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• Math Forum

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怎样写好作文？中国作家曹文轩为您幽默解答（详见视频23:36）

Every child is unique; every human with an entirely different set of fingerprints. Whether your child has the potential to be an engineer or a boss of their own, one thing remains inextricably part of life – math.

Take it from me, a 22-year-old business owner who used to flunk math. Your kids will hate maths until they start to see that they can actually do and get better at it. From F9 in A Maths, I studied hard and studied right to achieve A2. Your kids can do it with the right guidance and the right motivation.

And I’m not referring to scoring better than your neighbours or nephews and nieces. Your kids don’t care about that – and you shouldn’t too. Focus on the important things.

What are they? In this article, I’ll be sharing with you, parents, what will motivate your kids to want to be good at maths that are not grades.

Many kids have entrepreneurial blood and a knack for sales. Look at how well they persuade you to get what they want. Remember the times where they came up with the most ingenious of ideas – you were surprised; thought it could even become a business.

If your kids have a tendency to solve problems in the most creative ways possible and have a sense of leadership, you should get excited. They might be the next CEO of Amazon!

Math is crucial in starting and running a business. Whether it is running an eCommerce store (which is very profitable in 2019 and beyond) using platforms like www.shopify.com.sg or selling their artistic services online, math is a must.

Kids are motivated by things other than grades

You might think that this isn’t exciting for your kids.

Maybe they never thought it would be possible… Maybe all they knew was just the linear way of life…

What if they were interested in starting their own mini business? What if they got excited to be good at maths, motivated by the fact that they could apply to real life?

Now that I’ve sparked something in you, you might be thinking ‘Why does running a business need math?’

Reason #1: Doing their taxes

I wish my parents taught me how to do my taxes and to avoid ‘savings plans’ by a certain insurance company. These are the important things that will matter to your kids when they are adults – something that is missing in schools and not taught by most parents.

Being good at math will ensure that they don’t get lost in all the numbers, percentages, appreciation, depreciation, interest, and more. With a good foothold in working with numbers, your kids will not hate doing their taxes and avoid any penalties that come with incorrect tax payment or filing.

Starting their own business means they have no one to tell them how much they need to charge to have a good amount of profit. No teacher to tell them that they are spending way too much on unnecessary things and blowing out their expenditure. They have no tutor to guide them saying ‘to meet your financial goals and achieve sustainability in Singapore, you need to get $XXX a year.’ Running a business well demands good math skills to calculate and plan the finances. Now, your kids have a teacher, they have you and a math tutor. Bring math in real-life situations and you’ll start to see an increase of drive in their eyes. Conclusion Perhaps it’s time to unveil the a little bit more about reality to them. It could get them thrilled to head on to ace that math paper! Author: Jamie Posted in Uncategorized | Leave a comment How to speak to Human Singtel Customer Officer If you try calling the Singtel hotline 1688, you will spend most of your time to navigate the maze of options trying to speak to a human Singtel Customer Officer. I have not managed to successfully find the option to speak to a human Singtel Chat Agent through the hotline, if you know the method please comment below! Also, do not bother speaking to “Shirley” on the Contact Us page (https://www.singtel.com/contact-us). It is quite clear Shirley is not a human, but just a bot. The Trick to Chat with a Human Singtel Customer Officer 1. Go to the Contact Us page. 2. Click on Ask Shirley 3. Type “can i chat with customer service officer”. 4. Type in the category of your question, e.g. “billing”, “voucher”, etc. 5. Whatever Shirley says, just click “Submit Enquiry” 6. Bingo! You are now connected to a Human Chat Agent! From trial and error, this is the easiest way to get to speak to a Human Singtel Customer Service Officer/ Chat Agent. There is no direct link to chat with a Singtel Customer Representative. For the above method, you don’t even need to login to your Singtel account. But you may be asked your name and NRIC for verification purposes. Posted in Uncategorized | Tagged , , | Leave a comment Chinese Math Olympiad (Primary) Trick vs Singapore Modeling Math Both Methods (I) & (II) below does not use Algebra, which is not taught to primary school kids until secondary school (above 12 or 13 years old). (I) Ancient Chinese Arithmetic Method: 例2：The sister is 13 years old this year, while the brother is 9 years old. When the total of their ages is 40, how old will they be? 【这位妈妈太绝了！竟把小学6年奥数化为13句口诀】 Trick: Age difference does not change over time, they + or – in tandem. When 2 ages change, the multiple between them also changes. https://m.toutiaocdn.cn/group/6636154201682477582/?iid=65171531104&app=news_article_lite&timestamp=1552573996&group_id=6636154201682477582&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share (II) Singapore Modeling Math: ［例2］ Compare the Ancient Chinese Arithmetic (I) & Singapore Modeling Math (II): • (II) is better for young kids to understand visually the logic behind, • (I) is more a memorised trick but poor math education pedagogy. In [例 2] it is very hard for kids to understand why the 2 steps (40+4) & (40 – 4), although they lead to… View original post 130 more words Posted in Uncategorized | Leave a comment English Fun Math Different Maths: 1. English (UK/USA) Math is playfully tricky (Math Olympiad, Math Puzzles eg. this Numberpile video) 2. French Math is abstractly theoretical (Group theory explains Symmetry, Rubik’s cube game,… ) 3. Chinese Math (Abacus, “Chicken-Rabbits Problem” 鸡兔问题, Singapore Modeling Math) is applied & procedural (明朝 13CE invented “Determinant” 行列式 before the 19th CE “Matrix” by UK Sylvester，Chinese Remainder Theorem 韩信点兵). 4. Indian Math (Vedic Math , Factorization, Ramanujian-Style Math) is mysteriously spiritual. View original post Posted in Uncategorized | Leave a comment AI with Advanced Math helps in discovering new drugs Posted in Uncategorized | 1 Comment Why French excel in math ? Mathematics and quantitative finance, France Since 1990, there have been 22 winners of the Fields Medal, widely regarded as the Nobel Prize of mathematics. Thirteen came from just two countries, Russia and France. Russia has more winners (seven), but more than twice the population, so the honours go to France, with six winners. Cédric Villani, the 2010 Fields Medallist, cited national character. “Maths is an abstract way of looking at the world, which fits well with the French mentality. We apply algebra to everything.” Elite institutions help too. France’s brightest school leavers progress to the grandes écoles, which traditionally educate top scientists, administrators and presidents. For maths, you want Monsieur Villani’s alma mater, the École Normale Supérieure (ENS). All 10 French Fields Medallists learnt there. At ENS, no teacher can stay longer than 10 years. Instead of ancient dons, students get tutors at the forefront… View original post 190 more words Posted in Uncategorized | Leave a comment Happy Birthday To Urbain Le Verrier, Who Discovered Neptune With Math Alone Posted in Uncategorized | Leave a comment Percentage Mental Calculation Example: 4% of 75 = 75% of 4 Mental Steps: 75 x 4 – > 300 – > / 100 – > ＝ 3 (ANS. ) Is it easier ? View original post Posted in Uncategorized | Leave a comment The Laws of Mathematics Zermelo-Fraenkel Axioms Set Theory The Foundation of Modern Math which is based on the “Set Theory”, hit a crisis due to Bertrand Russell “Barber’s Paradox”, until the Zermelo-Fraenkel Axioms came to its rescue. Here is a humorous example of an ISP Internet Plan violating the 9 Z-F Axioms: How ISPs Violate the Laws of Mathematics: Video: View original post Posted in Uncategorized | Leave a comment Quora: Is Abstract Math a fluke (偶然) ？ Posted in Uncategorized | Leave a comment 通俗群论 Challenge: Put ’15’ and ’14’ in the right sequence (Impossible! ) 以下无解：群论 View original post Posted in Uncategorized | Leave a comment “Essential mathematical GIFs that will make mathematics finally make sense” “Essential mathematical GIFs that will make mathematics finally make sense” by Ali Kayaspor https://link.medium.com/z1nWgHm9GU View original post Posted in Uncategorized | Leave a comment RMM Olympiad 2019 Posted in Uncategorized | Leave a comment Best Machine Learning / Deep Learning Books After some research, I find that the best book on Machine Learning / Deep Learning currently on the market is: Deep Learning with Python. It is written by François Chollet, who is the creator of the famous Keras library (Google Tensorflow). The most popular language for machine learning is currently Python, which is the subject of this book. (Another language is R, but many people find R to be less user-friendly as compared to Python). The book is suitable for those who are studying deep learning from scratch, with zero prior knowledge. Currently, machine learning is at the peak of its hype, with many employers seeking to utilize machine learning in one way or another. It is very useful for students to pick up this skill for potential usage in the future. A key competitor to Keras/Tensorflow is Pytorch, developed by Facebook. It is supposedly even more user-friendly than Keras/Tensorflow. However, the drawback is that it is too new and few books/tutorials exist. Posted in Uncategorized | Leave a comment Alexa Ranking Below 1 Million Thanks to all readers, Mathtuition88 has reached Alexa Rank of below 1 Million! Current Global Rank: 983,883 SG Rank: 11,701 This is the first time Mathtuition88.com has broken the 1000,000 Alexa Rank barrier. For ranking, the lower the better. For instance Google is ranked number 1, and YouTube is number 2. Facebook is ranked number 3. Posted in Uncategorized | Tagged , | Leave a comment Powerpac Ceramic Cooker Review This should be the cheapest ceramic cooker on the market. PowerPac is a reliable Singaporean brand that has been on the market for quite some time. At the price of$29.90, the Ceramic Cooker even comes with a free stainless steel pot with cover (CNY Promo). Unbeatable price! It is also free delivery.

It is ideal for home steamboat / hotpot cooking. By the way, ceramic cooker can cook all types of pots and pans (unlike induction cookers).

[S$29.90](▼51%)[PowerPac Promo]PowerPac Ceramic Cooker (Any Pot) 2000 Watts (PPIC833) //Suitable for any use with any types of pots WWW.QOO10.SG Posted in Uncategorized | Leave a comment Free Philips Air Fryer (Enfagrow Promo) Official URL: Enfagrow Homepage Posted in Uncategorized | Leave a comment Group Theorems: Lagrange, Sylow, Cauchy 1. Lagrange Theorem: Order of subgroup H divides order of Group G Converse false: having h | g does not imply there exists a subgroup H of order h. Example: Z3 = {0,1,2} is not subgroup of Z6 although o(Z3)= 3 which divides o(Z6)= 6 However, if h = p (prime number), => 2. Cauchy Theorem: if p | g then G contains an element x (so a subgroup) of order p. ie.$latex x^{p} = e $∀x∈ G 3. Sylow Theorem : for p prime, if p^n | g => G has a subgroup H of order p^n:$latex h= p^{n}$Conclusion: h | g Lagrange (h) => Sylow (h=p^n) => Cauchy (h= p, n=1) Trick to Remember: g = kh (god =kind holy) => h | g g : order of group G h : order of subgroup H… View original post 83 more words Posted in Uncategorized | Leave a comment 陈省身 SS Chern – “The 2nd Gauss” 陈省身香港科技大学 演讲经典 (Highly Recommended – spoken in English & Chinese) http://www.bilibili.com/video/av5473133 他的女婿是香港科大校长。现任校长是 Prof 陈繁星 Tony F. Chan , the ‘Search Algorithm Thesis’ supervising Prof of the 2 Google founders in Stanford University, Applied Math Department) Key Points: 1. SS Chern won the “Wolf Prize” in the same year with the Hungarian “Vagabond” 流浪汉 Mathematician Erdos Paul. 2. He was appointed the Scientific Advisor of President Reagan, during which Chern recommended to build the USA Center of Math in Berkeley University. After retirement, Chern built a similar center in China at his alma mater Nankai University 南开大学 where he graduated in 1930. 3. SS Chern was an assistant lecturer of Prof Yang WuZhi 杨武之, who liked to invite Chern to his house for dinners, where he saw his 8-year old son Yang ZhenNing 杨振宁 (Nobel Prize Physics 1958). 4. SS Chern has guided great PhD students eg. James Simons (Billionaire Financial Investor applying… View original post 208 more words Posted in Uncategorized | Leave a comment 70-million Bounded Gap Between Primes Since Ancient Greek : 1. Euclid had proved there are infinite primes. 2. Sieve of Eratosthenes to enumerate the primes. 3. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap(N) of primes in infinity, but stuck at one critical step. 4. Dr. YiTang Zhang 张益唐 (1955 -) spent 7 years in solitude after failure in academic career, in 2013 during a 10-min walk at the deer backyard of his friend’s house, he found an Eureka solution for the GPY’s critical step:$latex boxed { epsilon = frac {1} {168}}&fg=aa0000&s=2 $which gave the first historical bounded Gap (N) from an infinity large number to a limit of 70 million. Notes: • Chinese love the number “8” ba which sounds like the word prosperity 发 fa (in Cantonese) . He could have instead used 160, so long as$latex epsilon is small. • The UltimateGoal of the Bounded… View original post 64 more words Posted in Uncategorized | Leave a comment Betta Fish Tricks Betta fish are quite intelligent and curious. I trained my Betta fish to do some simple tricks. I bought my 5 Gallon tank on Qoo10: Betta Fish Tank. The modern viewpoint is that Betta should not be kept in small bowls or vases (though they might still survive). A 2.5 gallon tank is considered the absolute minimum, with 5 gallon and above being a better choice. Jumping Trick and Going Through Hoop Trick Following Pen Trick Posted in Uncategorized | Tagged , , | Leave a comment 小算盘 大乾坤 Abacus 浙江临海市 算盘博物管主人 雷国华 收藏算盘20年，散尽储蓄，感慨涕下不已。 中国的算盘上面2珠 (2×5)，下面5珠(5)， 共15，加1 = 16 进位。古代是16位 (Hexadecimal) 制， 半斤 八两 (= 1/2 斤 x 16 两 = 8 两)。 日本改良成10位制: 上面1珠 (1×5)，下面4珠(4)， 共9，加1 = 10 进位。 View original post Posted in Uncategorized | Leave a comment 3D Rotation Matrices and Examples The following rotation matrices rotate vectors by an angle $\theta$ in an anticlockwise direction about the $x$-, $y$-, or $z$-axis respectively (the rotated axis points towards the observer). \begin{aligned} R_x(\theta)&=\begin{pmatrix}1 &0 &0\\ 0 &\cos\theta &-\sin\theta\\ 0 &\sin\theta &\cos\theta \end{pmatrix}\\ R_y(\theta)&=\begin{pmatrix}\cos\theta &0 &\sin\theta\\ 0 &1 &0\\ -\sin\theta &0 &\cos\theta \end{pmatrix}\\ R_z(\theta)&=\begin{pmatrix} \cos\theta &-\sin\theta &0\\ \sin\theta &\cos\theta &0\\ 0 &0 &1 \end{pmatrix} \end{aligned} Example 1 Rotating $\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}$ $45^\circ$ anticlockwise about $z$-axis: \begin{aligned} R_z(45^\circ)\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}&=\begin{pmatrix} \cos 45^\circ &-\sin 45^\circ &0\\ \sin 45^\circ &\cos 45^\circ &0\\ 0 &0 &1 \end{pmatrix} \begin{pmatrix}1\\ 0\\ 0\end{pmatrix}\\ &=\begin{pmatrix}\sqrt{2}/2\\\sqrt{2}/2\\0\end{pmatrix}. \end{aligned} Example 2 Rotating $\begin{pmatrix}0\\ 1\\ 0\end{pmatrix}$ $45^\circ$ anticlockwise about $z$-axis: \begin{aligned} R_z(45^\circ)\begin{pmatrix}0\\ 1\\ 0\end{pmatrix}&=\begin{pmatrix} \cos 45^\circ &-\sin 45^\circ &0\\ \sin 45^\circ &\cos 45^\circ &0\\ 0 &0 &1 \end{pmatrix} \begin{pmatrix}0\\ 1\\ 0\end{pmatrix}\\ &=\begin{pmatrix}-\sqrt{2}/2\\\sqrt{2}/2\\0\end{pmatrix}. \end{aligned} Posted in Uncategorized | 1 Comment 十二平均律 12-tone Equal Temperament 《十二平均律》 是明朝 ＂布衣王子＂ 朱载堉 (1536年－1610年) 发明的，由当时在中国传教的意大利人 利马窦 (Matteo Ricci, 传给欧洲的法国数学家 Marin Mersenne (Mersenne Prime ) 。现代音乐之父 巴哈 Bach 第一个采用，制作世界第一架钢琴有12黑白键，并作曲 《Bach 12-tone Equal Temperament》。 朱载堉把 “1” 到 “i” 的八度 (Octave) 分为等比 (ratio) 距离的12个半音 (half note), 每个音是前音的latex sqrt[12] {2 }$，第8高音频率 (frequency) “i” 巧好是第一音 “1”的2倍。他用81行的大算盘算出： Side Note: 1977年法国大学数学教授在课堂好奇地问我，你们祖先如何解代数？是用算盘吗？当时计算机还不流行，复杂的算法只能用Log Table 或 计算尺 (Slide Rule) 。 朱载堉的算盤算法就是个例子。 Bach 12-tone Equal Temperament https://zh.m.wikipedia.org/wiki/%E5%8D%81%E4%BA%8C%E5%B9%B3%E5%9D%87%E5%BE%8B 倍大吕： View original post Posted in Uncategorized | Leave a comment Richard Dedekind Julius Wilhelmina Richard Dedekind (6 Oct 1831 – 12 Feb 1916) – Last student of Gauss at Göttingen – Student and closed friend of Dirichlet who influenced his Mathematical education – Introduced the word Field (Körper) – Gave the first university course on Galois Theory – Developed Real Number ‘Dedekind Cut‘ in 1872 – Accomplished musician – Never married, lived with his unmarried sister until death “Whatever provable should be proved.” – By 1858: still yet established ?$latex sqrt{2}.sqrt{3} = sqrt{2.3} $– Gave strong support to Cantor on Infinite Set. http://www-history.mcs.st-and.ac.uk/Biographies/Dedekind.html View original post Posted in Uncategorized | Leave a comment HDB Low Water Pressure: Phone Hotline For those living near the top floor of HDB blocks, you may experience low water pressure since the water tanks are typically built at the rooftop of HDB flats. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation $\displaystyle\boxed{p=\rho gh},$ where g is the gravitational acceleration. By this equation, you can understand why those at the top floors experience low water pressure, due to the low height h (from the water tank). There is probably a need for a pump to increase the pressure. For low floors, it is typically ok, the natural pressure should be enough to make the water flow fast. Water Pressure Low Hotline: 1800-CALL-PUB The number you should call when experiencing low water pressure for HDB flats is: 1800-CALL-PUB (1800-2255-782) My Experience with Low Water Supply I experienced unbelievably quick action by PUB on Chinese New Year, around 9pm. I called the PUB hotline due to very low water pressure (insufficient for even bathing). Mentally, I was prepared that probably they could only fix it the next working day (which is 2 days later). To my amazement, a repairman arrived 15-20 minutes later, and proceeded to fix the water tank. The water pressure was back to normal in just half an hour from the time I dialed the hotline. I was quite impressed by the high efficiency. I am not sure what caused the problem in the first place though. This problem of low water pressure has been reported by Channel News Asia. HDB Low Water Pressure What To Do Firstly, you should check with neighbors on the same floor whether they experience the problem of low water pressure. This is to confirm whether the problem is with the water tank pump/pipes, or an isolated problem only pertaining to your unit. If your neighbors also experience low water pressure, then most likely it is a problem pertaining to the water tank pump/pipes. You should dial the PUB hotline (1800-2255-782) and inform them of the low water pressure. They will liaise with the Town Council and send a technician to investigate. (The service is free of charge.) If the situation still does not improve, you may wish to purchase this “Wind Storm” High Pressure Shower Head. Basically, it turns a low pressure stream of water into a high pressure spray of water, to the extent that you can feel a “wind” blowing. It also saves water so it will pay for itself in the long run (by reducing your water bills). [S$11.90](▼77%)[Restock] Wind Storm Shower Head ★Powerful High Pressure Shower heads ★ For Bath

WWW.QOO10.SG

Also see: Free Water Saving Kit (Singapore)

Dedekind Cut : “Prove 0.9999… = 1”

Key Notes:

1. Rational Numbers Q eg. 1/2, … Complete but non Continuous.
2. Irrational numbers eg. $latex sqrt {2}$
3. Real number is Complete and Continuous
4. Dedekind Cut

The Proof of “0.999… = 1” by using Set Theory :

$latex A subset B$
and
$latex B subset C$
$latex implies A = B$

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Bit Coin and Block Chain

Bit Coin is only one application of Block Chain.

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Happy Chinese New Year

Happy Chinese New Year to all readers of Mathtuition88.com!

Do check out and follow my Facebook page, where I post interesting news on Math/Education.

Formula for 3×3 Matrix Inverse

Let $\displaystyle A=\begin{pmatrix}a &b &c\\ d& e& f\\ g& h& i \end{pmatrix}.$

Then,
$\displaystyle A^{-1}=\frac{1}{\det(A)}\begin{pmatrix} ei-fh &ch-bi &bf-ce\\ fg-di &ai-cg &cd-af\\ dh-eg &bg-ah &ae-bd \end{pmatrix}.$

This method is about the same speed as the Gaussian-Elimination method. However, if you have already calculated det(A), using the formula may be slightly faster.

The formula provides an insight on why A is singular (not invertible) if det(A)=0. (Because, if det(A)=0, in the formula we would be dividing by 0 which is not allowed.)

Posted in Uncategorized | Tagged , | 1 Comment

Men’s wallet with coin compartment Singapore

Despite many cashless initiatives like PayLah, Singapore is not yet a truly cashless country. Coins are still needed to buy coffee or tea at the “Kopitiam”, or to put a $1 coin for pushing a trolley at supermarkets. Even if you carry paper notes, when you receive coins as change you will need a place to put them. Many wallets do not have coin compartments. On Qoo10, this brand “Arete First” is a Singaporean brand that sells Leather Wallets at a reasonable price, with coin compartment. The quality is good, and it is genuine leather. It can also put a decent number of cards (nine card slots). Do check it out if you are interested in a wallet with coin compartment. [S$19.90](▼88%)[Arete First] Genuine Leather Wallet for Men | RFID blocking | Bifold | Coin compartment

WWW.QOO10.SG

Horned Nerite Snails

Some video footage of my new Horned Nerite Snails in the Betta Tank. Really amazing and bright colors.

Taken using Canon PowerShot: Canon Camera and Camera Case Singapore

The fish tank is 5 Gallon: Betta Fish Tank

Imaginary Numbers

FINAL EPISODE – Riemann Complex Plane : 4 dimension but viewed in 3 dimensions

Episode 1 – 9 : History

Episode 10: Complex function

Function : 1 input mapped to 1 output

Multi-function : 1 input mapped to (n > 1 ) output

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My most exciting Bishop’s Opening ever

Game URL: https://lichess.org/pKHiu5ey/white#1

I did make a few serious blunders, hence it is not my best game. But it is certainly quite exciting. My heart pounded furiously as I played 22. f6! sacrificing my queen… If my opponent takes the queen, it will be checkmate in 3. (He didn’t.)

White has just played 22. f6!

My opponent, being 2000 rated, played quite well. He missed punishing my blunder at around move 14.

Currently, my white opening repertoire involves the Bishop’s opening (1. e4 e5 2. Bc4), with a view towards playing f4 whenever possible to transpose into Vienna/King’s Gambit.

Forest Man of India

Previously, I blogged about the Mountain Man of India:

Mountain Man Motivational Story

Today, I learnt that there is also a Forest Man of India.

By planting one tree a day (for many years), Jadav Payeng (a.k.a Forest Man of India) has planted a forest bigger than Central Park in New York!

This principle of doing small things everyday also applies to students and learning. By doing one Math question per day, at the end of one year, a student would have completed 365 Math questions! This would be a considerable amount that would certainly help to boost the student’s Math grade and also Math understanding.

Goby and Shrimp Video (GEP Science)

Amazing “teamwork” between a goby fish and a shrimp! Basically, the shrimp is in charge of digging the burrow, but it is almost blind. The goby fish acts as the sentry to alert the shrimp in case of danger.

This video may be useful for GEP science, it may be tested as an example of “symbiotic relationships” in animals. GEP Science syllabus includes a brief introduction to different types of symbiosis (Mutualism, Commensalism and parasitism).

It is also very entertaining and can promote interest in science for children.

Also check out:

If your child is interested in a Computer Science/Data Science career in the future, do consider learning Python beforehand. Computer Science is getting very popular in Singapore again. To see how popular it is, just check out the latest cut-off point for NUS computer science, it is close to perfect score (AAA/B) for A-levels.

According to many sources, the Singapore job market (including government sector) is very interested in skills like Machine Learning/ Deep Learning/Data Science. It seems that Machine Learning can be used to do almost anything and everything, from playing chess to data analytics. Majors such as accountancy and even law are in danger of being replaced by Machine Learning. Python is the key language for such applications.

I just completed a short course on Python: Python A-Z™: Python For Data Science With Real Exercises! The course fee is payable via Skillsfuture for Singaporeans, i.e. you don’t have to pay a single cent. (You have to purchase it first, then get a reimbursement from Skillsfuture.) At the end, you will get a Udemy certificate which you can put in your LinkedIn profile.

The course includes many things from the basic syntax to advanced visualization of data. It teaches at quite a basic level, I am sure most JC students (or even talented secondary students) with some very basic programming background can understand it.

The best programming language for data science is currently Python. Try not to learn “old” languages like C++ as it can become obsolete soon. Anyway the focus is on the programming structure, it is more or less universal across different languages.

Related posts on Python:

Superposition Principle

If $\mathbf{u}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{b}$, and $\mathbf{v}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{c}$, then $\mathbf{u}+\mathbf{v}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{b}+\mathbf{c}$.

Proof:
$\mathbf{A}(\mathbf{u}+\mathbf{v})=\mathbf{A}\mathbf{u}+\bf{A}\mathbf{v}=\mathbf{b}+\mathbf{c}$

Properties of Matrix Transpose

1) $(A^T)^T=A$
2) $(A+B)^T=A^T+B^T$
3) $(kA)^T=kA^T$
4) $(AB)^T=B^T A^T$

Hangout @ Chinatown

Includes a review on “The Coconut Club”, which serves one of the best Nasi Lemak in Singapore.

Well, today I have one day off and my husband also has time. We planned to go to Chinatown and have lunch there. He wanted to try a nasi lemak restaurant there. It’s the first time for us to go to Chinatown and hunt for non-Chinese food.

Chinatown of Singapore is really close to to the CBD. You can actually walk from Chinatown to CBD and also see blocks of tall buildings from Chinatown.

There are many places to have nice food in Chinatown, such as Amoy Street and Chinatown Food Street.

Chinatown has many traditional buildings of Nanyang style.

The restaurant we went is at Ann Siang Rd.

There are many bars, restaurants and cafes there.

The blue restaurant is the one we were going.

The Coconut Club.

It is not a very big restaurant. Their signature dish is nasi lemak, which can be told from the menu.

Actually…

View original post 487 more words

To those starting JC life in today’s Singapore

Excellent post by top GP tutor Mr Steven Ooi. This post sums up the current competitiveness of the Singaporean education system. Similarly for Math, there is a knowledge “arms-race” to the extent that a typical Primary 3 student should know how to calculate 1+2+3+…+100 in case this question pops up in the exam. The textbook syllabus remains just as easy as in the past, but what is tested has become 10 times more difficult.

Dear young friend,

I’m writing this to share some thoughts that I used to convey to every one of my students when I was still a full-time tutor in Singapore (I retired in 2016). It is just my personal opinion, formed through years of experience as a student in the 1980s and 1990s, then as a tutor in the 2000s and 2010s.

Observing student life in the 90s and then in the 2010s, I can only conclude that the school system in Singapore has become 10 times more competitive than during my time. At least 10 times. During the 90s, most of my junior college classmates didn’t even attend private tuition. We could hang out at the bowling alley, the arcade or the hawker centre most…

View original post 1,324 more words

Malayan Aqua Fern

This “Malayan Aqua Fern” is a very mysterious plant, there is very little information on Google about it.

There are two views on it, based on online writings.

First viewpoint on Malayan Aqua Fern:

The “Malayan Aqua Fern” is none other than Peacock Fern, or Selaginella willdenowii. It is NOT an aquatic plant, and will die if fully submerged under water. This is quite reasonable, based on the pictures of Peacock Fern online, it does look like the pictures of the “Malayan Aqua Fern”. Nonetheless, it can be planted in a crab/terrapin tank where it is not fully submerged under water.

The “Malayan Aqua Fern” may give the illusion of surviving under water when it may be slowly dying (takes around a month to die).

Websites that support this view:

Second view:

The “Malayan Aqua Fern” is an amphibious plant, able to live both submerged or in moist conditions. If this is true, then “Malayan Aqua Fern” would be an incredible aquarium plant as it looks very good in a fish tank.

Websites that support this view:

Is Malayan Aqua Fern Aquatic or Not?

The main question is whether the Malayan Aqua Fern is aquatic or not? Can it grow fully submerged under water? If you have experience with the Malayan Aqua Fern, please leave your comments below!

Malayan Aqua Fern and Betta

Chromatic Fingering for Moonlight Sonata 3rd Movement

In Beethoven’s Moonlight Sonata 3rd movement, there is a very fast stretch of chromatic notes in bar 187.

I was wondering if the most basic fingering is good, or a more advanced fingering involving the 4th or even 5th finger would be better. (Read more on advanced chromatic fingering here: http://www.pianisttopianist.com/?p=486)

Some people on Reddit suggest some very fanciful fingerings, including “using LH (Left Hand!!) (faster playing up)4321,4312,4321,4321. So, groups of 4321 with the exception starting on the C. That part goes 4312. Just play all the way up with the LH and smack that top A (was it?) with yer Right Hand”! This fingering is apparently attributed to Alfred Brendel.

It turns out that at least 2 professional pianists seem to use the basic chromatic fingering: 2 13 123 13 123 … etc. They do not use the fourth finger at all. The starting fingering of the first note (G#) may vary.

The first pianist is Valentina Lisitsa. Watch at 0.25 speed to see the fingering at around 6:07 time. Lisitsa seems to use a “special trick” by using her left hand to play the lowest G# in the chromatic range.

The second pianist is Rousseau. You can see his fingering clearly, it is the basic chromatic fingering at around 6:34 time.

Hence, it seems that for Moonlight sonata it is not needed to use the advanced chromatic fingering. Using the pedal during the chromatic (both pianists use it to some extent) gives the illusion of a fast chromatic.

For other pieces like Fantasie Impromptu, the advanced chromatic fingering works well for greater speed.

Posted in maths tuition | Tagged , | 4 Comments

BTS Fan Products

BTS is one of the most popular Korean bands. Previously, we wrote on how Scientists Use Math To Discover Why BTS Jin Is The Most Handsome. Their dance steps are also amazing, hence it is no question why they are so popular worldwide. Basically, nowadays top artistes need to be good at dance + singing in order to be popular.

BTS seems very popular locally in Singapore, their concert tickets are often sold out within an hour. By the way, if a youth says that they are in “the Army”, it may not mean that they are soldiers/National Cadet Corps. BTS fans are also known as “the Army”. I once conversed with a taxi driver who told me that his daughter is in RGS, and most of her classmates are fans of K-pop including BTS. Korea is also now a top tourist destination for Singaporeans.

Both Qoo10 and Amazon have BTS fan paraphernalia, with Amazon having a more extensive collection. Most of the items ship to Singapore, with the delivery charge being quite affordable considering the huge distance from America to Singapore.

An example of a BTS cosmetic set from Qoo10.

WWW.QOO10.SG

Mathematician Couple’s Wedding Math Questions

It is fun for the guests who are also mathematicians like the wedding couple…

Why don’t the IT couples do the same with computer questions (eg. private cloud, serverless, containers, DevOps,… ) , lawyers with legal cases, doctors with medical questions …

Example 1 is obvious to this guest whose PhD research topic is in Differential Geometry “Chern Class” invented by Prof S. S. Chern (陈省身) :

Example 2 is obvious to this guest unless he/she can’t count the number of sides (8):

Example 3 is to the guest with some background in secondary school organic chemistry but forgotten, definitely not linear…

Example 4 to the hobbyist of Rubik’s cube, but the answer can be guessed easily by elimination: definitely not 2019 (this year), or π.


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#### ACCELERATION SERVOSYSTEM

A servosystem that controls the acceleration (rate of change in velocity) of a load [15].

format: plain


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# ATNF VLBI Wiki

### Site Tools

lbaops:lbamay2005:recentchanges

# Differences

This shows you the differences between two versions of the page.

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Could the Sun have liquid iron in orbit?

How close of an orbit to the Sun could an iron meteor get before it melts into a ball?

1 Answer

As this source stats, galvanized building iron has an albedo of 0.351.

In general, we can assume, that a half of its total surface is shined by the Sun, with an average 45% angle. That means that it gets the radiation of the 6000 K Sun on $$\frac{1}{2} \cdot \frac{1}{\sqrt{2}} \approx 35\%$$, as if it would be shined directly on its whole surface. It radiates back 35% of it, the remaining 65% heats it. That means, in its equilibrial temperature, the iron meteor radiates $$\approx 23\%$$ in all direction due to its temperature, than it gets from the Sun.

Furthermore, being $$n$$ solar radii away from the Sun, it also gets the per-surface thermal energy of $$\frac{1}{n^2}$$. Here I committed yet another "approximation", because the Sun is not a pointlike radiator if $$n$$ is small, and the final result will be probably small, but it won't be too big.

The thermal radiation is proportional roughly with the 4th power of the temperature.2 Thus, $$n$$ solar radii away, it gets $$\frac{1}{n^2}$$ per-surface solar heating, it radiates away $$0.23\frac{1}{n^2}$$, what makes its equilibrial temperature $$\sqrt[4]{0.23 \cdot \frac{1}{n^2}} = 0.69\frac{1}{\sqrt n}$$ of the Sun's.

The average surface temperature of the Sun is 5778 K, the meltig point of iron is 1881K. Thus,

$$5778\ \mathrm K \cdot 0.69\frac{1}{\sqrt n} = 1881\ \mathrm K$$

$$\frac{1}{\sqrt n}=\frac{1881\ \mathrm K}{5778\ \mathrm K\cdot 0.69}=0.47$$

$$n=\frac{1}{0.47^2} \approx \underline{\underline {4.5}}$$

The answer is: 4.5 solar radius from the solar center, which is $$\approx$$ 1.8 solar diameter from the surface. It is far deeper than the orbit of the Mercury. As a comparison, the Parker Solar Probe will near the Sun 8 solar radii away. A 2000 K maximal temperature is predicted on its heat shield (note, that probe won't have an equilibrial temperature).

Another remark: liquid things in vacuum evaporate. The evaporation for molten metals near their melting point is slow, but it exists. Such an object, if it does not have something to keep the iron vapor around it (f.e., gravitation), will slowly disappear.

1Surprisingly, I did not found better data with google.

2Also this is not exact, because it is true only for absolute black body radiators, but the spectrum of most ordinary materials does not cause a huge error in the calculation.

• like a magnetic field – Muze the good Troll. Apr 14 at 3:09
• @Muze Yes, it would work to keep away the solar wind. But magnetic field keeps only moving charged particles away. It can affect neutral gases, like iron vapor, at most diamagnetically, which is a hundred million times weaker. And there is no way for a molten iron ball to have a natural magnetic field, even solid iron is no more ferromagnetic over its Curie point ($\approx$ 900C). Some artificial electronic should operate in the shadow of the iron ball. – peterh Apr 14 at 3:11
• True but it could be given a field by running electricity through it? – Muze the good Troll. Apr 14 at 3:38
• @Muze Yes it could work. The current could be also induced by an external EM field from the back. – peterh Apr 14 at 3:41


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#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Options

# Green mathematics

edited August 2015

David asked me to explain what I'm up to. Here's a quick sketch.

We all know that life doesn't violate the 2nd law of thermodynamics, because the 2nd law says that entropy increases in a closed system, but the Earth is not a closed system: we're powered by the Sun. So, the Earth doesn't go to equilibrium: instead, life figure out how to exploit sunlight and build beautiful ordered structures.

But the details still need to be understood. And it's not just a matter of understanding the details of one particular case; there's a quite general pattern that systems out of equilibrium evolve organized structures that exploit the flow of 'free energy' (in the technical sense) through that system.

Ilya Prigogine won the Nobel prize for his work on this; he's written lots of pop books and also technical books about it, and lots of other people have worked on these issues. So it's not as if this is unexplored territory! Anyone who wants to work on these issues has a lot to learn... and that includes me.

Nonetheless, I feel I have a certain edge over other people. (Feynman said that to succeed in research, it helps to feel you have an "inside track", or "edge" - some insight or trick up your sleeve that nobody else has. It's true.)

Part of this edge is category theory. Category theory lets us formalize the idea of networks, and flows through networks, in a very general way that can be tailored to whatever circumstances we're interested in.

In particular, my student Brendan Fong wrote a paper that provides general tools for building categories where the morphisms are networks:

We used this to "black-box" passive linear networks, like circuits made of resistors, inductors and capacitors, obtaining their external behavior. The key was to take advantage of the principle of minimum power:

With my student Blake Pollard we have just finished generalizing this work to detailed balanced Markov processes - the random processes to which thermodynamic concepts like "temperature" and "free energy" apply:

In parallel, Blake has found a generalization of the 2nd law that applies to open systems:

The next step is to:

1) work out the connection to thermodynamics in much more detail, and

2) apply this framework to chemical reaction networks, or equivalently, stochastic Petri nets.

The type of thing we expect to explain is how, for example, a cell in your body carries out chemical reactions in cycles, driven by the flow of free energy through that cell. In some sense people already understand the basic idea - but they don't have a sufficiently precise and general language to talk about these things.

• Options
1.

Here's a somewhat more focused blog article explaining my new paper with Blake and Brendan:

Comment Source:Here's a somewhat more focused blog article explaining my new paper with Blake and Brendan: * John Baez, [A compositional framework for Markov processes](https://johncarlosbaez.wordpress.com/2015/09/04/a-compositional-framework-for-markov-processes/).
• Options
2.

Thanks! Great material, I am reading through it.

Comment Source:Thanks! Great material, I am reading through it.
• Options
3.

It will take me a while to get through, because I have to unlearn some aspects of what you are trying to do. That stems from my experiences authoring a book called Markov Modeling for Reliability Analysis (still selling! Wiley Press) where the mantra was to conserve probability within a graph.

Comment Source:It will take me a while to get through, because I have to unlearn some aspects of what you are trying to do. That stems from my experiences authoring a book called Markov Modeling for Reliability Analysis (still selling! Wiley Press) where the mantra was to conserve probability within a graph.
• Options
4.

Yes, Markov processes conserve probability within a graph, but if you look at a smaller graph within that graph, probability can flow in and out. So, if you want to talk about a "piece" of a Markov process, you need a more general concept, which is what we're studying.

Comment Source:Yes, Markov processes conserve probability within a graph, but if you look at a smaller graph within that graph, probability can flow in and out. So, if you want to talk about a "piece" of a Markov process, you need a more general concept, which is what we're studying.


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Lecture 32 - Ideal Gas Laws

If you need a pdf version of these notes you can get it here

Video of lecture

The video should play in any browser, but works best in anything that isn't Internet Explorer. If you are having trouble watching the video within the page you can download the video and play it in Quicktime.

Note: In the messing around with the hotplate I forgot to start the screencapture. Thankfully I did remember to put the flip camera on..

Boyle's Law

At constant temperature, it is found that the product of the pressure and volume of an ideal gas are constant

$PV=\mathrm{constant}$

This is named Boyle's Law, after Robert Boyle who formulated it in 1662.

Charles' Laws

Joesph Louis Gay-Lussac published Charles' Law in 1802, attributing it to unpublished work of Jacques Charles in the 1780's (Gay-Lussac has his own law..though it's not clear he should!).

Charles' Law states that at constant pressure the volume of a gas is proportional to the temperature.

$V\propto T$

Gay-Lussac's law

Gay Lussac's Law states that for a fixed volume the pressure is proportional to the temperature

$P\propto T$

Ideal Gas Law

The combination of the previous 3 laws implies that

$PV\propto T$

Our previous laws were for systems of constant mass, but we can see that the amount of mass should effect the volume (at a given pressure) or the pressure (at a given volume).

$PV\propto mT$

Measuring the amount of mass in moles will allow us to write the ideal gas law in terms of a universal constant. A mole of gas is a given number of molecules, Avagadro's number, $N_{A}=6.02\times 10^{23}$. If we have a certain mass $m$ of a gas which has a certain molecular mass (measured in atomic mass units, $\mathrm{u}$, which are also the number of grams per mole.), the the number of moles $n$ is given by

$n=\frac{m[\mathrm{g}]}{\textrm{molecular mass}[\mathrm{g/mol}]}$

and

$PV=nRT$ where $R=8.314\mathrm{J/(mol.K)}$

This equation is the ideal gas law

Ideal Gas Law for a number of molecules

The ideal gas law can also be written in terms of the number of molecules $N$

$PV=nRT=\frac{N}{N_{A}}RT=NkT$

where $k=\frac{R}{N_{A}}=\frac{8.314\mathrm{J/(mol.K)}}{6.02\times 10^{23}}=1.38\times 10^{-23}\mathrm{J/K}$ is the Boltzmann Constant.

Using the Ideal Gas Law to determine Absolute Zero

If $PV=nRT$ the absolute zero temperature occurs when $P=0$. In practice most gases will liquefy before this point, but we can measure the pressure of fixed volume of gas at a couple of reference points and extrapolate down to zero pressure to get an estimate for absolute zero.

Through laser cooling and molecular trapping techniques it is now possible (but difficult!) for temperatures on the order of a $\mathrm{nK}$ to be achieved. Prof. Dominik Schneble produces ultra-cold ($\mu K$) Bose-Einstein condensates in the basement of this building! Prof. Hal Metcalf was one of the key players in the original development of laser cooling.

What makes a gas ideal?

There are a number of conditions which must be satisfied for a gas to be considered ideal

1. There must be a large number of molecules and they should move in random directions with a range of different speeds.
2. The spacing between molecules should be much greater than the size of the molecules.
3. Molecules are assumed to interact only through collisions.
4. The collisions are assumed to be elastic.

Ideal gas law from a molecular perspective

We can work out the pressure exerted by an ideal gas on it's container by starting from the change in momentum of a molecule when it strikes the container wall

The average force due to one molecule is then

$F=\frac{\Delta(mv)}{\Delta t}=\frac{2mv_{x}}{2l/v_{x}}=\frac{mv_{x}^{2}}{l}$

The net force on the wall will be the sum of the forces from all $N$ molecules

$F=\frac{m}{l}\Sigma_{i=1..N} v_{xi}^{2}$

$\frac{\Sigma_{i=1..N} v_{xi}^{2}}{N}=\bar{v_{x}^{2}}$ → $F=\frac{m}{l}N\bar{v_{x}^{2}}$

$v^{2}=v_{x}^{2}+v_{y}^{2}+v_{z}^{2}$ → $\bar{v^{2}}=\bar{v_{x}^{2}}+\bar{v_{y}^{2}}+\bar{v_{z}^{2}}=\bar{3v_{x}^{2}}$

$F=\frac{m}{l}N\frac{\bar{v^{2}}}{3}$

$P=\frac{F}{A}=\frac{1}{3}\frac{Nm\bar{v^{2}}}{Al}=\frac{1}{3}\frac{Nm\bar{v^{2}}}{V}$

$PV=\frac{2}{3}N(\frac{1}{2}m\bar{v^{2}})=NkT$

$\bar{KE}=\frac{1}{2}m\bar{v^{2}}=\frac{3}{2}kT$


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Cheap and Secure Web Hosting Provider : See Now

# [Solved]: How to read edge labels like "01, 1" on a state diagram?

, ,
Problem Detail:

Is this state machine a moore machine or a mealy machine? I am confused because the states have outputs and the transitions have output based on the input. I tried making a state table but I think its wrong. Can anyone provide the state machine?

Since the states define the output, it's a Moore machine.

The edge labels can be understood as follows: an edge $A \xrightarrow{w_1, \dots, w_k} B$ with $w \in \Sigma^*$ means that you can transition from $A$ to $B$ reading any of the words $w_1, \dots, w_k$.

Essentially, it's just a way to compact automata. As an exercise, you can expand the edges and see what you get. It's clear that this compactification is valid for finite automata, even if you add output (if you allow state output $\varepsilon$).


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Greens Functions

[SOLVED] Greens Functions

Homework Statement

show:
$$\int\int\int_{D}\vec{F}\cdot\vec{G}dV = 0$$
where:
$$\vec{F}=\nabla\phi$$
$$\vec{G}=\nabla\psi$$
$$\nabla\cdot\vec{F}=0$$
$$\psi|_{\partial D}=0$$

The Attempt at a Solution

This looks like a problem for Greens first theorem:

$$\int\int\int_{D}\phi\nabla^{2}\psi dV = \int\int_{\partial D}\phi\nabla\psi dS - \int\int\int_{D}\nabla\psi\cdot\nabla\phi dV$$

The very right term is clearly the integral that I'm looking for. So, i will set it to look like the requested answer. Also, I know that
$$\psi|_{\partial D}=0$$
meaning that I can also throw out the second term because that term wants me to integrate the gradient of psi over the surface, while I know that psi is 0 over the surface. So, I am left with this:

$$\int\int\int_{D}\phi\nabla^{2}\psi dV = - \int\int\int_{D}\vec{F}\cdot\vec{G} dV$$

So, this means that the term on the left mus equal zero. Does anyone know how I can show this? Psi is not zero through the domain, and the problem doesn't specify that it is a harmonic potential (although I suppose it could be). Could someone please help me with this step? Any help at all is greatly appreciated.

Related Calculus and Beyond Homework Help News on Phys.org
Dick
Homework Helper
Uh, phi is given to be harmonic, not psi. Since the divergence of it's gradient is zero. Why don't you move the laplacian operator over to phi?

Last edited:
Dick


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# Simpify large number using congruences

Using the language of congruences, find the remainder when $22^{104}$ is divided by $18$.

My attempt:

$22 \equiv 4(mod 18)$, this means $22^{104} \equiv 4^{104}(mod18)$

I am confused about what to do after this step.

Edit:

$4^{1} \equiv 4(mod18)$

$4^{2} \equiv 16(mod18)$

$4^{3} \equiv 10(mod18)$

$4^{4} \equiv 4(mod18)$

So this means that the congruence will repeat every 3 terms. $104 = 2 + 34 *3$

$4^2 \equiv 16 (mod 18)$

Is this the correct way to do the problem?

• $4^{3*34+2} = 10^34*4^2$ since $4^3=10 mod 18$ and continue from there, there are many ways, you can do whatever you like, just start decomposition the power.
– Rab
Apr 19, 2017 at 21:27

Your way is fine. Nothing wrong with it. Sometimes there are little short cuts like Fermat's Little Theorem or Euler's Theorem, but brute forcing it is onyl bad because of computation and time. Another way: Note that $4^2\equiv 16\equiv-2\pmod{18}$ so that $4^{104}\equiv (4^{2})^{52}\equiv(-2)^{52}\equiv (2^{4})^{13}\equiv(-2)^{13}\equiv (2^{4})^3\cdot(-2)\equiv8\cdot2\equiv-2\equiv16$

• I agree with anonymaker. What if a similar problem appeared in a future exam and you are working with larger numbers? Then Fermat's Little Theorem would really come in handy. Apr 19, 2017 at 22:32

Let $n$ be a natural number, with $u_n=22^n$

For $n=0$ : $u_n= 22^0 \equiv 1[18]$

For $n=1$ : $u_n= 22^1 = 1\cdot18 + 4 \equiv 4[18]$

For $n=2$ : $u_n= 22^2 \equiv 16[18]$

For $n=3$ : $u_n= 22^3 \equiv 10[18]$

For $n=4$ : $u_n= 22^4 \equiv 4[18]$

By This way, we have constructed a periodic sequence, with $p=3$

So $22^{3k+1} \equiv 4[18]$

$104 = 34\cdot3+2$

So $22^{104} = 22^{34\cdot3+2} = 22^{(34\cdot3+1)+1} = 22^{(34\cdot3+1)}\cdot22$

$22^{104} \equiv 22^{(34\cdot3+1)}\cdot22[18] \Leftrightarrow 22^{104} \equiv 4\cdot4[18] \Leftrightarrow 22^{104} \equiv 16[18]$


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Manuals not in the Library (wanted/needed)

Recommended Posts

As soon as it is decided what everyone's share will be I will send mine

Is this to be done by PayPal

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Now that we're talking about this here, I'm comfortable telling you all that I'm prepared to throw $250 at this from my end. So with everyone else's donations, we've got over$500 buying power - I'm thinking that should go a long way.

Also, after I thought about it a minute, I think it best NOT to post anything on this in the general forum. What do you guys think? Just let the seller think we lost interest all together, if in fact he's watching.

I concur. We can PM all the folks who were involved.

Should another 'find' we want for the community become available, we don't want to tip off the future seller as well.

Next time I run across something like this I will not bring it out into the open like I did, "I should had better sense than that"
I will PM one of the moderators of the site instead, of course I don't think I will be running across something like this everyday

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OH-MY-GOD,,,THEY ARE IN CHINESE....

That's OK
My wife is Chinese, she could translate

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Nice job guys.

Count me in to help monetarily. (is that a word)

That is, I will help to pay the money needed to acquire and scan the manuals.

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You know what? Nobody needs to send any money. I figure I can sell off the duplicates, keep the few we don't have and send the originals to whoever is stockpiling them. The dup's will be enough to recoup my outlay, I think. Who knows, it may be a bust and we get nothing we need. I took the gamble. My donation to the site. Maybe we should reserve the rare ones on to a disc for emailing or snail mailing, rather than risk disclosure and dispursion on the net??? Maybe it's best to have all access to them?

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I would be happy to scan as many manuals as you will send. I have access to a scanner that will do 11x17 in one page - no need to split it across two annoying 8.5x11.

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I would be happy to scan as many manuals as you will send. I have access to a scanner that will do 11x17 in one page - no need to split it across two annoying 8.5x11.

Yup I've got similar. My office has a flatbed capable of those.

We (and by we I also mean me) scan 1000000000 of medical records a year so it's no biggie lol.

It's a 7k scanner that can do up to 1200x1200 dpi whic would be overkill lol.

I also can manipulate the photos to make them more readable since my major was computer graphics ie photoshop.

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Anybody want to venture a guess as to what I did?

Nice work Kevin!! Since your negotiation skills seem to be stellar, you wanna call my wife real quick and convince her I need more Carver amps?

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Anybody want to venture a guess as to what I did?
Nice work Kevin!! Since your negotiation skills seem to be stellar, you wanna call my wife real quick and convince her I need more Carver amps?
LOL! Your on your own there bro, most of us are married and have our own selling to do. :-P

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For the library, Enjoy!

Attached / uploaded, is a PDF of the:

Carver CT-29v Audio/Video
Preamplifier/Tuner
with Dolby Pro Logic Surround
Owner's Manual

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Stickers

Delivery today! We get to find out if it was worth it!

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I never did know, is this a pretty heavy amount of manuals?

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Hopefully it fills any holes in the manual library, and that you can sell them on recover your expenses.

Thanks,
Wayne

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Donations can be made to: "my user name "@gmail.com. Don't do kev777! it's kve777.

Just sent a small donation!

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Looks like we will be adding a few SERVICE MANUALS...
C-2
C-6
C-11
C-16
M-1.5
TL-3100
TL-3200
TL-3300
TX-2
TX-10
TX-11
TX-11b
M2120
M2060
M4120
M4060
TD-1200
TD-1400
TD-1700
TDR-2400
PST-24
AVR-100
H-9AV
PM-CX4
AV-64
PT-1250
PM-100
PM-120
PM-175
PM-200
PM-600
PM-900
These were oddly organized, by strict numerical order. I put them together by type, in Alpha-Numerical order. Sort of. Easier for me to find. Some of these may be more inclusive or better detail of ones we have, too. In all about 67 Service Manuals, approx half of which we don't have. Good deal, I say.

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SUPER WOW.

At least 7 in that list I am looking for.

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Stickers

My donation will be coming this weekend (have to wait for payday)

This is PayPal "correct" ??

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Kev  just got around to reading this trend, if theres a change of mind and contributions are needed, count me in brutha

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Thank you Mark & Kev for snagging these!  Audentes fortuna iuvat!

While the donations are still rolling into the war chest: who do we have to bribe to get Sunfire schematics?

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I appreciate your PayPal donations. It will help in shipping these around for scanning.

I'd like to get all of these scanned and digital copies sent to Gene and I. I want to keep categories together.
Groupings like in our library. I will send the entire group to one person for scanning, they can judge if duplicates need to be scanned for better imaging, like the MXR-130 schematics, for instance. Some of the pages are quite large.
I need volunteers for-
Preamps-10
Amps-14
Pro Amps-14 (DennisMiller)
Car amps-5
Tuners-5
Tape Decks-5
CD Players-4 (DennisMiller)
Processors and Speakers- 3

There are Service Bulletins with the appropriate Manual, as found.

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I will do Pre Amps, Receivers, and CDP.

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Kev,

I noticed in the list you have the TL-3300 listed twice. Does this mean you have a TL-3200 manual (typo) or you just duplicated the TL-3300 entry (tired) ??

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Kev,

I noticed in the list you have the TL-3300 listed twice. Does this mean you have a TL-3200 manual (typo) or you just duplicated the TL-3300 entry (tired) ??

3200, too!

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I need volunteers for-
Preamps-10 (DennisMiller)

Amps-14
Pro Amps-14
Car amps-5
Tuners-5
Tape Decks-5
CD Players-4 (DennisMiller)
Processors and Speakers- 3

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text:
# pytket.passes¶

Module exposing various types of compiler pass.

class pytket.passes.BasePass

Base class for passes.

__init__()

Initialize self. See help(type(self)) for accurate signature.

apply(*args, **kwargs)

1. apply(self: pytket.passes.BasePass, compilation_unit: tket::CompilationUnit, safety_mode: pytket.passes.SafetyMode = SafetyMode.Default) -> bool

Apply to a CompilationUnit. Return true if and only if the pass modified the circuit.

1. apply(self: pytket.passes.BasePass, circuit: pytket.circuit.Circuit) -> bool

Apply to a Circuit in-place. Return true if and only if the pass modified the circuit.

class pytket.passes.RepeatPass

Repeat a pass until it has no effect.

__init__(self: pytket.passes.RepeatPass, compilation_pass: pytket.passes.BasePass)None

Construct from a compilation pass.

class pytket.passes.RepeatUntilSatisfiedPass

Repeat a compilation pass until a predicate on the circuit is satisfied.

__init__(*args, **kwargs)

1. __init__(self: pytket.passes.RepeatUntilSatisfiedPass, compilation_pass: pytket.passes.BasePass, predicate: tket::Predicate) -> None

Construct from a compilation pass and a predicate.

1. __init__(self: pytket.passes.RepeatUntilSatisfiedPass, compilation_pass: pytket.passes.BasePass, check_function: Callable[[pytket.circuit.Circuit], bool]) -> None

Construct from a compilation pass and a user-defined function from Circuit to bool.

class pytket.passes.RepeatWithMetricPass

Repeat a compilation pass until the given metric stops decreasing.

__init__(self: pytket.passes.RepeatWithMetricPass, compilation_pass: pytket.passes.BasePass, metric: Callable[[pytket.circuit.Circuit], int])None

Construct from a compilation pass and a metric function.

class pytket.passes.SafetyMode

Members:

Audit : Checks which predicates a circuit satisfies after the application of each base pass

Default : Only check that a circuit satisfies the preconditions of the overall pass at the start and the postconditions at the end

__init__(self: pytket.passes.SafetyMode, arg0: int)None
property name

(self: handle) -> str

class pytket.passes.SequencePass

A sequence of compilation passes.

__init__(self: pytket.passes.SequencePass, pass_list: List[pytket.passes.BasePass])None

Construct from a list of compilation passes arranged in order of application.

pytket.passes.CXMappingPass(device: pytket.device.Device, placer: pytket.routing.Placement, **kwargs)pytket.passes.BasePass

Construct a pass to convert all gates to CX, relabel Circuit Qubits to :py:class’Device’ Nodes, route to the connectivty graph of a Device and decompose additional routing gates (SWAP and BRIDGE) to CX gates.

Parameters
• device – The Device used for connectivity information.

• placer – The placement used for relabelling.

• **kwargs – Parameters for routing: (int)swap_lookahead=50, (int)bridge_lookahead=4, (int)bridge_interactions=2, (float)bridge_exponent=0, (RoutingMethod)routing_method=RoutingMethod.base, (bool)directed_cx=false, (bool)delay_measures=true

pytket.passes.CliffordSimp(allow_swaps: bool = True)pytket.passes.BasePass

An optimisation pass that performs a number of rewrite rules for simplifying Clifford gate sequences, similar to Duncan & Fagan (https://arxiv.org/abs/1901.10114). Given a circuit with CXs and any single-qubit gates, produces a circuit with Z, X, S, V, U1, U2, U3, CX gates.

Parameters

allow_swaps – dictates whether the rewriting will disregard CX placement or orientation and introduce wire swaps.

pytket.passes.CommuteThroughMultis()pytket.passes.BasePass

Moves single-qubit operations past multi-qubit operations that they commute with, towards the front of the circuit.

pytket.passes.DecomposeArbitrarilyControlledGates()pytket.passes.BasePass

Decomposes CnX and CnRy gates into Ry, CX, H, T and Tdg gates.

pytket.passes.DecomposeBoxes()pytket.passes.BasePass

Replaces all boxes by their decomposition into circuits.

pytket.passes.DecomposeMultiQubitsIBM()pytket.passes.BasePass

Converts all multi-qubit gates into CX and single-qubit gates.

pytket.passes.DecomposeSingleQubitsIBM()pytket.passes.BasePass

Converts all single-qubit gates into U1, U2 and U3 gates.

pytket.passes.DecomposeSwapsToCXs(device: pytket.device.Device, respect_direction: bool = False)pytket.passes.BasePass

Construct a pass to decompose SWAP and BRIDGE gates to CX gates, constraining connectivity to a Device, optionally taking the directedness of the connectivity graph into account.

Parameters
• device – The device to use for connectivity information.

• respect_direction – Optionally takes the directedness of the connectivity graph into account.

pytket.passes.DecomposeSwapsToCircuit(replacement_circuit: pytket.circuit.Circuit)pytket.passes.BasePass
Parameters

replacement_circuit – An equivalent circuit to replace a SWAP gate with in the desired basis.

pytket.passes.DefaultMappingPass(device: pytket.device.Device)pytket.passes.BasePass

Construct a pass to relabel Circuit Qubits to Device Nodes, and then route to the connectivity graph of a :py:class: ‘Device’. Edge direction is ignored. Placement used is GraphPlacement.

Parameters
• device – The Device used for connectivity information.

• **kwargs – Parameters for routing: (int)swap_lookahead=50, (int)bridge_lookahead=4, (int)bridge_interactions=2, (float)bridge_exponent=0, (RoutingMethod)routing_method = RoutingMethod.base.

pytket.passes.DelayMeasures()pytket.passes.BasePass

Commutes Measure operations to the end of the circuit. Throws an exception when this is not possible because of gates following the measure which are dependent on either the resulting quantum state or classical values.

pytket.passes.EulerAngleReduction(arg0: pytket.circuit.OpType, arg1: pytket.circuit.OpType)pytket.passes.BasePass

Uses Euler angle decompositions to reduce all chains of P and Q rotations to minimal P-Q-P triples, where P,Q ∈ {Rx,Ry,Rz}.

Parameters
• q – The type of the inner rotation of each triple.

• p – The type of the outer rotations of each triple.

pytket.passes.FlattenRegisters()pytket.passes.BasePass

Merges all quantum and classical registers into their respective default registers with contiguous indexing.

pytket.passes.FullMappingPass(device: pytket.device.Device, placer: pytket.routing.Placement, **kwargs)pytket.passes.BasePass

Construct a pass to relabel Circuit Qubits to Device Nodes, and then route to the connectivity graph of a Device. Edge direction is ignored.

Parameters
• device – The Device to use for connectivity information.

• placer – The Placement used for relabelling.

• **kwargs – Parameters for routing: (int)swap_lookahead=50, (int)bridge_lookahead=4, (int)bridge_interactions=2, (float)bridge_exponent=0, (RoutingMethod)routing_method = RoutingMethod.base.

pytket.passes.FullPeepholeOptimise()pytket.passes.BasePass

Performs full (and slow) peephole optimisation and converts to a circuit containing only CX, U1, U2 and U3 gates.

pytket.passes.GuidedPauliSimp(strat: pytket.transform.PauliSynthStrat = PauliSynthStrat.Sets, cx_config: pytket.transform.CXConfigType = CXConfigType.Snake)pytket.passes.BasePass

Applies the PauliSimp optimisation pass to any region of the circuit contained within a CircBox. This can be useful to focus the synthesis to target specific sets of commuting operations, rather than the default greedy approach.

Parameters
• strat – A synthesis strategy for the Pauli graph.

• cx_config – A configuration of CXs to convert Pauli gadgets into.

pytket.passes.KAKDecomposition()pytket.passes.BasePass

An optimisation pass that performs a Cartan/KAK Decomposition for 2 qubit gate sequences, well explained in Robert Tucci (https://arxiv.org/abs/quant-ph/0507171). Given a circuit with CXs, SWAPs and any single-qubit gates, produces a circuit with the same gates. This will not preserve CX orientation.

pytket.passes.O1Pass()pytket.passes.BasePass

A recommended, all-purpose circuit optimisation pass for fast compilation. Compiles to the gateset {CX, tk1, Reset, Measure}. This should be applied before the default compilation pass of the target backend.

Returns

An optimisation pass that performs only basic circuit simplifications for basic usage.

Return type

BasePass

pytket.passes.O2Pass()pytket.passes.BasePass

A recommended, all-purpose circuit optimisation pass for fast compilation. Compiles to the gateset {CX, tk1, Reset, Measure}. This should be applied before the default compilation pass of the target backend.

Returns

An optimisation pass that performs local circuit simplification techniques.

Return type

BasePass

pytket.passes.OptimisePhaseGadgets(cx_config: pytket.transform.CXConfigType = CXConfigType.Snake)pytket.passes.BasePass

Construct a pass that synthesises phase gadgets and converts to a circuit containing only CX, U1, U2 and U3 gates.

Parameters

cx_config – A configuration of CXs to convert phase gadgets into.

pytket.passes.PauliSimp(strat: pytket.transform.PauliSynthStrat = PauliSynthStrat.Sets, cx_config: pytket.transform.CXConfigType = CXConfigType.Snake)pytket.passes.BasePass

Construct a pass that converts a circuit into a graph of Pauli gadgets to account for commutation and phase folding, and resynthesises them as either individual gagdets, pairwise constructions, or by diagonalising sets of commuting gadgets.

Parameters
• strat – A synthesis strategy for the Pauli graph.

• cx_config – A configuration of CXs to convert Pauli gadgets into.

pytket.passes.PlacementPass(placer: pytket.routing.Placement)pytket.passes.BasePass

Construct a pass to relabel Circuit Qubits to Device Nodes.

Parameters

placer – The Placement used for relabelling.

pytket.passes.RebaseCirq()pytket.passes.BasePass

Converts all gates to CZ, PhasedX and Rz.

pytket.passes.RebaseCustom(multiqs: , cx_replacement: pytket.circuit.Circuit, singleqs: , tk1_replacement: Callable[[Expression, Expression, Expression], pytket.circuit.Circuit])pytket.passes.BasePass

Construct a custom rebase pass. This pass: (1) decomposes multi-qubit gates not in the set of gate types multiqs to CX gates; (2) if CX is not in multiqs, replaces CX gates with cx_replacement; (3) converts any single-qubit gates not in the gate type set singleqs to the form $$\mathrm{Rz}(a)\mathrm{Rx}(b)\mathrm{Rz}(c)$$ (in matrix-multiplication order, i.e. reverse order in the circuit); (4) applies the tk1_replacement function to each of these triples $$(a,b,c)$$ to generate replacement circuits.

Parameters
• multiqs – The allowed multi-qubit operations in the rebased circuit.

• cx_replacement – The equivalent circuit to replace a CX gate in the desired basis.

• singleqs – The allowed single-qubit operations in the rebased circuit.

• tk1_replacement – A function which, given the parameters of an Rz(a)Rx(b)Rz(c) triple, returns an equivalent circuit in the desired basis.

pytket.passes.RebaseHQS()pytket.passes.BasePass

Converts all gates to ZZMax, PhasedX and Rz.

pytket.passes.RebaseIBM()pytket.passes.BasePass

Converts all gates to CX, U1, U2 and U3 gates.

pytket.passes.RebaseProjectQ()pytket.passes.BasePass

Converts all gates to SWAP, CRz, CX, CZ, H, X, Y, Z, S, T, V, Rx, Ry and Rz.

pytket.passes.RebasePyZX()pytket.passes.BasePass

Converts all gates to SWAP, CX, CZ, H, X, Z, S, T, Rx and Rz.

pytket.passes.RebaseQuil()pytket.passes.BasePass

Converts all gates to CZ, Rx and Rz.

pytket.passes.RebaseTket()pytket.passes.BasePass

Converts all gates to CX and tk1.

pytket.passes.RebaseUMD()pytket.passes.BasePass

Converts all gates to XXPhase, PhasedX and Rz.

pytket.passes.RemoveRedundancies()pytket.passes.BasePass

Removes gate-inverse pairs, merges rotations, removes identity rotations, and removes redundant gates before measurement. Does not add any new gate types.

pytket.passes.RoutingPass(device: pytket.device.Device, **kwargs)pytket.passes.BasePass

Construct a pass to route to the connectivity graph of a Device. Edge direction is ignored.

Parameters
• device – The device to use for connectivity information.

• **kwargs – Parameters for routing: (int)swap_lookahead=50, (int)bridge_lookahead=4, (int)bridge_interactions=2, (float)bridge_exponent=0, (RoutingMethod)routing_method = RoutingMethod.base.

pytket.passes.SynthesiseHQS()pytket.passes.BasePass

Optimises and converts a circuit consisting of CX and single-qubit gates into one containing only ZZMax, PhasedX and Rz.

pytket.passes.SynthesiseIBM()pytket.passes.BasePass

Optimises and converts all gates to CX, U1, U2 and U3 gates.

pytket.passes.SynthesiseUMD()pytket.passes.BasePass

Optimises and converts all gates to XXPhase, PhasedX and Rz.

pytket.passes.USquashIBM()pytket.passes.BasePass

Squash U1, U2 and U3 gates by converting to them to Rz-Ry-Rz sequences and back. The only single-qubit gates in the resulting circuit are U1 and U3.


text:
Basic question about kinetic energy and momentum

grayb
Hi, I'm learning about momentum and kinetic energy and I wanted to know if the following relationships are true. I think they are true, but I am not sure:

1. If kinetic energy goes down and mass stays constant, momentum goes down
2. If kinetic energy stays constant and mass goes down, momentum goes down
3. If kinetic energy goes up and mass stays constant, then momentum goes up
4. If kinetic energy is constant and mass goes up, momentum goes up

Are they true? Thank you.

Staff Emeritus
KE = p$^{2}$/(2m)
KE $\propto$ p$^{2}$
m $\propto$ p$^{2}$


text:
# Zwitterion

Zwitterion or Zwitter ion is an important topic of organic chemistry. Every year many questions are asked from this topic in various examinations. So, in this article we are discussing zwitterion in detail. The word zwitterion is derived from the German language word Zwitter which means hermaphrodite.

## What is Zwitterion?

Zwitterion is an ion or molecule which contains an equal number of positively charged functional group’s and negatively charged functional group’s. It is also called neutral ion or inner salts. Zwitterionic polymers are also found which contain negatively and positive charged functional groups at either end of the chain. Zwitter ion is amphoteric in nature and during electrolysis it neither migrates to cathode nor to anode.

α – amino acids are best examples to understand the zwitterions. α – amino acids show crystalline properties due to zwitterion formation. When we dissolve . α – amino acids in aqueous solution, it gives zwitterion. For example, if we dissolve R-CH-NH2-COOH in an aqueous solution then the oxygen atom pulls electrons from hydrogen in the carboxyl function group. Thus, oxygen gets negative charge and formation of H+ ion takes place. Now this H+ ion gains a lone pair of nitrogen and gets bonded with it. Thus, nitrogen gains a positive charge with formation of NH3. Structure is given below –

Amino acids contain both basic and acidic groups. In them amine is basic while carboxylic is an acidic group. Amine being a stronger basic group gains H+ ion from COOH and leaves the carboxylic group as COO- ion. Thus, zwitterion forms.

Apart from amino acids sulfamic acid also crystallizes in the zwitterion form. Sulfamic acid is also called amidosulfonic acid, amidosulfuric acid, aminosulfonic acid or sulfamidic acid. It is an inorganic compound with the formula H3NSO3. In solid state its structure is explained by its zwitterionic form. Its zwitterionic form is given below –

Betaine – It is also an example of zwitterion. It is a neutral chemical compound with positively charged functional group quaternary ammonium or phosphonium and with a negatively charged functional group such as carboxylate group. Betaine is a specific type of zwitterion as it does not have any hydrogen atom on the atom which is bearing a formal positive charge.

Other examples of Zwitterion include trimethyl glycine, psilocybin, cocamidopropyl betaine etc. The only amino acid which is optically inactive is glycine. In Glycine, a carbon atom is bonded with two same groups or two hydrogen atoms due to which it lacks a chiral carbon atom, so it is optically inactive. Structure of glycine is given below –

If a chemical species is resonance stabilized then it can be called a zwitterion, only if its all forms of resonance follow the definition of zwitterion.

## Effect of pH

pH of the solution affects the zwitterions. If a solution of amino acids is prepared by using a low pH medium. Then, the amino group of amino acid accepts a proton and forms a positively charged ion. It happens due to the presence of H+ ions in acidic medium. During electrolysis this cation goes towards the negatively charged electrode.

If a solution of amino acids is prepared by using a high pH medium. Then, deprotonation takes place in amino acid and a carboxylic group of amino acid donates a proton and forms the negatively charged ion and H2O molecule. It happens due to the presence of OH- ions in the basic medium. During electrolysis, this anion goes towards the positively charged electrode.

Depending upon the level of pH of the solution amino acid can be found as anion, cation, or zwitterion in its aqueous solution.

## Isoelectric point

After understanding all three forms of amino acids in their aqueous solution. We are in the condition of understanding the isoelectric point of zwitterions. Each and every zwitterion has an isoelectric point. The isoelectric point is the pH at which a molecule (a polyatomic ion) carries no net electric charge. It is represented as pI, pH(I) or IEP although standard nomenclature to represent the isoelectric point is pH(I). pH of the surrounding environment of the molecule affects its net electrical charge. In an acidic medium it can become more positively charged by accepting protons. While in the basic medium it can become more negatively charged by donating protons. The pI value of zwitterion can affect the solubility of the molecule. The molecule will show less or even minimum solubility in water or salt solutions at the pH that corresponds to their pI. Generally, molecules form precipitate in the solution at their pI.

Thus, the pH at which zwitterion of a molecule is formed is called isoelectric point of that molecule. Isoelectric point affects various properties of the molecule such as solubility in a solution.

## Calculating pI values

pI values are calculated by taking the average of the pKas that involve the zwitterion. pKa is a negative log of Ka and Ka is acid dissociation constant. pI value of zwitterion can be represented by the following formula –

${\text{pl}} = \frac{{p{K_{a1}} + p{K_{a2}}}}{2}$

Let's understand it by taking an example of alanine. For alanine value of pK1 is 2.34 and pK2 is 9.64 then what will be the value of pI for alanine?

As we know,    ${\text{pl}} = \frac{{p{K_{a1}} + p{K_{a2}}}}{2}$

On keeping the values given in the questions = $\frac{{2.34 + 9.64}}{2}$

pI = 5.99

It means in an electrolytic solution at pH 5.99 alanine will neither migrate to cathode nor to anode. This question came in NEET 2016.

## Applications of Zwitterion

Few applications of zwitterions are listed below –

• SDS PAGE is a common practical procedure of molecular biology. It is used to separate protein molecules by molecular mass. Glycine is used in this method and zwitterionic properties of glycine play a vital role for separating proteins using this method.

• Zwitterionic polymers possess antifouling properties and prevent microbial adhesion and biofilm formation.

• These are useful in the medical field, drug delivery and medical implants etc.

This was all about Zwitterion, if you are looking for solutions of NCERT Textbook problems based on this topic, then log on to Vedantu website or download Vedantu Learning App. By doing so, you will be able to access free PDFs of NCERT Solutions as well as Revision notes, Mock Tests and much more.


text:
College Physics (4th Edition)

The artificial gravity created in the washer's drum has a strength of $16.1~g$
We can express the angular velocity in units of $rad/s$: $\omega = 4.0~rev/s \times \frac{2\pi~rad}{1~rev} = 8\pi~rad/s$ We can find the radial acceleration: $a_r = \omega^2~r$ $a_r = (8\pi~rad/s)^2~(0.25~m)$ $a_r = 157.9~m/s^2$ We can express the radial acceleration in terms of $g$: $a_r = 157.9~m/s^2\times \frac{1~g}{9.80~m/s^2} = 16.1~g$ The artificial gravity created in the washer's drum has a strength of $16.1~g$


text:
Not connected, Your IP: 54.236.62.49

# All Activity

1. Past hour
2. Yesterday
3. ## New AirVPN User - AirVPN is the best!

Not staff here, but an obvious place to start: https://airvpn.org/aboutus/ https://airvpn.org/mission/
4. ## Unable to start (No socket)

I have had this iritating problem for a while now & windows was previously updated. The only way around this problem, is I restart my laptop, which is not ideal. I use Airvpn on a desktop running Linux Mint, and no problems, but I have had nothing but hassel since trying to use it on a new laptop, which has all the latest updates. I followed the advice previously, but this only worked temporarily.
5. ## Eddie strict firewall requirements

Could somebody document what eddie needs open and to where? For example, if I needed to open firewall ports to a specific destination like port 443 to nl.vpn.airdns.org, what other EXACT destinations and ports does it need in order to function? What specific server does it connect to for authentication and could I put that i a host file so I would not need external DNS? Thanks in advance.
6. ## Can we get a server in Poland? They seem to like freedom of speech.

@kbps Hello! However, mega.nz operates servers in Luxembourg (at least from what we can see on the web site). We think that New Zealand poses no privacy problems at all. The issue is just finding a suitable datacenter. Kind regards
7. ## How to make Eddie change server on Line Issue/Packet Loss?

Yesterday it had a line issue at 'Peony' server that took 2:30h and Eddie didn't change the server automatically. Line issues and packet loss are recurring problems and finding/changing manually a working server are not always an option. Is there a way to detect and change server automatically when these issues pops up? I imagine that some rules would be perfect in that case, though I'm not sure how this works in Eddie.
8. ## Can we get a server in Poland? They seem to like freedom of speech.

Sorry Air, I must have missed Estonia. List updated. New Zealand would be good. Mega.nz is based there. As far as I am aware their data centers are all in NZ. The speeds for their servers are very impressive. Yes I am aware of potential privacy issues in that they are closed source, I am using them as an example of a privacy orientated large company that is based in NZ.
9. ## Bitcoin ATMs that don't require ID?

@OpenSourcerer Oh, OK, so it is impossible to identify someone in practice in the ATM described by @Mad_Max. We had the impression that you wanted to imply otherwise. About masks and other protections which make facial recognition fail, they are mandatory (in many countries in the EU you can be severely fined if you don't wear them outdoors and you don't have a medically motivated exemption, or even criminally prosecuted) or strongly recommended nowadays, so it's not a big deal, even if they were necessary. Kind regards
10. ## Copy Settings

yes you are right, working now. Thanks a lot
11. ## Copy Settings

Okay, weird. I haven't seen this XML since at least v2.16.3. In any case, should be automatically converted to the new format.

Yes.
13. ## Bitcoin ATMs that don't require ID?

You are interpreting way too much into my words. I never wrote anything about any aggregation. What I can write for sure is that if someone stole a credit card for example and attempted to withdraw money with that card, the police publically showed in the past that they have camera feeds from when it happened. They are matching this and other suspected faces with pan-European criminal databases (I wouldn't know which ones, I do not work in this field) and if unsuccessful, they ask the public if someone knows this and that face. I deduce that from every transaction WHEN, TO and HOW MUCH is known. Say, you repeat those transactions and someone finds that usage abnormal, there might be something off, like you transfer 1000€ daily to BTC, for 14 days in a row; in come the camera feeds: You can see if it was the same person for example. From there it's just a leap into checking such databases. Maybe it's someone wanted for laundering? Maybe that person is the case of a lawsuit involving a bank robbery? You never know. I wouldn't recommend it. Privacy should be about blending in, not standing out as the only one making a BTC transaction wearing a mask that day.
14. ## Eddie libappindicator dependencies

@Aghinix Hello! Can you tell us whether the AppImage's eddie-tray fails with the identical error, or you get a different one? What is your current Desktop Environment? Apart from the minimization problem, is anything else fine? What is your version of libappindicator? Can you please re-check whether libindicator is available? Kind regards
15. ## Japan needs more servers

@OpenSourcerer Hello! It's a good idea. Actually we already have it (it is shown only to special users, we don't know if you can see it) so it would be simple to make it available to anyone. We will consider it seriously. Kind regards
16. ## Bitcoin ATMs that don't require ID?

@OpenSourcerer So, how is it possible that the ATMs described by @Mad_Max (which actually exist for sure) can be used in Germany to aggregate ex-post all the anonymous transactions of each person performing them, and provided that this is possible, how is it possible to link that video footage to an identity (for example if the aggregated withdrawals total exceeds some anti-laundering limit by law). This is technically very interesting and raises questions on the fundamental right to privacy. If confirmed, it may be advisable to use ATM with facial masks, glasses and adequate hats, which make facial recognition impossible (currently). Kind regards
17. ## [SOLVED] ipv6 error 1

Have a lot of ipv6 errors lately. Windows 10 with eddie 2.19.7. See file. found problem, must open eddie as administrator, because I have windows open via linux and KRDC. Suddenly saw it in log file. 😏
18. ## Copy Settings

Inside the old Eddie portable Version
19. ## Bitcoin ATMs that don't require ID?

They… don't…? I never wrote this process is automatic.
20. ## Copy Settings

Yes, it's that. Wait. Where did you find that?
21. ## Eddie libappindicator dependencies

Did you try searching for that specific file? $xlocate -S$ xlocate libindicator.so .
22. ## Copy Settings

C:\Users\username\AppData\Local\ is not Eddie Directory. I guess its the default.profile inside my old portable Version. What is about the AirVPN.xml ?? Regards Firefox

Can confirm.
24. ## Copy Settings

In a PowerShell: > Copy-Item "C:\Users\username\AppData\Local\Eddie\default.profile" -Destination \path\to\where\the\portable\version\is\ Or in words, copy the default.profile file from C:\Users\username\AppData\Local\Eddie\default.profile to where the portable version is.
25. ## Japan needs more servers

I know you locked this, but could it help adding a CPU %usage rrdgraph to every server detail page?
26. ## Can we get a server in Poland? They seem to like freedom of speech.

Hello! You can add Estonia and update the list: we have a 1 Gbit/s server in Tallinn, Estonia: https://airvpn.org/servers/Alruba/ New Zealand would be great, especially when you consider the infamous and outrageous anti-encryption law which prevents us from operating in Australia: we have been and we are struggling to find the right infrastructure. We'll keep searching. Kind regards
27. ## Can we get a server in Poland? They seem to like freedom of speech.

Useful website. Did not know about it. It will be good for making decisions about services that I use in the future. https://rsf.org/en/ranking Good to see that Air has servers in nearly half of the top 14. Norway - Yes Finland - No Denmark - No Sweden - Yes Netherlands - Yes Jamica - No Costa Rica - No Switzerland - Yes New Zealand - No Portugal - No Germany - Yes Belgium - Yes Ireland - No Estonia - Yes Would be good to see at least one server in each of these locations. Could be a good marketing angle. I understand that geographically some countries are neighbours such as Norway and Finland so probably would not improve latency. However it would be nice to see somewhere like New Zealand or Costa Rica, primarily for latency reasons for people in or near those regions.
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text:
# Problems with trigonometry getting the power of this complex expression

I'm here because I can't finish this problem, that comes from a Russian book:

Calculate $z^{40}$ where $z = \dfrac{1+i\sqrt{3}}{1-i}$

Here $i=\sqrt{-1}$. All I know right now is I need to use the Moivre's formula $$\rho^n \left( \cos \varphi + i \sin \varphi \right)^n = \rho^n \left[ \cos (n\varphi) + i \sin (n\varphi) \right]$$

to get the answer of this.

First of all, I simplified $z$ using Algebra, and I got this:

$$z = \dfrac{1-\sqrt{3}}{2} + i \left[ \dfrac{1+\sqrt{3}}{2} \right]$$

Then, with that expression I got the module $|z| = \sqrt{x^2 + y^2}$, and its main argument $\text{arg}(z) = \tan^{-1} \left( \dfrac{y}{x} \right)$.

I didn't have problems with $|z| = \sqrt{2}$, but the trouble begins when I try to get $\text{arg}(z)$. Here is what I've done so far:

$$\alpha = \text{arg}(z) = \tan^{-1} \left[ \dfrac{1+\sqrt{3}}{1-\sqrt{3}} \right]$$

I thought there's little to do with that inverse tangent. So, I tried to use it as is, to get the power using the Moivre's formula.

$$z^{40} = 2^{20} \left[ \cos{40 \alpha} + i \sin{40 \alpha} \right]$$

As you can see, the problem is to reduce a expression like: $\cos{ \left[ 40 \tan^{-1} \left( \dfrac{1+\sqrt{3}}{1-\sqrt{3}} \right) \right] }$.

And the book says the answer is just $-2^{19} \left( 1+i\sqrt{3} \right)$.

I don't know if I'm wrong with the steps I followed, or if I can reduce those kind of expressions. I'll appreciate any help from you people :)

-
All you need to work out is what angle that arctangent represents; the rest follows straightly. – Semiclassical Aug 17 '14 at 23:03
Those russian texts are always fascinating by the manner they carefully choose the straightforward but nevertheless not so evident to work out problems :) – Math Gems Aug 17 '14 at 23:04
Yes, but the problem is I can't use a calculator to get that angle. Is there a way to do so w/o it? – TX286 Aug 17 '14 at 23:05
Hrm, you probably can but it gets a bit hairy. There's a better hint to start from, which I'll give below...actually, scratch that. My hint is superfluous given Troy's answer below. – Semiclassical Aug 17 '14 at 23:09
You're right @MathGems :) Ok, I'll check those answers ;) – TX286 Aug 17 '14 at 23:13

Oh my. We have: $$1+i\sqrt{3} = 2\exp\left(i\arctan\sqrt{3}\right)=2\exp\frac{\pi i}{3}$$ $$\frac{1}{1-i} = \frac{1}{2}(1+i) = \frac{1}{\sqrt{2}}\exp\frac{\pi i}{4},$$ hence: $$z=\frac{1+i\sqrt 3}{1-i} = \sqrt{2}\exp\frac{7\pi i}{12},$$ so: $$z^{40} = 2^{20}\exp\frac{70\pi i}{3}=2^{20}\exp\frac{4\pi i}{3}=-2^{20}\exp\frac{\pi i}{3}=-2^{19}(1+i\sqrt{3}).$$ As an alternative way, if you set $a=1+i\sqrt{3}$ and $b=\frac{1}{1-i}$ you have: $$a^3 = -2^3,\qquad b^4 = -2^{-2},$$ hence: $$z^{40} = a^{40} b^{40} = a(a^3)^{13} (b^4)^{10} = a\cdot(-2^{39})\cdot(2^{-20}) = -2^{19}(1+i\sqrt{3}).$$

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@jackdaurizio, thank you! You helped me a lot! Just one thing: I think pi/4 in the second exp would be -pi/4, am I right? – TX286 Aug 17 '14 at 23:51
No, it should be right, $(1+i)$ has a positive imaginary part. – Jack D'Aurizio Aug 17 '14 at 23:54
Oh, I see. You're right! Thank you again! ;) – TX286 Aug 17 '14 at 23:58

$$z=\sqrt 2\frac{\frac{1+\sqrt 3i}{2}}{\frac{\sqrt 2-\sqrt 2i}{2}}=\sqrt 2 e^{i(\pi/3-(-\pi/4))}$$ and therefore: $$z^{40}=2^{20}e^{i2\pi/3}=-2^{19}(1+i\sqrt3)$$

-

To tackle the arctangent head-on, we make use of an identity derived from the tangent angle addition formula:

$$\tan\left(\frac\pi4+x\right)=\frac{\tan\frac\pi4+\tan x}{1-\tan\frac\pi4 \tan x}=\frac{1+\tan x}{1-\tan x}$$ since $\tan \dfrac\pi4=1$. Recalling that $\tan\dfrac\pi3=\sqrt{3}$, then we immediately have $$\alpha=\tan^{-1}\left(\frac{1+\sqrt{3}}{1-\sqrt{3}}\right)=\tan^{-1}\left(\frac{1+\tan\frac\pi3}{1-\tan\frac\pi3}\right)=\tan^{-1}\left[\tan\left(\frac{\pi}{4}+\frac{\pi}{3}\right)\right]=-\frac{5\pi}{12}$$ since $\tan^{-1}$ takes values in $(-\pi/2,\pi/2]$.

From here, things are clear: $$\cos(40\alpha)+i\sin(40\alpha) =\cos\left(-\frac{2\pi}{3}-16\pi \right)+i\sin\left(-\frac{2\pi}{3}-16\pi \right)=-\frac{1+i\sqrt{3}}{2}$$ Multiplying through by the modulus $2^20$ gives the desired result.

-
Note that this is not the 'clever' approach; it is certainly better to recognize that $z$ is a quotient of simpler complex numbers. But the $\tan\left(\frac{\pi}{4}+x\right)$ identity given above is a nice addition to one's toolkit. – Semiclassical Aug 18 '14 at 0:12
Thank you very much @semiclassical, it's great to know this! ;) – TX286 Aug 18 '14 at 0:31


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# What is the equation of this curve?

1. Mar 14, 2010

### phantomcow2

1. The problem statement, all variables and given/known data

Let C be the circle with center (a/2, 0) and radius a/2. Let L be the line with equation x=a, find the polar equation of the curve produced in the following manner: FOr every angle $$\theta$$, -$$\pi/2$$ <$$\theta$$ < $$\pi/2$$, consider the ray from the origin that makes the angle $$\theta$$ with the positive x axis. This ray will intersect C at a point A and L at a point B. Let O be the origin. Then the point P on the ray is on the curve if line segment OP = line segment AB.

http://img341.imageshack.us/img341/8910/cireq.jpg [Broken]

If I trace it out, which I did in my example, it begins to look like a centroid. However I don't know how to verify this. I'm not sure exactly how to systematically approach this problem.
My idea is to break the equation of the resulting curve into two parts: first the length of the segment from the origin to when it hits the boundary of the circle, then the distance from the circle to the vertical line; the resulting curve being the difference between the former and the latter. I believe the distance of the line segment from O to A is simply cos$$\theta$$. I'm not sure how I'd express the rest of it though.

Last edited by a moderator: May 4, 2017
2. Mar 14, 2010

### LCKurtz

Hints:

What is the equation of the line in polar coordinates: r1 = ?? in terms of θ?

What is the equation of the circle in polar coordinates: r2 = ?? in terms of θ?

Then your curve, in polar equations is r = r1 - r2.

The curve approaches x = a as a vertical asymptote.

3. Mar 14, 2010

### phantomcow2

Darn, it's been too long since I've learned about polar coordinates. I know that the equation of the circle in polar coordinates is r=acos$$\theta$$. Some research is needed to find a straight line!

Thanks very much for your assistance!

Last edited: Mar 14, 2010
4. Mar 14, 2010

### phantomcow2

Okay, I looked through my old calculus books and have relearned that the equation of a vertical line is a=rcos(theta)

Resulting curve: acos(theta)-asec(theta)

5. Mar 14, 2010

### LCKurtz

Yes, but you mean r = a sec(theta) - a cos(theta)


text:
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# Iterating through OpenStudio Objects to get their "Types" and "Attributes"

Hi All,

For context this is being done using Python. I'm trying to see if there's a built-in method where I can load an existing OpenStudio model, use specific_object = osm.getObject(an_object_handle).get() to isolate a specific object (where osm is the whole model), and then pick apart and inspect what's in the object. If I use print(specific_object) I get a nice human-readable block of text. However I can't seem to figure out how to iterate through these fields beyond just specific_object.name().

I'd like to iteratively return if possible the type of object (Space, Thermal Zone, Construction, etc.), and its attributes. Like in the case of a space, returning Space Type Name, Default Construction Set Name, Default Schedule Set Name, etc.

I put types and attributes in quotes in the title because I think the nomenclature in OpenStudio is a little different which might be part of my problem.

I really appreciate any suggestions you all might have. I think if all else fails I could use str(specific_object) to get that human-readable output and then parse through that with other python tools. I just wasn't sure if there was a built-in way. My end goal for this project is to generate some reporting for myself about the model so I don't necessarily need to hang onto the OpenStudio objects themselves nor am I necessarily trying to change them. However, it would be nice to know what options I have should I want to later.

Thanks!

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You are looking for the OpenStudio SDK. Take a look at the documentation for the FanOnOff class. There are different methods to get everything about the fan, take a look at the example code below where I print the fan pressureRise parameter.

from openstudio import model
m = model.Model()
f = model.FanOnOff(m)
pressure_rise_si = f.pressureRise()
print('The fan Pressure Rise in Pa is ' + str(pressure_rise_si))

Output

The fan Pressure Rise in Pa is 300.0

You can get any parameter from a fan using similar methods, take a look at the SDK for the specific documentation.

Hmm interesting, I would like to ask you back what is the reason why you would do this. The following Python code should do what you are asking if I understand what you want to do.

# Create a fan
from openstudio import model
m = model.Model()
f = model.FanOnOff(m)
#  Get the fan iddObject
obj = f.iddObject()
fields = obj.numFields()
for i in range(fields):
print(f.getField(i))

Output:

{0fae4eb3-fe16-4c05-94f7-4ed150857507}
Fan On Off 1
{2f817562-e016-4118-9091-e4f096e2b345}
0.6
300
autosize
0.8
1

{668676fe-a69f-4db3-8e07-9953fa12b2d4}
{eb20ba76-8c87-412f-be6f-8d4b4c8af830}

more