Pub Date : 2022-08-02DOI: 10.3390/foundations2030043
Juan Núñez Valdés, Fernando de Pablos Pons, A. Ramos Carrillo
It is assumed that the history of modern science in Africa began between the last two decades of the 19th century and the first two or three of the 20th century [...]
据推测，非洲的现代科学史开始于19世纪最后20年和20世纪前两三十年之间[…]
{"title":"Pioneering Black African American Women Chemists and Pharmacists","authors":"Juan Núñez Valdés, Fernando de Pablos Pons, A. Ramos Carrillo","doi":"10.3390/foundations2030043","DOIUrl":"https://doi.org/10.3390/foundations2030043","url":null,"abstract":"It is assumed that the history of modern science in Africa began between the last two decades of the 19th century and the first two or three of the 20th century [...]","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"30 6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82998843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.3390/foundations2030042
S. George, I. Argyros, Christopher I. Argyros, Kedarnath Senapati
The Traub iterates generate a sequence that converges to a solution of a nonlinear equation given certain conditions. The order of convergence has been shown provided that the fifth Fréchet-derivative exists. Notice that this derivative does not appear on the Traub method. Therefore, according to the earlier results, there is no guarantee that the Traub method converges if the operator is not five times Fréchet-differentiable or more. However, the Traub method can converge, since these assumptions are only sufficient. The novelty of our new technique is the fact that only the Fréchet-derivative on the method is assumed to exist to prove convergence. Moreover, the new results does not depend on the Traub method. Consequently, the same technique can be applied on other methods. The dynamics of this method are also studied. Examples further explain the theoretical results.
{"title":"Approximating Solutions of Nonlinear Equations Using an Extended Traub Method","authors":"S. George, I. Argyros, Christopher I. Argyros, Kedarnath Senapati","doi":"10.3390/foundations2030042","DOIUrl":"https://doi.org/10.3390/foundations2030042","url":null,"abstract":"The Traub iterates generate a sequence that converges to a solution of a nonlinear equation given certain conditions. The order of convergence has been shown provided that the fifth Fréchet-derivative exists. Notice that this derivative does not appear on the Traub method. Therefore, according to the earlier results, there is no guarantee that the Traub method converges if the operator is not five times Fréchet-differentiable or more. However, the Traub method can converge, since these assumptions are only sufficient. The novelty of our new technique is the fact that only the Fréchet-derivative on the method is assumed to exist to prove convergence. Moreover, the new results does not depend on the Traub method. Consequently, the same technique can be applied on other methods. The dynamics of this method are also studied. Examples further explain the theoretical results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88160387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-25DOI: 10.3390/foundations2030041
Henok Desalegn, J. Mijena, E. Nwaeze, Tadesse Abdi
In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases of our results.
{"title":"Simpson’s Type Inequalities for s-Convex Functions via a Generalized Proportional Fractional Integral","authors":"Henok Desalegn, J. Mijena, E. Nwaeze, Tadesse Abdi","doi":"10.3390/foundations2030041","DOIUrl":"https://doi.org/10.3390/foundations2030041","url":null,"abstract":"In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases of our results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74027956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-24DOI: 10.3390/foundations2030040
D. Triantis, A. Loukidis, I. Stavrakas, E. Pasiou, S. Kourkoulis
The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant-load stage of each specific loading step. The experimental data are analyzed in terms of the interevent time intervals between any two successive acoustic hits (using the F-function concept) and, further, in terms of the power of the acoustic hits (in terms of the recently introduced P-function). It is indicated that while the mechanical load is kept constant, the acoustic activity attenuates steadily, and during the early steps of this attenuation phase, the temporal evolution of both the F- and P-functions is excellently described by an exponential law. Moreover, it is proven that for both the F- and P-functions, the relaxation exponents decrease monotonically with increasing load. This decrease becomes quite abrupt for loads exceeding about 80% of the fracture load, providing an interesting and promising pre-failure indicator, i.e., a warning signal that the specimen is entering into the stage of impending macroscopic fracture. The specific conclusions are in very satisfactory agreement, both qualitatively and quantitatively, with similar ones drawn by considering the temporal evolution of the respective b-value.
{"title":"Attenuation of the Acoustic Activity in Cement Beams under Constant Bending Load Closely Approaching the Fracture Load","authors":"D. Triantis, A. Loukidis, I. Stavrakas, E. Pasiou, S. Kourkoulis","doi":"10.3390/foundations2030040","DOIUrl":"https://doi.org/10.3390/foundations2030040","url":null,"abstract":"The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant-load stage of each specific loading step. The experimental data are analyzed in terms of the interevent time intervals between any two successive acoustic hits (using the F-function concept) and, further, in terms of the power of the acoustic hits (in terms of the recently introduced P-function). It is indicated that while the mechanical load is kept constant, the acoustic activity attenuates steadily, and during the early steps of this attenuation phase, the temporal evolution of both the F- and P-functions is excellently described by an exponential law. Moreover, it is proven that for both the F- and P-functions, the relaxation exponents decrease monotonically with increasing load. This decrease becomes quite abrupt for loads exceeding about 80% of the fracture load, providing an interesting and promising pre-failure indicator, i.e., a warning signal that the specimen is entering into the stage of impending macroscopic fracture. The specific conclusions are in very satisfactory agreement, both qualitatively and quantitatively, with similar ones drawn by considering the temporal evolution of the respective b-value.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76911422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-19DOI: 10.3390/foundations2030039
V. Pletser
In the first part of this paper, we considered several theoretical models, a static and four dynamic models without rebounds, of the throw of a fair coin landing on its edge, to demonstrate that the probability of heads or tails is less than 50%, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds that is the subject of this second part of the paper, it is found that the probability that a 50 Euro cent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.
{"title":"Is The Probability of Tossing a Coin Really 50–50%? Part 2: Dynamic Model with Rebounds","authors":"V. Pletser","doi":"10.3390/foundations2030039","DOIUrl":"https://doi.org/10.3390/foundations2030039","url":null,"abstract":"In the first part of this paper, we considered several theoretical models, a static and four dynamic models without rebounds, of the throw of a fair coin landing on its edge, to demonstrate that the probability of heads or tails is less than 50%, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds that is the subject of this second part of the paper, it is found that the probability that a 50 Euro cent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"10 6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89508429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-05DOI: 10.3390/foundations2030038
K. Romanevich, M. Lebedev, S. Andrianov, Sergey N. Mulev
Electromagnetic radiation (EMR) technology makes it possible to evaluate changes in the stress-strain state (SSS) in the “tunnel lining-enclosing rock mass” system at a high level of interference, and to create schemes of long-term EMR control in tunnels (geotechnical monitoring systems). The issues of the variations in EMR signals are extremely important for monitoring systems: based on anomalous deviations from the normal regime one can draw conclusions about changes in the SSS, leading to geodynamic phenomena (e.g., rock bursts). This article presents data obtained during laboratory studies on samples and field studies in transport tunnels. Also, some results of long-term geotechnical monitoring by a set of methods is presented: EMR and tensometry of the tunnel lining, both methods are in the automatic mode. The ability of an EMR control system to respond to earthquakes affecting tunnel structures is shown. An analysis of long-term EMR studies was conducted, which showed the periodic oscillation of the “tunnel lining-enclosing rock mass” system. In a stable compressed state, minima of EMR pulses are recorded; when the rock mass and lining material are stretched, charges are separated on the edges of micro-defects and EMR increases; complete separation of the edges of micro-defects leads to the termination of intense EMR. The same occurs in the opposite direction during the compression of micro-defects and micro-fractures in the rock mass and concrete lining. The periods of compression and expansion are closely related to temperature fluctuations. The results differ in detail and, therefore, in to be more confident, additional studies are needed in various host rock massifs and types of tunnel lining.
{"title":"Integrated Interpretation of the Results of Long-Term Geotechnical Monitoring in Underground Tunnels Using the Electromagnetic Radiation Method","authors":"K. Romanevich, M. Lebedev, S. Andrianov, Sergey N. Mulev","doi":"10.3390/foundations2030038","DOIUrl":"https://doi.org/10.3390/foundations2030038","url":null,"abstract":"Electromagnetic radiation (EMR) technology makes it possible to evaluate changes in the stress-strain state (SSS) in the “tunnel lining-enclosing rock mass” system at a high level of interference, and to create schemes of long-term EMR control in tunnels (geotechnical monitoring systems). The issues of the variations in EMR signals are extremely important for monitoring systems: based on anomalous deviations from the normal regime one can draw conclusions about changes in the SSS, leading to geodynamic phenomena (e.g., rock bursts). This article presents data obtained during laboratory studies on samples and field studies in transport tunnels. Also, some results of long-term geotechnical monitoring by a set of methods is presented: EMR and tensometry of the tunnel lining, both methods are in the automatic mode. The ability of an EMR control system to respond to earthquakes affecting tunnel structures is shown. An analysis of long-term EMR studies was conducted, which showed the periodic oscillation of the “tunnel lining-enclosing rock mass” system. In a stable compressed state, minima of EMR pulses are recorded; when the rock mass and lining material are stretched, charges are separated on the edges of micro-defects and EMR increases; complete separation of the edges of micro-defects leads to the termination of intense EMR. The same occurs in the opposite direction during the compression of micro-defects and micro-fractures in the rock mass and concrete lining. The periods of compression and expansion are closely related to temperature fluctuations. The results differ in detail and, therefore, in to be more confident, additional studies are needed in various host rock massifs and types of tunnel lining.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74729297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.3390/foundations2030037
Pletser Vladimir
Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails of less than 50%. In this first part, the theoretical models for a static case and for five dynamic cases, without rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. It is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand. In the second part of the paper, the dynamic model with rebounds is investigated.
{"title":"Is the Probability of Tossing A Coin Really 50–50%? Part 1: Static Model and Dynamic Models without Rebounds","authors":"Pletser Vladimir","doi":"10.3390/foundations2030037","DOIUrl":"https://doi.org/10.3390/foundations2030037","url":null,"abstract":"Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails of less than 50%. In this first part, the theoretical models for a static case and for five dynamic cases, without rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. It is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand. In the second part of the paper, the dynamic model with rebounds is investigated.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82138203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-26DOI: 10.3390/foundations2030036
E. Oks
For the excitation of the n = 2 states of hydrogen atoms due to electron impact, we compared the experimental and theoretical ratios of the cross-sections σ2s/σ2p. We found this theoretical ratio to be systematically higher than the corresponding experimental ratio by about 20%—far beyond the experimental error margins. We suggest that this discrepancy can be explained by the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental hydrogen gas. The explanation is based on the fact that, in the experiments, the cross-section σ2s was determined by using the quenching technique—by applying an electric field that mixed the 2s and 2p states, followed by the emission of the Lyman-alpha line from the 2p state. However, the SFHA only had the s-states, so the quenching technique would not count the excitation of the SFHA in the 2s state and, thus, lead to the underestimation of the cross-section σ2s. We estimates the share of the SFHA in the experimental hydrogen gas required for eliminating the above discrepancy and found this share to be about the same as the share of the usual hydrogen atoms. Thus, our results constitute the third proof from atomic experiments that the SFHA does exist, the first proof being related to the experimental distribution of the linear momentum in the ground state of hydrogen atoms, and the second proof being related to the experimental cross-section of charge exchange between hydrogen atoms and low-energy protons.
{"title":"Experiments on the Electron Impact Excitation of the 2s and 2p States of Hydrogen Atoms Confirm the Presence of Their Second Flavor as the Candidate for Dark Matter","authors":"E. Oks","doi":"10.3390/foundations2030036","DOIUrl":"https://doi.org/10.3390/foundations2030036","url":null,"abstract":"For the excitation of the n = 2 states of hydrogen atoms due to electron impact, we compared the experimental and theoretical ratios of the cross-sections σ2s/σ2p. We found this theoretical ratio to be systematically higher than the corresponding experimental ratio by about 20%—far beyond the experimental error margins. We suggest that this discrepancy can be explained by the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental hydrogen gas. The explanation is based on the fact that, in the experiments, the cross-section σ2s was determined by using the quenching technique—by applying an electric field that mixed the 2s and 2p states, followed by the emission of the Lyman-alpha line from the 2p state. However, the SFHA only had the s-states, so the quenching technique would not count the excitation of the SFHA in the 2s state and, thus, lead to the underestimation of the cross-section σ2s. We estimates the share of the SFHA in the experimental hydrogen gas required for eliminating the above discrepancy and found this share to be about the same as the share of the usual hydrogen atoms. Thus, our results constitute the third proof from atomic experiments that the SFHA does exist, the first proof being related to the experimental distribution of the linear momentum in the ground state of hydrogen atoms, and the second proof being related to the experimental cross-section of charge exchange between hydrogen atoms and low-energy protons.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77152202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.3390/foundations2030035
Te Ma, L. Schimleck, J. Dahlen, S. Yoon, T. Inagaki, S. Tsuchikawa, A. Sandak, J. Sandak
Near-infrared spectroscopy (NIRS) allows for the rapid estimation of a wide range of wood properties. Typically, NIRS studies on wood have utilized benchtop spectrometers, but efforts to utilize NIR hyperspectral imaging to examine wood and wood products have increased. Compared to benchtop NIR systems, hyperspectral imaging has several advantages (speed, visualization of spatial variability), but the data typically have a lower signal-to-noise ratio as well as fewer wavelengths saved; thus, hyperspectral imaging systems have a larger spectral sampling interval (SSI). Furthermore, the SSI and wavelength range varies considerably among different HSI cameras. NIR-HSI systems based on indium gallium arsenide (InGaAs) detectors have a wavelength range typically from 900 to 1700 nm, while short-wave infrared hyperspectral imaging (SWIR-HSI) systems based on mercury cadmium telluride (MCT) detectors have the ‘full’ NIR wavelength range from 1000 to 2500 nm. These factors may influence the performance of wood property calibrations. We compared one NIR-HSI (900–1700 nm) and three SWIR-HSI (1000–2500 nm) commercially available cameras with an NIRS benchtop spectrometer (1100–2500 nm). The performance of specific gravity (SG) and stiffness (MOE) calibration models was compared with one-hundred Douglas-fir (Pseudotsuga menziesii) samples. The limited wavelength range of an NIR-HSI camera provided the best models for MOE, whereas the NIR-HSI and two SWIR-HSI cameras provided similar SG results. SWIR-HSI models heavily favored wavelengths greater than 1900 nm.
{"title":"Comparative Performance of NIR-Hyperspectral Imaging Systems","authors":"Te Ma, L. Schimleck, J. Dahlen, S. Yoon, T. Inagaki, S. Tsuchikawa, A. Sandak, J. Sandak","doi":"10.3390/foundations2030035","DOIUrl":"https://doi.org/10.3390/foundations2030035","url":null,"abstract":"Near-infrared spectroscopy (NIRS) allows for the rapid estimation of a wide range of wood properties. Typically, NIRS studies on wood have utilized benchtop spectrometers, but efforts to utilize NIR hyperspectral imaging to examine wood and wood products have increased. Compared to benchtop NIR systems, hyperspectral imaging has several advantages (speed, visualization of spatial variability), but the data typically have a lower signal-to-noise ratio as well as fewer wavelengths saved; thus, hyperspectral imaging systems have a larger spectral sampling interval (SSI). Furthermore, the SSI and wavelength range varies considerably among different HSI cameras. NIR-HSI systems based on indium gallium arsenide (InGaAs) detectors have a wavelength range typically from 900 to 1700 nm, while short-wave infrared hyperspectral imaging (SWIR-HSI) systems based on mercury cadmium telluride (MCT) detectors have the ‘full’ NIR wavelength range from 1000 to 2500 nm. These factors may influence the performance of wood property calibrations. We compared one NIR-HSI (900–1700 nm) and three SWIR-HSI (1000–2500 nm) commercially available cameras with an NIRS benchtop spectrometer (1100–2500 nm). The performance of specific gravity (SG) and stiffness (MOE) calibration models was compared with one-hundred Douglas-fir (Pseudotsuga menziesii) samples. The limited wavelength range of an NIR-HSI camera provided the best models for MOE, whereas the NIR-HSI and two SWIR-HSI cameras provided similar SG results. SWIR-HSI models heavily favored wavelengths greater than 1900 nm.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72396528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-20DOI: 10.3390/foundations2020034
I. Argyros, J. P. Jaiswal, A. Saxena, M. Argyros
The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor–Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.
{"title":"On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations","authors":"I. Argyros, J. P. Jaiswal, A. Saxena, M. Argyros","doi":"10.3390/foundations2020034","DOIUrl":"https://doi.org/10.3390/foundations2020034","url":null,"abstract":"The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor–Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"252 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75808880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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