We've had smallest number of sunspots in this cycle since Cycle 14
This cycle reached its maximum solar activity in February of 1906
Low solar activity can lead to extended periods of cooling, researchers say
By ELLIE ZOLFAGHARIFARD FOR DAILYMAIL.COM
PUBLISHED: 19:02 GMT, 12 February 2016 | UPDATED: 20:25 GMT, 12 February 2016
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The sun is in the midst of its quietest period in more than a century.
Several days ago, it was in 'cue ball' mode, with an incredible image from Nasa showing no large visible sunspots seen on its surface.
Astronomers say this isn't unusual, and solar activity waxes and wanes in 11-year cycles, and we're currently in Cycle 24, which began in 2008.
However, if the current trend continues, then the Earth could be headed for a 'mini ice age' researchers have warned.
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The sun is in the midst of its quietest period in more than a century. Several days ago, it was in 'cue ball' mode, with an incredible image from Nasa showing no large visible sunspots seen on its surface
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The sun is in the midst of its quietest period in more than a century. Several days ago, it was in 'cue ball' mode, with an incredible image from Nasa showing no large visible sunspots seen on its surface
THE SOLAR CYCLE
Conventional wisdom holds that solar activity swings back and forth like a simple pendulum.
At one end of the cycle, there is a quiet time with few sunspots and flares.
At the other end, solar max brings high sunspot numbers and frequent solar storms.
It's a regular rhythm that repeats every 11 years.
Reality is more complicated.
Astronomers have been counting sunspots for centuries, and they have seen that the solar cycle is not perfectly regular.
We've had the smallest number of sunspots in this cycle since Cycle 14, which reached its maximum in February of 1906.
'With no sunspots actively flaring, the sun's X-ray output has flatlined,' wrote Vencore Weather.
'The number of nearly or completely spotless days should increase over the next few years as we continue to move away from the solar maximum phase of cycle 24 and approach the next solar minimum phase and the beginning of solar cycle 25.'
'The current level of activity of solar cycle 24 seems close to that of solar cycle number 5, which occurred beginning in May 1798 and ending in December 1810,' added an analysis by Watts Up With That.
The previous solar cycle, Solar Cycle 23, peaked in 2000-2002 with many furious solar storms.
During Solar Max, huge sunspots and intense solar flares are a daily occurrence. Auroras appear in Florida. Radiation storms knock out satellites.
The last such episode took place in the years around 2000-2001.
During Solar Minimum, the opposite occurs. Solar flares are almost non-existent while whole weeks go by without a single, tiny sunspot to break the monotony of the blank sun. This is what we are experiencing now.
NASA footage captures biggest solar flare of the year (related)
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The most recent image of our sun, taken this week, shows just a few sunspots (the top right dark freckles on the sun's surface). We've had the smallest number of sunspots in this cycle since Cycle 14, which reached its maximum in February of 1906
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The most recent image of our sun, taken this week, shows just a few sunspots (the top right dark freckles on the sun's surface). We've had the smallest number of sunspots in this cycle since Cycle 14, which reached its maximum in February of 1906
THE MAUNDER MINIMUM
Maunder Minimum (also known as the prolonged sunspot minimum) is the name used for the period starting in about 1645 and continuing to about 1715 when sunspots became exceedingly rare, as noted by solar observers of the time
Maunder Minimum (also known as the prolonged sunspot minimum) is the name used for the period starting in about 1645 and continuing to about 1715 when sunspots became exceedingly rare, as noted by solar observers of the time
The Maunder Minimum (also known as the prolonged sunspot minimum) is the name used for the period starting in about 1645 and continuing to about 1715 when sunspots became exceedingly rare, as noted by solar observers of the time.
It caused London's River Thames to freeze over, and 'frost fairs' became popular.
This period of solar inactivity also corresponds to a climatic period called the 'Little Ice Age' when rivers that are normally ice-free froze and snow fields remained year-round at lower altitudes.
There is evidence that the Sun has had similar periods of inactivity in the more distant past, Nasa says.
The connection between solar activity and terrestrial climate is an area of on-going research.
Some scientists hypothesize that the dense wood used in Stradivarius instruments was caused by slow tree growth during the cooler period.
Instrument maker Antonio Stradivari was born a year before the start of the Maunder Minimum.
The longest minimum on record, the Maunder Minimum of 1645-1715, lasted an incredible 70 years.
During this period, sunspots were rarely observed and the solar cycle seemed to have broken down completely.
The period of quiet coincided with the Little Ice Age, a series of extraordinarily bitter winters in Earth's northern hemisphere.
Many researchers are convinced that low solar activity, acting in concert with increased volcanism and possible changes in ocean current patterns, played a role in that 17th century cooling.
A study last year claimed to have cracked predicting solar cycles - and says that between 2020 and 2030 solar cycles will cancel each other out.
This, they say, will lead to another 'Maunder minimum' - which has previously been known as a mini ice age when it hit between 1646 and 1715.
The model of the sun's solar cycle produced unprecedentedly accurate predictions of irregularities within the sun's 11-year heartbeat.
Animation of the TVLM 513-46546 magnetic field
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Show here is a plot of the monthly sunspot number so far for the current cycle (red line) compared to the mean solar cycle (blue line) and the similar solar cycle no. 5 (black)
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Show here is a plot of the monthly sunspot number so far for the current cycle (red line) compared to the mean solar cycle (blue line) and the similar solar cycle no. 5 (black)
The Frozen Thames, 1677 - an oil painting by Abraham Hondius shows the old London Bridge during the Maunder Minimum
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The Frozen Thames, 1677 - an oil painting by Abraham Hondius shows the old London Bridge during the Maunder Minimum
It draws on dynamo effects in two layers of the sun, one close to the surface and one deep within its convection zone.
Predictions from the model suggest that solar activity will fall by 60 per cent during the 2030s to conditions last seen during the 'mini ice age' that began in 1645, according to the results presented by Prof Valentina Zharkova at the National Astronomy Meeting in Llandudno.
The model predicts that the pair of waves become increasingly offset during Cycle 25, which peaks in 2022.
During Cycle 26, which covers the decade from 2030-2040, the two waves will become exactly out of synch and this will cause a significant reduction in solar activity.
'In cycle 26, the two waves exactly mirror each other – peaking at the same time but in opposite hemispheres of the Sun,' said Zharkova.
'Their interaction will be disruptive, or they will nearly cancel each other.
'We predict that this will lead to the properties of a 'Maunder minimum'.
Solar Flares: See the sun as you've never seen it before
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Montage of images of solar activity between August 1991 and September 2001 taken by the Yohkoh Soft X-ray Telecope, showing variation in solar activity during a sunspot cycle
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Montage of images of solar activity between August 1991 and September 2001 taken by the Yohkoh Soft X-ray Telecope, showing variation in solar activity during a sunspot cycle
Read more:
www.vencoreweath...
Read more: http://www.dailymail.co.uk/sciencetech/article-3444633/What-happened-sun-Solar-activity-remains-quietest-century-trigger-mini-ice-age.html#ixzz4061UJ79G
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http://www.dailymail.co.uk/sciencetech/article-3444633/What-happened-sun-Solar-activity-remains-quietest-century-trigger-mini-ice-age.html
Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics\\
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
\date{\today}
\maketitle
{\bf Abstract: } In this announcement, we shall introduce the zero division $z/0=0$. The result is a definite one and it is fundamental in mathematics.
\bigskip
\section{Introduction}
%\label{sect1}
By a natural extension of the fractions
\begin{equation}
\frac{b}{a}
\end{equation}
for any complex numbers $a$ and $b$, we, recently, found the surprising result, for any complex number $b$
\begin{equation}
\frac{b}{0}=0,
\end{equation}
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices, and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers. The result is a very special case for general fractional functions in \cite{cs}.
The division by zero has a long and mysterious story over the world (see, for example, google site with division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei, Takahasi (\cite{taka}) (see also \cite{kmsy}) established a simple and decisive interpretation (1.2) by analyzing some full extensions of fractions and by showing the complete characterization for the property (1.2). His result will show that our mathematics says that the result (1.2) should be accepted as a natural one:
\bigskip
{\bf Proposition. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ such that
$$
F (b, a)F (c, d)= F (bc, ad)
$$
for all
$$
a, b, c, d \in {\bf C }
$$
and
$$
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
$$
Then, we obtain, for any $b \in {\bf C } $
$$
F (b, 0) = 0.
$$
}
\medskip
\section{What are the fractions $ b/a$?}
For many mathematicians, the division $b/a$ will be considered as the inverse of product;
that is, the fraction
\begin{equation}
\frac{b}{a}
\end{equation}
is defined as the solution of the equation
\begin{equation}
a\cdot x= b.
\end{equation}
The idea and the equation (2.2) show that the division by zero is impossible, with a strong conclusion. Meanwhile, the problem has been a long and old question:
As a typical example of the division by zero, we shall recall the fundamental law by Newton:
\begin{equation}
F = G \frac{m_1 m_2}{r^2}
\end{equation}
for two masses $m_1, m_2$ with a distance $r$ and for a constant $G$. Of course,
\begin{equation}
\lim_{r \to +0} F =\infty,
\end{equation}
however, in our fraction
\begin{equation}
F = G \frac{m_1 m_2}{0} = 0.
\end{equation}
\medskip
Now, we shall introduce an another approach. The division $b/a$ may be defined {\bf independently of the product}. Indeed, in Japan, the division $b/a$ ; $b$ {\bf raru} $a$ ({\bf jozan}) is defined as how many $a$ exists in $b$, this idea comes from subtraction $a$ repeatedly. (Meanwhile, product comes from addition).
In Japanese language for "division", there exists such a concept independently of product.
H. Michiwaki and his 6 years old girl said for the result $ 100/0=0$ that the result is clear, from the meaning of the fractions independently the concept of product and they said:
$100/0=0$ does not mean that $100= 0 \times 0$. Meanwhile, many mathematicians had a confusion for the result.
Her understanding is reasonable and may be acceptable:
$100/2=50 \quad$ will mean that we divide 100 by 2, then each will have 50.
$100/10=10 \quad$ will mean that we divide 100 by10, then each will have 10.
$100/0=0 \quad$ will mean that we do not divide 100, and then nobody will have at all and so 0.
Furthermore, she said then the rest is 100; that is, mathematically;
$$
100 = 0\cdot 0 + 100.
$$
Now, all the mathematicians may accept the division by zero $100/0=0$ with natural feelings as a trivial one?
\medskip
For simplicity, we shall consider the numbers on non-negative real numbers. We wish to define the division (or fraction) $b/a$ following the usual procedure for its calculation, however, we have to take care for the division by zero:
The first principle, for example, for $100/2 $ we shall consider it as follows:
$$
100-2-2-2-,...,-2.
$$
How may times can we subtract $2$? At this case, it is 50 times and so, the fraction is $50$.
The second case, for example, for $3/2$ we shall consider it as follows:
$$
3 - 2 = 1
$$
and the rest (remainder) is $1$, and for the rest $1$, we multiple $10$,
then we consider similarly as follows:
$$
10-2-2-2-2-2=0.
$$
Therefore $10/2=5$ and so we define as follows:
$$
\frac{3}{2} =1 + 0.5 = 1.5.
$$
By these procedures, for $a \ne 0$ we can define the fraction $b/a$, usually. Here we do not need the concept of product. Except the zero division, all the results for fractions are valid and accepted.
Now, we shall consider the zero division, for example, $100/0$. Since
$$
100 - 0 = 100,
$$
that is, by the subtraction $100 - 0$, 100 does not decrease, so we can not say we subtract any from $100$. Therefore, the subtract number should be understood as zero; that is,
$$
\frac{100}{0} = 0.
$$
We can understand this: the division by $0$ means that it does not divide $100$ and so, the result is $0$.
Similarly, we can see that
$$
\frac{0}{0} =0.
$$
As a conclusion, we should define the zero divison as, for any $b$
$$
\frac{b}{0} =0.
$$
See \cite{kmsy} for the details.
\medskip
\section{In complex analysis}
We thus should consider, for any complex number $b$, as (1.2);
that is, for the mapping
\begin{equation}
w = \frac{1}{z},
\end{equation}
the image of $z=0$ is $w=0$. 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.
However, we shall recall the elementary function
\begin{equation}
W(z) = \exp \frac{1}{z}
\end{equation}
$$
= 1 + \frac{1}{1! z} + \frac{1}{2! z^2} + \frac{1}{3! z^3} + \cdot \cdot \cdot .
$$
The function has an essential singularity around the origin. When we consider (1.2), meanwhile, surprisingly enough, we have:
\begin{equation}
W(0) = 1.
\end{equation}
{\bf The point at infinity is not a number} and so we will not be able to consider the function (3.2) at the zero point $z = 0$, meanwhile, we can consider the value $1$ as in (3.3) at the zero point $z = 0$. How do we consider these situations?
In the famous standard textbook on Complex Analysis, L. V. Ahlfors (\cite{ahlfors}) introduced the point at infinity as a number and the Riemann sphere model as well known, however, our interpretation will be suitable as a number. We will not be able to accept the point at infinity as a number.
As a typical result, we can derive the surprising result: {\it At an isolated singular point of an analytic function, it takes a definite value }{\bf with a natural meaning.} As the important applications for this result, the extension formula of functions with analytic parameters may be obtained and singular integrals may be interpretated with the division by zero, naturally (\cite{msty}).
\bigskip
\section{Conclusion}
The division by zero $b/0=0$ is possible and the result is naturally determined, uniquely.
The result does not contradict with the present mathematics - however, in complex analysis, we need only to change a little presentation for the pole; not essentially, because we did not consider the division by zero, essentially.
The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by {\it the method of Michiwaki} in the elementary school, even.
Should we teach the beautiful fact, widely?:
For the elementary graph of the fundamental function
$$
y = f(x) = \frac{1}{x},
$$
$$
f(0) = 0.
$$
The result is applicable widely and will give a new understanding for the universe ({\bf Announcement 166}).
\medskip
If the division by zero $b/0=0$ is not introduced, then it seems that mathematics is incomplete in a sense, and by the intoduction of the division by zero, mathematics will become complete in a sense and perfectly beautiful.
\bigskip
section{Remarks}
For the procedure of the developing of the division by zero and for some general ideas on the division by zero, we presented the following announcements in Japanese:
\medskip
{\bf Announcement 148} (2014.2.12): $100/0=0, 0/0=0$ -- by a natural extension of fractions -- A wish of the God
\medskip
{\bf Announcement 154} (2014.4.22): A new world: division by zero, a curious world, a new idea
\medskip
{\bf Announcement 157} (2014.5.8): We wish to know the idea of the God for the division by zero; why the infinity and zero point are coincident?
\medskip
{\bf Announcement 161} (2014.5.30): Learning from the division by zero, sprits of mathematics and of looking for the truth
\medskip
{\bf Announcement 163} (2014.6.17): The division by zero, an extremely pleasant mathematics - shall we look for the pleasant division by zero: a proposal for a fun club looking for the division by zero.
\medskip
{\bf Announcement 166} (2014.6.29): New general ideas for the universe from the viewpoint of the division by zero
\medskip
{\bf Announcement 171} (2014.7.30): The meanings of product and division -- The division by zero is trivial from the own sense of the division independently of the concept of product
\medskip
{\bf Announcement 176} (2014.8.9): Should be changed the education of the division by zero
\bigskip
\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{kmsy}
S. Koshiba, H. Michiwaki, S. Saitoh and M. Yamane,
An interpretation of the division by zero z/0=0 without the concept of product
(note).
\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. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{msty}
H. Michiwaki, S. Saitoh, M. Takagi and M. Yamada,
A new concept for the point at infinity and the division by zero z/0=0
(note).
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95. http://www.scirp.org/journal/ALAMT/
\bibitem{taka}
S.-E. Takahasi,
{On the identities $100/0=0$ and $ 0/0=0$}
(note).
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operators on the real and complex fields. (submitted)
\end{thebibliography}
\end{document}
アインシュタインも解決できなかった「ゼロで割る」問題
http://matome.naver.jp/odai/2135710882669605901
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.
https://notevenpast.org/dividing-nothing/
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。
1423793753.460.341866474681。
Einstein's Only Mistake: Division by Zero
http://refully.blogspot.jp/2012/05/einsteins-only-mistake-division-by-zero.html
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