Pub Date : 2022-09-19DOI: 10.3390/foundations2030055
R. Agarwal, Asif R Khan, Sumayyah Saadi
In this work, we use similarly separable vectors in separable Hilbert spaces to provide generalized integral results related to majorization, Niezgoda, and Ćebysév type inequalities. Next, we furnish some refinements of these inequalities. Theorems obtained in this work extend and improve several known results in the literature. An important aspect of our work is that these inequalities are directly related to Arithmetic, Geometric, Harmonic, and Power means. These means have played an important role in many branches of arts and sciences since the last 2600 years.
{"title":"Integral Results Related to Similarly Separable Vectors in Separable Hilbert Spaces","authors":"R. Agarwal, Asif R Khan, Sumayyah Saadi","doi":"10.3390/foundations2030055","DOIUrl":"https://doi.org/10.3390/foundations2030055","url":null,"abstract":"In this work, we use similarly separable vectors in separable Hilbert spaces to provide generalized integral results related to majorization, Niezgoda, and Ćebysév type inequalities. Next, we furnish some refinements of these inequalities. Theorems obtained in this work extend and improve several known results in the literature. An important aspect of our work is that these inequalities are directly related to Arithmetic, Geometric, Harmonic, and Power means. These means have played an important role in many branches of arts and sciences since the last 2600 years.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"143 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80280999","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 : 2022-09-19DOI: 10.3390/foundations2030054
V. D. Borisov
The work is devoted to the results of processing electromagnetic radiation signals obtained during laboratory loading of marble and diabase samples using a technique for determining the parameters of microcracks, developed and published by the author earlier. As a result of such processing, certain patterns were found in the nature of the evolution of the oscillatory process ensemble of microcracks. For example, solitary non-linear waves almost always preceded a sequence of High Frequency traces. Equations for straight lines approximating High Frequency traces in logarithmic coordinates, close to the equation of the Gutenberg–Richter law. Due to the similarity of seismic processes at different scale levels, the results of modeling at the microscale level can be used to describe seismic processes at the macroscale level, for example, to study the processes occurring immediately before destruction and at the time of destruction in order to search for repeatability and regularities. The regularities obtained can be used in the development of a predictive criterion that makes it possible to predict the time of one or another geophysical (seismic) event.
{"title":"Nonlinear Soliton-like Oscillations and Waves during Geomaterial Destruction Based on Electromagnetic Radiation Signals","authors":"V. D. Borisov","doi":"10.3390/foundations2030054","DOIUrl":"https://doi.org/10.3390/foundations2030054","url":null,"abstract":"The work is devoted to the results of processing electromagnetic radiation signals obtained during laboratory loading of marble and diabase samples using a technique for determining the parameters of microcracks, developed and published by the author earlier. As a result of such processing, certain patterns were found in the nature of the evolution of the oscillatory process ensemble of microcracks. For example, solitary non-linear waves almost always preceded a sequence of High Frequency traces. Equations for straight lines approximating High Frequency traces in logarithmic coordinates, close to the equation of the Gutenberg–Richter law. Due to the similarity of seismic processes at different scale levels, the results of modeling at the microscale level can be used to describe seismic processes at the macroscale level, for example, to study the processes occurring immediately before destruction and at the time of destruction in order to search for repeatability and regularities. The regularities obtained can be used in the development of a predictive criterion that makes it possible to predict the time of one or another geophysical (seismic) event.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77558464","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 : 2022-09-15DOI: 10.3390/foundations2030053
L. Jäntschi
Polyynes are alternations of single and triple bonds between carbon atoms, while cumulenes are successions of double bonds. Since the triple bond is the strongest bond between two carbon atoms, recent preoccupations included synthesizing and condensing cyclic polyynes and cumulenes and their clusters. Density functional theory calculations predicted stable monocyclic rings formation for a number of C atoms equal to or higher than 16. Alternative to the series of Carbon atoms are alternations of Boron and Nitrogen. Large rings (such as those of 24 atoms) can be crossed and thus small clusters can be formed. Patterns of three crosses seem to further stabilize the atomic ensemble. Clusters of 4C24 and 4B12N12 (96 atoms) as well as 4C26 (104 atoms) have been designed, and their conformation has been studied here.
{"title":"Energetics of C8B8N8, N12B12, and C24 Macrocycles and Two [4]Catenanes","authors":"L. Jäntschi","doi":"10.3390/foundations2030053","DOIUrl":"https://doi.org/10.3390/foundations2030053","url":null,"abstract":"Polyynes are alternations of single and triple bonds between carbon atoms, while cumulenes are successions of double bonds. Since the triple bond is the strongest bond between two carbon atoms, recent preoccupations included synthesizing and condensing cyclic polyynes and cumulenes and their clusters. Density functional theory calculations predicted stable monocyclic rings formation for a number of C atoms equal to or higher than 16. Alternative to the series of Carbon atoms are alternations of Boron and Nitrogen. Large rings (such as those of 24 atoms) can be crossed and thus small clusters can be formed. Patterns of three crosses seem to further stabilize the atomic ensemble. Clusters of 4C24 and 4B12N12 (96 atoms) as well as 4C26 (104 atoms) have been designed, and their conformation has been studied here.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89248549","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 : 2022-09-13DOI: 10.3390/foundations2030052
Zhonghui Li, Yueyu Lei, E. Wang, V. Frid, Dexing Li, Xiaofei Liu, Xuekun Ren
In order to explore the evolution characteristics of multi−scale rock−like material failure, we studied the acoustic emission (AE) and electromagnetic radiation (EMR) characteristics of different scale rock−like materials by using the AE−EMR experimental system of coal and rock failure, and the AE and EMR response law of rockburst in mining sites was analyzed. The results show that under uniaxial loading, the stress–strain curve of the specimen has a compaction stage, linear elastic stage, elastic–plastic stage and failure stage. The cumulative AE count, AE energy and stress level of the specimen have an exponential relationship during loading and compression. The cumulative EMR counts of loading and unloading showed a trend of first decreasing and then increasing with the increase in stress level. Electromagnetic radiation and microseismic hypocentral distance show an abnormal change trend when rockburst occurs, and this abnormal phenomenon can be used as a precursor feature signal for rockburst monitoring and early warning.
{"title":"Characteristics of Electromagnetic Radiation and the Acoustic Emission Response of Multi−Scale Rock−like Material Failure and Their Application","authors":"Zhonghui Li, Yueyu Lei, E. Wang, V. Frid, Dexing Li, Xiaofei Liu, Xuekun Ren","doi":"10.3390/foundations2030052","DOIUrl":"https://doi.org/10.3390/foundations2030052","url":null,"abstract":"In order to explore the evolution characteristics of multi−scale rock−like material failure, we studied the acoustic emission (AE) and electromagnetic radiation (EMR) characteristics of different scale rock−like materials by using the AE−EMR experimental system of coal and rock failure, and the AE and EMR response law of rockburst in mining sites was analyzed. The results show that under uniaxial loading, the stress–strain curve of the specimen has a compaction stage, linear elastic stage, elastic–plastic stage and failure stage. The cumulative AE count, AE energy and stress level of the specimen have an exponential relationship during loading and compression. The cumulative EMR counts of loading and unloading showed a trend of first decreasing and then increasing with the increase in stress level. Electromagnetic radiation and microseismic hypocentral distance show an abnormal change trend when rockburst occurs, and this abnormal phenomenon can be used as a precursor feature signal for rockburst monitoring and early warning.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"284 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76845826","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}
The accurate monitoring and early warning of coal and rock dynamic disasters become challenging in complex geological environments. Mostly, the signal information contains interferences, which misguides the technician, and thus leads to inaccurate monitoring results. To reduce the influence of interference signals, the synchronous response of the acoustic emission (AE) and electromagnetic emission (EME) signals before the failure of coal specimens during uniaxial loading was investigated in this study. Additionally, the coupling relationship between M value, AE energy/AE ringing count per unit time, and the damage of coal is established, and the early warning index of AE and EME (R value) was computed and verified through the field investigations. The results show that a strong synchronization of the acoustoelectric signals occurs only after the specimen enters the strain strengthening area. The analysis of the obtained results showed that the M value of the AE-EME synchronous response signal represents a strong degree of damage occurring in the coal body, however, this is still subject to false alarms. In contrast, the analysis of the R value accurately helped in determining the damage evaluation, thus, it can be regarded as one of the precursors of the imminent failure of coal. With R > 1, the specimen is closed to the failure state, thereby dangerous regions are identified with a dense concentration of R > 1 events. The obtained R value index through on-site AE and EME monitoring corresponds closely with the stress distribution cloud map of the roadway. It is inferred that the anti-interference ability and the reliability of the R value index are stronger than the routine early warning indicators of the single-AE or EME energy.
{"title":"Analyzing the Synchronous Acoustic and Electric Response of Coal Burst Failure: Validation through the On-Site Application","authors":"Yingjie Zhao, Da-zhao Song, Menghan Wei, Majid Khan, Zhenlei Li, Liming Qiu, Shan Yin","doi":"10.3390/foundations2030051","DOIUrl":"https://doi.org/10.3390/foundations2030051","url":null,"abstract":"The accurate monitoring and early warning of coal and rock dynamic disasters become challenging in complex geological environments. Mostly, the signal information contains interferences, which misguides the technician, and thus leads to inaccurate monitoring results. To reduce the influence of interference signals, the synchronous response of the acoustic emission (AE) and electromagnetic emission (EME) signals before the failure of coal specimens during uniaxial loading was investigated in this study. Additionally, the coupling relationship between M value, AE energy/AE ringing count per unit time, and the damage of coal is established, and the early warning index of AE and EME (R value) was computed and verified through the field investigations. The results show that a strong synchronization of the acoustoelectric signals occurs only after the specimen enters the strain strengthening area. The analysis of the obtained results showed that the M value of the AE-EME synchronous response signal represents a strong degree of damage occurring in the coal body, however, this is still subject to false alarms. In contrast, the analysis of the R value accurately helped in determining the damage evaluation, thus, it can be regarded as one of the precursors of the imminent failure of coal. With R > 1, the specimen is closed to the failure state, thereby dangerous regions are identified with a dense concentration of R > 1 events. The obtained R value index through on-site AE and EME monitoring corresponds closely with the stress distribution cloud map of the roadway. It is inferred that the anti-interference ability and the reliability of the R value index are stronger than the routine early warning indicators of the single-AE or EME energy.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89912108","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 : 2022-09-05DOI: 10.3390/foundations2030050
K. A. Lazopoulos
Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the Λ-fractional derivative conforms to all prerequisites demanded by differential topology. Hence, the various mathematical forms, including those derivatives, do not lack the mathematical accuracy or defects of the well-known fractional derivatives. A summary of the Λ-fractional analysis is presented with its influence on the sources of differential equations, such as fractional differential geometry, field theorems, and calculus of variations. Λ-fractional ordinary and partial differential equations will be discussed.
{"title":"On Λ-Fractional Differential Equations","authors":"K. A. Lazopoulos","doi":"10.3390/foundations2030050","DOIUrl":"https://doi.org/10.3390/foundations2030050","url":null,"abstract":"Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the Λ-fractional derivative conforms to all prerequisites demanded by differential topology. Hence, the various mathematical forms, including those derivatives, do not lack the mathematical accuracy or defects of the well-known fractional derivatives. A summary of the Λ-fractional analysis is presented with its influence on the sources of differential equations, such as fractional differential geometry, field theorems, and calculus of variations. Λ-fractional ordinary and partial differential equations will be discussed.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78455781","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 : 2022-08-23DOI: 10.3390/foundations2030048
R. Agarwal, H. Al-Hutami, B. Ahmad, Boshra Alharbi
This article is concerned with the study of a new class of hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals of different orders with a nonlocal q-integro-initial condition. An existence result for the given problem is obtained by means of Krasnoselskii’s fixed point theorem, whereas the uniqueness of its solutions is shown by applying the Banach contraction mapping principle. We also discuss the stability of solutions of the problem at hand and find that it depends on the nonlocal parameter in contrast to the initial position of the domain. To demonstrate the application of the obtained results, examples are constructed.
{"title":"Existence and Stability Results for Fractional Hybrid q-Difference Equations with q-Integro-Initial Condition","authors":"R. Agarwal, H. Al-Hutami, B. Ahmad, Boshra Alharbi","doi":"10.3390/foundations2030048","DOIUrl":"https://doi.org/10.3390/foundations2030048","url":null,"abstract":"This article is concerned with the study of a new class of hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals of different orders with a nonlocal q-integro-initial condition. An existence result for the given problem is obtained by means of Krasnoselskii’s fixed point theorem, whereas the uniqueness of its solutions is shown by applying the Banach contraction mapping principle. We also discuss the stability of solutions of the problem at hand and find that it depends on the nonlocal parameter in contrast to the initial position of the domain. To demonstrate the application of the obtained results, examples are constructed.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84573373","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 : 2022-08-19DOI: 10.3390/foundations2030047
E. Oks
In one of our previous papers, we performed a comparative analysis of the experimental and theoretical cross-sections for the excitation of atomic hydrogen by electrons. We found that the theoretical ratio of the cross-section σ2s of the excitation of the state 2s to the cross-section σ2p of the excitation of the state 2p was systematically higher than the corresponding experimental ratio by about 20% (far beyond the experimental error margins). We showed that this discrepancy can be due to the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental gas and that the share of the SFHA in the mixture, required for removing this discrepancy, was about the same as the share of the usual hydrogen atoms. The theory behind the SFHA was based on the standard quantum mechanics—on the second solution of the Dirac equation for hydrogen atoms—and on the experimental fact that the charge distribution inside the proton has the peak at the center of the proton; the term “flavor” was used by the analogy with flavors of quarks. In the present paper, we used the same guiding principles, as employed in that previous study, for the comparative analysis of the experimental and theoretical cross-sections for the excitation of molecular hydrogen by electrons. We found that presumably the most sophisticated calculations, using the convergent close-coupling method involving 491 states, very significantly underestimate the corresponding experimental cross-sections for the two lowest stable triplet states. We showed that if in some hydrogen molecules one or both atoms would be the SFHA, then the above very significant discrepancy could be eliminated. We estimated that it would take such unusual hydrogen molecules to be represented in the experimental gas by the share of about 0.26. This is just by about 40% smaller than the share 0.45 of the SFHA deduced in our previous analysis of the experiment on the electron impact excitation of hydrogen atoms (rather than hydrogen molecules). It should be emphasized that from the theoretical point of view, the share of the unusual hydrogen molecules in any experimental gas and the share of the unusual hydrogen atoms (SFHA) in any experimental gas should not be expected to coincide (it would be the comparison of “apples to oranges”, rather than “apples to apples”). In addition, given the roughness of the above estimates, we can state that the results of the present paper reinforce the main conclusion of our previous papers of the very significant share of the SFHA in the experimental hydrogen gases. Thus, the experiments on the electron impact excitation of hydrogen molecules are the fourth type of atomic experiments that proved the existence of the SFHA.
{"title":"Experiments on the Electron Impact Excitation of Hydrogen Molecules Indicate the Presence of the Second Flavor of Hydrogen Atoms","authors":"E. Oks","doi":"10.3390/foundations2030047","DOIUrl":"https://doi.org/10.3390/foundations2030047","url":null,"abstract":"In one of our previous papers, we performed a comparative analysis of the experimental and theoretical cross-sections for the excitation of atomic hydrogen by electrons. We found that the theoretical ratio of the cross-section σ2s of the excitation of the state 2s to the cross-section σ2p of the excitation of the state 2p was systematically higher than the corresponding experimental ratio by about 20% (far beyond the experimental error margins). We showed that this discrepancy can be due to the presence of the Second Flavor of Hydrogen Atoms (SFHA) in the experimental gas and that the share of the SFHA in the mixture, required for removing this discrepancy, was about the same as the share of the usual hydrogen atoms. The theory behind the SFHA was based on the standard quantum mechanics—on the second solution of the Dirac equation for hydrogen atoms—and on the experimental fact that the charge distribution inside the proton has the peak at the center of the proton; the term “flavor” was used by the analogy with flavors of quarks. In the present paper, we used the same guiding principles, as employed in that previous study, for the comparative analysis of the experimental and theoretical cross-sections for the excitation of molecular hydrogen by electrons. We found that presumably the most sophisticated calculations, using the convergent close-coupling method involving 491 states, very significantly underestimate the corresponding experimental cross-sections for the two lowest stable triplet states. We showed that if in some hydrogen molecules one or both atoms would be the SFHA, then the above very significant discrepancy could be eliminated. We estimated that it would take such unusual hydrogen molecules to be represented in the experimental gas by the share of about 0.26. This is just by about 40% smaller than the share 0.45 of the SFHA deduced in our previous analysis of the experiment on the electron impact excitation of hydrogen atoms (rather than hydrogen molecules). It should be emphasized that from the theoretical point of view, the share of the unusual hydrogen molecules in any experimental gas and the share of the unusual hydrogen atoms (SFHA) in any experimental gas should not be expected to coincide (it would be the comparison of “apples to oranges”, rather than “apples to apples”). In addition, given the roughness of the above estimates, we can state that the results of the present paper reinforce the main conclusion of our previous papers of the very significant share of the SFHA in the experimental hydrogen gases. Thus, the experiments on the electron impact excitation of hydrogen molecules are the fourth type of atomic experiments that proved the existence of the SFHA.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79039317","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 : 2022-08-19DOI: 10.3390/foundations2030046
S. Ntouyas, B. Ahmad, J. Tariboon
In the present research, single and multi-valued (k,ψ)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel’skiĭ fixed point theorems as well as the Leray–Schauder nonlinear alternative were used to establish the existence and uniqueness results. In the multi-valued case, when the right-hand side of the inclusion has convex values, we established an existence result via the Leray–Schauder nonlinear alternative method for multi-valued maps, while the second existence result, dealing with the non-convex valued right-hand side of the inclusion, was obtained by applying Covitz-Nadler fixed point theorem for multi-valued contractions. The obtained theoretical results are well illustrated by the numerical examples provided.
{"title":"Nonlocal Boundary Value Problems for (k,ψ)-Hilfer Fractional Differential Equations and Inclusions","authors":"S. Ntouyas, B. Ahmad, J. Tariboon","doi":"10.3390/foundations2030046","DOIUrl":"https://doi.org/10.3390/foundations2030046","url":null,"abstract":"In the present research, single and multi-valued (k,ψ)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel’skiĭ fixed point theorems as well as the Leray–Schauder nonlinear alternative were used to establish the existence and uniqueness results. In the multi-valued case, when the right-hand side of the inclusion has convex values, we established an existence result via the Leray–Schauder nonlinear alternative method for multi-valued maps, while the second existence result, dealing with the non-convex valued right-hand side of the inclusion, was obtained by applying Covitz-Nadler fixed point theorem for multi-valued contractions. The obtained theoretical results are well illustrated by the numerical examples provided.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82194583","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 : 2022-08-17DOI: 10.3390/foundations2030045
J. Nieto-Villar, R. Mansilla
From the perspectives of the thermodynamics of irreversible processes and the theory of complex systems, a characterization of longevity and aging and their relationships with the emergence and evolution of cancer was carried out. It was found that: (1) the rate of entropy production could be used as an index of the robustness, plasticity, and aggressiveness of cancer, as well as a measure of biological age; (2) the aging process, as well as the evolution of cancer, goes through what we call a “biological phase transition”; (3) the process of metastasis, which occurs during the epithelial–mesenchymal transition (EMT), appears to be a phase transition that is far from thermodynamic equilibrium and exhibits Shilnikov chaos-like dynamic behavior, which guarantees the robustness of the process and, in turn, its unpredictability; (4) as the ferroptosis process progresses, the complexity of the dynamics that are associated with the emergence and evolution of cancer decreases. The theoretical framework that was developed in this study could contribute to a better understanding of the biophysical and chemical phenomena of longevity and aging and their relationships with cancer.
{"title":"Longevity, Aging and Cancer: Thermodynamics and Complexity","authors":"J. Nieto-Villar, R. Mansilla","doi":"10.3390/foundations2030045","DOIUrl":"https://doi.org/10.3390/foundations2030045","url":null,"abstract":"From the perspectives of the thermodynamics of irreversible processes and the theory of complex systems, a characterization of longevity and aging and their relationships with the emergence and evolution of cancer was carried out. It was found that: (1) the rate of entropy production could be used as an index of the robustness, plasticity, and aggressiveness of cancer, as well as a measure of biological age; (2) the aging process, as well as the evolution of cancer, goes through what we call a “biological phase transition”; (3) the process of metastasis, which occurs during the epithelial–mesenchymal transition (EMT), appears to be a phase transition that is far from thermodynamic equilibrium and exhibits Shilnikov chaos-like dynamic behavior, which guarantees the robustness of the process and, in turn, its unpredictability; (4) as the ferroptosis process progresses, the complexity of the dynamics that are associated with the emergence and evolution of cancer decreases. The theoretical framework that was developed in this study could contribute to a better understanding of the biophysical and chemical phenomena of longevity and aging and their relationships with cancer.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82300785","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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