School of Basic Sciences

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Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces
(2023-01) Tamilvanan, K; Alkhaldi, A; Jakhar, J; Chugh, R; Jakhar, J
In this work, we investigate the refined stability of the additive, quartic, and quintic func tional equations in modular spaces with and without the ∆2-condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach space using the direct method. Additionally, using a suitable counterexample, we eventually demonstrate that the stability of these equations fails in a certain case.
Stochastic modeling and parameter estimation of turbogenerator unit of a thermal power plant under classical and Bayesian inferential framework
(2023-10) Kumar, A; Chaudhary, R; Kumar, K; Saini, M; Saini, D
The work reported in present study deals with the development of a novel stochastic model and estimation of parameters to assess reliability characteristics for a turbogenerator unit of thermal power plant under classical and Bayesian frameworks. Turbogenerator unit consists of five components namely turbine lubrication, turbine governing, generator oil system, gen erator gas system and generator excitation system. The concepts of cold standby redun dancy and Weibull distributed random variables are used in development of stochastic model. The shape parameter for all the random variables is same while scale parameter is different. Regenerative point technique and semi-Markov approach are used for evaluation of reliability characteristics. Sufficient repair facility always remains available in plant as well as repair done by the repairman is considered perfect. As the life testing experiments are time consuming, so to highlight the importance of proposed model Monte Carlo simulation study is carried out. A comparative analysis is done between true, classical and Bayesian results of MTSF, availability and profit function.
Sr(II) and Ba(II) Alkaline Earth Metal–Organic Frameworks (AE-MOFs) for Selective Gas Adsorption, Energy Storage, and Environmental Application
(2023-01) Sharma, A; Meynen, V; Király, N; Capková, D
Two new alkaline earth metal–organic frameworks (AE-MOFs) containing Sr(II) (UPJS-15) or Ba(II) (UPJS-16) cations and extended tetrahedral linker (MTA) were synthesized and characterized in detail (UPJS stands for University of Pavol Jozef Safarik). Single-crystal X-ray analysis (SC-XRD) revealed that the materials are isostructural and, in their frameworks, one-dimensional channels are present with the size of ~11 × 10 Å2 . The activation process of the compounds was studied by the combination of in situ heating infrared spectroscopy (IR), thermal analysis (TA) and in situ high-energy powder X-ray diffraction (HE-PXRD), which confirmed the stability of compounds after desolvation. The prepared compounds were investigated as adsorbents of different gases (Ar, N2 , CO2 , and H2 ). Nitrogen and argon adsorption measurements showed that UPJS-15 has SBET area of 1321 m2 g −1 (Ar) / 1250 m2 g −1 (N2 ), and UPJS-16 does not adsorb mentioned gases. From the environmental application, the materials were studied as CO2 adsorbents, and both compounds adsorb CO2 with a maximum capacity of 22.4 wt.% @ 0 ◦C; 14.7 wt.% @ 20 ◦C and 101 kPa for UPJS-15 and 11.5 wt.% @ 0◦C; 8.4 wt.% @ 20 ◦C and 101 kPa for UPJS-16. According to IAST calculations, UPJS-16 shows high selectivity (50 for CO2/N2 10:90 mixture and 455 for CO2/N2 50:50 mixture) and can be applied as CO2 adsorbent from the atmosphere even at low pressures. The increased affinity of materials for CO2 was also studied by DFT modelling, which revealed that the primary adsorption sites are coordinatively unsaturated sites on metal ions, azo bonds, and phenyl rings within the MTA linker. Regarding energy storage, the materials were studied as hydrogen adsorbents, but the materials showed low H2 adsorption properties: 0.19 wt.% for UPJS-15 and 0.04 wt.% for UPJS-16 @ −196 ◦C and 101 kPa. The enhanced CO2/H2 selectivity could be used to scavenge carbon dioxide from hydrogen in WGS and DSR reactions. The second method of applying samples in the area of energy storage was the use of UPJS-15 as an additive in a lithium-sulfur battery. Cyclic performance at a cycling rate of 0.2 C showed an initial discharge capacity of 337 mAh g−1 , which decreased smoothly to 235 mAh g−1 after 100 charge/discharge cycles.
Shifted fractional order Gegenbauer wavelets method for solving electrical circuits model of fractional order
(2023-10) Yadav, P; Jahan, S; Nisar, K
This study introduces a novel numerical approach based on shifted fractional-order Gegenbauer wavelets. The technique aims to provide approximate solutions for a certain class of extremely significant fractional models of electrical LC , RC , RL, and RLC circuits. We use a collocated approach to generate numerical solutions for these circuits model by making use of the beneficial characteristics of shifted fractional-order Gegenbauer polynomials (SFGBP). We include a parameter that characterizes the presence of fractional structures inside the models in order to retain the dimensional properties of the physical parameters in the electrical circuits. Several particular instances of the various source terms have also been examined. The main findings include the close resemblance of current fractional-order models to classical cases, variations in current with resistance values, and error reduction through additional series terms. Numerical simulations are shown through geometrical interpretation to illustrate the exactness and reliability of our technique.
Relativistic modeling of stellar objects in a Schwarzschild’s coordinates with embedded class one spacetime
(2023-06) Prasad, A; Kumar, M; Kumar, J
In this study, we investigate a new relativistic anisotropic Einstein field equations solution for compact stars under embedding class 1 conditions. In order to do this, we apply the Karmarkar condition and the embedding class one technique. By taking Buchdahl type metric poten tial grr into consideration, the precise analytical solution has been investigated. We have studied physical characteristics of various compact star using this analytical solution. Central singularities are absent from the solution. We have explored thermodynamic observables inside the stellar models, such as radial and tangential pressures, matter density, anisotropic factor, energy conditions, TOV, red-shift, and the speed of sound, etc., after establishing this space-time geometry for the stellar models. From the graphical representation of vari ous physical characteristics, it is demonstrated that our model meets all the specification for ultra-high density compact bodies.
Power Modified Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications
(2023-07) Kumar, D; Dey, S; Kharazmi, O
In this article, we explore a new probability density function, called the power modified Lindley distribution. Its main feature is to operate a simple trade-off among the general ized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible: its probability density function can be right skewed and its associated hazard rate function may be increasing, decreasing, unimodal and constant. First the model parameters of the proposed distribution are obtained by the maximum likelihood method. Next, Bayes estimators of the unknown parameters are obtained under different loss functions. In addi tion, bootstrap confidence intervals are provided to compare with Bayes credible intervals. Besides, log power modified Lindley regression model for censored data is proposed. Two real data sets are analyzed to illustrate the flexibility and importance of the proposed model.
PARAMETER INDEPENDENT SCHEME FOR SINGULARLY PERTURBED PROBLEMS INCLUDING A BOUNDARY TURNING POINT OF MULTIPLICITY ≥ 1
(2023-06) Kumari, P; Kumar, D; Ramos, H
A numerical scheme is developed for parabolic singularly per turbed boundary value problems, including multiple boundary turning points at the left endpoint of the spatial direction. The highest order derivative of these problems is multiplied by a small parameter ε (0 < ε ≪ 1), and when it is close to zero, the solution exhibits a parabolic type boundary layer near the left lateral surface of the domain of consideration. Thus, large oscillations appear when classical/standard numerical methods are used to solve the prob lem, and one cannot achieve the expected accuracy. Thus, the Crank-Nicolson scheme on a uniform mesh in the temporal direction and an upwind scheme on a Shishkin-type mesh in the spatial direction is constructed. The theoretical analysis shows that the method converges irrespective of the size of ε with accuracy O((∆t) 2 + N −1 ln N). Three test examples are presented to verify that the computational results agree with the theoretical ones.
PANI encapsulated α-MnO2 nanocomposites as photocatalytic, antibacterial and anticorrosive agents: Sustainable experimental and theoretical studies
(2023-06) Kumar, H; Luthra, M; Punia, M; Yadav, A
Metal nanoparticles and conducting polymers have applications in the fields like purification, separation, adsorption, photocatalytic, antibacterial, sensors, electrical conductivity, etc. The α-MnO2 nanoparticles, and polyaniline (PANI) were synthesized by the reverse micelle and chemical oxidative techniques, respectively. An in-situ technique was used for the synthesis of α-MnO2/PANI nanocomposites (NCs). The characterization of α-MnO2 nanoparticles and NCs was carried out by XRD, TEM, FTIR, and UV–visible techniques. The experimental data was supported by a theoretical (computational) study. Corrosion inhibition, antibacterial, and photo catalytic activity of α-MnO2/PANI NCs were explored. The NCs show a maximum of 87 ± 0.1% corrosion in hibition efficiency. The NCs (100 ppm concentration) degrade 89.15 ± 1.1% of methyl orange dye after 3 h of UV exposure. The photodegradation of dye follows pseudo-first order kinetics with a rate constant of 0.0657 min− 1 . The mechanism of photodegradation is supported by potentiostatic photocurrent measurement, imped ance spectroscopy, pH variation, and chemical oxygen demand. The antibacterial property of NCs was compared to standard Hexa disk against Gram-positive and Gram-negative bacterial strains. The NCs show 18.5 mm and 15.3 mm Zone of Inhibition (1000 ppm) for S. epidermis and E. coli, respectively. The α-MnO2/PANI NCs show very good anti-corrosive, antibacterial, and photocatalytic properties.
On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data
(2023-11) Alharb, R; Garg, R; Kumar, I; Kumari, A
The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent ran dom variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.
Metal oxide decorated polyaniline based multifunctional nanocomposites: An experimental and theoretical approach
(2023-05) Yadav, A; Kumar, H; Sharma, R
When combined with metal oxide nanoparticles, conducting polymers may result in unique or synergistic effects in their properties. Fe/Mn/CuO/PANI (FMC/PANI) based nanocomposites (NCs) were explored for five different novel applications. FTIR, UV–visible, XRD, Raman, and FESEM methods were used to identify the NCs. The anti corrosive, photocatalytic, magnetic, antibacterial, and electrical properties were investigated by experimental and theoretical (DFT) methods. The computational technique was used for frequency, geometry optimization, and energy study. Different thermodynamic, kinetic, and molecular orbital parameters were investigated by the DFT study for the NCs. The anti-corrosive, photocatalytic, antibacterial, electrical, and magnetic properties of NCs were investigated at different concentrations. The FMC/PANI NCs show a maximum of 85 ± 0.2% CIE for MS in 1.0 M HCl solution. The magnetic study proves the paramagnetic nature of NCs. The photocatalytic activity of FMC/PANI NCs was investigated against MO dye under UV light. The antibacterial property of FMC nano particles (NPs) was investigated against gram-positive and gram-negative bacterial strains, that is, B. subtilis and E. coli, respectively. The ZOI was compared with six standard antibiotics and found to be comparable with common antibiotics. The FMC/PANI-based NCs were proven to be perfect photocatalytic, magnetic, antibacte rial, electrical conductors, and anti-corrosive agents.
IoT-enabled technologies for controlling COVID-19 Spread: A scientometric analysis using CiteSpace
(2023-07) Kumar, D; Sood, S; Rawat, K
The COVID-19 outbreak has unleashed a cataclysmic impact on the daily existence of humanity, triggering a widespread upheaval in public health and wreaking havoc on the economies of affected nations. This lethal disease has emerged as a leading cause of substantial mortality and morbidity around the globe, and the emergence of new virus variants has confronted humanitarian society with formidable difficulties. In this tumultuous period, the Internet of Things (IoT) has played an indispensable role. IoT has offered various innovative solutions to curb the spread of the pandemic, providing a beacon of hope amidst the chaos. The current research delves into the literature on IoT-assisted COVID-19 research, utilizing a scientometric analysis to extensively examine the technological impact in the battle against the outbreak. It illuminates the multifaceted role of ICT in the ongoing pandemic by employing an array of empirical approaches such as publication patterns, citation structures, leading nations, literature co-citation network analysis, and knowledge mapping of scientific literature using the CiteSpace tool. Furthermore, the study uncovers the research frontiers, research hotspots, cluster analysis, and potential future directions in this knowledge domain, providing a visual narrative that inspires hope and a renewed commitment to our collective responsibility in the face of this global crisis.
Integrated Spatial Analysis of Forest Fire Susceptibility in the Indian Western Himalayas (IWH) Using Remote Sensing and GIS-Based Fuzzy AHP Approach
(2023-09) Pragya; Kumar, M; Tiwari, A
Forest fires have significant impacts on economies, cultures, and ecologies worldwide. Developing predictive models for forest fire probability is crucial for preventing and managing these fires. Such models contribute to reducing losses and the frequency of forest fires by informing prevention efforts effectively. The objective of this study was to assess and map the forest fire susceptibility (FFS) in the Indian Western Himalayas (IWH) region by employing a GIS-based fuzzy analytic hierarchy process (Fuzzy-AHP) technique, and to evaluate the FFS based on forest type and at district level in the states of Jammu and Kashmir, Himachal Pradesh, and Uttarakhand. Seventeen potential indicators were chosen for the vulnerability assessment of the IWH region to forest fires. These indicators encompassed physiographic factors, meteorological factors, and anthropogenic factors that significantly affect the susceptibility to fire in the region. The significant factors in FFS mapping included FCR, temperature, and distance to settlement. An FFS zone map of the IWH region was generated and classified into five categories of very low, low, medium, high, and very high FFS. The analysis of FFS based on the forest type revealed that tropical moist deciduous forests have a significant vulnerability to forest fire, with 86.85% of its total area having very high FFS. At the district level, FFS was found to be high in sixteen districts and very high in seventeen districts, constituting 25.7% and 22.6% of the area of the IWH region. Particularly, Lahul and Spiti had 63.9% of their total area designated as having very low FSS, making it the district least vulnerable to forest fires, while Udham Singh Nagar had a high vulnerability with approximately 86% of its area classified as having very high FFS. ROC-AUC analysis, which provided an appreciable accuracy of 79.9%, was used to assess the validity of the FFS map produced in the present study. Incorporating the FFS map into sustainable development planning will assist in devising a holistic strategy that harmonizes environmental conservation, community safety, and economic advancement. This approach can empower decision makers and relevant stakeholders to take more proactive and informed actions, promoting resilience and enhancing long-term well-being.
Hydrocarbons (C8–C12) separation in porous metallocavitand M-PPX (M = Cu, Ag, Au): From computational insight
(2023-09) Mohanty, B; Avashthi, G
High throughput computational approach has been employed to investigate the adsorption and separation of C8–C12 hydrocarbons (HCs) on a tube-shaped met allocavitand, pillarplex (PPX). The Cu (I), Ag (I), and Au (I) seamed PPX and their HC complexes has been examined using density functional theory (DFT), pro claiming Cu-PPX has a higher binding affinity with the HCs whereas Ag-PPX is lower. The thermodynamic properties reveal the host–guest complex is stable at ambient condition. Noncovalent interaction (NCI) analysis shows the interaction of guests within the cavity of PPX is mainly attributed by Van der Waals type. The energy decomposition analysis (EDA) enunciates the percentage contribution of dispersion interaction (ΔEdisp) is 59–62%, the electrostatic (ΔEelct) and orbital (ΔEorb) terms have a moderate contribution towards the total binding energy. The Grand canonical Monte Carlo (GCMC) simulation manifests the Cu-PPX and Au PPX are the ideal hosts with the optimum capacity to store HCs at ambient conditions. The octane uptake is 18.01, 17.50, and 25.31 cm3 STP/g in Cu, Ag and Au-PPX and the uptake reduces upon increasing the HC chain length. The isosteric heat of adsorption (Qst) is corroborated with the computed DFT data at ambient setup. The ideal adsorption solution theory (IAST) claims the C8 selectivity in Cu, Ag and Au-PPX is optimum at 298 K and the increasing temperature from 298 K to 323 K, the selectivity of the C9 and C12 in Cu-PPX and Au-PPX, respectively is remarkable after the complete separation of C8. Hence Cu-PPX and Au-PPX is the potential candidate for industrial use to separate the heavy HCs.
Fusion of Stable Odd-A isotope targets with Doubly Magic 16O Projectile
(2023-12) Vijay; Gautam, M; Chahal, R; Hitesh
Fusion excitation functions of stable odd-A targets 147,149Sm with 16O projectile are theoretically analyzed within view of the symmetric-asymmetric Gaussian barrier distribution (SAGBD) formalism. For the purposes of this study, we assumed that bombardment energies of the 16O + 147,149Sm reactions would be around nominal barrier. For these reactions, Wong based computations fails to retrace the fusion data whereas SAGBD predictions fairly retrace the fusion data in entire bombarding energy range. The evaluated values of channel coupling parameter (λ) and VCBRED from SAGBD outcomes are found larger for heavier (16O + 149Sm) over lighter (16O + 149Sm) system, which suggests that heavier system possess extra fusion enhancement in sub-barrier domain. Present theoretical investigation highlights the significant contributions of intrinsic channels that emerges due to structure of reacting nuclei and such effects are empirically included in SAGBD method.
Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator
(2023-09) Yadav, P; Jahan, S; Shah, K
This article aims to introduce and analyze a diabetes mellitus model of fractional order, utilizing the ABC derivative. Diabetes mellitus is a prevalent and significant disease worldwide, ranking among the top causes of mortality. It is characterized by chronic metabolic dysfunction, leading to elevated blood glucose levels and subsequent damage to vital organs including the nerves, kidneys, eyes, blood vessels, and heart. The fractional ABC derivative is used in this study to describe and analyze diabetes mellitus mathematically while removing hereditary influences. The investigation begins by exploring the initial points of the diabetes mellitus model. Under the fractional ABC operator, Picard’s theorem is used to prove the existence and uniqueness of solutions. For the numerical approximation of solutions in the fractional-order diabetes mellitus model, this study used a specialized technique that combines the principles of fractional calculus and a two-step Lagrange polynomial interpolation. Finally, the obtained results are visually presented through graphical representations, serving as empirical evidence to support our theoretical findings. The numerical experiments showed that the proportion of patients with diabetes mellitus increased as the fractional dimension (𝜃) reduced. The combination of mathematical modelling, analysis, and numerical simulations provides insights into the dynamics of diabetes mellitus, offering valuable contributions to the understanding and management of this prevalent disease. Additionally, the proposed scheme can be enhanced by incorporating the ABC operator, allowing for the simulation of real-world dynamics and behavior in the coexistence of diabetes mellitus and tuberculosis.
Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator
(2023-11) Yadav, P; Jahan, S; Nisar, K
The aim of this paper is to analyze a fractional model of the Ebola virus. This study is important because it contributes to our understanding of the Ebola virus transmission dynamics using the notion of non-local differential operators. We aim to apply the recently implemented Atangana– Baleanu–Caputo (ABC) fractional derivative with the Mittag-Leffler kernel to study the Ebola virus model closely. The Picard–Lindelof approach is used to do a comprehensive study of the existence and uniqueness of the model’s solutions. The approximate solutions of the fractional order Ebola virus model were obtained using a numerical technique with the ABC operator, a combination of the fundamental theorem of fractional calculus and the two-step Lagrange polynomial interpolation. This innovative approach may offer new insights into the Ebola virus model that were not previously explored. Finally, the numerical simulations illustrate how the control parameters impact specific compartments within the model. The geometrical representation gives significant information about the model’s complexity and reliable infor mation about the model. We simulate each model compartment at various fractional orders and compare them with integer-order simulations, highlighting the effectiveness of modern derivatives. The fractional analysis underscores the enhanced accuracy of non-integer order derivatives in capturing the Ebola virus model’s dynamics.
Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model
(2023-10) Jahan, S; Ahmed, S; Yadav, K; Nisar, K
In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that is solved by the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. Numerical examples are provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique, the approximate solutions of FROM are compared with the exact solution and other existing methods. This research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical problems in real-world systems.
Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method
(2024) Sharma, M; Gupta, R
In this work, the Benjamin-Bona-Mahoney-Burgers equation has been examined, which includes the dual power-law nonlinearity and diffraction term. By using the modified exp-function method, the exact solutions of the governing equation have been obtained. The resulting traveling wave solutions have been found to exhibit various characteristics, such as being dark solitons, periodic, and singular, depending on the values of certain constants. To further illustrate these solutions, 3D, 2D, and contour graphs have been displayed. To the best of our knowledge, this is the first time in literature that the dark solitons, periodic soliton, and singular soliton solutions of considered equations have been obtained by utilizing the modified exp-function method.
Co3O4 quantum dot decorated polypyrrole nanocomposites as a flexible, conducting, anticorrosive and antibacterial agent: sustainable experimental and theoretical approach†
(2023-02) Kumar, H; Luthra, M; Punia, M; Kaur, P
Self-assembled cobalt oxide quantum dots (QDs) were prepared by the inverse micelle technique. Polypyrrole (PPy) was synthesized by the chemical-oxidative method. Co3O4 QD-based PPy nanocomposites (NCs) were prepared by an in situ method. The Co3O4 QDs, PPy, and Co3O4@PPy NCs were characterized by TEM, FTIR, X-ray diffraction, and UV-visible techniques. The size of Co3O4 QDs, PPy, and Co3O4@PPy NCs was obtained by powder XRD and TEM methods. Computational (DFT) and adsorption (Langmuir and Henry) studies were carried out to support experimental data. Co3O4@PPy NCs show a maximum of 81.58% protection to mild steel in an acidic medium. The antibacterial activity of Co3O4@PPy NCs was comparable to that of Hexa disk (standard antibiotics). The Co3O4@PPy NCs were proven to be flexible, conducting, corrosion inhibiting, and possess antibacterial properties. The NCs find applications in soft electronics, the pharmaceutical industry, corrosion inhibitors for metals and their alloys, and flexible (moldable) display devices for sustainable developments
Bivariate Lupas¸-Durrmeyer type operators involving P ´olya distribution
(2023-03) Yadav, J; Mohiuddine, A; Kajla, A
In this paper, we consider a bivariate extension of blending type approximation by Lupas¸- Durrmeyer type operators involving Polya Distribution. We illustrate the convergence rate of these type ´ operators using Peetre’s K-functional, modulus of smoothness and for functions in a Lipschitz type space.

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