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FAMILY OF CONGRUENCES FOR (2, ?)?REGULAR BIPARTITION TRIPLES
Though congruences have their limitations, they have significant importance in the field of number theory and helps in proving many interesting results. Thus, this article has adopted the technique and properties of congruences to identify and prove a set of congruent properties for integer partition. The partition of a positive integer is a way of expressing the number as a sum of positive integers. One such partitions known as regular bipartition triple are discussed in this article. New congruences modulo even integers and modulo prime (p ? 5) powers are derived for (2, ?)?regular bipartition triples. Also infinite families of congruences modulo 2 for some (2, ?)?regular bipartition triples are derived. The theorems stated in this article are proved using the q?series notation and some of the prominent results such as Eulers pentagonal number theorem and Jacobis triple product identities. There are certain lemmas which are derived using these results that help in proving the major results of this article. 2022, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved. -
A FAMILY OF CONGRUENCES FOR (2, ?)?REGULAR BIPARTITIONS
The congruence of certain restricted partition functions known as regular bipartition is discussed in this paper. We particularly investigate the (2, ?)-regular bipartitions of n, denoted by B2,? (n), and establish certain congruences for B2,? (n) when ? ? 3. We derive infinite families of congruences modulo 4 for the (2, 3)-regular bipartition. We also obtain a generalisation of the regular bipartition for modulo p and p2. Indian Mathematical Society, 2022. -
Impact of bioconvection on the free stream flow of a pseudoplastic nanofluid past a rotating cone
In the current work, the repercussions of Brownian motion and thermophoresis on the three-dimensional free stream flow of tangent hyperbolic (pseudoplastic) nanofluid past a rotating cone are explored. The tangent hyperbolic model expresses the characteristics of a shear-thinning nanofluid. Furthermore, oxytactic microorganisms were used as mixers to actively stabilize the nanoparticles. The movement of these microorganisms within the nanofluid gives rise to a major phenomenon termed bioconvection. The flow of nanofluid past a rotating cone finds applications in the field of nuclear reactors, biomedical applications, solar power collectors, steam generators, and so on. The mathematical model is designed using Buongiorno's model that describes the two major slip mechanisms experienced by the nanoparticles moving within a fluid namely thermophoretic force and Brownian motion. The model thus formed is nondimensionalized using the apt similarity transformation. The resulting system is solved by the (Formula presented.) technique by adapting the shooting method. The velocity, temperature, concentration, and motile density profiles are graphically interpreted for different flow parameters involved in the study. It was observed that thermophoresis reduces concentration and enhances the temperature whereas Brownian motion enhanced both temperature and concentration profiles. Also, the increase in the mixed convection parameter effectively decreased the temperature of the nanofluid. 2022 Wiley Periodicals LLC. -
Flow of nanofluid past a stretching cylinder subject to Thompson and Troian slip in the presence of gyrotactic microorganisms
Incorporating the Thompson and Troian slip condition, this work studies the bioconvective flow of a nanofluid past a vertically stretching cylinder. The Thompson and Troian slip deals with the molecular scale interactions at the solidfluid interface, which plays a pivotal role in the fluid flow analysis. This study helps in understanding the behaviours of fluid flow in the presence of non-linear slip past a vertically stretching cylinder. The corresponding partial differential equations (PDEs) for momentum, energy, concentration of nanoparticles, and concentration of microbes are developed using Buongiornos model. A suitable similarity transformation is then applied to these PDEs, converting them into a set of ordinary differential equations (ODEs). The RungeKuttaFehlberg (RKF-45) method is utilized to calculate the numerical solution of the resulting ODE problem. The results demonstrate that the interaction of slip conditions, viscous dissipation, heat source, and bioconvection causes complex flow patterns and heat transfer characteristics. These observations are extremely relevant for applications including better oil recovery procedures, biomedical engineering, and microfluidic devices where exact control over nanofluid behaviour is necessary. Some of the major observations of the study include the enhancement of the temperature in the nanofluid for higher Eckert numbers, control of fluid flow through an external magnetic field, and Peclet number significantly decreased the motile density in the nanofluid. The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. -
Flow of nanofluid past a stretching cylinder subject to Thompson and Troian slip in the presence of gyrotactic microorganisms
Incorporating the Thompson and Troian slip condition, this work studies the bioconvective flow of a nanofluid past a vertically stretching cylinder. The Thompson and Troian slip deals with the molecular scale interactions at the solidfluid interface, which plays a pivotal role in the fluid flow analysis. This study helps in understanding the behaviours of fluid flow in the presence of non-linear slip past a vertically stretching cylinder. The corresponding partial differential equations (PDEs) for momentum, energy, concentration of nanoparticles, and concentration of microbes are developed using Buongiornos model. A suitable similarity transformation is then applied to these PDEs, converting them into a set of ordinary differential equations (ODEs). The RungeKuttaFehlberg (RKF-45) method is utilized to calculate the numerical solution of the resulting ODE problem. The results demonstrate that the interaction of slip conditions, viscous dissipation, heat source, and bioconvection causes complex flow patterns and heat transfer characteristics. These observations are extremely relevant for applications including better oil recovery procedures, biomedical engineering, and microfluidic devices where exact control over nanofluid behaviour is necessary. Some of the major observations of the study include the enhancement of the temperature in the nanofluid for higher Eckert numbers, control of fluid flow through an external magnetic field, and Peclet number significantly decreased the motile density in the nanofluid. The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. -
Crop Disease and Pest Management in Agriculture via UAV Remote Sensing and Advanced Machine Learning Models
Pests and diseases greatly reduce crop quality and yield; therefore, IA relies on effective pest and disease control. UAVs have become a crucial remote sensing (RS) tool for agricultural process monitoring and management. This study will examine major advances in this field using bibliometric methodologies including author co-occurrence and keyword co-contribution studies. The suggested technique involves preprocessing, feature extraction, and model training. Data quality improves with preprocessing. UAV images are used for feature extraction, focusing on canopy structure and height. PPO is trained the prediction model. Compared to ultramodern GANs and LSTM networks, the recommended model wins. The model consistently outperforms competitors with 91.17 percent accuracy. The study suggests employing UAVs in smart farming to reduce pests and diseases. The suggested model's accuracy and reliability improve crop quality and production by solving agricultural monitoring and management problems. 2025 IEEE. -
Enhancing Crude Oil Price Prediction with Neural Network Models
A nations economic, social, and national security are all severely affected by variations in crude oil prices, which is a basic energy source. Research on accurately forecasting price changes for crude oil is always progressing. This research presents a forecasting strategy for crude oil pricing using artificial neural networks. The presented model uses standardization techniques to prepare the historical data for the subsequent processes. It is possible to predict future prices by using a Feed Forward Neural Network (FFNN) with four layers. West Texas Intermediate (WTI) and Brent crude oil prices are utilized on a daily, weekly, and monthly basis to demonstration and confirmation. Directional statistic, accuracy of prediction, the model is evaluated using root mean square error and mean absolute error expressed as percentages. Empirical findings confirm that the suggested approach performs better than any of the previous approaches. Additionally, it is noted that the presented method achieved higher prediction in contrast to other methods. The Author(s), under exclusive license to Springer Nature Switzerland AG 2026. -
A Machine Learning Approach to Crude Oil Price Prediction Using Support Vector Machine (SVM)
Crude oil is one of the most important energy sources, and fluctuations in its international prices affect all aspects of the economy. The price of crude oil is influenced by several variables, and the length of time that each component has an effect differs giving an increase in non-linear oil price features. Although it is a complex task, identifying the most essential factor influencing for precise predicting, crude oil prices are essential. Therefore, this study aims to employ a machine learning model to address the intricate relationships among different factors. Primarily, it gathers data regarding West Texas Intermediate (WTI) and Brent crude oil prices as well as macroeconomic variables. Secondly, the data is normalized to prepare it for further analysis. Finally, a crude oil prediction model is constructed using Support Vector Machine (SVM) to predict future international crude oil prices. The daily, weekly, and monthly prices are used to confirm the models efficacy developed using WTI and Brent oil. The models performance is also evaluated by incorporating various combinations of macroeconomic variables to find the most influential factor. Results from experiments show indicates the benchmark model was much exceeded by the developed model and performed very well in terms of prediction accuracy. The findings reveal that selecting the appropriate variables can greatly enhance prediction accuracy. This model has the potential to provide valuable insights for traders, investors, and energy-related enterprises, offering beneficial guidance for decision-making purposes. The Author(s), under exclusive license to Springer Nature Switzerland AG 2026. -
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Polypyrrole/ silver/graphene ternary nanocomposite synthesis and study on photocatalytic property in degrading Congo red dye under visible light
In this report, a simple chemical synthesis of polypyrrole/silver/graphene (Ppy/Ag/Gr) ternary nanocomposites with varying concentrations of graphene are described. The XRD spectra of the samples polypyrrole/silver (Ppy/Ag) and Ppy/Ag/Gr show all the peaks of the face-centered cubic structure of silver. A broad peak between 10 and 20 and a peak at 26.7 corresponds to Ppy and graphene respectively. Using FTIR, and UVVis. spectroscopies the interaction between polypyrrole, silver, and graphene were studied. In our work, we explored the photocatalytic property of the synthesised samples by using them to degrade the aqueous solution of a cancer-causing dye, Congo red. The percentage degradation of Congo red dye using the sample Ppy/Ag/Gr (0.5 wt.%) is obtained as 96% and the reaction rate calculated is 0.162/min., greater than that of Ppy/Ag and Ppy/Gr binary composites. Thus, the addition of the optimum concentration of graphene into Ppy/Ag enhanced its photocatalytic property. The BET analysis shows an increased surface area for the sample Ppy/Ag/Gr (0.5 wt.%) and the reason for the enhancement of photocatalysis with this sample is confirmed since it is a surface-dependent property. The biodegradability of the dye solution was investigated by Chemical Oxygen Demand (COD) analysis and the COD value was reduced from 432 mg/L to 216 mg/L after 20 min of irradiation of light. 2023 -
Thermal diffusivity study of one-pot synthesised polypyrrole silver nanocomposite by thermal lens method
We are reporting the results of our exploration of the thermal lens method to determine the thermal diffusivity of Ppy and Ppy/Ag nanocomposites synthesised by simple, cost effective in situ chemical oxidative polymerisation. EDAX spectrum confirms the presence of silver in the samples. Raman analysis shows that the increase in the concentration of silver in composite results in an increase in the conjugation length of the samples. We have adopted the dual-beam pump-probe technique to determine the thermal diffusivity of polypyrrole and polypyrrole silver nanocomposite with varying silver concentrations. We report suppression of thermal diffusivity of polypyrrole with the addition of a small concentration of silver and an enhanced thermal diffusivity with an increase in the concentration of silver with ethanol as the base fluid. Increased thermal diffusivity of the samples makes them suitable for use as coolants. 2022 Elsevier Ltd -
Polypyrrole- silver nanocomposite for enhanced photocatalytic degradation of methylene blue under sunlight irradiation
Polypyrrole (Ppy) -Silver nanocomposite samples have been synthesised by chemical oxidative polymerisation. The characteristic peaks of face centered cubic (fcc) structure of silver in XRD confirmed its presence in Ppy. Shift in NH stretching frequency observed in FTIR spectroscopy revealed the coordination of silver into Ppy. The photocatalytic activity of the samples was studied by photocatalytic degradation of the aqueous solution of methylene blue (MB) under sunlight. The presence of Ag in polypyrrole (Ppy) enhanced its photocatalytic activity with respect to the reported values which further increased on increasing the silver concentration. 2021 Elsevier B.V. -
Polymeric Nanocomposites and Their Applications
A polymer is a macromolecule comprising numerous repeating subunits linked by covalent bonds. The word polymer arises from Greek, with polus denoting many and meros denoting parts. Although humans have used polymers long before, their chemical properties were studied only in the nineteenth century. The Author(s), under exclusive license to Springer Nature Switzerland AG 2025. -
Synthesis of polypyrrole silver graphene ternary nanocomposite and its thermal diffusivity study by thermal lens method
Efficient thermal management materials with tunable thermal diffusivity are increasingly required for advanced electronic, photonic, and energy applications. However, simultaneously achieving both thermal conductivity enhancement and thermal insulation within a single material system remains a significant challenge. In this work, we have synthesized polypyrrole silver graphene (PPy/Ag/Gr) ternary nanocomposites with varying concentrations of graphene by a simple one-pot chemical synthesis method.The photoluminescence spectrum of all the samples of PPy/Ag/Gr showed a quenching in the intensity due to the presence of graphene. Raman spectrum analysis confirmed good coordination of silver and graphene in the ternary composite. Morphological study was done using field emission scanning electron microscopy (FESEM). The thermal diffusivity of the binary composites polypyrrole silver (PPy/Ag) and polypyrrole graphene (PPy/Gr) as well as the ternary composites with varying concentrations of graphene were done using the highly sensitive thermal lens method using two laser sources, one as a pump source and the other as a probe beam. The results of the study show that the thermal diffusivity (D) of PPy/Ag/Gr with 0.2 wt.% of graphene is slightly greater than the binary composites and can be used as a coolant. Another exciting result of this study is that at higher concentrations of graphene the D values of the ternary composites decrease below the D value of the base fluid used. This interesting property of the samples can be exploited by using them as thermal insulators 2025 The Authors -
Polypyrrole/silver/graphene ternary composites for high-performance Ku-band electromagnetic interference shielding
Unwanted electromagnetic waves can significantly affect the performance of electronic devices and communication systems. A high-performance electromagnetic interference shielding (EMI) material is a solution to this issue. This study introduces a cost-effective one-pot synthesis method for polypyrrole/silver (Ppy/Ag), polypyrrole/graphene (Ppy/Gr) and polypyrrole/silver/graphene (Ppy/Ag/Gr) ternary composites with adjustable graphene concentrations. Detailed structural and morphological analyses using FTIR, XRD and STEM confirm the successful incorporation of Ag nanoparticles and graphene into the polypyrrole matrix. The total shielding effectiveness (SET) of the ternary composites in the Ku band shows an impressive 30.86 dB at 12.7 GHz for the 5 wt.% graphene composite, primarily driven by absorption mechanisms (SEA> SER). The synergistic interaction between Ag, which provides conductive pathways, and graphene, which offers structural reinforcement, significantly enhances interfacial polarisation and conductivity, surpassing the performance of binary counterparts (Ppy/Ag and Ppy/Gr. The results of this work introduce a lightweight, potent and economical composite material for EMI shielding applications in the Ku band. 2025 Elsevier B.V. -
Leveraging digital yarn dyeing for colour consistency in apparel weaving
When compared to traditional processes, digital yarn dyeing provides substantial benefits in terms of color control, versatility, and environmental impact. However, technological obstacles and constraints exist. The promise of digital dyeing may be realized by carefully selecting technology, optimizing ink consumption, and adopting stringent quality control methods, resulting in improved colour constancy and a more sustainable textile sector. -
Biosynthesis of ZnFe2O4@Ag hybrid nanocomposites for degradation of 2,4-Dichlorophenoxyacetic acid herbicide
This work demonstrates recent advancements in the phytosynthetic and environmentally friendly method of preparing ZnFe2O4 and ZnFe2O4@Ag hybrid nanocomposites using Pedalium murex L leaf extract as a stabilizing and reducing agent. The synthesized nanocomposite was characterized with UVvis, FTIR, TGA/DSC, XRD, FE-SEM, and EDX to investigate the electronic as well as morphological properties. Moreover, the photocatalytic behaviour of ZnFe2O4 and ZnFe2O4@Ag hybrid nanocomposites was evaluated with a breakdown of 2,4-dichlorophenoxyacetic acid (2,4-DPA) by exposing to UVVis light. The results obtained suggest that ZnFe2O4@Ag hybrid nanocomposite exhibited photocatalytic activity for the degradation of 2,4-DPA by approximately 94% in 60 min compared to ZnFe2O4. The hybrid nanostructure of ZnFe2O4@Ag significantly promoted charge transfer and prevented electron and hole recombination resulting in the enhancement of photocatalytic activity. Furthermore, ZnFe2O4@Ag nanocomposite showed the fair recyclable capacity for up to five catalytic cycles with an acceptable degradation percentage of 2,4-DPA. The findings of this study identify efficient charge transfer factor as a major contributor to the catalytic activity, with promising possibilities for the design of environmental remediation nanocomposite for harmful contaminants. 2023 The Author(s) -
Multifunctional characteristics of biosynthesized CoFe2O4@Ag nanocomposite by photocatalytic, antibacterial and cytotoxic applications
Carissa carandas, a traditional medicinal herb with a high concentration of antioxidant phytochemicals, has been used for thousands of years in the Ayurveda, Unani, and homoeopathic schools of medicine. By employing Carissa carandas bark extract as a reducing and capping agent in green biosynthesis, we extend this conventional application to produce CoFe2O4 and CoFe2O4@Ag nanocomposite. A variety of techniques have been used to characterize the synthesised nanocomposite, including UVVis, FTIR, XRD, FESEM, EDX, and BET. The CoFe2O4 and CoFe2O4@Ag nanocomposite demonstrated promising antibacterial action against human bacterial pathogens like B. subtilis and S. aureus as gram positive and P. aeruginosa and E. coli as gram negative with inhibition zones of 24.3 0.57, 17.4 0.75 and 20.5 0.5, 19.8 1.6 mm respectively, and the obtained results were superior to the nanocomposite without silver. Moreover, in-vitro cytotoxicity effects of biosynthesized CoFe2O4 and CoFe2O4@Ag were performed on the human breast cancer cell MCF-7. It was found that the MCF-7 cells' 50% inhibitory concentration (IC50) was 60 ?g/mL. Additionally, biosynthesized CoFe2O4 and CoFe2O4@Ag nanocomposite was used to demonstrate the photocatalytic eradication of Rhodamine Blue (RhB). Due to the addition of Ag, which increases surface area, conductivity, and increased charge carrier separation, the CoFe2O4@Ag nanocomposite exhibits a high percentage of photocatalytic degradation of ? 98% within 35 min under UV light irradiation. The photocatalytic performance of as-synthesised nanocomposite was evaluated using dye degradation-adsorption in both natural light and dark condition. Under dark conditions, it was found that 2 mg mL?1 CoFe2O4@Ag in RhB aqueous solution (5 ppm) causes dye adsorption in 30 min with an effectiveness of 72%. Consequently, it is anticipated that the CoFe2O4@Ag nanocomposite will be a promising photocatalyst and possibly a noble material for environmental remediation applications. 2023 Elsevier Ltd -
Biosynthesis of CuFe2O4@Ag hybrid nanocomposite: Ultrasensitive detection and catalytic reduction of 4-nitrophenol
Due to the dearth of extremely capable, sensitive, and stable catalysts, the efficient detection and catalytic removal of 4-nitrophenol (4-NP) in industrial wastewater remains a serious challenge. The detection and determination of 4-nitrophenol (4-NP) presence in the environment is a matter of paramount importance because it is a high-priority hazardous pollutant that can affect people, animals, and plants. Here, we present a promising and economically viable green synthetic route for fabricating CuFe2O4 and CuFe2O4@Ag hybrid nanocomposites from the leaf extract of Senna didymobotrya. The UVVis, FTIR, XRD, FE-SEM, EDXA, BET and VSM analysis were performed to characterize the synthesis of CuFe2O4@Ag nanocomposite. To evaluate the electrocatalytic capacity of CuFe2O4@Ag, electrochemical sensing stratergy was performed with cyclic voltammetry (CV) and differential pulse voltammetry (DPV). The modified CuFe2O4@Ag glassy carbon electrode (GCE) (CuFe2O4@Ag/GCE) demonstrated a linear response in the range of 0.01-15 ?g/ml (71 nm-107 ?M) and the ability to detect 4-NP at low concentration (0.006 ?g/ml (43 nM)). Due to the increased surface area of CuFe2O4@Ag/GCE by ? 1.5-fold, a greater cathodic current response (-16 ?A/cm2) at a low potential of -0.81 V was observed compared to CuFe2O4/GCE alone for the detection of 4-NP. Additonally, CuFe2O4@Ag showed excellent reduction ability towards 4-NP using NaBH4 with an efficiency of 96.4 % which was higher than the CuFe2O4 (only 87.3 %) in 12 min due to the synergistic relationship among Ag NPs and CuFe2O4 nanostructures. The outcomes from this study shows that the bi-functional electrocatalyst holds vast potential for environmental remediation. 2024 The Author(s) -
Classification and characterization using HCT/HFOSC spectra of carbon stars selected from the HES survey
We present results from the analysis of 88 carbon stars selected from Hamburg/ESO (HES) survey using low-resolution spectra (R ?1330 & 2190). The spectra were obtained with the Himalayan Faint Object Spectrograph Camera (HFOSC) attached to the 2-m Himalayan Chandra Telescope (HCT). Using well-defined spectral criteria based on the strength of carbon molecular bands, the stars are classified into different groups. In our sample, we have identified 53 CH stars, four C-R stars, and two C-N type stars. Twenty-nine stars could not be classified due to the absence of prominent C2 molecular bands in their spectra. We could derive the atmospheric parameters for 36 stars. The surface temperature was determined using photometric calibrations and synthesis of the H-alpha line profile. The surface gravity log g estimates are obtained using parallax estimates from the Gaia DR3 database whenever possible. Microturbulent velocity (?) was derived using calibration equation of log g & ? . We could determine metallicity for 48 objects from near-infrared Ca II triplet features using calibration equations. The derived metallicity ranges from ?0.43 ? [Fe/H] ? ?3.49. Nineteen objects were found to be metal-poor ([Fe/H] ? ?1), 14 very metal-poor ([Fe/H] ? ?2), and five extremely metal-poor ([Fe/H] ? ?3.0) stars. Eleven objects were found to have a metallicity in the range ?0.43 ? [Fe/H] ? ?0.97. We could derive the carbon abundance for 25 objects using the spectrum synthesis calculation of the C2 band around 5165 The most metal-poor objects found will make important targets for follow-up detailed chemical composition studies based on high-resolution spectroscopy, and are likely to provide insight into the Galactic chemical evolution. 2024, The Author(s), under exclusive licence to Springer Nature B.V.