# Blog

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Arvind Kumar and Kamlesh Kumar*

Departmen. of  Physics, Daryao Singh Rathore Mem. Degree College, Budaun (U.P)India

*Department. of Physics, Agra College Agra (U.P.)- 282002 India

Corresponding author email: arvindphy80@gmail.com

ABSTRACT:

Neglecting the effect of overtaking disturbances, the motion of strong plane shock wave in highly viscous medium has been investigated by Chester-Chisnell- Whitham method. The analytical expressions for shock strength decreases as shock advances for low viscous region of a medium to the high viscous region. The dependence of mach number on propagation distance, Pressure and Particle velocity as well as on adiabatic index has also been analyzed for the cases. The results obtained here are also compared Yadav et al. (2008) for a freely propagating shock. The obtained expansions are computed and discussed through table.

KEYWORDS: shock wave, CCW method and viscosity

ALOK MALVIYA1

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

MANINDER SINGH ARORA2

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

ABSTRACT:

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

DHRUTI K. PATEL1*
1*Lecturer in Mathematics Government Polytechnic, Himmatnagar-383001 (India)

ABSTRACT:

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

SUNDAR SINGH1*
1*Department of Physics, Bareilly College, Bareilly-243005 (India)
2Department of Applied Science and Humanities, Jamia Millia Islamia, New Delhi-110025 (India)

ABSTRACT:

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.

Bijendra Singh
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)
Rachana Khandelwal
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)
Nitu Trivedi
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)

ABSTRACT:

A prey-predator SIS model with logistic growth has been considered with parasitic infection in prey and more vulnerability of infected prey to predation. The combined harvesting of both species along with disease related death of prey has also been taken into account. It has been observed that the parameter concerned with disease related death affects the endemic state. Threshold numbers along with stability are also discussed. The contributions of Hethcote et. al.7 and Trivedi et. al.12 follows as corollary.

KEYWORDS: Prey-Predator model, Epidemiological model, Stability

B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)
M. KUMARA
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)

ABSTRACT:

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 ,...

V.R. KULLI
Department of Mathematics Gulbarga University, Gulbarga 585106 (India)
B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)
T.V. ASHA
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)

ABSTRACT:

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.

SUBHASH KUMAR SHARMA
Department of Electronics, M.G.P.G. College, Gorakhpur (India)
SHRI PRAKASH DUBEY
Department of Physics , M.G.P.G. College, Gorakhpur (India)
ANIL KUMAR MISHRA
Department of Physics , M.G.P.G. College, Gorakhpur (India)

ABSTRACT:

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

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

ABSTRACT:

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)

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

ABSTRACT:

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.