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Abstract Tuberculosis (TB) is a global health concern caused by the bacterium Mycobacterium tuberculosis. This infectious disease primarily affects the lungs but can also impact other organs. Effective TB control involves early diagnosis, appropriate treatment with a combination of antibiotics, and public health measures to prevent transmission. However, ongoing challenges include drug-resistant strains and socioeconomic factors influencing its prevalence. Drugs such as isoniazid, pyrazinamide, ethambutol, ethionamide, linezolid, and levofloxacin are approved for the treatment of drug-susceptible tuberculosis. The properties and other activities of the drug, can be analyzed by modelling its chemical structure in terms of a molecular graph $$G=\left(V,E\right)$$ , by considering the atoms as the vertex set $$V\left(G\right)$$ and the bonds between the two atoms as the edge set $$E\left(G\right)$$ . A molecular descriptor or topological index of $$G$$ represents the corresponding chemical molecule as a numerical value. Domination is one of the key concepts in the molecular structure used to analyze the properties of atoms. In this article, the domination distance-based topological indices of the drugs isoniazid, pyrazinamide, ethambutol, ethionamide, linezolid, and levofloxacin are computed to conduct QSPR (Quantitative Structure–Property Relationship) analysis, exploring their physicochemical and ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) properties. Quadratic regression is then used in the QSPR analysis to examine the physicochemical and ADMET properties of these drugs. The results of this analysis indicate that the domination Schultz index and domination SM index are the indices most strongly correlated with the majority of the physicochemical and ADMET properties. The QSPR analysis can also be extended to analogs of these drugs and to other treatment drugs, such as rifampin and rifapentine, to further explore their properties.

Abstract This work uses rational curve fitting models to investigate the complex link between topological indices and entropy metrics in calcium hydroxide $$(Ca(OH)_{2})$$ ( C a ( O H ) 2 ) networks. Entropy measurements shed light on the complexity and disorder of these networks, whereas topological indices are essential instruments for comprehending the structural characteristics of chemical substances. Our goal is to find new patterns and connections by merging these two fields, improving materials science’s prediction capacity. We calculate many topological indices, such as the Randic, Balaban, and Zagreb indices, and examine the relationship between them and entropy measurements obtained from $$(Ca(OH)_{2})$$ ( C a ( O H ) 2 ) structural arrangement.

Abstract This work initiates a concept of reduced reverse degree based $$\mathcal {RR_D\,M}$$ RR D M -Polynomial for a graph, and differential and integral operators by using this $$\mathcal {RR_D\,M}$$ RR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the $$\mathcal {RR_D\,M}$$ RR D M -Polynomial. The topological descriptors, denoted as $$\mathbb{T}\mathbb{D}$$ T D ’s, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

Magnesium alloys are increasingly valued for biomedical applications due to their biocompatibility. This study investigates Mg-AZ31B alloy samples treated with quartz and alumina grits (

Abstract The construction sector accounts for around 95% of the commercial usage of silicon dioxide (sand), for example, in the making of concrete. There are several uses for quartz, however in order to get a purer material, chemical processing is needed. Graph theory proved to be very beneficial for other research, especially in the applied sciences. In particular, graph theory has greatly influenced the field of chemistry. To do this, a transformation is needed to produce a graph with the vertices representing the atoms in the chemical compound and the edges indicating the bonds between the atoms. This graph then represents a chemical network or structure. In a graph, a vertex’s valency (or degree) is determined by the number of edges that are incident to it. The entropy of a probability quantifies a system’s level of uncertainty. In this article, we compute Zagreb-type indices and then compute the entropy measure. In order to evaluate the relevance of each kind, this article builds several edge degree-based entropies that link to the indices and establish how to adjust them. We also create the logarithmic regression model between indices and entropy.

Abstract In the context of graph theory and chemical graph theory, this research conducts a detailed mathematical investigation of reverse topological indices as they relate to iron telluride networks, clarifying their complex interactions. Graph theory is a branch of abstract mathematics that carefully studies the connections and structural features of graphs made up of edges and vertices. These theoretical ideas are expanded upon in chemical graph theory, which models molecular architectures with atoms acting as vertices and chemical bonds as edges. By extending these concepts, this work investigates the reverse topological indices in the context of Iron Telluride networks and outlines their significant effects on chemical reactivity, molecular topology and statistical modeling. By navigating intricate mathematical formalisms and algorithmic approaches, the analysis provides profound insights into the reactivity patterns and structural dynamics of Iron Telluride compounds, enhancing our knowledge of solid-state chemistry and materials science.

Abstract Vitamin A plays a critical role in various biological functions, including vision, cellular differentiation, and immune regulation. However, accurately assessing its status, particularly in obese individuals, presents challenges due to potential alterations in metabolism and distribution. This study utilized Liquid Chromatography–Tandem Mass Spectrometry (LC–MS/MS) methodology to precisely measure serum vitamin A concentrations in population of UAE. The methodology's reliability and precision, as demonstrated through validation procedures, underscore its potential utility in clinical settings. Employing the Multiple Reaction Monitoring mode of positive ion electrospray ionization, the LC–MS/MS system achieves a limit of detection (LOD) of 0.48 ng/mL in serum, while adhering to FDA-US regulations for accuracy and compliance. A key aspect of this study was the application of LC–MS/MS to assess vitamin A status in an obese population within UAE. By employing a diverse cohort of 452 Emirati participants, including 277 individuals from a randomized controlled trial who were assessed at baseline and at 6th month, and 175 healthy individuals aged 18–82 assessed at baseline, this study explores the relationship between obesity and vitamin A levels, shedding light on potential implications for health and well-being. It was an observational study based on a new vitamin A method and participants were asked to eat vitamin A rich foods. The robust performance of the LC–MS/MS methodology positions it as a valuable tool for clinical research. By accurately quantifying vitamin A levels in human serum, this methodology opens avenues for advancing our understanding of vitamin A physiology and its implications for health, particularly in obese populations. In summary, this LC–MS/MS methodology presents a potent tool for clinical studies, providing reliable, specific, and robust detection of vitamin A in human serum, thus, opening a new frontier for advancing our understanding of vitamin A related physiology and health in the obese population.

After a comprehensive taxonomic assessment of descriptions/ illustrations of all known (118) species of the spider mite genus Schizotetranychus Trägårdh (Acari: Prostigmata: Tetranychidae), five species groups are proposed based on the number of tactile setae on tibia II in female, i.e., vermiculatus with four setae (four spp.), schizopus with five setae (52 spp.), spireafolia with six setae (10 spp.), asparagi with seven setae (20 spp.), and bambusae with eight setae on tibia II (22 spp.). The species group schizopus is further divided into three species subgroups based on tactile setae on tibia I: schizopus with eight/ nine setae (21 spp.), andropogoni with seven setae (26 spp.), and taquarae with six tactile setae excluding the solenidion on tibia I (five spp.). Eight Schizotetranychus species were not assigned to any species group because of brief descriptions and/ or illustration and without information on the number of tactile setae on tibiae I and II. Moreover, two Schizotetranychus species, S. gausus Baker & Pritchard and S. luculentus Tseng that have six setae/ structures including a spinneret and a solenidion on the palp tarsus, are provisionally transferred to the genus Stigmaeopsis Banks. Finally, keys to species groups and subgroups of the world species of Schizotetranychus are provided.

Objective This study aimed to investigate the prevalence of paratuberculosis in cattle and buffaloes at twelve public dairy farms in Punjab, Pakistan. Methods A total of 2,181 more than two-year-old animals (1,242 cattle and 939 buffaloes) were tested by avian tuberculin, i.e., killed purified protein derivative of Mycobacterium avium paratuberculosis and indirect enzyme linked immunosorbent assay (ELISA). Blood and fecal samples were collected from tuberculin positive animals. These samples were further processed by indirect ELISA. The data were analyzed using frequency analysis and logistic analysis procedures. Results The prevalence of paratuberculosis at public dairy farms was 3.8%, as determined by tuberculin+ELISA test. It varied from 0.71% to 13.5% with a 100% herd prevalence. Multivariate logistic regression analysis revealed that species, milk production, total animals, total small ruminants, and total buffaloes were significantly associated with the occurrence of paratuberculosis. Odd ratio analysis revealed that with a one-kilogram increase in body weight, there will be a 0.006% increase in disease occurrence. With the increase in one animal in small ruminants and buffaloes, there will be 0.008% and 0.42% greater chances of developing paratuberculosis, respectively. Bivariate logistic regression analysis of cattle and buffaloes revealed that farm number, age, and total number of cattle were significantly associated with the occurrence of paratuberculosis. A one-month increase in lactation length increases the chance of tuberculosis by 0.004%; similarly, a one-liter increase in milk production increases the chance of disease by 10%. With each additional buffalo in the herd, there will be a 0.007% greater chance for the occurrence of paratuberculosis. Conclusion This study concluded that tuberculin testing can be used in conjunction with ELISA to screen animals for paratuberculosis in countries with scarce resources, such as Pakistan. The efficacy of disease diagnosis can be improved by combining multiple tests.

Abstract In this study, we conduct a comprehensive physical analysis of topological indices for the Iron Disulfide (FeS $$_{2}$$ 2 ) network using a curve-fitting model. Iron Disulfide is a cubic compound. In metamorphic rock, sedimentary rock, and quartz veins, it is typically found in combination with other sulfides or oxides. The numerical properties of molecular structures are referred to as topological indices. There are several different kinds of topological indices, including those that are based on distance, degree, or counting, among other factors. The real process of creating a topological index involves turning a chemical structure into a numerical value. In this paper, we calculate the iron disulfide network topological indices using the degrees of vertices in a chemical network of Iron Disulfide (FeS $$_{2}$$ 2 ). Thereafter, we discovered the physical parameters of FeS $$_{2}$$ 2 production, such as heat of formation. We then fitted curves between the thermodynamic properties and several indices. Several techniques based on rationality, linearity, and nonlinearity were used to fit curves in MATLAB. These quantitative results imply that a variety of thermodynamic characteristics of semiconducting materials may be accurately predicted by topological indices. These findings have significant ramifications as they provide the groundwork for the application of topological indices in semiconducting network design and optimization, which might result in more effective and economical material creation.

Abstract QSPR mathematically links physicochemical properties with the structure of a molecule. The physicochemical properties of chemical molecules can be predicted using topological indices. It is an effective method for eliminating costly and time-consuming laboratory tests. We established a QSPR between mev-degree and mve-degree-based indices and the physical properties of benzenoid hydrocarbons. To compute these indices, we designed a program using Maple software and the correlation between indices and physical properties was developed using the SPSS software. Our study reveals that the mve-degree-based sum-connectivity $$(\chi ^{mve})$$ ( χ mve ) and atom bond connectivity ( $$ABC^{mve}$$ A B C mve ) index, mev-degree-based Randić ( $$R^{mev}$$ R mev ) and Zagreb ( $$M^{mev}$$ M mev ) index are the three most significant parameters and have good prediction ability for the physicochemical properties. We examined that $$R^{mev}$$ R mev predicts the molar refractivity and boiling point, $${\chi }^{mve}$$ χ mve predicts the LogP and enthalpy, $$ABC^{mve}$$ A B C mve predicts the molecular weight, $$M^{mev}$$ M mev predicts the Gibb’s energy, Pie-electron energy and Henry’s law. Moreover, we computed the indices for the linear [n]-phenylen.

Abstract Quantitative structure relationships linked to a chemical structure that shed light on its properties and chemical reactions are called topological indices. This structure is upset by the addition of silicon (Si) doping, which changes the electrical and optical characteristics. In this article, we examine the connection between a chemical structure’s Gibbs energy (GE) and K-Banhatti indices. In this article, we compute the K-Banhatti indices and then show the correlation between the indices and Gibb’s energy of the molecule using curve fitting. Through the curve fitting, we see that there is a strong correlation between indices and Gibb’s energy of a molecule. We use the polynomial curve fitting approach to see the correlation between indices and Gibb’s energy.

This study aimed to examine the impact of the Theory of Planned Behavior on Malaysian luxury hotel selection. To achieve this objective, the study examined the influence of attitude, subjective norms, perceived behavioral control, and fake reviews on the choice of luxury hotels in Malaysia. The study also investigates whether intention mediates the relationship between these variables and luxury hotel selection. The research method was quantitative in nature and to collect the necessary data, convenience sampling was used on an online questionnaire, resulting in 400 valid responses. The respondents were residents of Malaysia aged over 18 years old who had stayed at luxury hotels before, as they are qualified to answer the research objectives. For this study, four- and five-star hotels are considered as luxury hotels. The collected data were then analyzed using IBM SPSS version 26, using descriptive, regression, and mediation analysis through Hayes process. The results from the regression analysis revealed the predictive power of each variable, while the mediation analysis demonstrated that intention mediates the relationship between attitude, subjective norms, and perceived behavioral control in luxury hotel selection. According to this study, attitude, subjective norms, perceived behavioral control, and fake reviews influence luxury hotel choices. Intention significantly mediates the association between attitude, subjective norms, perceived behavioral control, fake reviews, and luxury hotel choices.

Abstract The study explores the intricate relationship between topological indices and the heat of formation in the benzyl sulfamoyl network. Topological indices of benzyl sulfamoyl networks are studied and also emphasize their properties statistically. The benzyl sulfamoyl has unique properties due to its crystalline structure and it is used in the form of artificial substance. We analyze the distributions and correlations of the benzyl sulfamoyl network with others by using statistical methods and also build a computational analysis for topological indices. The findings show a strong association between the variables, indicating that topological indices may be used to accurately predict thermodynamic characteristics and improve the effectiveness of molecular modelling and simulation procedures.

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

Abstract This paper explores the complex interplay between topological indices and structural patterns in networks of iron telluride (FeTe). We want to analyses and characterize the distinct topological features of (FeTe) by utilizing an extensive set of topological indices. We investigate the relationship that these indicators have with the network’s physical characteristics by employing sophisticated statistical techniques and curve fitting models. Our results show important trends that contribute to our knowledge of the architecture of the (FeTe) network and shed light on its physiochemical properties. This study advances the area of material science by providing a solid foundation for using topological indices to predict and analyses the behavior of intricate network systems. More preciously, we study the topological indices of iron telluride networks, an artificial substance widely used with unique properties due to its crystal structure. We construct a series of topological indices for iron telluride networks with exact mathematical analysis and determine their distributions and correlations using statistical methods. Our results reveal significant patterns and trends in the network structure when the number of constituent atoms increases. These results shed new light on the fundamental factors that influence material behavior, thus offering a deeper understanding of the iron telluride network and may contribute to future research and engineering of these materials.

Abstract A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material’s various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work.

Abstract Eigenvalues have great importance in the field of mathematics, and their relevance extends beyond this area to include several other disciplines such as economics, chemistry, and numerous fields. According to our study, eigenvalues are utilized in chemistry to express a chemical compound’s numerous physical properties as well as its energy form. It is important to get a comprehensive understanding of the interrelationship underlying mathematics and chemistry. The anti-bonding phase is correlated with positive eigenvalues, whereas the bonding level is connected with negative eigenvalues. Additionally, the non-bonded level corresponds to eigenvalues of zero. This study focuses on the analysis of various structures of anticancer drugs, specifically examining their characteristic polynomials, eigenvalues of the adjacency matrix, matching number and nullity. Consequently, the selected structures of the aforementioned anticancer drugs exhibit stability since they are composed of closed-shell molecules, characterized by a nullity value of zero.

The construction phase of nuclear construction projects presents various risks and hazards, putting workers in potentially dangerous situations. Safety guidelines provided by Occupational Health and Safety Administration (OSHA) aim to address construction safety concerns, but limitations persist, especially in the context of workers safety and the transportation of Small Modular Reactors (SMRs) and Micro Reactors (MRs) in the nuclear construction domain. This research focuses on identifying issues related to safety guidelines in nuclear construction and aims to develop new guidelines and strengthen existing ones. Through a critical literature review, key factors influencing safety in nuclear construction were identified. A questionnaire survey was prepared in line with those identified key safety factors and distributed among 40 professionals from the United States to gather feedback on these factors in countering safety issues and developing new guidelines in the context of nuclear construction. The findings reveal a lack of specific guidelines concerning the safe transportation of SMRs and MRs, as well as a gap in understanding accidents during the construction and transportation phases of nuclear projects. The results of this research contribute to enhancing safety protocols and addressing the unique challenges faced in nuclear construction. The research has also highlighted the importance of digital technology tools such as Artificial Intelligence (AI), Augmented Reality (AR), Virtual Reality (VR), and Unmanned Aerial Vehicles (UAVs) as emerging digital tools, which could be helpful to counter safety concerns linked to SMRs and MRs in future.

Abstract Supramolecular chemistry is a fascinating field that explores the interactions between molecules to create higher-order structures. In the case of the supramolecular chain of Fuchsine acid, which is a type of dye molecule, several chemical applications are possible. Fuchsine acid helps to make better medicine carriers that deliver drugs where they’re needed in the body, making treatments more effective and reducing side effects. It also helps create smart materials like sensors and self-fixing plastics, which are useful in electronics, keeping our environment clean, and making new materials. In sensing and detection, the supramolecular chain of Fuchsine acid utilizes as a sensor or detector for specific analyzes. In drug delivery, the supramolecular chains of Fuchsine acid incorporated into drug delivery systems. In recent years, a common method is linking a graph to a chemical structure and using topological descriptors to study it. This technique is becoming increasingly important over time. Topological descriptors gives very useful information while studying the topology of chemical graph. In this paper, we have computed the 3D structure of supramolecular graph of Fuchsine acid. We have computed an explicit expressions of ABC index, GA index, General Randi $$\acute{c}$$ c ´ index, first and second Zagreb index, hyper Zagreb index, H-index and F-index of supramolecular structure of Fushine acid.

Abstract This study explores the complex relationships involving ecological footprints, energy use, carbon emissions, governance efficiency, economic prosperity, and financial stability in South Asian nations spanning the period from 2000 to 2022. Employing various methodologies such as cross-sectional dependence tests, co-integration analysis, and first- and second-generation unit-root tests, we use a panel Autoregressive Distributed Lag model, feasible generalized least squares, and Panel Corrected Standard Errors to ensure the robustness of our findings. We find noteworthy positive correlations between several variables, including heightened ecological consciousness, effective governance structures, increased GDP per capita, and amplified CO2 emissions. These relationships suggest potential pathways to strengthen the financial stability of the entire region; they also highlight the latent potential of embracing ecologically sustainable practices to fortify economic resilience. Our results also underscore the pivotal role of appropriate governance structures and higher income levels in bolstering financial stability in South Asian countries. Interestingly, we also find negative coefficients associated with the use of renewable energy, suggesting that escalating the adoption of renewable energy could create financial instability. This finding stresses the importance of diversification in energy strategies, cautioning policymakers to carefully consider the financial ramifications of potentially costly imports of renewable energy sources while seeking to reduce carbon emissions, emphasizing the need to strike a balance between ambitious sustainability goals and the pursuit of sustained economic robustness in the region. In considering the implications of these findings, it is crucial to consider each country’s broader socioeconomic context. Our results offer valuable insights for policymakers in developing renewable energy strategies.

Graph operations enable the modification and transformation of graphs, enhancing data representation as well as effectiveness in fields such as computer science, mathematics, and data analysis. Super line graph operations are a concept of advanced graph theory that is used in advanced mathematics and computer science. They are used to solve specific mathematical problems, especially in graph theory and Combinatorics. Topological numbers are numerical values connected with graph structures that are used to analyze structural characteristics and solve problems in fields such as chemistry and mathematics. They are important for simplifying complex data and enabling quantitative analysis. The general Randić number of some super line graph operations of number two with a three-diameter is investigated in this study. The pendant vertices are inserted without disturbing their diameter. Seven graphs of order five, each with a diameter of three, can be used to create twenty-three generalized super line graphs.

OBJECTIVES The primary objective of this study is to assess the degree of concordance and discordance between the interpretations of computed tomography (CT) brain images by resident and consultant radiologists while emphasizing the critical significance of accurate image interpretation for informed clinical decision-making. METHODOLOGY The evaluation of radiology reports for CT Brain interpretation through a prospective analysis at the Radiology Department of Rehman Medical Institute over two years, from 1st October 2020 to 31st October 2022. A total of 198 patients who underwent cranial CT scans were interpreted by residents (R1, R2, R3, R4). Following this, the consultant radiologists reviewed the images and completed their reports. The reports of the residents and the consultant radiologists were then compared, and concordance was achieved when the residents’ reports were consistent with the final radiologist’s reports. The data collected were recorded in Microsoft Excel. The statistical analysis was performed using SPSS version 22 (IBM Corp., Armonk, NY), and the kappa coefficient was used to determine the level of agreement between residents and consultants. RESULTS Among the 198 CT Head reports evaluated, 186 of them were in agreement with the final report of the consultant radiologist. Of the correctly diagnosed cases, R1 correctly diagnosed 46 cases, R2 correctly diagnosed 80 cases, R3 correctly diagnosed 54 cases, and R4 correctly diagnosed 6 cases. Our study achieved a percentage agreement of 93.93, with a Cohen's kappa coefficient of 0.8. CONCLUSION The overall concordance rate between residents and consultant radiologists was 93.93%, with a kappa coefficient 0.8. This high kappa coefficient indicates strong agreement between the two groups.

Pakistan is the fifth most populous country in the world. Its ecological environment is facing numerous stresses such as climate change, rapid urbanization, natural disasters, and a decline in air quality. Thus, the scientific understanding of spatial and temporal changes in Pakistan's ecological environment is crucial for formulating an informed strategy for regional sustainability. This study used the Google Earth Engine platform and the Remote Sensing Ecological Index (RSEI) to investigate ecological vulnerability in three provinces of Pakistan for 1990, 2000, 2010, and 2020. Landsat 5 and Landsat 8 datasets are used to construct RSEI indicators and Principal Component Analysis (PCA) is adopted to objectively compute RSEI for the past three decades. The results indicated that (1) the ecological vulnerability of the Punjab province exhibited a slightly improved trend from 1990 to 2020 with overall dominance of ‘moderate’ level vulnerability in all four years; (2) The Sindh province has exhibited a declining trend of the ecological environment with ‘poor’ ecological vulnerability contributing to 28.6% of the total area in 2020 as compared to 1.04% of the total area in 1990; and (3) The ecological environment of Balochistan province has shown resilience to some extent during 1900–2010 with the dominance of a ‘moderate’ level of ecological vulnerability. However, a decline is observed between 2010 and 2020. These research results can provide support for the Punjab, Sindh, and Balochistan provinces in achieving sustainable development while conserving the regional ecological environment.

The battery's performance heavily influences the safety, dependability, and operational efficiency of electric vehicles (EVs). This paper introduces an innovative hybrid deep learning architecture that dramatically enhances the estimation of the state of charge (SoC) of lithium-ion (Li-ion) batteries, crucial for efficient EV operation. Our model uniquely integrates a convolutional neural network (CNN) with bidirectional long short-term memory (Bi-LSTM), optimized through evolutionary intelligence, enabling an advanced level of precision in SoC estimation. A novel aspect of this work is the application of the Group Learning Algorithm (GLA) to tune the hyperparameters of the CNN–Bi-LSTM network meticulously. This approach not only refines the model's accuracy but also significantly enhances its efficiency by optimizing each parameter to best capture and integrate both spatial and temporal information from the battery data. This is in stark contrast to conventional models that typically focus on either spatial or temporal data, but not both effectively. The model's robustness is further demonstrated through its training across six diverse datasets that represent a range of EV discharge profiles, including the Highway Fuel Economy Test (HWFET), the US06 test, the Beijing Dynamic Stress Test (BJDST), the dynamic stress test (DST), the federal urban driving schedule (FUDS), and the urban development driving schedule (UDDS). These tests are crucial for ensuring that the model can perform under various real-world conditions. Experimentally, our hybrid model not only surpasses the performance of existing LSTM and CNN frameworks in tracking SoC estimation but also achieves an impressively quick convergence to true SoC values, maintaining an average root mean square error (RMSE) of less than 1 %. Furthermore, the experimental outcomes suggest that this new deep learning methodology outstrips conventional approaches in both convergence speed and estimation accuracy, thus promising to significantly enhance battery life and overall EV efficiency.

The industrial sector is one of the most energy-intensive sectors, with a share of nearly 38 % (156 EJ) of all energy used globally in 2020. Historical energy demand and consumption data from a poultry processing plant have been analyzed to lower greenhouse gas emissions (GHG) and reliance on traditional energy sources. The study includes energy, economic, and emissions analyses for (a) solar photovoltaic (PV) systems, (b) biomass fuels, and (c) coal-fired with wood. Fixed, single, and two-axis tracking solar PV systems that are company-owned and funded by banks are considered. The historical energy consumption data of the plant shows that 52.36 % of energy demand is met by electrical energy and 47.63 % by thermal energy. The yearly electricity demand is 9,938 MWh, costs $1,192,560, and emits 5117.6 tCO2. Thermal energy demand is based on an annual use of 898 tonnes of coal and 71.6 tonnes of liquefied petroleum gas (LPG), which costs $ 143,681 and emits 2977.7 tonnes of carbon dioxide (tCO2). Feasibility of 1.3 MW, fixed axis company-owned, solar PV plant shows an annual electricity production of 1876 MWh, GHG emission reduction of 965.9 tCO2 with a payback period of 3.4 years. Biomass system delivers yearly fuel cost savings of $25,724, reducing 2784 tCO2 with a 1.9-year payback period. Co-firing biomass offers a 3.58 % fuel cost saving and 557 tCO2 with a 0.93-year payback period. It concluded that the wood fuel feedstock biomass option is most suitable renewable energy resource for such large-scale poultry facilities.

Abstract Chemical graph theory, a subfield of graph theory, is used to investigate chemical substances and their characteristics. Chemical graph analysis sheds light on the connection, symmetry, and reactivity of molecules. It supports chemical property prediction, research of molecular reactions, drug development, and understanding of molecular networks. A crucial part of computational chemistry is chemical graph theory, which helps researchers analyze and manipulate chemical structures using graph algorithms and mathematical models. Beryllonitrene , a compound of interest due to its potential applications in various fields, is examined through the lens of graph theory and mathematical modeling. The study involves the calculation and interpretation of topological indices and graph entropy measures, which provide valuable insights into the structural and energetic properties of Beryllonitrene’s molecular graph. Logarithmic regression models are employed to establish correlations between these indices, entropy, and other relevant molecular attributes. The results contribute to a deeper understanding of Beryllonitrene’s complex characteristics, facilitating its potential applications in diverse scientific and technological domains. In this study, degree-based topological indices $$\text{TI}$$ TI are determined, as well as the entropy of graphs based on these $$\text{TI}$$ TI .

Abstract Background Dissolved organic matter (DOM) is the most active component of soil organic matter (SOM), playing a major role in regulating soil fertility and carbon cycling. However, the effects of different wolfberry (Lycium barbarum L.) planting ages on the chemical diversity of DOM and its interaction with soil physicochemical properties have not been comprehensively studied. In this context, we collected soil samples (0–10 cm) from wolfberry orchards at different planting ages (1, 4, 6, 10, and 13 years) and from a corn field (0 years) in the arid region of Northwest Ningxia in China to assess the changes in soil DOM quantity and quality using ultraviolet–visible absorbance, fluorescence spectroscopy, and parallel factor analysis. Results We found that the ages of the wolfberry plantation changed the contents of soil nutrients and SOM. In addition, significantly higher DOM concentrations were observed at wolfberry planting ages of 10 and 13 years than those in the control group (0 years) by 176.6 and 190.2%, respectively. The specific ultraviolet absorbance at 254 nm (SUVA254) and 254 nm to 365 nm ultraviolet absorbance ratio (E2/E3) values were decreased and increased, respectively, after wolfberry planting, indicating low aromatic and molecular weight compounds of soil DOM. The biogenic index (BIX) and fluorescence index (FI) of soil DOM ranged from 0.6 to 0.7 and 1.42 to 1.93, respectively, suggesting a combination of allochthonous and autochthonous sources. The short- and long-term wolfberry cultivations of 1 and 4 years decreased and increased the humification degrees of soil DOM, respectively. The contribution rate of the protein-like (C1) fluorescence intensity decreased, while that of the fulvic acid-like component (C3) increased with increasing wolfberry planting age, suggesting a change in the structure of soil DOM from protein-like to fulvic acids. In this study, total nitrogen (TN) and exchangeable Ca2+ were the main factors affecting the quantity and quality of soil DOM in the wolfberry orchards with different planting ages. Conclusions This study demonstrated that long-term wolfberry plantation enhances the accumulation of soil DOM and more complex compounds, thereby promoting soil organic carbon sequestration under different planting ages and land-use types in terrestrial ecosystems. Graphical Abstract

Abstract Covalent organic frameworks (ZnP-COFs) made of zinc-porphyrin have become effective materials with a variety of uses, including gas storage and catalysis. To simulate the structural and electrical features of ZnP-COFs, this study goes into the computation of polynomials utilizing degree-based indices. We gave a methodical study of these polynomial computations using Excel, illustrating the complex interrelationships between the various indices. Degree-based indices provide valuable insights into the connectivity of vertices within a network. M-polynomials, on the other hand, offer a mathematical framework for representing and studying the properties of 2D COFs. By encoding structural information into a polynomial form, M-polynomials facilitate the calculation of various topological indices, including the Wiener index, Zagreb indices, and more. The different behavior of ZnP-COFs based on degree-based indices was illustrated graphically, and this comparison provided insightful information for prospective applications and the construction of innovative ZnP-COF structures. Moreover, we discuss the relevance of these techniques in the broader context of materials science and the design of functional covalent organic frameworks.

Appropriate nitrogen (N) fertilization and planting density management are critical for efficient production of grain maize (Zea mays L.) and for environmental protection. However, the optimal N fertilization and planting density is still not established for forage maize that is cultivated to promote its vegetative growth and utilized for the above-ground vegetative mass. A two-year field experiment was conducted in the rainfed semiarid region of the Chinese Loess Plateau during the 2021 and 2022 growing seasons. The effects of N application rates and planting densities on the dry matter yields and the water- and N-use efficiencies of forage maize were studied. The experiment includes four N application rates (0, 90, 180, and 270 kg ha−1) and three plant densities (70000, 90000, and 110000 plants ha−1), covering the conventional practices of local farmers. The treatments were organized in a randomized complete block design with four replications. Averaged over the three plant densities, N application rate of 180 kg ha−1 resulted in the maximum average aboveground dry matter yield (18.6 t ha−1), crop N accumulation (228.5 kg ha−1), dry matter water productivity (51.9 kg ha−1 mm−1), and dry matter precipitation productivity (62.9 kg ha−1 mm−1) over the two years. Moreover, increasing N application rates significantly increased the soil nitrate-N accumulation (0–200 cm) but reduced the partial factor productivity of applied N fertilizer. Across the three plant densities, the two-year average soil nitrate-N accumulation was 12.6, 32.1, and 75.7 % higher with 90, 180, and 270 kg N ha−1 compared to no N treatment, respectively. The highest soil nitrate accumulation under 270 kg ha−1 N application rate in 2021 (229.5 kg ha−1) and in 2022 (329.7 kg ha−1) may cause severe nitrate leaching loss and potential soil water contamination, driven by intensive rainfalls. Averaged over the four N rates, planting density of 110000 plants ha−1 increased the crop N accumulation and PFP by 21.2 % and 15.8 % in 2021, compared to 70000 plants ha−1, respectively. The interaction of N application and planting density significantly affected the aboveground dry matter yield, crop water consumption, dry matter precipitation productivity, and crop N accumulation in 2021, but the effect was non-significant in 2022. Based on these findings, application of 180 kg N ha−1 and planting density of 110000 plants ha−1 are suggested as an efficient management strategy for improving productivity of forage maize and soil water and N resources utilization in the arid region of the Loess Plateau and similar areas.

In this study, we investigate entropy measurements for subdivided cage networks based on topological indices. We specifically calculate different entropy, redefining Zagreb entropy, [Formula: see text],[Formula: see text], [Formula: see text] entropy, atom bond connection entropy, and Randic entropy. We examine the graphical behavior of various entropy measures using the line fit approach. The results highlight patterns in the distribution of entropy values and interactions between them, which shed light on the intricate connectivity and structural properties of segmented cage networks. This work improves our understanding of cage network dynamics and provides a visual framework for interpreting their behavior.

AbstractMicroencapsulation improves the stability of liquid food by moving it to a free form of powder. In the current study, Nigella sativa Oil (NSO) emulsion mixture was spray dried under various operating conditions, including inlet air temperature (IAT) of 130, 145, and 160 °C, wall material (WM), 10, 15, and 20%; feed rate (FR), 6, 9, and 12 mL/min; and needle speeds (NS) of 6, 8, and 10 s. The conditions of 130 °C (IAT), 15% (WM), 9 mL/min (FR), and 6 s (NS) produced the highest encapsulation efficiency (EE) of 89.51 ± 0.90%. At 160 °C (IAT), 15% (WM), 9 mL/min (FR), as well as 8 s (NS), the minimum EE was observed to be 79.15 ± 0.61%, and the maximum model predicted value of (EE) was 89.46 ± 0.80%. IAT has a substantial impact on EE while improving the oxidative quality of spray-dried microcapsule (SDM) samples. The SDM sample sensory scores fell within acceptable limits. Therefore, the spray-drying method developed from Nigella sativa Oil can be recommended for different fortifying food products.

ABSTRACTOne of the most important fields in current materials research is the examination of materials through the prism of topological indices. An extensive statistical investigation of topological indices relevant to the characterization of copper(II) fluoride is presented in this paper. Our goal is to use the well-understood structural features of copper(II) fluoride, a chemical that is well known for its crystalline qualities, to uncover a variety of properties inherent in its network. This work makes use of the structural information available for copper(II) fluoride. After a thorough computational investigation, a rigorous statistical analysis is conducted to determine the distributions and correlations between heat of formation and the different topological indices. The findings reveal significant patterns and trends in the copper(II) fluoride network structure, providing insights into the underlying principles governing its material behavior.

Background: In Turkey, the SMART pharmacist program was launched to enable community pharmacists to deliver patient-centric care services. However, how far this programme has achieved success and what are the challenges faced by the programme need to be evaluated. Objective: This study aimed to explore the experiences of community pharmacists in providing person-centric care services in pharmacies and provide recommendations for improved care effectiveness. Methods: A phenomenological approach was adopted in this study. To conduct qualitative interviews, a semi-structured interview guide was devised to gather insights from the pharmacists. The interviews were coded verbatim. Subsequently, various themes and sub-themes were developed based on the aim and objectives of the study. A total of 14 pharmacists engaged in semi-structured interviews conducted between May and August 2023. Results: Two main themes emerged from the data: challenges in person-centric care and recommendations to improve person-centric care. Barriers were subdivided into patient-related challenges and personal challenges. Recommendations consisted of pharmacists’ professional tasks and recommendations. Conclusion: The findings of this study, suggest that the concerned healthcare authorities should re-evaluate the ‘SMART pharmacist’ program in Turkey and address professional and personal challenges faced by community pharmacists in delivering effective person-centric care. Pharmacists recommend patient follow-up (follow-ups), providing a counselling environment, collaboration with physicians, expansion of pharmacy services.

BackgroundControl of buffalo flies (Haematobia irritans exigua, BFs) relies mainly on chemical methods; however, resistance to insecticides is widespread in BF populations. Breeding for resistance to BFs represents a possible alternative, but direct phenotyping of animals is laborious and often inaccurate. The availability of reliable diagnostic biomarker(s) to identify low BF carrier cattle would facilitate rapid and accurate selection for genetic improvement. However, limited information is available regarding differences amongst cattle in host responses to BF infestation.MethodsThis study investigated the variation in Brangus cattle serum proteomic profiles before (naïve) and after peak BF exposure, in low (LF) and high BF burden (HF) cattle. Cattle were phenotyped for susceptibility based on BF counts on multiple dates using visual and photographic techniques. The relative abundance of serum proteins in cattle before and after exposure to BFs was analysed using sequential window acquisition of all theoretical fragment ion mass spectrometry (SWATH-MS).ResultsExposure to BFs elicited similar responses in HF and LF cattle, with 79 and 70 proteins, respectively, showing significantly different abundances post exposure as compared to their relevant naïve groups. The comparison of serum samples from naïve HF and LF cattle identified 44 significantly differentially abundant (DA) proteins, while 37 significantly DA proteins were identified from the comparison between HF and LF cattle post-exposure to BFs. Proteins with higher abundance in naïve LF cattle were enriched in blood coagulation mechanisms that were sustained after exposure to BFs. Strong immune response mechanisms were also identified in naïve LF cattle, whereas these responses developed in HF cattle only after exposure to BF. High BF cattle also showed active anticoagulation mechanisms in response to BF exposure, including downregulation of coagulation factor IX and upregulation of antithrombin-III, which might facilitate BF feeding.ConclusionUnderlying differences in the abundance of proteins related to blood coagulation and immune response pathways could potentially provide indirect indicators of susceptibility to BF infestation and biomarkers for selecting more BF-resistant cattle.

Background: This is a report from Multan Medical and Dental College about obesity among lady doctors and factors associated with it. Methodology: A cross sectional descriptive study was carried out in Multan medical & dental college and hospital from 1st January 2020 to 30th March 2020 after taking approval from institutional review board. Closed ended questionnaire was used to collect data from 159 lady doctors of age from 22 to 60 years including both married and unmarried females using simple random sampling technique. Results: Obesity was seen more in married lady doctors i.e. 64 (83.1%) as compared to 13 (16.88%) unmarried lady doctors and highest frequency of obesity was seen in 50 to 60 years age group i.e. 22 (88%) obese as compared to 3 (12%) non obese. The results were statistically significant. P=0.000. Conclusions: There is alarming rate of obesity among married lady doctors and also in upper age group i.e., 50 to 60 years.

Background: Prescribing errors are quite common and according to one estimate out of 100 patients admitted into UK hospitals 15 will have some form of prescribing error in their records. It is a general understanding that most of the time these errors are made due to lack of awareness. Severity of these errors can range from minor to major mistakes that can lead to fatal results. Materials and Methods: A simplified anonymous approach of identifying these errors and then using a step wise approach to educate the prescribers’ especially junior doctors can be quite fruitful in reducing these errors. Unfortunately there are not many studies or projects available to back our proposal however these seems a logical way forward and is exactly what we have shown in our study. Results: We performed a prospective snapshot study involving 100 inpatients to get baseline measurements. The errors and mistakes were identified and fed back to the junior doctors in an anonymous manner. Clear & legible writing, frequency of use, responsible consultant name, allergy box filled, VTE assessment, oxygen prescribing and labeling of medication discontinuation were the most common negligence identified. At the same time junior doctors were reminded of local prescription standards and guidelines which usually don’t form part of induction. Conclusion: Multiple deficient areas were identified during this audit like legible writing, dosage frequency, VTE prophylaxis and oxygen prescription. It was highlighted to junior doctors how important are these components as they play a key role in patient getting better after medical review. Above mentioned steps did improve prescription errors to an extent, but aim should be to achieve 100% results. Repeated reminders are important in this case as that helps to improve practice and avoid clinical accidents.

Background: The mean arterial pressure serves as an expression of blood pressure in patients on chronic hemodialysis. Serum calcium phosphorus product is considered as a risk factor of vascular calcification that is associated with hypertension in the patients of end stage renal disease. The literature regarding this relationship is inconsistent therefore this study is designed to determine the correlation between calcium phosphorus product and mean arterial pressure among hemodialysis patients with end stage renal disease. Methods: A total of 110 patients of end stage renal disease on hemodialysis for at least one year, 20 to 60 years of age were included. Patients with primary or tertiary hyperparathyroidism, peripheral vascular disease, malignancy, hypertension secondary to any cause other than kidney disease were excluded. Mean arterial pressure was calculated according to the standard protocol in lying position. Blood samples for estimation of serum calcium and phosphorous were taken and was sent immediately to the laboratory for serum analysis. Results: Mean age was 44.17 ± 10.94 years. Mean calcium phosphorous product was 46.71 ± 7.36 mg/dl and mean arterial pressure was 103.61 ± 12.77 mmHg. The values of Pearson correlation co-efficient (r) were 0.863 for age group 20 to 40 years and 0.589 for age group 41 to 60 years. This strong positive correlation means that high calcium phosphorous product goes with high mean arterial pressure (and vice versa) for both the age groups. Conclusion: A strong positive relationship exists between the mean arterial pressure and calcium phosphorous product and is independent of patients’ age.

Objective: Doxorubicin is presently a leading antineoplastic drug with promising efficacy. This study was designed to investigate the histological effects of doxorubicin toxicity on rat kidneys and how much protection is provided by Nigella Sativa. Materials & Methods: A randomized controlled trial conducted on thirty adult male wistar rats divided randomly into three equal groups. Group A served as a control. Group B was injected with weekly intraperitoneal injections of doxorubicin at a dose of 3mg/kg b.w. Group C rats received doxorubicin along with nigella sativa at a dose of 1000mg/kg b.w. orally daily. At the end of these interventions, animals were sacrificed and kidneys were removed for the purpose of histological staining. Renal glomerular and tubules related histopathological parameters were assessed qualitatively as mild, moderate & severe. Renal glomerular diameter was digitally measured by microscope. Ethical approval was taken from Ethical Committee, Jinnah Postgraduate Medical Centre (JPMC), Karachi. All the parameters were statistically analyzed. Results: Group B rats’ renal tissue was adversely affected by the drug showing marked necrosis of tubules and the glomeruli along with interstitial cells’ infiltration. Glomerular diameter was also significantly decreased in group B as compared to group A. These histological features in group C rats’ renal tissue were milder and glomerular diameter was close to that of group A. Conclusion: According to our study doxorubicin treatment proved noxious for the renal tissue, both tubules and glomeruli, while nigella sativa significantly competed against these pathological alterations.

Intercropping has been widely recognized to have great advantages in terms of increasing yield, controlling pests and diseases, and saving land, particularly in developing countries. Regulated deficit irrigation reduces water consumption and improves water productivity (WP). However, it is unclear whether the combination of intercropping and deficit irrigation could improve crop yield and WP simultaneously. In this experiment, three planting modes, including forage maize (Zea mays L.) monoculture (M), lablab bean (Lablab purpureus L.) monoculture (L), and maize-lablab bean intercropping (ML) were used. Six irrigation modes were set for each planting mode, including severe water deficit (W1), late water deficit (W2), alternate water deficit (W3), late moderate water deficit (W4), early moderate water deficit (W5), and full irrigation (W6). Results showed that compared with M, the ML treatment significantly increased the fresh forage yield (9.8%–17.0%), hay yield (9.5%–13.1%), crude protein yield (22.9%–25.9%), and WP (7.8%–8.7%). The W5 treatment achieved similar fresh forage yield, hay yield, and crude protein yield as that of the W6 treatment but reduced irrigation water by 25% and increased the WP (21.9%–24.8%). Intercropping achieved a high-water equivalence ratio (WER;1.52–1.81) and land equivalence ratio (LER;1.56–1.84), indicating its advantages over monocultures. The W6 treatment had the lowest WER and LER, suggesting that excessive irrigation can reduce the efficiency of utilizing land and water resource in maze-based forage production. Among all treatments, ML–W5 achieved the highest net income and output to input ratio. Overall, intercropping of forage maize and lablab bean with moderate deficit irrigation at an early stage could be used as a high-yield and efficient forage production system in the arid areas of northwest China.

Background: Dengue hemorrhagic fever (DHF) is a fatal manifestation of dengue disease. DHF’s risk factors profile holds significance importance in the clinical practice and efficient care plan are required during dengue disease flare-up. The aim of this study was to investigate the risk factors for pathogenesis of dengue disease and dengue hemorrhagic fever. Methods: In this descriptive cross-sectional study, data was obtained from 256 patients with diagnoses of Dengue hemorrhagic fever (DHF). Comprehensive history, physical assessment and biochemical estimations were recorded. Patients were followed to identify and assess the risk factors for DHF. The Statistical Package of Social Sciences for analysis of data. Stratification of residence and socioeconomic status to see effect of these on result variable by applying chi square test. p value of 0.05). All diseases were common in participants who belonged to the urban area. Conclusion: Secondary infection was most common risk factor in patients with DHF and found mostly in less than 40 age than older patients. Whereas, males were predominately affected more than the females (p

Smart energy management demands better ways to understand the energy consumption of buildings. Nonintrusive Load Monitoring (NILM) is an emerging technique that disaggregates total building consumption to individual appliances. However, low-power appliances pose a challenge as they exhibit similar power consumption patterns that are difficult to identify and distinguish from background noise. This research aims to bridge this gap by developing feature extraction and classification techniques specifically for low-power NILM. This may facilitate the development of targeted energy-saving strategies and result in more precise energy-use monitoring. To effectively identify and differentiate low-power appliances within a NILM system, this work proposes a novel feature extraction approach that combines mono-fractal and multifractal analysis of appliance startup current transients. Mono-fractal features, including fractal dimension and Hurst exponent, are extracted alongside Lacunarity and Multifractal features comprising the singularity spectrum and Hölder exponents. These features collectively create comprehensive appliance signatures that capture the unique characteristics of each appliance during its turn-on event. Building upon these extracted features, the work investigates the performance of three machine learning classifiers for appliance classification: deep neural network, support vector machine, and K-nearest neighbours. These classifiers are optimized using Bayesian optimization to achieve optimum performance. The proposed method demonstrates significant improvement over existing feature extraction approaches across all optimized classifiers, achieving an accuracy of up to 98.3% in classifying low-power appliances.

Business has a massive effect on both people and society as a whole in today’s culture. Businesses make significant contributions to humanity’s general well-being and progress by promoting economic growth, supporting innovation, producing wealth, and addressing social challenges. However, choosing the right location for a business is a complex task, involving multiple criteria and qualitative and quantitative factors that heavily rely on expert judgement. The researchers propose a unique approach called the SVNZN multi-attributed decision-making method to aid decision-makers in this process. They introduce new operating laws for SVNZNs based on the sine trigonometric (ST) function, known for its periodicity and symmetry over the origin, making it favorable for decision-makers over multi-time phase parameters. Additionally, novel AOs such as SVNZN weighted averaging and geometric operators are defined to combine SVNZNs effectively. Based on these AOs, a decision-making technique for MADM problems is presented, and its applicability is demonstrated through a numerical example of selecting the best location for a business. To validate and enhance the understanding of these proposed techniques, the researchers conducted a comprehensive comparison analysis, including a sensitivity analysis, considering existing literature on MADM difficulties. Figure 1 provides a thorough graphical summary by visually representing all of the contributions and outcomes.

In the aircraft sector, honeycomb composite materials are frequently employed. Recent research has demonstrated the benefits of honeycomb structures in applications involving nanohole arrays in anodized alumina, micro-porous arrays in polymer thin films, activated carbon honeycombs, and photonic band gap honeycomb structures. The resolvability parameter is the area of graph theory that is most commonly explored. This results in an original network reconfiguration. Occasionally in terms of atoms (metric dimension), and sometimes in terms of bounds (edge metric dimension). In this article, we examined the honeycomb rhombic torus’s metric, edge metric, mixed metric, and partition dimension. The application of edge metric dimension is also discussed in it.

The notion of partition dimension was initially introduced in the field of graph theory, primarily to examine distances between vertices. The local partition dimension extends this idea by incorporating specific conditions into how vertices are represented. In graph theory, it is customary to represent the partition dimension of a graph as $pd(G)$ . Network localization, on the other hand, is the process of precisely determining the position of nodes within a network concerning a selected subset of nodes, called the locating set. The smallest size of its locating set is used to represent the locating number of a network. The generalized hexagonal cellular network provides an innovative framework for network planning and analysis. In our study, we investigate the partition dimension of a generalized hexagonal cellular network and provide a rigorous proof of its exact partition dimension. Hence, our approach ensures the distinct recognition of each node within a generalized hexagonal cellular network. Additionally, we explore the utilization of the metric dimension in flood relief camping by the National Disaster Management Authority (NDMA) Pakistan during floods in 2022. NDMA established relief camps and relief centers with unique codes to rescue humans and animals.

Abstract In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least square homotopy perturbation method (LSHPM). The LSHPM is tested on various nonlinear problems documented in the existing literature. To evaluate the effectiveness of the proposed approach, the identified problems are also tackled using HPM and the MATLAB built-in function bvp5c, and then the results are compared with those obtained using LSHPM. In addition, a comparative analysis is carried out with the results of the AG method as found in the literature. The results show that LSHPM is a reliable and efficient method suitable for solving more complicated initial value problems in the fields of science and engineering.

A connected acyclic graph in which the degree of every vertex is at most four is called a molecular tree. A number associated with a molecular tree that can help to approximate the physical or chemical properties of the corresponding molecule is called a topological index. It is of great importance to investigate the relation between the structure and the thermodynamic properties of those molecules. In this paper, we investigated the extreme value of the first reformulated Zagreb index with a given order and degree of a graph. Further, we investigated the molecular trees that attain the maximum and minimum values. As an application, we presented the regression models to predict the acentric factor and entropy of octane isomers. Our extremal graphs give the minimum and the maximum acentric factor and entropy, which satisfied the experimental values.

Objectives: This study aims to determine the prevalence of knee osteoarthritis (OA) and associated risk factors in the contralateral limb after lower limb amputation. Methods: This cross-sectional survey included 500 lower limb amputees using prostheses for at least 1 year using convenience sampling from the Pakistan Institute of Prosthetic and Orthotic Sciences (PIPOS), Peshawar City, Pakistan rehabilitation services program (PRSP) and its satellite centers across Khyber Pakhtunkhwa. A sample included either gender aged 20 to 80 years. A basic demographic sheet and risk factors questionnaire and American College of Rheumatology (ACR) guidelines diagnostic knee OA criteria, such as using history, physical examination, and radiographic findings were used to collect data. Data were analyzed using SPSS software, version 21. T-test and analysis of variance (ANOVA) statistics were utilized to observe any relationship with P