APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

Evaluation of Certain Integrals Involving the Product of Classical Hermite's Polynomials Using Laplace Transform Technique and Hypergeometric Approach

In this paper some novel integrals associated with the product of classical Hermite＇s polynomials ∫-∞＋∞（x2）mexp（-x2）{Hr（x）}2dx,∫0∞exp（-x2）H2k（x）H2s＋1（x）dx,∫0∞exp（-x2）H2k（x）H2s（x）dx and ∫0∞exp（-x2）H2k＋1（x）H2s＋1（x）dx, are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of spe- cial functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite＇s polynomials by suitable simplifications of arbitrary parameters.

Testing Link of Climatic Factors and Air Pollution with COVID-19 amid the Second Wave in India

Several recent works indicated the association of climatic factors and air pollution with the spread of coronavirus disease-2019 (COVID-19, total daily confirmed deaths and new cases). Nonetheless, the impact of climatic and environmental conditions concerning virus spread and demise, yet not been solved. Present research work focuses on the spread of COVID-19 over five distinct states/territories of India;those have pretty different climatic conditions and the air quality index. The Kendall rank correlation and Spearman rank correlation tests at 95% significance were used from 3 Jan-15 May 15, 2021 (132 days), including April 2021, a month of sharp rise COVID-19 second wave. For all the regions, a significant positive correlation of temperature (>0.6) and a significant negative correlation of humidity (<-0.5) is found with COVID-19 except for Kerala (insignificant and weak relationship). However, in the case of wind speed, a lower correlation is found everywhere except over Andhra Pradesh (>0.5). For all the states, a significant and consistent inverse relationship (<-0.3) is found between COVID-19 and the daily Air Quality Index (AQI) from 1 Mar to 13 May 2021 (74 days). Thus, increase in temperature and winds, decrease in relative humidity were the climatic reasons, those chipped in COVID-19 cases surge and consequential enhancement of Air quality. These results are quite promising to comprehend the mutual tie-up between climate and COVID-19.

Fault Tree Analysis of the Reliability of Electric Vehicles in India

Innovations for electric vehicles have advanced quickly in latest decades. Large-scale business use of these vehicles is still constrained by reliability-related issues. By utilising fault tree (FT) and Monte Carlo simulation, a mathematical prototype is created that includes the reliability traits of all major electrical parts of the vehicle system, including the battery, motor, drive, controllers. The research demonstrates that by raising the component restoration rates, the vehicle’s survivability can be raised. A thorough discussion of this paradigm is provided, along with a presentation and analysis of the reliability estimations based on an electric vehicle. This research on the reliability design and maintenance of an electric vehicle can be supported by the ideas that are outlined in the paper. Additionally, the findings of this study may be helpful to those who build electric vehicle, especially when upgrading the components efficiency and planning for reliability increase.

Quantification of Organochlorine Pesticide Residues in the Buffalo Milk Samples of Delhi City, India

The ill effects of green revolution include residues of extensively used chemical pesticides in various environmental components. The present study was designed to analyze the levels of organochlorine pesticide residues along with chemical composition in buffalo milk samples collected from different localities of Delhi. Milk monitoring can yield information about the kinds and quantities of pesticides in the environment as well as in our daily diet. In this study, the residue of three different organochlorine pesticides, namely Hexachlorocyclohexane (HCH), Dichlorodiphenyltrichloroethane (DDT) and Endosulfan have been reported. Residues of Lindane exceeded the Maximum Residual Limit values in 50% of the samples is a cause of serious concern. The p,p’-DDT was detected in 70% of the samples with p,p’-DDE (dichlorodiphenyldichloroethylene) in 80% of the milk samples of different parts of Delhi state. DDD (Dichlorodiphenyldichloroethane) another metabolite of p,p’-DDT was detected in 65% of the milk samples. The analysis indicates that DDT is the major contaminants in different parts of Delhi state. α and β endosulfan were detected in 35% and 40% of the samples analyzed. The statistical correlation shows no significant correlation between chemical compositions of the samples. The presence of multiple chemicals in virtually all samples of buffalo milk raises new questions about the possible toxicological impacts of chemical mixtures on an infant’s developing nervous and immune systems and reproductive organs.

Regression analysis and features of negative activation energy for MHD nanofluid flow model:A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic(MHD)stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions.Negative activation energy is scarce in practice,but the impact of negative activation energy could not be neglected as it is noticed in chemical processes.The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies,such as exothermic binding of urea or water.In some processes,the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies.The present mathematical model is solved with successive linearization method(a spectral technique).A comparison of results is made for negative and positive values of activation energy.Apart from it,the quadratic multiple regression model is discussed briefly and explained with bar diagrams.It is observed that with rise in unsteadiness parameter from 0 to 1(taking positive activation energy),skin friction and Sherwood number are increased by 9.36%and 19%respectively,and Nusselt number is decreased by 26%.However,for negative activation energy,9.36%and 112%enhancement is observed in skin friction and Sherwood number,respectively.

Tailoring of structural,optical and electrical properties of anatase TiO_(2)via doping of cobalt and nitrogen ions

Pure(pristine)anatase and mono–doped and co–doped derivatives of TiO_(2)having nitrogen(N)and cobalt(Co)as dopants with respective fixed doping concentrations of 0.7 mol.%and 1.0 mol.%were synthesized using auto–combustion sol–gel technique.The doping effects at corresponding non–metal and transition metal sites of TiO_(2)on the basis of the structural,optical and electrical properties have been investigated.X–ray diffraction(XRD)measurement confirms the formation of pure anatase phase of TiO_(2)for all samples having I41/amd space group of tetragonal structure which has been also verified by the Raman spectroscopy measurement.Various crystallographic parameters have been calculated by performing Rietveld refinement of XRD data including average crystallite size that has been observed in the range of10–15 nm.Pure anatase phase indicates the incorporation of Co^(2+)into TiO_(2)lattice which assists the substitution of N in place of oxygen in co–doped TiO_(2).The band gap tuning towards the visible region from3.2 to 2.1 e V has been achieved with mono–doping and co–doping of the N and Co in TiO_(2)lattice.This can be described in terms of the formation of localized levels of N–2p and Co–3d states in mono–doping and an isolated intermediate band formation in co–doping case.Electrical properties have been investigated in details and explained as the synergetic effects of structural and inherent ionic characters of various dopants.The observed band gaps of all doped samples lie within the visible region which makes them pertinent as the solar energy harnessing materials for photocatalytic and photovoltaic applications.

Role of Al and Ti doping in modulating electrical properties of BIVOX system

The doubly-doped bismuth vanadate with Al and Ti having formula unit, Bi2V1–xAlx/2Tix/2O5.5–δ(0.10 ≤ x ≤ 0.25) was synthesized. The specimens were characterized by scanning electron microscopy(SEM), X-ray diffraction(XRD), Fourier transform infrared(FT-IR), differential scanning calorimetric(DSC), UV–Vis, and electrochemical impedance spectroscopy(EIS) for their structural, thermal, optical, and electrical studies. Influence of both dopant cations(Al and Ti) was observed in the gradual stabilization of the tetragonal phase of Bi2VO5.5–δ with dopant amount. A non-uniform grain growth phenomenon was observed up to x = 0.175, with dopant addition. UV–Vis study revealed the comparatively higher order of oxide ion vacancies for the composition x = 0.175. Impedance spectroscopy measurements indicate a significant decrease of both the grain(Rg) and grain boundary resistances(Rgb) with the rise in temperature and the overall resistance is found to be dominated by the grain interior contribution. Enhancement of ionic conductivity was found in all the compositions in the intermediate temperature range as compared to the parent compound, and the single Al-doped system and the highest value were obtained for x = 0.175.

VDTA-Based Wave Active Filter

In this paper we present a wave active filter based on Voltage Differencing Transconductance Amplifiers (VDTAs). The synthesis of active filters basically based on processing of wave quantities. The wave method is presented for basic building blocks of active filters i.e. a series inductor and parallel capacitor through which realization of various active circuits is made by appropriate connections. The proposed wave active filter is verified by realizing a 4th order low pass Butterworth filter using SPICE simulation with 0.18 μm TSMC CMOS technology parameters.

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

A review on emerging materials with focus on BiI_(3) for room-temperature semiconductor radiation detectors

Purpose Considerable advances in the fundamental knowledge and applications of radiation science have led to significant progress and development of room-temperature semiconductor radiation detectors(RTSD).The RTSDs technologies are continuously evolving with accelerated research and material engineering in the last decade.Significant scientific and technological advancements have led to development of high-performance radiation detectors with high signal-to-noise ratio(SNR),better sensitivity,faster response and higher-resolution with capability of desired room-temperature operation.This paper is a review on emerging semiconductor radiation detector materials with a deeper insight into the prospective role of Bismuth tri-iodide(BiI_(3))for room-temperature radiation detectors.Methods An introduction of the state of art of most developed semiconductor materials,i.e.,cadmium telluride(CdTe),mercury iodide(HgI_(2)),lead iodide(PbI_(2)),etc.,and a critical examination of properties,shortcomings and challenges related to their synthesis have been elaborated.Polymer-semiconductor composites with desirable properties and their integration into detector devices is also presented.Subsequent sections discuss the role of BiI_(3) as an emerging radiation detector material for room-temperature operation with an in-depth discussion on the role of defects in charge transportation and electrode configuration.Furthermore,the current challenges along with the future prospects of these materials for radiation detection to promote continuous innovation and practical applications are also elaborated.Conclusion The comprehensive review on latest developments in room-temperature radiation detector materials is expected to help establish a technological roadmap for the synthesis,fabrication and commercialization of novel materials for development of efficient radiation detectors.

TransientWaves Due to Mechanical Loads in Elasto-Thermo-Diffusive Solids

This paper deals with the study of transient waves in a homogeneous isotropic,solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion.The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary.The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique.Noting that the second sound effects are short lived,the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts.In case of continuous and periodic loads acting at the boundary,the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load.The temperature and concentration fields are found to be discontinuous at all the wave fronts.The displacement,temperature change and concentration deviation due to impulsive,continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform.The computer simulated numerical results have been presented graphically in respect of displacement,temperature change and concentration deviation for brass.A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.

A SIQ mathematical model on COVID-19 investigating the lockdown effect

This research paper aims at studying the impact of lockdown on the dynamics of novel Corona Virus Disease(COVID-19)emerged in Wuhan city of China in December 2019.Perceiving the pandemic situation throughout the world,Government of India restricted international passenger traffic through land check post(Liang,2020)and imposed complete lockdown in the country on 24 March 2020.To study the impact of lockdown on disease dynamics we consider a three-dimensional mathematical model using nonlinear ordinary differential equations.The proposed model has been studied using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is computed and significant parameters responsible to keep basic reproduction ratio less than one are identified.The study reveals that disease vanishes from the system only if complete lockdown is imposed otherwise disease will always persist in the population.However,disease can be kept under control by implementing contact tracing and quarantine measures as well along with lockdown if lockdown is imposed partially.