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揭开宇宙奥秘的“钥匙”
2018-05-30 22:58:00
英国著名理论物理学家斯蒂芬·霍金曾表示：“引力波提供了一种人们看待宇宙的全新方式。（人类）探测到引力波的这种能力，很有可能引发天文学革命。”由此可见，引力波探测对于天文学家和物理学家而言，有着至关重要的意义。
首先，对引力波的研究可以加深物理学家对广义相对论的理解。广义相对论在对一些强引力天体系统的精确描述中，起到关键性的作用。在这些强引力系统中，牛顿力学不再适用，我们只能使用广义相对论来研究它们。通过对引力波的研究，物理学家对广义相对论的理解将更加深入。
其次，借助引力波，可以直接判断某些天文现象的起源和本质。凭借天体辐射出的引力波，天文学家可以判断天体内部的信息。我们知道，传统天文学主要依赖电磁波观测，通过伽玛射线望远镜、X射线望远镜、紫外-可见光-红外望远镜与射电望远镜等，观测天体发出的各波段的电磁波，进而分析这些天体或者天体爆发现象的具体性质。但随着科学研究的发展，此类方法已经无法满足研究的需要。电磁波大多是天体表面发出的，无法提供天体核心的信息。许多天体（如太阳与超新星）内部产生的电磁波本是伽玛射线，但由于不断被自身物质吸收和再发射，到达表面时的光基本上变为紫外线、可见光与红外线，因此电磁波无法用以直接研究并推断天体内部的物理过程。而引力波则截然不同，它是时空本身的波动，所以不会被物质吸收。从天体中心发出之后，它在往外传播的整个过程中，始终保留其本来面目（只是强度随着距离变大而减弱）。当天文学家探测到引力波时，得到的信息几乎完全是天体核心的信息。这一优势是电磁波观测无法具备的。
举个例子，宇宙中有一种持续时间只有几毫秒到几千秒的伽玛射线爆发现象，被称为“伽玛射线暴”，简称“伽玛暴”。伽玛暴又被分为两大类，时间从几毫秒到2秒的是短伽玛暴；2秒以上的被称为长伽玛暴。此前天文学家一直推测短伽玛暴是由中子星与中子星并合或者中子星与黑洞并合而产生的，但并没有直接的观测证据。在2017 年 8 月17日，天文学家探测到引力波之后，很快就能够判定它来自中子星与中子星的并合，而且在探测到引力波之后仅1.7秒，天文学家在同一方位发现一个持续时间约2秒的短伽玛暴，分析表明它与该引力波起源相同。结合这些信息，天文学家首次直接证明：某些短伽玛暴确实由中子星与中子星并合产生。
最后，也是需要特别强调的一点是：对引力波的观测使科学家正式迈入全方位的“多信使天文学”时代。一个天体或是天体爆发事件往往会发出各种类型的信号，比如电磁波、中微子、宇宙射线和引力波等。这些信号带着天体的信息传了过来，因此被称为天文学上的“信使”。如果能够同时接收天体发出的多种此类信号，就是“多信使”探测，对应的天文学就是“多信使天文学”。
引力波与多信使天文学
一些天体爆发之后，有可能同时产生电磁波、宇宙射线、中微子和引力波这4类信使。在这4类信使中，电磁波的观测最早、最成熟也最容易。宇宙射线主要由速度接近光速的高能量质子或电子组成，但它们带电，在宇宙中穿行时，会因为受到磁场作用而产生偏转，因此对于接收到的宇宙射线，研究人员很难判断它们来自何方。
中微子不带电，也可以被作为直指天体本源的重要信使。人类在几十年前才首次探测到来自太阳的中微子。除了太阳的中微子之外，银河系外的中微子也已经被人类探测到，最著名的一次河外中微子爆发是1987年2月在银河系临近的星系“大麦哲伦云”发生的一次壮观的超新星事件（SN 1987A）。根据这些中微子，人们获得了超新星爆发机制的重要信息。
当天体或者天体爆发现象非常遥远时，人们一般只能探测到它们发出的电磁波，但如果它们距离比较近，就很可能探测到它们发出的宇宙射线与中微子。2015年之前，引力波在天文观测中一直缺席，直到人类首次探测到引力波，将多信使天文学中最后一位信使找到，从而完成了多信使天文学的完整拼图。
首次被“看到”的引力波
曾经，天文学家苦苦追寻着引力波；但在探测到引力波之后，天文学家们又不再满足于探测天体发出的引力波。他们更远大的目标是：同时探测到同一个天体发出的引力波和电磁波。由于在黑洞与黑洞并合中，除了产生引力波外，几乎没有其他伴随现象，天文学家就瞄准了双中子星或是中子星和黑洞并合事件。在这类并合事件发生时，不但会发出引力波，还能产生电磁波信号。这些电磁波信号是由中子星碎块引起的。在中子星即将与另一颗中子星或者黑洞并合时，中子星的一部分物质被强大的引力撕裂成碎块。这些被撕碎的中子星的一部分物质会堆积成“吸积盘”，然后回落到中心天体（可能为黑洞，也可能为大质量中子星），与中心天体构成一个“吸积”系统，朝中心天体旋转轴方向喷发喷流。与此同时，喷流内部辐射过程有可能产生伽玛射线暴。
中子星的另一部分碎块则逃逸出去，其质量大约是太阳的千分之一至十分之一（对应于300到3万个地球的质量），在逃逸过程中碎块内部的大量中子衰变为质子，与剩下的其余中子一起，快速形成富含中子的元素，如过渡金属元素（如金、银）、镧系元素（稀土元素）以及锕系元素（如铀、钚）。这些元素中有很多是放射性元素。
逃逸出的中子星碎块中具有放射性的元素会发生裂变、衰变并释放出大量能量，将其加热至通红状态，发出大量红外线、可见光和紫外线，最亮时甚至能够达到“新星”典型亮度的一千倍左右，因此被称为“千新星”或者“巨新星”。1998年，当时正在普林斯顿大学攻读博士学位的李立新（现为北京大学科维里天文与天体物理学研究所教授）与其导师帕钦斯基首次考虑这个过程，并初步计算了千新星的辐射。此后国际上多个小组发展、完善了千新星的理论。
2017年8月17日，LIGO探测到一个新的引力波；1.7秒后，美国宇航局（NASA）的伽玛射线卫星Fermi在同一片天区观测到一个持续约2秒的短伽玛暴。在LIGO和NASA相继发布此次预警之后，全世界超过70台各类望远镜都追踪观测到了这次震撼人心的引力波源，并相继发现了紫外线辐射、可见光辐射、红外线辐射、X射线辐射和射电辐射。
经过分析，天文学家们确认：观测到的引力波、短伽玛暴、红外线辐射、可见光辐射、紫外线辐射和射电辐射，全都来自距离地球1.3亿光年的星系NGC 4993的边缘。这是一次中子星与中子星并合导致的引力波事件。原本天文学家们预期，在2020年左右才有可能发现中子星并合产生的引力波以及伴随的电磁波辐射，因此2017年的这一次探测算是一个意外的惊喜。
经过国际上（特别是美国、欧洲、中国）的多个小组的观测、分析与计算，人们确定这次观测到的红外线、可见光、紫外线辐射来自千新星。这是首次以最直接、最强的证据证实了中子星与中子星并合会形成千新星，也直接证实这种并合过程会形成大量重元素（如金、银、镧系元素、锕系元素，等等）。与此同时，伴随的伽玛射线暴直接证实至少一部分短伽玛暴起源于中子星与中子星并合。
这次意义深远的观测，使人类不仅直接“听”到了引力波，而且还直接“看”到了伴随引力波出现的可见光辐射，首次实现包含引力波与电磁波的多信使观测。2017年10月16日，多国天文机构同步将此新闻向全球公布，这个重大的发现再次震撼了世界，引起无数媒体争相报道。如果不是因为引力波被人类的引力波探测器先探测到，那么这次双中子星并合事件中伴随引力波的可见光辐射（“千新星”辐射）不会受到如此密切的关注，天文学家们也许就此错失了它（它在几天时间内迅速变暗），也就失去首次直接检验千新星与重元素产生机制的机会。正因为引力波的探测表明它来自一个双中子星并合事件，才引发了非常及时的后续观测（1米口径的Swope可见光望远镜在引力波被探测到之后仅约11小时，就首次发现了这个千新星可见光辐射信号）。因此，引力波探测除了自身的极端重要性之外，它本身也像天文学家的预警机，及时报告目标，让天文学家在此后及时采取行动，探测可能伴随的其他种类的辐射。
ゼロ除算の発見は日本です：
∞？？？
∞は定まった数ではない・・・・・
人工知能はゼロ除算ができるでしょうか：
とても興味深く読みました：
ゼロ除算の発見と重要性を指摘した：日本、再生核研究所
ゼロ除算関係論文・本
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 412: The 4th birthday of the division by zero $z/0=0$ \\
(2018.2.2)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
}
\date{\today}
\maketitle
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0=1/0=z/0=0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristotelēs (BC384 - BC322) and Euclid (BC 3 Century - ), and the division by zero is since Brahmagupta (598 - 668 ?).
In particular, Brahmagupta defined as $0/0=0$ in Brāhmasphuṭasiddhānta (628), however, our world history stated that his definition $0/0=0$ is wrong over 1300 years, but, we showed that his definition is suitable.
For the details, see the references and the site: http://okmr.yamatoblog.net/
We wrote a global book manuscript \cite{s18} with 154 pages
and stated in the preface and last section of the manuscript as follows:
\bigskip
{\bf Preface}
\medskip
The division by zero has a long and mysterious story over the world (see, for example, H. G. Romig \cite{romig} and Google site with the division by zero) with its physical viewpoints since the document of zero in India on AD 628. In particular, note that Brahmagupta (598 -668 ?) established the four arithmetic operations by introducing $0$ and at the same time he defined as $0/0=0$ in
Brhmasphuasiddhnta. Our world history, however, stated that his definition $0/0=0$ is wrong over 1300 years, but, we will see that his definition is right and suitable.
The division by zero $1/0=0/0=z/0$ itself will be quite clear and trivial with several natural extensions of the fractions against the mysterously long history, as we can see from the concepts of the Moore-Penrose generalized inverses or the Tikhonov regularization method to the fundamental equation $az=b$, whose solution leads to the definition $z =b/a$.
However, the result (definition) will show that
for the elementary mapping
\begin{equation}
W = \frac{1}{z},
\end{equation}
the image of $z=0$ is $W=0$ ({\bf should be defined from the form}). This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere (\cite{ahlfors}). �As the representation of the point at infinity of the Riemann sphere by the
zero $z = 0$, we will see some delicate relations between $0$ and $\infty$ which show a strong
discontinuity at the point of infinity on the Riemann sphere. We did not consider any value of the elementary function $W =1/ z $ at the origin $z = 0$, because we did not consider the division by zero
$1/ 0$ in a good way. Many and many people consider its value by the limiting like $+\infty $ and $- \infty$ or the
point at infinity as $\infty$. However, their basic idea comes from {\bf continuity} with the common sense or
based on the basic idea of Aristotle. --
For the related Greece philosophy, see \cite{a,b,c}. However, as the division by zero we will consider its value of
the function $W =1 /z$ as zero at $z = 0$. We will see that this new definition is valid widely in
mathematics and mathematical sciences, see (\cite{mos,osm}) for example. Therefore, the division by zero will give great impacts to calculus, Euclidean geometry, analytic geometry, differential equations, complex analysis in the undergraduate level and to our basic ideas for the space and universe.
We have to arrange globally our modern mathematics in our undergraduate level. Our common sense on the division by zero will be wrong, with our basic idea on the space and the universe since Aristotle and Euclid. We would like to show clearly these facts in this book. The content is in the undergraduate level.
\bigskip
\bigskip
{\bf Conclusion}
\medskip
Apparently, the common sense on the division by zero with a long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on derivatives we have a great missing since $\tan (\pi/2) = 0$. Our mathematics is also wrong in elementary mathematics on the division by zero.
This book is an elementary mathematics on our division by zero as the first publication of books for the topics. The contents have wide connections to various fields beyond mathematics. The author expects the readers write some philosophy, papers and essays on the division by zero from this simple source book.
The division by zero theory may be developed and expanded greatly as in the author's conjecture whose break theory was recently given surprisingly and deeply by Professor Qi'an Guan \cite{guan} since 30 years proposed in \cite{s88} (the original is in \cite {s79}).
We have to arrange globally our modern mathematics with our division by zero in our undergraduate level.
We have to change our basic ideas for our space and world.
We have to change globally our textbooks and scientific books on the division by zero.
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{ahlfors}
L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.
\bibitem{cs}
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{guan}
Q. Guan, A proof of Saitoh's conjecture for conjugate Hardy H2 kernels, arXiv:1712.04207.
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{ms16}
T. Matsuura and S. Saitoh,
Matrices and division by zero z/0=0,
Advances in Linear Algebra \& Matrix Theory, {\bf 6}(2016), 51-58
Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt
\\ http://dx.doi.org/10.4236/alamt.2016.62007.
\bibitem{ms18}
T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication)
\bibitem{mms18}
T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.
\bibitem{msy}
H. Michiwaki, S. Saitoh and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. {\bf 6}(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
\bibitem{mos}
H. Michiwaki, H. Okumura and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces,
International Journal of Mathematics and Computation, {\bf 2}8(2017); Issue 1, 2017), 1-16.
\bibitem{osm}
H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), {\bf 1}(2017), 70-77.
\bibitem{os}
H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).
\bibitem{o}
H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.
\bibitem{os18}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
(Submitted for publication).
\bibitem{ps18}
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, Vol. {\bf 3}1, No. 8. (Oct., 1924), pp. 387-389.
\bibitem{s79}
S. Saitoh, The Bergman norm and the Szeg$\ddot{o}$ norm, Trans. Amer. Math. Soc. {\bf 249} (1979), no. 2, 261--279.
\bibitem{s88}
S. Saitoh, Theory of reproducing kernels and its applications. Pitman Research Notes in Mathematics Series, {\bf 189}. Longman Scientific \& Technical, Harlow; copublished in the United States with John Wiley \& Sons, Inc., New York, 1988. x+157 pp. ISBN: 0-582-03564-3
\bibitem{s14}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
\bibitem{s16}
S. Saitoh, A reproducing kernel theory with some general applications,
Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182. (Springer) .
\bibitem{s17}
S. Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM](2017.12.17).
\bibitem{s18}
S. Saitoh, Division by zero calculus (154 pages: draft): （http://okmr.yamatoblog.net/）
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.
\bibitem{a}
https://philosophy.kent.edu/OPA2/sites/default/files/012001.pdf
\bibitem{b}
http://publish.uwo.ca/~jbell/The 20Continuous.pdf
\bibitem{c}
http://www.mathpages.com/home/kmath526/kmath526.htm
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature - an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann281}
Announcement 281 (2016.2.1): The importance of the division by zero $z/0=0$.
\bibitem{ann282}
Announcement 282 (2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.
\bibitem{ann293}
Announcement 293 (2016.3.27): Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.
\bibitem{ann300}
Announcement 300 (2016.05.22): New challenges on the division by zero z/0=0.
\bibitem{ann326}
Announcement 326 (2016.10.17): The division by zero z/0=0 - its impact to human beings through education and research.
\bibitem{ann352}
Announcement 352(2017.2.2): On the third birthday of the division by zero z/0=0.
\bibitem{ann354}
Announcement 354(2017.2.8): What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.
\bibitem{362}
Announcement 362(2017.5.5): Discovery of the division by zero as $0/0=1/0=z/0=0$
\bibitem{380}
Announcement 380 (2017.8.21): What is the zero?
\bibitem{388}
Announcement 388(2017.10.29): Information and ideas on zero and division by zero (a project).
\bibitem{409}
Announcement 409 (2018.1.29.): Various Publication Projects on the Division by Zero.
\bibitem{410}
Announcement 410 (2018.1 30.): What is mathematics? -- beyond logic; for great challengers on the division by zero.
\end{thebibliography}
\end{document}
List of division by zero:
\bibitem{os18}
H. Okumura and S. Saitoh,
Remarks for The Twin Circles of Archimedes in a Skewed Arbelos by H. Okumura and M. Watanabe, Forum Geometricorum.
Saburou Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM]
arXiv:1712.09467 [math.GM]
Hiroshi Okumura and Saburou Saitoh
The Descartes circles theorem and division by zero calculus. ２０１７．１１．１４
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$, Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
T. Matsuura and S. Saitoh,
Matrices and division by zero z/0=0,
Advances in Linear Algebra \& Matrix Theory, 2016, 6, 51-58
Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt
\\ http://dx.doi.org/10.4236/alamt.2016.62007.
T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication).
T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.)
H. Michiwaki, S. Saitoh and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. 6(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
H. Michiwaki, H. Okumura and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces,
International Journal of Mathematics and Computation, 28(2017); Issue 1, 2017), 1-16.
H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), 1(2017), 70-77.
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics).
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
S. Saitoh, A reproducing kernel theory with some general applications,
Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182. (Springer) .
再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12276045402.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12263708422.html
1/0=0、0/0=0、z/0=0
ソクラテス・プラトン・アリストテレス その他
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか
〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか
〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか
再生核研究所声明 411(2018.02.02): ゼロ除算発見4周年を迎えて
ゼロ除算の論文
Mysterious Properties of the Point at Infinity
Mysterious Properties of the Point at Infinity
Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
2018.3.18．午前中 最後の講演： 日本数学会 東大駒場、函数方程式論分科会 講演書画カメラ用 原稿
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.
https://ameblo.jp/syoshinoris/entry-12361744016.html より
The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.
https://ameblo.jp/syoshinoris/entry-12361744016.html より
*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.):
Differential and Difference Equations with Applications:
ICDDEA, Amadora, 2017.
(Springer Proceedings in Mathematics and Statistics, Vol. 230)
May 2018 587 pp.
ゼロ除算の論文が２編、出版になりました：
ICDDEA: International Conference on Differential & Difference Equations and Applications
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
• Editors
• (view affiliations)
• Sandra Pinelas
• Tomás Caraballo
• Peter Kloeden
• John R. Graef
Conference proceedingsICDDEA 2017
log0=log∞=0log0=log∞=0 and Applications
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305
Division by Zero Calculus and Differential Equations
Sandra Pinelas, Saburou Saitoh
Pages 399-418
ICDDEA: International Conference on Differential & Difference Equations and Applications
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
• Editors
• (view affiliations)
• Sandra Pinelas
• Tomás Caraballo
• Peter Kloeden
• John R. Graef
Conference proceedingsICDDEA 2017
log0=log∞=0log0=log∞=0 and Applications
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305
Division by Zero Calculus and Differential Equations
Sandra Pinelas, Saburou Saitoh
Pages 399-418
2 件貼るもの
Message body
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
GLOBAL JOURNAL OF ADVANCED RESEARCH ON CLASSICAL AND MODERN GEOMETRIES” (GJARCMG)(in press).
Hiroshi O. Is It Really Impossible To Divide By Zero?. Biostat Biometrics Open Acc J. 2018; 7(1): 555703. DOI: 10.19080/BBOJ.2018.07.555703
ゼロで分裂するのは本当に不可能ですか？ - Juniper Publishers
1.
Differential and Difference Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
· Editors
· Sandra Pinelas
· Tomás Caraballo
· Peter Kloeden
· John R. Graef
Conference proceedingsICDDEA 2017
Hiroshi Michiwaki, Tsutomu Matuura, Saburou Saitoh
Pages 293-305
Sandra Pinelas, Saburou Saitoh
Pages 399-418
____________________________________________
The International Conference on Applied Physics and Mathematics, Tokyo, Japan, October 22-24, 2018,
John Martin
Program Coordinator
Program Coordinator
http://www.meetingsint.com/conferences/appliedphysics-mathematicsApplied Physics and Mathematics Conference 2018
Mail: appliedphysics@annualmeet.org
Mail: appliedphysics@annualmeet.org
Close the mysterious and long history of division by zero and open the new world since Aristotelēs-Eulcid.
Division by zero is trivial and clear from the concept of repeated subtraction - H. Michiwaki.
Recall the uniqueness theorem by S. Takahasi on the division by zero.
The simple field structure containing division by zero by M. Yamada.
The Yamane phenomena on the multiplication in the viewpoint of division by zero
Applications of the division by zero to Wazan geometry by H. Okumura.
______________________________________
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