Further Results on Maximal Domination in Graphs

Vidya And B. Chaluvaraju

Department of Mathematics, Bangalore University, Jnanabharathi
Campus Bangalore-560056 (India)

*Corresponding Author Email: bchaluvaraju@gmail.com/ vidyaraghut@gmail.com


In11, Kulli and Janakiram initiate the concept of maximal domination in graphs. In this paper, we obtained some bounds and characterizations. Also, we estimate the value of the maximal domination number of some graph products such as join of graphs, corona product, cartesian product and strong product.

KEYWORDS: Graph Product; Maximal Dominating Set; Maximal Domination Number.

Magnetized Bianchi Type-VIo String Cosmological Model for Anti-Stiff Fluid in General Relativity

Dhirendra Chhajed1, Ankita Choudhary*1, Atul Tyagi1

1Department of Mathematics & Statistics, University college of science,

Mohanlal Sukhadia University, Udaipur, 313001, Rajasthan, India

Corresponding author email:  ankitamaths1993@gmail.com


In this paper, we have investigated magnetized Bianchi type-VI0 string cosmological model for anti-stiff fluid in general relativity. We assume that F23 is the only survival component of electromagnetic field tensor Fij. For the absolute determination of the model, we assume the expansion in the model is proportional to the shear. The common measures of the Einstein’s field equations for the cosmological model have been acquired under the assumption of anti-stiff fluid i.e. p + ρ = 0, where ρ and p are the rest energy density and the pressure of the fluid, respectively. The physical and geometrical outcomes of the model in the presence of magnetic field are discussed.

KEYWORDS: Bianchi type-VI0, Anti-stiff fluid, Magnetic field, Cosmology (85A40).

Room Temperature Ferromagnetism in Chemically Synthesized Zno Nanoparticles

Veerendra Kumar1, Sundar Singh1* , And Pragati Kumar2

1Department of Physics, Bareilly College, Bareilly (affiliated to MJP Rohilkhand University, Bareilly)-243005, India

2Department of Nanosciences and Materials, Central University of Jammu, Rahya Suchani, Samba, Jammu-181143 India

Corresponding author email: ssg01bcb@gmail.com


Zinc Oxide (ZnO) is an intrinsic n-type metal oxide-based semiconductor with a wide bandgap and has attracted much attention of researchers due to its unique properties and applications in optoelectronic devices, ceramics, catalysis, pigments and many others. Herein, ZnO nanoparticles (NPs) have been successfully synthesised by a simple and cost-effective chemical co-precipitation method. The product is characterized by x-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and UV-Vis absorption spectroscopy (UV-Vis), photoluminescence spectroscopy (PL) and vibrating sample magnetometer (VSM). The XRD pattern confirms the formation of the wurtzite phase ZnO nanoparticles. The structural information and composition were further confirmed by FTIR where the stretching vibration bands appeared at 493 cm1, 562 cm1 and 831 cm1 are due to the Zn-O bond. The absorption edge is observed at 359 -nm which is due to its quantum confinement effect whereas the PL emission is observed in the range of 370 nm-600 nm. M-H loop shows the presence of room temperature ferromagnetism in ZnO nanoparticles possibly due to the presence of oxygen vacancies.

KEYWORDS: Co-Precipitation, Diluted Magnetic Semiconductor, RTFM, Spintronics.

Fourier Seriesand its Physical Application-A Study

Umesh  Kumar Gupta1  and Subhash Kumar Sharma2

Associate Professor Department of Mathematics   MGPG College, Gorakhpur  UP India

Assistant ProfessorDepartment of Electronics MGPG College,GorakhpurUP India

Corresponding Author Email: sksharma13@yahoo.co.uk


Fourier series are of great importance in both theoretical and applied mathematics. This paper will focus on the Fourier series of the complex exponentials of the many possible methods of estimating complex valued functions, Fourier series are especially attractive because uniform convergence of the Fourier series (as more terms are added) is guaranteed for continuous, bounded functions.After studying this paper we will learn about how Fourier transforms is useful in many physical applications, such as partial differential equations and heat transfer equations. one can solve many important problems of physics with very simple way.

KEYWORDS: Fourier Transform, Fourier Sine and Cosine Transform, Fourier Differential equation.

The Motion of Strong Plane Shock Wave in Highly Viscous Medium

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 E-mail : arvindphy80@gmail.com


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

Upconversion Luminescence Enhancement in Lanthanide Ions Doped Bismuth Tellurite Glasses

Yogesh K. Jayaswala, Ghizal F. Ansaria*, S. K. Patidara, Sunil Jatb

aPhysics department, Madhyanchal professional university Bhopal(M.P.)

bPhysics department, Govt. College Umarban, Dist. Dhar (M.P.)

Corresponding Author E-mail : ansarigf@rediffmail.com


Lanthanide ions doped glasses are studied by researchers for upconversion luminescence. Rare earth doped bismuth tellurite glasses codoped with and without silver nanoparticle were synthesized by melt and quench procedure for the study of enhanced upconversion luminescence. Physical parameters as molar mass, molar volume, and density were evaluated. Amorphous nature of samples was verified by x-ray diffraction. DSC is carried for information of thermal properties. UV-Visible absorption and fluorescence spectra is obtained to get detail information of upconversion luminescence. Upconversion mechanism of rare earth erbium and ytterbium ions discussed. Three prominent upconversion luminescence is observed two in green region  and one is in red.

KEYWORDS: Rare Earth Ions; Upconversion; Luminescence

Flow Of Visco Elastic {Oldroyd(1958)Model}Liquid Throughporous Medium And Theannular Space Between Tworightcircular Cylinders

Anil Tripathi

Department of Mathematics K.K.(P.G).College Etawah(U.P.)India

Corresponding Author Email:-   atkkdc@gmail.com


Present paper is concerned with the oscillatory motion of visco-elastic [Oldroyd  (1958) model] liquid through porous medium and the annular space between two right circular cylinders perpendicular to the flow of liquid when both the cylinders execute simple harmonic motion along the central axis of the cylinders. The amplitudes and frequencies have been taken different for both cylinders. The particular cases have also been discussed in detail. Thevelocity of visco-elastic liquid is effected by porous medium.

KEYWORDS: porous medium, oscillatory, harmonically, unsteady. Mathematical Subject Classification-76A10

Bianchi Type-I Inflationary Cosmological Models With Constant Deceleration Parameter For Perfect Fluid Distribution In General Relativity

Laxmi Lal Jat1, Atul Tyagi2,Barkha Rani Tripathi3


1Department of Mathematics & Statistics, UCOS, MLSU,Udaipur 313001,(India)
2Department of Mathematics & Statistics, UCOS, MLSU,Udaipur 313001,(India)
3Department of Mathematics,VidyaBhawanRural Institute,MLSU,Udaipur 313001, (India)

Corresponding Author Email: barkha1808@gmail.com, laxmilal000@gmail.com , tyagi.atul10@mlsu.ac.in


The models represent expanding and shearing universe and both models start with Big Bang initially and the expansion stops for large time. The spatial volume increases with time representing inflationary scenario. The shear is zero for large value of time representing isotropization of universe. The Hubble parameter determines the age of the universe. The expression for Hubble parameter matches with FRW model.


KEYWORDS: Keywords: Bianchi Type-I, Inflationary Universe, Perfect fluid, Cosmology (85A40).

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...