions of ALU’s and so on. Hence, we have utilized VHSIC Hardware Description Language and Xilinx in accomplishing this task of development of conversions processes of ALU

KEYWORDS: Binary, Decimal conversion, Floating point representation, Simulations and Device Utilization

A Fuzzy type Backlogging Production Inventory Model for Perishable Items with Time Dependent Exponential Demand Rate

Department of Mathematics & Astronomy, University of Lucknow- Lucknow,U. P. (India)


Production inventory models have an important role in production planning and scheduling. In any economic production quantity (EPQ) model, the production rate is dependent on demand. In this paper we have established a production inventory model for perishable items with partial backlogging and time dependent exponential demand rate. Allowing shortage, it is partially backlogged. The unsatisfied demand is backlogged and it is considered a function of waiting time. The aim of our study is to optimizing the total profit during a given cycle. A numerical example is given in showing the applicability of the developed model.

KEYWORDS: Inventory, , Backlogging and Time Dependent Exponential Demand Rate, Perishability, Subject Classification- MSC 2010 (90B05)

Mathematical Modelling of Solid Waste Management in a Higher Educational Institution

Assistant Professor, Department of Mathematics, Kakojan College, Jorhat, Assam (ICHANDRA CHUTIA
Associate Professor, Department of Mathematics, Jorhat Institute of Science and Technology (India)
Assistant Professor, Department of Civil Engineering, Jorhat Institute of Science and Technology (India)


In the present day scenario, in developing countries, solid waste management is declared as a dangerous issue. Population explosion, high standard of living, urbanization, lack of knowledge about management of waste etc. are the main cause of waste generation. An educational institution can play an important role in terms of waste management. It is observed that environmental studies is being introduced in all programs as a subject from lower primary up to higher level with the objectives to make concern everyone about their nature from childhood but it could not fulfill the objectives in deed. In this paper we propose a mathematical model using linear programming to manage the solid waste of an educational institution with minimum cost within the limited facilities there in.

KEYWORDS: Linear programming, Solid waste, ,Sensitivity analysis, AMS CLASSIFICATION: 90C05, 90C31.

Absolute temperature directly from plank’s profile: A simulation

B-111, Saivihar, Sector-15, CBD-Belapur, NaviMumbai-400614 (India)


The measured thermal radiation from a material surface will, in general, have a wave length (\lambda) dependent scale-factor to the Planck profile (PT) from the contributions of the emissivity (Є\lambda) of the surface, the response function (A\lambda) of the measurement setup, and the emission via non-Plank processes. For obtaining the absolute temperature from such a profile, a procedure that take care of these dependencies and which relay on a temperature grid searchis proposed. In the procedure, the deviation between the Plank profiles at various temperatures and the measured spectrum that is made equal to it at a selected wavelength, by scaling, is used. The response function (A\lambda) is eliminated at the measurement stage and the polynomial dependence of the remnant scale factor mostly dominated by Є\lambda) i s extracted from the measured spectrum by identifying its optimal \lambda dependence. It is shown that when such a computation is carried out over a temperature grid, the absolute temperature can be identified from the minimum of the above deviation. Here, search for T and Є\lambda) d elinked, unlike in the leastsquare approaches that are normally employed. Code that implements the procedure is tested with simulated Planck profile to which different viable values of Є\lambda) a nd noise is incorporated. It shown that if the \lambda dependence of scale-factor is not too high, the absolute temperature can be recovered. A large \lambda dependent scale-factor and the consequent possible error in the temperature obtained can also be identified.

KEYWORDS: Planck profile, Absolute Temperature scale, Temperature measurement

Thermo-Fluid Mechanics of gas-Solid Particle Flows over horizontal Flat Plate

Department of Mathematics, Osmania University, Hyderabad, Telangana-500007-India
Department of Mathematics, Osmania University, Hyderabad,Telangana-500007-India


Mathematical model has been developed to protect fluid and solid particle homogeneous mixture velocity concentration and temperature for a heated horizontal flat plate. Conversation equation based on Eulerian scale are approximated for small relaxation times through stream function and similarity transformations. Parametric database generated through computer program for arbitrary constants on comparison with clear fluid reveals the particle concentration has pronounced effect on velocity and temperature profiles.

KEYWORDS: Fluid Mechanics, Boundary layer equations, ordinary differential equation, AMS Subject Classification: 35Q35 37N10, 76A04, 78M15