The original online version of this article (Doroszlai, P. and Keller, H. (2022) The Symmetric Series of Multiples of Primes, Advances in Pure Mathematics, Vol. 12, 160-177. http://doi.org/10.4236/apm.2022.123014) unf...The original online version of this article (Doroszlai, P. and Keller, H. (2022) The Symmetric Series of Multiples of Primes, Advances in Pure Mathematics, Vol. 12, 160-177. http://doi.org/10.4236/apm.2022.123014) unfortunately contains some small mistakes. The author discovered the possible problem in Equations (1.6), (1.7) and in the last equation of the proof of lemma 2.3 and the numbering of the chapters 3 and 4 should be changed. To fix the problem, the author wishes to change these equations and titles.展开更多
The original online version of this article (Bibek Baran Nag (2021) An Elementary Proof of Fermat’s Last Theorem for Epsilons, Volume 11(8), 735-740 doi: https://doi.org/10.4236/apm.2021.118048) unfortunately contain...The original online version of this article (Bibek Baran Nag (2021) An Elementary Proof of Fermat’s Last Theorem for Epsilons, Volume 11(8), 735-740 doi: https://doi.org/10.4236/apm.2021.118048) unfortunately contains two typographical mistakes. The author wishes to correct the errors.展开更多
The original online version of this article (Zengyong Liang (2020) Solutions of Indefinite Equations, Volume 10(9), 540-544, doi: https://doi.org/10.4236/apm.2020.109033) unfortunately contains some mistakes. The auth...The original online version of this article (Zengyong Liang (2020) Solutions of Indefinite Equations, Volume 10(9), 540-544, doi: https://doi.org/10.4236/apm.2020.109033) unfortunately contains some mistakes. The author wishes to correct the errors. Sections 5, 6, 7, and 8 are supplemented here.展开更多
考虑方程z^((n))+f_1(t)x^((n-1))+f_2(t)x^((n-2))+……+f_(n-1)(t)x+f_n(t)=0 (1)在现有文献中,对方程(1)的研究几乎能集中在二阶,对于 n>2的情形,很少见到。本文应用变换技巧以及.直接方法,特别利用文[9]的推广了的方法研究了 n ...考虑方程z^((n))+f_1(t)x^((n-1))+f_2(t)x^((n-2))+……+f_(n-1)(t)x+f_n(t)=0 (1)在现有文献中,对方程(1)的研究几乎能集中在二阶,对于 n>2的情形,很少见到。本文应用变换技巧以及.直接方法,特别利用文[9]的推广了的方法研究了 n 为任意正整数的方程(1)的平凡解的稳定性,得到了其平凡解全局一致渐近稳定性的充分条件。特别当 n=2时所得的结果包含了文献[1-8]的有关结果。有些结果就非文[8]的条件所能得到,如本文定理4、5及其推论1。展开更多
Plotinus＇ account of matter in Ennead III 6[26] 11-15 serves two purposes. The terms, evil and ugly, present the negative side of matter＇s causality, providing for the change characteristic of the sensible world and...Plotinus＇ account of matter in Ennead III 6[26] 11-15 serves two purposes. The terms, evil and ugly, present the negative side of matter＇s causality, providing for the change characteristic of the sensible world and the possibility of ontological evil and privation as well as of moral evil among human beings. The receptacle and other images from Plato＇s Timaeus present the positive side of this causality, matter as allowing for the presence of forms in the bodies of the sensible world. Plotinus explicitly articulates the linguistic problem surrounding the nature of matter, since language is derived from the corporeal and thus needs constant correction when applied to matter as incorporeal. His use of language, thus, always has two phases, first, capturing the nature of matter as aptly as possible, and second, highlighting the difference between matter and the image, analogy, or metaphor used to help explain it.展开更多
As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bougue, Euler a...As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bougue, Euler and the Bernoullis. Despite unrelenting efforts institutionally, country-wide and world scale, the field remains relevant and of high focus, combining deep scientific basis with practical and ethical concerns stemming from a continually changing industry and society.展开更多
As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bouguer, Euler ...As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bouguer, Euler and the Bernoullis. Despite unrelenting effort the field remains topical, combining a deep scientific basis with very practical concerns continually coming from new trends in ship design.展开更多
Christopher Janaway＇s recent book on Plato＇s critique of the arts discusses, among other things, Book 10 of the Republic. This paper claims that his comments upon passages in Republic 10 overl Plato＇s ook the Ion a...Christopher Janaway＇s recent book on Plato＇s critique of the arts discusses, among other things, Book 10 of the Republic. This paper claims that his comments upon passages in Republic 10 overl Plato＇s ook the Ion and status of the Republic as itself a work of dramatic mimesis, ignore the dialectical form of the work, and miss that in various dialogues, Plato evinces a high view of poetry and the arts and even envisions a techne poietike. The paper defends these claims by constructing a three-stage argument that Plato holds a high view of poetry： （1） It first sketches an outline of a reading of the Ion as a dialogue that, despite being aporetic, nevertheless points ahead to a Socratic philosophizing that is craft-like and open to divine inspiration, and not only recognizes the value of poetry but also sometimes composes poetry; （2） Then, it discusses Socrates＇ use, in his conversational strategies in the Republic, of the techne of rhetoric described in the Phaedrus; and finally, （3） It considers four arguments against mimetic poetry in Republic 10 （598b8-606d7）, and sketches an interpretation of them that takes issue with Janaway＇s. It argues that they are meant to invite readers to a higher dialectical standpoint, from which might come into view the value of mimetic poetry to a community guided by a Basilike techne展开更多
文摘The original online version of this article (Doroszlai, P. and Keller, H. (2022) The Symmetric Series of Multiples of Primes, Advances in Pure Mathematics, Vol. 12, 160-177. http://doi.org/10.4236/apm.2022.123014) unfortunately contains some small mistakes. The author discovered the possible problem in Equations (1.6), (1.7) and in the last equation of the proof of lemma 2.3 and the numbering of the chapters 3 and 4 should be changed. To fix the problem, the author wishes to change these equations and titles.
文摘The original online version of this article (Bibek Baran Nag (2021) An Elementary Proof of Fermat’s Last Theorem for Epsilons, Volume 11(8), 735-740 doi: https://doi.org/10.4236/apm.2021.118048) unfortunately contains two typographical mistakes. The author wishes to correct the errors.
文摘The original online version of this article (Zengyong Liang (2020) Solutions of Indefinite Equations, Volume 10(9), 540-544, doi: https://doi.org/10.4236/apm.2020.109033) unfortunately contains some mistakes. The author wishes to correct the errors. Sections 5, 6, 7, and 8 are supplemented here.
文摘Plotinus＇ account of matter in Ennead III 6[26] 11-15 serves two purposes. The terms, evil and ugly, present the negative side of matter＇s causality, providing for the change characteristic of the sensible world and the possibility of ontological evil and privation as well as of moral evil among human beings. The receptacle and other images from Plato＇s Timaeus present the positive side of this causality, matter as allowing for the presence of forms in the bodies of the sensible world. Plotinus explicitly articulates the linguistic problem surrounding the nature of matter, since language is derived from the corporeal and thus needs constant correction when applied to matter as incorporeal. His use of language, thus, always has two phases, first, capturing the nature of matter as aptly as possible, and second, highlighting the difference between matter and the image, analogy, or metaphor used to help explain it.
文摘As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bougue, Euler and the Bernoullis. Despite unrelenting efforts institutionally, country-wide and world scale, the field remains relevant and of high focus, combining deep scientific basis with practical and ethical concerns stemming from a continually changing industry and society.
文摘As ancient as Archimedes （circa 250 BC）, the topic of stability of ships （and more generally of floating bodies） has fascinated eminent scientists throughout the centuries, of the likes of Huygens, Bouguer, Euler and the Bernoullis. Despite unrelenting effort the field remains topical, combining a deep scientific basis with very practical concerns continually coming from new trends in ship design.
文摘Christopher Janaway＇s recent book on Plato＇s critique of the arts discusses, among other things, Book 10 of the Republic. This paper claims that his comments upon passages in Republic 10 overl Plato＇s ook the Ion and status of the Republic as itself a work of dramatic mimesis, ignore the dialectical form of the work, and miss that in various dialogues, Plato evinces a high view of poetry and the arts and even envisions a techne poietike. The paper defends these claims by constructing a three-stage argument that Plato holds a high view of poetry： （1） It first sketches an outline of a reading of the Ion as a dialogue that, despite being aporetic, nevertheless points ahead to a Socratic philosophizing that is craft-like and open to divine inspiration, and not only recognizes the value of poetry but also sometimes composes poetry; （2） Then, it discusses Socrates＇ use, in his conversational strategies in the Republic, of the techne of rhetoric described in the Phaedrus; and finally, （3） It considers four arguments against mimetic poetry in Republic 10 （598b8-606d7）, and sketches an interpretation of them that takes issue with Janaway＇s. It argues that they are meant to invite readers to a higher dialectical standpoint, from which might come into view the value of mimetic poetry to a community guided by a Basilike techne
