Pub Date : 2023-03-09DOI: 10.3390/foundations3010011
P. Kärenlampi
Multiannual growth systems are modeled in generic terms and investigated using partial derivatives and Lagrange multipliers. Grown stock density and temperature sum are used as independent variables. Estate capitalization increases continuously with grown stock and temperature sum, whereas capital return rate and gross profit rate reach a maximum with respect to grown stock. As two restrictions are applied simultaneously, the results mostly but not always follow intuition. The derivative of capital return rate with respect to gross profit rate is positive, and negative with respect to capitalization. The derivative of capitalization with respect to capital return rate shows some positive values, as well as that with respect to gross profit rate. The derivative of the gross profit rate is positive with respect to both capitalization and capital return rate. The results indicate a variety of alternative strategies, which may or may not be multiobjective.
{"title":"Lagrangians of Multiannual Growth Systems","authors":"P. Kärenlampi","doi":"10.3390/foundations3010011","DOIUrl":"https://doi.org/10.3390/foundations3010011","url":null,"abstract":"Multiannual growth systems are modeled in generic terms and investigated using partial derivatives and Lagrange multipliers. Grown stock density and temperature sum are used as independent variables. Estate capitalization increases continuously with grown stock and temperature sum, whereas capital return rate and gross profit rate reach a maximum with respect to grown stock. As two restrictions are applied simultaneously, the results mostly but not always follow intuition. The derivative of capital return rate with respect to gross profit rate is positive, and negative with respect to capitalization. The derivative of capitalization with respect to capital return rate shows some positive values, as well as that with respect to gross profit rate. The derivative of the gross profit rate is positive with respect to both capitalization and capital return rate. The results indicate a variety of alternative strategies, which may or may not be multiobjective.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78865192","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 : 2023-02-23DOI: 10.3390/foundations3010010
Iván Lechuga, Karo Michaelian
Theories on life’s origin generally acknowledge the advantage of a semi-permeable vesicle (protocell) for enhancing the chemical reaction–diffusion processes involved in abiogenesis. However, more and more evidence indicates that the origin of life is concerned with the photo-chemical dissipative structuring of the fundamental molecules under soft UV-C light (245–275 nm). In this paper, we analyze the Mie UV scattering properties of such a vesicle created with long-chain fatty acids. We find that the vesicle could have provided early life with a shield from the faint but destructive hard UV-C ionizing light (180–210 nm) that probably bathed Earth’s surface from before the origin of life and at least until 1200 million years after, until the formation of a protective ozone layer as a result of the evolution of oxygenic photosynthesis.
{"title":"Fatty Acid Vesicles as Hard UV-C Shields for Early Life","authors":"Iván Lechuga, Karo Michaelian","doi":"10.3390/foundations3010010","DOIUrl":"https://doi.org/10.3390/foundations3010010","url":null,"abstract":"Theories on life’s origin generally acknowledge the advantage of a semi-permeable vesicle (protocell) for enhancing the chemical reaction–diffusion processes involved in abiogenesis. However, more and more evidence indicates that the origin of life is concerned with the photo-chemical dissipative structuring of the fundamental molecules under soft UV-C light (245–275 nm). In this paper, we analyze the Mie UV scattering properties of such a vesicle created with long-chain fatty acids. We find that the vesicle could have provided early life with a shield from the faint but destructive hard UV-C ionizing light (180–210 nm) that probably bathed Earth’s surface from before the origin of life and at least until 1200 million years after, until the formation of a protective ozone layer as a result of the evolution of oxygenic photosynthesis.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136173866","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 : 2023-02-21DOI: 10.3390/foundations3010009
I. Argyros, Gagan Deep, Samundra Regmi
In this study, we present a convergence analysis of a Newton-like midpoint method for solving nonlinear equations in a Banach space setting. The semilocal convergence is analyzed in two different ways. The first one is shown by replacing the existing conditions with weaker and tighter continuity conditions, thereby enhancing its applicability. The second one uses more general ω-continuity conditions and the majorizing principle. This approach includes only the first order Fréchet derivative and is applicable for problems that were otherwise hard to solve by using approaches seen in the literature. Moreover, the local convergence is established along with the existence and uniqueness region of the solution. The method is useful for solving Engineering and Applied Science problems. The paper ends with numerical examples that show the applicability of our convergence theorems in cases not covered in earlier studies.
{"title":"Extended Newton-like Midpoint Method for Solving Equations in Banach Space","authors":"I. Argyros, Gagan Deep, Samundra Regmi","doi":"10.3390/foundations3010009","DOIUrl":"https://doi.org/10.3390/foundations3010009","url":null,"abstract":"In this study, we present a convergence analysis of a Newton-like midpoint method for solving nonlinear equations in a Banach space setting. The semilocal convergence is analyzed in two different ways. The first one is shown by replacing the existing conditions with weaker and tighter continuity conditions, thereby enhancing its applicability. The second one uses more general ω-continuity conditions and the majorizing principle. This approach includes only the first order Fréchet derivative and is applicable for problems that were otherwise hard to solve by using approaches seen in the literature. Moreover, the local convergence is established along with the existence and uniqueness region of the solution. The method is useful for solving Engineering and Applied Science problems. The paper ends with numerical examples that show the applicability of our convergence theorems in cases not covered in earlier studies.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89390901","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 : 2023-02-16DOI: 10.3390/foundations3010008
V. Verdoliva, M. Saviano, S. De Luca
Zeolites, both natural and synthetic, are certainly some of the most versatile minerals for their applications. Since the 1940s, they have been used in the chemical industry as catalysts, adsorbents and ion exchanger extensively, and the development of their practical usage is expected to continue upon years. Their versatility is the result of the combination of peculiar and indispensable properties, each of which can be found in other material as a single property, but seldom all of them are found in combination. However, despite the success of their employment, the mechanisms of many important catalytic processes involving zeolites remained elusive. In particular, the comprehension of the structure–property relationships for emerging applications are highly required. In this perspective article we focus on the role of zeolites as solid acid-base catalysts. We go deeply into the structural properties of the LTA kind (Zeolite-Na A 4 Ångstrom) that was successfully employed as basic catalyst for several nucleophilic substitution reactions.
沸石，无论是天然的还是合成的，都是用途最广泛的矿物之一。自20世纪40年代以来，它们在化学工业中被广泛用作催化剂、吸附剂和离子交换剂，其实际应用的发展预计将持续数年。它们的多功能性是特殊的和不可或缺的性质组合的结果，其中每一种都可以在其他材料中作为一种特性发现，但很少能全部组合在一起。然而，尽管它们的应用取得了成功，但涉及沸石的许多重要催化过程的机制仍然难以捉摸。特别是，对新兴应用的结构-性质关系的理解是非常必要的。本文重点介绍了沸石作为固体酸碱催化剂的作用。我们深入研究了LTA类(沸石- na 4a Ångstrom)的结构性质，它被成功地用作几个亲核取代反应的基本催化剂。
{"title":"Investigation of the Acid/Basic Sites of Zeolite Trough Some Catalysed Nucleophilic Reactions","authors":"V. Verdoliva, M. Saviano, S. De Luca","doi":"10.3390/foundations3010008","DOIUrl":"https://doi.org/10.3390/foundations3010008","url":null,"abstract":"Zeolites, both natural and synthetic, are certainly some of the most versatile minerals for their applications. Since the 1940s, they have been used in the chemical industry as catalysts, adsorbents and ion exchanger extensively, and the development of their practical usage is expected to continue upon years. Their versatility is the result of the combination of peculiar and indispensable properties, each of which can be found in other material as a single property, but seldom all of them are found in combination. However, despite the success of their employment, the mechanisms of many important catalytic processes involving zeolites remained elusive. In particular, the comprehension of the structure–property relationships for emerging applications are highly required. In this perspective article we focus on the role of zeolites as solid acid-base catalysts. We go deeply into the structural properties of the LTA kind (Zeolite-Na A 4 Ångstrom) that was successfully employed as basic catalyst for several nucleophilic substitution reactions.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80132252","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 : 2023-02-06DOI: 10.3390/foundations3010007
E. Oks
There exists the following paradigm: for interaction potentials U(r) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E > 0 and for E = 0, bound states are considered to be impossible, both in classical and quantum mechanics. In the present paper we break this paradigm. Namely, we demonstrate the existence of bound states of E = 0 in neutron–neutron systems and in neutron–muon systems, specifically when the magnetic moments of the two particles in the pair are parallel to each other. As particular examples, we calculate the root-mean-square size of the bound states of these systems for the values of the lowest admissible values of the angular momentum, and show that it exceeds the neutron radius by an order of magnitude. We also estimate the average kinetic energy and demonstrate that it is nonrelativistic. The corresponding bound states of E = 0 may be called “neutronium” (for the neutron–neutron systems) and “neutron–muonic atoms” (for the neutron–muon systems). We also point out that this physical system possesses higher-than-geometric (i.e., algebraic) symmetry, leading to the approximate conservation of the square of the angular momentum, despite the geometric symmetry being axial. We use this fact for facilitating analytical and numerical calculations.
{"title":"Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems","authors":"E. Oks","doi":"10.3390/foundations3010007","DOIUrl":"https://doi.org/10.3390/foundations3010007","url":null,"abstract":"There exists the following paradigm: for interaction potentials U(r) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E > 0 and for E = 0, bound states are considered to be impossible, both in classical and quantum mechanics. In the present paper we break this paradigm. Namely, we demonstrate the existence of bound states of E = 0 in neutron–neutron systems and in neutron–muon systems, specifically when the magnetic moments of the two particles in the pair are parallel to each other. As particular examples, we calculate the root-mean-square size of the bound states of these systems for the values of the lowest admissible values of the angular momentum, and show that it exceeds the neutron radius by an order of magnitude. We also estimate the average kinetic energy and demonstrate that it is nonrelativistic. The corresponding bound states of E = 0 may be called “neutronium” (for the neutron–neutron systems) and “neutron–muonic atoms” (for the neutron–muon systems). We also point out that this physical system possesses higher-than-geometric (i.e., algebraic) symmetry, leading to the approximate conservation of the square of the angular momentum, despite the geometric symmetry being axial. We use this fact for facilitating analytical and numerical calculations.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"8 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88430540","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 : 2023-01-20DOI: 10.3390/foundations3010006
High-quality academic publishing is built on rigorous peer review [...]
高质量的学术出版建立在严格的同行评审的基础上[…]
{"title":"Acknowledgment to the Reviewers of Foundations in 2022","authors":"","doi":"10.3390/foundations3010006","DOIUrl":"https://doi.org/10.3390/foundations3010006","url":null,"abstract":"High-quality academic publishing is built on rigorous peer review [...]","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87330737","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 : 2023-01-11DOI: 10.3390/foundations3010005
Henok Desalegn Desta, E. Nwaeze, Tadesse Abdi, J. Mijena
In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k,ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.
{"title":"New Generalized Hermite–Hadamard–Mercer’s Type Inequalities Using (k, ψ)-Proportional Fractional Integral Operator","authors":"Henok Desalegn Desta, E. Nwaeze, Tadesse Abdi, J. Mijena","doi":"10.3390/foundations3010005","DOIUrl":"https://doi.org/10.3390/foundations3010005","url":null,"abstract":"In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k,ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85894439","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 : 2023-01-06DOI: 10.3390/foundations3010004
A. El-Sayed, Y. Omar, H. Hashem, S. Al-Issa
This article is devoted to the solvability and the asymptotic stability of a coupled system of a functional integral equation on the real half-axis. Our consideration is located in the space of bounded continuous functions on R+(BC(R+)). The main tool applied in this work is the technique associated with measures of noncompactness in BC(R+) by a given modulus of continuity. Next, we formulate and prove a sufficient condition for the solvability of that coupled system. We, additionally, provide an example and some particular cases to demonstrate the effectiveness and value of our results.
{"title":"Treatment of a Coupled System for Quadratic Functional Integral Equation on the Real Half-Line via Measure of Noncompactness","authors":"A. El-Sayed, Y. Omar, H. Hashem, S. Al-Issa","doi":"10.3390/foundations3010004","DOIUrl":"https://doi.org/10.3390/foundations3010004","url":null,"abstract":"This article is devoted to the solvability and the asymptotic stability of a coupled system of a functional integral equation on the real half-axis. Our consideration is located in the space of bounded continuous functions on R+(BC(R+)). The main tool applied in this work is the technique associated with measures of noncompactness in BC(R+) by a given modulus of continuity. Next, we formulate and prove a sufficient condition for the solvability of that coupled system. We, additionally, provide an example and some particular cases to demonstrate the effectiveness and value of our results.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78394896","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 : 2023-01-06DOI: 10.3390/foundations3010003
G. Deep, I. Argyros
In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given by Traub using divided differences. The first method requires three evaluations of the function and one evaluation of the first derivative, thereby enhancing the efficiency index. In the second method, the computation of a derivative is reduced by approximating it using divided differences. Various numerical experiments are performed which demonstrate the accuracy and efficacy of the proposed methods.
{"title":"Improved Higher Order Compositions for Nonlinear Equations","authors":"G. Deep, I. Argyros","doi":"10.3390/foundations3010003","DOIUrl":"https://doi.org/10.3390/foundations3010003","url":null,"abstract":"In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given by Traub using divided differences. The first method requires three evaluations of the function and one evaluation of the first derivative, thereby enhancing the efficiency index. In the second method, the computation of a derivative is reduced by approximating it using divided differences. Various numerical experiments are performed which demonstrate the accuracy and efficacy of the proposed methods.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74626019","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 : 2023-01-05DOI: 10.3390/foundations3010002
L. Nemes, C. Parigger
This work communicates cavity ring-down spectroscopy (CRDS) of methylidyne (CH) in a chemiluminescent plasma that is produced in a microwave cavity. Of interest are the rotational lines of the 0-0 vibrational transition for the A–X band and the 1-0 vibrational transition for the B–X band. The reported investigations originate from research on the CH radical in 1996, which constituted the first case of applying CRDS to the CH radical. The report also includes a recent analysis that shows excellent agreement of the measured and computed data, and it communicates CH line strength data. The CH radical is an important diatomic molecule in hydrocarbon combustion diagnosis and the analysis of stellar plasma emissions, to name just two examples of analytical plasma chemistry.
{"title":"Methylidyne Cavity Ring-Down Spectroscopy in a Microwave Plasma Discharge","authors":"L. Nemes, C. Parigger","doi":"10.3390/foundations3010002","DOIUrl":"https://doi.org/10.3390/foundations3010002","url":null,"abstract":"This work communicates cavity ring-down spectroscopy (CRDS) of methylidyne (CH) in a chemiluminescent plasma that is produced in a microwave cavity. Of interest are the rotational lines of the 0-0 vibrational transition for the A–X band and the 1-0 vibrational transition for the B–X band. The reported investigations originate from research on the CH radical in 1996, which constituted the first case of applying CRDS to the CH radical. The report also includes a recent analysis that shows excellent agreement of the measured and computed data, and it communicates CH line strength data. The CH radical is an important diatomic molecule in hydrocarbon combustion diagnosis and the analysis of stellar plasma emissions, to name just two examples of analytical plasma chemistry.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86498861","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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