Scientific African最新文献

{"title":"Mathematical model analysis of malaria transmission dynamics with induced complications","authors":"Bereket Hido Wako ,&nbsp;Mohammed Yiha Dawed ,&nbsp;Legesse Lemecha Obsu","doi":"10.1016/j.sciaf.2025.e02635","DOIUrl":"10.1016/j.sciaf.2025.e02635","url":null,"abstract":"<div><div>This study develops a mathematical model to analyze malaria transmission dynamics. It accounts for complications like severe anemia and organ dysfunction, which impact disease outcomes and healthcare systems. The study includes rigorous analysis to confirm the existence and uniqueness of the solution, positivity, boundedness, and stability of the equilibrium points. Stability analysis is done using the Routh–Hurwitz criteria and the Castillo-Chavez approach. It is verified that the malaria-free equilibrium point is globally asymptotically stable when <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is below one, with no backward bifurcation. A forward bifurcation exists with a smooth transition to endemic states as <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> crosses one. Local sensitivity analysis justifies a 10% increase in transmission rates <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> raises <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> by 5%, while a 10% increase in recovery rate <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> or mosquito mortality rate <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> reduce <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> by 1.3% and 5%, respectively. Global sensitivity analysis was conducted, and it identified that <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> has strong impact on the model’s output. Among all the parameters, <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> and the death rate of mosquitoes were found to be the most influential in determining the behavior of the model. We fit the mathematical model to malaria data from Ethiopia and estimate parameters using Matlab’s fminsearch routine. The effect of seasonal malaria transmission rate is also discussed. Simulation analysis show that increasing treatment and mosquito death rates, while reducing transmission rates, can reduce the malaria burden. The findings emphasize the need to control complications and improve vector management for effective malaria interventions in regions like Ethiopia.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02635"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MCMC-Driven mathematical modeling of the impact of HPV vaccine uptake in reducing cervical cancer","authors":"Sylas Oswald ,&nbsp;Eunice Mureithi ,&nbsp;Berge Tsanou ,&nbsp;Michael Chapwanya ,&nbsp;Kijakazi Mashoto ,&nbsp;Crispin Kahesa","doi":"10.1016/j.sciaf.2025.e02633","DOIUrl":"10.1016/j.sciaf.2025.e02633","url":null,"abstract":"<div><div>Human Papillomavirus (HPV) is a group of contagious viruses primarily transmitted through sexual contact and is a major cause of severe health issues, including cervical cancer. In Sub-Saharan Africa, including Tanzania, cervical cancer is the leading cause of cancer-related deaths among women of all ages. In 2022, there were 125,699 new cases and 80,614 deaths, making cervical cancer the second most common cancer. Of these, Tanzania recorded 10,868 cases and 6,832 deaths. To reduce the number of girls and female affected by HPV infections, particularly those vulnerable to cervical cancer, we have developed and analyzed a mathematical model for HPV transmission dynamics that incorporates vaccination. The analysis demonstrates the presence of both HPV-free and endemic equilibrium states. By applying the Graph Theoretic method, the reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> was computed. The results indicate that the HPV-free equilibrium is globally asymptotically stable when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, while the endemic equilibrium is globally asymptotically stable when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>. We employed a Markov Chain Monte Carlo (MCMC) method for model calibration, which highlighted several key factors. The interaction between vaccination rates for young girls and older females suggests long-term benefits from vaccinating both groups, contributing to increased herd immunity. Additionally, the strong identifiability of the recovery rate emphasizes its critical role in reducing HPV prevalence and cervical cancer progression. The correlations observed indicate the dual role of vaccination in both preventing infection and promoting recovery. On the other hand, the poor identifiability of the mortality rate points to gaps in understanding the long-term burden of cervical cancer. However, since the data used are synthetic, the uncertainties highlight how important it is to use real data and break it into groups to better understand how different factors affect the results. The herd immunity threshold was calculated to be 0.4417, recommending that at least 55.83% of the population be vaccinated to halt HPV transmission and reduce cervical cancer incidence.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02633"},"PeriodicalIF":2.7,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Detection of kidney stone from ultrasound images using machine learning algorithms","authors":"Yawukal Ashagrie Asaye,&nbsp;Pushparaghavan Annamalai,&nbsp;Lijaddis Getnet Ayalew","doi":"10.1016/j.sciaf.2025.e02618","DOIUrl":"10.1016/j.sciaf.2025.e02618","url":null,"abstract":"<div><div>Nephrolithiasis is a prevalent cause of chronic renal diseases which is extremely costly to treat. The diagnosis of nephrolithiasis is difficult since there aren’t enough radiologist interpreters to interpret pictures from imaging devices and make a decision. Machine Learning (ML) algorithms are currently used for the detection or diagnosis of kidney stones, with the major drawbacks of limited data, ionizing radiation from scanning devices, ex-vivo techniques, and cost. In this research, ultrasound images are collected from different hospitals and annotated by radiographers or experts. Preprocessing mainly focused on filtering and segmentation for feature extraction and stone size estimation. Entropy and Gray Level Co-occurrence Matrix (GLCM) feature descriptors are extracted. In the analysis process, Support Vector Classifiers (SVC), Decision Trees (DT), K-Nearest Neighbors (KNN), and Random Forest (RF) algorithms are considered. KNN and RF models outperform the provided datasets. The KNN achieves performance metrics of accuracy, precision, recall, and AUC; 98.4%, 0.97, 1.0, and 0.98, respectively, and 95.1%, 0.94, 0.97, and 0.9896, respectively, for RF. Estimation of stone size with the major axis length of 10.2235 mm is obtained for the actual stone size of 11.9 mm, as annotated by the expert. Hence, the proposed approach of detecting kidney stones using ML algorithms can enhance and improve the diagnosis and detection of kidney stones (renal calculi) from ultrasound images, which are non-invasive, simple to use, and affordable without any ionizing radiation to improve the quality of life of the patients.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02618"},"PeriodicalIF":2.7,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhanced LSTM model with integrated attention mechanism and data augmentation for projecting COVID-19 trends in Africa","authors":"Soufiana Mekouar","doi":"10.1016/j.sciaf.2025.e02617","DOIUrl":"10.1016/j.sciaf.2025.e02617","url":null,"abstract":"<div><div>Estimating the outcomes of epidemics promptly and precisely is crucial for decision-making and policy implementation. In this paper, we employ a long short-term memory (LSTM) method with an attention mechanism to discern the temporal correlation of COVID-19 growth. We propose a novel augmentation technique to enhance the regression model’s accuracy. A heuristic search identifies the optimal LSTM layer structure that maximizes the validation score. Initially, we trained the model on data containing confirmed cases and deaths from African countries, categorized by economic factors and GDP. The performance was better than the gated recurrent unit (GRU), LSTM, and BiLSTM methods, exhibiting a comparably low validation error. We assessed our LSTM-augmented model (LSTM-aug) using graph visualization and regression metrics on WHO COVID-19 data, demonstrating its superiority over existing methods.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02617"},"PeriodicalIF":2.7,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Artificial neural network-enhanced unconditionally stable finite-difference time-domain technique for multiscale problems","authors":"Oluwole John Famoriji,&nbsp;Thokozani Shongwe","doi":"10.1016/j.sciaf.2025.e02645","DOIUrl":"10.1016/j.sciaf.2025.e02645","url":null,"abstract":"<div><div>Electromagnetic sensing and system-level design challenges are often multiscale in nature, making them difficult to solve. These challenges will likely continue to hinder system-level sensing and design optimization for the foreseeable future. Typically, such multiscale problems involve three electrical scales: the fine scale, the coarse scale, and the intermediate scale that lies between them. The significant differences in scale across both spatial and temporal domains present major difficulties in numerical modeling and simulation. In this paper, a new artificial neural network (ANN) and unconditionally stable finite-difference time-domain (FDTD) technique for multiscale problems is proposed. The field data at these points is the output of ANN-FDTD, which takes as its input the point position of the spatial grid division in FDTD. Every time step, the output of the ANN and a known forced excitation source were used to build the hypothetical solution of Maxwell's equations. The gradient of the ANN's output with respect to the input vector indicates the error of the system. Labeled samples are not required for training as the backpropagation (BP) algorithm uses this error value to update the ANN parameters. In this case, ANN is trained to guarantee that the boundary requirements are satisfied by the hypothetical response. Every time-marching phase involves training a different ANN, so the results from one step do not impact the results from the next. With finely structured microwave components, the time step of the ANN-FDTD can be selected to be substantially bigger than that of the conventional FDTD. In addition, it is possible to partition each time step into blocks for parallel calculation. The accuracy and effectiveness of the proposed technique are verified by three numerical examples. The proposed method finds applications in antenna design, metamaterials, wireless communications, and wave propagation in complex environments.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02645"},"PeriodicalIF":2.7,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adansonia digitata and Daniella oliveri seed oils and cosmeceutical products exhibited potent pharmacological and marginal toxicity on fibroblast cells","authors":"O. Atolani ,&nbsp;A.T. Kola-Mustapha ,&nbsp;D.E. Tarigha ,&nbsp;E.T. Areh ,&nbsp;A.T. Hamzat ,&nbsp;O.S. Adeyemi","doi":"10.1016/j.sciaf.2025.e02643","DOIUrl":"10.1016/j.sciaf.2025.e02643","url":null,"abstract":"<div><div>There is a growing demand for the use of seed oils in food, pharmaceuticals, and cosmetics, especially in skincare and hair care products. The aim of this study was to formulate organic cosmetic products from underutilized seed oils and evaluate their pharmacological and toxicity potentials. Human foreskin fibroblast cells were used to evaluate the cytotoxicity of the sample, while using staurosporine as positive control drug. Standard agar diffusion assays were utilized to assess the in vitro antimicrobial activities against a variety of organisms, such as <em>Streptococcus aureus, Klebsiella pneumoniae, Bacillus subtilis, Escherichia coli, S. typhi, Pseudomonas aeruginosa, Candida albicans, Aspergillus niger, Penicillium notatam</em>, and <em>Rhizopus stoloniler</em> while the anti-inflammatory potential was evaluated using lipoxygenase inhibition assay. The ability of the seed oils and formulated cosmeceutical products to act as antioxidants were examined using complimentary DPPH and ABTS radical scavenging assays. In addition, the anti-parasitic effect of seed oil against <em>Toxoplasma gondii</em> was established. The green organic medicated soaps and emollients, free of all synthetic antioxidants, preservatives, colourants, stabilizers, perfumes and antibiotics were produced. The oils and their value-added cosmetic products from the seed of <em>A. digitata</em> and <em>D. oliveri</em> yielded 29 % and 16 % product and exhibited suitable physicochemical parameters comparable to edible oils used for industrial purposes. While <em>A. digitata</em> oil showed the presence of 22 fatty acids with oleic acid (46.04 %) and palmitic acid (19.98 %) as most predominant with total unsaturation of 60.55 %, <em>D. oliveri</em> showed 12-hydroxydodecanoic acid (23.25 %) and pentadecanoic acid (21.13 %) as the most predominant with total unsaturation of 20.54 %. The presence of essential fatty acids coupled with significant antioxidants, antimicrobial and low in vitro cytotoxicity underscore the cosmeceutical prospects of the plants. Although the Emollient exhibited a slightly reduced level of inhibition towards the tested clinical pathogens with a minimum inhibitory concentration value ranging from 50 to 100 mg/mL, the products hold huge promise as purely organic formulations with significant level of antimicrobial activities comparable to the standard drugs. While further in vivo toxicological evaluations would be required, the seed oils open up a channel of research for bountiful scientific explorations.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02643"},"PeriodicalIF":2.7,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of cytotoxic potential of Callistemon leaf extracts against breast and colon cancer: Metabolomic, flow cytometry and in silico studies","authors":"Amira Y. Eissa ,&nbsp;Kamilia F. Taha ,&nbsp;Abeer A. Dahab ,&nbsp;Usama R. Abdelmohsen ,&nbsp;Khayrya A. Youssif ,&nbsp;Mona H. Ibrahim ,&nbsp;Seham S. El-Hawary ,&nbsp;Manal M. Sabry","doi":"10.1016/j.sciaf.2025.e02638","DOIUrl":"10.1016/j.sciaf.2025.e02638","url":null,"abstract":"<div><div>This study explores the phytochemical and the cytotoxic prospective of leaf ethanol extracts from four <em>Callistemon</em> species (<em>C. citrinus, C. macropunctatus, C. viminalis, and C. subulatus</em>) against breast (MCF-7) and colon (Caco-2) cancer cell lines. Metabolomic profiling of the ethanolic extracts of the studied <em>Callistemon</em> species was performed using UPLC-ESI-MS/MS. <em>In-vitro</em> cytotoxicity effects were evaluated using 3-(4,5-dimethylthiazol-2- yl)-2,5-diphenyltetrazolium bromide (MTT) assay followed by flow cytometric analysis. In-silico docking studies of predominant compounds against cell cycle regulatory enzymes were conducted, followed by molecular dynamics simulations for top binding interactions. UPLC-ESI-MS/MS tentatively identified 20 compounds in the extracts, with lignans, and flavonoids being prominent. <em>C. macropunctatus</em> extract showed the strongest cytotoxicity against both cancer lines. Notably, this extract induced cell cycle arrest at S and G1 phases in both MCF-7 and Caco-2 cells, as well as promoted apoptosis. In-silico docking simulations further investigated that the evaluated compounds exhibited promising binding affinities (-6.6 to -11.2 kcal/mol) particularly cyanidin 3,5-diglucoside (-11.1), nilocitin (-10.9), and quercetin 3-<em>O</em>-(2′'-galloyl)-<em>β</em>-d-galactopyranoside (-11.2), exhibited the most favourable docking scores towards cyclin-dependent kinase-2 CDK2, a key cell cycle regulator, compared to the co-crystal ligand roniciclib (-9.5). These findings suggest strong interactions with crucial CDK2 amino acid residues. Collectively, this study highlights the cytotoxic potential of <em>Callistemon</em> leaf extracts, particularly <em>C. macropunctatus</em>, warranting further exploration of their anti-cancer properties, with a focus on CDK2 inhibition mechanisms.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02638"},"PeriodicalIF":2.7,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chromium bioremediation mechanistic action assessment using bacterial consortium isolated from Egyptian Petroleum Refining Company","authors":"Moaaz T. Hamed ,&nbsp;Bassma H. Elwakil ,&nbsp;Mohamed Hagar ,&nbsp;Doaa Ahmed Ghareeb ,&nbsp;Zakia A. Olama","doi":"10.1016/j.sciaf.2025.e02642","DOIUrl":"10.1016/j.sciaf.2025.e02642","url":null,"abstract":"<div><div>Bioremediation is a rising technique for heavy metals removal. The current study aimed to evaluate the removal of chromium using a native bacterial consortium. The bacterial consortium B (<em>Providencia rettgri</em> DSM 4542, <em>Bacillus altitudinis</em> 41KF2b and <em>Bacillus tropicus</em> MCCC1A01406) reported the maximum chromium tolerance. Taguchi statistical design was used for the optimization of the physiological factors affecting chromium bioremediation which revealed that 48 h incubation, pH 9; Cr concentration, 90 ppm; inoculum size, 15 ml; inoculum age, 72 h; peptone, 2.5 g; beef extract, 1.5 g; yeast extract, 1.5 g and NaCl, 0.5 g at 40 °C were the optimum conditions reaching 92.3 % chromium removal. The interactions between Cr⁶⁺ concentration (ppm) and inoculum size (ml) were the most significant factors. Electron microscopic and proteomic studies showed that the chromium ions were not adsorbed by the potent consortium but rather bioaccumulated via sulphate transporters with the release of the reduced chromium (Cr³⁺) in the surrounding medium. Furthermore, consortium B used malate dehydrogenase and a peptide-binding periplasmic ABC transporter to reduce Cr⁶⁺ to Cr³⁺. It can be concluded that the present consortia is a suitable bioremediation tool.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02642"},"PeriodicalIF":2.7,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating the evolutionary dynamics of second-line Mycobacterium tuberculosis drug resistance in Tanzania using hypercubic modelling and the Baum–Welch algorithm","authors":"Leonce Leandry ,&nbsp;Egbert Mujuni ,&nbsp;Eunice W. Mureithi ,&nbsp;Morten Brun ,&nbsp;Mary Mayige","doi":"10.1016/j.sciaf.2025.e02627","DOIUrl":"10.1016/j.sciaf.2025.e02627","url":null,"abstract":"<div><div><em>Mycobacterium tuberculosis</em> (MTB) continues to pose a significant threat to public health, particularly with the emergence of drug-resistant strains. Research shows that first-line anti-tuberculosis drugs are increasingly failing, and second-line drugs are also showing resistance. This study investigates the evolutionary dynamics of second-line drugs used against MTB, specifically Bedaquiline, Delamanid, Linezolid, Clofazimine, and Levofloxacin. Data were collected from the Tanzania National Institute of Medical Research (NIMR) at the Central Tuberculosis Reference Laborator Muhimbili Centre (CTRL). The data were analysed using a 5-hypercubic model, with parameters estimated using the Baum–Welch algorithm. The findings show that the most probable drug-resistant acquisition, independent of other drugs analysed, is Bedaquiline with a probability of 0.8660 and Levofloxacin with a probability of 0.134. The evolutionary pattern begins with Bedaquiline, followed by Levofloxacin, then Clofazimine, and finally either Linezolid or Delamanid, each with an equal probability of occurring. This highlights the evolutionary patterns of drug resistance, providing insights that can inform health experts and policymakers in developing evidence-based, effective interventions to combat this growing public health challenge.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02627"},"PeriodicalIF":2.7,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Density and dentability in norm-attainable classes","authors":"Joseph Owuor ,&nbsp;Benard Okelo ,&nbsp;Julia Owino ,&nbsp;Jeremiah Kinyanjui","doi":"10.1016/j.sciaf.2025.e02621","DOIUrl":"10.1016/j.sciaf.2025.e02621","url":null,"abstract":"<div><div>We establish the norm-denseness of the norm-attainable class <span><math><mrow><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> in the Banach algebra <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span>, which consists of all bounded linear operators on a complex Hilbert space <span><math><mi>H</mi></math></span>. Specifically, for every <span><math><mrow><mi>O</mi><mo>∈</mo><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> and each <span><math><mrow><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, there exists <span><math><mrow><msup><mrow><mi>O</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>∈</mo><mi>B</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> such that <span><math><mrow><mo>‖</mo><mi>O</mi><mo>−</mo><msup><mrow><mi>O</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>‖</mo><mo>&lt;</mo><mi>ϵ</mi></mrow></math></span>. This result is achieved through the convergence of sequences and the existence of limit points. The properties <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span> of Lindenstrauss ensure the density of <span><math><mrow><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span>, and we show that countable unions, finite intersections, countable tensor products, and countable Cartesian products preserve density in the associated classes. Furthermore, density in <span><math><mrow><mi>N</mi><mi>A</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span> exhibits transitivity. Building on this foundation of density, we next investigate the concept of dentability in norm-attainable classes within the Banach algebra <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math></span>. Dentability, which is closely related to density via Radon–Nikodým property, refers to the existence of a bounded linear norm-attainable operator within the class that lies outside the closed convex hull of the subclass obtained by excluding a sufficiently small ball around this operator. We provide conditions for dentability and <span><math><mi>s</mi></math></span>-dentability in subclasses, closures, closed convex hulls, and superclasses of norm-attainable classes. Moreover, we demonstrate that countable unions, Cartesian products, and finite intersections preserve dentability. We also prove that arbitrary unions, finite intersections, and arbitrary Cartesian products maintain the dentability of classes. Our work significantly contributes to the characterization and understanding of dentability in norm-attainable classes. The findings advance knowledge in operator analysis, operator theory, and optimization, particularly in relation to dentability. These results enhance the study of the lineability and spaceability of norm-attainable classes and Banach spaces.</div></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":"28 ","pages":"Article e02621"},"PeriodicalIF":2.7,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}