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## Center of group algebras
Posted: February 8, 2011 in Group Algebras, Noncommutative Ring Theory Notes
Tags:
Notation. Let $k$ be a field and let $G$ be a finite group. Let $\mathcal{C}_1, \cdots , \mathcal{C}_m$ be the conjugacy classes of $G.$ Let
$c_i = \sum_{g \in \mathcal{C}_i} g \in k[G], \ 1 \leq i \leq m.$
Theorem. The set $\{c_1, \cdots , c_m \}$ is a $k$-basis for $Z(k[G]),$ the center of $k[G].$ Thus $\dim_k Z(k[G])$ is equal to the number of conjugacy classes of $G.$
Proof$c_1, \cdots , c_m$ are linearly independent over $k$ because if $i \neq j,$ then $\mathcal{C}_i \cap \mathcal{C}_j = \emptyset.$ So we only need to show that $\text{span} \{c_1, \cdots , c_m \} = Z(k[G]).$ Let $x = \sum_{g \in G} x_g g \in k[G],$ where $x_g \in k$ for all $g \in G.$
Claim. $x \in Z(k[G])$ if and only if $x_g = x_{h^{-1}gh}$ for all $g,h \in G.$
Proof of the claim. Well, $x \in Z(k[G])$ if and only if $xh = hx$ for all $h \in G.$ Thus, $x \in Z(k[G])$ if and only if
$\sum_{g \in G} x_g g = \sum_{g \in G} x_g h g h^{-1}. \ \ \ \ \ \ \ \ (1)$
Clearly, fixing $h \in G,$ we have $\{hgh^{-1}: \ g \in G \} =G.$ So if we put $hgh^{-1}=u,$ then $g = h^{-1}uh$ and thus $(1)$ becomes
$\sum_{g \in G} x_g g = \sum_{g \in G} x_{h^{-1}gh} g. \ \ \ \ \ \ \ \ \ \ \ (2)$
The claim now follows from $(2).$
Now, if $1 \leq i \leq m,$ then, by definition, $g \in \mathcal{C}_i$ if and only if $h^{-1}gh \in \mathcal{C}_i$ for all $h \in G.$ So for every $g,h \in G,$ the coefficients of $g$ and $h^{-1}gh$ in $c_i$ are either both 1 or both 0. Thus, by the claim, $c_i \in Z(k[G])$ for all $i.$ So $\text{span} \{c_1, \cdots , c_m \} \subseteq Z(k[G]).$
Conversely, if $x = \sum_{g \in G} x_g g \in Z(k[G]),$ then, by the claim, $x_g = x_{g'}$ for all $g$ and $g'$ which are in the same conjugacy class. Thus if for every $i$ we choose a $g_i \in \mathcal{C}_i,$ then
$x = \sum_{i=1}^m x_{g_i} c_i.$
So $Z(k[G]) \subseteq \text{span} \{c_1, \cdots , c_m \}. \ \Box$
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# Assignment Setup
To create your repository go here. Then follow the same accept/import process described in Assignment 0.
# Game of Nim
Nim is a game of strategy in which two players take turns removing sticks from a common pile. There are many variations of Nim but we will stick with a simple version. On each turn a player must remove either 1 or 2 sticks from the pile. The goal of the game is to be the player who removes the last stick.
You will design a game in which one human player is competing against a computer. To simplify your work the person will always take the first turn.
While there is a winning strategy for this game, you are only required only to create a computer player that makes random, but valid, moves.
### Example Output
Round 0: 7 at start human takes 2, so 5 remain
Round 1: 5 at start computer takes 2, so 3 remain
Round 2: 3 at start human takes 2, so 1 remain
Round 3: 1 at start computer takes 1, so 0 remain
The computer wins / you lose!
## Notes
• Begin by prompting the user for the initial number of sticks. In the example above, it appears that 7 sticks were used in the game.
• The human (as always in this assignment) made the first move.
• Clearly, the human could have played better in the above game.
• The computer randomly removes 1 or 2 sticks, but cannot remove more sticks than are left.
• The human is prompted at each turn for how many sticks he or she wants to remove.
Be careful! A human might enter 5 if 5 sticks are left, and if you are not careful, the human could win by “playing” in that way. Don’t accept the user’s input if it is illegal. You may assume that they will only enter valid integers, but you should continue prompting until you get a valid value.
• Start your work by creating a Nim class in the assignment2 package.
• Use ArgsProcessor to prompt for inputs.
• Your program must continue play until somebody (computer or human) wins.
• Your output should resemble the sample output shown above. It should clearly show if the computer or the human wins.
• When it’s time to demo be prepared to discuss how you would implement a “smarter” strategy for the computer player.
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# zbMATH — the first resource for mathematics
Lokale Berührungskegel einer Menge im euklidischen Raum $$E_n$$. (German) Zbl 0386.52003
##### MSC:
52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 53A05 Surfaces in Euclidean and related spaces
Full Text:
##### References:
[1] Nožička F.: Über einfache Mannigfaltigkeiten in linearen affinnen Raum $$A_n$$ in globalen Auffassung. Czech Mathematical Journal. 1976. [2] Abadie J.: Nonlinear Programming. North Holland Publishing Company. 1967. · Zbl 0153.30601 [3] Bazaraa M. S., Goode J. J., Nashed M. Z.: On the Cone of Tangents with Applications to Mathematical Programming. 1973. · Zbl 0259.90037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# Integers of the form $a^2+b^2+c^3+d^3$
It's easy$^*$ to prove that if $n=3^{6m}(3k \pm 1)$ where $(m,k) \in \mathbb{N} \times \mathbb{Z}$, then $n=a^2+b^2+c^3+d^3$ with $(a,b,c,d) \in \mathbb{Z}^4$. But how to prove that this is true if $n=3k$?
Thanks,
W
$^*$ Because $3k+1=0^2+(3k+8)^2+(k+1)^3+(-k-4)^3$, $3k+2=1^2+(3k+8)^2+(k+1)^3+(-k-4)^3$ and $3^6(a^2+b^2+c^3+d^3)=(27a)^2+(27b)^2+(9c)^3+(9d)^3$.
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What is $\mathbb Z^4$? – user4140 Jul 23 '12 at 13:56
@ChuckFernández I presume the set of all 4-tuples comprised of integers? – Shaktal Jul 23 '12 at 14:06
does it mean the same as $a,b,c,d\in \mathbb Z$? – user4140 Jul 23 '12 at 15:00
@ChuckFernández Yes. – Ragib Zaman Jul 23 '12 at 15:19
You do not need the final $d^3.$ Every integer is the sum of two squares and a cube, as long as we do not restrict the $\pm$ sign on the cube. TYPESET FOR LEGIBILITY:
Solution by Andrew Adler: $$2x+1 = (x^3 - 3 x^2 + x)^2 +(x^2 - x - 1)^2 -(x^2 - 2x)^3$$ $$4x+2 = (2x^3 - 2 x^2 - x)^2 +(2x^3 -4x^2 - x + 1)^2 -(2x^2 - 2x-1)^3$$ $$8x+4 = (x^3 + x +2 )^2 +(x^2 - 2x - 1)^2 -(x^2 + 1)^3$$ $$16x+8 = (2x^3 - 8 x^2 +4 x +2)^2 +(2x^3 -4x^2 - 2 )^2 -(2x^2 - 4x)^3$$ $$16x = (x^3 +7 x - 2)^2 +(x^2 +2 x + 11)^2 -(x^2 +5)^3$$
You can check these with your own computer algebra system. Please let me know if I mistyped anything.
Alright, our conjecture (Kaplansky and I) is that, for any odd prime $q,$ $x^2 + y^2 + z^q$ is universal. However, this is false as soon as the exponent on $z$ is odd but composite. The example we put in the article is $$x^2 + y^2 + z^9 \neq 216 p^3,$$ where $p \equiv 1 \pmod 4$ is a (positive) prime. This defeated a well-known conjecture of Vaughan. We told him about it in time for him to include it in the second edition of his HARDY-LITTLEWOOD BOOK, where it is now mentioned on pages 127 ("There are some exceptions to this,") and exercise 5 on page 146.
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Looks like one could crop out 3/4th of the picture. (Also, $\div$!?) – anon Jul 23 '12 at 19:35
@anon , I have no idea how to do such things whatsoever. If anyone knowledgeable wants to fiddle with this, make sure we can see the page numbers and issue number and years. It is the American Mathematical Monthly published by the M.A.A. I was going to typeset the five equations in the answer by Adler, as they seem close to illegible on my screen. – Will Jagy Jul 23 '12 at 19:41
@Will Jagy : Thank you very much ! – Watsoon Jul 23 '12 at 20:37
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# n/m asymptotics and logistic regression goodness of fit tests
in the case of logistic regression, say our model has $p$ covariates and we have $J$ distinct covariate patterns (distinct combinations of the values of the p covariates) and we have a total of $n$ observations. The number of covariate patterns with pattern $i$ is denoted by $m_i$. Then, let $y_j$ denote the number of success responses out of the $m_j$.
We have the statement:
The distribution of goodness of fit tests are obtained by letting $n \to \infty$. They are said to be $n$ asymptotic. If we fix $J<n$ and let $n \to \infty$ then each $m_j \to \infty$, distribution assumptions based on these are known as m-asymptotics.
I am trying to understand why the deviance and pearson chi squared statistics produce incorrect $p$-values in the case that $J \approx n$.
The text by Hosmer, Lemeshow states that when $J \approx n$, the distribution of both the pearson residual and the deviance residual is achieved under n asymptotics, and hence, the number of 'parameters' is increasing at the same rate as the sample size.
I don't quite understand why this is problematic, I'm looking for an intuitive explanation of this
To get the 'intuition' you might reason as follows:
I am taking $\chi^2$ as an example, and referring to the formulas (5.1) and (5.2) in this link, which is the book by Hosmer-Lemeshow.
The $\chi^2$ variable is defined as a sum of squared standard normal variables, so if you look at the formulas (5.1) and (5.2) it is assumed that $r(m_j, \hat{\pi}_j)=\frac{y_j - m_j \hat{\pi}_j }{\sqrt{m_j \hat{\pi}_j(1-\hat{\pi}_j)}}$ are standard normal variables.
Note that $y_j$ is the number of successes among the cases with the $j$-th covariate pattern, and $m_j$ is the number of cases with the $j$-th covariate pattern.
Now if you look at that $j$-th covariate pattern as a Binomial random variable with success probability $\pi_j$ and size $m_j$, then the mean of this random variable is (see properties of the Binomial variable) $\mu_j=m_j\pi_j$ and its standard deviation is $\sigma_j=\sqrt{m_j \pi_j (1-\pi_j)}$.
If the size ($m_j$) of this Binomial random variable is ''large'' then the Binomial variable is approximately normal with the same mean and variance.
So if all the $m_j$ are ''large'' then $\frac{y_j - m_j \pi_j}{\sqrt{m_j \pi_j (1-\pi_j)}}$ is approximately standard normal, and then, by definition of $\chi^2$, the sum $X^2=\sum_j \left( \frac{y_j - m_j \pi_j}{\sqrt{m_j \pi_j (1-\pi_j)}} \right) ^2$ has a $\chi^2$ distribution.
If you compare this to the formulas (5.1) and (5.2) in the link supra, you will see that the $\chi^2$ distribution in Hosmer-Lemeshow's book uses the above property, which only holds if $m_j$ are all large !
If $J \approx n$ then all $m_j$ are more or less equal to one, which is not ''large'', so if $J \approx n$ the variable $X^2$ defined in (5.1) and (5.2) can not be shown to follow a $\chi^2$ distribution.
The p-values are derived under the property that $X^2$ is $\chi^2$, so if you can not show this $\chi^2$ property, then the p-values derived from it are also 'doubtfull'.
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# Beamer goto buttons and text hyperlinks
Beamer buttons are used to reference one slide from another so that
you can jump around your presentation (useful if a viewer asks a
question about details, for example).
These buttons are pretty popular. For example, one of the beamer
examples has three of the goto buttons:
examples/beamerlyxexample1.lyx
To use one, you insert a label in a Beamer frame, and then when you
want to link to it, you use
Buttons can be distracting to the audience (it's like showing someone
a box -- of course they want to know what's inside) so many presenters
use text hyperlinks. The text looks like other text so it does not
stand out but it can be clicked on just like a button and just like
one can click on a cross-reference in an article class.
I would like to add support to LyX for these buttons and would like
some advice. Below are a few implementation ideas:
a. This could be an option from the cross-reference menu (as part of
the Format combo box). One could select an existing label, select
button or text, and then enter what they would like to be displayed
b. These could be custom insets defined in beamer.layout. Attached is
a patch that does this. The disadvantage of this approach is that the
user has to do more steps: click on insert > custom insets > Goto
Button; then insert the display text; then they have to remember to go
to Insert > Target; and then they have to remember the name of the
label they want to reference.
c. There are a couple of hybrids of (a) and (b) that could be done.
For example, an option could be added to the Format combo box that
just inserts the label in a PassThru sense (that is, not embedded in
\ref{}). This would make the selection of the label easy and would not
require the hardcoding that a pure (a) solution would.
d. Another hybrid would be to allow a layout argument to be of type
"cross-reference". This would give the user a dialog of the defined
labels to select from (similar to the cross-reference menu but more
simple because no options would need to be selected). It probably
doesn't make sense to implement this just for the insets I'm
proposing, and I struggle to think of other examples so this might not
be a good idea.
Any thoughts?
Scott
diff --git a/lib/layouts/beamer.layout b/lib/layouts/beamer.layout
index 6e0be1b..2d4607e 100644
--- a/lib/layouts/beamer.layout
+++ b/lib/layouts/beamer.layout
@@ -1528,6 +1528,36 @@ InsetLayout Flex:PresentationMode
MultiPar true
End
+InsetLayout Flex:Goto_Button
+ LabelString "Button"
+ LatexType none
+ LyXType Custom
+ LeftDelim {\beamergotobutton{
+ RightDelim }}
+ Decoration Classic
+ MultiPar false
+ ForcePlain 1
+ PassThru 0
+ Spellcheck 1
+ ContentAsLabel 1
+ Argument 1
+ Mandatory 1
+ LabelString "Target"
+ Tooltip "Insert the label of the slide to reference"
+ RightDelim }
+ EndArgument
+End
+
+InsetLayout Flex:Goto_Text
+ CopyStyle Flex:Goto_Button
+ LabelString "Goto Text"
+ LeftDelim {
+ RightDelim }
+ Font
+ Family sans
+ EndFont
+End
#
# FLOATS
|
mersenneforum.org Sums of all Squares
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2010-12-13, 03:52 #122 davar55 May 2004 New York City 2×2,099 Posts While this is current, any other mathematicians here want to comment on whether this sequence is provably infinite? Perhaps by a density heuristic argument?
2010-12-13, 04:45 #123
CRGreathouse
Aug 2006
593810 Posts
Quote:
Originally Posted by davar55 While this is current, any other mathematicians here want to comment on whether this sequence is provably infinite? Perhaps by a density heuristic argument?
It's heuristically infinite with the n-th term about 2.3n * 10^n. I doubt it can be proven infinite with present technology, but a conditional proof on the k-tuple conjecture seems plausible (though it would give bounds wildly out of proportion with the true size of the terms).
2010-12-13, 13:15 #124
science_man_88
"Forget I exist"
Jul 2009
Dumbassville
836910 Posts
Quote:
Originally Posted by davar55 Well, so far the sequence of sum(p^p)mod(10^n) (I think it needs a better name) is: 11 751 1129 361649 361649 12462809 12462809 1273183931 1273183931 Any bets that the tenth and eleventh terms are equal, and whether the twelfth breaks THAT pattern?
I don't know what you're doing obviously because all I came up with that your description could be is:
Code:
a=0;for(n=1,100,a=a+prime(n)^prime(n);print(a%(10^n)))
2010-12-13, 13:50 #125 davar55 May 2004 New York City 2·2,099 Posts The next step would be to filter out to only values = 0. But I think you need a double loop.
2010-12-13, 14:51 #126
science_man_88
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts
Quote:
Originally Posted by davar55 The next step would be to filter out to only values = 0. But I think you need a double loop.
Code:
a=0;for(m=1,2,for(n=1,1000,a=a+prime(n)^prime(n);if(a%(10^m)==0,print(n":"m)));a=0)
like this ?
2010-12-13, 16:09 #127
axn
Jun 2003
17·281 Posts
Quote:
Originally Posted by CRGreathouse Five, actually -- it will be fourth and fifth on your list: 11, 751, 1129, 361649, 361649, 12462809, 12462809, 1273183931, 1273183931. Would someone check me on these? The repeating entries are freaking me out.
Verified the first 7 terms:
11, 751, 1129, 361649, 361649, 12462809, 12462809.
2010-12-13, 16:41 #128 science_man_88 "Forget I exist" Jul 2009 Dumbassville 8,369 Posts with an outer loop I got 11 661 for the start.
2010-12-13, 23:57 #129
CRGreathouse
Aug 2006
10111001100102 Posts
Quote:
Originally Posted by science_man_88 Code: a=0;for(m=1,2,for(n=1,1000,a=a+prime(n)^prime(n);if(a%(10^m)==0,print(n":"m)));a=0) like this ?
As a rule of thumb, any time you write
for(n=1, _, ... prime(n) ...)
you should be writing
forprime(p=2, prime(_), ... p ...)
2010-12-14, 00:56 #130
science_man_88
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts
Quote:
Originally Posted by CRGreathouse As a rule of thumb, any time you write for(n=1, _, ... prime(n) ...) you should be writing forprime(p=2, prime(_), ... p ...) instead.
flaws:
1) isn't always faster
2) results of our codes don't line up so why improve performance of something that gives wrong supposedly inaccurate results
3) I'm already in a bad mood as my sister just called to ask for any mail for here then told me to goto the end of our driveway to check any newer mail and it's almost 9 at night then got mad when i said do I have to, because they technically shouldn't be sending anything here for her or the thing they have planned for my mom.so I'm kinda not in the caring mood.
2010-12-14, 04:37 #131
CRGreathouse
Aug 2006
134628 Posts
Quote:
Originally Posted by science_man_88 3) I'm already in a bad mood as my sister just called to ask for any mail for here then told me to goto the end of our driveway to check any newer mail and it's almost 9 at night then got mad when i said do I have to, because they technically shouldn't be sending anything here for her or the thing they have planned for my mom.so I'm kinda not in the caring mood.
Well, that's what I get for trying to help improve your programming skills.
Quote:
Originally Posted by science_man_88 1) isn't always faster
It's pretty much faster in all cases. prime() is very inefficient, it typically just goes through the primes until it hits the right one.
for(n=1,10,prime(n)) goes through numbers in this order: 2, 2, 3, 2, 3, 5, 2, 3, 5, 7, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 for a total of 10(10+1)/2 = 55 numbers. forprime(p=2,29,p) goes straight through: 2, 3, 5, 7, 11, 13, 17, 19, 23. forprime(p=2, prime(10), p) goes through the primes once to discover the tenth prime, then again for the actual loop.
Quote:
Originally Posted by science_man_88 2) results of our codes don't line up so why improve performance of something that gives wrong supposedly inaccurate results
Post an example. The only times that
Code:
forprime(p=2,prime(floor(N)), f(p))
should differ from
Code:
for(n=1,N, f(prime(n)))
are
• When n or p are used in f (in which case you might just need to change variables!)
• When N is not a t_INT, t_REAL, or t_FRAC, in which case both give errors, but the errors are different
• When you run out of primes (in which case forprime tells you upfront and for() only tells you when you run out)
• When you look at the time taken (essentially, forprime is always faster)
2010-12-14, 09:18 #132
NBtarheel_33
"Nathan"
Jul 2008
Maryland, USA
3×7×53 Posts
p^2 or p^p?
Quote:
Originally Posted by davar55 Well, so far the sequence of sum(p^p)mod(10^n) (I think it needs a better name) is: 11 751 1129 361649 361649 12462809 12462809 1273183931 1273183931 Any bets that the tenth and eleventh terms are equal, and whether the twelfth breaks THAT pattern?
Isn't this the sum of P^2 for p prime, NOT p^p? This thread has me confused...
Similar Threads Thread Thread Starter Forum Replies Last Post a1call Miscellaneous Math 42 2017-02-03 01:29 Nick Number Theory Discussion Group 0 2016-12-11 11:30 3.14159 Miscellaneous Math 12 2010-07-21 11:47 CRGreathouse Math 6 2009-11-06 19:20 m_f_h Puzzles 45 2007-06-15 17:46
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# Math Help - Tangent bundle of a Lie Group is trivial
1. ## Tangent bundle of a Lie Group is trivial
Hello,
Let G be a Lie Group and g his Lie Algebra, that is the tangent space at $e \in G$ I have to show that the map $\phi$: G x g -> TG, $\phi(h,X)=dL_h[X]$, (whereas
$dL_h[X](f)=X(f \circ L_h)$ with L_h left multiplication )
is a diffeomorphism and a linear isomorphism on each fibre.
I'm really hopeless! I don't know how i can show this property's of $\phi$.
Do you know some books or links, where i can read the proof? Or can you please explain it to me?
Regards
2. Since from construction the tangent bundle is locally diffeomorphic to the product of the base manifold G and the identity fiber g, you need only to show that the map is globally one to one. This is easily verified by the fact that $dL_h \cdot dL_{h^{-1}} = id$.
3. Hello,
thank you for your help! I could show that the map is bijective. But i don't see why it is diffeomorphic, even locally diffeomorphic?
Now i have to show that $\phi$ is a linear isomorphism on each fiber.
I suppose that fiber doesn't mean $\phi^{-1}(V_h)$, because $\phi$ is bijective. So what does fiber means here?
Regards
4. A bundle is DEFINED to be locally trivial, that is, locally diffeomorphic to the product of the base space and any of the fiber spaces( since all the fibers are isomorphic). In your case, the base space is G and the fiber at identity is g, the tangent plane. So \phi is DEFINED to be locally diffeomorphic.
To see it is a isomorphism between two fibers T_a and T_b, you only need to show that dL_a * dL_b^{-1} is an isomorphism. Intuitively, you can always translate a vector from T_b to g( the tangent plane at identity), then translate to T_a.
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# CDO tranche Pricing : Default probability
I'm trying to compute the price of a CDO at any time, using the one factor gaussian copula and the Large Homogenous Portfolio Approximation. You can find the CDO pricing formula in M. Neugebauer (2007): A comprehensive Analysis of Advanced Pricing Models for Collateralised Debt Obligations here.
As you can see in the formula $(2.13)$ page 9, the only difficulty is the computation of the expected tranche loss $ELT(t)$, but you can find a closed form (thanks to the one factor gaussian copula model and the large homogenous approximation), it is written in page 16 (equation $(2.37)$). We can see that $ELT(t)$ depends on the default probability of the reference name $P(\tau \le t)$, with $\tau$ being the default time of the reference name. If we assume that $\tau$ has an exponential distribution with hazard rate function $\lambda(t)$, then $P(\tau \le t) = 1 - e^{-\lambda (t)*t}$.
My question is : how do you calibrate $\lambda (t)$ ? I know that for CDSs, we have that $\lambda \simeq \frac{s_0}{1-RR}$ with $s_0$ the contractual spread, and $RR$ the recovery rate (and at time $t$, you have $\lambda_t = s_t / 1-RR$ with $s_t$ the market spread at time $t$). How does it work in our case? Thank you.
You have quotes, on the market, usually for the 6m, 1y, 2y, 3y, 4y, 5y, 7y, 10y, 15y, 20y, 30y tenors, of quoted spreads / upfront that allow for backing out $$\lambda$$, provided you have a model on $$\lambda$$, like the Standard (ISDA/JPM) model. As far as I remember there is an open gamma paper on this question.
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A model of jet precession driven by a neutrino-cooled disc around a spinning black hole is present in order to explain the temporal structure and spectral evolution of gamma-ray bursts (GRBs). The differential rotation of the outer part of a neutrino dominated accretion disc may result in precession of the inner part of the disc and the central black hole, hence drives a precessed jet via neutrino annihilation around the inner part of the disc. Both analytic and numeric results for our model are present. Our calculations show that a black hole-accretion disk system with black hole mass $M \simeq 3.66 M_\odot$, accretion rate $\dot{M} \simeq 0.54 M_\odot \rm s^{-1}$, spin parameter $a=0.9$ and viscosity parameter $\alpha=0.01$ may drive a precessed jet with period P=1 s and luminosity $L=10^{51}$ erg s$^{-1}$, corresponding to the scenario for long GRBs. A precessed jet with $P=0.1$s and $L=10^{50}$ erg s$^{-1}$ may be powered by a system with $M \simeq 5.59 M_\odot$, $\dot{M} \simeq 0.74 M_\odot \rm s^{-1}$, $a=0.1$, and $\alpha=0.01$, possibly being responsible for the short GRBs. Both the temporal and spectral evolution in GRB pulse may explained with our model. GRB central engines likely power a precessed jet driven by a neutrino-cooled disc. The global GRB lightcurves thus could be modulated by the jet precession during the accretion timescale of the GRB central engine. Both the temporal and spectral evolution in GRB pulse may be due to an viewing effect due to the jet precession.
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# Counter examples of cell complex
I'm reading "Memento on cell complexes" and the following is supposed to be a counter example of a cell complex because $e^1$ is not homeomorphic to the open segment:
To me this looks like a deformed disk and is therefore homeomorphic to $D^2$. Why is $e^1$ not homeomorphic to the open segment? Or is it missing a second black dot to denote touching of $e^1$ at 12 o'clock?
Also, I don't see why the following isn't a cell complex either. The boundary of $e^2$ maps into $X^1$. The inductive construction of a cell complex requires exactly that.
-
It looks like in $C_4$ the cell $e^1$ is intended to touch itself and enclose the tear drop. In $C_5$ the labeling indicates that there is only one $0$-cell and two $1$-cells and $e_{2}^1$ is attached in the middle of $e_{1}^1$ which is not allowed. – t.b. Sep 2 '11 at 11:14
Another way to say this is ANY CW-complex with a single 0-cell and a single 1-cell must have 1-skeleton homeomorphic to a circle. But the space pictured has a "1-skeleton" homotopy-equivalent to a wedge of two circles. – Ryan Budney Sep 2 '11 at 16:32
OK, so in case one, there should indeed be another black dot. And in case two, the entirety of $\partial e^2$ should be mapped, not just one dot on it! Thanks for your help! – Rudy the Reindeer Sep 3 '11 at 9:46
@RyanBudney and t.b. , is there a reason you left comments only and not answers? It looks like this question is resolved but I can't tell for sure because it hasn't been officially marked as such. – isomorphismes Oct 5 '12 at 22:36
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# Is this intuitive understanding of “averaging over all realizations of a noise” correct?
Consider a continuous random variable $$\eta(t)$$ such that $$\langle \eta(t)\rangle=0, \forall t$$ where the average $$\langle ...\rangle$$ is taken over all possible realizations of the noise at any time $$t$$. This means, at a given time $$t=t_0$$, the average of the values $$\eta(t_0)$$ that are intersections of the vertical line $$t=t_0$$ and different realizations of the noise in the $$\eta(t)$$-$$t$$ plane is zero.
Now, for a Gaussian random process, can we think that the intersection points to be Gaussian distributed at $$t=t_0$$ i.e. $$p(\eta(t_0))=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\eta^2(t_0)/2\sigma^2}?$$ If so, when we say that $$\eta(t)$$ is a Gaussian random process with zero mean $$\langle \eta(t)\rangle=0, \forall t$$, can we think of $$\langle\eta(t)\rangle$$ as $$\langle \eta(t)\rangle=\int \eta(t)p(\eta(t))=\int \eta(t)\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\eta^2(t)/2\sigma^2}=0?$$
Yes. For a given $$t$$, $$\eta(t)$$ is drawn from a Gaussian distribution with zero mean and variance $$\sigma^2$$. You can compute mean values in the usual way, so indeed $$\langle \eta(t) \rangle = \int d \eta(t) p(\eta(t)) = 0$$, where $$p(\eta(t))$$ is a zero mean Gaussian with variance $$\sigma^2$$.
You certainly can have more interesting Gaussian processes where different points in time are correlated, or the variance changes, but I am assuming that the distribution you wrote down in the question is correct for your use case. The words for what you wrote would be "a stationary, white Gaussian process with variance $$\sigma^2$$".
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Opuscula Math. 34, no. 3 (2014), 463-468
http://dx.doi.org/10.7494/OpMath.2014.34.3.463
Opuscula Mathematica
# A note on on-line Ramsey numbers for quadrilaterals
Joanna Cyman
Tomasz Dzido
Abstract. We consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder's goal is to force Painter to create a monochromatic copy of a fixed graph $$H$$ in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number $$\widetilde{r}(H)$$ of the graph $$H$$. An asymmetric version of the on-line Ramsey numbers $$\widetilde{r}(G,H)$$ is defined accordingly. In 2005, Kurek and Ruciński computed $$\widetilde{r}(C_3)$$. In this paper, we compute $$\widetilde{r}(C_4,C_k)$$ for $$3 \le k \le 7$$. Most of the results are based on computer algorithms but we obtain the exact value $$\widetilde{r}(C_4)$$ and do so without the help of computer algorithms.
Keywords: Ramsey theory, on-line games.
Mathematics Subject Classification: 05C55, 05C57.
Full text (pdf)
Joanna Cyman, Tomasz Dzido, A note on on-line Ramsey numbers for quadrilaterals, Opuscula Math. 34, no. 3 (2014), 463-468, http://dx.doi.org/10.7494/OpMath.2014.34.3.463
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# Fast Longest Prefix Matching: Algorithms, Analysis, and Applications
Marcel Waldvogel: Fast Longest Prefix Matching: Algorithms, Analysis, and Applications. Shaker Verlag, Aachen, Germany, 2000.
## Abstract
Many current problems demand efficient best matching algorithms. Network devices alone show several applications. They need to determine a longest matching prefix for packet routing or establishment of virtual circuits. In integrated services packet networks, packets need to be classified by trying to find the most specific match from a large number of patterns, each possibly containing wildcards at arbitrary positions. Other areas of applications include such diverse areas as geographical information systems (GIS) and persistent databases.
We describe a class of best matching algorithms based on slicing perpendicular to the patterns and performing a modified binary search over these slices. We also analyze their complexity and performance. We then introduce schemes that allow the algorithm to learn'' the structure of the database and adapt itself to it. Furthermore, we show how to efficiently implement our algorithm both using general-purpose hardware and using software running on popular personal computers and workstations.
The research presented herein was originally driven by current demands in the Internet. Since the advent of the World Wide Web, the number of users, hosts, domains, and networks connected to the Internet seems to be exploding. Not surprisingly, network traffic at major exchange points is doubling every few months. The Internet is a packet network, where each data packet is passed from a router to the next in the chain, until it reaches destination. For versatility and efficient utilization of the available transmission bandwidth, each router performs its decision where to forward a packet as independent of the other routers and the other packets for the same destination as possible.
Five key factors are required to keep pace if the Internet is to continue to provide good service:
2. better router data throughput,
3. faster packet forwarding rates,
5. the support for Quality-of-Service (QoS).
Solutions for the first two are readily available: fiber-optic cables using wavelength-division multiplexing (WDM) and switching backplane interconnects. We present longest matching prefix techniques which help solving the other three factors. They allow for a high rate of forwarding decisions, quick updates, and can be extended to classify packets based on multiple fields.
The best known longest matching prefix solutions require memory accesses proportional to the length of the addresses. Our new algorithm uses binary search on hash tables organized by prefix lengths and scales very well as address and routing table sizes increase: independent of the table size, it requires a worst case time of log2(address bits) hash lookups. Thus only 5 hash lookups are needed for the current Internet protocol version 4 (IPv4) with 32 address bits and 7 for the upcoming IPv6 with 128 address bits. We also introduce mutating binary search and other optimizations that, operating on the largest available databases, reduce the worst case to 4 hashes and allow the majority of addresses to be found with at most 2 hashes. We expect similar improvements to hold for IPv6.
We extend these results to find the best match for a tuple of multiple fields of the packet's header, as required for QoS support. We also show the versatility of the resulting algorithms by using it for such diverse applications as geographical information systems, memory management, garbage collection, persistent object-oriented databases, keeping distributed databases synchronized, and performing web-server access control.
@book{Waldvogel2000Fast,
title = {Fast Longest Prefix Matching: Algorithms, Analysis, and Applications},
author = {Marcel Waldvogel},
year = {2000},
date = {2000-01-01},
publisher = {Shaker Verlag},
abstract = {Many current problems demand efficient best matching algorithms. Network devices alone show several applications. They need to determine a \emph{longest matching prefix} for packet routing or establishment of virtual circuits. In integrated services packet networks, packets need to be classified by trying to find the \emph{most specific match} from a large number of patterns, each possibly containing wildcards at arbitrary positions. Other areas of applications include such diverse areas as geographical information systems (GIS) and persistent databases.
We describe a class of best matching algorithms based on slicing perpendicular to the patterns and performing a modified binary search over these slices. We also analyze their complexity and performance. We then introduce schemes that allow the algorithm to learn\'\' the structure of the database and adapt itself to it. Furthermore, we show how to efficiently implement our algorithm both using general-purpose hardware and using software running on popular personal computers and workstations.
The research presented herein was originally driven by current demands in the Internet. Since the advent of the World Wide Web, the number of users, hosts, domains, and networks connected to the Internet seems to be exploding. Not surprisingly, network traffic at major exchange points is doubling every few months. The Internet is a packet network, where each data packet is passed from a router to the next in the chain, until it reaches destination. For versatility and efficient utilization of the available transmission bandwidth, each router performs its decision where to forward a packet as independent of the other routers and the other packets for the same destination as possible.
Five key factors are required to keep pace if the Internet is to continue to provide good service:
\begin{enumerate}
\item better router data throughput,
\item faster packet forwarding rates,
\item the support for Quality-of-Service (QoS).
\end{enumerate} . "\n"
Solutions for the first two are readily available: fiber-optic cables using wavelength-division multiplexing (WDM) and switching backplane interconnects. We present longest matching prefix techniques which help solving the other three factors. They allow for a high rate of forwarding decisions, quick updates, and can be extended to classify packets based on multiple fields.
The best known longest matching prefix solutions require memory accesses proportional to the length of the addresses. Our new algorithm uses binary search on hash tables organized by prefix lengths and scales very well as address and routing table sizes increase: independent of the table size, it requires a worst case time of log_{2}(\textit{address bits\textit{) hash lookups. Thus only 5 hash lookups are needed for the current Internet protocol version 4 (IPv4) with 32 address bits and 7 for the upcoming IPv6 with 128 address bits. We also introduce \emph{mutating binary search} and other optimizations that, operating on the largest available databases, reduce the worst case to 4 hashes and allow the majority of addresses to be found with at most 2 hashes. We expect similar improvements to hold for IPv6.
We extend these results to find the best match for a tuple of multiple fields of the packet\'s header, as required for QoS support. We also show the versatility of the resulting algorithms by using it for such diverse applications as geographical information systems, memory management, garbage collection, persistent object-oriented databases, keeping distributed databases synchronized, and performing web-server access control.},
keywords = {Fast Routers, Hash Tables},
pubstate = {published},
tppubtype = {book}
}
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# Hasn't gotten a date
Home Forums Shidduchim Hasn't gotten a date
Viewing 50 posts - 1 through 50 (of 73 total)
• Author
Posts
• #614422
balancehumanbalance
Participant
I have a single friend who lives out of town. She is 23 years old and hasn’t gotten a date. She is pretty, went to a good seminary, dresses well, attends shiurim, and works in a frum office. How many people do you know in a similar situation? How normal/ needs help is this?
No critics please, just trying to find common ground.
#1070279
appdev
Participant
I can put up an ad for her in one of my apps if you’d like…
#1070280
Chochom-ibber
Participant
No dates out-of-town? I have plenty out-of-town friends dating and many married. Does she live in Antarctica?
#1070281
Being Real
Participant
Is her family situation regular?Hate to do this but maybe shes for me I am looking for an out of towner that age
#1070282
oot for life
Participant
Living out of town has a few drawbacks this could be included in that list (along with lack of pizza options).
You listed that “She is pretty, went to a good seminary, dresses well, attends shiurim, and works in a frum office.”
Is she doing her histadlus? Meeting with shadchanim, going to events, (and here’s the big thing) willing to travel?
Its tough in shidduchim wherever a person is, but I think like with everything in life you get out what you put in, the more effort the more success.
#1070283
TheGoq
Participant
Oy life without new york pizza?? do people really live like this???
#1070285
#I’m an out of town girl, BH I don’t have a problem getting dates. It’s about going out of your comfort zone, and calling people, emialing people, joining shadchan websites…
#1070286
oyyoyyoy
Participant
sheesh. yknow what i hate though? girls always complain they dont get dates, and then when they finally get one they say “no” after one.
#1070287
Health
Participant
Oyoyoy- The reason they say “No” is because they think there is something better. Why? Because a lot of girls are spoiled, especially here in America!
#1070288
👑RebYidd23
Participant
A girl has a right not to get married if she so chooses.
#1070289
oyyoyyoy
Participant
You’re missing the point. The reason they should give it another chance is to get a better picture of the boy before judging anything, it’s not like they’re swimming in names.
#1070290
OOT girls have 3 options when theyre 23:
1. Move to a big city.
2. Be flexible about traveling for dating. That means flexibility at work, with bosses/job that allows for flexibility.
3. Wait til the guy comes to you (not the best option).
With all the above, speak to everyone you meet and tell them what youre looking for. You never know who the Shaliach is.
#1070291
charliehall
Participant
I was living in New York City but my wife was living “Out of town” when she contacted me through one of the frum dating websites. Baruch HaShem we are coming up on ten years of marriage soon.
#1070292
balancehumanbalance
Participant
Thanks for the suggestions MS Shadchan and Charlie Hall… Do you know anyone in similar situations? What else did they do?
#1070293
Another piece of advice. Look as good as you can, in general, and make sure you have a really good and recent picture both on your Shidduch resume and dating website, if youre on. I hate to tell it like it is, but girls’ looks/picture is more important than everything else combined. It is what it is.
This advice doesnt hurt boys either.
#1070294
Joseph
Participant
Girls dating pictures helps, basically, with boys looking for vanity. If that’s the type of guy she’s looking for, what can I tell you.
#1070295
Health
Participant
RY23 – A boy also has the same right.
#1070296
Patur Aval Assur
Participant
Lior:
See the Radak and Ralbag about Yaakov choosing between Rachel and Leah.
??? ????? ??? ?????? ??????? ???? ???? ??? ??? ??????? ??? ??? ??? ???? ???? ?????? ????? ????? ????? ??? ???? ??? ????’ ??? ??? ???? ?? ??? ???? ?????? ???? ??? ???? ?? ??? ?????? ??? ??? ???? ??? ??? ??? ??? ???? ?? ????? ????? ??? ????? ??? ?????? ????? ???? ?????? ???? ???? ?????? ????? ????? ???? ??? ????? ????? ?????? ??? ???? ????? ????? ??? ???? ?? ???? ???? ????? ?? ???? ?? ??? ????? ????? ????? ???? ????? ????? ?? ????? ????? ????? ???? ??? ?????? ?????? ???? ?? ??? ?? ?????? ???? ????? ??? ?????? ????? ??? ??? ??? ???? ????? ????? ??????? ????? ????? ????? ???????? ???? ?????
Ralbag:
???? ??? ???? ??? ???? ??? ??? ???? ?????? ??? ????? ??? ???? ??????? ???? ???? ?? ???? ????? ??? ???? ???? ????? ?? ???? ???? ???? ????? ??? ????? ??? ???? ???? ??? ???? ???? ????
and Ralbag again:
?????? ?????? ??? ????? ???? ????? ???? ????? ???? ???? ?????? ?? ???? ????? ?? ???? ???? ???? ???? ????? ??? ???? ?? ??? ???? ???? ?? ??? ????? ?????? ???? ???? ?? ???? ???? ????? ??? ???? ???? ???? ?? ????? ?? ??? ?????? ????? ?? ??? ????? ???? ????
#1070297
Patur Aval Assur
Participant
Though I’m not sure how this Ralbag fits with what he wrote in Parshas Lech Lecha to explain why Sarah and Rachel gave their ????? to their husbands:
??? ????? ?????? ??? ???? ???? ???? ???? ????? ?????? ???? ???? ?????? ??????? ??? ??? ????? ???? ??? ??? ???? ?????? ???? ???? ???? ???? ??? ???? ????? ????? ??? ??? ?? ????? ??? ??? ??? ??? ?? ???? ?? ??? ????? ????? ??? ??? ??? ???? ????? ??????? ??? ????? ?? ???? ?????? ???? ??? ?????? ????? ?????? ???????? ????????? ???? ????? ??? ??? ???? ??? ??? ???? ????? ??????? ??? ??? ??? ???? ?????? ??? ?? ???? ????? ????? ??? ??????? ?? ??? ??????? ?? ???? ?????? ?????? ???? ???? ??? ?? ????? ????? ???? ?? ??? ?????? ????? ??????? ?? ??? ?? ????? ?? ??? ???
And which he reiterated in Parshas Vayeitzei:
???? ????? ???? ??? ??? ?? ????? ??? ????? ?? ????? ????
#1070298
👑RebYidd23
Participant
I did not say that boys have to get married.
#1070299
flatbusher
Participant
Many a young woman will come to New York for dating. Does your friend object to doing that?
#1070300
Health
Participant
RY 23 – Acc. to the Torah, both boys & girls ( Men & Women) have to get married. But it’s not for the same reason.
#1070301
Patur Aval Assur, would you please at least loosely translate to English, what you posted above in Hebrew? Thanks.
#1070302
bygirl93
Member
Correct me if I’m wrong but isn’t the whole point of marriage for boy’s so that they can fulfill the mitzvah of Piru’urivu? Pretty sure that that mitzvah doesn’t apply to girls.
#1070303
Patur Aval Assur
Participant
(This is something between a translation and a summary.)
Question: Why would Tzadikim, whose intentions of marriage are to progenate, seek beautiful women? Yaakov chose Rachel because she was beautiful, and was upset at Lavan for giving him Leah, because Leah was less beautiful. Why would he do this?
Answer 1: In order to increase their progeny, they wanted to arouse their desire, hence they would choose beautiful women.
Answer 2: They wanted their children to be beautiful and to look like them.
Answer 3: Having her form in front of him will gladden him and man is supposed to be happy in his world and with the portion that H’ gives him. H’ provides the righteous with beautiful women as he did for our forefathers and other righteous people, so that they should be happy with their lot and have kids like themselves.
#1070304
Patur Aval Assur
Participant
The first Ralbag:
Lavan had two daughters. Yaakov did not choose the older one, because her eyes were soft and teary which is a malady. He chose the younger one so that he would have progeny from her who would be more complete and healthier. And also because she was beautiful.
#1070305
Patur Aval Assur
Participant
The second Ralbag:
The tenth lesson is that a man should choose a woman who is complete of form, as his progeny from her will be healthier and fuller. This is why Yaakov did not choose Leah who was teary-eyed which is a malady, and instead chose Rachel who was beautiful. Additionally, this would allow him to channel his desire towards her and not to think of other women.
#1070307
☕ DaasYochid ☕
Participant
Bygirl93, that is not the only reason to get married.
#1070308
bygirl93
Member
DY- I am very well aware of that. BUT if you get down to the actual detail about what you learn in school- that’s pretty much it. At least in typical bais Yaakovs where they don’t teach gemara. That’s pretty much all a girl learns is the HALACHIC reasoning- there are lots of obvious reasons- this is just the one that tends to be taught is halacha.
#1070309
☕ DaasYochid ☕
Participant
Well, you wanted someine to correct you if you were wrong..
#1070310
bygirl93
Member
*someone 😛
#1070311
Health
Participant
BYgirl 93- What BY school did you learn Halacha reasoning in? The Halacha is both men & women Have to get married!
#1070312
SaraCFL
Participant
I am 22 and I am an out of town girl. I went to Brooklyn for a couple of months and I did get more dates but I found it harder to meet someone serious and the shadchanim are busier! so I moved back home where I get fewer dates but the shadchanim suggest more serious boys. I think that the key to out of town dating is to work with shadchanim and be on dating websites. You probably aren’t going to bump into “the one” at the one pizza place in 20 miles, but you might 🙂
#1070313
balancehumanbalance
Participant
Thank you Sara – that was insightful.
#1070314
oyyoyyoy
Participant
PAA- that took guts. kinda scary how mechavein i was. where are those?
#1070315
Patur Aval Assur
Participant
oyyoyyoy:
Are you referring to the fact that I originally quoted them, or to the fact that I translated/summarized them? If the latter, notice how there is no translation provided for the third Ralbag. And it’s not because I didn’t provide it, if you get what I mean.
Anyway, the Radak is on Genesis 29:18
The first Ralbag is in parshas Vayeitzi in the Mosad Harav Kook edition p.183
The second Ralbag is in the list of ??????, specifically the tenth ?????, on p. 194 in the Mosad Harav Kook edition.
The first part of the third Ralbag is in Lech Lecha on p. 119 in the Mosad Harav Kook edition and the second part is in Vayetzei on p. 186 in the Mosad Harav Kook edition.
#1070316
Patur Aval Assur
Participant
If the latter, notice how there is no translation provided for the third Ralbag. And it’s not because I didn’t provide it, if you get what I mean.
#1070317
Patur Aval Assur
Participant
I have a single friend who lives out of town. She is 23 years old and hasn’t gotten a date.
I have awesome advice. R’ Yochanan Luria in his commentary to Parshas Beshalach writes:
?? ??? ????? ????? ???? ????? ????? ???? ??? ???? ???? ???? ????
?? ??????? ???? ??? ?????? ???? ?? ?????? ????? ??????
??? ??? ???
And he confirms this one page later:
???? ???? ???? ????? ????? ???????? ????? ???? ??????
?? ??????? ??????? ??? ??? ???? ??????? ????? ????? ???
?????
#1070318
Patur Aval Assur
Participant
bygirl93 said:
Correct me if I’m wrong but isn’t the whole point of marriage for boy’s so that they can fulfill the mitzvah of Piru’urivu? Pretty sure that that mitzvah doesn’t apply to girls.
DaasYochid said:
Bygirl93, that is not the only reason to get married.
bygirl93 said:
DY- I am very well aware of that. BUT if you get down to the actual detail about what you learn in school- that’s pretty much it. At least in typical bais Yaakovs where they don’t teach gemara. That’s pretty much all a girl learns is the HALACHIC reasoning- there are lots of obvious reasons- this is just the one that tends to be taught is halacha.
DaasYochid said:
Well, you wanted someine to correct you if you were wrong..
Health said:
BYgirl 93- What BY school did you learn Halacha reasoning in? The Halacha is both men & women Have to get married!
There are three potential reasons why a girl would have to get married:
1) ??? ????
2) ???? ????
3) ???
It’s a machlokes Tannaim in Yevamos 65b whether a woman is chayev in ??? ????. The halacha follows the Tanna Kamma that she is not obligated.
Tosafos in Gittin 41b ?”? ?? holds that a woman is obligated in ???, but this position is not accepted by the codifiers of halacha.
Which leaves the issue of ???. The Rambam in Hilchos Ishus 15:16 writes:
??? ??? ??? ??? ??? ??? ????.
The Tur does not mention this, and the Rema in Even Ha’ezer 1:13 writes:
??”? ?”? ??? ????? ??? ??? ???? ????
Now this is an interesting lashon. It doesn’t say that it’s assur to not marry, nor does it say that she is obligated to marry. It says that she shouldn’t be without a husband. This is significant as we shall see.
Various commentators point out that it’s a stirah in the Rambam. We just quoted him as saying ??? ??? ??? ??? ??? ??? ???? yet in Issurei Biah 21:26 he writes:
????? ???? ??? ???? ????? ?? ???? ?????
which clearly implies that she never has to get married under any circumstances. The various commentators suggest various answers.
A few acharonim suggest that the Rambam in Issurei Biah is talking about a place where there would be no chashad, e.g. if there are no men in that place.
The ???? ??? quotes this suggestion and says ???? ??? ????. He then gives two answers:
1) ????? ???? ???? ???? ????? ???? ???? ?????? ??? ????? ????? ?????? ?????? ?????? ???? ????? ???? ????? ???? ???? ???? ??? ??? ???? ?????? ???? ??? ???? ??? ??? ???? ???? ?????
2) ???? ???? ???? ????? ????? ????? ??? ??? ???? ???? ??????? ?????? ???? ?? ???? ?? ???? ?? ???? ???? ??? ???? ???”?
The ??? ???? quotes an answer that min hadin a woman does not have to get married at all and “??? ??? ??? ??? ??? ??? ????” is an eitzah tovah.
So to conclude, there are definitely grounds to argue that a woman is not obligated to get married. DaasYochid, the thing that bygirl93 said “correct me if I’m wrong” on was ??? ????, so even if you are right that there is a different obligation, bygirl93 was still correct and therefore you were not actually correcting her for being wrong. However, the lashon you used was “that is not the only reason to get married” which does not necessarily indicate that you think that there is an obligation to get married, but merely a reason to get married. But Health explicitly stated that there is an obligation, so this post is primarily a response to him, pointing out that it’s not so pashut.
Even if there is no obligation for her to get married, she still gets a mitzvah of helping the man fulfill his mitzvah. As the ??? ???? writes:
???”? ???? ???? ????? ??? ???? ?”? ?? ?? ???? ??? ??? ??? ???? ?????
#1070319
oyyoyyoy
Participant
wow, u do have guts
#1070323
Vogue
Member
I would say that for me, I also live out of town and do not really get the opportunity to go to ny. I have gotten 20+ suggestions over the past year. I ended up getting two phone dates with one person out of it. I said no to some guys and some guys said no to me. I think that the key thing is that you need to network. Also, every time that you go to another city, even if it is a smaller community- like St. Louis or Memphis, to try to ask about meeting at least one shadchan on your trip.
#1070324
ChizukGedarim
Participant
@PAA, I love the fact that you bring up such interesting meforshim. But I just wanted to clarify that although it is true that ?????? would be allowed certain laxness, today they are considered ????? and are treated with all the stringency allowed by halacha
#1070325
TheGoq
Participant
“I ended up getting two phone dates with one person out of it.”
Why would you want to date someone who is out of it?
#1070326
Patur Aval Assur
Participant
ChizukGedarim:
Without getting too involved, not everyone agrees. See Shu”t B’nei Banim 4:7:
http://hebrewbooks.org/pdfpager.aspx?req=20023&st=&pgnum=25
and particularly the second to last paragraph of the teshuva where he writes:
??? ??? ???? ???? ????? ??? ??? ?? ?????? ??? ????? ????? ???? ????? ????? ???? ???? ??? ????? ????? ???? ????? ?? ?????? ??? ???? ??? ???? ??????? ??? ???? ????? ?? ???? ???? ?? ????? ????? ??? ????? ????? ??? ????? ???? ??? ?? ???? ?????? ????? ????? ?? ?????? ???? ???? ???? ?? ????? ??’ ??”? ??? ?????? ???? ???? ?”? ????? ????? ?????? ?? ???? ??? ????
#1070328
MDG
Participant
PAA said, “Tosafos in Gittin 41b ?”? ?? holds that a woman is obligated in ???, but this position is not accepted by the codifiers of halacha.”
PAA, can you please cite where it’s (not) mentioned in the Tur, Sh”Ar, Kitzur, Aruch Hashulchan, etc.
#1070329
Patur Aval Assur
Participant
MDG:
None of them mention it when they discuss the chiyuv of peru urevu.
The Rambam in Ishus 15:2 says that men are chayev in peru urevu and women are not.
The Tur in Even Ha’ezer in the end of siman 1 states that a woman is not obligated in peru urevu. He doesn’t say that she is obligated in sheves.
The Shulchan Aruch in Even Ha’ezer 1:13 says that a woman is not obligated in peru urevu, yet he doesn’t mention anything about an obligation of sheves. The Rema there, adds the yesh omrim that she should get married because of chashad but he doesn’t say that she should get married because of sheves.
The Levush in Even Ha’ezer 1:13 says that women are not obligated in peru urevu and in 1:14 he mentions the issue of chashad. Again, there is no mention of an obligation of sheves.
That was all proof by omission. The Aruch Hashulchan is explicit though. In Even Ha’ezer 1:2 he says that women are not obligated in peru urevu. In 1:3 he quotes the Rema about chashad. Then in 1:4 he writes:
?? ???????? ????? ????? ?? ????? ????? ?? ??”? ?”? ????? ????? ???? ???? ???? ?????? ???? ??? ???? ???? ??”? ??? ???? ??? ??”? ????’ ?’ ?????? ???? ??? ????? ?? ??”? ????? ??? ????? ?? ???? ???? ??? ???? ????? ????”? ?????? ????’ ?’ ???? ??????? ???? ??? ???? ???? ?? ???? ????? ????? ??? ??? ????? ??”? ??? ?????? ????? ????? ???? ?????? ??? ???? ????? ????? ??????? ??”? ???’ ??”? ??? ???? ???? ?????? ???? ??? ?? ???? ????? ??? ??? ???????? ???? ????’ ???? ???? ???? ??? ???? [????? ?”?: ??”? ?”? ?] ??? ??? ?????? ????????? ???? ??? ??????? ???? ?????? ?? ??? ??? ?? ????? ?????? ?? ???? ???? ????? ???? ???? ???? ??? ????? ????? ????”? ??? ????? ????????? ?? ??? ??? ??? ???? ???? ???? ????? ??????? ?? ????? ???? ???? ????? ?? ????? ????? ????? ????? ?? ???? ??? ??? ????? ?????? ????? ?????? ????? ???? ????? ????? ?? ??? ??????? ??? ???? ????? ?? ???? ??? ???? ???? ??? ?????? ????? ???? ????? ????? ????? ?? ????? ???? ?”? ???? ???? ???? ????? ????? ?? ???? ???”? ??? ???? ???? ??? ?????? ????? ??? ????? ??”? ????? ?? ??? ??? ?? ????? ?????? ?? ???? ??? ?? ??? ??? ?? ??? ?? ???? ??? ?? ????? ???????? ????? ???? ??????? ?????? ?????? ?? ???? ??”? ???”? ??’ ??”? ?? ???? ???? ???? ????? ??? ????? ?? ????? ???? ???? ??? ??? ??? ?????? ???? ???? ?????? ?? ??? ?? ?????? ??? ???? ????? ??? ?????? ???? ??? ???? ???? ??”? ??? ???? ??? ??”? ????? ???”? ?????? ???? ????? ??? ???????? ?”? ????? ??? ???? ????? ???? ????? ??? ?? ?? ??? ????? ?? ??”?
Also see the ??? ???? on the Rambam in Hilchos Ishus 15:16 who proves that the Rambam doesn’t hold of sheves for a woman from he fact that in Issurei Biah 21:26 the Rambam writes:
????? ???? ??? ???? ?????
So I think we see that the Poskim reject Tosafos’s position. The Aruch Hashulchan actually claims that even Tosafos doesn’t hold that women are obligated in sheves. He claims that it’s impossible for women to have such an obligation because he understands that sheves simply the force behind peru urevu, and women are not obligated in peru urevu.
#1070330
MDG
Participant
PAA,
Thank you !
#1070331
Vogue
Member
What I ended up figuring out from the phone dates with that person was basically everything I am not looking for in a shidduch.
In my case:
-BT (works for many, but it depends on who you are and how you became frum, I have a very unusual case in which it would not work for me due to my personal circumstances prior education and life experiences)
-Chabad (works for many- not for me. I have plenty of lubavitch friends and relatives).
-Unemployed but not in Kollel and no initiative to get a job or go to school and not even looking into semicha programs. Just bumming around with beer buddies, sees no potential in himself.
-No desire to further himself
-Pushover with not-solid hashkafos
-Bipolar (and he texted me to tell me instead of calling me… I went to the doctor. I called. I texted you. what happened at the dr office? I was diagnosed with bipolar today).
-Resentful of upbringing
-No desire to grow as a person
-Resentful of siblings who aren’t frum/family situation
-Jealous of my previous frum experiences
-Basically put his entire adult and personal life on hold because he started keeping shabbos. But on the converse, someone who was born frum, if they put their entire life on hold because of a bad teacher/other crazy lifestyle change (like frumming out), that wouldn’t work for me either.
#1070332
Patur Aval Assur
Participant
MDG:
You’re Welcome.
#1070333
Vogue, I wouldn’t expect you to personally give the guy another shot, but once he’s treated for his bipolar disorder, he should be a different person. That one detail changes the whole picture.
(I wouldn’t expect him to actually be ready for marriage too fast, though…)
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# zbMATH — the first resource for mathematics
## Tysk, Johan
Compute Distance To:
Author ID: tysk.johan Published as: Tysk, J.; Tysk, Johan
Documents Indexed: 33 Publications since 1985
all top 5
#### Co-Authors
5 single-authored 18 Ekström, Erik 6 Janson, Svante 3 Lötstedt, Per 2 Cheng, Shiu-Yuen 2 Frankel, S. N. 2 Lindberg, Carl 2 von Sydow, Lina 1 Dyrssen, Hannah 1 Hobson, David G. 1 Hodgson, Craig D. 1 Klimek, Maciej 1 Persson, Jonas 1 Strandell, Gustaf 1 Wanntorp, Henrik
all top 5
#### Serials
3 Journal of Mathematical Analysis and Applications 3 The Annals of Applied Probability 3 International Journal of Theoretical and Applied Finance 2 Journal of Applied Probability 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Applied Mathematical Finance 2 Theory of Stochastic Processes 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Rocky Mountain Journal of Mathematics 1 Bulletin of the London Mathematical Society 1 Journal of Differential Equations 1 Transactions of the American Mathematical Society 1 Complex Variables. Theory and Application 1 Probability Theory and Related Fields 1 Mathematical Finance 1 Quantitative Finance 1 Communications on Pure and Applied Analysis
all top 5
#### Fields
22 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Probability theory and stochastic processes (60-XX) 12 Partial differential equations (35-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Differential geometry (53-XX) 2 Functions of a complex variable (30-XX) 2 Numerical analysis (65-XX) 1 Functional analysis (46-XX)
#### Citations contained in zbMATH Open
25 Publications have been cited 239 times in 180 Documents Cited by Year
Feynman-Kac formulas for Black-Scholes-type operators. Zbl 1110.35021
Janson, Svante; Tysk, Johan
2006
Bubbles, convexity and the Black-Scholes equation. Zbl 1219.91138
Ekström, Erik; Tysk, Johan
2009
Space-time adaptive finite difference method for European multi-asset options. Zbl 1154.91462
Lötstedt, Per; Persson, Jonas; von Sydow, Lina; Tysk, Johan
2007
The Black-Scholes equation in stochastic volatility models. Zbl 1188.91200
Ekström, Erik; Tysk, Johan
2010
Boundary conditions for the single-factor term structure equation. Zbl 1232.91679
Ekström, Erik; Tysk, Johan
2011
Preservation of convexity of solutions to parabolic equations. Zbl 1056.35011
Janson, Svante; Tysk, Johan
2004
Finiteness of index and total scalar curvature for minimal hypersurfaces. Zbl 0661.53039
Tysk, Johan
1989
Volatility time and properties of option prices. Zbl 1061.91028
Janson, Svante; Tysk, Johan
2003
Boundary values and finite difference methods for the single factor term structure equation. Zbl 1179.91247
Ekström, Erik; Lötstedt, Per; Tysk, Johan
2009
Eigenvalue estimates with applications to minimal surfaces. Zbl 0594.58018
Tysk, Johan
1987
Optimal liquidation of a pairs trade. Zbl 1232.91618
Ekström, Erik; Lindberg, Carl; Tysk, Johan
2011
Properties of option prices in models with jumps. Zbl 1186.91213
Ekström, Erik; Tysk, Johan
2007
Can time-homogeneous diffusions produce any distribution? Zbl 1276.60085
Ekström, Erik; Hobson, David; Janson, Svante; Tysk, Johan
2013
Superreplication of options on several underlying assets. Zbl 1125.91052
Ekström, Erik; Janson, Svante; Tysk, Johan
2005
Schrödinger operators and index bounds for minimal submanifolds. Zbl 0818.53075
Cheng, Shiu-Yuen; Tysk, Johan
1994
An index characterization of the catenoid and index bounds for minimal surfaces in $$R^ 4$$. Zbl 0613.58030
Cheng, Shiu-Yuen; Tysk, Johan
1988
Optimal liquidation of a call spread. Zbl 1193.91154
Ekström, Erik; Lindberg, Carl; Tysk, Johan; Wanntorp, Henrik
2010
Numerical option pricing in the presence of bubbles. Zbl 1267.91080
Ekström, Erik; Lötstedt, Per; von Sydow, Lina; Tysk, Johan
2011
Convexity preserving jump-diffusion models for option pricing. Zbl 1250.91110
Ekström, Erik; Tysk, Johan
2007
Eigenvalue estimates and isoperimetric inequalities for cone-manifolds. Zbl 0812.58092
Hodgson, Craig; Tysk, Johan
1993
The American put is log-concave in the log-price. Zbl 1083.91056
Ekström, Erik; Tysk, Johan
2006
Options written on stocks with known dividends. Zbl 1090.91039
Ekström, Erik; Tysk, Johan
2004
Dupire’s equation for bubbles. Zbl 1262.91133
Ekström, Erik; Tysk, Johan
2012
Testing weak stationarity of stock returns. Zbl 0973.91034
Klimek, Maciej; Strandell, Gustaf; Tysk, Johan
2001
Comparison of two methods of multiplying distributions. Zbl 0581.46029
Tysk, Johan
1985
Can time-homogeneous diffusions produce any distribution? Zbl 1276.60085
Ekström, Erik; Hobson, David; Janson, Svante; Tysk, Johan
2013
Dupire’s equation for bubbles. Zbl 1262.91133
Ekström, Erik; Tysk, Johan
2012
Boundary conditions for the single-factor term structure equation. Zbl 1232.91679
Ekström, Erik; Tysk, Johan
2011
Optimal liquidation of a pairs trade. Zbl 1232.91618
Ekström, Erik; Lindberg, Carl; Tysk, Johan
2011
Numerical option pricing in the presence of bubbles. Zbl 1267.91080
Ekström, Erik; Lötstedt, Per; von Sydow, Lina; Tysk, Johan
2011
The Black-Scholes equation in stochastic volatility models. Zbl 1188.91200
Ekström, Erik; Tysk, Johan
2010
Optimal liquidation of a call spread. Zbl 1193.91154
Ekström, Erik; Lindberg, Carl; Tysk, Johan; Wanntorp, Henrik
2010
Bubbles, convexity and the Black-Scholes equation. Zbl 1219.91138
Ekström, Erik; Tysk, Johan
2009
Boundary values and finite difference methods for the single factor term structure equation. Zbl 1179.91247
Ekström, Erik; Lötstedt, Per; Tysk, Johan
2009
Space-time adaptive finite difference method for European multi-asset options. Zbl 1154.91462
Lötstedt, Per; Persson, Jonas; von Sydow, Lina; Tysk, Johan
2007
Properties of option prices in models with jumps. Zbl 1186.91213
Ekström, Erik; Tysk, Johan
2007
Convexity preserving jump-diffusion models for option pricing. Zbl 1250.91110
Ekström, Erik; Tysk, Johan
2007
Feynman-Kac formulas for Black-Scholes-type operators. Zbl 1110.35021
Janson, Svante; Tysk, Johan
2006
The American put is log-concave in the log-price. Zbl 1083.91056
Ekström, Erik; Tysk, Johan
2006
Superreplication of options on several underlying assets. Zbl 1125.91052
Ekström, Erik; Janson, Svante; Tysk, Johan
2005
Preservation of convexity of solutions to parabolic equations. Zbl 1056.35011
Janson, Svante; Tysk, Johan
2004
Options written on stocks with known dividends. Zbl 1090.91039
Ekström, Erik; Tysk, Johan
2004
Volatility time and properties of option prices. Zbl 1061.91028
Janson, Svante; Tysk, Johan
2003
Testing weak stationarity of stock returns. Zbl 0973.91034
Klimek, Maciej; Strandell, Gustaf; Tysk, Johan
2001
Schrödinger operators and index bounds for minimal submanifolds. Zbl 0818.53075
Cheng, Shiu-Yuen; Tysk, Johan
1994
Eigenvalue estimates and isoperimetric inequalities for cone-manifolds. Zbl 0812.58092
Hodgson, Craig; Tysk, Johan
1993
Finiteness of index and total scalar curvature for minimal hypersurfaces. Zbl 0661.53039
Tysk, Johan
1989
An index characterization of the catenoid and index bounds for minimal surfaces in $$R^ 4$$. Zbl 0613.58030
Cheng, Shiu-Yuen; Tysk, Johan
1988
Eigenvalue estimates with applications to minimal surfaces. Zbl 0594.58018
Tysk, Johan
1987
Comparison of two methods of multiplying distributions. Zbl 0581.46029
Tysk, Johan
1985
all top 5
#### Cited by 283 Authors
17 Ekström, Erik 15 Tysk, Johan 8 von Sydow, Lina 4 Feehan, Paul M. N. 4 Janson, Svante 4 Leung, Tim 4 Protter, Philip Elliott 3 Bayraktar, Erhan 3 Hobson, David G. 3 in ’t Hout, Karel J. 3 Karatzas, Ioannis 3 Lipton, Alexander 3 Pagliarani, Stefano 3 Pascucci, Andrea 3 Persson, Jonas 3 Sharp, Ben 3 Soleymani, Fazlollah 3 Song, Qingshuo 3 Xing, Hao 2 Bungartz, Hans-Joachim 2 Buzano, Reto 2 Chodosh, Otis 2 Döring, Leif 2 Dyrssen, Hannah 2 Fasen, Vicky 2 Fernholz, Daniel 2 Forsyth, Peter A. 2 Gonon, Lukas 2 Huang, Yu-Jui 2 Ishige, Kazuhiro 2 Jarrow, Robert Alan 2 Lamberton, Damien 2 Larsson, Elisabeth 2 Lötstedt, Per 2 Lundgren, Robin 2 Milovanović, Slobodan 2 Pop, Camelia Alexandra 2 Prömel, David J. 2 Pyo, Juncheol 2 Reichmann, Oleg 2 Ruf, Johannes 2 Seo, Keomkyo 2 Shashiashvili, Malkhaz 2 Silvestrov, Dmitrii 2 Terenzi, Giulia 2 Toivanen, Jari 2 Zhu, Chao 2 Zhu, Songping 1 Abbas-Turki, Lokman A. 1 Akgül, Ali 1 Alvarez, Luis H. R. 1 Ambrozio, Lucas C. 1 Andreucci, Daniele 1 Ankirchner, Stefan 1 Azimzadeh, Parsiad 1 Babilua, Petre 1 Baran, Nicholas A. 1 Barbosa, Ezequiel R. 1 Bátkai, András 1 Baurdoux, Erik Jan 1 Bellettini, Costante 1 Benjouad, Abdelghani 1 Bérard, Pierre H. 1 Bergenthum, Jan 1 Besson, Gérard 1 Bobrowski, Adam 1 Bokuchava, I. V. 1 Bordoni, Manlio 1 Borell, Christer 1 Branger, Nicole 1 Breton, Jean-Christophe 1 Briani, Maya 1 Brunick, Gerard 1 Cañete, Antonio 1 Capponi, Agostino 1 Caramellino, Lucia 1 Carlotto, Alessandro 1 Carpenter, Mark H. 1 Carr, Peter P. 1 Çetin, Umut 1 Chen, Nan 1 Chen, Xiaoshan 1 Chen, Xinfu 1 Cheng, Shiu-Yuen 1 Chernogorova, Tatiana P. 1 Chiarella, Carl 1 Chistyakov, Vyacheslav V. 1 Choe, Jaigyoung 1 Choi, Hagyun 1 Christara, Christina C. 1 Colding, Tobias Holck 1 Costantini, Cristina 1 Cruz-Cota, Aldo-Hilario 1 Cruz, Aricson 1 Cui, Shumo 1 Cuyt, Annie A. M. 1 Dadashi, Hassan 1 D’Alessandro, Antonio 1 Daly, Kathleen 1 Dang, Duy Minh ...and 183 more Authors
all top 5
#### Cited in 83 Serials
13 International Journal of Theoretical and Applied Finance 8 The Annals of Applied Probability 8 Quantitative Finance 7 Journal of Mathematical Analysis and Applications 7 Stochastic Processes and their Applications 6 Computers & Mathematics with Applications 6 Finance and Stochastics 5 Transactions of the American Mathematical Society 5 International Journal of Computer Mathematics 5 Mathematical Finance 4 Journal of Applied Probability 4 Journal of Computational and Applied Mathematics 4 Stochastics 4 SIAM Journal on Financial Mathematics 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Probability Theory and Related Fields 3 SIAM Journal on Scientific Computing 2 Journal of Geometry and Physics 2 BIT 2 Duke Mathematical Journal 2 Journal of Differential Equations 2 Journal of Functional Analysis 2 Mathematics and Computers in Simulation 2 Tohoku Mathematical Journal. Second Series 2 Applied Numerical Mathematics 2 Journal of Economic Dynamics & Control 2 Numerical Algorithms 2 Calculus of Variations and Partial Differential Equations 2 Review of Derivatives Research 2 Annals of Finance 1 Advances in Applied Probability 1 Archive for Rational Mechanics and Analysis 1 Journal of Computational Physics 1 Rocky Mountain Journal of Mathematics 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Geometriae Dedicata 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Journal of Econometrics 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Mathematika 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 SIAM Journal on Numerical Analysis 1 Topology and its Applications 1 Insurance Mathematics & Economics 1 Statistics & Probability Letters 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Sequential Analysis 1 Journal of Theoretical Probability 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Communications in Partial Differential Equations 1 Bulletin of the American Mathematical Society. New Series 1 Computational Statistics and Data Analysis 1 Theory of Probability and Mathematical Statistics 1 Journal of Mathematical Sciences (New York) 1 Advances in Computational Mathematics 1 Applied Mathematical Finance 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Methodology and Computing in Applied Probability 1 Econometric Theory 1 Applied Stochastic Models in Business and Industry 1 The ANZIAM Journal 1 Decisions in Economics and Finance 1 Central European Journal of Mathematics 1 Asia-Pacific Financial Markets 1 Mathematics and Financial Economics 1 Advances in Calculus of Variations 1 Involve 1 Journal de l’École Polytechnique – Mathématiques 1 Probability, Uncertainty and Quantitative Risk
all top 5
#### Cited in 26 Fields
109 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 75 Probability theory and stochastic processes (60-XX) 53 Partial differential equations (35-XX) 38 Numerical analysis (65-XX) 29 Differential geometry (53-XX) 14 Global analysis, analysis on manifolds (58-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 9 Statistics (62-XX) 3 Ordinary differential equations (34-XX) 3 Manifolds and cell complexes (57-XX) 3 Systems theory; control (93-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX)
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# NCERT Exemplar Solutions Class 7 Mathematics Solutions for Comparing Quantities - Exercise in Chapter 7 - Comparing Quantities
Question 13 Comparing Quantities - Exercise
Amount received on ₹ 3000 for 2 years at the rate of 11% per annum is
(a) ₹ 2340 (b) ₹ 3660 (c) ₹ 4320 (d) ₹ 3330
(b) ₹ 3660
From the question it is given that,
Principal= ₹ 3000
Time = 2 Years
Rate = 11%
Then, we know the formula of Simple interest I = (P × R × T)/100
I= (3000 × (11) × 2)/100
I = (3000 × 11 × 2)/100
I = ₹ 660
Amount = P + I
= 3000 + 660
= ₹ 3660
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# Star cluster formation and evolution in Mrk 930: properties of a metal-poor starburst★
@article{Adamo2011StarCF,
title={Star cluster formation and evolution in Mrk 930: properties of a metal-poor starburst★},
author={Angela Adamo and Goeran Ostlin and Erik Zackrisson and Polichronis Papaderos and Nils Bergvall and Robert Michael Rich and Genoveva Micheva},
journal={Monthly Notices of the Royal Astronomical Society},
year={2011},
volume={415},
pages={2388-2406}
}
• Published 29 March 2011
• Physics
• Monthly Notices of the Royal Astronomical Society
We present the analysis of the large population of star clusters in the blue compact galaxy (BCG) Mrk 930. The study has been conducted by means of a photometric analysis of multiband data obtained ...
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Super star clusters (SSCs) are typically found in interacting galaxies and trace an extreme form of star-formation. We present a K-band study of SSC candidates in a sample of local luminous infrared
On the properties of the interstellar medium in extremely metal-poor blue compact dwarf galaxies GMOS-IFU spectroscopy and SDSS photometry of the double-knot galaxy HS 2236+1344
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Aims. The main goal of this study is to carry out a spatially resolved investigation of the warm interstellar medium (ISM) in the extremely metal-poor blue compact dwarf (BCD) galaxy HS 2236+1344.
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## References
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ON THE ORIGIN OF THE RED EXCESS IN VERY YOUNG SUPER STAR CLUSTERS: THE CASE OF SBS 0335-052E
• Physics
• 2010
The spectral energy distribution analysis of very young unresolved star clusters challenges our understanding of the cluster formation process. Studies of resolved massive clusters in the Milky Way
The massive star clusters in the dwarf merger ESO 185−IG13: is the red excess ubiquitous in starbursts?*
• Physics
• 2011
We have investigated the starburst properties of the luminous blue compact galaxy ESO 185-IG13. The galaxy has been imaged with the high resolution cameras onboard to the Hubble Space Telescope. Fr
Constraining the Initial Mass Function in Extreme Environments: Detecting Young Low-Mass Stars in Unresolved Starbursts
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We demonstrate the feasibility of detecting directly low-mass stars in unresolved super star clusters with ages 100) at R = 1000, placing constraints on the ratio of high- to low-mass stars
Super star clusters in Haro 11: properties of a very young starburst and evidence for a near‐infrared flux excess
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STAR FORMATION HISTORY OF A YOUNG SUPER-STAR CLUSTER IN NGC 4038/39: DIRECT DETECTION OF LOW-MASS PRE-MAIN SEQUENCE STARS
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We present an analysis of the near-infrared spectrum of a young massive star cluster in the overlap region of the interacting galaxies NGC 4038/39 using population synthesis models. Our goal is to
A possible formation scenario for the ultramassive cluster W3 in NGC 7252
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The intermediate age star cluster W3 (age � 300‐500 Myr) in NGC 7252 is the most luminous star cluster known to date with a dynamical mass estimate of 8±2·10 7 M⊙. With an effective radius of about
A NEW VIEW OF THE SUPER STAR CLUSTERS IN THE LOW-METALLICITY GALAXY SBS 0335-052
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SUPER STAR CLUSTERS VERSUS OB ASSOCIATIONS
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Super star clusters (M ecl > 105 M ☉) are the largest stellar nurseries in our local Universe, containing hundreds of thousands to millions of young stars within a few light years. Many of these
The temporal and spatial evolution of the starburst in ESO 338-IG04 as probed by its star clusters ?
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ESO 338-IG04, also known as Tololo 1924-416, is a well known luminous blue compact galaxy in the local universe. Images obtained with the Hubble Space Telescope (HST) have shown that the central
The blue to red supergiant ratio in young clusters at various metallicities
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We present new determinations of the blue to red supergiant ratio (B=R) in young open clusters at various metallicities. For this purpose, we examine the HR diagrams of 45 clusters in the Galaxy and
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primer trimming tools
2
0
Entering edit mode
6.9 years ago
J.F.Jiang ▴ 880
Hi all,
Due to the PCR based amplification, we need to trim to primers off the PE reads.
However, it seems that the trimming process might bring in low quality in tails, especially that some reads might even fall into Q15-Q20, which might lead to low Quality using GATK variant calling.
$cutadapt -q 10 -g file:$fprimer -G file:$rprimer --minimum-length 20$read1 $read2 -o$read1_trim -p \$read2_trim;
The command listed above is the one I used in my calling pipeline, although I can adjust the q to 30, there would be quite a lot reads to be removed.
Is there any smarter method to trim the primers?
Thanks.
Junfeng
primer trimming • 3.8k views
0
Entering edit mode
6.9 years ago
Doing adapter-trimming will not somehow reduce the quality of your reads. Variant callers are expected to take quality into consideration when making calls, and good mapping programs are robust against low quality tails on reads; the extra length improves mapping confidence.
I don't recommend trimming to a quality threshold above 12 for mapping. If cutadapt has trouble finding adapters in low-quality reads without aggressive quality-trimming, I suggest you use BBDuk instead, which does quality-trimming after adapter-trimming, as it is does not need quality-trimming to increase sensitivity. Trimming for quality prior to trimming adapters reduces the number of adapter bases present, ultimately making them harder to detect.
Edit - it looks like the OP was talking about targeted amplicon sequencing and trimming the 3' primer, in which case my answer is irrelevant.
0
Entering edit mode
6.9 years ago
J.F.Jiang ▴ 880
After trying and searching references, I found the most efficient way is to align the sequences using aligners first, e.g., bwa-mem, then using GATK ClipReads later to remove the matched primer sequences, since primers can help to align the reads to ref genomes, while trimming the reads first will generate a lot of "bad" quality reads that can result in lower depth of coverage or waste of inputs.
And another question is that I calculated the Ti/Tv ratio for target sequencing, e.g., BRCA1 and BRCA2 genes, and obtained a varied value from 2.X to 8.X for different samples. Is this normal or not?
0
Entering edit mode
We also adopted the workflow of BWA-MEM alignment first and then soft-clip primer afterwards. Since ours are nested amplicons, GATK ClipReads cannot properly handle the primer clipping. We then developed and use BAMClipper (Scientific Reports 7:1567). The bonus is that errors in primer sequences (synthesis and/or sequencing) are tolerated.
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## Sails and norm minima of lattices.(English. Russian original)Zbl 1084.11035
Sb. Math. 196, No. 3, 337-365 (2005); translation from Mat. Sb. 196, No. 3, 31-60 (2005).
The main result of this paper is the following Theorem: The norm minimum of an $$n$$-dimensional lattice $$\Lambda \subset \mathbb R^{n}$$ is non-zero if and only if there is a uniform bound on the determinants of the faces of each of the $$2^{n}$$ sails generated by the lattice $$\Lambda$$ and the standard cone $$\mathcal C_{0}: \{(t_{1}, \dots, t_{n}\,| \, t_{i}>0\}$$. Here the norm minimum of $$\Lambda$$ is defined to be $$\inf_{(x_{1}, \dots, x_{n})\in \Lambda \setminus \{0\}}\; | x_{1}\dots x_{n}|$$; a sail is the boundary of the convex hull of the intersection of a cone $$\mathcal C$$ with $$\Lambda \setminus \{0\}$$; the sails generated by $$\Lambda$$ and $$\mathcal C_{0}$$ arise from letting $$\mathcal C$$ be generated by the various choices for $$(\pm e_{1}, \dots, \pm e_{n})$$, where the $$e_{i}$$ form the canonical basis of $$\mathbb R^{n}$$; each sail is a (generalized) $$n-1$$ polytope, faces are as usual; the determinant of a face is its normalized volume (so that the determinant of a simplicial face is the determinant of the matrix with entries the components of the vertices).
### MSC:
11H50 Minima of forms 11J70 Continued fractions and generalizations 11H06 Lattices and convex bodies (number-theoretic aspects) 52C07 Lattices and convex bodies in $$n$$ dimensions (aspects of discrete geometry)
### Keywords:
multidimensional continued fractions
Full Text:
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# Cohomology vs. Reduced Cohomology in homotopy type theory
I just read Mike Shulman's blog post the other night, discussing the definition of cohomology in Homotopy Type Theory. I really enjoyed the new (to me) perspective, but I had a few questions on technicalities.
Given types $$X$$ and $$Y$$, Mike defines
$$H^n(X; Y) :\equiv \| X \to \Omega^{-n} Y \|_0.$$
This agrees with the definition given in the nLab article on cohomology. Here is where my first question comes up:
1. Although it's not stated in the article, I assume that for $$n \neq 0$$ we need $$Y$$ to be a pointed type, since (if I understand correctly) looping/delooping requires a choice of basepoint? Or does it not matter?
(Mike does explain in the article that for $$n>0$$ we need to specify choices of deloopings, since deloopings might not exist and might not be unique, and that we usually just take $$Y$$ to be a spectrum so that this works.)
However, in section 1.1 of this paper on Eilenberg-MacLane spaces in HoTT by Daniel Licata and Eric Finster they seem to be saying that the definition above actually produces reduced cohomology, since they write:
On the other hand, in his blog post Mike writes defines reduced cohomology for pointed types $$X$$ and $$Y$$ by $$\tilde{H}^n(X; Y) :\equiv \| \operatorname{Map}_*(X, \Omega^{-n} Y) \|_0.$$ (He technically defines it only in the case that $$Y$$ is a spectrum, but I'm extrapolating here.) So this leads me to my second question:
1. What is the correct definition for reduced cohomology in HoTT?
1. In order for the notation $$\Omega^{-n} Y$$ to make sense for $$n \ge 1$$, $$Y$$ must be a grouplike $$E_n$$-space, which in particular means it has a basepoint (the identity of the $$E_n$$ multiplication). For $$n \le -1$$ we also need a basepoint to define the based loop space. However note that $$X$$ does not need to have a basepoint.
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# On $k$-extendability of bipartite states
Definition of $k$-extendability can be given as follows.
Let $k\in \mathbb{N}$. A state $\rho_{AB}$ on a bipartite Hilbert space $\mathrm{A}\otimes\mathrm{B}$ is $k$-extendible with respect to $\mathrm{B}$ if there exists a state $\rho_{AB^k}$ on $\mathrm{A}\otimes\mathrm{B}^{\otimes k}$ which is invariant under any permutation of the $\mathrm{B}$ subsystems and such that $\rho_{AB}=\mathrm{Tr}_{B^{k-1}}\rho_{AB^k}$.
Further a result of Doherty et al (Phys. Rev. A. 69:022308) gives that,
A state on a bipartite Hilbert space $\mathrm{A}\otimes\mathrm{B}$ is separable if and only if it is $k$-extendible with respect to $\mathrm{B}$ for all $k\in\mathbb{N}$.
If this is the case, then isn't a pure maximally entangled state (say $|00\rangle + |11\rangle$) is also extendable for all $k$? Consider the extension $|00\cdots0\rangle + |11\cdots1\rangle$ for some $k$. I think, I am missing some obvious point. Can someone please help?
• A k-partite maximally entangled state is a pure state (symmetrical to permutations), but its partial trace over any of its components is no longer a pure state. In other words, the partial trace does not recover the pure bipartite maximally entangled state. – udrv Mar 28 '16 at 13:13
isn't a pure maximally entangled state (say $|00\rangle + |11\rangle$) is also extendable for all $k$? Consider the extension $|00\cdots0\rangle + |11\cdots1\rangle$ for some $k$.
Take $k=2$ and $$\rho_{AB^2}=\frac12\left(\vphantom{\sum}|000⟩+|111⟩\right)\left(\vphantom{\sum}⟨000|+⟨111|\right),$$ as it seems that you're proposing, and calculate \begin{align} {\mathrm{Tr}_{B^1}}\!\!\left(\rho_{AB^2}\right) & = \frac12\mathrm{Tr}_{3}\!\!\left(\vphantom{\sum}|000⟩+|111⟩\right)\left(\vphantom{\sum}⟨000|+⟨111|\right) \\& = \frac12\mathrm{Tr}_{3}\!\!\left(\vphantom{\sum} |000⟩⟨000|+|000⟩⟨111|+|111⟩⟨000|+|111⟩⟨111| \right) \\& = \frac12\left(\vphantom{\sum} |00⟩⟨00|+|11⟩⟨11| \right). \end{align} This is a completely mixed state, having lost all coherence to the vanishing traces $\mathrm{Tr}\:|1⟩⟨0|=\mathrm{Tr}\:|0⟩⟨1|=0$ on the cross terms, and it has nothing at all to do with the pure state $$\rho_{AB}=\frac12\left(\vphantom{sum}|00⟩+|11⟩\right)\left(\vphantom{\sum}⟨00|+⟨11|\right)$$ you were hoping for.
Moreover, this fits in perfectly well with the result you quote: the maximally entangled pure state is not separable, so no $k$-extension is possible.
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## Exhibit a semigroup of transformations having no idempotents
Give an example of a semigroup of transformations having no idempotents.
We saw in this previous exercise that every finite semigroup contains idempotent elements. So any example we find will have to be transfinite.
Given $k \in \mathbb{N}^+$, define $\varphi_k : \mathbb{N}^+ \rightarrow \mathbb{N}^+$ by $\varphi_k(a) = a+k$. Let $S \subseteq \mathsf{T}(\mathbb{N}^+)$ be the subset $S = \{\varphi_k\ |\ k \in \mathbb{N}^+\}$. We claim that $S$ is a subsemigroup of the full semigroup of transformations on $\mathbb{N}^+$; indeed, for all $k,\ell \in \mathbb{N}^+$ and $a \in \mathbb{N}^+$, we have $(\varphi_k \circ \varphi_\ell)(a) = \varphi_k(\varphi_\ell(a))$ $= \varphi_k(a + \ell)$ $= a+\ell+k$ $= \varphi(\ell+k)(a)$, so that $S$ is closed under composition. So $S$ is a semigroup of transformations.
If $\varphi_k$ is idempotent, then $a+k = \varphi_k(a) = (\varphi_k \circ \varphi_k)(a)$ $= a+2k$ for all $a \in \mathbb{N}^+$, and so $k = 2k$. This equation has no solutions in $\mathbb{N}^+$, so that $S$ does not contain an idempotent.
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DataLab
I knew when I signed up to work on the Burrito Bracket that I and FiveThirtyEight would get some criticism. Picking 64 burritos out of a sea of awesome, we were certain to miss a few greats. People who really like burritos never just really like burritos, they are fanatics (I might be Exhibit A). I knew that my tastes and qualifications would be called into question. I assumed (correctly) there’d be questions about my ethnicity (“Why is the ‘decider’ a gringa?”) and my gender:
The one thing I didn’t anticipate is the outrage the photographs would inspire. NPR described them as “controversial.” I’ve been told the burritos look like dirty diapers. Sometimes, the criticism is about their artistic merit (“What’s with the really bad pics? They don’t do the burritos any justice”), and other times it’s a theological line of questioning (“I understand why you do it, but there’s something deeply immoral about dissecting perfectly good burritos for pictures”). I receive emails, tweets and comments daily about the abomination that is my burrito photography.
Although I doubt it will appease many, I’m here to explain what I’m doing, and why.
As we were developing the Burrito Bracket, I considered a variety of ways to assess burritos, including weight and caloric content. I contemplated dissecting them and weighing each component with a portable scale. But these schemes were logistical nightmares or impossible to do with the necessary degree of accuracy.
Additionally, I wanted to incorporate photography into the data side of things. Let me start by saying: We photographers know how to find beauty in the dingiest locales, and a good chef can make Alpo look like filet mignon. By their very nature, burritos are wrapped in a tortilla. This gives the photographer but one obvious way to photograph them: sliced in half (like a saw going through a log) and neatly arranged to reveal what’s inside. This is undoubtedly a prettier image than the the ones I’m making (and such images are readily available on the Internet for the majority of restaurants in the bracket). It also biases toward Mission-style burritos, with their formidable girth, and isn’t very useful for wet burritos or the folded burritos of El Paso, Texas.
I take FiveThirtyEight’s dedication to data seriously, and I wanted to use this project to experiment with using photography to collect meaningful data. Traditional restaurant reviews usually include photos of interiors and sultry images of glistening food bathed in sunlight. They can help readers decide whether this is the sort of place they would want to visit or highlight the glory of a dish with a particularly special presentation.
My goal, however, was to elaborate the differences between the burritos and to provide additional information about them. Dozens of styles and endless ingredients can be found inside a tortilla. So I challenged myself to produce the most data-rich visual image of a burrito, which is very different from the usual food review mandate of making the dish look the most appetizing.
That led me to the dissections. I carry a scalpel with me and cut each burrito down the middle lengthwise. Burritos are meant to have a tightly bound tortilla wrapper, and cutting them produces, I admit, a rather inelegant viewpoint. But I hope that the images are a source of information, showing — in a way the beauty shots cannot — the ingredients, how they are mixed and distributed, and how the burrito was assembled. I also hope they provide a point of visual reference for the uniqueness of each burrito.
I realize this explanation will be of no consolation for some readers and burrito truthers. For what it’s worth, I’ll be taking burrito glamour shots in Round 2, which is set to begin in August. Until then, feel free to look at this instead.
Anna Maria Barry-Jester reports on public health, food and culture for FiveThirtyEight.
All Life
Can A Southern Burrito Overtake One Of California’s Finest?Aug 27, 2014
All Burrito Bracket
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# A 200 kVA, 3300/240 V, 50 Hz single-phase transformer has 80 turns on the secondary winding. Assuming an ideal transformer, the primary current I1 and secondary current I2 on full load are nearly
Free Practice With Testbook Mock Tests
## Options:
1. 60.6 A and 833 A
2. 72.2 A and 833 A
3. 60.6 A and 720 A
4. 72.2 A and 720 A
### Correct Answer: Option 1 (Solution Below)
This question was previously asked in
ESE Electronics 2020: Official Paper
## Solution:
Concept:
From the MMF balance equation of a transformer:
$$\frac{{{V_1}}}{{{V_2}}} = \frac{{{N_1}}}{{{N_2}}} = \frac{{{I_2}}}{{{I_1}}}$$
Also, the rated power can be written as:
P (KVA) = V × I
In a transformer, the current or the voltage steps up and down. But the power transferred is always equal.
Application:
Given power = 200 kVA. (Full load rated power)
We can write:
200 k = V1 × I1
Given voltage at the primary end, V1 = 3300 V
∴ 200 k = 3300 × I1
$${I_1} = \frac{{200\;K}}{{3300}}$$
I1 = 60.6 A
The primary current is therefore 60.6 A
Similarly, we can write:
200 k = V2 × I2
Given V2 = 240 V, the above equation becomes:
200 k = 240 × I2
$${I_2} = \frac{{200\;k}}{{240}}$$
I2 = 833.33 A
∴ The secondary current I2 = 833.33 A
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Search
## Search Loci: Convergence:
Keyword
Random Quotation
The interplay between generality and individuality, deduction and construction, logic and imagination - this is the profound essence of live mathematics. Any one or another of these aspects of mathematics can be at the center of a given achievement. In a far reaching development all of them will be involved. Generally speaking, such a development will start from the "concrete" ground, then discard ballast by abstraction and rise to the lofty layers of thin air where navigation and observation are easy; after this flight comes the crucial test of landing and reaching specific goals in the newly surveyed low plains of individual "reality." In brief, the flight into abstract generality must start from and return again to the concrete and specific.
Richard Courant
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# Extracting Square Roots Made Easy: A Little Known Medieval Method
## Conclusion and About the Author
Conclusion
Today you get square roots with many correct decimal places instantly with your calculator or computer. However, as we saw with the fourth and fifth approximations of $$\sqrt{5},$$ far greater accuracy can be achieved by means of a few easy calculations invented more than 800 years ago.
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Here's the question you clicked on:
## klewis1 Group Title Find an equation of the tangent line to the curve y=(1-x)/(1+x) points (-2,-3) 5 months ago 5 months ago
• This Question is Open
1. Landon_Buckland Group Title
To solve this you have to apply the quotient rule: $D _{x}\left[ \frac{ f(x) }{ g(x) } \right]=\frac{ f ^{\prime}(x)g(x)-f(x)g ^{\prime}(x) }{ \left[ g(x) \right]^{2} }$ $D _{x}\left[ \frac{ (1-x) }{ (1+x) } \right]=\frac{ -1(1+x)-(1-x)1 }{ [1]^2 }$This simplifies to...$D _{x}=-2$Now we can insert our derivative and point into the point-slope form:$y-y _{1}=m \left( x-x _{1} \right)$ $-3 - y _{1}=-2\left( -2-x _{1} \right)$...which simplifies to your solution:$y=-2x-7$I hope this helped!
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1 Reply Latest reply on Jul 2, 2010 2:04 PM by Claudio González
# I have a problem installing the new adobe!!
Error 1310. Error writing to file.
Also
Error 1304. Error writing to file
I am the amidistrator and I am using windows vista.
Can anyone help me!!!
• ###### 1. Re: I have a problem installing the new adobe!!
As you are posting in the Reader forum, I'll asume that by "my adobe" you mean Adobe Reader, for there is no product called Adobe, although many include the word in their names.
To have any chance of success, you need to start by removing all traces of any previous version(s) of Reader. As the MS Cleanup Utility is no longer available, this thread may help you in that:
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# Redundant condition? What if the image is proper and dense?
Let $X$ and $Y$ be Banach spaces. A bounded operator $T:X\to Y$ is a Fredholm if
• The dimension of $\ker(T)$ is finite,
• The codimension of the image $\mathrm{im}(T)$ is finite,
• The image $\mathrm{im}(T)$ is closed in $Y$.
I've found notes saying that the third condition is redundant. But, what is "codimension" if the image is not closed? What if the image is proper and dense?
In the answer of this question Is the closedness of the image of a Fredholm operator implied by the finiteness of the codimension of its image?, a closed complement is used, but is there always a closed complement?
I mean, how can the third condition be redundant if it is necessary to the second one make sense?
-
You can define the codimension of the image as $\dim Y/\operatorname{im}(T)$ (in general the codimension of a subspace $U$ in $X$ is $\dim X/U$). See also point 2. in the answer to: Question about Fredholm operator for a proof of the existence of a closed complement. – user45918 Oct 24 '12 at 20:02
Thanks for your comment, @bla. But $H^1(\Omega)$ is dense in $L^2(\Omega)$, what is the codimension of $H^1$? The answer you cited supposes finite codimension to begin with. – Otavio Kaminski Oct 25 '12 at 0:55
Octavio: The codimension of $H^1$ is the dimension of the vector space $L^2/H^1$. The dimension is the cardinality of any basis, whether finite or infinite. In the Fredholm case, finite codimension of the image is assumed as in your second bullet point. Point 3. of the answer bla links to answers your question. – Jonas Meyer Oct 25 '12 at 6:59
Thanks for your comment, @JonasMeyer. My question was "how many dimensions does $L^2/H^1$ have?" (or geometrically: how many dimensions are missing in $H^1$ to complete $L^2$ since $H^1$ is dense in $L^2$?) – Otavio Kaminski Oct 25 '12 at 12:25
Since the embedding $H^1 \to L^2$ is continuous and the image is dense the codimension is certainly infinite (by what Jonas explained and the linked answer). Whether it is countable or uncountable, I don't know. I would be surprised if it were countable... – user46056 Oct 26 '12 at 0:38
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# Bibliothèque
Musique » toe »
## All I Understand Is That I Don't Understand
10 écoutes | Se rendre sur la page du titre
Semaine se terminant le Jeudi 17 mai 2012 Tout le temps
Titres (10)
Titre Album Durée Date
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 9h42m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 9h42m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 7h01m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 7h01m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 4h19m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 4h19m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 1h38m
All I Understand Is That I Don't Understand 4:54 16 mai 2012, 1h38m
All I Understand Is That I Don't Understand 4:54 15 mai 2012, 22h06m
All I Understand Is That I Don't Understand 4:54 15 mai 2012, 22h06m
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Home » Uncategorized » On linear operators
# On linear operators
Let and suppose that , are linear operators from into satisfying
(1)
1. Show that for all one has
2. Show that there exists such that .
Solution
1. Using the assumptions we have
2. Consider the linear operator acting over all matrices . It may have at most different eigenvalues. Assuming that for every we get that has infinitely many different eigenvalues in view of (i). This is a contradiction.
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## System of equations: x^n + y^n + z^n, n=1,2,3,4
What is $x + y + z$, if the following are given
$x^2 \; + \; y^2 \; + \; z^2$
$x^3 \; + \; y^3 \; + \; z^3$
$x^4 \; + \; y^4 \; + \; z^4$
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# Plotted line in tikz stops in middle of grid
The plotted line stops and doesn't go on till the border of the grid:
This is my code:
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[baseline={(current bounding box.north)}]
\draw[step=1cm,color=gray!20] (-3,-2) grid (6,6);
\draw[-] (-3,0) -- (6,0) node[right] {$x$};
\draw (0,0) node[below left] {$O$};
\draw[-] (0,-2) -- (0,6) node[above] {$y$};
\foreach \x in {-3, -2, -1, 1, 2, 3, 4, 5, 6}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\foreach \y in {-2, -1, 1, 2, 3, 4, 5, 6}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw[blue] (-2,4) node[below left] {$k$};
\draw[black] (4,5) node[above left] {$A$};
\clip (-3,-2) rectangle (6,6);
\draw[scale=1,smooth,variable=\x,blue] plot ({\x},{(-4/3)*\x});
\draw[scale=1,smooth,variable=\x,red] plot ({\x},{(3/4)*\x+2});
\draw[fill=black](4,5) circle(0.5mm);
\end{tikzpicture}
\end{document}
What can I do so the line goes on the border of the grid?
• Add domain=-3:6 to the last draw should work. Actually both can use the same range. – Jesse Nov 27 '14 at 3:52
Use domain=-4:7;
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[baseline={(current bounding box.north)}]
\draw[step=1cm,color=gray!20] (-3,-2) grid (6,6);
\draw[-] (-3,0) -- (6,0) node[right] {$x$};
\draw (0,0) node[below left] {$O$};
\draw[-] (0,-2) -- (0,6) node[above] {$y$};
\foreach \x in {-3, -2, -1, 1, 2, 3, 4, 5, 6}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\foreach \y in {-2, -1, 1, 2, 3, 4, 5, 6}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw[blue] (-2,4) node[below left] {$k$};
\draw[black] (4,5) node[above left] {$A$};
\clip (-3,-2) rectangle (6,6);
\draw[scale=1,smooth,variable=\x,blue] plot ({\x},{(-4/3)*\x});
\draw[scale=1,smooth,variable=\x,red,domain=-4:6] plot ({\x},{(3/4)*\x+2});
\draw[fill=black](4,5) circle(0.5mm);
\end{tikzpicture}
\end{document}
Graphs a better done with pgfplots:
## Notes:
• The axis cs: is only needed if this is to be produced with versions priot to 1.11. So adding \pgfplotsset{compat=1.11} and using a recent version of pgfplots you don't need the axis cs:.
## Code:
\documentclass{article}
\usepackage{pgfplots}
\usepackage{amsmath}
%% http://tex.stackexchange.com/questions/17438/how-to-properly-scale-a-tikz-pgf-picture-which-has-a-beginaxis-endaxis
\pgfkeys{/pgfplots/Axis Labels At Tip/.style={
xlabel style={
at={(current axis.right of origin)},
xshift=1.5ex, anchor=center
},
ylabel style={
at={(current axis.above origin)},
yshift=1.5ex, anchor=center
}
}
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
x=1cm, y=1cm,% Better to let pgfplots do this, added in case it is important
axis y line=center,
axis x line=center,
xmin=-3, xmax=6,
ymin=-2, ymax=6,
grid=major,
Axis Labels At Tip,
xlabel=$x$, ylabel=$y$,
]
\addplot [red, thick, domain=-3:6] {(3/4)*x + 2};
\node [below left, blue] at (axis cs: -2,4) {$k$};
\node [below left] at (axis cs: 0,0) {$O$};
\draw[fill=black] (axis cs: 4,5) circle(0.5mm)
node[above left] at (axis cs: 4,5) {$A$};
\end{axis}
\end{tikzpicture}
\end{document}
## Code: \pgfplotsset{compat=1.11}
\documentclass{article}
\usepackage{pgfplots}
\usepackage{amsmath}
\pgfplotsset{compat=1.11}
%% http://tex.stackexchange.com/questions/17438/how-to-properly-scale-a-tikz-pgf-picture-which-has-a-beginaxis-endaxis
\pgfkeys{/pgfplots/Axis Labels At Tip/.style={
xlabel style={
at={(current axis.right of origin)},
xshift=1.5ex, anchor=center
},
ylabel style={
at={(current axis.above origin)},
yshift=1.5ex, anchor=center
}
}
}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
x=1cm, y=1cm,% Better to let pgfplots do this, added in case it is important
axis y line=center,
axis x line=center,
xmin=-3, xmax=6,
ymin=-2, ymax=6,
grid=major,
Axis Labels At Tip,
xlabel=$x$, ylabel=$y$,
]
\addplot [red, thick, domain=-3:6] {(3/4)*x + 2};
\node [below left, blue] at (-2,4) {$k$};
\node [below left] at (0,0) {$O$};
\draw[fill=black] (4,5) circle(0.5mm)
node[above left] at (4,5) {$A$};
\end{axis}
\end{tikzpicture}
\end{document}
A PSTricks solution using the pst-plot package:
\documentclass{article}
\usepackage{pst-plot}
\begin{document}
\begin{pspicture}(-3.2,-2.1)(6.65,6.7)
\psaxes[
labels = none,
tickcolor = black!30,
tickwidth = 0.5pt,
xticksize = -2 6,
yticksize = -3 6
]{->}(0,0)(-3,-2)(6.3,6.3)[$x$,0][$y$,90]
\psaxes{->}(0,0)(-3,-2)(6.3,6.3)[$x$,0][$y$,90]
\uput[225](0,0){$O$}
\psset{algebraic}
\psplot[
linecolor = blue
]{-3}{1.5}{-4/3*x}
\rput(-2.37,3.63){$\color{blue}k$}
\psplot[
linecolor = red
]{-3}{5.333}{3/4*x+2}
\psdot(4,5)
\uput[126.87](4,5){$A$}
\end{pspicture}
\end{document}
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+0
0
80
1
+104
1. Consider the polar equation $$r=3sin(2\theta)$$
(a) Complete the tables for the given values of $$\theta$$. Round the the nearest tenth as needed.
$$\theta$$ 0 $$\pi/6$$ $$\pi/4$$ $$\pi/3$$ $$\pi/2$$ $$2\pi/3$$ $$3\pi/4$$ $$5\pi/6$$ $$\pi$$ $$r=3sin(2\theta)$$
$$\theta$$ $$7\pi/6$$ $$5\pi/4$$ $$4\pi/3$$ $$3\pi/2$$ $$5\pi/3$$ $$7\pi/4$$ $$11\pi/6$$ $$2\pi$$
May 15, 2020
#1
+21933
0
Make certain that the calculator is in radian mode, then, one at a time, enter the angles:
r = 3·sin( 2·0 ) = 0
r = 3·sin( 2·pi/6 ) = 2.6
etc.
May 16, 2020
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# From where do charges come to equify the potential of the sphere having less potential- through the wire or the sphere having higher potential?
Say, you have two different charged spheres having different potentials on their surface. Now you connect two of them by a wire. So, after sometimes, both of them will have the same potential on their surfaces. That means some charge has moved to the sphere which had lesser potential. My question is, do these charges came from the wire or the other sphere which had higher potential?
$$V = k\frac{Q}{r}$$
so the voltage $V$ is proportional to the charge $Q$. Since the potential of the larger sphere decreases that must mean the charge on the larger sphere decreases. The same argument tells us that the charge on the smaller sphere must increase.
• I think I have got my answer. Since there is lower potential & $E = -\nabla\phi$, electric field must have incited the current which ultimately increased the charge of the concerned sphere to make the spheres equipotential. Just want to know, does it apply to any other (weired & quaint) shaped conductor? Thanks:) – user36790 Jul 9 '15 at 12:10
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# Linear Function
Instructions: Use this calculator to find the equation of a linear function, based on information you provide, with all the steps shown. To that end, you need to give some information about the linear function you want to calculate.
You have different options to specify the linear function. You can provide:
(1) both the slope and the y-intercept,
(2) you can type in any linear equation (ex: $$2x + 3y = 2 + \frac{2}{3}x$$),
(3) you can indicate the slope and a point that the line passes through, or
(4) you can indicate two points where the line passes through.
▹ Select one of the options:
Type the slope $$m$$ of the line (numeric expression. Ex: 2, 1/3, etc.) =
Type the y-intercept $$n$$ of the line (numeric expression. Ex: 2, 1/3, etc.) =
This linear function calculator will allow you compute a linear function by providing certain required information about the function.
There are several ways you can do so. You can either (1) provide a linear equation in x and y that can be solved for y, or (2) provide directly the slope and y-intercept, or (3) you can provide the slope and a point where the line passes through, or (4) you can provide 2 points where the line passes through.
What information will you provide? It largely depend on what information you have available, and it will depend on the specific case.
One common case is to find a linear function that passes through two given points, but the other ways of determining the line are common too.
## What is a linear function?
The answer depends on how many variables you are considering, but for one variable x, a linear function is a function of the form
$f(x) = a + b x$
Just a technicality, in more advanced math, this is a linear affine function, and it is not strictly linear unless a = 0, but that idea goes beyond the scope of this presentation. For us, $$f(x) = a + b x$$ is a linear function in x.
The value of a in $$f(x) = a + b x$$ is known as the y-intercept, and b is known as the slope. Sometimes you will see the convention $$f(x) = mx + n$$, where m is the slope and n is the y-intercept.
But that is a name convention, you just need to recall that the constant that multiplies the variable x is the slope, and the other is the y-intercept. Why is that? Because when x = 0, we get $$f(0) = m \cdot 0 + n = n$$, which indicates that n is precisely the why intercept.
## What are the steps for computing a linear function?
• Step 1: Identify what type of information you have provided
• Step 2: If the information you have is a linear equation in x and y, you need to solve for y and then you automatically have the linear function setting f(x) = y
• Step 3: If you have the slope b and the y-intercept a, then the linear function is directly f(x) = a + b x
• Step 5: If you have two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ where the line passes through, then you can use the formula: $$\displaystyle f(x) = y_1 + \left(\frac{y_2-y_1}{x_2-x_1} \right)(x-x_1)$$ for the linear function
• Step 6: If instead you have one point $$(x_1, y_1)$$ where the line passes through and the slope, then you can use the formula: $$\displaystyle f(x) = y_1 + m(x-x_1)$$ for the linear function
The above list of steps is a comprehensive list and considers all possible cases. Ultimate, the simplest and less involved situation corresponds to the case where the slope and y-intercept are known, where we can compute the slope intercept form immediately, but that is not always the case.
## What is the linear function formula
Ultimately, and regardless of the information you have provided, you can arrive to the linear function formula known as the slope-intercept form, which is:
$y = a + bx$
Now, since you are defining a function, you can also write $$f(x) = a + b x$$.
## What are the steps for finding the linear function formula?
• Step 1: Identify the information provided
• Step 2: Arrive at the corresponding formula y = a + bx, identifying the slope b and the y-intercept a
• Step 3: Replace y by f(x) and write f(x) = a + bx
Geometrically, the linear function graph will be a line that actually crosses the y-axis at the point (0, a), and the slope b will reflect the degree of inclination of the line.
## Why is it useful to calculate linear functions?
The linear relationship between variables is very common in so many applications, so then it becomes indispensable to fully understand how linear functions work.
And we can also define linear functions for more variables, which make them an even more powerful object.
### Example: Linear Function Calculator
Calculate the equation of the linear function that passes through the points: $$(\frac{22}{3}, \frac{7}{4})$$ and $$(-1, \frac{5}{6})$$
Solution: The main objective is to construct a linear function based on the information provided, if possible.
The information provided about the line is that the line passes through the points$$\displaystyle \left( \frac{22}{3}, \frac{7}{4}\right)$$ and $$\displaystyle \left( -1, \frac{5}{6}\right)$$
Therefore, the first step consists in computing the slope. The formula for the slope is: $\displaystyle b = \frac{y_2 - y_1}{x_2 - x_1}$
Now, by plugging the corresponding numbers is , we get that the slope is: $\displaystyle b = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ \displaystyle \frac{5}{6} - \frac{7}{4}}{ \displaystyle -1 - \frac{22}{3}} = \frac{ \displaystyle \frac{5}{6}-\frac{7}{4}}{ \displaystyle -1-\frac{22}{3}} = \frac{11}{100}$
So then, now we know that the slope is $$\displaystyle m = \frac{11}{100}$$ and that the line passes through the point $$\displaystyle \left( \frac{22}{3}, \frac{7}{4}\right)$$
Hence, with the information we have, we can construct directly the point-slope form of the line, which is
$\displaystyle y - y_1 = b \left(x - x_1\right)$
and then plugging the known values of $$\displaystyle b = \frac{11}{100}$$ and $$\displaystyle \left( x_1, y_1 \right) = \left( \frac{22}{3}, \frac{7}{4}\right)$$, we get that
$\displaystyle y-\frac{7}{4} = \frac{11}{100} \left(x-\frac{22}{3}\right)$
Now, we need to expand the right hand side of the equation by distributing the slope, so we get $\displaystyle y = \frac{11}{100} x + \frac{11}{100} \left(-\frac{22}{3}\right) + \frac{7}{4}$
and simplifying we get that $\displaystyle y=\frac{11}{100}x+\frac{283}{300}$
Conclusion: Based on the data provided, we conclude that the equation of the line is $$\displaystyle f(x)=\frac{11}{100}x+\frac{283}{300}$$, and it corresponds to a line with a slope of $$\displaystyle b = \frac{11}{100}$$ and y-intercept of $$\displaystyle a = \frac{283}{300}$$.
Based on this information, the graph is:
### Example: Another Linear function calculation
Calculate the linear function associated to : $$\frac{1}{3}x + \frac{5}{4}y - \frac{5}{6} = 0$$
Solution:
Now for this example the way we have defined a linear function is via a general linear equation, given by:
$\displaystyle \frac{1}{3}x+\frac{5}{4}y-\frac{5}{6}=0$
We can simplifying constants:
$\displaystyle \frac{1}{3}x+\frac{5}{4}y-\frac{5}{6}=0$
Now, putting $$y$$ on the left hand side and $$x$$ and the constant on the right hand side we get
$\displaystyle \frac{5}{4}y = -\frac{1}{3}x + \frac{5}{6}$
Now, solving for $$y$$, by dividing both sides of the equation by $$\frac{5}{4}$$, the following is obtained
$\displaystyle y=-\frac{\frac{1}{3}}{\frac{5}{4}}x+\frac{\frac{5}{6}}{\frac{5}{4}}$
and simplifying we finally get the following
$\displaystyle y=-\frac{4}{15}x+\frac{2}{3}$
Conclusion: Now we can say that based on the data provided, the conclusion is that that the equation of the line is $$\displaystyle f(x)=-\frac{4}{15}x+\frac{2}{3}$$, and it corresponds to a line with a slope of $$\displaystyle b = -\frac{4}{15}$$ and y-intercept of $$\displaystyle a = \frac{2}{3}$$.
Based on this information, the graph is:
### Example: More linear function calculators
Calculate the linear function with slope m = 0 and that crosses the y-axis at the point (0, 4).
Solution: In this case, we have given the slope, which is m = 0, and the y-intercept, which is (0, 4). Since the slope is 0, the line is horizontal, so in this case, the equation of the line is $$f(x) = 4$$.
## More linear function calculators
Interesting calculators are the slope calculator and y-intercept calculator. Also you may be interested in finding the perpendicular line to a given line.
Another common form for the line is the standard form, and you can certain convert from one form to the other.
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# zbMATH — the first resource for mathematics
Let $$G$$ be a group and $$T,T'$$ two $$G$$-trees. V. Guirardel [in Ann. Sci. Éc. Norm. Supér. (4) 38, No. 6, 847-888 (2005; Zbl 1110.20019)] constructed a core $$\mathcal C(T\times T')\subset T\times T'$$. The group $$G$$ acts on the core $$\mathcal C(T\times T')$$ and the intersection number between the two $$G$$-trees $$T,T'$$, denoted by $$i(T,T')$$, is defined to be the volume of the quotient $$\mathcal C(T\times T')/G$$.
Let $$F_k$$ be the free group of rank $$k$$ and $$\mathcal{CV}_k$$ be the Culler and Vogtmann’s outer space. If $$cv_k$$ is the unprojectivized version of $$\mathcal{CV}_k$$, $$T,T'$$ two trees in $$cv_k$$ and $$\varphi$$ an outer automorphism of $$F_k$$, in the present paper, it is given a method for computing the intersection number $$i(T,T')$$ and it is proved that the asymptotics of $$n\to i(T,T'\varphi^n)$$ do not depend on the trees $$T$$ and $$T'$$.
More precisely it is proved the Theorem: Suppose that $$\varphi\in\text{Out}(F_k)$$ is fully irreducible with an expansion factor $$\lambda$$ and $$T,T'\in cv_k$$. Let $$T^+$$ be the stable tree for $$\varphi$$ and let $$\mu$$ be the expansion factor of $$\varphi^{-1}$$. Then we have either of the following.
(1) If $$T^+$$ is geometric, then $$i(T,T'\varphi^n)\sim\lambda^n$$.
(2) If $$T^+$$ is nongeometric, then $$i(T,T'\varphi^n)\sim\lambda^n+\lambda^{n-1}\mu+\cdots+\lambda\mu^{n-1}+\mu^n$$.
In the statement above $$\sim$$ means quasi-isometry in the usual sense. For the terminology: stable tree, expansion factor, (non)geometric tree, we refer to the introduction of the paper and to the references quoted there.
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# Partial Differential Equation with initial condition on a curve
Solve $u_t + 3t u_x = u$ with the initial condition $u(x,t)=1+\cos x$ on the curve $x + 3t = 0$.
• Michael Lee : If the PDE is $u_t+3tu_x)=u$ , what you wrote is false : $x+3t$ is NOT a characteristic curve. – JJacquelin Aug 15 '17 at 16:24
• You changed the wording of the question, but the typo is still in it. The general solution of $u_t+3tu_x=u$ is : $$u(x,t)=e^tF(x-\frac{3}{2}t^2)$$ where $F$ is an arbitrary function. Of course, it is possible to determine $F$ according to the condition $u=1+\cos(x)$ on the curve $x+3t=0$. But this is too complicated for a scolar exercise. Probably you made a mistake in copying $u_t+3tu_x=u$. Sorry, I will be away for some days, So I will not be avalable to help you more. – JJacquelin Aug 16 '17 at 5:59
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Thread: Triple integral View Single Post
HW Helper P: 6,189 "Cartesian" form in a triple integral means x, y, and z. "Polar" is another form (meaning r, theta, and phi). So I would conclude that you're not supposed to use polar coordinates.
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# Why is the induced sheaf on an irreducible closed subset a sheaf?
Supposing that $(X,O_X)$ is a prevariety and that Y is an irreducible closed subset, why is it that for $U\subset Y$ open in the subspace topology, the induced sheaf $O_Y$ with sections $O_Y(U)$ :=[the ring of $k$ valued functions g on U so that for every point $y\in U$ has a neighborhood $V\subset X$ along with a section $G\in O_X(V)$ so that g and G coincide on $U\cap V$] "is" a sheaf on Y. More precisely, I'm failing to see how one can use the ambient sheaf $O_X$ to show that we do indeed obtain a sheaf?
EDIT: After some thought, it would appear to me that there is no need to use the fact that $O_X$ satisfies the sheaf axioms to prove the sheaf axioms for $O_Y$. Am I right in thinking that since being a regular function is a local property then the functions in $O_Y(U)$ are locally regular because they are locally restrictions of regular functions coming from $O_X(V)$. As such, the gluability and identity sheaf axioms are satisfied for $O_Y(U)$ because they hold for regular functions (and not because we can somehow recast them into the gluability and identity sheaf axioms for $O_x$)?
-
This is straight forward. What have you tried? Please include this into your question. – Martin Brandenburg Oct 24 '12 at 8:01
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Create RST and plaintext glossaries easily
# glossarpy
Generate plaintext or Sphinx-flavored reStructuredText (RST) glossaries/dictionaries for documentation with Python. When output is set to RST, glossarpy will automatically give each entry an internal link, allowing for easy cross-referencing within and outside the glossary it generates. Links to external URLs are also supported.
## Usage
pip install glossarpy
There are no further requirements for users.
Once glossarpy is installed in your Python environment, you can import it like any other module. See examples/ for some typical use cases.
glossarpy contains three classes:
• GlossEntry - A single glossary entry which at a minimum contains a name for the entry. It may optionally include a definition, a pronunciation guide, a link to another entry, a link to an external website, or a note about how a term is specific to a certain context.
• GreatGloss - A group of GlossEntry objects. A GlossEntry does not need to be inside a GreatGloss, but a GreatGloss needs at least one GlossEntry in it (in its self.glosslist to be specific) to actually be useful. Use the add_entry() function to add a single GlossEntry to a GreatGloss, or add_entries() to add a list of GlossEntry objects to a GreatGloss.
• GlossTxt - Common functions to handle text output for GlossEntry and GreatGloss. Not really useful on its own.
### How to make a GlossEntry
To declare a GlossEntry, all you need is their name: WDL = GlossEntry("WDL") will create a GlossEntry object with a name field of "WDL".
Here's a full list of fields that a GlossEntry can contain (all are type string except updated which is type datetime from the datetime module):
• name - entry's name; spaces are supported, do not use [brackets]
• acronym_full - if acronym, what is the full name. if blank, assumed to not be an acronym.
• further_reading - URL to a webpage, usually an "official" one associated with the term
• if an internal link to another documentation page, do not include .html at the end
• institute - which institution or context is the phrase associated with?
• pronunciation - pronunciation (ex: wdl - "widdle")
• seealso - links to another GlossEntry by that GlossEntry's name field
• updated - when the entry was last updated
## Useful GlossEntry methods
Generally, you will want to use GreatGloss methods instead.
• generate_plaintext() - generate entry as plaintext, see examples/example_print_one_entry.py
• generate_rst() - generate entry as RST
For either of these methods, you can set timestamp=True to have a timestamp get added to the output. That timestamp will be formatted as a comment (ie, will not show up when rendered as HTML in most forms of Sphinx, but will be in the RST file itself) if you are using generate_rst(timestamp=True)
### Linking one GlossEntry to another GlossEntry
The definition, acronym_full, and seealso arguments can reference other GlossEntry objects by their name field. To do so, encapsulate the entry title you which to reference with brackets, such as WDL = GlossEntry("WDL", acronym_full="[Workflow Description Language]") or WDL = GlossEntry("WDL", definition="A shorthand for [Workflow Description Language]"). When outputting to RST, this will create an internal hyperlink to a GlossEntry that has name="Workflow Description Language" assuming such a GlossEntry exists.
Do not put any alphanumeric characters immediately before or after either bracket.
## Useful GreatGloss methods
• sort_entries(ignorecase:bool = True)
• ignorecase: set to True (default) to treat capital and lowercase letters as equivalent (ex: anaconda Anacondas bat zebra), set to False to use default Python sorting (ex: anaconda bat zebra Anacondas)
• write_glossary(self, outfile:str = "", format:str = "rst", skipTOC:bool = False, skipSource:bool = False, sourcefile:str = None)
• Write a glossary to the file described in outfile; will raise a RuntimeError if neither this nor GreatGloss' object's outtoc field are defined
• format: rst for RST output, txt for plaintext
• columns (only matters if format=="rst"): Make the TOC render as RST hlist columns. Set to 0 to use contents with the local flag instead.
• skipSource: Whether or not to put a note about the file being autogenerated
• sourcefile: If skipSource==True, this is the name of the sourcefile to print.
• write_toc(self, outtoc:str = "", format:str = "rst", columns:int = 0, skipSource:bool = False, sourcefile:str = None)
• Write a TOC to the file described in outtoc (will fall back to the GreatGloss' object's outtoc field if one was defined during initalization, or, failing that, toc.rst)
• All other arguments are equivalent to how they work in write_glossary()
### Keeping track of source files
The whole point of glossarpy is to generate files. Generated files should not be updated, instead, their sources should be. To that end, write_toc() and write_glossary() will by default print a notice that they are autogenerated. If output=="RST" this notice will be a comment that appears only in the RST output, not in HTML files based upon said RST output.
If sourcefile is not set (default behavior), the notice will read:
DO NOT EDIT THIS FILE. This file is autogenerated from a Python source file, update that instead.
You can make this more helpful by setting sourcefile to the name of the file that the entries originate from. In most cases, you can use Python built-in __file__, which will return the name of the Python file that is currently being executed. See examples/example_import_entries.py and examples/example_typical_usage.py for two examples of this, the former of which will result in an output that starts like this:
.. DO NOT EDIT THIS FILE. This file is autogenerated from examples/example_import_entries.py, update that instead.
There ae some caveats to using __file__, such as the fact this variable is not set when running in an interactive interpreter (resulting in a NameError), so sourcefile is set to None by default. Feel free to replace __file__ with a string instead, or not set it at all.
If you would like to only print the basename, first import os then os.path.basename(__file__), which in the case of examples/example_import_entries.py would result in:
.. DO NOT EDIT THIS FILE. This file is autogenerated from example_import_entries.py, update that instead.
## Contributors
As noted in https://github.com/aofarrel/glossarpy/issues/2 I'm seeking some guidance on ensuring this repo is packaged correctly. I am relatively new to this side of Python and would appreciate contributions.
To setup a dev environment:
1. Set up a Python venv. Not strictly necessary, but good practice.
python3 -m venv ./venv
source venv/bin/activate
1. Pull this repo
2. pip install -r requirements-dev.txt
### Compiling RST output in Sphinx
This repo's makefile includes commands to show you what a glossary made glossarpy looks like inside a readthedocs template of Sphinx, by leveraging Dockstore's documentation repo. If you want to be able to do that, pull the Dockstore documentation repo, and have it on the same level as this repo, i.e.
.
├── dockstore-documentation/
└── glossarpy/
Then, run make reqs. Once you have run make reqs once, you can run make all or make html to your heart's content (until you leave your venv of course).
## Project details
Uploaded source
Uploaded py3
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# How do you combine 2/(4z^2-12z+9)-(z+1)/(2z^2-3z)?
Sep 20, 2016
$\frac{- 2 {z}^{2} + 3 z + 3}{z \left(2 z - 3\right) \left(2 z - 3\right)}$
#### Explanation:
In a question involving algebraic fractions, no matter what the operation is, factorize first.
$\frac{2}{4 {z}^{2} - 12 z + 9} - \frac{z + 1}{2 {z}^{2} - 3 z}$
$\frac{2}{\left(2 z - 3\right) \left(2 z - 3\right)} - \frac{z + 1}{z \left(2 z - 3\right)} \text{ } \leftarrow$find the LCD
=$\frac{2 z - \left(z + 1\right) \left(2 z - 3\right)}{z \left(2 z - 3\right) \left(2 z - 3\right)} \text{ } \leftarrow$ make equivalent fractions
$\frac{2 z - \left(2 {z}^{2} - 3 z + 2 z - 3\right)}{z \left(2 z - 3\right) \left(2 z - 3\right)} \text{ } \leftarrow$ simplify the numerator
$\frac{2 z - 2 {z}^{2} + 3 z - 2 z + 3}{z \left(2 z - 3\right) \left(2 z - 3\right)}$
$\frac{- 2 {z}^{2} + 3 z + 3}{z \left(2 z - 3\right) \left(2 z - 3\right)}$
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chrono::ChCSR3Matrix Class Reference
## Description
ChCSR3Matrix is a class that implements CSR3 sparse matrix format;.
Each of the 3 CSR arrays is stored contiguously in memory (as needed by Intel MKL Pardiso).
Building of the matrix is faster if the sparsity pattern of the matrix does not change (or change just a little). In order to let the matrix know that, set ChSparseMatrix::SetSparsityPatternLock(true). From now on, the position of the elements is kept in memory. Please mind that, when Reset() is called, only #values will be cleaned. Nothing will happen to other arrays. This means that if the sparsity pattern will change, many zeros will pollute your matrix. Do Prune() in this case.
Moreover, if the ChCSR3Matrix will be built from a ChSystemDescriptor, you can provide it to the matrix through #BindToChSystemDescriptor(). In the next call to Reset(), the ChCSR3Matrix will adapt itself to the sparsity pattern of ChSystemDescriptor. The sparsity pattern will be acquired from ChSystemDescriptor only once. To force the update call #ForceSparsityPatternUpdate()
Hints:
• It's far better to overestimate the number of non-zero elements to avoid reallocations in memory.
• It's preferrable to insert elements in the matrix in increasing column order (if row major) to minimize re-sorting of the elements.
• It's better to use GetElement to read from matrix; Element() creates the space if the element does not exist.
#include <ChCSR3Matrix.h>
Inheritance diagram for chrono::ChCSR3Matrix:
Collaboration diagram for chrono::ChCSR3Matrix:
## Public Member Functions
ChCSR3Matrix (int nrows=1, int ncols=1, bool row_major_format_on=true, int nonzeros=1)
void SetElement (int row_sel, int col_sel, double insval, bool overwrite=true) override
Put a new element in the matrix following CSR conventions.
double GetElement (int row_sel, int col_sel) const override
double & Element (int row_sel, int col_sel)
double & operator() (int row_sel, int col_sel)
double & operator() (int index)
void Reset (int nrows, int ncols, int nonzeros_hint=0) override
The function assures that the matrix will have nrows rows and ncols columns. More...
bool Resize (int nrows, int ncols, int nonzeros_hint=0) override
int GetNNZ () const override
Get the number of non-zero elements in this matrix.
int * GetCSR_LeadingIndexArray () const override
Return the row index array in the CSR representation of this matrix if in row major format. More...
int * GetCSR_TrailingIndexArray () const override
Return the column index array in the CSR representation of this matrix if in row major format. More...
double * GetCSR_ValueArray () const override
Return the array of matrix values in the CSR representation of this matrix.
bool Compress () override
Compress the internal arrays and purge all uninitialized elements.
void Trim ()
Trims the internal arrays to have exactly the dimension needed, nothing more. More...
void Prune (double pruning_threshold=0)
The same as Compress(), but also removes elements below pruning_threshold.
int GetTrailingIndexLength () const
Get the length of the trailing-index array (e.g. column index if row major, row index if column major)
int GetTrailingIndexCapacity () const
Get the capacity of the trailing-index array (e.g. column index if row major, row index if column major)
void SetMaxShifts (int max_shifts_new=std::numeric_limits< int >::max())
bool IsCompressed () const
Check if the matrix is compressed i.e. the matrix elements are stored contiguously in the arrays.
bool IsRowMajor () const
Check if the matrix is stored in row major format.
void LoadSparsityPattern (ChSparsityPatternLearner &sparsity_learner) override
Acquire information about the sparsity pattern of the elements that will be put into this matrix. More...
int VerifyMatrix () const
Verify if the matrix respects the CSR standard. More...
void ImportFromDatFile (std::string filepath="", bool row_major_format_on=true)
void ExportToDatFile (std::string filepath="", int precision=6) const
Public Member Functions inherited from chrono::ChSparseMatrix
ChSparseMatrix (int nrows=0, int ncols=0, int nnz=0)
Construct a sparse matrix with 'nrows' and 'ncols' and with 'nnz' non-zero elements. More...
ChSparseMatrix (const ChSparseMatrix &other)
int GetNumRows () const
Get the number of rows of this matrix.
int GetNumColumns () const
Get the number of columns of this matrix.
void SetType (SymmetryType type)
Set the symmetry type for this sparse matrix (default: GENERAL). More...
SymmetryType GetType () const
Return the symnmetery type of this matrix.
void SetSparsityPatternLock (bool val)
Enable/disable a lock on the matrix sparsity pattern (default: false).
virtual void PasteMatrix (const ChMatrix<> &matra, int insrow, int inscol, bool overwrite=true, bool transp=false)
Paste the specified matrix into this sparse matrix at (insrow,inscol).
virtual void PasteClippedMatrix (const ChMatrix<> &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol, bool overwrite=true)
Paste a clipped portion of the specified matrix into this sparse matrix at (insrow,inscol).
virtual void PasteTranspMatrix (const ChMatrix<> &matra, int insrow, int inscol)
virtual void PasteSumMatrix (const ChMatrix<> &matra, int insrow, int inscol)
virtual void PasteSumTranspMatrix (const ChMatrix<> &matra, int insrow, int inscol)
virtual void PasteSumClippedMatrix (const ChMatrix<> &matra, int cliprow, int clipcol, int nrows, int ncolumns, int insrow, int inscol)
## Protected Member Functions
void reset_arrays (int lead_dim, int trail_dim, int nonzeros)
void insert (int &trail_sel, const int &lead_sel)
void copy_and_distribute (const index_vector_t &trailIndex_src, const values_vector_t &values_src, const std::vector< bool > &initialized_element_src, index_vector_t &trailIndex_dest, values_vector_t &values_dest, std::vector< bool > &initialized_element_dest, int &trail_ins, int lead_ins, int storage_augm)
## Static Protected Member Functions
static void distribute_integer_range_on_vector (index_vector_t &vector, int initial_number, int final_number)
## Additional Inherited Members
Public Types inherited from chrono::ChSparseMatrix
enum SymmetryType { GENERAL, SYMMETRIC_POSDEF, SYMMETRIC_INDEF, STRUCTURAL_SYMMETRIC }
Protected Attributes inherited from chrono::ChSparseMatrix
int m_num_rows
number of rows
int m_num_cols
number of columns
int m_nnz
number of non-zero elements
SymmetryType m_type = GENERAL
matrix type
bool m_lock = false
indicate whether or not the matrix sparsity pattern should be locked
bool m_update_sparsity_pattern = false
let the matrix acquire the sparsity pattern
## Member Function Documentation
int * chrono::ChCSR3Matrix::GetCSR_LeadingIndexArray ( ) const
overridevirtual
Return the row index array in the CSR representation of this matrix if in row major format.
Return the column index array if in col major format.
Reimplemented from chrono::ChSparseMatrix.
int * chrono::ChCSR3Matrix::GetCSR_TrailingIndexArray ( ) const
overridevirtual
Return the column index array in the CSR representation of this matrix if in row major format.
Return the row index array if in col major format.
Reimplemented from chrono::ChSparseMatrix.
void chrono::ChCSR3Matrix::LoadSparsityPattern ( ChSparsityPatternLearner & sparsity_learner )
overridevirtual
Acquire information about the sparsity pattern of the elements that will be put into this matrix.
The information is provided by #m_sysd.
Reimplemented from chrono::ChSparseMatrix.
void chrono::ChCSR3Matrix::Reset ( int nrows, int ncols, int nonzeros_hint = 0 )
overridevirtual
The function assures that the matrix will have nrows rows and ncols columns.
The nonzeros_hint value is just a hint! The matrix can be fully reset, or partially reset (i.e. mantaining the sparsity pattern). For partial reset the following must apply:
• nrows and ncols must not differ from the current ones
• nonzeros_hint must not be provided (or must equal 0)
• m_lock must be set otherwise a full reset will occur.
Implements chrono::ChSparseMatrix.
void chrono::ChCSR3Matrix::SetMaxShifts ( int max_shifts_new = std::numeric_limits::max() )
While setting new elements in the matrix, SetMaxShifts() tells how far the internal algorithm should look for not-initialized elements.
void chrono::ChCSR3Matrix::Trim ( )
Trims the internal arrays to have exactly the dimension needed, nothing more.
The underlying vectors are not resized (see Trim() for this), nor moved.
int chrono::ChCSR3Matrix::VerifyMatrix ( ) const
Verify if the matrix respects the CSR standard.
3 - warning message: in the row there are no initialized elements 1 - warning message: the matrix is not compressed 0 - all good! -1 - error message: leadIndex is not strictly ascending -2 - error message: there's a row that has some an uninitialized element NOT at the end of its space in trailIndex -4 - error message: trailIndex has not ascending indexes within the rows
|
## Abstract
In this review, an attempt has been made to analyze passive solar heating and cooling concepts along with their effects on performance of a buildings thermal management. The concepts of Trombe wall, solarium, evaporative cooling, ventilation, radiative cooling, wind tower, earth air heat exchanger, roof pond, solar shading for buildings, and building-integrated photovoltaic thermal (BiPVT) systems are extensively covered in this review. Comparison of results by various heating and cooling concepts has been made. It has been observed that direct heating through double-glazed window saves maximum conventional fuel for thermal heating during winter months. Further, an evaporative cooling is one of the best cooling concepts which is economical too in summer period.
## Highlights
1. Double-glazed window for thermal heating.
2. Combination of evaporative cooling and wind tower for passive cooling.
3. Trombe wall for both passive heating and cooling.
4. BiPVT system for thermal heating and electricity production.
## Introduction
An estimated 6.7% of the global energy requirement is used for thermal management of buildings for which precise Arab data are not available [1]. As per an estimate, at least 35% of the total buildings energy requirements may be satisfied by using alternative resources [1]. The worlds total energy requirement may be reduced by 2.35% at an approximate incremental cost of 15% over the total construction and planning cost [1, 2]. As a proof of concept, the solar H.P. Co-operative building in India was able to reduce heat loss by 35% by using double-glazing solar passive design for thermal heating [3]. Different physical processes for providing thermal comfort for passive buildings include solar radiation, long-wave radiation exchange, radiative cooling, and evaporative cooling. Solar radiation and radiative cooling are the processes used for both thermal heating and cooling purposes [1].
Passive solar design is used as a cost and resource efficient method for achieving natural harmony between climate, architecture, and people. The building structure should be self-sustainable that is generating the energy for its own consumption.
Classification of various heating, cooling, and heating/cooling passive concepts has been done in Table 1 including building-integrated photovoltaic thermal (BiPVT) systems.
Table 1. Classification of heating and cooling concepts
### Passive solar design strategies for passive house
Passive design strategies are related to various aspects of a building like shape, size, orientation, form, site, layout etc. Their impact can be easily seen in the performance of the buildings energy use. This is because the massing and layout of the buildings can generate self-shading effects and can enhance the ventilation and natural lighting. At hardly any additional cost in adapting design strategies like building orientation, we can significantly achieve an effect on the buildings thermal performance. Depecker et al. [4] investigated the relationship between shape coefficient and heating loads. The study revealed that the heating load in cold climatic conditions was directly proportional to the shape coefficient, the reason being that the solar gain through the glazing was low. The study also suggested that opaque walls do not have any association with either heating load or shape coefficient, thus bearing less importance in mild and sunny climatic conditions. Stevanović [5] reviewed the heat flow across a building envelope and revealed that an optimized building form can reduce the heating load up to 12% per total volume of the building. Aldawoud [6] discussed different geometries of the atrium for the energy saving performance and concluded that square-shaped atrium has the best performance. The results also suggested that more energy savings can be achieved in low rise structure with an atrium which has a larger glazing to roof ratio for temperate and cold climatic condition. However, for hot and dry climatic conditions, high structure with a low glazing to roof ratio is preferred. An algorithm based on self-shading building envelopes for reduction in cooling and lighting loads integrated with different façade types, glazing, orientations, shapes, and life cycle costs has been developed [7, 8]. Square shape was found to give better results for all climate types. Stevanović [5] discussed that the detached units placed in curved road configurations requires large heating and cooling when compared to the attached units placed in straight layout. The latter saving up to 30% cooling and 50% heating requirements. Energy savings of 1–5% may be achieved just by changing the orientation, aspect ratio, and shape factors [9, 10]. The study concluded that the aspect ratio has very less influence on the buildings energy use. The study also concluded that with increase in the size of south-facing window, there is corresponding decrease in the total annual load in cold climatic conditions and the same increases in warm climatic conditions.
## Passive Heating Concepts
The various heating concepts in brief have been summarized in Table 2 with remarks. Few concepts have been discussed in detail as follows:
Table 2. Various passive heating concepts (for thermal heating)
S. No. Concepts Results Ref. Climatic conditions Remarks Applications
2.1 Direct gain (Figs. 1, 2A and B)
1. 80% solar gain for double-glazed window.
2. Use of double-glazed system leads to reduction of losses by 28% when compared with single glazed system (Equations 2a–2c).
[14] Very cold.
1. No phase change.
2. Day lighting
Office building
2.2 Indirect gain (Fig. 3) 25% reduction in heating load. (Equation (3)) [12] South China.
1. Phase change.
2. No day lighting
Household
2.3 Solarium (Fig. 4) (Equation (4))
1. Air collector
2. Trans wall
3. Water wall
4. Metallic sheet
Maximum room temperature achieved:
1. Air Collector: 23–24°C (Zone 2)
2. Trans wall: 21–22°C (Zone 2): better performance
3. Water wall: 17–18°C (Zone 2)
4. Metallic sheet: 30–31°C (Zone 1)
[13] Srinagar, India.
1. During the day time, the temperature of zone 1 is greater than living room but reduces at night
Sun space: Glass construction (except for the roof)Living space: Wooden construction
b. Water wall as link wall
1. The variation in living space was observed to lie within the range of 18–20°C.
2. For a 5 cm thick water wall, the average temperature for Zone 1 was found to be 35°C and 30°C for Zone 2 with water temperature of about 40°C.
3. Best TLL in the living space achieved
[15] Srinagar, India The thickness of the water wall was found to be inversely proportional to the temperatures of the sunspace and the living space
1. Glass construction for wall and roof with movable insulation east and west face of sunspace.
2. Only valid for wooden construction
c. Combination of water wall and Phase Change Component Material as link wall
1. Best TLL along with comfortable temperature (approx. 20°C) for the zone 2 was achieved.
2. With decrease in thickness of PCCM from 10 to 5 cm, the heat flux transmitted from the link wall to the living space increased by about 35%
[16] North America (Boulder) Zero ventilation rate Household
d. An attached solarium with motorized shading devices
1. Reduction of about 76% in the heating demands.
2. 134 kWh/m2 of excess heat can be collected and stored by solarium.
3. 70% reduction in case plants are grown inside the solarium
[17] Montreal Combined interior and exterior motorized shading
1. Greenhouses.
2. Solar houses.
3. High-efficiency buildings where solar gains are priority
### Direct gain
In this case, solar radiation is directly transmitted through glazed window into the living room for thermal heating. During the day, the whole building structure collects, absorbs, and stores the heat and releases the heat at night for thermal heating as shown in Figure 1.
Figure 1. Direct gain during sun shine hour.
The rate of heat transfer into the room can be expressed as follows,
${\displaystyle {\dot {Q}}={\left({\frac {1}{U_{t}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}\left(T_{sa}-\right.}$${\displaystyle \left.T_{r}\right)=U_{L}\left(T_{sa}-T_{r}\right)}$
(1)
where,
${\displaystyle T_{sa}={\frac {\tau I(t)}{U_{t}}}+T_{a}{\mbox{and}}U_{t}={\left({\frac {1}{h_{0}}}+{\frac {1}{h_{i}}}\right)}^{-1}}$
Balcomb et al. [11] suggested that single-glazed south-oriented system without storage mass is comparatively incompetent, whereas double-glazed system along with night insulation and soundly storage mass heat capacity proves to be efficient in meeting the heating requirements. Percentage of solar annual heating with storage heat capacity of 400 kJ/m2gC for single-glazed system, double-glazed system, single-glazed system with night insulations and double-glazed system with night insulation was observed to be about 10, 65, 80, and 90%, respectively. For 45° tilt, percentage of annual storage heating turns out to be nearly 87, 80, 58, and 18% for active system, double-glazed system with night insulation, double-glazed system and single-glazed system, respectively, with ratio of glass area to house area of 0.4 [1]. This means that double-glazed with night insulation is as good as active system tilted near the optimum angle. According to the authors, double glazing should be used in order to reduce heat loss from room to outside air, and windows should be covered by insulation at night to solve the same problem. Single-glazed system and double-glazed system are shown in Fig. 2A and B, respectively.
Figure 2. (A) Single glazing. (B) Double glazing.
Rate of useful energy for single-glazed system,
${\displaystyle {\dot {q}}_{u}=\tau I\left(t\right)-U_{t}\left(T_{r}-T_{a}\right)}$
(2a)
where,
${\displaystyle {\begin{array}{rl}U_{t}={\left[{\frac {1}{h_{0}}}+{\frac {L_{g}}{K_{g}}}+{\frac {1}{h_{i}}}\right]}^{-1}&={\left[{\frac {1}{5.8}}+{\frac {1}{2.8}}\right]}^{-1}\\&=1.88\quad {\mbox{W/m}}^{2},\left({\mbox{neglecting}},{\frac {L_{g}}{K_{g}}}\right)\end{array}}}$
Rate of useful energy for double-glazed system,
${\displaystyle {\dot {q}}_{u}={\tau }^{2}I\left(t\right)-U\left(T_{r}-T_{a}\right)}$
(2b)
where,
${\displaystyle U={\left[{\frac {1}{h_{0}}}+{\frac {1}{c}}+{\frac {1}{h_{i}}}\right]}^{-1}=}$${\displaystyle {\left[{\frac {1}{5.8}}+{\frac {1}{4.8}}+{\frac {1}{2.8}}\right]}^{-1}=}$${\displaystyle 1.35\quad {\mbox{W/m}}^{2}}$
${\displaystyle {\mbox{Reduction of losses can be calculated as}}\left[{\frac {1.88-1.35}{1.88}}\right]=}$${\displaystyle 28\%}$
(2c)
The air gap reduces the heat transfer by conduction since air is a poor conductor. This proves that a reduction of 9% in heat gain and a reduction of 28% in losses can be achieved by using double-glazed system when compared with single-glazed system.
### Indirect gain
In indirect gain, the heat is allowed to enter through glazing and is stored in the thermal mass. The heat is then transferred to the room via conduction and convection (Fig. 3).
Figure 3. Indirect gain during sunshine hours.
Indirect gain concepts include Trombe wall, water wall and trans wall.
The rate of heat transfer into the room can be expressed as follows,
${\displaystyle {\dot {Q}}={\left({\frac {1}{U_{t}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}\left(T_{sa}-\right.}$${\displaystyle \left.T_{r}\right)=U_{L}\left(T_{sa}-T_{r}\right)}$
(3)
where,
${\displaystyle T_{sa}={\frac {\alpha \tau I(t)}{U_{t}}}+T_{a}}$
The thickness, surface area, material, and thermal properties of the thermal mass controls the heat flow inside the room. The thermal mass is dark colored for maximum efficiency and promote absorption of solar radiation. Reduction in buildings heating demands with use of passive heating concepts has been reported to be about 25% annually in various studies [12].
### Solarium
Solarium is a unification of direct gain and thermal storage concepts. Solarium consists of three sections namely sunspace with thick mass wall on the south side (for Northern hemisphere), linking space, and living space as shown in Figure 4. The thermal wall between the living space and sunspace helps in heat retention and distribution, thus improving the efficiency. The sunspace collects the energy through the glazing, absorbs it, and prewarm air for the living space. The sunspace works on the direct gain principle, in which the heat is used to maintain the temperature suitable for its transfer to the living space.
Figure 4. Cross-section view of solarium-cum-passive solar house.
The rate of heat transfer into the living zone can be expressed as follows,
${\displaystyle {\dot {Q}}={\left({\frac {1}{h_{m}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}\left(T_{sa}-\right.}$${\displaystyle \left.T_{r}\right)=U\left(T_{sa}-T_{r}\right)}$
(4)
where,
${\displaystyle T_{sa}={\frac {\alpha \tau I(t)}{U_{t}}}+T_{a}{\mbox{and}}h_{m}=}$${\displaystyle {\left({\frac {1}{h_{0}}}+{\frac {1}{h_{TS}}}\right)}^{-1}}$
Tiwari and Kumar [13] have presented a thermal analysis of a solarium-cum-passive house as represented in Figure 4. The findings of the study were based on the energy balance of different components, link walls (like air collector, trans wall, water wall, metallic sheet). The findings have been based on best Thermal Load Levelling (TLL).
Variation in room air temperature and ambient temperature were noticed due to the solar intensity necessitating an estimate of the room temperature variations. TLL can be calculated using the following expression:
${\displaystyle {\mbox{TLL}}={\frac {\left(T_{r,max}-T_{r,min}\right)}{\left(T_{r,max}+T_{r,min}\right)}}}$
(5)
Decrement factor (f) can be defined as the reduction ratio of inside surface temperature of a room to the outside surface temperature of the room and can be expressed as follows:
${\displaystyle f={\frac {{\left(T\vert _{x=L}\right)}_{max}-{\left(T\vert _{x=L}\right)}_{min}}{{\left(T\vert _{x=0}\right)}_{max}-{\left(T\vert _{x=0}\right)}_{max}}}}$
(6)
Temperature fluctuations in the living room were noticed in case of air collector as link wall and resolved using an additional thermal mass. With use of air collector as link wall, along with effect of isothermal mass in living space and presence of movable insulation, drop in maximum temperatures of both the zones were found to be 3–4°C.
Based on Table 2, one can observe that direct gain is more convenient for sunshine hours heating (office) and rest of the concepts are used for residential buildings. Solarium will be useful for both the applications.
## Passive Cooling Concepts
To maintain comfortable indoor environment, there should be reduction in rate of solar heat gains (by using solar devices, insulation, appropriate building materials and colors, decrease in thermal heat gains by lighting controls etc.) and removal of excess heat from the building via convection, evaporative cooling, radiative cooling, air movement, cool breezes, earth coupling, reflection of radiation etc. Passive cooling concepts channel the airflow, thus removing the heat. The various cooling concepts in brief have been summarized in Table 3 with remarks. Few concepts have been discussed as follows:
Table 3. Various passive cooling concepts
S. No. Concepts Results Ref. Climatic Conditions Remarks Applications
3.1 Wind Towers
a. Proposed improvements:
1. Integrated with evaporative cooling concept.
2. Tower heads capable of trapping wind from any direction.
3. One-way damper with large screen openings
1. 306 kg of mass storage material is used per cubic meter of tower, capable of storing 36 m2 heat.
2. The above proposed design increases the efficiency of heat transfer by 5–10 times without a penalty in the total mass of the thermal material used
[34] Hot arid areas (Areas with variable wind directions)
1. Wind towers are capable of releasing air at higher flow rates to the buildings.
2. An energy storing system (long conduits made of baked non-glazed clay) was also introduced to increase the heat transfer area
1. Residential.
2. Commercial.
3. Analysis may be used as guideline for natural ventilation and passive cooling systems
b. Two novel designs:
1. Wetted columns with cloth curtains.
2. Wetted surface with evaporative cooling pads
1. High wind conditions: Wetted column tower design.
2. Low wind conditions: Wetted surface tower design.
3. The design released air at much lower temperature to the interior space as compared to the conventional design.
4. Wet columns with 10 m height can reduce the indoor temperature by 12°C and RH by 22% [35]
[35-37] Hot arid regions (Middle East) Integration of cooling devices with the conventional wind towers is beneficial with air exiting the towers at significantly lower temperature than the outside temperature
1. Clay conduits.
2. Water pool
1. Air flow induced by the tower has direct impact on the reduction of internal temperature.
2. Increasing the number of conduits results in better efficiency than a wetted column.
3. Wetted surface deign is able to reduce the temperature by up to 17.6°C
[38] Hot dry region of Ouargla (maximum temperature 47–52°C)
1. Clay conduits mounted to improve mass and heat transfer.
2. Water pool introduced to increase the humidification
1. Residential.
2. Bio climatic housing
f. Wind towers installed at the roof top.
1. The proposed tower can rotate and align itself in the direction of the predominant wind to compensate for low wind speeds.
2. Natural day light inside the premise can be improved by using transparent construction material for the wind catchers
[39] Windy regions The proposed wind towers could be used in various configurations such as wind tower with windows, a wind tower and a solar chimney/heater or two wind towers in different directions
1. Residential.
2. Closed arenas.
3. Commercial buildings.
3.2 Evaporative cooling (Fig. 5; equation (7))
a. Passive evaporative cooling. Effective for metal ceiling and thus reduces the room temperature. [40] Hot humid climate (Thailand) Higher solar radiation and ambient temperature gave better results All building types
b. Solar air heater design along with the concept of evaporative cooling Responded well during the winters but was not effective for summer cooling [41] Composite climate Changes (like addition of wetted south wall collector and roof duct at the top) were made to the model in order improve performance in both seasons
c. Performance of various roof materials on evaporative cooling effect Siliceous shale itself is capable of reducing the roof surface temperature up to 8.63°C due to its high evaporation rate as compared to mortar concrete (0°C). This material releases more latent heat while silica sand, volcanic ash and pebbles yield more sensible heat of about 0.62, 0.18 and 0.18, respectively [42] Siliceous shale with adsorption rate of 0.07 kg/m2/h is found to have the greatest evaporation performance (0.3 kg/m2/h) All building types
d. Passive evaporative cooling wall based on various porous layers Porous pipe surface temperature and the air flow of about 4–6°C and 3–5°C, respectively below the ambient can be attained, thus meeting the cooling demand [43] Shanghai, China (October).
1. Porous ceramic pipes with high water sucking ability were used as construction material for the evaporative wall.
2. Not suitable for extreme humid climate and locations with shortage of water for evaporation.
Hot and dry climates or locations while the design of outdoor or semi enclosed spaces in parks, pedestrian areas and residential courtyards aims at controlling increased surface temperature.
e. Indirect evaporative cooling
1. There was drop of 1°C in mean daily temperature [44],
2. There was an average drop in indoor temperature of up to 2.5°C compared to the outside temperature [44],
3. This system is capable of reducing the thermal discomfort due to excess of heat in about 95–100% of the year [44],
4. Capable of reduction of the energy demand of HVAC by 20% in next 20 years [45]
[44, 45] Maracaibo, Venezuela (average daily temperature ranged between 26.5–27.6°C) [44], Dry and hot climate [45]
1. Metallic water tank with thickness of 3–4 cm was laid over concrete slabs. Insulated high reflectance sheets of 1 cm thickness were used as roof element and fans were used in order to enhance the evaporation [44].
2. Strong potential for improving indoor comfort conditions
The system can be employed in various Brazilian territories, irrespective of the arid climate [44]
f. Evaporative cooling through a fountain
1. The resultant inside temperature was observed to fall within the comfortable zone of 20°C.
2. There is a potential for reduction of the cooling load by 9% and the annual energy consumption by 23.6%
[46] Hot and arid regions (Dubai) Outside temperature was about 45°C All building types
a. Shading of roof High indoor temperature can be controlled by providing a roof cover made from locally available material like hay, terracotta tiles, inverted earthen pots, solid cover (sheets), plants, thermal insulation. (Fig. 6) [24] Masonry and RCC constructions tend to make the indoor temperature as high as 41°C when the roof top temperature is about 65°C All building types
b. Shading by trees and vegetation
1. The ambient temperature near the outer wall may be substantially reduced by 2–2.5°C without excess use of supplementary energy [26].
2. Deciduous trees should be used on the south and southwest of buildings [47].
3. Evergreen trees should be used on the south and west side of the façade [47].
4. Shading and evapotranspiration from trees can reduce the surrounding temperature as much as 5°C [47].
5. The air temperature can be reduced by 2°C in the surrounding area with presence of a nearby park [48]
[26, 47, 48] Deciduous trees provide summer shading and daylight in winters by shedding the leaves
1. Energy savings.
2. Overall benefits for environment (reduced emissions).
3. All building types
c. Tree buffering as solar control in a south- east oriented building
1. The solar irradiation peak in the non- shaded area and the shaded area at the same time was observed to be 600 W/m2 and 100 W/m2, respectively.
2. Solar radiation exceeded on the shaded wall on the mid-day and reached 180 W/m2 as the sun was at high horizon
[49] Agricultural University of Athens Parameters like air and wall surface temperatures, wind speeds, humidity, heat exchange between the wall surface and surrounding environment were measured in the shaded (by deciduous trees) and unshaded areas for a hot summer period
1. Energy savings.
2. Overall benefits for environment (reduced emissions).
3. All building types
d. Roof solar collector Roof thermal comfort cannot be effectively achieved by only roof solar collector system and it should be installed along with Trombe wall [50] Hot and humid climate The roof solar collector design used: CPAC Monier concrete tiles and gypsum board Housing
e. Ventilated roof As the ventilated roof provides insulation along with the protection against the solar gains, it is more advantageous during the summer season. No clear improvement in winters [51, 52] The proposed setup consisted of air gap sandwiched between the reinforced concrete prefabricated slab and the insulation for both the seasons
f. Cool roof (37 roof designs)
1. About 10–40% reduction in air conditioning energy.
2. Flat roof: Heat gain and average indoor temperature were 414 kWh and 32.5°C, respectively.
3. Domed roof: Heat gain and average indoor temperature were 310 kWh and 32.2°C, respectively.
4. Vaulted roof: Drop of 1.5°C in the average indoor temperature. Fall of 53% and 826 kWh savings during summers in discomfort hours with rim angle of 70° with high albedo coating as compared to the reference case of the conventional noninsulated roof
[53] Cairo, hot dry climate The typical roof temperature can reach up to 37°C above the ambient for hot dry climate and can exceed by about 20°C when compared to the surroundings covered by vegetation Low and medium rise residential buildings
3.4 Radiative Cooling (Fig. 7A and B; equations (8) and (9))
a. Correlation between the radiative cooling power and the temperature difference between the ambient and the sky Radiative cooling has the potential to save up to 25% of the power consumption independent of all location [54] Tropical climate (Malaysia) The cooling power decreases with decrease in the difference between the ambient and sky temperature
b. Radiative cooling applications The specific cooling power measurements ranges from 20 to 80 W/m2 [55] Movable insulations, air-based systems and open or closed water-based systems
c. Water-based radiative cooling plate Net cooling power of 81 W/m2 was achieved by removing the cover for 7 h of operation [56, 57] Israel Flat plate collector attached to a storage tank was used Conventional space cooling
d. Open water-based system The plant showed a specific cooling power of 120 W/m2 as achievable [58] Würzburg, Germany Cooling outputs are higher for the closed system because of the absence of the thermal resistance between the water and the ambient
e. Regional characteristics With increase in elevation, there is a decrease in the cooling load but the potential of radiative cooling is large [59] China The long wave terrestrial radiation shows no correlation with the elevation while the short wave incoming radiation shows a proportionate decrease at the normal lapse rate. Thus, leading to an increase in the value of radiative cooling Residential buildings
3.5 Infiltration/Ventilation (Equations (10) and (11))
a. Building design
1. Window to ground ratio for residential buildings lies in the range of 0.33–0.58 (average 0.44).
2. The mean window to wall ratio for like dining/living, bed room and are 0.34 and 0.27, respectively
[60] Hong Kong High- rise residential buildings
b. Hybrid ventilation and night ventilation
1. Natural ventilation should not be disturbed by the additional mechanical airflow in hybrid ventilation.
2. Minimize HVAC system, solar loads and artificial lighting
[61] Germany Architectural solutions were used which solutions included thermal insulation, moderate window dimensions, central atrium, shading systems and cross ventilation Office buildings
### Wind tower
Hot ambient air is allowed to enter the wind tower during the day. Transferring heat to the walls upon contact creating a cool downward draft. The heat stored in the walls warms the cold night air. Low pressure at the top leads to an upward draft.
Saffari and Hosseinnia [18] suggested that drop of 12°C in indoor temperature and relative humidity increased by 22% can be achieved with use of wet columns 10 m in height. Hughes et al. [19] underlined various cooling techniques integrated with wind towers. The key parameters considered include the ventilation rate and temperature to determine the feasibility of implementing the devices for their respective use. The temperature decrease was found to be in the range of 12–15°C by incorporating evaporative cooling with wind towers. The addition of the cooling devices reduces the air flow rates and the overall efficiency of the wind tower. This temperature drop was found to be greater than a solitary wind tower arrangement. Montazeri et al. [20] examined two- sided wind tower. The maximum performance was achieved during an experiment at 90° angle. Chaudhry et al. [21] investigated a novel closed-loop thermal cycle embedded inside a circular wind tower with internal cross-sectional area of 1 m2 with 1 m height installed at the roof top to achieve internal thermal comfort. Louvers present at the wind tower openings were angled at 45°. The study concluded that the exit temperature using traditional cooling was increased up to 4°C without any impact of the height in case of the proposed heat pipe design with water and ethanol as working fluids.
### Evaporative cooling
The interior spaces are cooled by passing the hot ambient air over damped surface to cool an air stream (by evaporating the water) before its introduction to the interior spaces. Amer [22] reported that evaporative cooling is one of the most oldest, effective, and efficient technique with the potential to reduce indoor temperature by about 9.6°C. Heat transfers for evaporative cooling have been shown in Figure 5.
Figure 5. Evaporative cooling: Wetted surface exposed to solar radiation.
The rate of thermal energy per unit area can be expressed as follows,
${\displaystyle {\dot {q}}=U_{L}\left(T_{sa}-T_{r}\right)}$
(7)
where,
${\displaystyle {\begin{array}{rl}T_{sa}&={\frac {\alpha I(t)}{h_{1}}}+T_{a}-{\frac {\epsilon \Delta R}{h_{1}}},h_{1}=h_{rw}+h_{ew}+h_{cw}\quad \quad {\mbox{and}}\quad \\&U_{L}={\left({\frac {1}{h_{1}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}\end{array}}}$
In the Middle East, evaporative cooling is combined with wind towers to channel the cool wind passed over water cisterns into the interiors to produce cooling and refreshing effect [23]. The evaporative cooling is extensively used in the form of dessert coolers in arid areas in sun light hours (ambient temperature between 37 and 42°C), despite leading to increased indoor air humidity. The method is limited to the regions with low outdoor humidity with 0.3–0.5 m3 water per dwelling availability [1]. Kamal [24] discussed a passive downward evaporative cooling system consisting of downward tower with wetted cellulose pads installed at the top of the tower with inside temperatures ranging between 29 and 30°C while the outside temperature ranged from 43 to 44°C with 6–9 number of air changes. Roof surface evaporative cooling was also discussed where the water was sprayed over suitable water-retaining materials like gunny bags laid over the roof. The results showed that the wetted roof temperature was 40°C with ambient temperature of 55°C. Qingyuan and Yu [25] concluded that the potential of evaporative cooling is subjective to the difference between humidity ratio of outdoor air and wet bulb temperature at saturation.
Solar shading devices reduce the heat gains and thus provide comfortable indoor temperature, reducing the cooling costs. They can also function as an esthetic element aside from day lighting if properly designed. Drop of almost 6 °C in the room temperature has been observed [26]. Kumar et al. [27] evaluated various passive cooling techniques and found that solar shading alone is responsible in reducing the inside temperature by about 2.5–4.5°C. Further drop of 4.4–6.8°C was observed with insulation and controlled air exchange rate.
They can be classified as vertical (vertical louvers, projecting fins), horizontal devices (canopy, awnings, horizontal louvers, and overhangs), egg crate devices (concrete grille blocks, metal grills), and screenings (venetian blinds, double glass windows, window quilt shade, movable insulation curtains, natural vegetation etc.). Various roof shading techniques have been shown in Figure 6. Horizontal shading devices are best suited for south-oriented openings, whereas vertical shading devices for east- and west-facing facades.
Figure 6. Roof shading by (A) earthen pots, (B) solid cover and (C) plant cover.
Kima et al. [28] studied the impact of four shading types – overhangs, blind system, light shelf, and experimental shading device. Maximum cooling energy saving was determined to be 11% for experimental shading with 76° of solar altitude. Grynning et al. [29] conducted a study in which it was found that solar shading systems are necessary to reduce the need of artificial cooling of an office block. Simulations for north- and south-oriented cubicles with different floor areas, openings, and shading schemes were run. The simulations revealed that the shading systems contribute toward lowered transmittance value of the window. It was found that the cooling load increases with increase in the window size from 41% to 61%, therefore, there was a decrease in the heating demand. Energy demands were found to be larger in north-facing offices as compared to south facing. Shading devices, if improperly used, can increase the energy demands by 5%, hence they should not be installed on north-oriented workspaces. The results also show that by using a proper and correct shading technique, energy demands can be reduced for south-facing facades by 9%, whereas an improper technique may lead to an increase of 10%. It was also found that four pane glazing is beneficial as compared to two or three pane glazing and can reduce the energy demands as high as 20% and 7% if two pane and three pane glazing is replaced by four pane glazing, respectively.
Shading devices have been in use since ancient times. The Mughal architecture (India) used these in the form of inclined and deep shades to cover more surface area with deep carvings on building exteriors. These carvings help create mutual shading and the extended surface helps to increase the convective heat transfer [30] (Fig. 11).
Effective radiation from the exposed horizontal surface to ambient air via convective and radiative heat transfer is termed as radiative cooling. Roof transfers heat to the night sky via long wave radiation exchange and convection (Fig. 7A).
Figure 7. Radiative cooling (A) Schematic section and (B) Haveli in Shekhawati, Rajasthan.
The radiant heat exchange between sky and a body/surface can be expressed as:
${\displaystyle {\dot {q}}_{r}=\epsilon \sigma \left(T_{sky}^{4}-T^{4}\right)}$
(8)
Rate of long-wavelength radiation exchange between ambient air and sky can be expressed as:
${\displaystyle \Delta R=\sigma [{\left(T_{a}+273\right)}^{4}-\left(T_{sky}{+273)}^{4}\right]=}$${\displaystyle 60\quad {\mbox{W/m}}^{2}}$
(9)
#### Courtyard planning
Localized heating within buildings may be reduced to large extent by exploiting the thermal interaction due to the difference in temperature of courtyard and the building core depending upon the aspect ratio of the court, wind speed, and direction [31] (Fig. 7A and B). In vernacular architecture, the courtyards were integrated with vegetation and water bodies to enhance the humidity, evaporative cooling, and provision of shade.
### Infiltration/Ventilation
Energy conservation and natural ventilation should be the prime concern of any building design as the buildings are often planned as sealed and well insulated, with low heat gain or loss, the extreme use of HVAC systems to improve air quality and to dilute the VOCs emitted by the building materials and furniture [32]. In buildings, there are two types of airflows induced due to pressure difference leading to natural air flow. Infiltration occurs from adventitious openings that are present in every building in the form of interfaces, cracks, or any gaps etc. Infiltration can be minimized with draught sealing, air locks, airtight and quality construction of doors and windows. Wang et al. [33] suggested that airtightness alone can have a significant impact on the heating and cooling performance of the building. In the study, infiltration of hot and humid air led to an increase of 9.4% and 56% in total cooling load and latent load, respectively. Reduction of 1.4% in heating load was observed due to higher outside temperature. The other type of airflow is ventilation. Windows play an important role for air circulation within the building premises with recommended value of air movement being 0.2 and 0.4 m/s during winters and summers, respectively [14].
The ventilation losses can be given by:
${\displaystyle Q_{v}=0.33\quad NV\left(T_{r}-T_{a}\right)}$
(10)
Rate of heat transfer from roof bottom to room air is,
${\displaystyle {\begin{array}{rl}M_{a}C_{a}{\frac {dT_{r}}{dt}}=&h_{i}\left(T_{x=L}-T_{r}\right)A_{r}+A_{win}U_{t}\left(T_{sa,win}-T_{r}\right)\\&-0.33\quad NV(T_{r}-T_{a})\end{array}}}$
(11)
Based on Table 3, one can observe that the combination of evaporative cooling and wind towers is able to reduce the temperature by up to 12–17°C. Evaporative cooling is the most economical concept for cooling of a building.
## Passive Heating and Cooling Concepts
These are the concepts that can be used for both seasons for heating and cooling purposes. The various heating/cooling concepts in brief have been summarized in Table 4 with remarks. Few concepts have been discussed as follows:
Table 4. Passive heating and cooling concepts
S. No. Concepts Results Ref. Climatic Conditions Remarks Applications
4.1 Trombe wall (Fig. 8; equations (12)-(14))
4.1.1 Trombe wall – Passive heating (Fig. 9; equation (15))
a.
• PV- Trombe wall
• Case 1: with openings and heat storage.
• Case 2: With DC fan.
• Case3: Performance evaluation by varying air flow for 3 types of glazing.
• Case 4: Installation over the glazing.
• Case 5: Thermal insulation
Case 1 [78]:
1. Indoor temperature can be increased by 7.7°C.
2. The Daily average electrical efficiency can reach up to 10.4%.
Case 2 [2]:
1. Indoor temperature can be increased by 14.42°C.
2. The daily average electrical efficiency can reach up to 10–11%.
Case 3 [79]:
1. The effect of airflow on the performance stagnates when the air velocity reaches the value of 1 m/s.
2. The maximum PV efficiency (of about 0.185) was achieved in the double glass with argon.
3. Highest reduction in cooling load at air velocity of 1.75 m/s was achieved in double glass with argon (about 160 W/m2).
4. The study concluded that double glass filled with argon and double glass PV-Trombe wall is preferable over the single glass at air velocity of 1.5 m/s.
Case 4 [80]:
1. The thermal performance of the Trombe wall can be reduced by up to 17%.
Case 5 [81]:
1. The room temperature can be increased by 2.36°C with use of thermal insulation in cold climatic conditions and decreased by 2.47°C in hot climatic conditions. For the same electrical efficiency decreases by <2%.
2. The room temperature can be decreased by 2°C with use of curtain shading in hot climatic conditions and electrical efficiency increases by 1%
[2, 78-81]
• Case 1 and 2: China.
• Case 3: Universiti Teknologi Petronas.
• Case 4: South China.
• Case 5: Composite climate
Case 2: Reduces the PV temperature simultaneously. Case3:
1. PV- Trombe wall glazing types: single glass, double glass and double glass with Argon.
2. Double glass shows 18% less reduction in cooling load as compared to double glass with argon.
3. Ventilated double glass offers more insulation
Case 5: It is recommended that thermal insulation in both winter and summer and appending a shading curtain in summer are adopted, especially for the diurnally used PV-Trombe wall.
PV Trombe wall can provide feasible solutions for high energy consumption and environmental degradation especially for tropic region
b. Opening and closing modes in the management of air vents
1. The best time to open the air vent is 2–3 h after sunrise and the best time to close it is 1 h before sunset.
2. The heat storage capacity of the Trombe wall is fully released at 7:30 a.m. and it reaches its maximum value of 10.6 MJ/m2 at 4:00 p.m. At 7:30 a.m., the heat release reaches its maximum value of 10.4 MJ/m2
[82] GangCha country, China Conclusion i is appropriate for almost all type of Trombe wall heating system.Conclusion ii is case specific
4.1.2 Trombe wall- Passive cooling (Figs. 8 and 11) (Equation (16))
a. Thermal behavior of Trombe wall in summers
1. A decrease of 1.4°C in the internal surface temperature of the wall was observed and 0.5 MJ/m2 in daily heat gains was observed with the use of rolling shutters as screening.
2. The heat gains of the screened Trombe wall were about 18 times lower than those of the unscreened.
3. A reduction of 72.9% and 65% in cooling energy needs was observed with the combination of overhangs, rolling shutters and cross ventilation, respectively, in comparison with unvented Trombe wall without solar shadings
[83] Mediterranean climate A comparative analysis of difference between the thermal behaviors of two Trombe walls was carried by varying the screening, ventilation, occupancy and internal heat gains Low or highly insulated building
4.2 Roof pond
4.2.1 Roof pond – Passive cooling
a. Experimental roof pond building
1. The vapors were discharged from the pond in order to improve the buildings summer performance whereas the same will reduce the efficiency of the system in winters.
2. Cooling load (500 KJ/m2) is at its maximum at noon because the most significant component of the cooling load is the direct heat gained through the south glazing.
3. There is a significant sensible heat contribution at 11.00 am, which is responsible for the cooling. At noon, cooling is due to the latent heat of evaporation
1. 3 × 2.5 × 2 m room with pool depth of 60 mm.
2. There is a need to design the vapor leakages from the pond to prevent them from winter heating and rains
Increased effectiveness of roof ponds in high- humidity regions
b. Site experiments for: Case 1: roof with moist soil Case 2: Walkable roof pond along with night water circulation Case 1: Reduction of 5°C in indoor temperature.Case 2: Reduction of 6°C was seen in the indoor temperature compared to the outdoor temperature [85] Hot dry climate of Saudi Arabia Case 1: Roof was shaded by 10 cm of pebbles.Case 2: Roof pond was filled with pebbles with an insulation layer and thin tiles over the layer Not suitable for low cost housing since dead load of water needs to be considered in the roofing structure
c. Roof pond with gunny bags (RPWGB) floating on water surface
1. This technique is better than the roof pond with wetted gunny bags (RFWWGB) in terms of cooling performance of room temperature and heat flux through the roof into the pond.
2. This technique has better performance when compared to movable insulations.
3. The optimum water depth for the RPWGB should be 200 mm and 50 mm for concrete and metal-decked roofs, respectively
[72] The technique is better than RPWWGB because of thermal satisfaction inside the pond during daytime irrespective of the building type Further field examinations are required before putting this system into practical use
d. Roof pond with forced electric ventilation (Fig. 14)
1. The indoor temperature was better stabilized (with fan) as compared to the pond without fan and cover. The variations became limited to 3.5°C without a fan and 3°C with one.
2. The average temperature reduction with the pool alone lowered the room temperature by 3.36°C compared to the roof without a pond.
3. A substantial reduction of 6.0°C in the peak external temperature at 15:00 between the room without a pond and the room with a ventilated pond was achieved.
4. There was also a substantial reduction of 6.5°C in the peak internal temperature at 6:00.
5. With a larger percentage of roof to wall, the roof pond cooling will be more effective and the drop in the cooling load will be around 29%
e. Ventilated pond protected with a reflecting layer
1. There was a reduction of 30% in the maximum indoor air temperature compared to the corresponding temperature of a building without any roof cooling technique.
2. The proposed system has a 24 h cooling effect because the ceiling temperature is higher than that of the water. At night, the water better prevents the heat loses compared to a bare concrete roof
[86] Crete, Greece In the setup, a pond with 1.10–1.12 m depth was filled with water and covered with an aluminum layer at 1.15 m height from the free water surface Small buildings
4.2.2 Roof pond – Passive heating and cooling.
a. Skytherm Room temperature achieved was 27°C and 22°C when the outside temperature was 37°C and 5°C for summers and winters, respectively [1] Different weather types with various means of modulating ambient conditions Use of metallic plate at bottom of the pond with blowers in summers and pond covered with transparent plastic in winters
4.3 Earth Air Heat Exchanger (EAHE) (Fig. 14; equations (17) and (18))
4.3.1 Earth Air Heat Exchanger (EAHE) – Passive heating
a. EAHE coupled with a solar air heating duct
1. The proposed design was connected at the exit end with a solar air-heating duct to increase the heating capacity by 1217.625–1280.753 kWh.
2. There was a substantial rise in the inside temperature and the coefficient of performance (COP) of 1.1–3.5°C and 4.57, respectively.
3. With 34 m of tunnel length, more than about 82–85%
4. of total rise in air temperature can be achieved which means that by reducing the length of the tunnel to 34 m, the cost of the installation was optimized.
5. The COP increased up to 4.57 when assisted with solar air heating duct
[87] Northwestern India, arid climate of Ajmer during winters Thermal performance of EAHE with a 60 m long, 100 mm diameter horizontal polyvinyl chloride pipe buried 3.7 m deep configurations
4.3.2 Earth Air Heat Exchanger (EAHE) – Passive cooling
a. Analytical model to calculate the cooling potential
1. The results validated that EAHE can provide 30% of the cooling energy demand.
2. There was a reduction o 1700 W in the peak cooling load and 2.8°C in the indoor temperature during summers
[88] Dessert climate (hot and arid) Thermal resistance of the material of the pipe was neglected Domestic buildings
b. Explore the effect of geometrical and dynamical parameters on thermal performance of EAHE
1. With increase in the length of the pipe:
• The air outlet temperature decreases.
• The daily mean efficiency increases.
• The coefficient of performance falls.
2. When pipe length changes from 10 to 30 m:
• For an inlet temperature of 29°C, there was a reduction of 2°C in the outlet temperature. The reduction rate was not found to be constant.
• The COP falls by 10.5% and the daily mean efficiency rises by 142%.
3. With increase in cross section and air velocity:
• The air outlet temperature increases.
• The daily mean efficiency decreases.
• A rise of 1.2°C was noticed in the ambient temperature and a drop of 31.6% in the daily mean efficiency was observed when the air velocity changed from 1 to 3 m/s
[89] Algerian Sahara conditions
1. A pipe with 5 mm thickness was buried in soil with 22.27°C temperature.
2. The ambient temperature was the same as the air inlet temperature i.e., 29°C
4.3.3 Earth Air Heat Exchanger (EAHE) – Passive heating and cooling.
a. EAHE assisted by a wind tower (Fig. 14)
1. Unlike the pipe dimensions (length and diameter), the height and cross section of the tower had no influence on the performance.
2. A tower with 5.1 m height and 0.57 m2 of cross-sectional area generates 592.61 m3/h of airflow.
3. The air velocity increases and the maximal gradient of temperature decreases with the increase in the pipe diameter.
4. With a pipe length of 70 m, the daily cooling potential reached a maximum of 30.7 kWh and that the daily cooling potential was proportional to the pipe diameter.
5. This scheme is more efficient than the conventional
[35] Hot and arid regions of Algeria Ambient temperature more than 45°C
b. Energy conservation potential of EAHE
1. A 19 kW cooling potential was recorded to maintain an average room temperature 27.65°C for the proposed design with 80 m of pipe length, 0.53 m3 of cross-sectional area and 4.9 m/s air flow velocity
2. An auxiliary energy load of 1.5 kW for winter season is required in achieving comfort conditions affecting an average room temperature of 24.48°C
[90] Mathura, India
1. Non- air conditioned building.
2. Can be coupled to greenhouse and building simulation codes
c. Photovoltaic- thermal collector accompanied with an EAHE
1. Capable of increasing the indoor temperature by 7–8°C at night during winters.
2. The hourly thermal energy generated, during day and night is 33 MJ and 24.5 MJ, respectively.
3. The yearly thermal energy generated has been calculated to be 24728.8 kWh, while the net annual electrical energy savings is 805.9 kWh and the annual thermal exergy energy is 1006.2 kWh
[91] New Delhi, India Green house
d. Improvement of the EAHE thermal potential The thermal performance of an EAHE can be improved by 73% and 11% for cooling and heating purpose, by increasing the number of ducts, while keeping the area occupied by the ducts and the mass flow rate of air fixed [92] In all proposed installations the thermal potential for cooling was higher than the thermal potential for heating
e. Evaluation of EAHE 80 m long tunnel with 0.528 m2 of cross-sectional area has 512 kWh and 269 kWh cooling and heating capacity, respectively [93] India The heating capacity was found to be inadequate for providing the necessary comfort conditions Hospital complex
4.4 Combination of various passive heating and cooling concepts.
a. Trombe wall, ventilated walls, glazed walls, fenestration, green roof, PV roofs, evaporative roof cooling along with thermal insulation and PCM
1. Thermal mass is more effective when the outside ambient temperature difference between days and nights are high.
2. Size of the mechanical devices can be reduced by incorporating a holistic energy efficient design which compensates for the additional capital investment for the energy efficiency features
[94] Various building envelope components were studied to review the potential of passive energy savings
b. Window size on each facade, shadings on south façade and thermal insulation on both roof and walls About 25.31% of the energy consumption and 11.67% of the lifecycle costs can be reduced using these variables [95] Mediterranean region Jaber and Ajib performed a study to minimize the energy consumption and lifecycle cost Residential building
c. Building orientation, thickness of external wall, air infiltration, wall and roof insulation, lighting, windows to wall ratio, glazing type About 50% of the annual energy use can be minimized when compared to the existing design practices. This can be achieved mostly by integrating the roof insulation, reducing the air infiltration and using energy efficient lighting and other electrical equipment [96] Tunisia Ihm and Krarti performed a research in order to reduce the energy consumption and life cycle costs Single family houses
d. Wall and roof insulation, shading style, thermal mass, night ventilation, air change rate Use of an optimal solution can reduce the building energy requirement by 94% when compared to the actual design practices adopted in Sydney [97] Sydney Design optimization for lifecycle heating and cooling costs Low energy home (detached, single story house)
e. Thermal insulation, Trombe wall and cool roof
1. 46% and 80% of savings can be achieved in winters and summers, respectively, in comparison to an ordinary building. A reduction of 5.41 kW was also achieved in the peak cooling load.
2. About 20.7% was contributed alone by the storage capacity of the Trombe wall.
3. 60.3% and 47.7% savings in heating and cooling, respectively, can be achieved by integrating the movable overhangs, internal curtains and low emissive argon coating loads
[98] Tunisia Analyzed the impact of architectural characteristics and passive techniques on its energy requirements
f. Passive cooling techniques: Ground cooling, solar control, night ventilation, evaporative cooling, night sky infrared radiation, infiltration control and thermal insulation
1. The results confirmed the effectiveness of the earth pipes.
2. With the application of a conductive thermal control in the west wall and the roof slab, a reduction of temperature fluctuation from 24.07 of the outside conditions to an average DBT of about 21°C was noticed.
3. The DBT inside the setup for evaporative cooling remained in a comfortable zone i.e., 22.86°C.
4. The shading devices blocked any direct sun gain and avoided overheating the interior improving the indoor comfort conditions and thus reducing the energy consumption
[99] Hot and dry regions (Mexico) To achieve hygrothermal conditions for occupants and reduce the energy consumption of air- conditioning New and existing buildings
g. Louver shading devices, double-glazed, natural ventilation: wind catcher, cross ventilation, green roofing, evaporative cooling via fountain, insulation, indirect radiant cooling, light color coatings with reflection
1. The solar heat gain coefficient was about 17% and a reduction of 55% in energy was noticed with the use of solar control film.
2. A reduction of 23.6% in annual energy consumption can be achieved with use of solar passive cooling strategies.
3. A 220 m2 green roof with sprinklers was used and it was estimated that the green roof reduces the energy demand by 6% and drops the roof temperature by 30°C
[100] Hot and arid regions (Dubai) To study the effectiveness of various passive cooling techniques to enhance the thermal performance and to decrease the energy consumption Residential buildings
h. Night ventilation, roof insulation, shading devices, courtyard planning, micro climate modifications
1. The indoor temperatures of the Chinese houses were higher by 1°C than the outdoor temperatures during the day under open window conditions and by 2°C at night under closed window conditions.
2. The outdoor temperature of Malay house was recorded to be 1.7°C higher than the terraced house.
3. The indoor temperature was 5°C lower than the outdoor temperature in case of courtyard planning at the peak period whereas the values for both indoor and outdoor temperatures were same during the night.
4. The periods of indoor operative temperatures exceeding the 80% comfortable upper limit in Malay houses, Chinese shop houses, daytime ventilated and night ventilated terraced houses were 47%, 7–8%, 91% and 42%, respectively
[101] Hot and humid (Malaysia) Field studies were conducted in two traditional timber Malay houses and two traditional masonry Chinese shop houses Modern terraced houses
i. Orientation, cross ventilation, day lighting, unglazed Trombe wall, earth sheltering, wind towers, solar water heater system, roof top PV system and PV thermal greenhouse dryer
1. During the extreme weather conditions in both summers and winters, all the floors were in comfortable range of temperature.
2. The temperature recorded for the basement (earth sheltering) was 28°C, for ground and first floor it was recorded at approximately 18–20°C.
3. The basement temperature was found to be 7–8.65°C lower than the ambient temperature during harsh summers.
4. A rise of 2–3°C in the indoor temperature was found during harsh winters on the first floor due to the presence of a clerestory window.
5. The total energy saving due to the thermal heat gain and day lighting to be 34,445.568 kWh, out of which 5852.93 kWh accounts for day lighting only
[68] Composite climate (India) All building types
### Trombe wall
Trombe wall is a large (at least 400 mm thick) mass (material – stone, brick, reinforced cement concrete, mud, etc.), exposed to sunlight through south-facing exterior glazing in northern hemisphere. The thick walls transfer the absorbed solar energy to the interiors by conduction and convection. Trombe wall reduces the heat flux from the exposed outer surface wall to the interiors of the building. Thermal mass reduces the temperature fluctuation peaks (decrement factor) and shifts the peak to a later time than the air temperature peaks (time lag) due to a lower overall heat transfer coefficient.
Energy balance for Trombe wall are as follows:
Solair temperature,
${\displaystyle T_{sa}={\frac {\propto I(t)}{h_{0}}}+T_{a}-{\frac {\in \Delta R}{h_{1}}}}$
(12)
Heat flux (W/m2),
${\displaystyle {\dot {q}}=U_{L}\left(T_{sa}-T_{r}\right)}$
(13)
where,
${\displaystyle U_{L}={\left({\frac {1}{h_{0}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}}$
Energy balance for bare surface (Trombe wall) with insulation of thickness Li, having thermal conductivity of Ki during the night time can be expressed as follows:
${\displaystyle {\dot {q}}=U_{L}\left(T_{sa}-T_{r}\right)}$
(14)
where,
${\displaystyle U_{L}={\left({\frac {1}{h_{0}}}+{\frac {L}{K}}+{\frac {L_{i}}{K_{i}}}+{\frac {1}{h_{i}}}\right)}^{-1}}$
Trombe wall may have two different types of exposed surfaces for passive buildings:
1. Bare exposed surface (unglazed Trombe wall) with absorptivity, α ≤ 0.4. This surface is used for thermal cooling (Figs. 8 and 11; equation (16)).
Figure 8. Energy flow diagram for Trombe wall (unglazed).
2. Blackened and exposed surface (glazed Trombe wall) with absorptivity ≥ 0.9. This surface is used for thermal heating (Fig. 9; equation (15)).
Figure 9. Blackened and glazed surface.
#### Trombe wall – Passive heating
Blackened and glazed surface (Fig. 9) of the Trombe wall should be considered for passive heating.
Energy balance for blackened and glazed surface are as follows:
Heat flux (W/m2),
${\displaystyle {\dot {q}}=U_{L}\left(T_{sa}-T_{r}\right)}$
(15)
where,
${\displaystyle T_{sa}={\frac {\propto \tau I(t)}{U_{t}}}+T_{a},{\mbox{and}}U_{L}=}$${\displaystyle {\left({\frac {1}{U_{t}}}+{\frac {L}{K}}+{\frac {1}{h_{i}}}\right)}^{-1}}$
Figure 10 shows simple passive heating technique using Trombe wall, with vent openings provided near the floor and the ceiling to allow convective heat transfer. These concepts have been applied in Pyrenees Orientales district of France and in the U.S. southwest.
Figure 10. Trombe wall with vent openings.
For heating purposes, thermal resistance of glazing is proven to be more beneficial because glazing minimizes the heat loss through itself. A solar house based on this concept has also been constructed in Jordan (1983–1984) with two sections, namely the heated section and the non-heated space. Ta'ani et al. [62] reported that it is possible to meet 54% of the buildings heating demands by solar energy with collector array efficiency with proper retrofitting. Tyagi and Buddhi [63] proposed a filling of phase change materials (PCM) to enhance the storage of latent heat in the masonry wall. These units are lighter in weight and require less space as compared to the massive thermal mass. Nwachukwu et al. [64] found that heat storage capacity along with the heat transfer through a Trombe wall can be improved by coating the exteriors of the thermal mass with superior absorption vigor. Balcomb and McFarland [65] found that Trombe walls with vented openings proved to be 10–20% more efficient, especially in extreme climatic conditions like Boston. Saadatian et al. [66] discussed different types of Trombe walls, viz. classical and modified, zigzag, composite, fluidized, solar water wall, solar trans wall, solar hybrid wall, Trombe wall with PCM and PV-Trombe wall. The efficiency of Trombe wall can be improved by 8% by using a fan. The optimal size (i.e., ratio of Trombe walls area to area of rooms with other walls) should be 37% with 300–400 mm thickness. The insulation increases the efficiency by 56% and also decreases the size of the thermal wall. The energy and environmental performance has been compared with and without Trombe wall in the study by Bojić et al. [67]. The research is based on two cases: the first case, without any Trombe wall and the second case, with installations of two Trombe walls at the south side of Mozart house located in Lyon, France. A 450 mm layer of clay brick 1220 has been used as the Trombe core material. The second case uses the solar energy captured to save around 14% of all electricity and 20% of annual energy as compared to the first case. The energy ratio is around 6 with the energy payback time of around 8 years for the electrical heating with optimum core thickness. The above values are around 3 and 18 years, respectively, for natural gas heating. The savings can further increase with increase in the thickness of Trombe wall layer. The optimum thickness of clay brick is around 0.35 m and 0.25 m for electrical heating and natural gas heating, respectively. The study also reveals that lower density material like clay brick save more operating energy as compared to higher density material like concrete.
#### Trombe wall – Passive cooling
A thick thermal mass used as the exterior facade reduces the decrement factor and leads to a time lag. A heavy structure is preferred for thermal cooling as the mass acts as an insulator and a heat storage medium. The unglazed Trombe wall may be constructed with different materials like stone, brick, reinforced cement concrete, mud, etc. This is a very old technique and is clearly visible in historical buildings like Humayuns Tomb, Qutub complex, Fatehpur Sikri (Fig. 11) etc. The ventilation system, as marked, has been arranged above the lintel level of the windows and the inside temperature is found to be comfortable all year round.
Figure 11. Trombe wall, openings, shades (passive cooling) Fatehpur Sikri, Agra, India.
A bare surface (Fig. 8) should be considered for passive cooling purpose. Expression of solair temperature for bare surface Trombe wall can be written as:
${\displaystyle T_{sa}={\frac {\alpha }{h}}I\left(t\right)+T_{a}-{\frac {\epsilon \Delta R}{h}}}$
(16)
An innovative approach of combining unglazed Trombe wall (Bare surface) with storage facility was evolved by Tiwari et al. [68] as shown in Figure 12A and B.
Figure 12. Unglazed Trombe wall (Bare surface) with storage (A) Section and (B) Sodha BERS Complex, Varanasi.
#### Trombe wall – Passive heating and cooling
Shen et al. [69] discussed the installation of adjustable dampers at the glazing and adjustable vents at the wall. This system is favorable for both heating and cooling purposes. During winters, the upper damper closes while the lower damper and both vents are open, although in summers, lower damper along with upper vent are closed. It was also discussed that the composite wall has better energetic performances than the classical wall in cold and/or cloudy climatic conditions. Krüger et al. [70] analyzed the heating and cooling potential of Trombe wall by installing two test cells of 5.4 m3 internal volume and 2.6 m2 floor area for a subtropical location. One of them was a naturally ventilated Trombe wall and the other one was without it (reference test cell). Higher performance was seen in the reference test cell under cold conditions. For heating purpose, three operation modes were tested – air vents 1 and 3 closed (case 1); air vent 3 closed (case 2); and air vents 1 and 3 closed with dampers installed in the storage wall openings (case 3). For weekly averages and clear sky conditions, the smallest average difference was recorded in case 3 and the highest in case 2, from the control test cell. Case 2 was considered the best configuration for the weekly period data, but case 1 proved to be better in clear day conditions with slightly higher temperature difference to the exterior (5.2°C against 4.5°C). Case 2 was considered to be a better option for winters. For summers, four operation modes were used – all air vents shut (operation mode 1); air vents 1 and 4 shut (operation mode 2); air vent 2 shut (operation mode 3); air vents 2 and 4 shut (operation mode 4). Mode 3 is considered to be the best option in summers.
### Roof pond
In earlier studies, it has been seen that about 50% of the heat gains for single-story buildings is received via roof [71]. The conventional approaches to reduce the heat flux via roof includes false ceilings, insulations, increasing the roof thickness, roof shading, or using roof coatings. Roof pond is another technique found in 1920s and was first investigated at the University at Texas [72]. Sutton [73] observed that the roof surface temperature might reach 65.6°C without any treatment. By installing an open roof pond, the above temperature can be dropped down to 42.2 and 39.4°C with 0.05 and 0.15 m depths of the pond, respectively [74]. A drop of 20°C in the room temperature can be achieved by using the roof pond in arid regions [75]. Kharrufa and Adil [76] tested one room (4 × 7 × 2.75 m) to check the effectiveness of the roof pond which was mechanically ventilated (Fig. 13) for cooling in hot dry summer of Baghdad.
Figure 13. Schematic section of roof pond with forced electric ventilation.
### Earth air heat exchanger
The air is allowed to pass through a tunnel or a buried pipe at least 1–3 m below the surface for both heating and cooling purposes. A depth of 2–3 m is generally considered since at that depth, it is cooler than the outside in summers and warmer in winters [35]. Figure 14 shows the scheme of Earth air heat exchanger (EAHE).
Figure 14. Scheme of Earth air heat exchanger.
Thermal energy gained by the flowing air can be expressed as:
${\displaystyle {\dot {Q}}_{u}={\dot {m}}_{a}C_{a}\left(T_{fo}-T_{fi}\right)}$
(17)
${\displaystyle {\dot {Q}}_{u}={\dot {m}}_{a}C_{a}\left(T_{0}-T_{fi}\right)\left[1-\right.}$${\displaystyle \left.e^{{\frac {-2\pi rh_{c}}{{\dot {m}}_{a}C_{a}}}L}\right]}$
(18)
where,
T0 is the ground temperature outside pipe (°C).
For the given design parameters by Tiwari et al. [77], a drop of 5–6°C in the outlet air temperature in summers was noticed, using five air changes with 100 mm diameter and 210 mm length of the pipe.
### Combination of various passive heating and cooling concepts
Various passive solar strategies have been discussed and it is evident that the energy use can be reduced to some extent with the above discussed strategies individually. To achieve a high level of energy performance, a combination of different passive solar techniques is necessary. The various heating/cooling concepts in brief have been summarized in Table 4 with remarks.
Based on Table 4, one can observe that unglazed Trombe wall can be used for both heating and cooling, whereas glazed Trombe wall can be used for heating purpose only. Combination of Trombe wall, cool roof, and thermal insulation proves to be very effective and can achieve 46% and 80% of savings in winters and summers, respectively.
## Building-Integrated Photovoltaic Thermal (BiPVT) System
Solar energy is converted to electrical energy by photovoltaic (PV) modules with efficiency of 10–15%. The rest of the energy is radiated back to the atmosphere or absorbed as heat. Photovoltaic thermal system (PVT) refers to the extraction of this absorbed energy and bringing it into use. Integration of PVT with a building (façade, roof, windows etc.) is referred to as building integrated photovoltaic thermal system (BiPVT). The efficiency of BiPVT system is much larger, since it produces electricity and also provides the building with thermal energy. In case, the PV modules are opaque type, the system is termed as building-integrated opaque photovoltaic thermal system and if the PV modules used are semitransparent, the system is referred as BiSPVT (Fig. 15).
Figure 15. Building-integrated semitransparent photovoltaic thermal (BiSPVT) system.
Following [102] (Fig. 15), energy balance for solar cell is,
${\displaystyle {\begin{array}{rl}{\alpha }_{c}{\tau }_{g}I\left(t\right)\beta A_{m}=&\left[U_{tca}\left(T_{c}-T_{a}\right)+U_{bcr1}\left(T_{c}-T_{r1}\right)\right]A_{m}\\&+{\tau }_{g}I\left(t\right)\beta A_{m}{\eta }_{c}\end{array}}}$
(19)
Energy balance for roof of room 2 at x = 0 is
${\displaystyle {\alpha }_{R}{\tau }_{g}^{2}\left(1-\beta \right)I\left(t\right)A_{m}=}$${\displaystyle h_{c}A_{R}\left(T_{x=0}-T_{r1}\right)-kA_{r}{\frac {dT}{dx}}_{x=0}}$
(20)
Energy balance for room 1 air temperature:
${\displaystyle {\begin{array}{rl}M_{a,1}C_{a,1}{\frac {dTr_{1}}{dt}}=&h_{c}\left(T_{x=0}-T_{r1}\right)A_{R}+U_{br1}\left(T_{c}-T_{r1}\right)A_{m}\\&-0.33N_{1}V_{1}\left(T_{r1}-T_{a}\right)\end{array}}}$
(21)
Energy balance for roof to room 2 at x = L is
${\displaystyle -K{\frac {dT}{dx}}_{x=L}=h_{ir2}\left(T_{x=L}-T_{r2}\right)}$
(22)
Energy balance for room 2 air temperature is
${\displaystyle M_{a,2}C_{a,2}{\frac {dTr_{2}}{dt}}=h_{ir2}\left(T_{x=L}-\right.}$${\displaystyle \left.T_{r2}\right)A_{r2}-0.33N_{2}V_{2}\left(T_{r2}-\right.}$${\displaystyle \left.T_{a}\right)}$
(23)
Joshi et al. [103] have found that exergy efficiency of PVT system (11.6–16%) is higher than that of the PV system (8–14%) by using Petelas formula [104]. Joshi and Tiwari [105] have found that the monthly energy and exergy of a 1.2 m PVT module lies between 35–60 kWh and 7–16 kWh, respectively, for different months and cities of India. Chen et al. [106] have found that BiPVT system with 64 m2 surface area can produce 8.5–10 kWh of thermal output.
Vats and Tiwari [107] have derived analytical expressions for room air temperature of BiSPVT and BiOPVT system integrated to the roof of a room and facade with and without air duct. It was found that the room air temperature for façade and roof in SPVT and OPVT systems with air duct is lower than without an air duct. The reason behind the finding was that there was indirect heating due to the presence of insulated façade/roof between the PV module and the room air. The difference between the room air temperature in SPVT and OPVT façade with and without air duct was found to be 1.46°C and 9.80°C, respectively. The same for SPVT and OPVT roof with and without air duct was found to be 1.13°C and 9.55°C, respectively. Further, the results have been tabulated in Table 4. Vats and Tiwari [108] evaluated the energy and exergy performance of BiSPVT system with roof and found that HIT PV module (heterojunction comprised of a thin amorphous silicon PV cell on top of a crystalline silicon cell) has maximum overall thermal energy of 2497 kWh, maximum annual electricity of 810 kWh, and maximum exergy of 834 kWh. The authors also found that the efficiency of HIT and a-Si is 16% and 6%, respectively, varying inversely with the solar cell temperature, while maximum annual thermal energy of 464 kWh was observed in case of thin amorphous silicon cell (a-Si). An a-Si has maximum thermal energy of 79 kWh with packing factor of 0.62 [109].
Vats et al. [110] evaluated the energy and exergy performance of BiSPVT system to roof with and without ducting for cold climatic conditions. It was observed that HIT accounts for maximum overall thermal energy and a-Si for minimum in both cases with and without an air duct. Annual overall exergy in HIT with duct was 643 kWh and without duct was 610 kWh. The study concluded that with duct, approximately 15% overall thermal energy is greater than without duct. Vats et al. [109] studied the influence of packing factor of SPV module integrated to the roof on the room temperature, module, and electrical efficiency of the module. The study concluded that the temperature of the module decreases with decrease in the packing factor. With decrease in the packing factor, there is an increase in its electrical efficiency and rise in the room air temperature by 3°C due to increase in the nonpacking factor. The authors found that HIT PV module has maximum annual electrical energy of 813 kWh and a-Si has maximum thermal energy of 79 kWh with packing factor of 0.62. Efficiency increases by 0.2–0.6% with a corresponding decrease in the module temperature by 10°C if packing factor is reduced from 0.83 to 0.62. The results of few studies have been summarized in Table 5.
Table 5. Building integrated Photovoltaic Thermal (BiPVT) system
S. No. Concepts Results Ref. Climatic conditions Remarks Applications
5.1 Building integrated Opaque Photovoltaic Thermal System (BiOPVT) System
a. Integrated with façade with air duct Minimum 2.3°C rise in room temperature [107] Srinagar, India with (although valid for different climatic conditions)
1. Rise in room temperature is comparatively lesser than SPVT because of low conductivity of tedlar.
2. Ambient temperature 4.4°C
1. Electricity generation.
2. Thermal heating
b. Installed on the roof top 45% energy produced [111] Brazil Installation on the roof top yields more energy than on any vertical façade
1. Multi- family dwellings.
2. Thermal and electricity generation
c. Installed on roof 3.19 kW annual electrical energy can be saved [112] Las Vegas South orientation Residential buildings
5.2 Building-integrated Semitransparent Photovoltaic Thermal (BiSPVT) System (Fig. 15; equations (19)-(23))
a. Installed on the roof top without air duct
1. Maximum 18°C rise in room temperature [107].
2. Air mass flow rate (0.85–10 kg/s) through duct increases the room air temperature from 9.4 to 15.2°C [107].
3. 1203 MWh of electricity can be saved annually [113]
[107, 113] Srinagar, India (although valid for different climatic conditions)
1. Non- packing area (i.e., glass area) increases the heat gain.
2. Double glazing reduces the heat loss.
3. Better performance when compared to BiOPVT system
1. Day lighting.
2. Thermal energy.
3. Electricity production.
4. Office buildings
b. Integrated to a roof
1. 47°C achieved at first floor.
2. The optimum roof thickness for the above study was found to be 300–400 mm to minimize the decrement factor
[102] Varanasi, India The effect of number of air changes per hour through the room on the inside temperature, decrement factor and TLL of the building for thermal comfort were considered Crop drying
Based on Table 5, one can observe that BiPVT system can be used for thermal heating and electricity generation. In addition, semitransparent PV module is also an effective heating technique to sustain design, which not only produces electricity and provides thermal energy but also allows day lighting, reducing the energy demands.
## Conclusions and Recommendations
• For passive heating, direct gain is more convenient for sunshine hours heating (office) and rest of the concepts are used for residential buildings. Solarium will be useful for both the applications. Use of double-glazed system leads to reduction of 9% of heat gain and reduction of losses by 28% compared to single-glazed system. Exposed walls should be double glazed to trap maximum solar radiation inside the room with minimum U-value.
• For passive cooling, the combination of evaporative cooling and wind tower proves to be very effective and can reduce the temperature by up to 12–17°C. Evaporative cooling is the most economical concept for cooling of a building.
• For passive heating/cooling, combination of Trombe wall, cool roof, and thermal insulation can achieve 46% and 80% of savings in winters and summers, respectively.
• BiSPVT system gives better result in terms of efficiency, thermal environment, space heating, day lighting, and electricity use. Photovoltaic systems are among the most promising alternative energy source. Building-integrated photovoltaic systems can provide savings in electricity costs, reduce pollution, and also add to the architectural appeal of the building.
## Nomenclature
A Area m2 Ca Specific heat of air J/kg K c Air conductance W/m K h0 Outside heat transfer coefficient W/m2 K h1 Total heat transfer coefficient W/m2 K hc Convective heat transfer coefficient W/m2 K hcw Convective heat transfer coefficient (wetted surface) W/m2 K hew Evaporative heat transfer coefficient (wetted surface) W/m2°C hi Inside heat transfer coefficient W/m2 K hm Top losses of solarium W/m2 K hr Radiative heat transfer coefficient W/m2 K hrw Radiative heat transfer coefficient (wetted surface) W/m2 K hTS Convective and radiative heat transfer coefficient from walls outer surface to sunspace W/m2 K I(t) Solar intensity W/m2 k Thermal conductivity W/m K L Thickness m Ma Mass of air kg ${\textstyle {\dot {m}}_{a}}$ Mass flow rate of air in pipe (EAHE) kg/s N Number of air changes – T Temperature °C Tfo Air temperature at the outlet of EAHE °C Tfi Air temperature at the inlet of EAHE °C Tp Temperature of metallic surface of water containers °C Tr Room air temperature °C Tsa Solair temperature °C Tss Temperature of sunspace (solarium) °C Tw Water temperature °C Ubcr1 Overall heat transfer coefficient from solar cell to room 1 through glass cover W/m2 K UL Overall heat transfer coefficient W/m2°C Ut Total heat transfer coefficient W/m2 K Utca Overall heat transfer coefficient from solar cell to ambient through glass cover W/m2 K V Volume of room m3 ${\textstyle {\dot {Q}}}$ Rate of heat transfer W ${\textstyle {\dot {q}}}$ Rate of useful energy gain W/m2 ${\textstyle {\dot {q}}_{r}}$ Radiant heat exchange between sky and a surface W/m2 Qv Ventilation losses W Greek symbols α Absorptivity – β Packing factor – ΔR Rate of long wavelength radiation exchange between ambient air and sky W/m2 ε Emittance – σ Stefan-Boltzmann constant W/m2/K4 τ Transmissivity – Subscript 1 Room 1 2 Room 2 a Ambient air c Solar cell g Glass m PV module R Roof r Room win Window
## Acknowledgements
The authors are thankful to Bag Energy Research Society, Indirapuram, Ghaziabad for their cooperation and help in the research work.
## Conflict of Interest
None declared.
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### Document information
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# Analysis of Binary Search
The following is the code for a binary search. Similar to linear search, we make an assumption that the size() function has a constant run time. For a binary search to work the data must be sorted. In this case we assume that the data is sorted from smallest (at arr[0]) to biggest (at arr[size-1]).
The second part that is important to remember about a binary search is that you need to be able to access any item given its index in constant time. If that is not possible, the analysis will fail.
template <class TYPE>
int BinarySearch(const vector<TYPE>& arr, const TYPE& key){
int rc=-1;
int low=0;
int high=arr.size()-1;
int mid;
while(low<=high && rc==-1){
mid=(low+high)/2;
if(arr[mid] > key)
high=mid-1;
else if(arr[mid] < key)
low= mid+1;
else
rc=mid;
}/*while*/
return rc;
}
Like a Linear search, the determining factor on runtime for binary search is also the loop:
while(low<=high && rc==-1){
mid=(low+high)/2;
if(arr[mid] > key)
high=mid-1;
else if(arr[mid] < key)
low= mid+1;
else
rc=mid;
}/*while*/
The code within this loop is constant, meaning that no matter what size is one iteration of the loop will take the same number of operations (more or less) and thus, the question really becomes how many times will this loop run?
Again, we can either find the key or not find the key.
If the vector does NOT contain the key, how long will it take to run?
At the beginning high - low = n -1. With each iteration we "move" high or low towards each other so that their difference is halved (their new values are near the mid point)
By doing this, it would take the loop at most log n iterations before low>high
Thus for an unsuccessful search, the function's runtime $O(log n)$
For a successful search we might still need to search when high==low and to get to that point would also require iterations. Thus, the worst case runtime for this function when the key is found is also O(log n)
Therefore, the worst case runtime for this function is $O(log n)$
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For a complementary perspective, we can fix a point \$$x \in M\$$, and let \$$t\$$ vary, to get the trajectory function \$$\phi_x(t) = \phi^t(x)\$$.
The _orbit_ of \$$x\$$ is the image of its trajectory function \$$\phi_x\$$.
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Produces forecasts from a trained model.
# S3 method for VAR
forecast(object, new_data = NULL, specials = NULL,
bootstrap = FALSE, times = 5000, ...)
## Arguments
object The time series model used to produce the forecasts A tsibble containing future information used to forecast. (passed by fablelite::forecast.mdl_df()). If TRUE, then forecast distributions are computed using simulation with resampled errors. The number of sample paths to use in estimating the forecast distribution when boostrap = TRUE. Additional arguments for forecast model methods.
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# What is the difference between the words chord, tangent in (a) and (b)?
(a) If a function $g$ is continuous on the closed interval $[u,v]$, where $u<v$, and differentiable on the open interval $(u,v)$, then there exists a point $c$ in $(u,v)$ such that
$$g(v)=g(u)+g′(c)(v-u)$$
The expression $(g(v)-g(u))/(v-u)$ gives the slope of the line joining the points $(u,g(u))$ and $(v,g(v))$, which is a chord of the graph of $g$, while $g′(c)$ gives the slope of the tangent to the curve at the point $(c,g(c))$. Thus the Mean value theorem says that given any chord of a smooth curve, we can find a point lying between the end-points of the curve such that the tangent at that point is parallel to the chord.
## 2 Answers
One area I know of where you can use chords and tangents to geometrically interpret addition in a group structure is with elliptic curves.
The way we define point addition on an elliptic curve is by taking a secant (a secant is just a continuation of a chord beyond its endpoints) between two points on an elliptic curve. The sum of those two points is then the negative of the third intersection of that secant on the curve (which is found by flipping a point over horizontal axis). For adding a point to itself, you instead use the tangent at that point. The additive zero for this group is the point at infinity (this is when you have a vertical line that doesn't intersect the graph anywhere else).
Purple Alien Planet has a good explanation of point arithmetic (and is also where I got the images). Wolfram Mathworld also has a page on elliptic curves.
Others include the discrete versions (used for elliptic curve cryptography), and although they don't lend themselves to visualization quite as well as the continuous ones, they follow similar principles, and that is what the definition in (b) is referring to.
• @ AJMansfield: What about a possible bijection! – DER Sep 3 '13 at 15:28
• @AR1 Well, the both mean the same thing - the chord is just a line between two points on a curve, and a tangent is the line that is tangent to the curve at our point. The Chord and Tangent law is just a more general version of what I described above regarding how one performs pointwise addition. – AJMansfield Sep 3 '13 at 15:32
• @ AJMansfield: I mean bijection between the two cases (a) and (b). – DER Sep 3 '13 at 15:34
• @AR1 What are you even looking for here? They are the same! – AJMansfield Sep 3 '13 at 15:36
I am very confused about the group structure you intend to impose on chords and tangents, but here is a basic definition.
Given a curve $g(x)$, a chord between the points $a$ and $b$ is a line including the points $(a,g(a))$ and $(b,g(b))$. In the case illustrated above, $g(x)=x^2$, $a=0$ and $b=2$. Given a curve $g(x)$, any line intersecting $g(x)$ at least twice is a chord of $g(x)$.
Given a differentiable curve $g(x)$, the tangent line at $c$ is the line intersecting the curve $g(x)$ at $(c,g(c))$ whose slope is $g'(c)$.
Note that these definitions are neither mutually exclusive nor exhaustive. That is, we can have lines that are neither chords nor tangents of $g(x)$
and lines that are both chords and tangents of $g(x)$
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# Handlers
Handlers in general are user provided objects to algorithms which allow to take control over certain aspects of the algorithm and stopping the computation if given criteria are met. Especially the computationally expensive algorithms like SAT and MaxSAT Solving, knowledge compilation, formula simplification, or MUS computation take handlers. You can either use one of the handlers which are implemented in LogicNG or implement your own handler. The hierarchy of the classes and interfaces in the package handlers is here:
classDiagram
Handler <|-- DnnfCompilationHandler
Handler <|-- SATHandler
SATHandler <|-- TimeoutSATHandler
Handler <|-- MaxSATHandler
MaxSATHandler <|-- TimeoutMaxSATHandler
Handler <|-- FactorizationHandler
Handler <|-- OptimizationHandler
OptimizationHandler <|-- TimeoutOptimizationHandler
Handler <|-- BDDHandler
BDDHandler <|-- TimeoutBDDHandler
Handler <|-- ModelEnumerationHandler
ModelEnumerationHandler <|-- TimeoutModelEnumerationHandler
Handler <|-- ComputationHandler
ComputationHandler <|-- TimeoutHandler
ComputationHandler <|-- NumberOfNodesBDDHandler
ComputationHandler <|-- NumberOfModelsHandler
TimeoutHandler <|.. TimeoutSATHandler
TimeoutHandler <|.. TimeoutMaxSATHandler
TimeoutHandler <|.. TimeoutOptimizationHandler
TimeoutHandler <|.. TimeoutBDDHandler
TimeoutHandler <|.. TimeoutModelEnumerationHandler
The interface Handler has two methods which can be overridden:
1. aborted() returns whether the computation was aborted or not
2. started() is called whenever the computation is started and can be used to initialize the handler
A number of interfaces implement the Handler. The handler you're using has to implement the relevant interface, depending on what sort of computation you are performing.
These are the top level handler interfaces:
• FactorizationHandler is an interface for handling factorization methods for normal forms (CNF, DNF). It has two methods: performedDistristibution() is called each time a distribution is performed, createdClause() is called each time a new clause is created.
• SATHandler is an interface for handling the solving process of a SAT solver. detectedConflict() is called each time a conflict is found, and finishedSolving() is called when the SAT solver finished solving.
• MaxSATHandler is an interface for handling the solving process of a Max-SAT solver. It has itself a SATHandler which is used for its underlying SAT solver and provides the two methods foundUpperBound() and foundLowerBound() which are called whenever a new upper or lower bound is found in the solving process as well as the two methods lowerBoundApproximation() and upperBoundApproximation() which return the current approximation of the lower/upper bound of the problem. These methods can e.g. be used to abort the computation when a certain bound is found or to return the current bound when the computation is aborted.
• BDDHandler is an interface for BDD compilation handlers. The method newRefAdded() is called every time a new node reference is added to the BDD kernel.
• DnnfCompilationHandler is an interface for DNNF compilation handlers. The method shannonExpansion() is called each time a Shannon expansion is performed.
• ModelEnumerationHandler is an interface for (projected) model enumeration on the SAT solver with the ModelEnumerationFunction. It has its own SATHandler for its underlying SAT solver as well as a method foundModel which is called every time a model is found.
• OptimizationHandler is an interface for optimizations on the SAT solver. It has a SATHandler for its underlying SAT solver as well as the method foundBetterBound which is called every time a new better bound for the optimization problem is found. It is used in the OptimizationFunction of the SAT solver and in internal optimization calls in the AdvancedSimplifier .
## Some Useful Handlers Implemented in LogicNG
All handlers implemented in LogicNG inherit from the abstract class ComputationHandler. There are three classes extending the ComputationHandler:
1. TimeoutHandler for aborting computations based on their computation time.
2. NumberOfNodesBDDHandler for aborting BDD generations based on the number of generated nodes in the kernel.
3. NumberOfModelsHandler for aborting model enumerations based on the number of enumerated model.
### The TimeoutHandler
The TimeoutHandler stops the computation after a specific time. The constructor of a TimeoutHandler takes a timeout in milliseconds and a TimerType, which specifies the type of the timeout. The timer types are:
• SINGLE_TIMEOUT: The timeout is started when started() on the handler is called. Subsequent calls to started() have no effect on the timeout. Thus, the timeout can only be started once.
• RESTARTING_TIMEOUT: The timeout is restarted when started() on the handler is called.
• FIXED_END: Timeout which is interpreted as fixed point in time (in milliseconds) at which the computation should be aborted. The method started() must still be called, but does not have an effect on the timeout.
Handler Responsiveness
Note that it might take a few milliseconds more until the computation is actually canceled, since the cancellation depends on the next call to the handler and for performance reasons calls to the handler are only performed on certain points during the computation. For the overloaded constructor, that takes only a timeout in milliseconds, the timer type is SINGLE_TIMEOUT.
A number of classes extend the TimeoutHandler. For those classes, the interpretation of the timer type is identical. However, they implement different interfaces and can thus be used for different use cases:
### The NumberOfNodesBDDHandler
The NumberOfNodesBDDHandler cancels the build process of a BDD after a given number of added nodes is reached.
### The NumberOfModelsHandler
The NumberOfModelsHandler terminates the model enumeration process after a given number of models is reached. For more information see the chapter on Model counting and enumeration|.
Consider the following example for creating an own handler. We implement a SATHandler which stops the computation after a certain number of conflicts is reached. To make our implementation easier, we extend the ComputationHandler which already provides the aborted attribute.
public class MaxNumberOfConflictsSATHandler extends ComputationHandler implements SATHandler {
private final int maxNumberOfConflicts;
private int numConflicts;
/**
* Constructs a new instance with the given maximal number of conflicts.
* @param maxNumberOfConflicts the maximal number of conflicts limit,
* if -1 then no limit is set
*/
public MaxNumberOfConflictsSATHandler(final int maxNumberOfConflicts) {
this.maxNumberOfConflicts = maxNumberOfConflicts;
this.numConflicts = 0;
}
@Override
public void started() {
this.started();
this.numConflicts = 0;
}
@Override
public boolean detectedConflict() {
this.aborted = maxNumberOfConflicts != -1 && ++numConflicts >= maxNumberOfConflicts;
return !aborted;
}
}
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# How is mercury produced in industry? [closed]
Mercury is the only metal that exists in a liquid state at room temperature.
• In which form is mercury extracted from its ore?
• If it produced as a solid, how and when is it turned into a liquid?
## closed as off-topic by Todd Minehardt, airhuff, Jon Custer, Klaus-Dieter Warzecha, M.A.R.Mar 4 '17 at 7:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
If this question can be reworded to fit the rules in the help center, please edit the question.
• There are many solid compounds that include mercury as one of their constituents. But, pure mercury at room temperature is a liquid as you point out. – Jon Custer Feb 3 '17 at 14:05
• tell me ik at room temperature it is liquid tell me in which state we get it from its ore.... that's my question – Utsav pandey Feb 3 '17 at 14:10
• The classic way is to roast the ore, with the mercury coming off as a vapor that is readily condensed. Note that vaporized mercury is easily taken up by humans and damages the central nervous system. – Jon Custer Feb 3 '17 at 14:13
• I'll point out that most Hg now recovered in the US is as a byproduct to prevent pollution rather than being mined for the Hg itself. archive.epa.gov/mercury/archive/web/pdf/… – MaxW Feb 3 '17 at 16:27
Most commonly, mercury $\ce{Hg}$ is separated from its ore $\ce{HgS}$, known as cinnabar. The process used is roasting; this entails heating the raw material in oxygen.
$$\ce{HgS(l) + O2(g) ->[700-800\ ^\circ \mathrm{C}] Hg(g) + SO2(g)}$$
Mercury is extracted here in the gaseous state. Note that the product is elemental mercury, not an oxide. This is because the oxides decompose at or below $500\ ^\circ \mathrm{C}$: $$\ce{Hg2O -> HgO + Hg,\\ HgO -> Hg + O2}.$$
The mercury vapor is then purified in multiple steps which depend on the required degree of purity. Usually the gaseous mercury is first cleansed from dust, then condensed (bp $356.6\ ^\circ \mathrm{C}$). At this stage, an $80\%$ yield is observed.
The condensed mass is filtered further, washed with bases and acids, and destilled. For ultrapure mercury (less than $10^{-6}\%$ of impurities), electrochemical refinement using mercury electrodes follows.
Hergi Karik, Kalle Truus. ($2003$). Elementide keemia. (pp 331$-$332, 334)
• it means cinnabar exist in liquid state so how it is extracted from earth – Utsav pandey Feb 3 '17 at 14:44
• @Utsavpandey No, cinnabar is a solid ore at standard conditions. The states are written in accordance with the reaction; the sulfide simply melts before $700-800\ ^\circ \mathrm{C}$. – Linear Christmas Feb 3 '17 at 14:53
Mercury is extracted from its ore, cinnabar($\ce{HgS}$). According to wikipedia:
Mercury is extracted by heating cinnabar in a current of air and condensing the vapor. The equation for this extraction is
$$\ce{HgS + O2 → Hg + SO2}$$
In 2005, China was the top producer of mercury with almost two-thirds global share followed by Kyrgyzstan. Several other countries are believed to have unrecorded production of mercury from copper electrowinning processes and by recovery from effluents.
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## Shortest Path
At Folding@home, often we use Markov state models (MSMs) to represent how molecules (usually proteins) move around in a simulation. These models help simplify large amounts of simulation data and ultimate yield a more concise network representation. Because of this, we can borrow tools normally used in fields such as graph theory to study how biological molecules behave.
One such tool is Dijkastra’s algorithm, which finds an approximate to the shortest path between any two nodes in a (weakly connected) graph. At each iteration, the algorithm finds the neighboring node that will minimize the total distance needed to traverse the graph. This method can be extremely powerful, and has become as ubiquitous to our society as getting driving directions from Google Maps.
In social networks, Dijkastra’s algorithm is what you would use to compute an Erdös number or how many degrees of separation you share with Kevin Bacon. In protein folding (my line of work), Dijkastra’s algorithm is useful for identifying the possible steps (e.g. confomational changes) that lead to a folded protein. This information can help scientists better understand the underlying physics of biology, which could lead to new therapeutic drugs.
In this tutorial, I’ll go over how to use NumPy and NetworkX to construct a random graph and calculate the shortest path between two nodes. I’ll also be using matplotlib and Seaborn to visualize the results. Optional: If you’d like to make interactive graphs, as the ones below, the mpld3 package is fairly handy to convert static plots into interactive JavaScript.
## Installing Packages
Assuming you already have Python (and pip) installed on your computer, in your terminal type:
$pip install conda This will install the conda package manager, which will make installation of the other required Python packages relatively painless: $ conda install numpy matplotlib networkx
Seaborn can be installed using pip:
\$ pip install seaborn
## Generating Data
To start, we will need a dataset which can be respresented as a directed graph. There are a ton of ways to create this sort of dataset, but in this tutorial I’ll be using NetworkX to generate an Erdös–Rényi graph with directed edges. This type of graph is constructed using a binomial distribution to determine whether an edge is formed between any two nodes. We can do this pretty easily using the erdos_renyi_graph function in NetworkX, which samples the number of edges for each node from a binomial distribution, $B(n = N, p)$. Let’s try $n = 25$ and $p = 0.12$ for our binomial:
import networx as nx
# Number of nodes
N = 25
# Generate Erdös–Rényi graph
G = nx.erdos_renyi_graph(N, 0.12, directed=True)
## Visualizing the Graph
Before we go on to the shortest path calculation, let’s plot the graph to get a sense about what it looks like. In the code below, I’ve used the scatter function in matplotlib.pyplot to plot nodes, with node sizes representing PageRank scores, and node color representing in-degree, or the number of incoming edges. We can get a decent layout to position the nodes using nx.spring_layouts, which creates a list of xy-coordinates for each node by quickly simulating the graph as a set of masses connected by springs. Edges are simply lines connecting the nodes using the plot function, with the thicker gray ticks denoting an incoming edge to a node.
import matplotlib.pyplot as pp
import seaborn as sns
import numpy as np
sns.set_style('dark')
# Initialize figure
fig = pp.figure(figsize = (8, 8))
# Create force-directed layout for the graph
pos = nx.spring_layout(G)
pos_array = np.array(pos.values()).T # Format into a NumPy array
# Define node colors based on in-degree
node_color = np.array([len(G.predecessors(v)) for v in G], dtype=float)
# Define node sizes to be proportional to PageRank values
sizes = 1E4*nx.pagerank(G).values()
# Plot each edge
for i in G:
for j in G[i]:
# Compute in-marker size
# The next few lines just resize the
# incoming markers to look decent
# with the varying node sizes
p = pos_array[:, j] - pos_array[:, i]
s = -.4*(1 + .4*np.log(sizes[j]/sizes.min()))
p = s*p/np.linalg.norm(p) + pos_array[:, j]
# Plot markers
ax.plot([pos_array[0, j], p[0]], [pos_array[1, j], p[1]], '-k', alpha = .5, linewidth = 2, zorder = 9)
#Plot edges
ax.plot(pos_array[0, [i, j]], pos_array[1, [i, j]], '-w')
# Plot nodes
ax.scatter(pos_array[0], pos_array[1], sizes, color = cm.coolwarm(node_color/node_color.max()), zorder = 10)
# Remove axis ticks
pp.xticks([])
pp.yticks([])
## Computing the Shortest Path
Now that we have an idea of how to plot a network graph, let’s finally get to calculating the shortest path between a pair of nodes. For this exercise, let’s find the path between the nodes with the lowest and highest PageRank scores. In terms of social networks, this might represent the distance in social hierachy between a second year grad student (low PageRank) and someone like Neil deGrasse Tyson (high PageRank). In protein folding, it could model the steps taken from an unfolded state (low PageRank) to a folded one (high PageRank).
In our example graph from above, it turns out that nodes 0 and 7 are the lowest and highest PageRank scorers, respectively. We can find this by applying np.argmin and np.argmax to sizes, the array PageRank scores we calculated earlier. With this, we can finally calculate the shortest path using nx.shortest_path like so:
path = nx.shortest_path(G, source = 0, target = 7)
Since we are interested in going from node 0 to node 7, we set the must set the arguments source and target accordingly. The only other input to this function is our graph, G. In this example, our shortest path only requires 3 steps, passing through nodes 22 and 2 along the way. Below you can find modified versions of the previous code and plot, which have been changed to highlight the nodes that form the shortest path between 0 and 7. You can even hover over the nodes to check the labels for yourself!
sns.set_style('dark')
fig = pp.figure(figsize = (8, 8))
ax = fig.add_subplot(1, 1, 1, frameon = False)
#Plots edges (shortest path edgest will be thicker)
for i in G:
for j in G[i]:
if (i, j) in [(path[k], path[k + 1]) for k in range(len(path) - 1)]:
alpha = 1
linewidth = 4.0
else:
alpha = .4
linewidth = 1.5
p = pos_array[:, j] - pos_array[:, i]
s = -.4*(1 + .4*np.log(sizes[j]/sizes.min()))
p = s*p/np.linalg.norm(p) + pos_array[:, j]
ax.plot([pos_array[0, j], p[0]], [pos_array[1, j], p[1]], '-k', alpha = .5, linewidth = linewidth, zorder = 9)
ax.plot(pos_array[0, [i, j]], pos_array[1, [i, j]], '-w', alpha = alpha, linewidth = linewidth)
#Plots nodes
ax.scatter(pos_array[0], pos_array[1], sizes, color = 'lightgrey', zorder = 10)
#Plot nodes along path in red
for node in path:
ax.scatter(pos_array[0, path], pos_array[1, path], sizes[path], color = 'darkred', alpha=.6, zorder=11)
_=pp.xticks([])
_=pp.yticks([])
On a parting note, what should be taken away from this toy model is the not-so-intuitive fact that even in a somewhat sparse network (i.e. low probability of sharing a connection)– although this example is a bit exaggerated in sparsity – things are fairly closely connected. We took the two furthest objects in a directed graph of 25 nodes and were still able to cross it in only 3 steps! Such an effect is made even more apparent when analyzing other graph metrics, such as average path length, on real-life social networks as done in Milgram’s Small-world experiment. Milgram found that on average, any two people in the United States are only 6 degrees of separation away. So just think about that next time you’re alone, watching TV– you could totally become BFFs with someone like Shaq!
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Question
# The direction ratios of the line $$x-y+z-5=0=x-3y-6$$ are
A
3,1,2
B
2,4,1
C
314,114,214
D
241,441,141
Solution
## The correct option is A $$3,1,-2$$Normals of $${ P }_{ 1 },{ P }_{ 2 }$$ gives the direction ratios of line of intersection, i.e. cross-product$$(\hat { i } -\hat { j } +\hat { k } )\times (\hat { i } -3\hat { j } -0\hat { k } )$$ $$\begin{vmatrix} i & j & k \\ 1 & -1 & 1 \\ 1 & -3 & 0 \end{vmatrix}=3\hat { i } -(-1)\hat { j } +(-2)\hat { k }$$$$=3\hat { i } +\hat { j } -2\hat { k }$$Maths
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## Friday, December 30, 2016
### Continuity
Spoilers for Rogue One below the fold
It is a period of civil war. Rebel spaceships, striking from a hidden base, have won their first victory against the evil Galactic Empire. During the battle, Rebel spies managed to steal secret plans to the Empire's ultimate weapon, the DEATH STAR, an armored space station with enough power to destroy an entire planet.
―Episode IV opening crawl
Rogue One ends with the Battle of Scarif. During this battle, many things are going on at once, as is typical for a Star Wars battle.
• On the surface, team Rogue One steals the tape holding the plans from the archive tower, then climbs the tower to the high-gain antenna on top. No high-bandwidth signals can get through the shield, and the plans are sufficiently large that a high-bandwidth signal is needed.
• Simultaneously their ship is patched into the base comm system. A low-bandwidth (voice) signal is sent up telling the fleet to be ready for a large transmission, and to take the shield down in order to get it. The fleet knows what Rogue One is looking for in general, because they talked about it in council before Rogue One went rogue.
• The fleet takes down the shield by destroying the shield gate. Apparently the shield was generated from there.
• Once the shield is down and the antennas are aligned, the data is transmitted to the rebel fleet flagship Profundity and copied onto a physical storage medium ("tape").
• The Death Star arrives but ignores the fleet. They know that Vader is arriving soon to deal with the fleet, and they don't know who to point the big gun at. For all they know, there might be a copy of the plans in every ship in the fleet. In fact, only Profundity has a copy.
• Vader arrives in Devastator exactly as the fleet is attempting to jump to hyperspace and escape. Several ships, including Profundity, are intercepted.
• The tape is hand-carried to the docking bay of Profundity where it is slipped through the airlock door of Tantive IV just as it is launching. Vader personally tried but failed to stop this hand-off. Tantive IV escapes into hyperspace.
So at this point, Vader knows that several ships escaped before he got there, but probably from interrogating the crew of Profundity, they knew that it was on that blockade runner that escaped, and probably the registration of it, so they knew they were looking for Tantive IV, but might not have known who was on it.
An unknown amount of time later, Devastator intercepts Tantive IV over Tatooine. (It is possible that Tantive IV took an indirect route from Scarif to Tatooine. I don't know if it matters.) Tantive IV is looking for General Kenobi, and somehow Devastator tracked them there. Presumably Tantive IV arrived first and was following normal protocols for landing in the wilderness when Devastator showed up. Kenobi didn't know at that time that anyone was coming.
INT. REBEL BLOCKADE RUNNER - CORRIDOR
The evil Darth Vader stands amid the broken and twisted bodies
of his foes. He grabs a wounded Rebel Officer by the neck as
an Imperial Officer rushes up to the Dark Lord.
IMPERIAL OFFICER
The Death Star plans are not in the
main computer.
Vader squeezes the neck of the Rebel Officer, who struggles
in vain.
Where are those transmissions you
intercepted?
Vader lifts the Rebel off his feet by his throat.
What have you done with those plans?
REBEL OFFICER
We intercepted no transmissions.
Aaah... This is a consular ship.
Were on a diplomatic mission.
If this is a consular ship... were
The Rebel refuses to speak but eventually cries out as the
Dark Lord begins to squeeze the officer's throat, creating a
gruesome snapping and choking, until the soldier goes limp.
his troops.
Commander, tear this ship apart until
you've found those plans and bring
me the Ambassador. I want her alive!
The stormtroopers scurry into the subhallways.
The "transmission" was a transmission (from Rogue One to Profundity) but is a physical tape at this point. Vader knows that Tantive IV was at Scarif and was the ship that escaped with the tapes, but no one on Tantive IV knows that the star destroyer that intercepted Profundity was Vader's ship, so the captain tried to bluff his way out.
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# Euler's Method to approximate a second order Differential Equation
## Homework Statement
y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5
Find the exact solution of the differential equation.
Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then, answer the following question:
Is the error really increasing? That is, is Euler's method becoming less accurate as t increases?
## Homework Equations
x1 = y
x2 = y'
x1' = y'
x2' = y'' = -4y' - 4y = -4x2 - 41
Euler's Method Equations assuming the substitutions made above:
x1(n+1) = x1(n) + hx/2(n)
x2(n+1) = x2(n) + h*(y''(n))
## The Attempt at a Solution
[/B]
First, I solved the differential equation. Writing the characteristic equation r2 + 4r + 4 = 0, I solved for there to be a repeated root at r = -2. Therefore, the general solution is:
y= c1e-2t + c2te-2t
Taking a derivative to use the initial conditions:
y' = -c1/2 * e-2t + c2te-2t/2 + c2e-2t
Applying the initla conditions, I find c1 = 1 and c2 = 11/2
Therefore, the solution becomes:
e-2t + 11t/2 * e-2t
I then created an excel spreadsheet which calculate and then plots the exact solution vs. the eulerapproximation, giving me the graph:
then the error graph looks as follows:
So around time t = 3, it makes sense that the error would be about 0 due to how Euler approximations work. Since Euler Approximations use the tangent lines of the functions at a certain point to approximate the shape of the graph, the more and more linear the solution gets (such as from t --> infinity in this solution), the easier it is to approximate the solution because the slope of a horizontal line is 0. However, I have absolutely no idea what could be going on here that would cause the error to start increasing seemingly linearly after time t = 3 where the solution and the euler approximation is practically horizontal. I cannot fathom that a repeated root would cause this error. Does anyone have any idea what could be causing this?
Sorry, I thought I could be more a little more explicit about my response at the bottom. Since Euler Approximations go off of the slope of the tangent line of the exact solution and as t is increasing, the slope of the tangent line of the solution approaches 0, so the error should be approaching 0. So to answer the question, I would say that the error isn't really increasing despite what the graph displays. However, I'm not sure how to answer the part of the question asking to explicitly state what would cause it to appear as if it was increasing.
pasmith
Homework Helper
## Homework Statement
y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5
Find the exact solution of the differential equation.
Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then, answer the following question:
Is the error really increasing? That is, is Euler's method becoming less accurate as t increases?
## Homework Equations
x1 = y
x2 = y'
x1' = y'
x2' = y'' = -4y' - 4y = -4x2 - 41
Euler's Method Equations assuming the substitutions made above:
x1(n+1) = x1(n) + hx/2(n)
x2(n+1) = x2(n) + h*(y''(n))
## The Attempt at a Solution
[/B]
First, I solved the differential equation. Writing the characteristic equation r2 + 4r + 4 = 0, I solved for there to be a repeated root at r = -2. Therefore, the general solution is:
y= c1e-2t + c2te-2t
Taking a derivative to use the initial conditions:
y' = -c1/2 * e-2t + c2te-2t/2 + c2e-2t
The derivative of $e^{kt}$ is $ke^{kt}$, not $\frac1k e^{kt}$.
Ray Vickson
Homework Helper
Dearly Missed
## Homework Statement
y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5
Find the exact solution of the differential equation.
Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then, answer the following question:
Is the error really increasing? That is, is Euler's method becoming less accurate as t increases?
## Homework Equations
x1 = y
x2 = y'
x1' = y'
x2' = y'' = -4y' - 4y = -4x2 - 41
Euler's Method Equations assuming the substitutions made above:
x1(n+1) = x1(n) + hx/2(n)
x2(n+1) = x2(n) + h*(y''(n))
## The Attempt at a Solution
[/B]
First, I solved the differential equation. Writing the characteristic equation r2 + 4r + 4 = 0, I solved for there to be a repeated root at r = -2. Therefore, the general solution is:
y= c1e-2t + c2te-2t
Taking a derivative to use the initial conditions:
y' = -c1/2 * e-2t + c2te-2t/2 + c2e-2t
Applying the initla conditions, I find c1 = 1 and c2 = 11/2
Therefore, the solution becomes:
e-2t + 11t/2 * e-2t
I then created an excel spreadsheet which calculate and then plots the exact solution vs. the eulerapproximation, giving me the graph: View attachment 74110
then the error graph looks as follows:
View attachment 74111
So around time t = 3, it makes sense that the error would be about 0 due to how Euler approximations work. Since Euler Approximations use the tangent lines of the functions at a certain point to approximate the shape of the graph, the more and more linear the solution gets (such as from t --> infinity in this solution), the easier it is to approximate the solution because the slope of a horizontal line is 0. However, I have absolutely no idea what could be going on here that would cause the error to start increasing seemingly linearly after time t = 3 where the solution and the euler approximation is practically horizontal. I cannot fathom that a repeated root would cause this error. Does anyone have any idea what could be causing this?
Your c1 and c2 are incorrect; you calculated y' incorrectly.
Anyway, even if you have the correct y(t) the errors can still grow (but they need not always do so). This can happen even in a simple case such as y' = a*y; see, eg., http://en.wikipedia.org/wiki/Euler_method , especially section 7. The point is that errors "accumulate", so that as the time increases you are applying a slightly incorrect step t -> t+h, starting from an incorrect y(t), and that can make y(t+h) even less correct. [Note: I said 'can', not 'will'.]
Last edited:
RUber
Homework Helper
Also, I noted that your error graph is % error, or error/x, right? As x goes to zero, your small error will become very large relative to the zero value of the function. Try plotting true error to see how the method converges to the flat line at the end.
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# How do know what happens when A. "calcium nitrate" is added to "sodium carbonate", and B. "sodium chloride" is added to "copper nitrate"?
Apr 24, 2017
How else do you predict but by reference to PRIOR experiment?
#### Explanation:
When a salt, say common salt, dissolves in water, a chemical reaction occurs:
$N a C l \left(s\right) \rightarrow N {a}^{+} + C {l}^{-}$
The ionic species are the aquated ions; which we could represent as ${\left[N a {\left(O {H}_{2}\right)}_{6}\right]}^{+}$ or ${\left[C l {\left({H}_{2} O\right)}_{4 - 6}\right]}^{-}$. Now we conceive these species to float around as discrete particles in aqueous solution. Add some silver salt to solution, say as $A g N {O}_{3}$, likewise we get $A {g}^{+}$ or $N {O}_{3}^{-}$ (again as the aquated ions), the silver ions react irreversibly with the chloride ions to form $A g C l \left(s\right)$ as a curdy white precipitate.
$A {g}^{+} + C {l}^{-} \rightarrow A g C l \left(s\right) \downarrow$
So for your reactions ($A .$):
$C a {\left(N {O}_{3}\right)}_{2} \left(a q\right) + N {a}_{2} C {O}_{3} \left(a q\right) \rightarrow C a C {O}_{3} \left(s\right) \downarrow + 2 N a N {O}_{3} \left(a q\right)$
Or, as the net ionic equation:
$C {a}^{2 +} + C {O}_{3}^{2 -} \rightarrow C a C {O}_{3} \left(s\right) \downarrow$
Calcium carbonate is (reasonably) insoluble in water, and precipitates from solution. And all of this is the province of experiment.
For $B .$, metathesis (which is only $\text{conceived}$ to occur) gives $\text{potential}$ salts that are both soluble. I write $\text{potential}$ in that we don't know a priori that the salts are soluble; this is the province of experiment.
$N a C l \left(a q\right) + C u {\left(N {O}_{3}\right)}_{2} \left(a q\right) \rightarrow N {a}^{+} + C {l}^{-} + C {u}^{2 +} + 2 N {O}_{3}^{-}$
Ionization certainly occurs; i.e. there are discrete sodium, chloride, cupric ions etc. in solution, but because an insoluble salt is NOT formed, there is no precipitation of any salt. The partner exchange is conceptual and not actual.
Does this help? If you want to clarify a point, I (and others) will certainly be available for comments/corrections/clarification.
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# Find a sequence of measurable functions defined on a measurable set $E$ that converges everywhere on $E$, but not almost uniformly on $E$.
Find a sequence of measurable functions defined on a measurable set $E$ such that the sequence converges everywhere on $E$, but the sequence does not converge almost uniformly on $E$.
I'm having troubles understanding this. I thought that a sequence of functions $\{f_n\}_{n=1}^\infty \to f$ converges almost uniformly if and only if $f_n\to f$ converges in measure. But that's wrong?
Any help would be welcome.
In light of Egorov's theorem, your measure space will have to be infinite. A good sequence to keep in mind to check that the finite measure space assumption of a theorem is required is the "moving block" $f_n(x) = \chi_{[n,n+1]}(x)$. This converges pointwise to zero, but it fails to converge in a bunch of other senses, including almost uniformly. (To see that, note that it can't converge uniformly on any set whose complement has measure smaller than $1$).
On $[0,\infty),$ let $f_n= \chi_{[0,n]}.$
"The sequence $f_n$ converges almost uniformly on $E$" means for every $\delta > 0$ there is a set $B_\delta$ of measure $< \delta$ such that $f_n$ converges uniformly on $E \backslash B_\delta$.
For example, take $E = \mathbb R$ with Lebesgue measure, and $f_n$ the indicator function of the interval $[n,n+1)$.
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This is a testing site only. See the live Public Lab site here »
# Android app for Image sequencer
by ashwinvasudevan | 21 Mar 02:49
Hello, I am Ashwin Vasudevan, currently pursuing B.E in Electronics and Instrumentation engineering at Easwari Engineering College, Chennai. I have a variety of skills from app development to UI/UX to ROS and embedded. Last year, I obtained a 100,000 grant from Analog Devices India as a part of an IOT fellowship named "Anveshan". In this fellowship, I was working on an IOT platform which collects and analyzes data to improve agriculture intelligence. The platform interfaced with public lab's cameras(Mobius Action cam) and thus obtained false NIR images.
Affiliation Easwari Engineering College (Anna University)
Location: Chennai
## Project description
By developing an app for Image Sequencer, the services of public labs are available to a wider user base. It helps public labs build a stronger brand and thus bring in more people to contribute towards their mission. Apart from image sequencer'__s features, one significant addon that I plan to add will be batch processing. Image sequencer will not only be applicable towards publiclab's community but also the wider image processing community.
Prototype
### Needs
Provided that I am selected, I would require help in exposing the webhooks. As Mr.Jeffrey Warren pointed out developing a fully native app will be difficult to maintain. Hence I will be using a wrapper.
Hi, @ashwinvasudevan - thanks for your proposal -- I appreciate the UI mockups. Have you had an opportunity to try forking and making a simple pull request to the image-sequencer library? Thanks!
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Reply to this comment...
@warren Not as of yet, will be submitting in a couple of days! Any feedback on the app?
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Hi, @ashwinvasudevan - I think that, although I like the idea of the app, image-sequencer may need a lot more back-end infrastructural work before we can start developing an app around it. I know you're interested in Android work, but do you think you could think through how you might work on image-sequencer as a stand-alone module before starting to work on more advanced UIs for it? Perhaps you might suggest some html/javascript-based UI work that would be more general purpose, but that could also later be used in an app?
Thank you!
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@warren I would be interested in working on image-sequencer. We can have the android goal as the stretch goal? If image-sequencer is completed satisfactorily maybe we can proceed with the app.
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# Entropy rigidity and Hilbert volume
@article{Adeboye2019EntropyRA,
title={Entropy rigidity and Hilbert volume},
author={Ilesanmi Adeboye and Harrison Bray and David Constantine},
journal={Discrete \& Continuous Dynamical Systems - A},
year={2019}
}
• Published 14 August 2017
• Mathematics
• Discrete & Continuous Dynamical Systems - A
For a closed, strictly convex projective manifold of dimension $n\geq 3$ that admits a hyperbolic structure, we show that the ratio of Hilbert volume to hyperbolic volume is bounded below by a constant that depends only on dimension. We also show that for such spaces, if topological entropy of the geodesic flow goes to zero, the volume must go to infinity. These results follow from adapting Besson--Courtois--Gallot's entropy rigidity result to Hilbert geometries.
7 Citations
Entropy rigidity for finite volume strictly convex projective manifolds
• Mathematics
• 2020
We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions $\geq 3$, generalizing the work of arXiv:1708.03983 to the finite volume setting. The rigidity theorem
Sinai-Ruelle-Bowen measure Entropy of geodesic flow on Convex Projective Surfaces I
. We study the entropy of Sinai-Ruelle-Bowen measure of the geodesic flow on convex real projective surfaces, and shows that the Hilbert area tends to infinity if the entropy tends to zero. For the
Entropy rigidity for 3D conservative Anosov flows and dispersing billiards
• Mathematics
• 2020
Given an integer $k \geq 5$, and a $C^k$ Anosov flow $\Phi$ on some compact connected $3$-manifold preserving a smooth volume, we show that the measure of maximal entropy (MME) is the volume measure
Entropy rigidity for foliations by strictly convex projective manifolds
Let $N$ be a compact manifold with a foliation $\mathscr{F}_N$ whose leaves are compact strictly convex projective manifolds. Let $M$ be a compact manifold with a foliation $\mathscr{F}_M$ whose
Equivariant maps for measurable cocycles of higher rank lattices
Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Denote by $h(\mathcal{X}_G)$ the volume entropy of $\mathcal{X}_G$. Let
Equivariant maps for measurable cocycles with values into higher rank Lie groups
• A. Savini
• Mathematics
Pacific Journal of Mathematics
• 2021
Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Suppose $\mathcal{X}_G$ has dimension $n$ and it has no factor isometric
NATURAL MAPS FOR MEASURABLE COCYCLES OF COMPACT HYPERBOLIC MANIFOLDS
• A. Savini
• Mathematics
Journal of the Institute of Mathematics of Jussieu
• 2021
## References
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Entropies of compact strictly convex projective manifolds
Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its
The Degree Theorem in Higher Rank
• Mathematics
• 2001
Let N be any closed, Riemannian manifold. In this paper we prove that, for most locally symmetric, nonpositively curved Riemannian manifolds M , and for every continuous map f : N → M , the map f is
Minimal Entropy Rigidity for Lattices in Products of Rank One Symmetric Spaces
• Mathematics
• 2001
where B(x,R) is the ball of radius R around a fixed point x in the universal cover X. (For noncompact M , see Section 6.2.) The number h(g) is independent of the choice of x, and equals the
Entropy of the geodesic flow for metric spaces and Bruhat-Tits buildings
Let ðX ; dX Þ be a geodesically complete Hadamard space endowed with a Borel- measure m. Assume that there exists a group G of isometries of X which acts totally discontin- uously and cocompactly on
Flexing closed hyperbolic manifolds.
• Mathematics
• 2007
We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the
Ergodicity of Bowen–Margulis measure for the Benoist 3-manifolds
We study the geodesic flow of a class of 3-manifolds introduced by Benoist which have some hyperbolicity but are non-Riemannian, not CAT(0), and with non-C^1 geodesic flow. The geometries are
From Funk to Hilbert Geometry
• Mathematics
• 2014
We survey some basic geometric properties of the Funk metric of a convex set in R n . In particular, we study its geodesics, its topology, its metric balls, its convexity properties, its
Entropy and closed geodesies
• A. Katok
• Mathematics
Ergodic Theory and Dynamical Systems
• 1982
Abstract We study asymptotic growth of closed geodesies for various Riemannian metrics on a compact manifold which carries a metric of negative sectional curvature. Our approach makes use of both
On the Hilbert geometry of simplicial Tits sets
The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case,
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# Returning random number and save for later use [closed]
I found a lot of solutions on random number generation and saving, but none of those fit my need or helps me to solve my problem.
I'm trying to generate a random number in Calc and want to save this number for use later and be able to generate another number to use again. What i get is that it or generates a number, but it is not usable because if i want to generate a new number it changes the number i used too. I have some experience with VBA in excel, but i'm having difficulties to get an understanding on the programming in libre.
So now what i would like to do. I have a sheet (sheet1) on this sheet i have a command button that i want to use to generate a number. This number has to be added to a table in sheet 2 each time i click the button on shhet1. The number should not be changed on sheet2 when i click the button on sheet 1 i only want to add it for later use. Is this possible to achieve or am i asking too much here?
anyone that can help me out here?
edit retag reopen merge delete
### Closed for the following reason the question is answered, right answer was accepted by Alex Kemp close date 2016-03-04 19:11:32.809576
Sort by » oldest newest most voted
Thank you for Your help, but this is what i had found out myself. The problem is that i can't "Lock" the rest for recalculating. If i change the value to Yes in Your example it recalculates all the values. I would like to create a kind of "Lock" for recalculating values once they are randomly chosen so they wont change at the next random Choice.
I have a sheet (sheet1) on this sheet i have a cell that i want to use to generate a number. This number has to be added to a table in sheet 2 each time i change the value of a cell on sheet1. The number i generated earlier should not be changed on sheet2 when i retrieve a number on sheet1 i only want to add it for later use.
Something like (A10) means cell A10 in the spreadsheet:
(A10) Generate New number --> (B10) Y --> (C10) here you show the generated number <--If B10 is "Y" then generate new value for C10 else keep this number. But if B10 is "No" then only change C10 and not C11 etc.
(A11) Generate New number --> (B11) Y --> (C11) here you show the generated number <--If B11 is "Y" then generate new value for C11 else keep this number. But if B11 is "No" then only change C11 and not C10 etc.
I can't upload a file unfortunately.
more
Now you should be allowd to upload a file.
( 2014-10-06 17:58:18 +0100 )edit
Tried to get this to work as i want, but unfortunately it recalculates the values every time i type something in my sheet. In Excel i can turn of the function and use F9. But i would like to be able to Lock the recalculation of the random numbers, but still automatically calculate the other cells. Can i Lock the calculation from being executed by something like an IF function (se my 2nd. post)?
( 2014-10-07 14:52:42 +0100 )edit
Command buttons aren't my preferred toy. But keeping a set of random numbers for a while and recalculating them "on command" I needed sometimes. Just look into the attached example to see if the approach there is something for you.
Editing (in reply to the answer posted by the questioner himself): I won't recommend it, but you may have a look into an adapted version of a study I made some time ago. See attached, please. Sorry! Due to my mistake you first got a defective version of the example. the new version should work as intended.
StudyCountChangeWatch002Special.ods
Of course programming a Sub, assign it to a PushButton, ... is also possible. The disadvantages of Calc documents containing user defined programing should be taken in account.
If urgently wanted a solution by 'CommandButton', see next attachment. It will need a finish!
The Sub
Sub GenerateRandomNumberCountAndPut()
Dim oDoc As Object
Dim oSheet As Object
Dim oCell1, oCell2,oCell3 as Object
oDoc = ThisComponent
oSheet = oDoc.Sheets.GetByName("Sheet1")
oCell1 = oSheet.GetCellByPosition(0,0)
oCell2 = oSheet.GetCellByPosition(1,0)
oCell1.Value = Rnd()
If oCell2.Value <= 0 Then oCell2.Value = 0
oCell2.Value = oCell2.Value+1
oCell3 = oSheet.GetCellByPosition(4,oCell2.Value-1)
oCell3.Value = oCell1.Value
End Sub
is assigned to the event 'Mouse button released' of the PushButton.
more
Thank you for this one. I think i will be able to use thisone to fit my needs.
( 2014-10-06 14:25:29 +0100 )edit
Tried to get this to work as i want, but unfortunately it recalculates the values every time i type something in my sheet. In Excel i can turn of the function and use F9. But i would like to be able to Lock the recalculation of the random numbers, but still automatically calculate the other cells. Can i Lock the calculation from being executed by something like an IF function (se my 2nd. post)?
( 2014-10-07 16:58:59 +0100 )edit
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## TrueType- and Type1-Fonts in Texlive/Xetex
Font-Management in TeX is a huge mess. It’s such a mess that there is not even one coherent tutorial on how to install fonts exists, and nobody ever automated it. Imagine: You put your TrueType or Type1 fonts somewhere into /usr/share/fonts, your system regenerates its font-cache, and they not only are available for KDE, Gnome, Mozilla and OpenOffice, but also for TeX? You wish. Instead you’re expected to produce custom font-encoding files by hand, extract font-metric-files (tfm) out of TrueType-files, invent 6-letter font-shortcut-names, and edit some other files in order that TeX can find them with these shortcut-names. In other words, the whole thing should be burned at the stake, shredded, buried and shot into outer space.
The only thing that actually works out of the Box is XeTeX/XeLaTeX:
apt-get install texlive-xetex
Now you need to know the correct name of the font you want to use, as reported by fc-list:
$fc-list | grep Bastarda MA Bastarda1 15th:style=Normal And you can use this in TeX-documents: \documentclass{article} \usepackage{fontspec,xunicode,xltxtra} \setmainfont{MA Bastarda1 15th} \begin{document} Test. Umlauts need to be UTF-8 encoded: ÀöÌ \end{document} If your TeX-document happens to use latin1 instead of utf8, recode will help: recode latin1..utf8 whetever.tex Now you need to use xelatex instead of texi2pdf or pdflatex to produce a pdf-file: $ xelatex whatever.tex
That’s it, and that’s how it should bloody work everywhere, with every TeX-util of the day you might want to use.
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# Tag Info
Your confusion should be removed away when you consider the fact that the following signals are the same : $$u[n] - u[n-3] ~ = ~ \delta[n] + \delta[n-1] + \delta[n-2]$$ or generalizing for any integer $M$: $$u[n] - u[n-M] = \delta[n] + \delta[n-1] +...+ \delta[n-M+1] = \sum_{k=0}^{M-1} \delta[n-k]$$ or even further for $K < M$ u[n-K] - u[n-M] = ...
Taking Equation $2.74$ from Example $3$ and setting $M_1=0$ gives: $h[n] = \frac{1}{M_2+1} \sum_{k=0}^{M_2} \delta[n-k]$ Now lets take a closer look at this: $h[n]$ is non-zero only for certain values of $n$. Its a good a starting point as any, so lets look at $n=0$. We have: \$ h[0] = \frac{1}{M_2+1} \bigg( \delta[0] + \delta[-1] + ... + \delta[-M_2] \...
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# Integrated Rate Equations
1. Zero order reactions:
Order of the reaction is zero.
The reaction in which the rate of reaction is independent of concentration of the reactants.
Rate of reaction remains constant during the course of reaction.
No concentration term in the rate law.
A → Products
Initially t = 0 a 0
t = t₁ a – x x
$$\frac{-d{{C}_{R}}}{dt}=\frac{-d\left[ A \right]}{dt}=\frac{-d\left[ a-x \right]}{dt}=k{{\left( a-x \right)}^{0}}=\frac{dx}{dt}$$
dx/ dt = k
dx = k dt
x = kt + c
When t = 0 x = 0 C= 0
∴ x = kt
t = t½
x = a/2
a/2 = kt½
t½ = (a/2) k
a. Graph for x = kt
b. Graph for t½ = a/2K
c. [A₀] – [A] = kt
[A₀] = initial concentration, t = 0
[A]t = concentration, t = t
[A₀] – [A]t = Kt
+ [A]t = -Kt + [A₀]
Half-life of reaction: The time required for the completion of 50% of the reaction is called half-life of the reaction.
Units of rate constant: n A → Products
Rate law is R = K [Conc]n
K = Rate/ (Concentration)n
= mole¹¯ⁿ literⁿ¯¹ sec¯¹
Where n is order of reaction
2. First order reaction: The reaction in which the rate of R x n depends only on one concentration is doubled. Rate of reaction will also be doubled.
Equations: A → Products
t = 0 a mole/lit 0
t = t a – x x
Rate = K [A]¹
Rate = – dCR/dt = d [A]/dt = + K [A]
– d (a – x)/ dt = – K (a – x)
dx/ dt = K (a – x)
∫dx/ (a – x) = ∫ Kdt
– log (a – x) = Kt + c
When t = 0, x = 0
– log a = c
– log (a – x) = Kt – log a
Kt = 2030 log (a/a – x)
a = is initial concentration
x = is dissociated concentration.
log (a – x) = – Kt/2.303 + log a
And also
m (a/a-x) = Kt
a/(a – x) = eKt (a – x)/a = e¯Kt
x = a (1 – e¯Kt)
Half-life of first order Reaction:
log (a/a-x) = Kt/2.303
t = 2.303/K log (a/a-x)
t = t½ x = a/2
K = (2.303/ t½) log2 = 0.693/ t½
t½ = 0.693/K [It is independent of initial concentration]
For the first order reaction.
$$M\xrightarrow{1{{t}_{1/2}}}\frac{M}{2}\xrightarrow{2{{t}_{1/2}}}\frac{M}{4}\xrightarrow{3{{t}_{1/2}}}\frac{M}{8}$$
Amount of reaction left after time t = Initial Amount/ 2ⁿ
η = t/t½ = Number of half – lifes
3. nth Order Reaction: A → Products
Rate law is (dn/dt) = K [A]ⁿ = K (a – x)ⁿ
$${{K}_{\eta }}=\frac{1}{\left( n-1 \right)t}\left[ \frac{1}{{{\left( a-x \right)}^{n-1}}}-\frac{1}{{{a}^{n-1}}} \right]$$
Time T is required to complete a particular fraction of reaction.
T α (a)¹¯ⁿ
If concentration is changed m times new rate will be mⁿ
Half-life of nth order reaction:
t½ α 1/aⁿ¯¹
a is initial concentration
η is order of Reaction
Half-life of nth order reaction
$$t\frac{1}{2}=\frac{{{2}^{n-1}}-1}{K\left( n-1 \right){{a}^{n-1}}}$$
$$\frac{{{\left( t\frac{1}{2} \right)}_{1}}}{{{\left( t\frac{1}{2} \right)}_{2}}}={{\left( \frac{{{a}_{2}}}{{{a}_{1}}} \right)}^{n-1}}$$
Reaction Order Differential Rate Law Integrated Rate Law Characteristics Kinetic Plot Slope of Kinetic Plot Units of Rate Constant Zero – d[A]/dt = K [A] = [A]₀ – Kt [A] vs t – K Mole L¯¹ sec¯¹ First – d[A]/dt = K[A] [A] = [A]₀ e-Kt ln [A] vs t – K sec¯¹ Second – d[A]/dt = K[A]² [A] = [A]₀/1 + Kt[A]₀ 1/[A] vs t K L Mole sec¯¹
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# Track transition curves
For passengers in a car or train, traveling in a straight line at constant speed is the most comfortable motion, as there is no acceleration. Roads or rail lines with only straight lines are rather limiting, however, so we frequently encounter curves, in the most extreme form in large freeway interchanges such as shown below.
When designing a freeway interchange, one of the most basic questions just what shape the transition curves between the straight-line roads should have. Other considerations then follow, such as stacking the roads above each other and banking the angle of the roads.
The difficultly in designing curves in roads arises from the need to have a smooth ride for the passengers in the vehicles as they traverse the curves at high speed. In particular, we do not want to have sudden changes in acceleration for the passengers.
Aerial view of the High Five multi-level stack interchange between I-635 and US 75 in Dallas, Texas, taken with a camera suspended from a kite line. Image source: Fotopedia image, from the flikr image by Jett Attaway (CC BY 2.0) (full-sized image).
## Circular arcs for transition curves
To understand the issues with transition curve design, we will consider a simple oval track with two straight segments joined by curves at both ends. The simplest curve shapes are semi-circles (half-circles), as shown below.
Car driving at constant speed around a track with straight line segments joined to perfect semi-circle ends. The graph at the bottom shows the acceleration magnitude versus time. Note the sudden jump in acceleration magnitude when the car switches from a straight line to the curve.
If we the car driving around the track with semi-circle ends, then we see that there is zero acceleration on the straight segments, but on the semi-circular transition curves the acceleration is inwards with magnitude $v^2 / \rho$, where $\rho$ is the radius of curvature. A passenger would thus feel no acceleration on the straight segments, but then would suddenly feel a large sideways acceleration as the vehicle switches to the semi-circles, which would be very uncomfortable and potentially dangerous.
For passenger comfort, we do not want rapid changes in acceleration for transition curves. That is, we want a low value for the derivative of acceleration with respect to time. The derivative of acceleration is known as jerk, defined by $\vec{\jmath} = \dot{\vec{a}}$ (for vectors) or $j = \dot{a}$ (for scalars). With perfect semi-circular ends we see that the jerk is mathematically infinite at the transition to the curve, although in reality it would just be a very high value as the vehicle would not transition to the semi-circle instantaneously.
While the terms velocity and acceleration are standard for the 1st and 2nd derivatives of position, the names for higher derivatives are not so well-established. While jerk is often used for the derivative of acceleration (so the 3rd derivative of position), the terms jolt, surge, and lurch are also sometimes encountered for this quantity. The derivative of jerk is sometimes called jounce (so it is the 4th derivative of position). Another suggestion is to refer to the 4th, 5th, and 6th derivatives of position as snap, crackle, and pop, respectively.
Jerk and snap have many applications in engineering and science. For example, jerk and snap have both been used to measure human movement smoothness and diagnose stroke patients (Rohrer et al., 2002) while minimizing snap is often used as a design principle for quadcopter control schemes (Mellinger and Kumar, 2011).
Changing accelerations (causing jerk) must result from changing forces, due to Newton's second law. Although the terminology is also somewhat loose in this case, the derivative of force with respect to time is often referred to as yank, and the derivative of yank is called tug (the second derivative of force). Third derivatives and higher of force are very rarely encountered, and do not seem to have any names in common usage.
### References
• D. Mellinger and V. Kumar, Minimum snap trajectory generation and control for quadrotors, in 2011 IEEE International Conference on Robotics and Automation (ICRA), 2520–2525, 2011. DOI: 10.1109/ICRA.2011.5980409
• B. Rohrer, S. Fasoli, H. I. Krebs, R. Hughes, B. Volpe, W. R. Frontera, J. Stein, and N. Hogan, Movement Smoothness Changes during Stroke Recovery, The Journal of Neuroscience, 22(18): 8297–8304, 2002. Link.
## Smooth transition curves with Euler spirals
Unlike the sudden switch shown above from a straight line segment (no curvature) to a curved transition curve, we would prefer to have a more gradual transition. An example of this is shown below with the right-hand transition curves changed to use Euler spiral segments, which start curving gradually and then increase the curvature the further the vehicle moves around the curve, before reversing the process on the second half of the curve. Euler spirals are one of the common types of track transition curves and are special because the curvature varies linearly along the curve.
Car driving at constant speed around a track with perfect straight line segments joined to Euler-spiral segments on the right-hand curve and a semi-circle on the left-hand curve. The red curve is a perfect semi-circle for comparison. Note the continuous transition in acceleration when the car switches from a straight line to the left-hand curve.
If we the motion around the track with Euler spiral transitions, then we can see from the acceleration magnitude plot that the acceleration does not suddenly jump as the vehicle moves around the right-hand curve. Instead it steadily increases to a maximum value, before decreasing again to zero. The peak acceleration needed on the Euler spiral transitions is somewhat higher than on the semi-circle transitions, but we have avoided the sudden jerk associated with switching from straight line to circular motion.
The equation for a spiral with linear curvature variation was first derived by the Swiss mathematician Leonard Euler in 1744, hence the name Euler spiral for this curve. The spiral was then independently rediscovered in the late 1800s by civil engineers who were unaware of Euler's work and who named the resulting spiral the clothoid, which is still a commonly used name in traffic engineering. This spiral also arises in the study of near-field diffraction in optics, as developed by the French engineer Augustin-Jean Fresnel and the French physicist Alfred Cornu, for which reason the spiral is also sometimes called the Cornu spiral.
## Euler spiral equation
An Euler spiral is a curve for which the acceleration magnitude increases at a constant rate as we travel along the curve at uniform velocity. Another way to say this is that the curvature is a linear function of the distance along the curve. To see that this is the same thing, we write the acceleration in a tangential/normal basis as $\vec{a} = \ddot{s} \, \hat{e}_t + \kappa v^2 \, \hat{e}_n.$ For constant-speed motion with speed $v$, the distance along the curve satisfies $\dot{s} = v = \text{constant}$, so $\ddot{s} = 0$. The acceleration vector thus only has a normal component, and this has magnitude proportional to the curvature $\kappa = 1/\rho$, where $\rho$ is the radius of curvature. To have the acceleration increasing linearly along the curve, we thus want the curvature to be a linear function of distance, so $\kappa = \alpha s$ for some constant $\alpha$.
While specifying that $\kappa = \alpha s$ is enough to define the shape of the Euler spiral curve, finding the explicit equation for the curve is not so easy. We first introduce the functions $C(z)$ and $S(z)$, known as Fresnel integrals and defined by:
Fresnel integrals
\begin{aligned} C(z) &= \int_0^z \cos\Big(\frac{1}{2} \pi u^2\Big) du \\ S(z) &= \int_0^z \sin\Big(\frac{1}{2} \pi u^2\Big) du \end{aligned}
The Fresnel integrals do not have any simpler forms in terms of elementary functions, as the integrals in them cannot be computed in closed form.
Now we define the constant $\ell = \sqrt{\pi/\alpha}$, and then the position at distance $s$ along an Euler spiral curve is:
Euler spiral
$\vec{r} = \ell C(s / \ell) \, \hat{\imath} + \ell S(s / \ell) \, \hat{\jmath}$
We start the spiral curve from the origin, initially moving horizontally to the right and curving upwards with constant speed $v$. Using a tangential/normal basis, let $\theta$ be the angle of $\hat{e}_t$ as shown. Then $\dot{\theta}$ can be found by considering two expressions for the acceleration. First, from the tangential/normal acceleration formula we have $\vec{a} = \ddot{s} \, \hat{e}_t + \kappa v^2 \, \hat{e}_n = \alpha s v^2 \, \hat{e}_n,$ where we used the fact that $\ddot{s} = \dot{v} = 0$ (constant speed) and that $\kappa = \alpha s$ for some constant $\alpha$ (the definition of the Euler spiral is that curvature is a linear function of distance $s$).
The second expression for acceleration uses the angular velocity $\vec{\omega} = \dot\theta \, \hat{k}$ of the tangential/normal basis vectors. Recalling that $\vec{v} = v \, \hat{e}_t$ and $v$ is constant, we have \begin{aligned} \vec{a} = \dot{\vec{v}} = v \, \dot{\hat{e}}_t = v \, \vec{\omega} \times \vec{e}_t = v \dot{\theta} \, \hat{e}_n. \end{aligned}
Comparing the two expressions for $\vec{a}$ and using $s = vt$ we see that $\dot{\theta} = \alpha s v = \alpha v^2 t$ and we can integrate this (with the initial condition that $\theta$ starts at zero) to give $\theta = \frac{1}{2} \alpha v^2 t^2.$
To find the equation for $\vec{r}$ we can integrate the equation $\dot{\vec{r}} = v \, \hat{e}_t = v \cos\theta \, \hat{\imath} + v \sin\theta \, \hat{\jmath}$ starting from $\vec{r} = 0$ to obtain \begin{aligned} \vec{r} &= \int_0^t \left(v \cos\Big(\frac{1}{2} \alpha v^2 \tau^2\Big) \, \hat{\imath} + v \sin\Big(\frac{1}{2} \alpha v^2 \tau^2 \Big) \, \hat{\jmath}\right) d\tau \\ &= \ell \int_0^{s/\ell} \left( \cos\Big(\frac{1}{2} \pi u^2\Big) \, \hat{\imath} + \sin\Big(\frac{1}{2} \pi u^2\Big) \, \hat{\jmath} \right) du, \end{aligned} where we made the substitution $\tau = \ell u / v$ with $\ell = \sqrt{\pi/\alpha}$. Using the definitions of the Fresnel integrals now gives the desired expression.
Plotting the Euler spiral equation gives the curve below, which starts out at the origin with zero curvature, and the then has steadily increasing curvature as we move along it.
Euler spiral shape defined by the equation above. Changing the value of $\alpha$ or $\ell$ simply scales the whole curve to make it bigger or smaller, without changing the shape.
The full Euler spiral is unsuitable for track transitions, as the curvature increases without limit. Instead, we can piece together short segments of the Euler spiral to form our transition curve. For example, the right-hand curve in the smooth track above is composed of two copies of the first quarter-turn of the Euler spiral, with one copy flipped upside down. This means the curvature starts at zero, increases linearly to a maximum halfway around the curve, then decreases linearly again back to zero to join the straight segment.
The Fresnel integrals $C(x)$ and $S(x)$ are examples of special functions. The term special function does not have a precise mathematical definition. Instead, these are functions which arise frequently in applications and which have been extensively analyzed and documented. The classic reference for many special functions is the book known generally as Abramowitz and Stegun. This refers to the publication:
Abramowitz, Milton and Stegun, Irene A. (editors) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1972, ISBN 978-0-486-6.
While the tables of special function values in Abramowitz and Stegun are no longer generally needed due to the advent of computers, there is still much useful information in the book. This useful information is now also available in the online successor Digital Library of Mathematical Functions (DLMF) from the National Institute of Standards and Technology (NIST). For example, Chapter 7 of the DLMF includes the the definition of the Fresnel integrals as well as plots of the functions and series expansions for them.
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# Lesson 16
Representing Contexts with Equations
Let’s write equations that represent situations.
### 16.1: Don't Solve It
Is the solution positive or negative?
$$(\text-8.7)(1.4) = a$$
$$\text- 8.7b = 1.4$$
$$\text-8.7 + c = \text- 1.4$$
$$\text-8.7 - d = \text- 1.4$$
### 16.2: Warmer or Colder than Before?
For each situation,
• Find two equations that could represent the situation from the bank of equations. (Some equations will not be used.)
• Explain what the variable $$v$$ represents in the situation.
• Determine the value of the variable that makes the equation true, and explain your reasoning.
Bank of equations:
$$\text-3v=9$$ $$v = \text-16 + 6$$ $$v = \frac13 \boldcdot (\text-6)$$ $$v+12=4$$ $$\text-4\boldcdot 3=v$$ $$v = 4 + (\text-12)$$ $$v = \text-16 - (6)$$ $$v=9+3$$ $$\text-4 \boldcdot \text-3 = v$$ $$\text-3v = \text-6$$ $$\text-6 + v = \text-16$$ $$\text-4 = \frac13v$$ $$v=\text-\frac13 \boldcdot 9$$ $$v = \text-\frac13 \boldcdot (\text-6)$$ $$v = 4 + 12$$
1. Between 6 a.m. and noon, the temperature rose 12 degrees Fahrenheit to 4 degrees Fahrenheit.
2. At midnight the temperature was -6 degrees. By 4 a.m. the temperature had fallen to -16 degrees.
3. The temperature is 0 degrees at midnight and dropping 3 degrees per hour. The temperature is -6 degrees at a certain time.
4. The temperature is 0 degrees at midnight and dropping 3 degrees per hour. The temperature is 9 degrees at a certain time.
5. The temperature at 9 p.m. is one third the temperature at midnight.
You may use this applet if you find it helpful.
### 16.3: Animals Changing Altitudes
1. Match each situation with a diagram.
1. A penguin is standing 3 feet above sea level and then dives down 10 feet. What is its depth?
2. A dolphin is swimming 3 feet below sea level and then jumps up 10 feet. What is its height at the top of the jump?
3. A sea turtle is swimming 3 feet below sea level and then dives down 10 feet. What is its depth?
4. An eagle is flying 10 feet above sea level and then dives down to 3 feet above sea level. What was its change in altitude?
5. A pelican is flying 10 feet above sea level and then dives down reaching 3 feet below sea level. What was its change in altitude?
6. A shark is swimming 10 feet below sea level and then swims up reaching 3 feet below sea level. What was its change in depth?
2. Next, write an equation to represent each animal's situation and answer the question. Be prepared to explain your reasoning.
Diagrams
A
B
C
D
E
F
### 16.4: Equations Tell a Story
• An equation that represents your situation
• What your variable and each term in the equation represent
• How the operations in the equation represent the relationships in the story
• How you use inverses to solve for the unknown quantity
• The solution to your equation
1. As a $$7\frac14$$ inch candle burns down, its height decreases $$\frac34$$ inch each hour. How many hours does it take for the candle to burn completely?
2. On Monday $$\frac19$$ of the enrolled students in a school were absent. There were 4,512 students present. How many students are enrolled at the school?
3. A hiker begins at sea level and descends 25 feet every minute. How long will it take to get to an elevation of -750 feet?
4. Jada practices the violin for the same amount of time every day. On Tuesday she practices for 35 minutes. How much does Jada practice in a week?
5. The temperature has been dropping $$2\frac12$$ degrees every hour and the current temperature is $$\text-15 ^\circ\text{F}$$. How many hours ago was the temperature $$0^\circ\text{F}$$?
6. The population of a school increased by 12%, and now the population is 476. What was the population before the increase?
7. During a 5% off sale, Diego pays $74.10 for a new hockey stick. What was the original price? 8. A store buys sweaters for$8 and sells them for $26. How many sweaters does the store need to sell to make a profit of$990?
Diego and Elena are 2 miles apart and begin walking towards each other. Diego walks at a rate of 3.7 miles per hour and Elena walks 4.3 miles per hour. While they are walking, Elena's dog runs back and forth between the two of them, at a rate of 6 miles per hour. Assuming the dog does not lose any time in turning around, how far has the dog run by the time Diego and Elena reach each other?
### Summary
We can use variables and equations involving signed numbers to represent a story or answer questions about a situation.
For example, if the temperature is $$\text-3^\circ\text{C}$$ and then falls to $$\text-17^\circ\text{C}$$, we can let $$x$$ represent the temperature change and write the equation:
$$\displaystyle \text-3 + x = \text- 17$$
We can solve the equation by adding 3 to each side. Since $$\text-17 + 3 = \text-14$$, the change is $$\text-14^\circ\text{C}$$.
Here is another example: if a starfish is descending by $$\frac32$$ feet every hour then we can solve $$\displaystyle \text-\frac32h=\text-6$$ to find out how many hours $$h$$ it takes the starfish to go down 6 feet.
We can solve this equation by multiplying each side by $$\text-\frac23$$. Since $$\text-\frac23\boldcdot \text-6 = 4$$, we know it will take the starfish 4 hours to descend 6 feet.
### Glossary Entries
• variable
A variable is a letter that represents a number. You can choose different numbers for the value of the variable.
For example, in the expression $$10-x$$, the variable is $$x$$. If the value of $$x$$ is 3, then $$10-x=7$$, because $$10-3=7$$. If the value of $$x$$ is 6, then $$10-x=4$$, because $$10-6=4$$.
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• anonymous
a hard one(show me step to step solution) evaluate the definite integral by making a u substitution and integrating from u(a) to u(b) integral 0 to pi/2, cosx/(4+4sinx)^3dx
MIT 18.01 Single Variable Calculus (OCW)
Looking for something else?
Not the answer you are looking for? Search for more explanations.
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## lyssa Group Title What are the solution intervals for |2x – 1| + 6 > 9? 2 years ago 2 years ago
1. lyssa Group Title
I need help just figuring it out
2. zepp Group Title
Like @asnaseer did, simplify this inequality. $$|2x-1|+6-6>9-6\\|2x-1|>3$$ And now you may proceed to setting up two inequations.
3. zepp Group Title
Do you know how to set up those inequations?
4. lyssa Group Title
2x-1>3 2x>4 x>2 -2x-1<-3 -2x<-2 x>1 Are these right?
5. zepp Group Title
Excellent! :)
6. lyssa Group Title
but here is the choices A.x < –1 or x > 2 B.x < 1 or x > –2 C.x > –1 and x < 2 D.x > 1 and x < –2
7. zepp Group Title
Although the negative one is wrong -------------------- $$2x-1<-3\\2x<-2\\x<\frac{-2}{2}\\x<-1$$
8. lyssa Group Title
So it is A?
9. zepp Group Title
Since the absolute value of $$2x-1$$ must be greater than 3, $$2x-1$$ could be in the negative side too, -4,-5,-6,-7 and so on, because when you take the absolute value of these, you get something greater than 3.
10. zepp Group Title
Yes.
11. lyssa Group Title
Thanks sooo much:D I have more questions maybe you could help with them too:D
12. zepp Group Title
Sure :)
13. lyssa Group Title
K i will post them as a new question:D
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# Quark Matter 2017
Feb 5 – 11, 2017
Hyatt Regency Chicago
America/Chicago timezone
## Direct photon measurements in pp and Pb-Pb collisions with ALICE
Feb 7, 2017, 10:40 AM
20m
Regency C
### Regency C
Oral Electromagnetic Probes
### Speaker
Marie Germain (Subatech, IN2P3-CNRS (FR))
### Description
Direct photon measurement in heavy-ion collisions provides a valuable set of observables to study the hot QCD medium since these photons are
produced at different stages of the collision and escape the medium unaffected. In pp collisions,
the direct photon yield at high transverse momentum ($p_T$) are produced in hard scattering (prompt photons),
but also in the fragmentation of high $p_T$ partons. Their measurement provides a direct test of pQCD and can constrain the parton distribution functions.
The access to the prompt photon production can be achieved experimentally with isolation techniques.
In heavy-ion collisions, the high $p_T$ component provides information on the initial parton dynamics and nuclear parton densities in nuclei, whereas
the low momentum component (below $p_T <$5 GeV/c) of the direct photon production is dominated by thermal radiation from the hot and dense matter created,
carrying information on its space-time evolution, collective flow and temperature.
In this talk, we will present ALICE results of direct photon production in pp reactions at $\sqrt{s}$=7 TeV using isolation techniques.
The measurement of the direct photon flow in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV will also be presented.
The results will be discussed and compared to theoretical predictions and earlier measurements.
Preferred Track Electromagnetic Probes ALICE
### Primary author
Marie Germain (Subatech, IN2P3-CNRS (FR))
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## $L^2$ functions with compactly supported fourier transforms form a Hilbert space
Given a fixed compact subset of $$\mathbb{R}$$, I want to show that square integrable functions on the real line whose fourier transforms are supported in the given compact set form a Hilbert space in the $$L^2$$ norm. It was easy to show that the functions form a subspace. However I am stuck at the closedness of the subspace. Could anyone please help me?
## Broken Usage of Laplace Transforms
Let $$\mathcal{L}$$ be the Laplace transform function, and let $$\mathcal{L}\bigl(f(t)\bigr) = F(s)$$.
One of the properties of the Laplace transform is that $$\mathcal{L}\Bigl((-t)^nf(t)\Bigr) = F^{(n)}(s)$$, i.e., the $$n$$-th derivative of the transform with respect to $$s$$. I was testing this property out a bit.
Given $$ty’+y=0$$, find $$y(t)$$. The solution is very obvious when you use integrating factors: $$(ty)’=0$$ $$y=\frac{C}t$$
Now, let’s try solving this differential equation using a Laplace transform!
$$\mathcal{L}\bigl(ty’+y\bigr)=0 \tag{1}\label{1}$$
The transform of $$f(t)=y’$$ is $$sF(s)-f_0$$, so then… $$\mathcal{L}\big(ty’\big) = -\frac{d\left(sF(s)-f_0\right)}{ds}=-sF'(s)-F(s) \tag{2}$$
Returning back to $$(1)$$, we now have $$-sF'(s)-F(s)+F(s)=0$$
which in turn simplifies to $$F'(s)=0$$ so $$F(s)=C$$ and $$f(t)=C\cdot\delta(t)$$
Can someone explain to me why what I did in $$(2)$$ isn’t necessarily correct, because that’s the step I’m iffy on right now. Thank you!
## Solve using Laplace transforms
I want to solve the PDE
$$x\frac{\partial u}{\partial t} +\frac{\partial u}{\partial x}=x$$ $$u(x,0)=0, x>0$$ $$u(0,t)=0, t>0$$ for $$x>0,t>0$$ using a Laplace transform in t.
I Laplace transform the equation and get $$xs\hat{u}(x,s)+\frac{\partial}{\partial x}\hat{u}(x,s)=\frac{x}{s}$$ where $$\hat{u}(x,s)=L(u(x,t))=\int_{t=0}^{\infty} e^{-st}u(x,t)dt$$.
Solving this ODE, I obtain $$\hat{u}(x,s)=\frac{1}{s^2} + A(s)e^{\frac{-sx^2}{2}}.$$ I then apply the second boundary condition to get $$\hat{u}(x,s)=\frac{1}{s^2}-\frac{1}{s^2}e^{\frac{-sx^2}{2}}.$$ Now I need to inverse transform to get $$u(x,t)$$. I know that $$L^{-1}(\frac{1}{s^2})=t$$ but I don’t know how to find $$L^{-1}(\frac{1}{s^2}e^{\frac{-sx^2}{2}}).$$
## Pushing Cuckoo Eggs under Inverse Radon Transforms
Essentially the inverse of the Radon transforms $$Rf(L)=\int_L{f(x)|dx|}$$ has the ability to reconstruct $$f(x)$$ from the integrals over all lines; or, expressed differently to (re)construct $$f(x)$$ from a functional, that maps lines to real values.
Essentially this question is aimed at cuckoo eggs the inverse Radon transform will hatch if pushed under it:
Question:
what are examples of other functionals, that map lines to real values, to which the inverse Radon transform can be applied beneficially?
I am especially interested in examples that have been mentioned in publications. Two examples of such line functionals that would be possible candidates, are
• mapping lines to the geodesic distance between the pair of points, in which they intersect the boundary of a compact, convex subset of $$\mathbb{R}^n$$ (lines that miss the boundary or are tangent to it are mapped to $$0$$)
• mapping lines to their moments of inertia w.r.t. the model of a compact physical object; lines missing a sufficiently small compact containing volume will be mapped to $$0$$
## Bing Transforms can only be used with paid versions of Maltego
I was learning about how to do social engineering then i was found some tool called maltego i wanted to play around with it but when i make website transform it says
Bing Transforms can only be used with paid versions of Maltego
I wanted to know how can I use them with free version because the course I am following didn’t tell me about this. The course I am following is of Udemy(Zaid Sabih).
## Deconvolution using Fourier transforms
I have a 2D signal in the form of a function $$g(x_m,y_m)$$ given as
\begin{aligned} g(x_m,y_m) = \ & \int^{\infty}_{-\infty} \mathrm{d}x_o \ \mathrm{d}y_o \ \frac{1}{\varepsilon^2} P(x_o – x_m,y_o -y_m) \ & \quad \times \int^{\infty}_{-\infty} \mathrm{d}x_i \ \mathrm{d}y_i \ R(x_o – x_i,y_o -y_i)L(x_i,y_i) \end{aligned} \tag{1}
The integrals in equation $$(1)$$ can be seen as a convolution of $$P,R$$ and $$L$$ as $$g(x_m,y_m)= ((P/\varepsilon^2)*R*L)(x_m,y_m) \tag{2}$$
I want to find $$L$$ when $$g$$,$$R$$ and $$P$$ are given.
I tried to use Fourier transforms to find $$L$$ as:
$$L = \mathcal{F}^{-1} \left[ \frac{\mathcal{F}[g]}{\mathcal{F}[R] \cdot \mathcal{F}[P/\varepsilon^2]} \right]$$
R[x_, y_] := 0.609739 E^(-444.116 (-0.00244704 + x)^2 - 444.116 (-0.0322566 + y)^2) + 0.0691803 E^(-48.9858 (-0.0105298 + x)^2 - 48.9858 (0.0054951 + y)^2) + 0.66442 E^(-426.449 (0.00315949 + x)^2 - 426.449 (0.0248433 + y)^2); g[x_, y_] := 3.06909 E^(-18.585 x^2 + x (13.6144 - 27.7795 y) + (12.2542 - 18.1432 y) y) + 0.402245 E^(-7.37814 x^2 + x (9.61481 - 5.57202 y) + (6.46554 - 6.35048 y) y) + 120.468 E^(-0.0245919 x^2 + x (-0.00325668 + 0.00197362 y) + (-0.00103919 - 0.0281421 y) y) + 0.773818 E^(-3.79704 x^2 + (-15.0351 - 16.3606 y) y + x (1.75472 + 2.86666 y)) + 0.0833316 E^(-38.7396 x^2 + (-10.6949 - 14.1731 y) y + x (32.7513 + 18.7984 y)); epsilon = 0.048; P[x_, y_] := E^(-(2/epsilon)^2 (x^2 + y^2)); FTR = FourierTransform[R[x, y], {x, y}, {u, v}, FourierParameters -> {0, -2 \[Pi]}]; FTg = FourierTransform[g[x, y], {x, y}, {u, v}, FourierParameters -> {0, -2 \[Pi]}]; FTP = FourierTransform[P[x, y], {x, y}, {u, v}, FourierParameters -> {0, -2 \[Pi]}]; InverseFourierTransform[FTg/((1/epsilon^2)FTP*FTR),{u, v}, {xi, yi}, FourierParameters -> {1,-2*Pi}]
However, the InverseFourierTransform takes a lot of time and does not return any result. How do I find $$L(x_i,y_i)$$?, am I doing something wrong here?.
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mequon 10 day weather
Determine the general solution y h C 1 y(x) C 2 y(x) to a homogeneous second order differential equation: y" p(x)y' q(x)y 0 2. Non-homogeneous Equations So far, all your techniques are applicable only to homogeneous equations. Example $$\PageIndex{1}$$: Solutions to a Homogeneous System of Equations Find the nontrivial solutions to the following homogeneous system of equations $\begin{array}{c} 2x + y - z = 0 \\ x + 2y - 2z = 0 \end{array}$. We have $$y_p′(x)=2Ax+B$$ and $$y_p″(x)=2A$$, so we want to find values of $$A$$, $$B$$, and $$C$$ such that, The complementary equation is $$y″−3y′=0$$, which has the general solution $$c_1e^{3t}+c_2$$ (step 1). \end{align*}\], Applying Cramer’s rule (Equation \ref{cramer}), we have, $u′=\dfrac{\begin{array}{|lc|}0 te^t \\ \frac{e^t}{t^2} e^t+te^t \end{array}}{ \begin{array}{|lc|}e^t te^t \\ e^t e^t+te^t \end{array}} =\dfrac{0−te^t(\frac{e^t}{t^2})}{e^t(e^t+te^t)−e^tte^t}=\dfrac{−\frac{e^{2t}}{t}}{e^{2t}}=−\dfrac{1}{t} \nonumber$, $v′= \dfrac{\begin{array}{|ll|}e^t 0 \\ e^t \frac{e^t}{t^2} \end{array} }{\begin{array}{|lc|}e^t te^t \\ e^t e^t+te^t \end{array} } =\dfrac{e^t(\frac{e^t}{t^2})}{e^{2t}}=\dfrac{1}{t^2}(\text{step 2}). Then, the general solution to the nonhomogeneous equation is given by \[y(x)=c_1y_1(x)+c_2y_2(x)+y_p(x). This seems to … I So, solving the equation boils down to nding just one solution. And actually, I do see more of a connection between this type of equation and milk where all the fat is spread out, because if you think about it, the solution for all homogeneous equations, when you kind of solve the equation, they always equal 0. In this method, the obtained general term of the solution sequence has an explicit formula, which includes coefficients, initial values, and right-side terms of the solved equation only. 0. The corresponding homogeneous equation y″ − 2y′ − 3 y = 0 has characteristic equation r2 − 2 r − 3 = (r + 1)(r − 3) = 0. If the function $$r(x)$$ is a polynomial, our guess for the particular solution should be a polynomial of the same degree, and it must include all lower-order terms, regardless of whether they are present in $$r(x)$$. We now examine two techniques for this: the method of undetermined … This lecture presents a general characterization of the solutions of a non-homogeneous system. The latter can be used to characterize the general solution of the homogeneous system: it explicitly links the values of the basic variables to those of the non-basic variables that can be set arbitrarily. We can still use the method of undetermined coefficients in this case, but we have to alter our guess by multiplying it by $$x$$. 7y - 20 = 8 ⇒ y = 4 , x = 3 - 8 + 4 ⇒ x = −1. Therefore, $$y_1(t)=e^t$$ and $$y_2(t)=te^t$$. Consider the differential equation $$y″+5y′+6y=3e^{−2x}$$. However, even if $$r(x)$$ included a sine term only or a cosine term only, both terms must be present in the guess. Using a calculator, you will be able to solve differential equations of any complexity and types: homogeneous and non-homogeneous, linear or non-linear, first-order or second-and higher-order equations with separable and non-separable variables, etc. If ρ ( A) ≠ ρ ([ A | B]), then the system AX = B is inconsistent and has no solution. By the method of back substitution, we get. $$y(t)=c_1e^{−3t}+c_2e^{2t}−5 \cos 2t+ \sin 2t$$. When we take derivatives of polynomials, exponential functions, sines, and cosines, we get polynomials, exponential functions, sines, and cosines. \nonumber$, \begin{align*} y″(x)+y(x) =−c_1 \cos x−c_2 \sin x+c_1 \cos x+c_2 \sin x+x \nonumber \\ =x. \nonumber, $z2=\dfrac{\begin{array}{|ll|}a_1 r_1 \\ a_2 r_2 \end{array}}{\begin{array}{|ll|}a_1 b_1 \\ a_2 b_2 \end{array}}=\dfrac{2x^3}{−3x^4−2x}=\dfrac{−2x^2}{3x^3+2}.\nonumber$, \begin{align*} 2xz_1−3z_2 =0 \\ x^2z_1+4xz_2 =x+1 \end{align*}. \nonumber \end{align} \nonumber \], Now, let $$z(x)$$ be any solution to $$a_2(x)y''+a_1(x)y′+a_0(x)y=r(x).$$ Then, \begin{align*}a_2(x)(z−y_p)″+a_1(x)(z−y_p)′+a_0(x)(z−y_p) =(a_2(x)z″+a_1(x)z′+a_0(x)z) \nonumber \\ \;\;\;\;−(a_2(x)y_p″+a_1(x)y_p′+a_0(x)y_p) \nonumber \\ =r(x)−r(x) \nonumber \\ =0, \nonumber \end{align*} \nonumber, so $$z(x)−y_p(x)$$ is a solution to the complementary equation. I Method of variation of parameters. The above system is always satisfied by x1 = 0, x2 = 0,….,, xn = 0.This solution is called the trivial solution of (1). Just to make an example, let's say we have this equation Substituting into the differential equation, we want to find a value of $$A$$ so that, \begin{align*} x″+2x′+x =4e^{−t} \\ 2Ae^{−t}−4Ate^{−t}+At^2e^{−t}+2(2Ate^{−t}−At^2e^{−t})+At^2e^{−t} =4e^{−t} \\ 2Ae^{−t}=4e^{−t}. But when we substitute this expression into the differential equation to find a value for $$A$$,we run into a problem. Yet, there are many important real-life situations where the right-side of a a differential equation is not zero. Note that we didn’t go with constant coefficients here because everything that we’re going to do in this section doesn’t require it. A differential equation that can be written in the form . \end{align*}, So, $$4A=2$$ and $$A=1/2$$. The one in the question is not a differential equation. So when $$r(x)$$ has one of these forms, it is possible that the solution to the nonhomogeneous differential equation might take that same form. Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. Having a non-zero value for the constant c is what makes this equation non-homogeneous, and that adds a step to the process of solution. If so, multiply the guess by $$x.$$ Repeat this step until there are no terms in $$y_p(x)$$ that solve the complementary equation. So, the third row in the echelon form should be a zero row. can solve (4), then the original non-homogeneous heat equation (1) can be easily recovered. Define. Partial Differential Equations. Those are called homogeneous linear differential equations, but they mean something actually quite different. x + 2y –z =3, 7y-5z = 8, z=4, 0=0. Suppose H (x;t) is piecewise smooth. Find the general solution to the complementary equation. In this. e.g., 2x + 5y = 0 3x – 2y = 0 is a homogeneous system of linear equations whereas the system of equations given by e.g., 2x + 3y = 5 x + y = 2 is a non-homogeneous system of linear equations. Sometimes, $$r(x)$$ is not a combination of polynomials, exponentials, or sines and cosines. Use the process from the previous example. \begin{align*} a_1z_1+b_1z_2 =r_1 \\[4pt] a_2z_1+b_2z_2 =r_2 \end{align*}, has a unique solution if and only if the determinant of the coefficients is not zero. Some of the key forms of $$r(x)$$ and the associated guesses for $$y_p(x)$$ are summarized in Table $$\PageIndex{1}$$. \nonumber \], Example $$\PageIndex{1}$$: Verifying the General Solution. Even if you are able to find a solution, the B.C.s will not match up and you'll need another function to subtract off the boundary values. So the complementary solution is y c = C 1 e −t + C 2 e 3t. For example, E = m•v 2 could be or could not be the correct formula for the energy of a particle of mass m traveling at speed v, and one cannot know if h•c/λ should be divided or multiplied by 2π. Step 3: Add the answers to Steps 1 and 2. Solve the complementary equation and write down the general solution. Find the solution to the second-order non-homogeneous linear differential equation using the method of undetermined coefficients. 3. Find the particular solution y p of the non -homogeneous equation, using one of the methods below. \label{cramer}\], Example $$\PageIndex{4}$$: Using Cramer’s Rule. \nonumber\], Now, we integrate to find v. Using substitution (with $$w= \sin x$$), we get, $v= \int 3 \sin ^2 x \cos x dx=\int 3w^2dw=w^3=sin^3x.\nonumber$, \begin{align*}y_p =(\sin^2 x \cos x+2 \cos x) \cos x+(\sin^3 x)\sin x \\ =\sin_2 x \cos _2 x+2 \cos _2 x+ \sin _4x \\ =2 \cos_2 x+ \sin_2 x(\cos^2 x+\sin ^2 x) \; \; \; \; \; \; (\text{step 4}). Given that $$y_p(x)=x$$ is a particular solution to the differential equation $$y″+y=x,$$ write the general solution and check by verifying that the solution satisfies the equation. The general solution to this differential equation is y = c 1 y 1 ( x ) + c 2 y 2 ( x ) + ... + c n y n ( x ) + y p, where y p is a particular solution. So ρ (A) = ρ ([ A | B]) = 3 = Number of unknowns. Consider the nonhomogeneous linear differential equation, \[a_2(x)y″+a_1(x)y′+a_0(x)y=r(x). I Suppose we have one solution u. Notice that x = 0 is always solution of the homogeneous equation. Write the general solution to a nonhomogeneous differential equation. In the preceding section, we learned how to solve homogeneous equations with constant coefficients. Let $$y_p(x)$$ be any particular solution to the nonhomogeneous linear differential equation \[a_2(x)y''+a_1(x)y′+a_0(x)y=r(x), \nonumber and let $$c_1y_1(x)+c_2y_2(x)$$ denote the general solution to the complementary equation. None of the terms in $$y_p(x)$$ solve the complementary equation, so this is a valid guess (step 3). The general solution is, $y(t)=c_1e^t+c_2te^t−e^t \ln |t| \tag{step 5}$, \begin{align*} u′ \cos x+v′ \sin x =0 \\ −u′ \sin x+v′ \cos x =3 \sin _2 x \end{align*}., $u′= \dfrac{\begin{array}{|cc|}0 \sin x \\ 3 \sin ^2 x \cos x \end{array}}{ \begin{array}{|cc|} \cos x \sin x \\ − \sin x \cos x \end{array}}=\dfrac{0−3 \sin^3 x}{ \cos ^2 x+ \sin ^2 x}=−3 \sin^3 x \nonumber$, $v′=\dfrac{\begin{array}{|cc|} \cos x 0 \\ - \sin x 3 \sin^2 x \end{array}}{ \begin{array}{|cc|} \cos x \sin x \\ − \sin x \cos x \end{array}}=\dfrac{ 3 \sin^2x \cos x}{ 1}=3 \sin^2 x \cos x( \text{step 2}). is called a first-order homogeneous linear differential equation. There are no explicit methods to solve these types of equations, (only in dimension 1). We will see that solving the complementary equation is an important step in solving a nonhomogeneous differential equation. \nonumber$, $\begin{array}{|ll|}a_1 r_1 \\ a_2 r_2 \end{array}=\begin{array}{|ll|} x^2 0 \\ 1 2x \end{array}=2x^3−0=2x^3. 1.6 Slide 2 ’ & % (Non) Homogeneous systems De nition 1 A linear system of equations Ax = b is called homogeneous if b = 0, and non-homogeneous if b 6= 0. The method of undetermined coefficients is a technique that is used to find the particular solution of a non homogeneous linear ordinary differential equation. \[y_p′(x)=−3A \sin 3x+3B \cos 3x \text{ and } y_p″(x)=−9A \cos 3x−9B \sin 3x,$, \begin{align*}y″−9y =−6 \cos 3x \\−9A \cos 3x−9B \sin 3x−9(A \cos 3x+B \sin 3x) =−6 \cos 3x \\ −18A \cos 3x−18B \sin 3x =−6 \cos 3x. Non-homogeneous equations (Sect. Q: Check if the following equation is a non homogeneous equation. Particular Solution For Non Homogeneous Equation Class C • The particular solution of s is the smallest non-negative integer (s=0, 1, or 2) that will ensure that no term in Yi(t) is a solution of the corresponding homogeneous equation s is the number of time This method may not always work. (Non) Homogeneous systems De nition Examples Read Sec. Yes, that the sum of arbitrary constant multiples of solutions to a linear homogeneous differential equation is also a solution is called the superposition principle. is called the complementary equation. \end{align*}, Note that $$y_1$$ and $$y_2$$ are solutions to the complementary equation, so the first two terms are zero. Suppose H (x;t) is piecewise smooth. \end{align*}\]. Based on the form of $$r(x)=−6 \cos 3x,$$ our initial guess for the particular solution is $$y_p(x)=A \cos 3x+B \sin 3x$$ (step 2). Then the differential equation has the form, If the general solution to the complementary equation is given by $$c_1y_1(x)+c_2y_2(x)$$, we are going to look for a particular solution of the form, In this case, we use the two linearly independent solutions to the complementary equation to form our particular solution. Then, the general solution to the nonhomogeneous equation is given by, To prove $$y(x)$$ is the general solution, we must first show that it solves the differential equation and, second, that any solution to the differential equation can be written in that form. None of the terms in $$y_p(x)$$ solve the complementary equation, so this is a valid guess (step 3). Department of Mathematics & Statistics. \\ =2 \cos _2 x+\sin_2x \\ = \cos _2 x+1 \end{align*}\], $y(x)=c_1 \cos x+c_2 \sin x+1+ \cos^2 x(\text{step 5}).\nonumber$, $$y(x)=c_1 \cos x+c_2 \sin x+ \cos x \ln| \cos x|+x \sin x$$. In other words, the system (1) always possesses a solution. Therefore, for nonhomogeneous equations of the form we already know how to solve the complementary equation, and the problem boils down to finding a particular solution for the nonhomogeneous equation. This lecture presents a general characterization of the solutions of a non-homogeneous system. PROBLEM-SOLVING STRATEGY: METHOD OF UNDETERMINED COEFFICIENTS, Example $$\PageIndex{3}$$: Solving Nonhomogeneous Equations. For example, consider the wave equation with a source: utt = c2uxx +s(x;t) boundary conditions u(0;t) = u(L;t) = 0 (Non) Homogeneous systems De nition Examples Read Sec. x + y + 2z = 4 2x - y + 3z = 9 3x - y - z = 2 Writing in AX=B form, 1 1 2 X 4 2 -1 3 Y 9 3 -1 -1 = Z 2 AX=B As b ≠ 0, hence it is a non homogeneous equation. Missed the LibreFest? Nevertheless, there are some particular cases that we will be able to solve: Homogeneous systems of ode's with constant coefficients, Non homogeneous systems of linear ode's with constant coefficients, and Triangular systems of differential equations. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. The general solution of the homogeneous system is the set of all possible solutions, that is, the set of all that satisfy the system of equations. \nonumber\], When $$r(x)$$ is a combination of polynomials, exponential functions, sines, and cosines, use the method of undetermined coefficients to find the particular solution. Method of Undetermined Coefficients. Substitute $$y_p(x)$$ into the differential equation and equate like terms to find values for the unknown coefficients in $$y_p(x)$$. If this is the case, then we have $$y_p′(x)=A$$ and $$y_p″(x)=0$$. by Marco Taboga, PhD. Using a calculator, you will be able to solve differential equations of any complexity and types: homogeneous and non-homogeneous, linear or non-linear, first-order or second-and higher-order equations with separable and non-separable variables, etc. Since $$r(x)=3x$$, the particular solution might have the form $$y_p(x)=Ax+B$$. But, $$c_1y_1(x)+c_2y_2(x)$$ is the general solution to the complementary equation, so there are constants $$c_1$$ and $$c_2$$ such that, \[z(x)−y_p(x)=c_1y_1(x)+c_2y_2(x). This gives us the following general solution, \[y(x)=c_1e^{−2x}+c_2e^{−3x}+3xe^{−2x}. solving the non-homogeneous BVP 00(x) = 6x; 0 0 nding just one solution + amnxn + = 0 Verifying the general solution to (... Of constants on the right-hand side of the non-homogeneous heat equation with initial. + amnxn + = 0 umber of unknowns are many important real-life situations the! 2A−3B =0 equations is a non homogeneous equation homogeneous Definition, composed parts., sines, and step 3 is trivial t ) y0 + q ( t ) piecewise. Only to homogeneous equations y = r ( x ) =c_1y_1 ( )... The proof of the homogeneous system of linear equations in four unknowns that the solution... Has a detailed description not heterogeneous: a system of equations y_p t... Form of … solution: solving nonhomogeneous equations dimensions with non homogeneous bc y0 + (. Equations with constant coefficients no foolproof method for doing that ( for any arbitrary right-hand of! ≠ ρ ( non homogeneous equation ) = 3 = number of unknowns with associated general solution this. Example, let 's say we have this equation non-homogeneous ( y″−4y′+4y=7 \sin non homogeneous equation \cos )... This method of a first order linear non-homogeneous differential equation question is not a combination of polynomials exponentials... Libretexts content is licensed by CC BY-NC-SA 3.0, Chennai conditons PDE University 5 example lets! } 5A =10 \\ 5B−4A =−3 \\ 5C−2B+2A =−3 square matrix. necessarily. 2T+ \sin 2t\ ) and the solution to the nonhomogeneous equation the initial guess of the homogeneous equation differential.... ( ii ) a unique solution OpenStax is licensed by CC BY-NC-SA 3.0 the particular solution a... Y p of the homogeneous equation with boundary conditons PDE } y_p =uy_1+vy_2 \\ y_p′ =u′y_1+uy_1′+v′y_2+vy_2′ y_p″.
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# Math Help - Measuring distance using subtense method.
1. ## Measuring distance using subtense method.
cot(1degree23minutes12seconds) is the angle in a subtense bar method of measuring (computing) distance. The formula is d=b/2cot(1degree23minutes12seconds/2. or cot(1.38667degrees) My text uses this formula and gets a distance of 82.6341 cm. How did they do that? How does one use this formula and/or convert degrees to measurement?
2. ## Re: Measuring distance using subtense method.
Trig isn't one of my strong points, but I'll try to answer.
My text uses this formula and gets a distance of 82.6341 cm. How did they do that?
$d=\frac{b}{2}*cot(\frac{\theta}{2})$
$d=\frac{2}{2}cot({1.38667}{2})=82.6341 cm$
How does one use this formula and/or convert degrees to measurement?
You're trying to measure the distance d from point P to point Q. In order to do so, you place a bar of known length B such that point Q divides the length of the bar in half.
From the picture above, you can see that
$cot(\frac{\theta}{2})=\frac{d}{\frac{b}{2}}$
So
$d=\frac{b}{2}*cot(\frac{\theta}{2})$
I'm not sure if you were asking but to convert angles to decimal degrees it's simply
$\theta=1^{\circ} 23' 12''=\frac{degrees}{1}+\frac{minutes}{60}+\frac{se conds}{3600}$
3. ## Re: Measuring distance using subtense method.
downthesun01, Thank you for your response. Perhaps you can straighten me out. I input the equation into my TI-89 titanium using the equation you posted but my result is 41.3108. Your result is 82.6341 cm. There is something I am not getting right. Is it that my calculator is screwed up by not returning the cotangent as (1.386672) multiplied by (2/2) or am I unaware of something? I really cannot account for nor understand why my results are different than yours. I sure hope you get back to me because I am stuck.
4. ## Re: Measuring distance using subtense method.
downthesun01, I realize now what I was doing wrong. I was not dividing the cotangent by 2. Once I did that I got the same answer as you. One more thing though. In my text I have a similar problem. This problem has two cotangent angles. One each at the ends of distance. On your diagram ona at point P; in my text a similar distance line ending in point Q. The answer in the back of my book is 345.4 cm. The result for distance in my calculator is 86.3459. I am guessing the .345 is the answer they are lookong for. Does this mean the 86 is meters and the .345 is the centimeters? Sorry to ask such questions, but I am trying to truly know and understand what I am doing.
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# I have question about one integral
igoriance
## The Attempt at a Solution
∫[1/(1+x^2)^2] dx
## Answers and Replies
Homework Helper
What did you try?
Did you try integration by parts, substitution?
WhiteRae
I managed to get it by using substitution and then parts. Try making u=1/(1+x^2) and then when you get du, use u=1/(1+x^2) to solve for x to replace x with u. After that, use parts. Hope that helps I can give a more detailed answer if you still are having trouble.
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# Matlab, how read and extract matrices
1. May 25, 2012
### Valentina*
Hello,
I'm new here and in matlab, so if I do mistakes, please, tell me.
I'm working on my thesis and I need to extract some matrices and elements, but I can't write the for-loop exactly. For example, I have to read six matrices (but then I'll have more matrices) and this is too long
...
...
and so on. I'd like to do a for loop, to read the matrices, but I don't know how. I tried with something like
number = [1, 2, 3, 4, 5, 6];
for ii = 1 : 6
tmp = dlmread(sprintf('/scratch/matrix_$i', number[ii])); eval(sprintf('Matrix_final_$i = tmp', ii));
end
but it doesn't work :( In the same way, after, I have to extract the second column of each matrix, because is too long to do
n1 = matrix_1(:,2);
n2 = matrix_2(:,2);
...
...
I don't understand how to use the index ii in the for loop like a string in the name of the matrices. Does somebody know if it's possible?
Sorry for my English,
thank you!
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Amount of substance units converter
Converts amount of substance from one unit to another e.g. from millimoles (mmol) to number of particles (atoms or molecules depending on substance) or vice versa.
# Beta version#
BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !
# Symbolic algebra
ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations
# Inputs data - value and unit, which we're going to convert#
Value Unit yottamole [Ymol]zettamole [Zmol]examole [Emol]petamole [Pmol]teramole [Tmol]gigamole [Gmol]megamole [Mmol]kilomole [kmol]hektomole [hmol]mole [mol]decimole [dmol]centimole [cmol]milimole [mmol]micromole [µmol]nanomole [nmol]pikomole [pmol]femtomole [fmol]attomole [amol]zeptomole [zmol]yoctomole [ymol]number of particles [particles] Decimals 0123456789
# SI#
Unit Symbol Symbol(plain text) Value as symbolic Value as numeric Notes Unit conversion formula yottamole Show source$Ymol$ Ymol Show source$\text{...}$ - Derived amount of substance unit in SI system. One yottamole is equal to septylion of moles: $1\ Ymol= 10^{24}\ mol$ Show source$...$ zettamole Show source$Zmol$ Zmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One zettamole is equal to sextillion of moles: $1\ Zmol= 10^{21}\ mol$ Show source$...$ examole Show source$Emol$ Emol Show source$\text{...}$ - Derived amount of substance unit in SI system. One examole is equal to quintillion of moles: $1\ Emol= 10^{18}\ mol$ Show source$...$ petamole Show source$Pmol$ Pmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One petamole is equal to quadrillion of moles: $1\ Pmol= 10^{15}\ mol$ Show source$...$ teramole Show source$Tmol$ Tmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One teramole is equal to trillion of moles: $1\ Tmol= 10^{12}\ mol$ Show source$...$ gigamole Show source$Gmol$ Gmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One gigamole is equal to billion of moles: $1\ Gmol= 10^{9}\ mol$ Show source$...$ megamole Show source$Mmol$ Mmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One megamole is equal to million of moles: $1\ Mmol=1000000\ mol= 10^{6}\ mol$ Show source$...$ kilomole Show source$kmol$ kmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One kilomole is equal to thausand of moles: $1\ kmol=1000\ mol= 10^{3}\ mol$ Show source$...$ hektomole Show source$hmol$ hmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One hektomole is equal to hundred of moles: $1\ hmol=100\ mol= 10^{2}\ mol$ Show source$...$ mole Show source$mol$ mol Show source$\text{...}$ - The basic amount of substance unit in the SI system. One mole corresponds to the amount of substance that contains $6.023 \times 10^{23}$ particles (→ see Avogadro's number). Depending on the type of substance, it can be the number of atoms, ions or chemical molecules.$1\ mol = N_A\ \text{particles} = 6.023 \times 10^{23}\ \text{particles}$ Because definition and properties of the single particle depends on type of substance there is no constant relation between number of moles and mass. It means that, for example, one mole of water has different mass than one mole of atomic helium. Show source$...$ decimole Show source$dmol$ dmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One decimole is equal to one tenth of mole: $1\ dmol=0.1\ mol= 10^{-1}\ mol$ Show source$...$ centimole Show source$cmol$ cmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One centimole is equal to one hundredth of mole: $1\ cmol=0.01\ mol= 10^{-2}\ mol$ Show source$...$ milimole Show source$mmol$ mmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One milimole is equal to one thousandth of mole: $1\ mmol=0.001\ mol= 10^{-3}\ mol$ Show source$...$ micromole Show source$\mu mol$ µmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One micromole is equal to one millionth of mole: $1\ \mu mol=0.000001\ mol= 10^{-6}\ mol$ Show source$...$ nanomole Show source$nmol$ nmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One nanomole is equal to one billionth of mole: $1\ nmol= 10^{-9}\ mol$ Show source$...$ pikomole Show source$pmol$ pmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One pikomole is equal to one trillionth of mole: $1\ pmol= 10^{-12}\ mol$ Show source$...$ femtomole Show source$fmol$ fmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One femtomole is equal to one quadrillionth of mole: $1\ fmol= 10^{-15}\ mol$ Show source$...$ attomole Show source$amol$ amol Show source$\text{...}$ - Derived amount of substance unit in SI system. One attomole is equal to one quintillionth of mole: $1\ amol= 10^{-18}\ mol$ Show source$...$ zeptomole Show source$zmol$ zmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One zeptomole is equal to one sextillionth of mole: $1\ zmol= 10^{-21}\ mol$ Show source$...$ yoctomole Show source$ymol$ ymol Show source$\text{...}$ - Derived amount of substance unit in SI system. One yoctomole is equal to one septillionth of mole: $1\ ymol= 10^{-24}\ mol$ Show source$...$
# other#
Unit Symbol Symbol(plain text) Value as symbolic Value as numeric Notes Unit conversion formula number of particles Show source$particles$ particles Show source$\text{...}$ - Number of particles in the probe. Depending on the type of substance, it can be the number of atoms, ions or chemical molecules. Number of particles equals to Avogadro's number is one mole of substance.$N_A\ \text{particles} = 6.023 \times 10^{23}\ \text{particles} = 1\ mol$ Show source$...$
# Some facts#
• The basic SI unit of amount of substance is one mole.
• One mole of substance contains the same number of molecules (or atoms in the case of free elements that do create molecules) as 12 grams of carbon isotope 12C.
• In one mole there is 6,022140857 (74) × 10 23 particles (atoms, molecules, ions, etc.). This number is often called Avogadro number:
$N_A = 6,022140857(74) \times 10^{23}$
• One mole of substance may correspond to different mass. For example, one mole of water weighs 18,01528 g, but one mole of carbon dioxide 44,01 g. The mass of one mole of substance is called molar mass and is substance specific. You can read more about molar mass (including molar masses of selected substances) visiting our another calculator: Molar mass.
• One mole of perfect gas under normal conditions (temperature 273K, pressure 1023 hPa) occupies a volume of 22.42 dm3. You can find more about the volume occupied by various gases in our another calculators: Molar volume of gases and Clapeyron's equation.
# How to convert#
• Enter the number to field "value" - enter the NUMBER only, no other words, symbols or unit names. You can use dot (.) or comma (,) to enter fractions.
Examples:
• 1000000
• 123,23
• 999.99999
• Find and select your starting unit in field "unit". Some unit calculators have huge number of different units to select from - it's just how complicated our world is...
• And... you got the result in the table below. You'll find several results for many different units - we show you all results we know at once. Just find the one you're looking for.
# Tags and links to this website#
Tags:
Tags to Polish version:
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# Finding MLE by factor analyzing the correlation matrix
#### Blain Waan
##### New Member
In the book "Applied Multivariate Statistical Analysis" written by Johnson and Wichern, they have mentioned that the MLEs ($\hat{L_z}$) are obtained from the the correlation matrix $R$ by inserting $R$ in place of $[(n-1)/n] \times S$ (where $S$ is the sample covariance matrix) in the likelihood. They also mention that the likelihood is appropriate for $S$, not for $R$, but surprisingly it is equivalent to obtaining MLE ($\hat{L}$) from $S$ and then setting $\hat{L_z}=\hat{V}^{-1/2}\hat{L}$.
Is there any proof of this? Can anyone help?
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Tamil Nadu Board of Secondary EducationHSC Science Class 11th
# Determine the values of all the four quantum numbers of the 8th electron in the O-atom and 15th electron in Cl atom. - Chemistry
Determine the values of all the four quantum numbers of the 8th electron in the O-atom and 15th electron in Cl atom.
#### Solution
(1) O (Z = 8) 1s2 2s2 2px2py1 2pz1
Four quantum numbers for 2px1 electron in oxygen atom:
n = principal quantum number = 2
l = azimuthal quantum number = 1
m = magnetic quantum number = +1
s = spin quantum number = +1/2
(2) Cl (Z = 17) 1s2 2s2 2p6 3s2 3px2 3py2 3pz1
Four quantum numbers for 15th electron in chlorine atom:
n = 3, l = 1, m = 0, s = +1/2
(3) Cr (Z = 24) 1s2 2s2 2p2 3s2 3p2 3d2 4s1
n = 3, l = 2, m = +2, s = +1/2
Concept: Filling of Orbitals
Is there an error in this question or solution?
#### APPEARS IN
Tamil Nadu Board Samacheer Kalvi Class 11th Chemistry Volume 1 and 2 Answers Guide
Chapter 2 Quantum Mechanical Model of Atom
Evaluation | Q II. 10. | Page 64
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# Introduction
This is a guide to using the Shiny web ‘Viewer’ application created as part of The Concept Lab project. The purpose of the app is to visualize and explore the architecture of concepts inferred from large text corpora by means of statistical measures of the co-association of words in the text.
This document refers to the ‘October’ version of the app, completed in October 2018. A paper describing in full the natural language processing methods and some of the implementation details is available in the proceedings of IWCS 2017.1 Nulty, Paul. (2017). “Network Visualizations for Exploring Political Concepts”.Proceedings of the 12th International Conference on Computational Semantics (IWCS). For a more theoretical perspective on applying these methods to the study of the history of concepts, see the Concept Lab’s article published in Contributions to the History of Concepts.2 Distributional Concept Analysis: A Computational Model for Parsing Conceptual Forms. de Bolla, P., Jones, E., Recchia, G., Regan, J., & Nulty, P. (2019). Contributions to the History of Concepts
The app is now hosted on Cambridge University Library servers. Older versions were hosted on Amazon Web Services and served through port 3838. On some public wireless networks, this port may be restricted — if the app fails to load try to access it from an internet connection that does not restrict this port.
The app pane is composed of a sidebar (on the left) and a main panel, with a tab menu along the top of the screen to switch between panels showing different aspects of the app.
When the app is first opened in a browser, the sidebar and Configuration Panel are displayed.
# Configuration Panel
The Configuration Panel is the main screen from which the dataset and several universal preferences are selected. When the app is opened, the ECCO dataset will be loaded by default. This takes a few seconds, and when it is complete the sidebar text display will show ‘Co-occurrence counts loaded’ as well as several properties of the loaded data (see Figure ). The bottom of the sidebar shows the data file name from which the current co-occurrence counts are loaded, in this case ‘ECCO_100_dist_100_cut_10_2’. Also available are two sets of data constructed from libertarian and socialist text from reddit.
Configuration Panel
From the top down, the options available in the configuration panel are as follows:
• measure: The measure by which the association between words should be measured. Each of these measures are based on the number of times words co-occur in a certain context, adjusted for the number of times each word occurs independently. $DPF(A,B) = \frac{Co\mbox{-}occurrences(A, B)}{Freq(A)*Freq(B)}$
DPF (Distributional Probability Factor) is a measure similar to pointwise mutual information, with an extra parameter to downweight the score of very infrequent words. By default the log-dpf option is selected, as the association scores calclated by DPF tend to have a power-law distribution
• Dataset: Several datasets are available, with Eighteenth Century Collections Online the default.
• Concreteness threshold / filter concrete words: If the filter concrete words checkbox is ticked, then only words which appear in a contemporary vocabulary rated for concreteness by human annotators3 Brysbaert, Marc, Amy Beth Warriner, and Victor Kuperman. ‘Concreteness ratings for 40 thousand generally known English word lemmas.’ Behavior research methods 46.3 (2014): 904-911..Note that this annotated word list excludes many archaic terms and proper nouns. will appear. The words are rated on a scale from 0 (most abstract) to 5 (most concrete), and only words below the concreteness threshold set by the slider will be included. That is, if the slider is set to 4.5, words rated 4.5 and greater (the most concrete) will be filtered out.
• 2D node label size: This slider controls the size of the node labels for network panels that use 2D output. This is useful for setting an appropriate size for capturing readable screenshots for figures.
# Network Panels
The following options are only displayed in the side panel when one of the Network Visualisation panels is selected.
• Prune nodes of degree < : Only nodes with this number of connections or less will be displayed. The default setting is two, meaning that nodes that are only connected to one other node in the network are not shown.
• Steps from search nodes: The display shows a neighbourhood network, constructed by starting with nodes specified by the search terms and expanding to include their neighbours n hops away, where n is specified with this slider.
• Centrality sample size: The centrality panel shows a table of nodes ranked by their centrality score in the co-occurrence network specified by the dataset, thresholds, options, and search terms specified in the sidebar and configuration pane. The betweenness centrality is calculated by finding the length of shortest paths between random nodes in the network.4 Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001. As this algorithm is computationally intensive, only paths of length less than the value specified here are counted in the estimation. The higher the sample size, the more accurate the betweenness estimation but the longer the time taken to run.
# Exporting images
In the 2D network visualisation panels, a button labeled “Export as png” is available in the bottom right. The default filename of the downloaded image encodes the parameters used as follows:
keywords-dataset-distance-measure-threshold-rank-steps-pruned-concrete
For example in the filename democracy-prorogued-ecco-100-log-dpf-2.6-20-1-2-none.png, the final part (2-none) indicates the nodes with fewer than two links are pruned, and concrete words are not filtered out. If you check the “filter concrete words” box, this “none” will be replaced by the abstract/concrete filter threshold (default 4.5, i.e. exclude words that are > 4.5 on a five point scale from abstract (1) to concrete (5).
# Diff view
This pane compares two search terms with the following method: The common items from the lists of word1 and word2 are retrieved, and score_diff shows the score for each term in word2 subtracted from the score for the same term in word1. The result should be that words more associated with word1 get a higher score.
# Shortest Path
This pane shows the network plot of shortest route between two nodes. Exactly two search terms must be specified.
# Centrality
This tab shows a table of nodes ranked by their centrality score in the co-occurrence ntworek specified by the dataset, thresholds, options, and search terms specified in the sidebar and configuration pane.
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# A strongly open set which is not measurable in the weak operator topology
Let $H$ be a non-separable Hilbert space and $\{e_i\}_{i\in I}$ be an orthonormal basis for $H$. Let $J$ be a uncountable proper subset in $I$.
Let us put
One may check that $E$ is an open set in the strong operator topology but not in the weak operator topology.
Question1: I feel $E$ is not in the sigma algebra generated by the weak operator topology but have no evidence to prove it.
Question2: Let us assume that dimension of $H$ is of $c$. It seems that $E$ is WOT measurable if and only if every SOT open set is WOT measurable.
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### Still have math questions?
Find an equation of a parabola satisfying the given information. Focus $$( 0 , - 6 \pi )$$ , directrix $$y = 6 \pi$$ ,An equation for a parabola satisfying these conditions is $$\square$$ . (Type an equation. Type an exact answer, using $$\pi$$ as needed. Simplify your answer.)
$$x ^ { 2 } = - 24 \pi y$$
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# A solid shaft of 2 m diameter is used to transmit torque. The maximum shear stress induced to the shaft is 100 N/m2 . Determine the maximum torque transmitted by the shaft.
This question was previously asked in
DSSSB JE ME 2019 Official Paper Shift - 2 (Held on 06 Nov 2019)
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1. 146 N-m
2. 188 N-m
3. 165 N-m
4. 157 N-m
Option 4 : 157 N-m
## Detailed Solution
Concept:
Using torsion equation:
$$\frac{T}{{{I_P}}} = \frac{{{{\rm{τ }}_{max}}}}{R} = \frac{{G\theta }}{L}$$
Where,
T = applied torque, IP = Polar section modulus, τmax = Maximum shear stress in the shaft material, R = Radius of the shaft, G = Modulus of Rigidity, θ = Angle of twist, L = Length of the shaft
$${I_P} = \frac{π }{{32}}{D^4}$$
R = $$\frac{D}{2}$$
From shear stress criteria:
$$\frac{{{{\rm{τ }}_{{\rm{max}}\left( {allowable} \right)}} \times 2}}{D} = \frac{T}{{{I_P}}}$$
Substituting the values of $${I_P}$$ and R we get
Torque (T) = $$\frac{π }{{16}}τ {d^3}$$
Calculation:
Given:
d = 2 m, τ = 100 N/m2
T = $$\frac{π }{{16}}τ {d^3}$$
Taking π = 3.14
T = $$\frac{3.14\;\times\;100\;\times\;2^3}{16}$$ = 157 N-m
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# Aligning conditions in cases environment
I have a piecewise function with three "parts." I would like to have all three conditions aligned at the variable x. How do I achieve that? Here is the code I have so far:
$f(x) = \begin{cases} mx^2 +nx +1, & x \le -1 \\ 2m e^{|x|-1} + \sin \pi x - 3n, & -1 < x < 1 \\ 3x^2 - (m+n)x, & x \ge 1 \end{cases}$
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A different solution, which extends the cases environment. It adds an optional argument for defining array column options. The standard cases behavior is the default, so without optional argument it's like the normal amsmath's cases.
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\let\@ifnextchar\new@ifnextchar
\left\lbrace
\def\arraystretch{1.2}%
\array{#1}%
}
\makeatother
\begin{document}
$f(x) = \begin{cases}[@{}l@{\quad}r@{}l@{}] mx^2 +nx +1, & &x \le -1 \\ 2m e^{|x|-1} + \sin \pi x - 3n, & -1 < {} &x < 1 \\ 3x^2 - (m+n)x, & &x \ge 1 \end{cases}$
\end{document}
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Using the following generate errors with the redefinition of cases in this answer: $$\mathbf{l}=\begin{cases}[{-0.0095} \quad {11.7464} \quad { -0.1086} \\ \qquad {-0.4413} \quad {-0.3859} \quad {-0.1111}]&\text{for }x\le 0.34\ [{-4.5403} \quad {41.5374} \quad {-64.0957}\\ \qquad {50.2411} \quad {-19.2945} \quad {2.8837}]&\text{for }x>0.34\end{cases}$$ – Mobius Pizza Nov 22 '12 at 21:09
@MobiusPizza Check your argument in the square brackets, it should be the syntax for array column definitions. – Stefan Kottwitz Nov 22 '12 at 21:38
You could use alignedat instead, for aligning at several places, with a big brace on the left:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
f(x) = \left\{\begin{alignedat}{2} & mx^2 +nx +1, && x \le -1 \\ & 2m e^{|x|-1} + \sin \pi x - 3n, \qquad & -1 < {}&x < 1 \\ & 3x^2 - (m+n)x, && x \ge 1 \end{alignedat}\right.
\end{document}
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I would recommend using a \phantom{-1 <{}} to achieve the proper spacing. This will reserve as much space as is taken up by -1 < (with the additional {} to get the proper spacing on the right hand side of the <):
If you also want the 1 aligned on the right hand side you can add \phantom{-} before the 1 to get:
\documentclass{article}
\usepackage{amsmath}
\newcommand*{\Phantom}{\phantom{-1 <{}}}%
\begin{document}
$f(x) = \begin{cases} mx^2 +nx +1, & \Phantom x \le -1 \\ 2m e^{|x|-1} + \sin \pi x - 3n, & -1 < x < \phantom{-}1 \\ 3x^2 - (m+n)x, & \Phantom x \ge \phantom{-}1 \end{cases}$
\end{document}
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this approach re-uses ideas from other answers, but in a different way:
$f(x) = \begin{cases} mx^2 +nx +1, & x \le -1 \\ 2m e^{|x|-1} + \sin \pi x - 3n,\kern4em & \llap{-1 < {}} x < 1 \\ 3x^2 - (m+n)x, & x \ge 1 \end{cases}$
\qquad doesn't leave enough space on the second line, hence doubling it to \kern4em. the {} after the less than sign in the \llap ensures the correct spacing between it and the following "x". finally, since \llap puts you into horizontal mode, $...$ are needed to restore math mode.
the result:
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Tensor power- Notation question - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T10:05:28Z http://mathoverflow.net/feeds/question/65431 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65431/tensor-power-notation-question Tensor power- Notation question M.B 2011-05-19T13:05:19Z 2011-06-28T13:38:42Z <p>Hi everyone </p> <p>I have a notational question, which is written usually in papers, but I can not figure it out what could be. Let $M$ be an $A$-module. I have seen this notation $$M^{\otimes -n}$$</p> <p>I think this would mean $(Hom_A(M,A))^{\otimes n}$, but in the other way this can be denoted by $((M^*)^{\otimes n}$. Is this a standard notation? </p>
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Not too long ago, I was looking at some of the designs from MFOS(Music From Outer Space). They host analog synthesizer designs and sell kits and parts related to the designs. As I have an attraction to stochastic signals, the Noise Cornucopia caught my eye. In this design, white noise is generated with thermal noise from a BJT(Bipolar Junction Transistor). It is passed through some post-processing to get several outputs. Two of the outputs are dedicated to Grainy Noise, which sounds quite interesting. In order to make noise grainy, the below circuit was used:
The input is the random noise source and the potentiometer, R3, was used to control the grainyness of the signal. The output is a high passed grainy noise. The two op-amps are used in this context to generate a three state nonlinear function. When the noise is above some threshold value x, the top op-amp draws the signal to a high voltage. When the noise is below -x, the bottom op-amp pulls the signal to some negative value. When the noise is between the limits, the output of the non-linearity is near zero.
It would be possible to simply build the circuit and hear the sound, but I like to understand how to model phenomena. In modeling this circuit, it is useful and fun to have easy to manipulate audio as the output of a short program. To do this, I used Faust, which is an innovative method of writing out signal processing code for audio synthesis. Faust takes the description of a dsp algorithm with simple input definitions and translates it into a program with a compile time selected GUI and audio backend. In my opinion, the toolchain works well and has some good ideas.
For the replication of the above circuit the below code was used.
//+-----------------------+
//| Coarse Noise Generator |
//+-----------------------+
//Windowing parameters
window = hslider("Window Size", 0.9, 0.8, 1.0, 0.001);
win_h = window;
win_l = -window;
//White noise source [-1..1]
RANDMAX = 2147483647;
random = ffunction(int random(), <stdlib.h>, "");
noise = (random * (2.0/RANDMAX)) - 1.0;
//Windowed noise
process = noise <: (_,win_h : >), (_,win_l : <) : -;
This code simply takes random samples from random() and performs the previously described windowing functions. The faust code is terse, but the overall behavior is described by: (noise > window_high) - (noise < window_low). This can be seen with the attached svg diagram:
The final result can be heard here:
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A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform
MathematicS In Action, Volume 11 (2022) no. 1, pp. 3-42.
This study is a review of recent applications to seismic imaging of optimal transport based numerical tools. Modern seismic imaging methods used in the industry rely on the interpretation of the full signal. The characterization of the subsurface mechanical properties is formulated as a PDE-constrained optimization problem, solved through local optimization strategies. The choice of the misfit function used to measure the distance between actual seismic recordings and those synthetized by the solution of wave propagation PDE is crucial. Indeed, the conventional least-squares distance function leads to a non-convex optimization problem whose solution through local optimization then strongly depends on the initial guess. Using an optimal transport distance is an interesting alternative from its convexity properties with respect to translation and dilation. Specific strategies need however to be implemented as seismic data are oscillatory, while the optimal transport theory has been developed for the comparison of positive measures. In this study we review two optimal transport based misfit functions, from their mathematical formulation to their application to field data through their numerical implementation. Advantages and drawbacks of both strategies are discussed. Numerical experiments show that they represent two interesting and complementary alternative to the classical least-squares misfit function, mitigating the dependency to the choice of the initial guess.
Published online:
DOI: 10.5802/msia.15
Classification: 35R30, 86A22, 86A15
Keywords: Optimal transport, convexity, optimization, seismic imaging
Ludovic Métivier 1; Romain Brossier 2; Félix Kpadonou 3; Jérémie Messud 3; Arnaud Pladys 2
1 Laboratoire Jean Kuntzmann, Université Grenoble Alpes, France
2 ISTerre, Université Grenoble Alpes, France
3 CGG, Massy, France
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author = {Ludovic M\'etivier and Romain Brossier and F\'elix Kpadonou and J\'er\'emie Messud and Arnaud Pladys},
title = {A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform},
journal = {MathematicS In Action},
pages = {3--42},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {11},
number = {1},
year = {2022},
doi = {10.5802/msia.15},
language = {en},
url = {https://msia.centre-mersenne.org/articles/10.5802/msia.15/}
}
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TI - A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform
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PB - Société de Mathématiques Appliquées et Industrielles
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%0 Journal Article
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%A Romain Brossier
%A Jérémie Messud
%T A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform
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%D 2022
%P 3-42
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Ludovic Métivier; Romain Brossier; Félix Kpadonou; Jérémie Messud; Arnaud Pladys. A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform. MathematicS In Action, Volume 11 (2022) no. 1, pp. 3-42. doi : 10.5802/msia.15. https://msia.centre-mersenne.org/articles/10.5802/msia.15/
[1] H. Aghamiry; A. Gholami; S. Operto Improving full-waveform inversion by wavefield reconstruction with alternating direction method of multipliers, Geophysics, Volume 84 (2019) no. 1, p. R139-R162 | DOI
[2] M. Akgül A genuinely polynomial primal simplex algorithm for the assignment problem, Discrete Appl. Math., Volume 45 (1993) no. 2, pp. 93-115 | DOI | MR | Zbl
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# How do I calculate yield from a bond futures contract?
I would like to know how I can calculate the yield of a bond futures contract(say the 5 yr treasury "FVM05" is trading at 108.2)? I am not sure how to go about calculating the yield of the futures contract?
Need some guidance in doing so.
There's a lot of intracacies involved and you've got several options. Let's go through an example, using the current front-month 5-year contract FVU6 (FV expiring in September 2016).
• CTD Yield: The cheapest-to-deliver ("CTD") into FVU6 is the 1.625s of 11/30/2020 and its yield to maturity as of last close is 1.075%. You can simply use this as a proxy as the futures yield. This may seem dumb, but it's actually the one of the most prevalent choices in time series analyses. It works particularly well when the futures contract is fairly priced relative to cash bonds and the CTD is highly likely to be delivered into the contract (as it stands, 1.625s of 11/30/2020 has 100% delivery probability).
• CTD forward yield: Given that a futures contract more closely resemble a forward, it is natural to calculate the forward yield of the CTD. You can calculate the forward price for the CTD using the cash-carry formula, assuming that the forward date = delivery date (10/5/2016 in this case). The forward price can then be converted back into a forward yield. For FVU6, we'd have 1.105%.
• Futures implied yield: You can also calculate the so called futures implied yield. This is computed by assuming that the forward price of the CTD is the futures price multiplied by the conversion factor. In this case, the futures price is 121.46875, while the conversion factor for the 1.625s of 11/30/2020 is 0.8408, so you would assume that the CTD's forward price is $121.46875 \times 0.8408 = 102.130925$. Then you simply calculate the yield to maturity, assuming that the settlement date is the delivery date (10/5/2016), which nets you a yield of 1.099%.
These methods above assume that the CTD will not change between now and the delivery date. If that's not the case, you may want to calculate an average yield, weighted by CTD delivery probabilities.
• Where do the numbers 1.625 and 1.075% come from? Where does the date 11/30/2020 come from? I've come here hoping to see a formula and all I see are magic numbers – CashCow Nov 12 '19 at 8:56
• @CashCow it's the FUT_CTD Field on Bloomberg. It will tell you which Bond (Treasury) in the case of US Government is the Cheapest to Deliver for the given Bond Future. – bombayquant Dec 27 '19 at 15:57
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# Tag Info
97
As noted here before, Tardos' example clearly refutes the proof; it gives a monotone function, which agrees with CLIQUE on T0 and T1, but which lies in P. This would not be possible if the proof were correct, since the proof applies to this case too. However, can we pinpoint the mistake? Here is, from a post on the lipton's blog, what seems to be the place ...
95
I am familiar with Alexander Razborov whose previous work is extremely crucial and serves as a foundation for Blum's proof. I had the good luck of meeting him today and wasted no time in asking for his opinion on this whole matter, on whether he had even seen the proof or not and what are his thoughts about it if he did. To my surprise, he replied that he ...
41
Turing-machines and $\lambda$-calculus are equivalent only w.r.t. the functions $\mathbb{N} \rightarrow \mathbb{N}$ they can define. From the point of view of computational complexity they seem to behave differently. The main reason people use Turing machines and not $\lambda$-calculus to reason about complexity is that using $\lambda$-calculus naively ...
41
This is posted as community answer because (a) it's not my own words, but a citation from Luca Trevisan on a social media platform or from other people with no CSTheory.SE account; and (b) anyone should feel free to update this with updated, relevant information. Quoting Luca Trevisan from a public Facebook post (08/14/2017), replying to a question about ...
36
The correctness of the claimed proof is being discussed at Luca Trevisan's blog: https://lucatrevisan.wordpress.com/2017/08/15/on-norbert-blums-claimed-proof-that-p-does-not-equal-np/ In particular "anon" posted the following relevant comment: "Tardos observed that Razborov’s and Alon-Boppana’s arguments carry over to a function which is computed by a ...
33
A flip answer is that this isn't the first thing about complexity theory that I'd try to explain to a layperson! To even appreciate the idea of nonuniformity, and how it differs from nondeterminism, you need to be further down in the weeds with the definitions of complexity classes than many people are willing to get. Having said that, one perspective that ...
31
Yes. In fact, by the McCreight-Meyer Union Theorem (Theorem 5.5 of McCreight and Meyer, 1969, free version here) a result of that I believe is due to Manuel Blum, there is a single function $f$ such that $\mathsf{P} = \mathsf{DTIME}(f(n))$. This function is necessarily superpolynomial, but "just barely." The theorem applies more generally to any Blum ...
30
The paper "BQP and the Polynomial Hierarchy" by Scott Aaronson directly addresses your question. If P=NP, then PH would collapse. If furthermore BQP were in PH, then no quantum speed-up would be possible in that case. On the other hand, Aaronson gives evidence for a problem with quantum speedup outside PH, thus such a speed-up would survive a collapse of PH.
29
The Knot Equivalence Problem. Given two knots drawn in the plane, are they topologically the same? This problem is known to be decidable, and there do not seem to be any computational complexity obstructions to its being in P. The best upper bound currently known on its time complexity seems to be a tower of $2$s of height $c^n$, where $c = 10^{10^{6}}$, ...
28
Mulmuley's result (from Mulmuley's webpage without paywall) that, in the PRAM model without bit operations, "$\mathsf{P} \neq \mathsf{NC}$". (In the usual boolean model where $\mathsf{L}$ lives, $\mathsf{L} \subseteq \mathsf{NC}$.) This model is strong enough that the result implies any $\mathsf{L}$ algorithm for a $\mathsf{P}$-complete problem would have to ...
28
If $\mathsf{NP} = \mathsf{PSPACE}$, this would imply: $\mathsf{P^{\#P}} = \mathsf{NP}$That is, counting the solutions to a problem in $\mathsf{NP}$ would be polytime reducible to finding a single solution; $\mathsf{PP} = \mathsf{NP}$That is, polynomial-time randomized algorithms with success probability arbitrarily close to 1/2 is polynomial-time reducible ...
28
Here is a "smoothness" argument that I heard recently in defense of the claim that non-uniform models of computation should be more powerful than we suspect. On one hand, we know from the time hierarchy theorem that there are functions computable in time $O(2^{2n})$ that are not computable in time $O(2^{n})$, for example. On the other hand, by Lupanov's ...
27
The class ${\cal C}$ you are proposing is probably not $NP$. (If ${\cal C} = NP$, then every $NP$ language would have linear-size witnesses, which would imply that every $NP \subseteq TIME[2^{O(n)}]$ and $NP \neq EXP$, among other things). It is very natural to consider such classes; they arise in several settings. In this paper, Rahul Santhanam (...
27
25
There has, in fact, been quite a lot of recent works on proving quasi-polynomial running time lower bound for computational problems, mostly based on the exponential time hypothesis. Here are some results for problems that I consider quite natural (all results below are conditional on ETH): Aaronson, Impagliazzo and Moshkovitz [1] show a quasi-polynomial ...
25
Gustav Nordh commented on by Theorem 5 (page 29). Specifically, the function $$(x\lor y) \land (\lnot x \lor y) \land (x \lor \lnot y)$$ computes the function which is $1$ only if $x$ and $y$ are both $1$, hence it is monotone. The expression above for the function represents a "standard network" $\beta$ (where the only negations are to a literal) whose ...
24
Here's a version of the minimum circuit size problem (MCSP): given the $2^n$ bit truth table of a Boolean function, does it have a circuit of size at most $2^{n/2}$? Known to be not in $AC0$. Contained in $NP$. Generally believed to be $NP$-hard, but this is open. I believe it's not even known to be $AC0[2]$-hard. Indeed, recent work with Cody Murray (to ...
24
The complexity of computing a bit (specified in binary) of an irrational algebraic number (such as $\sqrt{2}$) has the best known upper bound of $\mathsf{P^{{{PP}^{PP}}^{PP}}}$ via a reduction to the problem $\mathsf{BitSLP}$ which known to have this upper bound [ABD14]. On the other hand we do not even know if this problem is harder than computing the ...
23
Wigderson proved that $NL/poly \subseteq \oplus L/poly$. By standard arguments, $L = \oplus L$ would imply $L/poly = NL/poly$. (Take a machine $M$ in $NL/poly$. It has an equivalent machine $M'$ in $\oplus L/poly$. Take the $\oplus L$ language of instance-advice pairs $S = \{(x,a)~|~M'(x,a)~\textrm{accepts}\}$. If this language is in $L$, then by ...
23
You need to understand that $\mathsf{CSP}$ problems have a structure that generic $\mathbf{SAT}$ problems do not have. I will give you a simple example. Let $\Gamma=\{\{(0,0),(1,1)\},\{(0,1),(1,0)\}\}$. This language is such that you can only express equality and inequality between two variables. Clearly any such set of constraints is ...
23
One point which has been implicitly but not explicitly mentioned yet is that we would get $\mathsf{NP} = \mathsf{coNP}$. Although this is equivalent to $\mathsf{PH}$ collapsing to $\mathsf{NP}$, it follows directly from the fact that $\mathsf{PSPACE}$ is closed under complement, which is trivial to prove. I think $\mathsf{NP} = \mathsf{coNP}$ is worth ...
22
Supposedly the reference "NP-complete problems on a 3-connected cubic planar graph and their applications" by Uehara (a paper I haven't actually seen) proves that independent set is NP-complete even for triangle-free planar graphs. But by Grötzsch's theorem they are always 3-colorable, and testing for smaller numbers of colors than 3 is easy in any graph, so ...
22
I recommend Jenga! Assuming you have two perfectly logical, sober, and dextrous players, Jenga is a perfect-information two-player game, just like Checkers or Go. Suppose the game starts with a stack of $3N$ bricks, with 3 bricks in each level. For most of the game, each player has $\Theta(N)$ choices at each turn for the next move, and in the absence of ...
22
In some technical sense you are asking whether $P = NP \cap coNP$. Suppose that $L \in NP \cap coNP$, thus there exists poly-time $F$ and $G$ so that $x \in L$ iff $\exists y: F(x,y)$ and $x \not\in L$ iff $\exists y: G(x,y)$. This can be recast as a minmax characterization by $f_x(y) = 1$ if $F(x,y)$ and $f_x(y) = 0$ otherwise; $g_x(y) = 0$ if $G(x,y)$ ...
22
$DTIME(n^{polylogn})$ is known as $QP$ (quasi-polynomial). It is widely believed that $NP\not \subset QP$, although it is a stronger statement than $P\neq NP$. Some common conjectures, such as the Exponential Time Hypothesis imply $NP\not \subset QP$.
22
3-SAT may be one such problem. Currently the best upper bound for Unique 3-SAT is exponentially faster than for general 3-SAT. (The speedup is exponential, although the reduction in the exponent is tiny.) The record-holder for the unique case is this paper by Timon Hertli. Hertli's algorithm builds upon the important PPSZ algorithm of Paturi, Pudlák, ...
22
Another natural topological problem, similar in spirit to Peter Shor's answer, is embeddability of 2-dimensional abstract simplicial complexes in $\mathbb{R}^3$. In general it's natural to ask when can we effectively/efficiently decide that an abstract $k$-dimensional simplicial complex can be embedded in $\mathbb{R}^d$. For $k=1$ and $d=2$ this is the graph ...
22
To have a list of such problems, you can look at the list of superpolynomial speed improvement at the quantum algorithm zoo (QAZ). The list below is based on this (see QAZ for precise definitions and references. This is another way to say I don’t even pretend to understand many of the problems of this list!) Algebraic and Number Theoretic Problems If I’m ...
Only top voted, non community-wiki answers of a minimum length are eligible
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Edge Expansion and Spectral Gap of Nonnegative Matrices
The classic graphical Cheeger inequalities state that if $M$ is an $n\times n$ \emph{symmetric} doubly stochastic matrix, then $\frac{1-\lambda_{2}(M)}{2}\leq\phi(M)\leq\sqrt{2\cdot(1-\lambda_{2}(M))}$ where $\phi(M)=\min_{S\subseteq[n],|S|\leq n/2}\left(\frac{1}{|S|}\sum_{i\in S,j\not\in S}M_{i,j}\right)$ is the edge expansion of $M$, and $\lambda_{2}(M)$ is the second largest eigenvalue of $M$. We study the relationship between $\phi(A)$ and the spectral gap $1-\re\lambda_{2}(A)$ for \emph{any} doubly stochastic matrix $A$ (not necessarily symmetric), where $\lambda_{2}(A)$ is a nontrivial eigenvalue of $A$ with maximum real part. Fiedler showed that the upper bound on $\phi(A)$ is unaffected, i.e., $\phi(A)\leq\sqrt{2\cdot(1-\re\lambda_{2}(A))}$. With regards to the lower bound on $\phi(A)$, there are known constructions with $\phi(A)\in\Theta\left(\frac{1-\re\lambda_{2}(A)}{\log n}\right),$ indicating that at least a mild dependence on $n$ is necessary to lower bound $\phi(A)$. In our first result, we provide an \emph{exponentially} better construction of $n\times n$ doubly stochastic matrices $A_{n}$, for which $\phi(A_{n})\leq\frac{1-\re\lambda_{2}(A_{n})}{\sqrt{n}}.$ In fact, \emph{all} nontrivial eigenvalues of our matrices are $0$, even though the matrices are highly \emph{nonexpanding}. We further show that this bound is in the correct range (up to the exponent of $n$), by showing that for any doubly stochastic matrix $A$, $\phi(A)\geq\frac{1-\re\lambda_{2}(A)}{35\cdot n}.$ As a consequence, unlike the symmetric case, there is a (necessary) loss of a factor of $n^{\alpha}$ for $\frac{1}{2}\leq\alpha\leq1$ in lower bounding $\phi$ by the spectral gap in the nonsymmetric setting. Our second result extends these bounds to general matrices $R$ with nonnegative entries, to obtain a more »
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NSF-PAR ID:
10190072
Journal Name:
Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms
National Science Foundation
##### More Like this
1. The cumulative empirical spectral measure (CESM) $\Phi[\mathbf{A}] : \mathbb{R} \to [0,1]$ of a $n\times n$ symmetric matrix $\mathbf{A}$ is defined as the fraction of eigenvalues of $\mathbf{A}$ less than a given threshold, i.e., $\Phi[\mathbf{A}](x) := \sum_{i=1}^{n} \frac{1}{n} {\large\unicode{x1D7D9}}[ \lambda_i[\mathbf{A}]\leq x]$. Spectral sums $\operatorname{tr}(f[\mathbf{A}])$ can be computed as the Riemann–Stieltjes integral of $f$ against $\Phi[\mathbf{A}]$, so the task of estimating CESM arises frequently in a number of applications, including machine learning. We present an error analysis for stochastic Lanczos quadrature (SLQ). We show that SLQ obtains an approximation to the CESM within a Wasserstein distance of $t \: | \lambda_{\text{max}}[\mathbf{A}] - \lambda_{\text{min}}[\mathbf{A}] |$ with probability at least $1-\eta$, by applying the Lanczos algorithm for $\lceil 12 t^{-1} + \frac{1}{2} \rceil$ iterations to $\lceil 4 ( n+2 )^{-1}t^{-2} \ln(2n\eta^{-1}) \rceil$ vectors sampled independently and uniformly from the unit sphere. We additionally provide (matrix-dependent) a posteriori error bounds for the Wasserstein and Kolmogorov–Smirnov distances between the output of this algorithm and the true CESM. The quality of our bounds is demonstrated using numerical experiments.
2. Abstract
Given a sequence $\{Z_d\}_{d\in \mathbb{N}}$ of smooth and compact hypersurfaces in ${\mathbb{R}}^{n-1}$, we prove that (up to extracting subsequences) there exists a regular definable hypersurface $\Gamma \subset {\mathbb{R}}\textrm{P}^n$ such that each manifold $Z_d$ is diffeomorphic to a component of the zero set on $\Gamma$ of some polynomial of degree $d$. (This is in sharp contrast with the case when $\Gamma$ is semialgebraic, where for example the homological complexity of the zero set of a polynomial $p$ on $\Gamma$ is bounded by a polynomial in $\deg (p)$.) More precisely, given the above sequence of hypersurfaces, we construct a regular, compact, semianalytic hypersurface $\Gamma \subset {\mathbb{R}}\textrm{P}^{n}$ containing a subset $D$ homeomorphic to a disk, and a family of polynomials $\{p_m\}_{m\in \mathbb{N}}$ of degree $\deg (p_m)=d_m$ such that $(D, Z(p_m)\cap D)\sim ({\mathbb{R}}^{n-1}, Z_{d_m}),$ i.e. the zero set of $p_m$ in $D$ is isotopic to $Z_{d_m}$ in ${\mathbb{R}}^{n-1}$. This says that, up to extracting subsequences, the intersection of $\Gamma$ with a hypersurface of degree $d$ can be as complicated as we want. We call these ‘pathological examples’. In particular, we show that for every $0 \leq k \leq n-2$ and every sequence of natural numbers $a=\{a_d\}_{d\in \mathbb{N}}$ there is a regular, compact semianalyticmore »
3. The densest subgraph problem in a graph (\dsg), in the simplest form, is the following. Given an undirected graph $G=(V,E)$ find a subset $S \subseteq V$ of vertices that maximizes the ratio $|E(S)|/|S|$ where $E(S)$ is the set of edges with both endpoints in $S$. \dsg and several of its variants are well-studied in theory and practice and have many applications in data mining and network analysis. In this paper we study fast algorithms and structural aspects of \dsg via the lens of \emph{supermodularity}. For this we consider the densest supermodular subset problem (\dssp): given a non-negative supermodular function $f: 2^V \rightarrow \mathbb{R}_+$, maximize $f(S)/|S|$. For \dsg we describe a simple flow-based algorithm that outputs a $(1-\eps)$-approximation in deterministic $\tilde{O}(m/\eps)$ time where $m$ is the number of edges. Our algorithm is the first to have a near-linear dependence on $m$ and $1/\eps$ and improves previous methods based on an LP relaxation. It generalizes to hypergraphs, and also yields a faster algorithm for directed \dsg. Greedy peeling algorithms have been very popular for \dsg and several variants due to their efficiency, empirical performance, and worst-case approximation guarantees. We describe a simple peeling algorithm for \dssp and analyze its approximation guarantee inmore »
4. Abstract
In this paper, we consider discrete Schrödinger operators of the form, $$\begin{equation*} (Hu)(n) = u({n+1})+u({n-1})+V(n)u(n). \end{equation*}$$We view $H$ as a perturbation of the free operator $H_0$, where $(H_0u)(n)= u({n+1})+u({n-1})$. For $H_0$ (no perturbation), $\sigma _{\textrm{ess}}(H_0)=\sigma _{\textrm{ac}}(H)=[-2,2]$ and $H_0$ does not have eigenvalues embedded into $(-2,2)$. It is an interesting and important problem to identify the perturbation such that the operator $H_0+V$ has one eigenvalue (finitely many eigenvalues or countable eigenvalues) embedded into $(-2,2)$. We introduce the almost sign type potentials and develop the Prüfer transformation to address this problem, which leads to the following five results. 1: We obtain the sharp spectral transition for the existence of irrational type eigenvalues or rational type eigenvalues with even denominators.2: Suppose $\limsup _{n\to \infty } n|V(n)|=a<\infty .$ We obtain a lower/upper bound of $a$ such that $H_0+V$ has one rational type eigenvalue with odd denominator.3: We obtain the asymptotical behavior of embedded eigenvalues around the boundaries of $(-2,2)$.4: Given any finite set of points $\{ E_j\}_{j=1}^N$ in $(-2,2)$ with $0\notin \{ E_j\}_{j=1}^N+\{ E_j\}_{j=1}^N$, we construct the explicit potential $V(n)=\frac{O(1)}{1+|n|}$ such that $H=H_0+V$ has eigenvalues $\{ E_j\}_{j=1}^N$.5: Given any countable set of points $\{ E_j\}$ in $(-2,2)$ with $0\notin \{ E_j\}+\{ E_j\}$, andmore »
5. Abstract
Let $f(z) = \sum_{n=1}^\infty a_f(n)q^n$ be a holomorphic cuspidal newform with even integral weight $k\geq 2$, level N, trivial nebentypus and no complex multiplication. For all primes p, we may define $\theta_p\in [0,\pi]$ such that $a_f(p) = 2p^{(k-1)/2}\cos \theta_p$. The Sato–Tate conjecture states that the angles θp are equidistributed with respect to the probability measure $\mu_{\textrm{ST}}(I) = \frac{2}{\pi}\int_I \sin^2 \theta \; d\theta$, where $I\subseteq [0,\pi]$. Using recent results on the automorphy of symmetric power L-functions due to Newton and Thorne, we explicitly bound the error term in the Sato–Tate conjecture when f corresponds to an elliptic curve over $\mathbb{Q}$ of arbitrary conductor or when f has square-free level. In these cases, if $\pi_{f,I}(x) := \#\{p \leq x : p \nmid N, \theta_p\in I\}$ and $\pi(x) := \# \{p \leq x \}$, we prove the following bound: $$\left| \frac{\pi_{f,I}(x)}{\pi(x)} - \mu_{\textrm{ST}}(I)\right| \leq 58.1\frac{\log((k-1)N \log{x})}{\sqrt{\log{x}}} \qquad \text{for} \quad x \geq 3.$$ As an application, we give an explicit bound for the number of primes up to x that violate the Atkin–Serre conjecture for f.
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From Dmitriy Setrakyan <[email protected]>
Subject Re: Ignite Web Control Center Architecture
Date Tue, 14 Jul 2015 17:12:31 GMT
Guys,
Neither 1st or 2nd approaches are secure. Keep in mind that agent has a
connection with the outside world, so it already will be considered a
higher security risk. The safest way for it to connect to the cluster is
via standard HTTP over port 80.
Generally, any approach that requires anything other than HTTP (port 80)
introduces higher security risk. On top of that, it requires punching holes
in a firewall, extra approvals, etc.
My strong preference is 3rd approach. Web agent is simply a proxy between
the web-control-center and the grid. It should simply forward
requests/responses and have almost no logic of its own.
D.
On Tue, Jul 14, 2015 at 9:57 AM, Alexey Kuznetsov <[email protected]>
wrote:
> We need web-agent for three use cases:
> #1 Grid monitoring.
> #2 SQL.
> #3 Collect metadata from RDBMS.
>
> #1 and #2 will require interaction with grid.
> #3 just connect to DB and grab metadata.
>
> So, in this thread three approaches to design web-agent were introduced.
> Let's see their pro and cons.
>
> First approach: implement web-agent as Ignite plugin that will start
> singleton service.
> Pro: Native to Ignite, automatic failover, easy to deploy (just put a
> jar into classpath).
> Cons: How to implement use case #3? What about security? Production grid
> usually deployed in closed network.
>
> Second approach: implement web-agent as separate application that will
> start daemon node inside when needed. Actually this is how Visor works.
> Pro: Also native to Ignite (could reuse Visor tasks already). Easy to
> deploy (as Visor) - just put some jars in bin/web-agent folder +
> bin\web-agent.sh
> Secure. Web-agent could use binary rest protocol as Visor and
> work even via ssh tunnel.
> Cons: No automatic failover.
>
> Third approach: implement web-agent as lightweight proxy between
> web-server and Ignite.
> Web-agent will retranslate http request to grid and retranslate results
> from grid to web control center.
> Pro: It is lightweight and could be implemented without dependencies
> from Ignite.
> Cons: Not native to Ignite. We need to implement two protocols:
> web-control-center <-> web agent and web agent <-> Ignite.
>
>
> As for me I most like second approach because we have a lot of experience
> with Visor and could reuse code.
>
>
> Thought?
>
>
> On Tue, Jul 14, 2015 at 11:38 PM, Nikita Ivanov <[email protected]>
> wrote:
>
> > +1 on Dmitriy's approach.
> >
> > --
> > Nikita Ivanov
> >
> >
> > On Tue, Jul 14, 2015 at 9:30 AM, Dmitriy Setrakyan <
> [email protected]>
> > wrote:
> >
> > > On Tue, Jul 14, 2015 at 8:30 AM, Yakov Zhdanov <[email protected]>
> > > wrote:
> > >
> > > > Why? Do you understand how many problems you bring with this
> approach?
> > > >
> > >
> > > Yakov, unfortunately this is not about ease of implementation, but
> > > security. We will not be allowed to connect to the grid cluster from
> > where
> > > the web agent is running.
> > >
> > > I also don't see how we are adding a lot of complexity either. The way
> I
> > > see it being implemented is by creating a set of tasks that will return
> > > JSON objects for metrics, topology, etc. which will be processed on the
> > > browser side. These tasks can be easily executed over HTTP REST
> protocol.
> > >
> > >
> > > >
> > > > --Yakov
> > > >
> > > > 2015-07-14 18:00 GMT+03:00 Dmitriy Setrakyan <[email protected]
> >:
> > > >
> > > > > Yakov,
> > > > >
> > > > > We cannot start a client inside of an agent simply because agent
> will
> > > be
> > > > > started outside of the cluster where grid is deployed. Agent will
> be
> > > > > connecting to the grid using HTTP Rest requests.
> > > > >
> > > > > D.
> > > > >
> > > > > On Tue, Jul 14, 2015 at 6:16 AM, Yakov Zhdanov <
> [email protected]>
> > > > > wrote:
> > > > >
> > > > > > I like the design where agent is a plugin to Ignite.
> > > > Agent-ControlCenter
> > > > > > can be incorporated into the singleton cluster-wide service
> > deployed
> > > by
> > > > > > plugin on start. This approach seems very good and clean to
me:
> > > > > > 1. Easy to config - just drop JAR with plugin to classpath
> > > > > > 2. It is native to the cluster - it operates inside.
> > > > > > 3. Failover works out of the box.
> > > > > >
> > > > > > Thanks!
> > > > > >
> > > > > > --Yakov
> > > > > >
> > > > > > 2015-07-02 19:35 GMT+03:00 Dmitriy Setrakyan <
> > [email protected]
> > > >:
> > > > > >
> > > > > > > On Thu, Jul 2, 2015 at 8:08 AM, Sergey Evdokimov <
> > > > > > [email protected]>
> > > > > > > wrote:
> > > > > > >
> > > > > > > > Yes, Web Agent can open connection to Control Center
at any
> > time.
> > > > Web
> > > > > > > Agent
> > > > > > > > is started up as much as started up cluster, but user
looks
> to
> > > > > Control
> > > > > > > > Center infrequently. Web Agent have to keep connection
always
> > > > opened
> > > > > or
> > > > > > > we
> > > > > > > > need a way to notify Web Agent about new web-session
on Web
> > > Control
> > > > > > > Center.
> > > > > > > >
> > > > > > >
> > > > > > > Sergey, the agent should automatically reconnect whenever
a
> > > > connection
> > > > > is
> > > > > > > lost. For example, it can send a keep-alive ping every
2
> seconds
> > > back
> > > > > to
> > > > > > > the web control center.
> > > > > > >
> > > > > > > If you having doubts in the approach, please ping me on
Skype
> so
> > we
> > > > > could
> > > > > > > flush out the details.
> > > > > > >
> > > > > > >
> > > > > > > >
> > > > > > > > On Thu, Jul 2, 2015 at 5:53 PM, Dmitriy Setrakyan
<
> > > > > > [email protected]
> > > > > > > >
> > > > > > > > wrote:
> > > > > > > >
> > > > > > > > > On Thu, Jul 2, 2015 at 7:29 AM, Sergey Evdokimov
<
> > > > > > > > [email protected]>
> > > > > > > > > wrote:
> > > > > > > > >
> > > > > > > > > > Web Agent can be shipped as Ignite plugin
and start
> inside
> > > the
> > > > > > > cluster
> > > > > > > > as
> > > > > > > > > > service to avoid unnecessary configuration.
> > > > > > > > > >
> > > > > > > > > > How Web Agent will detect that Web Control
Center need a
> > > data?
> > > > > Web
> > > > > > > > > Control
> > > > > > > > > > Center cannot open connection to cluster,
because cluster
> > may
> > > > be
> > > > > in
> > > > > > > > local
> > > > > > > > > > network without static IP. Do you mean that
Web Agent
> will
> > > keep
> > > > > > > opened
> > > > > > > > > > connection to Web Control Center always?
> > > > > > > > > >
> > > > > > > > >
> > > > > > > > > However, the Ignite web agent should be able
to open a
> > > connection
> > > > > to
> > > > > > > the
> > > > > > > > > web control center, no?
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > On Thu, Jul 2, 2015 at 5:12 PM, Alexey Kuznetsov
<
> > > > > > > > > [email protected]>
> > > > > > > > > > wrote:
> > > > > > > > > >
> > > > > > > > > > > Igniters,
> > > > > > > > > > >
> > > > > > > > > > > I'm working on Web Control Center and
first release is
> > > near.
> > > > > > > > > > > In first release we will provide UI
for cluster and
> > caches
> > > > > > > > > configuration.
> > > > > > > > > > >
> > > > > > > > > > > In next releases we will provide Monitoring,
SQL and
> > Schema
> > > > > > Import
> > > > > > > > > > Utility.
> > > > > > > > > > > But those advanced features require
> > > cluster
> > > > > (for
> > > > > > > > > > > Monitoring and SQL)
> > > > > > > > > > > and access to DB server for Schema
Import.
> > > > > > > > > > >
> > > > > > > > > > > After some thoughts we decided to create
a so-called
> "web
> > > > > agent"
> > > > > > it
> > > > > > > > > will
> > > > > > > > > > be
> > > > > > > > > > > started "near" cluster and DB will
connect to it and
> send
> > > all
> > > > > > > needed
> > > > > > > > > info
> > > > > > > > > > > to Web Control Center.
> > > > > > > > > > >
> > > > > > > > > > > Any ideas, thoughts and suggestions
are very welcome.
> > > > > > > > > > >
> > > > > > > > > > > Thanks.
> > > > > > > > > > >
> > > > > > > > > > > --
> > > > > > > > > > > Alexey Kuznetsov
> > > > > > > > > > > GridGain Systems
> > > > > > > > > > > www.gridgain.com
> > > > > > > > > > >
> > > > > > > > > >
> > > > > > > > >
> > > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
>
>
>
> --
> Alexey Kuznetsov
> GridGain Systems
> www.gridgain.com
>
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## Centripetal and tangential acceleration
Can someone help me make sense of this problem?
Thanks.
A race car, starting from rest, travels around a circular turn of radius 23.7 m. At a certain instant, the car is still accelerating, and its angular speed is 0.571 rad/s. At this time, the total acceleration (centripetal plus tangential) makes an angle of 35.0° with respect to the radius. (The situation is similar to that in Figure 8.15b.) What is the magnitude of the total acceleration?
PhysOrg.com science news on PhysOrg.com >> New language discovery reveals linguistic insights>> US official: Solar plane to help ground energy use (Update)>> Four microphones, computer algorithm enough to produce 3-D model of simple, convex room
Recognitions: Homework Help You know. $$|\vec{a}|^{2} = a_{radial}^{2} + a_{tangential}^{2}$$ and $$v = R \omega$$ With the angular speed and the radius you can calculate the radial acceleration, and with the angle information, you can calulate the modulus or magnitude of the acceleration, and if you want to the tangential acceleration...
Sorry, I was out of class for most of this week, so that doesn't make a lot of sense. Can you lay it out in equations?
Recognitions:
Gold Member
Homework Help
## Centripetal and tangential acceleration
If you missed class and did not understand the concepts, I strongly advise you take a good book like Resnick and Halliday and read the theory.
Similar discussions for: Centripetal and tangential acceleration Thread Forum Replies Classical Physics 4 General Physics 7 Advanced Physics Homework 1 Introductory Physics Homework 1 Introductory Physics Homework 10
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## Problem with localhost:Fixed. Now just setting everything
Help with Setup, Hardware, Performance or other Issues...Or just pimp your rig.
*Boinkage*!
Private First Class
Posts: 195
Joined: Wed May 02, 2007 1:49 am
Location: Behind you with a stealth flag.
### Problem with localhost:Fixed. Now just setting everything
I'm having problems with using localhost. I can do random maps fine, but when I attempt to do the same with one of my levels I'm screwing around with, it won't connect and will either just freeze or say error connecting to server. Trying again with random map works perfectly.
Also, weirder still, when I try to load a different level other than the one I named testing, they don't show up. It only shows testing and random map as choices.
I'm running Windows XP with 2.0.8.
I can't figure it out
Last edited by *Boinkage*! on Fri Aug 10, 2007 12:54 am, edited 1 time in total.
The Pen is Mightier Than the Sword.
Okay, you get a Bic, the orc gets a long sword.
He cuts the Bic in half.
Then he cuts you in half.
Oops, I meant quarters.
Longhair
Private First Class
Posts: 330
Joined: Tue Feb 08, 2005 6:06 pm
Location: Lancaster, PA
Contact:
Have you checked - with a fine tooth comb - the syntax of your maps? Try commenting out any code that might be questionable.
Also, have you tried using a map that you KNOW works elsewhere on your localhost?
blast
General
Posts: 4780
Joined: Fri Mar 21, 2003 3:49 pm
Location: playing.cxx
Contact:
Are you trying to run the server from the Start Server menu in the game? There is (was) a bug in the client that preventing it from showing every map in the worlds directory.
"In addition to knowing the secrets of the Universe, I can assure you that I am also quite potty trained." -Koenma (Yu Yu Hakusho)
*Boinkage*!
Private First Class
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Syntax?
I'm using BZEdit, and I have no clue what syntax is.
And what do you mean "elsewhere" on my localhost.
The Pen is Mightier Than the Sword.
Okay, you get a Bic, the orc gets a long sword.
He cuts the Bic in half.
Then he cuts you in half.
Oops, I meant quarters.
Longhair
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I'm using BZEdit, and I have no clue what syntax is.
I mean open up the resulting map in a text editor like notepad, and have a look at it.
And what do you mean "elsewhere" on my localhost.
Ah, that didn't come out quite the way I meant it. I mean that you should go to a public server with a working map, save the map, and run the saved map on your localhost server.
Looking at your first post again, are you starting bzfs from the command line with the -world option?
*Boinkage*!
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Well, I went over the world (turned into txt, right?). I found no errors. Everything was good. I changed it back to BZW format, but even when I removed everything else in the folder, I couldn't find it. It only had random map .
The Pen is Mightier Than the Sword.
Okay, you get a Bic, the orc gets a long sword.
He cuts the Bic in half.
Then he cuts you in half.
Oops, I meant quarters.
CannonBallGuy
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Merry Christmas!
"Look, if I don't buy booze for the kids, I don't get any incriminating pictures to show to their parents, my business goes down the sink, my girlfriend leaves me and the baby goes on ebay. So help me search..."
"go Play With Toys urself in a dark alley u donkey ******" - Lt-Kirby2007
Longhair
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Especially that command line bit.
From your posts, I think you are a bit confused about how maps work. ALL maps come in the form of plain text. I don't care what you made it in. They might import images, but the base map is a big text file.
To start a server, you need to be opening a command prompt. (click start --> run and put the letters: cmd hit enter.)
I'm a bit fuzzy in Windows, but you need to input a command something like:
Code: Select all
bzfs -world \path\to\map\file
If you have no clue what I'm talking about, do a search with your Internet search engine of choice on something like: "dos tutorial" or "windows command line tutorial" There's a base of knowledge that you need to have to even be able to run any sort of server other than a random map. It's not terribly difficult, but be prepared to spend the next week's evenings reading and practicing.
If you ARE clued in on how the command line bit works, you'll need to tell us what you're typing in.
*Boinkage*!
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Ok, so I put that code in to the command prompt and it said exactly this:
Code: Select all
'bzfs' is not a recognized as an internal or external command, operatable program or batch file.
I'm reading about the command line right now. What exactly do I need to know about on it? I'll check my directory is correct, and post later.
The Pen is Mightier Than the Sword.
Okay, you get a Bic, the orc gets a long sword.
He cuts the Bic in half.
Then he cuts you in half.
Oops, I meant quarters.
CannonBallGuy
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You would need to cd into the directory bzfs is in, or use the full path to it.
Merry Christmas!
"Look, if I don't buy booze for the kids, I don't get any incriminating pictures to show to their parents, my business goes down the sink, my girlfriend leaves me and the baby goes on ebay. So help me search..."
"go Play With Toys urself in a dark alley u donkey ******" - Lt-Kirby2007
Longhair
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Sorry I can't tell you 'what exactly you need to know' there is a basic set of skills you'll need to get together to use it. Otherwise, you'll just end up aping some commands, and have no real clue what they mean. For starters, you should be able to navigate around your computer using your command line interface with ease, be able to modify text files, and understand what PATH is. (hint: the reason bzfs isn't recognized as a command is because it isn't in your path) Keep at it with the tutorials, you'll get it soon enough, and be better for it.
Oh, if you're really frustrated with the DOS command line interface that comes with Windows, have a look at Cygwin. The BASH shell blows DOS right out of the water IMHO.
charg
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I think you might have a simple problem like the wrong port.
If you did not specifcly set a port in your config, make sure it is 5154 , also make sure you spell localhost correctly
Make sure you get my new Map Editor!: http://my.bzflag.org/bb/viewtopic.php?p=115526#115526
anomaly
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Make sure you have saved the file as a '.bzw' file. Without the extension bzflag will not list it. Also the command line that LongHair posted might not work in windows. It should be something like:
C:\Program Files\BZFlag2.0.8\bzfs .exe -world <path>
you should probably use the absolute path for the map file as well.
Like:
C:\path\to\world\file.bzw
Longhair
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Thanks, anomaly that looks more like the commands I remember from my Windows days.
Do be careful though, if you are running a version of BZFlag that isn't 2.0.8, the directory won't be the same. (on the other hand, if you're not running 2.0.8, why the heck not?)
Thumper
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### localhost vs 127.0.0.1
Try using 127.0.0.1 instead of localhost.
I vaguely remember some systems have problems resolving 'localhost' but it works with the IP.
HTH
anomaly
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Longhair wrote:Thanks, anomaly that looks more like the commands I remember from my Windows days.
yeah I still have to use windows at work. I'm not fond of that OS.
Btw, 127.0.0.1 (the loopback address) is not always in the hosts file on Windows. Using the address directly instead of localhost will always work. Good point Thumper.
Saber
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You can also put your map file in the My Bzflag Files folder. Then open the command prompt and type:
Code: Select all
cd C:\Program Files\Bzflag2.0.8
Hit enter.
That's the default path. If you installed Bzflag in another folder, just put the path to that folder. After you have done that, make sure you map file and BZFS are in the Bzflag2.0.8 folder. In the command prompt, type:
Code: Select all
bzfs.exe -world nameofyourmap.bzw
Hit enter.
Open a Bzflag client. Type localhost for the server and 5154 for the port. If you are using a router, I think you have to use Port Forwarding (but I'm not sure). Join the map and you will be able to play on it. You won't have any admin perms. You have to use a config file and set a password if you want to.
urbanracer34
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Put this command into AUTOEXEC.BAT and reboot:
Code: Select all
set path C:\Program Files\BZFlag2.0.8
This command looks for executables at startup. Then run:
Code: Select all
bzfs.exe -world nameofyourmap.bzw
No more having to run the blasted "cd" command when starting your server . Thank goodness for an old DOS 5.0 manual I had kicking around.
Oh, BTW, DO NOT close the DOS window down! It looks like it might be doing nada, but that window is what keeps your server running.
Macrosoft
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urbanracer34 wrote:Put this command into AUTOEXEC.BAT and reboot:
Code: Select all
set path C:\Program Files\BZFlag2.0.8
whoa there!,,, don't do that, you'll replace the previous path var, and that can cause problems on boot... instead make it...
Code: Select all
set path %PATH%; C:\Program Files\BZFlag2.0.8
that should append the directory to the path var instead of replacing it.
gazz: A bullet may have your name on it, but shrapnel is addressed "to whom it may concern".
http://bash.org/?785529
Saber
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Just use
cd C:\...
It will change the directory. Then, you don't have to enter the path for your BZFS.EXE and your map file (if they are both in the ...) There is no risk of boot problems (I hope ).
freebird1963
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anomaly wrote:Make sure you have saved the file as a '.bzw' file. Without the extension bzflag will not list it. Also the command line that LongHair posted might not work in windows. It should be something like:
C:\Program Files\BZFlag2.0.8\bzfs .exe -world <path>
you should probably use the absolute path for the map file as well.
Like:
C:\path\to\world\file.bzw
So files downloaded the end in .map need to be renamed to .bzw ?
IF so why even name them .map and if not how do you get them to run ?
'THanks
Mark
DTRemenak
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BZFlag worlds should be named .bzw, not .map. Some old ones are named .map; we changed bzfs to warn in this case to make things more consistent.
the_j0k3r
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When running servers on windows, i find the easiest way to do it is to just open up notepad, type in my "bzfs -world /path/to/map.bzw", press enter, then type "pause" (useful for when you come up with errors), then save it in your bzflag 2.0.8 directory as server.bat or something like that. Batch files make life easier, i dont have to retype code for everything and if i need to change the map i can just edit the file.
*Boinkage*!
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Thanks for all the help.
saber
EDIT AGAIN!: Im so stupid...Forgot to put the file in BZFlag2.0.8
Last edited by *Boinkage*! on Thu Aug 09, 2007 8:37 pm, edited 1 time in total.
The Pen is Mightier Than the Sword.
Okay, you get a Bic, the orc gets a long sword.
He cuts the Bic in half.
Then he cuts you in half.
Oops, I meant quarters.
CannonBallGuy
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Posts: 2083
Joined: Wed Apr 12, 2006 1:31 am
Contact:
What else did it say on the "bad arguement" line?
Merry Christmas!
"Look, if I don't buy booze for the kids, I don't get any incriminating pictures to show to their parents, my business goes down the sink, my girlfriend leaves me and the baby goes on ebay. So help me search..."
"go Play With Toys urself in a dark alley u donkey ******" - Lt-Kirby2007
|
## How to Turn 100 % Segment into XU and Vice Versa in TagEditor
You can turn 100 % segments into XU segments and vice versa even without TagEditor
It is very simple trick that can be done even without TagEditor.
To turn 100 % segments into XU segments (i. e., blocked protected segments) in a .ttx file, you need to make the following replacement:
<Tu MatchPercent="100">
to
<Tu MatchPercent="100" Origin="xtranslate">
To turn XU segments into 100 % segments, you need to make the reverse replacement:
<Tu MatchPercent="100" Origin="xtranslate">
to
<Tu MatchPercent="100">
or (since the order of attributes in such strings is arbitrary):
<Tu Origin="xtranslate" MatchPercent="100">
to
<Tu MatchPercent="100">
Please note the a .ttx file can be edited as if it is a regular text file (.txt), directly in any text editor, for example, in Notepad.
## Related posts
### Controlling faces
Surprise, we have a pseudo-anglicism here!
|
# Internal combustion engine
Engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber
Diagram of a cylinder as found in an overhead cam 4-stroke gasoline engine:
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combustion engine, the expansion of the high-temperature and high-pressure gases produced by combustion applies direct force to some component of the engine. The force is typically applied to pistons (piston engine), turbine blades (gas turbine), a rotor (Wankel engine), or a nozzle (jet engine). This force moves the component over a distance, transforming chemical energy into kinetic energy which is used to propel, move or power whatever the engine is attached to. This replaced the external combustion engine for applications where the weight or size of an engine was more important.[1][2][3]
The first commercially successful internal combustion engine was created by Étienne Lenoir around 1860,[4] and the first modern internal combustion engine, known as the Otto engine, was created in 1876 by Nicolaus Otto. The term internal combustion engine usually refers to an engine in which combustion is intermittent, such as the more familiar two-stroke and four-stroke piston engines, along with variants, such as the six-stroke piston engine and the Wankel rotary engine. A second class of internal combustion engines use continuous combustion: gas turbines, jet engines and most rocket engines, each of which are internal combustion engines on the same principle as previously described.[4][5] Firearms are also a form of internal combustion engine,[5] though of a type so specialized that they are commonly treated as a separate category, along with weaponry such as mortars and anti-aircraft cannons. In contrast, in external combustion engines, such as steam or Stirling engines, energy is delivered to a working fluid not consisting of, mixed with, or contaminated by combustion products. Working fluids for external combustion engines include air, hot water, pressurized water or even boiler-heated liquid sodium.
While there are many stationary applications, most ICEs are used in mobile applications and are the primary power supply for vehicles such as cars, aircraft and boats. ICEs are typically powered by hydrocarbon-based fuels like natural gas, gasoline, diesel fuel, or ethanol. Renewable fuels like biodiesel are used in compression ignition (CI) engines and bioethanol or ETBE (ethyl tert-butyl ether) produced from bioethanol in spark ignition (SI) engines. As early as 1900 the inventor of the diesel engine, Rudolf Diesel, was using peanut oil to run his engines.[6] Renewable fuels are commonly blended with fossil fuels. Hydrogen, which is rarely used, can be obtained from either fossil fuels or renewable energy.
## History
Various scientists and engineers contributed to the development of internal combustion engines. In 1791, John Barber developed the gas turbine. In 1794 Thomas Mead patented a gas engine. Also in 1794, Robert Street patented an internal combustion engine, which was also the first to use liquid fuel, and built an engine around that time. In 1798, John Stevens built the first American internal combustion engine. In 1807, French engineers Nicéphore Niépce (who went on to invent photography) and Claude Niépce ran a prototype internal combustion engine, using controlled dust explosions, the Pyréolophore, which was granted a patent by Napoleon Bonaparte. This engine powered a boat on the Saône river in France.[7][8] In the same year, Swiss engineer François Isaac de Rivaz invented a hydrogen-based internal combustion engine and powered the engine by electric spark. In 1808, De Rivaz fitted his invention to a primitive working vehicle – "the world's first internal combustion powered automobile".[9] In 1823, Samuel Brown patented the first internal combustion engine to be applied industrially.
In 1854 in the UK, the Italian inventors Eugenio Barsanti and Felice Matteucci obtained the certification: "Obtaining Motive Power by the Explosion of Gases". In 1857 the Great Seal Patent Office conceded them patent No.1655 for the invention of an "Improved Apparatus for Obtaining Motive Power from Gases".[10][11][12][13] Barsanti and Matteucci obtained other patents for the same invention in France, Belgium and Piedmont between 1857 and 1859.[14][15] In 1860, Belgian engineer Jean Joseph Etienne Lenoir produced a gas-fired internal combustion engine.[16] In 1864, Nicolaus Otto patented the first atmospheric gas engine. In 1872, American George Brayton invented the first commercial liquid-fueled internal combustion engine. In 1876, Nicolaus Otto began working with Gottlieb Daimler and Wilhelm Maybach, patented the compressed charge, four-cycle engine. In 1879, Karl Benz patented a reliable two-stroke gasoline engine. Later, in 1886, Benz began the first commercial production of motor vehicles with an internal combustion engine, in which a three-wheeled, four-cycle engine and chassis formed a single unit.[17] In 1892, Rudolf Diesel developed the first compressed charge, compression ignition engine. In 1926, Robert Goddard launched the first liquid-fueled rocket. In 1939, the Heinkel He 178 became the world's first jet aircraft.
## Etymology
At one time, the word engine (via Old French, from Latin ingenium, "ability") meant any piece of machinery—a sense that persists in expressions such as siege engine. A "motor" (from Latin motor, "mover") is any machine that produces mechanical power. Traditionally, electric motors are not referred to as "engines"; however, combustion engines are often referred to as "motors". (An electric engine refers to a locomotive operated by electricity.)
In boating, an internal combustion engine that is installed in the hull is referred to as an engine, but the engines that sit on the transom are referred to as motors.[18]
## Applications
Diesel generator for backup power
Reciprocating piston engines are by far the most common power source for land and water vehicles, including automobiles, motorcycles, ships and to a lesser extent, locomotives (some are electrical but most use Diesel engines[19][20]). Rotary engines of the Wankel design are used in some automobiles, aircraft and motorcycles. These are collectively known as internal-combustion-engine vehicles (ICEV).[21]
Where high power-to-weight ratios are required, internal combustion engines appear in the form of combustion turbines, or sometimes Wankel engines. Powered aircraft typically use an ICE which may be a reciprocating engine. Airplanes can instead use jet engines and helicopters can instead employ turboshafts; both of which are types of turbines. In addition to providing propulsion, airliners may employ a separate ICE as an auxiliary power unit. Wankel engines are fitted to many unmanned aerial vehicles.
ICEs drive large electric generators that power electrical grids. They are found in the form of combustion turbines with a typical electrical output in the range of some 100 MW. Combined cycle power plants use the high temperature exhaust to boil and superheat water steam to run a steam turbine. Thus, the efficiency is higher because more energy is extracted from the fuel than what could be extracted by the combustion engine alone. Combined cycle power plants achieve efficiencies in the range of 50% to 60%. In a smaller scale, stationary engines like gas engines or diesel generators are used for backup or for providing electrical power to areas not connected to an electric grid.
Small engines (usually 2‐stroke gasoline/petrol engines) are a common power source for lawnmowers, string trimmers, chain saws, leafblowers, pressure washers, snowmobiles, jet skis, outboard motors, mopeds, and motorcycles.
## Classification
There are several possible ways to classify internal combustion engines.
### Reciprocating
By number of strokes:
By type of ignition:
By mechanical/thermodynamic cycle (these cycles are infrequently used but are commonly found in hybrid vehicles, along with other vehicles manufactured for fuel efficiency[23]):
### Continuous combustion
• Gas turbine engine
• Turbojet, through a propelling nozzle
• Turbofan, through a duct-fan
• Turboprop, through an unducted propeller, usually with variable pitch
• Turboshaft, a gas turbine optimized for producing mechanical torque instead of thrust
• Ramjet,[24] similar to a turbojet but uses vehicle speed to compress (ram) the air instead of a compressor.
• Scramjet, a variant of the ramjet that uses supersonic combustion.
• Rocket engine
## Reciprocating engines
### Structure
Bare cylinder block of a V8 engine
Piston, piston ring, gudgeon pin and connecting rod
The base of a reciprocating internal combustion engine is the engine block, which is typically made of cast iron (due to its good wear resistance and low cost)[25] or aluminum. In the latter case, the cylinder liners are made of cast iron or steel,[26] or a coating such as nikasil or alusil. The engine block contains the cylinders. In engines with more than one cylinder they are usually arranged either in 1 row (straight engine) or 2 rows (boxer engine or V engine); 3 rows are occasionally used (W engine) in contemporary engines, and other engine configurations are possible and have been used. Single cylinder engines (or thumpers) are common for motorcycles and other small engines found in light machinery. On the outer side of the cylinder, passages that contain cooling fluid are cast into the engine block whereas, in some heavy duty engines, the passages are the types of removable cylinder sleeves which can be replaceable.[25] Water-cooled engines contain passages in the engine block where cooling fluid circulates (the water jacket). Some small engines are air-cooled, and instead of having a water jacket the cylinder block has fins protruding away from it to cool the engine by directly transferring heat to the air. The cylinder walls are usually finished by honing to obtain a cross hatch, which is able to retain more oil. A too rough surface would quickly harm the engine by excessive wear on the piston.
The pistons are short cylindrical parts which seal one end of the cylinder from the high pressure of the compressed air and combustion products and slide continuously within it while the engine is in operation. In smaller engines, the pistons are made of aluminum; while in larger applications, they are typically made of cast iron.[25] The top wall of the piston is termed its crown and is typically flat or concave. Some two-stroke engines use pistons with a deflector head. Pistons are open at the bottom and hollow except for an integral reinforcement structure (the piston web). When an engine is working, the gas pressure in the combustion chamber exerts a force on the piston crown which is transferred through its web to a gudgeon pin. Each piston has rings fitted around its circumference that mostly prevent the gases from leaking into the crankcase or the oil into the combustion chamber.[27] A ventilation system drives the small amount of gas that escapes past the pistons during normal operation (the blow-by gases) out of the crankcase so that it does not accumulate contaminating the oil and creating corrosion.[25] In two-stroke gasoline engines the crankcase is part of the air–fuel path and due to the continuous flow of it, two-stroke engines do not need a separate crankcase ventilation system.
Valve train above a Diesel engine cylinder head. This engine uses rocker arms but no pushrods.
The cylinder head is attached to the engine block by numerous bolts or studs. It has several functions. The cylinder head seals the cylinders on the side opposite to the pistons; it contains short ducts (the ports) for intake and exhaust and the associated intake valves that open to let the cylinder be filled with fresh air and exhaust valves that open to allow the combustion gases to escape. However, 2-stroke crankcase scavenged engines connect the gas ports directly to the cylinder wall without poppet valves; the piston controls their opening and occlusion instead. The cylinder head also holds the spark plug in the case of spark ignition engines and the injector for engines that use direct injection. All CI (compression ignition) engines use fuel injection, usually direct injection but some engines instead use indirect injection. SI (spark ignition) engines can use a carburetor or fuel injection as port injection or direct injection. Most SI engines have a single spark plug per cylinder but some have 2. A head gasket prevents the gas from leaking between the cylinder head and the engine block. The opening and closing of the valves is controlled by one or several camshafts and springs—or in some engines—a desmodromic mechanism that uses no springs. The camshaft may press directly the stem of the valve or may act upon a rocker arm, again, either directly or through a pushrod.
Engine block seen from below. The cylinders, oil spray nozzle and half of the main bearings are clearly visible.
The crankcase is sealed at the bottom with a sump that collects the falling oil during normal operation to be cycled again. The cavity created between the cylinder block and the sump houses a crankshaft that converts the reciprocating motion of the pistons to rotational motion. The crankshaft is held in place relative to the engine block by main bearings, which allow it to rotate. Bulkheads in the crankcase form a half of every main bearing; the other half is a detachable cap. In some cases a single main bearing deck is used rather than several smaller caps. A connecting rod is connected to offset sections of the crankshaft (the crankpins) in one end and to the piston in the other end through the gudgeon pin and thus transfers the force and translates the reciprocating motion of the pistons to the circular motion of the crankshaft. The end of the connecting rod attached to the gudgeon pin is called its small end, and the other end, where it is connected to the crankshaft, the big end. The big end has a detachable half to allow assembly around the crankshaft. It is kept together to the connecting rod by removable bolts.
The cylinder head has an intake manifold and an exhaust manifold attached to the corresponding ports. The intake manifold connects to the air filter directly, or to a carburetor when one is present, which is then connected to the air filter. It distributes the air incoming from these devices to the individual cylinders. The exhaust manifold is the first component in the exhaust system. It collects the exhaust gases from the cylinders and drives it to the following component in the path. The exhaust system of an ICE may also include a catalytic converter and muffler. The final section in the path of the exhaust gases is the tailpipe.
### 4-stroke engines
Diagram showing the operation of a 4-stroke SI engine. Labels:
1 ‐ Induction
2 ‐ Compression
3 ‐ Power
4 ‐ Exhaust
The top dead center (TDC) of a piston is the position where it is nearest to the valves; bottom dead center (BDC) is the opposite position where it is furthest from them. A stroke is the movement of a piston from TDC to BDC or vice versa, together with the associated process. While an engine is in operation, the crankshaft rotates continuously at a nearly constant speed. In a 4-stroke ICE, each piston experiences 2 strokes per crankshaft revolution in the following order. Starting the description at TDC, these are:[28][29]
1. Intake, induction or suction: The intake valves are open as a result of the cam lobe pressing down on the valve stem. The piston moves downward increasing the volume of the combustion chamber and allowing air to enter in the case of a CI engine or an air-fuel mix in the case of SI engines that do not use direct injection. The air or air-fuel mixture is called the charge in any case.
2. Compression: In this stroke, both valves are closed and the piston moves upward reducing the combustion chamber volume which reaches its minimum when the piston is at TDC. The piston performs work on the charge as it is being compressed; as a result, its pressure, temperature and density increase; an approximation to this behavior is provided by the ideal gas law. Just before the piston reaches TDC, ignition begins. In the case of a SI engine, the spark plug receives a high voltage pulse that generates the spark which gives it its name and ignites the charge. In the case of a CI engine, the fuel injector quickly injects fuel into the combustion chamber as a spray; the fuel ignites due to the high temperature.
3. Power or working stroke: The pressure of the combustion gases pushes the piston downward, generating more kinetic energy than is required to compress the charge. Complementary to the compression stroke, the combustion gases expand and as a result their temperature, pressure and density decreases. When the piston is near to BDC the exhaust valve opens. The combustion gases expand irreversibly due to the leftover pressure—in excess of back pressure, the gauge pressure on the exhaust port—; this is called the blowdown.
4. Exhaust: The exhaust valve remains open while the piston moves upward expelling the combustion gases. For naturally aspirated engines a small part of the combustion gases may remain in the cylinder during normal operation because the piston does not close the combustion chamber completely; these gases dissolve in the next charge. At the end of this stroke, the exhaust valve closes, the intake valve opens, and the sequence repeats in the next cycle. The intake valve may open before the exhaust valve closes to allow better scavenging.
### 2-stroke engines
The defining characteristic of this kind of engine is that each piston completes a cycle every crankshaft revolution. The 4 processes of intake, compression, power and exhaust take place in only 2 strokes so that it is not possible to dedicate a stroke exclusively for each of them. Starting at TDC the cycle consists of:
1. Power: While the piston is descending the combustion gases perform work on it, as in a 4-stroke engine. The same thermodynamic considerations about the expansion apply.
2. Scavenging: Around 75° of crankshaft rotation before BDC the exhaust valve or port opens, and blowdown occurs. Shortly thereafter the intake valve or transfer port opens. The incoming charge displaces the remaining combustion gases to the exhaust system and a part of the charge may enter the exhaust system as well. The piston reaches BDC and reverses direction. After the piston has traveled a short distance upwards into the cylinder the exhaust valve or port closes; shortly the intake valve or transfer port closes as well.
3. Compression: With both intake and exhaust closed the piston continues moving upwards compressing the charge and performing work on it. As in the case of a 4-stroke engine, ignition starts just before the piston reaches TDC and the same consideration on the thermodynamics of the compression on the charge apply.
While a 4-stroke engine uses the piston as a positive displacement pump to accomplish scavenging taking 2 of the 4 strokes, a 2-stroke engine uses the last part of the power stroke and the first part of the compression stroke for combined intake and exhaust. The work required to displace the charge and exhaust gases comes from either the crankcase or a separate blower. For scavenging, expulsion of burned gas and entry of fresh mix, two main approaches are described: Loop scavenging, and Uniflow scavenging. SAE news published in the 2010s that 'Loop Scavenging' is better under any circumstance than Uniflow Scavenging.[22]
#### Crankcase scavenged
Diagram of a crankcase scavenged 2-stroke engine in operation
Some SI engines are crankcase scavenged and do not use poppet valves. Instead, the crankcase and the part of the cylinder below the piston is used as a pump. The intake port is connected to the crankcase through a reed valve or a rotary disk valve driven by the engine. For each cylinder, a transfer port connects in one end to the crankcase and in the other end to the cylinder wall. The exhaust port is connected directly to the cylinder wall. The transfer and exhaust port are opened and closed by the piston. The reed valve opens when the crankcase pressure is slightly below intake pressure, to let it be filled with a new charge; this happens when the piston is moving upwards. When the piston is moving downwards the pressure in the crankcase increases and the reed valve closes promptly, then the charge in the crankcase is compressed. When the piston is moving downwards, it also uncovers the exhaust port and the transfer port and the higher pressure of the charge in the crankcase makes it enter the cylinder through the transfer port, blowing the exhaust gases. Lubrication is accomplished by adding 2-stroke oil to the fuel in small ratios. Petroil refers to the mix of gasoline with the aforesaid oil. This kind of 2-stroke engine has a lower efficiency than comparable 4-strokes engines and releases more polluting exhaust gases for the following conditions:
• They use a total-loss lubrication system: all the lubricating oil is eventually burned along with the fuel.
• There are conflicting requirements for scavenging: On one side, enough fresh charge needs to be introduced in each cycle to displace almost all the combustion gases but introducing too much of it means that a part of it gets in the exhaust.
• They must use the transfer port(s) as a carefully designed and placed nozzle so that a gas current is created in a way that it sweeps the whole cylinder before reaching the exhaust port so as to expel the combustion gases, but minimize the amount of charge exhausted. 4-stroke engines have the benefit of forcibly expelling almost all of the combustion gases because during exhaust the combustion chamber is reduced to its minimum volume. In crankcase scavenged 2-stroke engines, exhaust and intake are performed mostly simultaneously and with the combustion chamber at its maximum volume.
The main advantage of 2-stroke engines of this type is mechanical simplicity and a higher power-to-weight ratio than their 4-stroke counterparts. Despite having twice as many power strokes per cycle, less than twice the power of a comparable 4-stroke engine is attainable in practice.
In the US, 2-stroke engines were banned for road vehicles due to the pollution. Off-road only motorcycles are still often 2-stroke but are rarely road legal. However, many thousands of 2-stroke lawn maintenance engines are in use.[citation needed]
#### Blower scavenged
Diagram of uniflow scavenging
Using a separate blower avoids many of the shortcomings of crankcase scavenging, at the expense of increased complexity which means a higher cost and an increase in maintenance requirement. An engine of this type uses ports or valves for intake and valves for exhaust, except opposed piston engines, which may also use ports for exhaust. The blower is usually of the Roots-type but other types have been used too. This design is commonplace in CI engines, and has been occasionally used in SI engines.
CI engines that use a blower typically use uniflow scavenging. In this design the cylinder wall contains several intake ports placed uniformly spaced along the circumference just above the position that the piston crown reaches when at BDC. An exhaust valve or several like that of 4-stroke engines is used. The final part of the intake manifold is an air sleeve that feeds the intake ports. The intake ports are placed at a horizontal angle to the cylinder wall (I.e: they are in plane of the piston crown) to give a swirl to the incoming charge to improve combustion. The largest reciprocating IC are low speed CI engines of this type; they are used for marine propulsion (see marine diesel engine) or electric power generation and achieve the highest thermal efficiencies among internal combustion engines of any kind. Some Diesel-electric locomotive engines operate on the 2-stroke cycle. The most powerful of them have a brake power of around 4.5 MW or 6,000 HP. The EMD SD90MAC class of locomotives are an example of such. The comparable class GE AC6000CW whose prime mover has almost the same brake power uses a 4-stroke engine.
An example of this type of engine is the Wärtsilä-Sulzer RT-flex96-C turbocharged 2-stroke Diesel, used in large container ships. It is the most efficient and powerful reciprocating internal combustion engine in the world with a thermal efficiency over 50%.[30][31][32] For comparison, the most efficient small four-stroke engines are around 43% thermally-efficient (SAE 900648);[citation needed] size is an advantage for efficiency due to the increase in the ratio of volume to surface area.
See the external links for an in-cylinder combustion video in a 2-stroke, optically accessible motorcycle engine.
#### Historical design
Dugald Clerk developed the first two-cycle engine in 1879. It used a separate cylinder which functioned as a pump in order to transfer the fuel mixture to the cylinder.[22]
In 1899 John Day simplified Clerk's design into the type of 2 cycle engine that is very widely used today.[33] Day cycle engines are crankcase scavenged and port timed. The crankcase and the part of the cylinder below the exhaust port is used as a pump. The operation of the Day cycle engine begins when the crankshaft is turned so that the piston moves from BDC upward (toward the head) creating a vacuum in the crankcase/cylinder area. The carburetor then feeds the fuel mixture into the crankcase through a reed valve or a rotary disk valve (driven by the engine). There are cast in ducts from the crankcase to the port in the cylinder to provide for intake and another from the exhaust port to the exhaust pipe. The height of the port in relationship to the length of the cylinder is called the "port timing".
On the first upstroke of the engine there would be no fuel inducted into the cylinder as the crankcase was empty. On the downstroke, the piston now compresses the fuel mix, which has lubricated the piston in the cylinder and the bearings due to the fuel mix having oil added to it. As the piston moves downward it first uncovers the exhaust, but on the first stroke there is no burnt fuel to exhaust. As the piston moves downward further, it uncovers the intake port which has a duct that runs to the crankcase. Since the fuel mix in the crankcase is under pressure, the mix moves through the duct and into the cylinder.
Because there is no obstruction in the cylinder of the fuel to move directly out of the exhaust port prior to the piston rising far enough to close the port, early engines used a high domed piston to slow down the flow of fuel. Later the fuel was "resonated" back into the cylinder using an expansion chamber design. When the piston rose close to TDC, a spark ignited the fuel. As the piston is driven downward with power, it first uncovers the exhaust port where the burned fuel is expelled under high pressure and then the intake port where the process has been completed and will keep repeating.
Later engines used a type of porting devised by the Deutz company to improve performance. It was called the Schnurle Reverse Flow system. DKW licensed this design for all their motorcycles. Their DKW RT 125 was one of the first motor vehicles to achieve over 100 mpg as a result.[34]
### Ignition
Internal combustion engines require ignition of the mixture, either by spark ignition (SI) or compression ignition (CI). Before the invention of reliable electrical methods, hot tube and flame methods were used. Experimental engines with laser ignition have been built.[35]
#### Spark ignition process
Bosch magneto
Points and coil ignition
The spark-ignition engine was a refinement of the early engines which used Hot Tube ignition. When Bosch developed the magneto it became the primary system for producing electricity to energize a spark plug.[36] Many small engines still use magneto ignition. Small engines are started by hand cranking using a recoil starter or hand crank. Prior to Charles F. Kettering of Delco's development of the automotive starter all gasoline engined automobiles used a hand crank.[37]
Larger engines typically power their starting motors and ignition systems using the electrical energy stored in a lead–acid battery. The battery's charged state is maintained by an automotive alternator or (previously) a generator which uses engine power to create electrical energy storage.
The battery supplies electrical power for starting when the engine has a starting motor system, and supplies electrical power when the engine is off. The battery also supplies electrical power during rare run conditions where the alternator cannot maintain more than 13.8 volts (for a common 12V automotive electrical system). As alternator voltage falls below 13.8 volts, the lead-acid storage battery increasingly picks up electrical load. During virtually all running conditions, including normal idle conditions, the alternator supplies primary electrical power.
Some systems disable alternator field (rotor) power during wide-open throttle conditions. Disabling the field reduces alternator pulley mechanical loading to nearly zero, maximizing crankshaft power. In this case, the battery supplies all primary electrical power.
Gasoline engines take in a mixture of air and gasoline and compress it by the movement of the piston from bottom dead center to top dead center when the fuel is at maximum compression. The reduction in the size of the swept area of the cylinder and taking into account the volume of the combustion chamber is described by a ratio. Early engines had compression ratios of 6 to 1. As compression ratios were increased, the efficiency of the engine increased as well.
With early induction and ignition systems the compression ratios had to be kept low. With advances in fuel technology and combustion management, high-performance engines can run reliably at 12:1 ratio. With low octane fuel, a problem would occur as the compression ratio increased as the fuel was igniting due to the rise in temperature that resulted. Charles Kettering developed a lead additive which allowed higher compression ratios, which was progressively abandoned for automotive use from the 1970s onward, partly due to lead poisoning concerns.
The fuel mixture is ignited at different progressions of the piston in the cylinder. At low rpm, the spark is timed to occur close to the piston achieving top dead center. In order to produce more power, as rpm rises the spark is advanced sooner during piston movement. The spark occurs while the fuel is still being compressed progressively more as rpm rises.[38]
The necessary high voltage, typically 10,000 volts, is supplied by an induction coil or transformer. The induction coil is a fly-back system, using interruption of electrical primary system current through some type of synchronized interrupter. The interrupter can be either contact points or a power transistor. The problem with this type of ignition is that as RPM increases the availability of electrical energy decreases. This is especially a problem, since the amount of energy needed to ignite a more dense fuel mixture is higher. The result was often a high RPM misfire.
Capacitor discharge ignition was developed. It produces a rising voltage that is sent to the spark plug. CD system voltages can reach 60,000 volts.[39] CD ignitions use step-up transformers. The step-up transformer uses energy stored in a capacitance to generate electric spark. With either system, a mechanical or electrical control system provides a carefully timed high-voltage to the proper cylinder. This spark, via the spark plug, ignites the air-fuel mixture in the engine's cylinders.
While gasoline internal combustion engines are much easier to start in cold weather than diesel engines, they can still have cold weather starting problems under extreme conditions. For years, the solution was to park the car in heated areas. In some parts of the world, the oil was actually drained and heated overnight and returned to the engine for cold starts. In the early 1950s, the gasoline Gasifier unit was developed, where, on cold weather starts, raw gasoline was diverted to the unit where part of the fuel was burned causing the other part to become a hot vapor sent directly to the intake valve manifold. This unit was quite popular until electric engine block heaters became standard on gasoline engines sold in cold climates.[40]
#### Compression ignition process
For ignition, diesel, PPC and HCCI engines rely solely on the high temperature and pressure created by the engine in its compression process. The compression level that occurs is usually twice or more than a gasoline engine. Diesel engines take in air only, and shortly before peak compression, spray a small quantity of diesel fuel into the cylinder via a fuel injector that allows the fuel to instantly ignite. HCCI type engines take in both air and fuel, but continue to rely on an unaided auto-combustion process, due to higher pressures and temperature. This is also why diesel and HCCI engines are more susceptible to cold-starting issues, although they run just as well in cold weather once started. Light duty diesel engines with indirect injection in automobiles and light trucks employ glowplugs (or other pre-heating: see Cummins ISB#6BT) that pre-heat the combustion chamber just before starting to reduce no-start conditions in cold weather. Most diesels also have a battery and charging system; nevertheless, this system is secondary and is added by manufacturers as a luxury for the ease of starting, turning fuel on and off (which can also be done via a switch or mechanical apparatus), and for running auxiliary electrical components and accessories. Most new engines rely on electrical and electronic engine control units (ECU) that also adjust the combustion process to increase efficiency and reduce emissions.
### Lubrication
Diagram of an engine using pressurized lubrication
Wikimedia Commons has media related to Internal combustion piston engine lubrication systems.
Surfaces in contact and relative motion to other surfaces require lubrication to reduce wear, noise and increase efficiency by reducing the power wasting in overcoming friction, or to make the mechanism work at all. Also, the lubricant used can reduce excess heat and provide additional cooling to components. At the very least, an engine requires lubrication in the following parts:
• Between pistons and cylinders
• Small bearings
• Big end bearings
• Main bearings
• Valve gear (The following elements may not be present):
• Tappets
• Rocker arms
• Pushrods
• Timing chain or gears. Toothed belts do not require lubrication.
In 2-stroke crankcase scavenged engines, the interior of the crankcase, and therefore the crankshaft, connecting rod and bottom of the pistons are sprayed by the 2-stroke oil in the air-fuel-oil mixture which is then burned along with the fuel. The valve train may be contained in a compartment flooded with lubricant so that no oil pump is required.
In a splash lubrication system no oil pump is used. Instead the crankshaft dips into the oil in the sump and due to its high speed, it splashes the crankshaft, connecting rods and bottom of the pistons. The connecting rod big end caps may have an attached scoop to enhance this effect. The valve train may also be sealed in a flooded compartment, or open to the crankshaft in a way that it receives splashed oil and allows it to drain back to the sump. Splash lubrication is common for small 4-stroke engines.
In a forced (also called pressurized) lubrication system, lubrication is accomplished in a closed-loop which carries motor oil to the surfaces serviced by the system and then returns the oil to a reservoir. The auxiliary equipment of an engine is typically not serviced by this loop; for instance, an alternator may use ball bearings sealed with their own lubricant. The reservoir for the oil is usually the sump, and when this is the case, it is called a wet sump system. When there is a different oil reservoir the crankcase still catches it, but it is continuously drained by a dedicated pump; this is called a dry sump system.
On its bottom, the sump contains an oil intake covered by a mesh filter which is connected to an oil pump then to an oil filter outside the crankcase. From there it is diverted to the crankshaft main bearings and valve train. The crankcase contains at least one oil gallery (a conduit inside a crankcase wall) to which oil is introduced from the oil filter. The main bearings contain a groove through all or half its circumference; the oil enters these grooves from channels connected to the oil gallery. The crankshaft has drillings that take oil from these grooves and deliver it to the big end bearings. All big end bearings are lubricated this way. A single main bearing may provide oil for 0, 1 or 2 big end bearings. A similar system may be used to lubricate the piston, its gudgeon pin and the small end of its connecting rod; in this system, the connecting rod big end has a groove around the crankshaft and a drilling connected to the groove which distributes oil from there to the bottom of the piston and from then to the cylinder.
Other systems are also used to lubricate the cylinder and piston. The connecting rod may have a nozzle to throw an oil jet to the cylinder and bottom of the piston. That nozzle is in movement relative to the cylinder it lubricates, but always pointed towards it or the corresponding piston.
Typically forced lubrication systems have a lubricant flow higher than what is required to lubricate satisfactorily, in order to assist with cooling. Specifically, the lubricant system helps to move heat from the hot engine parts to the cooling liquid (in water-cooled engines) or fins (in air-cooled engines) which then transfer it to the environment. The lubricant must be designed to be chemically stable and maintain suitable viscosities within the temperature range it encounters in the engine.
### Cylinder configuration
Common cylinder configurations include the straight or inline configuration, the more compact V configuration, and the wider but smoother flat or boxer configuration. Aircraft engines can also adopt a radial configuration, which allows more effective cooling. More unusual configurations such as the H, U, X, and W have also been used.
Some popular cylinder configurations:
a – straight
b – V
c – opposed
d – W
Multiple cylinder engines have their valve train and crankshaft configured so that pistons are at different parts of their cycle. It is desirable to have the pistons' cycles uniformly spaced (this is called even firing) especially in forced induction engines; this reduces torque pulsations[41] and makes inline engines with more than 3 cylinders statically balanced in its primary forces. However, some engine configurations require odd firing to achieve better balance than what is possible with even firing. For instance, a 4-stroke I2 engine has better balance when the angle between the crankpins is 180° because the pistons move in opposite directions and inertial forces partially cancel, but this gives an odd firing pattern where one cylinder fires 180° of crankshaft rotation after the other, then no cylinder fires for 540°. With an even firing pattern, the pistons would move in unison and the associated forces would add.
Multiple crankshaft configurations do not necessarily need a cylinder head at all because they can instead have a piston at each end of the cylinder called an opposed piston design. Because fuel inlets and outlets are positioned at opposed ends of the cylinder, one can achieve uniflow scavenging, which, as in the four-stroke engine is efficient over a wide range of engine speeds. Thermal efficiency is improved because of a lack of cylinder heads. This design was used in the Junkers Jumo 205 diesel aircraft engine, using two crankshafts at either end of a single bank of cylinders, and most remarkably in the Napier Deltic diesel engines. These used three crankshafts to serve three banks of double-ended cylinders arranged in an equilateral triangle with the crankshafts at the corners. It was also used in single-bank locomotive engines, and is still used in marine propulsion engines and marine auxiliary generators.
### Diesel cycle
P-V diagram for the ideal Diesel cycle. The cycle follows the numbers 1–4 in clockwise direction.
Most truck and automotive diesel engines use a cycle reminiscent of a four-stroke cycle, but with temperature increase by compression causing ignition, rather than needing a separate ignition system. This variation is called the diesel cycle. In the diesel cycle, diesel fuel is injected directly into the cylinder so that combustion occurs at constant pressure, as the piston moves.
### Otto cycle
The Otto cycle is the most common cycle for most cars' internal combustion engines that use gasoline as a fuel. It consists of the same major steps as described for the four-stroke engine: Intake, compression, ignition, expansion and exhaust.
### Five-stroke engine
In 1879, Nicolaus Otto manufactured and sold a double expansion engine (the double and triple expansion principles had ample usage in steam engines), with two small cylinders at both sides of a low-pressure larger cylinder, where a second expansion of exhaust stroke gas took place; the owner returned it, alleging poor performance. In 1906, the concept was incorporated in a car built by EHV (Eisenhuth Horseless Vehicle Company);[42] and in the 21st century Ilmor designed and successfully tested a 5-stroke double expansion internal combustion engine, with high power output and low SFC (Specific Fuel Consumption).[43]
### Six-stroke engine
The six-stroke engine was invented in 1883. Four kinds of six-stroke engines use a regular piston in a regular cylinder (Griffin six-stroke, Bajulaz six-stroke, Velozeta six-stroke and Crower six-stroke), firing every three crankshaft revolutions. These systems capture the waste heat of the four-stroke Otto cycle with an injection of air or water.
The Beare Head and "piston charger" engines operate as opposed-piston engines, two pistons in a single cylinder, firing every two revolutions rather than every four like a four-stroke engine.
### Other cycles
The very first internal combustion engines did not compress the mixture. The first part of the piston downstroke drew in a fuel-air mixture, then the inlet valve closed and, in the remainder of the down-stroke, the fuel-air mixture fired. The exhaust valve opened for the piston upstroke. These attempts at imitating the principle of a steam engine were very inefficient. There are a number of variations of these cycles, most notably the Atkinson and Miller cycles.
Split-cycle engines separate the four strokes of intake, compression, combustion and exhaust into two separate but paired cylinders. The first cylinder is used for intake and compression. The compressed air is then transferred through a crossover passage from the compression cylinder into the second cylinder, where combustion and exhaust occur. A split-cycle engine is really an air compressor on one side with a combustion chamber on the other.
Previous split-cycle engines have had two major problems—poor breathing (volumetric efficiency) and low thermal efficiency. However, new designs are being introduced that seek to address these problems. The Scuderi Engine addresses the breathing problem by reducing the clearance between the piston and the cylinder head through various turbocharging techniques. The Scuderi design requires the use of outwardly opening valves that enable the piston to move very close to the cylinder head without the interference of the valves. Scuderi addresses the low thermal efficiency via firing after top dead center (ATDC).
Firing ATDC can be accomplished by using high-pressure air in the transfer passage to create sonic flow and high turbulence in the power cylinder.
The four-stroke crank-rocker engine with a curve cylinder was also invented to study its efficiency.[44]
## Combustion turbines
### Jet engine
Turbofan jet engine
Jet engines use a number of rows of fan blades to compress air which then enters a combustor where it is mixed with fuel (typically JP fuel) and then ignited. The burning of the fuel raises the temperature of the air which is then exhausted out of the engine creating thrust. A modern turbofan engine can operate at as high as 48% efficiency.[45]
There are six sections to a turbofan engine:
• Fan
• Compressor
• Combustor
• Turbine
• Mixer
• Nozzle[46]
### Gas turbines
Turbine power plant
A gas turbine compresses air and uses it to turn a turbine. It is essentially a jet engine which directs its output to a shaft. There are three stages to a turbine: 1) air is drawn through a compressor where the temperature rises due to compression, 2) fuel is added in the combuster, and 3) hot air is exhausted through turbine blades which rotate a shaft connected to the compressor.
A gas turbine is a rotary machine similar in principle to a steam turbine and it consists of three main components: a compressor, a combustion chamber, and a turbine. The temperature of the air, after being compressed in the compressor, is increased by burning fuel in it. The heated air and the products of combustion expand in a turbine, producing work output. About 23 of the work drives the compressor: the rest (about 13) is available as useful work output.[47]
Gas turbines are among the most efficient internal combustion engines. The General Electric 7HA and 9HA turbine combined cycle electrical plants are rated at over 61% efficiency.[48]
### Brayton cycle
Brayton cycle
A gas turbine is a rotary machine somewhat similar in principle to a steam turbine. It consists of three main components: compressor, combustion chamber, and turbine. The air is compressed by the compressor where a temperature rise occurs. The temperature of the compressed air is further increased by combustion of injected fuel in the combustion chamber which expands the air. This energy rotates the turbine which powers the compressor via a mechanical coupling. The hot gases are then exhausted to provide thrust.
Gas turbine cycle engines employ a continuous combustion system where compression, combustion, and expansion occur simultaneously at different places in the engine—giving continuous power. Notably, the combustion takes place at constant pressure, rather than with the Otto cycle, constant volume.
## Wankel engines
The Wankel rotary cycle. The shaft turns three times for each rotation of the rotor around the lobe and once for each orbital revolution around the eccentric shaft.
The Wankel engine (rotary engine) does not have piston strokes. It operates with the same separation of phases as the four-stroke engine with the phases taking place in separate locations in the engine. In thermodynamic terms it follows the Otto engine cycle, so may be thought of as a "four-phase" engine. While it is true that three power strokes typically occur per rotor revolution, due to the 3:1 revolution ratio of the rotor to the eccentric shaft, only one power stroke per shaft revolution actually occurs. The drive (eccentric) shaft rotates once during every power stroke instead of twice (crankshaft), as in the Otto cycle, giving it a greater power-to-weight ratio than piston engines. This type of engine was most notably used in the Mazda RX-8, the earlier RX-7, and other vehicle models. The engine is also used in unmanned aerial vehicles, where the small size and weight and the high power-to-weight ratio are advantageous.
## Forced induction
Forced induction is the process of delivering compressed air to the intake of an internal combustion engine. A forced induction engine uses a gas compressor to increase the pressure, temperature and density of the air. An engine without forced induction is considered a naturally aspirated engine.
Forced induction is used in the automotive and aviation industry to increase engine power and efficiency. It particularly helps aviation engines, as they need to operate at high altitude.
Forced induction is achieved by a supercharger, where the compressor is directly powered from the engine shaft or, in the turbocharger, from a turbine powered by the engine exhaust.
## Fuels and oxidizers
All internal combustion engines depend on combustion of a chemical fuel, typically with oxygen from the air (though it is possible to inject nitrous oxide to do more of the same thing and gain a power boost). The combustion process typically results in the production of a great quantity of thermal energy, as well as the production of steam and carbon dioxide and other chemicals at very high temperature; the temperature reached is determined by the chemical make up of the fuel and oxidizers (see stoichiometry), as well as by the compression and other factors.
### Fuels
The most common modern fuels are made up of hydrocarbons and are derived mostly from fossil fuels (petroleum). Fossil fuels include diesel fuel, gasoline and petroleum gas, and the rarer use of propane. Except for the fuel delivery components, most internal combustion engines that are designed for gasoline use can run on natural gas or liquefied petroleum gases without major modifications. Large diesels can run with air mixed with gases and a pilot diesel fuel ignition injection. Liquid and gaseous biofuels, such as ethanol and biodiesel (a form of diesel fuel that is produced from crops that yield triglycerides such as soybean oil), can also be used. Engines with appropriate modifications can also run on hydrogen gas, wood gas, or charcoal gas, as well as from so-called producer gas made from other convenient biomass. Experiments have also been conducted using powdered solid fuels, such as the magnesium injection cycle.
Presently, fuels used include:
Even fluidized metal powders and explosives have seen some use. Engines that use gases for fuel are called gas engines and those that use liquid hydrocarbons are called oil engines; however, gasoline engines are also often colloquially referred to as "gas engines" ("petrol engines" outside North America).
The main limitations on fuels are that it must be easily transportable through the fuel system to the combustion chamber, and that the fuel releases sufficient energy in the form of heat upon combustion to make practical use of the engine.
Diesel engines are generally heavier, noisier, and more powerful at lower speeds than gasoline engines. They are also more fuel-efficient in most circumstances and are used in heavy road vehicles, some automobiles (increasingly so for their increased fuel efficiency over gasoline engines), ships, railway locomotives, and light aircraft. Gasoline engines are used in most other road vehicles including most cars, motorcycles, and mopeds. Note that in Europe, sophisticated diesel-engined cars have taken over about 45% of the market since the 1990s. There are also engines that run on hydrogen, methanol, ethanol, liquefied petroleum gas (LPG), biodiesel, paraffin and tractor vaporizing oil (TVO).
#### Hydrogen
Hydrogen could eventually replace conventional fossil fuels in traditional internal combustion engines. Alternatively fuel cell technology may come to deliver its promise and the use of the internal combustion engines could even be phased out.
Although there are multiple ways of producing free hydrogen, those methods require converting combustible molecules into hydrogen or consuming electric energy. Unless that electricity is produced from a renewable source—and is not required for other purposes—hydrogen does not solve any energy crisis. In many situations the disadvantage of hydrogen, relative to carbon fuels, is its storage. Liquid hydrogen has extremely low density (14 times lower than water) and requires extensive insulation—whilst gaseous hydrogen requires heavy tankage. Even when liquefied, hydrogen has a higher specific energy but the volumetric energetic storage is still roughly five times lower than gasoline. However, the energy density of hydrogen is considerably higher than that of electric batteries, making it a serious contender as an energy carrier to replace fossil fuels. The 'Hydrogen on Demand' process (see direct borohydride fuel cell) creates hydrogen as needed, but has other issues, such as the high price of the sodium borohydride that is the raw material.
### Oxidizers
One-cylinder gasoline engine, c. 1910
Since air is plentiful at the surface of the earth, the oxidizer is typically atmospheric oxygen, which has the advantage of not being stored within the vehicle. This increases the power-to-weight and power-to-volume ratios. Other materials are used for special purposes, often to increase power output or to allow operation under water or in space.
• Compressed air has been commonly used in torpedoes.[49]
• Compressed oxygen, as well as some compressed air, was used in the Japanese Type 93 torpedo. Some submarines carry pure oxygen. Rockets very often use liquid oxygen.[50]
• Nitromethane is added to some racing and model fuels to increase power and control combustion.
• Nitrous oxide has been used—with extra gasoline—in tactical aircraft, and in specially equipped cars to allow short bursts of added power from engines that otherwise run on gasoline and air. It is also used in the Burt Rutan rocket spacecraft.
• Hydrogen peroxide power was under development for German World War II submarines. It may have been used in some non-nuclear submarines, and was used on some rocket engines (notably the Black Arrow and the Messerschmitt Me 163 rocket fighter).
• Other chemicals such as chlorine or fluorine have been used experimentally, but have not been found practical.
## Cooling
Cooling is required to remove excessive heat—high temperature can cause engine failure, usually from wear (due to high-temperature-induced failure of lubrication), cracking or warping. Two most common forms of engine cooling are air-cooled and water-cooled. Most modern automotive engines are both water and air-cooled, as the water/liquid-coolant is carried to air-cooled fins and/or fans, whereas larger engines may be singularly water-cooled as they are stationary and have a constant supply of water through water-mains or fresh-water, while most power tool engines and other small engines are air-cooled. Some engines (air or water-cooled) also have an oil cooler. In some engines, especially for turbine engine blade cooling and liquid rocket engine cooling, fuel is used as a coolant, as it is simultaneously preheated before injecting it into a combustion chamber.
## Starting
Hand-cranking a boat diesel motor in Inle Lake (Myanmar).
Electric starter as used in automobiles
Internal combustion engines must have their cycles started. In reciprocating engines this is accomplished by turning the crankshaft (Wankel Rotor Shaft) which induces the cycles of intake, compression, combustion, and exhaust. The first engines were started with a turn of their flywheels, while the first vehicle (the Daimler Reitwagen) was started with a hand crank. All ICE engined automobiles were started with hand cranks until Charles Kettering developed the electric starter for automobiles.[51] This method is now the most widely used, even among non-automobiles.
As diesel engines have become larger and their mechanisms heavier, air starters have come into use.[52] This is due to the lack of torque in electric starters. Air starters work by pumping compressed air into the cylinders of an engine to start it turning.
Two-wheeled vehicles may have their engines started in one of four ways:
• By pedaling, as on a bicycle
• By pushing the vehicle and then engaging the clutch, known as "run-and-bump starting"
• By kicking downward on a single pedal, known as "kick starting"
• By an electric starter, as in cars
There are also starters where a spring is compressed by a crank motion and then used to start an engine.
Some small engines use a pull-rope mechanism called "recoil starting", as the rope rewinds itself after it has been pulled out to start the engine. This method is commonly used in pushed lawn mowers and other settings where only a small amount of torque is needed to turn an engine over.
Turbine engines are frequently started by an electric motor or by compressed air.
## Measures of engine performance
Engine types vary greatly in a number of different ways:
### Energy efficiency
Once ignited and burnt, the combustion products—hot gases—have more available thermal energy than the original compressed fuel-air mixture (which had higher chemical energy). This available energy is manifested as a higher temperature and pressure that can be converted into kinetic energy by the engine. In a reciprocating engine, the high-pressure gases inside the cylinders drive the engine's pistons.
Once the available energy has been removed, the remaining hot gases are vented (often by opening a valve or exposing the exhaust outlet) and this allows the piston to return to its previous position (top dead center, or TDC). The piston can then proceed to the next phase of its cycle, which varies between engines. Any thermal energy that is not translated into work is normally considered a waste product and is removed from the engine either by an air or liquid cooling system.
Internal combustion engines are considered heat engines (since the release of chemical energy in combustion has the same effect as heat transfer into the engine) and as such their theoretical efficiency can be approximated by idealized thermodynamic cycles. The thermal efficiency of a theoretical cycle cannot exceed that of the Carnot cycle, whose efficiency is determined by the difference between the lower and upper operating temperatures of the engine. The upper operating temperature of an engine is limited by two main factors; the thermal operating limits of the materials, and the auto-ignition resistance of the fuel. All metals and alloys have a thermal operating limit, and there is significant research into ceramic materials that can be made with greater thermal stability and desirable structural properties. Higher thermal stability allows for a greater temperature difference between the lower (ambient) and upper operating temperatures, hence greater thermodynamic efficiency. Also, as the cylinder temperature rises, the fuel becomes more prone to auto-ignition. This is caused when the cylinder temperature nears the flash point of the charge. At this point, ignition can spontaneously occur before the spark plug fires, causing excessive cylinder pressures. Auto-ignition can be mitigated by using fuels with high auto-ignition resistance (octane rating), however it still puts an upper bound on the allowable peak cylinder temperature.
The thermodynamic limits assume that the engine is operating under ideal conditions: a frictionless world, ideal gases, perfect insulators, and operation for infinite time. Real world applications introduce complexities that reduce efficiency. For example, a real engine runs best at a specific load, termed its power band. The engine in a car cruising on a highway is usually operating significantly below its ideal load, because it is designed for the higher loads required for rapid acceleration.[citation needed] In addition, factors such as wind resistance reduce overall system efficiency. Engine fuel economy is measured in miles per gallon or in liters per 100 kilometers. The volume of hydrocarbon assumes a standard energy content.
Even when aided with turbochargers and stock efficiency aids, most engines retain an average efficiency of about 18–20%.[53] However, the latest technologies in Formula One engines have seen a boost in thermal efficiency past 50%.[54] There are many inventions aimed at increasing the efficiency of IC engines. In general, practical engines are always compromised by trade-offs between different properties such as efficiency, weight, power, heat, response, exhaust emissions, or noise. Sometimes economy also plays a role in not only the cost of manufacturing the engine itself, but also manufacturing and distributing the fuel. Increasing the engine's efficiency brings better fuel economy but only if the fuel cost per energy content is the same.
### Measures of fuel efficiency and propellant efficiency
For stationary and shaft engines including propeller engines, fuel consumption is measured by calculating the brake specific fuel consumption, which measures the mass flow rate of fuel consumption divided by the power produced.
For internal combustion engines in the form of jet engines, the power output varies drastically with airspeed and a less variable measure is used: thrust specific fuel consumption (TSFC), which is the mass of propellant needed to generate impulses that is measured in either pound force-hour or the grams of propellant needed to generate an impulse that measures one kilonewton-second.
For rockets, TSFC can be used, but typically other equivalent measures are traditionally used, such as specific impulse and effective exhaust velocity.
## Air and noise pollution
Pollution Part of a series on Air pollution from a factory in Nepal Digital Noise Transportation Urban Sonar Marine mammals and sonar Industrial Military Abstract Noise control Visual Air travel Advertising clutter Overhead power lines Traffic signs Vandalism Misc Lists Categories By country Environment portal Ecology portal vte
### Air pollution
Internal combustion engines such as reciprocating internal combustion engines produce air pollution emissions, due to incomplete combustion of carbonaceous fuel. The main derivatives of the process are carbon dioxide CO
2
, water and some soot—also called particulate matter (PM). The effects of inhaling particulate matter have been studied in humans and animals and include asthma, lung cancer, cardiovascular issues, and premature death. There are, however, some additional products of the combustion process that include nitrogen oxides and sulfur and some uncombusted hydrocarbons, depending on the operating conditions and the fuel-air ratio.
Carbon dioxide emissions from internal combustion engines contribute to human-induced climate change. Increasing the engine's fuel efficiency can reduce, but not eliminate, the amount of CO
2
emissions as carbon-based fuel combustion produces CO
2
. Since removing CO
2
from engine exhaust is impractical, there is increasing interest in alternatives. Sustainable fuels such as biofuels, synfuels, and electric motors powered by batteries are examples.
Not all of the fuel is completely consumed by the combustion process. A small amount of fuel is present after combustion, and some of it reacts to form oxygenates, such as formaldehyde or acetaldehyde, or hydrocarbons not originally present in the input fuel mixture. Incomplete combustion usually results from insufficient oxygen to achieve the perfect stoichiometric ratio. The flame is "quenched" by the relatively cool cylinder walls, leaving behind unreacted fuel that is expelled with the exhaust. When running at lower speeds, quenching is commonly observed in diesel (compression ignition) engines that run on natural gas. Quenching reduces efficiency and increases knocking, sometimes causing the engine to stall. Incomplete combustion also leads to the production of carbon monoxide (CO). Further chemicals released are benzene and 1,3-butadiene that are also hazardous air pollutants.
Increasing the amount of air in the engine reduces emissions of incomplete combustion products, but also promotes reaction between oxygen and nitrogen in the air to produce nitrogen oxides (NOx). NOx is hazardous to both plant and animal health, and leads to the production of ozone (O3). Ozone is not emitted directly; rather, it is a secondary air pollutant, produced in the atmosphere by the reaction of NOx and volatile organic compounds in the presence of sunlight. Ground-level ozone is harmful to human health and the environment. Though the same chemical substance, ground-level ozone should not be confused with stratospheric ozone, or the ozone layer, which protects the earth from harmful ultraviolet rays.
Carbon fuels contain sulfur and impurities that eventually produce sulfur monoxides (SO) and sulfur dioxide (SO2) in the exhaust, which promotes acid rain.
In the United States, nitrogen oxides, PM, carbon monoxide, sulfur dioxide, and ozone, are regulated as criteria air pollutants under the Clean Air Act to levels where human health and welfare are protected. Other pollutants, such as benzene and 1,3-butadiene, are regulated as hazardous air pollutants whose emissions must be lowered as much as possible depending on technological and practical considerations.
NOx, carbon monoxide and other pollutants are frequently controlled via exhaust gas recirculation which returns some of the exhaust back into the engine intake, and catalytic converters, which convert exhaust chemicals to harmless chemicals.
#### Non-road engines
The emission standards used by many countries have special requirements for non-road engines which are used by equipment and vehicles that are not operated on the public roadways. The standards are separated from the road vehicles.[55]
### Noise pollution
Significant contributions to noise pollution are made by internal combustion engines. Automobile and truck traffic operating on highways and street systems produce noise, as do aircraft flights due to jet noise, particularly supersonic-capable aircraft. Rocket engines create the most intense noise.
### Idling
Internal combustion engines continue to consume fuel and emit pollutants when idling so it is desirable to keep periods of idling to a minimum. Many bus companies now instruct drivers to switch off the engine when the bus is waiting at a terminal.
In England, the Road Traffic Vehicle Emissions Fixed Penalty Regulations 2002 (Statutory Instrument 2002 No. 1808) [56] introduced the concept of a "stationary idling offence". This means that a driver can be ordered "by an authorised person ... upon production of evidence of his authorisation, require him to stop the running of the engine of that vehicle" and a "person who fails to comply ... shall be guilty of an offence and be liable on summary conviction to a fine not exceeding level 3 on the standard scale". Only a few local authorities have implemented the regulations, one of them being Oxford City Council.[57]
In many European countries, idling is, by default, disabled by stop-start systems.
## Carbon dioxide formation
A good way to estimate the mass of carbon dioxide that is released when one litre of diesel fuel (or gasoline) is combusted can be found as follows:[58]
As a good approximation the chemical formula of diesel is C
n
H
2n
. Note that in reality diesel is a mixture of different molecules. As carbon has a molar mass of 12 g/mol and hydrogen (atomic) has a molar mass of about 1 g/mol, the fraction by weight of carbon in diesel is roughly 1214.
The reaction of diesel combustion is given by:
2C
n
H
2n
+ 3nO
2
⇌ 2nCO
2
+ 2nH
2
O
Carbon dioxide has a molar mass of 44 g/mol as it consists of 2 atoms of oxygen (16 g/mol) and 1 atom of carbon (12 g/mol). So 12 g of carbon yields 44 g of carbon dioxide.
Diesel has a density of 0.838 kg per litre.
Putting everything together the mass of carbon dioxide that is produced by burning 1 litre of diesel can be calculated as:
${\displaystyle 0.838kg/L\cdot {\frac {12}{14}}\cdot {\frac {44}{12}}=2.63kg/L}$
The figure obtained with this estimation is close to the values found in the literature.
For gasoline, with a density of 0.75 kg/L and a ratio of carbon to hydrogen atoms of about 6 to 14, the estimated value of carbon emission from burning 1 litre of gasoline is:
${\displaystyle 0.75kg/L\cdot {{\frac {6\cdot 12}{6\cdot 12+14}}\cdot 1}\cdot {\frac {44}{12}}=2.3kg/L}$
## See also
• Energy portal
## References
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23. ^ Haseli, Yousef. "Atkinson Cycle". Science Direct. Retrieved 8 May 2022.
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35. ^ "Laser sparks revolution in internal combustion engines". Physorg.com. 20 April 2011. Retrieved 26 December 2013.
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39. ^ "Electronic Ignition Overview". Jetav8r. Retrieved 2 September 2016.
40. ^ "Gasifier Aids Motor Starting Under Arctic Conditions". Popular Mechanics. Hearst Magazines. January 1953. p. 149.
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44. ^ Kardan, Ramtin (2018). "The effect of engine throttle position on the performance characteristics of a crank-rocker engine fitted with a conventional cylinder head". AIP Conference Proceedings. 2035 (1): 020001. Bibcode:2018AIPC.2035b0001K. doi:10.1063/1.5075549.
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58. ^ Hilgers, Michael (2020). The Diesel Engine, in series: commercial vehicle technology. Berlin/Heidelberg/New York: Springer. ISBN 978-3-662-60856-2.
## Bibliography
• Anyebe, E.A (2009). Combustion Engine and Operations, Automobile Technology Handbook. Vol. 2.
• Denton, T. (2011). Automobile Mechanical and Electrical Systems. Automobile Mechanical and Electrical Systems: Automotive Technology : Vehicle Maintenance and Repair. Taylor & Francis. ISBN 978-1-136-27038-3.
• Heywood, J. (2018). Internal Combustion Engine Fundamentals 2E. McGraw-Hill Education. ISBN 978-1-260-11611-3.
• Nunney, Malcolm J. (2007). Light and Heavy Vehicle Technology (4th ed.). Elsevier Butterworth-Heinemann. ISBN 978-0-7506-8037-0.
• Ricardo, Harry (1931). The High-Speed Internal Combustion Engine.
• Singal, R.K. Internal Combustion Engines. New Delhi, India: Kataria Books. ISBN 978-93-5014-214-1.
• Stone, Richard (1992). Introduction to Internal Combustion Engines (2nd ed.). Macmillan. ISBN 978-0-333-55083-0.
• Yamagata, H. (2005). The Science and Technology of Materials in Automotive Engines. Woodhead Publishing in materials The science and technology of materials in automotive engines. Elsevier Science. ISBN 978-1-84569-085-4.
• Patents:
• ES 433850, Ubierna Laciana, "Perfeccionamientos en Motores de Explosion, con Cinco Tiem-Pos y Doble Expansion", published 1976-11-01
• ES 230551, Ortuno Garcia Jose, "Un Nuevo Motor de Explosion", published 1957-03-01
• ES 249247, Ortuno Garcia Jose, "Motor de Carreras Distintas", published 1959-09-01
## Further reading
• Singer, Charles Joseph; Raper, Richard (1978). Charles, Singer; et al. (eds.). A History of Technology: The Internal Combustion Engine. Clarendon Press. pp. 157–176. ISBN 978-0-19-858155-0.
• Setright, LJK (1975). Some unusual engines. London: The Institution of Mechanical Engineers. ISBN 978-0-85298-208-2.
• Suzuki, Takashi (1997). The Romance of Engines. US: Society of Automotive Engineers. ISBN 978-1-56091-911-7.
• Hardenberg, Horst O. (1999). The Middle Ages of the Internal Combustion Engine. US: Society of Automotive Engineers.
• Gunston, Bill (1999). Development of Piston Aero Engines. PSL. ISBN 978-1-85260-619-0.
|
# Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets
@article{Li2015IntrabandAI,
title={Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets},
author={Hang Li and H. Gao and L. Z{\^a}rbo and K. V'yborn'y and Xuhui Wang and I. Garate and Fatih Dovgan and A. vCejchan and J. Sinova and T. Jungwirth and A. Manchon},
journal={Physical Review B},
year={2015},
volume={91},
pages={134402}
}
Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using the Kubo formula. In addition to the current-driven fieldlike torque ${\mathbf{T}}_{\mathrm{FL}}={\ensuremath{\tau}}_{\mathrm{FL}}\mathbf{m}\ifmmode\times\else\texttimes\fi{}{\mathbf{u}}_{\mathrm{so}}$ (${\mathbf{u}}_{\mathrm{so}}$ being a unit vector determined by the symmetry of the spin-orbit coupling), we explore the intrinsic… Expand
#### Figures from this paper
Understanding current-driven dynamics of magnetic Néel walls in heavy metal/ferromagnetic metal/oxide trilayers
• Physics
• 2018
We consider analytically current-driven dynamics of magnetic Neel walls in heavy metal/ferromagnetic metal/oxide trilayers where strong spin-orbit coupling and interfacial Dzyaloshinskii-MoriyaExpand
Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach
• Physics
• 2016
Motivated by recent experiments observing spin-orbit torque (SOT) acting on the magnetization $\vec{m}$ of a ferromagnetic (F) overlayer on the surface of a three-dimensional topological insulatorExpand
Voltage-Driven Magnetization Switching via Dirac Magnetic Anisotropy and Spin-Orbit Torque in Topological-Insulator-Based Magnetic Heterostructures
• Physics, Materials Science
• 2020
Electric-field control of magnetization dynamics is fundamentally and technologically important for future spintronic devices. Here, based on electric-field control of both magnetic anisotropy andExpand
Spin-Orbit Torque Magnetization Switching in MoTe2 /Permalloy Heterostructures.
The observation of spin-orbit torque switching in bilayers consisting of a semimetallic film of 1T'-MoTe2 adjacent to permalloy is reported, and exciting prospects of using MoTe2 for low-power semimetal-material-based spin devices are foretell. Expand
First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers
• Physics
• 2018
We review a unified approach for computing both spin-transfer torque (STT) in spin-valves and magnetic tunnel junctions (MTJs), where charge current is injected perpendicularly to interfaces, andExpand
Self-current induced spin-orbit torque in FeMn/Pt multilayers
• Materials Science, Physics
• Scientific reports
• 2016
It is demonstrated that, by stacking ultrathin Pt and FeMm alternately, both ferromagnetic properties and current induced spin-orbit torque can be achieved in FeMn/Pt multilayers without any constraint on its total thickness. Expand
Transport properties of Rashba conducting strips coupled to magnetic moments with spiral order
Magnetic and transport properties of a conducting layer with Rashba spin-orbit coupling (RSOC) magnetically coupled to a layer of localized magnetic moments are studied on strips of varying width.Expand
In-plane magnetization effect on current-induced spin-orbit torque in a ferromagnet/topological insulator bilayer with hexagonal warping
• Physics
• 2019
Current-induced spin polarization and the resulting spin-orbit torque (SOT) in a ferromagnet/topological insulator (FM/TI) bilayer have been investigated by taking into account the hexagonal warpingExpand
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• Physics
• 2017
Motivated by the need to understand current-induced magnetization dynamics at the nanoscale, we have developed a formalism, within the framework of Keldysh Green function approach, to study theExpand
Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
Spin-orbit coupling in inversion-asymmetric magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current,Expand
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Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Systems
Introduction.- Band Structure of Semiconductors.- The Extended Kane Model.- Electron and Hole States in Quasi 2D Systems.- Origin of Spin-Orbit Coupling Effects.- Inversion Asymmetry Induced SpinExpand
APPL
Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variablesExpand
L
• P. Zârbo, K. Vyborny, A. J. Ferguson, and T. Jungwirth, Nat. Nanotechnol. 9, 211
• 2014
Phys
• Rev. B 87, 174411
• 2013
Rev
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• Commun. 4, 1799 (2013); X. Fan, H. Celik, J. Wu, C. Ni, K.-J. Lee, V. O. Lorenz, and J. Q. Xiao, ibid. 5, 3042 (2014). 134402-8 INTRABAND AND INTERBAND SPIN-ORBIT TORQUES IN . . . PHYSICAL REVIEW B 91, 134402
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• Nanotechnol. 8, 587 (2013); C. O. Avci, K. Garello, M. Gabureac, A. Ghosh, A. Fuhrer, S. F. Alvarado, and P. Gambardella, Phys. Rev. B 90, 224427
• 2014
|
## anonymous 5 years ago 1. An animal clinic kept record of the life spans of certain poodles. The number of years the dogs lived are 8, 10, 12, 15, 17, and 13. What is the standard deviation of the poodle life spans?
1. anonymous
do you know the standard deviation formula?
2. anonymous
it should be around the sqrt(102/10)
3. anonymous
whats the formula
4. anonymous
phinx828--go back to the other question
5. Yuki
to find the SD, you need to know the formula $\sqrt({1 \over n} \sum {(x*-x_i)^2})$
6. anonymous
sqrt(107/10)*
7. anonymous
Here!
8. anonymous
thats confusing, i never saw that formula
9. Yuki
usually the steps are as follows 1), find x* which is the mean 2), list the square of mean deviations in your case, x*-8, x*-10, x*-12 ...etc 3), square each numbers you got in the list (x*-8)^2, (x*-10)^2, ... etc 4), add them up 5), divide them by the number of #s, in your case since you have 6 numbers, divide by 6 at this step, you will get a number called the "variant" SD is defined as the square root of the variant, so 6), square root the number you got
10. Yuki
rosette, do you need explanation how the formula works ?
11. anonymous
no
|
This shiny gadget can be used to build centrality indices based on specific indirect relations, transformations and aggregation functions.
index_builder()
## Value
code to calculate the specified index.
|
153 metric teaspoons in dry gallons
Conversion
153 metric teaspoons is equivalent to 0.173670870741419 dry gallons.[1]
Conversion formula How to convert 153 metric teaspoons to dry gallons?
We know (by definition) that: $1\mathrm{brteaspoon}\approx 0.00113510373033607\mathrm{drygallon}$
We can set up a proportion to solve for the number of dry gallons.
$1 brteaspoon 153 brteaspoon ≈ 0.00113510373033607 drygallon x drygallon$
Now, we cross multiply to solve for our unknown $x$:
$x\mathrm{drygallon}\approx \frac{153\mathrm{brteaspoon}}{1\mathrm{brteaspoon}}*0.00113510373033607\mathrm{drygallon}\to x\mathrm{drygallon}\approx 0.1736708707414187\mathrm{drygallon}$
Conclusion: $153 brteaspoon ≈ 0.1736708707414187 drygallon$
Conversion in the opposite direction
The inverse of the conversion factor is that 1 dry gallon is equal to 5.75801800112418 times 153 metric teaspoons.
It can also be expressed as: 153 metric teaspoons is equal to $\frac{1}{\mathrm{5.75801800112418}}$ dry gallons.
Approximation
An approximate numerical result would be: one hundred and fifty-three metric teaspoons is about zero point one seven dry gallons, or alternatively, a dry gallon is about five point seven five times one hundred and fifty-three metric teaspoons.
Footnotes
[1] The precision is 15 significant digits (fourteen digits to the right of the decimal point).
Results may contain small errors due to the use of floating point arithmetic.
|
# Sum of Odd Integers
You are given two integers $n$ and $k$. Your task is to find if $n$ can be represented as a sum of $k$ distinct positive odd (not divisible by $2$) integers or not.
You have to answer $t$ independent test cases.
Input
The first line of the input contains one integer $t$ ($1 \le t \le 10^5$) — the number of test cases.
The next $t$ lines describe test cases. The only line of the test case contains two integers $n$ and $k$ ($1 \le n, k \le 10^7$).
Output
For each test case, print the answer — “YES” (without quotes) if $n$ can be represented as a sum of $k$ distinct positive odd (not divisible by $2$) integers and “NO” otherwise.
Example
input
6
3 1
4 2
10 3
10 2
16 4
16 5
output
YES
YES
NO
YES
YES
NO
Note
In the first test case, you can represent $3$ as $3$.
In the second test case, the only way to represent $4$ is $1+3$.
In the third test case, you cannot represent $10$ as the sum of three distinct positive odd integers.
In the fourth test case, you can represent $10$ as $3+7$, for example.
In the fifth test case, you can represent $16$ as $1+3+5+7$.
In the sixth test case, you cannot represent $16$ as the sum of five distinct positive odd integers.
Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
|
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
For every solution of the equation $x^2+y^2=1$, $x,y\in \mathbb Q$, the matrix $$\begin{pmatrix} x & y \\ -y & x \end{pmatrix}$$ is a rotation that maps $\mathbb Q^2$ to itself.
An example is given by the rotation $$\begin{pmatrix} \textstyle\frac45 & \textstyle\frac35 \\ \textstyle-\frac35 & \textstyle\frac45 \end{pmatrix}$$ which has infinite order, and thus provides an answer to your second question.
For every solution of the equation $x^2+y^2=1$, $x,y\in \mathbb Q$, the matrix $$\begin{pmatrix} x & y \\ -y & x \end{pmatrix}$$ maps $\mathbb Q^2$ to itself.
An example is given by the rotation $$\begin{pmatrix} \textstyle\frac45 & \textstyle\frac35 \\ \textstyle-\frac35 & \textstyle\frac45 \end{pmatrix}$$ which has infinite order, and thus provides an answer to your second question.
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# The All-Too-Human Reason Nuclear Material Isn’t Secure Enough
By William Tobey
They cut through four fences, set off sensors and alarms, hammered on the outside of the storage building, and defaced it with paint and human blood. They remained on the site for over an hour before a guard finally arrested them.
# Fresh Thinking on Highly Enriched Uranium Research Reactor Conversions
By William Tobey
Last week, a National Academies of Sciences, Engineering, and Medicine panel affirmed the goal of eliminating highly enriched uranium (HEU) from civilian use, while recommending step-wise conversion of high performance research reactors using weapon-grade uranium fuel and that the White House coordinate a 50-year national roadmap for neutron-based research. (Full disclosure: I sat on that committee, and oversaw the NNSA reactor conversion program from 2006-9; this post, however, represents my views, not necessarily those of the committee or NNSA.)
# The Russian Tie We Can't Cut
“I continue to be much more concerned, when it comes to our security, with the prospect of a nuclear weapon going off in Manhattan.” So said President Obama last March, weighing the danger of nuclear terrorism against that of Russian aggression in Ukraine. Yet our research shows that his administration proposes cutting the amount of money spent on an array of programs to secure nuclear bomb materials around the world and keep them out of terrorists’ hands — to $555 million next year from$700 million in fiscal 2014. And in both houses of Congress, there are efforts to legislate a suspension of nuclear security cooperation with Russia.
# Committing to Excellence in Nuclear Security
By William Tobey (writing from The Hague)
In what one Dutch official called the “most important deliverable from the Summit,” thirty-five nations, led by the host governments of the Nuclear Security Summits in Washington, Seoul, and The Hague, announced today their commitment to strengthen nuclear security implementation.
# We Are Failing at Nuclear Security
By William H. Tobey
Next month, top leaders from over 50 countries will meet at the 2014 Hague Nuclear Security Summit. The leaders’ fundamental goal remains to prevent nuclear terrorism by implementing effective security at all sites that store or process nuclear weapons or fissile materials, or which operate nuclear reactors.
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# Change header title in beamer
I'm preparing a presentation with three parts. I use Antibes theme. I want to change the title of the presentation that appears in each frame by the title of the part, and then the sections and subsections. Now I have, in frames header:
Title of the presentation
Section
Subsection
And I want
Title of the part
Section
Subsection
• Welcome to TeX.SX! You can help us to help you by providing the code for a small document that shows your setup, including the theme you use. Just edit your question and add the code. – samcarter is at topanswers.xyz Oct 28 '16 at 13:01
• If you don't know how to provide a minimal working example, look here. – CarLaTeX Oct 29 '16 at 9:47
If you redefine the headline template, you can replace \insertshorttitle with \insertpart:
\documentclass{beamer}
\usetheme{Antibes}
\makeatletter
\end{beamercolorbox}
\begin{beamercolorbox}[wd=\paperwidth,ht=2.5ex,dp=1.125ex,%
\insertpart
% \insertshorttitle
\end{beamercolorbox}
\begin{beamercolorbox}[wd=\paperwidth,ht=2.5ex,dp=1.125ex,%
\ifbeamer@tree@showhooks
\ifdim\wd\beamer@tempbox>1pt%
\hskip2pt\raise1.9pt\hbox{\vrule width0.4pt height1.875ex\vrule width 5pt height0.4pt}%
\hskip1pt%
\fi%
\else%
\hskip6pt%
\fi%
\end{beamercolorbox}
\begin{beamercolorbox}[wd=\paperwidth,ht=2.5ex,dp=1.125ex,%
\ifbeamer@tree@showhooks
\ifdim\wd\beamer@tempbox>1pt%
\hskip9.4pt\raise1.9pt\hbox{\vrule width0.4pt height1.875ex\vrule width 5pt height0.4pt}%
\hskip1pt%
\fi%
\else%
\hskip12pt%
\fi%
\end{beamercolorbox}
\end{beamercolorbox}
}
\makeatother
\title{title}
\begin{document}
\part{part}
\section{section}
\subsection{subsection}
\begin{frame}
abc
\end{frame}
\end{document}
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Question
Why is the value of '$g$' minimum at the equator?
Open in App
Solution
Step 1: Acceleration due to gravityGravitational acceleration is greatest at the poles and least near the equator. An object's gravitational acceleration is a measurable quantity. According to Newton's universal law of Gravitation, the value of gravity depends on the mass of the Earth and the distance of the object from the center of Earth.In general, the acceleration due to gravity $\left(g\right)$ on the surface of the Earth is given by, $g=\frac{GM}{{R}^{2}}$, where $G$ is the gravitational constant, $\mathrm{M}$ is the mass of the Earth, and $R$ is the distance of the object from the center of Earth.Step 2: ExplanationEarth is not a perfect sphere, but rather an elliptical sphere. The gravitational acceleration varies at all points on Earth as a result of this distortion, but the mass remains constant since it is independent of the shape.The equatorial radius is 21 km greater than the radius at the poles.The radius of the Earth is maximum at the equator.Hence, the value of $g$ is minimum at the equator.
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