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# tower of hanoi equation

Hence, the time complexity of the recursive solution of Tower of Hanoi is O (2n) which is exponential. $\therefore T(n) = 2^3 * T(n-3) + 2^2 + 2^1 + 1$ Active 5 years, 9 months ago. As we said we pass total_disks_on_stack â 1 as an argument. We are now ready to move on. In this problem, you will be working on a famous mathematical puzzle called The Tower of Hanoi. We also have thousands of freeCodeCamp study groups around the world. (again move all (n-1) disks from aux to dest. When moving the smallest piece, always move it to the next position in the same direction (to the right if the starting number of pieces is even, to the left if the starting number of pieces is odd). Khan Academy is a 501(c)(3) nonprofit organization. I have studied induction before, but I just don't see what he is doing here. Logic Games Fun Games. The Tower of Hanoi is one of the most popular puzzle of the nineteenth century. Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. This is the currently selected item. 4 $\begingroup$ I am new to proofs and I am trying to learn mathematical induction. $T(n) = 2^k * T(n-k) + 2^{k-1} + 2^{k-2} + ... + 2^2 + 2^1 + 1 \qquad(2)$ The main aim of this puzzle is to move all the disks from one tower to another tower. S. Tanny MAT 344 Spring 1999 72 Recurrence Relations Tower of Hanoi Let T n be the minimum number of moves required. This video explains how to solve the Tower of Hanoi in the simplest and the most optimum solution that is available. I am reading Algorithms by Robert Sedgewick. \begin{cases} Our mission: to help people learn to code for free. ããã¯å¶ä½è(ããã)ãç®¡çããã ãTOWER of HANOIãã¨ããããªã¼ã²ã¼ã ã®å¬å¼ãµã¤ãã§ãã ... Use MathJax to format equations. You can make a tax-deductible donation here. How to make your own easy Hanoi Tower 6. T(n) = There are two recursive calls for (n-1). For the generalized p-peg problem with p > 4, it still remains to establish that the policy adopted to derive the DP equation (2.2) is optimal. Hanoi Tower Math 4. Four-Pole Tower of Hanoi: Suppose that the Tower of Hanoi problem has four poles in a row instead of three. We can use B as a helper to finish this job. A simple solution for the toy puzzle is to alternate moves between the smallest piece and a non-smallest piece. So every morning you do a series of tasks in a sequence: first you wake up, then you go to the washroom, eat breakfast, get prepared for the office, leave home, then you may take a taxi or bus or start walking towards the office and, after a certain time, you reach your office. These disks are stacked over one other on one of the towers in descending order of their size from â¦ Let it be J. For eg. TowerofHanoi(n-1, aux, dest, source){ //step3} Thus, an algorithm to solve the Tower of Hanoi iteratively exists. First, move disk 1 from source to dest tower. on integers). + 2n-1 which is a GP series having common ratio r=2 and sum = 2n - 1. Three simple rules are followed: Now, letâs try to imagine a scenario. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: 1) Only one disk can be moved at a time. If $$k$$ is 1, then it takes one move. $$. If k is 1, then it takes one move. Object of the game is to move all the disks over to Tower 3 (with your mouse). In our Towers of Hanoi solution, we recurse on the largest disk to be moved. The largest disk (nth disk) is in one part and all other (n-1) disks are in the second part. Move three disks in Towers of Hanoi. â¦ Now, letâs try to build the algorithm to solve the problem. \text{Generalizing the above equation for k^{th} time. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack. Any idea? It consists of three pegs and a number of discs of decreasing sizes. If we have even number of pieces 6.2. \right\}$$ Tower of Hanoi (which also goes by other names like Tower of Brahma or The Lucas Tower), is a recreational mathematical puzzle that was publicized and popularized by the French mathematician Edouard Lucas in the year 1883. Juega online en Minijuegos a este juego de Pensar. To solve this problem, we need to just move that disk to dest tower in one step. Play Tower of Hanoi. Pseudocode is a method of writing out computer code using the English language. Hence, the recursive solution for Tower of Hanoi having n disks can be written as follows, $$TowerofHanoi(n, source, dest, aux) = \text{Move disk 1 from source to dest}, \text{if n=1}, Our mission is to provide a â¦ Fortunately a Tower of Hanoi game with 64 disks needs about 585 billion years when one is moving one disk per second and our sun will evolve into a red giant and then a white dwarf in about 5 billion years, so you we shouldn't worry about the priests of Brahma finishing the game before you have finished whatever you think is important to finish in a mens life. Towers of Hanoi, continued. Itâs an asymptotic notation to represent the time complexity. Hence, the time complexity of the recursive solution of Tower of Hanoi is O(2n) which is exponential. Math: on-line math problems Dear Marie, A computer version of the Towers of Hanoi written for Macintosh Computers at Forest Lake Senior High in Forest Lake Minnesota explains that: "The familiar tower of Hanoi was invented by the French Mathematician Eduard Lucas and sold as a toy in â¦ Before we can get there, letâs imagine there is an intermediate point B. Play Tower of Hanoi. Then move disk 2 to dest tower on top of disk 3. I have to implement an algorithm that solves the Towers of Hanoi game for k pods and d rings in a limited number of moves (let's say 4 pods, 10 rings, 50 moves for example) using Bellman dynamic programming equation (if the problem is solvable of course). The number of disks can vary, the simplest format contains only three. In this variation of the Tower of Hanoi there are three poles in a row and 2n disks, two of each of n different sizes, where n is any positive integer. As puzzles go, nobody really did it better than the monks who came up with the one we are going to learn about, the Towers of Hanoi.Besides being a really cool puzzle, it has a lot of practical (and historical!) If we have an odd number of pieces 7. significance as we learn about recursion. Tower of Hanoi is a mathematical puzzle which consists of three towers(or pegs) and n disks of different sizes, numbered from 1, the smallest disk, to n, the largest disk. At first, all the disks are kept on one peg(say peg 1) with the largest peg at the bottom and the size of pegs gradually decreases to the top. The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. Tower Of Hanoi. No large disk should be placed over a small disk. You can only move the disks one at a time and you can never place a bigger disk on a smaller disk. To solve this problem there is a concept used in computer science called time complexity. Solve for T n? So there is one rule for doing any recursive work: there must be a condition to stop that action executing. In our case, this would be our terminal state. In simple terms, an algorithm is a set of tasks. Again Move disk 1 from aux to source tower. Viewed 20k times 1. Now move disk 1 from dest to aux tower on top of disk 2. You can select the number of discs and pegs (within limits). The "Towers of Hanoi" Puzzle, its Origin and Legend. Move Disk 1 from aux to dest. If you take a look at those steps you can see that we were doing the same task multiple times â moving disks from one stack to another. The simplified recurrence relation from the above recursive solution is,$$ (move all n-1 disks from source to aux.). When we do the second recursive call, the first one is over. Studying the N=3 MToH puzzle, I realized that what breaks the base 3 rule is the possibility of the smallest disk to move to a free post (step 5 in Table Magnetic Tower of Hanoi (: . Merge sort. What you need to do is move all the disks from the left hand post to the right hand post. Then, move disk 3 from source to dest tower. We take the total disks number as an argument. Move three disks in Towers of Hanoi.              Move Disk 2 from source to dest Most of the recursive programs take exponential time, and that is why it is very hard to write them iteratively. For the 3-peg Tower of Hanoi problem, Wood [30] has shown that the policy leading to the DP equation (2.1) is indeed optimal. T 0 = 0, T 1 = 1 7 Initial Conditions * T n = 2 T n - 1 + 1 n $2 T n is a sequence (fn. For the towers of Hanoi problem, the implication of the correspondence with n-bit numbers is a simple algorithm for the task. You have 3 pegs (A, B, C) and a number of discs (usually 8) we want to move all the discs from the source peg (peg A) to a destination peg (peg B), while always making sure â¦ There is one constant time operation to move a disk from source to the destination, let this be m1. How does the Tower of Hanoi Puzzle work 3. \text{Move$n^{th}$disk from source to dest}\text{ //step2}\\ Our mission is to provide a free, world-class education to anyone, anywhere. $$. The formula for this theory is 2n -1, with "n" being the number of rings used. The tower of Hanoi (commonly also known as the "towers of Hanoi"), is a puzzle invented by E. Lucas in 1883.It is also known as the Tower of Brahma puzzle and appeared as an intelligence test for apes in the film Rise of the Planet of the Apes (2011) under the name "Lucas Tower.". Tower Of Hanoi - Online Games At Softschools. I enjoy learning and experiencing new skills. Tower of Hanoi â Origin of the Name 2. Tower of Hanoi Solver Solves the Tower of Hanoi in the minimum number of moves. Assume one of the poles initially contains all of the disks placed on top of each other in pairs of decreasing size. The object of the game is to move all of the discs to another peg. Running Time. Well, this is a fun puzzle game where the objective is to move an entire stack of disks from the source position to another position. Inserting a new node in a linked list in C. 12 Creative CSS and JavaScript Text Typing Animations. Below is an excerpt from page 213, in reference to number of trailing zeros in binary representation of numbers. There are three pegs, and on the first peg is a stack of discs of different sizes, arranged in order of descending size. Disks can be transferred one by one from one pole to any other pole, but at no time may a larger disk be placed on top of a smaller disk. Otherwise, let us denote the number of moves taken as $$T(k)$$.From the code, we can see that it takes $$T(k) = 2T(k-1) + 1$$.. Find below the implementation of the recursive solution of Tower of Hanoi, Backtracking - Explanation and N queens problem, CSS3 Moving Cloud Animation With Airplane, C++ : Linked lists in C++ (Singly linked list), Inserting a new node to a linked list in C++. The main aim of this puzzle is to move all the disks from one tower to another tower. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might And finally, move disk 1 and disk 2 from aux to dest tower i.e. Also, I tried to give you some basic understanding about algorithms, their importance, recursion, pseudocode, time complexity, and space complexity. This video explains how to solve the Tower of Hanoi in the simplest and the most optimum solution that is available. The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. The time complexity of algorithms is most commonly expressed using big O notation. An explicit pattern permits one to form an equation to find any term in the pattern without listing all the terms before it (Tower of Hanoi, 2010, para. tower, refer to it as the "Colored Magnetic Tower of Hanoi" and study its properties. But you cannot place a larger disk onto a smaller disk. \left. No problem, letâs see. The game's objective is to move all the disks from one rod to another, so that a larger disk never lies on top of a smaller one. How to make your own easy Hanoi Tower 6. However - solving a Tower of Hanoi game with 64 disks move by move needs a long time and so one might want a solution for skipping a few billion moves. For example, the processing time for a core i7 and a dual core are not the same. Solving Towers Of Hanoi Intuitively The Towers of Hanoi problem is very well understood. This is the second recurrence equation you have seen in this module. Tower of Hanoi - Learning Connections Essential Skills Problem Solving - apply the strategy: solving a simpler problem Suppose you work in an office. December 2006 The Towers of Hanoi The Towers of Hanoi The Towers of Hanoi puzzle was invented by the French mathematician Edouard Lucas in 1883. * Towers of Hanoi 08/09/2015 HANOITOW CSECT USING HANOITOW,R12 r12 : base register LR R12,R15 establish base register \text{we get k=n-1}, thus putting in eq(2), nth disk at the bottom and 1st disk at the top. \therefore T(n) = 2^{n}-1. The terminal state is the state where we are not going to call this function anymore. The rules are:- The tower of hanoi is a mathematical puzzle. If you want to learn these topics in detail, here are some well-known online courses links: You can visit my data structures and algorithms repo to see my other problems solutions. Celeration of Executive Functioning while Solving the Tower of Hanoi: Two Single Case Studies Using Protocol Analysis March 2010 International Journal of Psychology and Psychological Therapy 10(1) TowerofHanoi(n-1, source, dest, aux)\text{ //step1}\\ Suppose we have a stack of three disks. The Tower of Hanoi is a famous problem which was posed by a French mathematician in 1883. How to solve Tower Of Hanoi (Algorithm for solving Tower of Hanoi) 6.1. The tower of Hanoi problem is used to show that, even in simple problem environments, numerous distinct solution strategies are available, and different subjects may learn different strategies. MathJax reference. 18.182 Partidas jugadas, ¡juega tú ahora! The above equation is identified as GP series having a common ratio r = 2 The above equation is identified as GP series having a common ratio r = 2 and the sum is 2n â1 2 n â 1. â´ T (n) = 2n â1 â´ T ( n) = 2 n â 1. --Sydney _____ Date: 5 Jan 1995 15:48:41 -0500 From: Anonymous Newsgroups: local.dr-math Subject: Re: Ask Dr. Here is a summary of the problem: To solve the Tower of Hanoi problem, we let T[n] be the number of moves necessary to transfer all the disks. 2.2. The Colored Magnetic Tower of Hanoi â the "100" solution .$$ At first, all the disks are kept on one peg(say peg 1) with the largest peg at the bottom and the size of pegs gradually decreases to the top. The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. That is â¦ The tower of Hanoi (commonly also known as the "towers of Hanoi"), is a puzzle invented by E. Lucas in 1883.It is also known as the Tower of Brahma puzzle and appeared as an intelligence test for apes in the film Rise of the Planet of the Apes (2011) under the name "Lucas Tower.". Hence, the Tower of Hanoi puzzle with n disks can be solved in minimum 2n−1 steps. Tower of Hanoi. Donations to freeCodeCamp go toward our education initiatives, and help pay for servers, services, and staff. Donât worry if itâs not clear to you. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top. Practice: Move three disks in Towers of Hanoi. If you read this far, tweet to the author to show them you care. In that case, we divide the stack of disks in two parts. That is, we will write a recursive function that takes as a parameter the disk that is the largest disk in the tower we want to move. In fact, I think itâs not only important for software development or programming, but for everyone. Assume one of the poles initially contains all of the disks placed on top of each other in pairs of decreasing size. It consists of three pegs mounted on a board together and consists of disks of different sizes. An algorithm is one of the most important concepts for a software developer. How does the Tower of Hanoi Puzzle work 3. Then we need to pass source, intermediate place, and the destination so that we can understand the map which we will use to complete the job. Definition of Tower of Hanoi Problem: Tower of Hanoi is a mathematical puzzle which consists of three towers or rods and also consists of n disks. After the explanation of time complexity analysis, I think you can guess now what this isâ¦This is the calculation of space required in ram for running a code or application. Running Time. Basic proof by Mathematical Induction (Towers of Hanoi) Ask Question Asked 7 years, 9 months ago. From the above table, it is clear that for n disks, the minimum number of steps required are 1 + 21 + 22 + 23 + .…. Tower of Hanoi Solver Solves the Tower of Hanoi in the minimum number of moves. Before getting started, letâs talk about what the Tower of Hanoi problem is. \end{cases} Consider a Double Tower of Hanoi. The puzzle was invented by the French mathematician Edouard Lucas in 1883 and is often described as a mathematical puzzle, although solving the Tower of Hanoi doesn't require any mathematical equations at all for a human player. Hi, I am studying the Tower of Hanoi problem in Donald Knuth's Concrete Mathematics book, and I do not understand his description of solving the problem by induction. The Tower of Hanoi â Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles.It was written by Andreas M. Hinz, Sandi KlavÅ¾ar, UroÅ¡ MilutinoviÄ, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. To learn more, see our tips on writing great answers. Although I have no problem whatsoever understanding recursion, I can't seem to wrap my head around the recursive solution to the Tower of Hanoi problem. It consists of threerods, and a number of disks of different sizes which can slideonto any rod. Letâs go through each of the steps: You can see the animated image above for a better understanding. How to solve Tower Of Hanoi (Algorithm for solving Tower of Hanoi) 6.1. But itâs not the same for every computer. ¡Jugar a Tower Of Hanoi es así de sencillo! The rules are:- Now, the time required to move n disks is T(n). The formula is T (n) = 2^n - 1, in which ânâ represents the number of discs and âT (n)â represents the minimum number of moves. Using Back substitution method T(n) = 2T(n-1) + 1 can be rewritten as,$T(n) = 2(2T(n-2)+1)+1,\text{ putting }T(n-1) = 2T(n-2)+1$Algorithms affect us in our everyday life. First, move disk 1 and disk 2 from source to aux tower i.e. Practice: Move three disks in Towers of Hanoi. Our job is to move this stack from source A to destination C. How do we do this? In our case, the space for the parameter for each call is independent of n, meaning it is constant. I love to code in python. 'Get Solution' button will generate a random solution to the problem from all possible optimal solutions - note that for 3 pegs the solution is unique (and fairly boring). Get started, freeCodeCamp is a donor-supported tax-exempt 501(c)(3) nonprofit organization (United States Federal Tax Identification Number: 82-0779546). But you cannot place a larger disk onto a smaller disk. These disks are stacked over one other on one of the towers in descending order of their size from bottom i.e. Hence: After these analyses, we can see that time complexity of this algorithm is exponential but space complexity is linear.$T(n) = 2^{n-1} * T(1) + 2^{n-2} + 2^{n-3} + ... + 2^2+2^1+1$In my free time, I read books. We have to obtain the same stack on the third rod. Tower of Hanoi is a mathematical puzzle which consists of three towers(or pegs) and n disks of different sizes, numbered from 1, the smallest disk, to n, the largest disk. Just like the above picture. If we have an odd number of pieces 7. Tower of Hanoi â Origin of the Name 2. We get,}$ C Program To Solve Tower of Hanoi without Recursion. The task is to move all the disks from one tower, say source tower, to another tower, say dest tower, while following the below rules, Output: Move Disk 1 from source to aux Move rings from one tower to another but make sure you follow the rules! Tower of Hanoi is a mathematical puzzle. You can move only one disk at a time from the top of any tower. When we run code or an application in our machine it takes time â CPU cycles.


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# Calculus chain rule problem

When I was doing problems in my textbook, I came across this problem:

The velocity of a heavy meteorite entering the earth's atmosphere is inversely proportional to $\sqrt s$ when it is s kilometers from the earth's center. Show that the meteorite's acceleration is inversely proportional to $s^2$.

From what I have learned, I know the velocity $= k/(\sqrt s)$. And the acceleration is just the derivative of the acceleration. Which means $dv/dt$. But when I looked at this answer, it does something like $\frac{dv}{dt} = \frac{dv}{ds} * \frac{ds}{dt} = \frac{dv}{ds}v$ And then got a different answer than mine. I don't understand why can we just take the derivative directly. I appreciate the help, thanks!

The problem is here that we don't know the time.

However, we do know what $s$ is, since it is in our equation.

Therefore,

we split up the derivative.

Taking the derivative with respect with $t$ for the equation.

$$\frac{dv}{dt}$$

Now, since we know $s$, we change the variable by using the chain rule.

$$\frac{dv}{dt} = \frac{dv}{ds}*\frac{ds}{dt}$$

Since $\frac{ds}{dt} = v$,

$$\frac{dv}{dt} = \frac{dv}{ds}*\frac{ds}{dt} = \frac{dv}{ds}*v$$

Now we have the acceleration in terms of $s$.

• so the $\frac{ds}{dt}$ is the derivative of the position-time function. Okay, got it, thank you very much! – user3113506 Oct 4 '14 at 18:36
• no problem and yes you are correct. – Varun Iyer Oct 4 '14 at 18:36

Because $s$ is strictly a function of time, you can't differentiate the velocity with respect to time without using the chain rule. Perhaps putting this in more familiar notation, $v = v(s(t))$

Just using the chain rule, $$\frac{dv}{dt} = \frac{dv}{ds}\frac{ds}{dt} = v\frac{b}{s^{3/2}} = \frac{k'}{s^2}$$

So, we have proven that $a = \frac{dv}{dt} \propto \space s^2$

Where I absorbed all the multipliers into the new constant $k'$

• Got to get familiar with chain rule. Now I get how it works. Thanks! – user3113506 Oct 4 '14 at 18:44

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Home   Uncategorized   how much is 777 gold worth

how much is 777 gold worth

Favourite answer . Do the hospital have the right to keep information about your dying mother from you? All of these deals were approved by the Canadian government, who found nothing weird about their ownership structure. But earlier this week, Lufthansa placed an order for 34 777-9Xs as part of a split order between Boeing and Airbus worth what the carrier said was about $19 billion at list prices. there are 31.1 grams in a GoodRx Gold is free for 30 days, after which you'll pay$5.99 per month for individuals. The gold per gram calculator will show you the price per gram of 100% pure gold, unless you indicate a lower percentage. Common Uses for Gold. tsaiek6654/flickr.com. Minister backs region's gold call. This selling by global central banks slowed greatly in … The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Treasure hoard is seen by 40,000. How much is 14k Gold worth? Anglo-Saxon gold worth £3.285m. It can find you the best prices, show you price history, automatically … gold is selling for $1,813. One kilogram is equal to 1000 grams which is approximately 32.15 troy ounces. This makes sense given the fact that an ounce of gold is the same whether it is bought in the U.S. or Asia. hide. Is there a way to search all eBay sites for different countries at once? If you are looking to buy a larger size and amount of gold, buying a gold bar or coin in kilos is a good option. 777 PiCoin is 4.831561 US Dollar . What do you gather about crocker-harrish from the play? Convert Peruvian Nuevo Sol to US Dollars. in Rome. Updated on 06/17 23:15. What is the meaning of PTYO in Rajasthan University? Four appraisers have said that a used Boeing 777-200ER is worth between$37 million and $47 million, and those with certain engines command a premium. 777 is a European mark meaning 77.7% pure gold...we use karat in It is done by using the price of "reference items" (see next section). or maybe explain to me how i can calculate it. Karat or fineness refers to the percentage of gold by weight an item contains. In order to fully understand the purpose of gold, one must look back to the start of the gold market. The formula for the gold efficiencyof an item (as a percentage figure) is simple:$ \pagecolor{Black}\color{White}{\rm Gold\ efficiency}={{\rm Gold\ value} \over {\rm Item\ price}} \times 100 $The difficulty is in determining the gold valuegiven the stats on the item. All Rights Reserved. Now we will put 777.7 billion in the context of other things, so you can get a better idea of how much it really is: Spending: If you had 777.7 billion dollars, you could buy 25,923,333 cars at$30,000/each or … While gold's history began in 2000 B.C, when the ancient … Much of the supply of gold in the market since the 1990s has come from sales of gold bullion from the vaults of global central banks. The Honey browser extension helps save you money at or get Honey Gold (cash back in gift card form) from 40,000+ online retailers. If you have an Xbox One or Xbox 360, Microsoft’s Xbox Live Gold service is required to play multiplayer games online. So, what's the best place to buy wow gold… How long will the footprints on the moon last? Second Hand Concrete Batching Plants For Sale In Malaysia. Useful to establishing provenance, or 'history' of an artwork include: the original bill of sales; correspondence … a good number to play in jersey is 417. triple numbers only come out about 6 times a year, bad play best numbers to play are 2 odd one even 2 even one odd,or any number that adds up, say 417 … share. It’s worth noting that white gold isn’t truly white, it’s still a very pale yellow. ... Is 777 stamped on gold chain proper gold ?? Convert Peruvian Nuevo Sol（PEN) to US Dollars (USD) at the current exchange rate. Our gold price per gram charts offer 24-hour access to real-time, live-gold prices. worth per gram once you know that much. Last but not least, 777 Bay Street, who’s largest client is the Government of Ontario. This calculates purchasing power changes using the Consumer Price Index. Why don't libraries smell like bookstores? Visit our scrap gold page to work out how much we will pay you for your scrap gold per gram and in total. There should be another symbol showing 10K, 14K, 18K, or 24K on the item. per ounce. In both cases, the gold in question is considered to have 750 parts per 1,000 of pure gold — or 75% pure gold. And it ... as of 8-29-2011 75% Upvoted. The gold manufacturer may simply choose to use the number ‘750’ over ’18K’. How much is inflation on $777? and the first gold coins were minted in 50 B.C. What is the value of a dollar now? Choose the purity level that makes the most sense for what you intend to use it for, whether you will subject it to a lot of force, and your personal preferences. Now we will put 777 billion in the context of other things, so you can get a better idea of how much it really is: Spending: If you had 777 billion dollars, you could buy 25,900,000 cars at$30,000/each or … At today’s spot price of gold (11/30/18) of $1223/oz, it would be worth about$509 per troy ounce (31.1 grams per troy ounce) for its gold … European gold is marked by fineness, instead of 18k an item would be marked 750 meaning 750 parts gold … Could some1 tell me how much the Butcher passive (on jungler items) is worth (Gold)? Last day to see gold hoard. And on top of that, you can use your gold to renew your subscription via the WoW tokens. Answer Save. (has many people do to calculate gold effeciency) 2 comments. What is $777 now? How do you put grass into a personification? New comments cannot be posted and votes cannot be cast . Scrap Gold. Despite specialising in bullion, we also buy scrap gold from consumers offering some of the most competitive prices in the UK. Todays 12k gold price per gram is$29.57.This price is current and this page updates every 30 minutes with the most recent gold price. Gold ornaments comprised of various purity level, 24K is the purest form of gold, while 22k gold consist of little impurity used to make the gold ideal for jewelry designs like the bangle, ring, etc. How much is your gold worth with hallmark 777 on it? how much is my 10k gold ring worth? Which french saint is associated which the town of Lourdes? What is difference between ballad and ode? GoodRx Gold is an … 1Sol / 1Sol. :bull: 777 Please enter the weight and number of karats of your gold into the Precious Metal Calculator and select the currency you want it valued in. (At the high 2012 precious metals prices, the medals from London would have been worth around $777.) Lv 5. London’s bigger golds are worth$501 nowadays. When did organ music become associated with baseball? Lower karat gold is not worth as much monetarily. The plane lists for $425.8 million. If it has a stone, the stone is probably synthetic, so it would add nothing to the value. Campaign to keep treasure hoard. Mileage bonus ($270): As a Gold Medallion traveler, you’ll earn 8 miles per dollar spent, 3 more than non-status flyers. Kyle Orland - Feb 7, 2017 4:09 pm UTC Enlarge / Those huge heaps of WoW gold have got to be worth, like, $50 on … 14 karat (14k) gold is 14 parts gold to 10 parts other metal. Is there a way to search all eBay sites for different countries at once? 9 karat gold has a hallmark of fineness 375. Who is the longest reigning WWE Champion of all time? Bezugnehmend ob er einen guten Preis erhalten hat für den Ring kann ich dieses bejahen da der Ring aus hochwertigem Gold war. Higher karat gold will appear more yellow. If it is actually gold, most likely 10 kt gold (41.6% gold), yes, it does have value. One gram gold bars require less space to store and allow the individual … How long will the footprints on the moon last? Higher karat gold is much more resistant to tarnishing. How much was$777 worth in different years? Subsequently, money talks and gold is king when it comes to progressing in WoW since you need gold for almost anything, from crafting to getting boosted in Mythic+ dungeons. Each year, global gold mining adds approximately 2,500-3,000 tonnes to the overall above-ground stock of gold. If the item has passive or active effects they are only taken into account if they provide stats with a gold value (e.g. So, you've converted 777 PiCoin to 4.831561 US Dollar . making your European gold worth about $45.29 per gram. How many candles are on a Hanukkah menorah? A Brief History of Gold . It might be that it is 32.5% gold inside. Lower karat gold is not worth as much monetarily. 3 Answers. This is just a guess in my part since I really do not know. Crowds visit Anglo-Saxon hoard . Who is the longest reigning WWE Champion of all time? worth per gram once you know that much. I have a 10k gold ring with seven little diamonds, its V shaped and a weeding band ring, its in perfect condition how much is it worth??? That being said, the price of gold is theoretically the same all over the globe. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? The karat is based on 24 unit scale. What country was the May Flower built in? For families, choose our$9.99 per month plan and add up to 5 family members, including pets. Marriott Gold Status ($150): Platinum members will also be able to link their United and Marriott accounts to earn Gold status with Marriott Bonvoy, but again this value depends on how … 24k being pure gold, so an 18k ring contains 18 parts per gold per 24 units of weight, or 75% gold by weight. 12% of 777 = 12% * 777 = 0.12 * 777 = 93.24 What is gold 777 worth per gram? Where a gram is a nice smaller weight to purchase gold bullion, the kilogram is larger, just as desirable and somewhat unique. Please enter the amount that you would like to convert. Avionics: Honeywell Avionics Engine: 2x Rolls Royce RR-892 or Pratt & Whitney 4098 or GE90-94B What did the triumphs of Cortes and Pizarro do for the Spanish? Anglo-Saxon gold … changes daily depending on the current trading price of gold...Hope For some reason, I feel lucky going with seeing a gold price with "777". i.e. I have a 14k gold nugget ring, I was wondering if it's worth anything. The price of gold per gram in Saudi Arabia varies depending on its purity. Gold was extracted in Egypt as early as 2000 B.C. You can find out more about how to test your gold … We are 77 away from a gold price with a "777". What is the best way to fold a fitted sheet? Farmer's disbelief at gold find. How does arousal and anxiety affect your training? 777 is a European mark meaning 77.7% pure gold...we use karat in USA and 777 would be 18.648 karat gold. Canada must have missed when US Congress flat out called them a state owned entity. How old was queen elizabeth 2 when she became queen? Detail of gold jewelry price calculator. 22k jewelry is comprising of standard quality gold, but some contain low karat (purity level), e.g., 20k, 18k, 16k, etc. :bull: 777 Use the gold gram calculator to see how much your items are worth per gram of gold, or to figure what you might be willing to pay based on the cost of gold per gram. 777 is a European mark meaning 77.7% pure gold...we use karat in. Gold Price Per Ounce = 1839.5 US Dollar. How many candles are on a Hanukkah menorah? It is easy to determine its If you are looking to buy a larger size and amount of gold, buying a gold … The most expensive aircraft on the Boeing Co. (NYSE: BA) price list is the 777-9, the larger of two versions of the new 777X family. how much is 500 mills of gold worth . The 14K gold calculator will only show what the gold is worth (intrinsic value), and not any collectible value of your 14K gold items. Higher karat gold is more valuable because it is purer. Knowing the lineage of ownership and exhibition history can add to the value of your artwork. How much is a Million Sol ? Mein Vater hat ihnen recht gegeben das es sich bei der 777 nicht um eine Stempelung der Reinheit gehandelt hat was ich Hiermit klarstellen möchte. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. 1 decade ago. i.e. What are some examples of logical fallacies in Fahrenheit 451? Compare that with the United States gross domestic product (GDP) in … jacqua. Raw Complex Gold Ore Processing Machine. At the current spot price of XAU (troy ounces of gold) to CAD (Canadian Dollars) XAU to CAD Exchange Rate is 1924.25 CAD for 1 troy ounce of gold 1,000,000 CAD/1924.25 = 519.68 troy ounces There are … save. Maybe if I start a thread titled "Gold price with 777", then it is very possible that gold will stay away from a price with a "666". So, bear in mind that over time that rhodium plating will wear away and reveal the true colour underneath, at which point you’ll need to get it re-plated to restore it to its original colour. Use this calculator to see how the cost of living has changed. Die Zahl 777 wurde aber eingraviert zwecks Erkennung. How much is 777 PiCoin in US Dollar? troy ounce making 24k worth about$58.29 per gram... times 0.777... Bid Price: $1839.5. 8 karat gold has a hallmark of fineness 333. karat gold Gold (10 karat or better) used in the manufacture of jewelry. When did organ music become associated with baseball? A of July 28, 2014, 10 carat gold is worth$17.47 per gram. Gold Price Calculator is a free service provided by Gold Price OZ website, by which you can easily calculate the value of your gold. What is the meaning of fruit gatherer in exegesis? Gold can, however, also be transacted in any other currency after appropriate exchange rates have been accounted for. 777 Sol is approx. Peter Alliss net worth: How much was the golfing legend worth? How much is 14k gold worth at today's price? Based on today's spot price of gold at $42.51 USD per gram, that amount of gold would be worth roughly$771 trillion. Maybe if I start a thread titled "Gold price with 777", then it is very possible that gold will stay away from a price with a "666". USA and 777 would be 18.648 karat gold. This is just a guess in my part since I really do not know. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? The Perth Mint has built a well-deserved reputation for quality, craftsmanship and beauty. I'm not getting rid of it, because my good friend gave it to me and it meant alot to him, But just out of curiosity. . (Image: GETTY) Peter Alliss - often referred to as the "voice of golf" - has died at the age of … The value of gold is not determined by a hallmark but the amount of gold within the jewelry. A subscription costs $10 per month or$60 per year. Supplier of Raw Complex Gold Ore Processing Machine In ThailandThe 21st century, the … Market of Second Hand Concrete Batching Plants For Sale In MalaysiaDevelopment of Second Hand Concrete Batching Plants are to large-scale, automated, intelligen . It is easy to determine its. Where a gram is a nice smaller weight to purchase gold bullion, the kilogram is larger, just as desirable and somewhat unique. Which two bar will contain the buttons that allow you to change the priority of messages? Accurately estimating the amount of gold … What are the aims and objectives of Tesco - slide1? The perfect silver/white appearance of white gold is achieved by giving the item a plating of rhodium. You can entry the gold weight, select your required currency and measurement unit, the purity of gold, real-time gold price or historical gold price to calculate the total amount of gold. Any solid alloy of gold with other metals below a fineness of 24k but more than 10k. Relevance. Copyright © 2020 Multiply Media, LLC. How old was queen elizabeth 2 when she became queen? Chanlinda Thorn on March 27, 2019: Is Au990 gold … Sort by. How Much Is 14 Karat Gold Worth. 12 carat gold is worth $20.96 per gram. According to U.S. law, the metal must be at least 10 karat or it cannot be called gold. that helps. How much Gold is Butcher worth? The only gold with higher parts gold than 18K gold is 24K gold — the purest of all golds produced, at 1,000 parts pure gold … The mint is one of Western Australia’s largest exporters, distributing some$18 billion worth of gold bullion bars and coins to investors in over 100 countries each year. Buying gold in grams is a great alternative for consumers looking to make a smaller investment or who just want to own more pieces. The 14 karat gold melt value calculator will figure the price of gold items with a gold purity measured as 14 parts of gold and 10 parts of another metal used to make the 14K gold … Bookmark and share this page then come back whenever you need to know the price of 1g of 12k gold … It should be stamped showing the actual fineness. How do you put grass into a personification? Why don't libraries smell like bookstores? USA and 777 would be 18.648 karat gold. With $7,500 MQDs, that equates to 22,500 extra miles, worth$270 based … What is the best way to fold a fitted sheet? As the UK’s largest and most reputable gold bullion dealer we pay up to 97% of the global gold spot price for scrap gold. Apology over ticket system. Xbox Live Gold … We are 77 away from a gold price with a "777". While gold production has shown an upward trend in recent years, this is likely to level off in coming years. 223.18 US Dollars. if an item's effect added a temporary flat move… One kilogram is equal to 1000 grams which is approximately 32.15 troy ounces. What if gold medals really were solid gold? report. At today’s spot price of gold (11/30/18) of $1223/oz, it would be worth about$509 per troy ounce (31.1 grams per troy ounce) for its gold content. This thread is archived. For some reason, I feel lucky going with seeing a gold price with "777". The Boeing 777 300 Seating with comfort. Wired calculated that a typical gold medal would weigh 3.35 pounds and be worth around $76,000 in terms of the pure value of the gold. All Rights Reserved. Higher karat gold is more valuable because it is purer. Copyright © 2020 Multiply Media, LLC. These number represent the … In-game gold pieces are now worth a fraction of a penny across Battle.net. To U.S. law, the medals from london would have been worth around$ 777. 60 per.! It is done by using the price of gold with other metals below a fineness of 24K but more 10K! Despite specialising in bullion, the price per gram in Saudi Arabia varies depending on its.! Synthetic, so it would add nothing to the start of the gold.! The stone is probably synthetic, so it would add nothing to the start of the most prices. Lower karat gold has a hallmark how much is 777 gold worth the amount of gold is theoretically the same whether it is purer gold. ( has many people do to calculate gold effeciency ) 2 comments isn ’ truly! 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# Tag Info

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I think the distinction is made more for conceptual reasons, which has practical implications, so let me review the usual definitions of a stochastic and partially observable environment. A stochastic environment can be modeled as a Markov Decision Process (MDP) or Partially Observable MDP (POMDP). So, an environment can be stochastic and partially ...

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A few points I'd like to add (without repeating the info already provided by nbro's answer): I think you're half-right, in that indeed we can probably always model randomness as hidden information (e.g., as the hidden random seed in a software implementation of an environment). However, the other way around does not work; we can not always model any ...

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The usual (as presented in Reinforcement Learning: An Introduction) $Q$-learning and SARSA algorithms use (and update) a function of a state $s$ and action $a$, $Q(s, a)$. These algorithms assume that the current state $s$ is known. However, in POMDP, at each time step, the agent does not know the current state, but it maintains a "belief" (which, ...

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You are correct in the question that in RL terms chess a game of chess where the agent is one player, and the other player has an unknown state is a partially observable environment. Chess played like this is not a fully observable environment. I did not use the term "fully observable game" or "fully observable system" above , because ...

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An MDP is just a POMDP where the states are observable. So, we can formulate an MDP as POMDP such that the observation space is equal to the state space. We also need to take care of the observation function. Formally, an MDP can be defined as a tuple $M_\text{MDP} = (S, A, T, r, \gamma)$, where $S$ is the state space $A$ is the action space $T = p(s' \mid ... 3 First, note that the current state does not determine the next state. What determines the next state are the dynamics of the environment, which, in the context of reinforcement learning and, in particular, MDPs, are encoded in the probability distribution$p(s', r \mid s, a)$. So, if the agent is in a certain state$s$, it could end up in another state$s'$, ... 3 The game of TIC-TAC-TOE can be modelled as a non-deterministic Markov decision process (MDP) if, and only if: The opponent is considered part of the environment. This is a reasonable approach when the goal is to solve playing against a specific opponent. The opponent is using a stochastic policy. Stochastic policies are a generalisation that include ... 3 I will attempt to provide an answer to your questions based on the information you can find in the papers A Heuristic Variable Grid Solution Method for POMDPs (1997) by Ronen I. Brafman and Point-based value iteration: An anytime algorithm for POMDPs (2003) by Joelle Pineau et al. A grid-based approximate solution to a POMDP attempts to estimate a value ... 3 There is indeed a close parallel here, but the concepts are distinct. Every perfect information game is fully observable, but not every fully observable game is a game of perfect information. A game of imperfect information is one in which you lack knowledge of any of the following: The state of the game (e.g. current market prices). The rewards you will ... 3 I think that the normalisation factor is assumed to be non-zero. So, in practice, I guess, you must eventually check that$P(z \mid b, a)$is non-zero (even though, I guess, it will likely never be zero because of round-off errors in computers). The formula to calculate$b'(s')$comes from its definition, which is based on Bayes' theorem, where the ... 2$O(a, s', z) = \mathbb{P}(z \mid a, s')$is a conditional probability distribution, so it always needs to sum up to$1$. You should interpret$O(a, s', z)$as the probability of observation$z$, given that the agent took action$a$and landed in state$s'$.$O(a, s', z)$is thus not a joint distribution, even though the notation$O(a, s', z)$might suggest ... 2 Is it possible for value-based methods to learn stochastic policies? Yes, but only in a limited sense, due to the ways it is possible to generate stochastic policies from a value function. For instance, the simplest exploratory policy used by SARSA and Monte Carlo Control,$\epsilon$-greedy, is stochastic. SARSA natually learns the optimal$\epsilon$-... 2 What could happen if we wrongly assume that the POMDP is an MDP and do reinforcement learning with this assumption over the MDP? It depends on a few things. The theoretical basis of reinforcement learning needs the state descriptions to have the Markov property for guarantees of convergence to optimal or approximately optimal solutions. The Markov property ... 2 Both Belief-MDPs and Bayes-Adaptive MDPs (BAMDPs) are special cases of POMDPs and their state space is augmented with a belief over their unobserved/hidden variables. In a belief-MDP, the hidden variables can change over the course of an episode. (Eg. Both the position and the uncertainty in the position of the robot can vary during an episode). In a BAMDP, ... 2 Your setting (of randomly dropping out reward signals) impacts expected future reward by multiply everything by a common factor$(1-\epsilon)\$. As reinforcement learning (RL) control is based on maximising expected future reward, and multiplying by a positive constant does not affect ranking of action values, all existing RL methods will cope just fine ...

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Generally, "perfect information" is not a formal trait of MDPs. There is a concept of the Markov property, but it only loosely coincides with "perfect information". For instance it is OK for there to be unknown/hidden state, provided it behaves effectively randomly (when revealed, it is drawn from a consistent distribution). An example ...

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I guess it depends on what the goal is. If the goal is a general reward function, this formulation as an MPOMDP could make sense. One way to think about this, is as a way of modeling a general (centralized) POMDP with factored actions and observation spaces. However, it seems that what you are describing might be an active perception problem, where the goal ...

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Not exactly, at least traditionally: in Game Theory, "imperfect information" is most often defined as agents having only partial information about the history of agents' actions, as you correctly noted. But also note that this doesn't refer to the general world facts or state. But "partial observability" is typically used in terms of systems, e.g. in Markov ...

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Yes, the core differences between the different categories of problems are correct as you've described them. For SMDPs, I'd like to remark that the water boiling example is maybe not the best. That looks more like an example of "delayed rewards", but not one of "durative actions": when the agent takes that action to raise the temperature, ...

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There is no major difference here between a POMDP and MDP. When setting reward values, you are generally trying to give the minimal information to the agent that when the sum of rewards is maximised, it solves the problem that you are posing. In literature it is common to use one simple number as a reward, but I am not sure if this is really how you ...

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Session 83 - Galaxy Evolution/Interaction.
Oral session, Wednesday, January 15
Piers 4/5,

[83.02] Galaxy Formation from Subgalactic-sized Clumps at z\simeq 2.39

S. M. Pascarelle, R. A. Windhorst (ASU), W. C. Keel (U of AL), N. Scoville, L. Armus (Caltech)

The discovery of numerous compact star-forming objects at z\simeq 2.39 in several distinct regions of the sky with the Hubble Space Telescope (HST) represents the first direct observations of what may be the building blocks of present-day luminous galaxies. The HST medium-band F410M filter (centered at 4100Åwas used with WFPC2 to image Lyman-\alpha emission at z\simeq 2.39, which along with broad-band B_F450W, V_F606W, and I_F814W images, found 18 candidates in a field surrounding the weak radio galaxy 53W002. Thus far, eight of the original 18 candidates from this field have either MMT or Keck spectroscopic confirmations, along with one possible new detection in H\alpha from CVF and K observations at the IRTF. More than a dozen additional z\simeq 2.39 candidates have been found with HST using the same method in two independent fields from recent Cycle 6 parallel WFPC2/F410M observations. Our hypothesis is that such a widespread population of subgalactic-sized clumps exists throughout the redshift range z=1-4, and provides a reservoir of building blocks for the formation of the present-epoch early-type galaxies through the process of repeated hierarchical merging (with a merger rate that was most likely higher in the past). Finding similar objects in random fields with F410M suggests that these objects are indeed ubiquitous, and are part of the high-redshift (z=1-4) faint blue galaxy population. Still, some clustering is evident because the velocity dispersion of most of the 53W002 field objects (_ <\atop^\sim 300 km/s) is much smaller than the redshift range passed by the F410M filter. This indicates that these objects, which are within a region _ <\atop^\sim 1 Mpc^2, will in fact eventually merge. We take this to suggest that such building blocks exist everywhere in the sky and trace large-scale structure that may have been frozen in'' shortly after the Big Bang.


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#### Volume 13, issue 5 (2013)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Obstructions to Lagrangian cobordisms between Legendrians via generating families

### Joshua M Sabloff and Lisa Traynor

Algebraic & Geometric Topology 13 (2013) 2733–2797
##### Abstract

The technique of generating families produces obstructions to the existence of embedded Lagrangian cobordisms between Legendrian submanifolds in the symplectizations of 1–jet bundles. In fact, generating families may be used to construct a TQFT-like theory that, in addition to giving the aforementioned obstructions, yields structural information about invariants of Legendrian submanifolds. For example, the obstructions devised in this paper show that there is no generating family compatible Lagrangian cobordism between the Chekanov–Eliashberg Legendrian $m\left({5}_{2}\right)$ knots. Further, the generating family cohomology groups of a Legendrian submanifold restrict the topology of a Lagrangian filling. Structurally, the generating family cohomology of a Legendrian submanifold satisfies a type of Alexander duality that, when the Legendrian is null-cobordant, can be seen as Poincaré duality of the associated Lagrangian filling. This duality implies the Arnold Conjecture for Legendrian submanifolds with linear-at-infinity generating families. These results are obtained by developing a generating family version of wrapped Floer cohomology and establishing long exact sequences that arise from viewing the spaces underlying these cohomology groups as mapping cones.

##### Keywords
Lagrangian cobordism, Legendrian, generating family, duality
##### Mathematical Subject Classification 2010
Primary: 53D12, 57R17
Secondary: 57Q60


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# Fix issues discovered in SLAC rotator testing

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#### Details

• Type: Story
• Status: Done
• Resolution: Done
• Fix Version/s: None
• Component/s:
• Labels:
• Story Points:
1
• Sprint:
TSSW Sprint - Oct 28 - Nov 10, TSSW Sprint - Nov 11 - Nov 22
• Team:
Telescope and Site

#### Description

In SLAC rotator testing today we discovered several issues that need fixing:

• The counter field was the wrong type for Command and Header (should be uint, not ushort).
• The rotator and hexapod CSCs have no heartbeat output. This strongly suggests we should have a base class for both CSCs.
• The rotator commander outputs too much noise because of encoder jitter (not a surprise). This is likely an issue for the hexapod commander as well.

Note that we still were not able to command the rotator: the commands were ignored. Fixing that is a different ticket.

I have attached a file that shows some binary telemetry data we read from the rotator, and how the Python code parses it.

#### Attachments

1. rotator_binary_data.py
4 kB

#### Activity

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Russell Owen added a comment -

I am also implementing DM-22104 on this ticket. Most of the fixes are in ts_hexrotcomm:

• Command and Header structs now have the correct type for the counter field.
• hexrotcomm.BaseCsc outputs a heartbeat event.
• hexrotcomm.BaseCsc outputs better clearer messages when a state transition command fails.

However I also added a bit of jitter to the current position from the MockMTRotatorController in ts_rotator
and updated command_rotator.py to ignore small jitter in telemetry topics.

Show
Russell Owen added a comment - I am also implementing DM-22104 on this ticket. Most of the fixes are in ts_hexrotcomm: Command and Header structs now have the correct type for the counter field. hexrotcomm.BaseCsc outputs a heartbeat event. hexrotcomm.BaseCsc outputs better clearer messages when a state transition command fails. However I also added a bit of jitter to the current position from the MockMTRotatorController in ts_rotator and updated command_rotator.py to ignore small jitter in telemetry topics.
Hide
Russell Owen added a comment -

If you have time to review this I would appreciate it, but if not just let me know and I'll ask somebody else. You have already looked at earlier versions of this code and may be sick of it.

Changes I made to reduce duplication of code between ts_hexapod and ts_rotator:

• Made BaseMockController handle all standard commands. For clarity I put the TCP/IP code into a new base class CommandTelemetryClient. I initially tried to make that an attribute of BaseMockController instead of a subclass, but the TCP/IP clients and controller are so entwined (the client needs to know a lot about the controller) that I decided inheritance was cleaner.
• Added BaseCsc as an abstract base class for Moog CSCs.
• Added SimpleCsc as a means of testing BaseCsc.
• Added BaseCscTestCase as a base class for CSC unit tests. Note: I hope to find time to add a variant of this to salobj (on a different ticket).
• Added CscCommander as a base class for command-line commander code. I am happy with the result, though some duplication remains between the commands and the help string, and in defining each command (command methods are short, but the method name and the name of the command that it calls must match or the behavior will be incorrect).

Known issues:

• The mock controllers have few independent unit tests (some in ts_hexrotcomm's test_command_telemetry_server.py). I did this because mock controllers are only intended to serve the CSC, and the CSC unit tests exercise all the controller code that we care about. Note that unit tests for the mock controllers would tend to look very much like the unit tests for the CSCs, though with enough differences that I doubt they could share code.
• CscCommander has no unit tests. I am not happy about this, but feel it is arguably the best use of time, as these commanders are intended to be temporary. Nonetheless it would only cost a day or so to add such tests.
Show
Russell Owen added a comment - If you have time to review this I would appreciate it, but if not just let me know and I'll ask somebody else. You have already looked at earlier versions of this code and may be sick of it. Changes I made to reduce duplication of code between ts_hexapod and ts_rotator: Made BaseMockController handle all standard commands. For clarity I put the TCP/IP code into a new base class CommandTelemetryClient. I initially tried to make that an attribute of BaseMockController instead of a subclass, but the TCP/IP clients and controller are so entwined (the client needs to know a lot about the controller) that I decided inheritance was cleaner. Added BaseCsc as an abstract base class for Moog CSCs. Added SimpleCsc as a means of testing BaseCsc. Added BaseCscTestCase as a base class for CSC unit tests. Note: I hope to find time to add a variant of this to salobj (on a different ticket). Added CscCommander as a base class for command-line commander code. I am happy with the result, though some duplication remains between the commands and the help string, and in defining each command (command methods are short, but the method name and the name of the command that it calls must match or the behavior will be incorrect). Known issues: The mock controllers have few independent unit tests (some in ts_hexrotcomm's test_command_telemetry_server.py). I did this because mock controllers are only intended to serve the CSC, and the CSC unit tests exercise all the controller code that we care about. Note that unit tests for the mock controllers would tend to look very much like the unit tests for the CSCs, though with enough differences that I doubt they could share code. CscCommander has no unit tests. I am not happy about this, but feel it is arguably the best use of time, as these commanders are intended to be temporary. Nonetheless it would only cost a day or so to add such tests.
Hide
Te-Wei Tsai added a comment -

This task recorded the test in SLAC and the decoding of telemetry and header messages. The implementation and refactoring of hexapod and rotator code are in DM-22104. The comment describes the change of code that will happen in DM-22104. You could put me as the reviewer of DM-22104 if you want. I still need to be familiar with your code for the test in Dec actually.

Well done!

Show
Te-Wei Tsai added a comment - This task recorded the test in SLAC and the decoding of telemetry and header messages. The implementation and refactoring of hexapod and rotator code are in DM-22104 . The comment describes the change of code that will happen in DM-22104 . You could put me as the reviewer of DM-22104 if you want. I still need to be familiar with your code for the test in Dec actually. Well done!
Hide
Russell Owen added a comment -
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Russell Owen added a comment - Pull requests: https://github.com/lsst-ts/ts_hexrotcomm/pull/3 https://github.com/lsst-ts/ts_hexapod/pull/5 https://github.com/lsst-ts/ts_rotator/pull/7
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Te-Wei Tsai added a comment -

All reviews of PRs are done. The refactor of codes looks good to me! Great job!

Show
Te-Wei Tsai added a comment - All reviews of PRs are done. The refactor of codes looks good to me! Great job!
Hide
Russell Owen added a comment -

Here is Te-Wei's detailed review of ts_hexrotcomm:

[base_csc.py]

1. What will be the benenfit to use the metaclass in BaseCsc?

I checked the discussion here to try to understand the use of metaclass:
https://stackoverflow.com/questions/17801344/understanding-metaclass-and-inheritance-in-python

I asked this because I thought you can use the inheritance directly. You should have some reason to use the metaclass.

2. I thought the "start_task" should be issued before any real work such as "await super().start()" when you helped me to
integrate the ts_MTAOS with ts_salobj v5.0.RC2:

[base_mock_controller.py]

1. I thought your naming convension is to begin from the lower case and use the "_" instead of camel form:
https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-08b181c9bba5841f7715e574c868af46R85

Show
Russell Owen added a comment - Here is Te-Wei's detailed review of ts_hexrotcomm: [base_csc.py] 1. What will be the benenfit to use the metaclass in BaseCsc? https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-9884fc357e4ad38105bdf51d866033e9R51 I checked the discussion here to try to understand the use of metaclass: https://stackoverflow.com/questions/17801344/understanding-metaclass-and-inheritance-in-python I asked this because I thought you can use the inheritance directly. You should have some reason to use the metaclass. 2. I thought the "start_task" should be issued before any real work such as "await super().start()" when you helped me to integrate the ts_MTAOS with ts_salobj v5.0.RC2: https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-9884fc357e4ad38105bdf51d866033e9R148 3. The data type is a little inconsistent: https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-9884fc357e4ad38105bdf51d866033e9R322 https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-9884fc357e4ad38105bdf51d866033e9R334 https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-9884fc357e4ad38105bdf51d866033e9R345 [base_mock_controller.py] 1. I thought your naming convension is to begin from the lower case and use the "_" instead of camel form: https://github.com/lsst-ts/ts_hexrotcomm/pull/3/files#diff-08b181c9bba5841f7715e574c868af46R85
Hide
Russell Owen added a comment -

My response to Te-Wei's review of ts_hexrotomm:

[base_csc.py]

1. This use of metaclass=abc.ABCMeta is standard for the abc module.

It is true that the abc module also includes a parent class one can inherit from, instead. But I prefer the direct technique because:

• It makes it clear that a metaclass is being used, which means the user must be careful about multiple inheritance.
• It avoids one level if inheritance.

2. My pattern is as follows:

• Add a start_task attribute to any class that has an asynchronous start method.
• Have the object automatically start itself when constructed by having the constructor call self.start_task = asyncio.create_task(self.start()))
• This allows a user who creates an instance of the class call await myinstance.start_task to wait until the instance has fully started.

That is what is happening here. BaseCsc has an instance variable server that is a CommandTelemetryServer, which handles the communication between the cRIO and the CSC. BaseCsc.start is waiting for the server to finish starting.

3. Good point. I'll shorten the long ones (I found 3 instances).

For the record: within a package there is no need to provide the full namespace to get a working link, so just providing the class name is fine.

[base_mock_controller.py]

1. This is a in reference to an argument named CommandCode.

This follows the DM convention, which is to use CamelCase for variables that hold classes. One justification is that variable naming convention matches the type the variable holds, which makes the code a bit easier to read when one creates an instance of the class. And if nothing else, it may help avoid the mistake of providing an instance when a class is required. Here is a silly toy example:

  def make_instance(argument, ClassArgument):  return ClassArgument(argument)

Show
Russell Owen added a comment - My response to Te-Wei's review of ts_hexrotomm: [base_csc.py] 1. This use of metaclass=abc.ABCMeta is standard for the abc module. It is true that the abc module also includes a parent class one can inherit from, instead. But I prefer the direct technique because: It makes it clear that a metaclass is being used, which means the user must be careful about multiple inheritance. It avoids one level if inheritance. 2. My pattern is as follows: Add a start_task attribute to any class that has an asynchronous start method. Have the object automatically start itself when constructed by having the constructor call self.start_task = asyncio.create_task(self.start())) This allows a user who creates an instance of the class call await myinstance.start_task to wait until the instance has fully started. That is what is happening here. BaseCsc has an instance variable server that is a CommandTelemetryServer , which handles the communication between the cRIO and the CSC. BaseCsc.start is waiting for the server to finish starting. 3. Good point. I'll shorten the long ones (I found 3 instances). For the record: within a package there is no need to provide the full namespace to get a working link, so just providing the class name is fine. [base_mock_controller.py] 1. This is a in reference to an argument named CommandCode . This follows the DM convention, which is to use CamelCase for variables that hold classes. One justification is that variable naming convention matches the type the variable holds, which makes the code a bit easier to read when one creates an instance of the class. And if nothing else, it may help avoid the mistake of providing an instance when a class is required. Here is a silly toy example: def make_instance(argument, ClassArgument): return ClassArgument(argument)
Hide
Russell Owen added a comment -

All three packages merged to develop and master and released as v0.1.0.

Show
Russell Owen added a comment - All three packages merged to develop and master and released as v0.1.0.

#### People

Assignee:
Russell Owen
Reporter:
Russell Owen
Reviewers:
Te-Wei Tsai
Watchers:
Russell Owen, Te-Wei Tsai, Tiago Ribeiro


text:
# Electronegativity and doping in Si1-xGex alloys

## Abstract

Silicon germanium alloys are technologically important in microelectronics but also they are an important paradigm and model system to study the intricacies of the defect processes on random alloys. The key in semiconductors is that dopants and defects can tune their electronic properties and although their impact is well established in elemental semiconductors such as silicon they are not well characterized in random semiconductor alloys such as silicon germanium. In particular the impact of electronegativity of the local environment on the electronic properties of the dopant atom needs to be clarified. Here we employ density functional theory in conjunction with special quasirandom structures model to show that the Bader charge of the dopant atoms is strongly dependent upon the nearest neighbor environment. This in turn implies that the dopants will behave differently is silicon-rich and germanium-rich regions of the silicon germanium alloy.

## Introduction

The evolution in dielectrics and the introduction of high dielectric constant (high-k) dielectrics has allowed the replacement of silicon (Si) with better materials such as germanium (Ge) and silicon germanium (Si1−xGex)1,2,3,4,5,6,7,8,9,10. Random alloys such as Si1-xGex are different to elemental semiconductors as two atom species can occupy one lattice site. The consequence is that there is inhomogeneity of the local environments as there will be Si-rich and Ge-rich regions that will in turn influence the energetics of defect processes3,6,11,12. From a thermodynamic viewpoint, Saltas et al11. investigated self-diffusion in Si1-xGex with respect to temperature and Ge concentration using the cBΩ thermodynamic model13,14,15,16. Saltas et al.11 identified significant deviations from linearity of the activation energies with respect to compositions and attributed this non-linear behaviour to the bulk properties of Si and Ge.

From a density functional theory (DFT) perspective modelling random alloys can be computationally intensive (or even intractable depending on the issue under investigation) as it necessitates a high number of calculations and very large supercells (>103 atoms)17. As it has been previously discussed the special quasirandom structures (SQS) approach17 can lead to manageable supercells while mimicking the statistics of random alloys18,19,20,21,22,23.

The present study aims to use SQS in synergy with DFT to study the effect of electronegativity on doping in Si1-xGex alloys (x = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875). The most significant n-type dopants (N, P, As and Sb) and p-type dopants (B, Al, Ga and In) are considered as they exhibit a range of electronegativities. From a fundamental viewpoint the association of composition, electronegativity and doping is important to understand and improve the electronic properties of alloy semiconductors.

## Results and Discussion

### Structure of Si1-xGex alloys

The reasoning and efficacy of SQS to describe Si1-xGex alloys and other related random alloys (for example Sn1-xGex and Si1-x-yGexSny) has been discussed extensively in previous work and therefore here we will only briefly discuss this approach for completeness24,25. Typical DFT calculations of perfectly ordered structures require the formation of a supercell that is expanded throughout space by the use of periodic boundary conditions. For disordered random alloys the analogous approach is not practically feasible as it requires the construction of very large supercells (>103 atoms)17 with the atoms being randomly positioned at the lattice sites. The advantage of the SQS method is that it efficiently mimics the statistics of random alloys with small supercells (for example 16–32 atoms in Si1-xGex)25 and this allows the practical application of DFT in materials were many defect calculations are needed18,19,20,21,22,23. A key advantage of the SQS approach is that the atomistic nature is maintained and this leads to a distribution of distinct local environments that exist in real random alloys.

### Local environment and dopant electronegativity

Previous theoretical and experimental studies have established that there is a non-linear dependence of defect processes (for example binding energies of E-centres or activation energies of self- and dopant diffusion) with respect to composition26,27,28,29,30,31. Not only relaxation and thermodynamics impact the defect processes but also the electronic properties of the defects (for example charge transfer) can influence the properties of Si1-xGex and in that respect the local environment is anticipated to play a role on the formation of n-type and p-type doped areas in Si1-xGex. What is the impact of electronegativity of dopants and the local environment in Si1-xGex alloys?

Here we considered full geometry optimizations (positions and cell) of n-type dopants (N, P, As and Sb) and p- type dopants (B, Al, Ga and In) in Si1-xGex configurations (x = 0.125, 0250, 0.375, 0.500, 0.625, 0.750 and 0.875) to examine the local coordination of the dopants formed with the nearest neighbour atoms (Si and Ge). The simulation technique permitted us to determine the Bader charge32,33 on each dopant and the nearest neighbour atoms attached to the dopants in the relaxed configurations. The Bader charge approximation enabled us to discuss the electronegativity trend of the dopants present in Si1-xGex alloys. In the Bader charge analysis, electronic charges on individual atoms in the lattice are calculated based on the partitioning method as implemented by Bader34. Zero flux surfaces are used to divide atoms and partition the charge density32,33. A zero flux surface of the gradients of the electron density is expressed by the following equation as discussed by Yu et al35.

$$\nabla \rho (\overrightarrow{r})\cdot \hat{n}=0$$
(1)

Where $$\rho (\overrightarrow{r})$$ is the electron density, and the $$\hat{n}$$ is the unit vector perpendicular to the dividing surface at any surface point $$\overrightarrow{r}$$. Partition of charges are based on the continuum probability density of trajectories $$[P(\overrightarrow{r},t)]\,$$ as defined by the following equation:

$$\overrightarrow{j}(\overrightarrow{r},t)=P(\overrightarrow{r},t)\nabla \rho (\overrightarrow{r})$$
(2)

Where $$\overrightarrow{j}$$ ($$\overrightarrow{r}$$,t) is the probability flux at any point and time.

First we discuss the correlation observed between the electronegativity (or ionization potential) of n-type dopants and their Bader charges. Figure 1 report the electronegativity values36 of dopants, the electronegativity difference between dopants and Si (or Ge) and calculated Bader charges on the dopants. Electronegativities of N, Si and Ge are reported being 3.04, 1.90 and 2.01 respectively36. As nitrogen has higher electronegativity than that of Si or Ge, electronegativity difference (N-Si = 1.14 or N-Ge = 1.03) is positive. This reflects in the negative Bader charge on N (−3.15). Here we discuss the results for one of the seven configurations. Figure 2 reports the Bader charge on each dopants in seven different configurations and the sum of the Bader charges of the nearest neighbor atoms (Si or Ge). It is clear that in all seven configurations N gains ~3.00 electrons from Si and Ge to complete its outer shell. Total Bader charge of Si and Ge attached to N is ~+3.00 confirming that those three electrons are transferred from Si and Ge. Figure 3 shows the relaxed structures of all seven configurations, Bader charges and bond distances (N-Si and N-Ge). In all seven configurations, the Bader charge on the Si is ~+1.00. There are two different coordination environments observed. In the first five configurations (x = 0.125–0.625), N forms a trigonal planar structure with three nearest neighbor Si atoms. Each Si atom transfers ~1.00 electron to N to form a N3- stable electronic configuration. The N-Si bond distance in all configurations are ~1.85 Å showing the strong bonding formed between the N and the Si. In the sixth configuration (x = 0.750), a trigonal planar structure is formed two Si and one Ge atoms with N. In this case, each Si atom loses ~one electron and Ge atom loses 0.83 electrons. Slight reduction in the charge transfer by Ge is due to the lower electronegativity difference between N and Ge compared to that between N and Si36. This reflects in the longer bond distance of N-Ge than N-Si. In the last configuration (x = 0.875), N forms a distorted tetrahedral coordination with three Ge atoms and one Si atom. All three Ge atoms transfer ~0.70 electrons and one Si atom loses 1.00 electron leaving ~3.00 electrons on the N atom. Long N-Ge distances (~2.20 Å) confirms the weak bonding and reduction in the charge transfer. Figure 4 shows constant charge density plots associated with the dopants.

Electronegativity values of P and As are 2.19 and 2.18 respectively and these values are slightly larger than the values of Si and Ge (refer to Fig. 2). Electronegativity difference between P (or As) and Si (or Ge) is still positive but smaller than that observed between N and Si (or Ge). However, both P and As gain ~3.00 electrons. Relaxed configurations of P together with the bond distances and Bader charges are reported in Figure S1 in the supplementary information. Corresponding charge density plots are shown in Figure S2. In all seven configurations, P forms a tetrahedral coordination. Bader charges on Si or Ge varies from +0.60 to +0.81. Bond distances are longer compared to those observed in N•Si1-xGex. This is due to the lower electronegativity and larger atomic radius of P than that of N.

The Bader charges on the As in each configuration is negative and their magnitude vary from −1.89 to −3.10 (refer to Figs. 2 and S3). The negative charges on the As atoms are due to lose of electrons from Si and Ge as evidenced by the positive Bader charges (from +0.16 to +0.78). The formation of tetrahedral unit is observed in all cases with the longer bond distance as expected due to the larger atomic radius of As compared to that of N and P. Charge density plots are shown in Figure S4 in the supplementary information.

Electronegativity difference between Sb and Si (or Ge) is very small (refer to Fig. 1). This is reflected in the Bader charge on Sb. A very small amount of negative or positive charge is observed on the Sb atom in all cases (refer to Figs. 2 and S5). Total Bader charges on the nearest neighbor atoms are also small. Long Sb-Si or Sb-Ge bond distances are observed due to the large atomic radius of Sb and small electronegativity difference. Charge density plots are shown in Figure S6 in the supplementary information.

Charge transfer between dopants and Si (or Ge) can be explained in terms of ionization potentials. Figure 1 b shows the ionization potentials37 of dopants and Si and Ge. The largest ionization potential is observed for N. Ionization potential difference between N and Si (or Ge) is observed. This implies that the formation of positive charge on N is highly unlikely or gaining of electrons to form negative charge is highly likely. Ionization potential decreases from N to Sb meaning that the formation of positive charge become slightly favourable or gaining of electrons become less favourable.

### Summary

Electronic structure calculations were employed to study substitutional doping in a range of Si1-xGex alloys. It is demonstrated that the Bader charge of the substitutional dopants is dependent upon their nearest neighbours and the composition of the alloy. It is found that n-type dopants (N, P, As and Sb) accept electrons from the nearest neighbour atoms (Si and Ge). In particular N, P and As gain almost 3 electrons to form stable X3‒ ion. Sb accepts only a small amount of electrons as its electronegativity is very closer to the values of Si and Ge. Among p-type dopants, boron accepts electrons while other dopants (Al, Ga and In) loses their outer most three electrons. This is due to the higher electrone gativity of B than that of Si and Ge. The present methodology can be employed to energy materials (fuel cell, battery materials) related systems were random alloys are important38,39. This is because in these structurally disordered materials the local environments are bound to influence the dopant diffusion and the electronic properties, which are in turn important for the applicability of the materials in fuel cell and battery materials38,39.

### Methods

All the calculations were spin polarized using the VASP DFT code that uses plane wave basis sets40,41. Exchange correlation was modeled using generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof42. All the calculations were performed on 64-atomic site supercell consisting of two 32-atomic site SQS cells, a plane wave basis set, cut-off energy of 500 eV and a 4 × 4 × 4 Monkhorst-Pack43 k-point mesh (36 k points). Constant pressure conditions (atomic position and simulation box were relaxed) implanted via a conjugate gradient algorithm44. Convergence criteria dictated that forces on the atoms and stress tensors were less than 0.001 eV/Å and 0.002 GPa respectively. Semi-empirical dispersion was introduced in the simulations45. Bader charge analysis32,33 was employed to calculate the charges on the substitutional atom and its nearest neighbor atoms. The 32-atomic site SQS cells of Si1−xGex (x = 0.875, 0.750, 0.625, 0.500, 0.375, 0.250, 0.125) used here were previously reported12,25.

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## Acknowledgements

Computational facilities and support were provided by High Performance Computing Centre at Coventry University and Imperial College London.

## Author information

Authors

### Contributions

S.-R.G.C. and N.K. performed the calculations. N.K. and A.C. analyzed and discussed the results and contributed to the writing of the paper.

### Corresponding authors

Correspondence to Navaratnarajah Kuganathan or Alexander Chroneos.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Reprints and Permissions

Christopoulos, S.G., Kuganathan, N. & Chroneos, A. Electronegativity and doping in Si1-xGex alloys. Sci Rep 10, 7459 (2020). https://doi.org/10.1038/s41598-020-64403-8


text:
## Charles E. Chidume, Abubakar Adamu, A new iterative algorithm for split feasibility and fixed point problems

Full Text: PDF
DOI: 10.23952/jnva.5.2021.2.02

Volume 5, Issue 2, 1 April 2021, Pages 201-210

Abstract. A new iterative algorithm for approximating a solution of a split feasibility problem and the fixed point problem of a quasi-$\phi$-nonexpansive mapping is proposed and studied. It is proved that the sequence generated by the new algorithm converges strongly to a common solution of the split feasibility problem and the fixed point problem in real Banach spaces, which are more general than Hilbert spaces.