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## a very quick Riddle
Posted in Books, Kids, pictures, R with tags , , , , , , on January 22, 2020 by xi'an
A very quick Riddler’s riddle last week with the question
Find the (integer) fraction with the smallest (integer) denominator strictly located between 1/2020 and 1/2019.
and the brute force resolution
```for (t in (2020*2019):2021){
a=ceiling(t/2020)
if (a*2019<t) sol=c(a,t)}
```
leading to 2/4039 as the target. Note that
$\dfrac{2}{4039}=\dfrac{1}{\dfrac{2020+2019}{2}}$
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# FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature
### Anikó Csébfalvi, György Csébfalvi, Sándor Danka
#### Abstract
In a recent article (Bhaskar et al., 2011) the authors proposed a heuristic method for the resource-constrained project scheduling problem (RCPSP) with fuzzy activity times. The apropos of this state-of-the-art work, we try identify and illuminate a popular misconception about fuzzification of RCPSP. The main statement of their approach, similarly to the other fuzzy approaches, is simple: the project completion time can be represented by a "good" fuzzy number. This statement is naturally true: in a practically axiomatic fuzzy thinking and model building environment, using only fuzzy operators and rules, we get a fuzzy output from the fuzzy inputs. But the real problem is deeper. The possibilistic (fuzzy) approach, traditionally, defines itself against the probabilistic approach, so in the "orthodox" fuzzy community everything is prohibited which is connected to somehow to the probability theory. For example, the Central Limit Theorem (CLT) is in the taboo list of this community. We have to emphasize, CLT is a humanized description of a miracle of nature. When we fight against CLT, we fight against nature. The situation in the "neologist" fuzzy community is not better, because they try to redefine somehow the probability theory within the fuzzy approach without using "forbidden" statistical terms. In this paper, we will show that the nature is working totally independently from our "magic" abstractions. According to the robustness of CLT, the distribution function of the completion time of real-size projects remains nearly normal, which is a manager friendly, natural and usable result. An abstraction and its "natural" operators are unable to modify the order of nature. When we want to add a practical scheduling method to the project managers we have to destroy the borders between the probabilistic and possibilistic approaches and have to define a "unified" approach to decrease the gap between scientific beliefs and reality. In this paper we present a unified (probabilistic/possibilistic) model for RCPSP with uncertain activity durations and a concept of a heuristic approach connected to the theoretical model. It will be shown, that the uncertainty management can be built into any heuristic algorithm developed to solve RCPSP with deterministic activity durations. The essence and viability of our unified model will be illustrated by a fuzzy example presented in the recent fuzzy RCPSP literature.
#### References
1. Alvarez-Valdés, R., Tamarit, J. M., 1993. The project scheduling polyhedron: Dimension, facets and lifting theorems, Journal of Operational Research, 96, 204- 220.
2. Bhaskar, T., Pal, M. N., Pal, A. K., 2011. A heuristic method for RCPSP with fuzzy activity times, European Journal of Operational Research, 208, 57- 66.
3. Csébfalvi, G., Csébfalvi, A., Szendroi, E., 2008. A harmony search metaheuristic for the resourceconstrained project scheduling problem and its multimode version, In Proceedings of the Eleventh International Workshop on Project Management and Scheduling, Istanbul, 56-59.
#### in Harvard Style
Csébfalvi A., Csébfalvi G. and Danka S. (2011). FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 286-291. DOI: 10.5220/0003644402860291
#### in Bibtex Style
@conference{ecta11,
author={Anikó Csébfalvi and György Csébfalvi and Sándor Danka},
title={FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)},
year={2011},
pages={286-291},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003644402860291},
isbn={978-989-8425-83-6},
}
#### in EndNote Style
TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)
TI - FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature
SN - 978-989-8425-83-6
AU - Csébfalvi A.
AU - Csébfalvi G.
AU - Danka S.
PY - 2011
SP - 286
EP - 291
DO - 10.5220/0003644402860291
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# 1000+ Trigonometry PDF (Questions & Solution with Shortcut Tricks) – Download Now
0
4286
## Trigonometry PDF Questions & Solution with Shortcut Tricks
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This video is provided as supplementary
material for courses taught at Howard Community College and in this video I’m going to talk about
decimal place value. So let’s start out with place value for
whole numbers. We’ll do that as a review and
then go on to decimals. I’ve got the whole number 384. We know that the 3, the digit 3 in this
numbers is in what we call the hundreds column. So I’m gonna write a 100 over the 3. I could also write 100 as a
power of 10, I could write that as 10 squared. Now what this means is that the value of
3 in this number is going to be 3 times 100, or 3 times 10-squared. When I move over one column and I get to the digit 8, that 8 is inwhat we call the tens column,
so I’ll write a 10 above it. And if I want to express that 10 as a
power of 10, I can write 10 to the first. And this is going to mean that 8, that the value of the digit 8, in this number is 8 times 10. Moving over one more column, I get to
the 4. That’s in the units or the ones column. So I’ll write a one over the 4. To express the one as a power of 10, I can
just write that as 10 to the zero. And that means the value of th3 4 in
this number is going to be 4 times 1. Now let’s start adding decimal places. I’ll write a decimal point and a 7. So what’s the value of this 7? Well, if I look at my powers of 10,
I started out with 10-squared, and then 10 to the first and 10 to the zero,
so it looks like I’m ready for ten to the negative 1. Now 10 to the negative 1
is the same as 1 over 10, or one tenth, so this is the tenths column. and that 7 has a value of 7 times 1 over 10. When we read that we’re going to read
it as 384 and seven-tenths. Let’s add another number, another digit. Let’s add the digit 5 after that, and let’s see what its value would be. Well its column would be… we have a 10-squared column, and 10 to the first,
10 to the zero, and 10 to the negative 1… I’m ready for 10 to the negative 2. 10 to the negative 2 is the same as
1 over 10-squared, or 1 over 100, and this is going to be the hundredths
column. So the value of that 5 is 5 times 1 over 100. When we read this number, we’ll read the 384 and… and we’ll take the decimal part and just say 75 hundredths. We can add another decimal place.
Let’s add a 2. So that’s going to be in the
10 to the negative 3 column. 10 to the negative 3 is 1 over 1000, so that’s the thousandths column. So the 2 will have a value of 2 times 1 over 1000. At this point when we’re reading the number we can say 384 and 752 thousandths, or we might want to start saying things
like 384 point seven five two. As we add more and more
decimal places, it’s going to be more and more likely that we’ll just say point seven five two and then whatever
other decimal numbers we have, but basically this is the way that
decimal place value works. It’s just a continuation of the regular place value that
you already know. That’s about it, take care, I’ll see you next time.
## One thought on “Decimal Place Value 127-4.0”
1. Atiksh Bhattacharya says:
It's 4×1 not 4×10
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Cody
# Problem 44273. Given a square and a circle, please decide whether the square covers more area.
Solution 1721413
Submitted on 5 Feb 2019 by Alfonso Nieto-Castanon
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
sq = 2; ci = 1; y_correct = (sq>ci); assert(isequal(sqci(sq,ci),y_correct))
2 Pass
sq = rand; ci = rand; y_correct = (4*sq^2>pi*ci^2); assert(isequal(sqci(sq,ci),y_correct))
3 Pass
sq = 0; ci = 0; y_correct = (0>0); assert(isequal(sqci(sq,ci),y_correct))
4 Pass
sq = 100; ci = 4; y_correct = (7>3); assert(isequal(sqci(sq,ci),y_correct))
5 Pass
sq = 21; ci = 127; y_correct = (3>7); assert(isequal(sqci(sq,ci),y_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
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Open In App
# Edit distance and LCS (Longest Common Subsequence)
In standard Edit Distance where we are allowed 3 operations, insert, delete, and replace. Consider a variation of edit distance where we are allowed only two operations insert and delete, find edit distance in this variation.
Examples:
Input : str1 = "cat", st2 = "cut"
Output : 2
We are allowed to insert and delete. We delete 'a'
from "cat" and insert "u" to make it "cut".
Input : str1 = "acb", st2 = "ab"
Output : 1
We can convert "acb" to "ab" by removing 'c'.
One solution is to simply modify the Edit Distance Solution by making two recursive calls instead of three. An interesting solution is based on LCS.
1. Find LCS of two strings. Let the length of LCS be x
2. Let the length of the first string be m and the length of the second string be n. Our result is (m – x) + (n – x). We basically need to do (m – x) delete operations and (n – x) insert operations.
Implementation:
## C++
// CPP program to find Edit Distance (when only two// operations are allowed, insert and delete) using LCS.#includeusing namespace std; int editDistanceWith2Ops(string &X, string &Y){ // Find LCS int m = X.length(), n = Y.length(); int L[m+1][n+1]; for (int i=0; i<=m; i++) { for (int j=0; j<=n; j++) { if (i == 0 || j == 0) L[i][j] = 0; else if (X[i-1] == Y[j-1]) L[i][j] = L[i-1][j-1] + 1; else L[i][j] = max(L[i-1][j], L[i][j-1]); } } int lcs = L[m][n]; // Edit distance is delete operations + // insert operations. return (m - lcs) + (n - lcs);} /* Driver program to test above function */int main(){ string X = "abc", Y = "acd"; cout << editDistanceWith2Ops(X, Y); return 0;}
## Java
//Java program to find Edit Distance (when only two// operations are allowed, insert and delete) using LCS. class GFG { static int editDistanceWith2Ops(String X, String Y) { // Find LCS int m = X.length(), n = Y.length(); int L[][] = new int[m + 1][n + 1]; for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) { L[i][j] = 0; } else if (X.charAt(i - 1) == Y.charAt(j - 1)) { L[i][j] = L[i - 1][j - 1] + 1; } else { L[i][j] = Math.max(L[i - 1][j], L[i][j - 1]); } } } int lcs = L[m][n]; // Edit distance is delete operations + // insert operations. return (m - lcs) + (n - lcs); } /* Driver program to test above function */ public static void main(String[] args) { String X = "abc", Y = "acd"; System.out.println(editDistanceWith2Ops(X, Y)); }}/* This Java code is contributed by 29AjayKumar*/
## Python 3
# Python 3 program to find Edit Distance# (when only two operations are allowed,# insert and delete) using LCS. def editDistanceWith2Ops(X, Y): # Find LCS m = len(X) n = len(Y) L = [[0 for x in range(n + 1)] for y in range(m + 1)] for i in range(m + 1): for j in range(n + 1): if (i == 0 or j == 0): L[i][j] = 0 elif (X[i - 1] == Y[j - 1]): L[i][j] = L[i - 1][j - 1] + 1 else: L[i][j] = max(L[i - 1][j], L[i][j - 1]) lcs = L[m][n] # Edit distance is delete operations + # insert operations. return (m - lcs) + (n - lcs) # Driver Codeif __name__ == "__main__": X = "abc" Y = "acd" print(editDistanceWith2Ops(X, Y)) # This code is contributed by ita_c
## C#
// C# program to find Edit Distance// (when only two operations are// allowed, insert and delete) using LCS.using System; class GFG{ static int editDistanceWith2Ops(String X, String Y){ // Find LCS int m = X.Length, n = Y.Length; int [ , ]L = new int[m + 1 , n + 1]; for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) { L[i , j] = 0; } else if (X[i - 1] == Y[j - 1]) { L[i , j] = L[i - 1 , j - 1] + 1; } else { L[i , j] = Math.Max(L[i - 1 , j], L[i , j - 1]); } } } int lcs = L[m , n]; // Edit distance is delete operations + // insert operations. return (m - lcs) + (n - lcs);} // Driver Codepublic static void Main(){ String X = "abc", Y = "acd"; Console.Write(editDistanceWith2Ops(X, Y));}} // This code is contributed// by 29AjayKumar
## Javascript
Output
2
Complexity Analysis:
• Time Complexity: O(m * n)
• Auxiliary Space: O(m * n)
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# Homework Help: Linear algebra: spanning
1. Oct 25, 2012
### phys2
1. The problem statement, all variables and given/known data
The problem is : Let S = [ (1,-1,3) , (-1,3, -7) , (2,1,0) ]. Do the vectors u = (5,1,3) and v = (2,3,6) belong to span(S)
2. Relevant equations
3. The attempt at a solution
So span means that I could take linear combinations of u and v and they should end up giving (1,-1,3) , (-1,3,-7) and (2,1,0). Right?
I could take x [5 1 3 ] + y [ 2 3 6 ] = [1 -1 3] or [-1 3 -7 ] or [2 1 0 ] (btw i meant to write [ 5 1 3] as a column matrix but I am not sure of how to using Latex. So anyway, is what I am trying to do correct? Is that what it means for the vectors to span S?
Thanks
2. Oct 25, 2012
### Staff: Mentor
No, it's the other way around.
Span(S) is the set of all linear combinations of the vectors in S. u is in Span(S) if there are constants a, b, and c for which a(1, -1, 3) + b(-1, 3, -7) + c(2, 1, 0) = u.
Similarly for v.
3. Oct 25, 2012
### Zondrina
Put your vectors from S into matrix form, augmenting them with either u or v ( You'll have to do both at some point so pick one at a time ).
Solve the corresponding system and check if the following system is linearly independent or dependent.
If the system is dependent for your choice of u or v, then you can conclude that the vector is not in the span of your set. Otherwise if your system is independent, you can exhibit a unique solution for your system implying that your vector IS in the span of your set.
4. Oct 25, 2012
### phys2
Ahh I see thanks
Yes, it works out...thanks
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# Too Good to be True
Today is a topical post! I don’t do these very often, but something has been floating around the news a bit today and I want to make a larger point about it.
To keep this relevant for future readers, let me give you the quick background. In the 2020 Democratic Primary race, candidate Mike Bloomberg spent a lot of money on his campaign for the party nomination. Like… a lot of money. Like half a billion dollars. Then he dropped out of the race after mediocre performance, so take that as you will.
Then someone tweeted this gem:
So, okay. They’re bad at math. But honestly, I don’t care about that. Lots of people are bad at math. Being bad at math is actually okay if you’re good at being reasonable.
Consider the following situation: you’re attempting to calculate the weight of your cat. It’s often hard to get pets to stay still on a scale, so a common method is to weigh yourself, then pick up your cat and weigh yourself again, and then subtract. Usually you get a close enough figure for what you need.
Now, let’s say you did that, and when you did the back-of-the-napkin math, you accidentally made a simple error and instead of your cat weighing 11 pounds you calculate it as weighing 110 pounds. Even if you didn’t spot the error in your math, what you should immediately catch is the absurdity of the result. No reasonable person would accept that their cat weighed over a hundred pounds without raising an eyebrow, which should in turn tell you that your math must have been wrong, even if you didn’t think it was. You’d go back and check again because the result was so bananas.
Now, when someone doesn’t get the right answer to a particular problem they’re working on, there’s usually one of three causes:
1. They didn’t have the correct inputs/knowledge in the first place. It happens.
2. They made a mistake during the process and didn’t pay enough attention to spot it.
3. They were highly motivated to get the wrong answer.
That last one happens a lot. Sometimes the wrong answer is exactly the answer we want. “Can I afford to quit my job and retire early,” you ask yourself. You do some math, and you make a mistake. As a result of the mistake, you believe that your current retirement savings will be enough to live comfortably, when in reality you’ll be stretched very thin and you should work for another 5 years. But because you really, really wanted the answer to be “yes I can,” you don’t spot the mistake.
Train yourself to be suspicious of good news. Extra suspicious, in fact. I love dispelling folksy truisms, so let me reverse a classic one: You should absolutely look a gift horse in the mouth.
First off, it might be filled with Trojan soldiers, so there’s that.
But second, if you really want something to be true, you will be less cautious than your baseline. So you should get into the habit of being MORE cautious than your baseline when you get good news, so hopefully the two effects will roughly balance out and you’ll be as smart as you always are.
In the above tweet, the person should have known that one person being able to casually send a million bucks to every American is as patently absurd as your cat that you just picked up and stepped on the scale with weighing a hundred pounds. But it supported the worldview she wanted to have, so she wanted it to be true, so she didn’t check hard. If someone with the opposite worldview had done the same math and gotten the same erroneous result, they’d have scowled and done the math again – to them, the answer would have been too bad to be true.
If you can train yourself to be as skeptical of news you want as you are of news you don’t, you’ll make far fewer mistakes.
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# Water mineral additions, losses to mash, and evaporation in the kettle. I.e., does water lost to the mash result in a proportionate loss of ions?
Rephrasing my question:
I see three separate ways of calculating the final ppm of various minerals in the end product.
Say I begin with 9 gallons of DH20. After the mash, I lost 1.5 gallons and end up with 7.5 gallons in the boil kettle. After boiling, I lose 1.5 gallons to evaporation and end up with 6 gallons of wort.
Let's pretend I'm aiming for 200ppm of Sulphate. CaSO4 gives 61.5ppm of Ca and 147.4ppm of SO4 for one gram in one water. Therefore, 1.36g/gallon of CaSO4 will result in ~200ppm of SO4 and ~84ppm Ca (200/147.4ppm = ~1.36g CaSO4).
Do I multiply 1.36g by 9 gallons of water - my total starting water? This assumes both that I lost 1.36g*1.5gal to the mash and also 1.36g*1.5gal to evaporation. (Obviously salts don't boil off so this is incorrect)
Do I multiple 1.36g by 7.5 gallons of water - my starting water less that which I lost to the mash? This assumes that by losing 1.5 gallons of water to the mash, I am also losing 1.36g*1.5gal, leaving me with 1.36g*6gal CaSO4/gal.
Do I multiply 1.36g by 6 gallons of water - my starting water less that which I lost to the mash less that which I lost to evaporation? This assumes that the 1.5gal I lost to the mash did not also lose the 1.36g*1.5gal CaSO4, leaving me with 1.36g*6gal CaSO4/gal.
I'm reading Brewing Better Beer and Gordon Strong states "Homebrewers should be aware that you don't have to put all the salts in the mash, and that not all salts in the mash carry over to the kettle." He doesn't however make explicit that which I am asking -- namely if I lose X gallons in the mash do I precisely lose the ratio of salt to X gallons as well.
• Why are you targeting 200pm of Cl, 200ppm SO₄ and 100ppm of Na in the first place? While those values might be appropriate for some water profiles, they're inappropriate for most. Looking through the Bru'nWater profile table (bottom of the Water Adjustment sheet), I can't find a profile that matches those values. Commented Jan 24, 2015 at 16:59
• 200ppm for Ca is insane. 50 is plenty for ales and even less for lagers. Martin Brungard, the technical editor of that book, has spoken about how the only real purpose of Ca is to aid flocculation. In ales, it doesn't take much. And since lagers are, well, lagered, that gets you the clearing and you can get by with even less Ca. Commented Jan 24, 2015 at 17:09
• 100ppm for Na is particularly high, probably to the point of being noticeably salty and with a negative effect on yeast health. Commented Jan 24, 2015 at 18:23
• Unless you're brewing a Gose! Commented Jan 24, 2015 at 18:30
• Why are you trying to max out these values? More is not necessarily better; you should not assume "when given a range of values that the highest in that range is always better". Commented Feb 4, 2015 at 3:28
You are targeting 200 ppm for your final 6 gallons of wort, but you need that same amount of mineral present in 7.5 gallons of wort, pre-boil. Not the same concentration (200 ppm), mind you, but the same absolute amount, since it will concentrate as evaporation occurs.
To calculate ppm in 7.5 gal:
200 ppm x 6 gallons / 7.5 gallons = 160 ppm
To get 160ppm (with 1 gram CaSO4 per gallon giving 147.4 ppm):
160 ppm / 147.4 = 1.085 grams per gallon
Here's where you account for your predicted 1.5 gallons left behind in the mash. Because the pre-mash water and the post-mash wort will both be 160 ppm (so will the water left behind) you have to have your full pre-boil volume + loss equal 160 ppm, hence:
(7.5 gallons + 1.5 gallons) x 1.085 grams/gallon = ~9.77 grams CaSO4
EDIT:
In regards to the last point in your post:
"if I lose X gallons in the mash do I precisely lose the ratio of salt to X gallons as well"
Sulfates and chlorides remain soluble during mashing so you should see a proportionate loss (~16.7% water retention would mean ~16.7% retention of Cl or SO4 in the spent grain, i.e. the ppm won't change). Calcium, however, reacts with phosphates released by the malt and forms an insoluble precipitate which will be left behind in the mash or precipitate later. So you would hypothetically see a higher loss for Ca than 16.7% in your finished beer.
EDIT 2:
To elucidate the point above a bit more, here's the reaction that occurs between CaSO4 and malt-derived phosphates that produces insoluble calcium phosphate:
3 CaSO4 + 4 K2HPO4 --> {Ca3(PO4)2}* + 2 KH2PO4 + 3 K2SO4
{...}* = insoluble/precipitate.
This formula is from The Practical Brewer
I believe the reaction is basically the same with chlorides. You can see that calcium phosphate is the only insoluble substance produced, so you should only see a higher ratio of calcium being lost to the mash, and it will depend very much on your water and malt composition.
AIUI, none of the minerals will boil off, so they will be concentrated by the boil, and you should factor that into your computations.
I don't believe you need to take the mash-captured volume into account in any particular way. If you're treating the mash liquor, then you want that liquor to have a particular profile uniformly. I don't believe that mash-captured liquor has any more or less of the ions, compared to the mash runnings.
• I think you would have to take that into account, because that extra 1.5 gallons doesn't make it to the kettle and therefore isn't being concentrated. Assuming there's no significant change of mineral concentration in the mash (i.e. the wort is also 200 ppm), rather than 300 ppm final concentration (200ppm x 9gal / 6gal), it's actually 250 ppm final (200ppm x 7.5gal / 6gal). Right? Commented Jan 24, 2015 at 18:18
• Right. But the only thing that matters there is the pre-/post-boil volume ratio, not the specific volume retained in the mash. Commented Jan 24, 2015 at 18:20
• Definitely true. I'm only saying that MM is asking whether he's ending with 300 ppm. He isn't, it's 250ppm, and I assume it's because he didn't take into account that the water that gets left behind is not contributing to the final mineral concentration. Commented Jan 24, 2015 at 18:25
• @FranklinPCombs Yes that calculation I did assumed that I didn't lose any salts to the mash. In the event that I lost a proportional amount of salts to the water I lost in the mash, your calculation is correct. Commented Feb 4, 2015 at 2:05
Your equation should only be adjusted for water loss due to boiling: for the above target use 1.088g per gallon assuming 7.5g of wort will boil down to 6g.
Losses in the mash are simply due to water sticking to the grains, the is no appreciable 'sticking' of salts to the grain, other than surface tension of water.
Furthermore even if your sparge water didn't have any salts, you could still recover the salts from the mash because the unidirectional flow through the grain bed will carry the salt down much faster than it can diffuse (using you don't do something silly like stirring the mash while lautering).
Most people put salts in pre-mash, according to the quantity of the final volume. So if you were brewing a 6 gallon batch, you'd calculate your salts based on 6 gallons, even though pre-mash you may have 9 or 10 gallons, and pre-boil you may have 7.5 gallons.
• Salts won't get 'filtered' out because they're in solution with the water. Unless they react with something in the mash to form an insoluble material, any water absorbed by the grain will have the same composition of dissolved salts as the water that passes through. This is why how many ppm you need pre-boil is the only important concentration to know. Commented Feb 4, 2015 at 15:19
• Since that's the case, then wouldn't you be targeting post-boil concentration? (Not pre-boil.) Commented Feb 5, 2015 at 15:16
• Also, the Gordon Strong comment seems to support some salts added pre-mash not making into the final volume. I think this is at the crux of the OP's question, though I do not have an answer to that. Commented Feb 5, 2015 at 15:23
• I guess I would say pre-boil is more important because that is the point at which the total mineral content of the wort in the kettle becomes fixed. No more minerals will be added (unless you add more water or salts during the boil) or taken away (except what's in the water that is absorbed by the hops). Only pure water leaves by evaporation, carrying no dissolved minerals out with it. So nothing changes the overall mineral content of the kettle wort, it only concentrates what's already there. Commented Feb 5, 2015 at 15:26
• Actually this whole entire question depends on whether the sparge water is treated with the same concentration of minerals or if the whole dose of salts goes in the mash and is then sparged with distilled water. Commented Feb 5, 2015 at 15:30
This is an interesting question, however I suspect there is no good answer because of the number of variables involved you would have to factor in reactions, precipitation, flocculation as well as additions of new ions from the grains and hops. Its also quite difficult to determine the exact concentration of various ions in your water supply. So why not determine the ion concentration after the boil (even though it will most likely change again after fermentation) if you are not determining it yourself then I would suggest you stick with your approximate formula.
(7.5/6)*1.36 = 1.7g/gallon of CaSO4
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
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## #1 2006-08-06 05:31:15
Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400
### Crashing into an Ocean on a Plane - How to Save Yourself from Dying?
The Mythbusters set out to prove if the special brace position while on a plane was a good position to protect yourself. Well, yes, it is, but which was the safest place on the plane, and what is the best position you could be in?
The Mythbusters were a bit puzzled on how they would set out to experiment with this. They said they could use a plane, but they would only have one shot at using a plane. So, they used a simulator - They dropped a similar model to a plane (made out of wood and metal ramps) as high as 15 feet, using test dummies the first time, of course. The dummies ended up with torn off limbs - Just the legs, though. The fact is, if you didn't protect yourself, you shouldn't put your feet under the seat in front of you, and worse yet, you shouldn't do nothing. If you did nothing, you'd break your neck as soon as the plane would hit the water - But the brace position was designed to prevent that fate, and keep you alive. When the Mythbusters were done experimenting, though, they weren't heppy. They needed real people, not dummies. Three of the Mythbusters bravely stepped forward, and accepted the task. They were about 10 feet up instead of 15 feet for their safety, though. Luckily, the Mythbusters team survived because of the brace position. Back at the lab, though, they were doing some other tests. In the end, they proved that the brace position, and buying First Class tickets could save your life. It turns out that the flight attendant's seat is the most safest of all on planes, though. The Mythbusters proved that the people at the back of the plane were in the most danger, as they would be killed by the flying debris from the back of the crashing plane. The people at the front, however, were under the most protection, because their seats were more spaced out, meaning they couldn't break their neck upon landing on a seat in front of them. Therefore, the Mythbusters had become successful in their experiment.
Thus, the Mythbusters proved that the brace position and First Class tickets could save your life - And that the flight attendant's area and seat were the safest part of the plane.
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## #2 2006-08-06 07:29:34
Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791
### Re: Crashing into an Ocean on a Plane - How to Save Yourself from Dying?
Be careful with that word, "Proved". Mythbusters has given some evidence that such is true, but they have proved nothing.
And that evidence, from your description, is shotty at best. Every plane is different, made out of different materials and constructed in a different way. There is no reason to believe what is true for one plane is true for all. Also, what they set up, as you said, was a model. There is no accurate way to test if the model is accurate. It gives a good idea, but like I said, is shotty at best.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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## #3 2006-08-06 09:47:05
MathsIsFun
Registered: 2005-01-21
Posts: 7,659
### Re: Crashing into an Ocean on a Plane - How to Save Yourself from Dying?
There is footage of a plane landing on water. The plane was hijacked in Africa and ordered to fly to Australia by some idiots who wouldn't believe the pilots when they said it couldn't get there on 5 hours of fuel. So the pilots did the best they could - aimed for an island. The plane ran out of fuel and the pilots attempted to land it near a beach. It actually looked to be going well, then a wing/jet touched the water and the plane broke apart. This was captured on film by someone on the beach. Tourists swam out, took boats etc, but only about 1/3rd of the passengers survived.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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## #4 2006-09-17 19:34:23
Chelsea
Member
Registered: 2005-06-16
Posts: 390
### Re: Crashing into an Ocean on a Plane - How to Save Yourself from Dying?
Wow thats amazing!!
Theres no other place like home or is there..............
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# Body Fat Calculation and Health
Body Fat Calculation and Health
The higher your percentage of fat above average levels, the higher your health risk for weight-related illness, like heart disease, high blood pressure, gallstones, type 2 diabetes, osteoarthritis, and certain cancers. Also, the higher your percentage of fat (and the smaller your percentage of muscle) the less calories you need to maintain your weight and therefore the easier it is to gain weight. This is because muscle is more metabolically active than fat tissue.
Body Fat Percentages and Lean Muscle Mass
When in ideal shape, body fat will make up about 15% – 18% of a male’s body
weight and 18% – 22% of a female’s. The remainder of the body’s lean weight
is composed of water (55%-60%), muscle and other lean tissue (10%-20%), and
bone and minerals (6%-8%). In other words, a 150-pound woman who is within or
close to her ideal body fat composition range at 22% will have approximately
33 pounds of fat, 86 pounds of weight composed primarily of water, 20 pounds
of muscle and other lean tissue, and 11 pounds of bone and mineral weight.
This total then makes up her total weight of 150 lbs.
Now take the example of another woman who weights 150 pounds, but has 30%
fat on her body. She would have 45 pounds of fat on her body, and the rest of
her weight would be divided among muscle, bone and water. Her non fat body
composition might look like this, 79 pounds of water (53%), 17 pounds of
muscle (12%), and 9 pounds of bone and minerals (6%). Both women weight 150
lbs. and are about the same height, but one looks much different because she
has less body fat.
Body fat percentage is generally accepted as a better gauge of weight loss
progress and fitness than scale weight. The method of calculating body fat
from body measurements as used by HealthSmart Nutrition is the fourth most
accurate method. Hydrostatic testing underwater is first. Electrical testing
of body mass resistance is second and body fat measurement by caliper is
third. Although it is not the most accurate, if you record your measurements
carefully and consistently using the measurement taking instructions given,
you will have a good relative gauge of how much body fat you are gaining or
losing. To our knowledge, the HealthKeeper software is the first program to offer this body fat percentage by measurement feature.
For higher accuracy you can override the automatic body fat measurement calculator and enter your body fat percentages done by hydrostatic testing underwater, electrostatic testing of body mass resistance or body fat percentage done by the caliper method. One product we highly recommend is the Tanita bathroom scale. It does very accurate electrostatic testing of body mass resistance to determine your body fat percentage in seconds.
The more accurate of method you use for tracking your body fat percentage the more accurately you will be able to use
the Lean Body Weight tracker.
The two most important graphs and statistics you want to watch to find out if you are making true and honest progress on your weight loss diet or body building program are, body fat percentage and lean body weight. Increasing lean body weight (mostly muscle mass) is important because if you body fat is going down into your ideal range and your lean body weight is going up you will be able to eat more calories without gaining weight and, it will be easier to maintain your desired body fat percentage when you reach your goal. This is because more lean body weight (composed of increased muscle mass) raises the body’s basal metabolic rate
(BMR) and the calories your body burns even when you are doing nothing.
If you body fat is going down to your ideal range and your lean body weight is going up you should be absolutely ecstatic. You have attained two of the three holy grails of honest and lasting weight loss. (The third is keeping within your ideal body fat range for 3-5 years after getting there.)
In spite of lean body weight being such a vital statistic to honest weight loss,
the Performance Diet is the only program and software we know that tracks it. (To track you lean body weight make sure you have used one of the 4 methods of body fat tracking and your body percentage is entered in your Personal Profile. Then go to the Graphing mode and select the correct date range and Lean Body Weight from among the various graphing options.)
The lean body weight tracking we use is based upon your current weight and the following formula. From your current weight calculate the number of pounds that is equal to your current �X� percentage of fat. (That is the number of pounds of fat on your body.) The remaining percentage of your weight is your non-fat lean body weight. This is composed of muscle and other lean tissue, water, bone, blood and minerals. Over an extended period of time (even considering periodic water retention,) the levels of water, bone, blood and minerals remain fairly constant.
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The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187165 Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2
%I
%S 0,96,1104,3984,9612,18888,32712,51984,77604,110472,151488,201552,
%T 261564,332424,415032,510288,619092,742344,880944,1035792,1207788,
%U 1397832,1606824,1835664,2085252,2356488,2650272,2967504,3309084,3675912,4068888
%N Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions.
%C Row 4 of A187162.
%H R. H. Hardin, <a href="/A187165/b187165.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 150*n^3 - 426*n^2 + 312*n - 48 for n>2.
%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F G.f.: 12*x^2*(8 + 60*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
%F (End)
%e A solution for 2 X 2 X 2:
%e ..2..0.....3..4
%e ..1..0.....0..0
%Y Cf. A187162.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2011
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# Bumpiness in event horizon due to infalling matter
+ 4 like - 0 dislike
1118 views
Classically, far-observers never see infalling matter to traverse the event horizon, they only see bumps that are progressively red-shifted. My question is: how quickly these bumps even out across the event horizon surface?
For instance, can I make a bump to grow faster than it spreads out in a steady manner? Can I make cusps in the event horizon via such methods?
If joining multiple of such bumps is physically possible, you could create an event horizon with a handle, which would be topologically equivalent to a toroidal black hole
edited Jun 16, 2014
+ 4 like - 0 dislike
These are called the black-hole normal mode decay rates, the decay is analogous to a membrane with a certain viscosity type friction which is dissipating it's energy, and the rate of exponential smoothing out of surface fluctuations is the rate at which the black hole equilibrates. The identity of the two processes, the membrane-paradigm surface smoothing from dissipative dynamics and the string-theoretic equilibration of the dual field theory, was a major motivator for the holographic principle in the 1990s. The normal mode rates are calculated in several places, I don't remember the rates offhand.
Regarding "making cusps", a steady insertion of matter flowing in a line-stream into a black hole should make something like this, but I never saw the precise form of the metric, or the deformation of the horizon, but it should make a cuspy structure of some kind. There are other singular constructions which are easier, involving time-reversal of black hole merger, but I don't remember how they work. Another cusp is the path of transition between a 5d linear black hole and a line of 5d sphere black holes, the Gregory Laflamme instability. The 5d black hole has to break up, but the way it does so is by producing many black holes linked by thin horizon tubes, which are singular cusps at the point where they connect with the large horizons. The scaling limit of this is computable, but it has never been done in the literature.
answered Jun 16, 2014 by (7,730 points)
edited Jun 16, 2014
Nice answer :-)! Is the link between the black holes in the line similar or related to the link between black holes by entanglement in the context of the ER/EPR correspondance?
Hi Ron. So, if doing cusps is physically allowed, then joining several cusps would also be possible, which would result in a toroidal event horizon (actually just an event horizon with a handle, but topologically equivalent)
In 5d, toroidal horizons exist, and exact solutions are known. The transition between these and spherical horizons are known. The problem with the cuspy type things is that they are unstable, and in 4d, when you try to link them into a loop they collapse too fast to do so. There is no problem in 5d, though.
@dilaton: I don't know, I don't understand ER/EPR well yet.
The problem with the cuspy type things is that they are unstable, and in 4d, when you try to link them into a loop they collapse too fast to do so
but wait a minute.. Once I'm growing the bump (feeding it at least an order of magnitude faster than it can spread out, I can assume that I'm firing mass at the bump relativistically if you like) why would it matter in what direction the bump is grown? The question is if it can be done fast enough so that some null rays can make it through the handle before it evens out.. Probably there is where the construction fails to achieve a true toroidal horizon, even transiently
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# Fractions of a number word problems Grade 3 - Third Grade
## Fractions of amounts word problems
Use these fractions of a number word problems to teach your kids how to multiply fractions by whole numbers. However, this activity will test your 3rd graders understanding of fractions and multiplication.
Of equal importance, you’ll discover the fastest ways to solve fractions of amounts word problems only in this great resource. As we can recall, a fraction tells you how many parts of a whole there are. So in a bid to solve fractions of an amount, we will discover how much that part is worth within the whole.
This activity is excellent for guiding kids in quickly calculating fractions in measurements, amounts, length, time, etc. For instance, we will often calculate the new price in a shop when given a discount.
### Simple methods for solving fraction of a number word problems
Below here are simple methods for solving fraction of a number word problems.
Before you begin solving, read the word problem carefully at least twice to have a perfect understanding. Next, set up a multiplication equation consisting of a whole number and a fraction.
When this is done, multiply the numerator of the fraction by the whole number, but keep the denominator the same
Finally, simplify the fraction where necessary.
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Concrete Mix
Topics: Concrete, Cement, Compressive strength Pages: 2 (439 words) Published: March 16, 2013
BRE Concrete mix design method
A popular simplified mix design method is that from BRE.
Compressive strength is, in general, related to durability. The greater the strength the more durable the concrete. To satisfy the required compressive strength, a value for water/cement (w/c) ratio is estimated for an appropriate test age (generally 28 days) and cement type. Tables in the BRE mix design handbook are consulted relating aggregate:cement (a/c) ratio, workability and water:cement (w/c) ratio for the different aggregate particle shapes and maximum size. From these tables the a/c ratio can be selected. A desired level of workability is chosen. The ratio of sand to coarse aggregate is chosen to produce a satisfactory plastic concrete. Generally there is a minimum amount of sand necessary to fill the voids between the course aggregate particles. Increasing the percentage of sand makes for a less harsh and more easily placed mix. While this is an over simplification, it does allow an assessment of the effects that changes to any of these controlling parameters have. Other methods include: ACI (1991) and Basic Mix Method (P L Owens, C&CA 1973) British method (BRE 1988)
The method of the Department of the Environment, revised in 1988 (BRE, 1988) and cited by Neville (1995), Step 1
Determination of water/cement ratio.
* A first constraint is imposed by durability concerns (maximum value). * Then the water/cement ratio is determined by the required compressive strength, for ages ranging from 3 to 91 days. Step 2
Determination of water content.
* The principle is very similar to that adopted in ACI 211. * A further refinement is brought by paying attention to the shape of particles (crushed vs. uncrushed), which is assumed to govern the water demand, together with the MSA and required slump. Step 3
Calculation of cement content, by dividing the water content by the water/cement ratio. Step 4
Determination of total mass of aggregate.
*...
Please join StudyMode to read the full document
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### New prefixes for the metric system
This exercise is a part of Educator Guide: The Metric System Has Gained New Prefixes / View Guide
Directions for teachers: Ask students to read the online Science News article “The metric system is growing. Here’s what you need to know,” which explores new prefixes for the metric system. A version of the article, “The metric system gains new prefixes,” appears in the January 14, 2023 issue of Science News.
1. What are the new metric system prefixes? How are they represented numerically compared with a base unit of measure, for example one meter?
The new metric system prefixes are ronna-, quetta-, ronto- and quecto-. One ronnameter is 1 x 1027 meters, and one quettameter is 1 x 1030 meters. One rontometer is 1 x 10-27 meters, and one quectometer is 1 x 10-30 meters.
2. When and where were the new prefixes adopted?
The new prefixes were adopted November 18 at the 27th General Conference on Weights and Measures in Versailles, France.
3. What was one sign that new prefixes were needed, according to Richard Brown?
People started coming up with their own prefixes, such as “bronto-.”
4. What is the global system of measurement called? Why is it beneficial for scientists to use a shared system and set of prefixes? Explain.
The International System of Units is the world’s most widely used system of measurement. If scientists agree on units and prefixes, they can communicate and understand each other with less room for confusion.
5. What are the masses of Earth and an electron using the new prefixes? Why might these prefixes be beneficial in some cases?
The mass of Earth is six ronnagrams. The mass of an electron is about one rontogram. In some cases, smaller numerical values might be easier to understand and compare.
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# Questions tagged [graphics]
Questions on the construction of 2D and 3D graphics through the direct use of primitives, directives, and functions. Include the graphics3d tag for questions specifically on 3D graphics. This tag is not to be used for basic questions on visualizing functions and lists using the various flavors of Plot commands.
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### 3D Ternary Plot - Triangular Prism?
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### Rewrite ListPlot using Graphics while perserving point color?
I have a lot of data points, and I have noticed that plotting using Graphics is usually much quicker than plotting with ListPlot. The problem is I am trying to color the data points based off some ...
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### How to remove the cap of a sphere in and chose the side where it cuts
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591 views
### Area/Volume of a 2D/3D object as it is filled up with water
How could I get the volume of water on a region as it is filled up with water from below? Assume gravity points in some appropriate downward axis like -y (or -z in 3D) so the water fills upward from ...
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### My plot is so tiny (and buggy)
This is a very weird question, I'm plotting impedance and admitance using parametric curves This is my code ...
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### Plots dashed when I don't specify them to be dashed?
I was plotting a function (F here) with selected values, and just wanted the plot to be solid lines with the selected colors specified with PlotStyle: ...
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### How can I label these three circles as A, B, C?
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### Placing labels “around” a GraphicsGrid
I have the following code, which produce the image shown. ...
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### Can this 2D-Venn diagram code--involving Disk--be “upgraded” to a 3D one, involving Sphere?
At https://wolfram.com/language/12/improved-visualization-labeling/venn-diagram.html?product=mathematica one finds the code ...
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### Create a Venn and/or related diagrams given the eight atoms of a three-set (A,B,C) 256-dimensional Boolean algebra
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### GeoListPlot - How can I create edges between points on a GeoGraphic object by clicking on them?
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### Raytracing using Regions & NSolve
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### RegionPlot3D is giving wrong plot
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### Help editing Graphics primitives in a variable
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### GraphicsGrid resizes plot when using SpanFromLeft
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### Problems exporting graphs with descriptions to raster image files
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### How to use “Style” properly with “ListPointPlot3D”?
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# Interpreting a Mining Cost Curve 101: the Basics
Updated on June 4, 2013
The cost curve is a widely used analytical framework in mining. What does it mean? Why does it matter? How can it help you make better mining corporate finance and strategy decisions?
The full name for the cost curve used in mining is the industry cost curve (“Cost Curve”). It can be used to analyse …
• Market structure
• Market dynamics and
• Market risk.
A thorough analysis of the Cost Curve should be completed to determine ...
• Relative cost
• Competitiveness and
• Expansion incentives.
This hub is the first in a series to help you become an expert user of the Cost Curve. This hub looks at the Cost Curve basics - so that you can start to use the Cost Curve to make better mining corporate finance and strategy decisions.
## FIRSTLY, THE COST CURVE IS NOT ...
There are a number of different types of (small c) cost curves in economic theory. Generally, they are used to show the cost of production at varying production levels for a company and can help management determine the production level that maximises profits. The:
• Cost of production (p) is shown on the y-axis and
• Quantity of production (q) is shown on the x-axis
The four primary types of cost curve are the:
• Short run average cost curve
• Short run marginal cost curve
• Long run average cost curve and
• Long run marginal cost curve
These cost curves can all be used for mines and or mining companies - read more about them on wikipedia. However, the cost curve referred to in mining is generally the (industry) Cost Curve, which is a little different.
## COST CURVE FUNDAMENTALS
### X-Axis
The estimated production capacity for the product, or its substitute along the x-axis on a mine or company basis. The width of the bars indicates the quantity each mine/(company) produces per annum.
### Y-Axis
The estimated cost of production per unit is shown in the height of each bar. Mines/(companies) are arranged in order from lowest cost producer on the left to highest cost producer on the right.
.
## THE ALL IMPORTANT DEMAND LINE
Typically, Cost Curves will not show the demand line, it changes frequently along with the price. You don't need to be given it because you can plot where it should be. The demand line's horizontal extent indicates the quantity of market demand and its vertical position is equal to the price sufficient to make the next producer marginally profitable. Using these rules you can estimate the position of the demand line.
In the Cost Curve above, if we knew that the price was currently \$32.50 we could estimate that demand was between 54 and 57mtpa and place the demand line on the Cost Curve as per the Cost Curve below.
In the example below the demand line indicates that:
• Current demand is equal 57Mtpa
• Current market price is \$32.50t
• Four mines are producing at full capacity
• Mine five is producing at approximately half capacity and
• The three highest cost mines are dormant.
Using the two rules for estimating the position of the demand line gives you a number of analytical tools. You can estimate the:
• Price if demand changes. What happens if demand is halved?
• Profitability of each miner at different levels of demand/ pricing
• Supply and demand assumptions of any price forecasts
• Pricing risk and competitiveness of any miner on the Cost Curve
## COMING UP
The Cost Curve can lead you to make significant errors if you don't understand the details. In the next post we will look at the assumptions behind the Cost Curve.
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## COMMENT
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• Linda Rogers
6 years ago from Minnesota
Great information here David. This is a topic I know little about, so I'll be learning a lot from you. Welcome to HubPages :-)
working
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Question
# The equivalent capacity of two 20 microfarad capacitor in parallel is: a. 10 Microfarad b. 20...
The equivalent capacity of two 20 microfarad capacitor in parallel is:
Here we have given that ,
Two capacitor connected in parallel having capacitance given as
C1 = C2 = 20 microfarad
Now in case of parallel connection of capacitor the charge across each will be divided directly proportional to their capacitance and voltages across them will be same
So that the net resultant capacitance will be given by simply adding both the capacitor
So thag total capacitance Ct = C1 + C2
Hence equivalent capacity Ct = 20 + 20 = 40 microfarad.
Therefore equivalent capacity of two 20 microfarad capacitor in parallel will be option (d) 40 Microfarad.
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
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## #1 2005-10-12 01:31:32
austin81
Member
Registered: 2005-03-21
Posts: 39
### Basic Algebra for Form1 students in secondary schl
How can Basic Algebra be introduced successful to year one students in secondary schools?
3bannanas+4bannanas=7bannanas
3pears+4pears=7pears
In general,3a+4a=7a?
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## #2 2005-10-12 09:46:57
MathsIsFun
Registered: 2005-01-21
Posts: 7,684
### Re: Basic Algebra for Form1 students in secondary schl
Hey, Members, how did you learn Algebra? What worked best?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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## #3 2005-10-12 10:34:21
Zach
Member
Registered: 2005-03-23
Posts: 2,075
### Re: Basic Algebra for Form1 students in secondary schl
By going to my maths lessons.
Plus, I have a very useful ability to understand things quickly.
Last edited by Zach (2005-10-12 10:34:43)
Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.
Offline
## #4 2005-10-13 06:08:58
kylekatarn
Member
Registered: 2005-07-24
Posts: 445
### Re: Basic Algebra for Form1 students in secondary schl
I started working with x and y directly and wasn't hard.
x=x
x+x=x+x
2x=x+x
2x+x=x+x+x
3x+x=x+x+x+x
now
a(z+z')=az+az'
b(a(z+z')=(ab)(z+z')=abz+abz'
I'm not a teacher, but if I were, I would shurelly avoid fruit-algebra in my classes.
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## #5 2005-10-13 09:46:10
MathsIsFun
Registered: 2005-01-21
Posts: 7,684
### Re: Basic Algebra for Form1 students in secondary schl
I actually have a page "in production" that starts something like:
2 + ? = 6
What does the "?" equal?
Then I go on to say that it is better to put an "x" instead:
2 + x = 6
What does the "x" equal?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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## #6 2005-10-13 16:29:16
ganesh
Registered: 2005-06-28
Posts: 24,312
### Re: Basic Algebra for Form1 students in secondary schl
I was first taught the difference between variables and constants.
Thereafter, the lessons were on simple operations of addition, division, multpilication, subtraction, extracting roots, exponentiation etc.
The next step was solving linear equations in one variable, simultaneous equations of two, three variables. A little later I learnt solving quadratic equations and their properties. I forgot to mention, I was also taught plotting graphs and solving equations with graphs.
The Binomial theorem was the last I was taught, and Pascal's triangle too.
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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## #7 2005-10-27 01:43:09
austin81
Member
Registered: 2005-03-21
Posts: 39
### Re: Basic Algebra for Form1 students in secondary schl
Thanks for the clues.
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## #8 2006-03-17 09:52:04
kafkan
Member
Registered: 2005-09-25
Posts: 2
### Re: Basic Algebra for Form1 students in secondary schl
this is my first time to use this forum, and i hope i will be ok for me
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## #9 2006-03-17 09:55:29
kafkan
Member
Registered: 2005-09-25
Posts: 2
### Re: Basic Algebra for Form1 students in secondary schl
math is hard not because it requires lots of figuring but because we take it to be something hard!
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## #10 2006-03-17 11:00:27
mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900
### Re: Basic Algebra for Form1 students in secondary schl
When I first came across algebra, I tried to solve the equations with trial and error.
Later on, I drew a set of scales to visualise the fact that I needed to do the same to each side.
Then I did the same method, but without the drawing, just lots of lines of working.
And now I'm able to do all kinds of crazy algebra in my head.
Just take small steps at a time.
Why did the vector cross the road?
It wanted to be normal.
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## #11 2006-03-17 16:48:52
MathsIsFun
Registered: 2005-01-21
Posts: 7,684
### Re: Basic Algebra for Form1 students in secondary schl
Hi kafkan, and welcome to the forum.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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## #12 2012-10-16 00:11:54
austin81
Member
Registered: 2005-03-21
Posts: 39
### Re: Basic Algebra for Form1 students in secondary schl
Thanks for all the assistance you give students and teachers of Mathematics in this forum. We greatly appreciate that
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## #13 2012-10-16 00:18:49
austin81
Member
Registered: 2005-03-21
Posts: 39
### Re: Basic Algebra for Form1 students in secondary schl
A number of books say we can use the substitution y=(m+1/m) to solve quartic equations that are symmetric i.e equations of the form ax^4 +bx^3+cx^2+bx+a=0, but do not talk much on quartic equations that are not symmetrical and are not easily factorised. The question is, are there other general methods of solving non-factorisable polynomial equations of degree greater than 3?
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## #14 2012-10-16 00:25:42
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Basic Algebra for Form1 students in secondary schl
Hi;
Welcome to the forum.
There are Descartes' and Ferrari's solutions for the general quartic but they are both difficult. There are no algebraic solutions for the general quintic or higher.
Download "First Course in the the Theory of Equations." It is free!
http://www.gutenberg.org/ebooks/29785
Down the page are the links.
Starting at page 56 of that book you will find everything you need.
If you need help with the examples he provides just post here.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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## #15 2012-10-16 09:23:53
ShivamS
Member
Registered: 2011-02-07
Posts: 3,648
### Re: Basic Algebra for Form1 students in secondary schl
I was taught adding variables in grade 4 and it seemed fairly easy. I was told that as long as the literal coefficients are the same, I can simply add and/or multiply the numerical coefficients depending on the operator.
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## #16 2012-10-18 00:21:52
austin81
Member
Registered: 2005-03-21
Posts: 39
Thanks
Offline
## #17 2012-10-18 00:23:45
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Basic Algebra for Form1 students in secondary schl
Hi austin81;
You are welcome. You will find several methods in that book,
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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# Tahun 5 - Peperiksaan Pertengahan Tahun 2012 - Kertas 2
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# Image Classification Using CNN | Step-wise Tutorial
Devansh Sharma 12 Jan, 2024 • 7 min read
Image classification using Convolutional Neural Networks (CNN) has revolutionized computer vision tasks by enabling automated and accurate recognition of objects within images. CNN-based image classification algorithms have gained immense popularity due to their ability to learn and extract intricate features from raw image data automatically. This article will explore the principles, techniques, and applications of image classification using CNNs. We will delve into the architecture, training process, and CNN image classification evaluation metrics. By understanding the workings of CNNs for image classification, we can unlock many possibilities for object recognition, scene understanding, and visual data analysis.
This article was published as a part of the Data Science Blogathon.
## Why CNN for Image Classification?
Image classification using CNN involves the extraction of features from the image to observe some patterns in the dataset. Using an ANN for the purpose of image classification would end up being very costly in terms of computation since the trainable parameters become extremely large.
For example, if we have a 50 X 50 image of a cat, and we want to train our traditional ANN on that image to classify it into a dog or a cat the trainable parameters become –
(50*50) * 100 image pixels multiplied by hidden layer + 100 bias + 2 * 100 output neurons + 2 bias = 2,50,302
We use filters when using CNNs. Filters exist of many different types according to their purpose.
Filters help us exploit the spatial locality of a particular image by enforcing a local connectivity pattern between neurons.
Convolution basically means a pointwise multiplication of two functions to produce a third function. Here one function is our image pixels matrix and another is our filter. We slide the filter over the image and get the dot product of the two matrices. The resulting matrix is called an “Activation Map” or “Feature Map”.
## How Are CNN Used Image Classification?
Image classification involves assigning labels or classes to input images. It is a supervised learning task where a model is trained on labeled image data to predict the class of unseen images. CNN are commonly used for image classification as they can learn hierarchical features like edges, textures, and shapes, enabling accurate object recognition in images. CNNs excel in this task because they can automatically extract meaningful spatial features from images. Here are different layers involved in the process:
### Input Layer
The input layer of a CNN takes in the raw image data as input. The images are typically represented as matrices of pixel values. The dimensions of the input layer correspond to the size of the input images (e.g., height, width, and color channels).
### Convolutional Layers
Convolutional layers are responsible for feature extraction. They consist of filters (also known as kernels) that are convolved with the input images to capture relevant patterns and features. These layers learn to detect edges, textures, shapes, and other important visual elements.
### Pooling Layers
Pooling layers reduce the spatial dimensions of the feature maps produced by the convolutional layers. They perform downsampling operations (e.g., max pooling) to retain the most salient information while discarding unnecessary details. This helps in achieving translation invariance and reducing computational complexity.
### Fully Connected Layers
The output of the last pooling layer is flattened and connected to one or more fully connected layers. These layers function as traditional neural network layers and classify the extracted features. The fully connected layers learn complex relationships between features and output class probabilities or predictions.
### Output Layer
The output layer represents the final layer of the CNN. It consists of neurons equal to the number of distinct classes in the classification task. The output layer provides each class’s classification probabilities or predictions, indicating the likelihood of the input image belonging to a particular class.
## Tutorial: CNN Image Classification with Keras and CIFAR-10
I will be working on Google Colab and I have connected the dataset through Google Drive, so the code provided by me should work if the same setup is being used. Remember to make appropriate changes according to your setup.
### Step 1: Choose a Dataset
Choose a dataset of your interest or you can also create your own image dataset for solving your own image classification problem. An easy place to choose a dataset is on kaggle.com.
The dataset I’m going with can be found here.
This dataset contains 12,500 augmented images of blood cells (JPEG) with accompanying cell type labels (CSV). There are approximately 3,000 images for each of 4 different cell types grouped into 4 different folders (according to cell type). The cell types are Eosinophil, Lymphocyte, Monocyte, and Neutrophil.
Here are all the libraries that we would require and the code for importing them:
``````from keras.models import Sequential
import tensorflow as tf
import tensorflow_datasets as tfds
tf.enable_eager_execution()
from keras.layers.core import Dense, Activation, Dropout, Flatten
from keras.layers.convolutional import Convolution2D, MaxPooling2D
from keras.optimizers import SGD, RMSprop, adam
from keras.utils import np_utils
from sklearn.tree import DecisionTreeClassifier # Import Decision Tree Classifier
from sklearn import metricsfrom sklearn.utils import shuffle
from sklearn.model_selection import train_test_splitimport matplotlib.image as mpimg
import matplotlib.pyplot as plt
import numpy as np
import os
import cv2
import randomfrom numpy import *
from PIL import Image
import theano``````
### Step 2: Prepare Dataset for Training
Preparing our dataset for training will involve assigning paths and creating categories(labels), resizing our images.
Resizing images into 200 X 200
``````path_test = "/content/drive/My Drive/semester 5 - ai ml/datasetHomeAssign/TRAIN"
CATEGORIES = ["EOSINOPHIL", "LYMPHOCYTE", "MONOCYTE", "NEUTROPHIL"]
print(img_array.shape)IMG_SIZE =200
new_array = cv2.resize(img_array, (IMG_SIZE, IMG_SIZE))``````
### Step 3: Create Training Data
Training is an array that will contain image pixel values and the index at which the image in the CATEGORIES list.
``````training = []def createTrainingData():
for category in CATEGORIES:
path = os.path.join(path_test, category)
class_num = CATEGORIES.index(category)
for img in os.listdir(path):
new_array = cv2.resize(img_array, (IMG_SIZE, IMG_SIZE))
training.append([new_array, class_num])createTrainingData()``````
### Step 4: Shuffle the Dataset
``random.shuffle(training)``
### Step 5: Assigning Labels and Features
This shape of both the lists will be used in Classification using the NEURAL NETWORKS.
``````X =[]
y =[]for features, label in training:
X.append(features)
y.append(label)
X = np.array(X).reshape(-1, IMG_SIZE, IMG_SIZE, 3)``````
### Step 6: Normalising X and Converting Labels to Categorical Data
``````X = X.astype('float32')
X /= 255
from keras.utils import np_utils
Y = np_utils.to_categorical(y, 4)
print(Y[100])
print(shape(Y))``````
### Step 7: Split X and Y for Use in CNN
``X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 4)``
### Step 8: Define, Compile and Train the CNN Model
``````batch_size = 16
nb_classes =4
nb_epochs = 5
img_rows, img_columns = 200, 200
img_channel = 3
nb_filters = 32
nb_pool = 2
nb_conv = 3
model = tf.keras.Sequential([
input_shape=(200, 200, 3)),
tf.keras.layers.MaxPooling2D((2, 2), strides=2),
tf.keras.layers.MaxPooling2D((2, 2), strides=2),
tf.keras.layers.Dropout(0.5),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(128, activation=tf.nn.relu),
tf.keras.layers.Dense(4, activation=tf.nn.softmax)
])
model.fit(X_train, y_train, batch_size = batch_size, epochs = nb_epochs, verbose = 1, validation_data = (X_test, y_test))``````
### Step 9: Accuracy and Score of Model
``````score = model.evaluate(X_test, y_test, verbose = 0 )
print("Test Score: ", score[0])
print("Test accuracy: ", score[1])``````
In these 9 simple steps, you would be ready to train your own Convolutional Neural Networks model and solve real-world problems using these skills. You can practice these skills on platforms like Analytics Vidhya and Kaggle. You can also play around by changing different parameters and discovering how you would get the best accuracy and score. Try changing the batch_size, the number of epochs or even adding/removing layers in the CNN model, and have fun!
## Conclusion
In conclusion, image classification using CNN has revolutionized the field of computer vision, enabling accurate recognition of objects within images. With its ability to automatically learn and extract complex features, CNNs have become a powerful tool for various applications. To further enhance your understanding and skills in image classification using CNN and other advanced data science techniques, consider enrolling in our Blackbelt Program. This comprehensive program offers in-depth knowledge and practical experience, empowering you to become a proficient data scientist. Ready to take the next step? Explore the possibilities of our Blackbelt Program today!
Q1. How to use CNN for image classification?
A. To use CNN for image classification, you need to define the architecture of the CNN, preprocess the input images, train the model on labeled data, and assess its performance on test images. Afterward, the trained CNN can classify new images based on the learned features.
Q2. What is CNN classifier for image classification?
A. CNN classifier for image classification is a CNN-based model specifically designed to classify images into different predefined classes. It learns to extract relevant features from input images and map them to the corresponding classes, enabling accurate image classification.
Q3. What is CNN in image captioning?
A. CNN in image captioning refers to using Convolutional Neural Networks as a component in the image captioning pipeline. CNNs are employed to extract visual features from input images, combined with text-based models to generate descriptive captions for the images.
Q4. How do I denoise an image in CNN?
A. You can train a CNN-based model on a dataset of noisy and corresponding clean images to denoise an image using CNN. The model learns to map the noisy images to their corresponding denoised versions. Once trained, the CNN can denoise new images by passing them through the network and obtaining the reconstructed clean images.
The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion.
Devansh Sharma 12 Jan 2024
Mushk Nizam 25 Feb, 2021
Hello. Thank you so much for the step to step guide to implement this. I have a question to ask. I hope to hear from you soon. I can not understand how was 'img_array' initialized in your work? What does img_array contain and how did you do that?
sarankumar 24 Apr, 2023
"print(img_array.shape)" when is try to run this line in colab I get error like "print(img_array.shape)" please help me to rectify this
Lisbertha 08 May, 2023
Hello! I was just wondering, in Step 2: Prepare Dataset for Training, where does the img_array variable come from? Is this just the path_test?
thurga 31 Aug, 2023
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# Order of Operations Fall 2008
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### PRODUCT DESCRIPTION
This is a worksheet for primarily algebra students who need a review of their order of operations.
Sadly, I often find that many of my students have been taught "PEMDAS" incorrectly, and they believe that you always do all of the multiplication operations before the division, and all of the addition before subtraction. I have to emphasize that multiplication and division are "tied," and to break a tie, you go left to right, just like you're reading a book. (And so on for addition and subtraction).
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Keywords: Jonnard
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1 hour
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1. ## L'Hosptial's Rule Question
I was wondering if someone could help me solve this problem:
The figure shows a sector of a circle with central angle θ. Let A(θ) be the area of the segment between chord PR and the arc PR. Let B(θ) be the area of the triangle PQR. Find
Thanks a lot!
2. Originally Posted by ty2391
I was wondering if someone could help me solve this problem:
The figure shows a sector of a circle with central angle θ. Let A(θ) be the area of the segment between chord PR and the arc PR. Let B(θ) be the area of the triangle PQR. Find
Thanks a lot!
I'm not going to work through all of the details of the area calculations. It's just elementary trigonometry.
The area of POR is $\frac{r^2}{2}\sin\theta$. The area of the whole sector is $\pi r^2\cdot\frac{\theta}{2\pi}=\frac{r^2\theta}{2}$. So the area of $A(\theta)$ is $\frac{r^2}{2}(\theta-\sin\theta)$.
Furthermore, the area of POQ is $\frac{r^2}{2}\cos\theta\sin\theta=\frac{r^2}{2}\cd ot\frac{\sin2\theta}{2}$ so $B(\theta)=\frac{r^2}{2}(\sin\theta-\frac{\sin2\theta}{2})$
$\lim_{\theta\to0^+}\frac{A(\theta)}{B(\theta)}=\fr ac{\frac{r^2}{2}(\theta-\sin\theta)}{\frac{r^2}{2}(\sin\theta-\frac{\sin2\theta}{2})}=$ $\lim_{\theta\to0^+}\frac{\theta-\sin\theta}{\sin\theta-\frac{\sin2\theta}{2}}$
Use L'Hopital's Rule thrice to get that the limit equals $\frac{1}{3}$.
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# Find the value
Question:
Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :
$3 y^{2}-x^{2}=108$
Solution:
Given Equation: $3 y^{2}-x^{2}=108 \Rightarrow \frac{y^{2}}{36}-\frac{x^{2}}{108}=1$
Comparing with the equation of hyperbola $\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$ we get,
$a=6$ and $b=\sqrt{108}=6 \sqrt{3}$
(i) Length of Transverse axis $=2 a=12$ units.
Length of Conjugate axis $=2 b=12 \sqrt{3}$ units.
(ii) Coordinates of the vertices $=(0, \pm a)=(0, \pm 6)$
(iv) Here, eccentricity, $e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\sqrt{1+\frac{108}{36}}=\sqrt{1+3}=2$
(iii) Coordinates of the foci $=(0, \pm a e)=(0, \pm 12)$
(v) Length of the rectum $=\frac{2 b^{2}}{a}=\frac{216}{6}=36$ units.
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# curve fitting toolbox F test ?
조회 수: 14(최근 30일)
EK 4 Dec 2019
편집: Navya Seelam 11 Dec 2019
Is it possible to extract/calculate the F test p-values from the output of a curve fitting toolbox?
#### 댓글 수: 1
Navya Seelam 9 Dec 2019
Hi,
What is the function you are using in the curve fitting tool box?
로그인 to comment.
### 답변(3개)
EK 9 Dec 2019
I am using linear fit and sigmoid (custom)
#### 댓글 수: 0
로그인 to comment.
Navya Seelam 10 Dec 2019
편집: Navya Seelam 11 Dec 2019
Hi,
You can use fitlm to extract p-values. The summary statistics of the model inlcudes p-value for the F-test on the model.
#### 댓글 수: 0
로그인 to comment.
EK 10 Dec 2019
Hi Navya
thank you very much for your suggestion. I do not understand how can I apply filtm function to my fitting parameter?
Below is a function I am using generated by fittin toolbox
function [fitresult, gof] = createFit(x, y)
%CREATEFIT(X,Y)
% Create a fit.
%
% Data for 'Sigmoid fit 1' fit:
% X Input : x
% Y Output: y
% Output:
% fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%% Fit: 'Sigmoid fit 1'.
[xData, yData] = prepareCurveData( x, y );
% Set up fittype and options.
ft = fittype( '1./(1 + exp(-a.*(x-c)))', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.77548254396942 0.353883903104256];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( 'Name', 'Sigmoid fit 1' );
#### 댓글 수: 0
로그인 to comment.
이 질문에 답변하려면 로그인을(를) 수행하십시오.
Translated by
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# Grade 9 Math: Intro to Geometry Area of a Composite
Back to Courses
### What is a composite figure?
a figure is a shape that can be divided into more than two basic figure
a figure is a shape that can be divided into more than one basic figure
a figure is a shape that can be divided into more than three basic figure
a figure is a shape that can be divided into more than four basic figure
### We have a right-angled triangle with a base of 11cm and height of 4cm. We also have a rectangle with base of 8 and a height of 5cm. What is the total area of both figures combined?
62cm$$^2$$
124cm$$^2$$
31cm$$^2$$
72cm$$^2$$
44cm$$^2$$
42cm$$^2$$
4040cm$$^2$$
22cm$$^2$$
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# 5.7 Transportation
The transportation function allows companies to gain company value by moving goods that have been sold on the market from the seller's city to the buyer's city. This is not necessary to complete the market transaction, which happens immediately; it is a separate opportunity for companies to grow.
Any company's transports may move any goods; the transporter does not need to be the buyer or the seller. Indeed, goods are assigned to transports in a city on a first-in, first-out basis.
On the transportation page, you may buy new vehicles. There are five vehicles to choose from and they all have different transportation capacity, max speed, price and fuel efficiency.
When you purchase a vehicle, it will appear in the city that you are based in. There is no limit to the number of vehicles you can own, but the price of each new vehicle of the same type will keep increasing.
US Game: The price for each new vehicle of the same type is multiplied by 2.5. For instance: if you buy three trucks and a trailer; the first truck will cost i\$950, the second truck costs 950 * 2.5 = i\$2375, and the third truck costs 2375 * 2.5 = i\$5938, while the 1st trailer is only i\$1350. The starting prices for each vehicle type are: Truck - i\$950 Trailer - i\$1350 Train - i\$2650 Airplane - i\$8000 Sweden Game: The price for each new vehicle of the same type is multiplied by 1.5. For instance: if you buy four trucks and a trailer; the first truck will cost 2400 iKr, the second truck costs 2400 * 1.5 = 3600 iKr, the third truck costs 3600 * 1.5 = 5400 iKr, and the forth truck costs 5400 * 1.5 = 8100 iKr while the 1st trailer is only 5400 iKr. The starting prices for each vehicle type are: Truck - 2400 iKr Trailer - 5400 iKr Ship - 10,600 iKr Airplane - 32,000 iKr
When buying a vehicle, you gain an increase to your company value equal to 1/15 of the purchase price. However, you will also lose 1/20 of the price due to the reduction in your savings, so your net CV gain will be 1/15 - 1/20 = 1/60 of the purchase price.
## Selling vehicles
When you sell a vehicle, the amount of CV loss and cash gain you will receive depends on how many vehicles you currently have.
Easy example:
You have one airplane and decide to sell it. The airplane costs 16 000 iKr to replace since it is your only vehicle.
You will receive 1/5 cash of the value and lose 1/40 CV. You gain 3 200 iKr and lose 400 CV. The net CV loss is 240 since the gain of 3 200 iKr offsets the loss. A 3 200 iKr gain raises your CV by 160.
Now for a more complicated calculation:
You have 2 trucks and want to sell one of them. The replacement cost on the truck is 3600 iKr since you have 2 trucks.
You will gain 1/5 iKr of 3600 and lose 1/40 CV of 3600. That is a 720 iKr gain and 90 CV loss. The net loss will be about 46 CV due to the gain of 608 iKr. I say about 46 because the numbers are rounded.
## Vehicle staff
An employee with a driver’s license must operate a vehicle. No matter what vehicle it is (whether it is a truck or an airplane), a driver's license is all the employee needs to operate the vehicle. The salary of an employee operating a vehicle is calculated with a market price of 25 iKr (check the staff section for how to calculate salaries).
Drivers are professional chauffeurs. They use their production points when operating a vehicle. Other staff can use their attribute points. The skill of the chauffeur determines the average speed of a vehicle, up to a max speed set for each type of vehicle.
When you view a vehicle's status page, the driver will be displayed along with his driving skill. A driver's skill is calculated with this formula: Number of production points (if driver) or number of attribute points (if other profession) / 2
You have a professional driver with 85 production points. How high driving skill does your driver have? 85 / 2 ~ 43. Your driver has a skill of 43%.
## Gasoline expenditure
Once a vehicle has been bought, it will need to tank up. It does so within the next ten minutes. When a vehicle tanks for gasoline, the gasoline is paid for from the gasoline account you can find on the "Transportation" page. If there is not enough money on the gasoline account for the vehicle to tank up, the vehicle will not function until money is deposited to the account, and it is able to purchase gasoline. The price per unit of gasoline is the same as the market price of gasoline.
Gasoline tanked by a vehicle is lost if the vehicle is sold.
Some vehicles have more gasoline capacity (the airplane, for instance), allowing them to travel further than other vehicles without tanking. Vehicles will tank only when they are running out of gasoline, and this will often be in the middle of an assignment. This means no vehicle types have limits to their reach. All vehicles may travel between all the possible routes in Tycoon Online.
US Game: Fuel efficiency is dependent on vehicle type: Tank size x Fuel efficiency = Distance per full tank Truck = 10 fuel x 250 mpg = 2500 miles Trailer = 20 fuel x 150 mpg = 3000 miles Train = 20 fuel x 500 mpg = 10,000 miles Airplane = 20 fuel x 200 mpg = 4000 miles Sweden Game: All vehicles consume one unit of gasoline per 200 kilometers traveled. Tank size x Fuel efficiency = Distance per full tank Truck = 10 fuel x 200 kmpg = 2000 km Trailer = 10 fuel x 200 kmpg = 2000 km Ship = 20 fuel x 200 kmpg = 4,000 km Airplane = 20 fuel x 200 kmpg = 4000 km
## Transporting goods
After having tanked, your vehicle will start receiving transportation assignments. These tasks are given to the vehicle automatically.
Goods that have been traded and made available for transportation are made unavailable for transportation if 48 hours pass without the goods being loaded by a vehicle.
When the bank purchases goods, no transportation assignments are created. However when the bank sell goods on the market, there will be transportation assignment created, from the city in which the company that sold the goods to the bank are located, to the buying company's city.
For instance: You have a truck in Malmö. It has a driver, has tanked up, and is ready for assignments. It is given the Malmö - Ystad route (the assignment appears under "Current assignments"). When a company in Ystad buys goods from the market sold by a company from Malmö, your vehicle will be loaded with these goods and sent to Ystad.
A vehicle will only head for its destination city once it has been fully loaded with goods or the amount of goods loaded has reached your chosen minimum capacity used. Thus, if a company in Ystad buys 10 goods from a company in Malmö, your truck will be loaded with 10 units of goods. Your truck can carry a total of 80 units of goods maximum, so it will remain in Malmö until more market transactions are made, or if you have set the truck's minimum carrying capacity to 10 units.
Trucks have a special ability, they can haul same-city cargo loads (those goods bought and sold in the same city). You do not need to do anything special to access this ability, however you can restrict individual trucks to only haul same-city goods, or to only haul goods to a different city.
When more vehicles are in need of transportation assignments than there is goods available for transportation, vehicles are queued in the cities they are currently in. Depending on the amount of market transactions, the queue will move forward as vehicles are loaded and sent to their destination cities.
You can order your vehicles to other cities yourself. To do this, enter the vehicle's profile, click the name of the city, and choose a city to go to. When choosing the city, you will be given information on goods currently in need of transportation in that city. When you give a vehicle such an order, it will not be transporting goods while moving to your chosen location. If the vehicle has already been assigned to another task, your order will be queued behind it. When looking at the 'Recent wait times' for a city, remember they are a lagging indicator, it shows the average waiting time of vehicles that recently departed and are still on route to the destination.
It is possible to delete tasks given to vehicles as long as the vehicle has not yet begun undertaking the assignment. Once it has arrived its destination city and has been awarded a transportation destination, it will remain there until it has been loaded and traveled to the given city. When deleting assignments, the latest given assignment must be deleted first.
If you click a task listed under "Current assignments", details about the amount of goods caried and company value increase gained from the task are displayed.
## FTL vs LTL
US Game: In the US version you can choose whether your vehicles will accept shipments that are smaller than the minimum you set for each vehicle. For example, if your vehicle is set to a minimum of 40 goods, and is in FTL (Full Truck Load) mode, you won't get stuck with a 5 unit load. Those 5 units may go to another player's LTL (Less-Than-Load) mode vehicle later in the queue. You will need to decide the best strategy for your transports. If you have a Gold Membership, you can set LTL/FTL mode individually for each vehicle, or set all vehicles to the same mode with one click. Players without GM can only choose one mode for their entire fleet. Sweden Game: All vehicles are LTL. They will start to fill up with the 1st available load of any size.
## Vehicle capacity
When entering a vehicle's profile, you may set the minimum capacity it may carry to its destination. By setting the minimum capacity used lower than a vehicle's maximum capacity, the vehicle is allowed to leave its city before it is fully loaded. This is especially helpful if the vehicle is "stuck" on a route between two cities where little goods need transportation. To escape such a situation, you may set your vehicle's minimum load below the load it has currently loaded to force it to move from the city it is stuck in.
These are the current maximum capacities of the various vehicles:
• Truck: 80 units
• Trailer: 120 units
• Airplane: 160 units
• Ship: 320 units
## Vehicle speed
Each vehicle has a max speed. This is the speed that a perfect driver may manoeuvre his or her vehicle: An employee with the driver profession, 100 in all attributes, and 100 profession points.
The speed that your vehicle moves with depends on your chauffeur's driving skill and is calculated with this formula: (max speed /2) + ((max speed / 2) * skill). This means that the lowest speed a vehicle can move with is half its max speed.
Your driver has 43% skill. He drives a truck, which has a maximum speed of 80 km/h. How fast will your driver be able to drive? (80 / 2 + ((80 / 2) * 0.43) = 40 + 17 = 57 km/h. Your driver will manoeuvre your truck at a speed of 57 km/h.
US Game: Vehicles will travel the calculated distance every 10 minutes. Sweden Game: Vehicles will travel the calculated distance every hour.
## Transportation rewards
When transporting goods, you earn 1 iKr/i\$ per unit of goods transported. The type of goods and the distance traveled has no influence on transportation payment.
More important is the increase in company value transportation produces.
US Game:
The company value gain is calculated with this formula:
Units transported x distance traveled / 1000
You transport 320 units 3000 miles. You receive 320 i\$ for the assignment. How much does your company value increase from the transportation assignment? 320 * 3000 / 1000 = 960 points of company value. For transporting 320 units 1000 miles, you gain 960 points of company value.
Sweden Game:
The company value gain is calculated with this formula:
Units transported x distance traveled / 300
You transport 320 units 100 km. You receive 320 iKr for the assignment. How much does your company value increase from the transportation assignment? 320 * 100 / 300 = 106 points of company value. For transporting 320 units 100 km, you gain 106 points of company value.
Hint: Transportation is a feature that serves wealthy companies the most. The income gained from transportation is low and does not cover your vehicles' gasoline and staff expenditures. Companies that have reached their maximum amount of buildings require new ways of increasing the company value growth, and it is the company value addition that is attractive when transporting goods. Therefore, the main purpose of vehicles' is to generate CV at a cash expense to the company. Which can sometimes bring greater returns than investing the cash.
Hint: Although vehicles function without supervision, you can greatly increase the company value you gain from them by keeping an eye on what cities have more goods available for transportation and directing your vehicles to these cities. If no cities have goods available for transportation, you can browse the current length of the queues for assignments in each city by changing the city viewed on the "Map" page.
## Transportation Map Tool
The transportation map tool shows an overview of all cities in the game and their current transport status. Information shown (when hovering over a city name) includes:
• Total cargo waiting
• Recent waiting times
• Vehicles waiting in, moving to or moving from the city
Each city name on the map will appear in different colours. Blue, Yellow or Red. The colour of the city name is determined by several factors including:
• Total goods waiting for transport
• Number of vehicles in the city
• Recent waiting times
Different points get assigned to each different criteria. City names in blue mean that they received more points and therefore meet the most criteria, names in red mean they meet the least. The criteria values can be modified by players with Gold Membership.
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1. Home
2. Knowledge Base
3. Financial Engineering – Definition
# Financial Engineering – Definition
### Financial Engineering
Financial engineering (or quantitative analysis) is the application of various technical fields, particularly applied mathematics and computer science, to the development of financial products – such as derivative assets.
Financial engineering is generally carried out by banks, managed funds, and insurance agencies.
### A Little More on What is Financial Engineering
Financial engineers or quantitative analysts employ mathematics and computer systems to develop approaches to analyzing and creating new investment vehicles, investment models, trading strategies, and other forms of financial instruments.
The objectives of these approaches are to develop new methods of investing money and determining how these investments will perform. Many derivative assets (investments that derive their value from other assets) were developed using financial engineering. High-powered computers applying sophisticated mathematical formulas are able to project how certain assets will perform with respect to other assets.
### Academic Research on Financial Engineering
Implementing Derivative Models (Wiley Series in Financial Engineering), Clewlow, L., & Strickland, C. (1996). Implementing Derivative Models (Wiley Series in Financial Engineering). This paper examines the increased global implementation of the Derivatives Models Les Clewlow and Chris Strickland Derivatives markets, particularly in the over-the-counter market in complex or exotic options. The paper further analyses the limited availability of information regarding the theory and applications of the numerical techniques required to succeed in these markets and the problems it could pose.
Financial engineering in corporate finance: An overview, Finnerty, J. D. (1988). Financial engineering in corporate finance: An overview. Financial management, 14-33. This introduction to the special issue provides an overview of financial engineering in corporate finance. It characterizes the process of financial innovation, describes the factors that stimulate financial innovation, and evaluates a variety of financial innovations within this framework in order to assess the sources of the value added by each.
Longevity bonds: financial engineering, valuation, and hedging, Blake, D., Cairns, A., Dowd, K., & MacMinn, R. (2006). Longevity bonds: financial engineering, valuation, and hedging. Journal of Risk and Insurance73(4), 647-672. This article examines the main characteristics of longevity bonds (LBs) and shows that they can take a large variety of forms which can vary enormously in their sensitivities to longevity shocks. The authors examine different ways of financially engineering LBs and consider problems arising from the dearth of ultra‐long government bonds and the choice of the reference population index. The article also looks at valuation issues in an incomplete markets context and finishes with an examination of how LBs can be used as a risk management tool for hedging longevity risks.
The determinants of stock price exposure: Financial engineering and the gold mining industry, Tufano, P. (1998). The determinants of stock price exposure: Financial engineering and the gold mining industry. The Journal of Finance53(3), 1015-1052. This paper studies the exposure of North American gold mining firms to changes in the price of gold.
How financial engineering can advance corporate strategy, Tufano, P. (1996). How financial engineering can advance corporate strategyHarvard Business Review74(1), 136-146. In this paper, the author looks at how financial engineering can help senior managers achieve their companies’ objectives. He presents five case studies that illustrate innovative applications of financial engineering and helps managers determine when such techniques are appropriate. The cases highlight five companies that faced different challenges: Enron Capital & Trade Resources, Tennessee Valley Authority, Rhone-Poulenc, Cemex, and MW Petroleum Corporation. The cases show that collaboration between managers and financial engineers can help create a competitive edge in a corporation.
Retail banking and behavioral financial engineering: The case of structured products, Breuer, W., & Perst, A. (2007). Retail banking and behavioral financial engineering: The case of structured products. Journal of Banking & Finance31(3), 827-844. In this paper, the authors apply cumulative prospect theory and hedonic framing to evaluate discount reverse convertibles (DRCs) and reverse convertible bonds (RCBs) as important examples of structured products from a boundedly rational investor’s point of view. Conclusions are documented withing the text.
Incoherence of contract-based Islamic financial jurisprudence in the age of financial engineering, El-Gamal, M. A. (2007). Incoherence of contract-based Islamic financial jurisprudence in the age of financial engineering. Wis. Int’l LJ25, 605. This paper analyses the Islamic financial jurisprudence and its impact on financial practices. It also analyses modernb day use of financial engineering in this jurisprudence. The paper shows that in today’s age of low-cost financial engineering, the regulatory substance of prohibitions, contract conditions, and other contract-based juristic rulings has been diluted to the point of rendering the contract-based jurisprudence incoherent.
Jump-diffusion models for asset pricing in financial engineering, Kou, S. G. (2007). Jump-diffusion models for asset pricing in financial engineering. Handbooks in operations research and management science15, 73-116. This survey focuses on the following issues related to jump-diffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as barrier and lookback options. (4) Difficulties associated with the partial integro-differential equations related to barrier-crossing problems. (5) Analytical approximations for finite-horizon American options with jump risk. (6) Multivariate jump-diffusion models.
Financial engineering in Islamic finance, Iqbal, Z. (1999). Financial engineering in Islamic finance. Thunderbird International Business Review41(4‐5), 541-559. The objective of this article is to examine the scope of financial innovation and engineering within an Islamic financial system. The article concludes that, contrary to common belief, Islamic finance provides the basic building blocks that can be used to construct more complex instruments that will enhance liquidity and offer risk management tools.
Financial engineering with Islamic options, Obaidullah, M. (1998). Financial engineering with Islamic options. In view of the central role which options play in mainstream financial engineering – in design of innovative financial products and management of risk, this paper undertakes an Islamic evaluation of options and its role in the Islamic system of financial contracting. It also proposes a comparison of istijrar to enable Islamic financial engineers to design contracts in a more efficient manner.
Financial engineering, consumer credit, and the stability of effective demand, Brown, C. (2007). Financial engineering, consumer credit, and the stability of effective demand. Journal of Post Keynesian Economics29(3), 427-450. This paper examines the macroeconomic implications of recent developments in financial engineering, with particular emphasis on the post-1987 growth of markets for securities backed by credit card, installment, student loan, and home equity receivables.
Financial engineering, corporate governance, and the collapse of Enron, Gillan, S., & Martin, J. D. (2002). Financial engineering, corporate governance, and the collapse of Enron. This paper presents an insight into the failure of Enron in less than one year after being named 7th largest US firm and six-time winner of Fortune’s most innovative firm. This paper aims to solve the cause of the company’s bankcrupty. Findings show that management used financial engineering and related-party transactions to disguise Enron’s financial condition for over three years. The authors document the existence of potential conflicts of interest throughout Enron’s governance structure, and conflicts that contributed to the firm’s bankruptcy.
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https://au.mathworks.com/matlabcentral/answers/72646-why-is-matlab-signrank-function-returns-the-same-signed-rank-statistic-values-when-flipping-the-sign
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# Why is Matlab signrank function returns the same signed rank statistic values when flipping the signs of the data points?
7 views (last 30 days)
Tim on 18 Apr 2013
Answered: Armando Angulo on 23 Nov 2017
Why is Matlab signrank function returns the same signed rank statistic values when flipping the signs of the data points?
I have a sequence of data points stored in vector x. I use signrank(x) to do sign rank test.
Matlab says
When you use the test for one sample, then W is the sum of the ranks of positive differences between the observations and the hypothesized median value M0 (which is 0 when you use signrank(x) and m when you use signrank(x,m)).
So I think the result signrank(x) and signrank(-x) should be different. But I have experienced some examples, and I get the same sign rank statistic value for x and -x. How is the signed rank statistic defined in Matlab signrank function?
Thanks!
Armando Angulo on 23 Nov 2017
I don't Know how matlab computes signrank, but the result it should be the same for x and -x because probability is compute with the smallest values of the independent sum of negative and positive ranks. So, in case x: negative sum = 8 positive sum = 16 you take 8 as W stat for compute p value
In contrast, in case -x: negative sum = 16 positive sum = 8 you take 8 as W stat for compute p value
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https://www.unitsconverters.com/en/Km2-To-Mm2/Utu-303-305
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Formula Used
1 Square Kilometer = 1000000 Square Meter
1 Square Meter = 1000000 Square Millimeter
1 Square Kilometer = 1000000000000 Square Millimeter
## km² to mm² Conversion
The abbreviation for km² and mm² is square kilometer and square millimeter respectively. 1 km² is 1000000000000 times bigger than a mm². To measure, units of measurement are needed and converting such units is an important task as well. unitsconverters.com is an online conversion tool to convert all types of measurement units including km² to mm² conversion.
## Square Kilometer to mm²
Check our Square Kilometer to mm² converter and click on formula to get the conversion factor. When you are converting area from Square Kilometer to mm², you need a converter that is elaborate and still easy to use. All you have to do is select the unit for which you want the conversion and enter the value and finally hit Convert.
## km² to Square Millimeter
The formula used to convert km² to Square Millimeter is 1 Square Kilometer = 1000000000000 Square Millimeter. Measurement is one of the most fundamental concepts. Note that we have Fahrenheit as the biggest unit for length while Per Degree Celsius is the smallest one.
## Convert km² to mm²
How to convert km² to mm²? Now you can do km² to mm² conversion with the help of this tool. In the length measurement, first choose km² from the left dropdown and mm² from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from mm² to km²? You can check our mm² to km² converter.
How to convert km² to mm²?
The formula to convert km² to mm² is 1 Square Kilometer = 1000000000000 Square Millimeter. km² is 1000000000000 times Bigger than mm². Enter the value of km² and hit Convert to get value in mm². Check our km² to mm² converter. Need a reverse calculation from mm² to km²? You can check our mm² to km² Converter.
How many m² is 1 km²?
1 km² is equal to 1000000 m². 1 km² is 1000000 times Bigger than 1 m².
How many cm² is 1 km²?
1 km² is equal to 10000000000 cm². 1 km² is 10000000000 times Bigger than 1 cm².
How many mm² is 1 km²?
1 km² is equal to 1000000000000 mm². 1 km² is 1000000000000 times Bigger than 1 mm².
How many ft² is 1 km²?
1 km² is equal to 10763910.4166236 ft². 1 km² is 10763910.4166236 times Bigger than 1 ft².
## km² to mm² Converter
Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Measurement like area finds its use in a number of places right from education to industrial usage. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. unitsconverters.com helps in the conversion of different units of measurement like km² to mm² through multiplicative conversion factors. When you are converting area, you need a Square Kilometer to Square Millimeter converter that is elaborate and still easy to use. Converting km² to Square Millimeter is easy, for you only have to select the units first and the value you want to convert. If you encounter any issues to convert Square Kilometer to mm², this tool is the answer that gives you the exact conversion of units. You can also get the formula used in km² to mm² conversion along with a table representing the entire conversion.
Let Others Know
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# Ez program
2
was8bit 2022-08-29 05:49
For those new to LowRes or programming in general ... :)
2022-08-29 05:55
2022-08-29 05:49
was8bit 2022-08-29 05:56
For those interested, in the first version, if you win or lose your face disappears without actually moving towards what it hit...
In the second version, I corrected this, moving the face BEFORE deciding if player has won or lost...
was8bit 2022-08-29 05:58
So, anyone can make mistakes... the key is to Test your program frequently, so as to be able to find a mistake and fix it quickly before adding more stuff to your game ;)
SP4CEBAR 2022-08-29 09:41 (Edited)
You can simplify
IF LEFT(0) THEN MX=-1 ELSE IF RIGHT(0) THEN MX=1 ELSE MX=0
With
MX=LEFT(0)-RIGHT(0)
was8bit 2022-08-29 09:57
That is quite clever :)
... as i am often programming while sleepy, i try to keep it more readable... math tricks made incorrectly are the ones i never seem to catch :/
Example, i might do right-left and never figure out the error with sleepy brains ;)
SP4CEBAR 2022-08-29 13:07
I'm usually not that worried about getting a value with the wrong sign (+/-), it usually moves the opposite way or something like that, whenever I see something like that, I invert it, (or a variable based on it), and usually that works just fine
was8bit 2022-08-29 15:59
Makes perfect sense :) but sometimes when sleepy my brain works in mysterious ways ;)
Also, the more math layers added to something the harder my brain has to work to understand it... i mean, for example yes i got the highest score in advanced calculus final exam, but also i took the longest time... typical time was 1-2 hours, i used the whole day, over 8 hours...
i have to break things down to their simplest steps with layered math.. so for example...
X/2=5
(X/2)*2=5*2
X*(2/2)=5*2
X*1=5*2
X=10
... where everyone else would have simply said
X=10
... could also be because i am a little dyslexic, so i might initially do
X/2=5
(X/2)*2=5*10
X*(2/2)=5*10
X*1=5*10
X=50
Which, actually, i actually did HERE just above, caught it, and fixed it, before i hit the POST button... and i can actually read thru the second incorrect one a few times before i realize my mistake...
Had i simply jumped to x=50, i would have never caught my mistake... my brain repeats the error as if it was still ok ....
Anyways, i have great respect for people who can get their math into tight little packages :)
McPepic 2022-08-29 16:57
@was8bit, kind of ironic that you happened to type 2 in binary instead of decimal.
was8bit 2022-08-29 17:27
:D
SP4CEBAR 2022-08-30 09:18 (Edited)
I'm a little slow with math too, but that is mostly caused by me double-checking every step of each calculation
Getting math right in programming is pretty hard sometimes, yesterday I spent quite a while debugging one line of code with a bunch of multiplications to try to get my multi-celled characters to go to the next line
was8bit 2022-08-30 12:28
Thats why i do a lot of testing as i add code... TRACE is wonderful :)
SP4CEBAR 2022-08-30 19:49
It really is
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http://openturns.github.io/openturns/latest/user_manual/response_surface/_generated/openturns.LinearTaylor.html
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# LinearTaylor¶
class LinearTaylor(*args)
First order polynomial response surface by Taylor expansion.
Available constructors:
LinearTaylor(center, function)
Parameters: center : sequence of float Point where the Taylor expansion of the function is performed. function : Function Function to be approximated.
Notes
The approximation of the model response around a specific set of input parameters may be of interest. One may then substitute for its Taylor expansion at point . Hence is replaced with a first or second-order polynomial whose evaluation is inexpensive, allowing the analyst to apply the uncertainty anaysis methods.
We consider here the first order Taylor expansion around .
Introducing a vector notation, the previous equation rewrites:
where:
• is the vector model response evaluated at ;
• is the current set of input parameters;
• is the transposed Jacobian matrix evaluated at .
Examples
>>> import openturns as ot
>>> formulas = ['x1 * sin(x2)', 'cos(x1 + x2)', '(x2 + 1) * exp(x1 - 2 * x2)']
>>> myFunc = ot.SymbolicFunction(['x1', 'x2'], formulas)
>>> myTaylor = ot.LinearTaylor([1, 2], myFunc)
>>> myTaylor.run()
>>> responseSurface = myTaylor.getResponseSurface()
>>> print(responseSurface([1.2,1.9]))
[1.13277,-1.0041,0.204127]
Methods
getCenter() Get the center. getClassName() Accessor to the object’s name. getConstant() Get the constant vector of the approximation. getId() Accessor to the object’s id. getInputFunction() Get the function. getLinear() Get the gradient of the function at . getName() Accessor to the object’s name. getResponseSurface() Get an approximation of the function. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. run() Perform the Linear Taylor expansion around . setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)
Initialize self. See help(type(self)) for accurate signature.
getCenter()
Get the center.
Returns: center : Point Point where the Taylor expansion of the function is performed.
getClassName()
Accessor to the object’s name.
Returns: class_name : str The object class name (object.__class__.__name__).
getConstant()
Get the constant vector of the approximation.
Returns: constantVector : Point Constant vector of the approximation, equal to .
getId()
Accessor to the object’s id.
Returns: id : int Internal unique identifier.
getInputFunction()
Get the function.
Returns: function : Function Function to be approximated.
getLinear()
Get the gradient of the function at .
Returns: gradient : Matrix Gradient of the function at the point (the transposition of the jacobian matrix).
getName()
Accessor to the object’s name.
Returns: name : str The name of the object.
getResponseSurface()
Get an approximation of the function.
Returns: approximation : Function An approximation of the function by a Linear Taylor expansion at the point .
getShadowedId()
Accessor to the object’s shadowed id.
Returns: id : int Internal unique identifier.
getVisibility()
Accessor to the object’s visibility state.
Returns: visible : bool Visibility flag.
hasName()
Test if the object is named.
Returns: hasName : bool True if the name is not empty.
hasVisibleName()
Test if the object has a distinguishable name.
Returns: hasVisibleName : bool True if the name is not empty and not the default one.
run()
Perform the Linear Taylor expansion around .
setName(name)
Accessor to the object’s name.
Parameters: name : str The name of the object.
setShadowedId(id)
Accessor to the object’s shadowed id.
Parameters: id : int Internal unique identifier.
setVisibility(visible)
Accessor to the object’s visibility state.
Parameters: visible : bool Visibility flag.
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https://www.pinterest.ca/pin/489555421966224400/
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▶ Measuring and Angle - YouTube teaching video
Find this Pin and more on MMS 4: angles & polygons by Sandra Riccardi.
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# Measuring and Angle
Measuring and Angle
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Worksheets: Measuring Angles
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Super fun powerpoint game to practice order of operations. Students tap the center of the wheel to spin, then tap again to stop. It really spins and stops whenever it is touched. Great practice and keeps them engaged!
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Complete info and lesson plan for teachers to use when teaching protractor skills. Includes links to interactive sites for kids.
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Angles Measures Task Cards - with or without QR codes!
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https://www.airmilescalculator.com/distance/sat-to-cgi/
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# Distance between San Antonio, TX (SAT) and Cape Girardeau, MO (CGI)
Flight distance from San Antonio to Cape Girardeau (San Antonio International Airport – Cape Girardeau Regional Airport) is 738 miles / 1188 kilometers / 641 nautical miles. Estimated flight time is 1 hour 53 minutes.
Driving distance from San Antonio (SAT) to Cape Girardeau (CGI) is 861 miles / 1386 kilometers and travel time by car is about 14 hours 43 minutes.
## Map of flight path and driving directions from San Antonio to Cape Girardeau.
Shortest flight path between San Antonio International Airport (SAT) and Cape Girardeau Regional Airport (CGI).
## How far is Cape Girardeau from San Antonio?
There are several ways to calculate distances between San Antonio and Cape Girardeau. Here are two common methods:
Vincenty's formula (applied above)
• 738.009 miles
• 1187.710 kilometers
• 641.312 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 738.222 miles
• 1188.054 kilometers
• 641.498 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## Airport information
A San Antonio International Airport
City: San Antonio, TX
Country: United States
IATA Code: SAT
ICAO Code: KSAT
Coordinates: 29°32′1″N, 98°28′11″W
B Cape Girardeau Regional Airport
City: Cape Girardeau, MO
Country: United States
IATA Code: CGI
ICAO Code: KCGI
Coordinates: 37°13′31″N, 89°34′14″W
## Time difference and current local times
There is no time difference between San Antonio and Cape Girardeau.
CST
CST
## Carbon dioxide emissions
Estimated CO2 emissions per passenger is 129 kg (284 pounds).
## Frequent Flyer Miles Calculator
San Antonio (SAT) → Cape Girardeau (CGI).
Distance:
738
Elite level bonus:
0
Booking class bonus:
0
### In total
Total frequent flyer miles:
738
Round trip?
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https://gamedev.stackexchange.com/questions/71303/modify-random-distribution-functions-make-it-less-likely-to-get-multiple-simi/71314
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# Modify random distribution functions :: Make it less likely to get multiple similar values in a sequence
I want to generate a sequence of numbers for procedurally generating planets in a galaxy sector. Each planet should be placed randomly, however it should be very unlikely that two planets are directly next to each other. How can I achieve that?
I know that you can modify the chances by applying a distribution function, but how can I control them in order to make specific values more/less likely?
• Simply adding a minimum distance would make sure a planet is not next to another. I estimate this is to simple so could you elaborate some more? Mar 3, 2014 at 15:57
• @MennoGouw Yes, that would solve it for this specific case, though I want to improve my understanding of probability so I am looking for a "softer" solution without hard limits/discarding generated numbers. Mar 3, 2014 at 16:14
• Clarify the "softer" solution. It's all about setting rules. When you need certain rules for procedural generation you need to add these rules. If you have special cases you set more or different rules for these. Mar 3, 2014 at 16:19
• I'm not sure why you don't just use a generator that has a great reputation about it's distribution? (I think the Mersenne twister is not bad.) Mar 3, 2014 at 16:22
• I agree. The random generation itself is not the problem. Doing this can even break your random generator by making it predictable. Rule generation is the way to go. Mar 3, 2014 at 17:25
If you do know the distribution you want, you can use rejection sampling.
Simplest way: In the graph above, pick points at random until you find one is below the curve. Then just use the x-coordinate.
For the actual distribution, there are various plausible approaches. For example, for planet number i at location p, and some strength parameter k (e.g. 0.5), define a function f_i(x)=abs(p-x)^k, then use distribution function g(x)=f_1(x)*f_2(x)*...*f_n(x).
In practice, compute and store results of g(x) to array t (t[x]=g(x)); remember the highest seen value h also. Pick a random position x in t, pick random value y between 0 and h, repeat if y>t[x]; otherwise the return value is x.
• Could you go a bit more in-depth about defining the distribution function? The rest should be pretty clear. Mar 3, 2014 at 19:11
• For example, if the current planets are at positions 0.1, 0.3 and 0.8, g(x) = (abs(x-0.1)*abs(x-0.3)*abs(x-0.8))^0.5, where "^" means exponentiation. (This is slightly differently written from the previous formula, but equivalent.) This distribution function looks roughly like the gif in your question and is not based on anything in particular. (Query string for WolframAlpha: "plot from 0 to 1 (abs(x-0.1)*abs(x-0.3)*abs(x-0.8))^0.5")
– yarr
Mar 3, 2014 at 21:14
• Wow, that function is pretty damn cool. Didn't know that a function like that is actually that simple :) Link for the lazy: bit.ly/1pWOZMJ Mar 3, 2014 at 22:05
I am not sure the problem is fully specified by the question, but I can provide some simple ideas, the second of these will provide numbers roughly in accordance with what your picture indicates you want.
Either way as you may realize the distribution function is changing after each number generated, and has a memory (ie: it is non-Markovian) and either of these method may prove impractical when the 'memory' (number of previously drawn numbers) gets very large.
1. Simple:
Generate random number form a flat distribution, compare with previously drawn nnumbers, repeat if 'too close'
2. This answer is more like your figure (assuming we want to draw from 0..1):
• create a new ordered list, insert 0 and 1
• generate random number from a flat distribution function: N_0
• add this number to the list
• on next call, draw a another number N_1,
• if N_1> N_0
• draw a new Gaussian Random number with mean=1 and a standard deviation o of whatever you want, a smaller number (compared with 1-N_1) will keep the random numbers further spaced apart. This will not guarantee a minimum distance between draws, but then again your figure doesn't seem to either.
• opposite case of N_1 < N_0 handled similarly
• on subsequent draws keep generating a random number (N_i) from a flat distribution
• traverse your list to see which two previously drawn numbers the new number lies between (N_-, N_+)
• create a new Gaussian random number with mean (N_- + N_+)/2
• add the flat distribution number (N_i) to your (ordered list) list
endpoint bins are a special case, but it should be simple enough for you to see how to handle them.
Think of the difference between 1 dice and 3 dice. 1 Dice gives you an even probability for all values, while 3 dice will tend to have a higher probability for the values towards the middle.
The more "dice" in your equation, the stronger your chance to get something towards the centre. So let's define a function that can handle any number evenly:
// Takes a random number between floor and ceil
// pow defines how strongly these results should gravitate towards the middle
// We also define a function TrueRand(floor, ceil) elsewhere where you should substitute your own random function
int CenterRandom(int floor, int ceil, int pow = 3)
{
if(ceil == floor)
return ceil; // don't care to compare
int total = 0;
for(int x = 0; x < pow; x++)
{
total += TrueRand(floor, ceil);
}
}
Now we can define an example function to use this:
// Distribues a number of points between floor and ceil
// We assume a function PlotPoint(int) exists to aid in creating the planet, etc...
void DistributePoints(int floor, int ceil, int numPoints)
{
// Could easily output this in the function parameters, but language wasn't specified
int[numPoints] breaks;
int numBreaks = 0;
// Special case for first pair
breaks[0] = CenterRandom(floor, ceil);
numBreaks++;
for(int x = 0; x < numPoints - 1; x++)
{
// Generate a random number linearly, this will be used for picking
// This way we have a greater chance of choosing a random value between larger pairs
int picker = TrueRandom(floor, ceil);
// Now we first find the pair of points that our picker exists on
// For simplicity, we handle the first and last pair separately
if(picker >= floor && picker < breaks[0])
{
breaks[x] = CenterRandom(floor, breaks[0] - 1);
}
for(int i = 0; i < numBreaks; i++)
{
if(picker > breaks[i] && picker < breaks[i+1])
{
breaks[x] = CenterRandom(breaks[i] + 1, breaks[i+1] - 1);
}
}
if(picker > breaks[numBreaks] && picker <= ceil)
{
breaks[x] = CenterRandom(breaks[numBreaks] + 1, ceil);
}
PlotPoint(breaks[x]); // Plot the point
}
}
Now the first to note is that this code really doesn't check if picker matches one of the points already. If it does then it's just not going to generate a point, possibly something you'd might like.
To explain what's going on here is that CenterRandom generates a bell curve of sorts. This function breaks up the plane into multiple bell curves, one per pair of points existing. The picker tells us which bell curve to generate from. Since we pick linearly, we can ensure that pairs with larger gaps between them will be chosen more often, but we still leave it completely random.
Hope this points you in the right direction.
I know you're asking about a sequence of random positions, but if you aren't restricted to generating the set sequentially, there's another approach: generate a set of points that has the desired spacing.
What I think you want is a set of planets that are reasonably spaced with some randomness. Instead of generating planet positions with a random number generator, generate planet spacing with a random number generator. This will let you directly control the distribution of spacing, by using a random number generator that picks from that distribution. This is straightforward in 1 dimension.
In 2 dimensions, I've seen some approaches that generate “blue noise” but I don't know a way to generate spacing with an arbitrary distribution. This article covers the standard “try placing it and reject if it's too close” approach, but you can generate them all at once, with a “softer” solution by placing all your points, then using Lloyd Relaxation to move all the planets to more desirable positions. It'll move the too-close planets farther apart. Recursive Wang Tiles are another approach that could be useful. This paper extends the problem to generating planets with one density and some other object like asteroids with another density. You might also be able to generate blue noise by using Fourier series; I'm not sure. The Fourier series approach would also let you use arbitrary distributions instead of only blue noise.
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# Excel VLOOKUP with Multiple Criteria in Column and Row
Get FREE Advanced Excel Exercises with Solutions!
In this article, we will learn to use the VLOOKUP function with criteria in the column and row in Excel. The VLOOKUP function looks for a value in the leftmost column of a table or array and returns a value from the same row from the specified column. Today, we will discuss 6 examples. Using these examples, you can easily use the VLOOKUP function with multiple criteria in the column and row. So, without any delay, let’s start the discussion.
## How to Use Excel VLOOKUP with Multiple Criteria in Column and Row: 6 Ideal Examples
To explain the examples, we will use a dataset that contains information about the First Name, Last Name, Level, and Department of some employees. Some employees have the same First Name while others have the same Last Name. Depending on the First and Last Name, we will look for the value of the Level and Department. For example, if the First Name is Peter and the Last Name is William, then the Level should be 3 and Department should be Sales.
### 1. Insert Ampersand (&) Inside Excel VLOOKUP to Join with Multiple Criteria in Column and Row
To use the VLOOKUP function with multiple criteria in the column and row, we need to join the criteria first. For that purpose, we can use the Ampersand (&) operator. Also, we must need a Helper column. Let’s follow the steps below to see how you can use the Ampersand (&) operator inside the VLOOKUP function.
STEPS:
• First of all, we need to insert a Helper column on the leftmost side of the table or range like the picture below.
Note: The range B4:E11 was the main dataset. After adding a Helper column, the range B4:F11 becomes the new dataset.
• Secondly, select Cell B5 and type the formula below:
`=C5&D5`
Here, we have used the Ampersand (&) operator to concatenate the texts of Cell C5 and Cell D5.
• Thirdly, press Enter and drag the Fill Handle down to copy the formula till Cell B13.
• After that, select Cell I6 and type the formula below:
`=VLOOKUP(\$I\$4&\$I\$5,\$B\$5:\$F\$11,4,FALSE)`
• Hit Enter to see the result.
This VLOOKUP formula looks for the value PeterWilliam in the range B5:F11 and extracts the Level value.
🔎 How Does the Formula Work?
• In this formula, the first argument (\$I\$4&\$I\$5) denotes PeterWilliam which is the lookup value. We have used absolute cell reference to lock the cells.
• The second argument (\$B\$5:\$F\$11) is the lookup array where the formula will search for the lookup value.
• We want to extract the desired Level value that is situated in the fourth column of the range B4:F11. That is why we have typed 4 in the third argument.
• As we needed the exact match, we typed FALSE in the fourth argument.
• Similarly, to get the value of the Department, type the formula below in Cell I7:
`=VLOOKUP(\$I\$4&\$I\$5,\$B\$5:\$F\$11,5,FALSE)`
Here, we have changed the Column Index Number to 5 as Department is the fifth column of the range B4:F11.
• Finally, if you change the Last Name, then the Level and Department will automatically update.
### 2. Excel VLOOKUP with CHOOSE Function to Add Multiple Criteria in Column and Row
If you want to avoid the Helper column, then, this example will certainly help you. We can use the CHOOSE function with the VLOOKUP function to add multiple criteria in columns and rows. The CHOOSE function chooses a value or action to perform from a list of values based on an index number. Here, we can use the CHOOSE function to create a concatenated lookup array. We will discuss the formula in the steps below. So, let’s pay attention to the steps below.
STEPS:
• In the first place, select Cell H6 and type the formula below:
`=VLOOKUP(\$H\$4&\$H\$5,CHOOSE({1,2},\$B\$5:\$B\$11&\$C\$5:\$C\$11,\$D\$5:\$D\$11),2,FALSE)`
• Press Enter to see the Level of Peter William.
In this formula, we have used the CHOOSE function in the second argument of the VLOOKUP function. Here, the CHOOSE function forms a table with Columns B, C, and D. In that table, Columns B and C are merged and Column D is the second column. So, the VLOOKUP formula looks for the value of Cell H4 and Cell H5 inside the newly formed table and extracts the row from the second column of that table. That is how we get the Level value of Peter William.
• After that, type the formula below in Cell H7 to get the Department name:
`=VLOOKUP(\$H\$4&\$H\$5,CHOOSE({1,2},\$B\$5:\$B\$11&\$C\$5:\$C\$11,\$E\$5:\$E\$11),2,FALSE)`
• In the end, press Enter to see the Department of Peter William.
Here, we have used \$E\$5:\$E\$11 in place of \$D\$5:\$D\$11. So, the CHOOSE function forms a table with Columns B, C, and E this time.
### 3. Join Multiple Criteria in Column and Row by Merging VLOOKUP with IF Function
Another way to use the VLOOKUP function for multiple criteria is to use it with the IF function. Also, you don’t need to add any helper columns. If we have two criteria, we will insert the first criteria in the first argument of the VLOOKUP function and the second one inside the IF function. In this way, we can use the VLOOKUP with the IF function. Let’s follow the steps below to learn about the formulas.
STEPS:
• In the beginning, select Cell H6 and type the formula below:
`=VLOOKUP(H4,IF(C5:C11=H5,B5:E11,""),3,FALSE)`
• Press Enter to see the Level value.
In this formula, the VLOOKUP function looks for the value of Cell H4 if Column C is equal to the value of Cell H5. Then, extract the row from Column D of the range B5:E11. You can also use the absolute cell reference to lock the cells.
• In the following step, select Cell H7 and type the formula below:
`=VLOOKUP(H4,IF(C5:C11=H5,B5:E11,""),4,FALSE)`
• Finally, press Enter to see the Department name in Cell H7.
### 4. Apply Excel VLOOKUP with MATCH Function for Multiple Criteria in Column and Row
If you need to use a Helper column, then you can use the VLOOKUP with the MATCH function for multiple criteria in columns and rows. The MATCH function returns the relative position of an item in an array that matches a specified value. Here, we will use the MATCH function to get the Column Index Number inside the VLOOKUP function. Let’s follow the steps below to learn more about it.
STEPS:
• Firstly, we need to add a Helper column in Column B.
• Secondly, select Cell B5 and type the formula below:
`=C5&D5`
• Hit Enter and drag the Fill Handle down to copy the formula to Cell B11.
• After that, you will see results like the picture below.
• In the following step, select Cell I6 and type the formula below:
`=VLOOKUP(\$I\$4&\$I\$5,B5:F11,MATCH(E4,B4:F4,0),FALSE)`
• Press Enter to get the Level value.
In this formula, the MATCH function returns the column index number of Cell E4 which is 4. So, the VLOOKUP formula becomes:
`=VLOOKUP(\$I\$4&\$I\$5,B5:F11,4,FALSE)`
which is the same as the formula of Example 1.
• Also, to get the Department name, type the formula below in Cell I7:
`=VLOOKUP(\$I\$4&\$I\$5,B5:F11,MATCH(F4,B4:F4,0),FALSE)`
The difference between this formula and the previous one is the part of the MATCH function. Here, we have used the MATCH function to look for the column index number of Cell F4 in the range B4:F4. This returns 5. This formula is also similar to the last formula of Example 1.
### 5. Use Excel VLOOKUP Function with Multiple Criteria in Single Column
In this example, we will use the VLOOKUP function with multiple criteria in a single column in Excel. To do so, we will use the dataset below. We will extract the Level number of two employees based on their First Names.
STEPS:
• First of all, select Cell E13 and type the formula below:
`=VLOOKUP(C13:C14,B5:E11,3,FALSE)`
• Now, press Ctrl + Shift + Enter to see the Level number of Peter and Sophie.
Note: This formula has a drawback. The VLOOKUP function always extracts the first matched data, that is why we are getting the Level value of Peter Smith, not of Peter William.
### 6. Insert Drop-Down Lists as Multiple Criteria in VLOOKUP
In Excel, we can also insert drop-down lists as multiple criteria in the VLOOKUP function. The advantage of drop-down lists is that you won’t have to type the criteria manually each time. Rather, you can select the First Name and Last Name using the drop-down list and the formula will return the desired Level value and Department name. Let’s pay attention to the steps below to see how we can insert drop-down lists as multiple criteria.
STEPS:
• In the first place, select Cell H4.
• Secondly, go to the Data tab and click on the Data Validation option. A dialog box will appear.
• Select List in the Allow field.
• Then, enable editing in the Source box and select the range B5:B11.
• Click OK to proceed.
• As a result, you will see a drop-down list in Cell H4.
• Repeat the same steps to get a drop-down list in Cell H5.
• At this moment, select the First and Last Names using the drop-down lists.
• In the following step, select Cell H6 and type the formula below to get the Level value:
`=VLOOKUP(H4,IF(C5:C11=H5,B5:E11,""),3,FALSE)`
• Press Enter to see the result.
• Finally, type the formula below in Cell H7 to find the Department name:
`=VLOOKUP(H4,IF(C5:C11=H5,B5:E11,""),4,FALSE)`
• Hit Enter for the result.
Note: We have used this VLOOKUP with the IF function formula in Example 3. You can find the explanation there.
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Convert grams per (cubic inch) to micrograms per cup
g/in³ to µg/US cup (µg/c) (g:gram, in:inch, µg:microgram, c:cup)
grams per cubic inch to micrograms per cup conversion cards
• 1
through
20
grams per cubic inch
• 1 g/in³ to µg/c = 14 437 500 µg/c
• 2 g/in³ to µg/c = 28 875 000 µg/c
• 3 g/in³ to µg/c = 43 312 500 µg/c
• 4 g/in³ to µg/c = 57 750 000 µg/c
• 5 g/in³ to µg/c = 72 187 500 µg/c
• 6 g/in³ to µg/c = 86 625 000 µg/c
• 7 g/in³ to µg/c = 101 062 500 µg/c
• 8 g/in³ to µg/c = 115 500 000 µg/c
• 9 g/in³ to µg/c = 129 937 500 µg/c
• 10 g/in³ to µg/c = 144 375 000 µg/c
• 11 g/in³ to µg/c = 158 812 500 µg/c
• 12 g/in³ to µg/c = 173 250 000 µg/c
• 13 g/in³ to µg/c = 187 687 500 µg/c
• 14 g/in³ to µg/c = 202 125 000 µg/c
• 15 g/in³ to µg/c = 216 562 500 µg/c
• 16 g/in³ to µg/c = 231 000 000 µg/c
• 17 g/in³ to µg/c = 245 437 500 µg/c
• 18 g/in³ to µg/c = 259 875 000 µg/c
• 19 g/in³ to µg/c = 274 312 500 µg/c
• 20 g/in³ to µg/c = 288 750 000 µg/c
• 21
through
40
grams per cubic inch
• 21 g/in³ to µg/c = 303 187 500 µg/c
• 22 g/in³ to µg/c = 317 625 000 µg/c
• 23 g/in³ to µg/c = 332 062 500 µg/c
• 24 g/in³ to µg/c = 346 500 000 µg/c
• 25 g/in³ to µg/c = 360 937 500 µg/c
• 26 g/in³ to µg/c = 375 375 000 µg/c
• 27 g/in³ to µg/c = 389 812 500 µg/c
• 28 g/in³ to µg/c = 404 250 000 µg/c
• 29 g/in³ to µg/c = 418 687 500 µg/c
• 30 g/in³ to µg/c = 433 125 000 µg/c
• 31 g/in³ to µg/c = 447 562 500 µg/c
• 32 g/in³ to µg/c = 462 000 000 µg/c
• 33 g/in³ to µg/c = 476 437 500 µg/c
• 34 g/in³ to µg/c = 490 875 000 µg/c
• 35 g/in³ to µg/c = 505 312 500 µg/c
• 36 g/in³ to µg/c = 519 750 000 µg/c
• 37 g/in³ to µg/c = 534 187 500 µg/c
• 38 g/in³ to µg/c = 548 625 000 µg/c
• 39 g/in³ to µg/c = 563 062 500 µg/c
• 40 g/in³ to µg/c = 577 500 000 µg/c
• 41
through
60
grams per cubic inch
• 41 g/in³ to µg/c = 591 937 500 µg/c
• 42 g/in³ to µg/c = 606 375 000 µg/c
• 43 g/in³ to µg/c = 620 812 500 µg/c
• 44 g/in³ to µg/c = 635 250 000 µg/c
• 45 g/in³ to µg/c = 649 687 500 µg/c
• 46 g/in³ to µg/c = 664 125 000 µg/c
• 47 g/in³ to µg/c = 678 562 500 µg/c
• 48 g/in³ to µg/c = 693 000 000 µg/c
• 49 g/in³ to µg/c = 707 437 500 µg/c
• 50 g/in³ to µg/c = 721 875 000 µg/c
• 51 g/in³ to µg/c = 736 312 500 µg/c
• 52 g/in³ to µg/c = 750 750 000 µg/c
• 53 g/in³ to µg/c = 765 187 500 µg/c
• 54 g/in³ to µg/c = 779 625 000 µg/c
• 55 g/in³ to µg/c = 794 062 500 µg/c
• 56 g/in³ to µg/c = 808 500 000 µg/c
• 57 g/in³ to µg/c = 822 937 500 µg/c
• 58 g/in³ to µg/c = 837 375 000 µg/c
• 59 g/in³ to µg/c = 851 812 500 µg/c
• 60 g/in³ to µg/c = 866 250 000 µg/c
• 61
through
80
grams per cubic inch
• 61 g/in³ to µg/c = 880 687 500 µg/c
• 62 g/in³ to µg/c = 895 125 000 µg/c
• 63 g/in³ to µg/c = 909 562 500 µg/c
• 64 g/in³ to µg/c = 924 000 000 µg/c
• 65 g/in³ to µg/c = 938 437 500 µg/c
• 66 g/in³ to µg/c = 952 875 000 µg/c
• 67 g/in³ to µg/c = 967 312 500 µg/c
• 68 g/in³ to µg/c = 981 750 000 µg/c
• 69 g/in³ to µg/c = 996 187 500 µg/c
• 70 g/in³ to µg/c = 1 010 625 000 µg/c
• 71 g/in³ to µg/c = 1 025 062 500 µg/c
• 72 g/in³ to µg/c = 1 039 500 000 µg/c
• 73 g/in³ to µg/c = 1 053 937 500 µg/c
• 74 g/in³ to µg/c = 1 068 375 000 µg/c
• 75 g/in³ to µg/c = 1 082 812 500 µg/c
• 76 g/in³ to µg/c = 1 097 250 000 µg/c
• 77 g/in³ to µg/c = 1 111 687 500 µg/c
• 78 g/in³ to µg/c = 1 126 125 000 µg/c
• 79 g/in³ to µg/c = 1 140 562 500 µg/c
• 80 g/in³ to µg/c = 1 155 000 000 µg/c
• 81
through
100
grams per cubic inch
• 81 g/in³ to µg/c = 1 169 437 500 µg/c
• 82 g/in³ to µg/c = 1 183 875 000 µg/c
• 83 g/in³ to µg/c = 1 198 312 500 µg/c
• 84 g/in³ to µg/c = 1 212 750 000 µg/c
• 85 g/in³ to µg/c = 1 227 187 500 µg/c
• 86 g/in³ to µg/c = 1 241 625 000 µg/c
• 87 g/in³ to µg/c = 1 256 062 500 µg/c
• 88 g/in³ to µg/c = 1 270 500 000 µg/c
• 89 g/in³ to µg/c = 1 284 937 500 µg/c
• 90 g/in³ to µg/c = 1 299 375 000 µg/c
• 91 g/in³ to µg/c = 1 313 812 500 µg/c
• 92 g/in³ to µg/c = 1 328 250 000 µg/c
• 93 g/in³ to µg/c = 1 342 687 500 µg/c
• 94 g/in³ to µg/c = 1 357 125 000 µg/c
• 95 g/in³ to µg/c = 1 371 562 500 µg/c
• 96 g/in³ to µg/c = 1 386 000 000 µg/c
• 97 g/in³ to µg/c = 1 400 437 500 µg/c
• 98 g/in³ to µg/c = 1 414 875 000 µg/c
• 99 g/in³ to µg/c = 1 429 312 500 µg/c
• 100 g/in³ to µg/c = 1 443 750 000 µg/c
• µg/c stands for µg/US c
• microgram per cup stands for microgram per US cup
• micrograms per cup stands for micrograms per US cup
Foods, Nutrients and Calories
ASADERO CHEESE, UPC: 216114804766 contain(s) 321 calories per 100 grams or ≈3.527 ounces [ price ]
GARDEIN, THE ULTIMATE BEEFLESS SLIDER, UPC: 842234001176 contain(s) 183 calories per 100 grams or ≈3.527 ounces [ price ]
Gravels, Substances and Oils
CaribSea, Freshwater, Flora Max, Original weighs 1 089.26 kg/m³ (68.00028 lb/ft³) with specific gravity of 1.08926 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Snow, compacted weighs 481 kg/m³ (30.02785 lb/ft³) [ weight to volume | volume to weight | price | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-502, liquid (R502) with temperature in the range of -51.12°C (-60.016°F) to 60°C (140°F)
Weights and Measurements
The troy pound per metric teaspoon density measurement unit is used to measure volume in metric teaspoons in order to estimate weight or mass in troy pounds
Torque can be defined as a turning or twisting action of the force F upon an object.
mg/dm³ to short tn/cm³ conversion table, mg/dm³ to short tn/cm³ unit converter or convert between all units of density measurement.
Calculators
Calculate volume of a spherical segment and its surface area
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CC-MAIN-2020-05
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https://www.entrepreneur.com/article/396697
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An Expert Shares the Truth Behind Bitcoin's All-Time Highs
Understanding the market cap of bitcoin and the TAM of the world's wealth reveals that bitcoin currently holds 0.504 per cent of worldwide wealth
By
Opinions expressed by Entrepreneur contributors are their own.
You're reading Entrepreneur India, an international franchise of Entrepreneur Media.
The CEO and founder of Out Of This World Investments holds extensive information surrounding bitcoin and more information will be released on a regular basis on his website. Having vast knowledge about the bitcoin market, he says that it’s understandable to feel that the price of Bitcoin at the moment is incredibly high due to the fact that throughout 2021, the price of BTC has been hitting ATH (all-time highs). Seeing a high number can easily give the impression that something is too expensive to buy. However, breaking an asset down into its smaller denominations may help to highlight its true cost. For example, although petrol costs £4,200, if you base the price on a full 3000-litre lorry load, looking at the price in terms of litres helps give a realistic assessment of cost.
Another example is the price of gold. Of course, £42,000 for a kilo can easily be considered a lot of money, but breaking it down into smaller denominations is how most people would use it. For instance, a kilo can be broken down into 1,000 grams; therefore, the price of 1 gram of gold seems significantly more affordable (£42). It’s even possible to break it down into 1,000,000 milligrams meaning the price would be £0.042.
Likewise, with both gold and fuel, 1 whole bitcoin can be broken down into smaller amounts. The smaller denominations are called Millibits (mBTC), Microbits (uBTC) and Satoshi’s (Sats). Thus, it is possible to buy 0.1 bitcoin, 0.000001 bitcoin or even 0.00000001 bitcoin.
Another aspect that is involved in this discussion regarding the price of bitcoin is how one tries to understand it. Firstly, it’s important to note that there will only ever be 21,000,000 bitcoin due to the way it was designed. To discover its market cap (total value of the bitcoin market), we multiply it by the current price of 1 bitcoin (\$60,000 x 21,000,00 = 1,260,000,000,000).
The next step is to evaluate what Bitcoin is designed to be. There have been many discussions based on this, but money is probably the most applicable to keep it simple. With this information, calculating what the TAM (Total Addressable Market) is will further help with understanding what the price of bitcoin is by understanding how much wealth there is in the world. Based on several sources, it is stated that the TAM of the world is roughly \$250 trillion which increases each day.
Therefore, understanding the market cap of bitcoin and the TAM of the world’s wealth, reveals that bitcoin currently holds 0.504 per cent of worldwide wealth. As this continues to increase, the growth of this new asset will continue also. For example, if the percentage doubled to 1.008 per cent then the price of a single bitcoin would be \$120,000. Ultimately though, it’s important to highlight that bitcoin has the potential to grow in a similar pattern as other technological inventions - and if it does, the price of it is incredibly low and affordable compared to what it will be in 5 to 10 years.
Another thing to point out here is that we tend to measure Bitcoin prices against currencies that are not fixed in supply. Each year, more dollars, pounds, and euros are created, but the amount of Bitcoin does not go up. This means that the price of bitcoin in dollar, pound, or euro terms can go up simply because it’s a deflationary currency being measured by inflationary ones.
The founder became so interested in Bitcoin primarily down to the fact that when he created a successful company, he had a huge cash balance to utilize. He started to look for ways to protect the purchasing power (Purchasing power is basically how much of something a currency can buy).
We all know that the price of our favorite chocolate bar or fuel is always increasing, for example, but this is not the “price going up” as such. It’s more about the currency we are buying the product with is losing its value because it’s inflated. In Bitcoin terms, the product has gotten cheaper year after year. Bitcoin has protected purchasing power since it was created in 2008. This is what it was designed to do. It’s programmed to do this at its very core and many people argue its inception was a reaction to the 2008 financial crisis which incompetent leaders caused.
To learn more about his story, Bitcoin, and some of the best startups trying to tackle the world's biggest problems using technology, visit his website, Out of This World Investments.
Note: Investment in cryptocurrency is subject to risk and readers should do their own due diligence. Entrepreneur Media does not endorse any such investment.
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| 2.6875
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https://aids.academickids.com/encyclopedia/index.php/Norton%27s_theorem
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Norton's theorem
Missing imageThevenin_and_norton_step_1.png The original circuit Missing imageNorton_step_2.png Calculating the equivalent output current Missing imageThevenin_and_norton_step_3.png Calculating the equivalent resistance Missing imageNorton_step_4.png The equivalent circuit
Norton's theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source I in parallel with a single resistor R. The theorem can also be applied to general impedances, not just resistors.
The theorem was published in 1926 by Bell Labs engineer Edward Lawry Norton (1898-1983).
To calculate the equivalent circuit:
1. Replace the load circuit with a short.
2. Calculate the current through that short, I, from the original sources.
3. Now replace voltage sources with shorts and current sources with open circuits.
4. Replace the load circuit with an imaginary ohm meter and measure the total resistance, R, with the sources removed.
5. The equivalent circuit is a current source with current I in parallel with a resistance R in parallel with the load.
In the example, the total current Itotal is given by:
[itex]
I_\mathrm{total} = {15 \mathrm{V} \over 2\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)} = 5.625 \mathrm{mA} [itex]
The current through the load is then:
[itex]
I = {1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \over (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)} \cdot I_\mathrm{total} [itex]
[itex]
= 2/3 \cdot 5.625 \mathrm{mA} = 3.75 \mathrm{mA} [itex]
And the equivalent resistance looking back into the circuit is:
[itex]
R = 1\,\mathrm{k}\Omega + 2\,\mathrm{k}\Omega \| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega) = 2\,\mathrm{k}\Omega [itex]
So the equivalent circuit is a 3.75 mA current source in parallel with a 2 kΩ resistor.
• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy
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https://reproducibility.org/RSF/book/rsf/tutorials/wedge.html
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```from rsf.proj import * y1=0.18 y2=0.30 x1=25 x2=150 a=(y1-y2)/(x1-x2) b=(y2*x1-y1*x2)/(x1-x2) Flow('layer1',None,'spike n1=500 d1=1 mag=0.18 label1=Trace unit1=') Flow('layer2','layer1','math output="%g*x1+%g" | clip2 lower=0.18 upper=0.3' % (a,b)) Flow('layers','layer1 layer2','cat axis=2 \${SOURCES[1]}') Result('layers','graph max2=0.6 min2=0 yreverse=y label2=Time unit2=s title=Layers') Flow('grid','layers','unif2 v00=1,2,3 n1=601 d1=0.001 label1=Time unit1=s') Result('grid','grey color=J mean=y wanttitle=n') vp=(3300,3200,3300) rho=(2600,2550,2650) ai = [str(vp[k]*rho[k]/1.0e6) for k in range(3)] Flow('ai','layers','unif2 v00=%s n1=601 d1=0.001 label1=Time unit1=s' % ','.join(ai)) Result('ai','grey color=lb mean=y title="Acoustic Impedance" barlabel=AI scalebar=y') Plot('sand1',None,'box x0=7.5 y0=7.5 label="shale 1" xt=0 yt=0') Plot('shale',None,'box x0=7.5 y0=5.9 label="sand" xt=0 yt=0') Plot('sand2',None,'box x0=7.5 y0=4.3 label="shale 2" xt=0 yt=0') for freq in (5,10,15): seismic = 'seismic%d' % freq Flow(seismic,'ai','ai2refl | ricker1 frequency=%d' % freq) Plot(seismic,'grey color=lb title="%d Hz wavelet" ' % freq) Result(seismic,seismic+' sand1 shale sand2','Overlay') End()```
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https://blog.csdn.net/qq_32817311/article/details/49928693
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# POJ 3702 距离排序
….(n-1,n)
#include<iostream>
#include<iomanip>
#include<math.h>
#include<algorithm>
using namespace std;
#define maxp 12
struct points{
int x,y,z;
};
typedef struct{
points p1,p2;
double val;
}Dis_t;
bool operator <(Dis_t a, Dis_t b){
return a.val < b.val;
}
ostream & operator<<(ostream &output,Dis_t src){
//(0,0,0)-(1,1,1)=1.73
cout<<"("<<src.p1.x<<","<<src.p1.y<<","<<src.p1.z<<")-(";
cout<<src.p2.x<<","<<src.p2.y<<","<<src.p2.z<<")=";
cout<<fixed<<setprecision(2)<<src.val;
}
points point[maxp]={0};
Dis_t dis[maxp*maxp]={0};
int n;
int discount = 0;
double calcu(int i,int j){
double dis0;
double dx = point[i].x - point[j].x;
double dy = point[i].y - point[j].y;
double dz = point[i].z - point[j].z;
dis0 = sqrt(dx*dx+dy*dy+dz*dz);
//cout<<dis0<<endl;
return dis0;
}
int main(){
cin>>n;
for(int i=0;i<n;++i){
cin>>point[i].x>>point[i].y>>point[i].z;
}
for(int i=0;i<n-1;++i){
for(int j=i+1;j<n;++j){
Dis_t tmp;
tmp.p1 = point[i];
tmp.p2 = point[j];
tmp.val = calcu(i,j);
dis[discount++] = tmp;
}
}
//sort(dis,dis+discount);
for(int i=0;i<discount-1;++i){
for(int j =0;j<discount-i-1;++j){
if(dis[j]<dis[j+1]){
Dis_t t = dis[j];
dis[j] = dis[j+1];
dis[j+1] = t;
}
}
}
for(int i=0;i<discount;++i){
cout<<dis[i]<<endl;
}
//system("pause");
return 0;
}
#### POJ 3214 Object Clustering 哈夫曼距离最小生成树
2016-08-13 16:54:38
#### poj1328 Radar Installation 贪心 （手动翻译）
2016-01-25 11:03:44
#### openjudge 距离排序
2014-03-26 17:44:31
#### Microsoft SQL Server，错误: 3702
2017-03-18 15:50:51
#### 无法删除数据库::提示:错误3702!无法除去数据库"test",因为它正在使用!!!
2007-01-04 19:48:00
#### POJ 上几个关于排列的题目
2015-05-10 20:00:25
#### POJ2388-排序水题
2016-09-08 11:19:30
#### POJ - 3241 Object Clustering 哈夫曼距离最小生成树
2017-06-13 18:06:57
#### cxf之HelloWorld版本实例
2014-01-28 21:39:22
#### DNA排序 代码
2013年11月28日 1KB 下载
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https://domyhomework123.com/parabola-calculator
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Get better grades,
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Forget about deadlines, with top 2% experts across the board. Your high school and college homework assignments are not your problem anymore.
# Parabola Equation Calculator For You To Use
What is a parabola? It is a U-shaped symmetrical curve with every point lying on it being equidistant from both a certain point.
Therefore, we can use a parabola calculator to calculate the path made by an object in projectile motion.
The parabola equation calculator displays the graph of the parabola after entering the required values. Our parabola generator makes the calculation faster and displays the parabola graph in a fraction of seconds.
It can serve as the following:
• Latus rectum calculator
• Focus and directrix calculator
• Parabola standard form calculator
• Focal parameter calculator
• Axis of symmetry and eccentricity calculator.
The parabola equation finder will help you solve your engineering algebraic problems and academic equations easily.
## How To Find the Equation of a Parabola
Use the formula to find the equation of a parabola calculator in vertex form:
Now, the standard form of a quadratic equation is y = ax² + bx + c
Therefore, the equation of a parabola calculator in its vertex form is y = a(x-h)² + k, where:
• a is similar to the a coefficient in the standard form;
• h is the parabola vertex x-coordinate
• k is the parabola vertex y-coordinate
To find the values of h and k, use the equations below:
h = - b/ (2a)
k = c - b²/ (4a)
On the other hand, the formula of the parabola standard form calculator is:
y = (x2 / (4a)) - (hx / 2a) + (k + (h2 / (4a)))
Where,
h = is the x-coordinate of parabola Vertex
k = is the y-coordinate of parabola Vertex
x = is the x-coordinate of parabola Focus
y = is the y-coordinate of parabola Focus
Here is an example:
#1: Find the directrix of the parabola. (using either the parabola calculator or the equation)
y = c - (b² + 1)/ (4a) = -4 - (9+1)/8 = -5.25
#2: Calculate the coordinates of the vertex, where a = 2, b = 3 and c = -4.
h = - b/ (2a) = -3/4 = -0.75
k = c - b²/ (4a) = -4 - 9/8 = -5.125
### Steps To Using the Parabola Equation Solver
The procedure is as simple as shown below:
1. Enter the necessary data in the input field
2. Hit the button “Submit”
3. The parabola graph will finally be displayed in the new window
You do not need any rocket science knowledge to use this parabola solver effectively. Provided you are armed with the formula; you can easily use the parabola equation calculator from points. On top of that, the parabola generator has a user-friendly site that can be used by amateurs and pros.
### Where Can I Get Homework Help With My Math Assignment?
We have the best math homework experts who can help students crack any mathematical problem online. Our rates are cheap and affordable for students of all levels.
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| 4.53125
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CC-MAIN-2023-06
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longest
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https://layton.fandom.com/wiki/Puzzle:Many_to_Cross...
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|
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2,511
pages
← 103 - Cogs & Pulleys 104 - Many to Cross... 105 - Bouquet Giveaway →
Many to Cross... (Bridgathon in the UK version) is a puzzle in Professor Layton and the Last Specter.
## Puzzle
US Version
A wanted to return a book to her friend B, but she couldn't remember where B lives. After walking around and crossing every bridge just once, she finally arrived at her friend's house.
Circle the number of B's house then touch Submit.
UK Version
A wanted to return a book to her friend B, but she couldn't remember where B lives. After walking around for a while and crossing every bridge just once, she finally determined which was her friend's house.
Circle the number of B's house.
## Hints
Click a Tab to reveal the Hint.
There seem to be many routes that A could take to get to B's house. Let's consider a single route.
First she started by walking past house number 4 and then number 3. At that point, she still had no idea how long her route would end up being.
US Version
After numbers 4 and 3, she would then visit 2, 1, 5, and 2 again. However, she still had not found her friend's house.
UK Version
After passing number 4 and number 3, she continued on to 2, 1, 5 and then 2 again.
Unfortunately, she still hadn't found her friend's house.
US Version
After arriving at number 2 the second time, she visited 6, 3, A, 6, 8, 7, 8, and then 7.
Even so, she could still not be sure which was the correct house. Had she overlooked something?
UK Version
Still determined after arriving at number 2 for the second time, she kept walking and went on to 6, 3, A, 6, 8, 9, 9 and then 7.
After all this, she still could not be sure which was the correct house. Had she overlooked something?
US Version
She had to cross every bridge to be sure. After arriving at number 7, she went to 8, 6, and 5 again. After crossing the last remaining bridge, she finally got to B's house. What a walk!
UK Version
You know that she had to cross every bridge before she was sure she'd found her friend's house.
From number 7 she went back to 8, 6 and then 5.
She then crossed the last remaining bridge and, with relief, realised that it was B's house without a doubt!
## Solution
### Incorrect
US Version
Try walking through the puzzle again.
UK Version
Try walking through the puzzle again.
### Correct
Correct!
US Version
If she walks over every bridge once, she will finally arrive at house number 7. Did you realize that whichever path she takes, she will arrive at number 7?
UK Version
B lives at house number 7!
After crossing every bridge once, she was finally certain that she had found her friend's house.
Did you realise she could have taken any route and still ended up at the same house?
A big thanks to http://professorlayton4walkthrough.blogspot.com
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| 3.515625
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https://sandbox.momath.org/home/momath-educator-sessions-cryptography/
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crawl-data/CC-MAIN-2020-05/segments/1579250591763.20/warc/CC-MAIN-20200118023429-20200118051429-00450.warc.gz
| 662,012,472
| 7,164
|
MoMath Educator Sessions: Cryptography (Grades 4 through 12)
By hiding messages in shapes, gibberish, and number codes, cryptography has allowed people, from the time of the ancient Greeks through today, to safely transmit secrets. Court intrigue, star-crossed love, and war have all benefited immensely from this method of communication. These days, cryptographers have traded the cipher disk for the computer screen, but cryptography still influences our life in covert ways. By harnessing statistics, abstract algebra, and other branches of mathematics, cryptography lets us breathe easier when we go to an ATM, create a password for our computer, or send money electronically.
The Secrets of Telling Secrets (Grades 4 through 12)
Students are introduced to the substitution cipher, which hides messages by replacing letters or groups of letters with other letters or groups of letters. Working with their classmates, students practice making and breaking different ciphers.
Keeping Secrets in Public (Grades 11 and 12)
Students are introduced to public key cryptography, which allows the public to encrypt but not decrypt, and only gives select individuals the decryption key. This type of cryptography solves the problem of passing along the key easily and securely. Using arithmetic and network graphs, students will explore this complex and fun type of secret-keeping!
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# Branch and Cut for TSP
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1 Branch and Cut for TSP Informatics and Mathematical Modelling Technical University of Denmark 1
2 Branch-and-Cut for TSP Branch-and-Cut is a general technique applicable e.g. to solve symmetric TSP problem. TSP is N P-hard no one believes that there exists a polynomial algorithm for the problem. TSP can be formulated as an integer programming problem for an n-vertex graph the number of binary variables becomes n(n 1) 2, and the problem has an exponential number of subtour elimination constraints. 2
3 The symmetric TSP min e E d ex e s.t. x(δ(v)) = 2, v {1,..., n} x(δ(s)) 2, S V x e {0, 1}, e E 3
4 The number of subtour elimination constraints is huge (2 V ) and even though we can remove half of those due to symmetry there are still exponentially many. therefore, in the relaxed version we remove the integrality constraints and the exponentially many subtour elimination constraints. 4
5 Challenges For the cutting plane approach to work we need to 1. be able to check whether any subtour elimination constraints are violated (efficiently) and 2. we must be able to solve the LP relaxation efficiently. 5
6 Problem 2 Start by solving a smaller variant of the original problem. Let E E and solve: min e E d e x e s.t. x(δ(v)) = 2, v {1,..., n} x(δ(s)) 2, S V 0 x e 1, e E An optimal solution x for this problem can be extended to a feasible solution for the original problem by x e = x e, e E and x e = 0, e E \ E. 6
7 BUT this solution might not be optimal in the original relaxed problem. Idea: Look at the dual problem. 7
8 Dual of the STSP max v V 2y v + S V 2Y S s.t. y u + y v + (u,v) δ(s) Y S d uv, (u, v) E Y S 0, S V If (y, Y ) is also feasible for the dual linear programming problem of the original problem then we know that x is optimal Otherwise add variables to E that violated the constraint of the dual linear programming problem and resolve. 8
9 Problem 1 Here we use branch-and-cut. Start of by removing the subtour elimination constraints. Then we get: min e E d ex e s.t. x(δ(v)) = 2, v {1,..., n} 0 x e 1, e E Let x be a feasible solution to the initial linear programming problem. 9
10 If the solution falls apart into several components then the node set S of each component violates a subtour elimination constraint. This situation is very easy to detect. We might end in a situation where the graph is not disconnected but there are actually subtour elimination constraints that are violated. How do we detect those? 10
11 The separation algorithm Use max-flow to find cuts that are violated in the present situation. Here we have two problems: Max-flow works on directed graphs this is a non-directed graph. We need a sink and a source to run the max-flow algorithm. 11
12 Now we are in a good position. We are now able to detect all possible subtour elimination constraints, but is that enough to solve the problem? 12
13 Consider the following part of a graph (dash is a flow of 0.5). 13
14 Comb inequalities Let C be a comb with a handle H and teeth T 1, T 2,..., T 2k+1 for k 1. Then the solution x for a feasible solution must satisfy: x(e(h))+ 2k+1 i=1 x(e(t i )) H + ( T i 1) (k +1) 2k+1 i=1 14
15 These cuts are generally still not enough but there are more cuts we could add: Grötschel and Padberg (1985) Jünger, Reinelt and Rinaldi (1995) Naddef (1990) Even these are not enough. There is today no full description of the convex hull for the TSP. Furthermore for some of the valid inequalities the exists no efficient (polynomial) separation algorithm. 15
16 THEREFORE branch after having added all the simple valid inequalities. Example: Upper bound: (simple heuristic) Lower bound: (LP-relaxation, subtour and simple comb-ineq) Gap: 0.2%!! 16
17 16 cities = = 120 variables. Let us keep the constraint that j x ij = 2, i = 1,..., N. Relax integrality constraints on variables to 0 x ij 1 17
18 Objective value: 920 Forbid the subtour Skagen- Thisted-Aalborg and resolve 18
19 Objective value: 960 Forbid the subtour Fredericia-Kolding-Vejle and resolve 19
20 Objective value: 982 Forbid the subtour Kolding- Fredericia-Vejle-Esbjerg- Aabenraa-Tønder-Ribe and resolve 20
21 Objective value: Identify a comb inequality: Handle being Thisted, Ringkøbing and Herning; teeth being (Thisted, Skagen), (Ringkøbing, Esbjerg) and (Herning, Vejle). 21
22 Objective value: Identify a comb inequality: Handle being Vejle, Silkeborg and Aarhus; teeth being (Vejle, Fredericia), (Silkeborg, Viborg) and (Aarhus, Randers). 22
23 Objective value: Identify a comb inequality: Handle being Viborg, Randers and Aalborg; teeth being (Viborg, Silkeborg), (Randers, Aarhus) and (Aalborg, Skagen). 23
24 Objective value: 996 Integer solution!!! 24
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| 8,035
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This is an oxidation-reduction (redox) reaction:
2 Br-I - 2 e- → 2 Br0 (oxidation)
CuII + 2 e- → Cu0 (reduction)
CuBr2 is a reducing agent, CuBr2 is an oxidizing agent.
### Word equation
cupric bromide → copper + bromine
### Input interpretation
CuBr2 → Cu + Br2
cupric bromide copper bromine
### Balanced equation
Balance the chemical equation algebraically:
CuBr2 → Cu + Br2
Add stoichiometric coefficients, c, to the reactants and products:
c1 CuBr2 → c2Cu + c3Br2
Set the number of atoms in the reactants equal to the number of atoms in the products for Br and Cu:
Br: 2c1 = 2c3
Cu: c1=c2
Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c1 = 1 and solve the system of equations for the remaining coefficients:
c1 = 1 c2=1
c3 = 1
Substitute the coefficients into the chemical reaction to obtain the balanced
equation:
| 271
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|
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longest
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https://tiphero.info/find-the-tiny-heart-hidden/
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# People Are Struggling to Find the Tiny Heart Hidden Among the Elephants
Gergely Dudas - Dudolf
If you’re ready for a brain break, we’re here for you. A hidden picture puzzle is a great way to rest your brain from whatever else it has been focusing on, like work, school or an endless to-do list. Giving yourself something else to focus on for a brief period of time can help you feel refreshed when you get back to whatever it is you were doing.
This particular brain break takes the form of a hidden picture puzzle, and it was created by artist Gergely Dudás, also known as the Dulof. Dudás has created many fun and challenging hidden picture puzzles that we enjoy solving (like this one and this one), and this new puzzle is no exception.
In this particular puzzle, at first glance, we see a lot of elephants in a variety of colors. We also see little yellow butterflies. The picture is entertaining even without looking for a hidden picture within the picture. We can’t help but look at the elephant in the top hat and the elephants that are wearing flowers.
It’s okay to get familiar with the picture before diving in and actually trying to solve the challenge, but be aware that simply looking at the picture and enjoying the nuances most likely won’t help you find the tiny hidden heart.
The hidden heart really is tiny, like, teeny tiny, and it requires paying close attention to detail to solve this puzzle. We suggest starting in one corner of the puzzle and carefully looking at every detail as you slowly move your eyes across the puzzle. The heart really is there, and you can find it if you take your time.
Here’s the puzzle. See how long it takes you to find the tiny hidden heart.
Did you find it? If not, and if you’re starting to need a brain break from solving this puzzle, you’ll be happy to know that there is an answer key; however, please don’t look at the answer until you’re really sure that you are done trying to solve it on your own.
Were you able to find the tiny hidden heart without looking at the answer key? Do you like solving hidden picture puzzles? Did you think this hidden picture puzzle was difficult or easy?
| 459
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# Toronto Math Forum
## MAT244--2019F => MAT244--Test & Quizzes => Quiz-2 => Topic started by: Junhong Zhou on October 04, 2019, 02:00:07 PM
Title: TUT0402 quiz2
Post by: Junhong Zhou on October 04, 2019, 02:00:07 PM
Question: Find an integrating factor and solve the given equation.
$$(3x^2y+2xy+y^3)+(x^2+y^2)y'=0$$
\begin{align}
M(x,y)=3x^2y+2xy+y^3 &\implies M_y=3x^2+2x+3y^2\notag\\
N(x,y)=x^2+y^2 &\implies N_x=2x\notag
\end{align}
Since $M_y \neq N_x$, this implies the given differential equation is not exact, so we need to find $\mu(x,y)$ such that the equation $\mu(3x^2+2xy+y^3)+\mu(x^2+y^2)y'=0$ is exact.
$$R(x)=\frac{M_y-N_x}{N}=\frac{3x^2+3y^2}{x^2+y^2}=3$$
then we can write $\mu$:
$$\mu(x,y)=e^{\int R(x)dx}=e^{\int 3 dx}=e^{3x}$$
multiply the given differential equation by $\mu$:
\begin{align}
\mu(3x^2y+2xy+y^3)+\mu(x^2+y^2)y' &= 0\notag\\
e^{3x}(3x^2y+2xy+y^3)+e^{3x}(x^2+y^2)y' &= 0\notag
\end{align}
Which is now an exact differential equation, this implies there exist $\varphi(x,y)$ such that $\varphi_x=M$ and $\varphi_y=N$.
\begin{align}
\varphi_y(x,y)=e^{3x}(x^2+y^2) &\implies \varphi(x,y)
=\int e^{3x}(x^2+y^2)dy\notag\\
&\implies \varphi(x,y)
= e^{3x}x^2y+\frac{1}{3}e^{3x}y^3+f(x)\notag
\end{align}
$$\varphi_x(x,y)=2e^{3x}xy+3e^{3x}x^2y+e^{3x}y^3+f'(x) \implies f'(x)=0 \implies f(x)=C\notag$$
Therefore:
$$\varphi(x,y)=e^{3x}x^2y+\frac{1}{3}e^{3x}y^3=C$$
$$e^{3x}x^2y+\frac{1}{3}e^{3x}y^3=C$$
| 675
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|
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Mr.Bool Editor - MrBool Space
Today we get to 1000 videos posted on the MrBool website. Among them you can find videos about Java, .NET, Front-End Development, Databases, and others. All material with high quality and renowned authors in TI world.
This number is growing continuously. We are publishing several posts on a daily basis for you!
Good studies.
MrBool Team.
-->">
2/20/2013 3:51:00 PM
Without a doubt, expressions are the main building blocks of a program. This is because there are so many different kinds of expressions that a majority of the source-code lines in a program end up being-you guessed it-expressions. There are expressions that result in numerical values. There are expressions that result in strings. There are simple expressions, complex expressions, and all manner of expressions in between.
In this post you'll learn not only more about those types of expressions, but also about logical expressions, which help a computer seem to be able to think and make choices. Along the way, you'll discover comparison and logical operators, which make logical expressions possible.
Types of Expressions
To put it simply, an expression is a line of code that can be reduced to a value or that assigns a value. For example, you know that the addition operator adds one expression to another, like this:
sum = expr1 + expr2;
In the preceding line, expr1 can be something as simple as the variable x or as complex as (4 + 5) * 2 * 5 / 7 + x / y. The same goes for expr2, of course. And, in fact, the first example containing expr1 and expr2 is an expression itself!
But no matter how complicated, all expressions can be classified into one of three main categories:
• Numerical expressions combine numbers, variables, or constants using mathematical operators. An nexample is 2 + 3 / x.
• Assignment expressions assign a value to a variable. An example is num = 3.
• Logical expressions are unique in that they result in a value of true or false. An example is x
Expressions Within Expressions
Look at the following assignment expression:
num = (5 - x) * (2 + y);
This is an assignment expression because it assigns a value to the variable num. However, the stuff on either side of the equals sign contains these other expressions:
num
(5 - x) * (2 + y)
Both of the above lines are numerical expressions because they can be reduced to a numerical value (assuming that you know the values of num, x, and y.
But, wait a second-you're not done yet. You can still find more sub-expressions. Look at the multiplication operation. Can you see that it's multiplying two expressions together? Those two expressions look like this:
(5 - x)
(2 + y)
And the above simplified expressions contain yet more sub-expressions. Those expressions are:
5
x
2
y
Expressions are what programmers like to call recursive, meaning that the definition of an expression keeps coming back on itself. An expression contains expressions that contain other expressions, which themselves contain other expressions. How deep you can dig depends on the complexity of the original expression. But, as you saw demonstrated, even the relatively simple expression
num = (5 - x) *
(2 + y) has four levels of depth.
Comparison Operators
Now that you've dug into the secrets of expressions, it's time to learn about a new type of operator. So far, you've gotten some practice with mathematical operators, which enable you to build various types of numerical and assignment expressions. Another type of operator you can use to build expressions is the comparison operator. Comparison operators are used to create logical expressions, which, if you recall, result in a value of true or false. Table 1 lists the logical expressions used in Java programming. C and C++ programmers will find these operators very familiar.
Table 1 Java's Logical Operators.
Operators - Description
== - Equal to
> - Greater than
>= - Greater than or equal to
!= - Not equal to
Example: Using Comparison Operators
Just how do you use comparison operators? As their name suggests, you use them to compare two expressions, with the result of the comparison being either true or false. For example, look at this logical expression:
3 == 2 + 1
The result of the above expression is true because the == operator determines whether the expressions on either side are equal to each other. If you were to change the expression to 3 == 2 + 2 the result would be false. That is, 3 does not equal 4. However, the previous sentence suggests a way to rewrite the expression, like this:
3 != 2 + 2
This expression results in a value of true, because 3 does not equal 4. The other logical ...
10/24/2011 2:16:00 PM
The Simplest Java Applet
The Java programming language and libraries enable you to create applets that are as simple or as complex as you like. In fact, you can write the simplest Java applet in only a few lines of code, as shown in Listing 1.
Listing 1 MyApplet.java: The Simplest Java Applet.
import java.applet.*;
public class MyApplet extends Applet
{
}
The first line of Listing 1 tells the Java compiler that this applet will be using some or all of the classes defined in the applet package (the asterisk acts as a wildcard, just as in DOS file names). All of the basic capabilities of an applet are provided for in these classes, which is why you can create a usable applet with so few lines of code.
The second line of code declares a new class called MyApplet. This new class is declared as public so that the class can be accessed when the applet is run in a Web browser or in the Appletviewer application. If you fail to declare the applet class as public, the code will compile fine, but the applet will refuse to run. In other words, all applet classes must be public.
As you can see, you take advantage of object-oriented programming (OOP) inheritance to declare your applet class by subclassing Java's Applet class. This inheritance works exactly the same as when you created your own classes as you can see in the post "Classes in Java - Introduction and Practical Examples". The only difference is that Applet is a class that's included with the Java Developer's Kit (JDK), rather than a class you created yourself.
You can actually compile the applet shown in Listing 1. When you do, you'll have the MyApplet.class file, which is the byte-code file that can be executed by the Java system. To run the applet, just create an HTML document like the one shown in Listing 2. If you need a refresher course on using the tag, take a look in the post "Running Java Applets." If you were to run the MyApplet applet, however, you wouldn't see anything much in Appletviewer or in your Web browser.
Listing 2 MYAPPLET.htmL: MyApplet's HTML Document.
Applet Test Page
Applet Test Page
code="MyApplet.class"
width=250
height=250
name="MyApplet">
The Five Stages of an Applet's Life Cycle
Every Java applet you create inherits a set of default behaviors from the Applet class. In most cases, these default behaviors do nothing, unless you override some of Applet's methods in order to extend the applet's basic functionality. However, although a simple applet like MyApplet in Listing 1 doesn't seem to do much, a lot is going on in the background. Some of this activity is important to your understanding of applets, and some of it can stay out of sight and out of mind.
Part of what goes on in a simple applet is the execution of the applet's life cycle. There are five parts to this cycle, each of which has a matching method that you can overr
...
10/13/2011 11:11:00 AM
When programming in a language such a C++, displaying graphics and playing sounds can be famously difficult, thanks to the fact that these languages provide no direct support for handling these types of files. Even the Windows API, as immense as it is, provides little help when it comes to handling these graphical and aural chores. Java, on the other hand, was designed to make creating applets as easy as possible. For that reason, Java's classes handle almost all the difficulties associated with displaying images (commonly called bitmaps) and playing sounds.
Image Types
In the world of computers, there are many types of images, each of which is associated with a specific file format. These image types are usually identified by their file extensions, which include PCX, BMP, GIF, JPEG (or JPG), TIFF (or TIF), TGA, and more. Each of these file types was created by third-party software companies for use with their products, but many became popular enough to grow into standards. The PCX graphics file type, for example, began as the format for PC Paintbrush files, whereas BMP files are usually associated with the Windows graphical interface.
If you were writing your Internet applications using a more conventional language like C++, you could choose to support whatever image type was most convenient for your use. This is because you'd have to write all the file-loading code from scratch, anyway. Java, on the other hand, comes complete with classes that are capable of loading image files for you. This convenience comes with a small price, however, since Java can load only GIF and JPEG image file formats. In this article, you'll use GIF files, which are more common, although JPEG files are rapidly gaining a reputation, especially for high-resolution, true-color images.
The first step in displaying an image in your applet is to load the image from disk. To do this, you must create an object of Java's Image class. This is fairly easy to do; however, in order to do so, you need to create an URL object that holds the location of the graphics file. You could just type the image's URL directly into your Java source code. If you do this, however, you have to change and recompile the applet whenever you move the graphics file to a different directory on your disk. A better way to create the image's URL object is to call either the getDocumentBase() or getCodeBase() method. The former returns the URL of the directory from which the current HTML file was loaded, whereas the latter returns the URL of the directory from which the applet was run.
Example: Using the getDocumentBase() Method
As I said previously, the getDocumentBase() method returns the URL of the directory from which the HTML document was loaded. If you're storing your images in the same directory (or a subdirectory of that directory) as your HTML files, you'd want to use this method to obtain an URL for an image.
Suppose you have your HTML documents in a directory called PUBLIC and the image you want, called IMAGE.gif, is stored in a subdirectory of PUBLIC called IMAGES. A call to getDocumentBase() will get you the appropriate base URL. That call looks like this:
URL url = getDocumentBase();
As you'll soon see, once you have the URL, you can load the file by using the URL along with the relative location of the image, which in this case would be IMAGES/IMAGE.gif. The full URL to the file would then be FILE:/C:/PUBLIC/IMAGES/IMAGE.gif. If you decided to move your public files to a directory called MYHOMEPAGE, the call to getDocumentBase() will give you the URL for that new directory, without your having to change the applet's source code. This new URL, once you included the relative location of the image file, would be FILE:/C:/MYHOMEPAGE/IMAGES/IMAGE.gif.
Example: Using the getCodeBase() Method
The getCodeBase() method works similarly to getDocumentBase(), except that it returns the URL of the directory from which the applet was loaded. If you're storing your images in the same directory (or a subdirectory of that directory) as your CLASS files, you'd want to call getCodeBase() to obtain an URL for an image.
Suppose you have your CLASS files in a directory called CLASSES and the image you want (still called IMAGE.gif) is stored in a subdirectory of CLASSES called IMAGES. A call to getCodeBase() will get you the base URL you need to load the image. That call looks like this:
URL url = getCodeBase();
Again, once you have the URL, you can load the file by using the URL along with the relative location of the image, which would still be IMAGES/IMAGE.gif. The full URL to the file would then be FILE:/C:/CLASSES/IMAGES/IMAGE.gif.
Once you have the image's base URL, you're ready to load the image and create the Image object. You can complete both of these tasks at the same time, by calling your applet's getImage() method, like this:
Image image = getImage(baseURL, relLocation);
The getImage() method's two arguments are the URL returned by your call to getCodeBase() or getDocumentBase() and the relative location of the image. For example, assuming that you've stored your CLASS files in the directory C:\CLASSES and your images in the directory C:\CLASSES\IMAGES, you'd have a code that looks something like this:
URL codeBase = getCodeBase();
Image myImage = getImage(codeBase, "images/myimage.gif");
After Java has executed the above lines, your image is loaded into the computer's memory and ready to display.
Displaying an Image
Displaying the image is a simple matter of calling the Graphics object's drawImage() method, like this:
g.drawImage(myImage, x, y, width, height, this);
This method's arguments are the image object to display, the X and Y coordinates at which to display the image, the width and height of the image, and the applet's this reference.
TIP
When you want to display an image with its normal width and height, you can call a simpler version of the drawImage() method, which leaves out the width and height arguments, like this: drawImage(image, x, y, this). This version of the method actually draws the image faster because it doesn't have to worry about reducing or expanding the image to the given width and height. It just blasts it on to the screen exactly as the image normally appears.
You may be wondering where you can get the width and the height of the image. As it turns out (no doubt thanks to careful consideration by Java's programmers over hundreds of cups of coffee), the Image class has two methods, getWidth() and getHeight(), that return the width and height of the image. The complete code for displaying the image, then, might look like this:
int width = image.getWidth(this);
int height = image.getHeight(this);
g.drawImage(image, x, y, width, height, this);
As you can see, the getWidth() and getHeight() methods require a single argument, which is the applet's this reference.
Example: Displaying an Image in an Applet
You're now ready to write an applet that can display images. Listing 1 is the Java source code for an applet called ImageApplet that displays a small image using the techniques described previously in this article. Make sure the SNAKE.gif image is in the same directory as the ImageApplet.class file, since that's where the program expects to find it.
Listing 1 - ImageApplet.java: An Applet That Displays an Image.
import java.awt.*;
import java.applet.*;
import java.net.*;
public class ImageApplet extends Applet
{
Image snake;
public void init()
{
URL codeBase = getCodeBase();
snake = getImage(codeBase, "snake.gif");
resize(250, 250);
}
public void paint(Graphics g)
{
int width = snake.getWidth(this);
int height = snake.getHeight(this);
g.drawRect(52, 52, width+10, height+10);
& ...
10/5/2011 4:58:00 PM
In this java tutorial, you get a look at configurable applets, which enable the applets user to modify how an applet looks and acts, all without having to change a line of Java code.
If you have questions about java applets, check out this free tutorial about java applets.
Most of the applets you've written so far have onething in common. Outside of the starting size of the applet, none of yourapplets are configurable. That is, the user can't configure the applet to fithis needs. In many cases, it doesn't make sense to give the user configurableoptions. But, just as often, someone who wants to use your applet in his ownhome page will want to make minor changes without having to change andrecompile the source code. In fact, the user probably won't even have access tothe source code.
Types of Users
Before you read further, it might be a good idea to define exactly what a user is. When it comes to applets, you could say that there are two kinds of users. The first kind is a net surfer who logs onto your home page and sees all the cool applets you've spent the last six months creating. Because this user is not installing your applets on his own Web pages, he's just a casual observer-he doesn't need access to the applet's parameters. In fact, if you want your Web pages to look right for different users, it just doesn't make sense to enable the surfer to configure an applet.
The other kind of user is the guy who found your applet on a server somewhere and wants to incorporate the applet into his own Web pages. Assuming that you've released your applet into the world for others to use, you want this type of user to find your applet to be as flexible as possible. However, you probably don't want to give this user your source code and expect him to make changes that require recompiling.
Hey, he could end up trashing the applet completely, right?
So, to make it easy for this user to modify the applet's appearance and functionality, you must build in support for parameters. To use these parameters, the user only needs to add a few lines to the HTML document that loads and runs the applet. For example, you may have written an applet that displays an awesome title on your home page. Now, you want to release the applet so that other netfolks can use it in their Web pages. However, these folks are going to want to display their own titles. So, you make the title string a parameter.
In this article, you'll not only learn how to support applet parameters, but you'll also learn how to make those parameters user-proof.
Parameters and Applets
When you want to use an applet that supports parameters, you must add the parameters and their values to the HTML document that loads and runs the applet. You do this using the tag, which has two parts. The NAME part of the tag specifies the parameter's name, and the VALUE part specifies the parameter's value. For example, suppose you want to provide a title parameter for that title applet you read about in the previous section. The parameter tag might look like this:
Here, the name of the parameter is title. The applet will use this name to identify the parameter. The value of the title parameter in the above line is the text string My first Home Page. The applet will retrieve this text string in order to display the title the user wants. A complete HTML document for the title applet might look something like Listing 1.
Listing1: Using a Parameter in an HTML Document.
Applet Test Page
Applet Test Page
code="TitleApplet.class"
width=250
height=150
name="TitleApplet">
As you can see, the tag is enclosed between the and tags, that is, the parameters are part of the applet's HTML code.
How does your applet retrieve the parameter at run time? An excellent question, and one for which I fortunately have the answer. To retrieve a parameter, you call the applet's getParameter() method, like this:
String param = getParameter(name);
The getParameter() method takes a single argument, which is a string containing the name of the parameter for which you want the value. The method always returns a string to your applet. This string is, of course, the part of the PARAM tag that follows the VALUE=.
Example: Setting and Retrieving a Parameter's Value
Suppose that you've written an applet that displays a fancy greeting to the viewer.
The parameter is defined in the HTML document like this:
When the applet runs, it has to find out what greeting to display. So, in the applet's init() method is the following line:
String str = getParameter("greeting");
Now that the applet has the text stored in the str variable, it can manipulate and display it any way it needs to.
Example: Using a Parameter in an Applet
Now that you know how to create HTML documents that set parameters, as well as how to obtain those parameters from within your applet, you'd probably like a real parameterized applet with which you can experiment. Listing 2 is an applet called ConfigApplet, which takes a single parameter. This parameter is the text string to display. Listing 3 is the HTML document that loads and runs the applet.
Listing 2 - ConfigApplet.java: An Applet with a Single Parameter.
import java.awt.*;
import java.applet.*;
public class ConfigApplet extends Applet
{
String str;
public void init()
{
str = getParameter("text");
Font font = new Font("TimesRoman", Font.BOLD, 24);
setFont(font);
}
public void paint(Graphics g)
{
g.drawString(str, 50, 50);
}
}
Line by line
- Tell Java that the applet uses the classes in the awt package.
- Tell Java that the applet uses the classes in the applet package.
- Derive the ConfigApplet class from Java's Applet class.
- Declare the class's data field.
- Override the init() method.
- Retrieve the value of the text parameter.
- Create and set the font for the applet.
- Override the paint() method.
- Display the given string.
Listing 3 - CONFIGAPPLET.htmL : HTML Document for ConfigApplet.
Applet Test Page
Applet Test Page
code="ConfigApplet.class"
width=250
height=150
name="ConfigApplet">
Once you get ConfigApplet compiled, try running the applet several times, each time changing the parameter in the HTML document to a new text string. This will give you a good example of how parameters work from the HTML document writer's point of view. Changing the value of the parameter in the HTML document is all you need to do to display a different text string. You don't have to change the applet's source code at all.
Multiple Parameters
When you're writing an application that others may use in their Web pages, it's important that you make the applet as flexible as possible. One way to do this is to use parameters for any applet value that the user might like to customize. Adding multiple parameters is just a matter of adding additional tags to the HTML document and then retrieving the values of the parameters in the applet. In the next example, you take a look at ConfigApplet2, which gives the user much more control over how the applet displays the text string.
Example: Using Multiple Parameters in an Applet
Suppose that you want to rewrite ConfigApplet so that the user can customize not just the text string the applet will display, but also the position of the text and the size of the font used to print the text. To do this, you need to create four parameters, one each for the text to display, the X position of the text, the Y position of the text, and ...
9/28/2011 6:17:00 PM
Classes and Objects
A class is the template for an object and a way to encapsulate both data (called fields in Java) and the functions (called methods) that operate on that data. The Inheritance, enables a class, called the subclass, inheriting the capabilities of a base class, called a superclass in Java. The polymorphism enables you to create virtual methods that can be implemented differently in derived classes. In this article, you'll apply what you know about object-oriented programming towards creating Java classes.
Defining a Simple Class
As I said, a class is sort of a template for an object. In this way, a class is equivalent to a data type such as int. The main difference is that Java already knows what an integer is. However, when you create a class, you must tell Java about the class's characteristics. You define a class by using the class keyword along with the class name, like this:
class MyClass
{
}
Believe it or not, the preceding lines are a complete Java class. If you save the lines in a file called MyClass.java, you could even compile the class into a .CLASS file, although the file won't actually do anything if you tried to run it. As you can see, the class definition begins with the keyword class followed by the name of the class. The body of the class is marked off by curly braces just like any other program block. In this case, the class's body is empty. Because its body is empty, this example class doesn't do anything. You can, however, compile the class and even create an object from it. To create an object from a class, you type the class's name followed by the name of the object. For example, the line below creates an object from the MyClass class:
MyClass myObject = new MyClass();
Declaring Fields for a Class
As I said, the MyClass example class doesn't do much yet. In order to be useful, it needs both data fields and methods. You declare fields for your class in much the same way you declare any variable in a program, by typing the data type of the field followed by the name of the field, like this:
int myField;
The above line declares a data field of type integer. However, looking at the above line doesn't tell you much about how data fields are used with classes. In fact, you can't tell from the above line whether myField is actually part of an object or just a normal variable. To clear up this ambiguity, you can plug the above line into the MyClass class definition, as shown in Listing1.
Listing 1: Adding a Data Field to a Class.
class MyClass
{
int myField;
}
Now you can see that myField is a data field of the MyClass class. Moreover, this data field is by default accessible only by methods in the same package. (For now, you can think of a package as a file.) You can change the rules of this access by using the public, protected, and private keywords. A public data field can be accessed by any part of a program, inside or outside of the class in which it's defined. A protected data field can only be accessed from within the class or from within a derived class (a subclass). A private data field cannot even be accessed by a derived class.
Defining a Constructor
You have now added a data field to MyClass. However, the class has no methods and so can do nothing with its data field. The next step in defining the class, then, is to create methods. One special type of method, called a constructor, enables an object to initialize itself when it's created. A constructor is a public method (a method that can be accessed anywhere in a program) with the same name as the class. Listing2 shows the MyClass class with its constructor in place.
Listing 2: Adding a Constructor to a Class.
class MyClass
{
int myField;
public MyClass(int value)
{
myField = value;
}
}
As you can see, the class's constructor starts with the public keyword. This is important because you want to be able to create an object from the class anywhere in your program, and when you create an object, you're actually calling its constructor. After the public keyword comes the name of the constructor followed by the constructor's arguments in parentheses. When you create an object of the class, you must also provide the required arguments.
Example: Creating an Object by Calling a Constructor
If you want to create an object from MyClass, you must supply an integer value that the class uses to initialize the myField data field. This integer is the MyClass constructor's single argument. You'd create an object of the class like this:
MyClass myObject = new MyClass(1);
This line not only creates an object of the MyClass class, but also initializes the myField data field to 1. The first word in the line tells Java that myObject is going to be an object of the MyClass class. The next word is the object's name. After the equals sign comes the keyword new and the call to the class's constructor.
Defining Methods
You just need to be sure to provide the proper type of access to your methods. That is, methods that must be called from outside the class, should be defined as public, methods that must be callable only from the class and its derived classes should be defined as protected, and methods that must be callable only from within the class should be declared as private.
Suppose myField is defined as private, and you now want to be able to set the value of myField from outside the MyClass class. Because that data field is defined as private, meaning it can be accessed only from within the same class, you cannot access it directly by name. To solve this problem, you can create a public method that can set the value for you. You might also want to create a method that returns the value of the field, as well, as shown in Listing3.
Listing 3: Adding a Method to the Class.
class MyClass
{
private int myField;
public MyClass(int value)
{
myField = value;
}
public void SetField(int value)
{
myField = value;
}
public int GetField()
{
return myField;
}
}
Line by line
- Start defining the MyClass class.
- Declare the class's myField data field.
- Define the class's constructor.
- Initialize the data field.
- Start defining the SetField() method.
- Set the data field to the value passed to SetField().
- Start Defining the GetField() method.
- Return the value of the myField data field.
NOTE
According to the rules of strict object-oriented design, all class data fields should be declared as private. Some programmers would go so far as to say that you should not even provide access to data fields through public methods. However, you'll see these rules broken a lot, even by programmers hired by big companies like Microsoft, Borland, and Sun. When you become more familiar with object-oriented programming, you'll better understand why the rules were made and when it's appropriate to break them.
Example: Using Classes in Applets
You've been writing applets using the classes already supplied as part of Java. Now, you'll see how to use your own classes in applets. This will help you understand not only how your own classes work, but also help you to understand why you used Java's classes as you did. Follow the steps below to see how all this class stuff works.
1. Type Listing3 and save it to your CLASSES folder under the name MyClass.java.
2. Start a DOS session by selecting Programs/MS-DOS Prompt from the Start menu.
3. Type CD C:\CLASSES to switch to your CLASSES folder.
4. Type javac MyClass.java to compile the MyClass class. You'll then find the MyClass.class file in your CLASSES folder.
5. Type Listing 4 and save it as Applet1.java in your CLASSES folder.
Listing 4 - Applet1 : An Applet That Uses the MyClass Class.
import java.awt.*;
import java.applet.*;
import MyClass;
public class Applet1 extends Applet
{
MyClass myObject;
TextField textField1;
public void init()
{
myObject = new MyClass(1);
textField1 = new TextField(10);
textField1.setText("1");
}
public void paint(Graphics g)
{
String s = textField1.getText();
int value = Integer.parseInt(s);
myObject.SetField(value);
value = myObject.GetField();
s = String.valueOf(value);
g.drawString("The data field of the object" ...
9/20/2011 6:28:00 PM
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9/20/2011 2:37:00 PM
An Introduction to Arrays
Often in your programs, you'll want to store many values that are related in some way. Suppose you manage a bowling league, and you want to keep track of each player's average. One way to do this is to give each player a variable in your program, as shown in Listing 1.
Listing 1 - Applet1.java: Using Variables to Track Scores.
import java.awt.*;
import java.applet.*;
public class Applet1 extends Applet
{
TextField textField1, textField2, textField3;
int avg1, avg2, avg3;
public void init()
{
textField1 = new TextField(5);
textField2 = new TextField(5);
textField3 = new TextField(5);
textField1.setText("0");
textField2.setText("0");
textField3.setText("0");
}
public void paint(Graphics g)
{
g.drawString("Your bowlers' averages are: ", 50, 80);
String s = textField1.getText();
g.drawString(s, 75, 110);
avg1 = Integer.parseInt(s);
s = textField2.getText();
g.drawString(s, 75, 125);
avg2 = Integer.parseInt(s);
s = textField3.getText();
g.drawString(s, 75, 140);
avg3 = Integer.parseInt(s);
}
public boolean action(Event event, Object arg)
{
repaint();
return true;
}
}
When you run Applet1, you can enter bowling scores into the three boxes at the top of the applet's display area. After you enter these averages, they're displayed on-screen as well as copied into the three variables avg1, avg2, and avg3.
Nothing too tricky going on here, right?
Now examine the listing. If you could find some way to make a loop out of this code, you could shorten the program significantly. How about a for loop that counts from 1 to 3?
But how can you use a loop when you're stuck with three different variables? The answer is an array. An array is a variable that can hold more than one value. As you know, a variable is like a box in memory that holds a single value. Now, if you take a bunch of these boxes and put them together, what do you have? You have an array. For example, to store the bowling averages for your three bowlers, you'd need an array that can hold three values. You could call this array avg. You can even create an array for a set of objects like the TextField objects Applet1 uses to get bowling scores from the user. You could call this array textField.
Now you have an array called avg that can hold three bowling averages and an array called textField that can hold three TextField objects. But how can you retrieve each individual average or object from the array? You do this by adding something called a subscript to the array's name. A subscript (also called an index) is a number that identifies the element of an array in which a value is stored. For example, to refer to the first average in your avg array, you'd write avg[0]. The subscript is the number in square brackets. In this case, you're referring to the first average in the array (array subscripts always start from zero.) To refer to the second average, you'd write avg[1]. The third average is avg[2].
In this case, the three bowling averages are 145, 192, and 160. The value of avg[0] is 145, the value of avg[1] is 192, and the value of avg[2] is 160.
Example: Creating an Array
Suppose that you need an array that can hold 30 floating-point numbers. First, you'd declare the array like this:
float numbers[];
Another way to declare the array is to move the square brackets to after the data type, like this:
float[] numbers;
After declaring the array, you need to create it in memory. Java lets you create arrays only using the new operator, like this:
numbers = new float[30];
The last step is to initialize the array, a task that you might perform using a for loop:
for (int x=0; x<30; ++x)
numbers[x] = (float)x;
These lines of Java source code initialize the numbers[] array to the numbers 0.0 to 29.0. Notice how the loop only goes up to 29. This is because, although there are 30 elements in the numbers[] array, those elements are indexed starting with 0, rather than 1. That is, the subscript is always one less than the number of the element you're accessing. The first element has a subscript of 0, the second a subscript of 1, the third a subscript of 2, and so on.
Example: Using a Variable as a Subscript
As you know, most numerical literals in a Java program can be replaced by numerical variables. Suppose you were to use the variable x as the subscript for the array avg[]. Then if the value of x is 1, the value of avg[x] is 192. If the value of x is 3, the value of avg[x] is 160.
Now take one last, gigantic, intuitive leap (c'mon, you can do it) and think about using your subscript variable x as both the control variable in a for loop and the subscript for the avg[] and textField arrays. If you use a for loop that counts from 0 to 2, you can handle all three averages with much less code than in the original program. Listing 2 shows how this is done.
Listing 2 - Applet2.java: Using Arrays.
import java.awt.*;
import java.applet.*;
public class Applet2 extends Applet
{
TextField textField[];
int avg[];
public void init()
{
textField = new TextField[3];
avg = new int[3];
for (int x=0; x<3; ++x)
{
textField[x] = new TextField(5);
textField[x].setText("0");
}
}
public void paint(Graphics g)
{
g.drawString("Your bowlers' averages are: ", 50, 80);
for (int x=0; x<3; ++x)
{
String s = textField[x].getText();
g.drawString(s, 75, 110 + x*15);
avg[x] = Integer.parseInt(s);
}
}
public boolean action(Event event, Object arg)
{
repaint();
return true;
}
}
Line by line
- Tell Java that the program uses classes in the awt package.
- Tell Java that the program uses classes in the applet package.
- Derive the Applet2 class from Java's Applet class.
- Declare TextField and int arrays.
- Override the Applet class's init() method.
- Create the textField and int arrays with three elements each.
- Loop from 0 to 2.
- Create a new TextField object and store it in the array.
- Add the new TextField object to the applet.
- Set the new TextField object's text.
- Override the Applet class's paint() method.
- Display ...
9/14/2011 11:31:00 AM
When you start writing real programs, however, you'll quickly discover that they can grow to many pages of code. When programs get long, they also get harder to organize and read. To overcome this problem, professional programmers break their programs down into individual functions, each of which completes a specific and well-defined task.
The Top-Down Approach to Programming
As I said, long programs are hard to organize and read. A full-length program contains many pages of code, and trying to find a specific part of the program in all that code can be tough. You can use modular program-design techniques to solve this problem. Using modular programming techniques, you can break a long program into individual modules, each of which performs a specific task.
In that article, I used the example of cleaning a house as a way to understand the process of breaking tasks up into specific steps. (The only reasonable way to clean my house is to douse it with gasoline and throw in a lighted match, but we won't get into that now.) You'll use that metaphor here, in preparation for learning about functions.
When cleaning a house, the main task might be called CLEAN HOUSE. Thinking about cleaning an entire house, however, can be overwhelming. So, to make the task easier, you can break it down into a number of smaller steps. These steps might be CLEAN LIVING ROOM, CLEAN BEDROOM, CLEAN KITCHEN, and CLEAN BATHROOM.
After breaking the housecleaning task down into room-by-room steps, you have a better idea of what to do. But cleaning a room is also a pretty big task-especially if it hasn't been done in a while or if you have cats coughing up fur balls all over the place. So why not break each room step down, too? For example, cleaning the living room could be broken down into PICK UP ROOM, DUST AND POLISH, CLEAN FURNITURE, and VACUUM RUG.
After breaking each room's cleaning down into steps, your housecleaning job is organized much like a pyramid, with the general task on the top. As you work your way down the pyramid, from the main task to the room-by-room list and finally to the tasks for each room, the tasks get more and more specific.
Of course, when cleaning a house, you don't usually write a list of steps. If you're an efficient housecleaner, the steps are organized in your mind. (If you clean house like I do, there are only two steps: TURN ON TV and COLLAPSE ON COUCH.) However, when writing a program, which is a more conceptual task, you may not have a clear idea of exactly what needs to be done. This can lead to your being overwhelmed by the project.
Breaking programming tasks down into steps, or modules, is called modular programming. And when you break your program's modules down into even smaller modules-as we did with the task of cleaning a house-you're using a top-down approach to program design. By using top-down programming techniques, you can write any program as a series of small, easy-to-handle tasks. In Java, the basic unit for organizing code in a top-down manner is the function.
Example: Using Functions as Subroutines
When programmers talk about subroutines, they usually mean program modules that return no value to your program. In a way, a subroutine is like a small program within your main program. If you write a housecleaning program, the subroutines in the main module might be called CleanLivingRoom(), CleanBedroom(), CleanKitchen(), and CleanBathroom(). The CleanLivingRoom() subroutine would contain all the steps needed to clean the living room, the CleanBedroom() subroutine would contain all the steps needed to clean a bedroom, and so on.
Of course, it takes an extremely talented programmer to get a computer to clean a house. (If you manage that trick, contact me immediately.) We need a more computer-oriented example. Suppose you want to write a program that displays game instructions on-screen. Listing 1 shows one way you might accomplish this task in a Java applet.
Listing 1 - Applet1.java: Printing Instructions in an Applet.
import java.awt.*;
import java.applet.*;
public class Applet1 extends Applet
{
public void paint(Graphics g)
{
g.drawString("Try to guess the number I am", 48, 65);
g.drawString("thinking of. The number will be", 48, 80);
g.drawString("between 0 and 100. You have an", 48, 95);
g.drawString("unlimited number of tries.", 48, 110);
g.drawString("Good Luck.", 95, 140);
}
}
Applet1 is about the simplest applet you can write. All it does is display text. The text comprises instructions for playing a simple number game. If you had to sum up in a couple of words the task performed by Applet1's paint() method, you might come up with something like "Draw Instructions," which is an excellent name for a function to handle that task. Listing 2 is a new version of the applet that isolates the instruction-display task in its own function. When you run this applet, it looks identical to Applet1.
Listing 2 - Applet2.java: Placing the Instructions in a Function.
import java.awt.*;
import java.applet.*;
public class Applet2 extends Applet
{
public void paint(Graphics g)
{
DrawInstructions(g);
}
void DrawInstructions(Graphics g)
{
g.drawString("Try to guess the number I am", 48, 65);
g.drawString("thinking of. The number will be", 48, 80);
g.drawString("between 0 and 100. You have an", 48, 95);
g.drawString("unlimited number of tries.", 48, 110);
g.drawString("Good Luck.", 95, 140);
}
}
Now for the million-dollar question: How does this Applet2 work? The program is divided into two functions. The first is the paint() method, which Java calls whenever the applet's display area must be redrawn. In this applet, paint() is at the highest level of your top-down design. That is, no other part of the program calls paint(), but paint() calls functions that are lower in level.
NOTE
You might be confused about the difference between methods, functions, and subroutines. The truth is that they are very similar. Specifically, a method is a function that is part of a class. So, in Applet2, both paint() and DrawInstructions() are methods of the Applet2 class. (They are also functions.) A subroutine is a function that returns no value. That is, it has the word void in front of its name.
The second function in Listing 2 is the DrawInstructions() subroutine, which is really just a Java function that returns no value to the calling function (paint(), in this case). DrawInstructions() is one level down from the main program in the top-down design. In paint(), instead of having all the code that's needed to display the instructions, you only have a line that calls the function that handles this task. This makes it easier to see what's going on in paint(). If you need to see more detail, you can always drop down a level in your program and take a look at DrawIns ...
9/2/2011 5:59:00 PM
If you are not familiar with the use of HTML (Hypertext Markup Language) for creating Web pages, you should pick up a book on HTML to get an idea of how this markup works. And even if you are an expert in HTML, you may not have seen the HTML extension that Sun Microsystems has created to support Java applets on Web pages. So, in this article, you not only will have the chance to see Java applets up and running but also will learn how to add them to your Web pages.
The Sample Java Applets
The Java Developer's Kit (JDK) includes many sample applets that you can test in your Web pages. (The HotJava browser, too, comes with a few of these sample applets.). As soon as you install the JDK, you're will ready to start experimenting with Java applets. In this section, you will use the Appletviewer tool-which comes with the JDK-to get a quick look at some applets. A following section, "Adding Applets to an HTML Document," will show you how to add an applet to a Web page.
The Appletviewer Tool
The truth is that you can write and run applets without even having a Java-compatible browser. This is thanks to the Appletviewer tool that comes as part of the JDK. Appletviewer is a Windows application (unless you're using a non-Windows version of the JDK) that you run from a DOS command line. Part of the command line is the applet that you want to run. When Appletviewer appears, the applet appears in the viewer's main window.
To run the Appletviewer application, first bring up an MS-DOS window by selecting the MS-DOS Prompt command from Programs on the Start menu. Then, switch to the folder containing the applet you want to run and type the command line C:\JAVA\BIN\APPLETVIEWER DOC.htmL.
In the preceding command line, DOC.htmL is the name of an HTML document that contains the tag for the applet you want to see.
Example: Running TicTacToe
Suppose you want to run the TicTacToe demo applet that comes with the JDK. To do this, just follow these steps:
- Select the Start/Programs/MS-DOS Prompt command. The DOS window appears.
- Change to the directory containing the TicTacToe applet
- Type the command line C:\JAVA\BIN\APPLETVIEWER EXAMPLE1.htmL.The
- Now that you have the applet started, try a few games of TicTacToe against the computer. To place an X, click the square you want. You'll quickly discover that the computer player is as dumb as yogurt. Let's just say that you don't have to be a rocket scientist to win.
TIP
If you want to avoid typing the full path name for Appletviewer every time you run it, type the command PATH=C:\JAVA\BIN at the MS-DOS prompt to add Appletviewer's directory to your path. (Of course, if you've installed the JDK somewhere else on your hard drive, you'll have to use a different path in the command.) After you type this command, MS-DOS will be able to find Appletviewer without your having to type the full path. For example, you'll be able to run TicTacToe by switching to the TicTacToe directory and simply typing APPLETVIEWER EXAMPLE1.htmL. You can also add Appletviewer's path to the PATH statement in your AUTOEXEC.BAT file and thus avoid having to type it in by hand every time you start your system and want to use Appletviewer.
The Animator Applet
Another applet that demonstrates some interesting facets of Java programming is the Animator applet, which not only displays various animation sequences, but also plays sound effects simultaneously. To run the Animator applet, switch to the C:\JAVA\DEMO\ANIMATOR folder and type the command line APPLETVIEWER EXAMPLE1.htmL. (The previous command line assumes that you've set your path to the JAVA\BIN directory.). (Yep, it's the ubiquitous Duke, waving at you from his very own applet.)
Animator is an example of a configurable applet. That is, by modifying the HTML tag that loads and runs the applet, the user can display his or her own custom animation sequence and sound effects. For now, though, it's enough for you to know that Java is capable of adding both animation sequences and sound effects to your Web pages.
NOTE
If you'd like to see what the applet's HTML tag looks like, select Appletviewer's Applet,Tag command.
The BarChart Applet
BarChart, another configurable applet, is especially useful when you need to graphically display data values in a Web page. To check out BarChart, switch to the JAVA\DEMO\BARCHART folder and type the command line APPLETVIEWER EXAMPLE1.htmL.
Because BarChart is configurable, you can create all sorts of different bar charts in your Web pages just by specifying different parameters in the applet's HTML tag. As you can see, applets can be powerful tools for creating dynamic and useful Web pages. (Try out Appletviewer's Applet,Tag command to see the code that specifies how the bar chart appears.)
Other Demo Applets
The DEMO folder contains many sample applets that you can experiment with using Appletviewer. All of the demo applets are run from HTML documents with names such as EXAMPLE1.htmL, EXAMPLE2.htmL, and so on. All demo applets have at least the EXAMPLE1.htmL document, while others have additional examples. To run any demo applet, change to the applet's folder and type APPLETVIEWER EXAMPLE1.htmL (assuming that you've set your path to the Appletviewer application). Use the DIR command to display the contents of an applet's directory in order to discover whether the applet features additional example HTML files.
NOTE
Adding Applets to an HTML Document
If you've created Web pages before, you know that you use HTML to create a template for the page. The commands in the template tell a Web browser how to display the Web page. When Sun Microsystems developed Java, they also had to come up with an extension to HTML that would enable Web pages to contain Java applets. That extension is the <applet> tag, which Sun Microsystems defines as shown in Listing 1.
Listing 1: The <applet> Tag Definition.
<applet attributes>
parameters
alternate -content
</applet>
In the preceding tag, the text in normal characters is typed literally; the text shown in italics is replaced by whatever is appropriate for the applet you're including in the document. As you can see, the <applet> tag is similar to other HTML tags with which you may be familiar. For example, the tag starts with <applet attributes> and ends with </applet>, which is not unlike the format of other HTML tags. The first and last lines are required. Other lines in the tag are optional.
The attributes section of the <applet> tag conta ...
9/1/2011 8:40:00 PM
Project coin is one of the projects that were developed for the implementation of Java 7.
The project idea was to add small changes in language, without having to depend on other projects, and without forcing developers to join the new syntax.
After several suggestions, was chosen about five modifications:
* Ability to use strings in switch
* Try-to-resources & Multi-catch
* Improvement in the creation of objects using generics (diamond)
* Simplify methods with variable number of arguments.
* Support for dynamic languages ??JSR 292
In this tutorial I will (try to) explain the use of the new syntax of the first three items on the list.
Strings in switch
The operator switch until the previous versions only supported types char, byte, short, int, Character, Byte, Short, Integer or enums.
In the new version, it is also possible to use Strings. Before, the only way was to make chains of if-else, for example:
String string = //anything
if(string.equals("one"){
} else if(string.equals("two"){
} else if(string.equals("three"){
} else if(string.equals("four"){
} else {
//default
}
In java 7 this same piece of code can be written with a switch:
String string = //anything
switch(string){
case "one":
//one
break;
case "two":
//two
break;
case "three":
//three
break;
case "four":
//four
break;
default :
//default
}
try-with-resources
It was created a new interface: AutoCloseable. All classes that implement (directly or indirectly) this interface are considered to be resources and have to be flushed (. Close ()) after use.
With the new try, it is possible that these resources are automatically closed after the execution of the block (either for normal execution or exception).
An example of code that can be modified to use the new feature is this: a method that makes a query to the database, and uses a statement as a resource:
public static void viewTable(Connection con) throws SQLException {
String query = "select COF_NAME, SUP_ID, PRICE, SALES, TOTAL from COFFEES";
Statement stmt;
try{
stmt = con.createStatement();
ResultSet rs = stmt.executeQuery(query);
while (rs.next()) {
String coffeeName = rs.getString("COF_NAME");
int supplierID = rs.getInt("SUP_ID");
float price = rs.getFloat("PRICE");
int sales = rs.getInt("SALES");
int total = rs.getInt("TOTAL");
...
8/31/2011 11:27:00 AM
This article introduces the Hibernate Validator, reference implementation of JSR 303 - Bean Validation API. This API allows you to easily validate, class objects that represent the application domain.
What is it for?
This article introduces developers to the Hibernate Validator API, which allows to incorporate data validation from the application through an easy to use and customizable API.
When this subject is useful:
Developers who want to learn how the Hibernate Validator works and how to integrate it into their applications will find detailed explanations in this article on how this API works.
Knowing the Hibernate Validator:
The Bean Validation API, represented by the JSR 303 was released in December 2009. Hibernate Validator has emerged as the reference implementation of this API and lets you use annotations to validate data quickly and easily. The biggest advantage is that the Bean Validation API is independent of the application layer where it is used and even in the way it is coded, allowing it to be used in various scenarios. This article discusses in detail how the Hibernate Validator works.
In December 2009, the final version of JSR 303 was released. It's about the Bean Validation API that allows quickly and easily data validation through the use of annotations. The purpose of this JSR is the validation of the data present in the classes that model the application domain, which usually follow the standard JavaBeans. What's interesting is that the Bean Validation API is independent of the application layer where it is used and even the way of how we code it. It can be used in both desktop and web applications, and isn't tied to the persistence mechanism used. Thus, can be used in various scenarios.
Data validation was always present in systems that receive input from the user. Each framework implements a proprietary mechanism to validate the information, which created incompatibility problems and was harder to integrate.
With the advent of JSR 303 has established a standard API for validation, which is flexible enough to be used for many different types of frameworks. In addition, the Bean Validation API provides data validation classes in the application domain, which is simpler than when the process is done by layer. In the layer validation, it is necessary to verify the same data several times (in the presentation layer, business, persistence, etc.). In order to ensure information consistency. By validating the data directly in the domain classes, the whole process is centralized, therefore the objects of these classes typically runs thru the application layers.
The JSR 303 implementation reference is the Hibernate Validator, which will be explained in detail throughout this article.
Configuring Hibernate Validator
To work with the API you must use Java version 5 or higher, since the Hibernate Validator is not compatible with earlier versions of JDK. Setting the application to use the API is simple. The first step is to download from the project official website, which can be found in the reference section. The version available until the time of this writing is 4.1.0.
After unpacking the file (which can be downloaded in ZIP or TGZ format), simply add the following JARs in your application's classpath: hibernate-validator-4.1.0.Final.jar, log4j-1.2.14.jar, slf4j-api-1.5.6.jar, slf4j-log4j12-1.5.6.jar and validation-api-1.0.0.Ga.jar.They are all inside of the downloaded compressed file. If your application use Java 5 instead of 6, you must also add the API JAXB JARs: JAXB-api-2.2.jar and JAXB-impl-2.1.12.jar.This set of files is the minimum necessary to set the Hibernate Validator to work.
Setting constraints using annotations
The constraints are used to define rules regarding the data of an object. You can, for example, define that a particular attribute can not be null or that a value of a numeric attribute must be within a defined interval. When the data validation process is performed, a verification is made to check if the data are consistent with the established rules.
When you need to add validation constraints in the code, this is done through the use of annotations. Hibernate Validator comes with a set of annotations for common validations, although the API allows the programmer to make customizations. The creation of custom constraints will be addressed later in this article.
There are two places where constraints may apply. The first is directly in the class attribute. In this case the Java directly accesses the attribute thru reflection in order to do the validation. Listing 1 shows an example. The second form of implementation of constraints can be used when the class follows the specification of a JavaBean. In this case you can use the annotation on the getter method of the attribute. Listing 2 shows how this can be done. You must choose only one option, because if both are used the validation will be done twice.
Listing 1.Using the constraint @NotNull on the attribute.
public class Student {
@NotNull
private String name;
}
Listing 2.Using the constraint @NotNull on the getter method.
public class Student {
@NotNull
public String getName () {
return name;
}
}
All elements of the Hibernate Validator (classes, interfaces, annotations, etc..) Used by your code belong to the package javax.validation.
In addition to the annotation @NotNull shown in the example, which verifies that the data is not null, there are other important annotations included in Hibernate Validator. Following we are going to discuss some of them in more details. For more information about these and other annotations, refer to JSR 303 and the Hibernate Validator documentation.
@AssertFalse and @AssertTrue
These annotations validate if the data is true or false, respectively. Should be implemented in Boolean data (the primitive type Boolean and Boolean class are supported).Listing 3 shows both constraints. The attribute hasWarnings shall be false while fullAge must be true.
Listing 3.Using the annotations @AssertTrue and @AssertFalse.
public class Student {
@AssertFalse
private boolean hasWarning;
@AssertTrue ...
7/29/2011 11:21:00 AM
Using validation groups
Often it is desirable to separate in groups the validations that should be accomplished. This allows the validation of only part of the constraints defined in the class, and not all of them at once.
Hibernate Validator support this separation. Each group is usually represented by a marker interface, which has no methods or attributes. It is important to understand that every time the validation process is invoked, you must specify one or more groups of validation. When a group is not explicitly provided, Hibernate Validator uses the group javax.validation.groups.Default as default. Listing 11 shows the class Student and the constraints made to its attributes. As the constraints do not refer to a specific group, the default is used.
Listing 11.Restrictions on Student class defined in the standard group validation.
public class Student {
@NotNull
private String name;
@Min(3)
private int age;
@Size (max = 10)
private String numEnrollment;
@NotNull
private Date dateEnrollment;
}
Validation should always be associated with one or more groups, which are passed as parameters to methods validate(), validateProperty() andvalidateValue(). To validate the default group, simply omit this information (the calls validate(student) and validate(studentjavax.validation.groups.Default.class) have exactly the same effect in this case). The invocation of the validation process takes into account only the constraints of the specified groups and ignores the rest. At this point, it is noteworthy that each constraint can belong to one or more groups.
Knowing now that every invocation of validation is done in one or more groups and that all constraints belong to at least one group, it is easy to understand the process of grouping constraints. The first step is the creation of groups, and Listing 12 shows the definition of two of them:PersonalData and EnrollmentData.
Listing 12.Definition of groups PersonalData and EnrollmentData.
public interface PersonalData {
}
public interface EnrollmentData {
}
Then you need to declare the constraints using the newly created groups, rather than the standard group. This is done through the attribute groupspresent in all annotations used for validation. Listing 13 shows the attributes name and age were assigned to the group PersonalData andnumEnrollment and dateEnrollment being assigned to EnrollmentData. If it is necessary to assign more than one group to a constraint, simply provide an array with the interfaces to the element groups from the annotation.If a constraint @NotNull is applied to both groups, for example, it could be declared as @NotNull (groups = {PersonalData.class, EnrollmentData.class}).
Listing 13.Organizing the constraints in groups.
public class Student {
@NotNull (groups = PersonalData.class)
private String name;
@Min (value = 3, groups = PersonalData.class)
private int age;
@Size (max = 10, groups = EnrollmentData.class)
private String numEnrollment;
@NotNull (groups = EnrollmentData.class)
private Date dateEnrollment;
}
Finally, just inform the group to be validated at the time of invoking the validation.Indeed, it is even possible to validate more than one group in one invocation. Listing 14 shows three examples of calls to the validate() method. The first two rely on validation to a group at a time, and the third for both groups. Always remember that the constraints that are not part of groups where the validation is being performed are ignored.
Listing 14.Invoking the validation per group.
validator.validate (student PersonalData.class);
validator.validate (student EnrollmentData.class);
validator.validate (student PersonalData.class, EnrollmentData.class);
Besides the separation of validation in groups, another important aspect should be considered. By default, there are no guarantees about the order of the validation of the constraints In cases where it is important to ensure the order, you can use the annotation @GroupSequence.
@GroupSequence allows to define an execution order for the groups. Suppose you want to perform validations in groups PersonalData andEnrollmentData respecting that order.For this you need to create a new group and define which groups it will check and in what order.Listing 15shows the creation of the group FullData, which defines that the first validation will be done on the group PersonalData and then in the group EnrollmentData. To validate this new group, just reference it at the time of validation. Invoking validate (student, FullData.class) will run the validation of the groups PersonalData and EnrollmentData in this order.
Listing 15.FullData group definition with an validation order set.
@GroupSequence ({PersonalData.class, EnrollmentData.class})
public interface FullData {
}
When a validation error is found in a group, the next groups are not validated.
Another function of the annotation @GroupSequence is redefining the standard group for a class, which by default is thejavax.validation.groups.Default.To change this setting, simply use @GroupSequence at class level.Listing 16 shows its use in theStudent.Now, when the validation is invoked for the default group, the groups PersonalData and EnrollmentData will be called and that order will continue to be respected. Another important point is to always add the class being annotated as a member of the group defined by@GroupSequence, as was done with the Student class in Listing 16. If this condi tion is not met, a GroupDefinitionException will be thrown.
Listing 16.Redefining the default group with the annotation @GroupSequence.
@GroupSequence ({Student.class, PersonalData.class, EnrollmentData.class})
public class Student {
//...
}
Customizing error messages
When you use the Hibernate Validator and validation problems occur and you are faced with messages like: "may not be null", "must be greater than or equal to 70" or "size Must Be Between 2 and 10."It is evident that not always these messages, which are set by default in the API, are ideal for your application.
For this reason, Hibernate Validator allows customizations to be made in the messages. To understand how this process works, you should keep in mind that each constraint has an associated message descriptor. A message descriptor is nothing more than a template that defines how will be the resulting message.
If we consider the annotations @NotNull @Min and @Size, for example, their respectives messages descriptors are{javax.validation.constraints.NotNull.message}, {javax.validation.constraints.Min.message} and{javax.validation.constraints.Size.message}.This information can easily be obtained if the method getMessageTemplate() is invoked on aConstraintViolation (which represents a validation error, as explained earlier).Any information of the message descriptor declared between braces, in fact, is a parameter that will be replaced in the time of the final message generation, a process known as interpolation.
To perform the interpolation Hibernate Validator queries parameter value in the file org/hibernate/validator/ValidationMessages.properties, which is located within the Hibernate Validator JAR. Listing 17 shows the portion that corresponds to the messages of the annotations @NotNull,@Min and @Size. This file maps a key to a value where the key is the parameter of the message descriptor and the value is what needs to be generated as output when occurs the interpolation process.
Listing 17.Part of the file ValidationMessages.properties provided by Hibernate Validator.
javax.validation.constraints.NotNull.message = may not be null
javax.validation.constraints.Min.message = must be greater than or equal to {value}
javax.validation.constraints.Size.message = size must be between {min} and {max}
To customize the error messages, you must create an ValidationMessages.properties file and redefine the messages. It should be at the root of the classpath of your application and has read precedence over the default Hibernate Validator file.Listing 18 shows how could be theValidationMessages.properties file of your application, which changes the messages generated for constraints with null value, minimum value and size.
Listing 18.ValidationMessages.properties file of the application.
javax.validat ion.constraints.NotNull.message = The data can not be null
javax.validation.constraints.Min.message = The value must be greater than or equal to {value}
javax.validation.constraints.Size.message = The data length must be between {min} and {max}
Another possibility which the API provides is to override the message descriptor of only one constraint.Thi ...
7/29/2011 11:21:00 AM
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https://www.answers.com/Q/How_do_you_beat_a_Rubik%27s_Cube
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# How do you beat a Rubik's Cube?
Matthew Colvin
2 June 2009
The Ways of the Cube Have you ever attempted to solve a Rubik's Cube? Are they one of the Seven
Wonders of the World? I don't think so but not many people can solve them. Although
these may be some of the most aggravating mechanisms you will ever face, there are
methods to solving these, and once you learn some of them, it will become very easy.
There are bad ideas you would want to avoid, basic solving, and speedcubing. These
will give you the basic ideas on what a Rubik's Cube is and some helpful tips on how to
solve them. To start off, here are some bad ideas that you would like to avoid, and some
solutions if you run into them. Number one, take off all the stickers and replace them.
Number two, buy a new cube in replace of the scrambled one. These are the solutions
to those problems if you really don't learn, don't have time to learn, or if just don't
want to do it at all. Solution to number one: twist the top or bottom layer half way to
pull out an edge piece; disassemble the cube and put it back together in the correct
solution. This leaves no stickers torn or messed up if you are careful. Solution to
number two: this way is better and more efficient on money; DO NOT buy a new one,
just disassemble it (stated above), and reassemble it in the correct solution. (If you
need help, there are tutorials on many websites). Second, the steps to solve a Rubik's Cube are actually quite simple and mostly
take common sense. All you need to do is focus on which pieces you are putting where
and how to get them there without messing up the other pieces you put into place.
The process in which you do that is by performing multiple and different algorithms. An
algorithm is a sequence of moves to solve the problem you have. There are many
algorithms; many of them you can learn by yourself although there are many more you
can find on a website to solve a certain parity you are stuck at. Parity is where pieces
are turned around or flipped from where they need to be. Although there are about 43
quintillion combinations for the Rubik's Cube, any way you mix it up beyond 18 moves
or so, the combinations change very slightly, and it's no more difficult to solve than the
last time. Eventually when you get really good at solving Rubik's Cubes and you want to
take it to the next level, there is Speedcubing. If you want to speedcube then, you
have to learn a method and get very accustomed to it meaning that you should be able
to think a couple moves ahead of time and flow very smoothly. Speedcubing is quite
simple; besides for finding the quickest algorithms to solve the cube you can use your
own that you know really good. When you are solving the cube, you need to learn
finger tricks that allow you to do your algorithms without stopping at all or using your
whole hand to move a side. Say you have your right thumb on the right side of the
bottom corner facing you, and your other fingers on the top of the cube; rotate the
right side up, use your thumb to twist the top to the right, and without stopping at all,
turn the right side up again. If you can do that without stopping and within half a
second, then you have the potential to learn other good finger tricks to be able to
speedcube. By now you should have a better idea of what not to do, what the Rubik's cube
is, what it is capable of, and lastly what and how to speedcube. Give it a shot and if
you fail, don't give up, keep working on it, and if you follow through all the steps you
will have it mastered in no time. If you can't figure out one method, try another; there
are many.
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https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/chapter-2-acute-angles-and-right-triangles-section-2-2-trigonometric-functions-of-non-acute-angles-2-2-exercises-page-62/45
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## Trigonometry (11th Edition) Clone
Published by Pearson
# Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 62: 45
#### Answer
$\sin$$^{2} 120^{\circ} + \cos$$^{2}$ 120$^{\circ}$ = 1
#### Work Step by Step
$\sin$$^{2} 120^{\circ} + \cos$$^{2}$ 120$^{\circ}$ $\sin$$^{2} 120^{\circ} = \frac{\sqrt3}{2} \cos$$^{2}$ 120$^{\circ}$ = -$\frac{1}{2}$ Therefore: = ($\frac{\sqrt3}{2}$)$^{2}$ + ($\frac{1}{2}$)$^{2}$ = ($\frac{3}{4}$) + ($\frac{1}{4}$) = 1 $\sin$$^{2} 120^{\circ} + \cos$$^{2}$ 120$^{\circ}$ = 1
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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+0
# system
0
223
1
Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 0
q - 2r = 8
p + r = 5
Aug 2, 2022
#1
+129742
+1
p - 2q = 0 → p = 2q (1)
q - 2r = 8 → r = (q - 8) / 2 (2)
p + r = 5 (3)
Sub (1) , (2) into (3)
2q + (q - 8) / 2 = 5
4q + q - 8 = 10
5q - 8 = 10
5q = 18
q = 18/5 p = 2(18/5) = 36/5 r = (18/5 - 8 ) / 2 = -11/5
Aug 2, 2022
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## Monday, October 21, 2019
### SHAPE UP!
How about some ideas for geometry? You can use these activities with young children or school age by adapting the shapes. You might even “spy” some of your state standards here!!!
The Shape Song (Tune: "I'm a Little Teapot"- "October Happies")
I am momma circle round like a pie. (Hands over head in a circle.)
I’m baby triangle three sides have I. (Use 3 fingers to make a triangle.)
I am papa square my sides are four. (Draw a square in the air.)
I’m cousin rectangle shaped like a door. (Draw a rectangle in the air and then knock.)
I am brother oval shaped like a zero. (Make oval with arms over head.)
I’m sister diamond with a sparkle and a glow. (Touch thumbs and index fingers and extend.)
We are the shapes that you all know. (Make circles with index fingers and thumbs and
Look for us wherever you go. place around your eyes like glasses.)
Note! Explain that “rhombus” is the correct term for the diamond shape. Sing the song calling sister a “rhombus” instead of a “diamond.”
*Have children draw shapes in the air with elbows, feet, noses, and other body parts.
*Place foam shapes or 3-dimensional shapes in a bottle filled with sand or salt. Children spin it around and try to identify the shapes. Can they draw the different shapes that they spy?
Body Shapes
Divide children into small groups and challenge them to lay on the floor and make various shapes with their bodies. How many friends will it take to make a triangle? A square? A pentagon? Take pictures and make a book.
*Make spyglasses for “spying” shapes by wrapping construction paper around paper towel rolls.
*Cut geometric shapes out of construction paper and let children use them to make a collage. Can they combine simple shapes to make larger shapes?
*Cut sponges into geometric shapes and have children dip them in paint and stamp on paper.
*Download highway shapes from makinglearningfun.com. Children can drive around these with toy cars or they can roll play dough and place it on the shapes.
*Go on a walk and look for shapes in your school and on the playground.
Shape Book
Fold two sheets of paper in half and staple. Children decorate the front of their book with shapes. Next, they walk around the room and draw shapes that they see. Can they label the shapes?
*This would be a good homework activity to help children be more aware of the shapes around their home.
Play Dough Book
Draw lines, curves, and geometric shapes with a marker on file folders. Laminate. Bind file folders with rings to make a book. Children roll play dough and place it on top of the shapes.
Bendables
Offer children pipe cleaners, Wikki stix, etc. and challenge them to make various shapes with the items.
Pretzel Shapes
Give children pretzel sticks and pretzel twists and challenge them to make geometric shapes. How many pretzel sticks will you need to make a hexagon? How many pretzel sticks will you need to make a triangle?
*Challenge them to make letters with the pretzels. This is fun to do with a partner as they take turns making letters and identifying them.
## Sunday, October 20, 2019
### MAGNETIC NUMBERS
What classroom doesn't have magnetic numbers?
They are a plentiful, multi-sensory tool to develop number concepts!
You can hide them, sort them, touch them, and take a look...
Numerical Order
Put numbers in order 0, 1, 2, 3…
Tens and Ones
How many tens? How many ones?
Can you make 56?
Fact Families
Give children two addends and the sum and have them make and write the
facts.
More? Less? Equal?
Place numbers in a bag. Children pull out two numbers. Which is more?
Which is less? Or, are they equal?
Pick a Number
Children choose a number from a bag and then make a set to equal that amount.
*Let children choose a number and then lead the class in doing that number of jumping jacks, toe touches, or other exercises.
Write addition and subtraction facts on a file folder. Children answer with a
magnetic number.
Daily Number
Put magnetic numbers in a bag. Each day select two from the bag and put
them together on the board. What’s the number? Count forwards. Count
backwards. How many tens? How many ones?
Number Sticks
Glue shapes and numerals to jumbo craft sticks. Children can match these up to shapes and numerals in the classroom. They can also use these as you count, tell number stories, or sing songs.
Little Red Number Box (Sarah Wilson)
Put magnetic numbers in a metal tin and then sing the song as you pull out a number. Then count to that number.
For example: I wish I had a little tin box to put a 6 in. I’d take it out and count 1, 2, 3, 4, 5, 6 and put it back in.
## Saturday, October 19, 2019
### WRITING NUMBERS
Oh, my! Those little hands may not be ready to write numerals, but the curriculum says they should. Believe it or not, 20 years ago we didn't even teach children to write numbers in kindergarten. We saved that for first grade. Now, we are expecting pre-k children to write numbers. I can't change your curriculum, but I can give you some songs and activities that may make it a little more positive and meaningful.
The Numeral Song (“Sing to Learn” CD)
This song goes to the tune of "Skip to My Lou." Have children stand and use their index finger to write in the air. Everybody's writing will look "good" when you do it in the air!
Come right down and that is all.
Come right down and that is all.
Come right down and that is all
To make the numeral one. (Hold up 1 finger.)
2 – Curve around and slide to the right…
3 – Curve in and around again…
4 – Down, over, down some more…
5 – Down, around, put on a hat…
6 – Curve in and around again…
7 – Slide to the right and slant it down…
8 – Make an “s” then close the gate…
9 – Circle around then come right down…
10 – Come right down, then make a zero…
We can sing the “Numeral Song”…
And make numerals all day long!
*Let children do air writing with other body parts, such as their elbow, foot, etc.
They can also practice writing on their palm or a friend's back.
*Squirt shaving cream on a safe surface so the children can practice making numbers.
*Have children practice writing numbers in salt, sand, and other sensory materials.
Number Chant
Children can associate numbers with the amount with this song and video. Encourage them to hold up the appropriate number of fingers as you sing.
Theme Books (Beth Cordier)
Let children make books for whatever theme you’re studying. Make a word wall with words from the theme. (Put magnetic tape on the back so children can take them off and copy them.) Children choose a different word for each page and illustrate it.
*Older children could write sentences with the words.
For example: Fall Theme
Page 1 “Pumpkin”
Page 2 “Leaves”
Page 3 “Squirrels”
Page 4 “Footballs”
Here's another song where children can stand and practice writing numerals without getting frustrated.
Chant and Write (“Totally Math” CD)
(Children echo each line.)
Zero is where it all begins- (Slap thighs to the beat.)
Curve down around and up again.
Number one is so much fun—
Pull straight down and you’ve got a one.
Number two is easy to do—
Up around down and across makes two.
Number three is simple to see—
Draw two humps sideways and that’s a three.
Go down, across, then down some more.
We’ve reached five, now let’s not stop—
Pull down, circle round, put a hat on top.
Number six is easy to fix—
Big curve, small loop will give you six.
Number seven is really sizzlin’—
Straight across, slant down, and that’s a seven.
Number eight isn’t very straight—
Make “S” then back up for an eight.
Number nine I think you’re fine—
A loop on top of a long straight line.
Number ten we’ve reached the end—
Put a one by a zero and count again:
1-2-3-4-5-6-7-8-9-10!
Highway Numbers
Children can trace over numerals with toy cars or they can roll play dough and place it on top of the numerals.
## Friday, October 18, 2019
### RHYME ON...
Rhymes are words that end with the same sound. Rhymes are common in poems, songs, and many children’s books. Cat, hat, rat, and bat are examples of words that rhyme. Being able to identify words that rhyme is key to developing phonological awareness.
Now, teaching children to identify words that rhyme doesn’t happen in one day. The curriculum guide may say, “The children will learn to rhyme today,” but you and I know it takes many, many, many activities where children listen, speak, sing, and chant to develop that skill. Traditional nursery rhymes, songs, and books are the most natural way to nurture rhymes, but here are a few more activities where children can rhyme in a “playful” way.
Handy Rhymes
Have children extend their arms as they say pairs of words that rhyme and sing to the tune of “Skip to My Lou.”
sun (extend right hand)
fun (extend left hand)
Those words rhyme.
sun (extend right hand)
fun (extend left hand)
Those words rhyme.
sun (extend right hand)
fun (extend left hand)
Those words rhyme.
They both end with “un.” (Roll arms around as you say this.)
*As they progress, the teacher says a word as children extend their right hand. Children say their own rhyming word as they extend their left hand.
Rhyme Detectives
Tell the children that they will get to be detectives and listen for words that rhyme. You’ll say two words, and if they rhyme they put their pinkies up. Pinkies down if the words don’t rhyme.
For example: Cat - hat (pinkies up), run - dog (pinkies down).
Rhythm Rhyme
Start a beat by slapping legs two times, clapping hands two times, and snapping fingers two times. On the first snapping beat the teacher says a word. On the second snapping beat the children say a word that rhymes.
Slap, slap, clap, clap, snap, snap.
Slap, slap, clap, clap, mitten. (Teacher says.)
Slap, slap, clap, clap, kitten. (Children say a word that rhymes.)
Rhyme Ball
You will need a ball, beanbag, or other object to toss for this game. Children sit or stand in a circle. The teacher says a word and then tosses the ball to a child. As the child catches the ball, she must say a word that rhymes.
Rhyming Puzzles
Glue rhyming pictures on opposite sides of a 3” x 5” index cards. Cut a puzzle shape between pictures. Mix up and have children put rhymes together.
*Make games with socks, mittens, shoes, etc. where children use clothes pins to put the rhyming pictures together.
*Mr. Google has some great free printables with rhyming pictures.
Riddle Rhyme Game
Let children make up their own rhymes in this game. First, they choose an object in the room. Next, they say a word that it rhymes with, along with another clue.
For example: “This rhymes with hair and it is something you sit on.” “This
rhymes with look and it is something you read.”
Rhyme Bag Homework
Give each child a paper lunch bag and ask them to bring in two objects from home that rhyme. As children share their items the following day encourage them to think of other words that rhyme.
## Thursday, October 17, 2019
### COOKING UP A NURSERY RHYME
You know it makes me sad that so many of you are not allowed to cook in your classrooms any more. When I think of the cooking experiences I had with my students it makes me smile. One of my favorite memories was when we were making pizzas. I said, “Let’s put them on the pan so I can bake them.” Floyd, a precious red head said, “That’s O.K., teacher, I’ll just eat my raw!”
Years ago a teacher sent me these recipes to tie in with nursery rhymes. I wish I could remember who to give them credit to! Even if you can’t have food in your classroom, you might enjoy making these with your own child, a neighbor, a scout troop, or a grown friend! They are too "sweet" to be forgotten!
Ole King Cole’s Coins
Every king has a treasure trove filled with coins so why not make these healthy coins to fill up your students.
Ingredients:
Fresh carrots
Ranch dressing
Have the students wash and scrub the carrots with a vegetable brush. Now slice them up so that they look like coins. Let the children dip their coins in the Ranch dressing.
Name Cakes
After singing the ABC’s the children can eat them with me!
Ingredients:
Rice cakes
Peanut butter, cream cheese or frosting
Find the letters of you name and place them on the table. Spread the topping of your choice over the rice cake and decorate with the letter that you name begins with.
Jack Horner’s Thumbprint Biscuits
Jack Horner stuck in his thumb and pulled out a plumb, but your children will get a kick out of sticking their thumbs in a biscuit.
Ingredients
Canned biscuits
Grape jelly
Give each child a biscuit and tell them to stick their thumb in the middle. Let them fill the hole in the middle with a spoonful of grape jelly. Bake according to directions on the package. Have your children say, “What a good (boy, girl) am I!
Moon Pizzas
The cow jumped over the moon and the astronauts landed on the moon. This recipe will add a whole new dimension to the rhyme or a study of the solar system.
Ingredients
English muffins
Pizza sauce
Shredded mozzarella
*Pepperoni, olive slices or cheeses shaped liked stars or moons are optional
Toast the English muffins ahead to time - especially if you like your pizza crust crunchy. Now spread the pizza sauce over the surface of the moon (English muffin) and add the mozzarella and other toppings of your choice. Bake at 350 degrees until the cheese melts.
Little Miss Muffet
Cottage cheese is very similar to curds and whey, so add a little fresh fruit to cottage cheese for snack.
Itsy Bitsy Spider Sandwich
Use a large plastic cup to cut a circle out of a piece of bread. Spread peanut butter, cream cheese, or Nutrella on the circle. Add eyes (raisins or chocolate chips), a mouth (M& M or cinnamon candy), and legs (pretzels, carrot sticks, or Cheetos).
*For a sweeter spider, put icing on a large sugar cookie and use licorice twists for legs.
Muffin Man Zucchini Muffins
The Muffin Man didn’t have this recipe in his cookbook, but now you do.
Ingredients
½ cup grated zucchini
1 egg
2 Tablespoons of oil
¼ cup of honey
¼ cup of grated lemon peel
¾ cup of flour
½ teaspoon of baking powder
¼ teaspoon salt
¼ cinnamon
Add the first five ingredients and mix well. Now add the rest and pour into muffin tins that have liners added. Bake at 400 degrees for twenty minutes. I’ll bet the Muffin man steals this recipe.
Humpty Dumpty
What could be better than hard boiled "Humpty Dumpty" eggs? Let children draw Humpty on a hard boiled egg, crack the shell, eat the egg, and then try to put the shell back together again.
## Wednesday, October 16, 2019
### DICTIONARY DAY
Did you know that October 16th is Dictionary Day? It's actually Noah Webster's birthday and a perfect day to let each child make her own personal dictionary.
Materials: pocket folder, prepared pages with alphabet letters, markers
Directions: Ask students to tell you what they know about dictionaries. Brainstorm the many uses of dictionaries. Model looking up words and reading definitions. Explain that each of them will get to create their own dictionary that they can use to help them the rest of the school year. First, let the children decorate the outside of their pocket folder. Insert the alphabet pages. As you add new words to the word wall or have new spelling words, ask the children to write them in their dictionary. These would also be a meaningful way to introduce vocabulary words. Encourage students to use their dictionaries when they write independently.
Hint! You might want to go ahead and type your core sight words on the pages before running them off.
Here are some other activities you can play with their dictionaries.
*Play “mystery word” where you give clues about words.
Can you find a word that starts with /m/ and ends with /d/?
Can you find a word that is the opposite of “fast”?
*Play the “rhyme” game.
Can you find a word that rhymes with “bike”?
Can you find a word that rhymes with “log” and is a pet?
*How many one letter words can you find? How many two letter words? Three letter words?
*Ask children to clap out the syllables in words.
*Can they match up words in their dictionaries with words in the classroom?
*Sort words that refer to people, things we do, describing words, etc.
*Have children find a word that starts with each letter in their name.
*Have children make up sentences (oral or written) with the words.
*Ask children to illustrate words or find magazine pictures that match the words.
## Tuesday, October 15, 2019
### TEACH ON WITH NURSERY RHYMES
You can take any rhyme and reinforce reading skills in a natural and meaningful way. Here are a few ideas you can adapt for large group or small group instruction.
FLUENCY
Take a Turn – The teacher reads a line and then the children read the next line and so forth.
Magic Word – Select a special word in the text. Every time you come to that word the children clap their hands or shout it out.
PHONOLOGICAL AWARENESS
Rimes - Make a list of words that rhyme. Circle the letters that are the same. Can the children think of additional words that end with the same sound?
Syllabication - Clap, jump, or snap to the beat of the rhyme.
PUNCTUATION
Use a highlighter to circle capital letters and punctuation.
VOCABULARY
When you come to unfamiliar words in rhymes model looking up definitions in a dictionary.
COMPREHENSION
Story Elements - Discuss the characters, setting, problem, resolution, etc. in the nursery rhyme.
Sequence - What happened first, next, last? What do you think will happen next?
PRINT CONCEPTS
Track the words from left to right and top to bottom. Identify letters in the rhymes.
WORD RECOGNITION
Identify high frequency words in rhymes.
KEY IDEAS AND DETAILS
Compare and contrast rhymes.
Describe the relationship between illustrations and rhymes.
CRAFTY IDEAS FROM NURSERY RHYMES
Jack and Jill
Trace around the puppet pattern on heavy paper. Challenge the children to make the puppet look like “Jack” on one side and “Jill” on the other side. Attach a straw and use as a puppet.
What happened after Jack fell down? Here’s more to the story!
So up got Jack
And said to Jill
As in his arms he took her.
You’re not hurt, brush off that dirt.
Now, let’s go fetch that water.
So up got Jack and
Up got Jill to fetch that pail of water.
They brought it back to mother dear
Who thanked her son and daughter.
Humpty Dumpty
Give children the oval shape and scrap paper. Have them tear the scrap paper into little pieces and then glue it on the oval to make a collage. Attach a stick and use it as a puppet.
What happened to Humpty Dumpty?
So the good children got
Some tape and some glue
Til’ he looked like new.
Then they carefully placed him
Back on the wall
And said, “Humpty Dumpty,
Baa Baa Black Sheep
Cut the sheep and the tops of the 3 bags of wool from the front of a file folder. Insert colored paper starting with black. Remove the black paper and then fill in the appropriate color word. (This would be something for the teacher to make and use with the children.)
Baa baa green sheep
Have you any wool?
Would you like patterns for the above craft activities?
Websites
Here are some good websites where you can download free nursery rhyme posters:
curry.virginia.edu/go/wil/rimes_and_rhymes.htm
enchantedlearning.com
prekinders.com
## Monday, October 14, 2019
### NEVER ENDING NURSERY RHYMES
A teacher recently told me that her administrator said, "Don't do nursery rhymes." What??? That administrator hasn't looked at the research!
rhymes:www.earlyliteracylearning.org
Saying nursery rhymes is a delightful way for children to practice oral language. Rhymes also develop auditory memory (good for the brain) and phonological awareness (key to beginning reading). Nursery rhymes have a simple plot and can be used to introduce story elements: characters, setting, problem, solution.
Nursery rhymes have been kept alive by children for hundreds of years. That is certainly testimony to their appealing quality to children. Nursery rhymes are short, simple, and are part of our literary heritage. Nursery rhymes are also FREE and can be integrated throughout the day to engage children.
What skills can children develop by saying nursery rhymes?
*oral language,
*auditory memory
*phonological awareness (rhyme, rhythm, alliteration)
*concepts about print (left to right, words)
*story elements (characters, setting, problem and resolution)
Hint! Although some claim nursery rhymes are violent and stereotypic, the children only hear the surface level and the music of the language.
Piggy Back Tunes
You can sing traditional nursery rhymes to tunes such as “100 Bottles
of Pop on the Wall,” “Yankee Doodle,” and ”Gilligan’s Island.”
Story Elements
Discuss the characters, setting, problem, resolution, etc. in nursery rhymes.
Rhyme of the Week
Select a rhyme each week and write it on a poster or language experience chart. Reread the rhyme each day.
*Clap the syllables.
*Find words that rhyme.
*Listen for words that start the same.
*Look up unusual words in the dictionary.
*Dramatize the rhyme.
*Say the rhyme the wrong way and let children correct you.
*Leave out a word and let the children fill in the missing word.
*Connect with art by letting children make puppets, play dough characters, etc.
Nursery Rhyme Club
Make a poster that says “Nursery Rhyme Club.” Whenever a child can say a rhyme, they get to sign their name on the poster. It would also be fun to give them a membership card!
Would you like some membership cards?
Rhyme Pops
Cut 3 1/2" circles out of heavy paper and glue them to jumbo craft sticks. As you learn new rhymes write them on the circles and save them in a can. When you have a few extra minutes children can pull out a "rhyme pop" and lead their classmates in saying the nursery rhyme.
Puzzles
Write rhymes on sentence strips. Cut between the words and let children put them in the correct order in a pocket chart.
My Nursery Rhyme Book
Every child will need a spiral notebook or composition book for this project. Each week run off a copy of a rhyme you want to focus on. (Be sure and increase the font for little eyes.) Children cut out the rhyme and glue it on the left and then illustrate the rhyme on the right. Use the rhyme for choral reading and to reinforce specific skills (letters, left to right, sight words, punctuation, etc.) throughout the week. On Friday children take home their books and read the rhyme to their parents. Encourage parents to write their "comments and compliments" in the book.
## Sunday, October 13, 2019
### I SEE THE MOON
I see the moon
And the moon sees me...
October 13th is a full moon and it's also called a HUNTER'S MOON because it lights up the sky.
From the time children are toddlers, most of them are fascinated with the moon. The moon is FREE and it belongs to EVERYONE! Wouldn’t it be interesting to have children look at the moon every night for a month with their parents and draw a picture of what the moon looks like? What a meaningful way for families to do a little science together.
Facts for kids about the moon:
The moon goes around the earth.
The moon has no light, but it reflects the sun’s light.
The light of sun on the moon creates the different phases of the moon.
That’s why it looks different to us throughout the month.
It’s called a new moon when you can’t see it.
When the moon gets a little larger at night it’s called waxing.
A full moon is when it looks like a circle.
As the moon gets smaller it’s called waning.
The moon is always up in the sky, but during the day when the sun is bright you can’t see it.
Here’s a neat website where you can get a calendar of the moon’s phases and other learning activities:
http://stardate.org/nightsky/moon.
*Let one child pretend to be the earth and stand in the middle of the room. Let another child pretend to be the moon and circle the earth.
*What other things can you see in the sky? Take children outside and let them draw pictures of the things they see.
*Is there really a man in the moon? The moon has craters that make it look like a face.
Give children uncolored play dough and let them make a moon/pancake. Have them make craters in their moon with a pencil eraser or the end of a marker.
Here’s a book from Scholastic with the phases of the moon:
http://www.scholastic.com/parents/resources/free-printable/science-printables/minibook-moon-phases
Don’t forget to read two of my favorite books GOOD NIGHT, MOON, and HAPPY BIRTHDAY MOON.
## Saturday, October 12, 2019
### SCHOOL GLUE - JUST A LITTLE DOT WILL DO!
Just think if you were a little kid and you had never held a bottle of glue before. Wouldn’t it be fun to squeeze it all out? Sometimes we forget that children need directions on how to use school materials. Tell children, “We just need to use a baby dot of glue. Not a mama dot or papa dot. Just a tiny, little baby dot.” (Be dramatic with this and say “baby dot” in a high little voice.) Demonstrate how to put a dot on a sheet of paper. “What does that look like? A little bug? A cookie crumb?”
*Put food coloring in a bottle of glue and use it at a center for children to practice making “baby dots.”
If you use glue sticks, you will also need to demonstrate how to use them. “If you barely touch the page you can’t see anything. That means nothing will stick to it. Press it gently down and then look to make sure you can see something. That means your paper will stick.”
School Glue
(Tune: “This Old Man”)
School glue, school glue,
Just a little dot will do.
Put a dot and spread it around.
It will hold your paper down.
School glue, school glue,
Don’t use more than a dab or two.
When it dries up, it will disappear.
Your work will look good never fear.
Glue Ghosts
Someone taught me how to make these years ago and I wanted to pass on the idea to you. Children squirt glue in the shape of a ghost on wax paper. Add googly eyes and let dry overnight. When they are dry, peel off the wax paper, punch a hole, and tie on a string for a necklace. If you didn't want to make ghosts, they could do aliens or other creatures. My kids loved these!
## Friday, October 11, 2019
### THE DOT
If you've never read THE DOT by Peter Reynolds you can find out more about it by visiting www.thedotclub.org.
I think we’ve all had experiences similar to the child in the book where we think, “I can’t draw.” “I can’t sing.” “I can’t dance.” “I can’t do statistics.” “I’ll never be able to cook.” Etcetera, etcetera. The book is a beautiful lesson for children about just getting started and TRYING!
THE DOT also reminded me of some simple art activities we can do with our students. These activities are open-ended and can be used with any age or integrated with a unit of study.
Sticky Dot
Materials: sticky dots, paper, crayons or markers
Directions: Give each child a sheet of paper and a sticky dot. Ask them to place the dot anywhere they’d like on the paper. Next, challenge them to create something out of the dot.
Dot to Dot
Materials: 2 dice, paper, crayons
Directions: Children roll the dice and add up the dots. They take a black crayon and make that number of dots randomly on a sheet of paper. Can they connect the dots and create something out of it?
*Have children make dots and then exchange papers with a friend.
Negative Space
Materials: paper, scissors, markers or crayons
Directions: Cut a hole out of the middle of each sheet of paper. Ask children to look at the hole and then create an object out of it.
*Extend the activity by having children write about their pictures.
Wiggles and Squiggles
Materials: crayons, paper
Directions: Have the children close their eyes and make a design on their paper with a black crayon. When they open their eyes, have them turn their paper all around and try to create something out of their design.
*Have children exchange papers of wiggles and squiggles with a friend.
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# Problem Solving Maths Ks2
For example: Some children will know immediately that the question is asking 3 x 5, the answer to which is 15.Others may not see this immediately and will need to draw the three boxes and then perhaps write '5' on each one, then count in 5s to find the answer.Our National Curriculum based workshops are a great way to improve the image of maths in your school.
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Then, when children had worked on the problems for a while, the ones with the same set* came together to compare their ideas and mathematical strategies. See how this works for you, I’d love to read your comments.
* For easy reference, we named each set of problems after a gem-stone.
You may need to show them your own pictures to help them, but make it very clear that they don't have to do these problems in their head (unless they want to! Children will also come across problems involving multiplication and division.
By the time they sit their KS1 SATs, they should know their 2, 5 and 10 times tables off by heart (as well as all the corresponding division facts that go with them).
Badger’s highly acclaimed Problem Solving series is designed to help teachers support the increased emphasis on using and applying mathematic skills.
It supports the teaching of both problem-solving skills and strategies for Years 1 to 6. ’ series is aimed at Key Stage 2 teachers who want to challenge and inspire their class with word problems in maths.
For example, children might come across a problem like this one: They might choose to solve this by working out 80 - 50, in which case, they might want to draw 8 circles, each representing 10, and then cross off 5 of them: Alternatively, they might want to draw a number line and write 50p on the left hand side, then jump in tens until they get to 80p.
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Operating systems: XP, Vista, 7, 8, 10, 11
Concentration follies - when concentration value seems stupid
There are situations when results of concentrations calculations look either funny or suspicious. Two of them are described - and explained - below.
What is molality of 99% w/w acetic acid?
Using formula derived in the concentration conversion section we have
13.1
(the same result can be obtained much faster using concentration calculator).
Something must be wrong. 1649 seems to be just too large.
But it isn't.
Molality is a number of moles per 1 kilogram of solvent. In 99% w/w acetic acid there are only 10g of water in every kilogram of solution. Thus we need 100 kg of solution for 1 kg of water - that gives 99 kg of acetic acid, or 1649 moles.
If the acetic acid is treated as solvent and water as dissolved substance the same solution has much more 'normal' molality of 0.5607.
What is mass-volume percentage of 80% w/w sulfuric acid?
Let's start finding conversion equation.
Mass percentage is defined as
13.2
Mass-volume percentage is defined as
13.3
msubstance is mass in g, Vsolution is volume in mL.
We know that
13.4
putting it all together yields
13.5
80 % w/w sulfuric acid has a density of 1.7323 g/mL (check our density tables or use our concentration calculator).
Thus mass-volume percentage is 1.7323×80=138.58%
Absurd? Yes. But mass-volume percentage is faulty by definition.
(this is taken from CASC help)
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mersenneforum.org Brimstone for cracking RSA. (jk)
Register FAQ Search Today's Posts Mark Forums Read
2020-08-09, 20:11 #1 SarK0Y Jan 2010 2×43 Posts Brimstone for cracking RSA. (jk) Story of tails, windows and how it impacts integer factorization.. In other words, MILESTONE has been done :D From the very start of my journey to discover the innards of stubborn IF, the prime goal was to have developed binary-search-tree algos. At some point, it seemed utterly impossible. But here we go.. Actually, algo consists of three stages.. it picks initial (probable) Z’s (pZ_L and pZ_R) up (Z = P + Q, N = P*Q). So, now algo needs to guess which one is closest to original Z. for pZ_L, it generates N_L which is closest to N from left/right and the same way for N_R of pZ_R. for N_R/L, it collects statistics of bit windows against N (their positions, widths..).. Window(N, EntryPoint, Width) == NOT Window(N_L, EntryPoint, Width). For instance, let Window(N, EntryPoint, Width) == “010”, then Window(N_L, EntryPoint, Width) == “101”. And now it’s possible to choose probable Z according collected statistics for given iteration. For tests, RSA-150 (https://en.wikipedia.org/wiki/RSA_numbers#RSA-150) has been taken, criterion to go left/right is widths of greatest windows. Output… test mode gets activated Wrong turn @ 1 Wrong turn @ 2 Wrong turn @ 3 Wrong turn @ 4 Wrong turn @ 5 Wrong turn @ 6 Wrong turn @ 7 Wrong turn @ 8 Wrong turn @ 9 Wrong turn @ 10 Wrong turn @ 11 Wrong turn @ 12 Wrong turn @ 13 Wrong turn @ 14 Wrong turn @ 15 Wrong turn @ 16 Wrong turn @ 17 Wrong turn @ 18 Wrong turn @ 19 Wrong turn @ 20 Wrong turn @ 21 Wrong turn @ 22 Wrong turn @ 23 Wrong turn @ 24 Wrong turn @ 25 Wrong turn @ 26 Wrong turn @ 27 Wrong turn @ 28 Wrong turn @ 29 Wrong turn @ 30 Wrong turn @ 31 Wrong turn @ 32 Wrong turn @ 33 Wrong turn @ 34 Wrong turn @ 35 Wrong turn @ 36 Wrong turn @ 37 Wrong turn @ 38 Wrong turn @ 39 Wrong turn @ 40 Wrong turns == 40 nice turns == 208 Total iterations == 248 In short, algo doesn’t do gaps (good and bad turns ain’t shuffled/mixed) even with such rather primitive criterion. Archive: https:// sourceforge . net /projects/fastprimecruncher/Mod note URL intentionally broken. Sourceforge reports it as malware. Password for archive: ᬓꨒꛏ78🁶 Last fiddled with by Uncwilly on 2020-08-11 at 15:30 Reason: Broke the URL
2020-08-10, 04:21 #2 CRGreathouse Aug 2006 3×1,987 Posts Fantastic! Unfortunately, Aoki, Kida, Shimoyama, & Ueda already factored RSA-150, so it's not a good way to show that your method works. Could you demonstrate it with this smaller number, please? 3817396723515136582858035291731476702231874047478035390874743899933916107585885458479075057627686466112442032963859000272684225286856787555319737 I promise that it was (pseudo-)randomly generated* and that I've kept the factorization a secret (even from myself). This number isn't considered hard to factor, and so it won't of itself demonstrate a breakthrough, but it would make a better example. (Of course if you could factor such examples quickly enough it would suggest either collusion or a breakthrough, either in factorization or RNG cracking.) * Brent's XORGEN.
2020-08-10, 10:32 #3
SarK0Y
Jan 2010
5616 Posts
Quote:
Originally Posted by CRGreathouse Fantastic! Unfortunately, Aoki, Kida, Shimoyama, & Ueda already factored RSA-150, so it's not a good way to show that your method works. Could you demonstrate it with this smaller number, please? 3817396723515136582858035291731476702231874047478035390874743899933916107585885458479075057627686466112442032963859000272684225286856787555319737
for now, it's just a test mode, so it takes original P & Q
2020-08-10, 12:23 #4
Dr Sardonicus
Feb 2017
Nowhere
26×5×13 Posts
MODERATOR NOTE: Thread moved to Miscellaneous Math
Quote:
Originally Posted by SarK0Y for now, it's just a test mode, so it takes original P & Q
In other words, your "method" depends on already having the factors (P and Q).
Last fiddled with by Dr Sardonicus on 2020-08-10 at 12:23 Reason: xifnig posty
2020-08-10, 15:22 #5 CRGreathouse Aug 2006 3×1,987 Posts ...so the "MILESTONE" is that, if you know the factorization, you can find it again very quickly?
2020-08-10, 21:10 #6
ewmayer
2ω=0
Sep 2002
República de California
2×7×827 Posts
Quote:
Originally Posted by SarK0Y for now, it's just a test mode, so it takes original P & Q
Well golly, my own top-sekrit factoring method for RSA-style moduli has that beat by a mile. You see, given a semiprime n = p*q, I only need *one* of p or q in order to quickly produce the other prime factor.
2020-08-11, 01:08 #7 SarK0Y Jan 2010 8610 Posts strictly speaking, it's not an actual factorization method, it's test bench to expose possible vectors of attack to crack IF.. so, yes == it takes P & Q to collect info for new methods. why "MILESTONE"? :) for instance, the're no division and no modular arithmetic, thereby test bench is rather fast. In fact, we use modular arithmetic for pseudorandom numbers, so it provides too wobbly ground to construct useful criteria + big matrices ain't good for multi-threaded solutions. in short, current methods already approached its deadline by algorithmic limits & hw ones as well.
2020-08-11, 02:54 #8
CRGreathouse
Aug 2006
3×1,987 Posts
Quote:
Originally Posted by SarK0Y strictly speaking, it's not an actual factorization method, it's test bench to expose possible vectors of attack to crack IF.
Could you give an example of what such a vector would look like?
Quote:
Originally Posted by SarK0Y why "MILESTONE"? :) for instance, the're no division and no modular arithmetic, thereby test bench is rather fast.
Could you give an example of a similar algorithm that already does the same thing (or a comparable thing), but which uses heavier operations like division or modular arithmetic? (Not that those are particularly costly, but I digress.) It would help us understand what, exactly, you're trying to do.
Quote:
Originally Posted by SarK0Y In fact, we use modular arithmetic for pseudorandom numbers, so it provides too wobbly ground to construct useful criteria + big matrices ain't good for multi-threaded solutions.
Are you saying
1. That your algorithm uses modular arithmetic, in particular for the generation of pseudorandom numbers (but I thought you said it didn't use modular arithmetic?), or
2. That some algorithms for generating pseudorandom numbers use modular arithmetic, and your method, not using modular arithmetic, is superior (but how does your method compare to generating pseudorandom numbers? seems like apples and oranges, or am I missing something?)
And what is this about big matrices?
Quote:
Originally Posted by SarK0Y In short, current methods already approached its deadline by algorithmic limits & hw ones as well.
Current methods for what, exactly?
2020-08-11, 15:22 #9
Till
"Tilman Neumann"
Jan 2016
Germany
6448 Posts
Quote:
Originally Posted by SarK0Y Archive: https:// sourceforge . net /projects/fastprimecruncher/ Password for archive: ᬓꨒꛏ78������
Somebody here with a virtual machine at hand including virus and malware scanner wants to try to open it?
Last fiddled with by Uncwilly on 2020-08-11 at 15:32 Reason: Broke the URL
2020-08-11, 15:32 #10
Uncwilly
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
67·137 Posts
Quote:
Originally Posted by Till SourceForge says "Malware detected. Download at own risk."
Thanks for catching that. I broke the link. If someone want to get it they can do so with full knowledge.
2020-08-11, 15:57 #11
kruoli
"Oliver"
Sep 2017
Porta Westfalica, DE
1100101102 Posts
Quote:
Originally Posted by Till Somebody here with a virtual machine at hand including virus and malware scanner wants to try to open it?
The file contains:
Code:
.:
total 16K
drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 ..
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 FastPrimeCruncher
-rwxrwxrwx 1 oliver oliver 15K Aug 9 20:49 MILESTONE.odt
./FastPrimeCruncher:
total 160K
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 ..
drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 bin
-rwxrwxrwx 1 oliver oliver 23K Jul 25 22:20 BuildLog.txt
drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 .clang
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 .codelite
-rwxrwxrwx 1 oliver oliver 287 Aug 3 00:33 compile_commands.json
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 Debug
-rwxrwxrwx 1 oliver oliver 1.1K Jul 19 23:59 FastPrimeCruncher.cbp
-rwxrwxrwx 1 oliver oliver 176 Jul 20 00:53 FastPrimeCruncher.layout
-rwxrwxrwx 1 oliver oliver 4.2K Aug 8 18:26 FastPrimeCruncher.mk
-rwxrwxrwx 1 oliver oliver 4.7K Aug 5 19:42 FastPrimeCruncher.project
-rwxrwxrwx 1 oliver oliver 39 Aug 8 18:26 FastPrimeCruncher.txt
-rwxrwxrwx 1 oliver oliver 594 Aug 8 06:01 FastPrimeCruncher.workspace
-rwxrwxrwx 1 oliver oliver 165 Jul 19 23:56 FastPrimeCruncher.workspace.layout
-rwxrwxrwx 1 oliver oliver 45K Aug 8 18:26 gears.cpp
-rwxrwxrwx 1 oliver oliver 5.2K Aug 4 00:29 headers.h
-rwxrwxrwx 1 oliver oliver 5.7K Feb 20 2019 konsole1.txt
-rwxrwxrwx 1 oliver oliver 14K Feb 20 2019 konsole.txt
-rwxrwxrwx 1 oliver oliver 2.4K Feb 20 2019 main0.cpp
-rwxrwxrwx 1 oliver oliver 1.8K Feb 20 2019 main1.cpp
-rwxrwxrwx 1 oliver oliver 4.4K Aug 8 17:50 main.cpp
-rwxrwxrwx 1 oliver oliver 267 Aug 8 18:26 Makefile
-rwxrwxrwx 1 oliver oliver 1.7K Aug 8 23:55 milestone.txt
-rwxrwxrwx 1 oliver oliver 11K Jul 28 04:56 out.txt
-rwxrwxrwx 1 oliver oliver 18 Aug 8 23:39 pswd.txt
drwxrwxrwx 1 oliver oliver 4.0K Jul 25 22:19 Release
-rwxrwxrwx 1 oliver oliver 581 Aug 8 18:14 run.gdb
-rwxrwxrwx 1 oliver oliver 193 Feb 20 2019 txt.txt
./FastPrimeCruncher/bin:
total 0
drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 ..
drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:47 Debug
./FastPrimeCruncher/bin/Debug:
total 0
drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:47 .
drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 ..
./FastPrimeCruncher/.clang:
total 0
drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 ..
./FastPrimeCruncher/.codelite:
total 524K
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 ..
-rwxrwxrwx 1 oliver oliver 7.0K Aug 8 18:26 compilation.db
-rwxrwxrwx 1 oliver oliver 539 Jul 25 22:17 compile_commands.json
-rwxrwxrwx 1 oliver oliver 3.5K Aug 8 06:01 FastPrimeCruncher.session
-rwxrwxrwx 1 oliver oliver 300K Aug 8 18:26 FastPrimeCruncher.tags
-rwxrwxrwx 1 oliver oliver 156 Feb 20 2019 FastPrimeCruncher.workspace.someone
-rwxrwxrwx 1 oliver oliver 210K Aug 8 16:44 refactoring.db
-rwxrwxrwx 1 oliver oliver 3 Feb 20 2019 sftp-workspace-settings.conf
-rwxrwxrwx 1 oliver oliver 44 Feb 20 2019 subversion.conf
drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 tabgroups
-rwxrwxrwx 1 oliver oliver 142 Feb 20 2019 .tern-project
-rwxrwxrwx 1 oliver oliver 3 Feb 20 2019 tweaks.conf
-rwxrwxrwx 1 oliver oliver 0 Feb 20 2019 valgrind.memcheck.supp
./FastPrimeCruncher/.codelite/tabgroups:
total 0
drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 ..
./FastPrimeCruncher/Debug:
total 2.1M
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 ..
-rwxrwxrwx 1 oliver oliver 1 Aug 8 18:26 .d
-rwxrwxrwx 1 oliver oliver 594K Aug 8 18:26 FastPrimeCruncher
-rwxrwxrwx 1 oliver oliver 980K Aug 8 18:26 gears.cpp.o
-rwxrwxrwx 1 oliver oliver 50 Aug 8 18:26 gears.cpp.o.d
-rwxrwxrwx 1 oliver oliver 500K Aug 8 17:57 main.cpp.o
-rwxrwxrwx 1 oliver oliver 48 Aug 8 17:57 main.cpp.o.d
./FastPrimeCruncher/Release:
total 220K
drwxrwxrwx 1 oliver oliver 4.0K Jul 25 22:19 .
drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 ..
-rwxrwxrwx 1 oliver oliver 1 Jul 25 22:19 .d
-rwxrwxrwx 1 oliver oliver 73K Jul 25 22:19 FastPrimeCruncher
-rwxrwxrwx 1 oliver oliver 121K Jul 25 22:19 gears.cpp.o
-rwxrwxrwx 1 oliver oliver 53 Jul 25 22:19 gears.cpp.o.d
-rwxrwxrwx 1 oliver oliver 20K Jul 25 22:19 main.cpp.o
-rwxrwxrwx 1 oliver oliver 51 Jul 25 22:19 main.cpp.o.d
Similar Threads Thread Thread Starter Forum Replies Last Post Owl Miscellaneous Math 11 2021-01-01 01:26 jasong Soap Box 9 2013-03-17 03:28
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1 February, 06:40
# the average daily maximum temperature is 21.85 Celsius and the average daily minimum temperature is - 4.7 Celsius the average daily maximum temperature is
0
1. 1 February, 07:11
0
Hello.
To find the answer you will have to add them then divide by 2.
So if you add 21.85+-4.7 you will get the answer of 17.15.
Then divide by two to get 8.575
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SSG_Chapter9
# A describe the features of the sample which make it
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a) describe the features of the sample which make it unrepresentative b) describe the features of the sample which bias it Passage 8 According to a new poll, 80% of Canadians would vote for President Barack Obama, if they could vote in the upcoming US Presidential Election. 1. The scheme contained in the passage is ________. a) generalization b) polling c) general causal reasoning 2. Considering the scheme involved and the premises it requires, the weakest point in the argument is ________. a) the first premise (in which S is a sample of X s) b) the second premise (in which Proportion 1 of X s in S are Y ) c) the conclusion (in which Proportion 2 of X s are Y ) 3. Considering the weakest point in the argument, the most effective way to argue against it would be to ________. a) describe the features of the sample which make it unrepresentative b) describe the features of the sample which bias it
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# Create a java program to determine what integers of two, three, and four digits are equal to the sum of the cubes of their digits?
Printable View
• October 25th, 2013, 12:07 AM
namenamename
Create a java program to determine what integers of two, three, and four digits are equal to the sum of the cubes of their digits?
Code :
```import java.util.*; import java.io.*; class Cubesum { public static void main(String args[]){ int input=0; int num1,num2,num3; //read the number System.out.print("Enter a positive integer: "); Scanner console = new Scanner(System.in); input= Integer.parseInt(console.nextLine()); int number = input; //number is a temp variable int counter = 0; //counter is used to count no of digits while(number>0){ int t= number%10; counter += t * t * t; number = number/10; } System.out.println("The sum of the cubes of the digits is: "+counter); } }```
Output:
Enter a positive integer: 223
The sum of the cubes of the digits is: 43
I want to get this output from the program:
371 = 3³+7³+1³
How would I do it?
• October 25th, 2013, 03:10 AM
D.K
Re: Create a java program to determine what integers of two, three, and four digits are equal to the sum of the cubes of their digits?
You have the wrong formula.
Hint: you need to use the math class.
Another hint: Math.pow(num1, 3) //example
• October 25th, 2013, 06:31 AM
rodiongork
Re: Create a java program to determine what integers of two, three, and four digits are equal to the sum of the cubes of their digits?
Formula is quite all right. This code sample calculates sum of cubes of digits for a single number.
Now you need simply enclose this calculation in a loop which iterates "number" from 10 to 9999 and print only those numbers for which "counter" equals to "number".
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Select Page
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Puzzles no. 399–403
### Puzzles
Author: ExcelBI
All files (xlsx with puzzle and R with solution) for each and every puzzle are available on my Github. Enjoy.
### Puzzle #399
Today we have been given a list of random strings containing of certain number of letters duplicated. And our task is to count how many of each letters are there and present it as alphabetically pasted string. Sounds nice and it is nice. Let’s go.
```library(tidyverse)
input = read_excel("Excel/399 Counter Dictionary.xlsx", range = "A1:A10")
test = read_excel("Excel/399 Counter Dictionary.xlsx", range = "B1:B10")```
#### Transformation
```count_chars = function(string) {
chars = string %>%
str_split(., pattern = "") %>%
unlist() %>%
tibble(char = .) %>%
group_by(char) %>%
summarise(count = n()) %>%
ungroup() %>%
arrange(char) %>%
unite("char_count", c("char", "count"), sep = ":") %>%
pull(char_count) %>%
str_c(collapse = ", ")
return(chars)
}
result = input %>%
mutate(`Answer Expected` = map_chr(String, count_chars)) %>%
select(-String)```
#### Validation
```identical(result, test)
# [1] TRUE```
### Puzzle #400
Once again we are playing with coordinates and checking if they form one structure. But this time vertices are mixed and we have some more to do.
In this puzzle I will give you one surprise. Be patient.
```library(tidyverse)
input = read_excel("Excel/400 Connected Points_v2.xlsx", range = "A1:D8")
test = read_excel("Excel/400 Connected Points_v2.xlsx", range = "E1:E8")```
#### Transformation
```result = input %>%
mutate(row = row_number()) %>%
select(row, everything()) %>%
pivot_longer(-row, names_to = "col", values_to = "value") %>%
select(-col) %>%
na.omit() %>%
group_by(row) %>%
separate_rows(value, sep = ", ") %>%
group_by(row, value) %>%
summarise(n = n()) %>%
ungroup() %>%
select(-value) %>%
group_by(n, row) %>%
summarise(count = n()) %>%
ungroup() %>%
filter(n == 1) %>%
mutate(`Answer Expected` = ifelse(count == 2, "Yes", "No")) %>%
#### Validation
```identical(test, result)
# [1] TRUE```
#### Optimized version
I asked AI chat to optimize my code from above, because I don’t really like when my code is to long without a purpose. So I tried it, and that is really a surprise.
```result2 <- input %>%
mutate(`Answer Expected` = pmap_chr(., ~ {
unique_values <- na.omit(c(...))
if (length(unique(unique_values)) == 2) "Yes" else "No"
})) %>%
identical(test, result2)
# [1] TRUE```
### Puzzle #401
I am not using matrices in my daily work often, but I really like puzzles in which I can use them to solve. Today we have to form triangle from string. We have to bend it to size of matrix. Let’s try.
```library(tidyverse)
range = "A2:A2", col_names = F) %>% pull()
range = "A5:A5", col_names = F) %>% pull()
range = "A9:A9", col_names = F) %>% pull()
range = "A14:A14", col_names = F) %>% pull()
range = "A19:A19", col_names = F) %>% pull()
range = "C2:D3", col_names = F) %>% as.matrix(.)
dimnames(test1) = list(NULL, NULL)
range = "C5:D7",col_names = F) %>% as.matrix(.)
dimnames(test2) = list(NULL, NULL)
range = "C9:E12",col_names = F) %>% as.matrix(.)
dimnames(test3) = list(NULL, NULL)
range = "C14:F17", col_names = F) %>% as.matrix(.)
dimnames(test4) = list(NULL, NULL)
range = "C19:G23", col_names = F) %>% as.matrix(.)
dimnames(test5) = list(NULL, NULL)```
#### Transformation and validation
```triangle = function(string) {
chars = str_split(string, "") %>% unlist()
nchars = length(chars)
positions = tibble(row = 1:10) %>%
mutate(start = cumsum(c(1, row[-5])),
end = start + row - 1)
nrow = positions %>%
mutate(nrow = map2_dbl(start, end, ~ sum(.x <= nchars &
nchars <= .y))) %>%
filter(nrow == 1) %>%
pull(row)
M = matrix(NA, nrow = nrow, ncol = nrow)
for (i in 1:nrow) {
M[i, 1:i] = chars[positions\$start[i]:positions\$end[i]]
}
FM = M %>%
as_tibble() %>%
select(where( ~ !all(is.na(.)))) %>%
as.matrix()
dimnames(FM) = list(NULL, NULL)
return(FM)
}
identical(triangle(input1), test1) # TRUE
identical(triangle(input2), test2) # TRUE
identical(triangle(input3), test3) # TRUE
identical(triangle(input4), test4) # TRUE
identical(triangle(input5), test5) # TRUE```
### Puzzle #402
One of common topics in our series is of course cyphering. And today we have again some spy level puzzle. We have some phrase and keyword using which we need to code given phrase. Few weeks ago there was puzzle when lacking letters in keyword were taken from coded phrase. Today we are repeating key how many times we need. And there is one more detail, we have to handle spaces as well. Not so simple, but satisfying.
```library(tidyverse)
input = read_excel("Excel/402 Vignere Cipher.xlsx", range = "A1:B10")
test = read_excel("Excel/402 Vignere Cipher.xlsx", range = "C1:C10")```
#### Transformation
```code = function(plain_text, key) {
coding_df = tibble(letters = letters, numbers = 0:25)
plain_text_clean = plain_text %>%
str_remove_all(pattern = "s") %>%
str_split(pattern = "") %>%
unlist()
key = str_split(key, "") %>% unlist()
key_full = rep(key, length.out = length(plain_text_clean))
df = data.frame(plain_text = plain_text_clean, key = key_full) %>%
left_join(coding_df, by = c("plain_text" = "letters")) %>%
left_join(coding_df, by = c("key" = "letters")) %>%
mutate(coded = (numbers.x + numbers.y) %% 26) %>%
select(coded) %>%
left_join(coding_df, by = c("coded" = "numbers")) %>%
pull(letters)
words_starts = str_split(plain_text, " ") %>%
unlist() %>%
str_length()
words = list()
for (i in 1:length(words_starts)) {
if (i == 1) {
words[[i]] = paste(df[1:words_starts[i]], collapse = "")
} else {
words[[i]] = paste(df[(sum(words_starts[1:(i-1)])+1):(sum(words_starts[1:i]))], collapse = "")
}
}
words = unlist(words) %>% str_c(collapse = " ")
return(words)
}
result = input %>%
mutate(`Answer Expected` = map2_chr(`Plain Text`, Keyword, code))```
#### Validation
```identical(result\$`Answer Expected`, test\$`Answer Expected`)
# [1] TRUE```
### Puzzle #403
We are summarizing some values into year brackets. Usually you do it using crosstab. And our job today is to make crosstab that is not excel crosstab, but should work like it. From R side usually you have to make pivot, but I didn’t. So we have pivot table (another word for crosstab), without using pivot neither in R nor in Excel. How? Look on it.
```library(tidyverse)
input = read_excel("Excel/403 Generate Pivot Table.xlsx", range = "A1:B100")
test = read_excel("Excel/403 Generate Pivot Table.xlsx", range = "D2:F9")```
#### Transformation
```result = input %>%
add_row(Year = 2024, Value = 0) %>% ## just to have proper year range at the end
mutate(group = cut(Year, breaks = seq(1989, 2024, 5), labels = FALSE, include.lowest = TRUE)) %>%
group_by(group) %>%
summarize(Year = paste0(min(Year), "-", max(Year)),
`Sum of Value` = sum(Value)) %>%
ungroup() %>%
mutate(`% of Value` = `Sum of Value`/sum(`Sum of Value`)) %>%
select(-group)```
#### Validation
```identical(result, test)
# [1] TRUE```
Feel free to comment, share and contact me with advices, questions and your ideas how to improve anything. Contact me on Linkedin if you wish as well.
R Solution for Excel Puzzles was originally published in Numbers around us on Medium, where people are continuing the conversation by highlighting and responding to this story.
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Continue reading: R Solution for Excel Puzzles
## Analysis
In this text, the author challenges the reader with multiple puzzles. These puzzles are a testament to the flexibility and efficiency of the R programming language, which is used to solve each problem. The incorporation of the tidyverse and readxl libraries into the solutions further showcase the power of R. The problems touch on data processing in different forms: string manipulation, coordinate transformation, matrix generation, cipher creation, and pivot table creation.
## Long-term Implications
The author demonstrates how R can be leveraged for data manipulation of various types, which provides insights into its potential uses for other data-related applications in the future. This includes data analysis, visualisation, machine learning, and modeling, with the possibility of extending R’s capabilities with libraries like tidyverse and readxl. This implies that learning and utilising R can be essential for analysts, data scientists and even business officials who engage with data regularly.
## Possible Future Developments
The R programming language will likely continue to evolve, with more powerful and efficient libraries being developed. These will likely improve the language’s data pre-processing functionalities further, making it an even more potent analytic instrument. As more individuals becomes aware and learn R, a possible future development could be the provision of simpler interface for R that allows even non-programmers to execute complex data manipulations.
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- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(g(X)) -> g(f(f(X))) [2] f(h(X)) -> h(g(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(g(X)) >= g(f(f(X))) ; f(h(X)) >= h(g(X)) ; Marked_f(g(X)) >= Marked_f(f(X)) ; Marked_f(g(X)) >= Marked_f(X) ; } + Disjunctions:{ { Marked_f(g(X)) > Marked_f(f(X)) ; } { Marked_f(g(X)) > Marked_f(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: f(g(X)) >= g(f(f(X))) constraint: f(h(X)) >= h(g(X)) constraint: Marked_f(g(X)) >= Marked_f(f(X)) constraint: Marked_f(g(X)) >= Marked_f(X) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(g(X)) -> g(f(f(X))) [2] f(h(X)) -> h(g(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ g ] (X0) = 2 + 2*X0 + 0; [ h ] (X0) = 0; [ f ] (X0) = 1*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; ]} ]} ]} Cime worked for 0.019474 seconds (real time) Cime Exit Status: 0
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Simple maths but i don't understand why (about recurring decimals or repeating)
Main Question or Discussion Point
Simple maths but i don't understand why (about recurring/repeating decimals)
When calculating recurring decimals, we let X to be that number to calculate it for example:
0.4* = x
4.4* = 10x
10x - x = 4.4* - 4*
9x = 4
x = 4/9
Therefore 0.4* = 4/9
But I when I calculate 0.9* this, i get
0.9* = X
9.9* = 10X
10X - X = 9.9* - 0.9*
9X = 9
X = 1
Therefore 0.9* = 1
but we know that 0.9* = 0.999999999............................. is close to 1 and not equal to 1
but how can we prove 0.9* is not equal to 1?
Last edited:
We can't because it IS equal to 1. Search for other threads like this on this forum, there have been a ton of them.
donaldcat said:
When calculating recurring decimals, we let X to be that number to calculate it for example:
0.4* = x
4.4* = 10x
10x - x = 4.4* - 4*
9x = 4
x = 4/9
Therefore 0.4* = 4/9
But I when I calculate 0.9* this, i get
0.9* = X
9.9* = 10X
10X - X = 9.9* - 0.9*
9X = 9
X = 1
Therefore 0.9* = 1
but we know that 0.9* = 0.999999999............................. is close to 1 and not equal to 1
but how can we prove 0.9* is not equal to 1?
The value 0.9* does not have any real meaning. Infinite numbers are irrelevant to mathematics as we can only deal with rational numbers (that are certain time approximation of irrational numbers). Letting this aside, 0.9* can be interpreted as the limit of a the geometrical sum:
9*(1/10) + 9*(1/10)^2 ...9*(1/10)^n
As n increases beyond all bounds (thus creating an "infinite" number). The limit is in fact 1.
Werg22 said:
The value 0.9* does not have any real meaning. Infinite numbers are irrelevant to mathematics as we can only deal with rational numbers (that are certain time approximation of irrational numbers). Letting this aside, 0.9* can be interpreted as the limit of a the geometrical sum:
What? Infinite numbers seem, to me at least, to definitely be relavent to mathematics, and are you seriously saying that we only deal with rational numbers? Are pi and e rational?
d_leet said:
What? Infinite numbers seem, to me at least, to definitely be relavent to mathematics, and are you seriously saying that we only deal with rational numbers? Are pi and e rational?
PI and e aren't rational, but we can only work with rational approximations. But the concept of "infinity" has no real meaning in mathematics. 0.9* dosen't mean anything if you don't take it as the previously mentionned limit.
Werg22 said:
PI and e aren't rational, but we can only work with rational approximations.
Yeah, but how often when working a calculus problem let's say do you really work with 3.14, or 2.718 instead of just calling it pi or e and having an exact answer?
Werg22 said:
But the concept of "infinity" has no real meaning in mathematics. 0.9* dosen't mean anything if you don't take it as the previously mentionned limit.
Would you care to explain this a little more in depth?
There is no single awnser. For example, the function 1/x has irrational values of rational x, but its integral from 1 to x will give an exact awnser for x = e^a.
Werg22 said:
There is no single awnser. For example, the function 1/x has irrational values of rational x, but its integral from 1 to x will give an exact awnser for x = e^a.
d_leet said:
Would you care to explain this a little more in depth?
How to explain? Mathematics has roots in the study of nature. From that point of view, we can only deal with rational approximations. 0.9* is simply another notation for:
C = 9(1/10) + 9(1/10)^2... 9(1/10)^n
Where C is always closer to reality as n grows. Thus the notation 0.9* for a value that C is never equal to, but always closer to it. It can also be written;
C = B + a
Where B = 1, and a can be as close to 0 as we wish, as long as n is big enough. Finally, the value 0.9* is thus equal to 1, since 1 is the value that "C is never equal to, but always closer to it".
d_leet said:
How often cannot be awnsered in mathematics :tongue:
An exact awnser will only occur if two inverse operations, involving e or pi, are made. For logs, trig and roots operations such as addition and multiplication can give a rational number (example: 3^1/2 * 3^1/2).
Werg22 said:
How to explain? Mathematics has roots in the study of nature. From that point of view, we can only deal with rational approximations. 0.9* is simply another notation for:
Ok. But that's a very experimentalist view in my opinion, and I will say again that we often deal with pi and e in problems and proofs as just that and take those to represent the irrational number.
Werg22 said:
C = 9(1/10) + 9(1/10)^2... 9(1/10)^n
Where C is always closer to reality as n grows. Thus the notation 0.9* for a value that C is never equal to, but always closer to it. It can also be written;
C = B + a
Where B = 1, and a can be as close to 0 as we wish, as long as n is big enough. Finally, the value 0.9* is thus equal to 1, since 1 is the value that "C is never equal to, but always closer to it".
I understand exactly why .999... is equal to 1 so you don't need to explain this to me or convince me of this fact, but the work you have here makes little sense and is certainly not rigorous. And the way you set this up makes it seem that you should have
C + a = B where B is 1 and a is as close to zero as you would like depending on the value of n using the above.
Werg22 said:
How often cannot be awnsered in mathematics :tongue:
An exact awnser will only occur if two inverse operations, involving e or pi, are made. For logs, trig and roots operations such as addition and multiplication can give a rational number (example: 3^1/2 * 3^1/2).
Give me more credit than that
I know how we can obtain exact answers using operations similar to those above, my question was asking you to justify your claim that infinite numbers are irrelevant to mathematics.
For your comment on how e an pi are used in proofs and problems, I would never go against that. But my point is e an pi are merely notations, when dealing with real data we can only use rational numbers. For the
C = 1 + a
What I meant to say is that, if a = a(x)
0<a(n+1) < a(n)
Also for how infinite numbers are irrelevant: they're not irrelevant as if they don't exist, they're irrelevant as in they are only notations of a limit. The dealing of infinity in mathematics only has a meaning when we look at the limit of the expressions.
Last edited:
Werg22 said:
For your comment on how e an pi are used in proofs and problems, I would never go against that. But my point is e an pi are merely notations, when dealing with real data we can only use rational numbers.
Again I agree with this, but I would think that in most cases when working specifically in pure mathematics the data is unlikely to be so experimental in nature that it is approximated by rational numbers.
Werg22 said:
C = 1 + a
What I meant to say is that, if a = a(x)
0<a(n+1) < a(n)
I understand what you mean, but the way you defined C makes it trivially less than 1 for all n and so I still think it should be
C + a = 1.
Werg22 said:
Also for how infinite numbers are irrelevant: their not irrelevant as if they don't exist, they're irrelevant as in they are only notations of a limit. The dealing of infinity in mathematics only has a meaning when we look at the limit of the expressions.
Ok that makes sense and I will agree with you on that for the most part.
Pardon my mistake on a, it should be
0 < |a(n+1)| < |a(n)|
Just consider my a to be negative
Sorry for the confusion.
Werg22 said:
Pardon my mistake on a, it should be
0 < |a(n+1)| < |a(n)|
Just consider my a to be negative
Sorry for the confusion.
Ok now that makes a lot more sense, sorry about that, and thanks for clearing that up.
uart
OK Werg22, lets assume that irrational numbers dont exist and then look at the problem of finding the zeros of the equation f(x) = x^2 + x - 1.
Assume that x can be written as p/q, where p and q have no common factors. This gives,
p^2/q^2 + p/q = 1
Multiply throughout by q and rearrange to get,
p^2/q = q - p
Notice that the RHS is an integer. This implies that q must be +/- 1, other wise LHS cannot be an integer.
Now take the original equation and multiply throughout by q^2/p. This gives,
q^2/p = p + q
Again the RHS is clearly an integer and so p must be equal to +/- 1, otherwist the LHS cannot be integer.
So what is our conclusion, if the original equation has any solution then it can only be +/-1. Sadly however you can easily verify that neither +1 or -1 is a solution to f(x)=0, so we'd have to conclude that the equation has no solutions! But f(0)=-1 and f(1)=+1, hence the function has to pass though zero somewhere in between. So we have a clear contradiction! You cant just ignore irrational numbers or you'll end up with all sorts of contradictions like this.
Hurkyl
Staff Emeritus
Gold Member
Sigh, I miss PF for a couple days, and my punishment is to have to clean up one of these messes.
donaldcat said:
but we know that 0.9* = 0.999999999............................. is close to 1 and not equal to 1
but how can we prove 0.9* is not equal to 1?
What you "know" is wrong. The decimal number system is defined so that 0.9* = 1, and calculations like the one you performed are the reasons such a definition was chosen.
Werg22 said:
The value 0.9* does not have any real meaning.
...
0.9* can be interpreted as the limit ... The limit is in fact 1.
Unless your arguing that 1 does not have any real meaning either, this contradiction sums up the primary objection I have to your posts.
0.9* is the notation for a decimal number. That decimal number has no more and no less meaning than any other decimal number. 1 just happens to be another notation for that same decimal number.
The secondary objection is that mathematics is a much, much broader subject than the study of the arithmetic of terminating decimal expansions. There is absolutely no trouble with working with numbers like pi or e in their exact form, even to a staunch constructivist.
Mathematics has roots in the study of nature.
A tertiary objection is that nature is full of irrational numbers. So, they better have some meaning, even if we can only approximate them. (As an aside, note that most rational numbers don't even have terminating decimal expansions)
Furthermore, approximating things with terminating decimals is a convenient course of action for scientific pursuits... not a necessary one. There is absolutely no reason at all why we couldn't approximate measured quantities with irrational values.
0.9* is simply another notation for:
C = 9(1/10) + 9(1/10)^2... 9(1/10)^n
Where C is always closer to reality as n grows.
And as a quaternary objection (I love that word), this is IMHO one of the most common fallacies that prevent a person from understanding decimal notation. :grumpy: 0.9* is a notation for one particular number... it is not some ambiguous number with an unspecified, but finite number of 9's. "0.9...9 (n 9's)" is a correct alternative notation for your C. 0.9* is not.
And, to be precise, you should write something like C(n), to express the fact that what you've written is a function of n.
Last edited:
HallsofIvy
Homework Helper
Werg22 said:
PI and e aren't rational, but we can only work with rational approximations. But the concept of "infinity" has no real meaning in mathematics. 0.9* dosen't mean anything if you don't take it as the previously mentionned limit.
No, that's not at all true. A person who has actually studied some "higher" mathematics ("Calculus and Beyond") can work very easily with $\pi$ and e- as easily as with $\sqrt{2}$, notapproximations. "0.9* dosen't mean anything if you don't take it as the previously mentionned limit" is very misleading since 0.999... is the "previously mentioned limit" by definition of the decimal numeral system. Would you say "2 doesn't mean anything unless you take it to be 1+ 1"?
Last edited by a moderator:
HallsofIvy
Homework Helper
Werg22 said:
How to explain? Mathematics has roots in the study of nature. From that point of view, we can only deal with rational approximations. 0.9* is simply another notation for:
C = 9(1/10) + 9(1/10)^2... 9(1/10)^n
Where C is always closer to reality as n grows. Thus the notation 0.9* for a value that C is never equal to, but always closer to it. It can also be written;
C = B + a
Where B = 1, and a can be as close to 0 as we wish, as long as n is big enough. Finally, the value 0.9* is thus equal to 1, since 1 is the value that "C is never equal to, but always closer to it".
This is absolute nonsense! I think we have another physicist trying to explain mathematics.
HallsofIvy
Homework Helper
Werg22 said:
There is no single awnser. For example, the function 1/x has irrational values of rational x, but its integral from 1 to x will give an exact awnser for x = e^a.
Can you give one example of a rational value of x such that 1/x is irrational?
HallsofIvy
Homework Helper
Werg22 said:
For your comment on how e an pi are used in proofs and problems, I would never go against that. But my point is e an pi are merely notations, when dealing with real data we can only use rational numbers. For the
C = 1 + a
What I meant to say is that, if a = a(x)
0<a(n+1) < a(n)
Also for how infinite numbers are irrelevant: they're not irrelevant as if they don't exist, they're irrelevant as in they are only notations of a limit. The dealing of infinity in mathematics only has a meaning when we look at the limit of the expressions.
Your use of the term "real data" makes it clear that you are not talking about mathematics.
Did anybody above catch his simple error? ".4 =x, 4.4 =10X" is wrong. It's 10x=4. Thus its 9X=3.6 and X=.4, just where we started!
robert Ihnot said:
Did anybody above catch his simple error? ".4 =x, 4.4 =10X" is wrong. It's 10x=4. Thus its 9X=3.6 and X=.4, just where we started!
Huh? He uses .4* representing .444444444.... with fours repeating forever, so I don't see a mistake unless I'm missing your point.
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In practice, what's the fastest method to find a least square solution rather than using SVD decompostion?
I'm working on a real-time implementation of Lucas-Kanade for optical flow. However, the SVD decomposition to do achieve the least square method to reduce the error seems to take too much time.
A brief explanation of the algorithm can be accessed here Lucas Kanade algorithm
• One might try using conjugate gradients in the case computing matrix factorizations like the SVD for one's problem is too computationally involving. This being said the computational complexity for each of these methods is in general $O(N^3)$. Oct 29, 2018 at 11:55
• I would recommend to try qr-factorization e.g. by using Gram-Schmidt orthogonalization. Oct 29, 2018 at 21:29
• @user35593 Why GS instead of Householder? Nov 28, 2018 at 23:52
In practice, the fastest direct method is normal equations $$A^TAx=A^Tb$$ + exploiting symmetry to compute $$A^TA$$ + Cholesky to solve the resulting linear system. It scales like $$mn^2 + o(mn^2)$$ for an $$m\times n$$ matrix $$A$$ with $$m\gg n$$, when most other algorithms cost $$2mn^2$$, and it is faster even in the case $$m\approx n$$. However, it may be dramatically unstable, especially if the value of that minimum norm is small.
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Home > Standard Error > Calculation Of Standard Error From Standard Deviation
# Calculation Of Standard Error From Standard Deviation
## Contents
R code to accompany Real-World Machine Learning (Chapter 2) GoodReads: Machine Learning (Part 3) One Way Analysis of Variance Exercises Most visited articles of the week How to write the first Larger sample sizes give smaller standard errors As would be expected, larger sample sizes give smaller standard errors. The sample mean will very rarely be equal to the population mean. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. http://bestwwws.com/standard-error/calculating-standard-error-without-standard-deviation.php
The researchers report that candidate A is expected to receive 52% of the final vote, with a margin of error of 2%. Steps Cheat Sheets Mean Cheat Sheet Standard Deviation Cheat Sheet Standard Error Cheat Sheet Method 1 The Data 1 Obtain a set of numbers you wish to analyze. Standard Error of the Estimate A related and similar concept to standard error of the mean is the standard error of the estimate. For the purpose of this example, the 9,732 runners who completed the 2012 run are the entire population of interest.
## Standard Error Example
Confidence intervals for means can also be used to calculate standard deviations. For illustration, the graph below shows the distribution of the sample means for 20,000 samples, where each sample is of size n=16. As an example, consider an experiment that measures the speed of sound in a material along the three directions (along x, y and z coordinates).
Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time. If the sample size is small (say less than 60 in each group) then confidence intervals should have been calculated using a value from a t distribution. ISBN 0-8493-2479-3 p. 626 ^ a b Dietz, David; Barr, Christopher; Çetinkaya-Rundel, Mine (2012), OpenIntro Statistics (Second ed.), openintro.org ^ T.P. Calculate Standard Error From Standard Deviation In Excel Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for
Wilson Mizner: "If you steal from one author it's plagiarism; if you steal from many it's research." Don't steal, do research. . How To Find Standard Error In Statistics doi:10.4103/2229-3485.100662. ^ Isserlis, L. (1918). "On the value of a mean as calculated from a sample". n is the size (number of observations) of the sample. http://stats.stackexchange.com/questions/15505/converting-standard-error-to-standard-deviation See unbiased estimation of standard deviation for further discussion.
For example if the 95% confidence intervals around the estimated fish sizes under Treatment A do not cross the estimated mean fish size under Treatment B then fish sizes are significantly Calculate Confidence Interval Standard Deviation The distribution of the mean age in all possible samples is called the sampling distribution of the mean. Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } The means of samples of size n, randomly drawn from a normally distributed source population, belong to a normally distributed sampling distribution whose overall mean is equal to the mean of
## How To Find Standard Error In Statistics
It can only be calculated if the mean is a non-zero value. The sample standard deviation s = 10.23 is greater than the true population standard deviation σ = 9.27 years. Standard Error Example Recent popular posts ggplot2 2.2.0 coming soon! Standard Error Formula As a result, we need to use a distribution that takes into account that spread of possible σ's.
Video How and why to calculate the standard error of the mean. http://bestwwws.com/standard-error/calculate-standard-deviation-from-standard-error-of-mean.php National Center for Health Statistics typically does not report an estimated mean if its relative standard error exceeds 30%. (NCHS also typically requires at least 30 observations – if not more By using this site, you agree to the Terms of Use and Privacy Policy. Bence (1995) Analysis of short time series: Correcting for autocorrelation. Standard Error Equation
Show more unanswered questions Ask a Question Submit Already answered Not a question Bad question Other If this question (or a similar one) is answered twice in this section, please click All the R Ladies One Way Analysis of Variance Exercises GoodReads: Machine Learning (Part 3) Danger, Caution H2O steam is very hot!! American Statistician. More about the author Sokal and Rohlf (1981)[7] give an equation of the correction factor for small samples ofn<20.
This often leads to confusion about their interchangeability. Calculate Variance Standard Deviation Standard error of the mean It is a measure of how precise is our estimate of the mean. #computation of the standard error of the mean sem<-sd(x)/sqrt(length(x)) #95% confidence intervals of Standard error of mean versus standard deviation In scientific and technical literature, experimental data are often summarized either using the mean and standard deviation or the mean with the standard error.
## Did this article help you?
A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample. The sample proportion of 52% is an estimate of the true proportion who will vote for candidate A in the actual election. The unbiased standard error plots as the ρ=0 diagonal line with log-log slope -½. Calculate Median Standard Deviation Standard error of the mean This section will focus on the standard error of the mean.
Download Explorable Now! A natural way to describe the variation of these sample means around the true population mean is the standard deviation of the distribution of the sample means. Community Q&A Search Add New Question How do you find the mean given number of observations? http://bestwwws.com/standard-error/calculate-standard-deviation-standard-error.php Get All Content From Explorable All Courses From Explorable Get All Courses Ready To Be Printed Get Printable Format Use It Anywhere While Travelling Get Offline Access For Laptops and
They may be used to calculate confidence intervals. R+H2O for marketing campaign modeling Watch: Highlights of the Microsoft Data Science Summit A simple workflow for deep learning gcbd 0.2.6 RcppCNPy 0.2.6 Using R to detect fraud at 1 million JSTOR2682923. ^ Sokal and Rohlf (1981) Biometry: Principles and Practice of Statistics in Biological Research , 2nd ed. Review authors should look for evidence of which one, and might use a t distribution if in doubt.
The standard error estimated using the sample standard deviation is 2.56. The larger the sample, the smaller the standard error, and the closer the sample mean approximates the population mean. Journal of the Royal Statistical Society. Follow us!
ISBN 0-7167-1254-7 , p 53 ^ Barde, M. (2012). "What to use to express the variability of data: Standard deviation or standard error of mean?". This is a sampling distribution. Similar Worksheets Calculate Standard Deviation from Standard Error How to Calculate Standard Deviation from Probability & Samples Worksheet for how to Calculate Antilog Worksheet for how to Calculate Permutations nPr and The graph below shows the distribution of the sample means for 20,000 samples, where each sample is of size n=16.
Answer this question Flag as... Notice that s x ¯ = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} is only an estimate of the true standard error, σ x ¯ = σ n If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of the true standard error of
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# physics
posted by .
two student walk in the same direction along a straight path, at a constant speed one at 0.90m/s and the other at 1.90m/s assuming that they start at the same point and the same time, how much sooner does the faster student arrive at a destination 780m away?
## Similar Questions
1. ### physics
This is a two-part question, and I got the first part, but I do not know how to do the second part. Two students walk in the same direction along a straight path, at a constant speed- one at 0.90 m/s and the other at 1.90 m/s. a) Assuming …
2. ### Physics (When will Kathy overtake Stan if )
Kathy has a sports car that can accelerate at the rate of 4.90m/s^2. She races with Stan. Both cars start from rest but experienced Stan leaves starting line 1.00s before her. Stan moves with a constant aceleration of 3.90m/s^2 and …
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When baseball outfielders throw the ball, they usually allow it to take one bounce on the theory that the ball arrives sooner this way. Suppose that after the bounce the ball rebounds at the same angle theta as it had when released, …
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7)A car is moving with a uniform speed of 15.0 m/s along a straight path. What is the distance covered by the car in 12.0 minutes?
5. ### Physics
Two students walk in the same direction along a straight path, at a constant speed - one at .90 m/s and the other at 1.90 m/s. a.) assuming that they start at the same point ant the same time, how much sooner does the faster arrive …
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Two cars travel westward along a straight highway, one at a constant velocity of 85 km/hr, and the other at a constant velocity of 115 km/hr. a) Sketch the velocity vs. time graph for both cars and paste your sketch in the space below. …
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Four race car drivers participate in a race on a loop track. All four are going at a constant speed. Assume that they did a flying start. That is, all four crossed the start line at the same instant while each was going their constant …
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Two walkers set off at the same time from a crossroad and walk along flat straight roads inclined to each other at 68 degrees.If they both walk at a speed of 6km/h,find their distance apart 10 minutes later.
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How tall is 5 ft 5 in centimeters? How high is 5 foot 5? Use this easy calculator to convert feet and inches to centimeters. Height Conversion Centimeters to Feet and Inches - The Short In my articles I sometimes refer to cm and meter, but other times I refer to feet and inches when talking about height or any other measurements. However I try always to include both feet + inches and cm or vice versa. If I forget to do that you might refer to the conversion chart chart below.
## A woman who is 5 feet and 4 inches tall (163 cm), should have a waist measurement below 32 inches (81 cm). A man who is 6 feet or 183 centimeters (cm) tall, should have a waist measurement below
Jan 14, 2016 · What’s my height measurement in feet and inches? Don’t know your height measurement in feet and inches?Don’t worry! You’re not alone. Just earlier today someone asked me what his height would be in feet and inches and he gave me his height in centimeters. Body length - body height - size and length - feet - inches The height of an average South American male is 165.5 cm, or a little over 5 foot five inches. The average female is 153 cm, or just over five feet. The height of the average North American male is 175.5 centimeters, a little over 5 foot 9 inches. Feet To Metres The converter above allows you to quickly convert between feet and inches and metres and centimetres when you need to find out your height in metres and centimetres. Just type your height into the feet and inches boxes to convert to metres or into the metres box to convert to feet and inches. Height Converter | Convert cm, feet & inches Height conversion Feet to Inches conversion. One feet is equal to 12 inches: 1ft = 12″ Inches to centimeters conversion. One inch is equal to 2.54 centimeters: 1″ = 2.54cm. Centimeters to meters conversion. One centimeter is equal to 0.01 meter: 1cm = 0.01m. One meter is equal to 100 centimeters: 1m = 100cm. Height conversion table
Have your desired Height of 5 feet 9 (175 cm) | Subliminal Feb 01, 2018 · All parts of my body are aligning perfectly proportional and are adjusting to my desired height of 175 cm. I am adjusting my height to 5’9 faster and faster. I am now adjusting my height to 175 How Much Should I Weigh for My Height? Jun 03, 2018 · What is the ideal weight-to-height ratio? How much should I weigh for my height? What is body mass index (BMI), and how it is calculated? Given here are the answers to all your height-related queries. How tall should my desk be? Correct desk height for better
If my height is 178cm , then am I 6 feet or 5 feet 10 inches Formula : inch to cm Ans : Multiply your length value by 2.54. One inch is equal to roughly 2.54 centimeters, so converting inches to centimeters means multiplying a value in inches by 2.54 5 feet 0 inches = 152.40 centimeters 5 feet 1 inches = 15 Have your desired Height of 5 feet 9 (175 cm) | Subliminal Feb 01, 2018 · All parts of my body are aligning perfectly proportional and are adjusting to my desired height of 175 cm. I am adjusting my height to 5’9 faster and faster. I am now adjusting my height to 175 How Much Should I Weigh for My Height? Jun 03, 2018 · What is the ideal weight-to-height ratio? How much should I weigh for my height? What is body mass index (BMI), and how it is calculated? Given here are the answers to all your height-related queries. How tall should my desk be? Correct desk height for better
## 2,925 Views · If my height is 178cm , then am I 6 feet or 5 feet 10 inches? So 157 centimeters divided by 5.15 feet would equal to 30.48centimeters. 5.15 feet is
Height Calculator - Calculator.net
### 162 Centimeters = 5 Feet, 3.7795 Inches. (rounded to 5 digits). Click here for the opposite calculation. Height Conversion Table. (some results rounded)
25 Nov 2019 You could also use the BMI calculator to find out if you are in the ideal weight category. You can convert your height from centimeters to feet Short stature - Wikipedia Short stature refers to a height of a human being which is below typical. Whether a person is. During World War I in Britain, the minimum height for soldiers was 5 feet 3 inches (160 cm). Thus thousands of men under this height were denied Is 176 cm / 5.9 foot normal for a guy? - The Student Room Trust me, that is normal height. I am shorter than all of my mates, and pretty much every girl/woman I meet and pretty much everyone I work with as well. I'm even BMI Calculator - BCBST.com Calculate BMI using feet/inches & pounds: Enter Height: Feet. and, Inches. Enter Weight: Pounds. (Please note: 8 ounces (Please note: 1 Meter = 100 cm).
What Size Bike Should I Get for My Height? | ApexBikes
How to convert my height (5'8") into centimeters? | Yahoo Answers Sep 28, 2013 · Move to a country that uses the metric system, and let your doctor worry about converting it. (Since there are only three countries that don't use metric, it should be easy to find one that does.) what is my height in feet i am 1.75cm? | Yahoo Answers Apr 17, 2014 · I think you mean that you are 175 cm (or 1.75 m). In feet and inches, you are nearly 5ft. 9in. tall. This is a bit above average height for women in the US, but not by much. Height Converter - Convert height in feet-inches to
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# Discussion 2: Environment Diagrams, Higher-Order Functions disc02.pdf
This is an online worksheet that you can work on during discussions. Your work is not graded and you do not need to submit anything.
Note on web discussions: In order to use the environment diagrams on the site, please log in using the account you use for Okpy.
# Call Expressions
Call expressions, such as `square(2)`, apply functions to arguments. When executing call expressions, we create a new frame in our diagram to keep track of local variables:
1. Evaluate the operator, which should evaluate to a function.
2. Evaluate the operands from left to right.
3. Draw a new frame, labelling it with the following:
• A unique index (`f1`, `f2`, `f3`, ...).
• The intrinsic name of the function, which is the name of the function object itself. For example, if the function object is `func square(x) [parent=Global]`, the intrinsic name is `square`.
• The parent frame ([`parent=Global`]).
4. Bind the formal parameters to the argument values obtained in step 2 (e.g. bind `x` to 3).
5. Evaluate the body of the function in this new frame until a return value is obtained. Write down the return value in the frame.
If a function does not have a return value, it implicitly returns `None`. In that case, the “Return value” box should contain `None`.
Note: Since we do not know how built-in functions like `min(...)` or imported functions like `add(...)` are implemented, we do not draw a new frame when we call them, since we would not be able to fill it out accurately.
### Q1: Call Diagram
Let’s put it all together! Draw an environment diagram for the following code. You may not have to use all of the blanks provided to you.
``````def double(x):
return x * 2
hmmm = double
wow = double(3)
hmmm(wow)``````
Objects
Global frame
f1: [parent=]
Return value
f2: [parent=]
Return value
### Q2: Nested Calls Diagrams
Draw the environment diagram that results from executing the code below. You may not need to use all of the frames and blanks provided to you.
``````def f(x):
return x
def g(x, y):
if x(y):
return not y
return y
x = 3
x = g(f, x)
f = g(f, 0)``````
Objects
Global frame
f1: [parent=]
Return value
f2: [parent=]
Return value
f3: [parent=]
Return value
f4: [parent=]
Return value
# Lambda Expressions
A lambda expression evaluates to a function, called a lambda function. For example, `lambda y: x + y` is a lambda expression, and can be read as "a function that takes in one parameter `y` and returns `x + y`."
A lambda expression by itself evaluates to a function but does not bind it to a name. Also note that the return expression of this function is not evaluated until the lambda is called. This is similar to how defining a new function using a def statement does not execute the function’s body until it is later called.
``````>>> what = lambda x : x + 5
>>> what
<function <lambda> at 0xf3f490>``````
Unlike `def` statements, lambda expressions can be used as an operator or an operand to a call expression. This is because they are simply one-line expressions that evaluate to functions. In the example below, `(lambda y: y + 5)` is the operator and `4` is the operand.
``````>>> (lambda y: y + 5)(4)
9
>>> (lambda f, x: f(x))(lambda y: y + 1, 10)
11``````
### Q3: Lambda the Environment Diagram
Draw the environment diagram for the following code and predict what Python will output.
``````a = lambda x: x * 2 + 1
def b(b, x):
return b(x + a(x))
x = 3
x = b(a, x)``````
Objects
Global frame
f1: [parent=]
Return value
f2: [parent=]
Return value
f3: [parent=]
Return value
# Higher Order Functions
A higher order function (HOF) is a function that manipulates other functions by taking in functions as arguments, returning a function, or both. For example, the function `compose` below takes in two functions as arguments and returns a function that is the composition of the two arguments.
``````def composer(func1, func2):
"""Return a function f, such that f(x) = func1(func2(x))."""
def f(x):
return func1(func2(x))
return f``````
HOFs are powerful abstraction tools that allow us to express certain general patterns as named concepts in our programs.
# HOFs in Environment Diagrams
An environment diagram keeps track of all the variables that have been defined and the values they are bound to. However, values are not necessarily only integers and strings. Environment diagrams can model more complex programs that utilize higher order functions.
Lambdas are represented similarly to functions in environment diagrams, but since they lack instrinsic names, the lambda symbol (λ) is used instead.
The parent of any function (including lambdas) is always the frame in which the function is defined. It is useful to include the parent in environment diagrams in order to find variables that are not defined in the current frame. In the previous example, when we call `add_two` (which is really the lambda function), we need to know what `x` is in order to compute `x + y`. Since `x` is not in the frame `f2`, we look at the frame’s parent, which is `f1`. There, we find `x` is bound to 2.
As illustrated above, higher order functions that return a function have their return value represented with a pointer to the function object.
### Q4: Make Adder
Draw the environment diagram for the following code:
``````n = 9
return lambda k: k + n
Objects
Global frame
f1: [parent=]
Return value
f2: [parent=]
Return value
There are 3 frames total (including the Global frame). In addition, consider the following questions:
1. In the Global frame, the name `add_ten` points to a function object. What is the intrinsic name of that function object, and what frame is its parent?
2. What name is frame `f2` labeled with (`add_ten` or λ)? Which frame is the parent of `f2`?
3. What value is the variable `result` bound to in the Global frame?
### Q5: Make Keeper
Write a function that takes in a number `n` and returns a function that can take in a single parameter `cond`. When we pass in some condition function `cond` into this returned function, it will print out numbers from 1 to `n` where calling `cond` on that number returns `True`.
Run in 61A Code
# Currying
One important application of HOFs is converting a function that takes multiple arguments into a chain of functions that each take a single argument. This is known as currying. For example, the function below converts the `pow` function into its curried form:
``````>>> def curried_pow(x):
def h(y):
return pow(x, y)
return h
>>> curried_pow(2)(3)
8``````
### Q6: Curry2 Diagram
Draw the environment diagram that results from executing the code below.
``````def curry2(h):
def f(x):
def g(y):
return h(x, y)
return g
return f
make_adder = curry2(lambda x, y: x + y)
Objects
Global frame
f1: [parent=]
Return value
f2: [parent=]
Return value
f3: [parent=]
Return value
f4: [parent=]
Return value
f5: [parent=]
Return value
# Extra Practice
This question is particuarly challenging, so it is recommended to attempt if you are feeling confident on the previous questions or are studying for the exam.
### Q7: Match Maker
Implement `match_k`, which takes in an integer `k` and returns a function that takes in a variable `x` and returns `True` if all the digits in `x` that are `k` apart are the same.
For example, `match_k(2)` returns a one argument function that takes in `x` and checks if digits that are 2 away in `x` are the same.
`match_k(2)(1010)` has the value of `x = 1010` and digits 1, 0, 1, 0 going from left to right. `1 == 1` and `0 == 0`, so the `match_k(2)(1010)` results in `True`.
`match_k(2)(2010)` has the value of `x = 2010` and digits 2, 0, 1, 0 going from left to right. `2 != 1` and `0 == 0`, so the `match_k(2)(2010)` results in `False`.
Important: You may not use strings or indexing for this problem. You do not have to use all the lines, one staff solution does not use the line directly above the while loop.
Hint: Floor dividing by powers of 10 gets rid of the rightmost digits.
Run in 61A Code
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# Annual Percentage Rate (APR)
Annual percentage rate (APR) is the annualized interest rate on a loan or investment which doesn’t account for the effect of compounding. It is the annualized form of the periodic rate which when applied to a loan or investment balance gives the interest expense or income for the period. In most cases it is the interest rate quoted by banks and other financial intermediaries on various products i.e. loans, mortgages, credit cards, deposits, etc. It is also called the nominal annual interest rate or simple interest rate.
Annual percentage rate (APR) is a useful measure when comparing different loans and investments because it standardizes the interest rates with reference to time. It is useful to quote an annual rate instead of quoting a 14-day rate for a 14-day loan or 30-year rate for a 30-year mortgage. Due to its simplicity, annual percentage rate is arguably the most commonly quoted rate even though effective annual interest rate is a better measure when there are more than one compounding periods per year.
Let’s say you obtained two loans, one for $150,000 requiring 6% interest rate for six months and another for$200,000 requiring 3.5% interest rate for three months. Annual percentage rate is helpful in this situation because it helps us compare the cost of loans. Annual percentage rate for the first loan is 12% (periodic rate of 6% multiplied by number of relevant periods in a year i.e. 2). Similarly, annual percentage rate for the second loan is 14% (periodic rate of 3.5% multiplied by number of periods in a year of 4). It helps us conclude that the second loan is expensive.
## Formula
Even though annual percentage rate (APR) is simple in concept, its calculation might be tricky when it is not specifically quoted. When periodic rate is given, we can use the following formula to calculate APR:
APR = periodic rate for m months × 12/m
It also depends on whether the loan is based on simple interest or discount. If the interest amount is deducted from the loan amount at the start of the loan period as in discount loans, the periodic rate is calculated by dividing the finance charge by the amount financed.
APR (discount loan) = finance charge/amount financed × 12/term of loan in months
Finance charge = principal × periodic rate × term of loan in months/12
Amount financed = principal – principal × periodic rate × term of loan in months/12
If you know the effective annual interest rate, you can find APR as follows:
APR = m × ((1 + EAR) ^ (1/m) – 1)
Where m is the number of compounding periods per year and n is number of years.
## Example
You are a personal finance expert advising three clients:
• Angela, who must choose between two payday loans, each for $3,000 and 14-days: Loan A with financial charge of$100 payable at the end of 14th day and Loan B with finance charge of $90 deducted from the principal balance at the start of the loan. • Ahsan, who must decide between two credit cards: Card C with 2.5% monthly charge and Card D with 7.1% quarterly charge. • Antonio, who wants to identify better investment for his$50,000 for 5 years: Investment E paying APR of 10.6% compounded semiannually and Investment F with effective interest rate of 11% compounded monthly.
In case of Angela, Loan B is better. This is because annual percentage rate (APR) of Loan B is lower than APR for the Loan A. APR of Loan A is 86.9% worked out through the following steps: (a) calculating periodic interest rate, which equals 3.33% (=$100/$3,000) for 14-day period, (b) annualizing the rate by dividing it by the term of the loan (i.e. 14) and multiplying by the number of days in a year (i.e. 3.33%/14×365 = 86.9%). APR of Loan B is 80.63% calculated as follows: (a) finding financial charge for 14 days which is $90, (b) finding amount financed, which is$2,910 ($3,000 total amount minus$90 interest because it is paid at the start of the loan), (c) finding periodic rate for the 14-days which is 3.093% (=$90/$2,910) and (d) annualizing the rate (i.e. 3.093%/14×365=80.63%).
In case of Ahsan, Card D is better because APR for Card C is 30% (=periodic rate of 2.5% × 12/1) and APR for Card D is 28.4% (= periodic rate of 7.1% * 12/3), which is lower.
In case of Antonio, we need to find out APR for Investment F to make a comparison.
Annual percentage rate (APR) – Investment F = 12 × ((1 + 11%)^(1/12) – 1) = 10.48%
We may quickly conclude that Investment E is better because it has higher annual percentage rate. However, this is exactly where the weakness of APR lies: it ignores the effect of compounding. In such a situation, we need to make a comparison based on effective annual interest rate. Effective annual interest rate (EAR) in case of Investment E is just 10.88% (as shown below) which is lower than the effective interest rate on Investment F i.e. 11%. Antonio should choose Investment F paying 11% effective rate instead of Investment E paying 10.6% annual percentage rate (APR) compounded semiannually.
Effective annual interest rate = (1 + 10.60%/2)^2 – 1 = 10.88%
Written by Obaidullah Jan, ACA, CFAhire me at
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# 1070674
## 1,070,674 is an even composite number composed of four prime numbers multiplied together.
1070674 is an even composite number. It is composed of four distinct prime numbers multiplied together. It has a total of sixteen divisors.
## Prime factorization of 1070674:
### 2 × 11 × 41 × 1187
See below for interesting mathematical facts about the number 1070674 from the Numbermatics database.
### Names of 1070674
• Cardinal: 1070674 can be written as One million, seventy thousand, six hundred seventy-four.
### Scientific notation
• Scientific notation: 1.070674 × 106
### Factors of 1070674
• Number of distinct prime factors ω(n): 4
• Total number of prime factors Ω(n): 4
• Sum of prime factors: 1241
### Divisors of 1070674
• Number of divisors d(n): 16
• Complete list of divisors:
• Sum of all divisors σ(n): 1796256
• Sum of proper divisors (its aliquot sum) s(n): 725582
• 1070674 is a deficient number, because the sum of its proper divisors (725582) is less than itself. Its deficiency is 345092
### Bases of 1070674
• Binary: 100000101011001010010 2
• Base-36: MY4Y
### Squares and roots of 1070674
• 1070674 squared (10706742) is 1146342814276
• 1070674 cubed (10706743) is 1227359446332142024
• The square root of 1070674 is 1034.7337821875
• The cube root of 1070674 is 102.3023834745
### Scales and comparisons
How big is 1070674?
• 1,070,674 seconds is equal to 1 week, 5 days, 9 hours, 24 minutes, 34 seconds.
• To count from 1 to 1,070,674 would take you about two weeks!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000.
Note: we do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!
• A cube with a volume of 1070674 cubic inches would be around 8.5 feet tall.
### Recreational maths with 1070674
• 1070674 backwards is 4760701
• The number of decimal digits it has is: 7
• The sum of 1070674's digits is 25
• More coming soon!
The information we have on file for 1070674 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 1070674, math, Factors of 1070674, curriculum, school, college, exams, university, STEM, science, technology, engineering, physics, economics, calculator.
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https://afides.org/it-can-be-played-in-a-syndicate/
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afides.org
afides.org
## It Can Be Played in a Syndicate
The Chinese Han Dynasty was the first civilization to record lottery slips, dated between 205 and 187 BC. It is believed that the game of chance was used as a way of financing major government projects. The Chinese Book of Songs even refers to the game of chance as a “drawing of wood” or “lots.”
## It’s a form of gambling
A lottery is a form of gambling, and it depends on chance to determine the winners. The game is a form of gambling because the winner receives money or prize money based on their chance of winning. All the tickets sold or offered for sale together form a pool, containing all the possible permutations of numbers. This pool is a way to ensure that every single ticket wins something, but the risk of addiction is relatively small.
## It raises money
Most states in the US use lottery proceeds for public works projects. While that may be a good idea, some people argue that using the money for public works creates an unfair burden on the least advantaged. Studies have shown that the people who lose the most money playing the lottery are blacks, Native Americans, and males living in disadvantaged neighborhoods. These are just a few of the reasons why we shouldn’t be promoting lottery play in our state.
## It has annuity payments
What are annuity payments? An annuity is a series of payments made at regular intervals, such as a monthly mortgage, insurance, or pension payment. Annuities are divided into types according to how often they are made – monthly, weekly, or quarterly, for example. Some annuities are calculated mathematically by using certain functions. Life annuities, for example, provide payments for a person’s lifetime.
## It can be played in a pool
There are many reasons why you might want to create a pool, and one of those reasons is to increase your chances of winning the lottery. You can win huge sums of money with the help of your pool, and you can even make it a social event. The most obvious reasons to have a pool are the obvious ones: to have a good time and make new friends. However, there are also more practical reasons. A pool can help you win some money and keep your team morale up.
## It can be played in a syndicate
It is possible to play It Can Be Played in a Syndicate. But before you do so, there are a few things that you should consider first. First, don’t make the syndicate comprise of your co-workers. The main reason for this is mutual trust, but it is also common sense to stick to everyday office partners and not your boss. However, if you are not sure whether your boss is the right person to be in your syndicate, don’t worry! Here are some guidelines to help you start:
## It encourages responsible gambling
Woolworths is a leading retailer of poker machines in Australia and is committed to promoting responsible gambling. The company recently announced its intention to introduce voluntary pre-commitment on its poker machines by 2014, two years ahead of the Federal Government’s timeline. The announcement comes just days before the company’s AGM, which will be held at the Adelaide Convention Centre on Thursday. The meeting will begin at 11am. It is hoped the announcement will encourage consumers to be more responsible about the way they gamble.
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# What Is A Dead End 3 Way?
## How do you wire a 3 way power switch and leg in the same box?
Since your incoming power and switch leg are in the same box we have to send power to the farthest switch ( switch #2 ), which we do with the white wire from the 12/3.
This will energize the travelers, the black and red wires from the 12/3.
We then attach the black wire from the fixture to the black screw on switch #1..
## How do you wire a 3 way switch using 14 2 wire?
3 Way Switch #1. Using a wire nut, connect the two white wires together. Connect the black wire from the 14/2 feed wire to the black common screw. … 3 Way Switch #2. Using a wire nut, connect the two white wires together. Connect the black wire from the 14/2 wire going to the light, to the black common screw.
## Why does my three way switch not work?
Sometimes, a 3-way circuit doesn’t work because someone tried to replace a defective switch and did not properly connect the wires. … Disconnect all three wires (or four, if the outlet is grounded) from both switches. Separate the wires so that they are as far away from each other as possible. 2) Turn the power back on.
## How many 3 and 4 way switches are required to control a light from 3 locations?
A four-way switch is similar to a three-way, except it has four terminals (plus a ground terminal) and controls one fixture from three locations. This type of switch must be combined between two three-way switches to form a circuit.
## Can you use a single pole switch as a 3 way switch?
Yes it can work. 3-way switches are spdt (single pole double throw) with 3 screw terminals, and regular switches are spst (single pole single throw) with 2 screw terminals. Just pick the correct two contacts and you are good to go. .
## Can you add an outlet to a 3 way switch?
If it’s a 3-way switch, then its two positions toggle a “common” conductor among two “traveler” conductors. … The neutral will be available at the light or at the other switch box. This means you cannot run a new outlet from the wires in this box – you need a neutral wire.
## Can a 3 way switch go bad?
Usually when a 3-way switch fails, lights can be toggled on and off at one switch, but not the other. If one of the two 3-way switches toggles the light(s) on and off, the other 3-way switch has probably failed. … If it does, it is a good switch and the other is bad.
## How do you wire a 3 way switch to 14 3?
Feed a length of 14-3 type NM cable (or 12-3, if you’re connecting to 12-gauge wire) between the two boxes. The 14-3 cable has three insulated conductors: white, black and red (plus a bare ground wire). Connect the wires to the new 3-way switches with ground screws using one of the two wiring diagrams (Fig.
## What color is the C wire on a thermostat?
BlueThe Rh wire connects to the heating system. This wire may be red without an “H” attached, in some cases. Blue. The blue wire on the thermostat is the Common or “C” wire.
## Can you use 2 wire for a 3 way switch?
Answer: No. There must be three wires between the two switches. You CAN use the switch with only two wires, but it will act as a regular switch, not a three-way switch.
## What color is the load wire?
The wire that causes the pen to glow red is the hot wire; also known as the Line wire. The wire that does not cause the pen to glow red is the Load wire.
## How can you tell which wire is hot?
The hot one will give a visual and audible alert. Most likely the neutral wire is white and the hot wire is red or black, but test to make sure. Identify the neutral wire in the fixture by looking at the wires. In most modern fixtures the neutral wire will be white and the hot wire is red or black.
## What is 2 way switch?
A two way light switch is a switch that can be used in conjunction with another two way light switch to turn a light (or lights) on and off from more than one location.
## What color wire goes to the black screw on a 3 way switch?
The black screw has the black (common) wire that runs up to the light through the yellow cable. The two grounds are connected together and then to the green ground screw on the switch. To summarize, the black screw gets either the wire from the electrical panel or the wire going to the light.
## How do I know if I have a 3 way switch?
A more positive way to identify a 3-way switch is to look at the body of the switch and count the number of screw terminals: a 3-way switch has three terminal screws plus a ground screw. Two of the terminals are a light color—bronze- or copper-colored—and are called travelers.
## How do you do a 3 way dead end?
Description Power and switch leg at one end, dead end of a 3 wire at the other. The hot and switch leg are extended over to the traveler terminals on the dead end 3way. The common terminals of each S3 are connected together and to nothing else.
## What is the difference between 2 way and 3 way switch?
The 2 way switch or single pole double throw switch is a three terminal switch. Here 1 terminal is the input and the other two are used as outputs. It’s okay if this is too complex for you….2 Way vs 3 Way Switch.2 Way Switch3 Way SwitchThese switches don’t have hot wires.These switches have hot wires4 more rows•Sep 27, 2019
## How do you bypass a 3 way switch?
3 Answers replace that switch with a single-pole switch. connect either of the “traveler” wires to the load side. remove the other (unwanted) switch and connect the traveler wire used in step-2 to the “switched hot” wire that goes to the lights. the unused “traveler” wire is abandoned.
## What is a 3 way switch wiring?
A three-way wall switch is a common type of light switch that makes it possible to control a ceiling light or other electrical fixture from two different locations in a room. … Three-way switches are always used in pairs and include special wiring connections.
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https://numberworld.info/402321430412110
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# Number 402321430412110
### Properties of number 402321430412110
Cross Sum:
Factorization:
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
16de8c1f1fb4e
Base 32:
bdt30v3uqe
sin(402321430412110)
0.95763165604531
cos(402321430412110)
-0.28799585299084
tan(402321430412110)
-3.3251577968929
ln(402321430412110)
33.628272463195
lg(402321430412110)
14.604573166705
sqrt(402321430412110)
20057951.800025
Square(402321430412110)
1.6186253336885E+29
### Number Look Up
402321430412110 (four hundred two trillion three hundred twenty-one billion four hundred thirty million four hundred twelve thousand one hundred ten) is a impressive number. The cross sum of 402321430412110 is 28. If you factorisate the figure 402321430412110 you will get these result 2 * 5 * 11 * 17 * 215145149953. 402321430412110 has 32 divisors ( 1, 2, 5, 10, 11, 17, 22, 34, 55, 85, 110, 170, 187, 374, 935, 1870, 215145149953, 430290299906, 1075725749765, 2151451499530, 2366596649483, 3657467549201, 4733193298966, 7314935098402, 11832983247415, 18287337746005, 23665966494830, 36574675492010, 40232143041211, 80464286082422, 201160715206055, 402321430412110 ) whith a sum of 836484343021152. The number 402321430412110 is not a prime number. The figure 402321430412110 is not a fibonacci number. The figure 402321430412110 is not a Bell Number. The number 402321430412110 is not a Catalan Number. The convertion of 402321430412110 to base 2 (Binary) is 1011011011110100011000001111100011111101101001110. The convertion of 402321430412110 to base 3 (Ternary) is 1221202111112221020010201122001. The convertion of 402321430412110 to base 4 (Quaternary) is 1123132203001330133231032. The convertion of 402321430412110 to base 5 (Quintal) is 410213113242141141420. The convertion of 402321430412110 to base 8 (Octal) is 13336430174375516. The convertion of 402321430412110 to base 16 (Hexadecimal) is 16de8c1f1fb4e. The convertion of 402321430412110 to base 32 is bdt30v3uqe. The sine of 402321430412110 is 0.95763165604531. The cosine of 402321430412110 is -0.28799585299084. The tangent of 402321430412110 is -3.3251577968929. The root of 402321430412110 is 20057951.800025.
If you square 402321430412110 you will get the following result 1.6186253336885E+29. The natural logarithm of 402321430412110 is 33.628272463195 and the decimal logarithm is 14.604573166705. that 402321430412110 is amazing figure!
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https://physics.stackexchange.com/questions/484907/a-paradox-between-quantum-and-statistical-mechanics
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# A paradox between quantum and statistical mechanics? [duplicate]
The Boltzmann distribution function tells us what is the probability of a given particle with a given energy to be at a certain state.
Now, this is in contrast with the state function the Schrodinger equation gives us. I mean, the quantum state gives us a probability distribution in energy space, and the statistical mechanics also gives us such a distribution, but why the two distribution differ?
## marked as duplicate by knzhou, John Rennie quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 10 at 10:53
As Emilio said in the comments. The two really describe two different scenarios. In the case of a wavefunction, we consider the system of interest as isolated and there is no notion of temperature (The notion of temperature most notably comes when our system is in contact with a heat reservoir). In such a case, the system has a fixed average energy i.e $$\langle\psi| H |\psi\rangle$$, that is the expectation value of the Hamiltonian with respect to the wavefunction $$|\psi\rangle$$.
This is different than the case when we attach our system to a heat reservoir of temperature T. Here, we consider an ensemble of wavefunctions $$|\psi_i\rangle$$ each of average energy $$\epsilon_i$$. Calculations of various properties of the system can be done by using the density operator (a.k.a density matrix) $$\sum_i p_i |\psi_i\rangle\langle\psi_i|$$, here $$p_i$$ will be the probability as per the Boltzmann distribution of $$|\psi_i\rangle$$, the wavefunctions present in the system. (note: one thing you should think is that ask yourself is that wither this different from a superposition of different wavefunctions). This is in a sense how one goes from quantum mechanics to quantum statistical mechanics.
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# The Electromagnet
We now know from the previous tutorials that a straight current carrying conductor produces a circular magnetic field around itself at all points along its length and that the direction of rotation of this magnetic field depends upon the direction of current flow through the conductor, the Left Hand Rule.
In the last tutorial about Electromagnetism we saw that if we bend the conductor into a single loop the current will flow in opposite directions through the loop producing a clockwise field and an anticlockwise field next to each other. The Electromagnet uses this principal by having several individual loops magnetically joined together to produce a single coil.
Electromagnets are basically coils of wire which behave like bar magnets with a distinct north and south pole when an electrical current passes through the coil. The static magnetic field produced by each individual coil loop is summed with its neighbour with the combined magnetic field concentrated like the single wire loop we looked at in the last tutorial in the centre of the coil. The resultant static magnetic field with a north pole at one end and a south pole at the other is uniform and a lot more stronger in the centre of the coil than around the exterior.
### Lines of Force around an Electromagnet
The magnetic field that this produces is stretched out in a form of a bar magnet giving a distinctive north and south pole with the flux being proportional to the amount of current flowing in the coil. If additional layers of wire are wound upon the same coil with the same current flowing, the magnetic field strength will be increased.
It can be seen from this therefore that the amount of flux available in any given magnetic circuit is directly proportional to the current flowing through it and the number of turns of wire within the coil. This relationship is called Magneto Motive Force or m.m.f. and is defined as:
Magneto Motive Force is expressed as a current, I flowing through a coil of N turns. The magnetic field strength of an electromagnet is therefore determined by the ampere turns of the coil with the more turns of wire in the coil the greater will be the strength of the magnetic field.
## The Magnetic Strength of the Electromagnet
We now know that were two adjacent conductors are carrying current, magnetic fields are set up according to the direction of the current flow. The resulting interaction of the two fields is such that a mechanical force is experienced by the two conductors.
When the current is flowing in the same direction (the same side of the coil) the field between the two conductors is weak causing a force of attraction as shown above. Likewise, when the current is flowing in opposite directions the field between them becomes intensified and the conductors are repelled.
The intensity of this field around the conductor is proportional to the distance from it with the strongest point being next to the conductor and progressively getting weaker further away from the conductor. In the case of a single straight conductor, the current flowing and the distance from it are factors which govern the intensity of the field.
The formula therefore for calculating the “Magnetic Field Strength”, H sometimes called “Magnetising Force” of a long straight current carrying conductor is derived from the current flowing through it and the distance from it.
### Magnetic Field Strength for Electromagnets
• Where:
• H – is the strength of the magnetic field in ampere-turns/metre, At/m
• N – is the number of turns of the coil
• I – is the current flowing through the coil in amps, A
• L – is the length of the coil in metres, m
Then to summarise, the strength or intensity of a coils magnetic field depends on the following factors.
• The number of turns of wire within the coil.
• The amount of current flowing in the coil.
• The type of core material.
The magnetic field strength of the electromagnet also depends upon the type of core material being used as the main purpose of the core is to concentrate the magnetic flux in a well defined and predictable path. So far only air cored (hollow) coils have been considered but the introduction of other materials into the core (the centre of the coil) has a very large controlling effect on the strength of the magnetic field.
Electromagnet using a nail
If the material is non-magnetic for example wood, for calculation purposes it can be regarded as free space as they have very low values of permeability. If however, the core material is made from a Ferromagnetic material such as iron, nickel, cobalt or any mixture of their alloys, a considerable difference in the flux density around the coil will be observed.
Ferromagnetic materials are those which can be magnetised and are usually made from soft iron, steel or various nickel alloys. The introduction of this type of material into a magnetic circuit has the effect of concentrating the magnetic flux making it more concentrated and dense and amplifies the magnetic field created by the current in the coil.
We can prove this by wrapping a coil of wire around a large soft-iron nail and connecting it to a battery as shown. This simple classroom experiment allows us to pick-up a large quantity of clips or pins and we can make the electromagnet stronger by adding more turns to the coil. This degree of intensity of the magnetic field either by a hollow air core or by introducing ferromagnetic materials into the core is called Magnetic Permeability.
## Permeability of Electromagnets
If cores of different materials with the same physical dimensions are used in the electromagnet, the strength of the magnet will vary in relation to the core material being used. This variation in the magnetic strength is due to the number of flux lines passing through the central core. if the magnetic material has a high permeability then the flux lines can easily be created and pass through the central core and permeability (μ) and it is a measure of the ease by which the core can be magnetised.
The numerical constant given for the permeability of a vacuum is given as: μo = 4.π.10-7 H/m with the relative permeability of free space (a vacuum) generally given a value of one. It is this value that is used as a reference in all calculations dealing with permeability and all materials have their own specific values of permeability.
The problem with using just the permeability of different iron, steel or alloy cores is that the calculations involved can become very large so it is more convenient to define the materials by their relative permeability.
Relative Permeability, symbol μr is the product of μ (absolute permeability) and μo the permeability of free space and is given as.
### Relative Permeability
Materials that have a permeability slightly less than that of free space (a vacuum) and have a weak, negative susceptibility to magnetic fields are said to be Diamagnetic in nature such as: water, copper, silver and gold. Those materials with a permeability slightly greater than that of free space and themselves are only slightly attracted by a magnetic field are said to be Paramagnetic in nature such as: gases, magnesium, and tantalum.
## Electromagnet Example No1
The absolute permeability of a soft iron core is given as 80 milli-henries/m (80.10-3). Calculate the equivalent relative permeability value.
When ferromagnetic materials are used in the core the use of relative permeability to define the field strength gives a better idea of the strength of the magnetic field for the different types of materials used. For example, a vacuum and air have a relative permeability of one and for an iron core it is around 500, so we can say that the field strength of an iron core is 500 times stronger than an equivalent hollow air coil and this relationship is much easier to understand than 0.628×10-3 H/m, ( 500.4.π.10-7).
While, air may have a permeability of just one, some ferrite and permalloy materials can have a permeability of 10,000 or more. However, there are limits to the amount of magnetic field strength that can be obtained from a single coil as the core becomes heavily saturated as the magnetic flux increases and this is looked at in the next tutorial about B-H curves and Hysteresis.
• D
D.NAGARAJ
Here i have a doubt I select X thickness of copper wire and it’s winded a Y length plastic bobbin holder center hollow type and I will give 5.2 v and 4 A current then how to Calculate the magnet flux for the coil
• b
babar ali
I want all formulas and detail or formula
• M
Micha
The coil diameter is 5cm. The soft iron insert has diameter 1cm and permeability 5000. How strong will be magnetic field (Tesla) inside the iron at coil current 1 amp. The coil length 15cm numbers of turns 150. Is the magnetic field in the iron of 4.9cm will be the same?
• L
Lily
I do not think this is important at all
• n
nick
Can u describe it in deep
h=i/2πr ?
By using derivation!
• Wayne Storr
Magnetic field strength (H or amperes per metre) is defined as the magnetomotive force per unit length of a magnetic circuit. For a straight conductor in air carrying a current of i amperes the generated magnetic field consists of circular lines of force eminating from and at a distance r metres to the conductor with its center at the center of the conductor.
Therefore the current i = H.2pi.r, thus H = i/(2pi.r). So if a straight conductor carries a current of 10 amperes, the magnetising force at a distance of 10cm from the center of the conductor will be: 10/(2pi x 0.1) = 16 A/m. Obviously, if there are “N” number of conductors together carrying the current then H = Ni/(2pi.r)
• A
Alex
Hello, Im trying to get a general idea about the electromagnet. How it works and its basic regulations.
• K
Kamalakanta Panda
wheather induced current will produce by moving both the magnet and the coil symultaneously or not?
• i
Does adding more soft iron in a coil increase or decrease the strength of an electromagnet?
• T
Taral Sharma
I have a question. when using electromagnet as poles i.e. one north and one south how does the strength of the electromagnet depends? Is it the same eq. ? The type of electromagnets that are used in production of electricity. please help.
• Wayne Storr
The strength of the magnetic field produced by an electromagnet depends on the number of turns of wire, the current flowing through the wire and permeability of the core.
• E
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Messages
Proposals
Variance Analysis
Homework ID: 926286 Client: karla9639D Budget: \$20-\$50 Deadline: 24 Hours Accounting & Finance Masters
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# Variance Analysis
Prior to beginning work on this assignment, read Chapter 4: Financial Forecasting in the textbook, and review the current financial statements of Starbucks through Yahoo! Finance (Links to an external site.)or the EDGAR | Company Filings (Links to an external site.)database in the Filings and Forms page. You can access the financial statements by going to the Yahoo! Finance webpage, typing in the stock symbol of Starbucks, and then clicking on the “Financials” tab. Watch the Week 1 Assignment video with Dr. Kevin Kuznia, DBA, CSSBB, PMP.
Reviewing the previous quarter’s financial statements will provide you with data to construct pro forma financial statements for Starbucks and make some basic projections. This week, you will be charged with constructing two pro forma financial statements and addressing some questions about your projections. The two financial statements will include an Income Statement and Balance Sheet.
Part 1
Use the EDGAR | Company Filings (Links to an external site.)or Yahoo! Finance (Links to an external site.)database to download the last 10-Q from Starbucks into Excel. Use the downloaded data to complete the Income Statement and Balance Sheet on the appropriate tabs in the Financial Forecasting Template. Assume the following:
Sales will increase for the next quarter by the same percentage increase from the previous quarter to the last reported quarter. For example, if sales increased 8% from the last quarter to the current reported quarter, you will use 8% as the sales increase for your pro formas.
Calculate the expenses to determine what will change and what will remain the same.
Note: Not all costs are associated with the cost of sales. It will be up to you to determine which line items need to be increased and which ones need to be left alone. This will require you to distinguish between fixed and variable costs. For a reminder of the difference between fixed and variable costs, please watch the video Business Costs (Fixed Costs and Variable Costs) Explained (Links to an external site.).
Within each line item expense explain your rationale, as well as provide a brief summary.
Part 2
Then, calculate a quarterly variance analysis using the Variance Analysis tab of the Financial Forecasting Template (the same template you used for Part 1). Complete the following in your variance analysis:
In the Excel template, insert the line items.
In Column C, (Q4, 20NN) enter the previous quarter’s numbers as the budget.
In Column D, (Q1, 20NN) enter the current quarter’s actual numbers.
In Column E, the spreadsheet will calculate the dollar difference between the budget and actual numbers.
In Column F, the spreadsheet will calculate the percentage change.
In Column G, analyze and speculate the rationale for the variances.
Submit your completed Financial Forecasting Template to Waypoint.
Accessibility Statement: If you have a disability that impacts your ability to successfully participate in this or any other course activity, please provide your instructor with your authorized Accommodation Request form from the Office of Student Access and Wellness so that they can discuss and arrange an alternative plan with you.
Carefully review the Grading Rubric (Links to an external site.) for the criteria that will be used to evaluate your assignment.
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Drawing line segments in a 3d plot
27 visualizzazioni (ultimi 30 giorni)
Harry il 12 Lug 2020
Risposto: jonas il 12 Lug 2020
Hi, given a matrix, such as
rand(6,5)
I want to create a 3d plot containing line segmentes, where each line segment is purple, begins at a blue point, with the x, y, z co ordinates taken from the entries in the 1st, 2nd and 5th columns of the matrix, and ends at a red point with the x, y, z co ordinates taken from the entries in the 3rd, 4th and 5th columns of the matrix.
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jonas il 12 Lug 2020
Something like this?
A = rand(6,5);
startv = [A(:,1),A(:,2),A(:,5)];
endv = [A(:,3),A(:,4),A(:,5)];
figure;hold on
scatter3(startv(:,1),startv(:,2),startv(:,3),[],'b','filled');
scatter3(endv(:,1),endv(:,2),endv(:,3),[],'r','filled');
h = plot3([startv(:,1)';endv(:,1)'],...
[startv(:,2)';endv(:,2)'],...
[startv(:,3)';endv(:,3)'])
set(h,'color',[128,0,128]./255);
view(3)
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Arbitrage betting is a way of making safe bets, especially on Esports. You can get stable and tangible income no matter the result of a sports event. How it’s possible? Find out in our article
Arbitrage bets: everything you need to know
Arbitrage bet or surebet – arbitrage situations in betting that arise due to bookmakers’ odds difference on opposite outcomes of the event. This situation allows a punter to place bets in such a way that he get guaranteed profit no matter the result.
The reasons of such a situation appear different, but the common are bookmaker mistakes, slow reaction to changing the situation in the match and simple competition for new clients between bookies.
Perhaps, this information did not give you a clear understanding of what arbitrage betting is – therefore, let’s consider a clear example of how the strategy works.
Surebet example
Let’s take for example a Dota 2 Esports match between Outsiders and Talon. As you can see at the screenshot – one bookmaker set 2.57 for TO 30.5 Team 1 kills and the second – 1.87 for TU 30.5 Team 1 kills.
Having such data, we’ll place bets of 84.23\$ on TO 30.5 and 115.77\$ on TU 30.5 (200\$ in total). And now we don’t need to worry about the final result, because we’ll get at least 16.47 of net profit:
2.57*84.23 = 216,47\$ – 200\$ = 16,47\$
1.87*115.77 = 216,49\$ – 200\$ = 16,49\$
Arbs: manual search vs surebet services
As you can see, surebets can surely bring a tangible and stable income. The main question here is how to search for arbitrage situations. Of course, you can search and calculate it on your own, but note that it’s a very hard and time consuming process. That is why punters more often use surebet services.
Surebet service – it’s a special software that analyses data from bookmaker lines and presents the complete list of arbitrage situations to its customers. Nowadays, one of the best products in this area is BetBurger.
The scanner analyse more than 200 bookies betting lines in 40+ kinds of sports and 210 markets. All the data updates in seconds, so the clients of BetBurger get a wide range of fresh and tangible surebets to place.
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# How is -Integer.MIN_VALUE Equal to Integer.MIN_VALUE
Ranch Hand
Posts: 31
I observed an interesting fact
System.out.println(-Integer.MIN_VALUE == Integer.MIN_VALUE);//output: true
System.out.println(-Integer.MIN_VALUE); // output : -2147483648
Why is that a negative int remains negative when negated???
----------------------------------
Regards
Avinash
Marshal
Posts: 62809
203
Write out its bit pattern. HInt: you can get it from Integer.toBinaryString(Integer.Min_VALUE). It might be 1 and thirty-one 0s. Or it might not be.
Work out its two's complement when negated: Hint: Write out the bit pattern for 2 to the 32nd. That is 1 and thirty-two 0s. Subtract the binary pattern for -2147483648 from that. And what do you get . . . Tadaaa!
Google for arithmetic overflow and two's complement binary integers, and you will get a different explanation of the same thing.
Campbell Ritchie
Marshal
Posts: 62809
203
Negating an int and getting the same value works for the value you have shown, and one other value. I shall let you guess which other value.
Avinash Haridasu
Ranch Hand
Posts: 31
Can any one tell me
how do we decide whether a number is negative or positive just by looking at the binary representation
0 0 0 0 0 0 0 1 = 1
1 1 1 1 1 1 1 1 = −1
and
System.out.println( 32 >> 37); // output: 1
System.out.println( 32 >> 5); // output: 1
How is this possible???
Ranch Hand
Posts: 247
• 1
Avinash Haridasu wrote:Can any one tell me
how do we decide whether a number is negative or positive just by looking at the binary representation
0 0 0 0 0 0 0 1 = 1
1 1 1 1 1 1 1 1 = −1
.
In binary number system we can use only 2 things and that is 0 and 1 and we have to use 0 and 1 for representing the negative numbers also.There is something known as MSB(most significant bit) and LSB(least significant bit). Now the left-most-bit is your MSB and right-most-bit is LSB. Example 01010101 Here the one in red color is MSB and the one in green color is LSB..
.
So you must have understood what is MSB and LSB. Now if the MSB is 0 then the number is positive and if the MSB is 1 then the number is negative. So the conclusion is MSB represents the sign of the number and other numbers(i would say bits ) are the actual value. So
Since MSB is 0 therefore number is positive and waht about the value 0000001 is equal to 1 and therefor ans is . Now Now MSB is 1 therefore number is negative and Java uses 2's complement for negative numbers and the 2's complement of 11111111 is 00000001 and therefore the ans is -1 (Please find out how to find 2's complement if you are not aware).
.
Campbell Ritchie
Marshal
Posts: 62809
203
Your description of the values of LSB and MSB is correct, but you ought to remember that only applies to two's complement numbers. The char for example is unsigned and behaves differently.
Campbell Ritchie
Marshal
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203
Look in the Java Language Specification and you find that the number of bits shifted is calculated % i where i is the number of bits in the datatype. So for everything except a long, shift 37 and shift 5 have the same effect.
i >> 5 is equivalent to i / 32
Rameshwar Soni
Ranch Hand
Posts: 247
Campbell Ritchie wrote:but you ought to remember that only applies to two's complement numbers. The char for example is unsigned and behaves differently.
Behaves differently ? Can you give an example so that i can understand it better?
Java Cowboy
Posts: 16084
88
char is like an unsigned 16-bit number. You can't store negative values in a char. So a char with the bit pattern 1111 1111 1111 1111 has the value 65536, not -32768. In other words, for a char, two's complement is not used.
Saloon Keeper
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192
Did you mean -1?
Campbell Ritchie
Marshal
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Actually it's not quite i % 32, but more like i & 31, which behaves similarly to i % 32 but gives a positive result from a negative left operand.
Campbell Ritchie
Marshal
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Stephan van Hulst wrote:Did you mean -1?
No, Jesper actually means 65535, assuming that is the bit pattern for a char. That is equivalent to the Unicode character for ffff, and you can find what that is here.
Stephan van Hulst
Saloon Keeper
Posts: 9703
192
Sorry, I was referring to Jesper's:
not -32768
Campbell Ritchie
Marshal
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Yes, I got confused about that. I agree that's "not -1".
Jesper de Jong
Java Cowboy
Posts: 16084
88
Ok, again...:
char is like an unsigned 16-bit number. You can't store negative values in a char. So a char with the bit pattern 1111 1111 1111 1111 has the value 65535, not -1. In other words, for a char, two's complement is not used.
Avinash Haridasu
Ranch Hand
Posts: 31
Campbell Ritchie wrote:Look in the Java Language Specification and you find that the number of bits shifted is calculated % i where i is the number of bits in the datatype. So for everything except a long, shift 37 and shift 5 have the same effect.
i >> 5 is equivalent to i / 32
As per Specification:
If the promoted type of the left-hand operand is int, only the five lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & with the mask value 0x1f. The shift distance actually used is therefore always in the range 0 to 31, inclusive.
But why it is "only the five lowest-order bits" ???
Can any one please explain ??
Stephan van Hulst
Saloon Keeper
Posts: 9703
192
Because you don't need any more than that. With 5 bits you can create the values 0-31, enough to perform any possible shift distance on an int.
Avinash Haridasu
Ranch Hand
Posts: 31
Need small clarification on shifting:
32 In Binary: 0000 0000 - 0000 0000 - 0000 0000 - 0010 0000
32>>1:
0000 0000 - 0000 0000 - 0000 0000 - 0001 0000
32>>2:
0000 0000 - 0000 0000 - 0000 0000 - 0000 1000
32>>1:
0000 0000 - 0000 0000 - 0000 0000 - 0000 0001
32>>6:
0000 0000 - 0000 0000 - 0000 0000 - 0000 0000
When 32>>6 is itself 0 - Then how 32>>33 is 16, 32>>38 is 0 ???
Campbell Ritchie
Marshal
Posts: 62809
203
The Java Language Specification link I gave you yesterday explains it all. There are 32 bits to an int, so you cannot shift an int more than 31 bits. You can fit 31 into 5 bits. [A long can be shifted up to 63 bits, and you can fit 63 into 6 bits.] If you shifted it 32 bits, you would come back to where you started, so i >> 32 is the same as i, which is the same as i >> 0. So you can shift an int by |n % 32| bits, where || is the absolute value operator. Now the absolute value of n % 32 is the same (in binary arithmetic) as n & 32 - 1. And as we all know, 32 - 1 = 0x1f. If you write the bit pattern for 0x1f you find it has 5 1s in. So you get 5 bits masked.
32 bits in an int.
32 = 2 to the 5th.
So you shift an int by the rightmost (least significant) five bits (six for a long).
All of the world's problems can be solved in a garden - Geoff Lawton. Tiny ad: RavenDB is an Open Source NoSQL Database that’s fully transactional (ACID) across your database https://coderanch.com/t/704633/RavenDB-Open-Source-NoSQL-Database
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# How should I start it?
Call a number $$\text{prime looking}$$ if it is composite but not divisible by $$2, 3, 5$$. The three smallest prime looking numbers are $$49, 77, 91$$. There are $$168$$ prime numbers less than $$1000$$. How many $$\text{prime looking}$$ numbers are there less than $$1000$$?
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+
# Why Is the Golden Ratio Important in Design & What Happens If You Don't Use It?
##### Rating:
(0)
Author: Tia Moreen
##### Description:
What Does It Mean?
In more specific terms, the golden ratio is a constant that describes the ratio between two quantities. It equates to roughly 1.6 and is oftentimes referred to as the perfect ratio (hence the name) due to its neat structure both visually and mathematically.
Some of the first and most famous examples of imagery that uses the golden ratio are Michelangelo's 'The Creation of Adam' and Botticelli's 'The Birth of Venus.'
The history and fields of application of the golden ratio are very interesting topics that could serve as a base for an entire essay. And if you dig deep enough, you'll discover that it transcends the boundaries of design and goes on to find its place in science and even in music. If you don't have time to do the research on your own, there are plenty of 'write my paper' services that will gladly do the research for you.
Flexible Boundaries
The orderly fashion in which the theory of the golden ratio is frequently presented might make it look like a pretty constricting system. It's not exactly correct. Attempting to use the golden ratio in your art doesn't remove the creative aspect.
Even as you work within its guidelines, you still have a lot of space for a creative maneuver. The human brain will do the work for you. If you ever tried sketching, you might have noticed an interesting thing. It is easier to find the image you are looking for in a messy drawing.
When you see a bunch of lines thrown together, your brain singles out the ones it finds the most logical and pushes all the rest to the background. That's why you can frequently see artists putting down multiple 'attempts' of one element of the picture only to pick the one they like best and erase the rest.
Our ability to detect the golden ratio in the things around us works similarly. Your art doesn't have to perfectly follow its geometrical proportions. Use it as a rough outline of where the main objects in your picture should be.
Once you start working on it, you'll find that your mind automatically guides you to the golden ratio. If you stray from it, your art will register as 'weird,' 'wrong,' or 'imperfect.'
Breaking the Rules
So what happens if you don't want to conform? Will breaking the rule prevent you from creating good imagery? Not at all.
The golden ratio is one of the most commonly used principles. But it is not the only approach. Even if you decide to ditch the golden ratio, there is no shortage of other systems to organize your art by:
Rule of thirds;
Silver ratio;
Rule of odds;
Lateral symmetry;
Besides, art isn't a stable field by any means. It changes and evolves constantly. Moreover, some pieces of art refuse to follow any sort of known guidelines, as artists prefer to rely on intuition.
If you feel like the golden ratio doesn't do it for you, feel free to look for other means of expressing yourself. Art is a subjective and individual field, after all. Finding your own style is a part of every artist's journey.
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### Developing Effective Teams
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Tutorial
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Next: Factors Up: The Garden of Previous: Systems of symbolic
# Ancestorless states for Rule 18
Rule 18, whose statistical properties have been extensively studied by Grassberger, is very similar to Rule 22, except for the fact that single cells die out rather than remaining to affect further evolution. The consequence is that isolated cells form growth clusters whose interiors die out, just as for Rule 22. However, the fate of colliding frontiers from two different clusters depends on the parity with which they collide, and as a result the evolution of Rule 18 is largely characterized by the conflict of neighboring domains of opposite parity. Occasionally a domain will shrink and disappear, allowing its two neighbors to coalesce. Grassberger was interested in the random walk involved.
The following script shows the subset machine for Rule 18.
```(2,1) Rule #18
Like LIFE but single cells die
(00*(0+10*1))*
Transitions from original machine
Transitions from subset machine
```
The next script shows the symbolic equation set of the subset machine for Rule 18. (The nodes have been relabelled according to , , , , , , , )
```
a=a.0+c.0+%
b=a.1+c.1
c=b.0
d=b.1+g.1
e=d.0
f=e.0+f.0
g=e.1+f.1+g.0
h=d.1
```
Since there are relatively few equations, we can write their symbolic coefficient matrix fairly easily. By partitioning it into submatrices certain characteristics of the equations are emphasized; namely that certain groups of nodes are selfcontained. Links lead into the group but there are no links leading out again. Figure shows the coefficient matrix (assuming the nodes to form a column vector) and the part of the subset diagram derived from the full subset.
Figure: Subset diagram for Rule 18.
The solutions for these equations can be obtained in a way which emphasizes the triangular nature of the coefficient matrix:
```
b=(0*1)(000*1+01)*
d=b.1((01+000*1)0*1)*
h=d.1
g=d.(01+000*1)0*
f=d.000*
e=d.0
a=b.000*+0*
c=b.0
```
The coefficients of b and d can be simplified slightly. The new coefficient means that (reading from left to right) after meeting the first 1, we can remain on the highest level only if 1's do not come in joined pairs. Having met the first such pair, we may now remain on the second level as long as the sequence repeats itself, which it will do unless three 1's come along in sequence, or else a pair of pairs enclosing a single isolated 1. Descent to level three ensues, finally leaving a sequence without an ancestor. Thus three ones in sequence is a sure mark of a Garden of Eden sequence, but the other condition is much less specific, as it does not refer to some sequence of fixed length.
Next: Factors Up: The Garden of Previous: Systems of symbolic
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx
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# Please explain why we only use the equation for the end of each period for a.
Please explain why we only use the equation for the end of each period for a.
Assume, you will receive rent payments over a time period of 120 years. For the first 60 years, you will receive a rent of $11 at the beginning of each year. For the next 60 years thereafter you will receive$11 at the end of each year. Assuming a discount rate of 11% calculate the net present value of this income stream. (a) Employing the equation for identical payments over a limited time period, show how you would alter this equation applied to this problem. (b) Calculate the NPV of the payments. (a) use the equation that is designed for equal payments over a limited time period at the END of each period. Subtract one period and add the undiscounted first rent. NPV = R + R/i[1 - 1/(1 + i)^60 - 1] + [1 - 1/(1 + i)^120] - R/i[1 - 1/(1 + i)^60] In this case this is NPV = 11 + 11/0.11 [1 - (1 + 0.11)^59] + 11/0.11[1 - 1/(1 + 0.11)^120] - 11/0.11[1 - 1/(1 + 0.11)^60] (b) NPV = 11 + 99.79 + 100.00 - 99. 81 = 110.98
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#### 期刊菜单
A Modified Level Bundle Method with Inexact Data for Nonsmooth Constrained Optimization
DOI: 10.12677/AAM.2019.89179, PDF, HTML, XML, 下载: 1,023 浏览: 1,397 国家自然科学基金支持
Abstract: This paper presents a modified level bundle method with inexact data for nonsmooth constrained optimization. In the method, the inexact data and the approximate improvement function are in-troduced. Moreover, in the projection subproblem, the Bregman distance is used to replace the classical Euclidean distance, in order that the geometric structure of the feasible set can be taken into account, which can reduce the computation of the algorithm. Global convergence of the algo-rithm is proved and the iterative complexity is analyzed.
1. 引言
$\begin{array}{l}{f}^{\ast }:=\mathrm{min}\text{\hspace{0.17em}}\text{\hspace{0.17em}}f\left(x\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{s}\text{.t}\text{.}\text{\hspace{0.17em}}\text{\hspace{0.17em}}c\left(x\right)\le 0,\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }\text{\hspace{0.17em}}\text{ }x\in X,\end{array}$ (1)
$h\left(x;{f}^{\ast }\right)=\mathrm{max}\left\{f\left(x\right)-{f}^{\ast },c\left(x\right)\right\}.$ (2)
2. 算法设计
$\left\{\begin{array}{l}f\left(x\right)\ge {f}_{x}\ge f\left(x\right)-{\epsilon }_{f}^{x},\text{ }\text{ }\text{ }\text{ }{\stackrel{˜}{g}}_{f}^{x}\in {\partial }_{{\epsilon }_{f}^{x}}f\left(x\right),\\ c\left(x\right)\ge {c}_{x}\ge c\left(x\right)-{\epsilon }_{c}^{x},\text{ }\text{ }\text{ }\text{ }{\stackrel{˜}{g}}_{c}^{x}\in {\partial }_{{\epsilon }_{c}^{x}}c\left(x\right),\end{array}$ (3)
${\partial }_{\delta }f\left(x\right)=\left\{g\in {R}^{n}:f\left(y\right)\ge f\left(x\right)+〈g,y-x〉-\delta ,\forall y\in X\right\}.$
$f\left(\cdot \right)\ge f\left(x\right)+〈{\stackrel{˜}{g}}_{f}^{x},\cdot -x〉-{\epsilon }_{f}^{x},\text{\hspace{0.17em}}\text{\hspace{0.17em}}c\left(\cdot \right)\ge c\left(x\right)+〈{\stackrel{˜}{g}}_{c}^{x},\cdot -x〉-{\epsilon }_{c}^{x}.$
${\epsilon }_{f}^{x}\le {\eta }_{f},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\epsilon }_{c}^{x}\le {\eta }_{c},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\forall x\in X.$
$\phi \left(x;\stackrel{^}{x}\right):=\omega \left(x\right)-\omega \left(\stackrel{^}{x}\right)-〈\nabla \omega \left(\stackrel{^}{x}\right),x-\stackrel{^}{x}〉,$
$\omega \left(y\right)\ge \omega \left(x\right)+〈\nabla \omega \left(x\right),y-x〉+\frac{{\sigma }_{\omega }}{2}{‖y-x‖}^{2},\text{\hspace{0.17em}}\forall x,y\in X.$
$〈\nabla \omega \left(x\right)-\nabla \omega \left(z\right),x-z〉\ge {\sigma }_{\omega }{‖x-z‖}^{2},\text{ }\text{ }\text{ }\text{ }\forall x,z\in X.$
${D}_{\omega ,X}^{2}:=\mathrm{max}\left\{\omega \left(x\right)-\left[\omega \left(z\right)+〈\nabla \omega \left(z\right),x-z〉\right],\forall x,z\in X\right\}.$ (4)
${‖x-z‖}^{2}\le \frac{2}{{\sigma }_{\omega }}{D}_{\omega ,X}^{2}=:{\Omega }_{\omega ,X},\text{ }\text{ }\text{ }\forall x,z\in X.$ (5)
$\left\{\begin{array}{l}{l}_{f}^{k}\left(\cdot \right):={f}_{{x}^{k}}+〈{\stackrel{˜}{g}}_{f}^{k},\cdot -{x}^{k}〉,\\ {l}_{c}^{k}\left(\cdot \right):={c}_{{x}^{k}}+〈{\stackrel{˜}{g}}_{c}^{k},\cdot -{x}^{k}〉.\end{array}$
${\stackrel{^}{f}}^{k}\left(x\right):=\underset{j\in {J}_{f}^{k}}{\mathrm{max}}{l}_{f}^{j}\left(x\right),\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{\stackrel{^}{c}}^{k}\left(x\right):=\underset{j\in {J}_{c}^{k}}{\mathrm{max}}{l}_{c}^{j}\left(x\right),$
(6)
${f}_{\text{low}}^{k}\left(\le {f}^{*}\right)$ 是问题最优值的一个下界，定义非精确改进函数如下：
$\stackrel{˜}{h}\left(x;{f}_{\text{low}}^{k}\right)=\mathrm{max}\left\{{f}_{x}-{f}_{\text{low}}^{k},{c}_{x}\right\}.$ (7)
${h}_{\text{rec}}^{k}:=\left\{\begin{array}{l}\stackrel{˜}{h}\left({x}^{0};{f}_{\text{low}}^{0}\right),\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }k=0,\text{ }\\ \mathrm{min}\left\{\underset{j\in {J}_{f}^{k}\cap {J}_{c}^{k}}{\mathrm{min}}\stackrel{˜}{h}\left({x}^{j};{f}_{\text{low}}^{k}\right),{h}_{\text{rec}}^{k-1}\right\}\text{ },\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }k>0,\end{array}$ (8)
${x}_{\text{rec}}^{k}\in {\left\{{x}^{j}\right\}}_{j\le k}\text{ }\text{ }\text{ }\text{ }\text{ }\text{s}\text{.t}\text{.}\text{ }\text{ }\text{ }\text{ }\text{ }\stackrel{˜}{h}\left({x}_{\text{rec}}^{k};{f}_{\text{low}}^{j}\right)={h}_{\text{rec}}^{k},$ (9)
${f}_{\text{lev}}^{k}$ 为当前水平值，采用上述邻近函数代替欧氏距离，本文算法每次迭代求解如下子问题：
${x}^{k+1}:=\mathrm{arg}\underset{x\in {X}^{k}}{\mathrm{min}}\phi \left(x;{\stackrel{^}{x}}^{k}\right),$ (10)
${X}^{k}:=\left\{x\in X:{\stackrel{^}{f}}^{k}\left(x\right)\le {f}_{\text{lev}}^{k},{\stackrel{^}{c}}^{k}\left(x\right)\le 0\right\}.$ (11)
$\nabla \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k}\right)+{s}^{k}+{\mu }_{f}^{k}{\stackrel{^}{g}}_{f}^{k}+{\mu }_{c}^{k}{\stackrel{^}{g}}_{c}^{k}=0,\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{\mu }_{f}^{k}\left({\stackrel{^}{f}}^{k}\left({x}^{k+1}\right)-{f}_{\text{lev}}^{k}\right)=0,\text{ }\text{ }\text{ }\text{ }\text{ }{\mu }_{c}^{k}{\stackrel{^}{c}}^{k}\left({x}^{k+1}\right)=0.$ (12)
${\stackrel{¯}{f}}^{{a}_{k}}\left(x\right):={\stackrel{^}{f}}^{k}\left({x}^{k+1}\right)+〈{\stackrel{^}{g}}_{f}^{k},x-{x}^{k+1}〉$ 满足 ${\stackrel{¯}{f}}^{{a}_{k}}\left(x\right)\le {\stackrel{^}{f}}^{k}\left(x\right)\le f\left(x\right),\text{ }\text{ }\text{ }\text{ }\text{ }\forall x\in X,$ (13)
${\stackrel{¯}{c}}^{{a}_{k}}\left(x\right):={\stackrel{^}{c}}^{k}\left({x}^{k+1}\right)+〈{\stackrel{^}{g}}_{c}^{k},x-{x}^{k+1}〉$ 满足 ${\stackrel{¯}{c}}^{{a}_{k}}\left(x\right)\le {\stackrel{^}{c}}^{k}\left(x\right)\le c\left(x\right),\text{ }\text{ }\text{ }\text{ }\text{ }\forall x\in X.$ (14)
$\underset{x\in {X}^{k}}{\mathrm{arg}\mathrm{min}}\phi \left(x;{\stackrel{^}{x}}^{k}\right)=\underset{x\in {X}^{{a}_{k}}}{\mathrm{arg}\mathrm{min}}\phi \left(x;{\stackrel{^}{x}}^{k}\right)$ (15)
a) 对于情形I，序列 $\left\{{x}_{\text{rec}}^{k}\right\}$ 的任意聚点都是问题(1)的 $\epsilon$ 最优解，其中 $\epsilon :=\mathrm{max}\left\{{\epsilon }_{f},{\epsilon }_{c}\right\}$
b) 对于情形II，序列 $\left\{{x}_{\text{rec}}^{k}\right\}$ 的任意聚点都是问题(1)的最优解。
$0\ge \underset{k}{\mathrm{lim}}\left({f}_{{x}_{\text{rec}}^{k}}-{f}_{\text{low}}^{{j}_{k}}\right)\ge \underset{k}{\mathrm{lim}}\left(f\left({x}_{\text{rec}}^{k}\right)-{\epsilon }_{f}^{{j}_{k}}-{f}_{\text{low}}^{{j}_{k}}\right)\ge \underset{k}{\mathrm{lim}}\left(f\left({x}_{\text{rec}}^{k}\right)-{\epsilon }_{f}^{{j}_{k}}-{f}^{\text{*}}\right),$
$0\ge \underset{k}{\mathrm{lim}}{c}_{{x}_{\text{rec}}^{k}}\ge \underset{k}{\mathrm{lim}}\left(c\left({x}_{\text{rec}}^{k}\right)-{\epsilon }_{c}^{{j}_{k}}\right).$
$\stackrel{¯}{x}$ 是序列 $\left\{{x}_{\text{rec}}^{k}\right\}$ 的一个聚点，对于情形I，由以上两个不等式可以得到 $f\left(\stackrel{¯}{x}\right)\le {f}^{*}+{\epsilon }_{f}$$c\left(\stackrel{¯}{x}\right)\le {\epsilon }_{c}$，因此 $\stackrel{¯}{x}$ 是问题(1)的 $\epsilon$ 最优解。对于情形II，再次利用以上两个不等式可得 $f\left(\stackrel{¯}{x}\right)\le {f}^{\text{*}}$$c\left(\stackrel{¯}{x}\right)\le 0$，故 $\stackrel{¯}{x}$ 是问题(1)的最优解。
3. 收敛性与复杂度分析
$‖{x}^{k+1}-{x}^{k}‖\ge \frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k},\text{ }\text{ }\text{ }\text{ }\text{ }k>k\left(l\right),$
$‖{x}^{k+1}-{\stackrel{^}{x}}^{k}‖\ge \frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k},\text{ }\text{ }\text{ }\text{ }\text{ }k=k\left(l\right).$
${f}_{{x}^{j}}+〈{\stackrel{˜}{g}}_{f}^{j},{x}^{k+1}-{x}^{j}〉\le {f}_{\text{lev}}^{k},$
${c}_{{x}^{j}}+〈{\stackrel{˜}{g}}_{c}^{j},{x}^{k+1}-{x}^{j}〉\le 0.$
${f}_{{x}^{j}}-{f}_{\text{lev}}^{k}\le 〈{\stackrel{˜}{g}}_{f}^{j},{x}^{k+1}-{x}^{j}〉,$
${c}_{{x}^{j}}\le 〈{\stackrel{˜}{g}}_{c}^{j},{x}^{k+1}-{x}^{j}〉.$
${f}_{{x}^{j}}-{f}_{\text{lev}}^{k}\le 〈{\stackrel{˜}{g}}_{f}^{j},{x}^{k+1}-{x}^{j}〉\le ‖{\stackrel{˜}{g}}_{f}^{j}‖‖{x}^{k+1}-{x}^{j}‖\le \Lambda ‖{x}^{k+1}-{x}^{j}‖.$
${c}_{{x}^{j}}\le 〈{\stackrel{˜}{g}}_{c}^{j},{x}^{k+1}-{x}^{j}〉\le ‖{\stackrel{˜}{g}}_{c}^{j}‖‖{x}^{k+1}-{x}^{j}‖\le \Lambda ‖{x}^{k+1}-{x}^{j}‖.$
$\begin{array}{c}\Lambda ‖{x}^{k+1}-{x}^{j}‖\ge \mathrm{max}\left\{{f}_{{x}^{j}}-{f}_{\text{low}}^{k}-\gamma {h}_{\text{rec}}^{k},{c}_{{x}^{j}}\right\}\\ \ge \mathrm{max}\left\{{f}_{{x}^{j}}-{f}_{\text{low}}^{k}-\gamma {h}_{\text{rec}}^{k},{c}_{{x}^{j}}-\gamma {h}_{\text{rec}}^{k}\right\}\\ =-\gamma {h}_{\text{rec}}^{k}+\mathrm{max}\left\{{f}_{{x}^{j}}-{f}_{\text{low}}^{k},{c}_{{x}^{j}}\right\}\end{array}$
$=-\gamma {h}_{\text{rec}}^{k}+\stackrel{˜}{h}\left({x}^{j};{f}_{\text{low}}^{k}\right)$(7)
$=\left(1-\gamma \right){h}_{\text{rec}}^{k}.$(8)
$k>k\left(l\right)$，则束管理确保 $k\in {J}_{f}^{k}\cap {J}_{c}^{k}$。故令使得 $‖{x}^{k+1}-{x}^{k}‖\ge \frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k}$ 成立，当 $k=k\left(l\right)$ 时，选取 ${\stackrel{^}{x}}^{k}$ 为稳定中心，故存在 $j\in {J}_{f}^{k}\cap {J}_{c}^{k}$ 使得 ${x}^{j}={\stackrel{^}{x}}^{k}$，即 $‖{x}^{k+1}-{\stackrel{^}{x}}^{k}‖\ge \frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k}$ 成立。
$k-k\left(l\right)+1\le {\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){h}_{\text{rec}}^{k}}\right)}^{2}+1.$
$〈\nabla \phi \left({x}^{k};{\stackrel{^}{x}}^{k-1}\right),x-{x}^{k}〉\ge 0,\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\forall x\in {X}^{k-1}.$ (16)
i) 假如在第 $k-1$ 步到第k步没有束压缩机制，那么根据 ${\stackrel{^}{f}}^{k}\left(x\right)$ 的定义(6)可知 ${\stackrel{^}{f}}^{k}\left(x\right)\ge {\stackrel{^}{f}}^{k-1}\left(x\right)$${\stackrel{^}{c}}^{k}\left(x\right)\ge {\stackrel{^}{c}}^{k-1}\left(x\right),\forall x\in {R}^{n}$。根据注1可得 ${f}_{\text{lev}}^{k}\le {f}_{\text{lev}}^{k-1}$，从而 ${X}^{k}\subseteq {X}^{k-1}$。因为 $k\in {K}^{l}$，所以有 ${X}^{k}$ 非空，并且 ${x}^{k+1}\in {X}^{k}$。又因为在每个 $l$ 循环中稳定中心不变，即： ${\stackrel{^}{x}}^{k-1}={\stackrel{^}{x}}^{k}$，从而可以得到 $〈\nabla \phi \left({x}^{k};{\stackrel{^}{x}}^{k}\right),{x}^{k+1}-{x}^{k}〉\ge 0$
ii) 若在第 $k-1$ 步到第k步有束压缩，则聚集指标 ${a}_{k}\in {J}_{f}^{k}$${a}_{k}\in {J}_{c}^{k}$，故 ${\stackrel{^}{f}}^{k}\left(x\right)\ge {\stackrel{¯}{f}}^{{a}_{k}}\left(x\right)$$\text{ }{\stackrel{^}{c}}^{k}\left(x\right)\ge {\stackrel{¯}{c}}^{{a}_{k}}\left(x\right)$$\forall x\in {R}^{n}$，从而 ${X}^{k}\subseteq {X}^{{a}_{k}}$。由(15)可知 ${x}^{k}=\mathrm{arg}\mathrm{min}\left\{\phi \left(x;{\stackrel{^}{x}}^{k-1}\right),x\in {X}^{{a}_{k}}\right\}$，根据一阶最优性条件有：
$〈\nabla \phi \left({x}^{k};{\stackrel{^}{x}}^{k-1}\right),x-{x}^{k}〉\ge 0,\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\forall x\in {X}^{{a}_{k}}.$ (17)
$〈\nabla \phi \left({x}^{k};{\stackrel{^}{x}}^{k\left(l\right)}\right),{x}^{k+1}-{x}^{k}〉\ge 0.$
$\phi \left(x;{\stackrel{^}{x}}^{k\left(l\right)}\right)$ 是强凸函数，有
$\frac{\sigma }{2}{‖{x}^{k+1}-{x}^{k}‖}^{2}\le \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)-\phi \left({x}^{k};{\stackrel{^}{x}}^{k\left(l\right)}\right)-〈\nabla \phi \left({x}^{k};{\stackrel{^}{x}}^{k\left(l\right)}\right),{x}^{k+1}-{x}^{k}〉\le \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)-\phi \left({x}^{k};{\stackrel{^}{x}}^{k\left(l\right)}\right).$
$\frac{\sigma }{2}{‖{x}^{k+1}-{x}^{k}‖}^{2}\le \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)-\phi \left({x}^{k};{\stackrel{^}{x}}^{k\left(l\right)}\right).$
$\frac{\sigma }{2}\underset{{}^{j=k\left(l\right)+1}}{\overset{k}{\sum }}{‖{x}^{j+1}-{x}^{j}‖}^{2}\le \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)-\phi \left({x}^{k\left(l\right)+1};{\stackrel{^}{x}}^{k\left(l\right)}\right).$ (18)
$\frac{\sigma }{2}\underset{{}^{j=k\left(l\right)+1}}{\overset{k}{\sum }}{‖{x}^{j+1}-{x}^{j}‖}^{2}\ge \frac{\sigma }{2}\underset{{}^{j=k\left(l\right)+1}}{\overset{k}{\sum }}{\left(\frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{j}\right)}^{2}\ge \frac{\sigma }{2}\underset{{}^{j=k\left(l\right)+1}}{\overset{k}{\sum }}{\left(\frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k}\right)}^{2}.$
$\begin{array}{l}\phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)-\phi \left({x}^{k\left(l\right)+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)\\ \le \phi \left({x}^{k+1};{\stackrel{^}{x}}^{k\left(l\right)}\right)\le \underset{x\in X}{\mathrm{max}}\left\{\phi \left(x;{\stackrel{^}{x}}^{k\left(l\right)}\right)\right\}\le \underset{x,y\in X}{\mathrm{max}}\left\{\phi \left(x;y\right)\right\}={D}_{\omega ,X}^{2}.\end{array}$
${D}_{\omega ,X}^{2}\ge \frac{\sigma }{2}\underset{{}^{j=k\left(l\right)+1}}{\overset{k}{\sum }}{\left(\frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k}\right)}^{2}=\frac{\sigma }{2}\left(k-k\left(l\right)\right){\left(\frac{1-\gamma }{\Lambda }{h}_{\text{rec}}^{k}\right)}^{2},$
$k-k\left(l\right)\le \frac{2{D}_{\omega ,X}^{2}}{\sigma }{\left(\frac{\Lambda }{\left(1-\gamma \right){h}_{\text{rec}}^{k}}\right)}^{2}={\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){h}_{\text{rec}}^{k}}\right)}^{2}.$
$\square$
a) 如果 ${\epsilon }_{f}^{k}\equiv {\epsilon }_{f}\ge 0$${\epsilon }_{c}^{k}\equiv {\epsilon }_{c}\ge 0$$\forall k$，则序列 $\left\{{x}_{\text{rec}}^{k}\right\}$ 的任意聚点是问题(1)的 $\epsilon$ 最优解，其中 $\epsilon :=\mathrm{max}\left\{{\epsilon }_{f},{\epsilon }_{c}\right\}$
b) 如果 ${\epsilon }_{f}^{k}\to 0$${\epsilon }_{c}^{k}\to 0$$k\to \infty$，则序列 $\left\{{x}_{\text{rec}}^{k}\right\}$ 的任意聚点是问题(1)的最优解。
$\square$
$\left(1+\frac{{f}^{*}-{f}_{\text{low}}^{0}}{\gamma {\delta }_{\text{Tol}}}\right)\left({\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){\delta }_{\text{Tol}}}\right)}^{2}+1\right).$
${f}^{\text{*}}\ge {f}_{\text{low}}^{0}+\gamma {h}_{\text{rec}}^{1}+\cdots +\gamma {h}_{\text{rec}}^{k}\ge {f}_{\text{low}}^{0}+\gamma {\delta }_{\text{Tol}}+\cdots +\gamma {\delta }_{\text{Tol}}.$
$N\le \frac{{f}^{\text{*}}-{f}_{\text{low}}^{0}}{\gamma {\delta }_{\text{Tol}}}.$
${\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){h}_{\text{rec}}^{k}}\right)}^{2}+1\le {\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){\delta }_{\text{Tol}}}\right)}^{2}+1.$
${k}_{{\delta }_{\text{Tol}}}$ 是使得 ${h}_{\text{rec}}^{k}>{\delta }_{\text{Tol}}\text{ }$ 成立的最大指标集，那么
${k}_{{\delta }_{\text{Tol}}}\le \left(1+\frac{{f}^{*}-{f}_{\text{low}}^{0}}{\gamma {\delta }_{\text{Tol}}}\right)\left({\Omega }_{\omega ,X}{\left(\frac{\Lambda }{\left(1-\gamma \right){\delta }_{\text{Tol}}}\right)}^{2}+1\right).$
$\square$
4. 结束语
NOTES
*通讯作者
[1] Kiwiel, K.C. (1985) An Exact Penalty Function Algorithm for Non-Smooth Convex Constrained Minimization Prob-lems. IMA Journal of Numerical Analysis, 5, 111-119. https://doi.org/10.1093/imanum/5.1.111 [2] Karas, E., Ribeiro, A., Sagastizábal, C., et al. (2009) A Bundle-Filter Method for Nonsmooth Convex Constrained Optimization. Mathematical Programming, 116, 297-320. https://doi.org/10.1007/s10107-007-0123-7 [3] Lemarechal, C., Nemirovskii, A. and Nesterov, Y. (1995) New Variants of Bundle Methods. Mathematical Programming, 69, 111-147. https://doi.org/10.1007/BF01585555 [4] Fletcher, R. and Leyffer, S. (2002) Nonlinear Programming without a Penalty Function. Mathematical Programming, 91, 239-269. https://doi.org/10.1007/s101070100244 [5] Van Ackooij, W. and De Oliveira, W. (2014) Level Bundle Methods for Constrained Convex Optimization with Various Oracles. Computational Optimization and Applications, 57, 555-597. https://doi.org/10.1007/s10589-013-9610-3 [6] Kiwiel, K.C. (1999) A Bundle Bregman Proximal Method for Convex Nondifferentiable Minimization. Mathematical Programming, 85, 241-258. https://doi.org/10.1007/s101070050056 [7] Ben-Tal, A. and Nemirovski, A. (2005) Non-Euclidean Restricted Memory Level Method for Large-Scale Convex Optimization. Mathematical Programming, 102, 407-456. https://doi.org/10.1007/s10107-004-0553-4 [8] 梁玲. 非光滑优化基于非精确数据的加速水平束方法[D]: [硕士学位论文]. 南宁: 广西大学, 2018. [9] 陈韵梅, 张维. 基于近似一阶信息的加速的bundle level算法[J]. 中国科学, 2017, 10(47): 1119-1142.
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Hide
Problem FPot
The teacher has sent an e-mail to her students with the following task: “Write a program that will determine and output the value of $X$ if given the statement:
$X = \mathit{number}_1^{\mathit{pow}_1} + \mathit{number}_2^{\mathit{pow}_2} + \ldots + \mathit{number}_ N^{\mathit{pow}_ N}$
and it holds that $\mathit{number}_1$, $\mathit{number}_2$ to $\mathit{number}_ N$ are integers, and $\mathit{pow}_1$, $\mathit{pow_2}$ to $\mathit{pow}_ N$ are one-digit integers.” Unfortunately, when the teacher downloaded the task to her computer, the text formatting was lost so the task transformed into a sum of $N$ integers:
$X = P_1 + P_2 + \ldots + P_ N$
For example, without text formatting, the original task in the form of $X = 21^2 + 125^3$ became a task in the form of $X = 212 + 1253$. Help the teacher by writing a program that will, for given $N$ integers from $P_1$ to $P_ N$ determine and output the value of $X$ from the original task.
Input
The first line of input contains the integer $N$ ($1 \leq N \leq 10$), the number of the addends from the task. Each of the following $N$ lines contains the integer $P_ i$ ($10 \leq P_ i \leq 9999$, $i = 1, \ldots , N$) from the task.
Output
The first and only line of output must contain the value of $X$ ($X \leq 1\, 000\, 000\, 000$) from the original task.
Sample Input 1 Sample Output 1
2
212
1253
1953566
Sample Input 2 Sample Output 2
5
23
17
43
52
22
102
Sample Input 3 Sample Output 3
3
213
102
45
10385
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swirl Lesson 1: Basic Building Blocks
| Please choose a course, or type 0 to exit swirl.
1: R Programming
2: Take me to the swirl course repository!
Selection: 1
1: Basic Building Blocks 2: Workspace and Files
3: Sequences of Numbers 4: Vectors
5: Missing Values 6: Subsetting Vectors
7: Matrices and Data Frames 8: Logic
9: Functions 10: lapply and sapply
11: vapply and tapply 12: Looking at Data
13: Simulation 14: Dates and Times
15: Base Graphics
Selection: 1
| | 0%
| In this lesson, we will explore some basic building blocks of the
| R programming language.
...
|== | 3%
| If at any point you'd like more information on a particular topic
| related to R, you can type help.start() at the prompt, which will
| open a menu of resources (either within RStudio or your default
| web browser, depending on your setup). Alternatively, a simple
| web search often yields the answer you're looking for.
...
|=== | 5%
| In its simplest form, R can be used as an interactive calculator.
| Type 5 + 7 and press Enter.
> 5+7
[1] 12
| All that practice is paying off!
|===== | 8%
| R simply prints the result of 12 by default. However, R is a
| programming language and often the reason we use a programming
| language as opposed to a calculator is to automate some process
| or avoid unnecessary repetition.
...
|====== | 11%
| In this case, we may want to use our result from above in a
| second calculation. Instead of retyping 5 + 7 every time we need
| it, we can just create a new variable that stores the result.
...
|======== | 13%
| The way you assign a value to a variable in R is by using the
| assignment operator, which is just a 'less than' symbol followed
| by a 'minus' sign. It looks like this: <-
...
|========= | 16%
| Think of the assignment operator as an arrow. You are assigning
| the value on the right side of the arrow to the variable name on
| the left side of the arrow.
...
|=========== | 18%
| To assign the result of 5 + 7 to a new variable called x, you
| type x <- 5 + 7. This can be read as 'x gets 5 plus 7'. Give it a
| try now.
> x<-5+7
| Keep working like that and you'll get there!
|============ | 21%
| You'll notice that R did not print the result of 12 this time.
| When you use the assignment operator, R assumes that you don't
| want to see the result immediately, but rather that you intend to
| use the result for something else later on.
...
|============== | 24%
| To view the contents of the variable x, just type x and press
| Enter. Try it now.
> x
[1] 12
| Nice work!
|=============== | 26%
| Now, store the result of x - 3 in a new variable called y.
> y<-x-3
| You got it!
|================= | 29%
| What is the value of y? Type y to find out.
> y
[1] 9
| All that practice is paying off!
|================== | 32%
| Now, let's create a small collection of numbers called a vector.
| Any object that contains data is called a data structure and
| numeric vectors are the simplest type of data structure in R. In
| fact, even a single number is considered a vector of length one.
...
|==================== | 34%
| The easiest way to create a vector is with the c() function,
| which stands for 'concatenate' or 'combine'. To create a vector
| containing the numbers 1.1, 9, and 3.14, type c(1.1, 9, 3.14).
| Try it now and store the result in a variable called z.
> z<-c(1.1,9,3.14)
|===================== | 37%
| Anytime you have questions about a particular function, you can
| access R's built-in help files via the ? command. For example,
| if you want more information on the c() function, type ?c without
| the parentheses that normally follow a function name. Give it a
| try.
> ?c
| Nice work!
|======================= | 39%
| Type z to view its contents. Notice that there are no commas
| separating the values in the output.
> z
[1] 1.10 9.00 3.14
| You are amazing!
|======================== | 42%
| You can combine vectors to make a new vector. Create a new vector
| that contains z, 555, then z again in that order. Don't assign
| this vector to a new variable, so that we can just see the result
| immediately.
> c(z,555,z)
[1] 1.10 9.00 3.14 555.00 1.10 9.00 3.14
| That's correct!
|========================== | 45%
| Numeric vectors can be used in arithmetic expressions. Type the
| following to see what happens: z * 2 + 100.
> z*2+100
[1] 102.20 118.00 106.28
| That's the answer I was looking for.
|=========================== | 47%
| First, R multiplied each of the three elements in z by 2. Then it
| added 100 to each element to get the result you see above.
...
|============================= | 50%
| Other common arithmetic operators are +, -, /, and ^
| (where x^2 means 'x squared'). To take the square root, use the
| sqrt() function and to take the absolute value, use the abs()
| function.
...
|=============================== | 53%
| Take the square root of z - 1 and assign it to a new variable
| called my_sqrt.
> my_sqrt<-sqrt(z-1)
| You got it right!
|================================ | 55%
| Before we view the contents of the my_sqrt variable, what do you
| think it contains?
1: a vector of length 0 (i.e. an empty vector)
2: a vector of length 3
3: a single number (i.e a vector of length 1)
Selection: 2
| You are quite good my friend!
|================================== | 58%
| Print the contents of my_sqrt.
> my_sqrt
[1] 0.3162278 2.8284271 1.4628739
| You are quite good my friend!
|=================================== | 61%
| As you may have guessed, R first subtracted 1 from each element
| of z, then took the square root of each element. This leaves you
| with a vector of the same length as the original vector z.
...
|===================================== | 63%
| Now, create a new variable called my_div that gets the value of z
| divided by my_sqrt.
> my_div<-z/my_sqrt
| You nailed it! Good job!
|====================================== | 66%
| Which statement do you think is true?
1: The first element of my_div is equal to the first element of z
divided by the first element of my_sqrt, and so on...
2: my_div is a single number (i.e a vector of length 1)
3: my_div is undefined
Selection: 1
| Great job!
|======================================== | 68%
| Go ahead and print the contents of my_div.
> my_div
[1] 3.478505 3.181981 2.146460
|========================================= | 71%
| When given two vectors of the same length, R simply performs the
| specified arithmetic operation (+, -, *, etc.)
| element-by-element. If the vectors are of different lengths, R
| 'recycles' the shorter vector until it is the same length as the
| longer vector.
...
|=========================================== | 74%
| When we did z * 2 + 100 in our earlier example, z was a vector of
| length 3, but technically 2 and 100 are each vectors of length 1.
...
|============================================ | 76%
| Behind the scenes, R is 'recycling' the 2 to make a vector of 2s
| and the 100 to make a vector of 100s. In other words, when you
| ask R to compute z * 2 + 100, what it really computes is this: z
| * c(2, 2, 2) + c(100, 100, 100).
...
|============================================== | 79%
| To see another example of how this vector 'recycling' works, try
| adding c(1, 2, 3, 4) and c(0, 10). Don't worry about saving the
| result in a new variable.
> c(1,2,3,4)+c(0,10)
[1] 1 12 3 14
| You got it right!
|=============================================== | 82%
| If the length of the shorter vector does not divide evenly into
| the length of the longer vector, R will still apply the
| 'recycling' method, but will throw a warning to let you know
| something fishy might be going on.
...
|================================================= | 84%
| Try c(1, 2, 3, 4) + c(0, 10, 100) for an example.
> c(1,2,3,4)+c(0,10,100)
[1] 1 12 103 4
Warning message:
In c(1, 2, 3, 4) + c(0, 10, 100) :
longer object length is not a multiple of shorter object length
| Excellent work!
|================================================== | 87%
| Before concluding this lesson, I'd like to show you a couple of
| time-saving tricks.
...
|==================================================== | 89%
| Earlier in the lesson, you computed z * 2 + 100. Let's pretend
| 100. You could either re-type the expression, or...
...
|===================================================== | 92%
| In many programming environments, the up arrow will cycle through
| previous commands. Try hitting the up arrow on your keyboard
| until you get to this command (z * 2 + 100), then change 100 to
| 1000 and hit Enter. If the up arrow doesn't work for you, just
| type the corrected command.
> z*2+1000
[1] 1002.20 1018.00 1006.28
| All that practice is paying off!
|======================================================= | 95%
| Finally, let's pretend you'd like to view the contents of a
| variable that you created earlier, but you can't seem to remember
| if you named it my_div or myDiv. You could try both and see what
| works, or...
...
|======================================================== | 97%
| You can type the first two letters of the variable name, then hit
| the Tab key (possibly more than once). Most programming
| environments will provide a list of variables that you've created
| that begin with 'my'. This is called auto-completion and can be
| quite handy when you have many variables in your workspace. Give
| it a try. (If auto-completion doesn't work for you, just type
| my_div and press Enter.)
>
> my_div
[1] 3.478505 3.181981 2.146460
| You are quite good my friend!
|==========================================================| 100%
| 2,717
| 10,755
|
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45343896145 http://1ucasvb.tumblr.com/post/45343896145/pis-parametric-coordinate-functions-this-is-the 1191 Pi’s parametric coordinate functions This is the...
## Pi’s parametric coordinate functions
This is the second of three animations I’ll be posting today (here’s the first). Be sure to check them out later if you miss them!
The polygonal trigonometric functions I described earlier were based on the interior angle, instead of the length along the polygon’s border.
This simplified things a lot, and created some interesting uses for the functions. However, since I could only have one value of radius for each angle (they were based on polar equations), I could not draw arbitrary shapes with a continuous line based on the [0,2π] interval.
The solution is to extend the idea to general closed curves, by using the position along the curve to define the sine and cosine analogues. In other words, we want “path trigonometric functions” for which the input parameter is the position along the path, and whose periods are the curve’s total arc-length.
But the concept of “sine” and “cosine”, as well as “trigonometric”, completely lose their meaning at this point. It has nothing to do with triangles or angles.
We’re now dealing with the functions x(s) (in blue) and y(s) (in red) that together describe the curve, by being used in the parametric equation r(s) = ( x(s) , y(s) ), where r(s) is a vector function and s is the arc-length. This is very standard stuff, so it isn’t incredibly exciting anymore.
Notice that if the green curve was a unit circle, the functions would become the usual sine and cosine.
But we do get to see what these functions look like and what they are doing. So here’s the coordinate functions for the arc-length parametrization of a pi curve!
Happy Pi day!
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# Sage Interactions - Geometry
## Intersecting tetrahedral reflections
by Marshall Hampton. Inspired by a question from Hans Schepker of Glass Geometry.
```#Pairs of tetrahedra, one the reflection of the other in the internal face, are joined by union operations:
p1 = Polyhedron(vertices = [[1,1,1],[1,1,0],[0,1,1],[1,0,1]])
p2 = Polyhedron(vertices = [[1/3,1/3,1/3],[1,1,0],[0,1,1],[1,0,1]])
p12 = p1.union(p2)
p3 = Polyhedron(vertices = [[0,0,1],[0,0,0],[0,1,1],[1,0,1]])
p4 = Polyhedron(vertices = [[2/3,2/3,1/3],[0,0,0],[0,1,1],[1,0,1]])
p34 = p3.union(p4)
p5 = Polyhedron(vertices = [[1,0,0],[1,0,1],[0,0,0],[1,1,0]])
p6 = Polyhedron(vertices = [[1/3,2/3,2/3],[1,0,1],[0,0,0],[1,1,0]])
p56 = p5.union(p6)
p7 = Polyhedron(vertices = [[0,1,0],[0,0,0],[1,1,0],[0,1,1]])
p8 = Polyhedron(vertices = [[2/3,1/3,2/3],[0,0,0],[1,1,0],[0,1,1]])
p78 = p7.union(p8)
pti = p12.intersection(p34).intersection(p56).intersection(p78)
@interact
def tetra_plot(opac = slider(srange(0,1.0,.25), default = .25)):
p12r = p12.render_wireframe()+p12.render_solid(opacity = opac)
p34r = p34.render_wireframe()+p34.render_solid(rgbcolor = (0,0,1),opacity = opac)
p56r = p56.render_wireframe()+p56.render_solid(rgbcolor = (0,1,0),opacity = opac)
p78r = p78.render_wireframe()+p78.render_solid(rgbcolor = (0,1,1),opacity = opac)
ptir = pti.render_wireframe()+pti.render_solid(rgbcolor = (1,0,1),opacity = .9)
show(p12r+p34r+p56r+p78r+ptir, frame = False)```
## Evolutes
by Pablo Angulo. Computes the evolute of a plane curve given in parametric coordinates. The curve must be parametrized from the interval [0,2pi].
```var('t');
def norma(v):
return sqrt(sum(x^2 for x in v))
paso_angulo=5
@interact
def _( gamma1=input_box(default=sin(t)), gamma2=input_box(default=1.3*cos(t)),
draw_normal_lines=True,
rango_angulos=range_slider(0,360,paso_angulo,(0,90),label='Draw lines for these angles'),
draw_osculating_circle=True,
t0=input_box(default=pi/3,label='parameter value for the osculating circle'),
auto_update=False ):
gamma=(gamma1,gamma2)
gammap=(gamma[0].derivative(),gamma[1].derivative())
normal=(gammap[1]/norma(gammap), -gammap[0]/norma(gammap))
gammapp=(gammap[0].derivative(),gammap[1].derivative())
np=norma(gammap)
npp=norma(gammapp)
pe=gammap[0]*gammapp[0]+gammap[1]*gammapp[1]
curvatura=(gammap[1]*gammapp[0]-gammap[0]*gammapp[1])/norma(gammap)^3
curva=parametric_plot(gamma,(t,0,2*pi))
evoluta=parametric_plot(centros,(t,0,2*pi), color='red')
grafica=curva+evoluta
if draw_normal_lines:
f=2*pi/360
lineas=sum(line2d( [ (gamma[0](t=i*f), gamma[1](t=i*f)),
(centros[0](t=i*f), centros[1](t=i*f)) ],
thickness=1,rgbcolor=(1,0.8,0.8))
for i in range(rango_angulos[0], rango_angulos[1]+paso_angulo, paso_angulo))
grafica+=lineas
if draw_osculating_circle and 0<t0<2*pi:
punto=point((gamma[0](t=t0), gamma[1](t=t0)), rgbcolor=hue(0),pointsize=30)
grafica+=punto+circulo
show(grafica,aspect_ratio=1,xmin=-2,xmax=2,ymin=-2,ymax=2)```
## Geodesics on a parametric surface
by Antonio Valdés and Pablo Angulo. A first interact allows the user to introduce a parametric surface, and draws it. Then a second interact draws a geodesic within the surface. The separation is so that after the first interact, the geodesic equations are "compiled", and then the second interact is faster.
```u, v, t = var('u v t')
@interact
def _(x = input_box(3*sin(u)*cos(v), 'x'),
y = input_box(sin(u)*sin(v), 'y'),
z = input_box(2*cos(u), 'z'),
_int_u = input_grid(1, 2, default = [[0,pi]], label = 'u -interval'),
_int_v = input_grid(1, 2, default = [[-pi,pi]], label = 'v -interval')):
global F, Fu, Fv, func, S_plot, int_u, int_v
int_u = _int_u[0]
int_v = _int_v[0]
def F(uu, vv):
X = vector([x, y, z])
return X.subs({u : uu, v : vv})
S_plot = parametric_plot3d( F(u, v),
(u, int_u[0], int_u[1]),
(v, int_v[0], int_v[1]))
show(S_plot, aspect_ratio = [1, 1, 1])
dFu = F(u, v).diff(u)
dFv = F(u, v).diff(v)
Fu = fast_float(dFu, u, v)
Fv = fast_float(dFv, u, v)
ufunc = function('ufunc', t)
vfunc = function('vfunc', t)
dFtt = F(ufunc, vfunc).diff(t, t)
ec1 = dFtt.dot_product(dFu(u=ufunc, v=vfunc))
ec2 = dFtt.dot_product(dFv(u=ufunc, v=vfunc))
dv, ddv, du, ddu = var('dv, ddv, du, ddu')
diffec1 = ec1.subs_expr(diff(ufunc, t) == du,
diff(ufunc, t, t) == ddu,
diff(vfunc, t) == dv,
diff(vfunc, t, t) == ddv,
ufunc == u, vfunc == v)
diffec2 = ec2.subs_expr(diff(ufunc, t) == du,
diff(ufunc, t, t) == ddu,
diff(vfunc, t) == dv,
diff(vfunc, t, t) == ddv,
ufunc == u, vfunc == v)
sols = solve([diffec1 == 0 , diffec2 == 0], ddu, ddv)
ddu_rhs = (sols[0][0]).rhs().full_simplify()
ddv_rhs = (sols[0][1]).rhs().full_simplify()
ddu_ff = fast_float(ddu_rhs, du, dv, u, v)
ddv_ff = fast_float(ddv_rhs, du, dv, u, v)
def func(y,t):
v = list(y)
return [ddu_ff(*v), ddv_ff(*v), v[0], v[1]]```
```from scipy.integrate import odeint
@interact
def _(u_0 = slider(int_u[0], int_u[1], default = (int_u[0] + int_u[1])/2, label = 'u_0'),
v_0 = slider(int_v[0], int_v[1], default = (int_v[0] + int_v[1])/2, label = 'v_0'),
V_u = slider(-10, 10, default = 1, label = 'V_u'),
V_v = slider(-10, 10, default = 0, label = 'V_v'),
int_s = range_slider(-10, 10, 0.1,
default = (0, (int_u[1] - int_u[0])/2),
label = 'geodesic interval') ):
du, dv, u, v = var('du dv u v')
Point = [u_0, v_0]
velocity = [V_u, V_v]
Point = map(float, Point)
velocity = map(float, velocity)
geo2D_aux = odeint(func,
y0 = [velocity[0], velocity[1], Point[0], Point[1]],
t = srange(int_s[0], int_s[1], 0.01))
geo3D = [F(l,r) for [j, k, l, r] in geo2D_aux]
g_plot = line3d(geo3D, rgbcolor = (1, 0, 0), thickness = 4)
P = F(Point[0], Point[1])
P_plot = point3d((P[0], P[1], P[2]), rgbcolor = (0, 0, 0))
V = velocity[0] * Fu(u = Point[0], v = Point[1]) + \
velocity[1] * Fv(u= Point[0], v = Point[1])
V_plot = arrow3d(P, P + V)
show(g_plot + S_plot + V_plot + P_plot,aspect_ratio = [1, 1, 1])```
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Determine the bending stress, Mechanical Engineering
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(a) What do you understand by the following : (i) Open System (ii) Closed System (iii) Concept of ‘Work' (b) 0.014 m 3 gas at a pressure of 2070 KPa expends to a pressure of
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explain with suitable eg. static and dynamic force analysis
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Compute the ratio of the torque: Compute the ratio of the torque transmitted by a hollow & a solid shaft of the similar material, length & weight. Solution d i = inte
Age-hardening of aluminium alloys, Age-hardening of Aluminium Alloys I...
Age-hardening of Aluminium Alloys In specific alloys precipitation from a single phase may arise. The precipitate phase might be in form of determine sub-microscopic particles
Interference, construction and working of michelsons interferometer
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https://www.huntthegoose.co.uk/on-line-casino-on-the-web-wagering-method-optimistic-development-system/
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# On line casino On the web Wagering Method – Optimistic Development System
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You can say this is a logic that tells you the opportunities of successful 4 times in a one row. At the commencing or just at the preliminary stage the wager is of one unit, the second wager is of three units, the 3rd wager is of two models and the fourth wager is of 6 units. Consequently it is also referred to as the one-three-two-6 method.
บาคาร่าออนไลน์ will illustrate this casino on the web betting method in element, to give you a obvious comprehending. For instance you spot your 1st guess of \$ten. The 2nd wager is meant to be \$thirty – when you acquire the initial wager, your \$10 receives additional up with the \$20 already placed on the table. The overall arrives to \$thirty.
So the second wager you spot would be of \$30. The grand total prior to you engage in the third wager will be of \$60 total (the \$30 wager put by you in the second guess mixed with each other with the 2nd guess successful presently positioned on the desk). From the \$sixty you just take away \$forty and the third wager is of \$20.
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# Clone a Linked List with next and Random Pointer
Given a linked list of size N where each node has two links: one pointer points to the next node and the second pointer points to any node in the list. The task is to create a clone of this linked list in O(N) time
Note: The pointer pointing to the next node is ‘next‘ pointer and the one pointing to an arbitrary node is called ‘arbit’ pointer as it can point to any arbitrary node in the linked list.
An example of the linked list is shown in the below image:
An example of linked list with a random pointerAn example of linked list with a random pointer
## Clone a Linked List with next and Random Pointer using Extra Space:
First create a single linked list with only the ‘next’ pointer and use a mapping to map the new nodes to their corresponding nodes in the given linked list. Now use this mapping to point the arbitrary node from any node in the newly created list.
Follow the steps mentioned below to implement the above idea:
• Create a duplicate (say Y) for each node (say X) and map them with corresponding old nodes (say mp, So mp[X] = Y).
• Create the single linked list of the duplicate nodes where each node only has the ‘next’ pointer.
• Now iterate over the old linked list and do the following:
• Find the duplicate node mapped with the current one. (i.e., if the current node is X then duplicate is mp[x])
• Make the arbit pointer of the duplicate node pointing to the duplicate of the current->arbit node (i.e., mp[x]->arbit will point to mp[X->arbit]).
• The linked list created in this way is the required linked list.
Follow the illustration below for a better understanding:
Illustration:
Consider the linked list shown below:
The green links are the arbit pointers
Creating copy of Nodes and next pointer:
Initially create single linked list of duplicate nodes with only the next pointers and map them with the old ones.
Here the blue coloured links are used to show the mapping.
New linked list mapped with old nodes
Linking the arbit pointers:
Now iterating the old array and update the arbit pointers as mentioned in the approach. The green coloured links are the arbit pointers.
At first node:
Linking arbit pointer of duplicate of 1st node
At second node:
Linking arbit pointer of duplicate of 2nd node
At third node:
Linking arbit pointer of duplicate of 3rd node
At fourth node:
Linking arbit pointer of duplicate of 4th node
At fifth node:
Linking arbit pointer of duplicate of 5th node
The final linked list is as shown below:
The original and the clone
Below is the implementation of the above approach:
## C++14
`// C++ code to implement the approach` `#include ``using` `namespace` `std;` `// Structure of a node of linked list``struct` `Node {`` ``int` `val;`` ``Node* next;`` ``Node* arbit;`` ` ` ``// Constructor`` ``Node(``int` `x)`` ``{`` ``this``->val = x;`` ``this``->next = NULL;`` ``this``->arbit = NULL;`` ``}``};` `// Function to clone the linked list``Node* cloneLinkedList(Node* head)``{`` ``// Map to store the mapping of `` ``// old nodes with new ones`` ``unordered_map mp;`` ``Node *temp, *nhead;`` ` ` ``// Duplicate of the first node`` ``temp = head;`` ``nhead = ``new` `Node(temp->val);`` ``mp[temp] = nhead;`` ` ` ``// Loop to create duplicates of nodes `` ``// with only next pointer`` ``while` `(temp->next != NULL) {`` ``nhead->next `` ``= ``new` `Node(temp->next->val);`` ``temp = temp->next;`` ``nhead = nhead->next;`` ``mp[temp] = nhead;`` ``}`` ``temp = head;`` ` ` ``// Loop to clone the arbit pointers`` ``while` `(temp != NULL) {`` ``mp[temp]->arbit = mp[temp->arbit];`` ``temp = temp->next;`` ``}`` ` ` ``// Return the head of the clone`` ``return` `mp[head];``}` `// Function to print the linked list``void` `printList(Node* head)``{`` ``cout << head->val << ``"("`` ``<< head->arbit->val << ``")"``;`` ``head = head->next;`` ``while` `(head != NULL) {`` ``cout << ``" -> "` `<< head->val << ``"("`` ``<< head->arbit->val << ``")"``;`` ``head = head->next;`` ``}`` ``cout << endl;``}` `// Driver code``int` `main()``{`` ``// Creating a linked list with random pointer`` ``Node* head = ``new` `Node(1);`` ``head->next = ``new` `Node(2);`` ``head->next->next = ``new` `Node(3);`` ``head->next->next->next = ``new` `Node(4);`` ``head->next->next->next->next `` ``= ``new` `Node(5);`` ``head->arbit = head->next->next;`` ``head->next->arbit = head;`` ``head->next->next->arbit `` ``= head->next->next->next->next;`` ``head->next->next->next->arbit `` ``= head->next->next;`` ``head->next->next->next->next->arbit `` ``= head->next;`` ` ` ``// Print the original list`` ``cout << ``"The original linked list:\n"``;`` ``printList(head);`` ` ` ``// Function call`` ``Node* sol = cloneLinkedList(head);`` ` ` ``cout << ``"The cloned linked list:\n"``;`` ``printList(sol);`` ` ` ``return` `0;``}`
## Java
`// Java code to implement the approach` `import` `java.io.*;``import` `java.util.HashMap;` `class` `Node {`` ``int` `val;`` ``Node next;`` ``Node arbit;` ` ``// Constructor`` ``Node(``int` `x)`` ``{`` ``this``.val = x;`` ``this``.next = ``null``;`` ``this``.arbit = ``null``;`` ``}``}` `class` `GFG {` ` ``static` `Node cloneLinkedList(Node head)`` ``{`` ``// Map to store the mapping of`` ``// old nodes with new ones`` ``HashMap mp = ``new` `HashMap<>();`` ``Node temp, nhead;` ` ``// Duplicate of the first node`` ``temp = head;`` ``nhead = ``new` `Node(temp.val);`` ``mp.put(temp, nhead);` ` ``// Loop to create duplicates of nodes`` ``// with only next pointer`` ``while` `(temp.next != ``null``) {`` ``nhead.next = ``new` `Node(temp.next.val);`` ``temp = temp.next;`` ``nhead = nhead.next;`` ``mp.put(temp, nhead);`` ``}`` ``temp = head;` ` ``// Loop to clone the arbit pointers`` ``while` `(temp != ``null``) {`` ``mp.get(temp).arbit = mp.get(temp.arbit);`` ``temp = temp.next;`` ``}` ` ``// Return the head of the clone`` ``return` `mp.get(head);`` ``}` ` ``static` `void` `printList(Node head)`` ``{`` ``System.out.print(head.val + ``"("` `+ head.arbit.val`` ``+ ``")"``);`` ``head = head.next;`` ``while` `(head != ``null``) {`` ``System.out.print(``" -> "` `+ head.val + ``"("`` ``+ head.arbit.val + ``")"``);`` ``head = head.next;`` ``}`` ``System.out.println();`` ``}` ` ``public` `static` `void` `main(String[] args)`` ``{`` ``// Creating a linked list with random pointer`` ``Node head = ``new` `Node(``1``);`` ``head.next = ``new` `Node(``2``);`` ``head.next.next = ``new` `Node(``3``);`` ``head.next.next.next = ``new` `Node(``4``);`` ``head.next.next.next.next = ``new` `Node(``5``);`` ``head.arbit = head.next.next;`` ``head.next.arbit = head;`` ``head.next.next.arbit = head.next.next.next.next;`` ``head.next.next.next.arbit = head.next.next;`` ``head.next.next.next.next.arbit = head.next;` ` ``// Print the original list`` ``System.out.println(``"The original linked list:"``);`` ``printList(head);` ` ``// Function call`` ``Node sol = cloneLinkedList(head);` ` ``System.out.println(``"The cloned linked list:"``);`` ``printList(sol);`` ``}``}` `/// This code is contributed by lokesh.`
## Python3
`# Structure of a node of linked list``class` `Node:`` ``def` `__init__(``self``, val):`` ``self``.val ``=` `val`` ``self``.``next` `=` `None`` ``self``.arbit ``=` `None` `# Function to clone the linked list``def` `cloneLinkedList(head):`` ``# Map to store the mapping of`` ``# old nodes with new ones`` ``mp ``=` `{}`` ``temp ``=` `head`` ``nhead ``=` `Node(temp.val)`` ``mp[temp] ``=` `nhead` ` ``# Loop to create duplicates of nodes`` ``# with only next pointer`` ``while` `temp.``next``:`` ``nhead.``next` `=` `Node(temp.``next``.val)`` ``temp ``=` `temp.``next`` ``nhead ``=` `nhead.``next`` ``mp[temp] ``=` `nhead` ` ``temp ``=` `head` ` ``# Loop to clone the arbit pointers`` ``while` `temp:`` ``mp[temp].arbit ``=` `mp[temp.arbit]`` ``temp ``=` `temp.``next` ` ``# Return the head of the clone`` ``return` `mp[head]` `# Function to print the linked list``def` `printList(head):`` ``result ``=` `[]`` ``while` `head:`` ``result.append(f``"{head.val}({head.arbit.val})"``)`` ``head ``=` `head.``next`` ``print``(``" -> "``.join(result))` `# Creating a linked list with random pointer``head ``=` `Node(``1``)``head.``next` `=` `Node(``2``)``head.``next``.``next` `=` `Node(``3``)``head.``next``.``next``.``next` `=` `Node(``4``)``head.``next``.``next``.``next``.``next` `=` `Node(``5``)``head.arbit ``=` `head.``next``.``next``head.``next``.arbit ``=` `head``head.``next``.``next``.arbit ``=` `head.``next``.``next``.``next``.``next``head.``next``.``next``.``next``.arbit ``=` `head.``next``.``next``head.``next``.``next``.``next``.``next``.arbit ``=` `head.``next` `# Print the original list``print``(``"The original linked list:"``)``printList(head)` `# Function call``sol ``=` `cloneLinkedList(head)` `print``(``"The cloned linked list:"``)``printList(sol)`
## C#
`// C# code to implement the approach``using` `System;``using` `System.Collections.Generic;` `class` `Node {`` ``public` `int` `val;`` ``public` `Node next;`` ``public` `Node arbit;` ` ``// Constructor`` ``public` `Node(``int` `x)`` ``{`` ``this``.val = x;`` ``this``.next = ``null``;`` ``this``.arbit = ``null``;`` ``}``}` `public` `class` `GFG {` ` ``static` `Node cloneLinkedList(Node head)`` ``{`` ``// Map to store the mapping of`` ``// old nodes with new ones`` ``Dictionary mp`` ``= ``new` `Dictionary();`` ``Node temp, nhead;` ` ``// Duplicate of the first node`` ``temp = head;`` ``nhead = ``new` `Node(temp.val);`` ``mp[temp] = nhead;` ` ``// Loop to create duplicates of nodes`` ``// with only next pointer`` ``while` `(temp.next != ``null``) {`` ``nhead.next = ``new` `Node(temp.next.val);`` ``temp = temp.next;`` ``nhead = nhead.next;`` ``mp[temp] = nhead;`` ``}`` ``temp = head;` ` ``// Loop to clone the arbit pointers`` ``while` `(temp != ``null``) {`` ``mp[temp].arbit = mp[temp.arbit];`` ``temp = temp.next;`` ``}` ` ``// Return the head of the clone`` ``return` `mp[head];`` ``}` ` ``static` `void` `printList(Node head)`` ``{`` ``Console.Write(head.val + ``"("` `+ head.arbit.val`` ``+ ``")"``);`` ``head = head.next;`` ``while` `(head != ``null``) {`` ``Console.Write(``" -> "` `+ head.val + ``"("`` ``+ head.arbit.val + ``")"``);`` ``head = head.next;`` ``}`` ``Console.WriteLine();`` ``}` ` ``static` `public` `void` `Main()`` ``{` ` ``// Code`` ``// Creating a linked list with random pointer`` ``Node head = ``new` `Node(1);`` ``head.next = ``new` `Node(2);`` ``head.next.next = ``new` `Node(3);`` ``head.next.next.next = ``new` `Node(4);`` ``head.next.next.next.next = ``new` `Node(5);`` ``head.arbit = head.next.next;`` ``head.next.arbit = head;`` ``head.next.next.arbit = head.next.next.next.next;`` ``head.next.next.next.arbit = head.next.next;`` ``head.next.next.next.next.arbit = head.next;` ` ``// Print the original list`` ``Console.WriteLine(``"The original linked list:"``);`` ``printList(head);` ` ``// Function call`` ``Node sol = cloneLinkedList(head);` ` ``Console.WriteLine(``"The cloned linked list:"``);`` ``printList(sol);`` ``}``}` `// This code is contributed by lokeshmvs21.`
## Javascript
`// Javascript code to implement the approach``class Node {`` ``constructor(val) {`` ``this``.val = val;`` ``this``.next = ``null``;`` ``this``.arbit = ``null``;`` ``}``}` `const cloneLinkedList = (head) => {` ` ``// Map to store the mapping of old nodes with new ones`` ``const mp = ``new` `Map();`` ``let temp = head;`` ``let nhead = ``new` `Node(temp.val);`` ``mp.set(temp, nhead);` ` ``// Loop to create duplicates of nodes with only next pointer`` ``while` `(temp.next) {`` ``nhead.next = ``new` `Node(temp.next.val);`` ``temp = temp.next;`` ``nhead = nhead.next;`` ``mp.set(temp, nhead);`` ``}`` ``temp = head;` ` ``// Loop to clone the arbit pointers`` ``while` `(temp) {`` ``mp.get(temp).arbit = mp.get(temp.arbit);`` ``temp = temp.next;`` ``}` ` ``// Return the head of the clone`` ``return` `mp.get(head);``}` `const printList = (head) => {`` ``let str = `\${head.val}(\${head.arbit.val})`;`` ``head = head.next;`` ``while` `(head) {`` ``str += ` -> \${head.val}(\${head.arbit.val})`;`` ``head = head.next;`` ``}`` ``console.log(str);``}` `// Creating a linked list with random pointer``const head = ``new` `Node(1);``head.next = ``new` `Node(2);``head.next.next = ``new` `Node(3);``head.next.next.next = ``new` `Node(4);``head.next.next.next.next = ``new` `Node(5);``head.arbit = head.next.next;``head.next.arbit = head;``head.next.next.arbit = head.next.next.next.next;``head.next.next.next.arbit = head.next.next;``head.next.next.next.next.arbit = head.next;` `// Print the original list``console.log(``"The original linked list:"``);``printList(head);` `// Function call``const sol = cloneLinkedList(head);` `console.log(``"The cloned linked list:"``);``printList(sol);` `// This code is contributed by shivamsharma215`
Output
```The original linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
The cloned linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
```
Time Complexity: O(N)
Auxiliary Space: O(N)
## Clone a Linked List with next and Random Pointer without using any Extra Space:
Create duplicate of a node and insert it in between that node and the node just next to it.
Now for a node X its duplicate will be X->next and the arbitrary pointer of the duplicate will point to X->arbit->next [as that is the duplicate of X->arbit]
Follow the steps mentioned below to implement the idea:
• Create the copy of node 1 and insert it between node 1 and node 2 in the original Linked List, create the copy of node 2 and insert it between 2nd and 3rd node and so on. Add the copy of N after the Nth node
• Now copy the arbitrary link in this fashion:
original->next->arbitrary = original->arbitrary->next
• Now restore the original and copy linked lists in this fashion in a single loop.
original->next = original->next->next;
copy->next = copy->next->next;
• Make sure that the last element of original->next is NULL.
## C++
`// C++ code to implement the approach` `#include ``using` `namespace` `std;` `struct` `Node {`` ``int` `data;`` ``Node *next, *random;`` ``Node(``int` `x) {`` ``data = x;`` ``next = random = NULL;`` ``}``};` `Node* cloneLinkedList(Node* head) {`` ``if` `(head == NULL) {`` ``return` `NULL;`` ``}`` ` ` ``// Step 1: Create new nodes and insert them next to the original nodes`` ``Node* curr = head;`` ``while` `(curr != NULL) {`` ``Node* newNode = ``new` `Node(curr->data);`` ``newNode->next = curr->next;`` ``curr->next = newNode;`` ``curr = newNode->next;`` ``}`` ` ` ``// Step 2: Set the random pointers of the new nodes`` ``curr = head;`` ``while` `(curr != NULL) {`` ``if` `(curr->random != NULL) {`` ``curr->next->random = curr->random->next;`` ``}`` ``curr = curr->next->next;`` ``}`` ` ` ``// Step 3: Separate the new nodes from the original nodes`` ``curr = head;`` ``Node* clonedHead = head->next;`` ``Node* clonedCurr = clonedHead;`` ``while` `(clonedCurr->next != NULL) {`` ``curr->next = curr->next->next;`` ``clonedCurr->next = clonedCurr->next->next;`` ``curr = curr->next;`` ``clonedCurr = clonedCurr->next;`` ``}`` ``curr->next = NULL;`` ``clonedCurr->next = NULL;`` ` ` ``return` `clonedHead;``}` `// Function to print the linked list``void` `printList(Node* head)``{`` ``cout << head->data << ``"("`` ``<< head->random->data << ``")"``;`` ``head = head->next;`` ``while` `(head != NULL) {`` ``cout << ``" -> "` `<< head->data << ``"("`` ``<< head->random->data << ``")"``;`` ``head = head->next;`` ``}`` ``cout << endl;``}` `// Driver code``int` `main()``{`` ``// Creating a linked list with random pointer`` ``Node* head = ``new` `Node(1);`` ``head->next = ``new` `Node(2);`` ``head->next->next = ``new` `Node(3);`` ``head->next->next->next = ``new` `Node(4);`` ``head->next->next->next->next`` ``= ``new` `Node(5);`` ``head->random = head->next->next;`` ``head->next->random = head;`` ``head->next->next->random`` ``= head->next->next->next->next;`` ``head->next->next->next->random`` ``= head->next->next;`` ``head->next->next->next->next->random`` ``= head->next;`` ` ` ``// Print the original list`` ``cout << ``"The original linked list:\n"``;`` ``printList(head);`` ` ` ``// Function call`` ``Node* sol = cloneLinkedList(head);`` ` ` ``cout << ``"The cloned linked list:\n"``;`` ``printList(sol);`` ` ` ``return` `0;``}`
## Java
`class` `Node {`` ``int` `data;`` ``Node next, random;` ` ``Node(``int` `x) {`` ``data = x;`` ``next = random = ``null``;`` ``}``}` `public` `class` `Main {`` ``public` `static` `void` `main(String[] args) {`` ``// Creating a linked list with random pointer`` ``Node head = ``new` `Node(``1``);`` ``head.next = ``new` `Node(``2``);`` ``head.next.next = ``new` `Node(``3``);`` ``head.next.next.next = ``new` `Node(``4``);`` ``head.next.next.next.next = ``new` `Node(``5``);`` ``head.random = head.next.next;`` ``head.next.random = head;`` ``head.next.next.random = head.next.next.next.next;`` ``head.next.next.next.random = head.next.next;`` ``head.next.next.next.next.random = head.next;` ` ``// Print the original list`` ``System.out.println(``"The original linked list:"``);`` ``printList(head);` ` ``// Function call`` ``Node sol = cloneLinkedList(head);` ` ``System.out.println(``"The cloned linked list:"``);`` ``printList(sol);`` ``}` ` ``public` `static` `Node cloneLinkedList(Node head) {`` ``if` `(head == ``null``) {`` ``return` `null``;`` ``}` ` ``// Step 1: Create new nodes and insert them next to the original nodes`` ``Node curr = head;`` ``while` `(curr != ``null``) {`` ``Node newNode = ``new` `Node(curr.data);`` ``newNode.next = curr.next;`` ``curr.next = newNode;`` ``curr = newNode.next;`` ``}` ` ``// Step 2: Set the random pointers of the new nodes`` ``curr = head;`` ``while` `(curr != ``null``) {`` ``if` `(curr.random != ``null``) {`` ``curr.next.random = curr.random.next;`` ``}`` ``curr = curr.next.next;`` ``}` ` ``// Step 3: Separate the new nodes from the original nodes`` ``curr = head;`` ``Node clonedHead = head.next;`` ``Node clonedCurr = clonedHead;`` ``while` `(clonedCurr.next != ``null``) {`` ``curr.next = curr.next.next;`` ``clonedCurr.next = clonedCurr.next.next;`` ``curr = curr.next;`` ``clonedCurr = clonedCurr.next;`` ``}`` ``curr.next = ``null``;`` ``clonedCurr.next = ``null``;` ` ``return` `clonedHead;`` ``}` ` ``// Function to print the linked list`` ``public` `static` `void` `printList(Node head) {`` ``System.out.print(head.data + ``"("` `+ head.random.data + ``")"``);`` ``head = head.next;`` ``while` `(head != ``null``) {`` ``System.out.print(``" -> "` `+ head.data + ``"("` `+ head.random.data + ``")"``);`` ``head = head.next;`` ``}`` ``System.out.println();`` ``}``}`
## Python3
`class` `Node:`` ``def` `__init__(``self``, x):`` ``self``.data ``=` `x`` ``self``.``next` `=` `None`` ``self``.random ``=` `None` `def` `cloneLinkedList(head):`` ``if` `head ``=``=` `None``:`` ``return` `None`` ``# Step 1: Create new nodes and insert them next to the original nodes`` ``curr ``=` `head`` ``while` `curr !``=` `None``:`` ``newNode ``=` `Node(curr.data)`` ``newNode.``next` `=` `curr.``next`` ``curr.``next` `=` `newNode`` ``curr ``=` `newNode.``next`` ``# Step 2: Set the random pointers of the new nodes`` ``curr ``=` `head`` ``while` `curr !``=` `None``:`` ``if` `curr.random !``=` `None``:`` ``curr.``next``.random ``=` `curr.random.``next`` ``curr ``=` `curr.``next``.``next`` ``# Step 3: Separate the new nodes from the original nodes`` ``curr ``=` `head`` ``clonedHead ``=` `head.``next`` ``clonedCurr ``=` `clonedHead`` ``while` `clonedCurr.``next` `!``=` `None``:`` ``curr.``next` `=` `curr.``next``.``next`` ``clonedCurr.``next` `=` `clonedCurr.``next``.``next`` ``curr ``=` `curr.``next`` ``clonedCurr ``=` `clonedCurr.``next`` ``curr.``next` `=` `None`` ``clonedCurr.``next` `=` `None`` ``return` `clonedHead` `# Function to print the linked list` `def` `printList(head):`` ``print``(head.data, ``"("``, head.random.data, ``")"``, end``=``"")`` ``head ``=` `head.``next`` ``while` `head !``=` `None``:`` ``print``(``"->"``, head.data, ``"("``, head.random.data, ``")"``, end``=``"")`` ``head ``=` `head.``next`` ``print``()` `# Driver code``if` `__name__ ``=``=` `'__main__'``:`` ``# Creating a linked list with random pointer`` ``head ``=` `Node(``1``)`` ``head.``next` `=` `Node(``2``)`` ``head.``next``.``next` `=` `Node(``3``)`` ``head.``next``.``next``.``next` `=` `Node(``4``)`` ``head.``next``.``next``.``next``.``next` `=` `Node(``5``)`` ``head.random ``=` `head.``next``.``next`` ``head.``next``.random ``=` `head`` ``head.``next``.``next``.random ``=` `head.``next``.``next``.``next``.``next`` ``head.``next``.``next``.``next``.random ``=` `head.``next``.``next`` ``head.``next``.``next``.``next``.``next``.random ``=` `head.``next` ` ``# Print the original list`` ``print``(``"The original linked list:"``)`` ``printList(head)` ` ``# Function call`` ``sol ``=` `cloneLinkedList(head)`` ``print``(``"The cloned linked list:"``)`` ``printList(sol)`
## C#
`using` `System;` `public` `class` `Node {`` ``public` `int` `data;`` ``public` `Node next, random;` ` ``public` `Node(``int` `x) {`` ``data = x;`` ``next = random = ``null``;`` ``}``}` `public` `class` `GFG {` ` ``public` `static` `Node CloneLinkedList(Node head) {`` ``if` `(head == ``null``) {`` ``return` `null``;`` ``}` ` ``// Step 1: Create new nodes and insert them next to the original nodes`` ``Node curr = head;`` ``while` `(curr != ``null``) {`` ``Node newNode = ``new` `Node(curr.data);`` ``newNode.next = curr.next;`` ``curr.next = newNode;`` ``curr = newNode.next;`` ``}` ` ``// Step 2: Set the random pointers of the new nodes`` ``curr = head;`` ``while` `(curr != ``null``) {`` ``if` `(curr.random != ``null``) {`` ``curr.next.random = curr.random.next;`` ``}`` ``curr = curr.next.next;`` ``}` ` ``// Step 3: Separate the new nodes from the original nodes`` ``curr = head;`` ``Node clonedHead = head.next;`` ``Node clonedCurr = clonedHead;`` ``while` `(clonedCurr.next != ``null``) {`` ``curr.next = curr.next.next;`` ``clonedCurr.next = clonedCurr.next.next;`` ``curr = curr.next;`` ``clonedCurr = clonedCurr.next;`` ``}`` ``curr.next = ``null``;`` ``clonedCurr.next = ``null``;` ` ``return` `clonedHead;`` ``}` ` ``// Function to print the linked list`` ``public` `static` `void` `PrintList(Node head) {`` ``Console.Write(head.data + ``"("` `+ head.random.data + ``")"``);`` ``head = head.next;`` ``while` `(head != ``null``) {`` ``Console.Write(``" -> "` `+ head.data + ``"("` `+ head.random.data + ``")"``);`` ``head = head.next;`` ``}`` ``Console.WriteLine();`` ``}`` ``public` `static` `void` `Main() {`` ``// Creating a linked list with random pointer`` ``Node head = ``new` `Node(1);`` ``head.next = ``new` `Node(2);`` ``head.next.next = ``new` `Node(3);`` ``head.next.next.next = ``new` `Node(4);`` ``head.next.next.next.next = ``new` `Node(5);`` ``head.random = head.next.next;`` ``head.next.random = head;`` ``head.next.next.random = head.next.next.next.next;`` ``head.next.next.next.random = head.next.next;`` ``head.next.next.next.next.random = head.next;` ` ``// Print the original list`` ``Console.WriteLine(``"The original linked list:"``);`` ``PrintList(head);` ` ``// Function call`` ``Node sol = CloneLinkedList(head);` ` ``Console.WriteLine(``"The cloned linked list:"``);`` ``PrintList(sol);`` ``}` `}`
## Javascript
`// JavaScript code to implement the approach` `class Node {`` ``constructor(x) {`` ``this``.data = x;`` ``this``.next = ``null``;`` ``this``.random = ``null``;`` ``}``}` `function` `cloneLinkedList(head) {`` ``if` `(head === ``null``) {`` ``return` `null``;`` ``}` ` ``// Step 1: Create new nodes and insert them next to the original nodes`` ``let curr = head;`` ``while` `(curr !== ``null``) {`` ``const newNode = ``new` `Node(curr.data);`` ``newNode.next = curr.next;`` ``curr.next = newNode;`` ``curr = newNode.next;`` ``}` ` ``// Step 2: Set the random pointers of the new nodes`` ``curr = head;`` ``while` `(curr !== ``null``) {`` ``if` `(curr.random !== ``null``) {`` ``curr.next.random = curr.random.next;`` ``}`` ``curr = curr.next.next;`` ``}` ` ``// Step 3: Separate the new nodes from the original nodes`` ``curr = head;`` ``const clonedHead = head.next;`` ``let clonedCurr = clonedHead;`` ``while` `(clonedCurr.next !== ``null``) {`` ``curr.next = curr.next.next;`` ``clonedCurr.next = clonedCurr.next.next;`` ``curr = curr.next;`` ``clonedCurr = clonedCurr.next;`` ``}`` ``curr.next = ``null``;`` ``clonedCurr.next = ``null``;` ` ``return` `clonedHead;``}` `// Function to print the linked list``function` `printList(head) {`` ``process.stdout.write(head.data + ``"("` `+ (head.random.data + ``")"``));`` ``head = head.next;`` ``while` `(head !== ``null``) {`` ``process.stdout.write(``" -> "` `+ head.data + ``"("` `+ (head.random.data + ``")"``));`` ``head = head.next;`` ``}`` ``console.log();``}` `// Driver code``// Creating a linked list with random pointer``const head = ``new` `Node(1);``head.next = ``new` `Node(2);``head.next.next = ``new` `Node(3);``head.next.next.next = ``new` `Node(4);``head.next.next.next.next = ``new` `Node(5);``head.random = head.next.next;``head.next.random = head;``head.next.next.random = head.next.next.next.next;``head.next.next.next.random = head.next.next;``head.next.next.next.next.random = head.next;` `// Print the original list``console.log(``"The original linked list:"``);``printList(head);` `// Function call``const sol = cloneLinkedList(head);` `console.log(``"The cloned linked list:"``);``printList(sol);` `// The code is contributed by Arushi Goel.`
Output
```The original linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
The cloned linked list:
1(3) -> 2(1) -> 3(5) -> 4(3) -> 5(2)
```
Time Complexity: O(N)
Auxiliary Space: O(1)
Related article:
Clone a linked list with next and random pointer | Set 2
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# Keno Odds and Payouts Explained
Home » Online Keno » Odds and Payouts
Updated on: June 13th, 2023
Welcome to our comprehensive guide on Keno Odds and Payouts! Whether new to the game or a seasoned player, this page is your go-to resource for understanding Keno’s probabilities and potential rewards. We’ll break down the odds, explain payout structures, and equip you with valuable strategies to enhance your chances of hitting it big. Get ready to dive into the fascinating world of Keno and take control of your winning destiny!
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## Understanding Keno Odds: Unveiling the Numbers Game
Keno is a thrilling numbers game that allows players to win big by selecting a set of numbers and matching them with the numbers drawn by the Keno machine. To make informed decisions and increase your chances of success, it’s crucial to understand Keno odds.
## How Keno Odds Work
Keno odds determine the likelihood of specific number combinations being drawn. The odds vary depending on how many numbers you choose and how many you match correctly. Generally, the more numbers you select, the higher the odds become, but the potential payouts also increase.
## Calculating Keno Odds
To calculate Keno odds, consider the total number of possible combinations and the number of ways to win. For example, if you choose 10 numbers, there are over 3.5 million possible combinations. However, the odds of hitting 10 out of 10 are significantly lower than hitting 2 out of 10.
## Strategies to Improve Keno Odds
When it comes to strategies to improve your Keno odds, there are a few key approaches you can consider:
### Select a balanced combination of numbers
Instead of solely relying on a random selection, choosing a balanced combination of numbers can increase your chances of hitting multiple matches. Aim for a mix of high and low numbers and even and odd numbers. This approach can diversify your ticket and improve your odds of success.
### Utilize number frequency analysis
Analyzing the frequency of numbers drawn in previous Keno games can provide valuable insights. While it does not guarantee a win, it allows you to identify patterns or trends influencing your number selection. Look for “hot” numbers frequently drawn and consider incorporating them into your chosen set. Similarly, be cautious of “cold” numbers drawn less frequently, as they may have a higher chance of appearing in the next draw.
Responsible bankroll management is one of the most important strategies in any gambling game. Before playing Keno, set a budget that you are comfortable with and stick to it. Avoid chasing losses or increasing your bets to recover. By playing within your means, you ensure that you can enjoy the game without risking more money than you can afford to lose. Responsible bankroll management allows for a more enjoyable and sustainable Keno experience.
## Exploring Keno Payouts: Unlocking the Rewards
Understanding Keno payouts is crucial for players aiming to maximize their gaming experience. Let’s delve into the world of Keno payouts and how they work.
### How Keno Payouts are Determined
Keno payouts are based on the number of matches you achieve and the amount you wagered. Each casino or gaming establishment may have a unique payout structure, so reviewing the specific rules before playing is important.
### Typical Keno Payout Table
Here’s a common example of a Keno payout table, illustrating the payouts for different numbers matched out of a 20-number draw:
• 1 out of 1 match: 3x payout
• 2 out of 3 match: 15x payout
• 5 out of 7 match: 250x payout
• 10 out of 10 match: 10,000x payout
It’s essential to understand that payout rates vary significantly between Keno games and establishments. Therefore, always refer to the specific payout table available at your chosen venue.
### Maximizing Payouts with Progressive Keno
Some Keno games offer progressive jackpots, where the potential winnings increase until someone hits the jackpot. These progressive games can result in life-changing payouts for lucky winners. However, remember that the odds of hitting the jackpot are usually much lower than hitting smaller payouts.
### Playing Responsibly and Setting Expectations
Keno is an entertaining game that should be enjoyed responsibly. Setting realistic expectations and understanding that Keno is primarily a game of chance is crucial. While winning substantial amounts is possible, having fun and gambling responsibly is equally important.
## Keno Odds and Payouts – Conclusion
In conclusion, understanding Keno odds and payouts is essential for anyone seeking to maximize their chances of winning in this exciting numbers game. By grasping the probabilities, employing smart strategies, and being aware of payout structures, you can make informed decisions and potentially enhance your Keno experience. Remember to play responsibly, have fun, and may luck be on your side as you explore the captivating world of Keno Odds and Payouts!
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What does 9 5 odds mean in horse racing?
What does 9 5 odds mean in horse racing?
How are horse racing odds calculated? To calculate the exact odds on your horse, simply subtract the take from the total pool, then subtract the amount bet on your horse to give you the cash amount to be paid.
What do odds mean in horse racing? Odds are simply how prizes and payouts are displayed on a racetrack. Numbers displayed as 4-7 or 2-5 tell you what you pay and how much you get back if the horse you bet on wins. The first number tells you how much you could win, the second number is the amount you bet.
What do the odds 9 4 mean? 9/4: For every 4 units you bet, you will receive 9 units if you win (plus your stake). If you see fractional odds the other way around – like 1/4 – it’s called odds and means the horse in question is a strong favorite to win the race. Again, this means the horse in question should win the race.
Related Articles
What Does 9 5 Odds Mean in Horse Racing – Related Questions
What happens if you bet \$100 on a +140 money line?
+200 odds on a Moneyline bet indicate how much money you would win if you bet \$100 and were right. If the New Orleans Saints have +200 moneyline odds and you bet \$100, you’ll get a \$300 payout if the Saint wins.
Are higher odds better?
Odds indicate how much money you will win if you bet that an event will occur. The higher the odds, the more you will win, relative to your stake. The lower the chances of a participant, the less money you will win.
What is 7 to 4 odds?
For every 11, there is a good chance that 7 is a particular event and 4 is another event. There is a 63.64% chance of one particular outcome and a 36.36% chance of another outcome. If you bet 1 on a game with odds of 7 to 4 and win, your total payout will be 2.75, which is your bet plus 1.75 profit.
What is the odds 7 to 2?
So odds of 7 to 2 means that for every \$2 invested, the bettor gets a profit of \$7 in return. This means that when you bet \$2, the total return if the bet is successful is \$9. Similarly, if a horse is tied (i.e. 1-1), that’s a profit of \$2 for every \$2 invested, or a total return of \$4.
What is the rating 7 5?
For every 12, there is a good chance that 7 is a particular event and 5 is another event. There is a 58.33% chance of one particular outcome and a 41.67% chance of another outcome. If you bet 1 on a game with odds of 7 to 5 and win, your total payout will be 2.40, which is your bet plus 1.40 profit.
What does odds of five to one mean?
This means that out of 6 possible results, there is a good chance that there will be 5 of one type of result and 1 of another type of result. For every 6, there is a good chance that 5 is a particular event and 1 is another event. odds of 5 to 1.
What are the odds from 1 to 4?
This means that out of 5 possible results, there is a good chance that there will be 1 of one type of result and 4 of another type of result. For every 5, the odds are that 1 will be a particular event and 4 will be another event.
What are the best odds?
Best Odds Guarantee is a concession or promotion offered by some bookmakers that applies to horse and greyhound racing. This means that when you take an early price or a fixed odds price on your selection for a particular race, if the SP (starting price) is higher, you are paid with the higher odds.
What do the odds 6 4 mean?
Fractional odds
Let’s say your bet is priced at 6/4 – in simple terms, this means you need to wager £4 to win £6 (on top of that, you’ll get your £4 stake back). In mathematical terms, another way to express 6/4 is 6 divided by 4, which equals 1.5. So, whatever your bet is, you can multiply it by 1.5 to calculate your profit.
Should you always bet on the favorite?
If you were hoping that a simple “always bet on the favorite” strategy was your path to profit, then think again. But there are a few key lessons to remember: betting on the favorite is rarely a bad bet. Shorter priced favorites are often more value for money than longer priced ones.
What does rating 33 1 mean?
This means that out of 34 possible results, there is a good chance that there will be 33 of one type of result and 1 of another type of result. For every 34, there is a good chance that 33 is a particular event and 1 is another event.
What is the payout on odds of 100 to 1?
The first number (100) is the amount you will win by betting the second number (1). So for every £1 or \$1 or €1 you spend, you will earn 100 back.
Is the moneyline a good bet?
What’s great about Moneyline betting is that they’re not only simple enough to understand and use correctly for beginner sports bettors, but they’re also widely used by professional sports bettors to land huge wins every time. day in sports betting around the world.
Why bet on negative odds?
Negative numbers mean the favorite on the betting line. The negative number indicates how much you need to bet to win \$100. If the number is positive, you are looking at the underdog, and the number refers to the amount of money you will win if you bet \$100.
What pays more moneyline or spread?
Spread betting gives a better payout
But other sports also offer spread bets. This bet is harder to win than a moneyline bet. However, there is also potential for a much better payout. Almost all the spread betting options you will find will have odds at -110 for each side.
What are good odds and bad odds?
“Low odds” means something is likely, and “high odds” means something is unlikely, but many people confuse the two. High odds means that if you placed a bet, you will win a high payout; and low odds mean that if you placed a bet, you will win a lower payout.
How do you know if the odds are good?
A positive value exists when the probability of a bet winning is greater than the probability reflected in the odds. In other words, a bet has positive value when it is MORE likely to win than the odds suggest. A bet has negative value when it is LESS likely to win than the odds suggest.
What is the meaning of against all odds?
: although success is very unlikely, he was able to do it, against all odds.
How do you calculate the odds?
Odds take the probability of an event occurring and divide it by the probability that the event does not occur. So, in case you roll a three on the first try, the probability is 1/6 that you would roll a three, while the probability that you would not roll a three is 5/6.
What does the rating 9 2 mean?
This means that out of 11 possible results, there is a good chance that there will be 9 of one type of result and 2 of another type of result. For every 11, there is a good chance that 9 is a particular event and 2 is another event.
What do the ratings 3 to 5 mean?
Odds of 3 to 5 indicate that your profit will be three-fifths of a dollar. In other words, for every \$5 you bet, you can earn \$3 in profit. To determine the profit, multiply the amount you bet by the fraction. If I spend \$15, my profit for winning is \$9 (15 x 3/5).
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## Engage NY Eureka Math Geometry Module 1 Lesson 12 Answer Key
### Eureka Math Geometry Module 1 Lesson 12 Exercise Answer Key
Opening Exercises
a. Find the measure of each lettered angle in the figure below.
a=115
b=115
c=67
d=23
e=115
f=124
g=101
h=79
i=79
j=101
b. Given: m∠CDE=m∠BAC
Prove: m∠DEC=m∠ABC
m∠CDE=m∠BAC Given
m∠CDE+m∠DCE+m∠DEC=180° Sum of the angle measures in a triangle is 180°
m∠BAC+m∠DCE+m∠ABC=180° Sum of the angle measures of a triangle is 180°
m∠CDE+m∠DCE+m∠DEC Substitution property of equality
m∠BAC+m∠DCE+m∠ABC
m∠DEC=m∠ABC Subtraction property of equality
Mathematical Modeling Exercise
You will work with a partner on this exercise and are allowed a protractor, compass, and straightedge.
→ Partner A: Use the card your teacher gives you. Without showing the card to your partner, describe to your partner how to draw the transformation indicated on the card. When you have finished, compare your partner’s drawing with the transformed image on your card. Did you describe the motion correctly?
→ Partner B: Your partner is going to describe a transformation to be performed on the figure on your card. Follow your partner’s instructions and then compare the image of your transformation to the image on your partner’s card.
Discussion
Explaining how to transform figures without the benefit of a coordinate plane can be difficult without some important vocabulary. Let’s review.
The word transformation has a specific meaning in geometry. A transformation F of the plane is a function that assigns to each point P of the plane a unique point F(P) in the plane. Transformations that preserve lengths of segments and measures of angles are called ___. A dilation is an example of a transformation that preserves ___ measures but not the lengths of segments. In this lesson, we work only with rigid transformations.
We call a figure that is about to undergo a transformation the ___, while the figure that has undergone the transformation is called the ___.
The word transformation has a specific meaning in geometry. A transformation F of the plane is a function that assigns to each point P of the plane a unique point F(P) in the plane. Transformations that preserve lengths of segments and measures of angles are called basic rigid motions. A dilation is an example of a transformation that preserves angle measures but not the lengths of segments. In this lesson, we work only with rigid transformations. We call a figure that is about to undergo a transformation the pre-image, while the figure that has undergone the transformation is called the image.
Using the figures above, identify specific information needed to perform the rigid motion shown.
For a rotation, we need to know:
Center of rotation, direction (Clockwise (CW) or Counterclockwise (CCW)) and number of degrees rotated.
For a reflection, we need to know:
The line of reflection acts as the perpendicular bisector of each segment that joins a given vertex of the pre-image with the respective vertex of the image.
For a translation, we need to know:
The point P to be translated, the length and degree measure of the angle that the vector makes with the line that passes through P, and the endpoint of the vector.
### Eureka Math Geometry Module 1 Lesson 12 Problem Set Answer Key
An example of a rotation applied to a figure and its image is provided. Use this representation to answer the questions that follow. For each question, a pair of figures (pre-image and image) is given as well as the center of rotation. For each question, identify and draw the following:
i. The circle that determines the rotation, using any point on the pre-image and its image.
ii. An angle, created with three points of your choice, which demonstrates the angle of rotation.
Example of a Rotation:
Pre-image: (solid line)
Image: (dotted line)
Center of rotation: P
Angle of rotation: ∠APA’
Question 1.
Pre-image: (solid line)
Image: (dotted line)
Center of rotation: P
Angle of rotation: _____
90°, 270° CW
Question 2.
Pre-image: △ABC
Image: △A’ B’ C’
Center: D
Angle of rotation: ___
300°, 60° CW
### Eureka Math Geometry Module 1 Lesson 12 Exit Ticket Answer Key
How are transformations and functions related? Provide a specific example to support your reasoning.
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# math help 40
Assignment 2: Use and Misuse of Percentages
One of the concepts you encountered in the readings this module was how to recognize the use and misuse of information presented in the form of percentages. In this discussion assignment, you will conduct an Internet search to find several examples of the use of percentages. These can be examples of percentages used in advertising claims, reported results from a study, or information shared by a government agency.
In a minimum of 200 words, post to the Discussion Area your response to the following:
Find an example of two of the following types of usage of percentages.
• Use of percentages as a fraction. Remember that this type will use the word of to imply multiplication. Explain whether this was an effective way to represent this information within the context of the example you found.
• Use of percentages to describe change. In the example you find, determine whether the reported percentage demonstrated absolute or relative change. Show your work. Explain whether this was an effective way to represent this information within the context of the example you found.
• Use of percentages for comparison. In the example you find, determine whether the reported percentage demonstrated absolute or relative change. Show your work. Explain whether this was an effective way to represent this information within the context of the example you found.
Now, find an example of two of the following misuses of percentages.
• Use of a shifting reference value. In this situation, the base values are changing as differing values of percentages are applied as increases, decreases, or both. Percentage increases, decreases, or both do not have a cumulative effect. Be sure to demonstrate why your example fits this category.
• Use of percentage to represent less than nothing. Look for an example where you are seeing a reduction of some percentage greater than 100. Be sure to demonstrate why your example fits this category.
• Situation where the average percentage is reported. In general, you can not average percentages. The result isn’t representative of what actually has occurred in the situation in question. Be sure to demonstrate why your example fits this category.
• Examine each example that the student provided. Did these examples sufficiently demonstrate the ways that percentages are used and misused? Explain.
• What have you learned regarding the necessity of carefully examining the percentages reported in advertising, news media, government reports, etc.?
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https://homework.cpm.org/category/ACC/textbook/gb8i/chapter/9%20Unit%203/lesson/CC3:%209.2.1/problem/9-57
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### Home > GB8I > Chapter 9 Unit 3 > Lesson CC3: 9.2.1 > Problem9-57
9-57.
Jenna is working with three squares. Their areas are $16 \text{ cm}^{2}, 9 \text{ cm}^{2}$, and $36 \text{ cm}^{2}$. She thinks they will make an obtuse triangle. Do you agree? Explain your reasoning.
What are the values of the sides of each square?
Try to predict what kind of triangle can be made from the squares below.
The sides of the squares are $4$ cm, $3$ cm, and $6$ cm.
These values make up the values of the sides of the triangle.
What kind of triangle do these squares make?
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https://brilliant.org/discussions/thread/proof-of-fermats-theorem-in-some-simple-way/
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# Proof of fermats theorem in some simple way
Fermats theorem
Note by Hardik Chandak
6 years, 9 months ago
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MathAppears as
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Sort by:
Are you looking for a simple proof of Fermat's Little Theorem or Fermat's Last Theorem or one of the many other theorems named after Fermat?
- 6 years, 9 months ago
FERMATS LAST THEOREM
- 4 years, 3 months ago
I'm pretty sure Fermat's Last Theorem
- 6 years, 9 months ago
Fermat's Little Theorem can be proved using induction.
- 6 years, 9 months ago
Can u prove it by induction plz show?
- 6 years, 9 months ago
It's not by induction, but an easy proof of Fermat's little theorem would be that $x^p \equiv (1+1+1+...+1)^p \equiv (1^p+1^p+...+1^p) \equiv x \pmod p$ with $x$ times number $1$. This is possible because in Pascal's triangle on prime rows the numbers are multiples of p except for the first and last terms which are $1$. This can be easily proven by using binomial formula.
- 6 years, 9 months ago
Okay get your calculators and try this:
$\sqrt[12]{1782^{12}+1841^{12}}$
$=1922$ right?
So this implies that ${1782^{12}+1841^{12}=1922^{12}}$
Does this disprove Fermat's Last Theorem?
Of course not!
The calculator is wrong.
- 6 years, 9 months ago
BTW: A quick check to see that $1782^{12}+1841^{12} \neq 1922^{12}$ is to note that the left side is odd whereas the right side is even.
- 6 years, 9 months ago
Took some time to realize... The actual answer is $1921.99999995586722540291132837029507293441170657370868230...$ Unfortunately, most calculators round the answer.
- 6 years, 9 months ago
If I remember correctly, that "equation" was from a Homer Simpson episode.
- 6 years, 9 months ago
I can give you a proof .
- 5 years, 7 months ago
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https://trustconverter.com/en/angle-conversion/sixth-circles/sixth-circles-to-twelfth-circles.html
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Sixth circles to Twelfth circles Conversion
Sixth circle to twelfth circle conversion allow you make a conversion between sixth circle and twelfth circle easily. You can find the tool in the following.
to
input
= 2.00000000
= 0.02 × 102
= 0.02E2
= 0.02e2
= 4.00000000
= 0.04 × 102
= 0.04E2
= 0.04e2
= 6.00000000
= 0.06 × 102
= 0.06E2
= 0.06e2
= 8.00000000
= 0.08 × 102
= 0.08E2
= 0.08e2
= 10.00000000
= 0.1 × 102
= 0.1E2
= 0.1e2
Quick Look: sixth circles to twelfth circles
sixth circle 1 1/6 circle 2 1/6 circle 3 1/6 circle 4 1/6 circle 5 1/6 circle 6 1/6 circle 7 1/6 circle 8 1/6 circle 9 1/6 circle 10 1/6 circle 11 1/6 circle 12 1/6 circle 13 1/6 circle 14 1/6 circle 15 1/6 circle 16 1/6 circle 17 1/6 circle 18 1/6 circle 19 1/6 circle 20 1/6 circle 21 1/6 circle 22 1/6 circle 23 1/6 circle 24 1/6 circle 25 1/6 circle 26 1/6 circle 27 1/6 circle 28 1/6 circle 29 1/6 circle 30 1/6 circle 31 1/6 circle 32 1/6 circle 33 1/6 circle 34 1/6 circle 35 1/6 circle 36 1/6 circle 37 1/6 circle 38 1/6 circle 39 1/6 circle 40 1/6 circle 41 1/6 circle 42 1/6 circle 43 1/6 circle 44 1/6 circle 45 1/6 circle 46 1/6 circle 47 1/6 circle 48 1/6 circle 49 1/6 circle 50 1/6 circle 51 1/6 circle 52 1/6 circle 53 1/6 circle 54 1/6 circle 55 1/6 circle 56 1/6 circle 57 1/6 circle 58 1/6 circle 59 1/6 circle 60 1/6 circle 61 1/6 circle 62 1/6 circle 63 1/6 circle 64 1/6 circle 65 1/6 circle 66 1/6 circle 67 1/6 circle 68 1/6 circle 69 1/6 circle 70 1/6 circle 71 1/6 circle 72 1/6 circle 73 1/6 circle 74 1/6 circle 75 1/6 circle 76 1/6 circle 77 1/6 circle 78 1/6 circle 79 1/6 circle 80 1/6 circle 81 1/6 circle 82 1/6 circle 83 1/6 circle 84 1/6 circle 85 1/6 circle 86 1/6 circle 87 1/6 circle 88 1/6 circle 89 1/6 circle 90 1/6 circle 91 1/6 circle 92 1/6 circle 93 1/6 circle 94 1/6 circle 95 1/6 circle 96 1/6 circle 97 1/6 circle 98 1/6 circle 99 1/6 circle 100 1/6 circle twelfth circle 2 1/12 circle 4 1/12 circle 6 1/12 circle 8 1/12 circle 10 1/12 circle 12 1/12 circle 14 1/12 circle 16 1/12 circle 18 1/12 circle 20 1/12 circle 22 1/12 circle 24 1/12 circle 26 1/12 circle 28 1/12 circle 30 1/12 circle 32 1/12 circle 34 1/12 circle 36 1/12 circle 38 1/12 circle 40 1/12 circle 42 1/12 circle 44 1/12 circle 46 1/12 circle 48 1/12 circle 50 1/12 circle 52 1/12 circle 54 1/12 circle 56 1/12 circle 58 1/12 circle 60 1/12 circle 62 1/12 circle 64 1/12 circle 66 1/12 circle 68 1/12 circle 70 1/12 circle 72 1/12 circle 74 1/12 circle 76 1/12 circle 78 1/12 circle 80 1/12 circle 82 1/12 circle 84 1/12 circle 86 1/12 circle 88 1/12 circle 90 1/12 circle 92 1/12 circle 94 1/12 circle 96 1/12 circle 98 1/12 circle 100 1/12 circle 102 1/12 circle 104 1/12 circle 106 1/12 circle 108 1/12 circle 110 1/12 circle 112 1/12 circle 114 1/12 circle 116 1/12 circle 118 1/12 circle 120 1/12 circle 122 1/12 circle 124 1/12 circle 126 1/12 circle 128 1/12 circle 130 1/12 circle 132 1/12 circle 134 1/12 circle 136 1/12 circle 138 1/12 circle 140 1/12 circle 142 1/12 circle 144 1/12 circle 146 1/12 circle 148 1/12 circle 150 1/12 circle 152 1/12 circle 154 1/12 circle 156 1/12 circle 158 1/12 circle 160 1/12 circle 162 1/12 circle 164 1/12 circle 166 1/12 circle 168 1/12 circle 170 1/12 circle 172 1/12 circle 174 1/12 circle 176 1/12 circle 178 1/12 circle 180 1/12 circle 182 1/12 circle 184 1/12 circle 186 1/12 circle 188 1/12 circle 190 1/12 circle 192 1/12 circle 194 1/12 circle 196 1/12 circle 198 1/12 circle 200 1/12 circle
1/6 circle or sixth circle is equal to 360°/6 = 60°. Plural name is sixth circles.
Name of unitSymbolDefinitionRelation to SI unitsUnit System
sixth circle1/6 circle
≡ 60°
Metric system SI
conversion table
sixth circlestwelfth circlessixth circlestwelfth circles
1= 26= 12
2= 47= 14
3= 68= 16
4= 89= 18
5= 1010= 20
1/12 circle or twelfth circle is equal to 360°/12 = 30°. Plural name is twelfth circles.
Name of unitSymbolDefinitionRelation to SI unitsUnit System
twelfth circle1/12 circle
≡ 30°
Metric system SI
conversion table
twelfth circlessixth circlestwelfth circlessixth circles
1= 0.56= 3
2= 17= 3.5
3= 1.58= 4
4= 29= 4.5
5= 2.510= 5
Conversion table
sixth circlestwelfth circles
1= 2
0.5= 1
Conversion in other languages
You can find the conversion in other languages in the following:
Legend
SymbolDefinition
exactly equal
approximately equal to
=equal to
digitsindicates that digits repeat infinitely (e.g. 8.294 369 corresponds to 8.294 369 369 369 369 …)
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CC-MAIN-2021-25
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http://mathoverflow.net/feeds/question/118834
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When does the cotangent complex vanish? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T01:18:34Z http://mathoverflow.net/feeds/question/118834 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118834/when-does-the-cotangent-complex-vanish When does the cotangent complex vanish? X-curious 2013-01-13T17:40:03Z 2013-01-16T17:05:58Z <p>The question is already in the title. Less succinctly, let's call a map $f:X \to Y$ of schemes <em>$L$-trivial</em> if its cotangent complex is quasi-isomorphic to $0$. Such maps have striking deformation-theoretic consequences; for example, any deformation of $Y$ can be followed uniquely by a deformation of $X$. </p> <p>My primary (and probably naive) question is:</p> <p> Is there a classification of $L$-trivial maps? </p> <p>I am sure this question has been asked before, but I did not find any literature that deals with it. The three examples of $L$-trivial maps I am familiar with are:</p> <ul> <li>Etale morphisms (and these are the <em>only</em> examples under finiteness constraints).</li> <li>Any map between perfect $\mathbb{F}_p$-schemes.</li> <li>The inclusion of the closed point in the spectrum of a valuation ring with divisible value group, or similar "divisible" constructions. For example, $\mathrm{Spec}(\mathbb{C}) \hookrightarrow \mathrm{Spec}(\mathbb{C}[ t^{\mathbb{Q}_{\geq 0}}])$ is $L$-trivial.</li> </ul> <p>[ <strong>Edit</strong>: I learnt the last one in conversation after positing the first version of this question. ]</p> <p>More examples can be obtained by taking filtered colimits of the above examples, but those are only slightly different. Hence, a second question is: are there other fundamentally different examples of $L$-trivial maps? </p> <p>Perhaps a classification is unreasonable to expect, so I am also happy to learn more about $L$-trivial maps in other geometric categories, like algebraic stacks, or derived/spectral schemes/stacks, or (complex/rigid) analytic spaces, etc.. In particular, I am especially curious to know if $L$-trivial maps can be better understood using derived algebraic geometry. </p> http://mathoverflow.net/questions/118834/when-does-the-cotangent-complex-vanish/118866#118866 Answer by Timo Schürg for When does the cotangent complex vanish? Timo Schürg 2013-01-14T10:51:18Z 2013-01-16T17:05:58Z <p><strong>Edit:</strong> Here is a possible characterization. As mentioned in the comments above, the vanishing of the 1-truncated cotangent complex $\tau_{\leq 1}L_{B/A}$ of a map of rings $f \colon A \to B$ is equivalent to a lifting property with respect to square-zero extensions $T' \to T$. This follows from the fact that the space $Map(L_{T/A},M[1])$ is equivalent to the groupoid of square-zero extensions of $T$ over $A$ with kernel $M$. Here $M$ is a $T$-module.</p> <p>Rephrasing this, $\tau_{\leq 1} L_{B/A}$ vanishes if and only if $f$ has a lifting property with respect to morphisms of 0-truncated simplicial algebras such that the kernel is concentrated in degree 0 and squares to 0. Let's call these 0-concentrated.</p> <p>Then we can go on to look at morphisms of 1-truncated simplicial algebras with kernel $K$ concentrated in degree 1. The squaring-to-zero property is vacuous here, because a product of two elements in $\pi_1(K)$ will be in $\pi_2(K)$, which is zero by assumption. Let's call these 1-concentrated Then we find that $\tau_{\leq 2} L_{B/A}$ vanishes if and only if $f$ has a lifting property with respect to all 0- and 1-concentrated maps. This again holds because the cotangent complex classifies 0- and 1-concentrated maps.</p> <p>I think now it's clear how to go on: $\tau_{\leq n+1}L_{B/A}$ vanishes if and only if $f$ has a lifting property with respect to all $m$-concentrated maps with $m \leq n$. And the full cotangent complex vanishes if and only if $f$ has the lifting property with respect to $n$-concentrated maps for all $n$.</p> <p>These directions one looks at if one starts to check with respect to $n$-concentrated maps for $n \geq 1$ are sometimes called the derived directions. So Avramov's theorem might be rephrased as saying that under strong finiteness assumptions, unobstructedness in the classical directions implies unobstructedness in all derived directions.</p> <hr> <p>This is an anwer to your last paragraph about L-trivial maps in other geometric categories. If you are only interested in schemes it doesn't tell you anything interesting.</p> <p>One thing that the cotangent complex is good at is measuring connectivity of a morphism of simplicial rings. This also holds without any finiteness assumptions on the ring.</p> <p>Recall that a morphism $f \colon A \to B$ of simplicial rings is called n-connective if it induces isomorphisms $\pi_i (A) \to \pi_i (B)$ in degrees $< n$ and a surjection $\pi_n (A) \to \pi_n (B)$ in degree $n$. There then is a result that states that if $f$ is $n$-connective, then the homology of the relative contangent complex $L_{B/A}$ vanishes in degrees $\leq n$. (I hope I got all the indices right.) So in particular, any equivalence of simplicial rings is L-trivial.</p> <p>One way of intepreting your question is to ask when the converse holds. What do I know if a morphism of simiplicial rings is L-trivial? There is a partial converse to the statement above. Namely, if a morphism $f \colon A \to B$ induces an isomorphism $\pi_0(A) \to \pi_0(B)$ and is L-trivial, then it is an equivalence! I find this pretty suprprising, as L is only a linear piece of data, but still manages to detect equivalences.</p>
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https://exercism.io/tracks/javascript/exercises/hamming/solutions/cb495809a29247e5a193ee3790fdf90e
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Exercism v3 launches on Sept 1st 2021. Learn more! ๐๐๐
# PatrickMcSweeny's solution
## to Hamming in the JavaScript Track
Published at Aug 24 2019 · 0 comments
Instructions
Test suite
Solution
#### Note:
This exercise has changed since this solution was written.
Calculate the Hamming Distance between two DNA strands.
Your body is made up of cells that contain DNA. Those cells regularly wear out and need replacing, which they achieve by dividing into daughter cells. In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime!
When cells divide, their DNA replicates too. Sometimes during this process mistakes happen and single pieces of DNA get encoded with the incorrect information. If we compare two strands of DNA and count the differences between them we can see how many mistakes occurred. This is known as the "Hamming Distance".
We read DNA using the letters C,A,G and T. Two strands might look like this:
``````GAGCCTACTAACGGGAT
CATCGTAATGACGGCCT
^ ^ ^ ^ ^ ^^
``````
They have 7 differences, and therefore the Hamming Distance is 7.
The Hamming Distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
# Implementation notes
The Hamming distance is only defined for sequences of equal length, so an attempt to calculate it between sequences of different lengths should not work. The general handling of this situation (e.g., raising an exception vs returning a special value) may differ between languages.
## Setup
Go through the setup instructions for Javascript to install the necessary dependencies:
https://exercism.io/tracks/javascript/installation
## Requirements
Install assignment dependencies:
``````\$ npm install
``````
## Making the test suite pass
Execute the tests with:
``````\$ npm test
``````
In the test suites all tests but the first have been skipped.
Once you get a test passing, you can enable the next one by changing `xtest` to `test`.
## Source
The Calculating Point Mutations problem at Rosalind http://rosalind.info/problems/hamm/
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
### hamming.spec.js
``````import { compute } from './hamming';
describe('Hamming', () => {
test('empty strands', () => {
expect(compute('', '')).toEqual(0);
});
xtest('single letter identical strands', () => {
expect(compute('A', 'A')).toEqual(0);
});
xtest('single letter different strands', () => {
expect(compute('G', 'T')).toEqual(1);
});
xtest('long identical strands', () => {
expect(compute('GGACTGAAATCTG', 'GGACTGAAATCTG')).toEqual(0);
});
xtest('long different strands', () => {
expect(compute('GGACGGATTCTG', 'AGGACGGATTCT')).toEqual(9);
});
xtest('disallow first strand longer', () => {
expect(() => compute('AATG', 'AAA')).toThrow(
new Error('left and right strands must be of equal length'),
);
});
xtest('disallow second strand longer', () => {
expect(() => compute('ATA', 'AGTG')).toThrow(
new Error('left and right strands must be of equal length'),
);
});
xtest('disallow left empty strand', () => {
expect(() => compute('', 'G')).toThrow(
new Error('left strand must not be empty'),
);
});
xtest('disallow right empty strand', () => {
expect(() => compute('G', '')).toThrow(
new Error('right strand must not be empty'),
);
});
});``````
``````export const compute = (leftStrand, rightStrand) => {
validateStrands(leftStrand, rightStrand);
let range = [...Array(leftStrand.length).keys()];
return range.filter((n, i) => {
return leftStrand[i] !== rightStrand[i];
}).length;
};
export const validateStrands = (leftStrand, rightStrand) => {
if (leftStrand.length === 0 && rightStrand.length > 0) {
throw new Error("left strand must not be empty");
}
if (rightStrand.length === 0 && leftStrand.length > 0) {
throw new Error("right strand must not be empty");
}
if (leftStrand.length !== rightStrand.length) {
throw new Error("left and right strands must be of equal length");
}
};``````
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|
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| 0.925471
|
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