1409.0065v1
TRANSCRIPT
The Future Science Institute (Print)
ISSN 2332-1792
The Future Science Institute (Online)
ISSN 2332-1784
Textbook of the Future Science Institute
A teaching guide for exercises, notes and open problems
Tianren Cheng
Volume I 2014-9-1
—English Chinese mixed version
UFO is for the stars which want to connect with others, also want to learn from
others and help others.
—The flying disk for interstellar travel
—The time machine from Venus aliens
Our universe is determined not only by its own law, but also by its civilizations.
Our galaxy—Sagittarius and Andromeda
Our universe is full of light and lives, full of emotions, full of connections.
Open your beautiful mind and share your ideas with others.
Our universe is like a pair of twin brothers, one holds material , the other is a
spiritual world.
—The infant universe
How do material and spiritual influence each other?
Who is the truly “shuiren shi”? Apollo and his burning mirror.
or
?
Apollonius of Perga (Greek: Ἀπολλώνιος; Latin: Apollonius Pergaeus; c. 262 BC – c. 190 BC) was
a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and
terminology, especially in the field of conics, influenced many later scholars including Ptolemy , Francesco
Maurolico, Johannes Kepler, Isaac Newton, and René Descartes. It was Apollonius who gave the ellipse,
the parabola, and the hyperbola the names by which we know them. The hypothesis of eccentric orbits, or
equivalently, deferent and epicycles, to explain the apparent motion of the planets and the varying speed of
the Moon, is also attributed to him. Ptolemy describes Apollonius' theorem in the Almagest XII.1. Apollonius
also researched the lunar history, for which he is said to have been called Epsilon (ε). The
crater Apollonius on the Moon is named in his honor.
If they are a same person, what our world will be?
+
= ?
So the God will guarantee a great task to such person,
his will must be practised,
his body must be suffered
make him hungry
make him poor
exercise his behavior
by which to improve his ability and thought
as well as develop himself
We prefer to live in a world where Karl Marx and Friedrich Nietzsche is a same
person. A world without world war and cold war, no racial discrimination, no
different beliefs . Everyone lives in a harmonic society where the gap between rich
and poor is not so big !
If the god can witness the tremendous progress we made, whether she will be moved by our
great spirit and effort ?
Since she gives us so equally and freely, how could we be so blind not to see ?
So what is the goal we pursuit for thousands of years ? What is the spirit we
insist in all ages ?
Now the answer is clearly，that’s because:
— She is hearting too，just as we !
Preface
This is a series of science textbook written by Professor Jeff, which
focus on mathematics and algorithm only in this volume. a person who has
professional research level or a student being educated in a graduate
school can read our textbook without much difficulty. Even though it need
very high background to read this material. but it is still not very impossible hard for amateurs in science, art and even litterateur.
On the other hand, since we proposed many most important and essential
problems in math and algorithm. So without our permission, please do not
cited so much unless you can understand the key idea in our textbook.
Now we introduce the content of this series, it can be summarized as 3 chapters:
1． The spirit of future science institute (1)
2. Professor Jeff’s mathematical exercises (1)
3. Professor Jeff’s algorithm notes (1)
— some remarks on ACM contest problems
The first chapter is a theological manuscript, which gives the rules
and character we future science academy’s person should obey and possess.
The second chapter is an exercise book for math department student. And
the last chapter is an algorithm notes for ACM competition questions. In
the second and the third paper, we try to introduce the most essential
topics in modern science, by proposing some challenge problems, we can
instill more basic concept and common technique in mathematic and computer
algorithm into the students in different level.
If you truly want to improve your knowledge by reading this textbook, it is better for you to study all the open problems mentioned in this
textbook carefully. To write down your unique solutions and opening
thought for these problems after your reading.
Any good idea about the problems appeared in this series can be mailed
to the author cheng ,via email: [email protected] or
We welcome any discussion from readers to improve our research.
Introduction
If you carefully and seriously study our exercises, solutions and the notes after them. You will find many interesting problems by yourself.
Don’t be worry, maybe the most important subject in this field is
concealed in the interesting story you just discovered. Search it, you
will find more and more joy in your reading. Now we give some examples, to teach you how to find these interesting problems fast and accurately.
Chapter 1: The spirit of future science institute (1)
If we want to achieve interstellar travel and time travel in the future,
what we should do now. what is our shortcomings and what is the gap between
us and other stars, how to overcome it .
Chapter 2: Professor Jeff’s mathematical exercises (1)
Part 1：Elementary exercises
1. exercise 1.2 (page 3)
The relation between the zero point theorem and the extreme point of the function:
The extreme point include arrest point and the non-differentiable point.
So by our solution to this problem, how about the number and the value
range of its extreme point? Whether we can use the zero point theorem to handle this problem ?
2. exercise 8.2 (page 36-37)
if we want to use 1i
a to omit i
a . Then in every step, we will get one
more term. They are: 1
a , 23
4a ,
32 a , ......
the hint is when we omit i
a , we can subtract the component of i
a in 1i
a ,
then the surplus term can be omitted.
Exercise 9.2 (page 40)
Use the conditions below to omit terms :
1. 0)21(2
ax
2. )1)(1(15 234
xxxxxx
3. 0)()1,0('
xfx
Part 2：Advanced exercises
Exercise 1.1 (page 2)
How to construct: n
Cn
f2
)12(
?
The hint is to use the Taylor expansion:
......2
!2
321
!1
21
1)(
2
......)(!2
)()(
!1
)()()(
1
2
)2()1(
x
CCC
x
CC
Cxf
k
axaf
axaf
afxf
to separate 122
n and )12( n
f and then ensure )12( n
f ！
Exercise 4.6 (page 15)
To study an arbitrary group, we always transform our object to its
permutation group. Since a permutation group can ensure invertible
property. Then by Cayley theorem, a group is isomorphic to a subgroup of
its permutation group. So our work is to calculate the rank and order of
the permutation group’s subgroup.
Exercise 5.5 (page 21)
The difficulty is that: if )1,0(]1,0( is not a bijection, how to ensure:
Exercise 5.7 (page 24)
Here we study its special minimizer 0:
If 01 u 1 u , then we can select the universal constant as :
R
C2
. Thus the minimizer 0 is obtained ！
Exercise 6.2 (page 29)
Recall the Crandall-liggett theorem :
Now it is clear that the Crandall-liggett theorem will lead to a semigroup.
Since every semigroup is rely on time and even the shape of the space,
that is the time discretion and the space discretion. So the time is
necessary here ！
Chapter 3: Professor Jeff’s algorithm notes (1)
— some remarks on ACM contest problems
Flip and shift (page 64)
一个更深层次的问题是：如何将随机抽取的黑球转化成按一定间隔排列的数？因为只有令黑
球所代表的数按照该区间的素数最大间隔排列, 才可以使得我们的搜索算法的效率最高。
Square destroyer (page 72)
这里，我们尝试寻找一个在每一个格子四周的木棍上填数的算法，使得对于按照幻方规则填
数的九宫格，问题总是可解的。即总是会剩下某一个正方形，它的四条边上的木棍是不可删
除的。
Color me less (page 141)
对于三维像素，DISTANCE 函数是决定存储效率的一个关键指标。
Bode plot (page 144)
See wiki: http://zh.wikipedia.org/wiki/%E6%B3%A2%E5%BE%B7%E5%9C%96
1. 电场回路是以匀速转动。所以，存在一个角频率之间的进制转换方法：
rcwangle
0.1arctan （其中，1.0 可以换算成 10.0， 100.0 等）
但是，如果我们采用正规化频率c
ww / ，则无需考虑进制转换。
2. 因为，当c
ww 时相位差可以忽略不计，即：
例如一个 Asin(ωt) 的信号进入系统后振幅变原来的 k 倍，相位落后原信号 Φ，则其输出信
号则为(A k) sin(ωt − Φ)，其中的 k 和 Φ 都是频率的函数。
此时的 Φ 可以近似地看作是 0。因此，我们需要为我们的电容电压公式加上一个条件，使得
我们的频率趋于无穷小 ：
0
)12
2(1
1
)12
2(1
)12
2(
)(1
22
2
2
m
jrc
m
jrc
m
j
rc
（ m ）
System overload (page 167) 这是一个关于贪心算法本质的问题，即按照贪心选择处理过的活动安排问题，是否总是可以
等价于一个模拟的约瑟夫环？
例如，我们考虑如下的例子：
我们按照贪心算法给出一个报数序列：
｛6，3，2，5，9，8，7，4，1，10，11｝
根据这个序列来看，它是一个模拟的约瑟夫环，即 1～n 之间每个数字均出现一次。而最关
键的问题则在于：最后报到的那个活动即标有特殊编号的活动应该如何作相应地选择呢？
THE WILLY MEMORIAL PROGRAM (page 52)
这里，我们尝试用 THE WILLY MEMORIAL PROGRAM 算法模拟汉诺塔的移动：
水管越粗，相应的就要移动越多的盘子到目标塔上，这就要求注水前该目标塔上最底层的盘
子要较其它的塔更大。因为，底层的盘子越大，就可以往该塔上堆叠越多的盘子。因此，为
了保证按照盘子按照从大到小的顺序往上堆叠，水管的粗细不仅代表了移动盘子的数目，还
代表了往该塔移动的盘子的大小：即移动越大的盘子，就需要往更粗的水管注水（这里，我
们可以依照盘子的大小编号，选取相应的宽度为 1~ n 的水管注水）。为了能够更快速的实现
汉诺塔算法，我们需要尽可能地优先选取位置更深的细管注水。位置越深，水管就越粗，注
水量也就越大。我们的目的就是要把最大的那些盘子优先叠到目标塔上，并且保证盘子是按
照从大到小的顺序往上堆叠。
另一方面，考虑到不同的细管之间有水平的管道相连，在若干次注水之后，所有细管内水量
的平均值肯定会有所增加。因此，我们可以为每一轮的注水设置一个水位的基准值。在一轮
注水过后，我们可以适当地提高基准值。然后，修改注水队列的头指针，选取最接近基准值
即水位最低的细管注水。
最后，我们注意到：水可以经过水平的管道在不同的细管中流动。所以，在停止注水后经过
一段时间 T，一般情况下，所有细管的水位都会持平。这就说明选取最接近基准值即水量最
少的细管注水，在某种意义上就等价于原题中每次都选取位置最低的细管注水这个条件。
注：我们可以把细管的容量设置为将所有盘子移动到目标塔所需要的移动次数的总和。
Future science: the next 10 years
New worlds, new life, new bodies: just some of the
breakthroughs we may see by 2020, predict our panel of
leading Australian scientists.
By Abbie Thomas
The hunt for dark energy, Science Online, 02 Apr 2009
Spare parts, Science Online, 31 Aug 2009
How epigenetics is changing our fight with disease, Science Online, 01 Oct 2009
Light-speed computing one step closer, Science Online, 03 Mar 2010
There have been some incredible leaps forward in science in the past decade. It's difficult to imagine
what life was like before Wi-Fi, and hard to believe how much we've discovered about Mars. And it's
only seven years since the entire human genome was sequenced, yet since then, scientists have
cracked the genomes of dozens more species.
So what's next? How many more amazing scientific discoveries will we see by the end of the next
decade? And how will these change our lives?
We asked some of Australia's most outstanding researchers in astronomy, health, technology and
the environment to gaze into the future and predict what the world will look like in 2020.
Deeper into space
WHAT'S NEXT: Bigger, better telescopes sweep the skies scrutinising the atmosphere of
planets in other solar systems while plutonium drills dig up alien life from 20 kilometres
beneath the ice of Saturn's moons.
"By 2020 I bet we'll be on the brink of a breakthrough in finding life out there in space,"
says Professor Fred Watson from the Anglo-Australian Observatory.
"Some of the moons of Jupiter and Saturn have ice 20 kilometres thick floating on liquid oceans: who
knows what could be living in them? Titan has lakes of liquid methane instead of water. There's a
good chance there are microbes living off these hydrocarbons — they would be amazing life forms if
we could find them."
Watson forecasts that a new generation of telescopes twice or even three times as large as today's
will make it possible to closely scrutinise the atmosphere of far-distant Earth-like planets for
indications of life.
We'll discover many Earth-like planets by 2020, says Dr Charley Lineweaver from the Australian
National University.
"This will inspire humanity's first mission to another star, using a spaceship that can travel many
times faster than any previous ship."
The search for extraterrestrial intelligence has the potential at any time to "unhinge our identities as
much or even more than Darwin did" says Lineweaver, adding "but I suspect it will be another quiet
decade for SETI", a project searching for other lifeforms in the universe.
Professor Mathew Colless, director of the Anglo-Australian Observatory is a little more hopeful.
"Maybe, just maybe — this is a real long-shot, we might even learn of other intelligences out there,
creatures who, like us, are capable of savouring knowledge about the universe we share."
WHAT'S NEXT: Cracking the mysteries of the universe.
"The Large Hadron Collider will find the Higgs Boson or something unexpected" - Dr Charley
Lineweaver (Source: CERN)
We are learning about our universe more rapidly than before and the next decade could herald some
exciting discoveries, says Colless.
"Particularly fascinating new discoveries to savour in the next ten years may well include where mass
comes from if the Large Hadron Collider identifies the Higgs boson; what most of the material in the
universe actually is if laboratory experiments detect the subatomic particles of 'dark matter'; what is
causing the expansion of the universe to accelerate if astronomical observations reveal the nature of
dark energy; and whether there are other Earth-like worlds around other stars."
Lineweaver agrees this will be the decade to find the elusive Higgs-boson particle.
"Our dark matter searches will find a dark matter particle (or particles) or something unexpected.
These results and the Planck cosmic microwave background observations could solve the mystery of
dark matter and dark energy," Lineweaver says.
The meaning of life
WHAT'S NEXT: A grand unifying theory of biology.
While discovering the Higgs-boson particle may help us understand how our universe works, a new
science called interactomics may help us understand the meaning of life on Earth.
Once upon a time, we thought genes could explain everything we observe in b iology. Then
epigenetics came along, revealing that our appearance and function are the result not just of our
genes but also their interaction with their environment.
Interactomics — a grand unifying theory of biology — could help us predict how a system will behave
based on information about the individual components that make up that system, says Professor
Stephen Simpson from the University of Sydney.
"A framework like this could help us predict how genes interact to produce an organism, how
neurones in the brain create consciousness; how thousands of people might behave if a fire broke
out in a football stadium; and even what the stock market might do in the future. Achieving such a
synthesis is one of the greatest challenges in modern biology, with imm ense practical implications,"
Simpson says.
New bodies
But what of our own biology? What will the human body look like a decade from now?
WHAT'S NEXT: Fat is the new thin, size 18 the new 12. We can choose from a swathe of
high tech pharmaceutical 'magic bullets' to help shed the kilos.
"More weight-loss drugs will be available on the market in 2020 than today" - Dr Nuala Byrne.(Source:
iStockphoto)
Obesity expert Dr Nuala Byrne from the Queensland University of Technology predicts even more
weight loss drugs will be available on the market in 2020 than today: some to slow the stomach
emptying, some to make you feel full, some to limit fat absorption, and others to increase metabolism.
"We may also see devices which use electrical impulses to control the nerves which regulate the
stomach and the pancreas and which tell you when you are full. Ultimately, there may be a genetic
test to tell you if you have the genes which increase propensity for weight gain — but it'll still be up to
you what you do about it."
WHAT'S NEXT: Your entire DNA sequenced for the cost of a new lounge suite.
It will be possible for you to see if you've inherited those obesity genes within 10 years, as fast and
cheap DNA sequencing technologies will make personal genomes a reality, predicts Professor
Arthur Georges from the University of Canberra.
"New machines which can yield terabytes of genetic information will make is possible for anyone to
have their entire DNA sequenced in less than a week for a $1000. Theoretically this information could
be used to predict diseases, cancer and obesity years ahead of when they actually develop," says
Georges.
New genomics technology will also transform forensics, making it increasingly difficult for
perpetrators to remain unconnected to their crime scene and victim.
And by 2020, laboratories will have sequenced the full genomes of 10,000 organisms, providing a
wealth of data to help understand how organisms function, how they respond to the environment and
ultimately how they evolve.
WHAT'S NEXT: Any wound can be healed by combining tissue engineering,
bioengineering and nanotechnology.
"We'll see the construction of three dimensional tissues in the lab such as skin, cartilage, cardiac and
bone tissue" - Professor Fiona Wood (Source: iStockphoto)
Genetics will be combined with other technologies in the future to heal the damage created by trauma,
burns and even cancer, says Australian of the Year Professor Fiona Wood from the University of
Western Australia.
"We'll see the construction of three dimensional tissues in the lab, such as skin, cartilage, cardiac and
bone tissue: growing organs in Petri dishes, if you like," predicts Wood.
We'll also start to see a multi-level characterisation of the wound, cancer or whatever is being treated,
from the external appearance right down to changes at the genetic level, she says.
"Once we understand what's going on at the genetic level, we'll enhance gene activity to make
wounds heal faster and better. Self-assembling nanoparticles will restore the tissue framework, and
ultimately in-situ tissue regeneration will become commonplace."
WHAT'S NEXT: Soldiers will be 40 per cent biology, 60 per cent technology.
New technology will deliver more than physical benefits in the next decade. Remembe r the
implantable memory chips in the 1984 science fiction classic Neuromancer?
Well, the reality of having direct access to cyberspace via implants in the brain is closer than you
think, saysProfessor Vaughan Macefield from the University of Western Sydney.
"Four people already have electrodes implanted in their brain — a neural interface system to help
them control a computer or prosthetic limb. In another decade, this system will give you a complete
sense of touch and of what's around you, allowing you to tell the difference between objects of
different weight, texture and softness," says Macefield.
"With the military's requirement for replacement limbs, the soldiers of tomorrow will be 40 per cent
biology, 60 per cent technology — perish the thought!"
Macefield also predicts we'll abolish memory loss, with implantable microelectrode arrays that allow
us to retrieve long forgotten memories.
Virtual friends and smart homes
WHAT'S NEXT: A life-size replica of your best friend.
A projector will create an image of your friend sitting next to you." - Dr Clio Creswell (Source: Thomas
Peter/Reuters)
By 2020, it will be possible to chat to a life-sized hologram of friends or colleagues, predicts TV
personality and lecturer Dr Clio Cresswell from the University of Sydney.
"A projector will create an image of your friend sitting next to you. It will be just like they are there,
except you can't touch them. And this won't happen without plenty of mathematics. Fourier
Transforms are sure to play a role in creating these holograms. That's the same mathematics
underlying MP3 players," says Creswell.
WHAT'S NEXT: Fast internet connected living.
If you're playing Monopoly with your virtual friend in 2020 the board will include an option to purchase
broadband along with water and electricity if Dr Alex Zelinsky, who heads CSIRO's Information
Sciences Group, has anything to do with it.
"Broadband is so essential to our lives it should be regarded as another utility," says Zelinsky.
"If everyone in Australia had access to cheap, fast broadband, it would pave the way for a whole host
of new services and technologies. These might include telemedicine, where medical information is
transferred through the internet to use for consulting, remote medical procedures or examinations."
Zelinsky believes national high-speed broadband would deliver many benefits such as 'smart' homes,
where the use of water and energy is monitored and controlled by internet-linked sensors. And we
could monitor every dam, river and reservoir and combine this information with weather forecasts,
allowing us to predict not only how much water we have today, but how much we will have in the
future.
Clean energy
WHAT'S NEXT: Cities supported by sustainable technology
"Unless we adopt clean technologies the prospects for human civilisation are bleak" - Ian Lowe (Source:
iStockphoto)
Clean energy technology is the key to the future, says Professor Ian Lowe from Griffith University.
Lowe envisions Australian cities will be powered by clean energy, and have the capacity to turn
energy and other resources efficiently into services within 10 years.
"Irrigation water will be used sustainably without depriving riverine ecological systems of the flows
they need ... well, that's my dream anyway.
"But unless we leave behind approaches and technologies that are clearly not sustainable within the
next decade, the prospects for the future of human civilisation are very bleak," he concludes.
WHAT'S NEXT: the big picture
Over the next decade, science will deliver environmental applications so we can live sustainably,
economic applications so we can enjoy prosperity, medical applications so we can enjoy health and
security applications so we can enjoy peace, says Colless.
But sometimes science supplies not just the means but also the end itself, he says.
"[Science is] something we enjoy because it is intrinsically valuable, not valuable because it leads to
something further."
"The end I have in mind is simply an appreciation of the universe we live in, an understanding of how
it works and why things are the way they are.
For those who share this view Colless predicts the next decade will be "an age of wonders and keen
pleasures".
Tags: obesity, pharmaceuticals, science-and-technology, astronomy-space, planets-and-asteroids,t
elescopes, the-universe, space-exploration, biology, computers-and-technology, energy,information-
technology, neuroscience, physics, robots-and-artificial-intelligence, genetics,brain-and-nervous-syst
em, nanotechnology, dna, environmental-technology
Published 11 March 2010
Email ABC Science
This paper is from : http://www.abc.net.au/science/articles/2010/03/11/2841781.htm
Reference：
1. https://www.researchgate.net/profile/Cheng_Tianren/?ev=hdr_xprf
2. http://scau.academia.edu/chengtianren
3. http://www.vixra.org/author/cheng_tianren
4. http://gsjournal.net/Science-Journals-Papers/Author/1423/cheng,%20tianren
5. https://www.quora.com/Cheng-Tianren
6.https://www.linkedin.com/profile/view?id=248782428&trk=nav_responsive_tab
_profile_pic
The Future Science Institute (Print)
ISSN 2332-1792
The Future Science Institute (Online)
ISSN 2332-1784
This is a book review for “Textbook of the future science institute”
(volume 1, 2014-9-1).It is a textbook written in English and Chinese mixed,
and it is adapt for the readers who major in science, especially for the
professors and graduate students who can master the basic knowledge in
mathematics and algorithms.
Now the first textbook published by our future science institute is online ,
and you can buy the copy from the following web:
1.
http://www.amazon.com/Textbook-Science-Institute-English-Chinese/dp/1501038001/ref=sr_1_1?
ie=UTF8&qid=1410330375&sr=8-1&keywords=textbook+of+the+future+science+institute
2.
http://www.lulu.com/shop/tianren-cheng/textbook-of-the-future-science-institute-volume-1-englis
h-chinese-mixed-version/paperback/product-21794629.html
3. http://www.magcloud.com/browse/issue/804782
Price:
1. print (51.3, 53.2, 54) per/dollars
2. digital (17.4, 19) per/dollars
Any good ideas about the problems appear in this book can be mail to the
author prof Jeff, via: