The present research aims at investigating the LRS Bianchi type I dark energy cosmological model within the framework of f(G) gravity. To obtain solutions for the field equations, a parametrization of the deceleration parameter is employed. The approximate best-fit values of the model parameters are obtained using the least squares method, incorporating observational constraints from available datasets such as the Hubble dataset and the Pantheon dataset by applying the Root Mean Square Error (RMSE) formula. The related cosmological parameters are graphed against redshift, and the universe's accelerated expansion is subsequently examined. Various physical parameters, including pressure, energy density, and energy conditions, are also discussed.
The FT-IR and FT-Raman spectra of 3-chloro-5-(trifluoromethyl)benzonitrile (TFMBN) are analysed using the hybrid correlation approach. Using density functional theory, B3LYP and the 6-311++G(d,p) basis set were utilised to determine the molecular structure, vibrational wavenumbers, infrared intensities, and Raman activities. The computational model's dependability was validated by comparing experimental and theoretical vibrational frequencies. The stability and chemical reactivity of the molecule were confirmed by the FMO orbital analysis, which also measured the energy gap between the HOMO and LUMO. The computed frequencies were also used to determine thermodynamic parameters, including heat capacity, entropies, enthalpy, and their relationships with temperatures.
The f(Q,T) gravity theory has been studied in the context of a spatially homogeneous and anisotropic Bianchi type-VI space-time in the presence of bulk viscous fluid. The field equations are solved explicitly with the help of hyperbolic hybrid scale factor R = eat[tanh(t)]b. The non-linear functional forms of f(Q,T) gravity: f(Q,T) = Q + αQ2 + βT where Q and T are non-metricity scalar and trace of energy momentum tensor respectively is considered. Some physical and geometrical properties are calculated and plotted their graphs in terms of time. For the considered model it is found that the coefficient of bulk viscosity appears to be positive and decreases over time. The cosmological behaviour of energy density, effective pressure, Equation of state parameter, and deceleration parameter are quite in good agreement with recent findings of cosmology. The energy conditions of the model are also studied.
Differential equations are the formulation of scientific theory for many real-world physical problems. Boundary value problems (BVPs) occur frequently in the fields of engineering and science, such as gas dynamics, nuclear physics, atomic structures, and chemical reactions. In most cases, BVPs do not always find the exact solutions to these problems. Boubaker wavelets are wavelet functions derived from Boubaker polynomials. They serve as an effective numerical tool for tackling a range of scientific and engineering problems, including differential and variational equations. Their strength lies in generating accurate approximate solutions by transforming complicated equations into simpler linear systems. In this paper, a wavelet-based Galerkin method using Boubaker wavelets for the numerical solution of BVPs is proposed. Here, Boubaker wavelets are used as weight functions that are the assumed basis elements that allow us to obtain the numerical solution of the BVPs. The numerical results from the proposed method are compared with the exact solution to assess accuracy against existing schemes (Galerkin method using other wavelets, such as Laguerre and Fibonacci wavelets). Some BVPs are taken to demonstrate the validity and applicability of the proposed method.
Heat exchangers are employed extensively in different industries such as ship building, chemical technology, power, food and beverage, and others. Maximum heat transfer in a heat exchanger is desired to achieve the highest possible efficiency and performance of the device. The heat transfer dynamics of a shell and tube heat exchanger with water as the heat transfer fluid are statistically examined in this study using the Full Factorial Design of Experiments approach. Input variables include the fluid flow parameters namely mass flow rates of the hot and cold water (50-250 L/h) as well as the temperature of the hot fluid entering (48.1-66 °C). The responses evaluated are the log mean temperature difference, heat transfer rate, effectiveness and overall heat transfer coefficient. The findings indicate that high flow rates and a high inlet temperature are the optimal input settings for maximum heat transfer. Low flow rates and high inlet temperature are the best settings for maximum effectiveness. The interactions between flow rates have a significant impact on the responses of heat transfer rate, overall heat transfer coefficient, and effectiveness. Effectiveness is also affected by the interaction of cold fluid’s flow rate and its inlet temperature.
This paper introduces a novel extension of the classical Banach Contraction Principle, focusing on "perimetric contractions" in n-gon. Unlike traditional contractions that deal with the distances between pairs of points, perimetric contractions are concerned with the contraction of the entire perimeter of an n-gon, considering the distances between consecutive points along the boundary. This new perspective enables the development of fixed-point results in higher-dimensional metric spaces. The core objective is to establish a fixed-point theorem for mappings that contract the perimeters of n-gon, providing a generalization of Banach's original theorem. The paper demonstrates that such mappings are continuous and presents conditions under which fixed points exist and are unique. Additionally, the relationships between perimetric contractions and conventional contraction mappings are examined, thus expanding the applicability of fixed-point theorems in more complex settings.
In this study, a comprehensive first-principles investigation has been carried out on ThH2 to evaluate its structural, electronic, elastic, phonon, thermodynamic, and hydrogen storage properties. The calculations were performed using DFT within the framework of the GGA-PBE approximation, employing the CASTEP module. Structural optimization confirmed that ThH2 crystallizes in a bct phase with space group I4/mmm, and the lattice parameters show good agreement with available experimental and computational data. Electronic band structure and DOS analyses reveal metallic behavior, with significant hybridization between Th-6d and H-1s orbitals. The elastic constants satisfy the mechanical stability criteria and indicate that ThH2 is ductile and elastically anisotropic. Phonon dispersion confirms the dynamical stability of the compound, with no imaginary frequencies across the Brillouin zone. Temperature-dependent thermodynamic properties such as Debye temperature, Helmholtz free energy, entropy, enthalpy, and heat capacity were also evaluated using the quasi-harmonic approximation. The volumetric hydrogen storage capacity of ThH2 (82.57 kg/m3) significantly exceeds the U.S. DOE’s 2025 target of 40 kg H2/m3, demonstrating its strong potential to meet and surpass future storage requirements. The findings establish ThH2 as a thermodynamically stable and mechanically robust material, making it a promising candidate for applications in advanced nuclear fuel systems and storage technologies.
This investigation analyzes the fundamental physical properties of UX (X = C, N, O) using the density functional theory-based CGA-PBE and CGA-PBEsol functionals implemented in the CASTEP code. The obtained lattice parameters of UX using the CGA-PBEsol technique demonstrate good agreement with previously reported results, and further calculations have been performed based on this technique. The electronic structure analysis reveals the metallic nature of UX. The dynamical stability of the studied structures has been checked through their phonon dispersion curves. The mechanical stability and ductile behavior of the studied compounds have been confirmed by the Born stability criterion, Cauchy pressures, Pugh’s ratio, and Poisson ratio. For the first time, the famous Slack equation has been utilized to calculate the lattice thermal conductivity of the studied compounds. From the thermophysical analysis, it is observed that UC has exhibited the highest Debye temperature and lattice thermal conductivity (kL) at room temperature, while UN has the highest melting temperature. Furthermore, UC and UN have displayed the lowest thermal expansion. Overall, this extensive study on the physical properties of UX (X = C, N, O) reveals the potential application of UC and UN solid fuel materials in nuclear power plants.
A comprehensive theoretical investigation of 8-hydroxy coumarin has been conducted to elucidate its geometrical, spectroscopic, and electronic properties. Geometrical analysis reveals the impact of the carbonyl and hydroxyl groups on bond lengths and bond angles. This is supported by consistent findings from Laplacian of electron density (∇²ρ) calculations. Natural Bond Orbital (NBO) analysis highlights significant conjugative and hyper-conjugative interactions that enhance molecular stability. Time-Dependent Density Functional Theory (TD-DFT) calculations identify a HOMO-LUMO energy gap of 4.32 eV, while simulated UV spectra feature sharp peaks at 220 nm and 289 nm, along with a small shoulder between 215–240 nm. Simulated Infrared (IR) and Nuclear Magnetic Resonance (NMR) spectra align well with experimental data. The electronic structure of 8-OH coumarin is explored through Electron Localization Function (ELF) and Localized Orbital Locator (LOL) studies. Density of States (DOS) studies unveils bonding, non-bonding, and antibonding interactions. Nonlinear optical (NLO) analysis reveals significant optical activity, while Reduced Density Gradient (RDG) analysis excludes intramolecular hydrogen bonding but indicates weak van der Waals and steric interactions.
Radiation safety is a key concern to protect workers, patients, and the public from ionizing radiation. This study investigates the status of radiation protection in 35 private medical facilities in Pirojpur district through field inspections, structured interviews, and radiation dose measurements, in accordance with national safety standards (BAER Act-2012, NSRC Rules-1997, and Regulatory Guides). The results show that 60 % of facilities lack a certified RCO, and 34 % of facility operators do not use a personal monitoring device, violating Sections 54.0, 58.1, and 59.1 of the NSRC Rules-1997. While most of the X-ray rooms are undersized, 86 % meet wall thickness requirements (Regulatory Guide for Diagnostic X-ray). 80 % of facilities have radiation warning signs and 88.5 % of facilities use PPE, which are safety requirements according to Sections 55.2 (a), 18.2 (22), and 83.1 (b) of NSRC Rules-1997. Radiation doses at control panels were within the limit in most cases, but the doses at the entrance doors were not satisfactory. The use of shielding materials was sufficient in most facilities. Compared with the previous regulatory survey, notable progress has been observed. However, to foster safe and effective radiological practice, awareness needs to increase by providing proper guidance, training, and regulatory support.
The L-Histidine Diglycine Picrate (LHSDGP) single crystal was carefully synthesized at room temperature using the slow evaporation solution technique (SEST), which allows for the gradual formation of LHSDGP crystals from a supersaturated solution under controlled conditions. The crystal's structure was confirmed through Single Crystal X-ray Diffraction, revealing an orthorhombic lattice within the P2₁2₁2₁ space group. To further validate its structural consistency, Powder X-ray Diffraction studies were also conducted. Fourier Transform Infrared (FTIR) spectroscopy was used for vibrational analysis, aiding in the identification of molecular groups and providing insight into the crystal's chemical composition. The mechanical properties of the crystal were assessed using microhardness testing, demonstrating its durability. Optical properties, including light absorption and transmission characteristics, were examined through UV-vis-NIR spectroscopy. The LHSDGP crystal's electrical response was analyzed through dielectric measurements, tracking changes in the dielectric constant and loss factor at three different temperatures. The TG/DTA analysis was conducted to determine the decomposition temperature and thermal endurance of the LHSDGP crystal. Notably, the laser damage threshold (LDT) of LHSDGP was found to be 2.7 GW/cm², highlighting its potential for high-power laser applications. Z-scan techniques evaluated the LHSDGP crystal's third-order nonlinear optical properties.
In the present work, the Bianchi Type III spacetime is taken into account in the presence of a cosmic string and a domain wall within the framework of f(R,T) theory of gravitation. A specific form of the f(R,T), theory, namely f(R,T) = R + 2f(T), is taken into account in this work. The modified field equations for cosmic string and domain wall models are solved using a particular form of the deceleration parameter, and their physical behaviors are analyzed. In addition, the EoS parameter, jerk parameter, statefinder pair, and Om(z) diagnostic are utilized to analyze the evolutionary behavior of the Universe under the considered modified gravity model, indicating a quintessence-type nature of the cosmic expansion.This research offers significant insights into the anisotropic behaviour of the Universe and effectively describes the cosmic acceleration observed during late times. Our findings are then compared to recent observational data and are found to be in agreement with the ΛCDM model.
An eco-friendly approach to soap production was explored using the semi-boiled saponification method with sodium methoxide (CH3ONa) as an efficient alkali. The performance of CH3ONa was compared with that of traditional alkalis (NaOH and KOH) in soap making from various vegetable oils (coconut, peanut, palm, olive, castor, and sesame) and blended oils. The soap yield and physicochemical properties, including pH, free alkali, foam stability, cleansing power, and hardness, were measured. Results showed that CH3ONa constantly produced the highest yields, up to 98 % for the coconut-sesame oil blend and 94 % for peanut oil. The pH of blended oil soaps with CH3ONa ranged from 9.60 to 10.00, which was closer to the commercial bathing soap (9.00 to 10.00). However, overall soap pH varied from 9.04 to 11.30. Free alkali was absent in most soaps, indicating proper neutralization. Coconut oil and its blends exhibited higher foam stability, cleansing ability, and balanced hardness. These findings suggest that combining CH3ONa with blended oils in saponification increases yield and optimizes physicochemical properties, providing an effective strategy for sustainable soap production in both industrial and household use.
Earlier studies have shown that in a two-component model of the universe with matter and the running vacuum energy, either eternal deceleration or acceleration is produced in the absence of a bare constant in the density of the running vacuum. Here, it is analytically solved for the Hubble parameter, in a spatially flat Friedmann universe with dark energy and matter as components, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. But along with the additive constant, equivalent to a cosmological constant, the model predicts a late time exponential acceleration in the expansion of the universe, and in the far future of the evolution it tends to de Sitter universe with deceleration parameter approaches -1. On contrasting the model with the cosmological data, it is favoured to the low value of present Hubble constant as measured from the CMB data.
This paper presents compact design of novel modified trident shaped 5G antenna for triple band operation. The key point of antenna design methodology is to increase the electrical length of antenna by defection in antenna patch in the form of three radiating tooth. The radiating patch tooth allows the excited surface current to flow along its periphery and at its center. This increases the electrical length of the antenna, which decreases lower edge frequency of operating band. The magnetic coupling developed between ground slot of plane and radiating patch generates multiple resonant frequency modes, which are merged to give rise enhanced bandwidth. The rejection filters embedded in the antenna geometry play important role in splitting the fractional wide bandwidth of 150 % into triple band operation by rejecting two frequency band centered at 3.5 GHz and 5.2 GHz. The triple band operation achieved impedance bandwidth of 1.07 GHz (2.39 GHz-3.46 GHz), 1.06 GHz (4.11 GHz-5.17 GHz), and 9.7 GHz (5.30 GHz-15 GHz), exhibiting fractional bandwidth of 36.58 %, 22.84 % and 95.57 % respectively. The antenna exhibits a peak gain of 9.32 dB. The proposed antenna is suitable for 5G applications, covering the sub 6 GHz (n77, n78), sub 7 GHz (n96) bands, and broadband communication.
In this paper, thermodynamic effects in modified (2+1)-dimensional FRW cosmology is explored. The impacts of fluctuations in the Hubble parameter and its derivatives on the universe's evolution and corresponding thermodynamic behavior are examined. Using the modified FRW metric as a starting point, and the conditions ∇μr∇μ=0, we obtained the adjusted apparent horizon radius rA-2 = H2 + k/a2 and matching surface gravity. The energy and generalized entropy at the horizon are obtained using the Misner–Sharp formalism. This is accomplished by using our modified (2+1)-dimensional FRW cosmology in conjunction with the unified first law of thermodynamics. The evolution equations were formulated for Ḣ and H2 based on modified Friedmann and acceleration equations with dimensionless constants α1, α2, β1 and β2. The dynamics of (2+1)-dimensional cosmology is improved by these changes. In order to guarantee conformity with the generalized first law, we apply requirements to the modified gravity parameters by examining the consistency of the thermodynamics equation Tds = dE +Wdv. These restrictions result in invariant relations between the corrections coefficients, namely α2/α1 = 1-β2/1-β1 and β2/β1 = 1-α2/1-α1, which are symmetric under the interchange αi ↔βi. This formulation establishes a connection between thermodynamics and gravitational dynamics in (2+1)-dimensions, thereby facilitating the systematic examination of the influence of modified gravity on cosmic evolution.
Dermatological diseases affect a significant portion of the global population. Traditional diagnostic methods such as visual inspection and biopsies are subjective, invasive, and time-consuming. To address these limitations, this study proposes an entropy-based texture analysis framework combined with Gray Level Co-occurrence Matrix (GLCM) features for the automated identification and classification of skin diseases using standard color dermatological images. The methodology involves pre-processing the input images through normalization and resizing, followed by the extraction of five key texture features: contrast, correlation, energy, homogeneity, and entropy. A comparative evaluation across four dermatological conditions Morgellons, Dermatitis, Psoriasis, and Vitiligo demonstrates that entropy and homogeneity are the most effective features in capturing disease-specific textures, whereas contrast, correlation, and energy exhibit limited discriminative capability. Furthermore, the study examines the impact of varying window sizes (5, 15, and 25) for texture extraction and identifies a 5×5 window as the optimal configuration for preserving critical lesion details. The proposed approach provides a lightweight, interpretable, and non-invasive solution that can serve as a valuable component in clinical decision-support systems. This work contributes to the advancement of AI-driven dermatological diagnostics by offering a cost-effective and accessible methodology for automated skin disease identification.
The vibrational frequency analysis of ionic liquids (ILs) interacting with CO₂ represents a rapidly emerging field, yet significant gaps persist in understanding microscopic interactions at the molecular level, particularly regarding solvation dynamics and structural relaxation. In this study, density functional theory (DFT) was employed to optimize the structures of the cation, anion, and cation–anion ion pairs of 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMImBF₄]), focusing on stable geometries. The structural properties and vibrational frequencies of the [EMImBF₄]₂ dimer were systematically investigated, followed by an analysis of the [EMImBF₄]₂-CO₂ complex. Scaled vibrational frequencies were compared with experimental far-infrared and Raman spectra, revealing critical insights into the ν₃ asymmetric stretching mode of CO₂. The dimer model demonstrated superior accuracy in representing CO₂ interactions compared to monomeric systems, with energy differences of 2.8 kcal·mol⁻¹ observed in the liquid phase. These findings enhance the understanding of CO₂ behavior in IL environments, offering implications for CO₂ capture technologies and spectroscopic interpretation.
The endophytic fungus, rich in potent bioactive compounds, exhibited notable antibacterial efficacy against pathogenic microorganisms. Our study delved into the efficacy of A. fumigatus, using in-vitro techniques to assess the bioactive potential (antibacterial and anticancer activity) of ethyl acetate extract from fermented broth, containing secondary metabolites. The crude extract demonstrated significant antibacterial activity against Multi-Drug Resistant (MDR) strains S. aureus and K. pneumoniae, and promising anti-cancer activity against HeLa cells. Chemical analysis of fermented extract via GC-MS unveiled a diverse array of constituents. In-silico analysis highlighted two compounds i.e. 1,3,6,9 b-tetraazaphenalene-4-carbonitrile and 4- isothiazolecarboxylic acid, 3,5-bis(methylthio)-, methyl ester, that are actively participating in biological activities, corroborated by in-vitro experiments. These findings underscore A. fumigatus' potential as a natural source of antibacterial and anticancer agents, with favorable pharmacokinetics and docking profiles, promising as drug candidates with minimal toxicity. Further research should explore their potential therapeutic applications through pre-clinical in-vivo studies.
During many visits to Lonar crater to study its formation, there is a clear indication of elevation from Talni village towards Lonar village and there is a sudden decline of elevation towards Sultanpur. From the observation point, it seems that Lonar crater region is earthquake disturbed zone and structural disturbance in Land pattern. Earthquake impact result in sharp certain elevation and depression on the land and the land pattern is not uniform i.e., there are crests and troughs (ups and downs). Lonar crater formation is due to maximum depression on the land due to land sliding, land sinking (land collapse) which is due to effect of earthquake. This study being a preliminary investigation to understand and keep on records, how Lonar crater was formed considering all the possibilities for its formation, which has been reported through this paper.
