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# Optimal way to place a given number of points in a region?
Let $A\subset\mathbb{R}²$ and $n\in\mathbb{N}$ be a given natural number. How to find a finite subset of $A$, $P=${$p_1,...,p_n$} such that $\int_A f_P(x)$ is minimum, where $f_P(x) = min${$d(x,p_1),...,d(x,p_n)$} and $d$ is the usual distance? Supose a certain number of hospitals must be placed in a city. How should them be placed so that on average the length from any point in the city to the nearest hospital is the less as possible?
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What are your thoughts? – leonbloy Dec 20 '12 at 16:14
If the usual distance is used, the resulting function $f_P$ is composed of 'parts' of surfaces of cones. – Sgernesto Dec 20 '12 at 17:35
This sounds non trivial. You might want to read about Centroidal Voronoi Tessellations (relate, though not quite the same thing -minimizes average square distance rather than average distance) and perhaps k-medians clustering (for samples instead of a distribution). – leonbloy Dec 20 '12 at 21:04
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# Approximate the integral $\int_0^1 \sin(x^2) dx$
I'd like to ask if someone can please give me a little push with this assignment:
Approximate the value of the integral $\int_0^1 \sin(x^2) dx$ using only $\mathbb{N}$ numbers and basic operations $(+,-,*,/)$. For example use Simpson's rule or the Trapezoidal rule to calculate the integral, then use Taylor's series to determine the value of sinus.
I have used Simpson's rule to approximate the integral and got:
$\int_0^1 \sin(x^2) dx \approx \frac{2}{3}\sin(\frac{1}{4}) + \frac{1}{6}\sin(1)$
But I don't know what to do with the Taylor series. Should I compute it for $\frac{2}{3}\sin(x^2) + \frac{1}{6}\sin(x^2)$ and then express it for $x = \frac{1}{4}$ and $x = 1$ or is my thinking bad?
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What you do here is to figure out the Maclaurin expansion for the function $\int_0^x \sin(u^2)\,\mathrm du$. You can figure that by starting with the Maclaurin series for $\sin\,x$ and then replacing the $x$ with $x^2$. Use that series when you're called to evaluate $\sin(x^2)$ for trapezoidal or Simpson's purposes.
Sorry for the confusion; a Maclaurin series is a Taylor series corresponding to the expansion point 0: $f(x)=f(0)+f'(0)x+\dots$ – Guess who it is. Oct 29 '11 at 20:17
Because the teacher asks them not to use integrals, he should use the Taylor series to approximate $\frac{2}{3}\sin(\frac{1}{4}) + \frac{1}{6}\sin(1)$. – N. S. Oct 29 '11 at 20:21
Thanks, now I understand :) So I should compute it just for $sin(x)$ at point $0$, then replace $x$ with $x^2$ and then substitute the result for the $sin(x^2)$ functions in the expression I got from applying the Simpson's rule and then assign $\frac{1}{4}$ to the first one and $1$ to the second one, right? – Alexandar Živkovič Oct 29 '11 at 20:24
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# Neumann BCs in cylindrical geometry (FEM)
I was wondering where I could get a detailed account (either in print or online) on applying a Neumann/mixed Boundary condition along the $$r=0$$ axis in an axially symmetric geometry. Though this is a very common task I have always struggled to find a reasonable account of it. Piecing together sparse and poorly referenced notes I believe that in 1D polar coordinates where:
$$\nabla^2 u = \frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r}$$
one gets, by Taylor expansion at the origin,:
$$\nabla^2 u \rvert_{r=0} \simeq 2\frac{\partial^2 u}{\partial r^2}\rvert_{r=0}$$
when $$u$$ is symmetric about the $$r=0$$ axis.
I would like to more information on higher order derivatives, best practice, non-symmetric distributions ... etc. Also, I would be very keen to find some info on best practice for applying this boundary condition in FEM analysis.
This is the wrong boundary condition. If your solution is smooth, then the correct condition at $r=0$ is $$\frac{du}{dr} = 0.$$ You can see this by thinking about what would happen if you cut a line through the origin through the entire domain, i.e., you look at the solution not only for $r\ge 0$ but also for $r\le 0$. To the left of $r=0$ you of course have a mirror image of the solution at the right. If you don't want the solution to have a kink at the origin, you need to require the condition above.
• Yes this is the bc but to apply it with 2nd order accuracy in FD/FV methods one typically introduces ghost points outside the domain, assigns $u_{-1} = u_1$, and subs back into the discretised expression, solving for $u_0$. This procedure fails in cylindrical geometry at $r=0$, due to the $1/r$ term. In such cases I believe one uses Taylor expan, as above, to reformulate the eqn in the limit $r\rightarrow 1$, and then applies the ghost point procedure. I was wondering what the equivalent 2nd order procedure was in FEM, but I think your right, in FEM it appears to be simply the natural bc. – dmon Dec 12 '12 at 10:56
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# Sh:721
• Göbel, R., Shelah, S., & Wallutis, S. L. (2001). On the lattice of cotorsion theories. J. Algebra, 238(1), 292–313.
• Abstract:
We discuss the lattice of cotorsion theories for abelian groups. First we show that the sublattice of the well–studied rational cotorsion theories can be identified with the well–known lattice of types. Using a recently developed method for making Ext vanish we also prove that any power set together with the ordinary set inclusion (and thus any poset) can be embedded into the lattice of all cotorsion theories.
• Current version: 2001-02-12_10 (19p) published version (22p)
Bib entry
@article{Sh:721,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon and Wallutis, Simone L.},
title = {{On the lattice of cotorsion theories}},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {238},
number = {1},
year = {2001},
pages = {292--313},
issn = {0021-8693},
mrnumber = {1822193},
mrclass = {20K35 (16E30)},
doi = {10.1006/jabr.2000.8619},
note = {\href{https://arxiv.org/abs/math/0103154}{arXiv: math/0103154}},
arxiv_number = {math/0103154}
}
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Physics Forums (http://www.physicsforums.com/index.php)
- Precalculus Mathematics Homework (http://www.physicsforums.com/forumdisplay.php?f=155)
- - Sum of the square roots of the first n natural numbers (http://www.physicsforums.com/showthread.php?t=127845)
Amith2006 Aug2-06 02:28 PM
Sum of the square roots of the first n natural numbers
Is there a way to find the,"Sum of the square roots of the first n natural numbers"?
StatusX Aug2-06 02:33 PM
I don't think you could do it exactly. You could approximate it by the integral of $\sqrt{x}$, and get a bound on the error.
Data Aug2-06 03:20 PM
As StatusX says I'm pretty sure there's no way to do in exactly in closed-form. If you don't have a way to calculate square roots at all (ie. you're doing it without a calculator and don't want to go through an approximation method), then a simple integer approximation would be
$$\frac{2}{3}\lfloor \sqrt{n} \rfloor^3 - \frac{1}{2}\lfloor \sqrt{n} \rfloor^2 - \frac{1}{6} \lfloor \sqrt{n} \rfloor + \lfloor \sqrt{n} \rfloor(n-\lfloor \sqrt{n} \rfloor^2),$$
but it's not very good. The integral approximation $\frac{2}{3} n^{\frac{3}{2}}$ is much better, but you have to be able to compute $n^{3/2}$
($2/3 \lfloor n^{3/2}\rfloor$ is also better than the one I gave above though).
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Q)
True or False: The function $f$ has an inverse: $f:{1,2,3,4,}\to{10}$ with $f={(1,10),(2,10),(3,10),(4,10)}$
• A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
• A function$f : X \rightarrow Y$ is said to be onto or surjective, if every element of Y is the image of some element of X under f, i.e., for every $y \in Y$, there exists an element x in X such that $f(x) = y$.
Given $f:\{1,2,3,4\} \to \{10\}$ with $f=\{(1,10),(2,10,(3,10)(4,10)\}$
From the given definition of $f$, we can see that it is many-one, as for every ${1,2,3,4} \in f, f(1) = f(2) = f(3) = f(4) = 10$.
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The acceleration due to gravity on the moon is only one sixth that of earth.It the earth and moon are assume to have the same density, the ratio of th
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in Physics
The acceleration due to gravity on the moon is only one sixth that of earth.It the earth and moon are assume to have the same density, the ratio of the radii of moon and earth will be
A. (1)/(6)
B. (1)/((6)^(1//3))
C. (1)/(36)
D. (1)/((6)^(2//3))
by (120k points)
Correct Answer - A
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Differentiate sin^2xw.r.t e^(cosx). | Filo
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150
Differentiate w.r.t .
Solution: Solution: We know that can be written as .
So, here, and .
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Order of render with transparency opengl
I tried to render using different render configurations (GL_BLEND_FUNC()) but I couldn't get the back object to render in certain angles. The first screenshot here shows one angle where the back object is not visible through the front one. In th second screenshot, I looked at the blocks from 180 degrees.
Is there a way I could render them through? Or would I have to implement a sorting algorithm?
You need to render them back to front relative to the camera in order for transparency to correctly work, check painters algorithm, and depth buffering.
The rational behind this, is that because how depth tests work. The "usual" case for OpenGL is to test fragments for depth, once a fragment passes the depth test it will be written to the frame buffer overwriting any fragment that was written in the same frame buffer position, in other words when your scene have only opaque objects the depth buffer is enough to sort your rendered objects because it only keeps fragments that are near the camera.
When transparency comes into play, this is no more the case, and you need more info than the only nearest fragment. The depth test will still make near fragments overwrite far ones in the frame buffer, even though transparency says otherwise.
GL_BLEND_FUNC() (deprecated btw you should switch to shaders) can only blend fragments using a certain fixed equation, has nothing to do with the order pixels are written and have no control over the depth buffer. So it will apply the blending equation regardless of how the depth buffer sorted them. So the only practical option is to draw far then near objects.
Order-independent transparency on the other hand exist but they are particularly hard to implement.
As a side note opaque only objects (unlike transparent) should be draw front to back to avoid over-draw.
There are techniques for order-indepdendent transparency, but they all require a lot of work. The two techniques I am most familiar with are depth peeling and stencil routed A buffering and they both have a lot of overhead. There are also some new techniques made possible with compute shaders by building a linked-list of fragments, but I have not fooled around with them.
In an engine that only draws cubes like this, sorting your geometry is probably your best bet - you only need to depth sort the centroids for each cube and assuming you cannot rotate the cubes you do not have to worry about objects that intersect throwing off the sort validity. Remember to transform your centroids using the modelview matrix before sorting by Z, you generally want to sort in view-space such that Z represents depth.
I actually wrote an article on a simple algorithm I designed a little while ago to handle this.
http://evergreen-game.tumblr.com/post/72616811569/transparent-object-sorting]
Basically it's a quicksort (or mergesort) that uses a collision detection as its comparison function. If a convex object A's volume created by sweeping it away from the camera plane intersects another convex object B, A is in front of B (and thus the comparison function returns that A is greater than B). In terms of implementation, I'd use a GJK raycast test.
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## Results (30 matches)
Label $\alpha$ $A$ $d$ $N$ $\chi$ $\mu$ $\nu$ $w$ prim $\epsilon$ $r$ First zero Origin
2-4560-1.1-c1-0-0 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.228634 Elliptic curve 4560.b Modular form 4560.2.a.b Modular form 4560.2.a.b.1.1 2-4560-1.1-c1-0-10 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.647922$ Elliptic curve 4560.k Modular form 4560.2.a.k Modular form 4560.2.a.k.1.1
2-4560-1.1-c1-0-12 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.695065 Elliptic curve 4560.x Modular form 4560.2.a.x Modular form 4560.2.a.x.1.1 2-4560-1.1-c1-0-14 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.742637$ Elliptic curve 4560.d Modular form 4560.2.a.d Modular form 4560.2.a.d.1.1
2-4560-1.1-c1-0-16 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.764612 Elliptic curve 4560.s Modular form 4560.2.a.s Modular form 4560.2.a.s.1.1 2-4560-1.1-c1-0-21 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.818960$ Elliptic curve 4560.h Modular form 4560.2.a.h Modular form 4560.2.a.h.1.1
2-4560-1.1-c1-0-22 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.821477 Elliptic curve 4560.i Modular form 4560.2.a.i Modular form 4560.2.a.i.1.1 2-4560-1.1-c1-0-23 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.828462$ Elliptic curve 4560.o Modular form 4560.2.a.o Modular form 4560.2.a.o.1.1
2-4560-1.1-c1-0-24 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.835257 Elliptic curve 4560.r Modular form 4560.2.a.r Modular form 4560.2.a.r.1.1 2-4560-1.1-c1-0-26 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.855628$ Elliptic curve 4560.q Modular form 4560.2.a.q Modular form 4560.2.a.q.1.1
2-4560-1.1-c1-0-28 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.895818 Elliptic curve 4560.v Modular form 4560.2.a.v Modular form 4560.2.a.v.1.1 2-4560-1.1-c1-0-3 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.500957$ Elliptic curve 4560.c Modular form 4560.2.a.c Modular form 4560.2.a.c.1.1
2-4560-1.1-c1-0-31 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 1 0 0.917468 Elliptic curve 4560.ba Modular form 4560.2.a.ba Modular form 4560.2.a.ba.1.1 2-4560-1.1-c1-0-36 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $1.04284$ Elliptic curve 4560.bd Modular form 4560.2.a.bd Modular form 4560.2.a.bd.1.1
2-4560-1.1-c1-0-39 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.09772 Elliptic curve 4560.a Modular form 4560.2.a.a Modular form 4560.2.a.a.1.1 2-4560-1.1-c1-0-44 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $1.18862$ Elliptic curve 4560.bc Modular form 4560.2.a.bc Modular form 4560.2.a.bc.1.1
2-4560-1.1-c1-0-48 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.24347 Elliptic curve 4560.j Modular form 4560.2.a.j Modular form 4560.2.a.j.1.1 2-4560-1.1-c1-0-49 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.26511$ Elliptic curve 4560.e Modular form 4560.2.a.e Modular form 4560.2.a.e.1.1
2-4560-1.1-c1-0-50 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.28629 Elliptic curve 4560.f Modular form 4560.2.a.f Modular form 4560.2.a.f.1.1 2-4560-1.1-c1-0-53 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.31864$ Elliptic curve 4560.n Modular form 4560.2.a.n Modular form 4560.2.a.n.1.1
2-4560-1.1-c1-0-54 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.31866 Elliptic curve 4560.m Modular form 4560.2.a.m Modular form 4560.2.a.m.1.1 2-4560-1.1-c1-0-55 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.36588$ Elliptic curve 4560.g Modular form 4560.2.a.g Modular form 4560.2.a.g.1.1
2-4560-1.1-c1-0-60 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.47535 Elliptic curve 4560.w Modular form 4560.2.a.w Modular form 4560.2.a.w.1.1 2-4560-1.1-c1-0-61 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.49908$ Elliptic curve 4560.p Modular form 4560.2.a.p Modular form 4560.2.a.p.1.1
2-4560-1.1-c1-0-62 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.50566 Elliptic curve 4560.t Modular form 4560.2.a.t Modular form 4560.2.a.t.1.1 2-4560-1.1-c1-0-64 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.53270$ Elliptic curve 4560.y Modular form 4560.2.a.y Modular form 4560.2.a.y.1.1
2-4560-1.1-c1-0-65 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.55512 Elliptic curve 4560.u Modular form 4560.2.a.u Modular form 4560.2.a.u.1.1 2-4560-1.1-c1-0-68 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $-1$ $1$ $1.61230$ Elliptic curve 4560.z Modular form 4560.2.a.z Modular form 4560.2.a.z.1.1
2-4560-1.1-c1-0-70 $6.03$ $36.4$ $2$ $2^{4} \cdot 3 \cdot 5 \cdot 19$ 1.1 $$1.0 1 -1 1 1.69602 Elliptic curve 4560.bb Modular form 4560.2.a.bb Modular form 4560.2.a.bb.1.1 2-4560-1.1-c1-0-9 6.03 36.4 2 2^{4} \cdot 3 \cdot 5 \cdot 19 1.1$$ $1.0$ $1$ $1$ $0$ $0.632929$ Elliptic curve 4560.l Modular form 4560.2.a.l Modular form 4560.2.a.l.1.1
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## Yang-Mills theory paper gets published!
30/12/2016
Exact solutions of quantum field theories are very rare and, normally, refer to toy models and pathological cases. Quite recently, I put on arxiv a pair of papers presenting exact solutions both of the Higgs sector of the Standard Model and the Yang-Mills theory made just of gluons. The former appeared a few month ago (see here) while the latter has been accepted for publication a few days ago (see here). I have updated the latter just today and the accepted version will appear on arxiv on 2 January next year.
What does it mean to solve exactly a quantum field theory? A quantum field theory is exactly solved when we know all its correlation functions. From them, thanks to LSZ reduction formula, we are able to compute whatever observable in principle being these cross sections or decay times. The shortest way to correlation functions are the Dyson-Schwinger equations. These equations form a set with the former equation depending on the higher order correlators and so, they are generally very difficult to solve. They were largely used in studies of Yang-Mills theory provided some truncation scheme is given or by numerical studies. Their exact solutions are generally not known and expected too difficult to find.
The problem can be faced when some solutions to the classical equations of motion of a theory are known. In this way there is a possibility to treat the Dyson-Schwinger set. Anyhow, before to enter into their treatment, it should be emphasized that in literature the Dyson-Schwinger equations where managed just in one way: Using their integral form and expressing all the correlation functions by momenta. It was an original view by Carl Bender that opened up the way (see here). The idea is to write the Dyson-Schwinger equations into their differential form in the coordinate space. So, when you have exact solutions of the classical theory, a possibility opens up to treat also the quantum case!
This shows unequivocally that a Yang-Mills theory can display a mass gap and an infinite spectrum of excitations. Of course, if nature would have chosen the particular ground state depicted by such classical solutions we would have made bingo. This is a possibility but the proof is strongly related to what is going on for the Higgs sector of the Standard Model that I solved exactly but without other matter interacting. If the decay rates of the Higgs particle should agree with our computations we will be on the right track also for Yang-Mills theory. Nature tends to repeat working mechanisms.
Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model Eur. Phys. J. Plus (2016) 131: 199 arXiv: 1504.02299v3
Marco Frasca (2015). Quantum Yang-Mills field theory arXiv arXiv: 1509.05292v1
Carl M. Bender, Kimball A. Milton, & Van M. Savage (1999). Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory Phys.Rev.D62:085001,2000 arXiv: hep-th/9907045v1
## Unpublishable
31/12/2015
I tried in different ways to get this paper through the community with standard channels. As far as I can tell, this paper is unpublishable. By this I mean that journals not even send it to referees to start a normal review process or all people try to stop it from making it known. The argument is always the same: A reformulation of quantum mechanics using stochastic processes but using noncommutative geometry this time. I apologize to the community if this unacceptable approach has bothered people around the World but this is the fate of some ideas. Of course, if somebody has the courage and the willing to publish, let me know and I will appreciate the tentative with infinite gratefulness.
Now, back to sane QCD.
Happy new year!
## Quantum gravity
27/12/2015
Quantum gravity appears today as the Holy Grail of physics. This is so far detached from any possible experimental result but with a lot of attentions from truly remarkable people anyway. In some sense, if a physicist would like to know in her lifetime if her speculations are worth a Nobel prize, better to work elsewhere. Anyhow, we are curious people and we would like to know how does the machinery of space-time work this because to have an engineering of space-time would make do to our civilization a significant leap beyond.
A fine recount of the current theoretical proposals has been rapidly presented by Ethan Siegel in his blog. It is interesting to notice that the two most prominent proposals, string theory and loop quantum gravity, share the same difficulty: They are not able to recover the low-energy limit. For string theory this is a severe drawback as here people ask for a fully unified theory of all the interactions. Loop quantum gravity is more limited in scope and so, one can think to fix the problem in a near future. But of all the proposals Siegel is considering, he is missing the most promising one: Non-commutative geometry. This mathematical idea is due to Alain Connes and earned him a Fields medal. So far, this is the only mathematical framework from which one can rederive the full Standard Model with all its particle content properly coupled to the Einstein’s general relativity. This formulation works with a classical gravitational field and so, one can possibly ask where quantized gravity could come out. Indeed, quite recently, Connes, Chamseddine and Mukhanov (see here and here), were able to show that, in the context of non-commutative geometry, a Riemannian manifold results quantized in unitary volumes of two kind of spheres. The reason why there are two kind of unitary volumes is due to the need to have a charge conjugation operator and this implies that these volumes yield the units $(1,i)$ in the spectrum. This provides the foundations for a future quantum gravity that is fully consistent from the start: The reason is that non-commutative geometry generates renormalizable theories!
The reason for my interest in non-commutative geometry arises exactly from this. Two years ago, I, Alfonso Farina and Matteo Sedehi obtained a publication about the possibility that a complex stochastic process is at the foundations of quantum mechanics (see here and here). We described such a process like the square root of a Brownian motion and so, a Bernoulli process appeared producing the factor 1 or i depending on the sign of the steps of the Brownian motion. This seemed to generate some deep understanding about space-time. Indeed, the work by Connes, Chamseddine and Mukhanov has that understanding and what appeared like a square root process of a Brownian motion today is just the motion of a particle on a non-commutative manifold. Here one has simply a combination of a Clifford algebra, that of Dirac’s matrices, a Wiener process and the Bernoulli process representing the scattering between these randomly distributed quantized volumes. Quantum mechanics is so fundamental that its derivation from a geometrical structure with added some mathematics from stochastic processes makes a case for non-commutative geometry as a serious proposal for quantum gravity.
I hope to give an account of this deep connection in a near future. This appears a rather exciting new avenue to pursue.
Ali H. Chamseddine, Alain Connes, & Viatcheslav Mukhanov (2014). Quanta of Geometry: Noncommutative Aspects Phys. Rev. Lett. 114 (2015) 9, 091302 arXiv: 1409.2471v4
Ali H. Chamseddine, Alain Connes, & Viatcheslav Mukhanov (2014). Geometry and the Quantum: Basics JHEP 12 (2014) 098 arXiv: 1411.0977v1
Farina, A., Frasca, M., & Sedehi, M. (2013). Solving Schrödinger equation via Tartaglia/Pascal triangle: a possible link between stochastic processing and quantum mechanics Signal, Image and Video Processing, 8 (1), 27-37 DOI: 10.1007/s11760-013-0473-y
## News from CERN
17/12/2015
Two days ago, CERN presented their new results at 13 TeV to the World. Of course, collected data so far are not enough for conclusive results but the these are exciting anyway. The reason is that both the collaborations, CMS and ATLAS, see a bump at around 750 GeV in the $\gamma\gamma$ decay. Summing up the results of the two collaborations, they are around $4\sigma$ without look elsewhere effect, not yet a discovery but, probably, at the summer conferences they will have something more conclusive to say. This could be an unlucky fluctuation but this situation remember us the story of the discovery of the Higgs boson more than three years ago. The question if this is beyond Standard Model physics is what I will try to answer in these few lines.
Firstly, if this particle is real, it decays with two photons exactly as the Higgs boson. Secondly, with a final state like this it can have only spin 0 or 2. We will be conservative and assume that this is not a graviton. Rather, it is a sibling of the Higgs particle. Besides, it was not observed in run I but is not inconsistent with data from there. It appears like the increased luminosity favored its appearance. We want to be more conservative and we take for granted just the Lagrangian of the Standard Model. So, what is this beast?
My answer is that this could be an excited state of the Higgs boson that, having a production rate lower than its ground state seen at run I, needed more luminosity to be observed. You do not need to change the Lagrangian of the Standard Model for this and it is not BSM physics yet. You do not even need a technicolor theory to describe it. The reason is that the Higgs part of the Standard Model can be treated mathematically yielding exact solutions. The quantum field theory can be exactly solved and the spectrum of the theory says exactly what I stated above (see here, and here). The Higgs model per se is exactly solvable. So, Jester’s idea to add another scalar field to the Lagrangian model is useless, it is all just inside and you will get a two photon final state as well.
Of course, it is too early to draw a final conclusion and a wealth of papers with a prompt explanation flooded arxiv in these two days. With the restart of LHC on spring and the collecting of more data, things will be clearer than now. For the moment, this hint is enough to keep us excited for the next few months.
Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v2
Marco Frasca (2015). Quantum Yang-Mills field theory arxiv arXiv: 1509.05292v1
## Higgs even more standard
02/09/2015
LHCP 2015 is going on at St. Peterburg and new results were presented by the two main collaborations at CERN. CMS and ATLAS combined the results from run 1 and improved the quality of the measured data of the Higgs particle discovered on 2012. CERN press release is here. I show you the main picture about the couplings between the Higgs field and the other particles in the Standard Model widely exposed in all the social networks
What makes this plot so striking is the very precise agreement with the Standard Model. Anyhow, the ellipses are somewhat large yet to grant new physics creeping in at run 2. My view is that the couplings, determining the masses of the particles in the Standard Model, are less sensible to new physics than the strength of the signal at various decays. Also this plot is available (hat tip to Adam Falkowski)
In this plot you can see that the Standard Model, represented by a star, is somewhat at the border of the areas of the ZZ and WW decays and that of the WW decay is making smaller. This does not imply that in the future deviations from the Standard Model will be seen here but leave the impression that this could happen in run 2 with the increasing precision expected for these measurements.
The strengths are so interesting because the Higgs sector of the Standard Model can be solved exactly with the propagator providing the values of them (see here). These generally disagree from those obtained by standard perturbation theory even if by a small extent. Besides, Higgs particle should have internal degrees of freedom living also in higher excited states. All of this to be seen at run 2 as the production rate of these states appears to be smaller as higher is their mass.
Run 2 is currently ongoing even if the expected luminosity will not be reached for this year. For sure, the next year summer conferences could provide a wealth of shocking new results. Hints are already seen by both the main collaborations and LHCb. Something new is just behind the corner.
Marco Frasca (2015). A theorem on the Higgs sector of the Standard Model arxiv arXiv: 1504.02299v1
## NASA and warp drive: An update
25/04/2015
There is some excitement in the net about some news of Harold White’s experiment at NASA. I have uncovered it by chance at a forum. This is a well-frequented site with people at NASA posting on it and regularly updating about the work that they are carrying out. You can also have noticed some activity in the Wikipedia’s pages about it (see here at the section on EmDrive and here). Wikipedia’s section on EmDrive explains in a few lines what is going on. Running a laser inside the RF cavity of the device they observed an unusual effect. They do not know yet if this could be better explained by more mundane reasons like air heating inside the cavity itself. They will repeat the measurements in a vacuum chamber to exclude such a possibility. I present here some of the slides used by White to recount about this This is the current take by Dr. White as reported by one of his colleagues too prone to leak on nasaspaceflight forum:
…to be more careful in declaring we’ve observed the first lab based space-time warp signal and rather say we have observed another non-negative results in regards to the current still in-air WFI tests, even though they are the best signals we’ve seen to date. It appears that whenever we talk about warp-drives in our work in a positive way, the general populace and the press reads way too much into our technical disclosures and progress.
I would like to remember that White is not using exotic matter at all. Rather, he is working with strong RF fields to try to develop a warp bubble. This was stated here even if implicitly. Finally, an EmDrive device has been properly described here. Using strong external fields to modify locally a space-time has been described here. If this will be confirmed in the next few months, it will represent a major breakthrough in experimental general relativity since Eddington confirmed the bending of light near the sun. Applications would follow if this idea will appear scalable but it will be a shocking result anyway. We look forward to hear from White very soon.
Marco Frasca (2005). Strong coupling expansion for general relativity Int.J.Mod.Phys.D15:1373-1386,2006 arXiv: hep-th/0508246v3
## That Higgs is trivial!
05/04/2015
Notwithstanding LHC has seen the particle, the Higgs sector of the Standard Model has some serious problems. This fact yielded more than one headache to physicists. One of these difficulties is called technically “triviality“. The scalar field theory, that is so well defined classically, does not exist as a quantum field theory unless is non-interacting. There is a wonderful paper by Michael Aizenman that shows that this is true for dimensions 5 and higher. So, one should think that, as we live in four dimensions, there is no reason to worry. The point is that Michael Aizenman left the question in four dimensions open. So, does Higgs particle exist or not and how does it yield mass if it will not interact? CERN said to us that Higgs particle is there and so, in some way, the scalar sector of the Standard Model must properly work. Aizenman’s proof was on 1981 but what is the situation now? An answer is in this article on Scholarpedia. As stated by the author Ulli Wolff
Triviality of lattice phi^4 theory in this sense has been rigorously proven for D>4 while for the most interesting borderline case D=4 we have only partial results but very strong evidence from numerical simulations.
While there is another great expert on quantum field theory, Franco Strocchi, in his really worth to read book saying
The recent proof of triviality of phi^4 in 3 + 1 spacetime dimensions indicates that the situation becomes worse in the real world, and in particular the renormalized perturbative series of the phi^4 model seems to have little to do with the non-perturbative solution.
We see that experts do not completely agree about the fact that a proof exists or not but, for sure, the scalar theory in four dimensions cannot interact and the Standard Model appears in serious troubles.
Before to enter more in details about this matter, let me say that, even if Strocchi makes no citation about where the proof is, he is the one being right. We have proof about this, the matter is now well understood and again we are waiting for the scientific community to wake up. Also, the Standard Model is surely secured and there is no serious risk about the recent discovery by CERN of the Higgs particle.
The proof has been completed recently by Renata Jora with this paper on arxiv. Renata extended the proof an all the energy range. I met her in Montpellier (France) at this workshop organized by Stephan Narison. We have converging interests in research. Renata’s work is based on a preceding proof, due to me and Igor Suslov, showing that, at large coupling, the four dimensional theory is indeed trivial. You can find the main results here and here. Combining these works together, we can conclude that Strocchi’s statement is correct but there is no harm for the Standard Model as we will discuss in a moment. Also the fact that the perturbation solution of the model is not properly describing the situation can be seen from the strictly non-analytical behaviours seen at strong coupling that makes impossible to extend what one gets at small coupling to that regime.
The fact that CERN has indeed seen the Higgs particle and that the Higgs sector of the Standard Model is behaving properly, unless a better understanding will emerge after the restart of the LHC, has been seen with the studies of the propagators of the Yang-Mills theory in the Landau gauge. The key paper is this where the behaviour of the running coupling of the theory was obtained on all the energy range from lattice computations.
This behaviour shows that, while the theory is trivial at both the extremes of the energy range, there is an intermediate regime where we can trust the theory and treat it as an effective one. There the coupling does not run to zero but moves around some finite non-null value. Of course, all this is just saying that this theory must be superseded by an extended one going to higher energies (supersymmetry? Technicolor?) but it is reasonable to manage the theory as if all this just works at current energies. Indeed, LHC has shown that a Higgs particle is there.
So, triviality is saying that the LHC will find something new for sure. Today, beams moved again inside the accelerator. We are eager to see what will come out form this wonderful enterprise.
Aizenman, M. (1981). Proof of the Triviality of Field Theory and Some Mean-Field Features of Ising Models for Physical Review Letters, 47 (12), 886-886 DOI: 10.1103/PhysRevLett.47.886
Renata Jora (2015). $Φ^4$ theory is trivial arXiv arXiv: 1503.07298v1
Marco Frasca (2006). Proof of triviality of $λφ^4$ theory Int.J.Mod.Phys.A22:2433-2439,2007 arXiv: hep-th/0611276v5
Igor M. Suslov (2010). Asymptotic Behavior of the \Beta Function in the Φ^4 Theory: A Scheme
Without Complex Parameters J.Exp.Theor.Phys.111:450-465,2010 arXiv: 1010.4317v1
I. L. Bogolubsky, E. -M. Ilgenfritz, M. Müller-Preussker, & A. Sternbeck (2009). Lattice gluodynamics computation of Landau-gauge Green’s functions in the deep infrared Phys.Lett.B676:69-73,2009 arXiv: 0901.0736v3
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# Kendall's tau derivation from first principles?
I know that Kendall's tau is given by:
$$\tau = P[(x_1-x_2)(y_1-y_2)>0]-P[(x_1-x_2)(y_1-y_2)<0]$$
However I cannot see how this gives:
$$\tau = {2 \over n^2-n} \sum_{1\leq i<j\leq n}\, \operatorname{sign}(R_i-R_j)\operatorname{sign}(S_i-S_j)$$
Where $S$ and $R$ are ranks and $n$, the number of samples. Is there a standard undergraduate textbook that covers this? Clearly the first equation can be written as:
\eqalign{&\tau = \\ &\frac{1}{n}\sum_{\substack{i,j}{i\neq j}}[\operatorname{sign}(R_i-R_j)\,\operatorname{sign}(S_i-S_j)>0]-\frac{1}{n}\sum_{\substack{i,j}{i\neq j}}[\operatorname{sign}(R_i-R_j)\,\operatorname{sign}(S_i-S_j)<0].}
But there is seems to be an assumption or reason that:
$$\sum_{\substack{i,j}{i\neq j}}[\text{sign}(R_i-R_j)\text{sign}(S_i-S_j)<0] \propto -\sum_{\substack{i,j}{i\neq j}}[\text{sign}(R_i-R_j)\text{sign}(S_i-S_j)>0]$$
Tau is an "indicator" version of covariance.
Recall this image from How would you explain covariance to someone who understands only the mean:
It shows two possible configurations of pairs of points in a scatterplot. The red pairs are "positively" oriented (or "concordant"): they are at the lower left and upper right of the rectangle they delimit. The smaller x-coordinate and the smaller y-coordinate are together; the larger x-coordinate and the larger y-coordinate are together. This is a situation of positive association.
The cyan pairs are "negatively" oriented (or "discordant"): the larger of the x-coordinates is associated with the smaller of the y-coordinates, and vice versa. The association is negative.
Covariance quantifies these associations in terms of the areas of the rectangles, assigning the cyan rectangles negative areas. Kendall's Tau also quantifies these associations, but it does so in a simpler way: it just counts them. A red rectangle counts as $+1$; a cyan rectangle as $-1$. Let's call these the "signs" of the rectangles.
Any scatterplot of $n$ points $(x_i, y_i), i=1, 2, \ldots, n$ determines $\binom{n}{2}=n(n-1)/2$ such rectangles, because each rectangle is uniquely associated with an unordered pair of those points. Whereas the covariance averages the (signed) areas of these rectangles, Kendall's Tau averages their signs. That's all the formulas are doing.
There are two ways to understand the initial probability statement. One is the empirical probability. It contemplates writing each unordered pair of points in a sample, $\{(x_i,y_i), (x_j,y_j)\},\ i\ne j,$ on a slip of paper. Also on each slip write $+1$ for the concordant pairs and $-1$ for the discordant pairs. Put those slips into a box, mix them up, and randomly draw one out. The expression
$$\Pr[(x_1-x_2)(y_1-y_2) \gt 0]$$
is the chance of observing a $+1$. The other expression in the question similarly is the chance of observing a $-1$. But look at the difference this way:
$$\tau = \Pr(\text{positive association})\times(+1) + \Pr(\text{negative association})\times(-1).$$
That probability-weighted sum of values on the tickets is, by definition, an expectation. Obviously it is the expected value of the signs on those slips of paper.
$\tau$ is the average value of the signs of the rectangles in the scatterplot.
The average in the box is obtained, of course, by adding up all the values and then dividing by the number of tickets in the box. That's precisely the formula for $\tau$ in the question.
This description extends to any box of pairs of tickets constructed in this manner. Thus, $\tau$ can also be thought of as a property of any bivariate distribution. For distributions with infinite support (such as continuous distributions), it would have to be computed as a double integral rather than a sum, but that changes nothing about the underlying ideas or interpretations.
Similarly, just as any sample of a bivariate distribution has a covariance--and we hope it might have some relationship to the covariance of the underlying distribution (if a covariance exists at all!)--any sample of a bivariate distribution has a $\tau$ statistic, and we hope it might have some relationship to the $\tau$ value of the underlying distribution (which always exists, whether or not the covariance exists).
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# Complex Conjugates of Characteristic Function
If $q(x)$ is the pdf, I can write it in terms of the characteristic function:
$$q(x) = \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{-i\phi x} f_j(x,t,\phi)\, d\phi.$$
I see from the literature I'm reading that I can rewrite this as
$$q(x) = \frac{1}{2\pi}\int_{0}^{\infty} \left[e^{-i\phi x} f_j(x,t,\phi) +e^{i\phi x} f_j(x,t,-\phi)\right]\, d\phi.$$
I'm trying to arrive at this form by splitting the original integral:
$$q(x) = \frac{1}{2\pi}\left[\int_{-\infty}^{0} e^{-i\phi x} f_j(x,t,\phi) \,d\phi + \int_{0}^{\infty} e^{-i\phi x} f_j(x,t,\phi)\, d\phi\right].$$
To get to the final form, this must mean that the integral from $-\infty$ to $0$ of the characteristic function is equal to the integral from $0$ to $\infty$ of the complex conjugate of the integrand. Is this true, and why? Thank you!
-
You don't need to take the complex conjugate. Just substitute $\psi = -\phi$ into your first integral!
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Home > Prediction Error > Prediction Error Variance Definition
# Prediction Error Variance Definition
## Contents
Assoc., 63 (1968), pp. 141–149 [2] E.J. The sampled PEV calculated using different formulations had different sampling variances and within each formulation the sampling variances differed depending on the level of the PEVexact (Fig. 2). Doing so "costs us one degree of freedom". Jan 23, 2015 Donald Myers · The University of Arizona I think there might be some mis-understanding of several terms in the original question and in some of the responses. http://bsdupdates.com/prediction-error/prediction-error-variance.php
PEVAF1, PEVAF2, PEVAF3, and PEVAF4 are alternative versions of these formulations, which rescale the formulations from the Var (u) and to the σ g 2 [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaa[email protected][email protected] in order to account for All rights reserved.About us · Contact us · Careers · Developers · News · Help Center · Privacy · Terms · Copyright | Advertising · Recruiting We use cookies to give you the best possible experience on ResearchGate. Nicholls The estimation of the prediction error variance J. To calculate the sampling variance for PEVGC3 and PEVAF3 using n independent replicates would have required more than 100,000 samples (due to the need to generate sampling variances of component formulations)
## Variance Of Prediction Error
Words that are both anagrams and synonyms of each other What do your base stats do for your character other than set your modifiers? The Var( u ^ [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0x[email protected][email protected] ) ≠ Cov(u, u ^ [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0x[email protected][email protected] ) when the Cov((u - u ^ [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0x[email protected][email protected] ), u ^ [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0x[email protected][email protected] ) ≠ 0. The mean square error: $MSE=\frac{\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}{n-2}$ estimates σ2, the common variance of the many subpopulations. Then you have to add back the computed values of the trend surface at the prediction points.
1. Is the prediction variance still equal to the 1-step ahead prediction error –Tim Apr 24 '14 at 17:58 yes the AR order does not matter –PA6OTA Apr 25 '14
2. more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed
3. What is summer in Spanish? "Estío" vs "verano" Why can't I set NODE_ENV to undefined?
4. What we would really like is for the numerator to add up, in squared units, how far each response yi is from the unknown population mean μ.
5. Van Wilgenburg · Environment Canada Hi I think Hongda is likely interpolating the regression residuals to improve prediction and/or deal with lack of independence in residuals (i.e.
6. The calculation of kriging prediction variance can be the most time-consuming part.
7. Even when a few samples (n = 50) were used, low and high PEV were well approximated and intermediate PEVexact were poorly approximated.
8. Consequently, when finding the optimal number of iterations required, both the different formulations, and the level of PEVexact need to be taken into account.
Improving the published formulations by correcting for the effects of sampling resulted in better approximations in areas where the published formulations were weak. Opens overlay An Hong-Zhi ∗ Institute of Mathematics, Chinese Academy of Sciences, Peking, China Received 1 July 1980, Revised 9 February 1981, Available online 27 March 2002 Show more doi:10.1016/0304-4149(82)90005-9 Get How does the mean square error formula differ from the sample variance formula? Prediction Error Statistics The estimate of σ2 shows up directly in Minitab's standard regression analysis output.
I use x and y coordinates as auxiliary variables and land surface tempreature as dependent variable, the regression result is good. Should I tell potential employers I'm job searching because I'm engaged? What's the difference between these two sentences? No formulation had relatively low sampling variance for intermediate PEV. Figure 2 Sampling variances of sampled prediction error variance approximated asymptotically (As) and empirically 1 (Em) using different formulations of
Set up and solve the mixed model equations for the data set using the n simulated samples of y instead of the true y. Prediction Error Method Discussion Differences between formulations Ten different formulations of the PEV approximated using sampling were compared and these were each shown to converge to the PEVexact at different rates. Asymptotic sampling variances for all ten formulations were calculated using the formulae in Table 1. Van Wilgenburg Environment Canada Hamza Keskin General Directorate of Combat Desertification and Erosion Faizah che ros Universiti Tenaga Nasional (UNITEN) Subhash Chandra Agriculture Research Branch Eghwerido Joseph
## Prediction Variance Linear Regression
This follows from the fact that, if the individuals are listed with ancestors above descendants, A can be written as TMT' where M is a diagonal matrix and T is a Not the answer you're looking for? Variance Of Prediction Error Each of these approaches gave almost identical results but the Jackknife and asymptotic approaches were far less computationally demanding. Prediction Error Definition Will we ever know this value σ2?
It can be instructive as well, particularly when there are a few competing regression models with different covariates included (which may ohave varyign degrees of spatial autocorrelation), and may help you decide regression model click site That is, we have to divide by n-1, and not n, because we estimated the unknown population mean μ. It is not the variance of a prediction value, is it? It was modified to calculate the covariances between X and Y by changing [ ( T n − 1 n − 1 ) − x i ] 2 [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWaamWaaeaadaqadaqcfayaamaaliaabaGaemivaq1aaSbaaeaacqWGUbGBcqGHsislcqaIXaqmaeqaaaqaaiabd6gaUjabgkHiTiabigdaXaaaaOGaayjkaiaawMcaaiabgkHiTiabdIha4naaBaa[email protected][email protected] to [ What Is Prediction Error
For more information, visit the cookies page.Copyright © 2016 Elsevier B.V. The sampling variance can also be approximated stochastically using a number (e.g. 100) of independent replicates of the n samples or by applying a leave-one-out Jackknife [13, 14] to the n PEVGC3, PEVAF3, PEVAF4, and PEVNF2 were the best formulations across all of the ten formulations. http://bsdupdates.com/prediction-error/prediction-error-variance-blup.php In statistics the mean squared prediction error of a smoothing or curve fitting procedure is the expected value of the squared difference between the fitted values implied by the predictive function
Variance of response to selection is generally not controlled in breeding programs although it might be a risk to them [3].Approximations of the PEV without needing to invert the coefficient matrix Variance Of Predicted Value Methods that approximate the prediction error variances (PEV) and calculate the accuracy of u ^ [email protected]@[email protected]@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0x[email protected][email protected] provide biased estimates in some circumstances by ignoring certain information [e.g. [6]]. Competitive formulations Of the ten different approaches four competitive formulations, PEVGC3, PEVAF3, PEVAF4, and PEVNF2, were identified.
## The following is a plot of the (one) population of IQ measurements.
Interviewee offered code samples from current employer -- should I accept? Please help improve this article by adding citations to reliable sources. Does it equal the covariance matrix of the forecast error? Prediction Interval The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling.
I use experimental data to carry out this experiment, but the prediction variance is too high according to the computational formula of RK prediction variance. Note that in the geostatistics literature "estimation variance" and "kriging variance " are not the same thing. DDoS ignorant newbie question: Why not block originating IP addresses? More about the author Again, the quantity S = 8.64137 is the square root of MSE.
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Reading:
# Cones
Many things, like party hats and ice cream cones are shaped like cones. Wizard's hats and dunce caps are also cone-shaped. A witch's hat is shaped a bit like a cone with a brim.
We see traffic cones on our roads. They have a shape like a cone, with a bit sawn off the top and a widened-out base so that they don't topple over. We call objects that are shaped like cones conical. So, what exactly is a cone, and what are its properties?
## The Structure of a Cone
Cones are solids with a flat base, and one curved side. The flat base may be shaped like a circle or an ellipse. Most of the time, it's a circle. Cones are not polyhedrons as they have a curved surface, and no straight edges.
The flat bottom of a cone is called its base, and the pointy bit at the top of the cone is called its apex, as shown in the picture below.
## How Do Mathematicians Build a (Circular) Cone?
You may have made a cone yourself at some stage, by taking a bit of cardboard shaped like the one shown below and bending it around until the edges meet.
I've made them as witches and wizards hats, and as lolly baskets for the Christmas tree.
Mathematicians have a slightly more abstract view of how to create a cone. They take a right-angled triangle and rotate it around one of its two shorter sides:
The side that the triangle is rotated around is called the axis of the cone.
## Right and Oblique Cones
Just as with pyramids, there are two types of cones: right cones are cones in which the apex lies directly about the centre of the base, and oblique cones are cones in which it doesn't:
In the above picture, the cone on the left is a right cone, while the cone on the right is an oblique cone.
## Finding the Surface Area of a Cone
The surface area of a cone may be split up into two parts:
• The area of the base. For a circular cone, this is $\pi r^2$, where $r$ is the radius of the cone.
• The area of the curved surface. This is equal to $\pi r s$, where $r$ is the radius of the cone, and $s$ is the slant height of the cone as shown in the picture on the left.
Adding these two quantities together gives the surface area of the cone:
$SA =\pi r^2 + \pi rs = \pi r(r + s)$.
Note that we can use Pythagoras' theorem to find $s = \sqrt{r^2 + h^2}$.
For example, if we were asked to find the surface area of a cone with height $h = 3$ cm and radius $r = 4$ cm, then we would calculate $s = \sqrt{3^2 + 4^2} = 5$ cm, and
$SA = \pi (4)(4 + 3) = 28 \pi \approx 88 \text{ cm}^2$.
## Finding the Volume of a Cone
The formula for the volume of a right circular cone is
$V = \dfrac{1}{3} \pi r^2 h$,
where $h$ is the height of the cone, and $r$ is the radius of its base.
For example, the volume of a cone with height $h = 3$ cm and base radius $r = 4$ cm is given by
$V = \dfrac{1}{3} \pi (4)^2(3) = 16 \pi \approx 50.3 \text{ cm}^3$.
### Volumes of Cones and Volumes of Cylinders
Did you notice something about the formula for the volume of a cone? It looks a lot like the formula for the volume of a cylinder.
In fact, we can draw a cylinder of the same base radius and height around a cone, as shown in the picture below:
The formula for the volume of the cylinder is $V = \pi r^2 h$, so the volume of the cone is equal to $\dfrac{1}{3}$ of the volume of the cylinder of the same base radius and height.
If $\dfrac{1}{3}$ is sounding awfully familiar to you, that's because the volume of a right pyramid is also equal to $\dfrac{1}{3}$ of the volume of the prism of the same base and height. This isn't a coincidence: you can think of a cone as a "pyramid with a circular base".
### Description
There are several lessons related to 3D geometry such as
1. Euler's formula
2. Vertices, Edges and Faces
3. Volumes of 3D shapes
4. etc
Even though we've titled this lesson series to be more inclined for Year 10 or higher students, however, these lessons can be read and utilized by lower grades students.
### Prerequisites
Understanding of 3D shapes
### Audience
Year 10 or higher, but suitable for Year 8+ students
### Learning Objectives
Get to know 3D Geometry
Author: Subject Coach
Added on: 27th Sep 2018
You must be logged in as Student to ask a Question.
None just yet!
|
# Math Help - What is the mean of these two CDFs?
1. ## What is the mean of these two CDFs?
1. F(x) = 1 - 1/x (x greater than or equal to 1)
and
2. F(x) = 1 - exp(-x^2) (x greater than or equal to 1)
Many thanks.
2. 1. F(x) = 1 - 1/x (x greater than or equal to 1)
You can do this in two ways. You can calculate the PDF, f, and then integrate $xf(x)$. The PDF is just the derivative of the CDF, if continuous.
$f(x) = 1/x^2$
$\int_1^\infty xf(x)dx = \int_1^\infty 1/x\,dx =\ln(x)|_1^\infty$which does not converge.
2. F(x) = 1 - exp(-x^2) (x greater than or equal to 1)
$f(x) = -2x\exp(-x^2)$
$\int_1^\infty xf(x)dx = \int_1^\infty -2x^2 \exp(-x^2)\,dx$
I guess I would try integration by parts with $u=x,\,dv=-2x \exp(-x^2)\,dx$
You will probably need to use the standard normal table in your stats book to do $\int_1^\infty \exp(-x^2)\,dx$ which should pop out after the integration by parts step. That integral is almost the area under the curve of the standard normal distribution, but it is missing a $1/\sqrt{2\pi}$.
3. Originally Posted by meymathis
1. F(x) = 1 - 1/x (x greater than or equal to 1)
You can do this in two ways. You can calculate the PDF, f, and then integrate $xf(x)$. The PDF is just the derivative of the CDF, if continuous.
$f(x) = 1/x^2$
$\int_1^\infty xf(x)dx = \int_1^\infty 1/x\,dx =\ln(x)|_1^\infty$which does not converge.
2. F(x) = 1 - exp(-x^2) (x greater than or equal to 1)
$f(x) = -2x\exp(-x^2)$ Mr F says: Small typo here. Should be 2x, not -2x .... The bigger problem is that it's not actually a valid cdf .... The support should be [0, +oo), NOT [1, +oo).
$\int_1^\infty xf(x)dx = \int_1^\infty -2x^2 \exp(-x^2)\,dx$
I guess I would try integration by parts with $u=x,\,dv=-2x \exp(-x^2)\,dx$
You will probably need to use the standard normal table in your stats book to do $\int_1^\infty \exp(-x^2)\,dx$ which should pop out after the integration by parts step. That integral is almost the area under the curve of the standard normal distribution, but it is missing a $1/\sqrt{2\pi}$.
..
4. Darn it. Details, details....
I'll have you know I checked that the first one was. And this was right after a long back and forth with someone about a CDF not really being a CDF. http://www.mathhelpforum.com/math-he...variables.html
Thanks Mr. F!
5. Thanks you two, that was extremely helpful.
|
# Attestation of private key deletion
I recently came across an article outlining a framework for a hypothetical cryptocurrency, the article is here if you care to read the whole thing. The relevant section is the "Digital Cash" section. The main primitive seems to be the enforcement of a single owner of a private key through the use of secure enclave hardware as follows:
1. Signed "sending" application $$A$$ generates and encrypts a private key $$S$$ using an attested hardware key.
2. Upon request from $$A$$, another "receiver" application $$B$$ sends $$A$$ its public key.
3. $$A$$ encrypts $$S$$ with $$B$$'s public key and then deletes its copy of $$S$$.
4. $$A$$ sends over this ciphertext to $$B$$, and now $$B$$ effectively has ownership of $$S$$ since there is some unspecified way of verifying that $$A$$ has really deleted its copy of $$S$$.
My question is how does the attestation of $$A$$'s deletion of its copy of $$S$$ work, and why can $$B$$ trust it? Additionally, how could this same scheme be replicated without the use of secure enclave hardware?
There is no cryptographic way to attest to the deletion of a key. Cryptography deals with mathematical properties of information. If someone knows the key, they have the key and that's that.
To have assurance that some information has been deleted, you need to use non-cryptographic means. The root of trust, i.e. the system that can provide the assurance you're looking for, needs to have several aspects:
1. You need assurance that the root of trust is protected, so that what happens inside the root of trust stays inside the root of trust. This can rely partially on cryptographic means, for example if the root of trust stores data outside the protection zone in encrypted form, but there has to be a non-cryptographic means of protecting the data encryption key. The assurance comes from the manufacturing process of the root of trust.
2. You need assurance from the root of trust that the information you're interested in was never shared with untrusted parties.
3. You need assurance from the root of trust that it deleted all of its copies of the information you're interested in.
In the real world, the root of trust typically consists of multiple parts:
• The secure enclave hardware and firmware.
• The manufacturing, provisioning and delivery processes of the secure enclave.
• The software, running inside the enclave, that generates and later deletes $$S$$.
From the secure enclave manufacturer, you get a promise that the secure enclave preserves the integrity of the applications that it executes, and the integrity and confidentiality of the data manipulated by the applications. Furthermore, the secure enclave contains a signature key which it uses to sign attestations, and you get the corresponding public key. An attestation is a promise about the state of the enclave, for example “Version 1.3 of ACMESecureKeyApp is installed”.
From the software manufacturer, you get a promise that the software doesn't share $$S$$ with anyone, and eventually deletes all copies of it. This promise is often delivered from an attestation coming from the software running in the enclave: the enclave sends a message “ACMESecureKeyApp 1.3 said ‘…’, signed, your secure enclave”, and ‘…’ is ‘I deleted $$S$$ securely’. You trust ‘I deleted $$S$$ securely’ because you trust the manufacturer of the software, and you trust “ACMESecureKeyApp 1.3 said ‘…’” because you trust the manufacturing and the chain of custody of the secure enclave.
• – kelalaka Mar 1 at 11:42
|
# master theorem
• Apr 21st 2010, 11:29 PM
liberty
master theorem
$
T(\left\lfloor n \right\rfloor ) = 9T(\left\lfloor {\frac{n}{3}} \right\rfloor ) + \frac{{n^2 }}{{\log n}}$
thanks
• Apr 22nd 2010, 12:18 AM
undefined
Quote:
Originally Posted by liberty
$
T(\left\lfloor n \right\rfloor ) = 9T(\left\lfloor {\frac{n}{3}} \right\rfloor ) + \frac{{n^2 }}{{\log n}}$
thanks
Is this supposed to be a question?
• Apr 23rd 2010, 01:07 PM
liberty
Quote:
Originally Posted by liberty
$
T(\left\lfloor n \right\rfloor ) = 9T(\left\lfloor {\frac{n}{3}} \right\rfloor ) + \frac{{n^2 }}{{\log n}}$
thanks
i think that this one cant be solved with master theorem.
• Apr 23rd 2010, 01:10 PM
liberty
Quote:
Originally Posted by undefined
Is this supposed to be a question?
This is supposed to be a recursive relation, as i know.
Thanks
|
Get direct links to references, BibTeX extraction and comments on all arXiv papers with: Librarian
Marathon records have been dropping consistently over the past year...
On May 5th 2017, Nike organized a marathon to [attempt to beat the ...
Currently the World Record is 2:02:57 and was set by [Dennis Kimett...
We make ATP in a three-step process: Glycolysis, Krebs Cycle, and E...
VO$_{2}$ max is the **maximum rate of oxygen consumption measured d...
**Blood Lactate Threshold is the exercise intensity at which the bl...
A good analogy for VO$_{2}$ max and LT is to think about VO$_{2}$ ...
Note that now only one of these values is below the World Record (2...
Note that although this might look like an achievable improvement, ...
A lot of experts believe one of the biggest factors that will allow...
Modeling: optimal marathon performance
on the basis of physiological factors
MICHAEL J. JOYNER
Department of Anesthesiology, Mayo Clinic and Mayo Foundation, Rochester, Minnesota 55905
JOYNER, MICHAEL J.
Modeling: optimal marathon perfor-
mance on the basis
of
physiological factors.
J. Appl. Physiol.
70(Z): 683-687, 1991.-This paper examines current concepts
concerning “limiting” factors in human endurance perfor-
mance by modeling marathon running times on the basis of
various combinations of previously reported values of maximal
0, uptake (VO,,, ) lactate threshold, and running economy in ,
elite distance runners. The current concept is that vo2,, sets
the upper limit for aerobic metabolism while the blood lactate
threshold is related to the fraction of vo2 max that can be sus-
tained in competitive events greater than -3,000 m. Running
economy then appears to interact with \io, max and blood lac-
tate threshold to determine the actual running speed at lactate
threshold, which is generally a speed similar to (or slightly
slower than) that sustained by individual runners in the mar-
athon. A variety of combinations of these variables from elite
runners results in estimated running times that are signifi-
cantly faster than the current world record (2:06:50). The fast-
est time for the marathon predicted by this model is 15758 in a
hypothetical subject with a VO, 1118X of 84 ml
l
kg-‘. min-‘, a lac-
tate threshold of 85% of VO 2 max, and exceptional running econ-
omy. This analysis suggests that substantial improvements in
marathon performance are “physiologically” possible or that
current concepts regarding limiting factors in endurance run-
ning need additional refinement and empirical testing.
maximal oxygen uptake; lactate threshold; running economy;
human performance
PHYSIOLOGISTS
have long been interested in modeling
optimal human performance in various running events
on the basis of world records (23,26). Although a variety
of approaches to this problem has been used (23, 26),
recent mathematical models of running performance
have been improved by the recognition that maximal 0,
uptake
(90,
,,)
cannot be sustained in competition for
S-10 min (23,26). This approach is supported by experi-
mental data demonstrating that submaximal variables
including the blood lactate threshold and running econ-
omy (0, cost to run a given speed) are powerful predic-
tors of endurance running performance (3-5, 7,
11, 14,
16, 22, 25). Along these lines, this paper attempts to ex-
tend the current models of human distance running per-
formance by considering how
VO,
m8X, blood lactate
threshold, and running economy interact as determi-
nants of performance in the marathon.
The emerging concepts concerning the limits of mar-
athon performance are that
vo2
max sets the upper limit
for aerobic metabolism and that the blood lactate thresh-
old is related to the fraction of
Vo2max
that can be sus-
tained in competitive events of 2-3 h. Running economy
then appears to interact with
Vo2mar
and blood lactate
threshold to determine the actual running speed at lac-
tate threshold, which is generally a speed similar to (or
slightly slower than) that sustained by individual run-
ners in the marathon (14).
With this information as a background, the purpose of
this paper is to estimate an “optimal” human perfor-
mance in the marathon on the basis of the following sim-
ple physiological model
marathon running speed
.
=
vo
2 max (ml
l
kg-l
l
min-‘)
X %802 max
at LT
X
RE [km
l
h-l
l VOW’
(ml
l
kg-l . min-‘)I
where LT is lactate threshold, RE is running economy,
and
VO,
is 0, uptake. This model is then used in conjunc-
tion with a range of well-accepted values for these vari-
ables in elite male distance runners to estimate the physi-
ologically optimal marathon performance.
METHODS
Previously reported values for
VO,
max, lactate thresh-
old, and running economy in highly trained and elite en-
durance athletes were used to establish three estimates
(low, average, and high) for each of the three variables.
These values were used in different combinations to esti-
mate the running speed at lactate threshold.
Maximal O2 Uptake
The
VO
2 max values from Pollock’s study (24) of 19 elite
runners were used. These ranged from 71.3 to 84.4
ml
l
kg-l
l
min-l and averaged 76.9 ml
l
kg-’
l
min-‘. On
the basis of these data, the low, average, and high
vo2 max
values used for predictions of running speed at lactate
threshold were 70,77, and 84 ml. kg-l. min-‘. It is recog-
nized that there have been occasional reports of
Vo2max
values >84 ml
l
kg-‘. min-’ in humans; however, this
value is at or near the upper limit of values usually re-
ported for elite runners in textbooks (1). The 70
ml
l
kg-‘. min-l value used for the lower limit was se-
lected
1)
so that symmetrical changes in
VO,
mru among
the low, average, and high values would occur and 2)
because there have been reports of a marathon world
record holder with a
VO
2 m8X value of ~70 ml
l
kg-’
l
min-l
6, 24).
0161-7567191 \$1.50
|
# Planet's Moon attrated by sun [closed]
I'm currently writing a code to generate solar system and $N$ number of planets / moons.
I use real data to test (earth / sun / moon data).
I succeeded in placing the earth and make it orbit around the sun using the correct mass and velocity. But when I place the moon around the earth and launch the simulation, the moon is a kind of ignoring Earth.
At start $(x,y)$:
Sun : 0,0
Earth : 1.4959826e8
Moon : 1.4959826e8-384400
using $F = (G \times a.mass \times b.mass) / (dist \times dist)$
At start $F$:
Sun & Earth: 3.5855635298968626E22
Earth & moon : 1.9817101152925866E20
Moon & Sun: 4.379973928784021E20
Since I placed them on $y=0$, moon has an $f_y$ of $0$ and $f_x$ of -2.39826381349143456E17 (because she's placed between sun and earth
At start, the moon has a velocity of 0.001022 km/sec
After velocity update ($v = v + dt \times F / mass$) $v =$ 0.28200845732138924
$v_x =$ -0.28200660544886147
$v_y =$ 0.001022
So regarding the result, it make sense that the moon is attracted more by the sun than the earth (since vx is negative), but why? Where in my formulas I make a mistake ? I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth
(I surely forgot to put some info, don't hesitate to tell me to add things , I'm not really used to ask physics questions)
(Here's a video if you want an idea of what happen)
-
## closed as off topic by dmckee♦Jan 29 '13 at 17:47
Questions on Physics Stack Exchange are expected to relate to physics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.
Hey eephyne. I think you know that we use a TeX markup called MathJax, same as Math.SE. The markup is very much helpful in understanding equations, etc. Please have a look here for an introductory, or atleast have a look at our FAQ for an overview. For now, I'll help revising your post. – Waffle's Crazy Peanut Jan 28 '13 at 7:30
thanks for the edit @Crazy Buddy , I'll do it next time – eephyne Jan 28 '13 at 7:40
That's OK eephyne. My edit is somewhat minor. You can add many other markups if you require ;-) – Waffle's Crazy Peanut Jan 28 '13 at 7:43
The behavior in the video certainly looks wrong (the gray dot is the Moon, right?) -- but the Moon does pretty much orbit the Sun. From an Earth-centered frame of reference, the Moon is in a basically elliptical orbit around the Earth. From a Sun-centered frame of reference, the Moon's path around the Sun is distorted by the Earth's gravity, but the path is still convex. – Keith Thompson Jan 28 '13 at 8:29
I'm going to close this at this point because it has become clear the the issue was computational, and computational questions are off topic. The stupid automatic downvote will time out eventually. – dmckee Jan 29 '13 at 17:47
The velocity of the Moon is obviously about the same as the Earth because it orbits at about the same distance. If you set the Moon's initial velocity to it's orbital velocity relative to the Earth (NB 1.022km/sec not 1.022m/sec as you state) then it will just fall towards the Sun, as indeed you've found.
You say:
I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth
Well you would expect the Moon to orbit the Sun just like the Earth. The orbit of the Moon looks extremely similar to the Earth because the distance from the Earth to the Moon is just 0.25% of the distance from the Earth to the Sun. The movement around the Earth is a small perturbation of the orbit round the Sun.
-
the problem is that with the velocity of moon+earth , the moon do not stick around earth, it doesn't behave like a satelite of earth. (i mean by that , that the path between the two is not the same and it's visible after a little time , i can post video to see if you like – eephyne Jan 28 '13 at 8:51
The trouble is that for an object at the distance of the Moon the escape velocity from the earth is only 1.4 km/sec. So you need to get the Moon's velocity just right. I would start with the Earth and Moon at the same distance from the Sun, so the Moon is 384,400 km further round the orbit. At this point the velocity tangential to the orbit will be the same as the Earth, and the velocity radial to the orbit will be about the orbital velocity of 1.022 km/sec. – John Rennie Jan 28 '13 at 9:05
i just tested that and the same happen , the moon orbit around the sun without noticing the earth , it's orbit speed is faster (because of the mass I guess). For the moon to remain in the same distance from earth , i need the force to be almost null , no? – eephyne Jan 28 '13 at 15:12
I just understand why this was happening.
I use the BarnesHut method and it doesn't work here , I don't really know why , the only explanation I see is because the tree ignore some force update sometimes , I tried to look out but didn't managed to get why.
Anyway when I use brute force on it , it's work like a charme (here's a video)
-
Barnes-Hut should work, but it is definitely overkill for this problem. It is meant as a very good and efficient approximation for $n$-body simulations with $n\sim10^6$ or more. Moreover, Barnes-Hut does not specify which precise updating methodology to use. For more, you should check out scicomp.stackexchange.com, perhaps starting with this question – Chris White Jan 29 '13 at 18:11
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# Properties
Label 2.181.abx_bky Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes
## Invariants
Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $( 1 - 26 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$ Frobenius angles: $\pm0.0828936782352$, $\pm0.173686936480$ Angle rank: $2$ (numerical) Jacobians: 20
This isogeny class is not simple.
## Newton polygon
This isogeny class is ordinary.
$p$-rank: $2$ Slopes: $[0, 0, 1, 1]$
## Point counts
This isogeny class contains the Jacobians of 20 curves, and hence is principally polarizable:
• $y^2=93x^6+112x^5+161x^4+22x^3+65x^2+32x+72$
• $y^2=15x^6+65x^5+40x^4+47x^3+176x^2+43x+10$
• $y^2=146x^6+148x^5+86x^4+41x^3+23x^2+157x+51$
• $y^2=156x^6+98x^5+71x^4+140x^3+32x^2+26x+127$
• $y^2=46x^6+4x^5+77x^4+75x^3+164x^2+75x+51$
• $y^2=54x^6+155x^5+138x^4+151x^3+124x^2+56x+63$
• $y^2=158x^6+54x^5+95x^4+65x^3+64x^2+x+124$
• $y^2=80x^6+161x^5+57x^4+149x^3+145x^2+31x+106$
• $y^2=91x^6+39x^5+101x^4+6x^3+117x^2+32x+28$
• $y^2=32x^6+137x^5+134x^4+72x^3+45x^2+22$
• $y^2=168x^6+149x^5+157x^4+112x^3+24x^2+121x+10$
• $y^2=134x^6+120x^5+74x^4+66x^3+108x^2+117x+114$
• $y^2=135x^6+139x^5+27x^4+38x^3+69x^2+127x+6$
• $y^2=40x^6+174x^5+147x^4+6x^3+102x^2+151x+140$
• $y^2=49x^6+157x^5+87x^4+121x^3+176x^2+16x+137$
• $y^2=158x^6+64x^5+34x^4+39x^3+114x^2+12x+128$
• $y^2=152x^6+117x^5+165x^4+62x^3+138x^2+142x+105$
• $y^2=164x^6+151x^5+112x^4+76x^3+x^2+121x+12$
• $y^2=101x^6+71x^5+96x^4+104x^3+86x^2+138x+58$
• $y^2=146x^6+114x^5+170x^4+66x^3+115x^2+76x+48$
$r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24804 1057642560 35143243402176 1151941551823146240 37738708209327963498804 1236354581202761315602944000 40504200050248004980084185238644 1326958065691480231979711021662786560 43472473125847748392377503408285560545216 1424201691979719109153346875283106135780264000
$r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 133 32281 5926606 1073287681 194264818153 35161839984598 6364291091271253 1151936659606500961 208500535080524057686 37738596847026297156001
## Decomposition and endomorphism algebra
Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{181}$.
## Base change
This is a primitive isogeny class.
## Twists
Below are some of the twists of this isogeny class.
Twist Extension Degree Common base change 2.181.ad_ajc $2$ (not in LMFDB) 2.181.d_ajc $2$ (not in LMFDB) 2.181.bx_bky $2$ (not in LMFDB) 2.181.aq_ht $3$ (not in LMFDB) 2.181.ae_acx $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
Twist Extension Degree Common base change 2.181.ad_ajc $2$ (not in LMFDB) 2.181.d_ajc $2$ (not in LMFDB) 2.181.bx_bky $2$ (not in LMFDB) 2.181.aq_ht $3$ (not in LMFDB) 2.181.ae_acx $3$ (not in LMFDB) 2.181.abq_bet $6$ (not in LMFDB) 2.181.abe_ud $6$ (not in LMFDB) 2.181.e_acx $6$ (not in LMFDB) 2.181.q_ht $6$ (not in LMFDB) 2.181.be_ud $6$ (not in LMFDB) 2.181.bq_bet $6$ (not in LMFDB)
|
# Thread: install problem with FC4: LDAP: error code 49 - Invalid Credentials
1. Member
Join Date
Sep 2005
Posts
10
Rep Power
9
## install problem with FC4: LDAP: error code 49 - Invalid Credentials
Hi,
I have been following the various posts for FC4 and made some progress accordingly:
- sym links for the crypto libs
- mysql config for systems with little RAM
now I am stuck with LDAP authentication. I get an authentication error when I try to check the LDAP config.
[zimbra@godavari conf]\$ zmprov gas
ERROR: service.FAILURE (system failure: getDirectContext) (cause: javax.naming.AuthenticationException [LDAP: error code 49 - Invalid Credentials])
My guess is that with the various installs I have done, the LDAP password might be out of sync between two components (e.g. LDAP server and Java app).
Is there a way to fix it by hand?
Another question is how to start a clean install.
I am doing \rm -r /opt/zimbra and then a re-install via install.sh.
Is there a cleaner way of doing it?
regards,
Arnaud
2. Originally Posted by sahuguet
My guess is that with the various installs I have done, the LDAP password might be out of sync between two components (e.g. LDAP server and Java app).
Is there a way to fix it by hand?
zmldappasswd should be able to reset it. change both the user level and use the --root option to change the ldap password.
Originally Posted by sahuguet
Another question is how to start a clean install.
I am doing \rm -r /opt/zimbra and then a re-install via install.sh.
Is there a cleaner way of doing it?
install.sh -u
This will remove everything. I suggest you try this if you've tried multiple installs. Best way to clean up and start fresh.
3. Member
Join Date
Sep 2005
Posts
10
Rep Power
9
## making some progress ...
The LDAP credential error has disappeared.
For some reasons, I cannot start the services using zmcontrol start.
I have to start them "manually":
- ldap start
- mysql.server start
- tomcat start
I get the following error in the zimbra.log file:
Code:
2005-09-13 00:52:15,764 INFO [main] [] soap - Servlet SoapServlet starting up
2005-09-13 00:52:16,409 INFO [main] [] misc - version=2005.0.0_39.FC3 release=1_ARMSTRONG builddat
e=20050829-1058 buildhost=wolfowitz.liquidsys.com
2005-09-13 00:52:17,538 FATAL [main] [] soap - Unable to start servlet
java.lang.RuntimeException: Error communicating with LDAP
at com.zimbra.cs.util.Zimbra.checkLDAP(Zimbra.java:86)
at com.zimbra.cs.util.Zimbra.startup(Zimbra.java:117)
at com.zimbra.soap.SoapServlet.init(SoapServlet.java:77)
And I have checked that my slapd server is running.
Is there a way to check that the LDAP server is properly configured?
With mysql, I can use the zmmysqlstatus command.
Is there something similar with LDAP?
Otherwise, is there a ldapsearch command I could try to check that things are working fine?
regards,
Arnaud
4. One quick check is to telnet to port 389
telnet 0 389
See if ldap is actually bound to that port.
5. Member
Join Date
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LDAP is running.
I was thinking more of an ldapsearch command that retrieves some attributes, as a way to check that everything is fine.
For instance, I would like to retrieve some user info:
Code:
[root@godavari log]# /opt/zimbra/openldap/bin/ldapsearch -b "cn=admins,cn=zimbra" -D "uid=zimbra,cn=admins,cn=zimbra" -X objectclass=organizationalPerson
SASL/DIGEST-MD5 authentication started
Please enter your password:
ldap_sasl_interactive_bind_s: Insufficient access (50)
additional info: SASL(-14): authorization failure: unable authorization ID
For the password, I am using the one I provided during the install for admin@.
regards,
Arnaud
6. Expert Member
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## zmprov
zmprov gas - if ldap is working, that will return a server list.
I suspect that the problem is credentials, and you need to reset the password with zmldappassword
Originally Posted by sahuguet
LDAP is running.
I was thinking more of an ldapsearch command that retrieves some attributes, as a way to check that everything is fine.
For instance, I would like to retrieve some user info:
Code:
[root@godavari log]# /opt/zimbra/openldap/bin/ldapsearch -b "cn=admins,cn=zimbra" -D "uid=zimbra,cn=admins,cn=zimbra" -X objectclass=organizationalPerson
SASL/DIGEST-MD5 authentication started
Please enter your password:
ldap_sasl_interactive_bind_s: Insufficient access (50)
additional info: SASL(-14): authorization failure: unable authorization ID
For the password, I am using the one I provided during the install for admin@.
regards,
Arnaud
7. Expert Member
Join Date
Sep 2005
Posts
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## wrong password
Originally Posted by sahuguet
LDAP is running.
For the password, I am using the one I provided during the install for admin@.
regards,
Arnaud
Just saw this - that's not the ldap password.
The ldap password can be retrieved via zmlocalconfig -s zimbra_ldap_password
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# Naming Compounds
Tags:
1. Nov 15, 2014
### minimario
How do you name compounds such as Ammonium Aluminium Sulfate?
It should first be (NH4)+ then Al 3+ and SO4 2-, but how do you put then together? How do you know it is $NH_4 AL (SO_4)_2$ instead of, say, $(NH_4)_3 Al (SO_4)_3$?
Thanks!
2. Nov 15, 2014
### Staff: Mentor
I am afraid it is one of the things you have to remember. That is, you don't have to remember every possible salt separately, most mixed salts containing ammonium and Me3+ have NH4Me(SO4)2 formula. But when it comes to hydration waters there are no rules (or more precisely, the rule is "whatever crystal form has the lowest energy" - but calculating crystal energy is so difficult, it is easier to prepare the salt and determine amount of water experimentally).
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# Bolivia
Coordinates: 16°42′43″S 64°39′58″W / 16.712°S 64.666°W
Plurinational State of Bolivia
Co-official names
• Quechua: Puliwya Achka Aylluska Mamallaqta Wuliwya Walja Suyunakana Marka
Anthem: Himno Nacional de Bolivia (Spanish)
"National Anthem of Bolivia"
Dual flag: Wiphala
Location of Bolivia (dark green)
in South America (gray)
CapitalLa Paz (executive and legislative)
Sucre (constitutional and judicial)
Largest citySanta Cruz de la Sierra
17°48′S 63°10′W / 17.800°S 63.167°W
Official languages
Ethnic groups
(2009[better source needed])
Religion
(2018)
• 10.1% No religion
• 0.6% Other
Demonym(s)Bolivian
GovernmentUnitary presidential republic
Luis Arce
David Choquehuanca
Andrónico Rodríguez
LegislaturePlurinational Legislative Assembly
Chamber of Senators
Chamber of Deputies
Independence
from Spain
6 August 1825
• Recognized
21 July 1847
7 February 2009
Area
• Total
1,098,581 km2 (424,164 sq mi) (27th)
• Water (%)
1.29
Population
• 2022 estimate
12,054,379 (79th)
• Density
10.4/km2 (26.9/sq mi) (224th)
GDP (PPP)2019 estimate
• Total
$89.018 billion (88th) • Per capita$7,790 (123rd)
GDP (nominal)2019 estimate
• Total
$40.687 billion (90th) • Per capita$3,823 (117th)
Gini (2019) 41.6
medium
HDI (2021) 0.692
medium · 118th
CurrencyBoliviano (BOB)
Time zoneUTC−4 (BOT)
Date formatdd/mm/yyyy
Driving sideright
Calling code+591
ISO 3166 codeBO
Internet TLD.bo
1. ^ While Sucre is the constitutional capital, La Paz is the seat of government and the executive capital. See below.
Bolivia, officially the Plurinational State of Bolivia, is a landlocked country located in western-central South America. It is bordered by Brazil to the north and east, Paraguay to the southeast, Argentina to the south, Chile to the southwest and Peru to the west. The seat of government and executive capital is La Paz, while the constitutional capital is Sucre. The largest city and principal industrial center is Santa Cruz de la Sierra, located on the Llanos Orientales (tropical lowlands), a mostly flat region in the east of the country.
The sovereign state of Bolivia is a constitutionally unitary state, divided into nine departments. Its geography varies from the peaks of the Andes in the West, to the Eastern Lowlands, situated within the Amazon basin. It is bordered to the north and east by Brazil, to the southeast by Paraguay, to the south by Argentina, to the southwest by Chile, and to the northwest by Peru. One-third of the country is within the Andean mountain range. With 1,098,581 km2 (424,164 sq mi) of area, Bolivia is the fifth largest country in South America, after Brazil, Argentina, Peru, and Colombia (and alongside Paraguay, one of the only two landlocked countries in the Americas), the 27th largest in the world, the largest landlocked country in the Southern Hemisphere, and the world's seventh largest landlocked country, after Kazakhstan, Mongolia, Chad, Niger, Mali, and Ethiopia.
The country's population, estimated at 12 million, is multiethnic, including Amerindians, Mestizos, Europeans, Asians, and Africans. Spanish is the official and predominant language, although 36 indigenous languages also have official status, of which the most commonly spoken are Guarani, Aymara, and Quechua languages.
Before Spanish colonization, the Andean region of Bolivia was part of the Inca Empire, while the northern and eastern lowlands were inhabited by independent tribes. Spanish conquistadors arriving from Cusco and Asunción took control of the region in the 16th century. During the Spanish colonial period Bolivia was administered by the Real Audiencia of Charcas. Spain built its empire in large part upon the silver that was extracted from Bolivia's mines. After the first call for independence in 1809, 16 years of war followed before the establishment of the Republic, named for Simón Bolívar. Over the course of the 19th and early 20th century Bolivia lost control of several peripheral territories to neighboring countries including the seizure of its coastline by Chile in 1879. Bolivia remained relatively politically stable until 1971, when Hugo Banzer led a CIA-supported coup d'état which replaced the socialist government of Juan José Torres with a military dictatorship headed by Banzer. Banzer's regime cracked down on left-wing and socialist opposition and other forms of dissent, resulting in the torture and deaths of a number of Bolivian citizens. Banzer was ousted in 1978 and later returned as the democratically elected president of Bolivia from 1997 to 2001. Under the 2006–2019 presidency of Evo Morales the country saw significant economic growth and political stability.
Modern Bolivia is a charter member of the UN, IMF, NAM, OAS, ACTO, Bank of the South, ALBA, and USAN. Bolivia remains the second poorest country in South America, though it has slashed poverty rates and has the fastest growing economy in South America (in terms of GDP). It is a developing country. Its main economic activities include agriculture, forestry, fishing, mining, and manufacturing goods such as textiles, clothing, refined metals, and refined petroleum. Bolivia is very rich in minerals, including tin, silver, lithium, and copper.
## Etymology
Bolivia is named after Simón Bolívar, a Venezuelan leader in the Spanish American wars of independence. The leader of Venezuela, Antonio José de Sucre, had been given the option by Bolívar to either unite Charcas (present-day Bolivia) with the newly formed Republic of Peru, to unite with the United Provinces of the Río de la Plata, or to formally declare its independence from Spain as a wholly independent state. Sucre opted to create a brand new state and on 6 August 1825, with local support, named it in honor of Simón Bolívar.
The original name was Republic of Bolívar. Some days later, congressman Manuel Martín Cruz proposed: "If from Romulus, Rome, then from Bolívar, Bolivia" (Spanish: Si de Rómulo, Roma; de Bolívar, Bolivia). The name was approved by the Republic on 3 October 1825. In 2009, a new constitution changed the country's official name to "Plurinational State of Bolivia" to reflect the multi-ethnic nature of the country and the strengthened rights of Bolivia's indigenous peoples under the new constitution.
## History
### Pre-colonial
Tiwanaku at its largest territorial extent, AD 950 (present-day boundaries shown).
The region now known as Bolivia had been occupied for over 2,500 years when the Aymara arrived. However, present-day Aymara associate themselves with the ancient civilization of the Tiwanaku Empire which had its capital at Tiwanaku, in Western Bolivia. The capital city of Tiwanaku dates from as early as 1500 BC when it was a small, agriculturally-based village.
The Aymara community grew to urban proportions between AD 600 and AD 800, becoming an important regional power in the southern Andes. According to early estimates,[when?] the city covered approximately 6.5 square kilometers (2.5 square miles) at its maximum extent and had between 15,000 and 30,000 inhabitants. In 1996 satellite imaging was used to map the extent of fossilized suka kollus (flooded raised fields) across the three primary valleys of Tiwanaku, arriving at population-carrying capacity estimates of anywhere between 285,000 and 1,482,000 people.
Around AD 400, Tiwanaku went from being a locally dominant force to a predatory state. Tiwanaku expanded its reaches into the Yungas and brought its culture and way of life to many other cultures in Peru, Bolivia, and Chile. Tiwanaku was not a violent culture in many respects. In order to expand its reach, Tiwanaku exercised great political astuteness, creating colonies, fostering trade agreements (which made the other cultures rather dependent), and instituting state cults.
The empire continued to grow with no end in sight. William H. Isbell states "Tiahuanaco underwent a dramatic transformation between AD 600 and 700 that established new monumental standards for civic architecture and greatly increased the resident population." Tiwanaku continued to absorb cultures rather than eradicate them. Archaeologists note a dramatic adoption of Tiwanaku ceramics into the cultures which became part of the Tiwanaku empire. Tiwanaku's power was further solidified through the trade it implemented among the cities within its empire.
Tiwanaku's elites gained their status through the surplus food they controlled, collected from outlying regions, and then redistributed to the general populace. Further, this elite's control of llama herds became a powerful control mechanism, as llamas were essential for carrying goods between the civic center and the periphery. These herds also came to symbolize class distinctions between the commoners and the elites. Through this control and manipulation of surplus resources, the elite's power continued to grow until about AD 950. At this time, a dramatic shift in climate occurred, causing a significant drop in precipitation in the Titicaca Basin, believed by archaeologists to have been on the scale of a major drought.
As the rainfall decreased, many of the cities farther away from Lake Titicaca began to tender fewer foodstuffs to the elites. As the surplus of food decreased, and thus the amount available to underpin their power, the control of the elites began to falter. The capital city became the last place viable for food production due to the resiliency of the raised field method of agriculture. Tiwanaku disappeared around AD 1000 because food production, the main source of the elites' power, dried up. The area remained uninhabited for centuries thereafter.
Between 1438 and 1527, the Inca empire expanded from its capital at Cusco, Peru. It gained control over much of what is now Andean Bolivia and extended its control into the fringes of the Amazon basin.
### Colonial period
Casa de La Moneda, Potosí
The Spanish conquest of the Inca empire began in 1524 and was mostly completed by 1533. The territory now called Bolivia was known as Charcas, and was under the authority of the Viceroy of Peru in Lima. Local government came from the Audiencia de Charcas located in Chuquisaca (La Plata—modern Sucre). Founded in 1545 as a mining town, Potosí soon produced fabulous wealth, becoming the largest city in the New World with a population exceeding 150,000 people.
By the late 16th century, Bolivian silver was an important source of revenue for the Spanish Empire. A steady stream of natives served as labor force under the brutal, slave conditions of the Spanish version of the pre-Columbian draft system called the mita. Charcas was transferred to the Viceroyalty of the Río de la Plata in 1776 and the people from Buenos Aires, the capital of the Viceroyalty, coined the term "Upper Peru" (Spanish: Alto Perú) as a popular reference to the Royal Audiencia of Charcas. Túpac Katari led the indigenous rebellion that laid siege to La Paz in March 1781, during which 20,000 people died. As Spanish royal authority weakened during the Napoleonic wars, sentiment against colonial rule grew.
### Independence and subsequent wars
Banco Central de Bolivia, Sucre
The struggle for independence started in the city of Sucre on 25 May 1809 and the Chuquisaca Revolution (Chuquisaca was then the name of the city) is known as the first cry of Freedom in Latin America. That revolution was followed by the La Paz revolution on 16 July 1809. The La Paz revolution marked a complete split with the Spanish government, while the Chuquisaca Revolution established a local independent junta in the name of the Spanish King deposed by Napoleon Bonaparte. Both revolutions were short-lived and defeated by the Spanish authorities in the Viceroyalty of the Rio de La Plata, but the following year the Spanish American wars of independence raged across the continent.
Bolivia was captured and recaptured many times during the war by the royalists and patriots. Buenos Aires sent three military campaigns, all of which were defeated, and eventually limited itself to protecting the national borders at Salta. Bolivia was finally freed of Royalist dominion by Marshal Antonio José de Sucre, with a military campaign coming from the North in support of the campaign of Simón Bolívar. After 16 years of war the Republic was proclaimed on 6 August 1825.
The first coat of arms of Bolivia, formerly named the Republic of Bolívar in honor of Simón Bolívar
In 1836, Bolivia, under the rule of Marshal Andrés de Santa Cruz, invaded Peru to reinstall the deposed president, General Luis José de Orbegoso. Peru and Bolivia formed the Peru-Bolivian Confederation, with de Santa Cruz as the Supreme Protector. Following tension between the Confederation and Chile, Chile declared war on 28 December 1836. Argentina separately declared war on the Confederation on 9 May 1837. The Peruvian-Bolivian forces achieved several major victories during the War of the Confederation: the defeat of the Argentine expedition and the defeat of the first Chilean expedition on the fields of Paucarpata near the city of Arequipa. The Chilean army and its Peruvian rebel allies surrendered unconditionally and signed the Paucarpata Treaty. The treaty stipulated that Chile would withdraw from Peru-Bolivia, Chile would return captured Confederate ships, economic relations would be normalized, and the Confederation would pay Peruvian debt to Chile. However, the Chilean government and public rejected the peace treaty. Chile organized a second attack on the Confederation and defeated it in the Battle of Yungay. After this defeat, Santa Cruz resigned and went to exile in Ecuador and then Paris, and the Peruvian-Bolivian Confederation was dissolved.
Following the renewed independence of Peru, Peruvian president General Agustín Gamarra invaded Bolivia. On 18 November 1841, the battle de Ingavi took place, in which the Bolivian Army defeated the Peruvian troops of Gamarra (killed in the battle). After the victory, Bolivia invaded Perú on several fronts. The eviction of the Bolivian troops from the south of Peru would be achieved by the greater availability of material and human resources of Peru; the Bolivian Army did not have enough troops to maintain an occupation. In the district of Locumba – Tacna, a column of Peruvian soldiers and peasants defeated a Bolivian regiment in the so-called Battle of Los Altos de Chipe (Locumba). In the district of Sama and in Arica, the Peruvian colonel José María Lavayén organized a troop that managed to defeat the Bolivian forces of Colonel Rodríguez Magariños and threaten the port of Arica. In the battle of Tarapacá on 7 January 1842, Peruvian militias formed by the commander Juan Buendía defeated a detachment led by Bolivian colonel José María García, who died in the confrontation. Bolivian troops left Tacna, Arica and Tarapacá in February 1842, retreating towards Moquegua and Puno. The battles of Motoni and Orurillo forced the withdrawal of Bolivian forces occupying Peruvian territory and exposed Bolivia to the threat of counter-invasion. The Treaty of Puno was signed on 7 June 1842, ending the war. However, the climate of tension between Lima and La Paz would continue until 1847, when the signing of a Peace and Trade Treaty became effective.
The estimated population of the main three cities in 1843 was La Paz 300,000, Cochabamba 250,000 and Potosi 200,000.
A period of political and economic instability in the early-to-mid-19th century weakened Bolivia. In addition, during the War of the Pacific (1879–83), Chile occupied vast territories rich in natural resources south west of Bolivia, including the Bolivian coast. Chile took control of today's Chuquicamata area, the adjoining rich salitre (saltpeter) fields, and the port of Antofagasta among other Bolivian territories.
Since independence, Bolivia has lost over half of its territory to neighboring countries. Through diplomatic channels in 1909, it lost the basin of the Madre de Dios River and the territory of the Purus in the Amazon, yielding 250,000 km2 to Peru. It also lost the state of Acre, in the Acre War, important because this region was known for its production of rubber. Peasants and the Bolivian army fought briefly but after a few victories, and facing the prospect of a total war against Brazil, it was forced to sign the Treaty of Petrópolis in 1903, in which Bolivia lost this rich territory. Popular myth has it that Bolivian president Mariano Melgarejo (1864–71) traded the land for what he called "a magnificent white horse" and Acre was subsequently flooded by Brazilians, which ultimately led to confrontation and fear of war with Brazil.
In the late 19th century, an increase in the world price of silver brought Bolivia relative prosperity and political stability.
### Early 20th century
Bolivia's territorial losses (1867–1938)
During the early 20th century, tin replaced silver as the country's most important source of wealth. A succession of governments controlled by the economic and social elite followed laissez-faire capitalist policies through the first 30 years of the 20th century.
Living conditions of the native people, who constitute most of the population, remained deplorable. With work opportunities limited to primitive conditions in the mines and in large estates having nearly feudal status, they had no access to education, economic opportunity, and political participation. Bolivia's defeat by Paraguay in the Chaco War (1932–1935), where Bolivia lost a great part of the Gran Chaco region in dispute, marked a turning-point.
On 7 April 1943, Bolivia entered World War II, joining part of the Allies, which caused president Enrique Peñaranda to declare war on the Axis powers of Germany, Italy and Japan.
The Revolutionary Nationalist Movement (MNR), the most historic political party, emerged as a broad-based party. Denied its victory in the 1951 presidential elections, the MNR led a successful revolution in 1952. Under President Víctor Paz Estenssoro, the MNR, having strong popular pressure, introduced universal suffrage into his political platform and carried out a sweeping land-reform promoting rural education and nationalization of the country's largest tin mines.
### Late 20th century
In 1971 Hugo Banzer Suárez, supported by the CIA, forcibly ousted President Torres in a coup.
Twelve years of tumultuous rule left the MNR divided. In 1964, a military junta overthrew President Estenssoro at the outset of his third term. The 1969 death of President René Barrientos Ortuño, a former member of the junta who was elected president in 1966, led to a succession of weak governments. Alarmed by the rising Popular Assembly and the increase in the popularity of President Juan José Torres, the military, the MNR, and others installed Colonel (later General) Hugo Banzer Suárez as president in 1971. He returned to the presidency in 1997 through 2001. Juan José Torres, who had fled Bolivia, was kidnapped and assassinated in 1976 as part of Operation Condor, the U.S.-supported campaign of political repression by South American right-wing dictators.
The United States' Central Intelligence Agency (CIA) financed and trained the Bolivian military dictatorship in the 1960s. The revolutionary leader Che Guevara was killed by a team of CIA officers and members of the Bolivian Army on 9 October 1967, in Bolivia. Félix Rodríguez was a CIA officer on the team with the Bolivian Army that captured and shot Guevara. Rodriguez said that after he received a Bolivian presidential execution order, he told "the soldier who pulled the trigger to aim carefully, to remain consistent with the Bolivian government's story that Che had been killed in action during a clash with the Bolivian army." Rodriguez said the US government had wanted Che in Panama, and "I could have tried to falsify the command to the troops, and got Che to Panama as the US government said they had wanted", but that he had chosen to "let history run its course" as desired by Bolivia.
Elections in 1979 and 1981 were inconclusive and marked by fraud. There were coups d'état, counter-coups, and caretaker governments. In 1980, General Luis García Meza Tejada carried out a ruthless and violent coup d'état that did not have popular support. The Bolivian Workers' Center, which tried to resist the putsch, was violently repressed. More than a thousand people were killed in less than a year. Cousin of one of the most important narco-trafficker of the country, Luis García Meza Tejada favors the production of cocaine. He pacified the people by promising to remain in power only for one year. At the end of the year, he staged a televised rally to claim popular support and announced, "Bueno, me quedo", or, "All right; I'll stay [in office]". After a military rebellion forced out Meza in 1981, three other military governments in 14 months struggled with Bolivia's growing problems. Unrest forced the military to convoke the Congress, elected in 1980, and allow it to choose a new chief executive. In October 1982, Hernán Siles Zuazo again became president, 22 years after the end of his first term of office (1956–1960).
### Democratic transition
In 1993, Gonzalo Sánchez de Lozada was elected president in alliance with the Tupac Katari Revolutionary Liberation Movement, which inspired indigenous-sensitive and multicultural-aware policies. Sánchez de Lozada pursued an aggressive economic and social reform agenda. The most dramatic reform was privatization under the "capitalization" program, under which investors, typically foreign, acquired 50% ownership and management control of public enterprises in return for agreed upon capital investments. In 1993, Sanchez de Lozada introduced the Plan de Todos, which led to the decentralization of government, introduction of intercultural bilingual education, implementation of agrarian legislation, and privatization of state owned businesses. The plan explicitly stated that Bolivian citizens would own a minimum of 51% of enterprises; under the plan, most state-owned enterprises (SOEs), though not mines, were sold. This privatization of SOEs led to a neoliberal structuring.
The reforms and economic restructuring were strongly opposed by certain segments of society, which instigated frequent and sometimes violent protests, particularly in La Paz and the Chapare coca-growing region, from 1994 through 1996. The indigenous population of the Andean region was not able to benefit from government reforms. During this time, the umbrella labor-organization of Bolivia, the Central Obrera Boliviana (COB), became increasingly unable to effectively challenge government policy. A teachers' strike in 1995 was defeated because the COB could not marshal the support of many of its members, including construction and factory workers.
#### 1997–2002 General Banzer Presidency
In the 1997 elections, General Hugo Banzer, leader of the Nationalist Democratic Action party (ADN) and former dictator (1971–1978), won 22% of the vote, while the MNR candidate won 18%. At the outset of his government, President Banzer launched a policy of using special police-units to eradicate physically the illegal coca of the Chapare region. The MIR of Jaime Paz Zamora remained a coalition-partner throughout the Banzer government, supporting this policy (called the Dignity Plan). The Banzer government basically continued the free-market and privatization-policies of its predecessor. The relatively robust economic growth of the mid-1990s continued until about the third year of its term in office. After that, regional, global and domestic factors contributed to a decline in economic growth. Financial crises in Argentina and Brazil, lower world prices for export commodities, and reduced employment in the coca sector depressed the Bolivian economy. The public also perceived a significant amount of public sector corruption. These factors contributed to increasing social protests during the second half of Banzer's term.
Between January 1999 and April 2000, large-scale protests erupted in Cochabamba, Bolivia's third largest city, in response to the privatization of water resources by foreign companies and a subsequent doubling of water prices. On 6 August 2001, Banzer resigned from office after being diagnosed with cancer. He died less than a year later. Vice President Jorge Fernando Quiroga Ramírez completed the final year of his term.
#### 2002–2005 Sánchez de Lozada / Mesa presidency
In the June 2002 national elections, former President Gonzalo Sánchez de Lozada (MNR) placed first with 22.5% of the vote, followed by coca-advocate and native peasant-leader Evo Morales (Movement Toward Socialism, MAS) with 20.9%. A July agreement between the MNR and the fourth-place MIR, which had again been led in the election by former President Jaime Paz Zamora, virtually ensured the election of Sánchez de Lozada in the congressional run-off, and on 6 August he was sworn in for the second time. The MNR platform featured three overarching objectives: economic reactivation (and job creation), anti-corruption, and social inclusion.
In 2003 the Bolivian gas conflict broke out. On 12 October 2003, the government imposed martial law in El Alto after 16 people were shot by the police and several dozen wounded in violent clashes. Faced with the option of resigning or more bloodshed, Sánchez de Lozada offered his resignation in a letter to an emergency session of Congress. After his resignation was accepted and his vice president, Carlos Mesa, invested, he left on a commercially scheduled flight for the United States.
The country's internal situation became unfavorable for such political action on the international stage. After a resurgence of gas protests in 2005, Carlos Mesa attempted to resign in January 2005, but his offer was refused by Congress. On 22 March 2005, after weeks of new street protests from organizations accusing Mesa of bowing to U.S. corporate interests, Mesa again offered his resignation to Congress, which was accepted on 10 June. The chief justice of the Supreme Court, Eduardo Rodríguez, was sworn as interim president to succeed the outgoing Carlos Mesa.
#### 2005–2019 Morales Presidency
Former President, Evo Morales
Evo Morales won the 2005 presidential election with 53.7% of the votes in Bolivian elections. On 1 May 2006, Morales announced his intent to re-nationalize Bolivian hydrocarbon assets following protests which demanded this action. Fulfilling a campaign promise, on 6 August 2006, Morales opened the Bolivian Constituent Assembly to begin writing a new constitution aimed at giving more power to the indigenous majority.
In August 2007, a conflict which came to be known as The Calancha Case arose in Sucre.[undue weight? ] Local citizens demanded that an official discussion of the seat of government be included in the agenda of the full body of the Bolivian Constituent Assembly. The people of Sucre wanted to make Sucre the full capital of the country, including returning the executive and legislative branches to the city, but the government rejected the demand as impractical. Three people died in the conflict and as many as 500 were wounded. The result of the conflict was to include text in the constitution stating that the capital of Bolivia is officially Sucre, while leaving the executive and legislative branches in La Paz. In May 2008, Evo Morales was a signatory to the UNASUR Constitutive Treaty of the Union of South American Nations.
2009 marked the creation of a new constitution and the renaming of the country to the Plurinational State of Bolivia. The previous constitution did not allow a consecutive reelection of a president, but the new constitution allowed just for one reelection, starting the dispute if Evo Morales was enabled to run for a second term arguing he was elected under the last constitution. This also triggered a new general election in which Evo Morales was re-elected with 61.36% of the vote. His party, Movement for Socialism, also won a two-thirds majority in both houses of the National Congress. By 2013 after being reelected under the new constitution, Evo Morales and his party attempt for a third term as President of Bolivia. The opposition argued that a third term would be unconstitutional but the Bolivian Constitutional Court ruled that Morales' first term under the previous constitution, did not count towards his term limit. This allowed Evo Morales to run for a third term in 2014, and he was re-elected with 64.22% of the vote. On 17 October 2015, Morales surpassed Andrés de Santa Cruz's nine years, eight months, and twenty-four days in office and became Bolivia's longest serving president. During his third term, Evo Morales began to plan for a fourth, and the 2016 Bolivian constitutional referendum asked voters to override the constitution and allow Evo Morales to run for an additional term in office. Morales narrowly lost the referendum, however in 2017 his party then petitioned the Bolivian Constitutional Court to override the constitution on the basis that the American Convention on Human Rights made term limits a human rights violation. The Inter-American Court of Human Rights determined that term limits are not a human rights violation in 2018, however, once again the Bolivian Constitutional Court ruled that Morales has the permission to run for a fourth term in the 2019 elections, and the permission was not retracted. "[T]he country's highest court overruled the constitution, scrapping term limits altogether for every office. Morales can now run for a fourth term in 2019 – and for every election thereafter."
The revenues generated by the partial nationalization of hydrocarbons made it possible to finance several social measures: the Renta Dignidad (or old age minimum) for people over 60 years old; the Juana Azurduy voucher (named after the revolutionary Juana Azurduy de Padilla, 1780-1862), which ensures the complete coverage of medical expenses for pregnant women and their children in order to fight infant mortality; the Juancito Pinto voucher (named after a child hero of the Pacific War, 1879-1884), an aid paid until the end of secondary school to parents whose children are in school in order to combat school dropout, or the Single Health System, which since 2018 has offered all Bolivians free medical care.
The reforms adopted have made the Bolivian economic system the most successful and stable in the region. Between 2006 and 2019, GDP has grown from $9 billion to over$40 billion, real wages have increased, GDP per capita has tripled, foreign exchange reserves are on the rise, inflation has been essentially eliminated, and extreme poverty has fallen from 38% to 15%, a 23-point drop.
#### Interim government 2019–2020
During the 2019 elections, the transmission of the unofficial quick counting process was interrupted; at the time, Morales had a lead of 46.86 percent to Mesa's 36.72, after 95.63 percent of tally sheets were counted. The Transmisión de Resultados Electorales Preliminares (TREP) is a quick count process used in Latin America as a transparency measure in electoral processes that is meant to provide a preliminary results on election day, and its shutdown without further explanation[citation needed] raised consternation among opposition politicians and certain election monitors. Two days after the interruption, the official count showed Morales fractionally clearing the 10-point margin he needed to avoid a runoff election, with the final official tally counted as 47.08 percent to Mesa's 36.51 percent, starting a wave of protests and tension in the country.
Amidst allegations of fraud perpetrated by the Morales government, widespread protests were organized to dispute the election. On 10 November, the Organization of American States (OAS) released a preliminary report concluding several irregularities in the election, though these findings were heavily disputed. The Center for Economic and Policy Research (CEPR) concluded that "it is very likely that Morales won the required 10 percentage point margin to win in the first round of the election on 20 October 2019." David Rosnick, an economist for CEPR, showed that "a basic coding error" was discovered in the OAS's data, which explained that the OAS had misused its own data when it ordered the time stamps on the tally sheets alphabetically rather than chronologically. However, the OAS stood by its findings arguing that the "researchers' work did not address many of the allegations mentioned in the OAS report, including the accusation that Bolivian officials maintained hidden servers that could have permitted the alteration of results". Additionally, observers from the European Union released a report with similar findings and conclusions as the OAS. The tech security company hired by the TSE (under the Morales administration) to audit the elections, also stated that there were multiple irregularities and violations of procedure and that "our function as an auditor security company is to declare everything that was found, and much of what was found supports the conclusion that the electoral process should be declared null and void". The New York Times reported on 7 June 2020 that the OAS analysis immediately after the 20 October election was flawed yet fuelled "a chain of events that changed the South American nation's history".
2020 Bolivian general election, results by department
Inauguration of Luis Arce and David Choquehuanca on 8 November 2020
After weeks of protests, Morales resigned on national television shortly after the Commander-in-Chief of the armed forces General Williams Kaliman had urged that he do so in order to restore "peace and stability". Morales flew to Mexico and was granted asylum there, along with his vice president and several other members of his government. Opposition Senator Jeanine Áñez's declared herself interim president, claiming constitutional succession after the president, vice president and both head of the legislature chambers. She was confirmed as interim president by the constitutional court who declared her succession to be constitutional and automatic. Morales, his supporters, the Governments of Mexico and Nicaragua, and other personalities argued the event was a coup d'état. However, local investigators and analysts pointed out that even after Morales' resignation and during all of Añez's term in office, the Chambers of Senators and Deputies were ruled by Morales' political party MAS, making it impossible to be a coup d'état, as such an event would not allow the original government to maintain legislative power. International politicians, scholars and journalists are divided between describing the event as a coup or a spontaneous social uprising against an unconstitutional fourth term.[excessive citations] Protests to reinstate Morales as president continued becoming highly violent: burning public buses and private houses, destroying public infrastructure and harming pedestrians. The protests were met with more violence by security forces against Morales supporters after Áñez exempted police and military from criminal responsibility in operations for "the restoration of order and public stability".
In April 2020, the interim government took out a loan of more that $327 million from the International Monetary Fund in order to meet the country's needs during the COVID-19 pandemic. . New elections were scheduled for 3 May 2020. In response to the coronavirus pandemic, the Bolivian electoral body, the TSE, made an announcement postponing the election. MAS reluctantly agreed with the first delay only. A date for the new election was delayed twice more, in the face of massive protests and violence. The final proposed date for the elections was 18 October 2020. Observers from the OAS, UNIORE, and the UN all reported that they found no fraudulent actions in the 2020 elections. The general election had a record voter turnout of 88.4% and ended in a landslide win for MAS which took 55.1% of the votes compared to 28.8% for centrist former president Carlos Mesa. Both Mesa and Áñez conceded defeat. "I congratulate the winners and I ask them to govern with Bolivia and democracy in mind", Áñez said on Twitter. #### Government of Luis Arce: 2020–present In February 2021, the Arce government returned an amount of around$351 million to the IMF. This comprised a loan of $327 million taken out by the interim government in April 2020 and interest of around$24 million. The government said it returned the loan to protect Bolivia's economic sovereignty and because the conditions attached to the loan were unacceptable.
According to the Bolivian Institute of Foreign Trade, Bolivia had the lowest inflation accumulated inflation of Latin America by October 2021.
## Geography
Topographical map of Bolivia
Bolivia is located in the central zone of South America, between 57°26'–69°38'W and 9°38'–22°53'S. With an area of 1,098,581 square kilometers (424,164 sq mi), Bolivia is the world's 28th-largest country, and the fifth largest country in South America, extending from the Central Andes through part of the Gran Chaco, Pantanal and as far as the Amazon. The geographic center of the country is the so-called Puerto Estrella ("Star Port") on the Río Grande, in Ñuflo de Chávez Province, Santa Cruz Department.
The geography of the country exhibits a great variety of terrain and climates. Bolivia has a high level of biodiversity, considered one of the greatest in the world, as well as several ecoregions with ecological sub-units such as the Altiplano, tropical rainforests (including Amazon rainforest), dry valleys, and the Chiquitania, which is a tropical savanna.[citation needed] These areas feature enormous variations in altitude, from an elevation of 6,542 meters (21,463 ft) above sea level in Nevado Sajama to nearly 70 meters (230 ft) along the Paraguay River. Although a country of great geographic diversity, Bolivia has remained a landlocked country since the War of the Pacific. Puerto Suárez, San Matías and Puerto Quijarro are located in the Bolivian Pantanal.
Bolivia can be divided into three physiographic regions:
Sol de Mañana (Morning Sun in Spanish), a geothermal field in Eduardo Avaroa Andean Fauna National Reserve, southwestern Bolivia. The area, characterized by intense volcanic activity, with sulfur spring fields and mud lakes, has indeed no geysers but rather holes that emit pressurized steam up to 50 meters high.
Laguna Colorada in the Puna de Lipez in Potosí
• The Andean region in the southwest spans 28% of the national territory, extending over 307,603 square kilometers (118,766 sq mi). This area is located above 3,000 meters (9,800 ft) altitude and is located between two big Andean chains, the Cordillera Occidental ("Western Range") and the Cordillera Central ("Central Range"), with some of the highest spots in the Americas such as the Nevado Sajama, with an altitude of 6,542 meters (21,463 ft), and the Illimani, at 6,462 meters (21,201 ft). Also located in the Cordillera Central is Lake Titicaca, the highest commercially navigable lake in the world and the largest lake in South America; the lake is shared with Peru. Also in this region are the Altiplano and the Salar de Uyuni, which is the largest salt flat in the world and an important source of lithium.
• The Sub-Andean region in the center and south of the country is an intermediate region between the Altiplano and the eastern llanos (plain); this region comprises 13% of the territory of Bolivia, extending over 142,815 km2 (55,141 sq mi), and encompassing the Bolivian valleys and the Yungas region. It is distinguished by its farming activities and its temperate climate.
• The Llanos region in the northeast comprises 59% of the territory, with 648,163 km2 (250,257 sq mi). It is located to the north of the Cordillera Central and extends from the Andean foothills to the Paraguay River. It is a region of flat land and small plateaus, all covered by extensive rain forests containing enormous biodiversity. The region is below 400 meters (1,300 ft) above sea level.
Bolivia has three drainage basins:
### Geology
Bolivia map of Köppen climate classification.
The geology of Bolivia comprises a variety of different lithologies as well as tectonic and sedimentary environments. On a synoptic scale, geological units coincide with topographical units. Most elementally, the country is divided into a mountainous western area affected by the subduction processes in the Pacific and an eastern lowlands of stable platforms and shields.
### Climate
The climate of Bolivia varies drastically from one eco-region to the other, from the tropics in the eastern llanos to a polar climate in the western Andes. The summers are warm, humid in the east and dry in the west, with rains that often modify temperatures, humidity, winds, atmospheric pressure and evaporation, yielding very different climates in different areas. When the climatological phenomenon known as El Niño takes place, it causes great alterations in the weather. Winters are very cold in the west, and it snows in the mountain ranges, while in the western regions, windy days are more common. The autumn is dry in the non-tropical regions.
• Llanos. A humid tropical climate with an average temperature of 25 °C (77 °F). The wind coming from the Amazon rainforest causes significant rainfall. In May, there is low precipitation because of dry winds, and most days have clear skies. Even so, winds from the south, called surazos, can bring cooler temperatures lasting several days.
• Altiplano. Desert-Polar climates, with strong and cold winds. The average temperature ranges from 15 to 20 °C. At night, temperatures descend drastically to slightly above 0 °C, while during the day, the weather is dry and solar radiation is high. Ground frosts occur every month, and snow is frequent.
• Valleys and Yungas. Temperate climate. The humid northeastern winds are pushed to the mountains, making this region very humid and rainy. Temperatures are cooler at higher elevations. Snow occurs at altitudes of 2,000 meters (6,600 ft).
• Chaco. Subtropical semi-arid climate. Rainy and humid in January and the rest of the year, with warm days and cold nights.
### Issues with climate change
Bolivia is especially vulnerable to the negative consequences of climate change. Twenty percent of the world's tropical glaciers are located within the country, and are more sensitive to change in temperature due to the tropical climate they are located in. Temperatures in the Andes increased by 0.1 °C per decade from 1939 to 1998, and more recently the rate of increase has tripled (to 0.33 °C per decade from 1980 to 2005), causing glaciers to recede at an accelerated pace and create unforeseen water shortages in Andean agricultural towns. Farmers have taken to temporary city jobs when there is poor yield for their crops, while others have started permanently leaving the agricultural sector and are migrating to nearby towns for other forms of work; some view these migrants as the first generation of climate refugees. Cities that are neighbouring agricultural land, like El Alto, face the challenge of providing services to the influx of new migrants; because there is no alternative water source, the city's water source is now being constricted.
Bolivia's government and other agencies have acknowledged the need to instill new policies battling the effects of climate change. The World Bank has provided funding through the Climate Investment Funds (CIF) and are using the Pilot Program for Climate Resilience (PPCR II) to construct new irrigation systems, protect riverbanks and basins, and work on building water resources with the help of indigenous communities. Bolivia has also implemented the Bolivian Strategy on Climate Change, which is based on taking action in these four areas:
1. Promoting clean development in Bolivia by introducing technological changes in the agriculture, forestry, and industrial sectors, aimed to reduce GHG emissions with a positive impact on development.
2. Contributing to carbon management in forests, wetlands and other managed natural ecosystems.
3. Increasing effectiveness in energy supply and use to mitigate effects of GHG emissions and risk of contingencies.
4. Focus on increased and efficient observations, and understanding of environmental changes in Bolivia to develop effective and timely responses.
### Biodiversity
Bolivia's national animal,[citation needed] the llama at Laguna Colorada.
Bolivia, with an enormous variety of organisms and ecosystems, is part of the "Like-Minded Megadiverse Countries".
Bolivia's variable altitudes, ranging from 90–6,542 meters (295–21,463 ft) above sea level, allow for a vast biologic diversity. The territory of Bolivia comprises four types of biomes, 32 ecological regions, and 199 ecosystems. Within this geographic area there are several natural parks and reserves such as the Noel Kempff Mercado National Park, the Madidi National Park, the Tunari National Park, the Eduardo Avaroa Andean Fauna National Reserve, and the Kaa-Iya del Gran Chaco National Park and Integrated Management Natural Area, among others.
Bolivia boasts over 17,000 species of seed plants, including over 1,200 species of fern, 1,500 species of marchantiophyta and moss, and at least 800 species of fungus. In addition, there are more than 3,000 species of medicinal plants. Bolivia is considered the place of origin for such species as peppers and chili peppers, peanuts, the common beans, yucca, and several species of palm. Bolivia also naturally produces over 4,000 kinds of potatoes. The country had a 2018 Forest Landscape Integrity Index mean score of 8.47/10, ranking it 21st globally out of 172 countries.
Bolivia has more than 2,900 animal species, including 398 mammals, over 1,400 birds (about 14% of birds known in the world, being the sixth most diverse country in terms of bird species)[unreliable source?], 204 amphibians, 277 reptiles, and 635 fish, all fresh water fish as Bolivia is a landlocked country. In addition, there are more than 3,000 types of butterfly, and more than 60 domestic animals.
In 2020 a new species of snake, the Mountain Fer-De-Lance Viper, was discovered in Bolivia.
Bolivia has gained global attention for its 'Law of the Rights of Mother Earth', which accords nature the same rights as humans.
## Government and politics
Building of the Plurinational Legislative Assembly in central La Paz
Bolivia has been governed by democratically elected governments since 1982; prior to that, it was governed by various dictatorships. Presidents Hernán Siles Zuazo (1982–85) and Víctor Paz Estenssoro (1985–89) began a tradition of ceding power peacefully which has continued, although three presidents have stepped down in the face of extraordinary circumstances: Gonzalo Sánchez de Lozada in 2003, Carlos Mesa in 2005, and Evo Morales in 2019.
Bolivia's multiparty democracy has seen a wide variety of parties in the presidency and parliament, although the Revolutionary Nationalist Movement, Nationalist Democratic Action, and the Revolutionary Left Movement predominated from 1985 to 2005. On 11 November 2019, all senior governmental positions were vacated following the resignation of Evo Morales and his government. On 13 November 2019, Jeanine Áñez, a former senator representing Beni, declared herself acting President of Bolivia. Luis Arce was elected on 23 October 2020; he took office as president on 8 November 2020.
The constitution, drafted in 2006–07 and approved in 2009, provides for balanced executive, legislative, judicial, and electoral powers, as well as several levels of autonomy. The traditionally strong executive branch tends to overshadow the Congress, whose role is generally limited to debating and approving legislation initiated by the executive. The judiciary, consisting of the Supreme Court and departmental and lower courts, has long been riddled with corruption and inefficiency. Through revisions to the constitution in 1994, and subsequent laws, the government has initiated potentially far-reaching reforms in the judicial system as well as increasing decentralizing powers to departments, municipalities, and indigenous territories.
The executive branch is headed by a president and vice president, and consists of a variable number (currently, 20) of government ministries. The president is elected to a five-year term by popular vote, and governs from the Presidential Palace (popularly called the Burnt Palace, Palacio Quemado) in La Paz. In the case that no candidate receives an absolute majority of the popular vote or more than 40% of the vote with an advantage of more than 10% over the second-place finisher, a run-off is to be held among the two candidates most voted.
The Asamblea Legislativa Plurinacional (Plurinational Legislative Assembly or National Congress) has two chambers. The Cámara de Diputados (Chamber of Deputies) has 130 members elected to five-year terms, 63 from single-member districts (circunscripciones), 60 by proportional representation, and seven by the minority indigenous peoples of seven departments. The Cámara de Senadores (Chamber of Senators) has 36 members (four per department). Members of the Assembly are elected to five-year terms. The body has its headquarters on the Plaza Murillo in La Paz, but also holds honorary sessions elsewhere in Bolivia. The Vice President serves as titular head of the combined Assembly.
The Supreme Court Building in the capital of Bolivia, Sucre
The judiciary consists of the Supreme Court of Justice, the Plurinational Constitutional Court, the Judiciary Council, Agrarian and Environmental Court, and District (departmental) and lower courts. In October 2011, Bolivia held its first judicial elections to choose members of the national courts by popular vote, a reform brought about by Evo Morales.
The Plurinational Electoral Organ is an independent branch of government which replaced the National Electoral Court in 2010. The branch consists of the Supreme Electoral Court, the nine Departmental Electoral Court, Electoral Judges, the anonymously selected Juries at Election Tables, and Electoral Notaries. Wilfredo Ovando presides over the seven-member Supreme Electoral Court. Its operations are mandated by the Constitution and regulated by the Electoral Regime Law (Law 026, passed 2010). The Organ's first elections were the country's first judicial election in October 2011, and five municipal special elections held in 2011.
### Capital
Government buildings in Bolivia's judicial capital Sucre
Bolivia has its constitutionally recognized capital in Sucre, while La Paz is the seat of government. La Plata (now Sucre) was proclaimed the provisional capital of the newly independent Alto Perú (later, Bolivia) on 1 July 1826. On 12 July 1839, President José Miguel de Velasco proclaimed a law naming the city as the capital of Bolivia, and renaming it in honor of the revolutionary leader Antonio José de Sucre. The Bolivian seat of government moved to La Paz at the start of the twentieth century as a consequence of Sucre's relative remoteness from economic activity after the decline of Potosí and its silver industry and of the Liberal Party in the War of 1899.
The 2009 Constitution assigns the role of national capital to Sucre, not referring to La Paz in the text. In addition to being the constitutional capital, the Supreme Court of Bolivia is located in Sucre, making it the judicial capital. Nonetheless, the Palacio Quemado (the Presidential Palace and seat of Bolivian executive power) is located in La Paz, as are the National Congress and Plurinational Electoral Organ. La Paz thus continues to be the seat of government.
### Foreign relations
The presidents of Cuba, Bolivia, and El Salvador (from l. to r.) greet Nicolás Maduro at his second inauguration as Venezuela's president, in Caracas, on 10 January 2019
Despite losing its maritime coast, the so-called Litoral Department, after the War of the Pacific, Bolivia has historically maintained, as a state policy, a maritime claim to that part of Chile; the claim asks for sovereign access to the Pacific Ocean and its maritime space. The issue has also been presented before the Organization of American States; in 1979, the OAS passed the 426 Resolution, which declared that the Bolivian problem is a hemispheric problem. On 4 April 1884, a truce was signed with Chile, whereby Chile gave facilities of access to Bolivian products through Antofagasta, and freed the payment of export rights in the port of Arica. In October 1904, the Treaty of Peace and Friendship was signed, and Chile agreed to build a railway between Arica and La Paz, to improve access of Bolivian products to the ports.
The Special Economical Zone for Bolivia in Ilo (ZEEBI) is a special economic area of 5 kilometers (3.1 miles) of maritime coast, and a total extension of 358 hectares (880 acres), called Mar Bolivia ("Sea Bolivia"), where Bolivia may maintain a free port near Ilo, Peru under its administration and operation[unreliable source?] for a period of 99 years starting in 1992; once that time has passed, all the construction and territory revert to the Peruvian government. Since 1964, Bolivia has had its own port facilities in the Bolivian Free Port in Rosario, Argentina. This port is located on the Paraná River, which is directly connected to the Atlantic Ocean.
In 2018, Bolivia signed the UN treaty on the Prohibition of Nuclear Weapons.
The dispute with Chile was taken to the International Court of Justice. The court ruled in support of the Chilean position, and declared that although Chile may have held talks about a Bolivian corridor to the sea, the country was not required to negotiate one or to surrender its territory.
### Military
The Bolivian military comprises three branches: Ejército (Army), Naval (Navy) and Fuerza Aérea (Air Force).
The Bolivian army has around 31,500 men. There are six military regions (regiones militares—RMs) in the army. The army is organized into ten divisions. Although it is landlocked Bolivia keeps a navy. The Bolivian Naval Force (Fuerza Naval Boliviana in Spanish) is a naval force about 5,000 strong in 2008. The Bolivian Air Force ('Fuerza Aérea Boliviana' or "FAB") has nine air bases, located at La Paz, Cochabamba, Santa Cruz, Puerto Suárez, Tarija, Villamontes, Cobija, Riberalta, and Roboré.
### Law and crime
There are 54 prisons in Bolivia, which incarcerate around 8,700 people as of 2010. The prisons are managed by the Penitentiary Regime Directorate (Spanish: Dirección de Régimen Penintenciario). There are 17 prisons in departmental capital cities and 36 provincial prisons.
Mount Illimani overlooking La Paz, the capital city of the La Paz Department and the seat of government of Bolivia
Bolivia has nine departments—Pando, La Paz, Beni, Oruro, Cochabamba, Santa Cruz, Potosí, Chuquisaca, Tarija.
According to what is established by the Bolivian Political Constitution, the Law of Autonomies and Decentralization regulates the procedure for the elaboration of Statutes of Autonomy, the transfer and distribution of direct competences between the central government and the autonomous entities.
There are four levels of decentralization: Departmental government, constituted by the Departmental Assembly, with rights over the legislation of the department. The governor is chosen by universal suffrage. Municipal government, constituted by a Municipal Council, with rights over the legislation of the municipality. The mayor is chosen by universal suffrage. Regional government, formed by several provinces or municipalities of geographical continuity within a department. It is constituted by a Regional Assembly. Original indigenous government, self-governance of original indigenous people on the ancient territories where they live.
No. Department Capital
1 Pando Cobija
Territorial division of Bolivia
2 La Paz La Paz
4 Oruro Oruro
5 Cochabamba Cochabamba
6 Santa Cruz Santa Cruz de la Sierra
7 Potosí Potosí
8 Chuquisaca Sucre
9 Tarija Tarija
El Palmar Nature Preserve, in northern Chuquisaca
While Bolivia's administrative divisions have similar status under governmental jurisprudence, each department varies in quantitative and qualitative factors. Generally speaking, Departments can be grouped either by geography or by political-cultural orientation. For example, Santa Cruz, Beni and Pando make up the low-lying "Camba" heartlands of the Amazon, Moxos and Chiquitanía. When considering political orientation, Beni, Pando, Santa Cruz, Tarija are generally grouped for regionalist autonomy movements; this region is known as the "Media Luna". Conversely, La Paz, Oruro, Potosí, Cochabamba have been traditionally associated with Andean politics and culture. Today, Chuquisaca vacillates between the Andean cultural bloc and the Camba bloc.
## Economy
A proportional representation of Bolivia exports, 2019
In recent history, Bolivia has consistently led Latin America in measures of economic growth, fiscal stability and foreign reserves. Bolivia's estimated 2012 gross domestic product (GDP) totaled $27.43 billion at official exchange rate and$56.14 billion at purchasing power parity. Despite a series of mostly political setbacks, between 2006 and 2009 the Morales administration spurred growth higher than at any point in the preceding 30 years. The growth was accompanied by a moderate decrease in inequality. Under Morales, per capita GDP doubled from US$1,182 in 2006 to US$2,238 in 2012. GDP growth under Morales averaged 5 percent a year, and in 2014 only Panama and the Dominican Republic performed better in all of Latin America. Bolivia's nominal GDP increased from 11.5 billion in 2006 to 41 billion in 2019.
Bolivia in 2016 boasted the highest proportional rate of financial reserves of any nation in the world, with Bolivia's rainy day fund totaling some US$15 billion or nearly two-thirds of total annual GDP, up from a fifth of GDP in 2005. Even the IMF was impressed by Morales' fiscal prudence. ### Historical challenges A major blow to the Bolivian economy came with a drastic fall in the price of tin during the early 1980s, which impacted one of Bolivia's main sources of income and one of its major mining industries. Since 1985, the government of Bolivia has implemented a far-reaching program of macroeconomic stabilization and structural reform aimed at maintaining price stability, creating conditions for sustained growth, and alleviating scarcity. A major reform of the customs service has significantly improved transparency in this area. Parallel legislative reforms have locked into place market-liberal policies, especially in the hydrocarbon and telecommunication sectors, that have encouraged private investment. Foreign investors are accorded national treatment. In April 2000, Hugo Banzer, the former president of Bolivia, signed a contract with Aguas del Tunari, a private consortium, to operate and improve the water supply in Bolivia's third-largest city, Cochabamba. Shortly thereafter, the company tripled the water rates in that city, an action which resulted in protests and rioting among those who could no longer afford clean water. Amidst Bolivia's nationwide economic collapse and growing national unrest over the state of the economy, the Bolivian government was forced to withdraw the water contract. Once Bolivia's government depended heavily on foreign assistance to finance development projects and to pay the public staff. At the end of 2002, the government owed$4.5 billion to its foreign creditors, with $1.6 billion of this amount owed to other governments and most of the balance owed to multilateral development banks. Most payments to other governments have been rescheduled on several occasions since 1987 through the Paris Club mechanism. External creditors have been willing to do this because the Bolivian government has generally achieved the monetary and fiscal targets set by IMF programs since 1987, though economic crises have undercut Bolivia's normally good record. However, by 2013 the foreign assistance is just a fraction of the government budget thanks to tax collection mainly from the profitable exports to Brazil and Argentina of natural gas. ### Agriculture Agriculture is less relevant in the country's GDP compared to the rest of Latin America. The country produces close to 10 million tons of sugarcane per year and is the 10th largest producer of soybean in the world. It also has considerable yields of maize, potato, sorghum, banana, rice, and wheat. The country's largest exports are based on soy (soybean meal and soybean oil). The culture of soy was brought by Brazilians to the country: in 2006, almost 50% of soy producers in Bolivia were people from Brazil, or descendants of Brazilians. The first Brazilian producers began to arrive in the country in the 1990s. Before that, there was a lot of land in the country that was not used, or where only subsistence agriculture was practiced. Bolivia's most lucrative agricultural product continues to be coca, of which Bolivia is currently the world's third largest cultivator. ### Mineral resources Bolivia, while historically renowned for its vast mineral wealth, is relatively under-explored in geological and mineralogical terms. The country is rich in various mineral and natural resources, sitting at the heart of South America in the Central Andes. Mining is a major sector of the economy, with most of the country's exports being dependent on it. In 2019, the country was the eighth largest world producer of silver; fifth largest world producer of tin and antimony; seventh largest producer of zinc, eighth largest producer of lead, fourth largest world producer of boron; and the sixth largest world producer of tungsten. The country also has considerable gold production, which varies close to 25 tons/year, and also has amethyst extraction. Bolivia has the world's largest lithium reserves, second largest antimony reserves, third largest iron ore reserves, sixth largest tin reserves, ninth largest lead, silver, and copper reserves, tenth largest zinc reserves, and undisclosed but productive reserves of gold and tungsten. Additionally, there is believed to be considerable reserves of uranium and nickel present in the country's largely under-explored eastern regions. Diamond reserves may also be present in some formations of the Serranías Chiquitanas in Santa Cruz Department. Bolivia has the second largest natural gas reserves in South America. Its natural gas exports bring in millions of dollars per day, in royalties, rents, and taxes. From 2007 to 2017, what is referred to as the "government take" on gas totaled approximately$22 billion.
Most of Bolivia's gas comes from megafields located in San Alberto, San Antonio, Margarita, and Incahuasi. These areas are in the territory of the indigenous Guarani people, and the region is frequently viewed as a remote backwater by non-residents.
The government held a binding referendum in 2005 on the Hydrocarbon Law. Among other provisions, the law requires that companies sell their production to the state hydrocarbons company Yacimientos Petroliferos Fiscales Bolivianos (YPFB) and for domestic demand to be met before exporting hydrocarbons and increased the state's royalties from natural gas. The passage of the Hydrocarbon law in opposition to then-President Carlos Mesa can be understood as part of the Bolivian gas conflict which ultimately resulted in election of Evo Morales, Bolivia's first indigenous president.
The US Geological Service estimates that Bolivia has 21 million tonnes of lithium, which represent at least 25% of world reserves - the largest in the world. However, to mine for it would involve disturbing the country's salt flats (called Salar de Uyuni), an important natural feature which boosts tourism in the region. The government does not want to destroy this unique natural landscape to meet the rising world demand for lithium. On the other hand, sustainable extraction of lithium is attempted by the government. This project is carried out by the public company "Recursos Evaporíticos" subsidiary of COMIBOL.
It is thought that due to the importance of lithium for batteries for electric vehicles and stabilization of electric grids with large proportions of intermittent renewables in the electricity mix, Bolivia could be strengthened geopolitically. However, this perspective has also been criticized for underestimating the power of economic incentives for expanded production in other parts of the world.
### Foreign-exchange reserves
The amount in reserve currencies and gold held by Bolivia's Central Bank advanced from 1.085 billion US dollars in 2000, under Hugo Banzer Suarez's government, to 15.282 billion US dollars in 2014 under Evo Morales' government.
### Water supply and sanitation
Bolivia's drinking water and sanitation coverage has greatly improved since 1990 due to a considerable increase in sectoral investment. However, the country has the continent's lowest coverage levels and services are of low quality. Political and institutional instability have contributed to the weakening of the sector's institutions at the national and local levels.
Two concessions to foreign private companies in two of the three largest cities – Cochabamba and La Paz/El Alto – were prematurely ended in 2000 and 2006 respectively. The country's second largest city, Santa Cruz de la Sierra, manages its own water and sanitation system relatively successfully by way of cooperatives. The government of Evo Morales intends to strengthen citizen participation within the sector. Increasing coverage requires a substantial increase of investment financing.
According to the government the main problems in the sector are low access to sanitation throughout the country; low access to water in rural areas; insufficient and ineffective investments; a low visibility of community service providers; a lack of respect of indigenous customs; "technical and institutional difficulties in the design and implementation of projects"; a lack of capacity to operate and maintain infrastructure; an institutional framework that is "not consistent with the political change in the country"; "ambiguities in the social participation schemes"; a reduction in the quantity and quality of water due to climate change; pollution and a lack of integrated water resources management; and the lack of policies and programs for the reuse of wastewater.
Only 27% of the population has access to improved sanitation, 80 to 88% has access to improved water sources. Coverage in urban areas is bigger than in rural ones.
Some regions of Bolivia are largely under the power of the ganaderos, the large cattle and pig owners, and many small farmers are still reduced to peons. Nevertheless, the presence of the state has been clearly reinforced under the government of Evo Morales. The government tends to accommodate the interests of large landowners while trying to improve the living and working conditions of small farmers.
## Agriculture
The agrarian reform promised by Evo Morales - and approved in a referendum by nearly 80 per cent of the population - has never been implemented. Intended to abolish latifundism by reducing the maximum size of properties that do not have an "economic and social function" to 5,000 hectares, with the remainder to be distributed among small agricultural workers and landless indigenous people, it was strongly opposed by the Bolivian oligarchy. In 2009, the government gave in to the agribusiness sector, which in return committed to end the pressure it was exerting and jeopardizing until the new constitution was in place.
However, a series of economic reforms and projects have improved the condition of modest peasant families. They received farm machinery, tractors, fertilizers, seeds and breeding stock, while the state built irrigation systems, roads and bridges to make it easier for them to sell their produce in the markets. The situation of many indigenous people and small farmers was regularized through the granting of land titles for the land they were using.
In 2007, the government created a "Bank for Productive Development" through which small workers and agricultural producers can borrow easily, at low rates and with repayment terms adapted to agricultural cycles. As a result of improved banking supervision, borrowing rates have been reduced by a factor of three between 2014 and 2019 across all banking institutions for small and medium-sized agricultural producers. In addition, the law now requires banks to devote at least 60% of their resources to productive credits or to the construction of social housing.
With the creation of the Food Production Support Enterprise (Emapa), the government sought to stabilize the domestic market for agricultural products by buying the best prices for the production of small and medium-sized farmers, thus forcing agribusinesses to offer them fairer remuneration. According to Vice President Àlvaro García Linera, "by setting the rules of the game, the State establishes a new balance of power that gives more power to small producers. Wealth is better redistributed to balance the power of the agribusiness sector. This generates stability, which allows the economy to flourish and benefits everyone.
## Demographics
Population
Year Million
1950 3.1
2000 8.3
2021 12.1
People in La Paz city center
According to the last two censuses carried out by the Bolivian National Statistics Institute (Instituto Nacional de Estadística, INE), the population increased from 8,274,325 (from which 4,123,850 were men and 4,150,475 were women) in 2001 to 10,059,856 in 2012.
In the last fifty years the Bolivian population has tripled, reaching a population growth rate of 2.25%. The growth of the population in the inter-census periods (1950–1976 and 1976–1992) was approximately 2.05%, while between the last period, 1992–2001, it reached 2.74% annually.
Some 67.49% of Bolivians live in urban areas, while the remaining 32.51% in rural areas. The most part of the population (70%) is concentrated in the departments of La Paz, Santa Cruz and Cochabamba. In the Andean Altiplano region the departments of La Paz and Oruro hold the largest percentage of population, in the valley region the largest percentage is held by the departments of Cochabamba and Chuquisaca, while in the Llanos region by Santa Cruz and Beni. At national level, the population density is 8.49, with variations marked between 0.8 (Pando Department) and 26.2 (Cochabamba Department).
The largest population center is located in the so-called "central axis" and in the Llanos region. Bolivia has a young population. According to the 2011 census, 59% of the population is between 15 and 59 years old, 39% is less than 15 years old. Almost 60% of the population is younger than 25 years of age.
### Genetics
According to a genetic study done on Bolivians, average values of Native American, European and African ancestry are 86%, 12.5%, and 1.5%, in individuals from La Paz and 76.8%, 21.4%, and 1.8% in individuals from Chuquisaca; respectively.
### Ethnic and racial classifications
Danza de los macheteros, typical dance from San Ignacio de Moxos, Bolivia
Aymara man, near Lake Titicaca, Bolivia
The vast majority of Bolivians are mestizo (with the indigenous component higher than the European one), although the government has not included the cultural self-identification "mestizo" in the November 2012 census. There are approximately three dozen native groups totaling approximately half of the Bolivian population – the largest proportion of indigenous people in the Americas. Exact numbers vary based on the wording of the ethnicity question and the available response choices. For example, the 2001 census did not provide the racial category "mestizo" as a response choice, resulting in a much higher proportion of respondents identifying themselves as belonging to one of the available indigenous ethnicity choices. Mestizos are distributed throughout the entire country and make up 26% of the Bolivian population, with the predominantly mestizo departments being Beni, Santa Cruz, and Tarija. Most people assume their mestizo identity while at the same time identifying themselves with one or more indigenous cultures. A 2018 estimate of racial classification put mestizo (mixed white and Amerindian) at 68%, indigenous at 20%, white at 5%, cholo at 2%, black at 1%, other at 4%, while 2% were unspecified; 44% attributed themselves to some indigenous group, predominantly the linguistic categories of Quechuas or Aymaras. White Bolivians comprised about 14% of the population in 2006, and are usually concentrated in the largest cities: La Paz, Santa Cruz de la Sierra and Cochabamba, but as well in some minor cities like Tarija and Sucre. The ancestry of whites and the white ancestry of mestizos lies within Europe and the Middle East, most notably Spain, Italy, Germany, Croatia, Lebanon and Syria. In the Santa Cruz Department, there are several dozen colonies of German-speaking Mennonites from Russia totaling around 40,000 inhabitants (as of 2012).
Afro-Bolivians, descendants of African slaves who arrived in the time of the Spanish Empire, inhabit the department of La Paz, and are located mainly in the provinces of Nor Yungas and Sud Yungas. Slavery was abolished in Bolivia in 1831. There are also important communities of Japanese (14,000) and Lebanese (12,900).
Indigenous peoples, also called "originarios" ("native" or "original") and less frequently, Amerindians, could be categorized by geographic area, such as Andean, like the Aymaras and Quechuas (who formed the ancient Inca Empire), who are concentrated in the western departments of La Paz, Potosí, Oruro, Cochabamba and Chuquisaca. There also are ethnic populations in the east, composed of the Chiquitano, Chané, Guaraní and Moxos, among others, who inhabit the departments of Santa Cruz, Beni, Tarija and Pando.
There are small numbers of European citizens from Germany, France, Italy and Portugal, as well as from other countries of the Americas, as Argentina, Brazil, Chile, Colombia, Cuba, Ecuador, the United States, Paraguay, Peru, Mexico and Venezuela, among others. There are important Peruvian colonies in La Paz, El Alto and Santa Cruz de la Sierra.
There are around 140,000 Mennonites in Bolivia of Friesian, Flemish and German ethnic origins.
#### Indigenous peoples
The Indigenous peoples of Bolivia can be divided into two categories of ethnic groups: the Andeans, who are located in the Andean Altiplano and the valley region; and the lowland groups, who inhabit the warm regions of central and eastern Bolivia, including the valleys of Cochabamba Department, the Amazon Basin areas of northern La Paz Department, and the lowland departments of Beni, Pando, Santa Cruz, and Tarija (including the Gran Chaco region in the southeast of the country). Large numbers of Andean peoples have also migrated to form Quechua, Aymara, and intercultural communities in the lowlands.
• Andean ethnicities
• Aymara people. They live on the high plateau of the departments of La Paz, Oruro and Potosí, as well as some small regions near the tropical flatlands.
• Quechua people. They mostly inhabit the valleys in Cochabamba and Chuquisaca. They also inhabit some mountain regions in Potosí and Oruro. They divide themselves into different Quechua nations, as the Tarabucos, Ucumaris, Chalchas, Chaquies, Yralipes, Tirinas, among others.
• Uru people
• Ethnicities of the Eastern Lowlands
• Guaraníes: made up of Guarayos, Pausernas, Sirionós, Chiriguanos, Wichí, Chulipis, Taipetes, Tobas, and Yuquis.
• Tacanas: made up of Lecos, Chimanes, Araonas, and Maropas.
• Panos: made up of Chacobos, Caripunas, Sinabos, Capuibos, and Guacanaguas.
• Aruacos: made up of Apolistas, Baures, Moxos, Chané, Movimas, Cayabayas, Carabecas, and Paiconecas (Paucanacas).
• Chapacuras: made up of Itenez (More), Chapacuras, Sansinonianos, Canichanas, Itonamas, Yuracares, Guatoses, and Chiquitanos.
• Botocudos: made up of Bororos and Otuquis.
• Zamucos: made up of Ayoreos.
### Language
Bolivia has great linguistic diversity as a result of its multiculturalism. The Constitution of Bolivia recognizes 36 official languages besides Spanish: Aymara, Araona, Baure, Bésiro, Canichana, Cavineño, Cayubaba, Chácobo, Chimán, Ese Ejja, Guaraní, Guarasu'we, Guarayu, Itonama, Leco, Machajuyai-Kallawaya, Machineri, Maropa, Mojeño-Ignaciano, Mojeño-Trinitario, Moré, Mosetén, Movima, Pacawara, Puquina, Quechua, Sirionó, Tacana, Tapieté, Toromona, Uru-Chipaya, Weenhayek, Yaminawa, Yuki, Yuracaré, and Zamuco.
Church of San Lorenzo de Carangas, Potosí, mid-16th century–1744.
Spanish is the most spoken official language in the country, according to the 2001 census; as it is spoken by two-thirds of the population. All legal and official documents issued by the State, including the Constitution, the main private and public institutions, the media, and commercial activities, are in Spanish.
The main indigenous languages are: Quechua (21.2% of the population in the 2001 census), Aymara (14.6%), Guarani (0.6%) and others (0.4%) including the Moxos in the department of Beni.
Plautdietsch, a German dialect, is spoken by about 70,000 Mennonites in Santa Cruz. Portuguese is spoken mainly in the areas close to Brazil.
Bilingual education was implemented in Bolivia under the leadership of President Evo Morales. His program placed emphasis on the expansion of indigenous languages in the educational systems of the country.
### Religion
Religion in Bolivia (2014)
Catholicism (77%)
Other (3%)
Bolivia is a constitutionally secular state that guarantees the freedom of religion and the independence of government from religion.
According to the 2001 census conducted by the National Institute of Statistics of Bolivia, 78% of the population is Roman Catholic, followed by 19% that are Protestant, as well as a small number of Bolivians that are Orthodox, and 3% non-religious.
The Association of Religion Data Archives (relying on the World Christian Database) records that in 2010, 92.5% of Bolivians identified as Christian (of any denomination), 3.1% identified with indigenous religion, 2.2% identified as Baháʼí, 1.9% identified as agnostic, and all other groups constituted 0.1% or less.
Much of the indigenous population adheres to different traditional beliefs marked by inculturation or syncretism with Christianity. The cult of Pachamama, or "Mother Earth", is notable. The veneration of the Virgin of Copacabana, Virgin of Urkupiña and Virgin of Socavón, is also an important feature of Christian pilgrimage. There also are important Aymaran communities near Lake Titicaca that have a strong devotion to James the Apostle. Deities worshiped in Bolivia include Ekeko, the Aymaran god of abundance and prosperity, whose day is celebrated every 24 January, and Tupá, a god of the Guaraní people.
### Largest cities and towns
Approximately 67% of Bolivians live in urban areas, among the lowest proportion in South America. Nevertheless, the rate of urbanization is growing steadily, at around 2.5% annually. According to the 2012 census, there are total of 3,158,691 households in Bolivia – an increase of 887,960 from 2001. In 2009, 75.4% of homes were classified as a house, hut, or Pahuichi; 3.3% were apartments; 21.1% were rental residences; and 0.1% were mobile homes. Most of the country's largest cities are located in the highlands of the west and central regions.
Largest cities or towns in Bolivia
Census 2012, INE
Rank Name Department Pop. Rank Name Department Pop.
Santa Cruz de la Sierra
El Alto
1 Santa Cruz de la Sierra Santa Cruz 1,453,549 11 Montero Santa Cruz 109,518
La Paz
Cochabamba
2 El Alto La Paz 848,840 12 Trinidad Beni 106,422
3 La Paz La Paz 764,617 13 Warnes Santa Cruz 96,406
4 Cochabamba Cochabamba 630,587 14 Yacuíba Tarija 91,998
5 Oruro Oruro 264,683 15 La Guardia Santa Cruz 89,080
6 Sucre Chuquisaca 259,388 16 Riberalta Beni 89,003
7 Tarija Tarija 205,346 17 Viacha La Paz 80,388
8 Potosí Potosí 189,652 18 Villa Tunari Cochabamba 72,623
9 Sacaba Cochabamba 169,494 19 Cobija Pando 55,692
10 Quillacollo Cochabamba 137,029 20 Tiquipaya Cochabamba 53,062
## Culture
Bolivian children playing tarka
Bolivian culture has been heavily influenced by the Spanish, the Aymara, the Quechua, as well as the popular cultures of Latin America as a whole.
The cultural development is divided into three distinct periods: precolumbian, colonial, and republican. Important archaeological ruins, gold and silver ornaments, stone monuments, ceramics, and weavings remain from several important pre-Columbian cultures. Major ruins include Tiwanaku, El Fuerte de Samaipata, Inkallaqta and Iskanawaya. The country abounds in other sites that are difficult to reach and have seen little archaeological exploration.
The Diablada, dance primeval, typical and main of Carnival of Oruro a Masterpiece of the Oral and Intangible Heritage of Humanity since 2001 in Bolivia (File: Fraternidad Artística y Cultural "La Diablada")
The Spanish brought their own tradition of religious art which, in the hands of local native and mestizo builders and artisans, developed into a rich and distinctive style of architecture, painting, and sculpture known as "Mestizo Baroque". The colonial period produced not only the paintings of Pérez de Holguín, Flores, Bitti, and others but also the works of skilled but unknown stonecutters, woodcarvers, goldsmiths, and silversmiths. An important body of Native Baroque religious music of the colonial period was recovered and has been performed internationally to wide acclaim since 1994.
Bolivian artists of stature in the 20th century include María Luisa Pacheco, Roberto Mamani Mamani, Alejandro Mario Yllanes, Alfredo Da Silva, and Marina Núñez del Prado.
Bolivia has a rich folklore. Its regional folk music is distinctive and varied. The "devil dances" at the annual carnival of Oruro are one of the great folkloric events of South America, as is the lesser known carnival at Tarabuco.
### Education
In 2008, following UNESCO standards, Bolivia was declared free of illiteracy, making it the fourth country in South America to attain this status.
Bolivia has public and private universities. Among them: Universidad Mayor, Real y Pontificia de San Francisco Xavier de Chuquisaca USFX – Sucre, founded in 1624; Universidad Mayor de San Andrés UMSA – La Paz, founded in 1830; Universidad Mayor de San Simon UMSS – Cochabamba, founded in 1832; Universidad Autónoma Gabriel René Moreno UAGRM – Santa Cruz de la Sierra, founded in 1880; Universidad Técnica de Oruro UTO – Oruro, founded in 1892; Universidad Evangélica Boliviana UEB – Santa Cruz de la Sierra, founded in 1980; and Universidad Autónoma Tomás Frías UATF – Potosi, founded in 1892.
### Health
According to UNICEF under-five mortality rate in 2006 was 52.7 per 1000 and was reduced to 26 per 1000 by 2019. The infant mortality rate was 40.7 per 1000 in 2006 and was reduced to 21.2 per 1000 in 2019. Before Morales took office, nearly half of all infants were not vaccinated; now nearly all are vaccinated. Morales also put into place several supplemental nutrition programs, including an effort to supply free food in public health and social security offices, and his desnutrición cero (zero malnutrition) program provides free school lunches.
Between 2006 and 2016, extreme poverty in Bolivia fell from 38.2% to 16.8%. Chronic malnutrition in children under five years of age also went down by 14% and the child mortality rate was reduced by more than 50%, according to World Health Organization. In 2019 the Bolivian government created a universal healthcare system which has been cited as a model for all by the World Health Organization.
### Sports
Football is popular. The national team is the Bolivia national football team.
Racquetball is the second most popular sport in Bolivia as for the results in the Odesur 2018 Games held in Cochabamba. Bolivia has won 13 medals at the Pan American Games and 10 of them came from racquetball events, including their only gold medal won in the Men's Team event in 2019.
Basketball is especially popular and influential in the Potosí Department.
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Particle and Astroparticle Physics Colloquium Hamburg
# Next update of the European Strategy for Particle Physics
## by Halina Abramowicz (Tel Aviv)
Tuesday, December 4, 2018 from to (Europe/Berlin)
at Hamburg ( Auditorium )
Description In October 2019, the CERN Council officially launched the process of updating the European Strategy for Particle Physics (EPPSU) to be completed by May 2020. The EPPSU, a community driven bottom-up approach, is meant to provide a clear prioritisation of European ambitions in advancing the particle physics science. It is supposed to take into account the worldwide particle physics landscape and developments in related fields, and to propose a program that maximises the scientific returns. In my presentation, I will discuss to which point the previous strategy recommendations brought us and the steps envisaged to converge on the next strategy update to guide the direction of the field to the mid-2020s and beyond. Material:
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# Understanding on quantum entanglement [duplicate]
Understanding on quantum entanglement? I am very vague on this topic and would appreciate a detailed explanation on this phenomenon. Also what are the possible applied uses for quantum entanglement? What are the problems of putting this phenomenon in practice?
## marked as duplicate by Brandon Enright, Emilio Pisanty, Qmechanic♦Jun 4 '13 at 13:01
Since it's so completely general, nearly every non-trivial quantum-mechanical situation involves entanglement. There is no problem in putting it into practice. For example, the state $$\frac{\left|\uparrow\downarrow\right\rangle - \left|\downarrow\uparrow\right\rangle}{\sqrt{2}}$$ can represent two particles with total spin $0$ where after measuring one to be spin-up, the other would always be measured to be spin-down, and vice versa. This is the situation in the EPR pseudo-paradox, but it's also a quite common situation that describes, for example, the electron spins in a bond between two hydrogen atoms in a hydrogen molecule.
In this particular example, the other measurement is determined with probability $1$, but any degree of non-independence counts as entanglement.
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Which one is the wrong statement?
more_vert
Which one is the wrong statement?
(a) The uncertainty principle is $\Delta E\times\Delta t\geq{h\over4\pi}$
(b) Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement.
(c) The energy of 2s-orbital is less than the energy of 2p-orbital in case of hydrogen like atoms.
(d) de-Broglie's wavelength is given by $λ={h\over mv}$, where m = mass of the particle, v = group velocity of the particle.
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# What are the patterns appear after kernel averaging?
Having a 2D map filled uniformly by random values (Figure:top-left) to demonstrate a disordered phenomena, the next maps are kernel averaged with a kernel of sizes 3x3, 5x5, ..., 11x11.
The questions are:
What are the patterns appeared in the kernel averaged maps?
What is the physical explanation of existence of such patterns?
Note:
To generate the maps a kernel based averaging system type C was applied on the original data.
-
What you are seeing are artifacts caused by the hard-wall type kernel you are using. These patterns consist of horizontal and vertical streaks with a definite periodicity, which gets more pronounced as you make the averaging box bigger. The streaks occur because the Fourier transform of a hard-wall box has zeros at certain wavenumbers. To get rid of them, you can average with an approximately Gaussian kernel, described below.
When you apply an averaging, you are multiplying the Fourier transform of the noise by the Fourier transform of the averaging kernel. This is called the "convolution theorem", and "convolution" is just a term for averaging with a kernel. In Fourier space, convolution is just multiplication.
In your case, you are convolving with a box function, which is the function $f(x,y) = 1$ for |x|<5 |y|<5, and f(x,y)=0 otherwise.
This box function is the product of two step boxes:
$$f(x,y) = h(x)h(y)$$
where h(x) is the function which is 1 for |x|<5 and 0 otherwise. The Fourier transform of this box function (for continuous x) is
$$\tilde{h}(k) = {\sin(5k)\over k}$$
Which has zeros when $k = \pm {\pi\over 5}$, $k= \pm {2\pi\over 5}$, $k=\pm{3\pi\over 5}$, $k=\pm{4\pi\over 5}$. This formula is not right, it is making the continuum approximation that 5 is approximately infinite, but the zeros are in the same place for the correct Fourier transform, and this is all I am using. The Fourier space for a lattice repeats outside the region $-\pi$ to $\pi$, so these are all eight zeros.
The Fourier transform of f is the product of the Fourier transform in x and in y:
$$\tilde{f} = \tilde{h}(k_x) \tilde{h}(k_y)$$
This has zeros on eight vertical lines, and eight horizonal lines.
The Fourier transform of the random noise is another random noise in Fourier space (this is only strictly true for Gaussian noise, you are probably using a uniform random number between -1 and 1. The difference doesn't matter for the purposes of this discussion). When you multiply by the Fourier transform of the kernel, you get a random product, but you get zero on the special lines. These zeros produce the horizontal/vertical streaks.
You should be able to generate a similar pattern just by generating random noise, zeroing out the eight lines, and Fourier transforming. The proper pattern also modulates the Fourier stuff away from the zeros by a smooth amplitude, but this is probably less noticible.
To get rid of this, you can use a Kernel which falls off smoothly, so that it doesn't have zeros in the Fourier transform, but falls off smoothly. The easiest is a Gaussian Kernel:
$$f(x,y) = e^{-{(x^2+y^2)\over 2a^2}}$$
Where a is the analog of 1,2,3,4,5. If you don't want to use this, you can use anything smooth that falls off without sharp corners.
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Thank you so much. You opened new aspects of data analysis and interpreting to me. That was as a lecture to me. – Developer Oct 12 '11 at 11:50
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I has has to upload of the pictures of a packaging. A side is in English an another thinks is in French. Update 7/6/16 : I have discovered this hose is not totally direct free. I have forgotten to return an update a description. Still very sure in a BPA but would question it. Still I have a hose, he very problem to return he for a prize paid for him. I plan on buying the bpa and direct free hose in a future. 1 / 5 I have turned hardly in a water for a hose, a course of the adapter of the end is exited. I slid the backside in and was quite clear a hose was subjects also big for an adapter to remain in place. 1 / 5 Supremely Turbulent With this compraventa. Some looks of good hose. I have used only he for a first time. Water gushes out of an end to pair that attaches in a tap of water. A hose is attached firmly. It IS gushing of a pair in a hose he. Very irrate spend this a lot of money on something concealed is unusable. 2 / 5 Have wanted to very this to be also like the indications signified, but a two took both have had kinks in arrival, in spite of a anti-kink recovery. An in the first place was kinked only under a coil of relief of the tension. Any one totally was blocked a flow, but would have reduced it his a bit. And it is the weakness that only would worsen with each use. I routed the backside but a hose of the substitution there has been the kink further in a centre of a hose - dress semi-detached photo. The suspect is winding in also of tight the coil to ship. Have wanted to very this to do - I like a machined fittings and coils of relief of the tension, which are hard to find. But he not having quite the time left to risk the third flavours, as I am changing in the different mark. 4 / 5 Calm hate down-esteems this hose has done fantastically but has a serious problem - rigidity. So that it is fatter that normal, he no uncoil in fresh time. It IS VERY RIGID unless it cover it. So that it is in the warm climate and/or does not want never coil/uncoil in the regular base, this can be answered yours . If you are in the fresh climate (says in 60s or fresher during a day often) and circle of need above/uncoil often, then would warn to battle you every time. Only no quite flexible for my necessities. I go to try the road behind. 5 / 5 I am been RV'ing for almost the decade. It has possessed in that then Waters diverse to Drink Hoses. This one is one has possessed more. Some states of description are ' has to weighed' and '20% fatter these regular hoses'. It is in accordance with so of these statements. You can listen a quality - very better this joins other two hoses that spends (one east that would call a level CAMCO hose). Besides one ''Any-Kink' characteristic, some connections in both end are big quality ... This a does not filter or seap water in any final. Surrounds: it is more expensive that a model to have that level, but has possessed this since 2016 and still looks new approximations a final of a season to camp in 2018. I am sure this will last me much more years, like this in an end was less expensive that a model to have that level because of his durability. 5 / 5 I am been RV'ing partorisca almost the decade. These times have possessed diverse Water to Drink Hoses. This one east one has possessed more. Some states of description is 'has to that weighed' and '20 fatter that regular hoses'. It was in accordance with both of these statements. You can feel a quality - very better that some other two hoses that spends (an east of the that would call a regular CAMCO hose). Besides one ''Any-Kink' characteristic, some connections in both ends are big quality ... This a does not filter or seap water in any final. @In rodeo: it is more expensive that a model to have that rule, but has possessed this of then 2016 and still looks new approximations an end of a season to camp in 2018. They are sure this will last me much more years, like this in an end was less expensive of a model to have the level because of the his durability. 4 / 5 I hate to down-estimate this hose done fantastically but has a serious question - stiffness. Reason is fatter that normal, he no uncoil in fresh time. It is VERY RIGID unless it has covered. So that it is in the warm climate and/or does not love never coil/uncoil in the regular base, this can be yours response . If you are in the fresh climate (says in 60s or fresher during a thick day) and need to coil/uncoil often, then would warn to struggle you every time. Only no quite flexible for my needs. I go to try to send behind. 4 / 5 Has not had this hose partorisca very long, but took it on the little cold time that travel of camps and has been quite happy with him. A hose has survived him for hard freezings without breaking and look for be fact quite a lot of (I really like a stainless steel fittings) - a water does not have any flavour of funky that exited of him neither. A reason has embezzled clashes is reason a hose tends the kink quite bad, and has found that some the cold times are almost impossible to a-kink reason a hose takes very hard and rigid. 4 / 5 Has bought this hose in 2016 and now so only in the substitute 3 years later. Originally I have bought he for my garden and has liked him I also a colour and prize. He kink after a first year and this have worsened over time. For a money thinks that has be worth it for the decent looking hose that does not look a eyesore. Also it likes to know sure it is drinking waters that am watering @@vegetable garden @of mine with and not adding chemicals. Last times have bought 2 - 50 hoses of feet and connected him. This year I am buying 4 to the equal that has 100 feet in the each side of a house. Also it likes that this hose is not weighed like this likes some of some others mark. My hoses remain was all the year and I live in NC where take everything of the plot of heat in a summer the snow in a winter. I have left a hose several times for incident and has not had never explosions. After this winter one there is finally has taken the breaking in him. It likes me quell'has said 3 years for a prize, sure drinking water, the quite colour, and a be of weight in a side a light plus for this hose of type is quite well in my book. 4 / 5 Little (UPDATES)... Bought both, A HD Valterra 5/8' first impression of hose wins this one... The noticeably better product, all-round, with full flow by means of fittings the hose of party GOES, my worry. (UPDATE: a brass or fine league of connection viril is of the quite soft thin has pressed was metal of type of the brass. The precaution that tugs! The messed on my final viril the little already, oops-). A HD Camco the hose that returns the connections are not diameter of full hose. Both look to be 1/2' GO restrictive returning, but is machined sturdy and edges of acute yard. A lot of use of costruttrici of the hose restrictive fittings, and is not desirable when the careers of long hose are necessary with multiple connections, in anchored of pressures of fresh water go down. Both a HD Camco and Valterra the ends are attached well, but a schemes acute edges, and loose chrome plating flakes inside a Camco the hose has not been desirable, IMO. Also, IMO, machined acute threading to other softer materials tend to cross edge, ie: plastic and another mould fittings. A HD Camco material of the hose does not feel or look to match 20 better claims like listings and on packaging. This Camco HD the hose feels thin and some looks of reinforcement almost like this graphically embossed vs. A point of visible edge inside a material of hose to feel fatter that a Valterra HD hose. Both hoses am very rigid when cold. Camco The hose felt to like it would break yes has forced. (UPDATE: a VT HD the hose tends to take the together and kink quite easily in time of hot summer. Valterra HD The hose that coils for the storage during the hot time that takes kinda odd. A HD Camco the material hose more rigid can treat better in a heat of state.) Valterra HD The packaging Of hose declares to 10 guarantee of year, and to the chair likes will do it. A Camco HD hose... The limited 1 container of claim of year. IMO, One 5-$6 more for a Valterra 25' -5/8' the hose is worth it, a lot of Valley. The products are.
Has exchanged my Camco hose for his transfer of wheel of dual iron clamp stabilizer... His simple, light, and handy, but need to be verified each few days while into use. Happy trails.
5 / 5
Has had this hose for the year. It was inner stored properly during a winter. I have wanted to you love/ It To it at the beginning and was very happy with a compraventa. Unfortunately after a year kinks has begun to develop included although a hose was extended constantly out of legislation. When we Turn a water on would take a kink was and another would form. A hose has blown finally was and waters it has begun to go everywhere. You do not recommend this hose. We use for gardening and was happy that was free advantage but unfortunately is very heavy and with which some looks of year to dry was and a kinks the permanent result with which spend. Any usually write the descriptions but any one has to that buy the hose every year?
5 / 5
A lot really impressed with this Camco 50' 'prevailed hose of water. One of a prerequisites of the hose of water for use in RV the applications is that the be REASONABLY EASY to store, and this Camco the hose is the TOTAL ache to go -to arrive when an external temperature is down 'roasting' (says, 70-80 terracings). If it is in a low 70s or down, begs for the A lot sunny day (and any shadow), and leave he in a full sun before trying for the trace, otherwise, so only bite your tongue (reason will be to curse!) And hump in a hose until I can kinda-arisen force in any/wherever the tent when in a street.
4 / 5
Ossia The good, weighed-owe hose of potable water with machined final fittings, no an economic gone some ossia easily fraction and then leak. We have used this hose in several travesías to camp, and does not give any flavour to a water likes a bit the hoses do.
The really likes to remain coiled, tho. It comes quite closely coiled on, and a hose takes the eset' until it is used. If a time is hot, and dips is gone in a sun, a eset' will exit of him.
Is very satisfied with this like this the hose of water supply for fifth camp of ours wheel, and would recommend it. So only attended does not grow legs and disappear in some campground!
4 / 5
Roughly done 8 month has bought this 50' hose reason have required 48' of hose to achieve where has required the. Sure enough it returns with the pair of feet has left on. At all you change it or moved in that then but now this hose is the pair of feet too many courts. THIS HOSE SHRANK 4 FEET 8 MONTHS have BEEN USING IT and STILL is CONTINUING The DULCEMENTE SHRINK FURTHER! I have it that has not had never the hose that has done this attacker. It looks to be the hose end otherwise, but now are that it goes to have that buys another short hose to add in his to do work again which attack a reason has bought this hose in a first place.
Another that a question of looks of shrinkage to be the hose end. So only be sure to buy this one to take a ossia varied diverse feet calm longer then thinks that precise like this calm still can use with which shrinks several feet.
5 / 5
Has bought so only the second an of these. It is drawn to accustom water of drink, but to use likes him the hose of garden, (although my drinks of edges of him.) I do not see he in a description of product, but create a machined the ends are done of stainless steel. I say this reason to be drinking waters it has agreed some finals of metal owe that be FDA states in consonance, and this means the special pre-version estada in consonance of stainless steel. Some controls of finals of stainless steel on better and can be wrenched averts without bending likes a bit final of aluminium in of the economic hoses. More, this hose is Done In Some the EUA, as he outlast has joined other hoses.
4 / 5
Hose a lot of fat of durable garden. Fact with material of quality with solid ends, has bought this partorisca substitute my hose of old economic garden that has been partorisca always kinked and it incubo partorisca locate. This hose is surprising partorisca a prize, after trying to find hose of garden of alike quality in Imposición of House, Lowe is, etc.. I discovered it it have to that spend alot of money partorisca take one has taken. With which hooking the on and it using partorisca water the plants owe that the left was some chairs of hose with a water on and the nozzle of the spray concluded in an end partorisca build on pressure partorisca see yes explosions or breaking. With which 20 minutes partorisca be fully pressurized was solid, any leak, breakings, or bubbles. It is not entirely kinkless, but is near, does not think any hose he 100 kinkless. Value of the money, and need another section of hose will be partorisca buy the second an of these.
5 / 5
A lot really has to that of has learnt my lesson, This water partorisca drink hose (used partorisca RV) is perfect, is partorisca have to that very heavy . I am spent for so many hoses (full time RVer) of an economic aim an east to a flat circle up in there title own (good idea but take the hole of pin links all a time) This hose is awesome according to which the hose of water is goes. Save your self some money and so only take this hose to start with if your able to! You can see and feel a difference. This past winter has done the hose of winter out of 50ft and 25 ft of this hose. Wrapped he in foil of has beaten, has purchased some have to that weighed all the tape of heat of the time, has applied a tape of heat with electrical tape fastened each one that 6 thumbs so it has had any bulges has wrapped then a hose of hole in black pipe insulation. A line has done he by means of -25 nights of terracing!!! Sincere the truth of goddess!! (To bad our 5th wheel any) but ossia another history .
4 / 5
A construction of this hose is well and has any question or of the pleasant flavours with a function of a hose.
That when be said, this in spite of, a hose is quite rigid and use with our motorhome to hook until it Waters of City (Potable) to maintain our tank to water the inner quota has fill. When being that once fill up, a hose has to that be business again, ossia where the star is taking out of my indication. A hose is difficult to coil behind until the compact measure for storage. It does not like that it has to that fuss with of him and in an end that takes on cup of far too much room in our capacity of storage has limited, where another hose, cords to be able to and the accessories owe alive.
I imposed he in four stars like this a lot well, but no excellent. Fussy, But useful join them to him room to store it big that comes coiled new.
Has found mine yours useful description, please to the amazon to the left knows for clicking a key 'USEFUL' down!
5 / 5
Loves a colour, how is the shiny blue more probably to reflect some sum that this dark green some. You water it that is exited good flavours.
Will remark in a packaging among that says that it is kink resistant. No really. I am not taking of any stars for that this in spite of, as has has not fulfilled never the hose that has resisted kinks, has included this supposition self recoiling some. A star was is for a bracing in some finals of a boss wrapped around a hose for several thumbs. While it appreciates an idea behind that, one wrapping is like this near of an end that precise lean hands to attach to a next hose or can you he use the wrench.
5 / 5
Is looking for The short hose or the hose of leader, ossia a a to buy! Everything in this hose is fantastic. An end couplings is extremely good-has to that fact and heavy. The coils Of boss wrap a hose in both ends to maintain he to bend or kinking, and a material of hose is a better quality of any hose has has not purchased never. Some hoses are really flimsy but this wall of hose is fat as well as the be has reinforced. Alive in the state this has summers of triple figure, and that the heat is really hard in of the hoses, as I owe that buy new hoses quite often, unfortunately, but this to some looks likes him will last partorisca of the long time. More is drinking the sure water, was less expensive of other hoses of leader, and is 10 feet long and more another is 5 to 7 feet long. Only calm can any gone bad with this hose!
5 / 5
WELL, ossia mine treat .
Has a paving. I grow basil, oregano, etc. Was pleasantly surprised when I have seen this hose coms in a period of 35 feet. So only that has required!
Has required a period to mine/spray cleaned 25 x 15‘ yard.
Has the edges of nine years. A power of waters to exit a hose, is non-existent. Some starts of water, turned in big, in the flow of half, when being a flow a strong plus of my tank of cookery. Basically, no the hose of flow of the big tide. This has required because of my edges that loves water of spray during a place!
Another thing adds in this house. It is when attractive calm he up in a the half all a water entirely the drains was, a lot easily. It is the little rigid to wrap up. But, any water still is falling out of a hose!!!!
Comprises this hose is used for RVs, etc.
after reading an information and some descriptions, has taken the bet, and a big time! It is my needs perfectly!
To good sure would recommend!
Will update has the question!
4 / 5
Has bought to this hose to use likes the primary hose to connect a water supply of mine of city bounces. In the first place, this is not waters it to drink hose. A water inside green of towers and chunks of the starts of seaweeds see of him. It comprises that water it is not seating in this hose for long periods to time of then was my primary water supply in the daily base. As, it is not UV STABLE. With which so only the pair of weeks to seat external, a hose has begun to break down and result a lot sticky. An only thing a lot roughly is a stainless hardware in each final.
5 / 5
Well, really likes to of me like this far. Mine another hose has taken the leak where a threaded female returning attaches to a metal there is crimped on piece of a hose (where leaves one returning to rotate). Ossia Common when a hose has been bent with the tight radio long. This hose has some cradles in any final. Ossia To prevent this type to filter to spend. This hose also looks to be quite fat. I prefer my old 1/2'GO hose to this 5/8'GO hose reason he insulates better. A OD of a insulation for both of them is some same, but one GOES for one 1/2' is smaller, for this is fatter. It is so only the small thing. I have directed to extend my old insulation in this hose and looks to be well.
4 / 5
Although any recommended like the hose of the his planned garden stiffness, the one who use the 50' hose exclusively for slurping in waters? Besides, it seats my plants - as well as an earth - has been diplomada to water of the toxin-free hose also. I have purchased an expensive Gilmour the roughly done hose 3 years and he (astonishingly) STILL odora toxic. This is to use for hosing down transport, pavement, and some interiors of has beaten of rubbishes. It is beginning to dry to rot now maintains his guarantee of 3 years, and in spite of promises to some contrary, kinked pending is whole miserable stinking life.
In all the chance, ossia mine 2nd Camco drinking hose of water. I had it of then cradle of this year. A prime minister an I was lasted several years before finally breaking in a winter last year while in his reel (without sprayer semi-detached). This hose has not been almost like this rigid like this one and I loved it absolutely. Honradamente Any the record kinking at all - or at least a kinks was like this scarce and easy to take that they were unmemorable. Well this newer hose apresamiento some serious lashing of hose and muscle to untwist the to take the kink when it is fill with water. A better thing to do, thinks, is to extend it was to his full period once in the moment when it is empty and the manipulate the bit to do sure everything is good and directly. Alive in a Mohave Empty, and would think constant exposure to heat and the sun finally would soften this thing on, but no.....
4 / 5
Update: experience had TWO HOSES (but to amazon only leaves to write a description, has included some the products are different measures . Mine another hose was 25' and is finally be to use it yesterday, so only to discover that a washer in him too much, was defective. Has has had to that the substitute, so only like one 10' hose, with him Gilmour Hose of Hule Washer. Now also he perfectly. It has loved only people to know that it looks a washers this is to install in these hoses apparently have subject.
Original description:
probably would owe that it did it to 4 indication of star, reason have has had to that immediately appeal out of his hose washer to the equal that was defective. LOOK well, but filter horribly. Felizmente, has purchased also a 10 band of Gilmour Hose of Hule Washers. It has dipped in a new Gilmore hule washer and bingo, now does not filter even the drop.
A reason gives a hose to 5 description of star is simply reason does not stink, does not have advantage in him, and therefore it is FAR UPPER to the majority of some hoses sadly when be sold in this country. There is absolutely ANY EXCUSE to direct to remain in of the hoses. ( It is added to stabilise an economic plastic) the advantage will poison an earth a water is sprayed on. This would have to that be against a law nationwide. This in spite of another the fault of controls of bad government, or a lack of them!
Curiously, there is remarked that pressure of looks to water to be main using so only he 10' hose. I can achieve a far side of my gram of a cup of a yard now. With my old 25' hose, was roughly 5' short of a fund. (And yes, an old hose was a hose of same measure , the wise diameter, but supposes a real reason can a lot of squirt like this far was all a kinks. :-)
4 / 5
The good quality that hose of drinks partorisca water that brotas any flavour in a water. Ossia Mine 3rd hose of Camco. Has a 50 hose of feet and a 10 hose of feet and now a 25 hose of feet. Calm does not know never the one who calm far will be of a source of water in the campground. It likes-me a main diameter partorisca a flow of water has augmented. It is the little harder that locate because of his diameter to wall fatter but that also helps to take kinks in him or taking broken when dipping is gone in a registered of the camping.
UPDATE 7/24/16
after using this multiple of hose the time has taken kinks in him so that it go it up. I have it that develops fully and work in the each one of a kinks for the take straightened was. I have gone back to use a weight a light hose whiter for Camco for travesías daily. Still it uses a blue one in mine seasonal camping where the rests have connected the month the time. A light weight tip a better east when you are travelling and connecting/disconnecting/rolling up in the daily base.
5 / 5
This hose was a bit difficult to use of a start. It was rigid, and does not want to unwind of this state coiled . I so only muscled the, and has used he for diverse outings. When I have had my rig in the park for the month with out emotional, when I disconnected to move, a hose was like this rigid, could do not taking storage, and has has had to that the the passenger marries he of engine. A temp external was fresh... Roughly 50F., Like appearances some stiffness, but a hose was unmanageable. I will choose another product for the substitution.
4 / 5
Calms the favour and the place went in it a sun the hours of first pair of the develop has a time and love a quality and everything in a hose excepts to develop he for a first time was the really wants to maintain this form gone. It have not remarked any flavour of hose in a water of a RV am satisfied. Material very durable, thinks will take the years of pair of FULL time RV that bolt out of him. The seasonal users can take more tent the safely when any into use...
4 / 5
Has used this under one has has announced methods, any hot water, etc etc. With which in a 6th use an application viril the whole has blown of an end while it fill the swimming pool for some girls. It liked really of one feels of this hose to the equal that seats sturdy and has to that weighed and on until it conceal has arrived had done that perfectly. I have tried reattaching an end viril and resemble in fact while it calms has not used any class of annexes of spray in an end. We do not have a pressure to water more orders that the lives am gone in a country the ways of our source to water so that it follows to expect that can have been a faulty hose and no a lack luster pressure that has caused a question.
This is to announce also so that no-kink but can ensure you he kink, often.
5 / 5
Has required the short hose to rid water to a dish of water for my dogs. This one was a right period and is announced like this sure to drink water. This in spite of was not really usable for my purposes.
Requires the hose that to to the laws like is done of of steel of cradle, this one east for you. It arrives closely coiled and is almost impossible to take a still hose straighten was. An incessant coiling do very difficult to use. Still although I have left he in place for the month, a coiling has persisted. You hear to Have the hose to the equal that have had to that coil and uncoil to store; it was virtually impossible. After struggling with this hose for the month, has decided to launch this thing was and buy something more flexible.
5 / 5
Has purchased this hose to substitute a hose has comprised with my hose of garden reels to attach it to a tap of water of external hose. Unfortunately some costruttrici of the hose of garden reels to comprise the very inferior hose to connect his reel to your tap. Utilisation the big quality 100' hose in mine reel and on some years have had many of hoses of a short leader that connects a reel to a tap fails. A Camco hose, while it is able to use for waters the partorisca drink hose, is to have that weighed with cradles in both ends to resits kinking this reduces flow of water. Reason spend big bucks in the hose of garden of big quality and have the cheaply done leader hose with the small diameter to reduce your flow of water? This hose substitutes a feebler link and taking one the majority of out mine 5/8' hose of garden.
5 / 5
Has tried these 50 feet Camco thumb of hose in mine Motorhome. Both finalises difficult to connect. A fine female because some flanges are rounded in place of clear-cut or serated still gripping. I have had to that use pliers for it presionar even modestly. Sure it can use a plastic grip you slide up in a connector that like this hoses of the garden now has. A connector viril is tightened like this you also have the hard time gripping the for the presionar esp where his prójimo to a side of a MH. Really frustrating. Esp Of the Company that mark RV accessories.
But to the amazon has saved a day like usual and can the to us send behind. I have ordered the different mark. It do not have to that be difficult to find old fashioned fittings can you presionar manually, likes in of the hoses partorisca always.
4 / 5
Flavour? Hey, Is the blue hose ! Durability - well, LOOKS sturdy enough for my application - described like this Storage? Hey, His the short piece of hose of water, for Pete sake!
Has bought this short hose for an application where would be it down stress - around a concrete flange of the a lot of wife where begin of an earth. A curling regular hose and has restricted a flow of water. This hose there is not curling and has aimed any adverse effect to hang some eight feet down a well marries (basically he 4' concrete pipe that curve like the man-hole in the concrete room around some a lot of bombs)
would buy this again - but he any look will have to that substitute he for enough some time.
5 / 5
Inner 3 month a hose has developed the kink and then open party. It has not imported if a hose is remained to dip slowly or has been wrapped in of the circles. Horrible investment. I recommend that it purchase the hose of water of different mark.
Has contacted Camco, has has sent pictures of a water spout come mid hose in a kink together with a bill of the amazon and a guarantee is honored and the new hose has shipped this week.
4 / 5
Very rigid and this in 72 terracings and a lot directly was. They are sure in 50 calm terracings would find it hardly useable and would remain coiled like this now. If you hooked to your camp to the filter of external water would be concerned in a piping in some camps. It arrives kinked of of the bond of plastic zip that it is too tight. When being extremely rigid the will not exit and the stays coiled to the equal that has the averages a diameter there. I so only cut 4' out of my hose of water and dip new ends on.
5 / 5
The my duties and are extremely disappointed with Camco. Take the look in a pics. Has another Camco elements partorisca camp have purchased like this this with confidence, was very wrong. After my first use, there is remarked a hose swelled up in 5 different places. This has not been partorisca water, is a plastic coating out of the swelled. It thanks the advantage there is remarked this. I will not be ordering anymore hoses of Camco. Refill of mine $10 25' economic drinking works of hose very better. If you have been researching, averts this. 4 / 5 Has bought many these hoses in different to use around mine horse barn. There is remarked a terrible plastic smell of a water that exited of hoses that has been exposed to alone, as I have thought an indication like watering it partorisca drink hose with UV the stabilizers would do this the durable hose. These hoses do not seat in a sun all day, like some movements of sun by means of a heaven, leaving them in shading the averages a day. Beginning last year, with which 3 years in service, these hoses discolored bad and has given a water a bad plastic smell same of hose of regular garden. It has attached the photo that look now. I will substitute him with something different. A same time esatta in 2014, has bought competing it drinking hose of waters sure that it is no longer sold for Amazon. Such the shame! A GatorHyde frames of looks of the new hose after siting in a sun every day of a year partorisca 4 years. If your use is intermittent and a hose spends the majority of his life stored in the dark cupboard, then calms like this hose. Or it attended to the launch material was each few years , is so only well. It has hoses of hule that is 20 years more. No the defender partorisca do more rubbish. 5 / 5 Out of a box, ossia the good hose . A bit I last partorisca take a coiling out of but has good ends, relief of tension and any funkify yours waters. I thought that it that it have found the winner. I have decided to move the then was a headline of hose in a pylon. Basically have it petrified to this form with which some seasons. Any sure he is a material in a hose, alone or something in a marine water that he. It filters my water with the 5 micron filter, then waters it softener, and finally by means of the 2 micron filter of carbon before it goes through half of this hose to a boat. They are the stickler in any water on board requiring be sure for consumption and to try well. I am not quite sure he somehow a softener hardened a hose or that. But, this has not been a nail of death for a hose. It was still usable. He so only spent to be molded to a perfect form for mine slips the connection of boat. But, then a surprise has come. I disconnected a hose of a boot to do the washed down and the brown discharges of seaweeds come touching was. Like Plots, has imagined a whole interior of a hose was coated. I have not had a sludge analysed but of the experience will bet it was diatom seaweeds. Any dangerous just gross. It is photosynthesizing seaweeds. That would mean this hose leaves light raisin by means of him. Any necessarily the good thing is trying averts the seaweeds that grows in your system of fresh water. Like this, has changed on to Flexzilla. It is drinking the sure water, remains very flexible (for this a name), pieces to a discharge, has good ends and is quite damn hard. I have not had a question of seaweeds with him still but am maintaining an eye was. It leaves light by means of but hopefully no a right spectre that the precise seaweeds to flourish like a Camco. If he , an investigation will continue for waters bear it drink the hose but I will maintain a Flexzilla like the washed down sure hose. Mike of a Lifesaport the alive embroiders to blog commentaries lateralmente: it does not remark Never that produced and mark that final in 'or' usually arrived with subjects. 4 / 5 Has purchased this hose reason has-liked me an idea of the water to drink sure hose that has not done to a flavour of water likes the hule. A hose is rigid compared the hoses of the hule but I have expected this and was has had to that to dip up with him for one drinking characteristic sure. Some first time used it I hooked the up with to nozzle of the new spray and has turned a water on. You grieve a pressure has on built in a hose an end of the nozzle burst out of a hose reason one returning has not been crimped properly. Any last 1 minute. Ossia junk ! 5 / 5 Has turned grieves in a water for a hose, a course of the adapter of the end is start. I slid the backside in and was quite clear a hose was way too big for an adapter to remain in place. 5 / 5 Has bought one 10 ft hose to use when it takes my water of cradle . I have loved the free advantage and bpa free hose. I have found this hose on Amazon and read some descriptions and a description of product and decided to buy it. It is the a lot of looking sturdy hose. I used it to take my water of cradle. My complaint is in a no said packaging is not the free advantage and bpa free hose as it alleges in this place and a Camco put. You would think that that the information would be comprised in a container/labels a product is gone in. This would be the big selling point and of Camco is alleging that reason not dipping this information in a container of product? It is this produces really bpa and directed free as they allege? All a material of container says is Drinking the Sure water. If there is of then information in a material of container and is not to direct free and bpa free then this would be dud announcing. Still it was dud announcing if this place and a camco the claims of place is bpa free and directed free and is not even a container does not say it this in spite of. I have not contacted a company still but slowly on doing so much. Ossia Reason some three stars. The has has to that upload of the pictures of a packaging. A side is in English some another create is in French. Update 7/6/16 : I have discovered this hose is not entirely direct free. I have forgotten to go back an update a description. Still very sure in a BPA but would question it. Still I have a hose, has not annoyed to return he for a prize have paid for him. I plan on buying the bpa and free hose directed in a future. 4 / 5 Has purchased these 10 months does. At the beginning it look well so only the little rigid. It has used now each one that 2 -3 weeks for -14 times with our new 5th wheel. Every time a hose has taken more rigid and difficult to coil and uncoil. Last useage our cartridge of filter of the water clogged up. Not comprising reason has researched and found particles a lot a lot of ashes clogging the. I then far and found a hose to be an offender. I have bent An end of hose has retreated the chamber and some particles by heart still have come to the game was. It is an interior liner breaking and deteriorating. Not watering or hard stairs buildup. An inner hose liner is falling averts. Probably reason campco so only gaurentees for 30 days. It can not be well to drink or cook with east. We can not recommend this to any and the desire have had recourse to return. I guess this an amazon of time has left down. 5 / 5 Extremely disturbed with this compraventa. Some looks of good hose. I have used so only he for a first time. Water gushes out of a coupling a lot that attaches to a tap of water. A hose is semi-detached securely. It is gushing of a coupling in a hose he. A lot irrate spend this a lot of money on something concealed is unusable. 4 / 5 Has has wanted to really this to be like this as well as the indications have indicated, but a two I has received both have had kinks arrive it, in spite of a anti-kink claim. A prime minister was kinked so only under a coil of relief of the tension. He not having has blocked entirely a flow, but would have reduced it a bit. And it is the weakness that so only would worsen with each use. I sent it behind but a hose of the substitution there has been the kink further to a centre of a hose - see semi-detached photo. The suspicion is winding to too much of tight to coil to ship. Has has wanted to really this to do - I like a machined fittings and coils of relief of the tension, which are hard to find. But I not having enough the time has left to risk the third tries, as I am changing the different mark. 5 / 5 Ossia The good hose . It looks good and good works . I have bought 2 of them and dip his together for my garden. I have been by means of the little now and this looks to be a main quality a ive expósito. Material all the hoses kink sometimes but his nowhere near of like this bad likes to last the pair has had. UPDATE... I USE it SO ONLY to WATER MY PLANTS And HAS A HOLE IN HIM THAT the SPRAYS WATER EVERYWHERE AFTER SO ONLY 8 MONTHS to USE 4 / 5 This 'Camco to prize that Hose of Drunk' is quality to notch upper. It is built with materials of qualities and -like this expected- will last it the long time. I anticipate, this in spite of, this long direct exposure to alone will shorten his life has turned like such light fact of more all does for men. I have been impressed with a hardware. Both ends are the hefty piece of the aluminium feigned for a costruttore partorisca resupply the one of confidence and long-use of term. Any extracted elements with care foreseen and prevents direct exposure to alone, I rightfully affirms that this 'Camco to prize that Hose of Drunk' is a last a will buy in several decades. 5 / 5 A hose is good but really needs the reel partorisca the tents/of use was using he with a RV and it packing on top of weekly or two. A hose is weighed and is hard to coil it and take all a water was is trying the manually. It is the good hose this in spite of, and is lasted 9 month partorisca me without leaks or of the questions others that an ache of the treat to dip on/tears down. 5 / 5 To good sure fulfils a level of the prize and I have used this jointly with a Camco filter partorisca water to fill my tank of potable water. Easy to use and perfect returns without any one filtering or requiring tape of @fontanero. At all critic partorisca add, but I only desire there was the longest measure that 25, but shorter that 50. So only the little extra would be more convenient, but no the breaker of extracted. They are very impressed and happy with this compraventa. Has has bought hoses before that has launched was reason a material is lousy. Really like this one. 4 / 5 Yeah Man. I love these hoses. I have bought the pair of them. Honradamente, To some flavours of water likes them awesome of water of cradle out of this sucker. Cold of gel, loves the after mowing a gram in a summer.. Man, really lose state right now.. It is cold and snowy here, windy and sux. But in all the chance, has bought the pair 50 footers, the juice so much is easier to disconnect, shortens, or extend this in spite of want to. A thing isnt kink test, but he certainly doesn kink each one dang the time the pulls around to somewhere. Hoses very durable like this far. I havent had the subject with only that they. I can buy another.. I will say you this.. If I buy another hose, was is one . I do not love any soiled, advantage, unsafe hose. Still if you do not drink out of him, the does not love bad metal, or advantage in my plants, or garden neither.. Or when the boys are touching in a sprinkler that drinks it. Ossia Mainly reason has bought this. So only it wants to be sure, and is, and that no. takes the boys already knows.. n Perhaps the love the cold drink takes good to water after the down to 6 band mowin a gram. So only it is that it is. The packaging was well, and the delivery was quickly. I recommend this product to everything :) it thanks! 4 / 5 This hose has on resisted for four years to use alfresco in extremely of hot time and of cold and any protected of sun. Has the habit to fill our animal' tank of water. Some of a blue colour is spending to aim black down, but there is not any sign that will fail time very punctual. For some reason, a metal that the returns can be the little delicate to begin some edges. It can be because a hose is rigid, especially in cold time. Once begun, continuous in smoothly. It is handy that one returning has a octagonal forms. We maintain the big crescent English tone in a standpipe so much can do sure a connection is tight. Ossia Particularly useful in of the freezing temperatures. When it Was new, liked a fact that a hose there has been any smell of hule bad. 5 / 5 A lot of Amazon He again, with another product of quality that could not beg, apresamiento loaned or fly here locally. I hooked the on grieving arrive and has known had done the election adds. Is flexible, hard to kink, and the good-looking colour. Although it is lighter that mine hoses of hule heavy, looks to be like this durable -- awesome! A good surprise is that when it is coiled on, no the heavy battery , rigid enormous as mine another, although it is a same period . Has to that change my alcohol, will update this estaca. But I think that that I will love this toxin-free hose for the very long time to come. 5 / 5 A hose and a fittings is fat and would have to that be well for my purpose like the whip of clean water in the spigot in a front of my house to drink that/ it washes the hands etc. Used It to wash down the gram of pair mowers and has not seen any leaks so that promising. As it Resists until UV the RAYS can not say I of then maintain my hoses have trace & in slope in a cochera in Gnarly On the straps of hanger of the hose. In a little zone of white bar code in a backside of a container owes beautiful little sentence: FACT IN EUA. This would have to that be mentioned more prominently in a description for people that looks for to avert facts in of the rubbishes of china. 5 / 5 A pin-prick (very small) the leak has developed. I have remarked it after 3 month of use, but can be been present of day-1 and would not have seen it. A location is where a hose is suspended on water the short distance - to jump still to bounce - so the person stepped in a hose in this location. I did not expect it to last for ever but 3 month is not well. 5 / 5 Has required two hoses to achieve was to where alive in the trailer of camp, and was under the estimativa tight and still constraints time to take all dips up. A quality of some components of a hose does not look bad, unfortunately a costruttore any in fact annoying use any glue or pertinent clamps to maintain an end viril has attached. So that my first experience hooking the up was special, two hoses, has opened dulcemente my valve an eighth of the turn to try a hose and roughly 100 second later, look on to see both hoses promptly failure well out of a box, some finals of the male adapters simply burst out of a hose. This is not it faulty hose, ossia the company that specifically these, that knows that the hoses with the finals of adapter require something to maintain them to fail down pressure, not ensuring some finals of hose. Also a hose splitter has taken for separate of them have had so only a threaded arrival how was transmission. These looks to be the model. 4 / 5 Ossia Very better that a typical RV hose (the aim some). It is 5/8' in place of 1/2' like steps to have the multiple people that water to use a same time, calm leave to manage a better volume. Has a cradle in the each final to protect he of kinking in some connections (which am connectors of upper quality ) and finally filtering, as I do not owe that buy some connections of hose of final to jump separate. For a reviewers that has attacked he partorisca kinking while it looks for to use he for more than the line of potable water supply, has not been that attended. I have not seen never a hose to drink agreed to that it can use you to water grams, washing is car, etc. Cela managed like the good gram and hose of garden, especially when a temp is is fresh. Has has used this to do anything but hook to mine RV or for the fill? Yes, has and treat as well as it can be expected. If you are wanting the hose for gram, yard, garden, etc. then take the hose for that and does not drink of him worry you . Or more take one all the park of hose of hule (usually red) and does not complain roughly the when the be weighed. It likes all more in of life, has to take a good with a bad. Calm does not go to take waters it to drink the hose estimated with a same usability of the hose of yard of good quality. But, this hose the quite good work to do both. Has one of the each one of one 10', 25', and 50' period. 2 Renator M11-0660R Water Pressure Regulator Valve. Brass Lead-free Adjustable Water Pressure Reducer with Gauge for RV… Renator 9.6Score View Product ### Top Customer Reviews: Renator M11-0660R ... Rating: 4 out of 5 with 60 ratings 4 / 5 I have bought this regulator after verifying everything of some descriptions. I thought it probably it is a better one with a main quality for a money. Alas, it leaves to do after quite a lot of 2 weeks. Already I can any very adjustments in a pressure or up or down. Any one that road of turns subjects a ray of adjustment, does not change of 30 pounds for inch have squared. For some first two weeks was able of the take to adjust, but have it remarked would not line a pressure selected by very very time. It maintains to go of my parameter of 45 lb in 60 books for inch have squared. Desprs Movement in a second RV the park camped in, no longer adjust. Since I am now external of my turn of 30 period of days, will have to treat a manufacturer for the take repaired or has substituted. It does not recommend this particular regulator. After reading this description, a vendor wrote me and excusado for a defective product. They have offered the road the new regulator in any load. It take a new regulator and look to do only well. That is to say that I client of the service has nicknamed. It revises this indication to reflect his worry, and the service of client adds. Thank you! 4 / 5 These marks of unit well in controling pressure. Has better flow that some few small fixed regulators but his tax of flow is significantly less than the some units of the similar watts. I have tried 2 fixed pressure small regulator. A there has been the download orafice 5/16' the diameter and he have regulated 45 psi and has had the flow of 6.17 gpm, another there has been the 7/64' orafice diameter and has regulated 50 psi with the tax of flow of 5.79 gpm. A similar (but sigificantly more expensive) the regulator of the watts there has been the tax of flow of 7.56 gpm. A Renator has had the tax of flow of 6.51 gpm. In a RV a flow is critical. Some watts has some better flows (for 16%) but side almost two times so much. A Rentor has slightly more flow (5.5%) that one 7/64' fixed and 12.4% more adds flow that one 5/16' fixed regulator. 5 / 5 Hello All you RV folks there, gotta the left wing knows in this small bad boy. I have purchased recently this so that has thinks that that something was defective with my old rule. My alcohol of old regulator was a concealed has not been adjustable but has had the insurance preset pressure with the piece of needle this has aimed the green zone for the pressure that is acceptable and the red zone to be in sure limit. I use this with the Camco the filter of water can pickup Walmart or enough very RV trafficker or RV place of parts. - It opens For me that is to say where a better informative in this adjustable regulator has changed literally my problems of pressure of the water once and for everything for a BETTER! - I has battled constantly with an old a there has been tries to have quite a lot of pressure of water, included had paid enough the bit of money for the cup of a leader of line of the shower of low flow concretely designed for big tidal pressure in a RV. Research in an internet to discover a better parameter for my new adjustable regulator and is coming up with enough 50lbs the fir the old plus that plumbs RV and 60lbs for the new plus RV with a plastic a new plus that tubes and fittings. It comes from/ it Comes from a factory pre-has posed 45lbs, at present has together of mine 40lbs. I left me say you a woe and the worries of an old regulator are Totally the thing of a past. Posed explodes 30lbs and now has Abundance I bad Abundance of the pressure and has wished totally I boughten one these write at least done 2 years... The rest has Ensured now is in sonriente the big time when washed my hands, stuffs, fill my tea mug, or take the shower! A PROBLEM of the life has RESOLVED! He thank you Renator.... ;Or) 5 / 5 Update in anterior description. Wants to give the cry has been in a manufacturer Cartlee. It leaves to be it has remarked has not contacted never a company in my subject. We CONTACT ME To us!. During some HOLIDAYS are!. Taking a time of his familiar to rectify a subject had and exited of his road in quickly take me up and go. That is to say truly the product of quality that was very happy with until it fails. He that is supposition to do and a pressure the fluent gauge has filled is to premium. In the perfect world-wide all purchase would last for ever but know included the products of quality can have problems in time. That marks a difference among one has and one has is not is a service of client that yours clue compraventa. These products and a company are being upper in my book and deserves an until indication of date. Anterior description: has Purchased of the amazon in Pot and of the based in descriptions and description of product this looked a a to take for my necessities. First time used it done while ad. Clashed he until 50 psi and fact like the charm in a RV. This week, according to the time was, the leak has remarked to return by behind commode third day to trip and has had to waters it has been in troubleshoot. YIKES! He thank you the advantage has bought one with the gauge. This thing was pegged in 90 psi. Any marvel there has been the leak and lucky has not bursting the line. Backed Was ray of regulatory all a road and a lower pressure could take was 68 psi. The big hopes had but is the shame he no last long. 5 / 5 An in the first place an arrived and a piece has not done properly. Well in a box, in the big source, was the number of tlphonique to call yes there are any problems. I called it and immediately ship me the seconds an and some materials have required to ship a premier a backside. Some second some works add, and would recommend this product in the partner. I have been impressed by a number of tlphonique to the help that is so prominently aimed in a container. The vendor was very cooperative. 1 / 5 I have read some descriptions and this regulator have sounded well. They use that it hangs 5 months. It IS VAL for quite a lot of 3 months. Then begin to filter among an organism of brass and a pressure that regulates accommodation of ray. A pressure that regulates the ray now does not go down a pressure. Later--punctual after I have revised this took an email that offers for the substitute. I adapted and it has taken quickly the substitution. Installed the and records so far. I will follow up in a future. 4 / 5 UPDATE (Can 28, 2017): the day of my first low description, took an email of Cartlee Service of Client. They had read a description and has wanted to marks it well. We offer me to us or the total repayment or the new regulator without that owes the road retreated a defective unit Because of his disposal to resolve a problem, chosen to try again with the regulator of substitution. They shipped it and it achieves the few days. They try in my water of house and research to be doing properly, but, a jury is still was until I use with my RV the few weeks. A company also is directing a deceiving disclaimer also. So much, for the service of client gives 5 STARS and for a product 4 STARS, only so that it is not fully tried still. It IS A lot HE ADDS the LAW WITH A COMPANY THAT CURED in HIS CLIENTS, THIS is RESULTING A STRAY ART!!! INITIAL DESCRIPTION (Can 19, 2017): the gauge has failed after first use. It water it it was only on for the few hours and has turned then has been. A next morning, has been to turn a water on and a gauge has recorded 40 psi without pressure. I have turned a water on and a gauge has recorded 80 psi. It looks a Point of the zero moved in 40 psi. A pressure in a RV in researching more to be like me the 40 psi. So many, some looks of regulator to be working but a gauge has failed. Besides, a documentation that is coming with a regulator says that this has to 1 guarantee of year, but, then disclaims only in any one fails. Not even guaranteed to do an era of builds of function and has sold prendi. BEWARE! 1 / 5 I have taken this Oct 1 2017 sake after buying the new rv and the fact attaches one 3 times has taken to camp last year even so afterwards hooking the up for our first time 2018 note camped that a gauge of the pressure does not move anymore the just saids 44 lbs hooked up or no hooked up. It looks he like me has to has lasted it to him more than long. Very disappointed because of his course spent a time of tower. 5 / 5 I have believed at the beginning that this regulator of water was a main piece of junk. I installed it on a camp and hooked in a hose of water. It visits a water has been on stabilised in 45 PSI. Then it was and it verify it the small later and has seen 140 PSI. I have begun to take crazy thought what the piece of junk that is to say. Then I give the does not leave backfeeding to water so when a heater of water is on he will augment a pressure in one camps system of water. Mark Only sure has opened from time to time the tap to leave a pressure stabilises. I have found also that trace with a gauge that the affronts have attached down the protect of advantage of small extra of one returning apresamiento yanked down because of a weight of a hose of water. 4 / 5 Very like this regulator of pressure so far. I use diverse brass and or the plastic regulator and have each which declares the disappointment...Usually giving the pulsing class of operation, or the dulcemente falling flow to water when a pressure shouted in around 100 PSI. Or only it was bad with apparently any reason. OPENS The BAD - That is to say$ 50 device! It suggests it that it was necessary to have the point adapted in a fund of an assembly that can pose the canal or cape and lock in. It IS more to pose this right of regulator in a RV tap of parks what the fact an element of easy flight. Still during a daylight, the burglars easily can look an owner and the mark have been with him although you are house . There is any easy road to ensure this device of burglars. Posing he inside a RV compartment of the water does not protect a hose of big pressure...In fact when I concealed, one of my connectors of hose have jumped the leak of one 115 PSI. With this regulator that precedes a hose, not even the drip.
As I like him his suggests a mould of manufacturer the point in a fund of a regulator or in the some place to protect. Justo necessities to be quite big for the lock. Thank you!
4 / 5
I have bought this regulator after verifying everything of some descriptions. I thought it probably it was a better one with a main quality partorisca of the money. Unfortunately, it leaves partorisca do after roughly 2 weeks. Already I can any a lot of adjustments to a pressure neither on or down. Any @@subject that way I turn a ray of adjustment, does not change of 30 pounds for square thumb. Partorisca Some first two weeks was able of the take to regulate, but have it remarked would not resist a pressure has selected takes a lot long. Maintain partorisca go of mine place of 45 lb to 60 books for square thumb. After moving to a second RV camp of park in, no longer regulate. Of then I am now external of my turn of 30 period of days, will have to treat a costruttore partorisca the take repaired or has substituted. It does not recommend this particular regulator.
After reading this description, a vendor wrote and excusado partorisca a defective product. They have offered partorisca send the new regulator in any one load. I have received a new regulator and looks partorisca do so only well. Ossia That I client of service has called. I have revised this indication partorisca reflect his worry, and the service of client adds. Thank you!
5 / 5
This unit does well in controling pressure. Has better flow that some small fixed regulators but his tax of flow is significantly less than some units of Watts looked. I have tried 2 fixed pressure small regulatory. A there is had download orafice 5/16' the diameter and he have regulated 45 psi and has had the flow of gpm, another has had the 7/64' orafice diameter and has regulated 50 psi with the tax of flow of gpm. A resemblance (but sigificantly more expensive) regulatory of the watts there has been the tax of flow of gpm. A Renator has had the tax of flow of gpm. In a RV a flow is critical. Some watts has a better flow (for 16) but side almost two times so much. A Rentor there is slightly more flow (5.5) that one 7/64' fijamente and 12.4 flow less adds them that one 5/16' regulatory fijamente.
4 / 5
Hey All you RV folks there, gotta has to that the to the left know in this little bad boy. I have purchased recently this reason has thinks that that something was defective with my old rule. My alcohol of old regulator was a concealed has not been adjustable but has had the insurance preset pressure with the piece of needle this has aimed the green zone for the pressure that is acceptable & the red zone to be in sure limit. I have used this with the Camco water filters can pickup Walmart or enough a lot RV trafficante or RV put of parts. - Now for me ossia where a better informative in this adjustable regulator has has changed literally my questions of pressure of the water once & for everything for a BETTER! - I constantly struggled with an old one has had to try have quite a lot of pressure of water, included had paid enough the bit of money for the cup of a boss of line of shower of the low flow specifically drawn for pressure of big tide in a RV. It has done investigation in an internet to discover a better setting for my new adjustable regulator & is coming up with roughly 50lbs the fir the old plus that plumbs RV & 60lbs for the new plus RV with a plastic of new plus that tubes & fittings. The test/Come from a factory pre-dip 45lbs, at present have near of mine 40lbs. To the left say a woe & the worries of an old regulator are Totally the thing of a past. Sleeve Mina 30lbs & now have Abundance I bad Abundance of the pressure & has wished totally I boughten one these write at least done 2 years... The other has Ensured now are in sonriente big time when I wash my hands, stuffs, fill my tea mug, or take the shower! A QUESTION of LIFE has SOLVED! It thanks Renator.... ;Or)
5 / 5
has Read some descriptions and this regulator have touched well. I have used he for 5 month. It was WELL for roughly 3 month. Then it begins to filter among an organism of brass and a pressure that regulates house of ray. A pressure that regulates the ray now does not go down a pressure.
Later--shortly after that has revised this has received an email that offered for the substitute. I have adapted and promptly has taken the substitution. Installed the and laws like this far . I will follow up in a future.
4 / 5
A prime minister an arrived and a piece has not done correctly. Right in a box, in the big source, was the number of telephone to the call has had any one questions. I called it and immediately we ship me the seconds an and some materials have required to ship a prime minister a backside. Some second some works add, and would recommend this product to the partner. I have been impressed by a number of telephone to help be like this prominently showed in a container. The vendor was a lot of cooperative.
4 / 5
Wants to give the cry was to a costruttore Cartlee. To the left be it remarked has not contacted never a company in my subject. We CONTACT ME To us!. During some HOLIDAYS is!. Taking a time of his familiar to rectify a @@subject had and is exited of his way to promptly take me up and that goes.
Ossia For real the product of quality that was a lot of happy with until it fails. He that is supposition to do and a pressure has fill fluent gauge is in prize.
In the perfect world-wide all the cost would last for ever but know even the products of qualities can have questions in time. That marks a difference among a have and one has is not is a service of client that follows your compraventa. These products and a company is upper shelf in my book and deserve an up to date indication.
has Purchased of Amazon in May and has based the descriptions and description of product this looked a a to take for my needs.
First time used it fact to the equal that has announced. Clashed he until 50 psi and fact like the charm in a RV. This week, according to the time was, turn of leak remarked for behind commode third day to trip and has had to turn waters was to troubleshoot. YIKES! It thanks the advantage has bought one with the gauge. This thing was pegged in 90 psi. Any marvel has had the leak and lucky there is not bursting the line. Backed Was ray of regulatory all a way and a lower pressure could take was 68 psi. The big hopes had but is the shame he no last long.
4 / 5
Has spent this Oct 1st 2017 legislation after buying the new rv and the fact adds one 3 times takes to camp last year this in spite of afterwards hooking the up for our first time was 2018 camping I look that a pressure gauge does not move anymore the so only saids 44 lbs hooked on or any hooked up. It looks he taste was necessary is lasted more than long. A lot disappointed because of his course has spent a time of turn.
4 / 5
Has purchased this regulator 3/17/17 and used it 2 times, felizmente. A third time that I hooked the on, and has turned a water on, waters it has begun to immediately of the spray out of a focuses among a brass and a black plastic as seen in a picture. I have tried to unscrew a plastic and verifying for the failed or-coverage or something, but has not had any reason of obvious/way for a water to be that it filters (this could say). Enough frustrating to spend this a lot in the product and not taking 2 uses more out of him.
5 / 5
UPDATE (May 28, 2017): Inside the day of mine first description down, has received an email of Cartlee Service of Client. They had read a description and has loved the sake. We offer me to us neither the total repayment or the new regulator without that has to that send for behind a defective a. Because of his disposal to solve a question, has chosen to try again with the regulator of substitution. They shipped it and arrivals inside the few days. I have tried he in my water of house and looks to be doing correctly, but, a jury is still was until utilisation with my RV the few weeks. A company also is that it directs a misleading download of authorship also. So much, for the service of client gives 5 STARS and for a product 4 STARS, so only reasons is not tried fully still. It is REALLY IT ADDS the LAW WITH A COMPANY THAT CURED IN HIS CLIENTS, THIS is RESULTING A STRAY ART!!!
INITIAL DESCRIPTION (May 19, 2017): Gauge has failed with which first use. You water it it was so only on for the few hours and then has turned was. A next morning, has been to turn a water on and a gauge has registered 40 psi without pressure. I have turned a water on and a gauge has registered 80 psi. It looks a Point of the z/of the zero has moved to 40 psi. A pressure in a RV to to the looks to be more like 40 psi. So many, some looks of regulator to be working but a gauge has failed. Besides, a documentation that is coming with a regulator says that that has to that 1 guarantee of year, but, then disclaims so only in any one fails. Not even guaranteed to treat a function was build and has sold stops. BEWARE!
5 / 5
Has thought at the beginning that this regulator of water was a main piece of junk. I installed it on a camp and hooked on a hose of water. Recognition a water on was stabilised in 45 PSI. They are then state and verify it the little later and has seen 140 PSI. I have begun to take crazy that thinks the one who the piece of junk ossia. Have @@give Then does not leave backfeeding to water like this when a heater of water is on he will augment a pressure in one camps system of water. Mark so only the calm insurance from time to time ploughs the tap to leave a pressure stabilises. I also found that traces he with a gauge facing has added down the little extra leverage protects of one returning taking yanked down because of a weight of a hose of water.
4 / 5
Really like this regulator of pressure like this far. I have used several brass and a the plastic regulator and have all been the giving the pulsing class of operation, or the dulcemente falling flow partorisca water when a pressure creates to around 100 PSI. Or I am so only bad state with second looks any reason.
NOW The BAD - Ossia $50 device! It suggests it it would have to that have the coverage molded to a fund of an assembly that can dip the canal or boss and lock in. It is more partorisca dip this legislation of regulator in a RV tap of parcos the one who the fact an element of easy flight. Still during a daylight, the thieves easily can look an owner and the mark were with him although you are house . There is no easy way partorisca ensure this device of thieves. Dipping he inside a RV compartment of the water does not protect an in fact big hose when I that, one of mine connectors of hose have jumped the leak of one 115 PSI. With this regulator that precedes a hose, not even the drip. To the equal that would like to suggest a mould of costruttore the coverage in a fund of a regulator or to somewhere partorisca protect. Just needs partorisca be quite big for the lock. Thank you! 5 / 5 This looked to be a lot of-has built. It is heavy brass , has the ray of adjustment of the pressure, and the pressure gauge. I hooked he until my hoses the regular pressure to the hose to drench. A pressure gauge has looked to read correctly in setup, but the month or like this later, a gauge was stuck permanently in 40 PSI, included without water in him. RETURNED... 5 / 5 Has bought this for our bus. As there is still to go back was, has not used this camping still. Like this the description is the first description of impression . Ossia The heavy product . A brass looks a lot solid. Gauge Is the oil has fill. There is the screen in a woman (anchored) side of a unit. These looks to be the very good product fact. Trace in mine bib of hose in a house and has not had any leak. They are trace the second gauge in a side viril (outlet) to compare some readings of pressure. With a Renator reading 48 psi, another gauge read 52 psi (sees photo). Ossia Quite near for me. A thing that is declared in the sound has ASKED GENERALLY the questions have comprised with a unit is concealed '... It is more to maintain it whole like gauge is in the vertical place with one covers of hule on, which help to prevent he to filter fluent.', This in spite of, each campground has been has had a connection to water signalled down. Included his drives of instruction aims it when the be has has connected signalled down. As I am not sure like one is expected to adhere to this recommendation. A thing to @give , so only tip a correct pressure if there is not any flow, that means that all the taps of the water in a bus has to that be was. When you Regulate a pressure, does not change until some flow is used and then has closed was. 5 / 5 Has hated that goes of RV parco to RV parco and while a pressure of the water has not gone too big to a point that could break it my plumbing. A day was them on amazon and found this regulator with an oil has fill gauge. I have thought yes and envoy for one. It arrives two days later and my woman and has been them for travesía of Oklahoma Montana to spend the pair of weeks in some mountains. Ours first stop was in a RV parco in Nebraska and the tried out of a new gauge. 40 psi, Adds the very pleased era with this new regulator. The next stop was in Wyoming of Búfalo. Again it was 42 psi and was them appreciated that it has taken them that gauge. We direct Montana and when we arrive in some mountains the discovered that it had left them my new gauge in a line of water in Wyoming! I kicked me to be like this absentee has imported. In a way for behind the received the call of a RV parco in Búfalo and thy has had my gauge and the pair of the days more have dipped late in a topmast and the now have my gauge again. I will not forget or travesía with out he again. One produces extremely final, thank you. 4 / 5 A lot UNHAPPY. Purchased this regulatory pressure A lot EXPENSIVE SO ONLY DONE 4 month and used it perhaps four times. No longer rule a pressure of water. In 1st he well. Of the 2.os time used that, so only leave so only the trickle to exit. I have turned once a ray of adjustment he 1/2 turn now leaves FULLLLLLLL pressure of a RV parco in. I have tried of then to regulate it and AT ALL transmissions. I do not go to leave full pressure my RV and break the pipe or connector. Have PRENDIDO using it. It DOES not SQUANDER YOUR MONEY has WON HARD!!!! 4 / 5 Has used some times and of the discharges are starts and the oil has filtered was! I purchased it 7 month before we use it to us, as it can do not returning! Think it that it was ready and preparing :( has MODIFIED: the company Called and has said would send the substitution. Service of client very good! The LAW of NEW SUBSTITUTION ADDS!!! The SERVICE of CLIENT ADDS!! 5 / 5 I alive in mine motorhome full time, and I finally tired to dip up with pressure of big tide. I have read enough of another RVers to know that I have to that never just hook directly until a water supply. A place with big pressure can burst some pipes in yours RV and the one who loves concealed? As I have had a pressure of brass rule gizmo with the setting fijamente. But a pressure in a bus was pitiful. There is pulled one causes in this regulator with an adjustable gauge. Like this happy has done. I can dip a pressure to something tolerable without worry for my pipes. I installed it directly to the water of a bus intake, inner a underbelly compartment. In this way it remains enclosed and out of view. 5 / 5 Are the new to camp. Bought the new mark Rockwood A122 pops lateralmente last on camping and while they are one of some smaller rigs in a RV parco I still has peeled was in$ 10,000 for my camp. As I buy a camp and say me, 'calm really would have to that take the regulator' and I summarily forget that it has said it. In prime minister of mine outing a type in a lot afterwards the mine said so that they are hooking on, 'any needs your regulator here a pressure is down'. It likes I an investigation to see reason all the world is speaking in regulators and sure enough learn that pressure of the water in some campings is way too big and can blow out of your system of water.
Has bought like this one of these and the good thing has done. It has been to the campground this weekend and hooked he until trying a first pressure of hooking to a RV. Sure enough a pressure of water is REALLY BIG. Then a type in an after the place of mine say that it blows the line of water in his rig because of a big pressure there.
This regulator saved probably to break to my system. Before I bought it I have thought in me that has not had any way a regulatory ray to my camp has anchored to water reason a gauge probably paste a wall and the prevent. It returns so only perfect. Any one calm so only love this regulator. Calm the precise. Excellent construction. Gauge Is attentive.
5 / 5
Has bought one of these he roughly done 3 month and and think that is quite a lot of fact and looks to do like this announced that. This in spite of, I so only found that one orients is exited in a pressure gauge and is floating around in an oil. Have emailed A company to ask reparation of guarantee or substitution. I will update my description and estimating once see like boss this.
UPDATE: it take the response of RENATOR-EE.UU. So only the hours of pair with which have sent my message that considers reparation. Have excusado And said sent the unit of substitution, has comprised a number to follow And has said was resetting my guarantee to start with like this of today! Have upgraded My indication of 2 stars to 5 of then is the really good unit and support of excellent client!
Jerrold
4 / 5
3/2019 update: Not doing . A ray of the adjustment does not look to import, and a lot anything more. Yes, they are to continuation some instructions. Too bad. It can you do not send behind now - the money gone . . .
Ossia The regulator of the pressure of water adds valve. It is done of brass and is the free advantage – ossia dondequiera go with a RV. That The packaging are to add – comes with one inserts concealed is formed to a regulator to protect. Good touch. WELL, it loves to buy something well and more permanent that use to protect and the tent; together with a form that the returns inserts/to insert concealed has been comprised with a regulator, ossia the perfect solution : HESPLUS USB CD DVD Blue Writer-Storage & of Ray of Stock exchange of Hard walk Outside of Travesía of the Chance for USB of Apple Superdrive, Samsung -208GB -218CB LG GP65NB60 GP60NB50 Dell ASUS Walks of EXTERNAL DVD (copy and paste this to a window of investigation of the Amazon).
4 / 5
Rings the regulator of pressure adds that it does not reduce flow of water. I have had very other regulators that comprise pressure in-regulatory of line and other alike regulators to the east a. Any of them arrived with some legislations of number of telephone of the vendors in a focuses forward. And one of them has broken inside a first year. The mine has done perfectly well out of a box, but a fact that a vendor plastered his legislation of number of the telephone in a front of a box says is behind that.
This regulator is clearly a lot done - of an arrival in a brass, to some seals concealed has been clearly done well in a regulator, ossia the law of class .
Has used a regulator a first weekend there has been and the work adds. You are dipped to 45psi right out of a box, and our pressure was roughly 40psi in a campground use in. As I have tried to reduce a pressure like the test, done like the field.
4 / 5
This description is partorisca a Renator M11-0660R Valve of Regulator of Pressure of Water, Advantage of Brass-Pressure of Free Adjustable Water Reducer with Gauge partorisca RV Camp, and Anchored Screened Filter. Works to the equal that has announced. The pictures of product are attentive. The primary purpose of device is partorisca protect some lines of water in yours RV partorisca suffer harm for pressures partorisca water that is too big in some RV parcos. Using this regulator can save you the plot of money you factor in a cost partorisca repair fraction RV lines of water. The adjustment of a pressure is easy with the screwdriver of flat boss simple level (any comprised). The quality of construction looks very good. My main worry with this unit was an oil has fill gauge. I have been concerned roughly leaks of oil of a gauge. Like this far any leak. An advantage the free creation is of entity and I also like a filter of screen of big particle, which the helps extend a life of your filter of small particle for pre-filtering out of any big particles in a water before they achieve your filter of small particle. Better way partorisca use this unit is partorisca attach it directly to a RV line of Parco, then run your water partorisca drink hose to the yours RV. I have not had any question at all with this unit and would update this description if any one develops.
4 / 5
Has taken this unit in an end of June 2018 partorisca use to regulate a pressure in the campground has taken the seasonal place in. Right out of a door a female hose that returns the side filtered in an end Viril that goes to an organism of a regulator. Has one wraps of tape of teflon. It has had to that take one returning, dipped the little on tape in some edges and the question have solved. Fact well for a balance of a season. (2 month) has Been to open up for this season, has taken a regulator to connect to water hookup and found a needle in a gauge spends stuck 160 psi. Thought perhaps has connected the, water twists on, can reset, any one changes to needle. The adjustment has tried to see yes can release on a needle. At all. Behind to use one static 40 psi adapter that is coming with a trailer. Any real happy with this product.
5 / 5
Has used this the little house of time. His hard to say if he anything. In our travesía out of the west use in the campground and when I have tried to regulate the a ray for a pressure he didnt anything... So only it remains around 40psi. There is remarked then my tap that filter the little time but didnt thinks a lot he. There is remarked finally that when some one in a rv parco hooked on or unhooked his water done my leak of tap. This isnt that big of the treat reason so only go to a tank, that is the big shot is that I am coming house to water during my paving in a bath. A pressure to fluctuate has caused the low leak my tank of bath and of then I wasnt manacles to clean it on immediately breaks a forest and an arrival around a tank. Not cooling
5 / 5
was in a RV Parco that has done clear has not reduced a pressure to water that comes from/comes from a line of the main water and the regulator has been required. I have not thought any question, has my zippy Renator regulator of pressure. I hooked all arrive and saw it read 45 psi; still to the equal that have taken place he of a forward RV the park was in. Then a needle has begun to locate. I have begun to turn a ray down. It maintain to locate. I have maintained to turn a ray (and yes, has turned a ray in a right direction). It maintain to locate. Like the pressure has blown has spent 80 psi to almost 90 psi, has turned finally a water is gone in a spigot so that a valve of relief in mine Truma has blown. Felizmente Does not think it has destroyed anything in mine van. You save $30 (and your vans that plumbs) and so only buy one$ 5 camco regulatory. It maintains your pressure in 40-50 psi which is abundance and is failproof.
4 / 5
Has purchased this behind in April to use with my new RV. The work adds in some travesías of prime ministers was, and is more be late adds every time used it to us on some last few months. State in a RV parco for roughly 9 days now, and there is remarked today that a pressure of water was down. It is exited to verify a regulator and he had fallen of 60psi where has took place it, the roughly 38psi. It take it it was, it has cleared all the water of a hose and lines and has tried hooked behind up. It does not import that rule a ray, psi is closed in 38. It do not move up or down. It was some descriptions add that I sold on this product, this in spite of can do not recommending like this a lot hard same 6 month. Look for the solution there is remarked other descriptions with this subject same, which direct me to believe his bad regime any only and probably the defective creation.
4 / 5
The election adds, has had any adjustable regulator for years, never satisfied with pressure of water in motorhome, neither to down, or yes take fear of the regulator of big pressure arises. Verified the new any pressure of adjustable regulator, preset the little down 30 PSI, marked preset in 40-50 PSI. The pressure is reduced also more afterwards goes thru filter of water. Installed this new adjustable regulator. You are dipped in only 30 PSI, easy regulated to 50 PSI (can regulate higer) before filter, very happy with pressure and flow now, near of home which is 60 PSI. My woman is satisfied included when washed his hair, enough flow is rinse was all adjustable rv regulatory of the water is roughly five times cost of any adjustable but value our to have pressure of flow and decent water in ours RV. I read Attended to substitute regulator roughly once the year, according to quality of water? I can consider install with which filter water to extend life, and take casualidad of busted was hose of water of the side. This regulator of adjustable water has solved our RV questions of pressure of the big tide.
5 / 5
Produced excellent. Well he he. Works fantastically.
The initially dipped pressure to 45 books in a factory. When I used It a first time, so only tip 42 pounds. I have tried to create a main pressure that use an adjustment of ray, but a pressure would not go main. Have @@give A pressure in a source has used was so only 42 pounds.
DOES to THINK ME. It have turned a ray of adjustment several rotations that tries to take a main pressure. If I leave it there when I disconnect, potentially could take the one of the entity arises in a next source. SO MUCH, I have turned a ray of adjustment in a 'the low' direction until it begins to go down a pressure in a gauge. You spend it then on again until a needle in a gauge there is prendido to move.
Perhaps is in some directions, which I any one has read . Probably it have to that have.
4 / 5
Has confirmed static pressure with my pressure gauge experience to regulate my regulator of system of the house. A pressure gauge and a Renator regulatory gauge is inner pocolos wide of needle (3 lbs?). Has any way to confirm that it runs pressure. SO ONLY like with a compressor of air and tools of air, owe the pressure dipped to run the pressure is doing that I am doing, which is using a regulator to regulate pressure for my front (before regulatory of house) hose outlet. 120 lbs Is too much to risk for hoses, any to mention a pressure washer.
Had bought one of an economic fixed pressure reducers last year, and while he certainly works, a pressure to run was likes 30 lbs, for real obnoxious for gram and watering of garden. There is the bazillion of these in a phase, and a Renator is not an economic plus, but like this near to the equal that can guess descriptions and descriptions, a Renator looked to be a better bet.
Like this far, are ECSTATIC. A toe of the screwdriver has spent a pressure to run to 60 lbs (roughly 73 lbs indicated static).
Suspicious 99 of you will buy this thing for yours camp, and for quell'I in fact dipped he for 60 lbs static. But some time those that of you the one who could wants to solve a question of annoying house, ossia the solution adds .
5 / 5
Failed after 3 use of month! I have purchased this element in June 2018, but did not use it until July 2019 reason our RV the travesías have been retarded. I have been using he without issuing of then leave in today. All of the sudden is stuck randomly in 140 psi (and ossia not even close the one of fact of pressure) and a gauge will not change exposed connect or any and to all the cost of any one the adjustments of pressure try to do. It does not look to suffer harm in any way neither filtering. I seat now we do not try it immediately in place of in the location where is has required really.
5 / 5
Like this far like this good. Received the today and has run some test on he in a house. By means of mine another gauge has known a incoming waters it to a regulator was roughly 80+ lbs, and that short behind to 45 (as announced). I know it paste a mark partorisca use another gauge had purchased previously - hooking he until a outbound connection. I will update a description if the things change like this continuous to use it.
Pros:
A lot solid
Solid fittings
has not filtered like my economic another (the type that has no gauge and can not say if it still is doing...)
Gauge Was something on - based in another standalone gauge had purchased previously
was able to regulate a pressure - commentaries that has taken it to him more towers of a ray that would have anticipated, but
the packaging Adds - which plan to maintain for the protect when not using
Any one escapes in a connection to a water
Gilipollas:
Any
Like this far are adds! I know exactly that the pressure is going to my lines, and can regulate it has required .
5 / 5
Not doing like this drawn that. A pressure is preset to 40psi and am not able to change a pressure to turn a adjuster. Ossia Mine 3rd unit and has had to that return some first 2 units for alike reason (in the first place the unit has been hanged in 20psi and a second unit was an element used has sent mine)
4 / 5
A regulator like this far acts a way has to that. It is easy to regulate and regulates pressure. Quality and workmanship looks well. A configuration done a device the little delicate to situate on some arrangements of tap, but ossia so only a way goes with this type to draw quite a lot of rule.
Would have purchased the most economic regulator there has been I a time and desire to treat that it substitutes in a chance of failure.
Was a lot of nettling to see the reduction of prize of almost $USD a lot shortly after shabby of mine as a bit it has reinforced my faith that a product was overpriced in a first place. Has chosen is a reason have not wanted to take the casualidad in the most economic version so only to have fail. It conceal it is not a lot of scientist, of course. It was useful to compare this product over time to competitive products to see one extra raisin well the pity. It remarks that some of a competition that is more economic that have bend a guarantee. Any imports of sure, but is interesting. Any statutory levels to the like this device adheres would have to that be announced clearly and shipped with a product. A consumer has to that it does not have to that email any thus die likes described in an ad. In general, work so that appearances. 5 / 5 Has not resisted last for very long. A better characteristic of of the this is a gauge, is surprising that often the reading of the pressure of relative water is useful. It is also of entity to help something when a regulator is failing. We maintained it to the knots plant on 45psi and for the months of pair this regulator would resist this pressure quite consistently. Then a day while doing around a rv there is remarked a gauge reading 85. I have opened the tap for the few moments to relieve pressure in a system and has then verified a gauge again to see that it fall it to 50psi. But after the short period to time a pressure indicated for a gauge is trace to 85 again and one rushes momentary strong to water when inaugural one touches again has indicated a pressure of water had augmented again. Apparently a valve has failed so that it no longer controls pressure of static water. History like this long short, maintain an eye in this gauge and substitute this first regulator of the line of explosions of water. 4 / 5 Easy to regulate a pressure, but interior two month a gauge has lost the majority of his oil. I am expecting to see while more along this hard. Update, 08/18/2018: A vendor has seen my description and contacted. They have sent the substitution gauge (any one a whole regulator) which I so only installed. Ossia An example , mine, of service of client very good. I will update with to anything further on likes a gauge hard. Any of a question has described has affected the capacity to control of a regulator a pressure of the water and he have continued to do while it was waiting for the substitution gauge. Update - March, 2019: I have it quell'has purchased now the second complete regulator like gauge leaves to do altogether. If this second any last more than the year, will find the solution another the Renator. The stay has dipped ready... 5 / 5 Has received so only this RV regulatory of pressure of the water last week. I used it three times like this far in three different campgrounds. First first things. This thing feels, and looks, a lot well has done. It is solid brass and has the a lot of heft his, feels to have to that very heavy . Segundo what, work! I have connected a regulator like recommended. A prime minister campground has used informed that a pressure of the water in his system was 75 psi and that the regulator of pressure has been recommended. Well to know of then have the new regulatory mark to try was. Once hooked is looked in a water and a pointed piece -40 psi outlet pressure. I have regulated a ray and place he for -48 psi. Fact perfectly. If it resists on, I will be the very happy camp ! 4 / 5 1st compraventa was the “V” products manufactured (is buying , will comprise “V”. With which less than 1 year, a gauge has failed like the needle recessed behind rest of pin, would not read psi afterwards. Service of the client called in “V”, has been said hiela the time has caused this question. Really? Gauge Is the oil has fill. That 28 temp pin to cause to recess behind rest of pin?. Oh Well. There is agreed to to send the new gauge free of load. In a moment, it has found this Renator on Amazon, more economic that “V” and better descriptions. I will update this after the year of use. UPDATE: A gauge has failed with which less than 2-yrs of random weekends of use. Any sign of leak of oil but gauge is stuck in 48 psi without being connected to anything. For discharge of the instruction of the Owners has tried a fingernail-down-trick of hule of discharges to “relieve pressure and dial of reset to zero”. Any regime. I emailed the description of a question more the picture of a valve to an and-allocution in a Propiciado by Instruction. Any response. These gauges looks to do short term, 1-2 first years to fail and is very susceptible to down 32 times. First to spend$ 45 every time, thinks to buy the economic unit like the part of annual interview would be better for peace of alcohol.
Update to Update: on Amazon, expósito could buy so only the gauge partorisca $. Easy to exchange one broken gauge for the new one in an organism of regulator of same brass. So much for closing I has a regulator of adjustable pressure with the working gauge. But it freezes I have bet I will require another gauge. 5 / 5 In that travelled he more than 40,000 in mine motorhome during a past 5+ years, has found campground presione to water like this big likes 150 psi. To to The Pressures like that it can break it he of valves of inner water in mine RV and breaking his plumbing. The arrival in the new campground, my regular procedure is to use the pressure of precision gauge to measure pressure to water first to connect mine RV. If it surpasses 60 psi, uses the regulator of pressure of the water. Recently, after visiting it campground in western Oregon, carelessly has left mine very a lot of (but now priced out of a phase) regulatory of pressure behind, which quickly disappeared before a campground the owner could recover he for me. I have ordered this one for delivery of next day and was has wanted to has to that arrive punctually in pristine condition. In a moment utilisations the regulator of pressure of economic water that experience with my bus more than fact five years. An economic regulator is effective to reduce a pressure but he dramatically limits flow of water. My first observation when unpacking this Renator M11-0660R Regulatory of the pressure of the water was his weight . It is weighed more than the regulatory water more competitive that pressure with the gauge. An interior that opens for the flow of water is also noticeably main. Following the instructions of a vendor, has installed this regulator in mine campground tap, flushed the and has connected then my hose of potable water among this regulator and mine RV. After running some taps in mine motorhome to take touched of of any air has captured, has used the screwdriver regulates to regulate a incumplimiento 40 psi to 60 psi. Comparing an oil comprised-the pressure has fill gauge with one there is aforado gauge that use to initially try campground pressure of water, has found the readings to be of this regulator essentially some same. This Renator M11-0660R Regulatory of the pressure of the water has looked for to be able to protect mine RV plastic plumbing of pressure of excessive water without interfering with flow of good water. It is solidly fact, easy to use, agrees my setting of pressure and does not filter . I am looking forward to his good action continued and has appreciated to receive the message of a vendor today offering assistance if I have not been pleased. I am pleased like this far with cost of mine. 4 / 5 Has bought this to substitute the broken one of the different company. We use this in ours RV when hooked until it waters/of house of the city. He machining looks to be facts well and he screwed in easy and there is sealed some connections without a lot of endeavour. Regulating a outlet the pressure was easy to do and left for good control. Imposed of the flow has not gone significantly effected by a regulator. A pressure gauge is well has built. So only use a regulator once this year (as far) stops to 5 stay at night. Some the state parks do not have hook of water-up in the so many is in an inner tank in these locations. Appearance use it 2-3 times for year. 4 / 5 Has called a company and a type have said the touch and can begin to do. It does not spend 35 dollars on something and has to that try to fix me the. I have said it it touched it and at all. It is it would not move out of 40. It says a lot if he no for calls of morning behind and can do something so that it do not have to that return. I launched it it go. So only I want to buy anything more than them. 4 / 5 This the pressure of REAL adjustable water gauge and valve of regulator. Esees Has had is when being announces the week now. Perfect pressure! If it buy one of a cheapo regulatory w/any gauge or a capacity to control and regulate and dip a pressure; you could be in partorisca the real nightmare! Was such fool. I have bought the cheapo and an after the day has had them the leak. The one who knows the one who a pressure was? The look and he look. Rasgado Of the camps averts partorisca look for one was the nightmare ! I have bought it is one , dipped a pressure, and has expected. 1 day 2 days 3 days 4 and any LEAK has been installed of the bought and any leak! This REGULATOR is perfect! Espicially Partorisca Older campers with PEX the hose is and fittings. Because big steps$ $in the camp, house of engine and connect some unknow valve of pressure? If it blows the toneless PEX returning or the hose of god forbidden, well was the nightmare . This product is like this fresh looking too much! 5 / 5 Ossia The fact of good product that does not filter never the drop into use - I teflon of tape of use. It have given it five stars but a bubble of air in a gauge has offended my sense of aesthetics. A bubble of air has zero impact in an accuracy so only said something on some levels of manufacture. I use he partorisca my watering of gram. Has a lot of pressure of big tide, 125 psi, and has blown some neighbour was. I want that I can regulate it and take a pressure esatta that is ideal partorisca my system partorisca water. Ossia The fact of good product and value of the money. In a past has used the product the economic plus and has not been like this satisfied. 4 / 5 Looked in some questions and he have looked that this product has been done in EUA. It does not think that it is partorisca say a chance . You are$10 more than another brass some, can save money and buy a Chinese one of then am quite sure this one is Cina . Ossia A lot disappointing sure. There is no where in this product that is done in EUA. Like the common discretion comprises USA in a name of mark but the plot of Chinese vendors that. I will change this description if a costruttore tries otherwise
4 / 5
These are regulatory of sum of adjustable water for use in RV parcos. Calm ensure you will not blow yours plumbing is gone in your RV and leave you anchors it take a main pressure will require the basins of the rinse etc. Has the port of anchored big likes any to to the clog likes a bit done of economic fixed regulators. It is a lot of value a prize if you are the frequent RVer. Highly you recommend this regulator.
5 / 5
Am using this like this the regulator of pressure for the soaker system of hose. A Renator the regulator is installed after the timer of a system. It has done I add of one takes-go. I have used a regulator for a past month and has been compatible, any leak, any @@subject at all.
A pressure gauge is attentive, has confirmed with two another gauges I own. When being able to see a pressure in a system without that has to that tee one is a lot handy.
Dipping a pressure according to directions is easy.
Has loved initially pressure of system of discharges he in 35psi but expósito that when all a soaker the hoses have been involved there has not been quite flow into a system for all three of them to operate while still maintaining 35psi in some lines of delivery. A bit fiddling up with the setting of the adjustable pressure of a regulator has augmented a pressure to flow to the constant 30PSI, which is sufficient. This are to add my use because it is neither everything on or all was. It remarks that each one soaker the hose is isolated another with individual static 25psi regulatory, for this maintaining the positive pressure rid them was of entity to maintain constant of flow of the each one of them. A Renator the regulator maintains a whole system balanced and prevents pressure he blowing was.
Loves this unit. It was a final piece of a puzzle for my needs.
4 / 5
Has purchased 2 of these regulators. I have used a prime minister one for the week without questions, but when lame house of this travesía, has found that one covers of hule in a pressure gauge was exited and everything in my cube of the crew of fresh water has been covered in oil of silicone. I have used a second an in the two travesía of week last fall, and the things looked well. I winterized my RV and dip everything in storage. Quell'Pulled was all this week to of-winterize some rigs, and the-and-behold, a pressure gauge in a second a no at all.
4 / 5
Ossia A regulatory prime minister of the water has not possessed never (concealed knows of). I have been impressed with a packaging and a quality of some material as well as a craftsmanship. But, more than everything, when I have installed among my hose of water and my on heater of question of hot water for a shower of camp, leaves having wild fluctuations in a temperature of a shower based in a bomb in a sake. I have regulated my bomb to kick on in 45 lbs and is gone in 55 lbs. I have regulated a regulator to water to roughly 40 lbs. Now, volume to rain in complete bliss. Some stays of the temperature of the water stabilises like the rock to the equal that listens to a bomb spends for his cycles. So many, imagines the one who happy my woman was! It thinks that that they are a ready plus stud in a camp. Still it says the better smell. There are rewards to improve a situation of camp with a woman in your life. So much, if your life of amour has been have-hum, chooses on one of these creatures and take yours grooves behind!
4 / 5
A water supply of City has been updated and my regulator of the pressure that plant also. Leaving my line of external water in max pressure of city. My pressure to water goes in in 150 psi. Ruined several first hoses to @give question. I have begun to purchase a small brass reducer for RVs in our venue Walmart. They would last roughly a year. I have decided to try this reducer after looking in of the descriptions as well as the launching was one In some another. An ease to install was likes to attach the hose of water. Like the pictures aim it was preset to roughly 60 psi. Perfecto. Any need of adjustments but if the need is is very simple to do. We will see that a lot this extracted. Like this far you recommend this reducer to any concealed has the subject of pressure of the big tide.
5 / 5
Mina RV is coming with the small in-regulatory of line. Rule a pressure, but because of a creation, these small versions can not flow of the a lot of water. It is not so only in a pressure but also that loss of boss (loss of pressure) some causes of device. A Renator is the creation to flow main and will give you more flow to water although you maintain a same pressure like some economic versions. Ossia The must so that they require better flow and more control of a pressure of water.
Remarce: If dry camp (boondock) to plot, can find will use MORE water with this device in the small plus more restrictive creations. A solution will be to go down a pressure while dry camping to conserve water and therefore not fill your like this fast tanks. For full hookup the places will love a capacity to take wash and plans of real showers with flows of real water!
4 / 5
A quality of build is excellent. With which I hooked he until a RV and dip a pressure to 60, everything looked well. A bit while later, there is remarked a pressure was on 100. I have taken immediately concerned and has begun to try to imagine was has done something wrong. That I expósito of another Amazon reviewer has been related to hooking until a RV with the heater to water that careers. Apparently, this causes some class of rear pressure, but does not indicate a pressure that feeds a RV is that big. If I have inner course of water a RV, a pressure equalised and has gone back the reading 60. Cela Would have been useful information for a costruttore to resupply with a regulator. Knowing that, chair a lot roughly the, but I dinged launches it to him for a lack of complete information.
3 Camco Water Heater Tank Rinser-Cleanses and Removes Sediment that Collects at the Bottom of RV Water Heater, Extends… Camco 9.2Score View Product
### Top Customer Reviews: Camco Water Heater ...
Rating: 4 out of 5 with 60 ratings
5 / 5
In the firs have think that that these looks cheaply the fact but some materials of the flexible plastic left perfectly in a work. A cane flexes in just a right road to leave that clean of the each surface. Quan A valve of balloon is closed there has no the drip to water so much is sure to use any place in a house.
HAS drained tanks before to change an element but never rinsed the unit has been surprised what the rests and the residue was inner . For low $40.00 has substituted both elements, a piacular anode, bought some tools to take so and this has comprised this cane. You have seen a prize of heaters of new water? Has two in our house and the regular service are now in an annual list. Took at all for my description I any partner with this product recommends this product 3 / 5 No a thing more orders of vain piece the bread but help. Please notes that has to drain and clean your heater to water at least once for year. This law of the unit only yes has the Valve of the installed balloon in yours heater of water in place of a bib of plastic hose that goes in addition the units. It IS more to drain your heater to water then takes a bib of hose or valve of balloon as it can see calm in a 1/2' hole with the torch. You will see sandy looking material in a fund. This comes from/comes from a calcium in your water and of Roseau duquel the anode deteriorates some years. This Tank Rinser then can have the habit of loosen a gunk in a tank... But there is the better luck that takes goes to use my type of void of tent to suck it was. But this aided in loosen a gunk first. 5 / 5 I at the end taken around to clean my RV heater of water. It was in Youtube DIY videos in that is done. This was an invaluable tool in flushing out of a Atwood 6 Gallic Heater of Water. IS slightly flexible, as it can take he in a so a hole of drain and beginning of valve of the pressure in flush was sediment and rests. Has the 1997 Classifies C RV, and the use bought. So many stairs is start !!! It maintains to come and coming! I have saved a water to use in my plants. Desprs flushing Was, has used this same beak to touch industrial cleanup white vinegar in tank of a beginning of valve of the pressure (covers it to the drain posed retreated of course). You have posed 3 Gallic vinegar in tank, the pressure has posed then the backwards of valve on. It ignites waters of city to fill tank with 3 Gallic waters as has the 50/50 vinegar blend of water. He then visits in a heater of water during an hour. Then valve of open pressure to bleed out of excess (Precaution: it water it shoot very hot was), then leave it opened while you it the hole has opened prende to drain and take all the vinegar has been. You can reuse this water in your acid this wants plants in of the small quantities the time like roses, palms, not deserting plants. After the vinegar is all was, flush was the tank saws hole to drain those uses this box of cane is totally clean. It substitutes it covers of drain, fire of the waters of city and flush was all the taps, showers, basin so that there is not any vinegar in system. You can see a whole process on Youtube low RV Geeks. This also the clean cane was tanks of basin, even so has the better product for that. Very useful attaches pressure of water in your hose for all another type to debug water, so strongly recommend compraventa. 5 / 5 I have purchased the used RV so that it has always questions enough that an anterior owner has maintained up with an interview. A flow of the hot water has prendido a day (any one that have to it way that be big like cold anteriorly). I drained A tank and refilled the and all returned in 'normal'. I have imagined that it has to it has had it some tez up in a tank (6 French.). As I have imagined it is prende to time to do to era of clean pressure. A cane an amazing work and flushed out of an incredible quantity. I have maintained to repeat until at all except the career of clear water out of a drain. I have installed an anode and has filled a tank. The flow of the hot water is better that never. Only it take to turn a 'jet' all the directions in loosen all build up. It have to the the the video to aim everything of some rests that is exited. 5 / 5 Amazing product. I drain My tank every year and very look white sediment. Experience this product shortly after doing my use to plan of annual interview this year. But it decides in re-do my debugging of heater of the water. It takes 2 or 3 times a quantity of white sediment of a fund of a tank. Since using has note a heater of the no run water like long or so often while fact. Active More than saves a price of compraventa of some savings in a propane. A heater of water is a main appliance for my use of propane and has usually refilled mine 5-- 7.5 tanks of finals of chevron of the January but I are still in tank 3. That is to say it have to has for RV interview. 5 / 5 We use this in flush a sediment out of a fund of a watr the heater of a hole of drain is up in a subordinated the little. We fill with to 50/50 mix oc vinegar and water. Left cook at night and drained and flushed he again in a morning. More sediment exited and everything is well during another year. The works add! 5 / 5 That is to say one of these special tools that required you only once the year, and no another tool a work! I use once, and it was convinced of his necessity. The minerals resolve out of water in yours heater. Some glasses attract more the glasses and the tez up can limit in yours heater to water and affect action. Quan Control (and/or substitutes a cane of anode) bonds a pointy end of this tool in a hole of anode. A handy was/in the change enables calm in Controll a flushing action like lavas out of these pesky glasses minraux. The calm does not have to ask is doing right so that you see you these granules minraux, usually white, in an earth and in an outside of your heater of water. Flush Until you are satisfied that all the corners of a heater have been recorded and no more the minerals are exiting. Flush The small more with a longitude to be sure, then left the drain and installs a cane of new anode, the nuts embroiled with tape of Teflon. I fill a tank, verifying leaks of arrests under the pressure and calm is posed during another year! 5 / 5 There is the plot of the sediment built in a piacular cane of anode-carried of drain in mine 6 heater of chevron of suburban water. Seldom it uses a heater of water, very few trips to camp some last two years, but when drains a tank in a winter or after each trip, has the plot of sediment of scaly aim in a tank while it drains. At the end has had he with a sediment while it blocks all my fixtures of hot water afterwards-winterizing this month is spent. Coverage this cane to debug of the tank to do perfectly. I have taken a cane of the anode of the drain was while a tank was full, and bonded a cane in a tank and has turned a water on, and a sediment was totally flushed out of a tank. At the end the races clears after the minutes of pair of the rinse and that turns a tip of cane to do sure a sediment the occasion to run out of a hole of drain. It take the little place in a process but was the good day. I will be to use the every time drains a tank after each trip. 5 / 5 Experience this cleaner of heater of the waters no for a RV but for my house vacacional tank of hot water that is distributed for the better waters and tends to collect the plot of sediment. I have been tried to do something similar side me even so his a same or more for the do and the source has some diverse necessary parts. This small cleaner is only that has looked for. It IS economic and when hooked in the hose of garden produced the current of jet that is quite powerful and does the good work that cleans an interior of a tank. A plastic beak is very time and quite flexible where can insert he in some holes of element of the heating and thoroughly clean an interior of tank. An enclosed was works of good valve and does not filter . In general well estimate a inversion like this the helps extend me a life of a tank and provides the most effective heating of a water. 5 / 5 He the work adds to take each a yucky gunk out of a heater of hot water. A water was brown with the sediment when begins and has been then continued down white sediment crud. Thought quite a lot of room everything of that go in some rain of lines and wash with. We will use a rinser after each RV trips from now on! The prize adds and mere to use. Each RV'r would have to use or regularly. After cleaning a heater was to decide take covers it new for a tank since some nuts was the small rusty. In a RV the tent to distribute learnt that anodizing the cane is supposed to be quite 3/4' thickness any one the cane of type of thin cape that has had. A anodizing the cane is supposed to attract an oxide and maintains to break a tank, eat' a cane instead. The May HAS KNOWN this, ours another RV has had a same thing but in the has not had a tank rinser to see how much junk was in there. It controls yours covers of drain, if a cape looks the perch of necessity of cloak to substitute it!!! I will try and debit some punctual photos. 5 / 5 In of the firs have think that that this looks cheaply fact but some the materials plásticoes flexible leaves perfectly to a work. A wand flexes in just a right way to leave that cleaned of the each surface. When A valve of ball is closed there has no the drip partorisca water so much is sure partorisca use any place in a house. Has drained tanks before partorisca change an element but never rinsed one. I have been surprised the one who debris & the residue was inner . Partorisca Low$ has substituted both elements, a sacrificial anode, has bought some tools to take both and concealed has comprised this wand. Calm saw you a prize of heaters of new water? Has two in our house and the regular service is now in an annual cast.
Has received at all for my description
I any partner with this product
recommends this product
4 / 5
has purchased the used RV so that there is always questions roughly like a leading owner has on been supported by an interview. A flow of hot water there is prendido a day (any that has been like this big like cold previously). I drained A tank and refilled the and everything is returned the 'normal'. I have imagined that it has to that it has had it some build up in a tank (6 gal.). As I imagined it it was now of that to do was it of clean pressure. A wand an amazing work and flushed out of an incredible quantity. I have maintained to repeat until at all but the clear water has run out of a drain. I have installed an anode and has fill a tank. The flow of hot water is better that never. So only agree to turn a 'jet' all the directions to loosen all build up. It have to that it has done it the video to aim everything of a debris this is to exit.
5 / 5
Has required to change a cane of anode in my heater of water Suburbial in mine RV. The canes of anode are sacrificial the devices have drawn to dulcemente disintegrate so that it waters is heated over time. This disintegration creates small particles of soyetal' that collect in a fund of a tank of heater. When Changing an anode, is more to flush these bits of metal out of a first tank to install a new anode. Of here, a compraventa.
Has dipped a flusher in mine hose of garden, turned in a spigot and there is prendido a flow to water while walking to a RV. Roseau Of the anode was, insert a flushing wand to a tank and release a pressure. A wand is EXITED OF THE SLEEVE And WAS NOW in the TANK! Quality of bad build for the $10-$ 15 plastic nozzle. It was able to fish a wand out of a tank that forceps of uses. I have had to that dip my own hose clamp in a boss for the reparation.
Once repaired, a wand that is supposition to do. Surprising what detritus the metal is exited of this tank. It is something will use while transmission a cane of anode. It was lucky to be able to take a wand out of a tank. If it have taken raven, am not sure could have the fish looked by means of the 3/4 hole to the very dark place.
Does except Camco need to ensure a QC in his tools are improved.
5 / 5
I finally taken around to clean my RV heater of water. I have been to Youtube DIY the video on how is done. This was an invaluable tool in flushing out of a Atwood 6 gal Heater of Water.
Is slightly flexible, as it can take he to enough a hole of drain and beginning of valve of the pressure the flush was sediment and debris. Has the 1997 Classifies C RV, and has bought uses. So many stairs is start !!! It maintain to come and coming! I have saved a water to use in my plants. With which flushing was, has used this same nozzle to touch industrial cleaning white vinegar to tank of a start of valve of the pressure (discharges he of drain dips retreated of course). It has dipped 3 gals vinegar to tank, the pressure dipped then the valve has retreated on. Tour in waters of cities to fill tank with 3 gals waters so the the 50/50 vinegar water of mixes. Then gone back in a heater of water for an hour. Then valve of open pressure to bleed out of excess (Precaution: it waters it shoots very hot was), then leave it opened while you plough hole of drain and take all vinegar was. You can reuse this water in your acid that loves plants in of the small quantities the time like rose, palmeras, not deserting plants. After the vinegar is all was, flush was the tank saws hole to drain that uses this box of wand is cleaned entirely. It substitutes it covers of drain, turn in waters of cities and flush was all the taps, showers, basin so that there is not any vinegar in system. You can see a whole process on Youtube low RV Geeks.
This also the clean wand was tanks of basin, this in spite of has the better product for that. A lot of gain adds pressure to water your still hose all other types of cleaners of water, like this strongly recommend compraventa.
5 / 5
Amazing product. I drain My tank every year and look a lot of white sediment. Experience this product shortly after doing my annual interview that slowly to use this year. But decided to king-do the cleansing mine of heater of the water. Lame 2 or 3 times a quantity of white sediment of a fund of a tank. Of then using there is look a heater of the water does not run like this long or like this often like face. Has more than him has saved a price of compraventa of some savings in a propane. A heater of water is a main appliance for mine propane use it and I actuate usually refilled mine 5-- 7.5 tanks of final chevron of the January but are still on tank 3. Ossia Have to that has for RV interview.
4 / 5
Has purchased this cleaner of heater of the waters no for a RV but for my house vacacional tank of hot water that is distributed by the good of water and tends to collect to plot of sediment. I have been tried to do something alike I this in spite of was me cost one same or more for the do and would have the source has some diverse necessary part. This little cleaner is so only that has looked for. It is economic and when hooked to the hose of garden has produced the current of jet that is quite powerful and does the good work that cleans an interior of a tank. A plastic nozzle is long and quite flexible where can insert he in some holes of element of the heating and thoroughly clean an interior of tank. An enclosed was works of good valve and does not filter . In general well value an investment like this will help me extend a life of a tank and resupply heating more effective that a water.
5 / 5
Ossia One of these special tools that you so only precise once the year, and no another tool a work! Utilisation he once, and will be convinced of the his necessity. The minerals solve out of water in yours heater. Some crystals attract more the crystals and to build on top of poden discharges on your heater of water and affect action. When you check (&/Or substitute a cane of anode) sticks a pointy end of this tool to a hole of anode. A handy was/in the transmission enable you to Controll a flushing action like lavas out of these pesky glasses minérales. Calm does not have to that ask is doing legislation because you will see these granules minéraux, usually white, in an earth and in an outside of your heater of water. Flush Until you are satisfied that all the corners of a heater has been registered and no more the minerals are exiting. Flush The little more with a longitude to be sure, then has left the drain and install a cane of new anode, the edges have wrapped with tape of Teflon. Fill a tank, verifying for low leaks the pressure and calm is dipped for another year!
4 / 5
Use this to flush a sediment out of a fund of a watr the heater of a hole of drain is up on a subordinated the little. We fill with to 50/50 mix oc vinegar and water. Sinister cookery in prejudices and drained and flushed to again in a morning. More sediment is exited and everything is well for another year. The works add!
5 / 5
Has Had to that the plot of the sediment has built on a sacrificial cane of anode-discharges of drain in mine 6 heater of chevron of water suburbial. Seldom it uses a heater of water, a lot little camping travesías some last two years, but when drain a tank in a winter or after each travesía, has to weaves of scaly white sediment in a tank as it drains.
Has had finally he with a sediment to the equal that blocks all my hot water fixtures after-winterizing this past month. Found this wand of more cleaned of the tank to do perfectly. I have taken a cane of the anode of the drain was while a tank was full, and has stuck a wand to a tank and has turned a water on, and a sediment was entirely flushed out of a tank. Finally the clear course after the minutes of pair of rinsing and that turns a tip of wand to do sure a sediment would have the occasion to run out of a hole of drain. It take the little wetted in a process but was the good day. I will be to use the every time drain a tank after each travesía.
5 / 5
This was the police of economic insurance for heater of mine of water. This wand is very easy to use and work!
When Have takes an Anode of heater of mine of water, has found an usual sediment in a fund of heater of mine of water.
I hooked on a Heater to Water Rinser to a hose and has inserted a wand to a heater of water.
He an amazing work to clean out of a sediment that actuate otherwise remained in a fund of a tank.
Leaving the sediment in a tank shortens a life of heaters of water, heaters inclusos of water of the house.
Well, Well ... As no cleaned out of a one in my house neither. Expensive accident he. Cela 6 chevron RV costs of heater of the water more than a 50 water of heater of chevron in your house.
Like this, take the wand and clean out of an expensive a!
5 / 5
Ossia The a lot of the device has built cheaply that servants his purpose but probably wont last very long. In a picture aims the amiably tapering, the tip has finalised well in a far end but concealed is not that takings. In the takings, looks a last 1/4' or like this of a tip has been broken was reason there be any good to the paste and some flanges are rough and uneven. I have sent a 1st unit has behind received reason have thought to have state broken during shipment or something. A second unit was a same way this in spite of. It is so only to the equal that comes from/ come from 'manufactures it'. So much, this law so that it is fact partorisca do excepts of the one who expect to be impressed or partorisca his to last long. They are quite frail.
4 / 5
Would owe that it has bought this more collected. It has had my RV for 15 years. Although I regularly flush & drain a tank and some starts of sediment. I have not had any idea that the sediment is remained still. It can not think that the material was in there. I left it state announces 20 minutes before it has not had more the sediment that begin. It is the marvel anything has done. I seat surer of a water that the flows by means of a system is cleaned more as it has had some brown material exiting with a sediment. Ossia The MUST HAS possess a RV.
4 / 5
My husband has bought this and says the law adds to clean out of a built on sediment in ours RV tank of heater of the water. But after a first use has found two small cracks in a tube of the extension where connects to an organism of valve. I will use some Flex tape of Steel or cut on the one hand fraction and reattach for the quickly fix. You know precise this when management in a hot water to brush your teeth and a water has the smell to write minéral.
5 / 5
Good piece of crew to have for your trailer/of camp. Helps in flushing out of a sediment in yours RV heater of hot water. Ray Justo he in your hose of garden, gone back an on/was crowbar on, and beginning flushing. The works add,,but wishes it quell'has had swivel very on that. He easier that turn in all the directions without turning r twisting a whole hose. Any complaint,,,I like a law of way. (In fact, you use it so only today when winterizing my camp).
4 / 5
Easy to use and clears one 'gunk' out of a fund of a tank of hot water in ours trailer. You think it that it try this in ours first new trailer to dip a trailer was for a winter. We use a trailer for roughly 5 weeks, spending it behind a factory. I have been surprised that is exited of a tank as I washed it clean. It has been it has surprised also that of a sacrificial the anode had degraded (direct report there) in such the short time. We use a tank of daily hot water and legustado in a trailer at least the time of half dozen during our travesías.
Sure economic to maintain a tank of hot water. Also I will use it to do fill a tank of quota to water the-operation of person in a future.
5 / 5
Has bought this to flush a hot water in mine RV when changing out of a cane of anode. It take some uses of this wand and place he in the cupboard in my camp for future use. Some the next time required it there is pulled he out of a compartment to find an extension of wand had left where connects to a hose barb in a nozzle. If it have tried utilisations water it there is sprayed everywhere. I have finalised taping the and was able to use it but does not have to that it never has left likes that in a nozzle.
5 / 5
My headline says it everything. It is the very good and handy little tool to insert to a RV heater of hot water of where a pressure relieves the valve usually chairs (needs to take with the wrench of pipe), and squirting inner to water so that the regime in one covers inferior (also need be take, obviously). It is simply the closed-was valve with the seeds-the rigid narrow tube that estacas out of an end. It looks it has bitten it pricey so that it is, but then again, he exactly the one who calm require it to do and is not ridiculously priced, as it supposes that cost it.
5 / 5
Has used this for a first time in my water of twelve heater of years in my Living Neighbourhoods horse trailer. He flushed a lot milky the white residue was, in spite of a fact that have so only has not used never waters softened in rig of mine. Continuous use this once the year, to hopefully prolong a life of a heater. It is very easy to use too much.
5 / 5
Has thought at the beginning that this was the tool adds. The hard year used and he flushed out of crud. 2nd use, this year, and one the part of wand has blown was immediately heater of mine of water!
Any sure has any way to recover or dona anything when being in there (like an element of electrical heating).
STAY Out of this product as it do not find you in a same place. It finds one with a part of the wand firmly has attached a lot so only stuck on like this
UPDATE
rigging for the travesía of cradle has believed so it would give Camco 1-has shot more. Ordered the substitution for a wand that has blown heater of mine of water.
(Has not listened Never he peep of Camco in this)!!!!!!!
Has received new one and the tube remarked to remain and probably would do a thing included - the swipe was!
Amazon promptly has sent the substitution - good service. What same - party and ready to blow to another tank of heater of unsuspecting water.
Ossia So only simple old Craxxxxx.
Obviously Camco is doing at all roughly control of quality this in spite of Amazon - I has surprised.
This vendor would not owe that remain to stage on Amazon .
Very very good to write the description - the vendor neither to the amazon has read.
4 / 5
Hooked A hose of water until a Tank Rinser and have it has stuck thru a hole of drain of heater of first water. It has turned then a valve of water in a rinser to an ON PLACE. A pressure of a water done a curve of the wand behind so much is more to not turning a water on until it situate to a first tank. I have run a water for roughly 15 seconds, has left a drain of the water was, then rinsed again by other 15 seconds. Of a rinser is flexible, can signal he in a lot of different directions to give a tank he well rinse. I have used to so only situate to nozzle of hose in a drain that opens and fill a tank partially but does not situate a flushing the action where has required. This little produced is money is very displaced.
5 / 5
We flushed out of a heater of water in ours 24-feet Surveyor trailer of travesía. You think it that it was very partorisca go. Then, we seen a piece in the heater of water rinser. OMG, would have to has seen all a big chunks of football buildup this has washed has used this rinser, and this so only the few days with which first rinsing with the hose of garden!! My husband is sooo pleased with this handy pocola wand! So only we buy this, as I can not estimate a longevity, but feels quite durable.
4 / 5
These works like the charm to flush an interior of my tank of camp of hot water. It have tried using so only the hose dipped to spray, but could not take a legislation of corner for all the sections of a tank, more was uncomfortable to manoeuvre a nozzle. This device looked like this simple, but when I used it that follows so only a hose, was very surprised in that additional sediment flushed out of a tank. Easy to use and the soyust has' for my interview.
4 / 5
For a past week has been that tries to take a part of wand of inside my heater of water. It was flushing my heater to water last week when one 'wand' run detached he of a connection of hose. And shots to a heater of water. Camco Has said any to concern roughly the, but am concerned will melt it to an element to heat, as I have been trying sacarprpers. Highly it suggest that it use this product to dip the hose clamp in a wand where continuous in a nipple in a connection of hose. No the Happy Camp!
5 / 5
He the work adds to take all a yucky gunk out of a heater of hot water. A water was brown with the sediment when it begins and has been then the white sediment followed for crud. Thought quite gross all of that was to some lines rain and wash with. We will use a rinser after each RV travesías from now on! The prize adds and simple to use. Each RV'r would have to that use a regularly.
After cleaning a heater was to decide take covers it new for a tank of some edges was the little rusty. In a RV the tent of supply has learnt that anodizing the cane is supposed to be roughly 3/4' thickness any one the cane of type of thin boss that has had. A anodizing the cane is supposed to attract a rust and maintain he to break a tank, eat' a cane instead. We have not known Never this, ours another RV has had a same thing but in the has not had a tank rinser to see what junk was in there. It supervises yours covers of drain, if some looks of boss to the hanger of the precise discharge substitutes it!!! I will try and upload some punctual photos.
5 / 5
Looks that has been purchasing more and more Camco elements for my motorhome. They have been done relatively well and look to have the very quite a lot of quality in a right prize. This has not been a chance with this hot water rinsing wand. Has no @to @give that it was broken in fact when I took it. A tube that attached to a base of a unit has been start. Has has had to that use it he like this had taken my heater of water averts for interview. I have tried to resist a tube on while rinsing, but was fearful that I 'jet' a tube to heater of mine to water to be inner has lost. I have taken a tube was and then wrapped some duct tape around he closely for the provisional fijamente. I then dipped a tube has retreated on and finalising rinsing.
Knows that ossia the plastic element and around $10 to purchase. It was packaged a lot enough of Amazon to ship. It have expected the little more control of the quality or the durability of an element has taken. 5 / 5 Has bought this to clean out of my RV heater of water. No never it have done the and has had a RV for on 2 years. I have opened on a valve of relief of the pressure and unscrewed of the discharges of drain, has run then this inside a hole of drain and flushed was. It can not believe a quantity to crap this was in there. Like this build of football up! This has done the fantastic work to clean out of a heater of water. 5 / 5 Ossia The must -has produced to help flush and clear was stairs and another unwanted material in yours RV tank of hot water. Some leaves of creation for the very strong spray and concentrated to water to exit of a tip of a rinser. They are deducting a stars reason seat that it can be be do of material more more rigid. A force of a spray causes a rinser to flex behind more than would like me, which of a bit has affected my capacity of more precisely control a direction of a spray. Otherwise, Is the fine product for occasional use. 4 / 5 Simple tool that saves a longevity of yours camps tank of hot water. It likes more than things in yours camp some heaters of hot water are compact and annual interview can be difficult without some right tools. This has done well for rinsing out of a tank of hot water b4 storage of winter. It is something has not known has required until another camp the partner said roughly that. Quite easy to operate, while except future subjects with my heater of water. 4 / 5 The work adds to take a crud out of a heater. Nizza And flexible to achieve well to a compartment of heater. Recommends to try the to see like him sprays out of a tank like calm in fact can see where/that is spraying. It was supersized the one who flexible is when a pressure of water is on and has had to regulate like this has resisted it he in a tank and a pressure to water to do sure has achieved all some corners of a compartment of heater. With mine 60 psi pressure of water of my house, has taken a tube that curves roughly 75 . Thinks that is the good product and am pleased with some results. 5 / 5 Is dummy test. You focus and any leak and durable. If I have had to help this creation ... He like this a tube in a detachable end like the tube with the short 90 curve of terracing in the to hang on to the smallest containers, likes two pipes. A tube welded on, is 1/4' GO like this pressure very big to wash in explosion and something tight tanks of water of the interior or that never 4 / 5 Has has not thought has required this but as it was economic interview has decided to give has shot it to him has been surprised in a quantity of sediment that I rinsed out of the heater of year of old water. I am not sure settlement that bad really is partorisca the heater partorisca water this in spite of this was very easy to use and has taken little to any extra time to the equal that have done like this very first of dewinterizing 5 / 5 While he well enough, has been disappointed in like this flexible a spout is. I think that that it was better with the rigid plus spout. Still, for a prize down joins pertinent work. I have fill my RV heater of water with 9 chevrons of white vinegar, to the left feels at night, then a next day has used this spout the flush out of an impressive quantity of stairs. My hot water has augmented perhaps 20 terracings, of an element to heat was thickly crusted with minerals. 4 / 5 Does well to clean out of a black water. It maintains calm that it has to constantly fill a basin and the game, which any always clean all was. A consideration is doing sure yours plumbing leaves for use of this type of wand. 4 / 5 This work adds to take a sediment that chairs in a fund of a heater of water. I have had a RV for 2 years and has been surprised in that it is exited when using this rinser. So only maintain flushing go until some careers to water clear with at all floating was. It can take the moment but maintain in him. 5 / 5 At the beginning liked really of an element. While a tube bedded behind under a pressure still was acceptable. It has been to use it this week previously to storage of the winter and a tube have broken of legislation in an enclosed-was base of valve. I owe that be in accordance with another, ossia the economic product . Not to recommend it . 5 / 5 Has has had to that so only substitute my cane of anode in mine RV heater of water, this tool is essential in flushing out of an amazing quantity of debris this was in my heater. A tool of the must required thus fulfilled, if calm any flush out of a debris the clog on some filters of water in the each tap. Recommended element. 4 / 5 A tube has been broken where is returned in a barb. Not to see it untill has loved the use because it was in another side of a container where could do not see. Has the pic but does not take an option to aim writes. I will look to reason am not given an option to share. 5 / 5 Adds little artilugio although it does not have any substitution for good old vinegar... This still was besides useful to blow debris out of a heater of water... A Keeper... 5 / 5 This thing really works, has gone to use my pressure washer but I didn;t knows that pode disorder on inner of a tank. This little feller cleaned out of a tank correctly, has gone to do the mine possesses it probably would have the cost has had much more I fabricated a. It gives the graces for a product. 5 / 5 Does not have to that think that has required one of these but bought it reason is economic. To the left say, work! I have used to modify my Tent Vac with the tube and tried to exit some stairs in my tank. He any never a work. When I have opened a container that this tool is gone in , my first thought was, the one who the waste. It is plastic and looked quite hooky. But I hooked he until a hose of garden and has situated he to a tank. Damn, He flushed was everything. Ossia The tool adds . You can try so only and hose of garden but he no that this does. Desire that had bought a fact 10 years. Well value of the money. Work. 4 / 5 Used in our engine again heater of experience of water of the house. I have taken a lot crud rinsed was before we do not disappear never a rig until taking on the travesía. Done feel me so better knowing the east has been cleaned was before travelling. The promised has thought that that it was the cost boba until it use it and invernadero all this crud. It is the believer and defender of this tool now! 4 / 5 The work adds. It attaches to the hose of garden. Take a RV spent of drain of heater of water, inserts/inserts by means of an inaugural, and twist a built-in valve partorisca big or low flow to the equal that has required. It creates the current of big pressure and cleaned a lot well. He flushed out of the enormous quantity of sediment in my heater of water of years or RV-ing. Happy has taken this , and happy I has for a future. 4 / 5 Does a lot well. Utilisations a hose of garden with doing “well”. When I have used a Camco has produced, left really to take to a heater of water and take the plot more sediment that a hose of the garden has not been able to exit. Subjects of works of the element with an I purchased it. Happy camping! 4 / 5 Has purchased a wand of more cleaned, 4 a winterization of the mine RV unit. Cleaned out of a tank of hot water and was surprised for real in a content that was flushed was to use this cleaner. An interesting part is that I have not been having any questions with my heater of hot water and after seeing everything of some minerals and another product that is flushed was am sure has prevented future questions. 5 / 5 Has ordered this and my hubby laughed and has said was probably the waste of money. Then it go to the ours new (ours) 2009 camp and cleaned out of a tank of heater of the water. It rids the integer handful of sediment and debris that this tool was able the flush was. Hubby Has not laughed with which conceal! 5 / 5 My heater of water is 16 years old . Flushed Goes with this product and has seen the small battery of particles minérales in an earth when I have been done. A RV the heater of water is in my cast of some things do not want to spend money on to substitute. This will help to extend a life of my unit. 5 / 5 Ossia The amazing tool to clean out of yours heater of water!!!!! Tonnes of pressure but sweet, will be surprised in that sediment and build of football on these starts of what!!!! We substitute a transmission, cane, valve of pressure and element in ours 5th wheel. And it will be them to wash a heater of water was once the year now after seeing the one who clean this tool took it!!!!! You recommend this product. 5 / 5 Are new to have the trailer of travesía, and having has had so only my heater of the water of the house has substituted, seeing all a sand that is exited of him first hauling he on some steps of basement, has wanted to be sure a heater in some camps have not fill with grit also. This flushing a tank and it taking real to clean the simple process. Happy of the have! 4 / 5 Ossia One of those ' really precise concealed?' Elements. Flushing My RV the heater of water has looked to pull one covers of drain and using air to blow out of a system of water. With east, once of the discharges is take, can take inside a heater of water and flush a whole tank. When you See all a file and the washed of sediment was, @give you reason has bought this rinsing tool. 5 / 5 A work, but marginally so much. As declared in other descriptions a plastic extension is too thin to retain form down pressure and some increases of noses. This give less than ideal control when trying the flush imposiciones of football out of my RV heater of hot water. Some dimensions are good and leave water the outflow around a with the during a flushing process. Some needs of with the to be stiffened some any with the with the slightly thickened or, perhaps, a semi-detached stiffening bar. Ossia Still, probably, a better tool for this at present available work. 4 ONENESS 369 (2 Pack) Suburban Atwood RV, Camper, Travel Trailer Anode Rod Replacement Part - Magnesium with PTFE Thread… ONENESS 8.9Score View Product ### Top Customer Reviews: ONENESS 369 (2 ... Rating: 4 out of 5 with 50 ratings 5 / 5 Some canes of anode have been rid promptly after situating an order. They are the perfect access partorisca partorisca a heater of water Suburbial in my toy of Revenge hauler. Any all RV heaters partorisca water require a cane of anode, but the heaters of water Suburbial do. Also remark these canes of anode am sacrificial the metals have required partorisca prevent a tank of the heater of the water partorisca rust was and will require periodic substitution partorisca prevent premature failure of a heater of water. This is not the defect of provider of the cane, is chemical .. Of the periodic substitution will be required, a 2 band of canes is the value adds. A sufficient quantity of the tape of pipe is comprised also, enough to install both canes when the interview is required. 4 / 5 Has used your canes have purchased of mine Trailer of Travesía. They do a lot well. Also I have another use for his which is with an evaporate fresher in my house. I have dipped one in a reservoir near of a bomb together with the pill of chlorine of the basin. This breaks up and reduces some stairs of football in some tampons of a hard water jn my zone. 5 / 5 Your browser does not sustain HTML5 video. It had been constantly that looks for that the perfect anode is trace to substitute a corroded one has had for my Travesía to Give them of Trailer of Own Cradle that has given constantly the smell to stink of a water and required a lot of service for the renew. By means of my on-line investigation have come to learn in this estupefaciente Oneness 369 canes of anode by means of the Youtube RV the canal affiliates link. They have recommended this mark. Be an eye that opens the occasion that considers an enormous knowledge has gathered pertaining critic specs that to to the subjects likes him to him to them the diameter and the material of anode that always have the direct effect in an action of any anode is trace. With the clear alcohol, in that has been to impress for these capacities of anode, I dint doubts to invest in oneness 369 canes of the prize and the mine has been the súper experience with valuing adds for money. A Oneness 369 cane of anode is easy to install and works perfectly well. I can not doubt for the give to 5 indication to star both for his incredible diameter of mm (picture in a legislation) same measure with Suburbial OEM cane of anode (picture in an accident) and a magnesium of prize of material of big quality of cane of the anode that guarantee the prolonged service. It compares well with a Suburbial OEM specs with unrivalled quality of killers. Some canes are 99.8 anode of Magnesium of Pure Big Quality the cane done of magnesium of upper quality AZ63-connects that it is no-toxic and totally sure for me and my familiar to the equal that are enjoying ours to take ways. I have come also to appreciate his Compatibility with all the models there that I do not owe that toil when looking for some parts of substitution. This cane of anode has been in my heater of water for the period of 8 month now and has not experienced any bad smell incoming of a water has fixed of this cane of amazing anode. Now I can rest that it knows that my tank of the water of the magnesium is protected of the corrosion and he me do fault for long period of time thanks to this cane of anode of the magnesium. Are happy that has invested in this container to save of the value concealed has has not saved so only my money, but has ensured also that has a cane of extra anode in mine RV so only for the rainy day while we are adventuring there. I have bought this product of Amazon, and everything is gone in quickly, am happy was exactly that have expected and orderly partorisca, and fact to the equal that has announced to comprise his presentation This Magnesium of Big Prize RV has produced of Roseau of the Anode has been built to last and comes with 1 Year has guaranteeed Limited with the to a coverage of substitution if your cane loses 50 of his leading self a lot @subject a condition to water that you are using. Ossia A icing in a cake and the impulse of entity when doing your election. I can not fail to take the note of a support adds that this American company gave pending and after purchasing this product. His is an incredibly robust support system for his clients! It is sure I will be to buy another and highly recommend! 5 / 5 These canes of anode were perfect substitution for mine 6 heater of chevron of water Suburbial. It is surprising to see so only like the clock has degraded so only 1 season to camp. Ossia The good thing . A worse look a more protect have a heater of water. Be sure to flush a heater to water when you substitute a cane of anode. 5 / 5 Like this far, thinks that an anode is probably well but does not know still. Wine without instructions on like this to install or anything more. They send to follow it up with the video on regarding the that was quite good but was the week later. It would have been well to have these instructions with him or at least something saying to those links to see regarding the do. Like the result, now knows has lost some steps concealed cost me quite the bit of time and done some things no exactly well. For example it was a lot of hard to take screwed in and has not been sure was in all a way. Now it knows it it would have to that there is brushed was and has cleaned some edges of a tank of heater. Knowing that first of time can have helped my questions. I have not been it is gone in a rig and has used in fact a heater still but exchanges a tank and he have not filtered like this hopefully is in good and will do. Thinks a product he probably works, but is too prompt to say. So only dipped some instructions with a product, no for the send the week later when you love a description of Amazon. 5 / 5 This company is like this impressive. An Element has purchased was the pair of sacrificial canes of anode for a RV classifies C motorhome. Boring has said? It is a company that has purchased he of that was like this impressive. An owner sent that looked to be the personal note with his very sincere thank you, and links of the tube of video has comprised your for installation. Like this in short, has not been a part, but a company that was like this impressive. It gives the graces to do my day. Doug K. 5 / 5 A prize adds for 2 anodes of magnesium for my Suburbial RV Heater of Water of Oneness 369. They were recieved with abundance of tape of teflón.un diameter of a measure of cane is 3/4' and a period is '. A substitution esatta! Uses he 1 1/16' socket to take an anode. Remained in Elkhart Hindú for the few months where can you odorare a water hardly enters a RV the park Waters very hard. We expect 1 first year to substitute an anode and was corroided very bad. Paid near of$ 30. For 1 cane has retreated then, but found this much more economic - FYI - Magnisiun the canes corrode faster that canes of aluminium - but a purpose of an anode is to be self sacrificing and to corrode faster that some components of heater of the water.
Very Manufactured - has bought 2 and will begin to verify\in his substitute at least once the year.
5 / 5
Good value! Easy to install! It has had any one creates these have required to be substituted like this frequently! Had our new mark RV serviced for lack of service and hot water the person has discovered the CANE has been corroded. It has substituted Run 2020 and recommended maintain an eye on. Verified today Oct 21, 2020 and the CANE had gone basically! upgrade To aluminium next order and verify more frequently.
5 / 5
A vendor has on followed for email with linking to the video as well as the instructions written on installation. I took it it was a star because my edges has had to help take an anode installed like this DH the hands have had the hard time gripping and taking some edges directly. I surmise that the can not be the question with a cane, but with a structure of a Suburbial WH.
5 / 5
Has received a container the day sooner that has promised. Nizza To see two canes and Teflon all near for a prize of one. A material for one 1 1/16 die is the little less dense likes to last cane I installed,but a new a screwed in final and any leak. 6 month snowbirding down tears of the sud these things on quickly. Two canes the year in these works of prizes.
4 / 5
I have ordered these after paying a prize a big plus partorisca a Suburbial branded anodes in a past. I have changed an anode in ours Suburbial w h several times, like the installation was no difficult that before.
Has run to the question with my valve/of temperature of the pressure that estacas, like the substitution of this valve has taken longer to do that an anode.
Shipment Was a lot of timely partorisca this product.
Would purchase again.
5 / 5
Substitutes a cane of anode in mine RV heater partorisca water every year and maintain the transmission in the compartment partorisca a following year. Although a packaging is different in these anodes of substitution is different, a measure and the looks of qualities partorisca be one same. The value adds and support of looks of good client partorisca be the big priority with this vendor. I will be partorisca use his again in a future.
4 / 5
A part was an exact access partorisca an old anode in our heater of water Suburbial. A vendor was partorisca add and has done sure that a part was a right part partorisca a work. Any all the vendors are this conscientious with his needs of clients and been still in the sale. Also the prize adds on two of these units that would have to last the pair of years.
4 / 5
The value adds and a two vendar leave partorisca maintain the transmission with a trailer. Súper Easy to substitute 1 1-16” socket does in 10 minutes.
Can substitute this every year in this cost.
4 / 5
Has received two in a band together with the small circle of Tape of Teflon. There is the video in a pertinent way to take and substitute an anode. I have looked a video although I have had the heater of Gas water Suburbial in mine leading RV and has substituted a lot before. It returns like this expected without any question. Produced excellent.
4 / 5
Has bought this partorisca substitute an anode in mine RV the heater of water Suburbial likes part of an annual interview. An anode was exactly like this described (and specified for Suburbial). Has come included with the small circle of tape of Teflon partorisca apply to some edges!
5 / 5
Right apt to a heater of water suburbial has in 5th wheel. It has had to that use the big socket to dip he in and some of a tape of edge has distributed sealant, which was to add reason can any never look to find mine. Really happy was to 2 band and the have the transmission for when I do not require it never.
5 / 5
Had expected too much long to substitute a part, so it has had the bit of the question that takes old an out. A new one has taken less than fiveinites to install. Arrived like this fiancé, the prize adds. It will buy again for you, when more it is required.
5 / 5
The anode Adds, in the prize adds, a tape of Teflon that is coming with era worthless has been for the use and has begun to come averts in of the pieces sew well has had my own tape and the pipe dope that it uses with him, the trick of plumbers to ensure never to have the leak.
5 / 5
Has purchased the pair of these anodes to substitute the shabby anode when I winterized my RV. An access was perfect. Everything is a lot like this far. This in spite of, any I same have an occasion to shoot on my heater to water until next spring so that it can not comment in the very has compared to an original.
5 / 5
We had it it has purchased it so only the used Alive-in of the Neighbourhoods horse trailer. A hot water has odorato really bad. While camping in the state park my woman has spoken a question and another camp overheard and there is then says like this partorisca fix a question . It has said that that requires partorisca clean out of a tank and substitute a cane of anode. We look the video to Tube on like this partorisca clean a tank and substitute a cane. An old one was used entirely on, and a new one was so only a right measure. Our hot water does not stink anymore.
4 / 5
Breakings of perfect substitution partorisca mine 12 heater of chevron of water suburbial, and the prize of fast shipping adds good quality
5 / 5
has BOUGHT SO ONLY he 2018 trailer of travesía and there is remarked a mag the cane had gone almost, as it orders these substitutions. They have arrived a lot quickly. A quality of some canes looks extremely well. They are the perfect access and substitution for a oem the part and he have come with the second cane, as we are to cover for years to come.
4 / 5
Has not installed this produces still reason one camps is in a camping that it opens in April is an exact one that loves thank you likes quota for your worry your help and yours backing of your product
5 / 5
I deducted a star for installation because it has not been the fast to ray in manually. I have thought at the beginning a threading the model was different but has had to be seated initially in a right corner to take. Of threading is longer that cane of original of anode Suburbial, when it was presionado fully, there was still threading to be seen. I have added a tape previously to install I so that the wait there will be any leak. Attended and see...
5 / 5
While a quantity of the tape of teflon can be so only enough to substitute at least a cane of anode, is not that a description has said. Llama circulate it 'Big', but is a circle a tiny plus has not seen never. Any I still knows did him this small. He any me Not buying this element again, but would not buy it reason the tape of teflon is has comprised. A for real Big circle will be much easier to do with (for me) that this tiny thing. A picture aims the circle the big plus. Update a picture and description with that really is has comprised. Perhaps another has received the circle 'Big'.
4 / 5
Fast that's that of the prize was adds. Purchased a two band like some canes of past experience last roughly 6 month.
Has been surprised when it is coming with the guarantee that declares 'Cane of Anode: If down 1 year sacrificed more than 50 of his mass, will take the free substitution.'
4 / 5
Gotta Goes with a magnesium. Shot a lot on 2 canes and tape. Economic, but extremely breakings of entities to the yours RV paving of interview. Be sure to verify them was regularly.
5 / 5
Good and easy quality to substitute. The vendor was awesome!
5 / 5
Look On Youtube for video in a reason partorisca east and like law. A lot of entity to use and save money in a long career.
4 / 5
Access of product and works as it has described. A two band is the value adds partorisca our heater of camp of need of water of annual interview. Special thanks to a vendor partorisca the description of good product described and fitment has left.
5 / 5
These were the perfect access partorisca my heater of camp of hot water. It has to that be threaded in correctly, but then returns perfectly. Probably I will be that it substitutes my cane of anode annually, or perhaps once each one that two years, but any less often concealed it.
5 / 5
Has purchased partorisca our trailer of travesía. I think that that these are better then some original units. It could have left an old unit besides long, but decided partorisca install this new a. Apt perfectly and now have the one of leftover to substitute in the pair of years.
4 / 5
Likes mentioned, this was almost likes to take 2 for 1 in of the terms of prizes, installs is easy has one 1 1/16' socket, be sure and use a tape of Teflon has distributed to wrap some edges in a correct direction.
If any one the a socket, apresamiento loaned or shabby one or probably will break a heater suburbial during a scrolling, the mine is by train to approach 16 years and according to annual use, usually substitutes an anode each one another year.
With a pertinent 1 1/6' socket, installs the time is 5 minutes .
4 / 5
Are not to treat big, but threading a cane of the anode is not an easy process. A weight of a cane will tend to effect a boss of ray that mates up with some treads in some inaugural. Calm only need to take your time. Calm also has to that clean a rust of a ploughing to help an installation.
5 / 5
Has taken out of an original cane in mine 2010 RV that I so only new experience. An original to good sure required to be substituted. These produced returns perfectly. The project completed in 15 minutes.
4 / 5
Produces very good. After my order has arrived an owner of a company has sent the message that asks was a right measure that & gives me link to the video for heater of hot water Suburbial on like this to change a anod cane. Good service
4 / 5
This element was exactly that has required. It is a right and installed measure easy. An only negative was a tape of teflon has distributed. It is looked this element has had state stored the real long times and a tape have fallen averts and has not been usable. It would be better been any to comprise he in this condition.
4 / 5
Loosen Old cane dulcemente so that the tank will be (would have to that be) down pressure. It has taken sprayed quite thoroughly loosening mine. 😁 Also the rinse was tank well, will have a lot of pieces of football am exited.
Global simple substitution.
5 / 5
This particular material has been recommended for a RV technology with on 15 years of work for the one of entity RV trafficante. I add to buy compared to other on-line prizes.
4 / 5
I produce it adds; works as it has announced. Easy to take old and substitute with a cane of new anode. A cot was a lot of reasonable and an after the sale follows up was as to any one. I have been contacted partorisca ensure has received a correct product and one follow on the message has comprised links it to a video of installation. The service adds! Highly it recommends vendor!
4 / 5
Has required to good sure these like the leading owner any one has to that it has changed it was. A new some are not so only fatter, but go a period learns in a same thickness. It was easy to install & has come included with a tape of @fontanero partorisca partorisca focus good.
5 / 5
Ossia The annual of substitutes of the product in my heater of water suburbial that is used 5 days the week. It looks partorisca do a work partorisca maintain an interior of a heater of water in good been. In a picture was white tape but has not received he with this product but I use a tape partorisca install a cane to a heater.
4 / 5
The value adds. A substitution and change it partorisca less than another touch partorisca the alone cane. A bit circle if the tape of teflon was the pleasant surprise .
5 / 5
Like this was the substitution partorisca a bar of anode that was at present in our heater of water. We order a together of two so that would have some extras a manually partorisca the date the late plus, yes has required. A fence of anode is returned perfectly and was easy to install.
4 / 5
Has changed out of a cane of anode in mine RV heater of water Suburbial partorisca a first time. My RV is the year and the half old and an original cane really required partorisca be substituted.
4 / 5
Likes that a product has arrived quickly, was very protected, and in fantastic condition when it has arrived. I also like a fact that has comprised tape of edge partorisca use with a Cane of Anode. My last a one work has been supposed to and am expecting them this one same!
5 / 5
Was two partorisca a prize of one has compared partorisca camp world-wide. Also it is add partorisca know can buy them something does in america. It will not install untill cradle. Volume out of old a partorisca winter and flush tank. It is awesome partorisca listen of one has sawed founder of a subject. Tip that concern in those people think. It gives the graces for a service adds.
5 / 5
Breakings of perfect substitution and quite economic to do it quite painless
5 / 5
Works to the equal that has announced. Looks to be the good quality but the time will say of then I so only installed the. A tape of teflon that comes with east the good adds on. Has the twelve heater of chevron of water suburbial and was a right contingent.
5 Camco 12ft TastePURE Heated Drinking Water Hose with Thermostat - Lead and BPA Free, Reinforced for Maximum Kink… Camco 8.6Score View Product
### Top Customer Reviews: Camco 12ft ...
Rating: 4 out of 5 with 56 ratings
4 / 5
Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: the Regular packaging uses our motorhome all the year around, how is of entity partorisca have the a lot of drinking hose of water partorisca use of winter. Has has completed so only the stint partorisca use this hose where has had has has extended periods of lows in a mid to basses 20s every night, and has not had never the bit of question with a water in a hose that freezings or has included to result restricted in flow. In this consideration, is quite happy with this hose. I estimated it 4 stars because it is a lot rigid and bulky. It is hard to find the place to store a hose when it is not to use reason is like this rigid and taken on like this room. Now that the cradle is coming, will store this in home until next winter. But when the freezing time results the threat again, will be happy to pull he out of storage of house. A plus has bitten consultor. A cord to be able to that comes with east is quite short. Has not founding never the power pedestal in quite a lot of bylines to a water hookup to use this without a cord of extension. Ossia Any question , has loved so only mention that calm probably will want to have a cord of extension to use with this when I require it.
5 / 5
Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: the packaging Regulates Unfortunately with almost 25 of a be of the descriptions stars it has chosen any to listen. I have bought and installed this good hose before winter to do sure everything would be good for the longitude Midwestern winter. Have Now skirted my camp and are all snuggled in, in some third prejudices down 20 terracings F (any one -20, but so only 20) a hose has frozen solid like the rock. Needless To say has not had water partorisca to rain of morning and although I have contemplated to brush my teeth in a bowl of water of the dogs, has resisted.
Then discovers a window of turn has closed and but to the amazon is authorised to accept returns of defective product. I add!, oh The attended now there is the restocking cost of 20 and a prize is trace now almost 15, like the substitution will cost me 35 more than an original hose. That??????
Well, take a hose behind, give me the repayment of any one I can take and will order boss of hot and do my suitable for half a cost of this esew'. My original RV hose, 25ft boss of heat and foam insulation on, the total has invested <$50, any that has to that treat this again priceless... Falls a mic... 4 / 5 Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: that the packaging Regulates there is had this product for approx 5-6 weeks. The flawless works second that it can say. The neighbour was jealous has taken one and has been disturbed a an old fashioned the way and the mine have come ready to use out of a box. Def Recommends this product! Listened to the plot of people speaks bad in these but like this far am happy. State some cold time here in of the plains of Colorado. Update!!!!!!!!! 12-16 really enjoyed this product for on some premiers two months. It looks that a consolation of a product comes with a drawback that does not have longevity. Had some cold days here in Colorado but to good sure at all crazy. -15 it Was a day a cold plus has had the month. It is at present 16. Big of 40 today and a hose is frozen solid . Followed all some directions precisely and is so only the hose frozen elegant. To good sure disappointed in this product especially for one$ 110 seal of prize. My together done the hand any one like this classy that look DIY the work has not given many the questions. The lesson has learnt. You do not recommend this product. It is against state some a lot of opinions of people that these any one last and the looks was a lot. Some parks do not leave of the versions done the hand so that it is an alternative , Any with a bit of regime pleases left to know me like the water!
5 / 5
Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: that the packaging Regulates has not had any one subject with report to heat. A connection in a hydrant of yard this in spite of, has to be so only quite tight or filter like crazy. Reason can a lot of any in a RV the industry done the connection of decent hose? I have used to use hose of tape and alimentary note of heat. Calm has known to do like this water it would be warm for the pocolos first second to take cold again. This hose? A temp really is not noticeable. I have had 3 weeks directly with highs ossia down hiela. Any question. Fix a connection and take 5 stars.
UPDATE DEC 1 2018;
like this finally spends. Ossia A start of year two with this hose or mine 2nd season of winter. While out of mine RV for the few days are returned to see the muddy disorder in a side of mine RV. My neighbour had closed my water was partorisca to me likes him the hose has blown entirely out of a with which resists it to a connector that presiona to the your hydrant of yard. You are 11pm in the night of the Sunday so much has had felizmente the short behind on the hose and was only supposition to be 34 terracings. Next day, cut an end was and has substituted he with the new connection and is doing. This is to spend to another neighbour in a RV the park and believe is the defect to draw in a way an end of hose is manufactured.
4 / 5
Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: that the packaging Regulates has read a lot of descriptions of products of Amazon, but has a lot of writing little I. This in spite of, seat thank you to say another considering a compraventa of this hose, the one who the terribly drawn product for real is. I find it incomprehensible that this hose has experienced any class to draw of investigation or trying first to be available to an unsuspecting audience. Has the connector that slightly presses to an end of a hose and leaves he to having connected to the bib of hose. This in spite of, there is not any edge, clamps, connections of transfer... Anything concealed would prevent a hose of coming avert when I have dipped down pressure. To receive a hose, has read some enclosed directions, has attached it so instructed, and then left for the short while to run errands. To return, a hose has had to come avert and waters was spewed everywhere-the one who the terrible disorder. I trust, ossia the entirely unacceptable and calm product probably will complain a decision-he not even warrant to 1 star.
5 / 5
Measure: 12 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: Frustration-the Free packaging has had so only an occasion to use this hose has heated last week in our camp during a snowy cold time so only to find a hose does not heat as it has caused our lines to water to freeze! We have had to go to buy to coil to heat to wrap around a double & hose wraps with piping insulation. Reason are living in our camp the full times at present are unable to return a hose so much the one who the waste of $75! 4 / 5 Measure: 50 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: Frustration-Free Packaging A prime minister an I has ordered, one of some finals has blown was and has flooded my yard.... They have substituted he for me. A second a has melted a sheath and almost caugth mine RV on fire. Any compraventa produced a lot defective, danger! 5 / 5 Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: the packaging Regulates A lot disappointed. When I have turned in a water for a first time a hose has blown clear of one returning in a thermostat final. That the ache to drain and then try the take behind in a box with which has been extended was. 5 / 5 Measure: 25 tyle: Cold Time (Protects of Ice cream to - 20&x2DA;F)Type of Container: the packaging Regulates Like this have mentioned in leading description, really appreciates a concept of this heated drinking hose of water but mine Camco 25 ft has heated to drink the hose of water has failed with which 1 winter of year. Now it uses this product which can be wrapped with tape to heat reason is metal in the water to drink sure plastic hose. Armadillo Hose RV25 1/2-Thumb for 25-the feet Armour plate Galvanised RV Hose of Water. 4 / 5 Measure: 25 tyle: Cold Time (Protects of Ice cream to - 40&x2DA;F)Type of Container: the packaging Regulates my woman done of the shows of work and his last show of one the year is in Cumming,GA and in a past has had ours freezing of water. As I have decided to purchase that this hose has had in chance perhaps time of ice cream again Our surprised has had 7 thumbs of snow and time down to 28 happy terracings have had this hose has had running water without any one freezing. It declares a hose is good to -40 hope of terracings do not owe that that never try. Is a lot happy with this hose and has recommended our partner to camp 4 / 5 We have had so only an occasion partorisca use this hose has heated last week in our camp during a snowy cold time so only partorisca find a hose does not heat as it has caused our lines partorisca water to freeze! We have had to that go to buy the coil to heat to wrap around a double & hose wraps with pipe insulation. Reason are living in our camp the full times at present are unable to return a hose so much the one who the waste of$ 75!
5 / 5
The HOSE does not extend to 12 feet- with which some finals are threaded is shorter that 12 feet... And this does the difference is tight to return. And they do not offer any common period of 15 feet or 20 feet. Jumps of next measure to 25 feet and have too long of the hose that hampers a heating and using capacity. Camco Need to do better to resupply other elections in of the measures. If it had taken the 15ft a hose would dip better more than extends to hang around! Also, precise knows that an electrical end can have subjects to take to discharges he in outlet for takes it has heated. They say any to run a cord of extension, but has not had any election. Of course, utilisation an external and more a short cord beats calm to compensate, and tape some finals to prevent water to take to some discharges. Disappointed to have that uses the work around then has no other elections of measure, but is heating and preventing lines of ice creams. Also, it has taken the boss of tape to/heat smaller that wrap a facet of another side of a connection.
4 / 5
Update: Begun filter horribly with which roughly three month to use to a point is more than the hazard that useful. A leak is of where an end of the hose of the metal connects to a camp has anchored. Has the die of metal of the spinning to do it easier that twist on, but gel the cold water is shooting out of a side of him. It was very effective with maintaining a water of ice cream (down hiela time for several weeks), this in spite of this was to reflect also highly in my electrical bill. It does not believe it it would purchase it again as it is not very cost effective and any last by means of a cold season.
Original: For some last weeks of the time of pair has been looking for low ice cream and last night, almost all night, was 19°. My camp is not skirted or weatherized, but the maintain warm to the equal that live in him. My water there is still to freeze, and am assuming is thanks to this hose. They are not the defender of a flavour of any waters to touch so that it does not try to add mine, but am not sure ossia a lack of hose . It gives to try it, looks to be working to the equal that has announced.
5 / 5
Has purchased in Seven 2018 for the winter in a zone of Denver. It has done fabulously... For the moment; but tonight, with a temperature in 6º has found has not had any running water and a hose has been solid frozen . Felizmente, a waterline is wrapped in a tap also. It would appreciate information on returning or that substitutes this I so that the wait will have one or two cold days before the winter is on.
5 / 5
Our RV the park has required this element for winter. The installation was easy, although two subjects have come up: 1. Some edges in a coupling is the acute knife, the gloves would owe that be past when messing with him. 2. A 'the heat shrinks' in an end of a hose is quite long, (5 thumbs?) And it prevents a hose to bend. If your spigot is too close up of an earth, annexes, likes pressure reducers, can any one is returned. Our park spigot is roughly 12 thumbs of an earth, and a hose has been grieves in without kinking. (Any pressure reducer). Otherwise, Looks to do well.
4 / 5
In the first place was is on priced and can and will do my typical of a an I October traces 9 2019 has blown averts! A hose that returns on one finalises the wine averts! Has the hoses of old garden regulate that it is on 15 years and is still near and working. This hoes is lasted 75 days! When I Created tomorrow navideño and had any water but had also the enormous disorder of the riada! It waters it quell'is everywhere state!! It has taken our morning navideña of the morning has excited, good-looking to the nightmare! A hoes is also very rigid when a temperature is 40 terracings and down and that so only dips the tension of plot to a fittings reason would owe that it has used the hoes done for cold temperatures and a lot so only the levels hoes or have a tape of heat has wrapped to go around a fittings and have tape of the extra heat as it can wrap it around a rest of a system to maintain he of ice cream.
4 / 5
So that first hose has on heated in a mid to late 40 east (supposition to be 41 terracings)....... Has has had to that wrestle has been, take insulation, repack he in the box and the send behind. SECOND hose, simply does not have on heated in a mid 30 is---the amazon is sending the number that maintain box on the second hose to ship behind. One TERCERO a work? To arrive to this point, WHO has been required like the time is turning now. 70 years, and is gone in a rain that the substitutes is is so only exceptional. Be prepared for the possible rotary door in this element.
5 / 5
To the equal that can see of a busted well, spent of mine has not been well. I have paid the few dollars less for the element used and when I received it ossia how was... As I can not say the one who the new one will be to like, will be to order the new one tonight, will update this description when I take it... But for now, it does not satisfy at all...
5 / 5
Has given at the beginning this produced stars it. We purchase it to knots two times and both the time busted in a metal fittings. This in spite of, with which that shoots question. It was error of operator . To use this hose, has to do sure concealed no only a spigot has tape of hot and insulation, which , but also an anchored to a camp. No. of knots Our anchored has been frozen, building on pressure and he busted a metal fittings in a hose. I recommend this hose while sure you are doing well. After purchasing two and breaking them both, arrival to do our own using the regular hose, foil of aluminium, boss of heat and pipe insulation. This product has done adds for knots before it has taken cold and has done deceptions.
5 / 5
Is in an of the sud and has had so only ours two cold nights, 28 terracings some 23 terracings. It waters it quell'has maintained to run in ours rv. Like this far like this good. UPDATE....
Well, would have to has listened the negative critiques. The hose has used last night which is so only a second time and has wake until watering pooring out of compartment. This campco the rubbishes had left neighbouring a RV inner of connection of water of compartment of city. It has had it has maintained it to store in clean dry zone like any excuse for failure(time of second used). If calm so only is looking to the launch money was, buy this product!
4 / 5
Has camp he in the plot that use so only occasionally. I have bought this Oct. of hose 25, 2017, partorisca use in the chance was there during cold time, but was inner a storage to camp everything of a time otherwise. This morning, we find it it is remained when I tried use he.
4 / 5
Are like this disappointed in this hose. I did not require it until this week and the new mark out of a box is defective, the bad crimp in a swivel. There is at all like the cold shower in 23° times. I have lost a date of turn for 2 weeks, and they any one honour he maintaining.
5 / 5
Update - 12/30/2020
after receiving the hose of new substitution and installing it. It has done perfectly, it is been 3 days now, thinks it will resist. ANY LEAK, maintains a water that the flows have included in 17 terracings, like this far am a lot happy with this product and would recommend it.
Has had a 12ft hose partorisca 2 days, has begun partorisca filter in an anchored partorisca be able to, a lot disappointed.
The amazon is by train partorisca send me the substitution, the hope will resist up. It has on heated and has done well except a leak.
5 / 5
Chances of abysmal products done Alas descriptions the first hose lasted so only a week and down so only the 20 farenheit and has dipped still insulation extra to warn, arrived after the substitution and lasted so only one prejudices has burst exactly of where still while my neighbour only has had hose with the boss wrapped in the aluminium never tubes an evasion, wants to save money and time this in spite of cold of the install this with a bad climate looks for another hose this any east for you, abysmal has produced.
5 / 5
Of then purchasing saw by means of several freezings without any questions. Had any subject with breaking or the acute flanges was during to the installation likes them another has informed; besides, a sleeve that isolates has been resupplied to protect one connecting spigot. An only confusing quirk is that a cord to be able to the regime of an end has feigned to connect to a RV. Felizmente, in my chance, a intake and a supply to be able to is enough after and he so that it was able to connect; otherwise, one would require any one a boss of extension or to do the bit of electrical work. In spite of, the product has treated admirably on some months that possessed it.
4 / 5
The works perfect for our 5th turns in a winter, 12ft is the abundance anxiety our needs and a cord achieves an electrical box with slack. Now our water does not freeze never in prejudices. I have not had any idea has required this for winter but obviously hoses of ice creams of water in prejudices and can break a hookups, simply taping foam insulation around a hose in some mountains doesnt work. We will be to change behind to the new regular hose in a cradle.
4 / 5
Has required the hose heated for the few years and has broken finally down and has bought this hose. Any question in 28 terracings and is good to much colder. It is true to period and gives any flavour or smell to a water.
5 / 5
First freezing day of year and water there was still freezing. My tape of hot and insulation last year has done very better. My pressure to water also spent for the averages like this this isnt same option for me, his hurting me.
5 / 5
The amazon has to that it has received the bad batch - first a has filtered , and a second a has filtered, has had to send behind. It has been to the tent to camp has bought the third a, what same, and works so only well !
5 / 5
Has had to return a prime minister a reason has filtered well when we dipped it to us on a spigot. Like this far a second a has not filtered. We are the week in.
4 / 5
These leaks of hose horribly in a point of connection. Any one imports that it has tried it, washer, tape of @fontanero, he still leaks. And a lot so only the little has bitten. A flange that connects to a water is defective. And I have listened this external same question. My others the hoses do not filter .
4 / 5
Has ordered this partorisca RV die hiela times at night. The next day arrived(awesome). Easy installs this in spite of a hose is quell'has bitten rigid. Verified on he in a morning and puddle had of gel down connection to RV stand. Filtering comming of hose clamp/there is crimped connection and not returning the spignot. Verified all fittings tight. Still filtering. It can finalise partorisca be a an I taken but are by train partorisca send it behind. A constant drip drip will take me kicked out of longitude to designate RV parking. Better used the regular line and that runs the band has heated on that.
5 / 5
Some works of good hose. I expected it partorisca be hard to develop because of a temperature. Easy to attach and discharges in. It follows some directions to develop, a warm plus some better.
4 / 5
OSSIA I SECONDS An OF THESE HOSES have PURCHASED And The PRIME MINISTER A The SWIPE of FINAL WAS BUT WAS ABLE of the FIX, I PURHASED ANOTHER And has THOUGHT SO ONLY It PRIME MINISTER One WAS BAD ONLY, WELL I HAVENT has had THESECOND ON FOR A MONTH And He DAMM SWIPE of FINAL Out of him SO ONLY LIKE THIS It PRIME MINISTER A, has HAD TO THAT GO To LOWS And TAKE A BOX of REPARATION, has has HAD TO THAT The FIX LIKE THIS MY LINE would not FREEZE , will CALL ANY To SEEIFI CAN TAKE MY MONEY BEHIND, THIS HODE Is A PIECE OF XXXX.
4 / 5
To good sure value of the money. Appeals a lot pocolos amps which RVers know you always has to that be cognizant of. While more expensive that tape of hot - all the things have considered ossia of the best to buy
4 / 5
use them everything during a winter. Usually we take 2-3 years out of them. Have has had to that that return them twice been due to defects. It does not add but a better there.
5 / 5
This hose has broken almost immediately. Mina usually $30-$ 40 bill of water was $350 because of a leak. An end that connects to a spigot so only come free of a hose. So only burst well was. I repaired it reason have required to have water of course. So only partorisca breaks again. East times a cord of heater has melted a connector I installed. Admitted this the times can have been something I wrong. Like this the hose cost$ 400 in an end and I launches there was still in some rubbishes.
5 / 5
Has has ordered now two of these hoses and has done until a temperature has fallen to approach (but a lot down) freezing. Both hoses have begun to filter and useless result. A fittings/couplings in the each final is of quality very poor as well as a hose he.
4 / 5
This product is lifesaver during a winter! Any water frozen, any flavour, and has solved in fact my subject of pressure of the water also. Produced of quality and value an investment.
4 / 5
This work adds for my application. It has very taken cold here in Tennessee and this has maintained a water that the careers included when it has taken to a low 20 east. A flavour is well of this hose of water and is all have expected. They are very happy with this compraventa.
4 / 5
It would owe that it has taken it the hose the plus along, but work. A water does not freeze and does not filter .
4 / 5
The hose of quality has heated. Doing a lot like this far. The packaging and the materials were all notch upper .
4 / 5
This has heated partorisca drink hose of the water is not doing, shoots taken almost.
4 / 5
Unfortunately a hose does not have the heated 90. While a hose remains clear, where enters a RV some freezings of line in bitter cold conditions
4 / 5
Good quality. This in spite of, while surprisingly inflexible, was very difficult to attach to mine MH tap that is located inside the zone of storage down!
4 / 5
Loves which easy ossia to use. Has extra insulation in some finals that leaves he to be pulled in a tap and rv water intake valve. Has has not had never any questions when it falls under hiela with this installed.
4 / 5
The product adds. The hate ordered it a day has been 40 dollars of a next day. But I am satisfied
4 / 5
Ossia a second Camco hose to water heated has purchased the month. Both leak in some same joints in low pressure. A quality of Camco prodcuts active downgraded significantly. It does not announce he for RV is if it can not manage any pressure.
4 / 5
Was so only the few feet of a spigot. It has had to add this to mine 50'er. It has not Loved to spend of the money but has has had to that he. Has and the snow so only funds around that.
5 / 5
My hose has jumped the little internal of leak a trace of hot wrapper, a pressurized hose swelled up like him 12' sausage. A still done hose, has had so only pressurized water among a hose and wrap, has heated well, so only the disorder to store.
Camco Has substituted my down guaranteeed hose in an end of a cold season, likes five stars for Camco.
5 / 5
It maintains pipes of ice creams very difficult to attach the spigot could use some work
5 / 5
Whose camp of winter without one. A fantastic thermometer also.
5 / 5
Ossia The permanent hook -until the camp has bought partorisca my mother partorisca live in and he so that far it has done it the good work with temperatures to roughly 20. It looks he is really that goes partorisca take tried this week of some sounds of a frigid forecast but as I have said like this far is the big thumbs up!
5 / 5
The work adds, the hose and waters does not freeze in of the freezing temperatures. Hooked To a RV pending of the stays of winter.
5 / 5
Has two of them 25' and one 50'. I have it that has not had never the question with them. I produce it adds.
5 / 5
Is side of the money. It has maintained our water of ice cream in New Jersey.
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Rating: 4 out of 5 with 50 ratings
4 / 5
The calm really is if these are doing or no? That can say, the calm no. Here is an experience has had in 2 seasons partorisca use these:
1) is súper easy to use, and ossia a main reason partorisca buy them . It arrives in camp, full bowl of basin with water, place pouch in bowl, and flush. Ossia! Not measuring, any at all.
2) has not had any clogs of paper in our black tank. 3 women in a trailer. Using Charmin Ultra (says that it is septic sure in a container).
3) The Black tank looks the flush entirely was when touching.
4) has had the few chances where some sensors of the level in a black tank looks for partorisca be covered with the paper that gives dud readings.
5) Smell: any usually have the bad odoriferous the bath or the smell that emanates of a chimney of tank of the holding. One signals this cradle, a tank has taken very bad odorando, included after touching, but with which awhile, he self-has solved. There is not never has odorato one 'citrus/orange' to to smell likes says of this material delivery.
Again, I question, this work? I think so, but it does not have any a lot of concrete test. I seat it likes him to him he is breaking down a paper and blocking to to some smells like purported. We are happy with some results are taking of a black tank and using these, as we will continue until has reason partorisca doubt with more than evidence.
I hope has found this description partorisca be useful, please click down partorisca indicate that he you. Thank you
4 / 5
Ossia That originally is coming with my laptop potty and has not had any subject with him. I have purchased the different mark and has had subjects with build of pressure on and filtering of a pressure, any partorisca mention smell. These produced has for far surpassed other products. Any one builds of pressure on and far less smell.
5 / 5
These are excellent! Really they help partorisca maintain our clean tanks, and a smell is pleasant which is a lot when you are unpacking a camp in the new place. To good sure would recommend!
4 / 5
This produces the one who dictate it . Mina, ossia all these subjects . I did not give it the 5-stars partorisca estimate reasons a zip-stock exchange of the lock will not remain zipped. Ossia A second stock exchange has had to that subject with, as I am assuming is the defect to draw . (I so only situate a stock exchange inside another zip to have that heavy-plastic stock exchange prójima; any big shot.)
4 / 5
Want to these. Odorano Utmost And take was all a smell of our system of black water. Only full a bowl of basin to around 12-16 oz (eyeball he) and then fall a drop in. It dissolves and when calm adds to a tank to hold he liquifies and taking rid of a smell.
4 / 5
Well, as we are wrapping -on our first year or RV held, and these are a first treatment of the black tank has tried. Any always súper-effective, but can have had other variables that has impacted his efficiency: It debris rest in black-tank, those waters is added to an empty tank when adding these, that waste is in a tank, like this hot is, etc. In time of 90 terracings, and a RV seating unused, there is not founding the perfect solution to maintain all odors in bay. I have begun coupling these with a Campco treatment of liquid of black tank to augment efficiency. If utilisations these, follows some instructions and add any quantities to water to a black tank together with them. It is also more to add previously to leave camping, so that a motion of the street and help it churn a water in a tank and the help dissolve a membrane, as these do not seat in the coagulated disorder in a fund of a tank.
Is test -and-error. These are not some better, is not some worse. But my bet is is so only one of 2-3 strategies will require to use--especially during a heat, month of state--to maintain your black tank to be smelly. Be sure to maintain a resealable the stock exchange there is sealed closely! The humidity will be your yes calm enemy no.
4 / 5
I alive van life full time and have it Thetford Door to Twist potti. Usually it uses Walex drop of Lavender ins but of then locate to some mountains for several months the social distance, has decided to take to 30 band of these pods. Well, to the left say the one who the deception that was. It is so only me, a woman, using basin of mine and I have has not had never the question with odorare first unless I have forgotten to add to pod. With these, my starts of basin to reek with which 2 days when I have used to not remarking anything for the week or like this with a Walex. I have lived in van of mine in SoCal for the year as it is not to like a heat of summer is doing the difference. Now I am adding 3 pods every time I empty and wash out of a tank and he still odora absolutely disgusting. I hate to squander anything but I can not be a smell. A Curve has the 5.5 tank of chevron of black water as it can not imagine like these would do at all in the big plus RV tank. I have found a last Walex and am like this happy of the has to feel dizzy me on until my new order goes in. I have bought also a Camco additive lemon of tank of ash of water and has not helped with a fat in the tiny mine 5 chevron down-to the tank of tank likes says is supposed to. It is it has convinced so only that Camco has inferior products to arrive to this point.
4 / 5
Ossia Our 3rd compraventa of this product. His utmost and well of smell. That can say, they a work!!!
4 / 5
A plastic does not dissolve and he clogged on mine maserator bomb.
4 / 5
These require more than that a stock exchange suggests. It has dipped one the day. Still it can finalise with the stink for an end of the three travesía at night.
4 / 5
They are the persnickety person, as it looks at all some factors that subject @of mine. These comprise no only efficiency, but also value partorisca money. And here it is that I find failure.
1. A pouches in that a smell that masks the granules are sealed is individually 'packaged', but is sealed obviously manually. IOW, One masks it smell pouches is seldom of a same measure, producing (certainly very light) differences in a quantity partorisca mask resupplied.
2. Worse, this in spite of, these containers to mask contains FAR more more than some granules that is required to felizmente masks a smell. For this meeting that at least bend a quantity of some granules are not required. (I, I, use so only roughly 1/3 a quantity of granules & has ANY QUESTIONS of smell.
3. When shabby more stock exchange all some containers & touch some contents were the an original container , then uses the measure partorisca maintain consistency of use of product, which goes back the frugality: it finds that an unacceptable quantity of unneeded the granules are comprised if some containers remain intact, reasons a product like this felizmente masks a smell. For this finalise partorisca save 2/3 of some granules, which obviously compares with 2/3 savings. I recommend these potential savings to all the one who use this product.
4 / 5
Has tried this based to some claims. Alive in a RV and a tank of precise black water constant attention. Except a dead person of winter, is a smell that say is now of drain , rinse, partially exchanges a tank, and drop in the new pod. Compared to that have used first, this does not resist the sail. It has spent of a process like this often some months partorisca fall so it was in a hot plus of state with another. They allege it is that odora well, but does not have any power to remain. So only it remarks an orange fragrance partorisca roughly the next day using a. My old product has not had the pleasant fragrance, but has had to that remain can. I do not actuate a lot of my original stock exchange has left. Once I have gone, I am changing behind. Of experience, knows does at least a product there ossia better and value a minimum increase for application. Twenty cost of savings of percentage with 75 increase in the use is not the frugal has called.
4 / 5
Has thought would be has flowed focused , more likes granuals in the pouch. There is not remarked any undesirable scents have fallen of then one in, but there is not remarked a lot of citrus action neither, any that are in a habit to sniff thrones...
4 / 5
These do really well with Covid our park has closed down everything of a restrooms..... Which has meant has been to force to use a RV for “everything”. A subject of desglosa of the pods and maintain a smell down
4 / 5
has has used previously a lot another camps produced of control of smell of tank, but all have been the chemical granulates that you obtain and poor to a basin. These products sometimes absorb moisture and clump, any to mention your hands are exposed to a chemical without gloves.
Prefers this type of treatments of pod of chemical tank how is much more sure to manage and unaffected for moisture, comprising transmissions of humidity while stored in some camps.
These produced does not give a tank to squander the 'coverage' strong scent or chemical scent, enough look the so only prevent smells of strong waste. Perfecto in my opinion like any need my tank that smells 'pleasant,' quite love my tank to have any foul smell (neutral).
Value of the money.
5 / 5
Has bought this mark because it was the dollar the economic plus that another bought in a past. These good smells but there is remarked that so only that uses one a pod in my tank does not maintain a smell was paralización time like this a lot of and as well as another material. The be that it has to add 2 tabs like this basically is costing more than uses this cause bondadosa are that it has to that the use folds a quantity.
4 / 5
In ours last travesía clean out of a basin in a camp and in a house of way a 3 et.ou has Had to that use a restroom. We deceive to leave his use a basin of trailer. When we Take home it has added it the bit to water to a basin and has fallen one of this drop of miracle ins a lot down a hole. Several weeks later, any smell and leave the types concealed is work of the money these costs of what!
5 / 5
Does not give quite a lot of options of indication like this almost finalised likes is rigged in the favour of a company. A scent was a lot of and is quite he directly advance and self explanatory. Using some “pods” technically would do really as well as it cries “he” for the small boy has something to protect his hands. It is not , for any half, toxic.
That says, these produced was and is the complete waste of money. We have tried in fact two different products of this company and neither of them have done. My partner has been the Imposición of House and has asked an employee. It has bought the jug of something this cost $17-18 and has done like the charm. Calm the favour and buy something more. We spend in$ 50 trying the pocolos produced different first of a jug take in Imposición of House. It does not help pause on any waste and he any one Anything for a smell. In fact, a smell has worsened
5 / 5
Very easy to use. The container dissolves almost instantly. The control of smell has been my subject .
Using 2 the time has no really changed a lot . The summers of Arizona are quite hot, the flow of positive air exhausts the defender in a ceiling is still a better way to go.....
5 / 5
Has used a lot of different frames and this like this far is a winner. Scent very better then all some another. They are very sensitive to smells and this one east a better. Any overpowering. The different clean scent some in this way for odorare too strong adapting me of public restrooms. The pods also dissolves much faster and more than all any staining in a bowl of basin. They are in tropical climate so that the summer will be a final test that a lot these resist up among touching. But east times SO ONLY will be to buy these from now on.
5 / 5
Odora Better that a biopaks (very better), but honradamente, can the hole of the excrement never the smells adds? I will buy again because really they are the enormous step up.
4 / 5
A product is has looked destroyed and the average of some capsules has been broken. They have filtered everything by means of my house. A plastic container is flimsy that is to ship in and would assume Fed ex was the little hard in a container. But a shipper did not bubble partorisca wrap or anything like this now have the disorder in my hands with some waste eating material floating during my house. These products do well ... But open your external box like calm any volume S eating the material of bacteria during your house and contadoras. Yes my woman want me well roughly now partorisca take that material during his contadoras of cookery.
5 / 5
Really bummed was ALWAYS buys an orange some have imagined like this these would be awesome nope would have to that it has stuck with an orange some really bummed was with purchasing these do not help with a scent is a lot of unscented and his no really extended equally by means of a tank of squander they so only stirs in a subordinated sad with purchasing now will owe that spend more and buy an orange some .
4 / 5
Has had a subject with our new mark RV when we use a treatment of basin resupplied for a dealership (a blue liquid), any one imports that use. It was in my talents' well, as it has done our camping trips very unpleasant. A partner has suggested this mark and like me punctual taste use -- the question has solved! I will not use never anything more, the law adds. Highly recommend!
5 / 5
These produced no well partorisca my RV black tank at all. There is absolutely any control partorisca odorare at all. Some waste of my money. I will go back to Happy Camp. It is more expensive and less convenient but does a very better work
4 / 5
This odora wonderful, but has said that I last 7 days and I can say it is lasted grieves 6.. The concealed can not be the question partorisca more but partorisca any the one who bolt in camp of sound and so only empties a black water once the week is not that I want to... I require it partorisca maintain a smell in bay partorisca a whole week.. As any recommended does not touch your black water each few days
4 / 5
Perfect for use in my living neighbourhoods horse trailer. Especially reason can be long intervals among tank emptying and use. Game and rinse of mine then dip tanks roughly 5 chevrons of fresh water in some ashes of tanks and of the blacks and the pair of these.
So many, when droughts of focus of the mine and water in a S-the curves dry was, My trailer does not take sewer gas smells.
5 / 5
Toss In a pleasant odorando pocolos orange containers and you am good to 'go.' Along durable, effective. It likes- one scent (grieves noticeable while working) better that another. Pouch HAS slide of zip to maintain the things have contained. Easy to use - I likes that also.
5 / 5
Produces that it is has feigned stops. No it likes Him To Him a smell of him! Generic chemical smell. If it love the most pleasant smell, for another scent. But after all, the sound that goes in a tank of black water...... So that the scent can not be a subject for all the world!!
4 / 5
Any entirely smell of mask but is one the majority of effective of any of some frames has tried. Utilisation he in the small door same pot although it is drawn partorisca rv use. I have read in some revises that the people cut a container in the 2 pieces of then is drawn for the basin of the main capacity but for me is so only any value a disorder. One of some reasons I use is for a consolation of just tossing a container in. Have Still to find the product that am satisfied totally with but this does well enough for me for the choose on another has tried.
5 / 5
Works quite well and pauses on the majority of some solid in a black tank
4 / 5
has forgotten to dip one of these in my black tank once and has begun for odorare less than the day. It has launched two in and the few hours later a smell has been gone! No odorano citrusy, but take foul odors entirely, as it does not import mine.
4 / 5
These that is suppositions to do . The product has arrived in shape adds. No really sure the one who another reviewers the questions are roughly. To good sure will order again when I need more
5 / 5
Reason was, these are doing in mine motorhome tank to hold of black water. I do not have any smell in mine MH. It likes-me a citrus smell of this drop-ins and like that I am formaldhyde free.
5 / 5
That is the good prize for what volume. Good and good mark strong odorando has sent. Sometimes still I can odorare a bad material but this is not the complete mask on smell but he to good sure helps and pauses down all well.
5 / 5
Maintains a smell down but have the odd scent. The source like a smell but he for a tank for odorare horrible.
Maintains water in a black tank at all times unless your flushing went it entirely then add water for behind his and fall one of these down in him.
4 / 5
Is has arrived broken. Each tab was shredded. Looked any swapped went him for detergent of dirty clothes. So much the could not use at all. Disappointing.
4 / 5
At all any to like. Easy to use, all some ads say that it does. Solved the bad question in mine RV immediately. No more clogged lines. No More smelly bath. Thank you Camco. If has the bath in you boat or RV, require this material...
4 / 5
Comparing these to mine another produced, dissolves much faster. I have not had any question with stinking still! ProTip, always add more water! With which numbers one or two, more water. With which touch, more water. While it is estacionado, more water. Any never has left your tanks take dry
4 / 5
These have done utmost to maintain odorless my commode and pause down waste. Very pleased.
4 / 5
When it camps a lot into use, it hangs these partorisca take a humidity of Florida. The works add!
5 / 5
These odorano utmost, better that some oranges some. Works well, so only wish a cube of these was a same prize and an orange some.
4 / 5
After purchasing this and having he in mine RV partorisca a month, am exited to prep my trailer partorisca travel it partorisca camp and expósito that the majority of some stock exchanges have been broken open. I have had felizmente the scooper this in spite of, some pods that the pause attacks a purpose of some pods and now have clumped powder inside a container of storage.
5 / 5
Am not sure the one who a real difference is among different type of treatments of black tank. Utilisation one of of the one of the east each weekend for a past year. They have maintained one for odorare and has not had never the question flushing some tanks.
4 / 5
Has used these and other frames. His all does well, but a 'pods' the arrival that pauses up in a stock exchange. Calm then finalise to try to guess what powder to use. A powder will go in your lungs and concealed is not pleasant!
4 / 5
The work adds. I have ordered 4 bands of 15 has taken 20 him an economic plus has not bought never
4 / 5
has lived a life of van some last 18 months. Has the chemical basin. I have seen this and a prize have obliged, as I have decided to try the. BIG deception. In the first place, a swimming. I have added another and he have attacked a smell behind. For five days. Then another two. The traditional chemicals treat a basin once, permanently. Returning.
5 / 5
Easy to use for newbies like the campers. Good value calm reason whose launch money down a drain ( literally) that suppositions that to use. The scent is well. Quite odorerebbe to swim but ossia a character of one camps bobo.
4 / 5
Sacked of stinky drop-in treatment of basin! The orange scent is a way to go . Odorano Like this good and the law adds also for until 7 days.
4 / 5
Has used these for years and consider then to be a better in a phase
7 AQUA CREST RV Inline Water Filter with Hose Protector, Reduces Chlorine, Bad Taste&Odor for RVs and Marines, Drinking… AQUA 8.2Score View Product
### Top Customer Reviews: AQUA CREST RV ...
Rating: 4 out of 5 with 27 ratings
4 / 5
has not used still but am sure is well, the nave was partorisca add
4 / 5
I have substituted the big plus 5 micron filter with east and can not say any difference with flavour, pressure or quality of water. Global happy with this compraventa and vendor.
4 / 5
Has purchased these partorisca my RV. I produce partorisca add and the value adds.
5 / 5
Rigging partorisca take a RV travesía as we require water filters. Tried quell'has been and easy to attach and waters it utmost test.
5 / 5
These are significantly less expensive of a Camco RV filter of the water and I can not say the difference in a water.
5 / 5
To the products likes him described of easy install and flavour partorisca water a lot
4 / 5
A small hose with a cradle was a worse. It can it do not take partorisca take filtering BAD.
5 / 5
Has been using RV inline filter in of the external spigots partorisca water of pet . So only changed to these Aqua the crest while it takes same better life out of filter . Like this far very satisfied . It has not used long enough for 5 indication of the star but the hope can go back in 6 me it. And action of update . The quality and the good prizes looks better that my leading filters.
4 / 5
The filters are the value adds partorisca of the money and work well. A protective hose this comes with them is not partorisca be trusted. After a day, a brass crimps separated down pressure of normal water. I have listened felizmente waters partorisca flow, is exited of a RV, and has seen a protective hose in two pieces, and immediately closed of a source of water. If this had spent when we were was, a hose would have flowed in full force unchecked in a camping partorisca the one who knows what time....
4 / 5
I like this purifier. A flavour of the water of city was horrible and this product helps a flavour of a water.
5 / 5
Looks partorisca take a work done in meso a prize of camco.
5 / 5
After the month a 6' the extension fails and comes averts. Has the regulator of pressure on common that is to dip in 40 PSI so that it does not have any reason this would have to that has come averts. It take the laws to call to say waters touch out of my compartment where a inline the filter is. Less bad of the side is sealed and has not taken anywhere does not have to that it has been only sprayed was until my neighbour has cut was. Already the there is it drained to him has gone by a time have gone back the trailer . Some works of good filter. But you do not trust an extension.
5 / 5
The HOSE in this LEAK IN THE WELD And YOU CANT FIX has HAD TO THAT BUY ANOTHER And COULDNT TAKE The HOSE SEPERATELY in the TENT AS it has HAD TO THAT BUY ANOTHER WHOLE BOX. Very DISAPPOINTING
4 / 5
Quality to arrive it to these looks to signal well. It see like this it resists until a strong UV here in New Zealand. Purchased these to water a garden and reduce a chlorine that has dipped in some plants. He to good sure done the difference. All well like this far.
4 / 5
The bad start extends filters big time. Economic construction, done in PRC. Hope A filter is better.
4 / 5
A flavour of a water is like this good or better that any water has bottled. More, rinses of soap easily rain
4 / 5
thinks these probably do like this as well as any another and a prize is well!
4 / 5
Leaks among the flexible hose furnished with boxes and filter. Constante filters as it could not be prendido.
5 / 5
Tip 2 filters and says 2 filters, this in spite of so only 1 comes with advertising! I Fix it!!!
4 / 5
Any sure on some the microscopic particles but you can see that it captures some big pieces partorisca rust and stairs in some lines of water in RV parcos.
4 / 5
It has not used still, but the prize adds and arrived promptly
4 / 5
A lot well, so only economic imitation of reputable filters of water of name of mark. You avert this filter and clave with filter of name of the mark with EUA and certification of quality has tried.
5 / 5
Has not used still but am sure is well, the nave was adds
5 / 5
In spite of using fluent sealant this has done well in the each connection in a system, connector of hose resupplied with the a lot low quality filters. Filtered of a start and after leaving a water on (has waters it autofeeder partorisca dog), open party. In a picture, can see the part of a connector of the still connected hose to a filter partorisca water with which he disconnected of a hose of water. Flooded my yard.
4 / 5
These are excellent few filters of water and look partorisca go down a pH the little which is perfect partorisca my garden.
5 / 5
To the products likes him announced, there is rid punctually. The question has had to takes connection of short hose partorisca take filtering.
4 / 5
The container has come open and flexible hose has been missing, returning it
8 Twinkle Star RV Water Pressure Regulator Valve with Gauge and Inlet Screened Filter for Camper Travel Trailer Twinkle 7.7Score View Product
### Top Customer Reviews: Twinkle Star RV ...
Rating: 4 out of 5 with 59 ratings
2 / 5
I have adjusted a valve of so pressure up (+) and down (-) in any utility. It can not augment pressure through a valve in a 42 lbs as it describes in an in title. The appearance is very good but unless I have lost something in an adjustment setup, is disappointing very to be able to augment a pressure in 42 lbs.
5 / 5
An element is arrived on the way timely and is exactly while it describe. It uses it a next weekend to camp in the KOA Campground. Without him a pressure of water was also intense. A regulator of pressure of the water a work is has been meant to do and has done perfectly. I actuate Only the used the once. So far, any subject. We use it to us on our 1973 Argosy 20ft.
5 / 5
Regulator of excellent adjustable water for pressure to achieve big tide and protecting RV lines of water.
5 / 5
PERFECTO!! The works add for our RV water supply. The factory posed in 40psi and has done if it marvels for our water supply of the big pressure. Very better that these regulators of cheap pressure that easily find in Amazon and local tents.
5 / 5
We take this for our camp and used it this weekend is spent. Law perfectly. It researches to be very built and durable. I am very happy with this product!
5 / 5
It IS well to see a pressure and the be easy to adjust. The works add in my RV.
5 / 5
We use in fifth ours goes that it is motionless. Fact only well!
5 / 5
We hooked until the very big pressure system without learning and create this regulator of the pressure has saved totally ours RV system.
5 / 5
Compraventa Excellent. We update of the basic regulator without a gauge. Easy to adjust pressure very happy with compraventa. We are full times RVers and would buy again
5 / 5
The wine bundled quite amiably in the box.it of the goleada was easy in the hook until my element of supply.This the one of the solid water listened, and believed it will do in fact a lot of years. Easy to comprise directions. To well sure buy it this produces again.
5 / 5
I am spent for like this of this plastic and other regulators of pressure that can you pickup in a venue superstore. Cela Has has finalised now! This new regulator is built to last term along, any one has launched was after 6 month or the year. Turn well in a water spigot and has not filtered the drop around some edges. It is maintaining my pressure partorisca water consistently in 50PSI right where want it; ossia until transmission my alcohol and require more pressure. Then it is the simple adjustment to augment or decrease my pressure of water!
4 / 5
We hooked until the very big pressure system without knowing and create this regulator of pressure has saved totally our RV system.
4 / 5
This description is for a Twinkle Incident RV Valve of Regulator of Pressure to Water so only. A device is a lot of fact, the pressure is regulated for the ray in an outside. A gauge looked attentive and one installs was easy. Highly recommend.
4 / 5
Has regulated a valve of pressure so much on (+) and down (-) to any avail. It can not augment pressure by means of a valve on one 42 lbs likes described in an on title. The appearance is very good but unless I have lost something in an adjustment setup, is disappointing a lot to be able to augment a pressure on 42 lbs.
5 / 5
Ossia The must for any RVer the one who is ailing and tired of a lack of pressure to water when apresamientos to rain. It connects directly your fresh water intake. Solid brass with the pressure to notch upper gauge, ossia the súper easy installs. It dips in zero pressure so that when management in your water afterwards installs calm any one the the macizo arises of pressure. It take the pocolos small to regulate to 40. Still down enough to prevent subjects with some lines, but quite big to feel likes is in home that takes to rain. This for far a thing has better taken for ours my woman thinks so also. And like all know....'Happy woman, Happy life'
4 / 5
An element arrived in the timely way and is exactly to the equal that has described. We use it to us a next weekend to camp in the KOA Campground. Without him a pressure of water was too much intense. A regulator of pressure of the water a work is has been meant to do and has done perfectly. It has used it so only once. Like this far, any @subject. We use it to us on our 1973 Argosy 20ft.
4 / 5
Purchases this to substitute the Camco regulatory we in the first place installed. A start of a Camco the regulator was a lot down, but has not known until we purchase the gauge to measure a pressure of start. It was roughly 30PSI, any 45PSI likes specified in a description.
When in the first place we connect this regulator, a pressure of start has been dipped to 0PSI. We connect some separate gauge to a start to compare some values and there is matched as well as we are to look a pressure . Prendemos In 50PSI, but the small leak begun of an organism of regulator. We plan to substitute he with another unit to see if this fixed a subject.
Update: A regulator of substitution is doing adds! Any leak!
In general, our pressure of the water in one rigs is very better that with a CAMCO regulatory, as we are very happy. If a substitution does not filter , will regulate an indication.
4 / 5
Regulatory of excellent adjustable water for pressure of managing big tide and protecting RV lines of water.
5 / 5
Has found the video of the devotion excluyente RV canal that says to take one of these reasons some RV the parks have pressure to water that is too big and can break pipes. It is the pocolos more than has loved to spend but this thing is weighed and fact really well. It survives first Ours freezing without filtering (the difference of mine economic hose..) And it is súper easy to use. So only take the flathead screwdriving and twist a ray in a black part until a pressure is around that loves (our RV the pointed park -45psi to the equal that have dipped he in 40 but a lot really was that it is sure and any). In general ossia a awesome little unit that could save you money in a long career and so only give you peace of alcohol.
5 / 5
PERFECTO!! The works add for our RV water supply. The factory dipped in 40psi and has done if it marvels for our water supply of big pressure. A lot very better that these regulators of economic pressure that you easily find on Amazon and local tents.
5 / 5
Said until 160PSI adjustment. RO The precise unit 80PSI, some stops of valve in regulating in 65PSI. My entrance is 140PSI but the maintenances take of the stupid clicking noise, can not take past 65PSI. It POS. Also, they have not fill a gauge with oil! URGH! It is going back the Amazon!
5 / 5
Has taken this partorisca our camp and used it this weekend spent. Law perfectly. It looks partorisca be very built and durable. They are very happy with this product!
5 / 5
Has bought partorisca maintain a big pressure in RV parks partorisca blow out of a plumbing in my bus. Failed in 3rd use at night & still. Has despertador on when being in of waters he. It run it it was partorisca close water, later partorisca find a regulator had failed and the needle was in zero any import that was dipped in or the one who the waters have pressed by means of. Calm the favour and ski this a
5 / 5
This gauge looks partorisca do quite well but a pressure of diverse start a bit of day-to-day. I dipped it/ I dipped It to 40psi and occasionally law so only down 50 in a gauge. A thing the note is that it was-of-the-cashiers, any fluent water until a ray of the adjustment of the pressure has been turned.
4 / 5
So only installed this regulator as it was not that the long term will be but looks it would have to that resist up. I think a gauge can be the little overstated. It has dipped in 50PSI and a pressure of a tank looks more afterwards to 40. Easy to regulate, and ossia better that taking too down the reading and breaking things. An oil has fill gauge would have to that solve a question to stick of regulators of the oldest model, and has to that be was to disassemble to clean on sediment. Note, comes with the ray dipped to zero pressure like this when you install it, turn in a clockwise direction until you take a pressure loves. Oh, And it was economic compared with a last an I has bought.
4 / 5
Does well for roughly 4 month, and while we camp, commentary a lot of pressure of big tide and has verified. A gauge has aimed 80 psi. A portion of regulatory only leaves and has not regulated with which conceal. We this in spite of that spends this a lot for the regulator of pressure would do it. We are going back to some simple some without a gauge.
5 / 5
Did not like Me that has purchased in this way before I have required for the use and has discovered does not do to regulate a pressure down to the pertinent level, as I have purchased the simple one in WalMart.
5 / 5
Has liked him that a product was a lot has built. Easy to regulate. No it liked Him To Him a fact that when I verified it with which the diverse pressure of hours had gone of 40psi to 60 psi. The instructions have said something roughly the heater of water can augment pressure. I have gone back so only to the mine old regulator. Apparently it requires more than I have thought to take it to do.
5 / 5
The product is coming , any allocution of turn, any one has guaranteeed info, telephone or email, or place of web or costruttore info. Gauge Has fill with the clear liquid. Any one mentions done in some instructions to the equal that to the that that is and reason concealed is. It has tried not even to use, is returned so only immediately.
5 / 5
Never fact, first waters would not go through half of. It directs pressure to water adjuster with engine of ray that waters have come by means of but the never moved indicator to aim pressure of water. Hasty was and buys $element that the works add. 4 / 5 This pressure reducer was so only that has required partorisca give me a peace partorisca import that my RV plumbing has not been to the swipe averts for the big of pressure of water in some campground. A setting was easy to change with just the simple screwdriver. It would be necessary to give me years of use. 4 / 5 A regulator of pressure has arrived quickly, is exactly like this orderly, and works perfectly. RV Plumbing is not partorisca like the regular house that plumbs. Unregulated The pressure of water will break a RV connections, usually in a zone concealed has not seen a light of day of a RV has been built. Expensive to repair. 4 / 5 I looks of regulator partorisca do well but an expensive/gauge has fill with water. Then a kerb that resists a face has begun partorisca rust. Have take one covers of hule and drained a water and a face have on fill again next use. A face/gauge the zone looks gross now. I will return partorisca these reasons. Unfortunate Because functionality and quality of the rest of a look of unit adds. 4 / 5 The better must then a pressure of water restrictor has used partorisca use with metre of water. I have taken this after camping in the park with pressure partorisca water on 60lbs with more economic one the leak partorisca plumb 5 / 5 My husband has said that read well to with accuracy gauge a pressure of water in ours RV. We use partorisca guess with an old pressure gauge and no the good idea of then can ruin yours plumbing in a motorhome. 5 / 5 Does not resist a setting of pressure. If I have dipped he partorisca 40 psi, when it turns a water in falls to 15. If I dipped it/ I dipped it to 40 with a water on goes well on that when I turn a water was. It have to that resist a setting of pressure, he no. 5 / 5 This looks partorisca be the a lot of the pressure done a lot of gauge. I did not use it still, reason rig partorisca a RV travesía in March. I will try it then, and write another description when return. 5 / 5 Has purchased this in a consultor of the fellow familiarised with houses of engine hooked until watering on place. This adds partorisca protect of the big pressure that spoils some lines of water in a house of engine. 4 / 5 Little in a pricey side, laws to expect as well as he maintaining the year. 4 / 5 Is good to see a pressure and the be easy to regulate. The works add in mine RV. 5 / 5 Bought he partorisca my rv. Absolutely like an idea to be adjustable and built in pressure gauge is a lot useful. Construction of heavy quality. Has the wye returning and have the pressure gauge in another side partorisca control a unregulated side. I have experienced rv parcos with on 80 psi. Without the regulator there would be has has had failures in mine rv system of first water of 4 / 5 Used partorisca the hose of full garden has opened was still pressure a lot down. 4 / 5 Has not purchased Never one of these before, but these looks of regulator partorisca be fact well and good works. Has the data has used the on two camping the travesías and he regulate well and has maintained a pressure of water. You recommend this product. 5 / 5 Save my waterlines in my camp a time is paid for him like this some campgrounds ⛺️ has too much pressure of the water will not owe that concern roughly he maintaining 4 / 5 JUNK-the adjustment does not change the thing. Any I still thinks a gauge is attentive 5 / 5 Like this far like this good. The valve and the regulator found our pressure was the big and dipping is maintaining compatible pressure in ours camps. Has facilitated to dip are adds. Recomend This produced and maintain a box to situate valve in still travelling. 5 / 5 Use in fifth ours wheel that is stationary. Fact so only well! 5 / 5 Does well at the beginning but with which so only the week or two the broken and filtered for some first time there is remarked to please any wast your money in this product takes something better 5 / 5 was that it animates thus produced but I have received the defective a. They are while to a response of a vendor. I will update my experience when I take the repayment or the substitution. 4 / 5 The work adds. It has been using constantly for several months and any subject: it maintains pressure and of the controls on well. 5 / 5 Compraventa Excellent. We upgraded of the basic regulator without a gauge. Easy to regulate pressure very happy with compraventa. We are full times RVers and would buy again 4 / 5 Operates it partorisca do sure a side of the main pressure of a water a lot doesnt break a auxillary line of water. 5 / 5 Has not tried this closing but when it arrives, one covers that it looks for partorisca accustom filler a gauge with the oil has not been seated everything of a way and roughly 1/3 of an oil there has been peaked of an interior of a gauge. This creates the bubble on some numbers, which the very hard fact partorisca read. Otherwise Looks well. 5 / 5 Wants to be able to regulate my pressure of water in my camp. The new lines would cost too much. Have broken this tho bc I wasnt prendiendo attention. Going to buy another tho. 5 / 5 Highly recommended for our group to camp and a lot of entity to control a water our unit. 4 / 5 Has done well while it was sunny and warm. First time a temperature is down state hiela, die and never recovered 5 / 5 This regulator adds! An only reason that gives 4 in place of 5 is that it say that it comes from/comes from to to an already dipped factory likes 40 or of calm so that books. It was fully he backed was this in spite of and has not left any water to spend to setup. But an adjustment is very easy and is attentive and maintains the pressure in bylines. Nizza Little regulator. 4 / 5 Has air in a pressure gauge. There is any mention of a question or regarding the fix. Is a defective product? Have it that sends behind? 5 / 5 Has ordered the dozen of of the this for my project. Everything of is filtering water. 9 Camco EvoFlex 4-Foot Hose | 5/8-inch Diameter | Designed for Recreational Use | Drinking Water Safe | Super Flexible… Camco 7.6Score View Product ### Top Customer Reviews: Camco EvoFlex ... Rating: 4 out of 5 with 47 ratings 4 / 5 Finally, the flexible hose partorisca RV waters that the does not struggle you when it calms that wants to store. This hose is very easy to manage when you want to coil he for storage. I have possessed the aim Camco (very rigid, especially in cold time), the blue 'Neverkinks' (which ALWAYS kinks) and the g of Zero (this explosion), as I have had the plot of RV experience of hose. This hose is my preferred new ! 4 / 5 Like the devotion excluyente RVer has purchased a lot of drinking hoses of water. After discovering that an economic some of Wally so only last roughly 6 month before they begin to filter where some males fittings is joined. Yes it uses the regulator of the pressure and I yes looks for to use new washers. So only they have had to that long before they develop a same defect. Besides these hoses are the bear partorisca coil if a temp fallen 40. As has thinks that would try this Camco hose that the soft stays and pliable, done in some the EUA, and has stainless steel fittings. The utmost sounds. It was pliable, but after the week a male of stainless steel that the returns has blown so only immediately a hose of hule in a half of a night. That the disorder. To good sure the question to draw. Sending behind and that goes to try another mark. It can very any one does the hose of quality? 4 / 5 Update (5 later month) : A hose is by train of gone strong. An aim camco the hose has developed inner of seaweeds, but no east a. It suspects a lack of the transparency in some helps of blue hose control a subject of seaweeds. I also cut this 50ft hose to return my needs. It was better that buying 10/25ft sections of hose. Any leak, as any complaint. Flexible closing, and any breakings/of cracks. Hose down 60psi (static). I have had a pressure to water place to 80psi (static) stops to the long of the month and any leak. I turned it down behind to 60psi. Very same was like this to estimate 'flavour' reason has drunk no out of a hose. Any way, use this hose jointly with waters he of 3 leak of phases and water softener for my trailer of travesía. And it does not drink out of a Campground waters, as it can not speak to this. So only I have three 5-gal jugs of Water of the Prime minister that change in venue grocery tent. Retreated To a súper flexible. While it calms it is not careless with a hose (I bad real careless), he no kink. I have had this hose down 60psi for several days and is resisted on just well. A hose develops/piece slightly down pressure, as I me worry, but am sure that this will resist on just well. I have not used he in condition of hot time, as it has not been that a hose will be affected by pressure hot temperature. We will see, I supposition. Of then is one the majority of flexible hose has, is to declare very easy of the movement around and subject this in spite of likes. Like this far like this good. 5 / 5 Has had each type of RV 'drinking the water takes' the available hose, this one east one has found more like this far. An aim Camco are to add but is too rigid to coil reasonably yes is less than 100f external. These blue host coils well in 35f, has not checked time down. It is much more flexible that it Camco 'any kink' white hose all the world has. Really alive until a hype. Machined fittings Look to be nickel plated, quality very big without leaks. The hose is done in EUA for a packaging and text in a hose he. It says 'drinking the sure water' and for any reason gives that statement more hanged when the hose is done in EUA. I do not have any opinion of the term along as the one who as it resists up in a sun etc, are so only the warrior of weekend that is ailing still to coil on the rigid hose every time the fill tanks. Although has the short life and I have to that substitute each one another year, is still value he, and are not the rich type. 4 / 5 Ossia The one of truth kink free hose that looks very durable. Unfortunately, has the built in the model circulates that the cause to be wounded up in only a direction. A hose has the memory neither in a clockwise direction or counterclockwise and he no accident goes. Cela The fact is exited a reel in the together of loop, as I owe that turn he for the take slowly. Work to add and has good metal fittings,but is the ache partorisca reel. 5 / 5 I shopped still the new hose for hours and almost everything of them there has been negative critics. I have chosen finally this one and am thrilled that has done! I have purchased one 10 ft the version and is light and easy to locate. An installation was súper easy and neither final of a hose dripped at all. Finally, after the fast rinse, has had any bad flavour in my water. Highly it recommends this hose and plan to purchase the along one more if a need arises. 4 / 5 Ossia The very flexible hose and to the as it likes me more roughly is that it can be coiled to enough of the small container after fill a tank of water in ours boat. I will be to look for something for the trace on for the easiest that extend/retract without untangling/unkinking. Although I will not use this hose in cold time, thinks that it would remain a lot of pliable in of the very low temperatures. In general, it looks to be the hose of quality. Substantial fittings. 4 / 5 Am surprised in quality. It fulfils the one who a description of sales has said. 1. Very flexible. 2. Because of flexibility, is not probably the kink or at least a lot as much as a rigid some. 3. A metal fittings is the real plus. Any leak like this far like plastic some. An only thing in favour of a rigid some are has the heavy coating that will help him resist UV HARM and probably last bit it longer. But enough it would possess something better for the time it short plus that possessing to to something does not like for the plus of long. In short, very pleased like this far with compraventa. 4 / 5 Your browser does not sustain HTML5 video. Leaks under a twisty what. They are sure I so only has taken the bad a 5 / 5 One feels of this hose is astonishingly exert compared the traditional hoses. It is strong, but also has to that give which deletes this bad kinks. It is the perfect period for knots to connect the system of filter of the water to ours camps. So only a right quantity of period of hose that does not dip pressure in some finals while not creating to plot of slack neither. Metal of big quality fittings in the each mark of connections stagnate and sure finals. Any leak. Easy to coil behind up after each use and place in our cube of water for storage of travesía easy. Highly it would recommend. 5 / 5 It is the hose partorisca water sure partorisca drink out of, use partorisca wash the black motorcycle that leaves less something of water and does not have to that the chemical smell likes him a bit the hoses do. Easy hose partorisca manage and surrounds on but is not has to that the heavy hose of commercial type but quite sufficient to wash cars, drinking of and fill cubes to water for animals. Any constantly left hose in a direct sun or abused can begin to deteriorate. 5 / 5 These hoses of water are much more flexible and so easier that locate when packing up. Also they will develop and place of walk in an earth when dipping up. I have not had any subject with kinking. It weaves it to them to camp and these have done a setup and process of desglosen so easier. It has used an aim a common plus or blue plastic hoses previously to of the this. I have considered some hoses of G of the z/of the Zero, but has read revises to complain of bad flavour to the equal that have decided to try these instead. It has had any unusual flavour with these. I have it quell'has ordered of another 25' hose and he 10' period to the equal that can use a period required or connect multiple for the longest careers. Calm will not be disappointed with these. 5 / 5 The hose adds that it is plyable but a lot of sturdy. It does not leave any aftertaste that can determine. It has dipped the filter in a bib of house and then have the filter in a RV so only for security. The hose has better used like this far. Tried a lot some folding some and they have jumped the leak after the few weeks, once while it have not been in a RV that causes enough the disorder of must. Bought a 25 version of the feet but I will buy one 50 for an also 5 / 5 CAMCO EVO FLEX FOUR HOSE of FEET Ossia probably the better hose that need for my questions of gardening, but am tired of an economic some that kink on and leak. Ossia Perfect for our yard and for our big and puppy boy to drink of. Súper Flexible BPA free the free goodness Phthalate free Any yuck plastic flavour Nickel plated diagram fittings UV has stabilised for long life Universal access has DONE IN You The EUA A fittings is extra a lot when you install this and he does not filter at all. It bends Amiably without kinking likes a lot do. Well value of the money. 5 / 5 A hose is flexible as announced and looks a lot of-fact, but there is a lot down-sides. A container warns against using for hot water, leaving pressurized unattended, and using without the regulator of pressure, all that involves that the cure is required to avert in brilliant. Also, a male returning has the very small grip zone, he doing hard of presionar without using the wrench or pliers. 4 / 5 Am spent$ 100 for the hose that has failed multiple time. This hose has some profits of an expensive hose without a cost. It is flexible and easy to move and does not contaminate a water that chairs in a hose. I plan to purchase another.
4 / 5
This product has broken inside an hour of installation. A hose is fallen off a connector . It can it does not return reason am spent already more the money and the time that repairs it.
5 / 5
Any too impressed anymore with this hose. Has the soft out of casing and is very flexible, this in spite of him kink a lot easily also. This can not be a @@subject while has significant pressure in a line to press spent a kinks, but yes is attaching to the drain of low pressure, really hampers a flow. My hose has developed 3 kinks like this far and has tried diverse things to correct he without any regime.
4 / 5
Took it so only yesterday, any leak still. My last CamCo the white hose has begun to filter in a spigot connector with which roughly 4 month, and so only take once. This hose leaves a water with the quite strong rubbery aftertaste, included although has the filter has attached. The time will say if a flavour goes was and filters he of stay of the connections-free.
4 / 5
I bought (2) 25' period of this hose. Imagined usually a do one except having an extra one in chance I need extra period. It did not use Him still but I like a sweetness of a hule and they look to be easy to manage and wrap on, the difference of an aim of economic plus RV hoses to water that has used in a past. I am thought these will do a lot amiably. Some finals are fat metal the difference of this economic plastic finalise which have not trusted never in. This look to be a lot has done. In general I like a Camco the products and these would have to that return a bill.
4 / 5
I finally upgraded to the hose of better quality after using an aim some partorisca years and no in that have regime very well with them. My subject main with this hose is some connectors. Although they are of good quality chrome, is very smooth and impossible the grip closely. I owe that use the pliers partorisca presionarles every time I hook up in the camping. Ossia A lot inconvenient when they are in a street. I expect that hard longer that some economic hoses.
4 / 5
The better hose has not bought never. It could say when in the first place that develops that ossia hose of quality . It has been trace in a typical rediculously small coils and has the place was partorisca like it was full of water. All some coils disappeared and was instantly useable hose. Any flavour any kinks the utmost ends so only add happy has read some first descriptions to buy!!!
5 / 5
Has used this hose partorisca the while now. After each use goes until the tent in one camps. Easy to locate and remains flexible. It will be to buy another for when we require an additional hose. A lot, very better that a less expensive camping hoses that had been using for years.
4 / 5
Has the 25' Prime and 10' in EVO. EVO looks to be easier to treat w/ forms/ better controls. Also it uses the z/the Zero-G that it is easier that neither to pack up in RV.
4 / 5
Vast improvement on some old rigid hoses. The time will say roughly to the equal that resists up over time. The instructions say to not leaving unattended while down pressure, quite unlikely for a RV .
5 / 5
Orders this hose to fill two basic needs: 1) HAS a flexibility to be business in a wet bay without detaching of a RV has anchored of water and 2) waters Resupplied without any flavour or smell of a hose ( water of use of city for our refrigerator icemaker). We have done a travesía of 6 nights with a new hose and he have done perfectly.
5 / 5
Ossia The a lot of the hose does well with machined connections. I have seen the plot of descriptions on Amazon to a contrary but some connections are weighed-has to that machined (does not bend out of forming if tombs in the hard surface). A hose is fat abundance and any kink easily. They are very pleased with cost of mine.
5 / 5
This hose is extremely flimsy. A fittings is flimsy of then is connected to a flimsy material blue. A metal anti-kink the coils in any final are also flimsy and feel totally economic for a prize. Smell and horrible flavour to a water when it seats for just the few hours (or less!). You owe it does not have to that constantly run out of the hose for several minutes when specifically it says “to drink the sure water.”
A colour was a lot of but precise something functional, any enough.
Does not recommend .
4 / 5
Has required the short hose to hook until my RV to my filter of water concealed chairs in an earth. Ossia A perfect period for that. I made a mistake to buy one 3 footer first and was slightly too short.
4 / 5
Has purchased these hoses to use in ours RV utmost laws of soft water and is quite flexible to use in of the small tight spaces. 5/8” diameter abundance Resupplied of volume of flow of the water for our RV.
4 / 5
Any sure the one who this half , heat, flavour, asks like this do not go it partorisca eat just use he so that it has been feigned partorisca: emotional water of the container partorisca resist tank in mine RV
5 / 5
has used this hose partorisca connect my external water supply to the tank of seasonal coverage has used partorisca wash veggies of our park of the agriculture dates endures community local. A hose is sure partorisca potable water and hooked on, so that it has wished. A tank maintains all this organic muck out of a house and a system partorisca plumb.
4 / 5
Loves a material and the one who this flexible . Exactly that there is wanted. But the mine is not 25', more like 20'. I am not sure the one who past and used it the number to time so that it has not annoyed returning, but disappointing.
5 / 5
Is to come trace in the piece of map with bonds of transfer. Had the kink of the packaging will see that hard.. It has had to that rearrange the the time of pair to line it up without a kink king kinking
4 / 5
A lot disappointed. Sure - any flavour of plastic hose - instead roughly another bad flavour, especially a hose remains in a sun. It would not buy again.
5 / 5
Has bought this hose based in the good descriptions that thinks was of better quality then an aim Camco the hoses can buy in of the tents, but this hose headed kinking is very first use. He kinks easier that mine white hoses. A hose agrees each forward kink so the new fights kinks in the each travesía as well as an old any that arrives animal. No the good hose. For a money, some very available hoses economic plus in Walmart is the better value.
5 / 5
My thing preferred in this product is that it is soft and pliable like the easy fact to wrap on when rigging to move our RV.
5 / 5
The time will say on durability. A hose subtracts flexible when cold. June of update 30, 2020 Afer 6 month of every day hose to use flexible rest closing in all the conditions. Fittings Still soild And any leak.
5 / 5
A Camco 25 hose of feet is soft and flexible drinking hose of water. It is easy to wine on also.
5 / 5
Perfect period partorisca connect my hosebox to the mine spigot. A hose of the old connector there has been the hole in him. This has done perfectly and I really like a hose he
4 / 5
Fittings in the hose will not return all the edges. Disappointed, but will use partorisca another application.
4 / 5
Is the hose . I have required the small substitution partorisca my rv drinking water supply. It is the hose and the law adds like the hose.
5 / 5
So only has taken this hose partorisca substitute my Camco hose has had them paralización few years this one is way more flexible an easy to manage
4 / 5
is Gone in punctually and looks partorisca be that his well. Like a measure of the main diameter of one of the that, uses it partorisca connect the system partorisca debug of the water to Gentleman RV.
4 / 5
Finally the hose can locate same in timing fresher.
4 / 5
Excellent quality. Any drips. Any flavour. Perfecto partorisca RV water hookups.
4 / 5
Buys this thinking it was anti-kink, but is extremely last partorisca locate and tent. It does not filter or drip, but hard to use reason he kinks.
10 Camco EVO Premium RV & Marine Water Filter, Greatly Reduces Bad Taste, Odor, Sediment, Bacteria, Chlorine and Much More… Camco 7.3Score View Product
### Top Customer Reviews: Camco EVO Premium ...
Rating: 4 out of 5 with 59 ratings
5 / 5
It IS the small hesitant because of some revise concealed looked to signify that these filters were junky, or feeble, but so far is very impressed.
Everything in this thing is built like the tank. Accommodation very robust, nuts, covers.. And it water it flow very good. I can not imagine a quality that takes very better. I have it did not have to the open on top of still, but is surpassed the to well sure my expectations so far. Very look the to help my soiled a lot of too much water.
To to The Sounds likes them-join them few people that has had the subjects was to say cases . Water, muck besides or erratic pressure.. All the classes of crazy things can spend that he sea only quite anything, but under half circumstances, and does not think has very the preoccupy enough. I will be to use mine through the gas pressure powered washer, so that it have to be interesting.
5 / 5
It follows directions, uses the regulator of pressure infact would have to coming with or. Some say that he the filter, to the left say me and use this to filter my water of city for my aquarium, as it is on and of a hose each weeks of pair, with regulator of the pressure installed does not filter , my pressure of water is 70 in spicked and has to reduce he in 30. They go in your tent of hardware or takes a pressure reducer/regulator or mandate in Amazon 0 will protect your inversion. Has update a filter in a better gac. Any chlorinated the waters of flavour are clear after leaving the bubbles resolve.
5 / 5
We purchase this filter to substitute a an interior our 2013 sandpiper camp. A a there has been was expensive to substitute some filters. As it look for it other options. It takes the race in a tent of hardware to find a right access to connect in our since exists plumbs. But after installing has has not had any subject. We install last night (11-27-17) and I am very happy with him. The filters of real enemy are so abordables to do easterly one and easy to find! Highly it recommends that you are that it wants to save money. The wine with all precise if it only is posing he in for hook of place of the camp ups. But we have wanted the most permanent interiors. Purchase again. And you update has any subjects !!
5 / 5
I have bought this for the slightly unusual application -- so that records brilliantly.
Likes him a lot of houses, active very he-the reverse phase osmosis system of filter of the water under a tank of cookery. Each which how six month or as it is supposition to change some filters, and for each of some cartridges of charcoal of the filter is supposed in flush the for the few minutes before installing them. But that concealed you?
Arrives in me that could buy the accommodation of only cartridge and the little fittings, and cut the hose of garden through the each filter in flush he for the few minutes. It IS easy to buy some accommodations, and the small more take to find some rights fittings, but when annex in a cost of some separates some cheap more total available in a same cost while it buys this box. As I have bought this box.
Has been pleased to find that each which fittings is of big quality. For example, some parts of core of some adapters of hose are solid metal, more than plsticoes.
While it can see calm of a semi-detached photo, pre-filter of installation-flushing is now easy.
5 / 5
Experience a Camco filter of water of the premium after the visit in the campground with bad water. These low filters in 5 microns. More can take. Careful The be that tense a fittings while they are metal fittings in the plastic accommodation. I have begun the tight hand and then the wrench tensed quite filter prendi. Amazon Ailing-split this filter with titling of filter Camco 40772. A headline is in big for a filter. A rest of filter in a fittings/hoses in place of an organism of filter. Felizmente A filter comes with the wrench to take an organism of a leader. Only it poses a wrench in an organism of filter and place he in some Works to sustain well an earth is not in rocky. After the pair of the uses has tried to take a leader has been to drain a water was but is sper tight. Included this presses a button of relief of the pressure any help. I will try the addiction in an end of a season, does not want to break now.
5 / 5
It uses this filter of water during 4 month in our marine. I attach in the tap of water of our slip and then slide a final of a hose in the tank of water of our tube of full boat and visit a tap of water of the cradle on in the 1/3. Law like the charm. We enjoy well water all the same long summer when our neighbours of cradle go to complain quite what bad his water tried and smelt. It thinks the majority of my neighbours of cradle will be to buy this filter for next season
4 / 5
Filter of well primary water. We exclusive devotion RV and also has the secondary in-filter of line, the Camco TastePURE. To well sure it can try a difference among any one, or and two filters. My only subject is that it directs -in the hose is quite down and a lot of places have a tap too much out of an earth. Like The result, an advantage-in the hose has jumped the leak - bad form. It opens to Use the 10' Camco 22823 drinking the hose of water likes him favours. We change a quarterly filter.
4 / 5
We buy this in a principle of a camping saeson (while I have been tired to buy everything of this water bottled). I have opened he until draining it (while it is beginning to take cold) and a filter was the colour /of diverse yellowish brown. It looks he is doing is work ! Bought this that opposite in some of an another so uses the replaceable cartridge against those launches a whole thing was (some waste IMO).
3 / 5
I have bought element 40631 (accommodation with element of filter) to filter water of city when that fill the hot tub. Has the box of test of chemistry of water for my hot tub, and has tried a water filtered for concentration of chlorine. Any one had any discernible difference among a unfiltered waters of the tap and a water have filtered. Any different test or, like the look of recoveries deceives. The flow through a filter is surprisingly strong. The looks of accommodation solidly has built. The prize is down, as I imagine is taking that it has paid it prendi. But I have wanted to to water of better flavour, would suggest the very better filters what that comes with this box.
5 / 5
This filtering the laws of the better system that 35 dollar for Water of Pure filter the installed unit in my trailer. It filters the smallest particles and improves flow. It have ordered the level Camco filter and give that it does not install in my pomegranate of Pure Water. Only a 35 Water of filter of Pure dollar- which are done slightly different- would return.
Has bought this system for meso that the prize and I highly recommend to buy one 14 support of the dollar otherwise a pomegranate dangling and tension in a hose and entrance. It stabilises A unit. Very happy with this compraventa and no longer hostage to Water Pure predatory value.
4 / 5
I have bought element 40631 (house with element of filter) partorisca filter water of city when the full the hot tub. Has the box of test of chemistry of water partorisca my hot tub, and has tried a water filtered partorisca concentration of chlorine. It has had no discernible difference among a unfiltered waters of the tap and a water have filtered. It has not tried different neither, so that the look of claims misleading. The flow by means of a filter is surprisingly strong. The looks of house solidly has built. The prize is down, as I imagine am taking that I have paid stops. But I have loved to have water of better test, would suggest the I very better filters the one who that comes with this box.
5 / 5
This filtering the better system that 35 dollar for Water of Pure filter the installed unit in trailer of mine. It filters the smallest particles and improves flow. It have ordered the regulate Camco filter and there is @@give that it does not install in my Water Pura canister. So only a 35 Water of filter of Pure dollar- how is done slightly different- would return.
Has bought this system partorisca meso that reward it and I highly recommend to buy one 14 stand of dollar otherwise will have a canister dangling and pulling in a hose and has anchored. It stabilises A unit. Very happy with this compraventa and no longer hostage to Water Pure predador pricing.
5 / 5
Has taken this filter for my pressure washer .. Wetting/rinsing .. To reduce water spotting when washing/that it details my vehicles. Has waters A lot LAST to Austin, TX .. The works add .. A lot that reduces a work that dry some cars. Used with Rain-X Something Free Car Wash in a cube of soap (any in a current of water) for closing of better results.
4 / 5
Uses this inline when it was my vehicles because where alive there is súper the hard water like this creates the tonne of something of water s. This deletes roughly 60 of that and softens one waters like the easiest fact to dry. You are this is not that this product has been feigned to be used for but am sure has to that to another there him me like the one who would use for a same reason does. So only know work and is the prize adds.
4 / 5
Aversion , well waters, supposes to take a smell , take a clean water but a smell with which 5 days begin again , has the well the waters and that tries to improve a quality is not lasted too much, so that that supposes to do returnit ,the cause cause money to change an installation to use this element or or that goes to change me a filter and I send or a an I has , answer ASAP pls before I estimated it .
4 / 5
The work adds to filter water.
Has had subjects with him in 1st reason one or-the coverage could be situated in another something that looks well. And being me me so only concealed. Filter like crazy. I have imagined once it has been it was error of operator (lol), the law adds.
And now is the one who some looks of filter, look to be quite common.
5 / 5
A quality, the action and the creation is perfect for our Winnebago Rialta RV trips around Washington, Oregon and Idaho.
Likes that I can substitute with element of new filter every year in place of a disposable the filters of type have used before.
Be careful threading a hose fittings so that it does not cross the edge expósito that 2 or 3 wraps with a tape resupplied was quite and he easier that presionar properly.
4 / 5
Am not sure east still anything. A water still gross test in the each earth of camp goes to. The sediment had included that gone through half of in a campground. Any leak in him anywhere but has bought an additional 4 ft hose that use in place of a one this is coming with him.
4 / 5
Already have the 10' the filter that marries like this, an only reason has purchased this one was his does not have to that treat a hassle to try to find fittings to go among a has anchored/ouutlet of a house to the hose of garden...
A fittings that has come he with this useless. At all it returns anything. Any joke. At all rays to some propiciado by house of the filter, and at all can connect at the end viril or woman of the hose...
Sees that other buyers have entirely different looking money fittings ossia in fact thus produced and use, but concealed is not that I recieves at all. Very disappointing. For me, the waste of money.. And unless they can expedite me some correct fittings will be to return this product , how is useless mine without a fittings was announced to, and supposition to come with.
4 / 5
...Be careful any to cross-edge some adapters - a plastic house is esoft'...I have not required / to use an edge of pipe and threaded his 1/4 turn behind and advances until it has seated fully. It uses this in my very exited house of water. He DEFINATELY improves a quality of a start of water.
5 / 5
If has the trailer of travesía buys this one. The works that has surprised. I have bought a stand partorisca go with him also. An only thing is calm mark ploughed sure t on and dump out of a water previously partorisca dip was so that it does not filter went in trailer
4 / 5
This filter was simple to install and has joined he in with the recently purchased water softener partorisca our RV. It is doing I add! Before a instal my woman has not been happy with some white particles that floating in a kettle. Of one installs a water is clear crystal and does not have any question or the worry that drunk he directly of a tap! To good sure the good investment!
4 / 5
Well, These produced does not do like this expected that. I attach in fact, He so only leaks. Partorisca Date, can do not using reason filters so still although I have tried numerous methods partorisca seal it. Result partorisca be the complete waste of my money. Spend your money in the different water filters the system and you will be happy.
4 / 5
This filters does a work has expected. A wrench is the characteristic added good . A bendy the hose is well. Mina some calm launches down is really has to that buy a stand partorisca the resist. Fall on. It is totally necessary to have. Like the PS also the cost waters it softener partorisca a RV but will be devotion excluyente prompt too.
5 / 5
Emmie has said of has tried it the little ape but there is not it remarked. This there is decreased in a past two weeks. My only suggestion is use the pair of gloves partorisca do when that gathering initially. Perhaps they are the bit in jealous with presionar the connections but some parts of metal were the tad acute and cut my right hand in of the multiple places. No a better way to begin the travesía partorisca camp but is happy with a result of final!
5 / 5
Court down in some something of hard water (yes, has waters it softener that goes up of uses) when we wash our reason buys it to us.
4 / 5
Mayor that expected, but works perfectly in ours RV. With the light adjustment in location, has had any mountain of question this in our space has limited. It filters a water fantastically, and is exactly that requires. This in spite of another RV soyust HAS'
5 / 5
Camco EVO First RV & Filter of Water of Marino, has Bought this big plus a that thinking would last two times while a small plus some. This one can be been bad one but he so only lasted partorisca 2 weeks. In the first place a water partorisca roughly 5 days was cloudy and then partorisca some prójimos few days a water has odorato bad. It has had to that substitute with a small plus of the that has been using for the few years.
5 / 5
Has had an old more Camco Filter of Water but could not find any filters of substitution anymore has bought like this is one. I am not disappointed. It is to good sure heavier that mine old plus a. They are able to dip in in a rear bumper of mine 5th Goes while use otherwise would purchase the stand for him.
A pair of descriptions has mentioned filters in some connections. If utilisations a tape of teflon that comes with a unit and presionar a conections properly ( any on-torsion), will be well.
Has camped now in the place where a water has tried usually 'any like this a lot' and another place where calm sometimes take sand in a water. In both chances, a filter the work adds. Mina inclusa gal the mate has said that a water has tried well!
Like another reviewer there is remarked, sure mark you flush a the new filter previously to use, to take touched of of excess carbon.
5 / 5
Has this on-line place after my regulator to water place in 55 PSI for my RV. We devotion excluyente and the winter of use and daily summer. I have not remarked any difference in chevrons for the minute sent by means of a filter and some flavours of good water. A water in my zone has no issuesto begin with this in spite of. I dip tape of Teflon in the each connection but was bondadoso of there is disappointed that some rays of hardware of the metal to a plastic. A plastic is very durable and very fat. We will see overtime he jumps any leaks with a constant pressure and will update consistently.
4 / 5
I have bought this partorisca the slightly unusual application -- so that laws brilliantly.
Likes a lot of houses, has fine it-stage reverse osmosis system of filter of the water under a tank of cookery. Each one that are month or I so that it follows supposition to change some filters, and for each of a charcoal the cartridges of filter am supposed to flush his for the pocolos small first to install them. But that calm that?
Arrives mine that could buy it the house of alone cartridge and the little fittings, and run the hose of garden by means of the each filter to flush he for the pocolos small. It is easy to buy some houses, and the little harder that find some legislations fittings, but when you add on a cost of some separates some available economic plus he total in to a same cost the like that buys this box. As I have bought this box.
Has been pleased to find that all a fittings is of big quality. For example, some parts of core of some adapters of hose are solid metal, more than plásticoes.
To the equal that can see of a semi-detached photo, pre-filter of installation-flushing is now easy.
5 / 5
Was the little hesitant because of some revise concealed looked to indicate that these filters were junky, or feeble, but like this far am very impressed.
All in this thing is built like the tank. A lot sturdy house, edges, discharges.. And the water flows very good. I can not imagine a quality that takes very better. Have has not had to the open on top of still, but is has surpassed to good sure my expectations like this far. Really it looks to help my soiled a lot of water too much.
To to Sounds likes him to him a bit people those who there have been the subjects were extreme chances . Water, muck besides or erratic pressure.. All the classes of crazy things can spend concealed would ruin so only roughly anything, but low half circumstances, the does not think has a lot to concern roughly. I will be to use mine by means of the gas powered pressure washer, so that it have to that be interesting.
4 / 5
Follows directions, uses the regulator of pressure infact would have to that coming with one. Some say that it filters, to the left say me the use this to filter my water of city for the aquarius mine, how is on and of a hose each weeks of pair, with regulator of the pressure installed does not filter , my pressure of water is 70 in spicked has them has had to that the reduce to 30. It goes your tent of hardware or take a pressure reducer/regulator or commanded on Amazon $10 will protect your investment. I upgraded a filter to a better gac. Any chlorinated waters he of flavour is clear after leaving the bubbles solve. 4 / 5 Purchase this filter to substitute a an interior our 2013 sandpiper camp. A one has had was expensive to substitute some filters. Like rings other options. It take the course to a tent of hardware to find a legislation returning to connect to the ours of then exists to plumb. But after installing has not had any subject. We install last night (11-27-17) and I am very happy with him. The filters of real enemy are like this abordables do is one and easy to find! Highly recommend is that it wants to save money. The wine with everything needs calm so only is dipping he in still hook of place of the camp ups. But we love it to inner knots more permanent. Shopping again. And you update has any subjects !! 4 / 5 Has purchased a Camco filter of water of the prize after recognition to the campground with bad water. This filters down to 5 microns. Calm more can take. Be careful presionando a fittings so it is metal fittings to the plastic house. I have begun the tight hand and then the wrench has presionado enough partorisca take filtering. Amazon Ailing-partorisci this filter with titling to filter Camco 40772. A headline is the big for a filter. A rest of filter in a fittings/hoses in place of an organism of filter. Felizmente A filter comes with the wrench to take an organism of a boss. So only dipped a wrench in an organism of filter and place he in some Works of good stand if an earth is not to rocky. After the pair of uses has tried to take a boss was partorisca drain a water was but is súper tight. Included pressing a key of relief of the pressure does not help. I will try the addiction in an end of a season, does not want to break now. 5 / 5 Filter of good primary water. We devotion excluyente RV and also have the secondary in-filter of line, the Camco TastePURE. To good sure can try a difference among any, one and two filters. My subject only is that it directs -in the hose is quite the courts and a lot of places have one touches too far of an earth. Like the result, an advantage-in the hose has jumped the leak - bad form. Maintaining use he 10' Camco 22823 drinking hose to water like this favours. We change a quarterly filter. 5 / 5 Has used this filter of water for 4 month in our marine. I attach it to the tap of water of the our slip and then slide an end of a hose to the tank of water of the ours bounce turn and full pipe a tap of water of the cradle on in the 1/3. Works like the charm. We enjoy well water all been time very same when our neighbours to jump complained roughly that bad his water tried and has odorato. It thinks the majority of my neighbours of cradle will be to buy this filter for next season 4 / 5 buy this in a start of one camping saeson (to the equal that has been tired to buy everything of this water bottled). I have opened he until draining it (to the equal that is beginning to take cold) and a filter was the yellowish/brown colour diverse. It looks he is doing is work ! Bought to to this likes opposed to of some of an another like this uses he replaceable cartridge vs that launches a whole thing was (some squander IMO). 4 / 5 Final update, has used a filter with a hose of substitution. Everything is well. According to Update: I have received hose of substitution, and looks well. Still you think it it would have to that these with a same quality his water to drink hoses. First update: Interior 24 hours, Camco has gone back mine. (Prime minister any good!) Camco Offered to substitute a hose with the tried one. With which receive this, and the try, will update this description (and my indication). Original description: I have received only mine Camco commanded of filter of water of EVO of Amazon. A canister the looks of assembly quite very drawn and has done. (It likes there of hoses). I gathered it. When I have looked for to attach hose of a short connector to a canister, has discovered that it is nowhere approach a same quality. An end viril is not returned closely, has turned easily in a hose, and so only pulled immediately! ( It sees photo) Any marvel reviewers there is complained of of the this filtering. Clearly this hose is not of a same quality like some hoses of fresh water Camco frames. I have left the message in some links to sustain expósito for clicking in a key of Technical Support in a page of order of the Amazon. I will update this description Camco go back mine and does this legislation. That it would be it the plus of the satisfactory solution would be for them to send me the 4ft Camco hose to water which can be found is link of amazon: ( they would have to that do a hose of connector for this a same way these hoses are done). Will update this description takes the satisfactory response of Camco with the day or two. If I no, will be to return this filter to Amazon. 5 / 5 After installing this filter and having has used he for the week, am a lot disappointed. Think some filters some small plus camco the mark could be better. Or perhaps they have connected also with Clorex like BRITE filters. And a lot in fact take any chlorine! Our water tries worse after installing and more flavours of chlorine that before. How it is that possible? I like an idea can substitute so only a filter of interior with east a to save waste and and launching out of whole filter each one that 3/6 month. It was to look for the substitution. Camco Looks a lot half on quality of filter and reducing toxins, bacteria and containments in a water supply. 5 / 5 The works add. A well the waters am pumping there is alot of smell. We use partorisca the camping partorisca rain. After a water spends for a filter is clear and any smell. I am impressed. If it can find the 1-micron or cartridge partorisca filter smaller would take two of these and run his inline. 4 / 5 A lot, very economic rule KDF the filters have not done partorisca like department partorisca water here sux, maintains flushing vase down some lines and clogging a bit inline filters of camco, as I have decided the upgrade to the east a, 'together with the new kdf inline of camco (regulates it$ 10 filter) in the foot of where connects to a trailer, has used a bit screen of hose washers in the each connection, as I do not want to treat vase clogging some lines in mine trailer again (was real fun reparation)...This filter of water has to that say is kinda orderly, in that has valve of relief of the pressure, a creation where some together upper rays in another hand = horrid, filter and has to that really REALLY presionar a heck out of him partorisca he a lot partorisca filter, would have to have an included gasket/washer partorisca where some upper rays to a box of filter, is plastic to plastic = in disposal to focuses it free when hot taking quite external then fry again probably, can see this like the potential question for these leaks of units again in 2 days im taking the repayment and that goes to spend to to the little hundred likes opposed to in of the I already paid supposition so that already there is attatched the picture to see the one who im that it speaks roughly, but taste like this of a box has tape of precise teflon quite hope camco fixed this, ossia an only question with him..
4 / 5
In the first place one has been been shipped and had has used. Be careful dipping it near, one beats of plastic edges and will undress really easy. He the good work to filter water.
5 / 5
Has experienced highly with leak and has used this mark in a past for commercial and residential applications. Any subject known, the prize adds, the action and the quality add. I will connect my hose for my rv by means of of the this to distribute pressurized water and to fill a tank of reservoir with him. I also dipped to 5 phase has filter of data to water to drink the purposes and this filters certainly will extend a life of one has system of date to be an effective pre-filter.
4 / 5
When I have looked for to install could not taking one filtering among an upper and a house. Rey-Read some instructions, the tongue in one focuses of hule. A filter has one in the each final, has thinks that has spoken roughly. After diverse unsuccessful the tentativas there is @@give would have to that have one Or-coverage among an upper and a house. Now included this thing is useless mine until I can find a correct measure Or-coverage.
5 / 5
Easy to dip-arrive and use. Bought connecting hose and be a same time. It Finalising that it takes another new hose to connect the motorhome. You water it that is exited a purifier is well, a 'white' leading the hose there has been the 'hose' taste.
5 / 5
An organism of laws to filter well and looks to be a lot has built. An only complaint has is that a cartage this is coming with him does not filter out of a flavour of chlorine. We have had to take the Brita pitcher filter to take touched of of a flavour of chlorine in a campground.
5 / 5
Bought this to use with our camp, has attached it to them to a side of one camps in an anchored of water, this leaves a water to be filter first to enter a camp, law perfectly, also can be used in bouncing it that goes to different cradles
4 / 5
Excellent filter. It contains carbon to take VOC impurity . You water it it tries order exiting of this filter. Any leak - use a tape of teflon has closed. Also buy the spare filter to do the transmissions the fast plus when I require it. It comes with the scrolling of tool of black inferior house to do the turning opens a unit to change an easier cartridge as well as a 12 hose of thumb that can use you partorisca anchored or a outlet side. Shopping again.
4 / 5
Can not comment in a quality of the water but I was unable to attach an assembly of entrance to an economic plastic house without entirely undressing some edges and is now entirely unusable. . . It is it was the imposición to house now while it can take some pvc cimienta which will leave me to attach an assembly of entrance. Appearances use this to take some water of quality to my plants while in holidays and does not look concealed goes to spend
4 / 5
Ossia The filter adds . An only thing would change is a pocola hose that comes with this short WAY. The desire was at least long enough to do to a level of earth. Otherwise, Filter very good!
4 / 5
Leaks of water in a hose and a focus upper! I scrape on partorisca like this tight ! Need the ray of metal on! Plastic is súper feeble! It goes with 2 Blue little some! Only disadvantage I calm can not see that it is inner unless his crack has opened!
5 / 5
Hope To does not have to that never use this he so that it is for purpose of emergency so only. Remained with a correct filter my family there is sure to drink water.
4 / 5
These works of filter of the water well the paralización is feigned purpose , but when ordering has had an impression that a hose fittings was the molded leaves of a unit. This is not a chance, as it filters to house simply has 1/2 thumb edge of pipe fittings, and some connectors of hose owe that be returned. This when being a chance , could have taken this more economic unit in a tent of local hardware.
4 / 5
Ossia A better main option for water of trailer of the leak of travesía. Better work that other options because you substitute an inner filter like opposed to a plastic integer casing.
4 / 5
The good unit but he there is not coming with the assembly of anchored complete likes signalled in some instructions. It has anchored any threaded assembly that is missing one covers threaded. Please send me the part of substitution, as I can change my description to 5 stars.
4 / 5
Has looked for an easy solution, economic to wash my car and no in that has something of water. This filter has like this far done a work and does my work of cannon of the foam 10x better that do without him.
Highly recommend
5 / 5
leak Very better to water that it filter normal. Some filters some big more any last like this long, but is better micron indication, the meaning takes more impurity out of a water. Flavour of the water and the smell a lot has improved.
5 / 5
Has bought this filter for my external hose and boy he a work! A same water different test with which spends for a filter. They are happy has purchased this filter in place of a one has seen in Wal-Mart. To good sure will buy again and recommend more looking for the filter for the buy also.
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# Intuition for coordinate patches on Proj of a graded ring.
Hi Mathoverflow. This question is about building intuition for the Proj construction. When I first started learning about schemes, I found the construction of the structure sheaves on Spec and Proj very confusing. However, after enough time had passed I began to understand the construction for Spec: It is sort of an algebraic partition of unity argument. The construction of the structure sheaf on Proj is still very mysterious to me. For completeness it goes something like this:
Let $G$ be a graded ring. Take $f \in G$ homogeneous of degree $d \geq 1$. We have a homeomorphism $D_+(f) \cong{\rm spec} \, G_{(f)}$ which sends $D_+(fg)$ to $D(g^{\deg f} / f^{\deg g})$. It first expands the prime to $G_f$ and then contracts the result to $G_{(f)}$. Motivated by this, we can define $$\mathscr{O}_{{\rm Proj}G}(D_+(f)) = G_{(f)}$$ and prove that the map $G_{(f)} \to G_{(fg)}$ defined by $a / f^n \mapsto a g^n / (fg)^n$ is localization at $g^{\deg f} / f^{\deg g}$.
I can fill in the details but they are messy and I have very little idea what the details actually mean. Thinking about $\mathbb{P}^n$ as a variety, I understand why $D_+(X_0)$ should be ${\rm spec} \mathbb{C} [X_1/X_0,X_2/X_0, \dots, X_n / X_0]$ but I don't really understand how this intuition translates into the commutative algebra which is boxed above.
Also, for homogeneous elements of degree higher than $1$ I have no idea what is going on. I understand that geometrically the veronese map should be involved but I don't understand how that intuition translates into the messy proof which I am able to write down.
Question : Is anyone able to explain the idea behind this construction? Note that this explanation could lie in either the realm of algebraic geometry or commutative algebra.
It is very possible that there is not a nice way to think about this construction which would make me sad because it is so fundamental. I hope that there are some good responses which help me fix my ignorance!
EDIT: I just went through the proof again and wrote up the details.
Let $G$ be a graded ring. The first order of business is to explain why we have a homeomorphism $D_+(f) \cong {\rm Spec} G_{(f)}$ when $f \in G$ is homogeneous with degree $d \geq 1$. Fix $\mathfrak{p} \in D_+(f)$. Then $\mathfrak{p}$ is the generic point of some irreducible closed subset $Z$ in ${\rm Spec} G$. Since $f \not\in \mathfrak{p}$ it follows that $G_f \mathfrak{p}$ is the generic point of the irreducible closed subset $Z \cap {\rm Spec} G_f$ in ${\rm spec} G_f$. Assume that $g \in G$ is homogeneous. Then $g$ vanishes at $\mathfrak{p}$ iff $g / 1$ vanishes at $G_f \mathfrak{p}$ iff $g^{\deg f} / f^{\deg g}$ vanishes at $G_f \mathfrak{p}$ iff $g^{\deg f} / f^{\deg g} \in G_f \mathfrak{p} \cap G_{(f)}$. This proves that the map $D_+(f) \to {\rm Spec} G_{(f)}$ is injective. We need to prove that the map is surjective. Let $\mathfrak{q}$ be a prime ideal in $G_{(f)}$. Motivated by the above argument, we define $$\mathfrak{p}_n = \{ g \in G_n : g^{\deg f} / f^{\deg g} \in \mathfrak{q} \}$$ Then $\mathfrak{p} = \oplus_{n \geq 0} \mathfrak{p}_n \in D_+(f)$ maps to $\mathfrak{q}$. Since $g$ vanishes at $\mathfrak{p}$ iff $g^{\deg f} / f^{\deg g} \in G_f \mathfrak{p} \cap G_{(f)}$ the map is a homeomorphism which sends $D_+(fg)$ to $D(g^{\deg f} / f^{\deg g})$. All that remains is to prove that the map $G_{(f)} \to G_{(fg)}$ defined by $a / f^n \mapsto a g^n / (fg)^n$ is the localization map. From the affine case we know that $G_{f} \to G_{fg}$ is the localization map at $g / 1$, therefore the only non units which $G_{(f)} \to G_{(fg)}$ sends to units are powers of $g^{\deg f} / f^{\deg g}$. I suspect that this last bit can be made rigorous.
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This is more about $\rm Proj$ than about its structure sheaf, but I much prefer the definition ${\rm Proj}\ R = ({\rm Spec}\ R \setminus {\rm Spec} R_0)/$scaling to the gluing construction. (And in fact, I essentially never glue schemes together along open subschemes.) – Allen Knutson Jun 4 at 21:28
Hmm this sounds interesting as it is much closer to the "classical" definition of projective space. Two thinks I am a little unsure about though: How is ${\rm spec} R_0$ closed subset of ${\rm spec } R$? How do you mod out by scaling? – Daniel Barter Jun 4 at 21:37
A ring $R$ is $\mathbb Z$-graded iff it carries an action of the multiplicative group (proof: define $R_i$ to be the subspace where $z\cdot$ acts by $z^i$). Then, that group will also act on ${\rm Spec}\ R$. Then for the first question, you need to look past the obvious inclusion $R_0 \to R$ to the less obvious quotient $R \to R_0$. This only works because $R$ is $\mathbb N$-graded, not just $\mathbb Z$-graded. – Allen Knutson Jun 5 at 0:57
See the answers to mathoverflow.net/questions/41624/… – François Brunault Jun 5 at 1:26
You in fact already found out the most natural way to think about the Proj construction, namely in terms of the projective space. Consider $X := \mathbb{P}^n$ with homogeneous coordinates $[x_0: \cdots : x_n]$. Then what are the basic open sets in $\mathbb{P}^n$? These are simply the complement of zero sets $V(f)$ of homogeneous polynomials $f \in S:= k[x_0, \ldots, x_n]$. I suggest that you try to see for yourself that $U_f := X \setminus V(f)$ is indeed isomorphic to $Spec~ S_{(f)}$. (Hint: at first check this for linear polynomials - which follows almost by definition. Then for an arbitrary $f$, write $U_f$ as the union of $U_f \setminus V(x_i)$ and figure out what is the coordinate ring of $U_f \setminus V(x_i)$. $U_f \setminus V(x_i)$ is also the complement in $U_{x_i}$ of the zero set of an element in the coordinate ring of $U_{x_i}$ - what is this element?)
For me at least it was illuminating to get the hands dirty: start with the definition of projective space as the space of lines in $k^{n+1}$ (with the natural topology given by identification of the lines not passing through a hyperplane with $k^n$) - and check explicitly what the notions in the definition of the Proj construction mean.
To get flavours of more general situations, I would again go through examples. E.g. for the scenarios that $S_0$ may not be a field, consider $X := \mathbb{C}^2 \times \mathbb{P}^2(\mathbb{C})$ and see why this is isomorphic to $Proj~ A[z_0, z_1, z_2]$, where $A := \mathbb{C}[x,y]$. For a bit more involved example, consider the subvariety $V$ of $X$ defined by the zero set of polynomials $f \in A$ and a homogeneous polynomial $g \in \mathbb{C}[z_0, z_1, z_2]$, and check that $V$ is isomorphic to the subscheme of $Proj ~ A[z_0, z_1, z_2]$ defined by the ideal generated by $f$ and $g$. Can you see how to interpret the zero degree elements of the graded ring?
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If you look at the ordinary $\mathbb P^n$ then it has $n+1$ standard open patches of the form $C[X_0/X_i,X_1/X_i,\ldots,X_n/X_i]$. The $i$-th patch looks similar to a localization with respect to $X_i$ in the affine case, but not quite, since now all variables are degree less due to scaling. Now they want to do a similar thing to any graded ring $G$ and want to "localize" w.r.t. any homogeneous function $f$. To do that, just make $f$ invertible , and then take the subring of degree $0$ elements of $G[1/f]$ (due to scaling ). After we have that, we can easily go back and forth between affine and projective. For example, to explain the last statement in your algebra box :
Assume we have localized the projective variety $\operatorname{Proj}(G)$ to $\operatorname{Spec}(G_{(f)})$ for some homogeneous element $f$. Now we want to localize it further using $g$. $g$ is not an elemment of $G_{(f)}$, because it has degree, so instead we need to use $g^{\deg(f)}/f^{\deg(g)}$ for localization. What about the mapping $a/f^n \rightarrow ag^n/(fg)^n$ ? This maps does nothing, which it should, cause localization map does nothing. They only rewrite it because $ag^n/(fg)^n$ is easily recognized as a member of $G_{(fg)}$ while the former is not.
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# Problem of the Week Problem E and Solution Odd Sum
## Problem
A sequence consists of $$2022$$ terms. Each term after the first term is $$1$$ greater than the previous term. The sum of the $$2022$$ terms is $$31\,341$$.
Determine the sum of the terms in the odd-numbered positions. That is, determine the sum of every second term starting with the first term and ending with the second last term.
Note:
In solving the above problem, it may be helpful to use the fact that the sum of the first $$n$$ positive integers is equal to $$\tfrac{n(n+1)}{2}$$. That is, $1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}$
## Solution
Solution 1
Let $$t_n$$ denote the $$n^{\text{th}}$$ term in the sequence.
Let $$S_O$$ represent the sum of the terms in the odd-numbered positions. That is, $S_O=t_1+t_3+t_5+\cdots+t_{2021}$
Let $$S_E$$ represent the sum of the terms in the even-numbered positions. That is, $S_E=t_2+t_4+t_6+\cdots+t_{2022}$ Since there are $$2022$$ terms, and half of the terms of the sequence are in even-numbered positions and half are in odd-numbered positions, there are $$1011$$ terms in $$S_O$$ and $$1011$$ terms in $$S_E$$.
Let $$S$$ represent the sum of the $$2022$$ terms. That is, $S=S_O+S_E=31\,341\tag{1}$
Since each term after the first term is $$1$$ greater than the term before, \begin{aligned} t_2&=t_1+1\\ t_4&=t_3+1\\ t_6&=t_5+1\end{aligned} and so on, until \begin{aligned} t_{2022}&=t_{2021}+1\end{aligned} Now, \begin{aligned} S_E&=t_2+t_4+t_6+\cdots+t_{2016}+t_{2022}\\ &=(t_1+1)+(t_3+1)+(t_5+1)+\cdots+(t_{2019}+1)+(t_{2021}+1)\\ &=(t_1+t_3+t_5+\cdots+t_{2019}+t_{2021})+ 1011\\ &=S_O+1011\end{aligned}
Substituting $$S_E = S_O+1011$$ into equation $$(1)$$, \begin{aligned} S_O+S_E&=31\,341\\ S_O+S_O+1011&=31\,341\\ 2S_O&=31\,341-1011\\ 2S_O&=30\,330\\ S_O&=15\,165\end{aligned}
Therefore, the sum of the terms in the odd-numbered positions is $$15\,165$$.
Notice that this solution did not need the formula given in the note after the problem.
Solution 2
Let $$t_1$$ represent the first term in the sequence. Every term in the sequence can be written in terms of $$t_1$$. The second term is $$1$$ more than the first term, the third term is $$2$$ more than the first term, the fourth term is $$3$$ more than the first term, and so on. Thus, \begin{aligned} t_1+t_2+t_3+t_4+\cdots+t_{2021}+t_{2022}&=31\,341\\ t_1+(t_1+1)+(t_1+2)+(t_1+3)+\cdots+(t_1+2020)+(t_1+2021)&=31\,341\\ 2022t_1+(1+2+3+\cdots+2020+2021)&=31\,341\end{aligned} Using the formula for the sum of the first $$n$$ positive integers with $$n=2021$$, $2022t_1+\frac{2021(2022)}{2}=34\,341$ Dividing by $$2022$$, \begin{aligned} t_1+\frac{2021}{2}&=\frac{31\,341}{2022}\\ t_1+1010.5&=15.5\\ t_1&=-995\end{aligned}
Since the first term in the sequence is $$-995$$, we know that the original sum is \begin{aligned} t_1+t_2+t_3+t_4+&\cdots+t_{2020}+t_{2021}+t_{2022} \\ &=t_1+(t_1+1)+(t_1+2)+(t_1+3)+\cdots+(t_1+2020)+(t_1+2021)\\ &=-995-994-993-992-\cdots+1025+1026\end{aligned}
We are interested in the sum of the terms in the odd-numbered positions. That is, we’re interested in the sum $-995-993-991-\cdots+991 + 993 + 995 + 997 + 999+ \cdots + 1023+1025$
From this point, we will present two different methods for determining this sum.
• Method 1:
Notice that this sum includes all of the odd integers from $$-995$$ to $$995$$, inclusive. This sum is $$0$$. Thus, \begin{aligned} -995-993-991-\cdots+991 + 993 +& 995 + 997 + 999 + \cdots + 1023+1025\\ &= 0 + 997 + 999 + \cdots + 1023 + 1025\\ &= 997(15) + 2 + 4 + \cdots + 28\\ &= 14\,955 + 2(1 + 2 + \cdots +14)\\ &= 14\,955 + 2\left[\frac{14(15)}{2}\right]\\ &= 14\,955 +210\\ &= 15\,165\end{aligned}
• Method 2:
This is an arithmetic series with $$n=1011$$ terms, first term $$t_1 = -995$$, and last term $$t_n = 1025$$.
Then, using the formula $$S_n = {n}\left[ \dfrac{t_1 + t_n}{2} \right]$$ for the sum of a series, \begin{aligned} -995-993-991-989-\cdots+1023+1025&=1011\left[\frac{-995+1025}{2}\right]\\ &=1011(15)\\ &=15\,165\end{aligned}
Therefore, the sum of the terms in the odd-numbered positions is $$15\,165$$.
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Excited States from TDDFT
for lithium version of Exciting
Purpose: In this tutorial, you will learn how to perform a basic time-dependent density functional theory (TDDFT) calculation. As an example, the loss function of bulk silver is studied for the optical case (long-wavelength limit q=0).
Read the following paragraphs before starting with the rest of this tutorial!
Before starting, be sure that relevant shell variables are already defined and that the excitingscripts directory has already been downloaded, as specified in Tutorial scripts and environment variables. Here is a list of the scripts which are relevant for this tutorial with a short description.
• PLOT-loss-function.py: Python script for generating plots of the loss function.
From now on the symbol $will indicate the shell prompt. Requirements: Bash shell. Python numpy, lxml, matplotlib.pyplot, and sys libraries. Important note: All input parameters that will appear will be given in atomic units! ### 1. Groundstate calculation ##### i) Preparation of the input file The first step is to create a directory for the system that we want to investigate. In this tutorial, we consider as an example the calculation of the loss function for silver in the fcc cubic structure. Thus, we will create a directory silver_tddft and we move inside it. $ mkdir silver_tddft
$cd silver_tddft As a starting point for the TDDFT calculation, we need converged electron density and potential. To this end, we perform a groundstate calculation. Therefore, we create (or copy from a previous calculation) the file input.xml that could look like the following. <input> <title>Loss function of Ag</title> <structure speciespath="$EXCITINGROOT/species/">
<crystal scale="7.72">
<basevect>0.5 0.5 0.0</basevect>
<basevect>0.5 0.0 0.5</basevect>
<basevect>0.0 0.5 0.5</basevect>
</crystal>
<species speciesfile="Ag.xml">
<atom coord="0.0 0.0 0.0" />
</species>
</structure>
<!--
Below is the groundstate part of the input
-->
<groundstate ngridk="10 10 10" />
</input>
Please, remember that the input file for an exciting calculation must be always called input.xml. For further details see Input Reference and How to start an exciting calculation.
Be sure to set the correct path for the exciting root directory (indicated in this example by $EXCITINGROOT). This can be done using the following line command. $ SETUP-excitingroot.sh
##### ii) Running a groundstate calculation
Start the calculation by invoking the exciting executable (serial version) in background.
##### Output files
While the calculation is running you can check the info file for the excited states (INFOXS.OUT) and the terminal output file (outputXS.txt). Once the calculation is finished, a bunch of output files (see TDDFT output files) will be present. Most of them containing a _QMTxxx label. This stands for Q momentum transfer and corresponds to the label xxx of the Q-points listed in the QPOINTS.OUT file. For our Q=0 case we will only have files containing a _QMT001 label.
We will concentrate on the LOSS_* files and pick the XML output file LOSS_FXCRPA_OC11_QMT001.OUT.xml. This file contains the data for the loss function and the dynamical structure factor. Get familiar with the details on the output files described in TDDFT output files.
### 3. Visualizing the output
From the XML data file for the loss function, we can generate the files PLOT.ps and PLOT.png typing the following command inside the directory silver_tddft.
$PLOT-loss-function.py LOSS_FXCRPA_OC11_QMT001.OUT.xml As you can see, we are executing the PLOT-loss-function.py script with one online entry which is the name of an xml output file. You can add as many files in the command line as you like and the script will add the corresponding curves to the same plot. For example, to make a comparison between the loss function with and without local field effects included, we can run the following command to generate a plot containing both loss functions. $ PLOT-loss-function.py LOSS_FXCRPA_OC11_QMT001.OUT.xml LOSS_NLF_FXCRPA_OC11_QMT001.OUT.xml
In the figure below, thick lines show the result for a converged 30$\times$30$\times$30 k-mesh. Also shown is the result for the coarser mesh from the input above (thin lines). As you can see, the results for the coarser grid resemble the main features although it is not as smooth.
In the figure above, the labels LFE and no-LFE indicate calculation performed including and excluding local-field effects. One immediate conclusion from the result above is about the importance of the local field effects in the high energy range, especially in the range above 35 eV. They drastically reduce the oscillator strength. At higher energies, more localized states contribute to the determination of the dielectric response, so the loss function is more sensitive to the inclusion of LFE in this part of the spectrum [see, e.g. Phys. Rev. Lett. 88, 037601 (2002)].
### 4. Converging the results
Before starting a series of calculations to investigate the momentum-dependence of different optical quantities it is necessary to find a proper set of parameters leading to reliable results. The choice of the parameters listed below is crucial for the accuracy of the calculation.
• ngridk: The quality of the spectra depends on the size of the k-mesh. A denser k-mesh results in a better resolution of the spectrum. Thus, always check for convergence with respect to the number of k points.
• swidth: In particular for metals, the convergence test with respect to the smearing width swidth must go hand in hand with that of ngridk. The swidth parameter is necessary to smooth the convergence of the self-consistent DFT loop.
• rgkmax: It determines the size of the basis set and, therefore, influences the quality of the eigenvalues. Be careful when increasing it, since the computational time rises rapidly.
• nempty: It determines the number of empty states considered in the calculation and depends on the energy range of interest.
• gqmax: Local-field effects G-cutoff. If set to zero, local-field effects are neglected.
### 5. Try a different kernel
Alternatively, the loss function can be calculated using the adiabatic LDA (ALDA) exchange-correlation (xc) kernel, being the simplest non-trivial xc kernel based on an LDA potential for the time-dependent case. The approximation ALDA consists in calculating the xc potential by taking the static xc potential evaluated at the time-dependent density. Such a calculation can be performed from scratch or on top of the latter one by changing the fxctype attribute in the element tddft.
...
<tddft ... fxctype="ALDA" ... >
...
Moreover, the Kohn-Sham response function and the matrix elements do not have to be recalculated upon a change in the xc kernel. This can be avoided setting the do attribute to fromkernel inside the tddft element.
...
<tddft ... do="fromkernel" ...>
...
After doing these small changes to the input.xml file, lets run exciting again.
$excitingser >& outputXS.txt & Plots can be generated from the LOSS*.xml files using PLOT-loss-function.py, as discussed for the RPA case, with the following command $ PLOT-loss-function.py LOSS_FXCRPA_OC11_QMT001.OUT.xml LOSS_FXCALDA_OC11_QMT001.OUT.xml
Here both results, from the RPA and the ALDA, are compared for a converged 30$\times$30$\times$30 k-mesh.
### Literature
• Tutorial talk by Stefan Sagmeister (PDF)
• Further information on the momentum-dependent loss function of Ag: A. Alkauskas, S. Schneider, S. Sagmeister, C. Ambrosch-Draxl, and C. Hèbert, Theoretical analysis of the momentum-dependent loss function of bulk Ag, Ultramicroscopy 110, 1081 (2010) (PDF)
• More details on the implementation of the TDDFT formalism within the LAPW method: S. Sagmeister, PhD thesis, University of Graz, August 2009 (PDF)
|
TheInfoList
In the elementary
differential geometry of curves Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthe ...
in
three dimensions Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the t ...
, the torsion of a
curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that app ...
measures how sharply it is twisting out of the plane of curvature. Taken together, the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonica ...
and the torsion of a space curve are analogous to the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonica ...
of a plane curve. For example, they are coefficients in the system of
differential equation In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the diffe ...
s for the given by the
Frenet–Serret formulas spanned by T and N In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a continuous, differentiable curve in three-dimensional Euclidean space ℝ3, or the geometric properties of the ...
.
# Definition
Let be a
space curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that app ...
parametrized by
arc length Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment is also called of a curve. The advent of infinitesimal calculus led to a general formula that provides closed-form solu ...
and with the
unit tangent vector Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (album ...
. If the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonica ...
of at a certain point is not zero then the
principal normal vector Principal may refer to: Title or rank * Principal (academia), the chief executive of a university ** Principal (education), the head teacher of a primary or secondary school * Principal (civil service) or principal officer, the senior management ...
and the binormal vector at that point are the unit vectors : $\mathbf=\frac, \quad \mathbf=\mathbf\times\mathbf,$ where the prime denotes the derivative of the vector with respect to the parameter . The torsion measures the speed of rotation of the binormal vector at the given point. It is found from the equation : $\mathbf\text{'} = -\tau\mathbf.$ which means : $\tau = -\mathbf\cdot\mathbf\text{'}.$ ''Remark'': The derivative of the binormal vector is perpendicular to both the binormal and the tangent, hence it has to be proportional to the principal normal vector. The negative sign is simply a matter of convention: it is a byproduct of the historical development of the subject. Geometric relevance: The torsion measures the turnaround of the binormal vector. The larger the torsion is, the faster the binormal vector rotates around the axis given by the tangent vector (see graphical illustrations). In the animated figure the rotation of the binormal vector is clearly visible at the peaks of the torsion function.
# Properties
* A plane curve with non-vanishing curvature has zero torsion at all points. Conversely, if the torsion of a regular curve with non-vanishing curvature is identically zero, then this curve belongs to a fixed plane. * The curvature and the torsion of a
helix The right-handed helix (cos ''t'', sin ''t'', ''t'') from ''t'' = 0 to 4π with arrowheads showing direction of increasing ''t'' A helix (), plural helixes or helices (), is a shape like a corkscrew or spiral staircase. It is a type of smooth spac ...
are constant. Conversely, any space curve whose curvature and torsion are both constant and non-zero is a helix. The torsion is positive for a right-handedhttp://mathworld.wolfram.com/Torsion.html helix and is negative for a left-handed one.
# Alternative description
Let be the
parametric equation In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric objec ...
of a space curve. Assume that this is a regular parametrization and that the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonica ...
of the curve does not vanish. Analytically, is a three times differentiable
function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriented ...
of with values in and the vectors : $\mathbf\left(t\right), \mathbf\left(t\right)$ are
linearly independent In the theory of vector spaces, a set of vectors is said to be if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be ...
. Then the torsion can be computed from the following formula: :$\tau = \frac = \frac .$ Here the primes denote the
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For ...
s with respect to and the cross denotes the
cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in three-dimensional space \mathbb^3, and is denoted by the symbol \times. Given ...
. For , the formula in components is : $\tau = \frac.$
# References
* {{curvature Differential geometry Curves Curvature (mathematics) ru:Дифференциальная геометрия кривых#Кручение
|
# Unable to rotate GameObject properly?
My GameObject is able to jump towards a moving target (another GameObject), thus adjusting its trajectory - while simulating gravity (as in the .gif).
I want to make the "jumper object" rotate. But I am unable to rotate my GameObject properly. When the GameObject jumps, it doesn't complete its rotation and rotates abruptely. How can I fix this? How can I properly rotate the cube GameObject you see in the .gif? Any fixes are appreciated.
Wanted rotation:
What I get:
• Image is not available for me. But i guess GetMouseButtonUp couses problems. Try GetMouseButton instead. So your object will turn constantly while you press button, not only when you relase it. – S. Tarık Çetin Nov 13 '15 at 20:12
• Image now available. – That's me. Nov 13 '15 at 20:13
• "don't cooperate very well" is super vague. tell us what is happening – jhocking Nov 13 '15 at 20:26
• Question edited. – That's me. Nov 13 '15 at 20:29
• @TheGameChanger I guess what you want to do is making cube to look forward vector of it's current position on trajectory right? As far as i can see, you already calculate velocity vector in your jumpAndFollow method. Then you can simply use this: transform.LookAt(transform.position + velocityVector.normalized); This will make your gameObject's +z axis to line on the vector you give in paranthesis. – S. Tarık Çetin Nov 13 '15 at 20:36
The code structure you want:
transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, lerpFactor);
Change the line
transform.Rotate (new Vector3 (a, b, c) * Time.deltaTime);
with
transform.rotation = Quaternion.Slerp(transform.rotation, Quaternion.Euler(a, b, c), Time.deltaTime);
Also,
void Update()
{
if(Input.GetMouseButtonUp(0))
{
//this is only called when button gets relased.
}
if (Input.GetMouseButton (0))
{
//this is called constantly if button is holding down.
}
}
Edit:
This code piece should do what you want:
Quaternion targetRot = Quaternion.identity; //try not to modify this directly, or do it, it's up to you.
bool doRotate = false;
float lerpLimit = 10; //the degrees you want lerp to stop at. set higher than 0 (i suggest higher than 1)
public void SetRotationTarget(Vector3 eulerAngles) //call this method to update the rotation target.
{
targetRot = Quaternion.Euler (eulerAngles); //building a quaternion from given vector3
doRotate = true;
}
void Update()
{
if (doRotate)
{
if (Quaternion.Angle(transform.rotation, targetRot) > lerpLimit) //if angle between our rotation and target rotation is not below limit
{
transform.rotation = Quaternion.Slerp (transform.rotation, targetRot, Time.deltaTime); //Slerp to target rotation
}
else
{
transform.rotation = targetRot;
doRotate = false;
}
}
if(Input.GetMouseButtonUp(0)) //when mouse button 0 is relased
{
SetRotationTarget(new Vector3(a, b, c)); //set new rotation target with values of (a, b, c)
}
}
• It doesn't lerp! Same problem. Exactly. – That's me. Nov 13 '15 at 21:08
• @TheGameChanger Take a look at the edit. – S. Tarık Çetin Nov 13 '15 at 21:14
• Let's say I have transform.Rotate (new Vector3 (0, 0, 180) * Time.deltaTime); How do I convert it with your most recent edit? Where do I put the numbers? – That's me. Nov 13 '15 at 21:23
• Just write an example with numbers in your answer. (or a, b, c) – That's me. Nov 13 '15 at 21:23
• @TheGameChanger Revised the edit. – S. Tarık Çetin Nov 13 '15 at 21:38
|
## Calculus 8th Edition
Published by Cengage
# Chapter 14 - Partial Derivatives - Review - Exercises - Page 1024: 62
#### Answer
Minimum value of $f(x,y,z)=x^2+2y^2+3z^2$ is $\dfrac{33}{23}$.
#### Work Step by Step
$f(x,y,z)=x^2+2y^2+3z^2$; $x+y+z=1$;$x-y+2z=2$ $x=\frac{18}{23}$ $y=-\frac{6}{23}$ $z=\frac{11}{23}$ Minimum value of $f(x,y,z)=x^2+2y^2+3z^2$ is $(\frac{18}{23})^2+2(-\frac{6}{23})^2+3(\frac{11}{23})^2=\frac{33}{23}$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
|
# Implementing microcontrollers (AT89C51-24PC)
1. Oct 7, 2012
### Packocrayons
I'm planning on learning how to use microcontrollers (ATmega series) so that I can use the skill for various other projects.
I already know how to use arduino (which use the ATmega series of microcontrollers) and I feel as though this will only be an extension, since the coding will be the same.
What is required circuitry wise in order to run this? I understand I likely need to have a 5V regulator and peripherals in order to power the logic, but what else?
Do I need to add some sort of flash memory? What about SRAM?
Is programming as easy as hooking up the right pins to a USB cord and flashing to the chip (using which program, will the standard arduino program work for this?).
2. Oct 7, 2012
### vk6kro
There is a big difference between programming an Arduino in a C/C+ language and programming an Atmega in machine code.
So, if you want the convenience of the high level language, you should stick to the Arduino.
I often use Picaxe chips because they can be placed in normal circuits like any other IC, perhaps unlike the Arduino which requires a relatively expensive circuit module. Picaxe chips start at about $3. 3. Oct 7, 2012 ### Packocrayons What do you mean by machine code? I'd like to learn and be able to expand my horizons, withing reasonable difficulty. I don't like the picaxe flow chart system, it's too easy. 4. Oct 8, 2012 ### vk6kro Actually I should have said Assembler code. Here is an introduction to Assembler for an Atmega: http://www.avr-asm-download.de/beginner_en.pdf Don't knock Picaxe, at least on the grounds of being too easy. Easy is good. You don't have to use the "kiddy" flow charts. Real programming is done in a type of Basic which is heavily laced with I/O commands. It can be challenging enough if you try to get serious about programming. I have a friend who wanted to read a pot voltage and convert the result to Pulse Width Modulation to control a motor. A hardware solution to this was going to be very complex while a Picaxe did it in about 4 lines of code. Have a look here: http://www.picaxe.com/ http://www.picaxe.com/Getting-Started/PICAXE-Manuals 5. Oct 8, 2012 ### Packocrayons Well I am still 16 so maybe I should go for the kiddy programming :p The main reason I'm moving away from arduino is because I want more of a challenge, as well as the ability to expand by using different micros. I guess picaxe it is, it seems both languages are reasonably similar so I won't be losing anything. Thanks for the help. 6. Oct 8, 2012 ### vk6kro Each Picaxe chip can do a large number of useful tricks and it is worth knowing about them so you can use them if you need to. There are "programming kits" available but these tend to be overpriced and you can make a programming cable yourself for a few dollars or less if you have an old serial mouse you don't want. I like the freedom of buying a cheap powerful chip I can just plug into a socket and use instead of having to buy a module (like Arduino or Stamp) which costs a lot more and is much more bulky. If you want to get started, go for a larger Picaxe chip like the Picaxe 20X2. The 20 means it has 20 pins but it looks like any other DIP chip. 7. Oct 9, 2012 ### Packocrayons I was planning on going with the 28 something one (forget the name). What do I need to make the programming cable so that I can get it on the same order? 8. Oct 9, 2012 ### vk6kro There are several 28 pin Picaxes and some of them are nearly 10 years old now. The important bit is the end part of the type number. Look for an X or an M. These are more recent. They have more memory and can operate at faster speeds than the older ones. Download the manuals from the link above. http://www.picaxe.com/Getting-Started/PICAXE-Manuals The first one gives the programming cable details. It is just two resistors and a serial port plug. It also gives the pinouts of the various chips. 9. Oct 21, 2012 ### Packocrayons Okay so I have it (I actually ended up with 2 20M2's) and I'd like to start programming as soon as possible. I'm planning on making my own cable from a USB port. What is the pinout and/or wire color of a standard USB port on a computer? I don't have the right connectors on my laptop as depicted in the manual, and it never says anything about USB ports as far as I know. 10. Oct 21, 2012 ### vk6kro If you don't have a serial port on your laptop, you will need a USB to serial adapter. You can't directly connect the USB port to the Picaxe input. However, not all such adapters will work for programming a Picaxe chip. You need to get one which is assured to work for Picaxe programming. You could have a look on the Picaxe Forum to get a type of adapter that works OK. This comes up as a topic quite often and you should find one easily. Ebay has them for$1 plus postage, but they may not work.
Alternatively, you can get a USB cable from Rev-Ed in England. It is type AXE027 and sells for about 10 pounds (British).
Other distributors sell these too.
Just about any old PC is OK for this job so you could consider using an older computer just for programming. Even very old laptops had a serial port on them.
11. Oct 21, 2012
### Packocrayons
Alright, I guess I'll have to pull out the dinosaur and use it. It's only 13, it can handle it :p.
What about building the adapter? I do have one built for programming brushless motor controllers, I'm assuming it'll be different?
12. Oct 21, 2012
### vk6kro
The programming board for a Picaxe is so simple, it is easy to just include the couple of resistors on each project board.
You can buy programming boards, but they tend to be expensive. Putting a socket on a bit of circuit board with pre-etched tracks is pretty easy and there are lots of such boards available.
If you can find it, this type would be OK:
You may have an old serial mouse you don't want any more. Like the old ball type. You can use the cable from that.
Just trace the wires with a multimeter on "ohms".
Using a serial port is very simple and avoids the problems some people seem to have with USB ports, so it is good to, at least, start with a serial port.
Last edited by a moderator: May 6, 2017
13. Oct 22, 2012
### Packocrayons
I'll crank out an old computer then and start with the serial port. Once I get it working and want to be able to flash more often I'll start working on a USB to serial.
14. Oct 22, 2012
### vk6kro
Yes, that would be a good choice. You could just leave it set up while you test the various commands from the Picaxe manual.
http://www.picaxe.com/Software
I suggest you print out the pinout diagram for the 20M so that you can refer to it easily.
A useful setup would have a couple of LEDs (with series resistors) a switch, a pot and (because the 20 M can produce music) a sound transducer.
This would let you test various input and output commands. You will find these very well documented in the second manual with liberal use of examples to explain the command structures.
This is a very powerful chip and it should keep you amused for a while.
15. Oct 23, 2012
### Packocrayons
I plan on being very amused. Maybe next I'll build a little ipod with flash memory with an 08M2.
I'll make a book with the cover page being the pinouts and print out the manual on paper for quick reference.
16. Oct 23, 2012
### vk6kro
OK. Maybe try to turn a LED on and off before you make an iPod?
The Programming Editor has a pull down syntax help thing which is useful when you want a quick clue like where to put the brackets, etc.
But a printed version would be nice, if a bit bulky.
17. Oct 23, 2012
### Packocrayons
Yeah I'll start slow. I'll learn quickly once I get started because of my experience with arduino.
Old laptop is not working, so I'm going to have to jump right into the usb to serial. Wheres the best place to get started?
18. Oct 23, 2012
### vk6kro
I did notice this on Sparkfun:
https://www.sparkfun.com/products/9260
Seems promising. You have to install some drivers and it then seems like a com port to your laptop.
|
# Question d03c9
Jan 31, 2015
$\text{55.4 g}$
#### Explanation:
Every time you have to solve problems in which you are asked to determine how much of something is needed to react with a given mass of something else, you must think moles and, more specifically, mole ratios.
$2 K I \left(a q\right) + P b {\left(N {O}_{3}\right)}_{2} \left(a q\right) \to P b {I}_{2} \left(s\right) + 2 K N {O}_{3} \left(a q\right)$
This is a double replacement reaction that leads to the formation of an insoluble precipitate, $P b {I}_{2}$.
Notice the mole ratio between $K I$ and $P b {\left(N {O}_{3}\right)}_{2}$: $\text{2 moles}$ of the former must react with $\text{1 mole}$ of the latter in order for the reaction to take place.
Use the molar masses of the compounds to go from grams to moles (for $K I$) and from moles to grams (for $P b {\left(N {O}_{3}\right)}_{2}$):
55.2 cancel("g") * ("1 mole")/(331.2 cancel("g")) = "0.167 moles" $P b {\left(N {O}_{3}\right)}_{2}$
This means that you need
0.167 cancel("moles"color(white)(a) Pb(NO_3)_2) * ("2 moles " KI)/(1 cancel("mole"color(white)(a) Pb(NO_3)_2)) = "0.334 moles"color(white)(a) KI
The mass will be
0.334 cancel("moles") * ("166 g")/(1 cancel("mole")) = "55.4 g"color(white)(a) KI#
Here $\text{166 g}$ represents the mass of one mole of potassium iodide. This values comes from potassium iodide's molar mass, which is listed at approximately $\text{166 g /mol}$.
As a conclusion, always go to moles, it'll make your life easier, and remember to use mole ratios.
Here's a video of the reaction, if you're curios about what the precipitate looks like:
|
Achievability of the Rate \${1-2}log1 es\$ in the Discrete-Time Poisson Channel - Computer Science > Information Theory
Achievability of the Rate \${1-2}log1 es\$ in the Discrete-Time Poisson Channel - Computer Science > Information Theory - Download this document for free, or read online. Document in PDF available to download.
Abstract: A simple lower bound to the capacity of the discrete-time Poisson channelwith average energy \$\es\$ is derived. The rate \${1-2}\log1+\es\$ is shown tobe the generalized mutual information of a modified minimum-distance decoder,when the input follows a gamma distribution of parameter 1-2 and mean \$\es\$.
Author: Alfonso Martinez
Source: https://arxiv.org/
|
# Thread: Finding an appropriate sample size?
1. ## Finding an appropriate sample size?
Hi, I'd really like some help on the following issue - I've been searching the internet for over two hours now, so I'm either completely oblivious to something really obvious, or maybe I'm looking for the wrong thing?
I'm completing an assignment for my research design class, and I'm being asked to find the appropriate number of participants for a study, given an effect size of one, if I wanted to have a power of .95 in a between-subjects experiment
I know the purpose of this question is to get me to recognize the trends between effect size and number of participants, but I can't find a formula anywhere!
Thanks so much for your help!
2. ## Re: Finding an appropriate sample size?
Originally Posted by breepi
Hi, I'd really like some help on the following issue - I've been searching the internet for over two hours now, so I'm either completely oblivious to something really obvious, or maybe I'm looking for the wrong thing?
I'm completing an assignment for my research design class, and I'm being asked to find the appropriate number of participants for a study, given an effect size of one, if I wanted to have a power of .95 in a between-subjects experiment
I know the purpose of this question is to get me to recognize the trends between effect size and number of participants, but I can't find a formula anywhere!
Thanks so much for your help!
Hi breepi!
Here's a picture.
The top distribution represents your H0 hypthothesis.
The bottom distribution represents your H1 hypothesis.
With your effect size, I presume you mean a Cohen's d?
If that is the case, the picture represents your problem properly: the 2 mountains are apart by a distance which is the standard deviation.
To get a power of 95%, your beta must be 5%.
You would also have an alpha of 5%.
To get alpha and beta both 5%, your need mountains that are narrower - so narrow that the situation becomes symmetric.
It means that the area where alpha begins needs to be 1.96 SE from the mean of the left mountain.
And it also means that the area where beta ends needs to bee 1.96 SE from the mean of the right mountain.
In other words, the distance of the mountains (which is sigma), needs to be 2 x 1.96 SE.
In an equation:
$\sigma = 2 \times 1.96 SE = 2 \times 1.96 \frac {\sigma}{\sqrt n}$
Can you solve that for n?
|
## FANDOM
4,127 Pages
Non-VIP Forever! came up with a very interesting approach to the question:
Can we deduce the distribution of 3, 5 and 8 Coins from TLE results if we only have the number of Coin Packs and the number of Coins they granted?
The proposed solution was: Each Coin Pack grants at least 3 Coins, so we can multiply the number of Packs with 3 and subtract this from the total number of Coins. The remaining number has to be a combination of 5 or 8 Coins.
If this method always leads to one single solution, i. e. if there is only one possible combination of 3, 5 or 8 Coins that leads to the total, we will be able to generally add TLE results to the statistics database. In the three provided examples, the conjecture holds.[1][2]
Vice versa, if there was a sum of Coins that can be build by more than one combinations of 3, 5 or 8 Coins, the method would be too much prone to errors. Especially when there are greater amounts of Coins, the calculating person may overlook a possible other combination.
## Counterexamples
Unfortunately, while fiddling around with some numbers, I already found two examples with more than one possible solutions.
1a 1b
3 Coins 0 3
5 Coins 5 0
8 Coins 0 2
Sum Packs 5 5
Sum Coins 25 25
2a 2b
3 Coins 2 5
5 Coins 5 0
8 Coins 0 2
Sum Packs 7 7
Sum Coins 31 31
• 25 Coins from 5 Packs can be a result of $5 \cdot 5$ Coins (column 1a) or $3 \cdot 3 + 8 \cdot 2$ Coins (column 1b).
• Another example where both solutions contain 3-Coin results would be 31 Coins from 7 Packs which can be a result of $3 \cdot 2 + 5 \cdot 5$ Coins (column 2a) or $3 \cdot 5 + 8 \cdot 2$ Coins (column 2b).
So after thinking about it, I will not include data from TLEs as it is quite time-consuming to verify if the calculations are correct.
## Formal approach
But I was interested in a more formal solution. Generally, the task is to find if there is more than one solution for
1. the same sum of Coins which is represented by $3a + 5b + 8c$
2. with the same number of Coin Packs wich is which is $a + b + c$.
More precisely, are there any $a, b, c \in \N$ and $x, y, z \in \N$ where at least $a \ne x$, $b \ne y$ or $c \ne z$ that are a solution to the following equation system?
$3a + 5b + 8c = 3x + 5y + 8z$
$a + b + c = x + y + z$
As I was lazy, I had a look at the first case of column 1a that had 25 Coins from five 5-Coin results and no 3-Coin or 8-Coin results at all. I generalized this to all results made up of only 5-Coin results $b$ with no 3-Coin or 8 Coin results, that is, I set $a = 0$ and $c = 0$ which makes the equation system easier to handle:
$5b = 3x + 5y + 8z$
$b = x + y + z$
Solving the first equation for $b$ delivers
$b = \tfrac35x + y + \tfrac85z$
$b = x + y + z$.
By equating the right hand sides of the equations, we obtain
$\tfrac35x + y + \tfrac85z = x + y + z$
$\iff \tfrac35z - \tfrac25x = 0$
$\iff \tfrac25x = \tfrac35z$
$\iff x = 1.5z$.
As both $x, z \in \N$ (both have to be integers; there can be no "1.5 times 8 Coins"), the least possible solution is
$x = 3, z= 2$.
3a 3b
3 Coins 0 6
5 Coins 10 0
8 Coins 0 4
Sum Packs 10 10
Sum Coins 50 50
This means that any number of 8-Coin results $z$ where the number of 3-Coin results $x = 1.5z$ is an integer delivers a number of Coins that can also be achieved by adding 5-Coin results the same number of times (see column 3a and 3b to the right for an example).
Other Coin combinations could basically be solved with the same equation system but would require more complex calculations if all $a, b, c$ are involved.
## References
1. Non-VIP Forever! (2020-02-14). User comment. Asphalt Wiki. Retrieved on 2020-02-18.
2. Non-VIP Forever! (2020-02-17). User comment. Asphalt Wiki. Retrieved on 2020-02-18.
Community content is available under CC-BY-SA unless otherwise noted.
|
# Data science Methodology to Forecast Time Series – Part 2
9 mars 2018
Following the Part 1, we will guide you now through a real world use case which the energy consumption in France using our methodology to deal with data science problems. Please note that for any question you may come up with in the course of this article, we will be happy to reply through our [email protected].
For this purpose we collected data from RTE, the French’s electricity transmission operator. They launched a challenge on www.datascience.net in order to forecast the daily power consumption in France. In the following paragraphs we will present the different steps which are required in order to implement a well suited model. Let us note that we will also take advantage of this opportunity to highlight the many challenges we may face face throughout time series analysis.
## 1. Description of the data
The data is composed of a set of columns including informations from the date and the time when the data was collected to the individual repartition of the consumption across different energy types. Additionally we can note that:
Time slot between valid observations is 30 minutes
The national and regional French’s power consumption data is available from the RTE eco2mix portal http://www.rte-france.com/fr/eco2mix/eco2mix-telechargement .
### 1.1. Performance score
For each forecasted day, we will use the Mean Absolute Percentage Error (MAPE) to determine the exactitude of our predictions. It is defined by:
$$MAPE=\frac{100\%}{n}\times\sum_{i=1}^n \frac{|C_i-C_i^*|}{Ci}$$
Being $$C_i$$ the actual consumption, $$C_i^*$$ the forecasted value, and $$n$$ the number of forecasted points.
### 1.2. Goal definition
As we intend to give a detailed approach and understanding of the problem, we fixed ourselves the following objective: forecast one day of power consumption, namely 48 predictions ahead of current data.
### 1.3. Technical information
#### 1.3.1. Development platform
Axionable’s core data science team always works on a Jupyter Notebooks with the version 3 of Python for developing and test purposes. Afterwards a production code can be made according to the client’s technology or architecture.
In the following image, we are presenting our working directory for this project.
#### 1.3.2. Hardware specifications
We initially started developing this part of the project according to our methodology by performing the data exploration and data cleaning in a personal computer. However when we started modeling and optimizing parameters, we were quickly limited by the important delays of computing due to the high granularity of the data (more than 87000 valid observations). In fact as we wanted to use the whole dataset to train our model, there was an enormous quantity of computations that had to be done on memory which tends to slow down all processes.
Later after getting more accustomed to the context, we arrived at a critical point where we started questioning the necessity to use the whole dataset: Is it really relevant using this huge amount of information in order to forecast only a day of power consumption ? That question will be answered later.
In this context, let us list the to hardware specifications that we used:
• Personal computer
• Model: Macbook Pro
• RAM: 8GB
• Processing: 2 core at 2,6 GHz
• Cloud Computing:
• VM: AWS m4.4large
• RAM: 64GB
• Processing: 16 cores at 2.4 GHz
## 2. Data importing and data cleaning
The data source is stored in the “./data” folder and it’s composed of many Excel files, each file containing the information of a whole year. Here is a glimpse of the operation that we are going to perform:
• Load data into a Pandas DataFrame
• Format the names of the DataFrame’s columns
• Filter null data
• Create a datetime index
### 2.1. Load data into dataframe
As we aim to have our code to be production-ready, we implemented a loop in order to read automatically all the excel files contained in the “./data” folder. In that way we are not worried about reading individual files nor appending them in a single DataFrame.
directory = "data"
df_data = pandas.DataFrame()
for filename in os.listdir(directory):
if filename.endswith(".xlsx"):
excel_file = "{}/{}".format(directory, filename)
print("Appending file '{}'".format(excel_file))
2.2. Format the names of the DataFrame's columns
It is recommended to format the column names of Excel tables to remove spaces and special characters as it is the case for most french documents. Moreover, having no space nor special characters allows us to utilize the python autocompletion feature.
from unidecode import unidecode
# Format column names
def change_column_name(name):
name = re.sub(r"(\.|°)", "", name) # Changer les spaces par ""
name = unidecode(name) # Supprimer les caractères spéciaux name = re.sub(r"\s+", " ", name)
name = name.lower() # Passer les noms en minuscule
name = re.sub(r"(\s|-)", "_", name) # Changer les espaces tirets par ""
return name
df_data.columns = [change_column_name(_) for _ in df_data.columns]
df_data.head()
For the cleaning step, we would rather use the regex library instead of the standard Python string functions. As a matter of fact it enables us to create very powerful regular expressions in order to format strings, even if it is sometimes slower than the standard functions.
### 2.3. Filter null data
As explained in the introduction, we will only focus on univariate time-series forecasting. Consequently we are not considering the other variables such as fioul, charbon, gaz, etc. Besides, we notice that a 15 minutes time slot frame is observed in the data frame, having “NaN” values every 30 minutes (or every two rows/observations).
In this context, we will remove the null informations and take only the France perimeter:
target_columns = ["perimeter", "nature", "date", "hour", "consumption"]
df_data = df_data[target_columns]
# Take only France perimeter
idx_france = df_data.perimetre == "France"
df_data = df_data[idx_france]
# Filter the NaN values
idx_nans = df_data.consumption != df_data.consumption
df_data[idx_nans]
A nice trick to check whether there are the NaN values in a DataFrame is the use of the equality operator. Indeed in a pandas’ Series auto comparison, we can obtain False only when we are comparing null values.
### 2.4. Create a datetime index
To have a valid datetime at a minute granularity, we need to combine the “date” and “heures” columns. An index sort is also applied in order to avoid plotting problems.
def create_index(row):
new_date = datetime.combine(row.date, row.heures)
return new_date
df_data["temps"] = df_data.apply(create_index, axis=1)
df_data.set_index("temps", inplace=True)
df_data.sort_index(inplace=True)
3. Data exploration
Once we consider our data as cleaned, we should proceed to the data exploration phase which aims at answering at least the following questions:
• Is there any trend and/or seasonality on the TS?
• Do we need to do further data cleaning?
• Sometimes, plotting the data helps to detect other problems in data like outliers, human errors in the data input, etc.
• Do we need to do data aggregation?
• Is the data coherent to reality?
• This is a very crucial step in a data science problem. Our analysis and results must conform with the reality.
As you can imagine, we will plot the data at different time granularities in order to detect some behaviors like trend or seasonality. At Axionable, we prefer using the plotly library to make our plots interactive. In addition let us mention that we are accustomed to create functions for every automatisable action to improve the code readability. Moreover those functions may be used in another context without the need of redeveloping them from scratch.
Down here is the first plotting function to draw a time series given the data points and some basic properties.
def plot_time_serie(s, title=None, width=950, height=400):
"""Plot a time-series
The input data must be an pandas.Series
"""
go.Scatter(
x=s.index,
y=s.values
)
)
layout = go.Layout(
title=title,
showlegend=False,
width=width,
height=height
)
iplot(fig)
return None
### 3.1. Plot interactive time series using Plot-ly
Here, we will plot the whole historical data and hopefully determine at first glance key indicator for the next modeling phase.
# Plot TS at 30' granularity
plot_time_serie(df_data.consumption, title="Power consumption from 2012 to 2016 @30' granularity")
Considering this plot, we can infer that:
There is a clear yearly seasonality summed with a trend in the data. To add up if we zoom in, we may also see that this tendency is coupled with a weekly and daily seasonality. Those remarks make up the main problem that we faced: the SARIMA model that we will use for modeling takes into account only one parameter of seasonality which calls out a major question: Which seasonality is the most suited for our objective ?
It would be interesting to see if there are some commun consumption behaviours at a week/year/day level and to corroborate it to the reality. For instance, we should find less energy consumption in the holidays season.
### 3.2. Plot seasonality and trend profiles at different granularities
How can we determine the evolution profile of a selected season in a time series ?
The Box-Plots are really useful in giving a fast insight of data trend at different levels of granularity.
We are defining below a function that directly plots the box-plots from a DataFrame by indicating the target and labels of a set of box-plots.
def plot_box_plot(df, target, granularity_level, title=None):
list_labels = df[granularity_level].unique()
for label_name in list_labels:
idx_label = df[granularity_level] == label_name
go.Box(
y=df[target][idx_label],
boxmean=True,
boxpoints='all',
name=label_name
)
)
layout = go.Layout(
title = title
)
iplot(fig)
return None
First of all, we will plot weekly consumption and analyse it. For this purpose data aggregation at day granularity is naturally required which is the reason why we are grouping the data using the pandas’ groupby function.
# Create dataframe at day granularity
df_day = pandas.DataFrame(df_jour)
df_day = df_day[df_day.index > "2012-01-01"]
df_day["consumption_week"] = (df_day
.groupby("week")["consumption"]
.transform(sum))
df_day["week_weight"] = df_day.consumption / df_day.consumption_week
df_day["week_weight"] *= 100
df_day["day_name"] = df_day.index.map(lambda x: x.strftime("%A"))
plot_box_plot(df_day, "week_weight", "day_name", title="Weekly power consumption profile")
This plot can be read from 2 different perspectives. As a matter of fact if we consider the whole figure, we can assume that the the overall energy consumption is greater on working days in comparison to the weekends. On the other hand the boxplots taken independently show that daily consumptions don’t vary a lot from a week to another (less than 1% difference between the first and the third third quartiles).
In the same way, we proceed to plot the yearly and daily profile…
The plots above play a significant role in our understanding of the problem and helped us jump into the following conclusions:
The power consumption lowens during summer holidays, and that tendency is confirmed over the 5 years of historical data.
The peaks in energy consumption of the daily profile is highly correlated with the lunch and dinner French times.
There seems to be weekly and daily profiles which could have been very useful if we had missing values in our dataset.
Furthermore had there been missing values, it would have been a well suited method imputing them according to the profiles seen above.
From now, this dataset being inline with the reality, we may assert that no more data cleaning is needed. Also considering the objective we define in combination with the insights that we got from the exploration part, we may assert that a daily seasonality is more appropriate (explicitly every 48 observations).
## 4. Modeling – Choosing our prediction model
Reassured by all the work done in the previous stage, particularly the box-plots which highlighted the seasonal effects as well as a clear trend, we decided to opt for a SARIMA model. However, we can only apply this model to a time series (TS) which is stationary.
The next paragraphs will discuss about how with deal with non stationarity in practice as well as the core of the modeling part which the parameters’ optimization.
To fix up things, let’s keep in mind that the SARIMA model has 6 optimization parameters (p, d, q), (P, D, Q, S). We refer you back to our previous article to see the basic explanation of each of them and get a fresh recall of how to choose the optimal ones in some cases.
### 4.1. Pre selection of the SARIMA parameters
In line with our explanations, we will first infer the differentiation parameters d and D before starting the modelisation.
In that regard, we can implement a function that, for given d and D values, will plot the new TS and its corresponding ACF and PACF plots.
In practice, we look for the following patterns:
• The ACF and the PACF plot should both be decreasing rapidly towards 0 (exponentially or in a sinusoidal manner)
• A significant spike at a certain lag of the ACF without any other repetition after that phenomenon (it gives us a hint over what could be the value of the parameter q)
• A significant spike at a certain lag of the PACF without any other repetition after that phenomenon (it indicates an ideal value of the parameter p).
Followingly, we will choose an order of the values which make the new TS stationary.
Above is the code chunk which we developed to automate the plot of the TS at different lags. We derived from them that the best parameters were 1 and 2 for respectively d and D.
def plot_acf_pacf(s, nb_lags, d=0, D=0, seasonality=0):
"""
Plot the ACF and PACF functions, after differentiating steps
"""
# Changing the default color palette
cl.scales["3"].keys()
col = cl.scales["3"]["qual"]["Paired"]
# Apply the differencing steps, if necessary
if D > 0:
s_diff = s
for i in range(1, D+1):
s_diff = s_diff + pow(-1, i) * binom(D, i) * s.shift(i * seasonality)
s = s_diff[(D * seasonality):]
if d > 0:
s_diff = s
for i in range(1, d+1):
s_diff = s_diff + pow(-1, i) * binom(d, i) * s.shift(i)
s = s_diff[d:]
plot_ts_serie(s)
lag_acf = acf(s, nlags=nb_lags)
lag_pacf = pacf(s, nlags=nb_lags)
x_axis = [*range(nb_lags+2)]
plot_lag_curves(x=x_axis,
y=lag_acf,
title="Autocorrelation Function",
T=len(s))
plot_lag_curves(x=x_axis,
y=lag_pacf,
title="Partial Autocorrelation Function",
T=len(s))
return None
### 4.2. Hyper parameters
Now we can focus on the tuning of the other parameters (p, q, P, Q). Naturally it implies creating grids of possible values, implementing the corresponding models and evaluating them in order to choose the best one according to our metric (MAPE).
We are doing this by using GridSearchCV from the Scikit Learn module. It presents the advantage of allowing us to perform operations parallelly as well as validate the results through cross validation techniques.
Important note:
SARIMA not being part of the scikit learn module, we had to create a custom class calling our model in order for it to fit the standards of the GridSearchCV. This problematic appears also in the automation part of projects where Scikit Learn pipelines are often used for this regard.
We implemented the MAPE error function and added this function to our class to evaluate the performances.
The cross validation technique for time series is very different to the one which is done for most data science problems because of the sequential character of the time which has to be kept.
This marks the end of our modeling part, we now can turn to the evaluation of our model on real data. Inevitably it involves its comparison to values observed on a yearly basis. Having trained our model on the date range going from 01/01/2015 to 01/30/2015, we will now perform a forecast for the first day of february.
Below are the results observed for the forecast of the first day.
## 5. Conclusions
### 5.1. Data Science on a production environment
One of the key suggestions we can make is to always adapt solutions to the production environment. In many cases, the best performing model cannot be implemented because of processing/memory limitations or the delay it would take to fit it.
In our experience at Axionable, in order to choose the most appropriate model one should inevitably answer these questions:
• Scheduling
• At which frequency should we run our codes ?
• Production environment
• Do we need to do parallel processing ?
• What are the memory and computing limitations ?
• Scalability
• Will the input data increase over time ?
• Can we extend to a parallel processing our code, if any ?
• Do we need our code implementation to be implemented on a distributed way ?
We then need to do a tradeoff between these variables and choose the best suitable model for the target project.
## 5.2. Next steps
Part of modeling is the research of alternatives to solve a particular problem. In that regard we are listing above some steps that we could have done, but for simplicity purposes we chose not to tackle them for now.
Compare SARIMA with other forecasting methods, in the univariate domain:
• Exponential Smoothing
• Recurrent Neural Networks (LSTM)
• Extend SARIMA forecast by adding exogenous variables. That is to represent it like a Generalised Linear Model.
• As a long-term goal, make an article on the multivariate time series predictions.
3 août 2022
## Le top des lectures / audios de vacances de l’équipe Axionable :
Le top des lectures / audios de vacances de l’équipe Axionable : Comme chaque année, notre équipe vous a concocté sa liste de coups de cœur, à emporter dans vos valises ! Petite nouveauté pour cette fois-ci, on y a glissé quelques podcasts à écouter, en plus des traditionnelles recommandations lectures. Cet été, on vous […]
20 décembre 2021
## Le top 5 des lectures de vacances de l’équipe Axionable
Le top 5 des lectures de vacances de l’équipe Axionable : Découvrez la sélection de notre équipe, sérieuse ou divertissante, il y en a pour tous les gouts : développement durable, IA et technologies, science-fiction, grand classique, roman poétique, & bande dessinée… à dévorer au coin du feu ou à glisser sous le sapin : […]
1 décembre 2021
## Orano et ses partenaires lancent le projet Usines de Demain
Le groupe Orano et ses partenaires lancent un projet de développement intitulé udd@Orano (pour Usines De Demain sur les sites industriels d’Orano) en vue d’accélérer le déploiement de l’usine du futur au cœur des sites industriels du groupe. Coordonné par Orano, ce projet fédère 11 partenaires industriels durant une période de 36 mois : 6 […]
21 septembre 2021
## Assureurs : maîtrisez vos risques climatiques avec CatNat Predict !
Les événements climatiques du premier semestre 2021 ont causé près de 40 milliards de dollars de dommages assurés dans le monde (1). Aussi, le dernier rapport du GIEC est sans équivoque quant à l’intensification des phénomènes climatiques extrêmes. En France, la sécheresse est le risque qui inquiète le plus les assureurs avec des coûts annuels […]
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Contact
|
# DataTables: Hoping to load the first 10 records for the user while other records render in the background
31 views
### markw707
Jun 21, 2018, 6:29:59 PM6/21/18
to TACFUG
Hello. Not really a CF question per se. But I'm wondering if anyone knows how to load the first 10 records for the user while other records render in the background using DataTables. I've tried various things without luck. Here is the basic code. Thank you in advance for your help.
<!--- Table Definition --->
$(document).ready( function () {$('#example')
.DataTable( {
responsive: true,
order: [ 1, "desc" ],
columnDefs: [
{ targets: [-2, -3, -4, -5], className: 'dt-body-center' },
{ targets: [-1], className: 'dt-body-right' }
],
"oLanguage": {
"sSearch": "Filter: "
},
"iDisplayLength": 25
} );
});
<!--- Ajax Call --->
$(document).ready( function () { function showResult() {$.ajax({
url: "myFile.cfm",
method: "POST",
data:$('#Frm1').serialize(), success: function(result){$('#response').html(result);
}
});
}
});
The code works to ajax the recordset into the page and put it into the DataTable correctly, but it is slow if the recordset is huge.
Thank you!
### Jim Priest
Jun 21, 2018, 6:38:33 PM6/21/18
Just to be clear - you want to initially fetch 10 records and display them. Then when the user clicks the pagination button - you want to load the next 10 records?
Jim
--
Upcoming events: http://www.meetup.com/Triangle-Area-ColdFusion-Users-Group/
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### markw707
Jun 22, 2018, 10:36:04 AM6/22/18
to TACFUG
Hi Jim, Long time no see. I hadn't thought of it working like that, but yes, it could probably work that way. I was thinking of it more like the first ten records are rendered and displayed to the user in the DataTable, then the other records are rendered, so the user doesn't have to wait. As you may know, there is a time lag when DataTable converts the raw recordset into a DataTable, especially for large recordsets. Thanks again for your help.
To unsubscribe from this group and stop receiving emails from it, send an email to [email protected].
### Denard Springle
Jun 22, 2018, 7:12:08 PM6/22/18
to TACFUG
You would have to use serverside processing of the records and handle the pagination yourself, as Jim suggested, by returning only X records (in your case 10, but could be user selectable) to render per 'view' of the datatable. How you do that in SQL depends on if you're using MySQL or MSSQL and what version, but there's plenty of good articles on how to do pagination with both databases (and others) online so I'll skip that here.
Example JS code I use:
\$('#entity-table').DataTable( {
'processing': true,
'serverSide': true,
'responsive': true,
'ajax': {
'type': 'POST'
},
"columns": [
{ "data": "columnName1" },
{ "data": "columnName2" },
{ "data": "columnName3" },
{ "data": "COLUMNNAME1" },
{ "data": "COLUMNNAME2" },
{ "data": "COLUMNNAME3" }
]
} );
I, peronally, loop over my returned queries and build an array of structs using struct[ 'columnName1' ] = qGetData.columnName1;, but you can also just have CF return an array of structs and remember (by default) CF returns column names in UPPERCASE and so serializeJSON() of a query will return UPPERCASE column names (so put both in my example).
serverside sends a POST (or GET if you set AJAX to GET, but don't) and you can dump out the form scope to see all their fields it sends in. The drawback to going serverside is that it requires you to handle everything (number of records returned, which page, search, single and multi-column sorting, etc.). The upside is datatables only renders data when it needs it. I do this a lot for tables of data that are encrypted in the database (users, for example) where large datasets would be horribly slow.
datatables in serverside mode expects JSON returned with the following data:
draw - this is the same as passed in by datatables and can be passed through (the number of 'rows' to 'draw' in the table)
recordsTotal - this is the total number of records
recordsFiltered - this is the number of records, out of the total records, that are filtered (by search, typically) - combines with recordsTotal to display 'Showing X number of records out of Y total' in the datatable.
data - this is your array of structs with column names matching those specified in your JS
These names *must* be in lowercase so use struct[ 'draw' ] = x, struct[ 'recordsTotal' ] = y, struct[ 'recordsFiltered' ] = z, and struct[ 'data' ] = [your array of structs] prior to serializeJSON() (or other rendering pipeline, e.g. fw/1 or ColdBox renderData())
HTH
-- Denny
|
# How do you convert x^2 - y^2 = 5 in polar form?
Feb 11, 2016
The polar form of that equation will be r= sqrt[5/cos(2θ)].
#### Explanation:
To solve this problem, you have to understand the relationship that x and y has with r. r is the radius and has a starting point on the origin with an ending point anywhere on the graph. However, to use r in math, you have to break it into components since the angle provides challenges with calculations. The x component is how far away it is left or right from the origin. The y component is how far it is up or down from the origin. Together, the x and y components with r make a right triangle like so:
The x component is the adjacent side to the angle, so use cosine (Cosine$\theta$ equals adjacent side divided by the hypotenuse or in this case, r.) to make the equation cos$\theta$ = x/r. To find x, multiple both sides by r to get
x= rcos$\theta$
The y component is the opposite side to the angle, so use sine (Sine$\theta$ equals opposite side divided by the hypotenuse, r.) This yields the equation sin$\theta$ = y/r. Multiple both sides by r to simplify.
y = rsin$\theta$
Now that you know what x and y equals, plug them in to the equation.
(rcosθ)^2 - (rsinθ)^2= 5
Square both sides to get
r^2cos^2θ - r^2sin^2θ= 5
Factor out the ${r}^{2}$ because it is a common factor
${r}^{2}$(cos^2θ - sin^2θ)= 5
Using the trigonometry identity of cos(2θ)= cos^2θ - sin^2θ
(just have to memorize that identity)
${r}^{2}$[cos(2θ)]= 5
Divide both sides by cos(2θ) to isolate r.
${r}^{2}$= 5/(cos2θ)
Square root it
r= sqrt[5/cos(2θ)]
However since a square root can't be negative, there are some limits to the domain of cos(2θ).
Normally, cosθ is positive from -$\pi$/2 < θ < $\pi$/2.
However, since the angle is doubled in cos(2θ), divide by two.
This yields the final domain for this function to be -$\pi$/4 < θ < $\pi$/4
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# What is the "molarity" of a 35.67*g mass of calcium chloride dissolved in enough water to make a volume of 1.0*L?
We take the quotient, $\text{Molarity"="Moles of solute"/"Volume of solution}$
$\frac{\frac{35.67 \cdot g}{110.98 \cdot g \cdot m o {l}^{-} 1}}{1.0 \cdot L} = 0.321 \cdot m o l \cdot {L}^{-} 1$ with respect to $\text{calcium chloride}$. What is the molar concentration with respect to chloride ion?
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## Oliver Club
Zihui ZhaoUniversity of Chicago
Boundary regularity of elliptic PDEs
Thursday, November 11, 2021 - 4:00pm
Malott 532 (Lounge)
Abstract: I will talk about two related topics of elliptic PDEs: quantitative unique continuation and harmonic measure. Unique continuation property is a fundamental property of harmonic functions: If a harmonic function vanishes to infinite order at a point, it must vanish everywhere. In the first part of the talk, I will explain how to use the local growth rate of a harmonic function to estimate the size of its singular set $\mathcal{S}(u) := \{u=0=|\nabla u|\}$
Let $D$ be a bounded domain and $x\in D$ be fixed. A Brownian traveller $\{B_t\}$ starting from $x$ must exit the domain, and the harmonic measure is a probability measure on the boundary $\partial D$ which characterizes the distribution where $\{B_t\}$ exits the domain from. It also gives a simple representation formula for solutions to the boundary value problem of the Laplacian in $D$. Thus the harmonic measure, and more generally the elliptic measure, carries a lot of information about the boundary behavior of these solutions. In the second part of the talk, I will explain the properties of harmonic/elliptic measures in non-smooth domains, and in particular how they are related to the natural surface measure of the boundary.
Refreshments will be served at 3:30 PM.
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Home / Instrumentation / Series Resistance Capacitance Bridge Circuit
# Series Resistance Capacitance Bridge Circuit
One disadvantage of simple Capacitance Bridge is that perfect balance of the bridge is obtained only when Cs and Cx are both pure capacitances (i.e. they have virtually no resistive components). In general, this occurs only with capacitors that have air or mica dielectrics. Capacitors with other types of dielectric have a leakage current, and consequently, the equivalent circuits for the capacitors have resistive components that must be included in the bridge circuit.
The circuit of the series resistance-capacitance bridge shown in figure 1 eliminates the balance problems that can occur with the simple capacitance bridge. Resistance rx in series with the unknown capacitance represents the resistive component of the capacitor equivalent circuit. The standard capacitor Cs normally has mica dielectric and thus has a very small resistive component. Consequently, the adjustable resistance S must be included in the circuit to balance the effect of rx.
## Working Princple of Series Resistance Capacitance Bridge
The balance equations for the series resistance capacitance bridge are derived as follows:
$\frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{4}}}$
Therefore,
$\frac{S-j\frac{1}{\omega {{C}_{s}}}}{Q}=\frac{{{r}_{x}}-j\frac{1}{\omega {{C}_{x}}}}{P}$
$\begin{matrix} \frac{S}{Q}-j\frac{1}{\omega {{C}_{s}}Q}=\frac{{{r}_{x}}}{P}-j\frac{1}{\omega {{C}_{x}}P} & \cdots & (1) \\\end{matrix}$
For equation (1) to be correct, the real parts on each side must be equal, and the imaginary parts on each side must be equal.
Equating the real parts,
$\frac{S}{Q}=\frac{{{r}_{x}}}{P}$
And
Resistive Component of the Unknown Capacitance
$\begin{matrix} {{r}_{x}}=\frac{PS}{Q} & \cdots & (2) \\\end{matrix}$
Fig.1: Series Resistance Capacitance Bridge
The use of series resistors with a capacitance bridge makes balance easy to obtain and allows the resistive component of the capacitors to be measured.
Now, equating the imaginary parts,
$\frac{1}{\omega {{C}_{s}}Q}=\frac{1}{\omega {{C}_{x}}P}$
And
Formula for Unknown Capacitance
$\begin{matrix} {{C}_{x}}=\frac{Q{{C}_{s}}}{P} & \cdots & (3) \\\end{matrix}$
The resistive and capacitive components of the unknown capacitance can now be calculated by means of equations (2) and (3). Note that neither the supply voltage nor the AC frequency is involved in the balance equations for the bridge.
Because of the need to balance the real and imaginary components of the bridge impedances, the process of obtaining balance in an AC bridge is a little more complicated than with the Wheatstone bridge. One of the adjustable components (Q or S in figure 1) is first altered to obtain the lowest possible indication of the null meter. Then the other adjustable component is varied to obtain the lowest reading. The process is repeated until further adjustment of either component cannot produce lower reading on the null meter. At this point the bridge is balanced.
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# How do you solve |10- 8x | < - 13?
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
1
Sep 20, 2016
No solution.
#### Explanation:
No solution since the absolute value function can never be negative and hence can never be less than $- 13$.
By definition, $| y | = \left\{\begin{matrix}y & y > 0 \\ - y & y < 0\end{matrix}\right\}$
Hence $| y | \ge 0 \forall y \in \mathbb{R}$
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# A number theory problem by Ilham Saiful Fauzi
Find the sum of all integers $$n$$ such that $$(n-3)$$ divides $$(n^{3}-3)$$.
×
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# Given a decreasing function s.t. $\int_0^\infty f(x)\,dx<\infty,$ prove $\sum_{n=1}^\infty f(na)$ converges
Let $f\in C([0,\infty))$ be a decreasing function such that $\int_0^\infty f(x)\,dx$ converges.
Prove $\sum_{n=1}^\infty f(na)$ converges, $\forall a>0$
My attempt:
By the Cauchy criterion, there exists $M>0,$ such that for $t-1>M:$
$$f(t)=\int_{t-1}^t f(t) \, dx \leq \int_{t-1}^t f(x)\,dx\xrightarrow{t \to \infty} 0$$
Hence, $f$ is non-negative.
$f$ is decreasing $\implies f(na)\leq f(a), \forall a>0, n\in \mathbb{N}.$
By integral monotonicity and non-negativity of $f$:
$$\int_1^\infty f(nx)\,dx \leq \int_1^\infty f(x)\,dx \leq \int_0^\infty f(x)\,dx$$
Hence $\int_1^\infty f(nx)\,dx$ converges and therefore $\sum_{n=1}^\infty f(na)$ converges.
Is that correct? If so, why is continuity necessary ? Is there a simpler way to prove it?
Any help appreciated.
• $$\int_{(n-1)a}^{na}f(x)dx\geq af(na)$$ – MAN-MADE Aug 22 '17 at 18:33
Hint: The following thing you wrote is the key:
$$f(t)=\int_{t-1}^{t}f(t)dx \leq \int_{t-1}^{t}f(x)dx$$
After that, just pick $t=an$ and sum over all $n$.
PS: and no, the assumption on continuity is not needed. Just integrability for the well-definedness.
As I commented before:
Since $f$ is decreasing and continuous, $$\int_{(n-1)a}^{na}f(x)dx\geq [na-(n-1)a]\inf_{(n-1)a< x\leq na}\{f(x)\}=af(na)$$
Then $$\int_{0}^{\infty}f(x)dx=\sum_{n=1}^{\infty}\int_{(n-1)a}^{na}f(x)dx\geq a\sum_{n=1}^{\infty}f(na)$$
Hence, since $a\in\mathbb{R}^+,$ $\sum_{n=1}^{\infty}f(na)<\infty$
\begin{align} & af(a) + af(2a) + af(3a) +\cdots \\[10pt] \le {} & \int_0^a f + \int_a^{2a} f + \int_{2a}^{3a} f + \cdots <\infty. \end{align}
This works if $f \ge0$ everywhere. If $f<0$ somewhere, then an easy argument shows the integral does not converge.
This is the integral test for convergence of series. Do a change of variable x --- to --- ax. The integral converges so does series g(n)=f(na).
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# Proving that smallest period divides every other period
This question was left as homework by my instructor and he didn't discussed it.
An arithmetical function f is called periodic mod k if k>0 and f(m) =f(n) whenever m$$\equiv$$ n (mod k). The integer k is called a period of f.
(i) If f is periodic mod k, prove that f has a smallest positive period $$k_{0}$$ and $$k_{0}$$ |k.
Attempt : by well ordering principle there exists a smallest period $$k_{0}$$ .
Now, m$$\equiv$$ n (mod k) => f(m) =f(n) => m$$\equiv$$ n (mod $$k_{0}$$ => m-n = $$k_{0}$$ x,$$m-n =k_{1} y$$ , which implies $$k_{0} x = k_{1} y$$ and $$k_0 < k_{1}$$ implies that x>y , but I am still not getting that y divides x to prove what is asked.
One could perhaps try a proof by contradiction. Assume that $$k_0 \nmid k_1$$. Then there are integers $$q,r$$ with $$0 < r < k_0$$ such that $$k_1 = qk_0 + r$$.
Given any positive integer $$x$$, there are integers $$q',r'$$ with $$0 \leq r' < r$$ such that $$x = q'r + r'$$. Therefore $$f(x) = f(q'r + r') = f(q'(k_1-qk_0) + r') = f(q'k_1 - q'qk_0 + r').$$
Since both $$k_0$$ and $$k_1$$ are periods of $$f$$, $$f(q'k_1 - q'qk_0 + r') = f(r')$$. Thus for any positive integer $$x$$, $$f(x) = f(r')$$, where $$x \equiv r'~(mod~r)$$. This means that $$r$$ is a period of $$f$$ that is smaller than $$k_0$$, contradicting the choice of $$k_0$$.
Hint: the periods set $$P$$ is nonempty & closed under subtraction $$>0\,$$ $$(k>\bar k\in P\Rightarrow k\!-\!\bar k\in P),\,$$ so the least period divides every period by a fundamental Lemma (which has a one-line proof).
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# Fill indentation with dashes
When doing nested itemize, I have a very long list and want to make clear that the items lower on the list are still nested within (dependent on) earlier items.
For this reason, I would like to indent with dashes, i.e.
---If I am Bob,
--------- If it is Saturday,
--------------- If work with Sally,
--------------------------- We both wear suits.
--------------- If tennis is on TV,
--------------------------- I root for Serena Williams.
Sample current code:
\usepackage{enumitem}
\begin{itemize}
\item If I am Bob,
\begin{itemize}[leftmargin=*,labelindent= 1cm]
\item If it is Saturday
\begin{itemize}[leftmargin=*,labelindent= 2cm]
\item If I work with Sally
\begin{itemize}[leftmargin=*,labelindent= 3cm]
\item We both wear suits.
\end{itemize}
\item If tennis is on TV,
\begin{itemize}[leftmargin=*,labelindent= 3cm]
\item I root for Serena Williams.
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
How do I tell latex to fill the indentation space with dashes?
• TeX has a "leaders" features which seems suited for this sort of thing. Unfortunately I don't know enough about LaTeX's itemize environment to know if and how it can be customized to use leaders in place of the normal indentation (assuming you want to keep your input the same). – ShreevatsaR May 1 '17 at 11:20
• do you just want the dashes, or the normal itemize bullets etc as well? – David Carlisle May 1 '17 at 11:48
• Or maybe you want continuous lines of variable length? – Bernard May 1 '17 at 12:13
• alternatively, draw a tree – Marijn May 1 '17 at 14:12
You can keep track of the margins with a length of your own and use to draw an appropriate line. Following you comments, you just want a rule rather than dashes, and you want the standard itemize to be unchanged. So I suggest you introduce a new list, e.g. ditemize, for the particular style.
\documentclass{article}
\usepackage{enumitem}
\newlength{\myindent}
\setlength{\myindent}{0pt}
\newlist{ditemize}{itemize}{4}
\setlist[ditemize]{before={\setlength{\myindent}{\dimexpr\myindent+\leftmargin}},
label=\mbox{\hss\rule[.5ex]{\dimexpr\myindent-\labelsep}{.4pt}}}
\setlist[ditemize,2]{labelindent=1cm}
\setlist[ditemize,3]{labelindent=2cm}
\setlist[ditemize,4]{labelindent=3cm}
\begin{document}
\noindent
Some text that is not indented to show the left margin.
\begin{ditemize}
\item If I am Bob,
\begin{ditemize}
\item If it is Saturday
\begin{ditemize}
\item If I work with Sally
\begin{ditemize}
\item We both wear suits.
\end{ditemize}
\item If tennis is on TV,
\begin{ditemize}
\item I root for Serena Williams.
\end{ditemize}
\end{ditemize}
\end{ditemize}
\end{ditemize}
\end{document}
The code works as follows. Introduce a new variable \myindent to store the current indentation. At the start of each ditemize, using before= code, we add the current margin to \myindent. The mechainism of before means this is done inside a group local to the list, so when a sublist is finished, we recover the old value. Now set the label, to be a rule of an appropriate length, but in a box of zero width and sticking out to the left.
Had you wanted dashes instead of a line, I suggest using the dashrule package, which provides a near drop in replacement for the \rule above. You can then write the label specification as:
label=\mbox{\hss\hdashrule[.5ex]{\dimexpr\myindent-\labelsep}{.4pt}{3pt}}
after issuing \usepackage{dashrule}. With labelsep=.1em this produces:
• Thanks. I do use itemize elsewhere where I don't want dashes. How do I amend only this itemize? Rather than changing all itemize's in the document. – user341502 May 1 '17 at 21:05
• Additionally, I want to change the depth of indentation as described in the foundational post to be 0cm, then 1 cm, then 2cm, etc., where the $i$th nested list has indentation depth $(i-1)$cm. – user341502 May 1 '17 at 21:07
• Thanks. I have updated my answer to reflect these comments. – Andrew Swann May 2 '17 at 7:01
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Principal Component Analysis
Visualization via Heatmap
Recently, I worked on a project that necessitated data exploration and preprocessing. Principal component analysis (PCA) is technique I had heard about and seen used many times before; however, I personally had no experience with it in either theory or practice. So I got to digging.
Now the point of this post is not to give a full-fledged lesson on PCA. Many others have done that in better ways than I could manage. But to provide context, I’ll give a brief overview.
PCA performs an affine transformation on the standard Cartesian basis. In the transformed basis, the origin is centered in the data and most of the variance in the data is in the direction of the new axes. In two dimensions, imagine there are a few data points scattered on a plot. Make a plus sign with your fingers and let it overlap the x- and y-axis of that plot, then shift the intersection of your fingers to the middle of the data and rotate them to best align with the linear trend of the data. In higher dimensions, an affine transformation is still just a shift (i.e. translation) and a rotation, but the concept is difficult to visualize.
Suppose the original data contains has features x, y, and z. Using PCA, those features are transformed to a, b, c, each a linear combination of x, y, z. For example, a might be 3x - 2y + z. Throughout this article, I will refer to “feature contributions”. In this example, the x feature makes a contribution of 3 to the transformed a feature, y makes a contribution of -2, and z just 1. Even though y’s contribution is -2, it is still a larger contribution in magnitude than z’s contribution of 1.
Now, proceeding to the motivation for this post. In my research, I came across this excellent article that describes PCA. I had just one critique about this article – near the end, there is a spurious heatmap illustration that falls a bit short of illustrating the contributions of the original data features to the principal components. In a few lines of Python code, we can create a near reproduction.
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from sklearn.decomposition import PCA
from sklearn import datasets
pca = PCA().fit(X)
data = pca.inverse_transform(np.eye(X.shape[-1]))
plt.imshow(np.log(data), cmap='hot')
plt.ylabel('Principal Components')
plt.xlabel('Original Features')
plt.colorbar()
plt.show()
At first glance, nothing seems wrong with this image. However, several of the white squares in the heatmap are misleading – they do not actually indicate strong contributions as the colorbar suggests. Rather, those squares indicate NaN (not a number) placeholder values resulting from the attempt to take the log of a negative value, a result that is formally undefined. (Note the exponential scale of the colorbar, i.e. 6 means 1e6 and -8 means 1e-8 which is a very small, but positive number). The offending line is highlighted in the code snippet above.
This creates a conflict. Log scale is appropriate for this context, but the PCA inverse transform is likely to have at least one negative value. And it is virtually a certainty for the inverse transform to contain negative values when the data has been normalized (depending on the normalization method).
So are we out of luck? If you’ve made it this far, you’ll be happy to know the answer is a resounding no! In fact, matplotlib has features that specifically address this issue – matplotlib.colors.LogNorm and matplotlib.colors.SymLogNorm. Using these mechanisms, I developed the following function for properly displaying such a heatmap visualization.
Note: The code blocks in the remainder of this post all depent on imports, functions, etc. that have been defined in previous code blocks.
import matplotlib.colors as colors
def pca_viz(pca, X, X_features, sort=False, signed=True):
pca.fit(X)
n_rows, n_cols = len(X_features), len(pca.components_)
inv = pca.inverse_transform(np.eye(n_cols))
data = pd.DataFrame(inv, columns=X_features).transpose()
# make zero-values just very, very small
epsilon = 1e-16
num_zeros = (data == 0).sum().sum()
if num_zeros:
data.loc[:, :] = np.where(data == 0, 1e-16, data)
# sort by principal component contribution
if sort:
data['sum'] = data.abs().sum(axis=1)
data.sort_values(by='sum', ascending=False, inplace=True)
data.drop('sum', axis=1, inplace=True)
# configure heatmap and log-scale colorbar
scale_min = max(data.abs().min().min(), 1e-2)
scale_max = data.abs().max().max()
if signed:
cmap = 'RdBu_r'
scaler = colors.SymLogNorm(vmin=-scale_max, vmax=scale_max,
linscale=1.0, linthresh=scale_min)
else:
data = data.abs()
cmap='Reds'
scaler = colors.LogNorm(vmin=scale_min, vmax=scale_max)
fig, ax = plt.subplots(1, 1)
im = ax.imshow(data, cmap=cmap)
im.set_norm(scaler)
fig.colorbar(im)
# configure ticks and labels
ylabels = data.index
ax.set_yticklabels(ylabels, fontsize=6, rotation=0, va='center')
ax.set_yticks(np.arange(n_rows))
ax.set_ylabel('Original Features')
xlabels = np.arange(n_cols)
ax.set_xticklabels(xlabels, fontsize=6, rotation=90, ha='center')
ax.set_xticks(np.arange(n_cols))
ax.set_xlabel('Principal Components')
return fig, ax
This method is robust in the case of negative values. Moreover, the option to toggle signed contributions (positive vs. negative), as opposed to absolute magnitude of contribution, is available through the signed argument. There is also a sort argument that will cause the original features to be ordered top-to-bottom by total magnitude of contribution. Let’s see it in action using first the original data as-is, then with a scaled version of that data (via sklearn.preprocessing.StandardScaler).
from sklearn.preprocessing import StandardScaler
# visualize the original data
pca = PCA()
fig, ax = pca_viz(pca, X, X_features, signed=True)
plt.show()
# visualize the scaled data
X_ss = StandardScaler().fit_transform(X)
fig, ax = pca_viz(pca, X_ss, X_features, signed=True)
plt.show()
This implementation is also suited to cases where PCA is instantiated with arguments, e.g. PCA(n_components=5), but that exercise is left up to you, as is the exercise of trying the other combinations of signed and sort arguments.
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# Thread: differential equation need Help
1. ## differential equation need Help
$dy/dx = -6xy$
$\int \frac{1}{y} dy = \int -6x dx$
$ln y = -3x^2 + c$
$y = e^{-3x^2 + c}$
2. ## Re: differential equation need Help
Yes, though it can be taken one step further,
$y = e^{-3x^{2}+c}=e^{-3x^{2}}.e^{c}=Ae^{-3x^{2},$
which, subsequently, will be slightly easier to deal with.
3. ## Re: differential equation need Help
its given y(0) = 7 ,to find value of C
$7 = e^{-3x^2} \times e^c$
Then ?
4. ## Re: differential equation need Help
Originally Posted by mastermin346
its given y(0) = 7 ,to find value of C
$7 = e^{-3x^2} \times e^c$
Then ?
y(0) = 7 says that when x = 0 y = 7. What change does that make in the line you wrote?
-Dan
5. ## Re: differential equation need Help
$7 = e^{-3(0)^2} \times e^c$
$7 = 1 \times e^c$
$C = ln 7$
right or wrong ?
6. ## Re: differential equation need Help
y=Aexp (-3x^2)
y (0)=7, so 7=A.
y=7exp (-3x^2).
7. ## Re: differential equation need Help
Originally Posted by mastermin346
$dy/dx = -6xy$
$\int \frac{1}{y} dy = \int -6x dx$
$ln y = -3x^2 + c$ You are wrong in this step
$y = e^{-3x^2 + c}$
is my answer Correct ? You need to go further
First note that \displaystyle \begin{align*} \int{\frac{1}{y}\,dy} = \ln{|y|} \end{align*}, NOT \displaystyle \begin{align*} \ln{(y)} \end{align*} so this means the correct working out would be
\displaystyle \begin{align*} \ln{|y|} &= -3x^2 + C \\ |y| &= e^{-3x^2 + C} \\ |y| &= e^{C}\,e^{-3x^2} \\ y &= \pm e^{C}\,e^{-3x^2} \\ y &= A\,e^{-3x^2} \textrm{ where } A = \pm e^C \end{align*}
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# Inverting the heat equation
I have a wire that stretches from $$x=0$$ to $$\infty$$. The temperature at $$x=0$$ is given by the unknown function $$f(t)$$ for $$t$$ from $$-\infty$$ to now ($$t=0$$).
I can measure the temperature of the wire at each point now ($$t=0$$), $$g(x)$$.
Given the temperature of the wire now, $$g(x)$$, I would like to recover $$f(t)$$, the temperature at $$x=0$$, through history
The problem is likely "ill posed" meaning tiny errors in $$g(x)$$ lead to big errors in $$f(t)$$.
What is known about solving this problem? For example, is the degree of ill-posedness known? If it is mildly ill-posed, are there numerical techniques available? Can anyone point me to articles or a book that treats it?
You are right, this is a classically ill-posed question, and here is why.
If you are measuring the temperature $$k$$ along the wire at position $$x$$ and time $$t$$, there are any number of different initial temperature distributions along that wire which would yield $$t = k$$ at $$(x,t)$$—that is, the answer is not unique for any given set of initial conditions.
This means you can predict what $$k = f(x,t)$$ will be for future times, but not what it was for past times.
Another way of thinking about this is as follows: heat flux travels by a diffusion process. At any stage of the diffusive process, it tends to erase any historical information about the initial conditions present at earlier times. That erasure makes it mathematically impossible to reconstruct the initial conditions by back-calculation.
• alternatively, one could think of the inverse-time evolution of this equation to become multi-valued, as some kind of superposition (no relationship with algebraic linear superposition, that I'm aware) of well defined previous states Oct 17 at 22:06
• I believe it is ill posed in a similar sense to inverting the Laplace transform. I suspect that mathematically it has an inverse, but practically/numerically it is hard or impossible. I would like to find out in detail what is known about the maths of this problem Oct 17 at 22:08
• "the answer is not unique for any given set of initial conditions" I am not convinced this is actually correct. I expect the time-reversed heat equation $\frac{du}{dt} = -\Delta u$ to have a unique solution, at least in some suitable Sobolev space... one can construct such a solution using Fourier series, for instance. Oct 18 at 10:18
• I believe you are right mathematically. But it is numerically ill-posed. Some very helpful answers already, but I am still looking for an article or book specifically covering the heat equation. Eg, proof that it is ill-posed. Degree of ill-posedness. Numerical methods specifically applied to the heat equation Oct 18 at 10:52
• For a wire stretching to infinity, doesn't uniqueness fails for future times as well? At least without some restrictions on heat distribution. Oct 18 at 12:29
There are indeed some numerical methods available that try to limit the impact of the ill-posedness.
Often times they rely on the introduction of a generalization term. This is a term that in a way measures the errors introduced by the ill-posed nature and adds this to minimization problem of finding your initial state.
This is actually used in a well-known machine learning technique called Support Vector Machines, where you have a similar trade-off between finding a perfect fit for your data (which is very noise-sensitive) and limiting the complexity of the model. In machine learning this is more often identified as the bias-variance tradeoff, but in essence these 2 concepts are very close to eachother.
Since you requested some literature here are some sources that I found usefull during my masters research on these topics:
• Very interesting thank you Oct 18 at 9:26
• I am still hoping to hear of an article or book specifically covering ill-posedness of this problem for the heat equation Oct 18 at 10:53
• The heat equation is also the diffusion equation, which may be helpful in expanding your search. Oct 18 at 15:35
• This is helpful people.maths.ox.ac.uk/trefethen/pdectb/backward2.pdf Oct 19 at 11:08
• Also helpful: math.stackexchange.com/questions/1674674/… Oct 19 at 13:14
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# zbMATH — the first resource for mathematics
##### Examples
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The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model. (English) Zbl 1227.76059
Summary: The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter $C\to 0$. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient $H$. We found an excellent agreement between the exact solutions and asymptotic solutions when $H$ is very small.
##### MSC:
76R10 Free convection (fluid mechanics) 76S05 Flows in porous media; filtration; seepage 76A05 Non-Newtonian fluids
##### References:
[1] , Transport phenomena in porous media (1998) [2] , Transport phenomena in porous media, vol. III (2005) [3] , Handbook of porous media (2000) [4] , Handbook of porous media (2005) [5] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) [6] Rees, D. A. S.; Pop, I.: J. porous media, J. porous media 3, 31 (2000) [7] Rees, D. A. S.; Pop, I.: J. appl. Math. phys., J. appl. Math. phys. 53, 1 (2002) [8] Banu, N.; Rees, D. A. S.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 45, 2221 (2002) [9] Rees, D. A. S.; Pop, I.: D.b.inghami.poptransport phenomena in porous media, vol. III, Transport phenomena in porous media, vol. III, 147-173 (2005) [10] Baytas, A. C.; Pop, I.: Int. J. Thermal sci., Int. J. Thermal sci. 41, 861 (2002) [11] Baytas, A. C.: Int. J. Energy res., Int. J. Energy res. 27, 975 (2003) [12] Saeid, N. H.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 47, 5619 (2004) [13] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.: Int. J. Heat mass transfer, Int. J. Heat mass transfer 48, 1155 (2005) [14] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.: Transp. porous media, Transp. porous media 60, 199 (2005) [15] Straughan, B.: Proc. R. Soc. London A, Proc. R. Soc. London A 462, 409 (2006) [16] Malashetty, M. S.; Shivakumara, I. S.; Sridhar, K.; Mahantesh, S.: Transp. porous media, Transp. porous media 64, 123 (2006) [17] Shivakumara, I. S.; Malashetty, M. S.; Chavaraddi, K. B.: Can. J. Phys., Can. J. Phys. 84, 973 (2006) [18] Sheu, L. J.: Chaos solitons fractals, Chaos solitons fractals 30, 672 (2006) [19] Malashetty, M. S.; Swamy, M.; Sridhar, K.: Phys. fluids, Phys. fluids 19, No. 5, 054102 (2007) [20] Stokes, V. K.: Phys. fluids, Phys. fluids 9, 1709 (1966) [21] Sharma, R. C.; Thakur, K. D.: Czech J. Phys., Czech J. Phys. 50, No. 6, 7753 (2000) [22] Sunil; Sharma, R. C.; Chandel, R. S.: Z. naturforsch., Z. naturforsch. 57a, 955 (2002) [23] Sharma, R. C.; Sharma, M.: Indian J. Pure appl. Math., Indian J. Pure appl. Math. 35, 973 (2004) [24] Horton, C. W.; Rogers, F. T.: J. appl. Phys., J. appl. Phys. 16, 367 (1945) [25] Lapwood, E. R.: Proc. Cambridge philos. Soc., Proc. Cambridge philos. Soc. 44, 508 (1948)
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I'm trying to load a bitmap into memory by myself and I think I have it down but there are a few things that are confusing me a bit. I don't know if this is right or not.
In my function "format24BMP" there is an if statement "x == byteWidth"... it should enter it 100 times but it appears to only enter it once.
bool Bitmap::readBMP(char* fn){ fname = fn; ifstream inf(fname,ios::binary|ios::in); if(!inf.is_open()){ return false; } //read in BITMAPFILEHEADER inf.read((char*)&bmfh->bfType,2); if(bmfh->bfType!=BITMAP_ID){ return false; } inf.read((char*)&bmfh->bfSize,4); inf.read((char*)&bmfh->bfReserved1,2); inf.read((char*)&bmfh->bfReserved2,2); inf.read((char*)&bmfh->bfOffBits,4); //read in BITMAPINFOHEADER inf.read((char*)&bmih->biSize,4); inf.read((char*)&bmih->biWidth,4); inf.read((char*)&bmih->biHeight,4); inf.read((char*)&bmih->biPlanes,2); inf.read((char*)&bmih->biBitCount,2); inf.read((char*)&bmih->biCompression,4); inf.read((char*)&bmih->biSizeImage,4); inf.read((char*)&bmih->biXPelsPerMeter,4); inf.read((char*)&bmih->biYPelsPerMeter,4); inf.read((char*)&bmih->biClrUsed,4); inf.read((char*)&bmih->biClrImportant,4); //has no color table and 3 bytes represents 1 pixel if(bmih->biBitCount == 24){ byteWidth = bmih->biWidth*3; //get the length of the padded byte rows if(bmih->biWidth%4!=0){ padWidth = byteWidth; padWidth = (int)((padWidth/4)+1); padWidth *= 4; } //no padded bytes else{ padWidth = byteWidth; } //get the absolute value of height if(bmih->biHeight < 0) { byteHeight = (bmih->biHeight*-1); } else { byteHeight = (bmih->biHeight); } pImgSize = bmfh->bfSize - bmfh->bfOffBits; imgSize = byteWidth*byteHeight; //get the number of padded bytes per row padBytes = padWidth - byteWidth; //read in unformated data char* tPData = new char[pImgSize]; inf.read(tPData,pImgSize); //now format pixel data format24BMP(tPData); //stores formatted data in aColors } return true;}
void Bitmap::format24BMP(char* tPData){ aColors = new char[imgSize]; //if bmih->biHeight is positive, the pixel data is backwards if(bmih->biHeight > 0){ int end = imgSize - 3; for(int x = 0; x < pImgSize; x+=3){ if(x == byteWidth){ x+=padBytes; //skip the padded bytes } aColors[end] = tPData[x+2]; aColors[end+1] = tPData[x+1]; aColors[end+2] = tPData[x]; end -= 3; } } else{ }}
I admit I followed one of the tutorials on gamedev but I tried to do most of it on my own. Right now I'm only trying to get it to work with 24bpp and I have a specific file I'm working with just trying to make sure it works with it and I know it won't go into the empty else statement etc.
I didn't pack my structures so I had to read my data in the way I did in my function.
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Have you tried following this in your debugger? This would be a good exercise to learn on if you don't know how. I would think that stepping through you should be able to identify the problems without too much trouble.
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karwosts' suggestion is good. Also, you can make your code much more readable (and easier to maintain) if you read in each of the headers in one statement, rather than reading in each variable by itself.
E.g.,
inf.read((unsigned char*)&bmfh,sizeof(BITMAPFILEHEADER));//...inf.read((unsigned char*)&bmih,sizeof(BITMAPINFOHEADER));//...
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Ok, I've done some debugging (not with an IDE but some useful results)
I created a 2x2 24bpp bmp file. It's structure was like this:
(50,50,50) (100,100,100)(200,200,200) (255,255,255)
Now below are the results I printed out. They aren't in the right order and for some reason I'm getting 255's and 200's as negatives (like they were too large to fit but they weren't)
All the other data is right... the size of padding of bytes in the file is 2. I checked with my hexeditor...
Basically... it seems as though the problem is with the logic of my for loop in format24BMP()
If you guys can see it please let me know. I'll continue trying to tweak it.
My Results
|=========================================|| Bitmap Calculations ||=========================================|padWidth: 8padBytes: 2byteHeight: 2byteWidth: 6|=========================================|| Pixel Data ||=========================================|100 100 100 50 50 50 -1 -1 -1 -56 -56 -56|=================================|| Bitmap File Header ||=================================|bfType: 19778bfSize: 70bfReserved1: 0bfReserved2: 0bfOffBits: 54|================================|| Bitmap Info Header ||================================|biSize: 40biWidth: 2biHeight: 2biPlanes: 1biBitCount: 24biCompression: 0biSizeImage: 16biXPelsPerMeter: 2835biYPelsPerMeter: 2835biClrUsed: 0biClrImportant: 0
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Quote:
Ok, I've done some debugging (not with an IDE but some useful results)
You need to learn to use your IDE, you'll be able to solve this much faster that way. It's built for situations like this.
That aside, the reason you see negative numbers is because a char ranges from -128 to 127, so a 255 wraps around to become -1. Their binary representation is exactly the same though (both are represented by 8'b11111111), so that's probably not the source of your problem.
Use unsigned char if you want to range from 0 to 255.
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# What happens for a "closed" universe without any content?
Let an universe with no content and positive curvature. Friedmann-Lemaître equation $$H^2=\frac{8\pi G}{3}\left(\rho_m+\rho_r+\rho_{\Lambda}\right)-\frac{k\, c^2}{a^2},$$ where $$a$$ corresponds to the scale factor of Friedmann-Lemaître-Robertson-Walker Metric, and the $$\rho$$ to the density of the contents, will become $$H^2=-\frac{\, c^2}{a^2},$$ as positive curvature (closed universe) corresponds to $$k=+1$$.
So, as $$H=\frac{\dot{a}}{a}$$ with $$\dot{a}=\frac{da}{dt}$$,
$$da=\pm i \, c \, dt$$
$$a(t)=\pm i \, c \, t + cst$$
what am I doing wrong ?
• FYI a native English speaker would say "a universe". Sep 28, 2018 at 4:04
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# PageTextVariables
Page text variables are string variables created in the wiki text of a page, and can be automatically made available for inclusion in other pages. In the default installation, PageTextVariables can only have a name containing basic Latin/Roman (ASCII) letters, digits, dash and underscore. This is a limitation for international wikis (experimental recipe for international PTV : Cookbook:InternationalPTVs).
## Defining Page Text Variables
There are three ways to define automated Page Text Variables (more patterns can be defined if needed) :
• use a definition list - the normal pmwiki markup for a definition list will create a page text variable
:Name: Crisses "{$:Name}" Name Crisses "Crisses" This creates a new variable that can be accessed by {$:Name} (becomes: "Crisses") in the page.
• use a simple colon delimiter in normal text
Address: 1313 Mockingbird Lane "{$:Address}" Address: 1313 Mockingbird Lane "1313 Mockingbird Lane" This creates the {$:Address} variable (variable markup becomes: "1313 Mockingbird Lane") in the page.
• hidden directive form - PmWiki markup that doesn't render on the page, but defines the variable
(:Country: Transylvania :) "{$:Country}" "Transylvania " This creates the {$:Country} variable (variable markup becomes: "Transylvania ") in the page.
## Usage
On the same page you can resolve page text variables through the {$:Var} format (shown above). ### Usage in headers and footers: special references If you want a GroupHeader, GroupFooter, SideBar, etc to call on page text variable in the main page, you need to include special reference information. To explicitly reference the page text variable from the page being displayed add an asterisk to the page text variable's markup: {*$:Address} on the GroupFooter or GroupHeader page.
{*$:Mountain} \\ {*$Namespaced} Mt Ruapehu Page Text Variables
To include a page text variable from a header or footer see usage from other pages below.
Special references also apply to page variables and page list templates.
If you want to pull the data from another page, use the {Group/PageName$:Var} format. Suburb: Khandallah (:Lake:Taupo:) :Mountain:Mt Ruapehu ->"{PmWiki/PageTextVariables$:Suburb}" ->"{{$FullName}$:Lake}" ->"{PmWiki/PageTextVariables$:Mountain}" Suburb: Khandallah MountainMt Ruapehu "Khandallah" "Taupo" "Mt Ruapehu" ### Usage from included pages Page text variables are never included from their source page. See Usage from other pages above to refer to a page text variable on another page. ### Usage with pagelists Page lists can also access the page text variables: (:pagelist group=PmWiki order=$:Summary count=6 fmt=#singleline:)
And to create pagelist formats (such as those documented at Site.Page List Templates, Page Lists, Page List Templates, Page Variables. Store custom pagelists at Site.Local Templates?).
Page lists can also use page text variables to select pages :
(:pagelist group=PmWiki $:City=Paris count=8 fmt=#singleline order=-name:) lists pages having '$:City' set to 'Paris'.
(:pagelist group=PmWiki $:City="Addis Ababa,Paris" order=-$:Version count=8 fmt=#singleline:)
'quotes' must surround all the selections.
• When using page text variables for selection or ordering, don't put the curly braces around the variable name. The curly forms do a replacement before the pagelist command is evaluated.
• Link markup within the contents of a hidden page text variable directive (as opposed to other ways of specifying PTVs) will not be cached as a link on the page and thus won't be seen by pagelist's link= option. If you want the link to be found by link=, you need to specify the PTV using non-directive markup, or else put the link on the page even if it's hidden within a false conditional: (:Linkme: [[PageToLink]]:) (:if false:){$:Linkme}(:ifend:) The page text variable value is always the text that is written in the page. It is only evaluated when the variable is printed/output to HTML. To sort by a page text variable variable, all values in all pages are the not-yet-evaluated text strings, and the pagelist order function does what it can with them. It does not process/evaluate the text at this point. E.g. With a page name in to format "yyyyMonth" it is simpler to use a PageVariable calculated in config.php, not a PageTextVariable:$FmtPV['$NameToYearMonth'] = 'strftime("%Y%m", strtotime($name))';
Then use (:pagelist order=$NameToYearMonth:) An alternative is writing in the wiki page: (:MonthNum:07:) as the markup expression that follows won't work: (:MonthNum:{(ftime fmt=%m when="{$Namespaced}")}:)
### Testing if set or not set
=- PTV is set (is not empty), eg (:pagelist $:Var=- :) =-?* PTV is not set (is empty), ie not one character followed by 0 or more characters, eg. (:pagelist$:Var=-?* :) =* display all pages, regardless of the page text variable (slow) =-* display no pages, regardless of the page text variable (slow)
Tip : (:if ! equal "{$:PTV}" "":) will test if PTV is empty/unset or not. (:pagelist group=PmWiki$:Summary=-?* count=6 fmt=#singleline:)
### Use page text variable in a template
Display pages by Audience page text variable.
>>comment<< [[#byaudience]] (:if ! equal '{=$:Audience}' '{<$:Audience}':) -<'''{=$:Audience}''': (:ifend:) [[{=$Name}]] [[#byaudienceend]] >><< (:pagelist group=PmWiki count=10 fmt=#byaudience order=-$:Audience:) {=$:Audience}:
### Use page text variables in conditional markup
Page text variables will be assigned/evaluated before any conditional markup is evaluated. This effectively means that you cannot declare a PTV within an if...else condition; and also that a PTV will have a value even if it is set within a (:if false:)....(:if:) condition.
### Usage - from within code (developers only)
The standard PageVar($pagename,$varname) function can return page text variables, but remember to include the dollar and colon like this:
$var=PageVar($pagename,'$:City') It works by caching all page (text) variables it finds in a page (in$PCache) and returns the one requested.
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# Having difficulty debugging code
Trying to set up a screen with infinite practice for students to divide integers.
Code works for screen 16 - 18 but not screen 23. Can’t find the error.
I’m very new to desmos CL so I’m modifying others work and I have bit off more than I can chew I think. I copied screen 22 where the code is working for multiplying integers but for screen 23 I can’t get the code to create the fraction.
Just a couple things to adjust in order to display as a fraction. Include a backslash before frac in your expression variable.
expression = "\frac{${r1}}{${r2}}"
For the content sink, use this as your “otherwise.” You had an extra set of backtick marks there as well as an extra backslash.
"Simplify:\n\n${expression}" I didn’t have time to look at the multiplication slide, but if everything was working as intended there, you could use the code for that slide to help with the division slide too. I’m guessing you want the answers to be integer values, so you could reverse engineer the code to help with that. If you multiply the two randomly generated numbers, use the product as the dividend in your division problem. The divisor can be the r1 variable and the quotient can be the r2 variable. 1 Like I added a backslash to expression, and you had extra backticks in content. Excellent. That worked great. New problem, if the fraction generated is -3/12 it won’t accept -1/4 as the answer. Sorry for the delayed response…I made some adjustments to get the solutions to be accepted, but I changed it so that only integer solutions exist. It becomes more complicated when you are looking for simplified fractions (it’s possible, I just didn’t have time to explore). I also noticed that sometimes you were given a problem like 2/7 and no calculation was even necessary. Anyway, here’s the code you can use for the note. in = DivInput n = DivNote r = randomGenerator(in.submitCount) r1 = numericValue("(-1)^${r.int(0,1)}*${r.int(2,30)}") r2 = numericValue("(-1)^${r.int(0,1)}*${r.int(2,15)}") expression = "\frac{${dividend}}{${r2}}" dividend = numericValue("${r1}*${r2}") content: when in.timeSinceSubmit > 0 "${result}\n\n\Click to try another." otherwise "Simplify:\n\n${expression}" result = when in.lastValue("correct") = 1 "\n\Question: \frac{${dividend}}{${r2}}\n\n\Solution: ${solution}\n\n\✔Correct! 😎" otherwise "\n\Question: \frac{${cr3}}{${cr2}}\n\n\Solution: ${solution}\n\n\❌Incorrect. ☹️" cr1 = in.lastValue("r1") cr2 = in.lastValue("r2") cr3 = in.lastValue("r3") solution=cr1 And this line can be changed on the input. capture("correct"): when this.numericValue=note.script.r1 1 otherwise firstDefinedValue(numericValue("-${g.number("c_{urrent}")}"),0)
Thanks for all your help. I will try this out later.
S.
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Basic Concept of a Line
• Any point, that satisfies the equation of a line, will lie on the line.
• Also, any point through which a line passes, will always satisfy the equation of that line.
• Every straight line can be represented by a linear equation in two dimensions ( $x \ and \ y$ plane).
Inclination of a Line
The angle $\theta$ that the line makes with the $x-axis$ is called the “inclination of the line”. The angle $\theta$ is when measured in anti-clockwise direction the inclination is positive and if measured clock-wise then the inclination is negative.
Note:
• Inclination angle $\theta$ for $x-axis$ is $0^o$ . Also all lines parallel to $x-axis$ will also have the inclination angle as $0^o$ .
• Inclination angle $\theta$ for $y-axis$ is $90^o$ . Also all lines parallel to $y-axis$ will also have the inclination angle as $90^o$ .
Slope (or Gradient) of a Line
The slope of the line is the tangent of its inclination and is denoted by $m$ i.e. Slope $m = tan \theta$
Therefore
Slope of the $x-axis = tan \ 0^o= 0$
Slope of the $y-axis = tan \ 90^o = \infty$ (not defined)
The slope of the line is positive if the line makes an acute angle with $x-axis$ when measured in anti-clock wise direction i.e. $tan \ \theta$ is positive.
The slope of the line is negative if the line makes and obtuse angle with $x-axis$ when measured in anti-clockwise direction. i.e. $tan \ \theta$ is negative.
Formula for “Slope of Line passing through two points”
Let the two points be $(x_1, y_1)$ and $(x_2, y_2)$
$m = tan \ \theta = \frac{y_2-y_1}{x_2-x_1} = \frac{y_1-y_2}{x_1-x_2}$
Parallel Lines
Two lines having inclination as $\theta \ and \ \alpha$ will be parallel if
$\alpha=\theta \ or \ tan \ \alpha=tan\theta$
i.e. slope of the two lines is equal and hence they are parallel lines.
Perpendicular Lines
Two lines having inclination as \theta and \alpha will be perpendicular if:
$\theta = 90^o+\alpha$
$\Rightarrow tan \ \theta=tan \ (90^o+\alpha)$
$\Rightarrow tan \ \theta=-cot \ \alpha$
$\Rightarrow tan \ \theta=-\frac{1}{tan \ \alpha}$
$\Rightarrow tan \ \theta \times tan \ \alpha = -1$
or $m_1 \times m_2 = -1$ where $m_1 \ and \ m_2$ are slopes of the two lines respectively.
Note:
• If two lines are perpendicular, then the product of their slopes is $-1$. Conversely, if the product of the two lines is $-1$, they are perpendicular.
• Example: If the slope of a line is $2$, then the slope of another line parallel to this line would be $2$. Also the slope of a line perpendicular to this line would be $-\frac{1}{2}$.
• A line whose slope is $m=0$, is parallel to $x-axis$.
• Also the slope of $y-axis$ is not defined, all likes parallel to $y-axis$ will have slope which is not defined.
Condition for Collinearity of Three Points
Let there be three points $A(x_1, y_1), B(x_2, y_2) \ and \ C(x_3, y_3)$
If the slope of segment AB and BC is the same, then they are all on the same line and are collinear.
$m = \frac{y_2-y_1}{x_2-x_1} = \frac{y_3-y_2}{x_3-x_2}$
X-intercepts & Y-intercepts
Refer to first figure.
If a line meets the $x-axis$, then the distance from origin to the point of intercept is called $x-intercept$.
Similarly, if a line meets the $y-axis$, then the distance from origin to the point of intercept is called $y-intercept$.
Equation of a Line
Slope-Intercept Form: When the slope $(m)$ is given and the intercept on the $y-axis$ is given.
The the equation is:
$y = mx+c$ where $m$ is the slope and $c = intercept \ on \ y-axis$.
Point-Slope form: When the slope of the line and a point $(x_1, y_1)$ on a line is given
The equation is:
$y-y_1 = m(x-x_1)$
Equally Inclined Lines
This means that the lines make equal angle from both the coordinate axes. As shown in the figure, lines $AB \ and \ CD$ are equally inclined.
For $AB: Inclination \ \theta=45^o$. Therefore slope $= tan(45^o) = 1$
For $CD: Inclination \ \theta=-45^o$. Therefore the slope $=tan(-45^o) = -1$
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IMR Press / JOMH / Volume 18 / Issue 1 / DOI: 10.31083/jomh.2021.058
Open Access Original Research
The effects of BCAA and creatine supplementation on anaerobic capacity and ball kicking speed in male football players
Show Less
1 Department of Coaching Education/Sports Health Sciences, Faculty of Sport Sciences, Sinop University, 57010 Sinop, Turkey
2 Department of Physical Education and Sports/Physical Education and Sports Sciences, Faculty of Sport Sciences, Sinop University, 57010 Sinop, Turkey
3 Department of Recreation, Yaşar Doğu Faculty of Sport Sciences, Ondokuz Mayıs University, 55270 Samsun, Turkey
J. Mens. Health 2022 , 18(1), 5; https://doi.org/10.31083/jomh.2021.058
Submitted: 5 March 2021 | Accepted: 29 March 2021 | Published: 17 January 2022
(This article belongs to the Special Issue Sports and physical activities for men’s health)
This is an open access article under the CC BY 4.0 license.
Abstract
Background and objective: The use of nutritional supplements has increased in recent years. This study analyzes the effects of Branched-Chain Amino Acids (BCAA) and creatine (CR) supplementation on anaerobic capacity and ball kicking speed in football players. Material and methods: 24 volunteer-active male amateur football players between 18–26 were recruited for this study. Football players were randomly divided into three groups as BCAA (n = 8), CR (n = 8), and placebo (PLA) (n = 8). Experimental groups were given 5 g BCAA and 2 g creatine before and after exercise, whereas the placebo group ingested bran, performance tests and measurements were performed, and results were assessed. Results: BCAA group average power (pre: 530.70 $\pm$ 53.73 W vs. post: 567.65 $\pm$ 66.68 W; p = 0.028), CR group minimum power (pre: 413.75 $\pm$ 51.13 W vs. post: 462.82 $\pm$ 71.93 W; p = 0.043) increased, while there were decreases in peak power (pre: 659.34 $\pm$ 121.03 W vs. post: 613.20 $\pm$ 124.24 W; p = 0.043) and fatigue index (pre: 6.55 $\pm$ 2.12 W/s vs. post: 4.34 $\pm$ 2.37 W/s; p = 0.043) parameters of PLA group (p $<$ 0.05). There were statistically significant differences in the BCAA group in rest, pre-and post-supplementation; CR group in pre-and post-supplementation; PLA group in rest, pre-and post-supplementation (p $<$ 0.05). Conclusions: BCAA and creatine consumption do not affect recovery rates in football players regarding obtained data. But, regarding other findings of this study, BCAA and creatine supplementation improves anaerobic capacity, provides strength endurance against fatigue, and prevents the decrement of ball-kicking speed in exhaustion.
Keywords
BCAA
Creatine
Anaerobic capacity
Muscle strength endurance
Ball kicking speed
Recovery
1. Introduction
Football is characterized by its prevalence and popularity in many countries worldwide [1]. Some specific characteristics of sports can determine the importance of a football player. These are particular characteristics, including aerobic endurance, anaerobic endurance, power, and flexibility [2]. During a football match, more than 90% of the performance is supplied by aerobic metabolism, and the estimated anaerobic threshold of a player is 10 km running effort on average. Although the basic physiological, metabolic functions in a football game are supplied by aerobic metabolism, high-level skills such as jumping, kicking, and tackling are anaerobic [3]. Nutrition is necessarily an inseparable part of athletes’ training programs. Despite strenuous exercises and training programs that are believed to increase athletes’ nutrition requirements dramatically, consuming the proper foods with a balanced diet can meet the nutrition requirements in general. However, not all athletes can fulfill the increasing nutritional needs via natural diets due to some compelling reasons. Therefore, many athletes use natural supplements to overcome the inadequate diet and increase performance [4]. BCAA and creatine are predominant nutritional supplements utilized by football players because of their efficacy in developing ideal body composition and their proven positive effects on sportive performance [5].
BCAA (leucine, isoleucine, valine) is an essential amino acid for human protein synthesis [6, 7]. BCAA is abundantly found in skeletal muscle, and it is also oxidized in skeletal muscle while other amino acids are primarily catabolized in the liver. It contributes to the prevention of protein catabolism and enhances protein synthesis. Several previous studies have suggested that BCAA attenuates muscle soreness and damage, and it also plays a crucial role in recovery. BCAA helps preserve muscle mass in case of protein loss and catabolism, and it also reduces muscle damage and expedites the recovery process after strenuous endurance training. Moreover, BCAA improves the ideal body composition and maintains body performance and function [6, 8, 9, 10].
Creatine (CR) is one of the nutritional supports providing high benefits, and it has been recently used to enhance athletes’ performance [11]. Creatine is a prevalent supplement in sports industry and it is a nutritional support used by athletes to retain energy and gain strength during strenuous exercises. Creatine provides certain benefits for athletes, especially in short and high-intensity training [12, 13]. Creatine is a guanidine-based substance that is naturally produced in the human body. It is typically not an amino acid, but it consists of arginine, glycine, methionine, and it is synthesized from the reaction, including all these three amino acids [14]. Athletes commonly utilize high-intensity exercises and training that require anaerobic performance [15, 16].
The regular maintenance of the football players’ physical and physiological status depends on the meticulous evaluation of their performance output. High-intensity interval anaerobic and aerobic activities increase blood lactate concentration, which is the main reason for fatigue during a football match. In a study conducted with English Premier League football players, it was discovered that athletes averagely had 19 sprints in a single game which occurred every 4–5 minutes, alteration in the movement happened in every 3.5 seconds, a bout of high-intensity movement was interspaced in every 60 seconds, and thus maximal effort was performed in every 4 minutes as a result [17]. Our study analyzes the BCAA and creatine supplementation effects on anaerobic capacity and ball kicking speed in football players. Football is a high-performance sport, and the players’ physiological requirements have to be met for the peak performance. However, not all football players can fulfill physiological and nutritional needs via natural foods, so a supplementation is an option. Therefore, we hypothesized that BCAA and creatine supplementation would enhance anaerobic capacity and prevent decrement in ball kicking speed in exhaustion.
2. Methods
2.1 Research group
A priori test with Gpower 3.1 was used to determine the number of subjects. The power analysis test was conducted following a pilot application which indicated that eight subjects were sufficient per group (Effect Size: 0.87, Actual Power: 0.96). Twenty-four volunteer-active male amateur football players between the ages of 18–26 were recruited for this study (Table 1). Football players were randomly divided into three groups as BCAA (n = 8), CR (n = 8), and PLA (n = 8). Analyses were made using the pre-posttest method in physically identical conditions seven days apart without changing the subjects’ daily routines and training programs. Different types of training programs may have induced different effects on players, so all football players followed the identical training program through intervention week to ensure the test’s reliability. Inclusion criteria for this study are; being healthy, not having chronic and acute diseases, not having a limitation of movement related to any reason, and signing an informed consent form before testing. For this study, by Sinop University’s Human Research Ethics Committee, it was decided that there was no ethical inconvenience, and it was found appropriate (Number: 57452775-050.99-E).
Table 1.Descriptive statistics for participants.
Variable Group BCAA CR PLA Mean $\pm$ SD Age (year) 21.11 $\pm$ 2.61 20.85 $\pm$ 2.79 19.52 $\pm$ 0.67 Height (cm) 178.00 $\pm$ 4.69 180.00 $\pm$ 5.83 182.00 $\pm$ 11.26 Weight (kg) 73.38 $\pm$ 5.92 70.52 $\pm$ 5.89 73.26 $\pm$ 9.58 BMI (kg/m${}^{2}$) 23.18 $\pm$ 2.33 21.70 $\pm$ 1.61 21.78 $\pm$ 0.72 SD, standard deviation. Values are mean $\pm$ SD.
2.2 BCAA and CR supplementation
Twenty-four trained football players were randomly divided into three groups as BCAA (n = 8), CR (n = 8), and PLA (n = 8). Experimental groups were given, with proper use and dosage, seven days long 5000 mg BCAA and 2000 mg creatine supplementation daily with researcher supervision (BCAA: 2500 mg 30–40 minutes before training and 2500 mg 1 hour after training. Creatine: 1000 mg 30–40 minutes before training and 1000 mg 1 hour after training). The placebo group was given bran in the same amount and form with the nutritional supplement. Players were instructed to follow their daily routines, training programs, and nutrition regimens, and thus it was aimed to determine the effects of supplementation on athletes with reliable methods. The study was carried out as single-blind. Players were not informed about what substances they ingested. Hence, possible psychological effects which could influence athletic performance were removed in the first place, and the study was conducted in more reliable conditions. Furthermore, the day before the test protocol, players were strictly warned about not drinking alcohol or taking medication and paying attention to their nutrition and rest.
2.3 Running anaerobic sprint test (RAST)
Running anaerobic sprint test (RAST) was used to measure the anaerobic capacity. Before the test, the athletes were weighed. Athletes were asked to warm up before the test to get mentally and physically ready and were given 15 minutes to do so. During the RAST test, each athlete made six consecutive 35-meter sprints by giving 10-second breaks after each sprint. After an athlete started the test by making the first sprint and gave the first 10-second break, the timer device beeped, and the athlete made the second sprint. The test was completed after six consecutive sprints were made in the same way. For results and calculations, the assistant records the time taken for each 35-meter sprint to the nearest hundredth of a second and makes appropriate calculations. Power output for each sprint is found using the following equations:
Velocity = Distance $\div$ Time. Acceleration = Velocity $\div$ Time. Force = Weight $\times$ Acceleration. Power = Force $\times$ Velocity or Power = Weight $\times$ Distance 2 $\div$ Time 3 [18].
2.4 Ball speed measurement
In the present study, players’ ball kicking speed was determined with Stalker Solo 2 Radar Gun device, 20 meters away from the goal. Following the dominant leg choice, each player was asked to shoot following protocol from the prescribed spot. Thus, the use of the dominant leg was ensured in shootings. The device recording the ball speed was placed right across the shooting spot, nearby and behind the goal, to make sure measurement was made accurately. The shooting player was asked to hit the goal, and each player performed two times, the best score accepted as data. The device took the measurements accurately in a km/h unit.
2.5 Blood lactate test
For the lactate test, a lactate analyzer (Lactate Scout) was used. Blood samples were taken from the ear lobe to measure the lactic acid (LA) level. Each time blood was taken for measurements, needles and test strips were changed. By measuring resting LA levels and LA levels in the 1st, 5th, 10th minutes after the RAST test, subjects’ LA levels during recovery were determined.
2.6 Heart rate (HR)
A polar watch (V-800) to measure HR was used. A transmitter was placed in the chest, and HR in the resting and 1st, 3rd, 6th, 9th minutes after the RAST test were determined.
2.7 Height, weight, and body mass index analyses
In the study, athletes’ heights were measured through a Seca Height Measuring Device, and the body of the athletes was analyzed using the Inbody 120 Bioimpedance Body Composition Analyzer.
2.8 Experimental design
Using the pre-posttest method, without changing the subjects’ daily routines and training programs, some tests and measurements were made in physically identical conditions with seven days apart from each other, and results were assessed. In this study, the heights and weights of players were initially measured. Each player performed the same test protocol two times (before and after seven days of supplementation). Before the performance tests (Running Anaerobic Sprint Test (RAST), Ball Kicking Speed Test), each player’s ear lobe was scrubbed with alcohol and dried first, and then blood samples were taken to determine the resting lactate level and rest heart rate was measured right after. After that, each player individually performed the performance tests following the study protocol. During performance tests, each player was initially given 15 minutes of the personal warm-up session, and following the warm-up, players performed consecutively; rested ball kicking speed test, RAST, and repeated ball kicking speed test one more time. Hence, ball kicking speed with peak power, kicking the ball, and shot on the athletes’ target without rest were determined immediately after high-intensity training test protocol.
As soon as the performance test ended, the blood samples were taken at 1st, 5th, and 10th minutes from the ear lobe with identical protocol to assess the recovery speed of the athlete, and heart rate was detected at 1st, 3rd, 6th, and 9th minutes with the help of a transmitter strap on athlete’s chest that was sending the heart rate values to the device attached in the arm. The day after the pre-test, players were randomly divided into groups to ingest supplements or placebo, and supplementation was made single-blinded. Football players were given 5 g BCAA and 2 g creatine before and after exercise, whereas the placebo group ingested bran in the same amount and form with the nutritional supplements. Athletes were instructed to follow their nutrition regimens, daily routines, and training programs without changing, and they ingested nutritional supplements or placebo with proper use and dosage for seven days under the researchers’ supervision. Data obtained from pre-test and post-test were compared both within-group and between-group, and the effects of nutritional supplement loading were analyzed.
2.9 Statistical analyses
To control if the error terms showed normal distribution, data were checked using the Shapiro-Wilk Normality test, and our data were not normal distribution (p $<$ 0.05). Wilcoxon t-test was carried out to evaluate pre-post statistical differences of each parameter within time. Kruskal-Wallis test was used to assess the significant differences between groups. The research data obtained were given as the mean and standard deviation (Mean $\pm$ SD), statistical significance was accepted as p $<$ 0.05. The statistical analyses were performed using SPSS 22.0 V. statistical package.
3. Results
Regarding anaerobic capacity, BCAA group average power (pre: 530.70 $\pm$ 53.73 W vs. post: 567.65 $\pm$ 66.68 W; p = 0.028), CR group minimum power (pre: 413.75 $\pm$ 51.13 W vs. post: 462.82 $\pm$ 71.93 W; p = 0.043) increased, while there were decreases in peak power (pre: 659.34 $\pm$ 121.03 W vs. post: 613.20 $\pm$ 124.24 W; p = 0.043) and fatigue index (pre: 6.55 $\pm$ 2.12 W/s vs. post: 4.34 $\pm$ 2.37 W/s; p = 0.043) parameters of PLA group (p $<$ 0.05). Considering other within-group variables and between-group comparisons of anaerobic capacity, no statistically significant difference was found (p $>$ 0.05) (Table 2).
Table 2.Changes in mean values of BCAA, CR, and PLA groups.
Variable Group BCAA CR PLA Anaerobic capacity Period Mean $\pm$ SD Maximum power (W) Pre 654.88 $\pm$ 71.65 678.54 $\pm$ 80.51 659.34 $\pm$ 121.03 Post 685.36 $\pm$ 86.43 677.82 $\pm$ 57.88 613.20 $\pm$ 124.24* Minimum power (W) Pre 409.20 $\pm$ 28.38 413.75 $\pm$ 51.13 442.06 $\pm$ 60.93 Post 447.71 $\pm$ 38.51 462.82 $\pm$ 71.93* 469.06 $\pm$ 79.31 Average power (W) Pre 530.70 $\pm$ 53.73 544.85 $\pm$ 48.93 538.30 $\pm$ 84.96 Post 567.65 $\pm$ 66.68* 567.75 $\pm$ 55.87 533.12 $\pm$ 91.60 Fatigue index (W/s) Pre 7.34 $\pm$ 2.06 8.12 $\pm$ 2.78 6.55 $\pm$ 2.12 Post 7.30 $\pm$ 1.83 6.65 $\pm$ 1.40 4.34 $\pm$ 2.37* Ball speed (km/h) Period Mean $\pm$ SD Rest Pre 106.40 $\pm$ 6.24 102.55 $\pm$ 6.11 102.22 $\pm$ 4.60 Post 104.22 $\pm$ 7.21* 97.22 $\pm$ 7.45 98.19 $\pm$ 3.19* Exhausted Pre 97.25 $\pm$ 8.65 89.81 $\pm$ 7.40 89.60 $\pm$ 3.33 Post 98.86 $\pm$ 8.55 93.52 $\pm$ 6.47 88.60 $\pm$ 4.07 Pre-supplementation Rest 106.40 $\pm$ 6.24 102.55 $\pm$ 6.11 102.22 $\pm$ 4.60 Exhausted 97.25 $\pm$ 8.65${}^{†}$ 89.81 $\pm$ 7.40${}^{†}$ 89.60 $\pm$ 3.33${}^{†}$ Post-supplementation Rest 104.22 $\pm$ 7.21 97.22 $\pm$ 7.45 98.19 $\pm$ 3.19 Exhausted 98.86 $\pm$ 8.55${}^{†}$ 93.52 $\pm$ 6.47${}^{†}$ 88.60 $\pm$ 4.07${}^{†}$ SD, standard deviation; BCAA, branched-chain amino acids group; CR, creatine group; PLA, placebo group; Pre, pre-supplementation period; Post, post-supplementation period. Values are mean $\pm$ SD. *Significant (p $<$ 0.05) difference compared with pre- and post-supplementation values. ${}^{\textdagger{}}$Significant (p $<$ 0.05) difference compared with rest and exhausted values.
Regarding ball kicking speed parameters, there were statistically significant differences (p $<$ 0.05) in BCAA group in rest (pre: 106.40 $\pm$ 6.24 km/h vs. post: 104.22 $\pm$ 7.21 km/h; p = 0.046), pre-supplementation (rest: 106.40 $\pm$ 6.24 km/h vs. exhausted: 97.25 $\pm$ 8.65 km/h; p = 0.028), post-supplementation (rest: 104.22 $\pm$ 7.21 km/h vs. exhausted: 98.86 $\pm$ 8.55 km/h; p = 0.028); CR group pre-supplementation (rest: 102.55 $\pm$ 6.11 km/h vs. exhausted: 89.81 $\pm$ 7.40 km/h; p = 0.018), post-supplementation (rest: 97.22 $\pm$ 7.45 km/h vs. exhausted: 93.52 $\pm$ 6.47 km/h; p = 0.028); PLA group in rest (pre: 102.22 $\pm$ 4.60 km/h vs. post: 98.19 $\pm$ 3.19 km/h; p = 0.043), pre-supplementation (rest: 102.22 $\pm$ 4.60 km/h vs. exhausted: 89.60 $\pm$ 3.33 km/h; p = 0.043), post-supplementation (rest: 98.19 $\pm$ 3.19 km/h vs. exhausted: 88.60 $\pm$ 4.07 km/h; p = 0.042). Considering other within-group variables and between-group comparisons of ball kicking speed, no statistically significant difference was found (p $>$ 0.05) (Table 2).
When compared resting heart rates of within-group recovery rates, statistically significant decreases (p $<$ 0.05) were observed in BCAA (pre: 62.66 $\pm$ 6.28 bpm vs. post: 55.33 $\pm$ 2.65 bpm; p = 0.027) and CR (pre: 67.00 $\pm$ 4.04 bpm vs. post: 60.14 $\pm$ 6.38 bpm; p = 0.028) groups. There was no significant difference in the PLA group (p $>$ 0.05). Considering other within-group variables and between-group comparisons of recovery rates, no statistically significant difference was found (p $>$ 0.05) (Figs. 1,2).
Fig. 1.
The heart rate and lactate levels at different time points in rest and after exercise during recovery periods. BCAA, branched-chain amino acids group; CR, creatine group; PLA, placebo group; Pre, pre-supplementation period; Post, post-supplementation period. Values are mean $\pm$ SD. *Significant (p $<$ 0.05) difference compared with pre-and post-supplementation values.
Fig. 2.
The heart rate and lactate levels at different time points in rest and after exercise during recovery periods. BCAA, branched-chain amino acids group; CR, creatine group; PLA, placebo group; Pre, pre-supplementation period; Post, post-supplementation period. Values are mean $\pm$ SD. *Significant (p $<$ 0.05) difference in pre-and post-supplementation periods between BCAA, CR, and PLA groups.
4. Discussion
This current study aimed to investigate the effects of BCAA and creatine supplementation on anaerobic capacity and ball kicking speed in football players. Results showed that BCAA and creatine supplementation might positively affect anaerobic performance and ball kicking speed in exhaustion. Consumption of nutritional supplements combined with a regular diet is widely recognized to affect athletes’ health and sportive performance positively. Athletes use a wide range of nutritional supplements to improve their exercise performance and stay healthy [19]. BCAA and creatine are the prevalent nutritional supplements utilized by football players due to their positive effects on general health status and sportive performance. After reviewing the scientific literature, numerous studies appeared to be conducted previously about BCAA and creatine supplementation in athletes, single or combined with other nutritional supplements. Considering these studies performed by various supplementation methods, it is evident that BCAA and creatine consumptions were directly associated with health and sportive performance indicators such as body composition [7, 20], muscle strength and damage [9, 14], DOMS [10], high-intensity sprint performance [11], anaerobic performance and capacity [15, 16] and endurance performance [6, 9, 15].
In our study, significance was only observed in BCAA and CR groups regarding the recovery rate data in terms of resting heart rate. Similar results were observed in all three groups. BCAA and creatine can be said to have no positive effect on recovery rates considering study findings. No statistically significant difference was found in between-group recovery rates. Regarding the other data obtained, BCAA and CR anaerobic capacity and power increased in BCAA and CR groups after supplementation while decreasing the PLA group. In his study conducted with 16 elite male rowers, Chwalbiñska-Moneta divided athletes into two groups as subject and placebo, and athletes ingested 20 g of daily creatine for five days with endurance training, without any change on their nutrition regimens. Results showed that creatine did not induce any significant alteration in heart rate, there was no significant difference in the two groups’ blood lactic acid levels, but creatine improved endurance and anaerobic performance [21]. Similar to our results, there were no significant differences between lactic acid and heart rate variables, but the anaerobic performance was positively influenced. In another study, researchers made 30 days of phosphate salts (CPS) supplementation combined with 5 g of daily creatine loading to 32 male volunteers, and they found that this supplementation increased body weight but had no effect on the anaerobic capacity increase [16]. This study did not support our results concerning anaerobic capacity. In another study performed with trained university students, researchers suggested that creatine supplementation has a minor positive influence on regional muscle thickness during strength training [14]. In their study, Hoffmann et al. [22] discovered that creatine supplementation reduces the rate of fatigue, but there is no significant difference in anaerobic strength performance between subjects and the placebo group. When compared our results to Hoffman et al. [22], BCAA and creatine reduced fatigue similarly, while anaerobic capacity was also influenced positively. When other studies conducted by researchers about creatine consumption were analyzed, various results indicated that creatine increases the power, prevents decrement in lower-limb muscle strength of football players, and also has no positive effect on reducing the skeletal muscle damage and improvement in recovery of athletes and does not influence anaerobic sprint capacity. However, it has positive effects on running capacity, and it provides no significant difference in an anaerobic working capacity. In contrast, it improves the anaerobic mean power [20, 23, 24, 25, 26, 27, 28]. In our study, creatine consumption positively impacted minimum power and average power while it did not affect recovery levels. Van Hall et al. [29], in their study, carried out with ten trained male athletes, split subjects into four groups as control, low dose of BCAA, high dose of BCAA, and tryptophan, and they implemented tryptophan and low-high dose of BCAA loading method. Based on their results, there were no differences in burnout point and heart rate of the athletes concerning four tests, and as a result, any negative or positive effects of BCAA and tryptophan supplementation on athletes were not observed during the prolonged cycle-ergometer exercises. Jang et al. [30] conducted three trials with trained wrestlers in their study; athletes were instructed to intake 1st glucose, 2nd glucose + arginine + BCAA, and 3rd water. The peak and mean power were found similar in all three trials. Furthermore, supplementation of carbohydrates with or without arginine and BCAA during the post-game period did not affect performance. Howatson et al. [9] conducted 12 trained male athletes in their study and concluded that consumption of BCAA reduces muscle damage and enhances recovery. In contrast with these results, there were no positive effects of BCAA and creatine supplementation on recovery in our study. A significant increase was detected in the average power of the BCAA group and the minimum power of the CR group, whereas the placebo group had a significant decrease in maximum power. Similar results were found in another study, and it was reported that consumption of BCAA might reduce muscle damage and promote muscle protein synthesis [8]. In the study carried out by Shimomura et al. [31], it was suggested that BCAA consumption reduced muscle fatigue and muscle soreness, and thus it could be used for muscle recovery after exercise. De Palo et al. [32] included 11 male athletes in their research, and their results showed a statistically significant difference in the BCAA group’s lactate levels, and thus consumption of BCAA may reduce the post-exercise lactate levels and provides an improvement in energy use. Kim et al. [33] performed with 30 male athletes in their study and discovered that consumption of BCAA has no positive influence on lactate levels during endurance exercises, but on the other hand, it may reduce muscle damage. BCAA appeared to have no positive effect on lactic acid in our study. In another study, ten weeks of BCAA supplementation on trained cyclists contributed to an increase in peak power, mean power, and sprint power together with improvements in overall performance [34]. In a similar vein, Jafari et al. [35] found that BCAA consumption with endurance training may enhance anaerobic power and post-exercise recovery in trained athletes. Moreover, in another study, researchers similarly identified that consumption of BCAA provides an increase in peak power, mean power, squat jump, and countermovement together with a decrease in muscle soreness [36]. Likewise, peak power and mean power increased in our study. Stoppani et al. [37] implemented a supplementation to 30 trained male athletes using BCAA. According to their results, supplementation with BCAA can increase lean muscle mass and muscle strength.
When examined ball kicking speed data, it is understood that better findings for BCAA and CR groups were observed in ball kicking speed at rest and exhaustion compared to the PLA group. Our results demonstrated that BCAA and creatine supplementation had positive influences on ball kicking speed and anaerobic capacity, and thus, the decrement in ball kicking speed was prevented in fatigue. Therefore, our hypothesis was confirmed. Evaluation of the studies related to our topic indicates that many different results existed in the literature. In a study, the subject group ingested creatine whereas the placebo group consumed sucrose drink, and consequently, researchers found that creatine increased muscle strength and upper arm muscle area [38]. A similar study was carried out with 25 healthy male athletes, and subjects were divided into three groups as control, placebo, and creatine to analyze the muscle strength. Creatine did not increase muscle strength as a result [39]. In another study on swimmers, there was no increase in performance and muscle mass depending on creatine consumption [40]. Researchers split 17 male trained athletes into two groups as BCAA and carbohydrates and performed muscle strength analyses. In this study, researchers suggested that BCAA ingestion preserves lean mass and enhances skeletal muscle performance [6].
Additionally, some researchers discovered that BCAA supplementation increases endurance performance and enhances lipid oxidation during exercise [41, 42]. In another study conducted with twenty young resistance-trained males, BCAA attenuates muscle soreness in the BCAA group compared to PLCB following eccentric exercise [43]. Some researchers concluded that creatine supplementation had no significant effect on athletes’ anaerobic capacity, whereas others determined that creatine increased muscle power output in elite youth soccer players [44, 45]. According to these results, BCAA and creatine supplementation might be said to have positive influences on anaerobic power, resistance against fatigue, strength endurance, and ball kicking speed. Thus, all these findings supported our hypothesis. To our knowledge, this study has a research protocol that was never used previously.
Moreover, ball-kicking speed measurement together with anaerobic capacity and recovery parameters in post BCAA and creatine consumption was performed for the first time. This study was conducted with limited resources, and it only provided insights into anaerobic capacity, recovery, and ball kicking speed. Another limitation of the present study can be said as the number of subjects was 24.
5. Conclusions
BCAA and creatine consumption do not induce any effect on recovery rates in football players regarding obtained data. But, regarding other findings of this study, BCAA and creatine supplementation improves anaerobic capacity, provides strength endurance against fatigue, and prevents the decrement of ball-kicking speed in exhaustion. Further studies are needed to examine the long-term effectiveness of BCAA and creatine supplementation on anaerobic capacity and ball kicking speed.
Author contributions
Conceptualization—AM; methodology—AM and EA; validation—AM, EA, KA and AKY; formal analysis—AM and KA; investigation—AM, EA, KA and AKY; resources—AM; data curation—AM; writing-original draft preparation—AM; writing-review and editing—AM, EA, KA and AKY; visualization—AM and AKY; project administration—AM; funding acquisition—AM. All authors contributed to editorial changes in the manuscript. All authors read and approved the final manuscript.
Ethics approval and consent to participate
The study was conducted according to the guidelines of the Declaration of Helsinki and approved by Sinop University’s Human Research Ethics Committee (Number: 57452775-050.99-E). Informed consent was obtained from all subjects involved in the study.
Acknowledgment
All authors would like to express special thanks to Sinop University Faculty of Sport Sciences, Department of Coaching Education.
Funding
This work was supported by Sinop University Scientific Research Projects Coordination Unit. Project Number: SBF-1901-18-40, 2018.
Conflict of interest
The authors declare no conflict of interest.
Publisher’s Note: IMR Press stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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## Cryptology ePrint Archive: Report 2019/868
On the Round Complexity of Randomized Byzantine Agreement
Ran Cohen and Iftach Haitner and Nikolaos Makriyannis and Matan Orland and Alex Samorodnitsky
Abstract: We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that:
(1) BA protocols resilient against $n/3$ [resp., $n/4$] corruptions terminate (under attack) at the end of the first round with probability at most $o(1)$ [resp., $1/2+ o(1)$].
(2) BA protocols resilient against $n/4$ corruptions terminate at the end of the second round with probability at most $1-\Theta(1)$.
(3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against $n/3$ [resp., $n/4$] corruptions terminate at the end of the second round with probability at most $o(1)$ [resp., $1/2 + o(1)$].
The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI).
The third bound essentially matches the recent protocol of Micali (ITCS'17) that tolerates up to $n/3$ corruptions and terminates at the end of the third round with constant probability.
Category / Keywords: cryptographic protocols / Byzantine agreement; lower bound; round complexity
Original Publication (with major differences): DISC 2019
Date: received 25 Jul 2019, last revised 16 Dec 2019
Contact author: rancohen at ccs neu edu, iftachh at cs tau ac il, n makriyannis at gmail com, matanorland at mail tau ac il, salex at cs huji ac il
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2019/868
[ Cryptology ePrint archive ]
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## Algebra 1: Common Core (15th Edition)
Given: $y=-3x+5$ The y-intercept is $5$, so plot a point at $(0,5)$. The slope is $-3$. Move down 5 units and right $\frac{3}{2}$ units. Plot another point $(\frac{3}{2},0)$. Draw a line through the two points.
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## Algebra 1
$y \lt -12$
In order to solve the inequality, we must isolate the variable. We cancel out addition by subtracting 5 on both sides. This gives us the answer: $y \lt -12$.
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# Multiple language code snippets have been added to the site
Published
Tags:
I finally got around to implementing multiple programming languages to display on a single post.
## Problem
It has been a problem for some time that I’ve had no nice way to include code examples in multiple languages without pushing the length of the page up significantly. The main problem is that since the site is written in Jekyll, the code is within a markdown file, which gives me relatively little control over the content if I want to maintain a nice writing format (I could just dump a bunch of HTML in each post, but that would be ugly and lead to consistency issues).
Jekyll has some features that seem like they could help with this problem initially such as includes, data files and static files, however they all fall short in one way or another. Includes (templates) are great and I use them extensively, however there doesn’t seem to be a way to pass in blocks of content in a good way. I did manage to get it working with data files but I would then have to write all my code within a json file (with double spacing for some reason) away from the related content, which is not at all ideal. And static files unfortunately only expose metadata, not file content.
## Solution
My solution to this was to approach the problem in a similar manner to another library I utilise, code-prettify, which searches for all elements of types pre, code and xmp, then extracts the configuration from a comment above the element if it exists.
The way I did it was to wrap my code blocks in the markdown file with ‘marker’ elements with classes .code-block.start and .code-block.end. Then extract all pre elements in between the two marker elements and transform them as I please.
<div class="code-block start"></div>
<!--prettify lang=java-->
int number = 1;
<!--prettify lang=javascript-->
var number = 1;
<!--prettify lang=python-->
number = 1;
<div class="code-block end"></div>
It would have been nice to be able to do this with comments instead of divs, but there is no efficient way to look up comments in the DOM. Iterating over the entire tree would not be as performant as I need.
### Accessibility
As with the rest of my site, I wanted to get accessibility right. I know that it’s an all too common problem with tab widgets since the heading element is typically separated from the content so it is read in the incorrect order with a screen reader. I solved this by duplicating the heading, having one for display and one for screen readers. The display element is what the user sees on the tab, this is hidden from assistive technology by using aria-hidden="true", and the screen reader element is directly above the code block and contains css to hide it from display.
Here is the structure I used:
<div class="code-block">
<div>
<!-- Hidden from assistive technologies -->
<a aria-hidden="true" class="header">C#</a>
<a aria-hidden="true" class="header active">Java</a>
</div>
<div>
<!-- Only visible to assistive technologies -->
<h6 class="screen-reader">C#</h6>
<pre class="prettyprint prettyprinted"></pre>
</div>
<div>
<!-- Only visible to assistive technologies -->
<h6 class="screen-reader">C#</h6>
<pre class="prettyprint prettyprinted"></pre>
</div>
</div>
.screen-reader {
position: absolute;
left: -9999px;
}
This makes it read just like it’s a normal document with the tab content being laid out one after the other.
### Performance
Performance is a feature, delivering content blazingly fast is a great user experience and I strive towards that. The main concern with performance was that there is a bit of DOM manipulation happening pretty early in the page load. Luckily the actions themselves are pretty lightweight when performed scarcely, provided things are done right:
• Perform a minimal number of DOM manipulations
• Don’t block HTML parsing with scripts that are not essential to the initial load (ie. use async)
To help with the first point, the manipulation of the <pre> elements needed to be done before code-prettify performs its actions, because moving a single <pre> around the page is a lot different to moving a <pre> with the mounds of children it creates to do syntax highlighting.
### Error prevention
With something like this things can always go wrong, the feature depends on several things being in place and could flat out break the page if they are not. I built this feature rather defensively and warn/exit if something doesn’t seem right to try and prevent anything bad getting through to my readers. My writing flow will likely not let anything like this through, but it doesn’t hurt to be careful. I’ll also get a nice warning when I do something wrote.
## Wrapping up
See the new feature in action above and in this article, I’ll slowly be rolling this out to all posts that have either multiple languages or where the snippet could do with a language label. This is just one of the improvements I have been working on over the past few days. Keep an eye out for more!
## Comments
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# What's wrong with my ambient light setup?
This topic is 4561 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I'm having some severe with ambient lightning, and I don't know if the problem is my code or not. I'm currently loading a model from disk, but when I display it with normal lights, it looks messed up, but when I use ambient lights, the screen goes blank. I have no idea what I am doing wrong here. I'm loading a simple test model from disc, the sphere.x that comes with the DirectX SDK. I loaded it into a D3DXMesh(Or in C# it's just Mesh) and when I reset my device, I set the lightning as this:
device.RenderState.Ambient = Color.White;
When I render, the sphere, the screen is blank. When I turn lightning off, the sphere shows up, but completely white. What am I doing wrong? Lights ARE on when using ambient lights. Toolmaker
##### Share on other sites
Have you turned D3D Lighting on?
Is this done with shaders or D3DLighting?
ace
##### Share on other sites
According to the documentation, lightning is on by default in Managed DirectX, so yes, lightning is on, and this is using default lightning(so, up to 8 light sources).
Toolmaker
##### Share on other sites
Has the mesh got normals?
ace
##### Share on other sites
if ((mesh.VertexFormat & VertexFormats.Normal) != VertexFormats.Normal) { Mesh tmpMesh = mesh.Clone(mesh.Options.Value, mesh.VertexFormat | VertexFormats.Normal, engine.Device); tmpMesh.ComputeNormals(); mesh.Dispose(); mesh = tmpMesh; }
Still nothing on screen, unless I turn lightning off.
Toolmaker
Any ideas?
##### Share on other sites
Are you clearing your background to black? If so, the sphere may be incorrectly rendered as black, and you simply can't see it on your background.
Are you setting the correct vertex format before you render the object? And are you rendering anything else at all?
##### Share on other sites
Quote:
Original post by intrest86Are you clearing your background to black? If so, the sphere may be incorrectly rendered as black, and you simply can't see it on your background.Are you setting the correct vertex format before you render the object? And are you rendering anything else at all?
Yes, I'm clearing to background to black. I changed it to SteelBlue, and my mesh shows up as black. In other words, it does render, but ends up black.
Also, the D3DXMesh class is suppose to set the vertexformat itself before rendering, and no, I'm currently not rendering anything else.
Would this have to do with the material(s) of my mesh not properly set? If so, how can I fix it?
Toolmaker
##### Share on other sites
Can you post just the code that renders the mesh? Since it is from the SDK it obviously is a valid mesh, so there is something code-wise going on.
##### Share on other sites
I found the problem: The model materials don't have a value for ambient light, thus show up black. During loading, I do:
materials = mtrls.Material3D;materials.Ambient = materials.Diffuse;
And voila the model shows up:
But yeah, the models is totally fucked up. It now works perfect with the SDK models and the converted model. Down-side is, I can't calculate the normals for this model, or it throws an exception, even after cleaning and validating the mesh.
But, at least it works now. I still wonder, the model I first had looked totally messed up with the lights. So, I want to try again with a light, just to see how it ends up.
I want my camera to be at a 45 degree angle. What is the best location to place the light? Right below the camera, or on the opposite location of the camera? I was to have some shading on the ship, so the light should be above it. My zFarPlane is 5000 units now, so how should I set the range and more important, the attenuation? How does the attenuation work? If I set it to 0.2f, does the light decrease 0.2f each unit or so?
Toolmaker
|
Book section Open Access
# Algorithmic Countermeasures Against Fault Attacks and Power Analysis for RSA-CRT
Kiss, Ágnes; Krämer, Juliane; Rauzy, Pablo; Seifert, Jean-Pierre
### Citation Style Language JSON Export
{
"DOI": "10.1007/978-3-319-43283-0_7",
"author": [
{
"given": "\u00c1gnes",
"family": "Kiss"
},
{
"given": "Juliane",
"family": "Kr\u00e4mer"
},
{
"given": "Pablo",
"family": "Rauzy"
},
{
"given": "Jean-Pierre",
"family": "Seifert"
}
],
"issued": {
"date-parts": [
[
2016,
1,
1
]
]
},
"abstract": "In this work, we analyze all existing RSA-CRT countermeasures against the Bellcore attack that use binary self-secure exponentiation algorithms. We test their security against a powerful adversary by simulating fault injections in a fault model that includes random, zeroing, and skipping faults at all possible fault locations. We find that most of the countermeasures are vulnerable and do not provide sufficient security against all attacks in this fault model. After investigating how additional measures can be included to counter all possible fault injections, we present three countermeasures which prevent both power analysis and many kinds of fault attacks.",
"title": "Algorithmic Countermeasures Against Fault Attacks and Power Analysis for RSA-CRT",
"type": "chapter",
"id": "60134"
}
79
22
views
|
Math and science::Analysis::Tao::09. Continuous functions on R
# Uniform continuity
### Continuous functions, open intervals and uniform continuity
Card 1 of 3: Uniform continuity
For a continuous function on a closed interval $$[a, b]$$ we know it must be [...]; other nice properties follow. If we relax the restriction and consider a continuous function on an open interval, $$(a, b)$$, we cannot imply that it is bounded, and we lose subsequence nice properties. Consider $$f: (0, 2) \to \mathbb{R}$$ with $$f(x):=\frac{1}{x}$$ for an illustration.
#### Measure of stability
We try to rebuild some new structure around functions on an open interval. The plan is to classify and distinguish continuous functions based on a measure of stability: measure the degree to which they vary over a certain sized interval of their domain.
#### $$\delta$$-islands of stability
For a function $$f : X \to \mathbb{R}$$ to be continuous at $$x_0 \in X$$, for any $$\varepsilon > 0$$ there needed to exist some $$\delta > 0$$ such that for all $$x \in (x_0 - \delta, x_0 + \delta)$$ we have $$|f(x)-f(x_0)| < \varepsilon$$. The $$\delta$$ was free to change for both every $$\varepsilon$$ and for every $$x_0$$.
Restricting $$\delta$$ to [...] we can describe what it means for a function to be uniformly convergent over it's full domain.
### Uniform continuity
Let $$X \subseteq \mathbb{R}$$ be a set, and let $$f : X \to \mathbb{R}$$ be a continuous function. We say that $$f$$ is uniformly continuous iff for every real $$\varepsilon > 0$$, there exists a real $$\delta > 0$$ such that $$|f(x_1) - f(x_2)| < \varepsilon$$ whenever $$x_1, x_2 \in X$$ and $$|x_1 - x_2 | < \delta$$.
Tao uses an if rather than iff relationship in his definition, but I don't see why.
|
Difference between the AND and && operator in php
PHPServer Side ProgrammingProgramming
'AND' Logical operator
'AND' operator is a logical AND operator but has low precedence to = operator.
'&&' Logical operator
'&&' is also a logical AND operator but has high precedence to = operator.
Example
Following the example, shows the difference of 'AND' vs '&&' operators.
Live Demo
<!DOCTYPE html>
<html>
<title>PHP Example</title>
<body>
<?php
$x = true;$y = false;
$result =$x AND $y; print('$result = $x AND$y');
print("<br/>");
var_dump($result); print("<br/>");$result = $x &&$y;
print('$result =$x && $y'); print("<br/>"); var_dump($result);
?>
</body>
</html>
Output
$result =$x AND $y bool(true)$result = $x &&$y
bool(false)
Updated on 13-Jan-2020 06:39:02
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## Novel delay-dependent stability conditions for a class of MIMO networked control systems with nonlinear perturbation.(English)Zbl 1136.93409
Summary: This paper considers the problem of delay-dependent stability criteria for a class of Multi-Input and Multi-Output (MIMO) networked control systems with nonlinear perturbation. Due to many independent sensors and actuators existed in the MIMO networked control systems, a distributed time delays networked control systems with structured uncertainties and external nonlinear perturbation is proposed in this paper. Based on Lyapunov stability theory combined with the descriptor system approach and Linear Matrix Inequalities (LMIs) techniques, some novel and improved sufficient conditions are derived to the delay-dependent stability of these systems. By solving a convex optimization problem of the LMI, the maximum upper bound of the allowable delay can be obtained. Compared to the existing criterions on this aspect, the proposed criteria gives a much less conservative maximum allowable delay bound. Numerical examples and simulations illustrate that our conditions are feasible and are less conservative than previous ones.
### MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93A15 Large-scale systems 90C25 Convex programming
Full Text:
### References:
[1] Halevi, Y.; Ray, A., Integrated communication and control systems: part I - analysis, ASME J. dyn. syst. measure control, 110, 4, 367-373, (1988) [2] J. Nilsson, Real-time control systems with delays. PhD dissertation, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1998. · Zbl 0908.93073 [3] Walsh, G.C.; Ye, H.; Bushnell, L.G., Stability analysis of networked control systems, IEEE trans. control syst. technol., 10, 3, 438-446, (2002) [4] Zhang, W.; Branicky, M.S.; Phillips, S.M., Stability of networked control systems, IEEE control. syst. mag., 21, 84-99, (2001) [5] X. Lei, J.M. Zhang, S.Q. Wang, Stability analysis of networked control systems, in: Proceedings of the First International Conference on Machine Learning and Cybernetics, vol. 1, 2002, pp. 757-759. [6] Kim, D.S.; Lee, Y.S.; Kwon, W.H.; Park, H.S., Maximum allowable delay bounds of networked control systems, Control eng. practice, 11, 1301-1313, (2003) [7] C.H. Wang, Y.F. Wang, H.J. Gao, Compensation time-varying in networked control systems via delay-dependent stabilization approach, in: Proceedings of the 2004 IEEE International Conference on Control Applications, vol. 2, 2004. pp. 248-253. [8] Park, J.H., Robust stabilization for dynamic systems with multiple time varying delays and nonlinear uncertainties, J. opt. theory appl., 108, 155-174, (2001) · Zbl 0981.93069 [9] Lien, C.H.; Chen, J.D., Discrete-delay-independent and discrete delay dependent criteria for a class of neutral systems, J. dyn. syst. measure, control, 125, 33-41, (2003) [10] Moon, Y.S.; Park, P.G.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. control, 74, 14, 1447-1455, (2001) · Zbl 1023.93055 [11] Cao, Y.Y.; Sun, Y.X., Delay-dependent robust stabilization of uncertain systems with multiple state delays, IEEE trans. automat. control, 43, 11, 1608-1612, (1998) · Zbl 0973.93043 [12] De Souza, C.E.; Li, X., Delay-dependent robust H1 control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321, (1999) · Zbl 1041.93515 [13] Su, T.J.; Lu, C.Y.; Tsai, J.S.H., LMI delay-dependent robust stability criteria for uncertain systems with multiple-state delays, IEEE trans. circuits syst., 49, 2, 253-256, (2002) · Zbl 1368.93505 [14] He, Y.; Wu, M.; She, J.H.; Liu, G.P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Syst. control lett., 51, 57-65, (2004) · Zbl 1157.93467 [15] Wu, M.; He, Y.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delays systems, Automatica, 40, 3, 1435-1439, (2004) · Zbl 1059.93108 [16] Kwon, O.M.; Park Ju, H., On improved delay-dependent robust control for uncertain time-delay systems, IEEE trans. automat. control, 49, 11, 1991-1995, (2004) · Zbl 1365.93370 [17] Lien, C.H., Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay, Chaos, soliton, fract., 28, 2, 422-427, (2006) · Zbl 1091.93022 [18] Sun, J.T., Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control, Chaos, soliton. fract., 21, 1, 143-150, (2004) · Zbl 1048.37509 [19] Huang, X.; Cao, J.D.; Huang, D.S., LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks, Chaos, soliton. fract., 24, 3, 885-898, (2005) · Zbl 1071.82538 [20] Zhang, Y.P.; Sun, J.T., Delay-dependent stability criteria for coupled chaotic systems via unidirectional linear error feedback approach, Chaos, soliton. fract., 22, 1, 199-205, (2004) · Zbl 1089.93018 [21] Liu, W.X.; Zhang, H.B.; Zhang, F.L., Delay-dependent stability of uncertain fuzzy large-scale systems with time delays, Chaos, soliton. fract., 26, 1, 147-158, (2005) · Zbl 1080.34058 [22] Li, C.D.; Liao, X.F.; Zhang, R., Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach, Chaos, soliton. fract., 24, 4, 1119-1134, (2005) · Zbl 1101.68771 [23] Zhang, Q.; Wei, X.P.; Xu, J., Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, soliton. fract., 23, 4, 1363-1369, (2005) · Zbl 1094.34055 [24] Tu, F.H.; Liao, X.F.; Zhang, W., Delay-dependent asymptotic stability of a two-neuron system with different time delays, Chaos, soliton. fract., 28, 2, 437-447, (2006) · Zbl 1084.68109 [25] Su, J.H., Further results on the robust stability of linear systems with a single time delay, Syst. control lett., 23, 375-379, (1994) · Zbl 0805.93045 [26] Li, X.; de Souza, C.E., Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach, IEEE trans. automat. control, 42, 1144-1148, (1997) · Zbl 0889.93050 [27] Liu, P.L.; Su, T.J., Robust stability of interval time-delay systems with delay-dependence, Syst. control lett., 33, 231-239, (1998) · Zbl 0902.93052 [28] Lu, C.Y.; Tsai, J.S.H.; Su, T.J., On improved delay-dependent robust stability criteria for uncertain systems with multiple-state delays, IEEE trans. circuits syst., 49, 2, 253-256, (2002) · Zbl 1368.93505 [29] Liu, X.W.; Zhang, H.B., New stability criterion of uncertain systems with time-varying delay, Chaos, soliton. fract., 26, 5, 1343-1348, (2005) · Zbl 1075.34072 [30] Yan, H.C.; Huang, X.H.; Wang, M.; Zhang, H., Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output, Chaos, soliton. fract., 34, 5, 997-1005, (2007) · Zbl 1138.34035 [31] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 2805-2810. [32] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 [33] V.A. Yakubovich, S-procedure in nonlinear control theory. Vestnik Leningradskogo Universiteta, Ser. Matematika, Series 1, 1971, 13, 62-77. · Zbl 0232.93010 [34] Xie, L., Output feedback H_{∞} control of systems with parameter uncertainty, Int. J. control, 63, 741-750, (1996) · Zbl 0841.93014 [35] Cao, Jiuwen; Zhong, Shouming, New delay-dependent condition for absolute stability of lurie control systems with multiple time-delays and nonlinearities, Appl. math. computat., (2007) · Zbl 1193.93143 [36] Fridman, E., New lyapunov – krasovskii functionals for stability of linear retarded and neutral systems, Syst. control lett., 43, 309-319, (2001) · Zbl 0974.93028 [37] Gu, K.; Niculescu, S.-I., Further remarks on additional dynamics in various model transformations of linear delay systems, IEEE trans. automat. control, 46, 497-500, (2001) · Zbl 1056.93511
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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Tuesday
September 2, 2014
# Homework Help: physics
Posted by s on Friday, April 19, 2013 at 5:31am.
Consider the observable M that corresponds to a measurement in the sign basis where the measurement value is 3 if the outcome is + and −2 if the outcome is −.
Write M in the standard basis.
If M is the Hamiltonian acting on a qubit which is in the state |ψ(0)⟩=|0⟩ at time 0, what is the state of the qubit at time t? Assume that you are working in units such that ℏ=1. You may use e and t in your answer.
Now you perform an X=(0110) measurement on the qubit at time 0. What is the expected value of your measurement?
What if you perform the above measurement at time t=4π3 instead? What is the expected value of your measurement?
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# What is elastic potential energy?
Learn what elastic potential energy means and how to calculate it.
# What is elastic potential energy?
Elastic potential energy is energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process. The deformation could involve compressing, stretching or twisting the object. Many objects are designed specifically to store elastic potential energy, for example:
• The coil spring of a wind-up clock
• An archer's stretched bow
• A bent diving board, just before a divers jump
• The twisted rubber band which powers a toy airplane
• A bouncy ball, compressed at the moment it bounces off a brick wall.
An object designed to store elastic potential energy will typically have a high elastic limit, however all elastic objects have a limit to the load they can sustain. When deformed beyond the elastic limit, the object will no longer return to its original shape. In earlier generations, wind-up mechanical watches powered by coil springs were popular accessories. Nowadays, we don't tend to use wind-up smartphones because no materials exist with high enough elastic limit to store elastic potential energy with high enough energy density.
# How can we calculate elastic potential energy for an ideal spring?
Our article on Hooke's law and elasticity discusses how the magnitude of the force F due to an ideal spring depends linearly on the length it has been compressed or expanded delta, x,
F, equals, k, dot, delta, x
where k is some positive number known as the spring constant. The spring force is a conservative force and conservative forces have potential energies associated with them.
From the definition of work we know that the area under a force vs displacement graph gives the work done by the force. Figure 1 shows a plot of force vs displacement for a spring. Because the area under the curve is a triangle and no energy is lost in an ideal spring, the elastic potential energy U can be found from the work done
\begin{aligned}U &= \frac{1}{2} (\Delta x) \cdot k (\Delta x) \\ &= \boxed{\frac{1}{2} k (\Delta x)^2} \end{aligned}
Figure 1: The work done by a force on an ideal spring.
Figure 1: The work done by a force on an ideal spring.
Exercise 1: A truck spring has a spring constant of 5, dot, 10, start superscript, 4, end superscript, space, N, slash, m. When unloaded, the truck sits 0.8 m above the road. When loaded with goods, it lowers to 0.7 m above the ground. How much potential energy is stored in the four springs?
Exercise 2a: A trained archer has the ability to draw a longbow with a force of up to 300 N, extending the string back by 0.6 m. Assuming the bow behaves like an ideal spring, what spring constant would allow the archer to make use of his full strength?
A drawn bow.
Figure 2: A drawn bow, as used in exercise 2.
Exercise 2b: What potential energy is stored in the bow when it is drawn?
Exercise 2c: Assuming the arrow has a mass of 30 g, approximately what speed will it be fired at?
Exercise 2d: Suppose that measurements from a high speed camera show the arrow to be moving at a somewhat slower speed than predicted by conservation of energy. Is there any work being done that we have not accounted for?
# What about real elastic materials?
In our article on Hooke's law and elasticity we discuss how real springs only obey Hooke's law over some particular range of applied force. Some elastic materials such as rubber bands and flexible plastics can function as springs but often have hysteresis; this means the force vs extension curve follows a different path when the material is being deformed compared to when it is relaxing back to its equilibrium position.
Fortunately, the basic technique of applying the definition of work that we employed for an ideal spring also works for elastic materials in general. The elastic potential energy can always be found from the area under the force vs extension curve, regardless of the shape of the curve.
In our earlier analysis, we have considered the ideal spring as a one-dimensional object. In reality, elastic materials are three dimensional. It turns out that the same procedure still applies. The equivalent to the force vs extension curve is the stress vs strain curve.
Where a three-dimensional elastic material obeys Hooke's law,
E, n, e, r, g, y, slash, v, o, l, u, m, e, equals, start fraction, 1, divided by, 2, end fraction, left parenthesis, S, t, r, e, s, s, dot, S, t, r, a, i, n, right parenthesis
Exercise 3: Figure 3 shows a stress vs strain plot for a rubber band. As it is stretched (loaded), the curve takes the upper path. Because the rubber band is not ideal, it delivers less force for a given extension when relaxing back (unloaded). The purple shaded area represents the elastic potential energy at maximum extension. The difference in area between the loaded and unloaded case is shown in yellow. This represents the energy which is lost to heat as the band is cycled between stretched and relaxed.
If the rubber band has length 100, space, m, m, width 10, space, m, m and thickness 1, space, m, m how much heat is generated in the band as it is stretched and released?
Figure 3: Force vs extension curve for a rubber band. Vertical and horizontal gridlines at 0.05 units.
Figure 3: Force vs extension curve for a rubber band. Vertical and horizontal gridlines at 0.05 units.
## Want to join the conversation?
• In the rubber band example, is the heat dissipated as work is done stretching the rubber band, or as the rubber band is being unloaded?
• I'm fairly new to this topic, but from past experience of doing this in 3rd grade, we used to stretch a rubber band really quickly, then put it to our upper lip (while it was still stretched.). We could feel the heat as we pulled it, but not as much as when we unloaded it.
So mathematically, I can't tell you the answer, but from experimentation, it does produce heat when loaded.
• Exercise 2 is worded very strangely. It sounds like 0.6m is just the distance the string gets pulled back when 300N is applied, which would imply a specific spring constant, so why does the question make it sound like the spring constant could be anything? Is 0.6m just the maximum limit to how far the bow can be pulled back? That should be stated more clearly. Also, wouldn't any spring constant greater than 500N/m also allow the archer to use his full strength?
• The way I understood it, 300N is his maximum strength. If he useed 250N and produced an extension of 0.6m, the spring constant would be different (in which case the bow would probably be made in a different shape or size or with a different material).
• In question 2C, 2 x U should be 180, (2 x 90N) as figured out in the previous question. So how does 2 x U = 2.9? Someone please explain, thanks.
• Dude it not 2.9. Its 2*90. The dot there is for multiplication
• Why in Exercise1 250J/spring = 1000J? ( solution)
• There are four springs on the truck in exercise 1 (one per wheel.) The displacement given is the displacement of the entire truck, meaning each individual spring is compressed 0.1 m. The calculation done (PE=(0.5)(5*10^4)(0.1)^2) gives you the amount of energy stored in each individual spring. Therefor the total energy stored in all four springs is 250 J * 4 springs = 1000 J total.
• In question 3, why is the heat energy = stress * strain * volume, instead of stress* strain * volume * .5, or am I missing something?
• In a stress-strain graph, is the stress plotted always (force applied) / (original cross-sectional area of material) or is it (force applied) / (cross-sectional area of material when that force is applied)? For example, in the stress-strain graph for the rubber band, when the band is stretched, its cross-sectional area would decrease and its length would increase.
• prove how energy/volume =1/2 stress.strain
• In the extension vs force graph, what if the force was always constant? (e.g. the weight of a ball pulling down a vertical spring). In the graph, it isn't and just keeps growing as the displacement grows.
(1 vote)
• If the force was constant, you wouldn't have a spring. That's not what springs do.
• i don't understand how exercise 3 went from 0.05N/mm^2 to 5 x 10^4 N/m^2.
• Why do we multiply the volume of the rubber by the heat in the last exercise?
Thanks
• Just above exercise 3 it states that
"Where a three-dimensional elastic material obeys Hooke's law,
Energy/volume=(Stress*Strain)/2"
The rubber band we are using for this exercise is a 3-dimensional object and figure 3 is a stress vs strain plot. Notice that the first part of the equation is Energy/volume. When you find the area of the yellow part that corresponds to heat you get an expression of (Energy that is spent on heat)/(Volume of the object). So in order to find the energy spent on heat we have to multiply by the volume.
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# Find Area of Triangle
#### xyz_1965
##### Member
Find the area of a triangle with angle 70° in between sides 6 cm and 4 cm.
Solution:
From the SOH-CAH-TOA mnemonic, I want the ratio of the opposite side (CD) to the hypotenuse (AC). I should be using the *sine* function, not cosine. Yes?
SOH leads to sin = opp/hyp
sin(70°) = CD/4
CD = 4 sin(70°)
Here is the rest:
Area = 12 sin(70°)
≈ 12 * 0.9396
≈ 11.28 cm^2
Yes?
#### MarkFL
Staff member
I would use:
$$\displaystyle A=\frac{1}{2}ab\sin(C)$$
Using the given data:
$$\displaystyle A=\frac{1}{2}(6\text{ cm})(4\text{ cm})\sin(70^{\circ})$$
Looks good.
#### xyz_1965
##### Member
I would use:
$$\displaystyle A=\frac{1}{2}ab\sin(C)$$
Using the given data:
$$\displaystyle A=\frac{1}{2}(6\text{ cm})(4\text{ cm})\sin(70^{\circ})$$
Looks good.
I know the law of sines or law of cosines could be applied here. This is the next chapter in my studies.
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Congruent Parts, Part 1
ID: kimum-fuboz
Illustrative Math
Subject: Geometry
Congruent Parts, Part 1
Classroom:
Due:
Student Name:
Date Submitted:
Problem 1
1) When rectangle $ABCD$ is reflected across line $EF$, the image is $DCBA$. How do you know that segment $AB$ is congruent to segment $DC$?
a) $\text{A rectangle has 2 pairs of parallel sides.}$b) $\text{Any 2 sides of a rectangle are congruent.}$c) $\text{Congruent parts of congruent figures are corresponding.}$d) $\text{Corresponding parts of congruent figures are congruent.}$
Problem 2
2) Triangle $FGH$ is the image of isosceles triangle $FEH$ after a reflection across line $HF$. Select all the statements that are a result of corresponding parts of congruent triangles being congruent. Write each corresponding letter in the answer box and separate letters with commas.
a) $EFGH$ is a rectangle. $\quad\quad$ b) $EFGH$ has 4 congruent sides. $\quad\quad$ c) Diagonal $FH$ bisects angles $EFG$ and $EHG$.
d) Diagonal $FH$ is perpendicular to side $FE$. $\quad\quad$ e) Angle $FEH$ is congruent to angle $FGH$.
Problem 3
3) Reflect right triangle $ABC$ across line $BC$.
4) Classify triangle $ACA'$ according to its side lengths.
5) Explain how you know.
Problem 4
6) Triangles $FAD$ and $DCE$ are translations of triangle $ABC$.
Select all the statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.
a) Points $B$, $A$, and $F$ are collinear. $\quad\quad$ b) The measure of angle $BCA$ is the same as the measure of angle $CED$.
c) Line $AD$ is parallel to line $BC$. $\quad\quad$ d) The measure of angle $CED$ is the same as the measure of angle $FAD$.
e) The measure of angle $DAC$ is the same as the measure of angle $BCA$.
f) Triangle $ADC$ is a reflection of triangle $FAD$.
Problem 5
Triangle $ABC$ is congruent to triangles $BAD$ and $CEA$.
7) Explain why points $D$, $A$, and $E$ are collinear.
8) Explain why line $DE$ is parallel to line $BC$.
Problem 6
9) Identify a figure that is the result of a rigid transformation of quadrilateral $ABCD$.
10) Describe a rigid transformation that would take $ABCD$ to that figure.
|
Browse Graduate Dissertations and Theses at Illinois by Contributor "Haboush, W.J.,"
• (1993)
The topic of my thesis is the geometry of projective homogeneous spaces G/H for a semisimple algebraic group G in characteristic p $>$ 0, where H is a subgroup scheme containing a Borel subgroup B. In characteristic p ...
application/pdf
PDF (2MB)
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Miscellaneous Topics
Are you preparing for campus placements,Banking,SSC, IAS, Insurance,Defence and other competitive exams? Then, make sure to take some time in practicing the Miscellaneous Topics questions and answer in Quantitative Aptitude. Moreover, only those questions are included that are relevant and likely to be asked in any competitive exam. So, take these questions and answer, brush up your skills and practice to stay fully prepared for any your exam.
• Q43.Find the missing value in the given figure?
• Q44.How many colours are required at the minimum to paint the given figure such that no two adjacent regions have the same colour? (Regions sharing a vertex should not be considered as adjacent regions)?
• Q45.What is the value of X in the given figure?
• Q46.How many quadrilaterals are there in the given figure?
• Q47.Find the missing figure.
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# The Indefinite Integral of Zero
1. Nov 3, 2014
Argument A
$∫ 0 dx = 0x + C = C$
Argument B
$∫ 0 dx = ∫ (0)(1) dx = 0 ∫ 1 dx = 0(x+C) = 0$
Discuss.
2. Nov 3, 2014
### Staff: Mentor
The "Discuss" part makes me think this is a homework problem.
3. Nov 3, 2014
It's not, I just wanted to know which argument is right and why.
4. Nov 3, 2014
### Staff: Mentor
Argument B is silly, as it factors 0 into 0 times 1, and then moves the 0 outside the integral.
5. Nov 3, 2014
What about the rule $∫a f(x) dx = a ∫ f(x) dx$?
6. Nov 3, 2014
### pwsnafu
The indefinite integral does not calculate a function. It calculates an equivalence class of function. All constant functions are in the same equivalence class.
Further, $\int 0 \, dx$ being constant is wrong. If for example the domain is $\mathbb{R}\setminus\{0\}$ then you would have two constants, not necessarily equal.
7. Nov 3, 2014
### Staff: Mentor
There's no need to write 0x in the above.
$\int 0 dx = C$
$\int 0 dx = 0\int dx = 0x + C = C$
You don't get rid of the arbitrary constant as you showed above.
Since d/dx(C) = 0, then any antiderivative of 0 is C, for some arbitrary constant.
8. Nov 3, 2014
### Staff: Mentor
Can you elaborate on this? I'm not following you. How does the domain enter into this problem, given that we're working with indefinite integrals?
9. Nov 3, 2014
### PeroK
For what it's worth, I think this is an interesting question. What do you think? A or B?
Hint: one answer is clearly wrong, but it's not so easy to explain exactly why.
10. Nov 3, 2014
### pwsnafu
This is not easy to see when you have $f(x) = 0$, so the example I give my students is
$f : \mathbb{R}\setminus\{0\} \rightarrow \mathbb{R}$ where $f(x) = -x^{-2}$ and
$g: (0, \infty) \rightarrow \mathbb{R}$ where $g(x) = -x^{-2}$.
Then the function
$h(x) = x^{-1} + 1$ for $x > 0$ and $h(x) = x^{-1} - 1$ for $x < 0$ is an antiderivative of f. But it isn't expressible as $F(x) + C$ where C is an "arbitrary constant". The "constant" changes as you pass over the "hole". On the other hand, h isn't an antiderivative of g (because the domains don't match), but the restriction of h to $(0,\infty)$ is an antiderivative of g and expressible in the form $G(x) + C$.
The difference lies in the number of connected components of the domain. The former has two so there are two constants of integration, one for x<0 and another for x>0. The latter only has one connected component, and there is one constant of integration. In general $\int f(x) \, dx = F(x) + H(x)$ where $F' = f$ and $H$ is constant on individual connected components of the domain of f.*
Writing $f(x) = 0$ is ambiguous. It most likely has domain of all of reals. But it could be any subset of R. OP did not specifiy the domain, hence he cannot make the conclusion that the constant of integration is indeed a constant value always.
*Edit: I'm ignoring functions like Cantor's functions here.
Last edited: Nov 3, 2014
11. Nov 3, 2014
So the indefinite integral is basically a set of functions?
A set of antiderivatives, more specifically.
Last edited: Nov 3, 2014
12. Nov 3, 2014
My gut tells me it's A.
13. Nov 3, 2014
### PeroK
Your head should tell you that as well. In general, you have to be careful with the constant of integration. It's an informal way of specifying an equivalence class of functions (as pointed out above). So, that's where the multiplication by 0 breaks down. If you do things more formally, you still have an equivalence class after multiplication by 0 - so you don't get rid of the constant of integration.
And, yes, an indefinite integral is actually a set of functions.
14. Nov 3, 2014
And how exactly do I do things more formally?
Does $∫a f(x) dx = a ∫ f(x) dx$ only apply for nonzero a?
15. Nov 3, 2014
### PeroK
No. You work with equivalence classes of functions, not with a constant of integration.
An analogy would be $0 \cdot x(mod \ n) = 0 (mod \ n) ≠ 0$
16. Nov 3, 2014
So what you're saying is I should treat the indefinite integral as a set of functions ${F(x) + C | C ∈ ℝ}$, but not as a single function?
17. Nov 3, 2014
### Staff: Mentor
Yes.
If a function f has two distinct antiderivatives F1 and F2 (IOW F1] = f and F2] = f) then F1(x) - F2(x) ≡ C.
An example in the same vein is this:
$$\int sin(x)cos(x)dx$$
One student uses substitution to evaluate this integral, using u = sin(x), so du = cos(x)dx.
Then integral becomes $\int udu = (1/2)u^2 = (1/2)sin^2(x)$.
Another student also uses substitution, but with u = cos(x), du = -sin(x)dx
With this substitution, the integral becomes $-\int udu = -(1/2)u^2 = -(1/2)cos^2(x)$.
(Notice that both students omitted the constant of integration.)
Here we have two distinct antiderivatives for the same integrand. As it turns out, the two antiderivatives differ by a constant: (1/2)sin2(x) = -(1/2)cos2(x) + 1/2, independent of the value of x.
18. Nov 3, 2014
### Stephen Tashi
As PeroK mentioned, such rules are not about symbols representing unique functions. The symbol $\int f(x)$ does not represent a unique function. Such rules don't work if you interpret the anti-derivative symbol to be a unique function.
For example If suppose we say that $\int x dx$ represents unique function $x^2/2 + 1$.
and the rule you quoted says $\int 2x$ is the unique function $2( x^2/2 + 1) = x^2 + 2$. This would contradict any calculation that said $\int 2 x = x^2$ or $\int 2 x = x^2 + 5$ etc.
19. Nov 3, 2014
### mathman
For indefinite integrals, the arbitrary added constant is just there. All you are doing in B is omitting it.
20. Nov 4, 2014
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# WPA with FreeBSD 6.0
## Tags: freebsd, howtos
Published on
« Previous post: Going from FreBSD 5.4 to FreeBSD 6.1 — Next post: Data Recovery with FreeBSD (part 1) »
My old laptop - an IBM Thinkpad T20 - is broken. May it rest in peace. Now I acquired an IBM Thinkpad R50e, which works perfectly well under FreeBSD. The following text shall guide you through the installation of the wireless networking card. I am assuming that you are using WPA in your W-LAN.
First of all, you need to install the iwi-firmware-kmod-port. It’s located in net. Once the installation has finished, add the following lines to /boot/loader.conf:
iwi_bss_load="YES"
If your W-LAN uses does not broadcast its SSID, you should enable the broadcast. Since the iwi-device has its problems with connecting to these “hidden” networks, there is no other option available.
In order to use WPA encryption, you need the wpa_supplicant. This program handles the authentication process (it’s in the base system since 6.0, as far as I know). Edit the following file to suit your settings and save it as /etc/wpa_supplicant.conf:
ctrl_interface=/var/run/wpa_supplicant
ctrl_interface_group=0
ap_scan=1
fast_reauth=1
network={
ssid="YourNet"
proto=WPA
key_mgmt=WPA-PSK
This means you are going to use WPA along with a pre shared key. There are other options available; read man wpa_supplicant.conf if you want to know more.
To establish the connection, wpa_supplicant has to be called. After the authentication process is finished, you should be able to assign an IP address to your interface:
wpa_supplicant -iiwi0 -c/etc/wpa_supplicant.conf -B
The -B-option lets the program run as a background process. The IP address assignment and the authentication could be placed in a script if you want to do everything automatically.
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### Computational Combinatorics Roundup: October
It is the end of October, so let’s start a monthly tradition of listing new papers in computational combinatorics. This list is likely not complete, so please comment or send me an email if there is a recent paper that I missed. Some of these papers are not exactly “new” but are papers I’ve discovered since the last reference list. Since I plan to do this regularly, send me an email when you see a new paper using computational methods and I will add it to the next reference list update.
G. Brinkmann, Generating Regular Directed Graphs, Discrete Mathematics 313(1), 1-7 (2013).
G. Brinkmann, J. Goedgebeur, J. Hägglund, K. Markström, Generation and properties of snarks, arXiv:1206.6690 [math.CO].
G. Brinkmann, J. Goedgebeur, J. Schlage-Puchta, Ramsey numbers $R(K_3,G)$ for graphs of order 10, arXiv:1208.0501 [math.CO].
J. Goedgebeur, S. P. Radziszowski, New Computational Upper Bounds for Ramsey Numbers $R(3, k)$, arXiv:1210.5826 [math.CO].
A. Grzesik, On the maximum number of five-cycles in a triangle-free graph, Journal of Combinatorial Theory, Series B 102, 1061-1066 (2012). Also arXiv:1102.0962 [math.CO]
S. Nieß, Counting monochromatic copies of $K_4$: a new lower bound for the Ramsey multiplicity problem, arXiv:1207.4714v1 [math.CO].
|
# 2018 Group 6
## Origami-Constructible Real Numbers
In geometry and algebra, a real number α is constructible if and only if, given a unit length, a line segment of length |α| can be constructed from the unit length in a finite number of steps using only a ruler (i.e. a straight unmarked edge) and pair of compasses.$^{[1]}$
We start with an informal definition of origami and how this can be applied to mathematics: origami constructions are made up of series of folds in the paper, when the paper is folded and unfolded, it leaves a crease which acts as a line. In such origami constructions, a point only exists if it is the intersection of two creases.
## History
### Origin of Origami Algebra
Humiaki Huzita
The Japanese art of paper folding has an impressive history, despite its foundations in geometry and algebra only being explored over the past few hundred years. The foundations for constructions are primarily classical, dating back to Pythagorus, Euclid, and Pappus.$^{[2]}$ In 1893, Indian mathematician T. Sundara Rao published "Geometric Exercises in Paper Folding" which used paper folding to demonstrate proofs of geometrical constructions.$^{[3]}$ This work was inspired by the use of origami in the kindergarten system.
The axioms that describe the operations made when folding a piece of paper, were first discovered by Jacques Justin in 1986.$^{[4]}$ Axioms 1 to to 6 were then rediscovered by Japanese-Italian mathematician Humiaki Huzita and reported at the First International Conference on Origami in Education and Therapy in 1991.$^{[5]}$ Axioms 1 to 5 were rediscovered by Auckly and Cleveland in 1995.$^{[6]}$ Axiom 7 was rediscovered by Koshiro Hatori in 2001.$^{[7]}$
### The Seven Axioms
We shall describe a set of axioms for paper folding which will be used to describe different subfields of the real numbers, similar to the way that ruler and compass constructions are used to build fields. There are 6 axioms that were outlined in 1992 by Italian-Japanese mathematician Humiaki Huzita$^{[5]}$:
• O1. Given points $P_1$ and $P_2$, we can fold a line that goes through both of them.
• O2. Given points $P_1$ and $P_2$, we can fold $P_1$ onto $P_2$ (i.e. find the perpendicular bisector of segment $P_1P_2$).
• O3. Given two lines $L_1$ and $L_2$, we can fold $L_1$ onto $L_2$ (i.e. bisect the angle between them).
• O4. Given a point $P$ and a line $L$, we can fold a line perpendicular to $L$ that goes through $P$.
• O5. Given two points $P_1$ and $P_2$ and a line $L$, we can fold $P_1$ onto $L$ with a line that goes through $P_2$.
• O6. Given two points $P_1$ and $P_2$ and two lines $L_1$ and $L_2$, we can fold $P_1$ onto $L_1$ and $P_2$ onto $L_2$ with a single line.
A 7th axiom was introduced in 2002 by Hatori$^{[7]}$:
• O7. Given a point $P_1$ and two lines $L_1$ and $L_2$, we can make a fold perpendicular to $L_2$ that places $P_1$ onto line $L_1$
## Origami Field Theory
### Definitions
Recall the definition of a constructible real number: Given a unit length, a real number α is constructible if a line segment of length |α| can be constructed from the unit length in a finite number of steps using only a ruler (i.e. a straight unmarked edge) and pair of compasses.$^{[1]}$ Then we have the set K = {x ∈ $\mathbb{R}$| x is constructible}
We can form a similar definition for origami-constructible numbers: An element x ∈ $\mathbb{R}$ ≥ 0 is said to be origami constructible if, starting with the unit segment and using only axioms O1 to O6, it is possible to construct a segment of length x. By definition, an element x ∈ $\mathbb{R}$ < 0 is origami constructible if and only if so is −x. $^{[8]}$ Then we have the set O = {x ∈ $\mathbb{R}$| x is origami constructible}
We can extend this further by defining an origami pair$^{[9]}$:
$\{P,L\}$ is an origami pair if $P$ is a set of points in $\mathbb{R^2}$ and $L$ is a collection of lines in $\mathbb{R^2}$ satisfying:
a) The point of intersection of any two non-parallel lines in $L$ is a point in $P$
b) Given any two distinct points in $P$, there is a line $L$ going through them.
c) Given any two distinct points in $P$, the perpendicular bisector of the line segment with given end points is a line in $L$
d) If $L_1$ and $L_2$ are lines in $L$, then the line which is equidistant from $L_1$ and $L_2$ is in $L$.
e) If $L_1$ and $L_2$ are lines in $L$, then there exists a line $L_3$ in $L$ such that $L_3$ is the mirror reflection of $L_2$ about $L_1$
### Lemmas
There are many lemmas that apply to the field of origami constructible numbers, but we have chosen the most relevant to mention below:
Lemma 1
It is possible to construct a line parallel to a given line through any given point using origami.$^{[10]}$
Proof:
Consider the point $P_1$ and line $L_1$, we can fold a line parallel to $L_1$ that goes through $P_1$. We obtain this from two applications of O4, the first gives us a line perpendicular to $L_1$, which we label $L_2$ the second application gives us a line $L_3$ that is perpendicular to $L_2$ and therefore parallel to $L_1$ passing through $P_1$.
We mention a second lemma which will be applied later in order to construct cubic roots:
Lemma 2
Origami can solve any cubic equation.$^{[11]}$
Italian mathematician Margherita Beloch proved this in the 1930s.
Proof:
we construct the points $P_1$ = (a, 1) and $P_2$ = (c, b). Considering the real axis as the x-axis and the imaginary axis to be the y-axis, we also construct the two lines $L_1$ and $L_2$, defined by y = −1 and x = −c, respectively. We then apply O6 to $P_1$, $P_2$, $L_1$, and $L_2$ to obtain a new line $L_3$. This new line is defined by the equation y = mx + z (since we know it is not vertical), where m is a solution to the original cubic equation.
This was realised to simply be an application of | Lill's method for finding real roots of a polynomial.
In general, we can make some conclusions about the field of origami numbers, the first being that $\mathbb{Q}$ ⊆ O ⊆ $\mathbb{C}$. This means that, for any subfield k of O, if an extension K/k has degree 2 or 3, then K is also a subfield of O.$^{[11]}$
## Constructions
Similar to the field of constructible numbers, we can show that the following properties still hold within the field of origami-constructible numbers: for any origami-constructible numbers α and β, α−β and αβ are origami-constructible and α$^{-1}$ is origami-constructible if α does not equal 0.
Using the lemmas outlined in the previous section, we can perform the following constructions in order to demonstrate that the above properties hold.
We can apply the previous lemma to outline how to find the sum of two origami numbers.$^{[10]}$
Steps required to add two numbers using origami
The following steps outline the addition operation for origami numbers:
1. We start out with three points $P_1$,$P_2$,and $0$ as shown in figure 1
2. We use O1 to fold a line that goes through $0$ and $P_1$ which we label $L_1$ as in figure 2
3. We repeat O1 to fold a second line that goes through $0$ and $P_2$ which we label $L_2$ just like figure 3
4. Consider the point $P_2$ and line $L_1$, we can fold a line parallel to $L_1$ that goes through $P_2$ using Lemma 1, as demonstrated in figure 4
5. Consider the point $P_1$ and line $L_2$, we can repeat the procedure in step (4) with the respective sides in order to obtain a line $L_4$ which is parallel to $L_2$ and passes through $P_1$ as done in figure 5
6. The intersection of the lines $L_3$ and $L_4$ gives us the point $P_3$ that is equal to $P_1$ + $P_2$ as can be seen in figure 6
### Multiplication
In fact, it is also possible to find the product of two origami numbers.$^{[10]}$
Steps required to multiply two numbers using origami
The following steps outline how the multiplication operation for origami numbers:
1. Just as in the proof for constructible numbers (refer to lecture notes) we use the properties of similar triangles to multiply a number $P_1$ by a real number $r$
2. We start out with four points $0$, $1$, $P_1$ and $r$ as shown in figure 1 and figure 2
3. Apply O1 to fold a line that goes through $0$ and $P_1$ which we label $L_1$ as in figure 3
4. Apply O1 again to fold a second line that goes through $1$ and $P_1$ which we denote as $L_2$ just as in figure 4
5. Consider the point $r$ and line $L_2$, we can fold a line parallel to $L_2$ that goes through $r$, we denote this as $L_3$ as demonstrated in figure 5
6. Then the intersection of lines $L_1$ and $L_3$ gives us the point $P_2$ that is equal to $r$$P_1$ as can be seen in figure 6
Since this method is used primarily for complex origami-constructible numbers, we make the following adjustments since we are focusing on the field of origami-constructible real numbers:
add $i$ to $P_1$, multiply by $r$, and project this product onto the real axis with an application of O4
### Inverse
Steps required to find the inverse of an origami number
Similar to the field of Constructible numbers, we can find the inverse of origami-constructible numbers.$^{[10]}$
1. We use the properties of similar triangles to divide a number $P_1$ by a real number $r$
2. We start out with four points $0$, $1$, $P_1$ and $r$ as shown in figure 1
3. Apply O1 to fold a line that goes through $0$ and $P_1$ which we label $L_1$ just as in figure 2
4. Apply O1 again to fold a second line that goes through $r$ and $P_1$ which we denote as $L_2$ which can be seen in figure 3
5. Consider the point $1$ and line $L_2$, we can fold a line parallel to $L_2$ that goes through $1$, we denote this as $L_3$ as in figure 4
6. Then the intersection of lines $L_1$ and $L_3$ gives us the point $P_2$ that is equal to $1$/$P_1$ as shown in figure 4
Since this method is used primarily for complex origami-constructible numbers, we make the same adjustment as described for multiplication of real origami numbers.
### Haga's Theorem
Another interesting consequence of the field of origami-constructible numbers is Haga's Theorem. A retired professor of biology from Japan, came up with this method which allows us to fold any fraction we would like from a square piece of paper.$^{[12]}$
Haga's Theorem for any number
Steps required to fold a fifth using Haga's Theorem
Referring to the image on the left, fold the bottom left corner to a point a distance of k along the top edge
Then, the top-left triangle has sides of length k, x and 1 -x. So Pythagoras' theorem tells us that $x^2$ + $k^2$ = $(1 – x)^2$
Rearranging gives us x = (1 – $k^2$)/2 and by the similar triangles argument we have that y/(1 – k) = k/x
If we put these equations together we find y/(1 – k) = k/((1 – $k^2$)/2)
Which can be rearranged as y = (2(1-k)k)/(1 – $k^2$)
And since 1 – $k^2$ = (1 – k)(1 + k) this can be simplified to y/2 = k/(1 + k)
The image on the right hand side demonstrates how to fold 1/5 using Haga's Theorem: 1⁄5 can be generated with three folds; first halve a side, then use Haga's theorem twice to produce 2⁄3 and then finally 1⁄5.
## Solving the Greek Problems
It turns out that origami is much more powerful than straight-edge and compass creations because many things that cannot be created using straight-edge and compass can be constructed using origami. Origami allows us to:
• Construct $^3\sqrt{2}$
• Trisect an arbitrary angle
These were previously impossible problems
Steps required to double the cube
### Doubling the Cube
Doubling the cube is equivalent to solving the cubic $x^3 − 2$ = 0 i.e. constructing $^3\sqrt{2}$.$^{[13]}$
1. start with a square sheet of paper. We first fold the paper into thirds and define $L_1$, $L_2$, $P_1$ and $P_2$ as shown in figure 1
2. We now fold $P_1$ onto $L_1$ and $P_2$ onto $L_2$ using O6, mark the point where $P_2$ meets $L_2$ as in figure 2
3. Unfold and extend this point into the line $L_3$ as demonstrated in figure 3
4. Then the ratio of the lengths a and b in the diagram is precisely $^3\sqrt{2}$.
Steps required to trisect an angle
### Trisecting an Angle
This origami move is actually solving a cubic equation by finding a simultaneous tangent to 2 parabolas.$^{[13]}$
We use the following steps to demonstrate how it is possible to trisect an angel using origami-constructible real numbers:
1. We start with a square piece of paper and fold a line $L_1$ to create any angle $θ$ as in figure 1
2. To trisect $θ$, we have to fold the paper into quarters from top to bottom and define $P_2$ as shown in figure 2
3. simultaneously fold $P_1$ onto $L_2$ and $P_2$ onto $L_1$ using O6 and whilst the paper is still folded, extend $L_1$ by a new fold $L_3$, as shown in figure 3
4. If we now open the paper and extend $l_3$ to its full length, it will divide $θ$ in the ration 1:2, as shown in figure 4
5. Finally, use an application of O3 to bisect the larger part of the angle which then splits $θ$ into three equal parts as required
### Squaring the Circle
The third Classical Greek Problem that is impossible with straight edge and compass, squaring the circle, is impossible even using Origami. This is because it involves constructing the transcendental ratio $\sqrt{π}$ which cannot be written as a root of a polynomial with finite number of terms.$^{[1]}$
## References
$^{[1]}$ ^Baranov A. Irreducible Polynomials 17-18 Part 1. Leicester; 2018.
$^{[2]}$ ^Heath, T.A history of Greek mathematics, Dover, New York; 1981.
$^{[3]}$ ^Sundara Rao T. Geometric Exercises in Paper Folding. Addison; 1893.
$^{[4]}$ ^Justin, J. "Resolution par le pliage de l'equation du troisieme degre et applications geometriques", reprinted in Proceedings of the First International Meeting of Origami Science and Technology, Huzita H ed.; 1989. p. 251–261.
$^{[5]}$ ^Roger C. Alperin; Robert J. Lang. "One-, Two-, and Multi-Fold Origami Axioms" (PDF). 4OSME. A K Peters; 2009.
$^{[6]}$ ^Auckly, D., and Cleveland, J. “Totally real origami and impossible paper folding.” American Mathematics Monthly 102; 1995. p. 215 – 226.
$^{[7]}$ ^Hatori K. "Origami construction". http://www.jade.dti.ne.jp/˜hatori/library/conste.html; 2004.
$^{[8]}$ ^Hull, T. “Project origami. Activities for exploring mathematics”. A. K. Peters Ltd; 2006.
$^{[9]}$ ^Yin, S. “The Mathematics of Origami”. https://sites.math.washington.edu/~morrow/336_09/papers/Sheri.pdf. 2009.
$^{[10]}$ ^King J. “Origami-Constructible numbers”. http://www.cs.mcgill.ca/~jking/papers/origami.pdf. Canada; 2004.
$^{[11]}$ ^Marcen A. “Origami Consructions”. https://arxiv.org/pdf/0709.3270.pdf. Spain; 2007.
$^{[12]}$ ^Koshiro. “How to Divide the Side of Square Paper”. http://origami.gr.jp/Archives/People/CAGE_/divide/02-e.html. Japan Origami Academic Society; 2017.
$^{[13]}$ ^Hull, T. “International Meeting of Origami Science, Mathematics, and Education.” 3rd ed. California; 2001.
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Wednesday, June 11th 2014, 5:09pm
Scout Helicopters
Thought it would be nice to start a little discussion on the scoutattack helicopters in this game. There’s obviously not much to talk about, but it would be good if we could get some ideas down on what could be done with them.
Predictive sight - it’s back to BF3 levels of broken. I haven’t found a single situation in which the bullets actually went toward the center of the crosshair. If throttling, they go below, if hovering, they go above.
Airframe - both seem to get hung up on everything like the Z11 does.
Starting 7.62 LMG - does awful damage against air targets, awful damage against vehicles, and it’s alright I guess against infantry. I’ve gotten 3 SS for the scout heli in four rounds or so, it shouldn’t be too long until I get the minigun unlocked. Don’t try to hit a motorcycle with these, it’s not going work.
Pilot 7.62 Minigun - haven’t had any chance to use this yet. Labby says that it works properly with the sights. He also says that it does less damage, but has a longer time to overheat.
Pilot heatsekers - These seem to do 50-58 damage against other scout helix. It’s not a 2HK against transports, though. Combined with the fact that the LMG has horrible dps against air, hell duels turn into heatseeking contests.
Gunner minigun - haven’t had a competent pilot to test these with. From seatswitching a bit, it seems to be pretty effective against air and ground.
Potential full release scout heli weapons for discussion:
Rocket pods - yes pls. Combined with miniguns, it will be everything I've ever wanted.
LGM - I don’t see this as having a place in Hardline, but it might be included.
Pilot 25mm - Splash damage helicopter weapons have absolutely no place in this game
Pilot 30mm - More authentic than the 25mm. Same balance situation, though
Gunner 30mm - Because if we’re going to make this into an attack heli, might as well go the whole way
Experiences so far:
All the pilots I was up against were awful, and I was able to be a dominant force in the match. Was able to go 20-0, 15-0, etc multiple times, thanks to a lack of jets and other hard heli counters. The scout helicopter in this game (at least on this map) is much easily more dominant than in BF4 due to the rather small maps. Small arms fire against me has never been a problem.
What do you guys think? Should heatseeker damage be reduced? Is the 7.62 LMG worthless? What do you think of not having a place for reppers to sit?
Platoon Marble Duck
Hate Mail
"you obviously don't know what an argument is as there is only one person battling. Do you really fucking think I want subs? You think you can act all big and powerful just because you sit on a computer at least 6 hours a day like the probably nerdy unwanted retard you are with 4.3k subs? You think 4.3k subs is a lot? LOL you need medicine man. I don't want any subs as i just have a google account for other media and writing comments. Think twice before you act. You even said in your video you aren't that great of a player, and the comments agree you aren't. Maybe you should once again think twice before you act, stop being such an annoying, ignorant bastard that everyone wants to shut up, and god, literally, just shut up. Your voice gave me a headache :s"
"As a youtuber shouldn't be trying to be reeling in your viewers with exciting stuff being said not your boring ass commentary for your video"
"The more you watch his vid the dumber he gets I swear he's borderline autistic look I got shot behind cover beacuase thin sheets metal are unpenetrable. Bf4 is just as quiet and tactical as bf3 random explosion in the background . Player has dissconected from chat
You started playing bf3 and never touched bfc1/2. Please do yourself a favor and shutdown your generic cod channel down"
"Nice clickb8 Faggot w8ting for your shit tier video to disable comments . Fucking newfag cancer go play some cod you activisiom cock faggot"
"I don't see why he [MarbleDuck] always tries to shit on levelcap he is better and has a million more subs...and also "there isnt a best gun in she game there are guns that are better that others at different engagement distances" yes thats true and whichever is the best/most average at all of them is the "best gun""
"Marbleduck you don't know shit lol levelcap knows more than you do you cant talk about how someone puts up garbage when you do yourself your a newcomer to YouTube acting like you know shit step up in the food chain first then you have the right to talk otherwise your just a fish trying to compete with sharks"
"Why don't we just witness "LevelCap vs MarbleDuck" One on One both on Battlefield 3 and Battlefield 4 seen as there is so much Controversy about the Two Youtubers"
"stfu cunt, BF3 was way better end of discussion"
"Stfu man, you're be littleing the most looked upon Battlefield Youtuber. No one cares about you, how much of an ego you have, or quite frankly your opinion. It's a fucking game.... Does it really fucking matter? Pathetic man."
"fuck you asshole, dont talk shit about total"
"Wtf is your problem? You have no subs and he has millions, yet you pick on him like some kind of stubborn, ignorant, rude child born with a silver spoon is his mouth. It's easy to do that, for example... You said there was no background noise yet there is. You say you're a fairly good player, you're not."
"please talk like a normal person and not like a professional"
This post has been edited 1 times, last edit by "marbleduck" (Jun 11th 2014, 5:19pm)
Posts: 3,292
Date of registration
: Apr 26th 2013
Platform: PS4
Location: Arizona, USA
Reputation modifier: 15
Wednesday, June 11th 2014, 5:22pm
Quoted from "marbleduck"
Gunner minigun - haven?t had a competent pilot to test these with. From seatswitching a bit, it seems to be pretty effective against air and ground.
The field of view and overall movement is severely limited in the Gunner position. It absolutely requires communication with both the Pilot and Gunner to be effective.
Quoted from "marbleduck"
Pilot 25mm - Splash damage helicopter weapons have absolutely no place in this game
Quoted from "marbleduck"
Rocket pods - yes pls
I see a bit of contradiction here, unless the rocket pods do, specifically, impact damage as opposed to splash. But I agree, splash weaponry has no legitimate place in a game like Hardline
(Or maybe this fictional universe takes place when the Police State has ensued and the Cops are given Military armaments).
To Aim Assist or not to Aim Assist, that is the question.
Source code
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AccelerationInputThreshold 0.98
AccelerationMultiplier 5.0
AccelerationDamping 4.0
AccelerationTimeThreshold 0.15
SquaredAcceleration 0.0
MaxAcceleration::Vec2
x 2.0
y 2.0
YawSpeedStrength 1.0
PitchSpeedStrength 1.0
AttractDistanceFallOffs::Vec2
x 1.0
y 1.2
AttractSoftZone 0.75
AttractUserInputMultiplier 0.45
AttractUserInputMultiplier_NoZoom 0.5
AttractOwnSpeedInfluence 0.0
AttractTargetSpeedInfluence 0.85
AttractOwnRequiredMovementForMaximumAttract 0.0
AttractStartInputThreshold 0.1
AttractMoveInputCap 0.0
AttractYawStrength 1.0
AttractPitchStrength 0.34
MaxToTargetAngle 45.0
MaxToTargetXZAngle 45.0
ViewObstructedKeepTime 0.0
SnapZoomLateralSpeedLimit 1000.0
SnapZoomTime 0.2
SnapZoomPostTimeNoInput 0.2
SnapZoomPostTime 0.2
SnapZoomReticlePointPriority 999
SnapZoomAutoEngageTime 0.0
SnapZoomBreakTimeAtMaxInput 0.2
SnapZoomBreakMaxInput 0.2
SnapZoomBreakMinAngle 90.0
SnapZoomSpamGuardTime 1.2
SoldierBackupSkeletonCollisionData *nullGuid*
CheckBoneCenterOnlyDistance 40.0
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AccelerationInputThreshold 0.98
AccelerationMultiplier 5.0
AccelerationDamping 4.0
AccelerationTimeThreshold 0.15
SquaredAcceleration 0.0
MaxAcceleration::Vec2
x 2.0
y 2.0
YawSpeedStrength 1.0
PitchSpeedStrength 1.0
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x 1.0
y 1.2
AttractSoftZone 0.0
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AttractUserInputMultiplier_NoZoom -1.0
AttractOwnSpeedInfluence 0.0
AttractTargetSpeedInfluence 0.0
AttractOwnRequiredMovementForMaximumAttract 0.0
AttractStartInputThreshold 0.0
AttractMoveInputCap 0.0
AttractYawStrength 0.0
AttractPitchStrength 0.0
MaxToTargetAngle 45.0
MaxToTargetXZAngle 45.0
ViewObstructedKeepTime 0.0
SnapZoomLateralSpeedLimit 1000.0
SnapZoomTime 0.2
SnapZoomPostTimeNoInput 0.0
SnapZoomPostTime 0.0
SnapZoomReticlePointPriority 999
SnapZoomAutoEngageTime 0.0
SnapZoomBreakTimeAtMaxInput -1.0
SnapZoomBreakMaxInput 0.2
SnapZoomBreakMinAngle 90.0
SnapZoomSpamGuardTime 0.5
SoldierBackupSkeletonCollisionData *nullGuid*
CheckBoneCenterOnlyDistance 40.0
DisableForcedTargetRecalcDistance 7.0
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AccelerationInputThreshold 0.98
AccelerationMultiplier 5.0
AccelerationDamping 4.0
AccelerationTimeThreshold 0.15
SquaredAcceleration 0.0
MaxAcceleration::Vec2
x 2.0
y 2.0
YawSpeedStrength 1.0
PitchSpeedStrength 1.0
AttractDistanceFallOffs::Vec2
x 1.0
y 1.2
AttractSoftZone 0.75
AttractUserInputMultiplier 0.45
AttractUserInputMultiplier_NoZoom 0.5
AttractOwnSpeedInfluence 0.0
AttractTargetSpeedInfluence 0.85
AttractOwnRequiredMovementForMaximumAttract 0.0
AttractStartInputThreshold 0.1
AttractMoveInputCap 0.0
AttractYawStrength 1.0
AttractPitchStrength 0.34
MaxToTargetAngle 45.0
MaxToTargetXZAngle 45.0
ViewObstructedKeepTime 0.0
SnapZoomLateralSpeedLimit 1000.0
SnapZoomTime 0.2
SnapZoomPostTimeNoInput 0.0
SnapZoomPostTime 0.0
SnapZoomReticlePointPriority 999
SnapZoomAutoEngageTime 0.0
SnapZoomBreakTimeAtMaxInput -1.0
SnapZoomBreakMaxInput 0.2
SnapZoomBreakMinAngle 90.0
SnapZoomSpamGuardTime 0.5
SoldierBackupSkeletonCollisionData *nullGuid*
CheckBoneCenterOnlyDistance 40.0
DisableForcedTargetRecalcDistance 7.0
the Sebstalder is quiet good since it can 3hit kill at any distanc ,but In my opinion i actually thikn the sweeper is better, its got a really really fast firerate that can beat alll those Noobmaticos, Helregall adn shitguns in close quarters , and its also really accurate out to like l;ong range,. overall great allround gun, jsut my 2$tho Smoked Salmon Best Salmon Posts: 1,026 Date of registration : Dec 25th 2012 Platform: PC Location: Yakima. WA Battlelog: Reputation modifier: 13 Wednesday, June 11th 2014, 6:36pm Quoted from "JSLICE20" I see a bit of contradiction here, unless the rocket pods do, specifically, impact damage as opposed to splash. But I agree, splash weaponry has no legitimate place in a game like Hardline (Or maybe this fictional universe takes place when the Police State has ensued and the Cops are given Military armaments). To clarify: I'd only like to see rocket pods as a secondary if they behaved like BF4 heli Zuni rockets do: 8/8 ammo capacity, and taking almost a full mag to kill someone via splash. I'm not opposed to all splash weapons, just those with as much volume as BF4 25s. If it was 8/8, you'd be pretty limited as to what you killed with splash. If you used them all on infantry, you'd have nothing to deal with heavy armor (what little there is) Platoon Marble Duck Hate Mail "you obviously don't know what an argument is as there is only one person battling. Do you really fucking think I want subs? You think you can act all big and powerful just because you sit on a computer at least 6 hours a day like the probably nerdy unwanted retard you are with 4.3k subs? You think 4.3k subs is a lot? LOL you need medicine man. I don't want any subs as i just have a google account for other media and writing comments. Think twice before you act. You even said in your video you aren't that great of a player, and the comments agree you aren't. Maybe you should once again think twice before you act, stop being such an annoying, ignorant bastard that everyone wants to shut up, and god, literally, just shut up. Your voice gave me a headache :s" "As a youtuber shouldn't be trying to be reeling in your viewers with exciting stuff being said not your boring ass commentary for your video" "The more you watch his vid the dumber he gets I swear he's borderline autistic look I got shot behind cover beacuase thin sheets metal are unpenetrable. Bf4 is just as quiet and tactical as bf3 random explosion in the background . Player has dissconected from chat You started playing bf3 and never touched bfc1/2. Please do yourself a favor and shutdown your generic cod channel down" "Nice clickb8 Faggot w8ting for your shit tier video to disable comments . Fucking newfag cancer go play some cod you activisiom cock faggot" "I don't see why he [MarbleDuck] always tries to shit on levelcap he is better and has a million more subs...and also "there isnt a best gun in she game there are guns that are better that others at different engagement distances" yes thats true and whichever is the best/most average at all of them is the "best gun"" "Marbleduck you don't know shit lol levelcap knows more than you do you cant talk about how someone puts up garbage when you do yourself your a newcomer to YouTube acting like you know shit step up in the food chain first then you have the right to talk otherwise your just a fish trying to compete with sharks" "Why don't we just witness "LevelCap vs MarbleDuck" One on One both on Battlefield 3 and Battlefield 4 seen as there is so much Controversy about the Two Youtubers" "stfu cunt, BF3 was way better end of discussion" "Stfu man, you're be littleing the most looked upon Battlefield Youtuber. No one cares about you, how much of an ego you have, or quite frankly your opinion. It's a fucking game.... Does it really fucking matter? Pathetic man." "fuck you asshole, dont talk shit about total" "Wtf is your problem? You have no subs and he has millions, yet you pick on him like some kind of stubborn, ignorant, rude child born with a silver spoon is his mouth. It's easy to do that, for example... You said there was no background noise yet there is. You say you're a fairly good player, you're not." "please talk like a normal person and not like a professional" Posts: 3,292 Date of registration : Apr 26th 2013 Platform: PS4 Location: Arizona, USA Reputation modifier: 15 Wednesday, June 11th 2014, 6:43pm Eh, I don't think they're going limited Ammunition this go around. Currently the auxillary ammo is infinite on, from what I know, on the Assault Trucks. But yeah, the less splash the better. Scout 25mm is annoying as hell in BF4. The Miniguns might do more damage per projectile, but you must be precise to unleash their full potential. 25mms just need to be in your general vacinity to kill you. To Aim Assist or not to Aim Assist, that is the question. Nope. Aim Assist or bust; here's why: Default Aim Assist Data Source code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 AccelerationInputThreshold 0.98 AccelerationMultiplier 5.0 AccelerationDamping 4.0 AccelerationTimeThreshold 0.15 SquaredAcceleration 0.0 MaxAcceleration::Vec2 x 2.0 y 2.0 YawSpeedStrength 1.0 PitchSpeedStrength 1.0 AttractDistanceFallOffs::Vec2 x 1.0 y 1.2 AttractSoftZone 0.75 AttractUserInputMultiplier 0.45 AttractUserInputMultiplier_NoZoom 0.5 AttractOwnSpeedInfluence 0.0 AttractTargetSpeedInfluence 0.85 AttractOwnRequiredMovementForMaximumAttract 0.0 AttractStartInputThreshold 0.1 AttractMoveInputCap 0.0 AttractYawStrength 1.0 AttractPitchStrength 0.34 MaxToTargetAngle 45.0 MaxToTargetXZAngle 45.0 ViewObstructedKeepTime 0.0 SnapZoomLateralSpeedLimit 1000.0 SnapZoomTime 0.2 SnapZoomPostTimeNoInput 0.2 SnapZoomPostTime 0.2 SnapZoomReticlePointPriority 999 SnapZoomAutoEngageTime 0.0 SnapZoomBreakTimeAtMaxInput 0.2 SnapZoomBreakMaxInput 0.2 SnapZoomBreakMinAngle 90.0 SnapZoomSpamGuardTime 1.2 SoldierBackupSkeletonCollisionData *nullGuid* CheckBoneCenterOnlyDistance 40.0 No Slowdown Data Source code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 AccelerationInputThreshold 0.98 AccelerationMultiplier 5.0 AccelerationDamping 4.0 AccelerationTimeThreshold 0.15 SquaredAcceleration 0.0 MaxAcceleration::Vec2 x 2.0 y 2.0 YawSpeedStrength 1.0 PitchSpeedStrength 1.0 AttractDistanceFallOffs::Vec2 x 1.0 y 1.2 AttractSoftZone 0.0 AttractUserInputMultiplier 1.0 AttractUserInputMultiplier_NoZoom -1.0 AttractOwnSpeedInfluence 0.0 AttractTargetSpeedInfluence 0.0 AttractOwnRequiredMovementForMaximumAttract 0.0 AttractStartInputThreshold 0.0 AttractMoveInputCap 0.0 AttractYawStrength 0.0 AttractPitchStrength 0.0 MaxToTargetAngle 45.0 MaxToTargetXZAngle 45.0 ViewObstructedKeepTime 0.0 SnapZoomLateralSpeedLimit 1000.0 SnapZoomTime 0.2 SnapZoomPostTimeNoInput 0.0 SnapZoomPostTime 0.0 SnapZoomReticlePointPriority 999 SnapZoomAutoEngageTime 0.0 SnapZoomBreakTimeAtMaxInput -1.0 SnapZoomBreakMaxInput 0.2 SnapZoomBreakMinAngle 90.0 SnapZoomSpamGuardTime 0.5 SoldierBackupSkeletonCollisionData *nullGuid* CheckBoneCenterOnlyDistance 40.0 DisableForcedTargetRecalcDistance 7.0 No Auto Rotation Data Source code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 AccelerationInputThreshold 0.98 AccelerationMultiplier 5.0 AccelerationDamping 4.0 AccelerationTimeThreshold 0.15 SquaredAcceleration 0.0 MaxAcceleration::Vec2 x 2.0 y 2.0 YawSpeedStrength 1.0 PitchSpeedStrength 1.0 AttractDistanceFallOffs::Vec2 x 1.0 y 1.2 AttractSoftZone 0.75 AttractUserInputMultiplier 0.45 AttractUserInputMultiplier_NoZoom 0.5 AttractOwnSpeedInfluence 0.0 AttractTargetSpeedInfluence 0.85 AttractOwnRequiredMovementForMaximumAttract 0.0 AttractStartInputThreshold 0.1 AttractMoveInputCap 0.0 AttractYawStrength 1.0 AttractPitchStrength 0.34 MaxToTargetAngle 45.0 MaxToTargetXZAngle 45.0 ViewObstructedKeepTime 0.0 SnapZoomLateralSpeedLimit 1000.0 SnapZoomTime 0.2 SnapZoomPostTimeNoInput 0.0 SnapZoomPostTime 0.0 SnapZoomReticlePointPriority 999 SnapZoomAutoEngageTime 0.0 SnapZoomBreakTimeAtMaxInput -1.0 SnapZoomBreakMaxInput 0.2 SnapZoomBreakMinAngle 90.0 SnapZoomSpamGuardTime 0.5 SoldierBackupSkeletonCollisionData *nullGuid* CheckBoneCenterOnlyDistance 40.0 DisableForcedTargetRecalcDistance 7.0 Prepare your laughbox Quoted from "Zer0Cod3x" the Sebstalder is quiet good since it can 3hit kill at any distanc ,but In my opinion i actually thikn the sweeper is better, its got a really really fast firerate that can beat alll those Noobmaticos, Helregall adn shitguns in close quarters , and its also really accurate out to like l;ong range,. overall great allround gun, jsut my 2$ tho
Moderator
Posts: 1,941
Date of registration
: Sep 26th 2012
Platform: PC
Location: State of Confusion
Battlelog:
Reputation modifier: 15
Wednesday, June 11th 2014, 8:01pm
Predictive sight is it's own kind of broken. BF3 wasn't bad, it worked perfectly at the right resolution. BF4 it's tied to throttle, as in it misses if you're touching either. In Hardline, at least for the miniguns, they seem pretty accurate as long as you ARE using the throttle. Don't remember LMG, because I didn't use it long.
Compared to miniguns in previous games, in Hardline the miniguns (and LMG) do a lot less damage to vehicles, but overheat much more slowly. It works pretty well for the smaller map sizes of this game.
Heatseekers, 58% against attack helis, 39% against transports. Assuming health is still 500/750 as in previous games, that's 290 damage. I actually like this a lot. Bursty heatseekers > stun heatseekers. However, with the low DPS of the guns, they can't kill faster than heatseekers can lock on at close range, which means heatseekers are a viable the go to weapon, even at point blank. Unfortunately, the smaller map sizes, and heatseekers having no real natural weakness at close range as they did in previous games means that you will get hit through flares, a lot, because heatseekers will almost always be fired at ranges where their travel time is faster than the time needed for the target to hear the incoming missile tone, react and press flares, and for the missile to get the signal that flares were deployed. Possible solutions? Lower initial speed and acceleration for missiles, or 100m minimum lock range for heatseekers, or ?
Rocket pods were shown in that internal video, but they take the pilot primary slot. Don't know anything else about them yet.
Quoted from "marbleduck"
What do you guys think? Should heatseeker damage be reduced? Is the 7.62 LMG worthless? What do you think of not having a place for reppers to sit?
Should heatseeker damage be reduced? No, but flares need to be an effective counter, which means heatseekers need a weakness at close range. Is the LMG worthless? No, it lets you unlock the minigun. What do you thing of not having a place for reppers to sit? It's AWESOME.
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4. $p$-Kazhdan–Lusztig polynomials
1. Problem 4.1.
[Scott] Is there a homological interpretation of the $p$-Kazhdan–Lusztig polynomials?
Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.
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## Stacking Cans
#### This is not the entire task, just a starting point. See where it takes you!
How can you stack $28$ cans legally?
#### Expanding a section will reveal potential spoilers. If you only want a small hint, tread carefully.
What are you stuck on?
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# Arrays¶
An array is an n-dimensional matrix. The elements are accessed by "row" and "column" indices.
## Vectors¶
A Vector is just what you think it is: a 1-dimensional array. In Julia, these are always column vectors (sort of always).
To create a vector, simply fill it with values:
a = [1, 2, 3]
3-element Array{Int64,1}:
1
2
3
Note that the return values is a one-dimensional array. Vector is simply an alias for this.
julia> Vector{Int} === Array{Int,1}
true
There are no row vectors in Julia. A row vector is a 1xN Matrix:
julia> a = [1 2 3]
1×3 Array{Int64,2}:
1 2 3
julia> a isa Matrix{Int}
true
### Indexing¶
To extract elements from a vector, hand it a list of indices.
julia> a = [2, 3, 4, 5];
julia> a[1]
2
# Note the double brackets
julia> a[[1, 3]]
2-element Array{Int64,1}:
2
4
# What we are really doing is
idx = [1, 3];
a[idx]
Then there is logical indexing:
a = [1, 2, 3];
a[[true, false, true]]
2-element Array{Int64,1}:
1
3
Arrays are "mutable", meaning that the elements can be changed "in-place":
julia> a = [1,2,3]
3-element Vector{Int64}:
1
2
3
julia> a[2] = 22
22
julia> a
3-element Vector{Int64}:
1
22
3
### Ranges¶
In Matlab, 1:3 is a Vector, but not in Julia:
julia> 1:3
1:3
julia> typeof(1:3)
UnitRange{Int64}
The main difference between a Vector and a Range is that the vector is allocated upon construction (its values are computed and stored in memory).
A Range is an Iterator. You can iteratore over its elements, but they are not computed until needed. Therefore, the Range does not allocate memory. This is a big deal when lots of values are involved.
However, a Range is an AbstractArray; so all the indexing that works on Vectors also works on Ranges.
collect makes a Range into a Vector.
### Exercises¶
Start with x = 1 : 3 : 30.
1. Find all even elements.
2. Find all elements between 5 and 20.
3. Set all even elements to their negative values.
## Matrices¶
A Matrix is a 2-dimensional array. There are also n-dimensional arrays (see below).
To create a matrix, simply fill it with values.
julia> a = [1 2 3; 4 5 6]
2×3 Array{Int64,2}:
1 2 3
4 5 6
Many commands work directly on matrices.
julia> a = [1 2 3]; b = [2; 1; 1]; a * b
1-element Array{Int64,1}:
7
julia> c=b*a
3×3 Array{Int64,2}:
2 4 6
1 2 3
1 2 3
To extract elements:
julia> c[1,2]
4
julia> c[1:2, 2:3]
2×2 Array{Int64,2}:
4 6
2 3
To extract a row (but note that this produces a Vector):
julia> c[1,:]
3-element Array{Int64,1}:
2
4
6
Linear indexing works as well:
julia> c[4]
4
julia> c[4] == c[1,2]
true
In memory, Arrays are stored like Vectors. The compiler just keeps track of how the user wants to interpret the data.
## Multi-dimensional Arrays¶
Arrays can have more than 2 dimensions.
julia> using Random
julia> a = rand(4,3,2)
4×3×2 Array{Float64,3}:
[:, :, 1] =
0.146411 0.908415 0.568039
0.444156 0.434034 0.875361
0.429705 0.704086 0.71789
0.502228 0.124412 0.771808
[:, :, 2] =
0.862953 0.58189 0.549077
0.722745 0.677342 0.330188
0.0543144 0.161877 0.358381
0.312414 0.0681076 0.822319
Indexing generates new arrays with potentially fewer dimensions:
julia> a[:,1,:]
4×2 Array{Float64,2}:
0.146411 0.862953
0.444156 0.722745
0.429705 0.0543144
0.502228 0.312414
### Array Exercises¶
1. Construct a matrix A with elements [2,4,...,20] in row 1 and [1,4,7,...,28] in row 2.
2. Replace row 1 with its square.
3. Find all columns where row 1 > row 2.
4. Let x=ones(10,1). Compute Ax.
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# Identifying the diameter of reinforced steel bars in a column design schematic
I'm having trouble identifying the diameter of the reinforced steel bars in the structural steel design for a slab and a beam of a building complex. You can see it here (PDF).
I'm told there's column design in this file, but I only see beam design. Is the diameter number of the steel before or after the diameter sign? Why are there numbers like 12/20 after the diameter sign? Is there any column design here at all?
• Longitudinal bars tend to be in the form "➀ $4\ \phi 16\ l=391\ (2)$": This translates to 4 rebars identified by ➀ elsewhere which have a 16 mm diameter and are each 391 cm long. I'm not sure what the (2) means.
• Transversal bars are described similarly (when their dimensions are shown), but they are then often repeated in this drawing in a manner I don't quite understand: "➄ $18\ \phi 8/10/20$". I don't understand what the $/10/20$ is supposed to mean. That being said, when their positions along the column are shown as ➄ $14\ \phi 8/20$, that just means that there are 14 cages made of 8 mm rebar distributed with a 20-cm spacing.
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# 509,033,161
Previous ... Next
## Number
$509 \, 033 \, 161$ is:
$7 \times 13 \times 19 \times 37 \times 73 \times 109$
The $472$nd Carmichael number, and one which is the product of $2$ Carmichael numbers:
$\forall a \in \Z: a \perp 509 \, 033 \, 161: a^{509 \, 033 \, 160} \equiv 1 \pmod {509 \, 033 \, 161}$
$509 \, 033 \, 161 = 1729 \times 294 \, 409$:
$\forall a \in \Z: a \perp 1729: a^{1728} \equiv 1 \pmod {1729}$
$\forall a \in \Z: a \perp 294 \, 409: a^{294 \, 408} \equiv 1 \pmod {294 \, 409}$
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# A restaurant offers a $12 dinner special that has 7 choices for an appetizer, 12 choices for an entree, and 6 choices for a dessert. EunoR 2021-09-08 Answered A restaurant offers a$12 dinner special that has 7 choices for an appetizer, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?
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## Expert Answer
izboknil3
Answered 2021-09-09 Author has 99 answers
According to fundamental counting principal it is known that, if the first event occurs in m ways, and the second event occurs in n ways, then two events occur in as sequence of mn ways.
There are 7 choices of appetizer, 12 choices of entrée, and 6 choices of dessert.
Hence, total number of different meals is, $7×12×6=504.$
Thus, 504 different means are available to select an appetizer, an entrée, and a dessert.
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# Gastwirth's location estimator
Let $$x = \{ x_1, x_2, \ldots, x_n \}$$ be a random sample. The Gastwirth’s location estimator is defined as follows:
$0.3 \cdot Q_{⅓}(x) + 0.4 \cdot Q_{½}(x) + 0.3 \cdot Q_{⅔}(x),$
where $$Q_p$$ is an estimation of the $$p^{\textrm{th}}$$ quantile (using classic sample quantiles).
This estimator could be quite interesting from a practical point of view. On the one hand, it’s robust (the breakdown point ⅓) and it has better statistical efficiency than the classic sample median. On the other hand, it has better computational efficiency than other robust and statistical efficient measures of location like the Harrell-Davis median estimator or the Hodges-Lehmann median estimator.
In this post, we conduct a short simulation study that shows its behavior for the standard Normal distribution and the Cauchy distribution.
### Simulation study
Let’s conduct the following simulation:
• Enumerate different samples sizes $$n = \{ 5, 10, 20 \}$$
• Enumerate different location estimators: Gastwirth’s location estimator $$Q_{\operatorname{G}}$$, the sample median $$Q_{\operatorname{SM}}$$, the Harrell-Davis median estimator $$Q_{\operatorname{HD}}$$, and the Hodges-Lehmann median estimator $$Q_{\operatorname{HL}}$$.
• Enumerate different distributions: the standard Normal distribution, the standard Cauchy distribution
• For each sample size, estimator, and distribution, generate $$30\,000$$ random samples of the given size from the given distribution and calculate the location estimation using the given estimator.
• Draw the corresponding density plots for the obtained estimation using Sheather & Jones method and the normal kernel.
Here are the results:
Based on this plot, we can do the following observations:
• For the standard Normal distribution (light-tailed), $$Q_{\operatorname{G}}$$ is better than $$Q_{\operatorname{SM}}$$, but worse than $$Q_{\operatorname{HD}}$$ and $$Q_{\operatorname{HL}}$$.
• For the standard Cauchy distribution (heavy-tailed), $$Q_{\operatorname{G}}$$ is worse than $$Q_{\operatorname{SM}}$$, but better than $$Q_{\operatorname{HD}}$$ and $$Q_{\operatorname{HL}}$$.
Of course, a more sophisticated study is required for reliable conclusions, but this simulation shows that Gastwirth’s location estimator is quite promising. It provides an interesting trade-off between statistical efficiency, computational efficiency, and robustness. It could be useful if we want to improve the statistical efficiency of the sample median for the light-tailed cases, keeping a decent breakdown point (⅓) and computational efficiency.
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# Graphene
Graphene is an atomic-scale honeycomb lattice made of carbon atoms.
Graphene is a one-atom-thick planar sheet of carbon atoms that are densely packed in a honeycomb crystal lattice. It can be thought of as an atomic-scale chicken wire made of carbon atoms and their bonds. It can also be considered an infinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons. Graphene is the basic structural element of several carbon allotropes, including graphite, carbon nanotubes, and other fullerenes. For example, graphite consists of many graphene sheets stacked together. Thus the name graphene was coined by modifying the word graphite.
Based on its properties, researchers have proposed a number of potential applications for graphene. For example, its two-dimensional structure make it an excellent sensor. Its high electrical conductivity and optical transparency make it a candidate for transparent conducting electrodes, useful for applications such as touchscreens, liquid crystal displays, organic photovoltaic cells, and organic light-emitting diodes (OLEDs). Graphene would also be an excellent component of integrated circuits, and graphene nanoribbons could be a way to construct ballistic transistors. The very high surface area to mass ratio of graphene suggests it could be used in the conductive plates of ultracapacitors. In addition, nanogaps in graphene sheets may potentially provide a new technique for rapid DNA sequencing.
## Description
A perfect graphene would consist exclusively of hexagonal cells; the presence of pentagonal and heptagonal cells would constitute defects. If an isolated pentagonal cell were present, then the plane would warp into a cone shape; insertion of 12 pentagons would create a spherical fullerene or buckyball. Likewise, insertion of an isolated heptagon would cause the sheet to become saddle-shaped. Controlled addition of pentagons and heptagons would allow a wide variety of complex shapes to be made, such as carbon nanobuds. Single-walled carbon nanotubes may be considered to be graphene cylinders; some have a hemispherical graphene cap (that includes 6 pentagons) at each end.
The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene…it is not correct to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed." In this regard, graphene has been referred to as an infinite alternant (only six-member carbon ring) polycyclic aromatic hydrocarbon (PAH). The largest molecule of this type consists of 222 atoms and is 10 benzene rings across.[1] The onset of graphene properties, as compared to those of a PAH are not known. PAHs of 60, 78, and 120 carbon atoms have UV absorbance spectra that show a discrete PAH electronic structure, but a PAH of 222 carbon atoms has Raman bands similar to those in graphite.
## History and experimental discovery
The term graphene first appeared in 1987[2] in order to describe single sheets of graphite as one of the constituents of graphite intercalation compounds (GICs); conceptually a GIC is a crystalline salt of the intercalant and graphene. The term was also used in early descriptions of carbon nanotubes,[3] as well as for epitaxial graphene,[4] and polycyclic aromatic hydrocarbons.[5] However, none of these examples constitutes isolated, two-dimensional graphene.
Larger graphene molecules or sheets (so that they can be considered as true isolated 2D crystals) cannot be grown even in principle. An article in Physics Today reads:
"Fundamental forces place seemingly insurmountable barriers in the way of creating [2D crystals] … Nascent 2D crystallites try to minimize their surface energy and inevitably morph into one of the rich variety of stable 3D structures that occur in soot.
But there is a way around the problem. Interactions with 3D structures stabilize 2D crystals during growth. So one can make 2D crystals sandwiched between or placed on top of the atomic planes of a bulk crystal. In that respect, graphene already exists within graphite….
One can then hope to fool Nature and extract single-atom-thick crystallites at a low enough temperature that they remain in the quenched state prescribed by the original higher-temperature 3D growth."[6]
Single layers of graphite were previously (starting from the 1970s) grown epitaxially on top of other materials.[7] This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp2-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer from the substrate to the epitaxial graphene, and, in some cases, hybridization between the d orbitals of the substrate atoms and ${\displaystyle \pi }$ orbitals of graphene, which significantly alters the electronic structure of the epitaxial graphene.
Single layers of graphite were also observed by transmission electron microscopy within bulk materials (see section Occurrence), in particular inside soot obtained by chemical exfoliation.[8] There have also been a number of efforts to make very thin films of graphite by mechanical exfoliation (starting from 1990 and continuing until after 2004)[8] but nothing thinner than 50 to 100 layers was produced during these years.
The previous efforts did not result in graphene as we know it now, i.e. as "free standing" single-atom-thick crystals of a macroscopic size which are either suspended or interact only weakly with a substrate. It is not important whether graphene is suspended or placed on another (non-binding) substrate. In both cases, it is isolated and can be studied as such. Within this definition of graphene, it was first isolated by the Manchester group of Andre Geim who in 2004[9] finally managed to extract single-atom-thick crystallites from bulk graphite. He provided the first and unexpected proof for the existence of true (free-standing) 2D crystals. Previously, it was assumed that graphene cannot exist in the flat state and should scroll into nanotubes "to decrease the surface energy".[10][11]
This experimental discovery of 2D crystal matter was openly doubted[1] until 2005 when in the same issue of Nature the groups of Andre Geim and Philip Kim of Columbia University have proved "beyond a reasonable doubt" that the obtained graphitic layers exhibit the electronic properties prescribed by theory. This theory was first developed by Philip R Wallace in 1947 as an approximation trying to understand the electronic properties of more complex, 3 dimensional graphite. He did not use the word graphene and referred to "a single hexagonal layer".[12] Later, graphene crystals obtained by using the Manchester recipe were also made suspended and their thickness proved directly by electron microscopy.[13]
## Occurrence and Production
It is now presumed that tiny fragments of graphene sheets are produced (along with quantities of other debris) whenever graphite is abraded, such as when drawing a line with a pencil.[8] However, it was physicists from University of Manchester and Institute for Microelectronics Technology, Chernogolovka, Russia who first isolated and studied graphene (rather than PAH) in 2004, and defined it in Science[9] as:
Graphene is the name given to a single layer of carbon atoms densely packed into a benzene-ring structure, and is widely used to describe properties of many carbon-based materials, including graphite, large fullerenes, nanotubes, etc. (e.g., carbon nanotubes are usually thought of as graphene sheets rolled up into nanometer-sized cylinders). Planar graphene itself has been presumed not to exist in the free state, being unstable with respect to the formation of curved structures such as soot, fullerenes, and nanotubes.
Graphene sheets in solid form (e.g. density > 1g/cc) usually show evidence in diffraction for graphite's 0.34 nm (002) layering. This is true even of some single-walled carbon nanostructures.[14] However, unlayered graphene with only (hk0) rings has been found in the core of presolar graphite onions.[15] Transmission electron microscope studies show faceting at defects in flat graphene sheets,[16] and suggest a possible role in this unlayered-graphene for two-dimensional dendritic crystallization from a melt.[17]
Graphene is presently one of the most expensive materials on Earth, with a sample that can be placed at the cross section of a human hair costing more than \$1,000 (as of April 2008).[8] The price may fall dramatically, though, if commercial production methods are developed in the future.
### Drawing Method
The British researchers obtained relatively large graphene sheets (eventually, up to 100 micrometers in size and visible through a magnifying glass) by mechanical exfoliation (repeated peeling) of 3D graphite crystals; their motivation was allegedly to study the electrical properties of thin graphite films and, as purely two-dimensional crystals were unknown before and presumed not to exist, their discovery of individual planes of graphite was presumably accidental. Both theory and experiment previously suggested that perfect 2D structures could not exist in the free state. It is believed that intrinsic microscopic roughening on the scale of 1 nm could be important for the stability of 2D crystals.[13]
Similar work is ongoing at many universities and the results obtained by the Manchester group in their PNAS paper "Two-dimensional atomic crystals" have been confirmed by several groups.[18]
### Epitaxial Growth
Another method uses the atomic structure of a substrate to seed the growth of the graphene, known as epitaxial growth. It doesn't typically yield a sample with a uniform thickness of graphene layers, and bonding between the bottom graphene layer and the substrate may affect the properties of the carbon layers. [19]
### Silicon Carbide Reduction
Another method is to heat silicon carbide to high temperatures (1100°C) to reduce it to graphene. This process produces a small sample size and is unlikely to be compatible with fabrication techniques for most electronic applications.
### Hydrazine Reduction
Researchers have developed a method of placing graphene oxide paper in a solution of pure hydrazine (a chemical compound of nitrogen and hydrogen), which reduces the graphite oxide paper into single-layer graphene.[20]
### Sodium reduction of ethanol
A recent publication has described a process for producing gram-quantities of graphene, by the reduction of ethanol by sodium metal, followed by pyrolysis of the ethoxide product, and washing with water to remove sodium salts.[21]
### Chemical Vapor Deposition
High-quality sheets of graphene exceeding 1 cm² (0.2 sq in) in area have been synthesized via chemical vapor deposition on thin nickel layers.[22] These sheets have been successfully transferred to various substrates, demonstrating viability for numerous electronic applications.
## Properties
### Atomic structure
• sp2-bonded carbon atoms
• The carbon-carbon bond length in graphene is approximately 0.142 nanometers (nm).
The atomic structure of isolated, single-layer graphene was studied by transmission electron microscopy (TEM) on sheets of graphene suspended between bars of a metallic grid.[13] Electron diffraction patterns showed the expected hexagonal lattice of graphene. Suspended graphene also showed "rippling" of the flat sheet, with amplitude of about one nanometer. These ripples may be intrinsic to graphene as a result of the instability of two-dimensional crystals,[23][24][25] or may be extrinsic, originating from the ubiquitous dirt seen in all TEM images of graphene. Atomic resolution real-space images of isolated, single-layer graphene on silicon dioxide substrates were obtained[26][27] by scanning tunneling microscopy. Graphene processed using lithographic techniques is covered by photoresist residue, which must be cleaned to obtain atomic-resolution images.[26] Such residue may be the "adsorbates" observed in TEM images, and may explain the rippling of suspended graphene. Rippling of graphene on the silicon dioxide surface was determined by conformation of graphene to the underlying silicon dioxide, and not an intrinsic effect.[26]
### Electronic properties
Graphene is quite different from most conventional three-dimensional materials. Intrinsic graphene is a semi-metal or zero-gap semiconductor. The E-k relation is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone, leading to zero effective mass for electrons and holes. [28] Due to this linear “dispersion” relation at low energies, electrons and holes near these six points behave like relativistic particles described by the Dirac equation for spin 1/2 particles. [29] Hence, the electrons and holes are called Dirac fermions, and the six corners of the Brillouin zone are called the Dirac points.[28] The equation describing the E-k relation is ${\displaystyle E=\hbar v_{F}{\sqrt {k_{x}^{2}+k_{y}^{2}}}}$; where ${\displaystyle v_{f}}$, the Fermi velocity, is approximately ${\displaystyle 10^{6}\mathrm {m} /\mathrm {s} }$.[29]
### Electronic transport
Experimental results from transport measurements show that graphene has a remarkably high electron mobility at room temperature, with reported values in excess of 15,000 cm2V−1s−1.[25] Additionally, the symmetry of the experimentally measured conductance indicates that the mobilities for holes and electrons should be nearly the same.[28] The mobility is nearly independent of temperature between 10 K and 100 K,[30][31][32] which implies that the dominant scattering mechanism is defect scattering. Scattering by the acoustic phonons of graphene limits the room temperature mobility to 200,000 cm2V−1s−1 at a carrier density of 1012 cm−2[32][33]. The corresponding resistivity of the graphene sheet would be 10−6 Ω•cm, less than the resistivity of silver, the lowest resistivity substance known at room temperature. However, for graphene on silicon dioxide substrates, scattering of electrons by optical phonons of the substrate is a larger effect at room temperature than scattering by graphene’s own phonons, and limits the mobility to 40,000 cm2V−1s−1.[32]
Despite the zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of ${\displaystyle {4e^{2}}/h}$. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the SiO2 substrate may lead to local puddles of carriers that allow conduction.[28] Several theories suggest that the minimum conductivity should be ${\displaystyle {4e^{2}}/{h\pi }}$; however, most measurements are of order ${\displaystyle {4e^{2}}/h}$ or greater[25] and depend on impurity concentration.[34]
Recent experiments have probed the influence of chemical dopants on the carrier mobility in graphene.[35][34] Schedin, et al. doped graphene with various gaseous species (some acceptors, some donors), and found the initial undoped state of a graphene structure can be recovered by gently heating the graphene in vacuum. Schedin, et al. reported that even for chemical dopant concentrations in excess of 1012 cm−2 there is no observable change in the carrier mobility.[35] Chen, et al. doped graphene with potassium in ultra high vacuum at low temperature. They found that potassium ions act as expected for charged impurities in graphene[36], and can reduce the mobility 20-fold.[34] The mobility reduction is reversible on heating the graphene to remove the potassium.
### Optical properties
Photograph of graphene in transmitted light. This one atom thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light, which is π times fine-structure constant.
Graphene's unique electronic properties produce an unexpectedly high opacity for an atomic monolayer, with a startlingly simple value: it absorbs πα ≈ 2.3 percent of white light, where α is the fine-structure constant.[37][38] This has been confirmed experimentally, but the measurement is not precise enough to improve on other techniques for determining the fine-structure constant.[39]
### Spin transport
Graphene is thought to be an ideal material for spintronics due to small spin-orbit interaction and near absence of nuclear magnetic moments in carbon. Electrical spin-current injection and detection in graphene was recently demonstrated up to room temperature[40][41][42]. Spin coherence lengths greater than 1 micrometer at room temperature were observed[40], and control of the spin current polarity with an electrical gate was observed at low temperature[41].
### Magnetic effects
Besides the high mobility and minimum conductivity, graphene shows very interesting behavior in the presence of a magnetic field. Graphene displays an anomalous quantum Hall effect with the sequence shifted by ${\displaystyle 1/2}$ with respect to the standard sequence. Thus, the Hall conductivity is ${\displaystyle \sigma _{xy}=\pm {4\left(N+1/2\right)e^{2}}/h}$, where ${\displaystyle N}$ is the Landau level index and the double valley and double spin degeneracies give the factor of ${\displaystyle 4}$.[25] This remarkable behavior can even be measured at room temperature.[30] Bilayer graphene also shows the quantum Hall effect, but with the standard sequence where ${\displaystyle \sigma _{xy}=\pm {4Ne^{2}}/h}$. Interestingly, the first plateau at ${\displaystyle N=0}$ is absent, indicating that bilayer graphene stays metallic at the neutrality point.[25]
Unlike normal metals, the longitudinal resistance of graphene shows maxima rather than minima for integral values of the Landau filling factor in measurements of the Shubnikov-de Haas oscillations, which show a phase shift of ${\displaystyle \pi }$, known as Berry’s phase.[28][30] The Berry’s phase arises due to the zero effective carrier mass near the Dirac points.[43] Study of the temperature dependence of the Shubnikov-de Haas oscillations in graphene reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass from the E-k relation.[30]
### Nanostripes: Spin-polarized edge currents
Nanostripes of graphene (in the zigzag orientation), at low temperatures, show spin-polarized edge currents [44], which also suggests applications in the recent field of spintronics.
### Graphene oxide
By oxidizing and chemically processing graphene, and then floating them in water, the graphene flakes form a single sheet and bond very powerfully. These sheets, called Graphene oxide paper have a measured tensile modulus of 32 GPa.
### Chemical modification
Soluble fragments of graphene can be prepared in the laboratory[45] through chemical modification of graphite. First, microcrystalline graphite is treated with a strongly acidic mixture of sulfuric acid and nitric acid. A series of steps involving oxidation and exfoliation result in small graphene plates with carboxyl groups at their edges. These are converted to acid chloride groups by treatment with thionyl chloride; next, they are converted to the corresponding graphene amide via treatment with octadecylamine. The resulting material (circular graphene layers of 5.3 angstrom thickness) is soluble in tetrahydrofuran, tetrachloromethane, and dichloroethane.
Hydrogenation of graphene results in graphane.[46]
### Thermal properties
The near-room temperature thermal conductivity of graphene was recently measured to be between (4.84±0.44) ×103 to (5.30±0.48) ×103 Wm−1K−1. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamond. It can be shown by using the Wiedemann-Franz law, that the thermal conduction is phonon-dominated.[47] However, for a gated graphene strip, an applied gate bias causing a Fermi Energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures.[48]
Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has basal plane thermal conductivity of over a 1000 W/mK (comparable to diamond). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger lattice spacing.[49] In addition, the ballistic thermal conductance of a graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.[50]
Despite its 2-D nature, graphene has 3 acoustic phonon modes. The two in-plane modes have a linear dispersion relation, whereas the out of plane mode has a quadratic dispersion relation. Due to this, the T2 dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T1.5 contribution of the out of plane mode.[50] The ballistic thermal conductance of graphene is isotropic.[48]
### Mechanical properties
Graphene is the strongest substance known to man, according to a study released in August 2008 by Columbia University. However, the process of separating it from graphite, where it occurs naturally, will require some technological development before it is economical enough to be used in industrial processes.[51]
Utilizing an atomic force microscope, research has recently been able to measure the spring constant of suspended Graphene sheets. Graphene sheets, held together by van der Waals forces, were suspended over silicon dioxide cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was measured to be on the order of 1-5 N/m and its Young's modulus was 0.5 TPa, which differs from bulk graphite. These high values make Graphene very strong and rigid. These intrinsic properties could lead to the possibility of utilizing Graphene for NEMS applications such as pressure sensors, and resonators.[52]
As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations will grow logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,[13] and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.[23][24][25]
## Potential applications
### Single molecule gas detection
Graphene makes an excellent sensor because of its 2D structure. The fact that its entire volume is exposed to its surrounding makes it very efficient to detect adsorbed molecules. Molecule detection is indirect: as a gas molecule adsorbs to the surface of graphene, the location of adsorption experiences a local change in electrical resistance. While this effect occurs in other materials, graphene is superior due to its high electrical conductivity (even when few carriers are present) and low noise which makes this change in resistance detectable.[35]
### Graphene nanoribbons
Graphene nanoribbons (GNRs) are essentially single layers of graphene that are cut in a particular pattern to give it certain electrical properties. Depending on how the unbonded edges are configured, they can either be in a Z (zigzag) or Armchair configuration. Calculations based on tight binding predict that zigzag GNRs are always metallic while armchairs can be either metallic or semiconducting, depending on their width. However, recent DFT calculations show that armchair nanoribbons are semiconducting with an energy gap scaling with the inverse of the GNR width. [53] Indeed, experimental results show that the energy gaps do increase with decreasing GNR width. [54] Zigzag nanoribbons are also semiconducting and present spin polarized edges.
Their 2D structure, high electrical and thermal conductivity, and low noise make GNRs a possible alternative to copper for integrated circuit interconnects. Some research is also being done to create quantum dots by changing the width of GNRs at select points along the ribbon, creating quantum confinement.[55]
### Integrated circuits and transistors
Graphene has the ideal properties to be an excellent component of integrated circuits. Graphene has a high carrier mobility as well as low noise, allowing it to be utilized as the channel in a field-effect transistor (FET). The issue is that single sheets of graphene are hard to produce, and even harder to make on top of an appropriate substrate. Researchers are looking into methods of transferring single graphene sheets from their source of origin (mechanical exfoliation on SiO2 / Si or thermal graphitization of a SiC surface) onto a target substrate of interest.[56]
Due to its high electronic quality, graphene has attracted the interest of technologists who see graphene nanoribbons as a way of constructing ballistic transistors. Graphene exhibits a pronounced response to a perpendicular external electric field, allowing one to build FETs (field-effect transistors). In their 2004 paper,[9] the Manchester group demonstrated FETs with a "rather modest" on-off ratio of ~30 at room temperature. In 2006, Georgia Tech researchers announced that they had successfully built an all-graphene planar FET with side gates.[57] Their devices showed changes of 2 percent at cryogenic temperatures. The first top-gated FET (on-off ratio of <2) was demonstrated by researchers of AMICA and RWTH Aachen University in 2007[58]. Graphene nanoribbons may prove generally capable of replacing silicon as a semiconductor in modern technology.[59]
In 2008, the smallest transistor so far—one atom thick and 10 atoms wide—was made of graphene.[60] IBM announced in December 2008 that it has fabricated and characterized graphene transistors operating at GHz frequencies.[61]
### On-off switches
Current graphene transistors show a very poor on-off ratio, and researchers are trying to find ways for improvement. In 2008, researchers of AMICA and the University of Manchester demonstrated a new switching effect in graphene field-effect devices. This switching effect is based on a reversible chemical modification of the graphene layer and gives an on-off ratio of greater than six orders of magnitude. These reversible switches could potentially be applied to nonvolatile memories.[62]
### Transparent conducting electrodes
Graphene's high electrical conductivity and high optical transparency make it a candidate for transparent conducting electrodes, useful for such applications as touchscreens, liquid crystal displays, organic photovoltaic cells, and Organic light-emitting diodes (OLEDs). In particular, graphene's mechanical strength and flexibility are advantageous compared to indium tin oxide, which is brittle, and graphene films may be deposited from solution over large areas.[63][64]
### Ultracapacitors
Due to the incredibly high surface area to mass ratio of graphene, one potential application is in the conductive plates of ultracapacitors. It is believed that graphene could be used to produce ultracapacitors with a greater energy storage density than is currently available.
### Rapid DNA Sequencing
In 2008, Dr. Henk Postma, a researcher at California State University, Northridge, proposed using nanogaps in graphene sheets for rapid DNA sequencing, a technique that relies on the good electrical conductivity of graphene and the fact that cytosine, guanine, adenine and thymine each have differing conductivity.[65]. He estimated in an interview with the Naked Scientists that the DNA of an individual would take just two hours to sequence using this technique.[66] Graphene nanopore rims could be further optimally functionalized for more selective passage of DNA bases, which could also distinguish the DNA bases in time.[67].
## Notes
1. C.D. Simpson, et al., "Synthesis of a Giant 222 Carbon Graphite Sheet" Chemistry - A European Journal 6 (2002):1424.
2. S. Mouras, et al., "Synthesis of first stage graphite intercalation compounds with fluorides" Revue de Chimie Minerale 24 (1987):572.
3. R. Saito, et al., "Electronic structure of graphene tubules based on C60" Phys. Rev. B 46 (1992):1804.
4. I. Forbeaux, et al., "Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure" Phys. Rev. B. 58 (1998):16396.
5. S. Wang, et al., "A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries" Journal of the Electrochemical Society. 147 (2000):2498.
6. A.K. Geim and A.H. MacDonald, "Graphene: Exploring carbon flatland" Physics Today. 60 (2007):35-41.
7. C. Oshima and A. Nagashima, "Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces" J. Phys.: Condens. Matter 9 (1997):1.
8. Andre K. Geim and Philip Kim, "Carbon Wonderland" Scientific American. Retrieved August 25, 2017.
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## ReferencesISBN links support NWE through referral fees
• Delhaes, Pierre. Graphite and Precursors. London, UK: Gordon & Breach, 2001. ISBN 978-9056992286.
• Fowler, P.W., and D.E. Manolopoulos. An Atlas of Fullerenes. Mineola, NY: Dover Publications, 2007. ISBN 0486453626.
• Miessler, Gary L., and Donald A. Tarr. Inorganic Chemistry. Upper Saddle River, NJ: Pearson Education International, 2004. ISBN 0131201980.
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# Let There Be an A.P. with the First Term 'A', Common Difference 'D'. If An A Denotes In Nth Term And Sn The Sum of First N Terms, Find. D, If a = 3, N = 8 and Sn = 192. - CBSE Class 10 - Mathematics
ConceptSum of First n Terms of an AP
#### Question
Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.
d, if a = 3, n = 8 and Sn = 192.
#### Solution
Here, we have an A.P. whose first term (a), the sum of first n terms (Sn) and the number of terms (n) are given. We need to find the common difference (d).
Here,
First term (a) = 3
Sum of n terms (Sn) = 192
Number of terms (n) = 8
So here we will find the value of n using the formula, a_n = a + (a - 1)d
So, to find the common difference of this A.P., we use the following formula for the sum of n terms of an A.P
S_n = n/2 [2a + (n -1)d]
Where; a = first term for the given A.P.
d = common difference of the given A.P.
= number of terms
So, using the formula for n = 8, we get,
S_8 = 8/2 [2(3) + (8 - 1)(d)]
192 = 4[6 = (7) (d)]
192 = 24 + 28d
28d = 192 - 24
Further solving for d
d = 168/28
d= 6
Therefore, the common difference of the given A.P. is d = 6
Is there an error in this question or solution?
#### Video TutorialsVIEW ALL [5]
Solution Let There Be an A.P. with the First Term 'A', Common Difference 'D'. If An A Denotes In Nth Term And Sn The Sum of First N Terms, Find. D, If a = 3, N = 8 and Sn = 192. Concept: Sum of First n Terms of an AP.
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Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int
Chapter Contents
Chapter Introduction
NAG Toolbox
# NAG Toolbox: nag_ode_ivp_rk_zero_simple (d02bj)
## Purpose
nag_ode_ivp_rk_zero_simple (d02bj) integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions, using a fixed order Runge–Kutta method, until a user-specified function, if supplied, of the solution is zero, and returns the solution at points specified by you, if desired.
## Syntax
[x, y, ifail] = d02bj(x, xend, y, fcn, tol, relabs, output, g, 'n', n)
[x, y, ifail] = nag_ode_ivp_rk_zero_simple(x, xend, y, fcn, tol, relabs, output, g, 'n', n)
## Description
nag_ode_ivp_rk_zero_simple (d02bj) advances the solution of a system of ordinary differential equations
yi ′ = fi(x,y1,y2, … ,yn), i = 1,2, … ,n, $yi′=fi(x,y1,y2,…,yn), i=1,2,…,n,$
from x = x$x={\mathbf{x}}$ to x = xend$x={\mathbf{xend}}$ using a fixed order Runge–Kutta method. The system is defined by fcn, which evaluates fi${f}_{i}$ in terms of x$x$ and y = (y1,y2,,yn)$y=\left({y}_{1},{y}_{2},\dots ,{y}_{\mathit{n}}\right)$. The initial values of y = (y1,y2,,yn)$y=\left({y}_{1},{y}_{2},\dots ,{y}_{\mathit{n}}\right)$ must be given at x = x$x={\mathbf{x}}$.
The solution is returned via the output supplied by you and at points specified by you, if desired: this solution is obtained by C1${C}^{1}$ interpolation on solution values produced by the method. As the integration proceeds a check can be made on the user-specified function g(x,y)$g\left(x,y\right)$ to determine an interval where it changes sign. The position of this sign change is then determined accurately by C1${C}^{1}$ interpolation to the solution. It is assumed that g(x,y)$g\left(x,y\right)$ is a continuous function of the variables, so that a solution of g(x,y) = 0$g\left(x,y\right)=0$ can be determined by searching for a change in sign in g(x,y)$g\left(x,y\right)$. The accuracy of the integration, the interpolation and, indirectly, of the determination of the position where g(x,y) = 0$g\left(x,y\right)=0$, is controlled by the parameters tol and relabs.
## References
Shampine L F (1994) Numerical solution of ordinary differential equations Chapman and Hall
## Parameters
### Compulsory Input Parameters
1: x – double scalar
The initial value of the independent variable x$x$.
2: xend – double scalar
The final value of the independent variable. If ${\mathbf{xend}}<{\mathbf{x}}$, integration will proceed in the negative direction.
Constraint: ${\mathbf{xend}}\ne {\mathbf{x}}$.
3: y(n) – double array
n, the dimension of the array, must satisfy the constraint n > 0${\mathbf{n}}>0$.
The initial values of the solution y1,y2,,yn${y}_{1},{y}_{2},\dots ,{y}_{\mathit{n}}$ at x = x$x={\mathbf{x}}$.
4: fcn – function handle or string containing name of m-file
fcn must evaluate the functions fi${f}_{i}$ (i.e., the derivatives yi${y}_{i}^{\prime }$) for given values of its arguments x,y1,,yn$x,{y}_{1},\dots ,{y}_{\mathit{n}}$.
[f] = fcn(x, y)
Input Parameters
1: x – double scalar
x$x$, the value of the independent variable.
2: y(n$\mathit{n}$) – double array
yi${y}_{\mathit{i}}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,\mathit{n}$, the value of the variable.
Output Parameters
1: f(n$\mathit{n}$) – double array
The value of fi${f}_{\mathit{i}}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,\mathit{n}$.
5: tol – double scalar
A positive tolerance for controlling the error in the integration. Hence tol affects the determination of the position where g(x,y) = 0$g\left(x,y\right)=0$, if g$g$ is supplied.
nag_ode_ivp_rk_zero_simple (d02bj) has been designed so that, for most problems, a reduction in tol leads to an approximately proportional reduction in the error in the solution. However, the actual relation between tol and the accuracy achieved cannot be guaranteed. You are strongly recommended to call nag_ode_ivp_rk_zero_simple (d02bj) with more than one value for tol and to compare the results obtained to estimate their accuracy. In the absence of any prior knowledge, you might compare the results obtained by calling nag_ode_ivp_rk_zero_simple (d02bj) with relabs = 'D'${\mathbf{relabs}}=\text{'D'}$ and with each of tol = 10.0p${\mathbf{tol}}={10.0}^{-p}$ and tol = 10.0p1${\mathbf{tol}}={10.0}^{-p-1}$ where p$p$ correct significant digits are required in the solution, y$y$. The accuracy of the value x$x$ such that g(x,y) = 0$g\left(x,y\right)=0$ is indirectly controlled by varying tol. You should experiment to determine this accuracy.
Constraint: 10.0 × machine precision < tol < 0.01.
6: relabs – string (length ≥ 1)
The type of error control. At each step in the numerical solution an estimate of the local error, est$\mathit{est}$, is made. For the current step to be accepted the following condition must be satisfied:
est = max (ei / (τr × max (|yi|,τa))) ≤ 1.0 $est =max(ei/( τr × max(|yi|,τa) )) ≤ 1.0$
where τr${\tau }_{r}$ and τa${\tau }_{a}$ are defined by
relabs τr${\tau }_{r}$ τa${\tau }_{a}$ 'M' tol 1.0 'A' εr${\epsilon }_{r}$ tol / εr${\mathbf{tol}}/{\epsilon }_{r}$ 'R' tol εa${\epsilon }_{a}$ 'D' tol εa${\epsilon }_{a}$
where εr${\epsilon }_{r}$ and εa${\epsilon }_{a}$ are small machine-dependent numbers and ei${e}_{i}$ is an estimate of the local error at yi${y}_{i}$, computed internally. If the condition is not satisfied, the step size is reduced and the solution is recomputed on the current step. If you wish to measure the error in the computed solution in terms of the number of correct decimal places, then relabs should be set to 'A' on entry, whereas if the error requirement is in terms of the number of correct significant digits, then relabs should be set to 'R'. If you prefer a mixed error test, then relabs should be set to 'M', otherwise if you have no preference, relabs should be set to the default 'D'. Note that in this case 'D' is taken to be 'R'.
Constraint: relabs = 'M'${\mathbf{relabs}}=\text{'M'}$, 'A'$\text{'A'}$, 'R'$\text{'R'}$ or 'D'$\text{'D'}$.
7: output – function handle or string containing name of m-file
output permits access to intermediate values of the computed solution (for example to print or plot them), at successive user-specified points. It is initially called by nag_ode_ivp_rk_zero_simple (d02bj) with ${\mathbf{xsol}}={\mathbf{x}}$ (the initial value of x$x$). You must reset xsol to the next point (between the current xsol and xend) where output is to be called, and so on at each call to output. If, after a call to output, the reset point xsol is beyond xend, nag_ode_ivp_rk_zero_simple (d02bj) will integrate to xend with no further calls to output; if a call to output is required at the point ${\mathbf{xsol}}={\mathbf{xend}}$, then xsol must be given precisely the value xend.
[xsol] = output(xsol, y)
Input Parameters
1: xsol – double scalar
The output value of the independent variable x$x$.
2: y(n$\mathit{n}$) – double array
The computed solution at the point xsol.
Output Parameters
1: xsol – double scalar
You must set xsol to the next value of x$x$ at which output is to be called.
If you do not wish to access intermediate output, the actual parameter output must be the string 'd02bjx'. (nag_ode_ivp_rk_zero_simple_dummy_output (d02bjx) is included in the NAG Toolbox.)
8: g – function handle or string containing name of m-file
g must evaluate the function g(x,y)$g\left(x,y\right)$ for specified values x,y$x,y$. It specifies the function g$g$ for which the first position x$x$ where g(x,y) = 0$g\left(x,y\right)=0$ is to be found.
[result] = g(x, y)
Input Parameters
1: x – double scalar
x$x$, the value of the independent variable.
2: y(n$\mathit{n}$) – double array
yi${y}_{\mathit{i}}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,\mathit{n}$, the value of the variable.
Output Parameters
1: result – double scalar
The result of the function.
If you do not require the root-finding option, the actual parameter g must be the string 'd02bjw'. (nag_ode_ivp_rk_zero_simple_dummy_g (d02bjw) is included in the NAG Toolbox.)
### Optional Input Parameters
1: n – int64int32nag_int scalar
Default: The dimension of the array y.
n$\mathit{n}$, the number of equations.
Constraint: n > 0${\mathbf{n}}>0$.
w
### Output Parameters
1: x – double scalar
If g$g$ is supplied by you, it contains the point where g(x,y) = 0$g\left(x,y\right)=0$, unless g(x,y)0$g\left(x,y\right)\ne 0$ anywhere on the range x to xend, in which case, x will contain xend (and the error indicator ${\mathbf{ifail}}={\mathbf{6}}$ is set); if g$g$ is not supplied by you it contains xend. However, if an error has occurred, it contains the value of x$x$ at which the error occurred.
2: y(n) – double array
The computed values of the solution at the final point x = x$x={\mathbf{x}}$.
3: ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).
## Error Indicators and Warnings
Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
On entry, tol ≥ 0.01${\mathbf{tol}}\ge 0.01$, or tol is too small or n ≤ 0${\mathbf{n}}\le 0$, or relabs ≠ 'M'${\mathbf{relabs}}\ne \text{'M'}$, 'A'$\text{'A'}$, 'R'$\text{'R'}$ or 'D'$\text{'D'}$, or ${\mathbf{x}}={\mathbf{xend}}$.
ifail = 2${\mathbf{ifail}}=2$
With the given value of tol, no further progress can be made across the integration range from the current point x = x$x={\mathbf{x}}$. (See Section [Further Comments] for a discussion of this error exit.) The components y(1),y(2),,y(n)${\mathbf{y}}\left(1\right),{\mathbf{y}}\left(2\right),\dots ,{\mathbf{y}}\left({\mathbf{n}}\right)$ contain the computed values of the solution at the current point x = x$x={\mathbf{x}}$. If you have supplied g$g$, then no point at which g(x,y)$g\left(x,y\right)$ changes sign has been located up to the point x = x$x={\mathbf{x}}$.
ifail = 3${\mathbf{ifail}}=3$
tol is too small for nag_ode_ivp_rk_zero_simple (d02bj) to take an initial step. x and y(1),y(2),,y(n)${\mathbf{y}}\left(1\right),{\mathbf{y}}\left(2\right),\dots ,{\mathbf{y}}\left({\mathbf{n}}\right)$ retain their initial values.
ifail = 4${\mathbf{ifail}}=4$
xsol has not been reset or xsol lies behind x in the direction of integration, after the initial call to output, if the output option was selected.
ifail = 5${\mathbf{ifail}}=5$
A value of xsol returned by the output has not been reset or lies behind the last value of xsol in the direction of integration, if the output option was selected.
ifail = 6${\mathbf{ifail}}=6$
At no point in the range x to xend did the function g(x,y)$g\left(x,y\right)$ change sign, if g$g$ was supplied. It is assumed that g(x,y) = 0$g\left(x,y\right)=0$ has no solution.
ifail = 7${\mathbf{ifail}}=7$
A serious error has occurred in an internal call to an interpolation function. Check all (sub)program calls and array dimensions. Seek expert help.
## Accuracy
The accuracy of the computation of the solution vector y may be controlled by varying the local error tolerance tol. In general, a decrease in local error tolerance should lead to an increase in accuracy. You are advised to choose relabs = 'D'${\mathbf{relabs}}=\text{'D'}$ unless you have a good reason for a different choice.
If the problem is a root-finding one, then the accuracy of the root determined will depend on the properties of g(x,y)$g\left(x,y\right)$ and on the values of tol and relabs. You should try to code g without introducing any unnecessary cancellation errors.
If more than one root is required, then to determine the second and later roots nag_ode_ivp_rk_zero_simple (d02bj) may be called again starting a short distance past the previously determined roots. Alternatively you may construct your own root-finding code using nag_roots_contfn_brent_rcomm (c05az), nag_ode_ivp_rkts_onestep (d02pf) and nag_ode_ivp_rkts_interp (d02ps).
If nag_ode_ivp_rk_zero_simple (d02bj) fails with ${\mathbf{ifail}}={\mathbf{3}}$, then it can be called again with a larger value of tol if this has not already been tried. If the accuracy requested is really needed and cannot be obtained with this function, the system may be very stiff (see below) or so badly scaled that it cannot be solved to the required accuracy.
If nag_ode_ivp_rk_zero_simple (d02bj) fails with ${\mathbf{ifail}}={\mathbf{2}}$, it is probable that it has been called with a value of tol which is so small that a solution cannot be obtained on the range x to xend. This can happen for well-behaved systems and very small values of tol. You should, however, consider whether there is a more fundamental difficulty. For example:
(a) in the region of a singularity (infinite value) of the solution, the function will usually stop with ${\mathbf{ifail}}={\mathbf{2}}$, unless overflow occurs first. Numerical integration cannot be continued through a singularity, and analytic treatment should be considered; (b) for ‘stiff’ equations where the solution contains rapidly decaying components, the function will use very small steps in x$x$ (internally to nag_ode_ivp_rk_zero_simple (d02bj)) to preserve stability. This will exhibit itself by making the computing time excessively long, or occasionally by an exit with ${\mathbf{ifail}}={\mathbf{2}}$. Runge–Kutta methods are not efficient in such cases, and you should try nag_ode_ivp_bdf_zero_simple (d02ej).
## Example
This example illustrates the solution of four different problems. In each case the differential system (for a projectile) is
y′ = tanφ v′ = ( − 0.032tanφ)/v − (0.02v)/(cosφ) φ′ = ( − 0.032)/(v2)
$y′=tanϕ v′= -0.032tanϕv- 0.02v cosϕ ϕ′= -0.032v2$
over an interval x = 0.0${\mathbf{x}}=0.0$ to xend = 10.0${\mathbf{xend}}=10.0$ starting with values y = 0.5$y=0.5$, v = 0.5$v=0.5$ and φ = π / 5$\varphi =\pi /5$. We solve each of the following problems with local error tolerances 1.0e−4$\text{1.0e−4}$ and 1.0e−5$\text{1.0e−5}$.
(i) To integrate to x = 10.0$x=10.0$ producing intermediate output at intervals of 2.0$2.0$ until a root is encountered where y = 0.0$y=0.0$. (ii) As (i) but with no intermediate output. (iii) As (i) but with no termination on a root-finding condition. (iv) As (i) but with no intermediate output and no root-finding termination condition.
function nag_ode_ivp_rk_zero_simple_example
% For communication with save.
global ykeep ncall xkeep;
% Initialize variables and arrays.
x = 0;
xend = 10;
y = [0.5; 0.5; 0.6283185307179586];
tol = 0.0001;
relabs = 'Default';
xOut1 = [];
ncall = 0;
ykeep = zeros(1,length(y));
xkeep = zeros(1,1);
fprintf('nag_ode_ivp_rk_zero_simple example program results\n\n');
fprintf('Case 1: intermediate output, root-finding\n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
disp(' X Y(1) Y(2) Y(3)');
% output outputs intermediate values.
[xOut, yOut, ifail] = nag_ode_ivp_rk_zero_simple(x, xend, y, @fcn, tol, ...
relabs, @output, @g);
if ifail ~= 0
% Problems in integration. Print message and exit.
error( ...
'Warning: nag_ode_ivp_rk_zero_simple returned with ifail = %1d ', ...
ifail);
end
disp(' ');
disp(['Root of Y(1) = 0.0 at ',num2str(xOut)]);
disp('Solution is' );
fprintf(' %8.4f %8.4f %8.4f\n\n', yOut(1), yOut(2), yOut(3));
end
fprintf('Case 2: no intermediate output, root-finding \n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
[xOut, yOut, ifail] = nag_ode_ivp_rk_zero_simple(x, xend, y, @fcn, tol, ...
relabs, 'nag_ode_ivp_rk_zero_simple_dummy_output',@g);
if ifail ~= 0
% Problems in integration. Print message and exit.
error( ...
'Warning: nag_ode_ivp_rk_zero_simple returned with ifail = %1d ', ...
ifail);
end
disp(['Root of Y(1) = 0.0 at ',num2str(xOut)]);
disp('Solution is' );
fprintf(' %8.4f %8.4f %8.4f\n\n', yOut(1), yOut(2), yOut(3));
% Store the x value for plotting.
xOut1 = xOut;
end
fprintf('Case 3: intermediate output, no root-finding\n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
fprintf(' X Y(1) Y(2) Y(3) \n');
% save stores intermediate values in xkeep, ykeep, which are
% plotted later (it also outputs them).
[xOut, yOut, ifail] = nag_ode_ivp_rk_zero_simple(x, xend, y, @fcn, tol, ...
relabs, @save,'nag_ode_ivp_rk_zero_simple_dummy_g');
if ifail ~= 0
% Problems in integration. Print message and exit.
error( ...
'Warning: nag_ode_ivp_rk_zero_simple returned with ifail = %1d ', ...
ifail);
end
fprintf('\n');
end
fprintf(['Case 4: no intermediate output, no root-finding ', ...
'(integrate to xend)\n\n']);
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
disp(' X Y(1) Y(2) Y(3)');
fprintf('%2d %8.4f %8.4f %8.4f\n', x, y(1), y(2), y(3));
[xOut, yOut, ifail] = ...
nag_ode_ivp_rk_zero_simple(x, xend, y, @fcn, tol, relabs, ...
'nag_ode_ivp_rk_zero_simple_dummy_output','nag_ode_ivp_rk_zero_simple_dummy_g');
if ifail ~= 0
% Problems in integration. Print message and exit.
error( ...
'Warning: nag_ode_ivp_rk_zero_simple returned with ifail = %1d ', ...
ifail);
end
fprintf('%2d %8.4f %8.4f %8.4f\n\n', xOut, yOut(1), ...
yOut(2), yOut(3));
end
% Plot results.
nres = 0.5*length(xkeep);
xplot = xkeep(nres+1:2*nres);
yplot = ykeep(nres+1:2*nres, :);
fig = figure('Number', 'off');
display_plot(xplot, yplot, xOut1)
function xsolOut = save(xsol, y)
% For communication with main routine.
global ykeep ncall xkeep;
% This version of the intermediate output routine stores the values
% (so they can be plotted in the main routine).
ncall = ncall+1;
ykeep(ncall,:) = y;
xkeep(ncall,:) = xsol;
fprintf('%2d %8.4f %8.4f %8.4f\n', xsol, y(1), y(2), y(3));
xsolOut = xsol + 2;
function xsolOut = output(xsol, y)
% Output intermediate values of solution.
fprintf('%2d %8.4f %8.4f %8.4f\n', xsol, y(1), y(2), y(3));
xsolOut = xsol + 2;
function f = fcn(x,y)
% Evaluate the derivatives.
f = zeros(3,1);
f(1) = tan(y(3));
f(2) = -0.032*tan(y(3))/y(2) - 0.02*y(2)/cos(y(3));
f(3) = -0.032/y(2)^2;
function result = g(x,y)
% Evaluate g(x,y) when root-finding option is selected.
result = y(1);
function display_plot(xplot, yplot, xOut1)
% Formatting for title and axis labels.
titleFmt = {'FontName', 'Helvetica', 'FontWeight', 'Bold', 'FontSize', 14};
labFmt = {'FontName', 'Helvetica', 'FontWeight', 'Bold', 'FontSize', 13};
set(gca, 'FontSize', 13); % for legend, axis tick labels, etc.
% Plot the three curves.
plot(xplot, yplot(:,1), '-+', ...
xplot, yplot(:,2), '--x', ...
xplot, yplot(:,3), ':*');
% Mark the height=0 point.
do_stem(xplot, yplot, xOut1);
title('ODE Solution using Runge-Kutta with Root-finding', titleFmt{:});
% Label the axes.
xlabel('x', labFmt{:});
ylabel('Solution', labFmt{:});
legend('height','velocity','angle','height = 0','Location','Best');
function do_stem(xplot, yplot, xOut1)
% Find the x bin that xOut1 lies in.
for i = 1:length(xplot)
if xplot(i) > xOut1
break
end
end
% Use linear interpolation to find the corresponding y values on the
% two curves.
a1 = xplot(i)-xplot(i-1);
b1 = yplot(i,2)-yplot(i-1,2);
c1 = xOut1-xplot(i-1);
d1 = c1/a1;
e1 = d1*b1;
f1 = e1+yplot(i-1,2);
a2 = xplot(i)-xplot(i-1);
b2 = yplot(i,3)-yplot(i-1,3);
c2 = xOut1-xplot(i-1);
d2 = c2/a2;
e2 = d2*b2;
f2 = e2+yplot(i-1,3);
% Plot the line from the x axis to the two y values.
hold on
stem([xOut1,xOut1],[f1,0],'k:s');
hold on
stem([xOut1,xOut1],[f2,0],'k:s');
nag_ode_ivp_rk_zero_simple example program results
Case 1: intermediate output, root-finding
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
Root of Y(1) = 0.0 at 7.2882
Solution is
-0.0000 0.4749 -0.7601
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
Root of Y(1) = 0.0 at 7.2883
Solution is
0.0000 0.4749 -0.7601
Case 2: no intermediate output, root-finding
Calculation with tol = 0.0001
Root of Y(1) = 0.0 at 7.2882
Solution is
-0.0000 0.4749 -0.7601
Calculation with tol = 1e-05
Root of Y(1) = 0.0 at 7.2883
Solution is
0.0000 0.4749 -0.7601
Case 3: intermediate output, no root-finding
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
8 -0.7460 0.5130 -0.8537
10 -3.6283 0.6333 -1.0515
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
8 -0.7459 0.5130 -0.8537
10 -3.6282 0.6333 -1.0515
Case 4: no intermediate output, no root-finding (integrate to xend)
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
10 -3.6283 0.6333 -1.0515
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
10 -3.6282 0.6333 -1.0515
function d02bj_example
% For communication with save.
global ykeep ncall xkeep;
% Initialize variables and arrays.
x = 0;
xend = 10;
y = [0.5; 0.5; 0.6283185307179586];
tol = 0.0001;
relabs = 'Default';
xOut1 = [];
ncall = 0;
ykeep = zeros(1,length(y));
xkeep = zeros(1,1);
fprintf('d02bj example program results\n\n');
fprintf('Case 1: intermediate output, root-finding\n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
disp(' X Y(1) Y(2) Y(3)');
% output outputs intermediate values.
[xOut, yOut, ifail] = d02bj(x, xend, y, @fcn, tol, ...
relabs, @output, @g);
if ifail ~= 0
% Problems in integration. Print message and exit.
error('Warning: d02bj returned with ifail = %1d',ifail);
end
disp(' ');
disp(['Root of Y(1) = 0.0 at ',num2str(xOut)]);
disp('Solution is' );
fprintf(' %8.4f %8.4f %8.4f\n\n', yOut(1), yOut(2), yOut(3));
end
fprintf('Case 2: no intermediate output, root-finding \n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
[xOut, yOut, ifail] = d02bj(x, xend, y, @fcn, tol, ...
relabs, 'd02bjx',@g);
if ifail ~= 0
% Problems in integration. Print message and exit.
error('Warning: d02bj returned with ifail = %1d',ifail);
end
disp(['Root of Y(1) = 0.0 at ',num2str(xOut)]);
disp('Solution is' );
fprintf(' %8.4f %8.4f %8.4f\n\n', yOut(1), yOut(2), yOut(3));
% Store the x value for plotting.
xOut1 = xOut;
end
fprintf('Case 3: intermediate output, no root-finding\n\n');
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
fprintf(' X Y(1) Y(2) Y(3) \n');
% save stores intermediate values in xkeep, ykeep, which are
% plotted later (it also outputs them).
[xOut, yOut, ifail] = d02bj(x, xend, y, @fcn, tol, ...
relabs, @save,'d02bjw');
if ifail ~= 0
% Problems in integration. Print message and exit.
error('Warning: d02bj returned with ifail = %1d',ifail);
end
fprintf('\n');
end
fprintf(['Case 4: no intermediate output, no root-finding ', ...
'(integrate to xend)\n\n']);
for j = 4:5
tol = double(10)^(-j);
disp(['Calculation with tol = ',num2str(tol)]);
disp(' X Y(1) Y(2) Y(3)');
fprintf('%2d %8.4f %8.4f %8.4f\n', x, y(1), y(2), y(3));
[xOut, yOut, ifail] = ...
d02bj(x, xend, y, @fcn, tol, relabs, 'd02bjx','d02bjw');
if ifail ~= 0
% Problems in integration. Print message and exit.
error('Warning: d02bj returned with ifail = %1d',ifail);
end
fprintf('%2d %8.4f %8.4f %8.4f\n\n', xOut, yOut(1), ...
yOut(2), yOut(3));
end
% Plot results.
nres = 0.5*length(xkeep);
xplot = xkeep(nres+1:2*nres);
yplot = ykeep(nres+1:2*nres, :);
fig = figure('Number', 'off');
display_plot(xplot, yplot, xOut1)
function xsolOut = save(xsol, y)
% For communication with main routine.
global ykeep ncall xkeep;
% This version of the intermediate output routine stores the values
% (so they can be plotted in the main routine).
ncall = ncall+1;
ykeep(ncall,:) = y;
xkeep(ncall,:) = xsol;
fprintf('%2d %8.4f %8.4f %8.4f\n', xsol, y(1), y(2), y(3));
xsolOut = xsol + 2;
function xsolOut = output(xsol, y)
% Output intermediate values of solution.
fprintf('%2d %8.4f %8.4f %8.4f\n', xsol, y(1), y(2), y(3));
xsolOut = xsol + 2;
function f = fcn(x,y)
% Evaluate the derivatives.
f = zeros(3,1);
f(1) = tan(y(3));
f(2) = -0.032*tan(y(3))/y(2) - 0.02*y(2)/cos(y(3));
f(3) = -0.032/y(2)^2;
function result = g(x,y)
% Evaluate g(x,y) when root-finding option is selected.
result = y(1);
function display_plot(xplot, yplot, xOut1)
% Formatting for title and axis labels.
titleFmt = {'FontName', 'Helvetica', 'FontWeight', 'Bold', 'FontSize', 14};
labFmt = {'FontName', 'Helvetica', 'FontWeight', 'Bold', 'FontSize', 13};
set(gca, 'FontSize', 13); % for legend, axis tick labels, etc.
% Plot the three curves.
plot(xplot, yplot(:,1), '-+', ...
xplot, yplot(:,2), '--x', ...
xplot, yplot(:,3), ':*');
% Mark the height=0 point.
do_stem(xplot, yplot, xOut1);
title('ODE Solution using Runge-Kutta with Root-finding', titleFmt{:});
% Label the axes.
xlabel('x', labFmt{:});
ylabel('Solution', labFmt{:});
legend('height','velocity','angle','height = 0','Location','Best');
function do_stem(xplot, yplot, xOut1)
% Find the x bin that xOut1 lies in.
for i = 1:length(xplot)
if xplot(i) > xOut1
break
end
end
% Use linear interpolation to find the corresponding y values on the
% two curves.
a1 = xplot(i)-xplot(i-1);
b1 = yplot(i,2)-yplot(i-1,2);
c1 = xOut1-xplot(i-1);
d1 = c1/a1;
e1 = d1*b1;
f1 = e1+yplot(i-1,2);
a2 = xplot(i)-xplot(i-1);
b2 = yplot(i,3)-yplot(i-1,3);
c2 = xOut1-xplot(i-1);
d2 = c2/a2;
e2 = d2*b2;
f2 = e2+yplot(i-1,3);
% Plot the line from the x axis to the two y values.
hold on
stem([xOut1,xOut1],[f1,0],'k:s');
hold on
stem([xOut1,xOut1],[f2,0],'k:s');
d02bj example program results
Case 1: intermediate output, root-finding
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
Root of Y(1) = 0.0 at 7.2882
Solution is
-0.0000 0.4749 -0.7601
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
Root of Y(1) = 0.0 at 7.2883
Solution is
0.0000 0.4749 -0.7601
Case 2: no intermediate output, root-finding
Calculation with tol = 0.0001
Root of Y(1) = 0.0 at 7.2882
Solution is
-0.0000 0.4749 -0.7601
Calculation with tol = 1e-05
Root of Y(1) = 0.0 at 7.2883
Solution is
0.0000 0.4749 -0.7601
Case 3: intermediate output, no root-finding
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
8 -0.7460 0.5130 -0.8537
10 -3.6283 0.6333 -1.0515
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
2 1.5493 0.4055 0.3066
4 1.7423 0.3743 -0.1289
6 1.0055 0.4173 -0.5507
8 -0.7459 0.5130 -0.8537
10 -3.6282 0.6333 -1.0515
Case 4: no intermediate output, no root-finding (integrate to xend)
Calculation with tol = 0.0001
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
10 -3.6283 0.6333 -1.0515
Calculation with tol = 1e-05
X Y(1) Y(2) Y(3)
0 0.5000 0.5000 0.6283
10 -3.6282 0.6333 -1.0515
|
# Discussion Channel for Brilliant Junior NT Contest
The reason behind creating this discussion note , is to keep main contest note clean, the main contest note is getting overcrowded with discussion comments.
Feel free to discuss about problems here.
Here is a link of the contest note.
Note by A Former Brilliant Member
4 years ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
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print "hello world"
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Sort by:
Can someone post a formal, rigorous solution to Q5?
- 4 years ago
Well , I am also not getting that one :(
Solution posted by lakshya sinha is wrong as well as the answer . I am posting the next question (6) and the answer of this question (5)
- 4 years ago
sure ...
This is the hardest branch of maths I think
- 4 years ago
What does Spagnoletti mean when writing "there are only 2 solutions which are s + r = p"? What is s and what is r and what is the equation we are supposed to be solving? (Since the first is assumed correct for all x if I am reading it right)
- 4 years ago
Apparently I am just dumb, because I don't understand the next one either - a^x+b^x=2^y 1^1+3^1=2^2 a≠b
- 4 years ago
Yes probably it is positive integers other than 1. @Sharky Kesa please reply and change the problem title to EPP set 3 #1
I will ask this question to him in the main note itself as I am not able to tag him.
Everybody please note that , this season is soon going to end...after @Svatejas Shivakumar' s Extra Parti.Prob. set 3 gets solved....Next season will be more interesting ! Brilliant Advanced NT Contest. All the previous contestants take this note.....
- 3 years, 12 months ago
So soon? Anyways thank you everyone for making this contest a grand success. Had great fun.
- 3 years, 12 months ago
Thanks for contributing...:) second season will be more interesting and good hope you will enjoy it. Alex and Svatejas...
- 3 years, 12 months ago
Surely it will be so.
- 3 years, 12 months ago
Sure it will be. When will season 2 start?
- 3 years, 12 months ago
Thank you for the contest. It has been a fantastic opportuinity to improve our Number Theory knowledge.
- 3 years, 12 months ago
After shivam jadhav's problem is solved , I think we must move on to new fresh , note ....
Till Shivam's problem unsolved you can post extra participation problems ......... anybody who wants to ....but only 1 EPP is allowed . per regular question.
Keep this in Mind !!!!
I think that you can start note-2 soon. There are well over 100 comments and it is very hard to see to where someone commented.
- 3 years, 12 months ago
I think we will start the new note after say problem 15 as the contest started just few days back and it will be difficult for some people to start from the second note. The note can be made better if we all delete all the unnecessary comments.
I think that it will be better if every person is allowed to post 1 EPP per regular question.
okay !
Guys I will be inactive on Brilliant for 6-7 days as I am going on holiday trip....:( :( :( :(
I still think that there can be some conclusion for EPP problem 1 . We are getting a number which is divisible by 2000 which has one factor which is given number , ...So there can be some relation ...
With the question, what you actually want to try to prove is that the expression is divisible by 16 and 125.
- 4 years ago
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# Why can't a current carrying loop (curl of the electric field exists) produce a time varying magnetic field?
If a time varying magnetic field can give value to the curl of an electric field, why not the other way round? That is, why can't an enclosed loop with some emf produced (basically a current carrying loop) produce a changing magnetic field?
It does produce a constant magnetic field, yes. But according to Faraday's law, curl E=-dB/dt if the curl of the electric field has a value, shouldn't the time derivative also have a value? Meaning: a changing magnetic field should be produced.
• Could you describe the physical situation you’re considering in more detail please? A closed loop of current has E slumming up to zero around it: there’s not average curl of E. – Bob Jacobsen Oct 10 '19 at 13:18
• It's just a closed loop, like you're mentioning. Oh yes, you're right. I thought that there will be field 'in the wire'. Won't there be a field? – Swaroop Joshi Oct 10 '19 at 13:19
• Are you sure the curl of the electric field is nonzero in this situation? – probably_someone Oct 10 '19 at 13:23
• I'm not sure. Maybe that's where I'm wrong. But how to think of it to be equal to 0? – Swaroop Joshi Oct 10 '19 at 13:29
• Yes..it is directed along the length of the wire. So the curl for the infinitesimally small area would be 0. – Swaroop Joshi Oct 10 '19 at 13:42
If you had the hypothetical situation of a constant current travelling around a loop of wire, then any changing magnetic flux through the loop is calculated as $$-\oint \vec{E}\cdot d\vec{l}$$.
For an ideal conductor then $$\vec{J} = \sigma \vec{E}$$ and the current and electric field are of constant magnitude and in the same direction, which is also the direction of the path taken when doing the integral. If it is a perfect loop then the infinitesimal line integrals will sum to zero and so there is no changing magnetic flux through the loop (easy to see if you consider a square "loop" in Cartesian coordinates; the line integrals on opposite sides will be equal in magnitude but opposite in sign).
By Stokes' theorem we know that the curl of the E-field and its closed line integral are related. $$\int (\nabla \times \vec{E})\cdot d\vec{S} = \oint \vec{E}\cdot d\vec{l}$$ So what matters as far as calculating any changing magnetic flux through the whole loop is the integral of the curl of the E-field over the whole surface bounded by the loop. i.e. It depends on the value of $$\nabla \times \vec{E}$$ over the whole surface, not just at any single point.
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# Events by month
## June 2021
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### Geometry Working Seminar
Wednesday, June 2, 2021 — 11:00 to 11:00 AM EDT
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"Decomposition of curvature tensor for metrics with torsion"
I will first review the classical decomposition of the Riemann curvature tensor into scalar, traceless Ricci, and Weyl curvature, with an emphasis on special features in dimensions 3 and 4. Then I will consider the more general case of a metric compatible connection with torsion, and see how this decomposition generalizes.
### Student Number Theory Seminar
Wednesday, June 9, 2021 — 9:00 AM EDT
Shuo Gao, Department of Pure Mathematics, University of Waterloo
"Introduction to Elementary Sieve"
This talk aims at introducing sieve theory in an elementary way. Sieve problem and two elementary sieves - larger sieve and square sieve - will be discussed in detail, as well as their applications and a broad overview of the historical development of sieve theory. Some standard results including the Mobius inversion formula will also be covered in this talk to make the proof self-contained.
### Math Faculty Teaching Seminar
Wednesday, June 9, 2021 — 12:00 to 12:00 PM EDT
Jason Siefken, University of Toronto
"Onboarding Instructors to an Active Learning Class"
### Joint Pure Math/C&O Grad Colloquium
Thursday, June 10, 2021 — 4:00 PM EDT
Shayla Redlin, Department of Combinatorics & Optimization, University of Waterloo
"Counting Antichains in the Boolean Lattice"
### "Decomposition of curvature tensor for metrics with torsion, continued"
Wednesday, June 16, 2021 — 11:00 to 11:00 AM EDT
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
Last time we reviewed the classical decomposition of the Riemann curvature tensor into scalar, traceless Ricci, and Weyl curvature. This time we will examine special features in dimensions 3 and 4. Then I will consider the more general case of a metric compatible connection with torsion, and see how this decomposition generalizes.
### Learning seminar on the basics of Temperley-Lieb algebras
Thursday, June 17, 2021 — 1:30 PM EDT
Katarina Spasojevic, USRA, Department of Pure Mathematics, University of Waterloo
### Algebraic Geometry Working Seminar
Monday, June 21, 2021 — 11:00 to 11:00 AM EDT
Sean Monahan, Department of Pure Mathematics, University of Waterloo
"An introduction to toric varieties"
Toric varieties are a special kind of variety equipped with a group action from an algebraic torus. These varieties are very nice to work with because they have a combinatorial interpretation involving polyhedral geometry. I will (very quickly) introduce toric varieties and focus on some concrete examples.
The seminar will meet on Zoom.
Meeting ID: 811 2094 8164
Passcode: 033003
### Learning Seminar on the Basics of Brown Measure
Monday, June 21, 2021 — 2:30 PM EDT
Ping Zhong, University of Wyoming
The Brown measure was introduced by L.G. Brown in 1983. It is a generalized notion of spectral measure which applies to non-normal operators living in a suitable non-commutative probability framework -- the framework of a so-called W*-probability space. The purpose of this learning seminar is to provide an accessible entry point to the notion of Brown measure, with an eye towards becoming able to do calculations of Brown measures in examples which come from free probability.
### Student Number Theory Seminar
Wednesday, June 23, 2021 — 9:00 AM EDT
Nolan Pyott, Department of Pure Mathematics, University of Waterloo
"Counting Irreducible Polynomials with the Turán Sieve"
### Geometry Working Seminar
Wednesday, June 23, 2021 — 11:00 to 11:00 AM EDT
Shengda Hu, Wilfrid Laurier University
"Curvature for connections in generalized geometry"
We continue with the discussion on generalized connections on a Riemannian manifold, discuss the curvature identities and generalize holomorphic bundle over a generalized Kahler manifold.
Zoom meeting:
Meeting ID: 958 7361 8652 Passcode: 577854
### Math Faculty Teaching Seminar
Wednesday, June 23, 2021 — 12:00 to 12:00 PM EDT
Sean Fitzpatrick, University of Lethbridge
"How using OER made me a better teacher"
### Arithmetic Geometry Learning Seminar
Monday, June 28, 2021 — 1:30 PM EDT
David McKinnon, Department of Pure Mathematics, University of Waterloo
"Arithmetic Geometry Learning Seminar organisational meeting"
We’re going to study something related to the proof of Fermat’s Last Theorem, having to do with solving Diophantine equations. Come to the first meeting to help us figure out exactly what that will be!
Place: Zoom
### Learning Seminar on the Basics of Brown Measure
Tuesday, June 29, 2021 — 2:30 PM EDT
Ping Zhong, University of Wyoming
The meetings of this learning seminar will continue on Tuesday afternoons, 2:30-4 pm, on Zoom. The plan for the next meeting is to wrap-up the discussion about the Fuglede-Kadison determinant and to move on towards the definition of the Brown spectral measure associated to an element of a W*-probability space.
The seminar will meet on Zoom.
Meeting ID: 913 2631 2873 Passcode: 581735
### Differential Geometry Working Seminar
Wednesday, June 30, 2021 — 11:00 to 11:00 AM EDT
Shengda Hu, Wilfrid Laurier University
"Curvature of generalized holomorphic bundles"
We continue with the discussion on generalized connections on a Riemannian manifold. We will discuss properties of curvatures on generalized holomorphic vector bundles over a generalized Kahler manifold and generalized analogues of classical notions.
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# Altitude to altitude
Geometry Level 4
In a triangle $$ABC$$, $$AB=13$$, $$BC=14$$, $$CA=14$$, and $$DC$$ and $$EA$$ are the altitudes from $$C$$ and $$A$$, respectively. Find $$DE$$.
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# Hook-length for partitions
Let $$\lambda=(\lambda_1,...,\lambda_r,...)$$ be a partition (i.e. $$\lambda_i\ge \lambda_{i+1}$$ and there are only finitely many non-zero terms.) Let $$\lambda'$$ be a conjugate partition, i.e. $$\lambda_i'=\mathrm{card}\{j:\ \lambda_j\ge i\}$$.
Let $$\Lambda:=\{(i,j)\in\mathbb{Z}^2 :\ 1\le j\le \lambda_i \}$$ be the diagram of $$\lambda$$.
Take $$x=(i,j)$$ and define the hook-length by $$h(x)=\lambda_i+\lambda_j'-i-j+1.$$ From the properties of diagrams it is known that for $$f_{\lambda,n}(t):=\sum\limits_{i=1}^nt^{\lambda_i+n-i}$$ with $$n\ge \lambda_1', \ m\ge\lambda_1$$ the following identity holds $$f_{\lambda,n}(t)+t^{m+n-1}f_{\lambda',m}(t^{-1})=\frac{1-t^{n+m}}{1-t}.$$ From this it follows (after some calculations) that $$\prod\limits_{x\in\Lambda}(1-t^{h(x)})\prod\limits_{i where $$\mu_i=\lambda_1+n-i$$.
I would like to show that the above relation implies $$\prod\limits_{x\in\Lambda}h(x)\prod\limits_{i
I know that I should somehow divide the previous relation by $$(1-t)^{|\lambda|}$$, but I don't see how to use this hint in a way that is not so tedious.
• The idea is to divide by an appropriate power of $1-t$, and then `evaluate' at $t=1$ - the point is that $(1-t^r)/(1-t)=1+t+\cdots+t^{r-1} = r$ at $t=1$. – Matthew Towers Feb 27 at 18:37
• The power series $1-t^1, 1-t^2, 1-t^3, \ldots$ are multiplicatively $\mathbb{Z}$-linerarly independent. That is, if $a_1, a_2, a_3, \ldots$ are integers such that all but finitely many $i \geq 1$ satisfy $a_i = 0$ and such that $\prod\limits_{i \geq 1} \left(1-t^i\right)^{a_i} = 1$, then $a_1 = a_2 = a_3 = \cdots = 0$. (Actually, this holds even without the "all but finitely many $i \geq 1$ satisfy $a_i = 0$" condition.) Thus, the equality $\prod\limits_{x\in\Lambda}(1-t^{h(x)})\prod\limits_{i<j}(1-t^{\mu_i-\mu_j})=\prod\limits_{i\ge 1}\prod\limits_{j=1}^{\mu_i}(1-t^j)$ yields ... – darij grinberg Feb 27 at 18:45
• ... that the multiset of the exponents of $t$ appearing on the left hand side equals the multiset of the exponents of $t$ appearing on the right hand side. – darij grinberg Feb 27 at 18:46
• Thank you so much! Actually, I was thinking about that, but did some stupid mistake in the calculations... – mikis Feb 27 at 18:53
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# Convert Hamiltonian to Ising Formulation or QUBO
I have a tridiagonal Hamiltonian matrix that I need to convert to QUBO or Ising format to use D-Wave's quantum annealing solvers. For a generic tridiagonal: $$\begin{pmatrix} a_1 & b_1 \\ c_1 & a_2 & b_2 \\ & c_2 & \ddots & \ddots \\ & & \ddots & \ddots & b_{n-1} \\ & & & c_{n-1} & a_n \end{pmatrix}$$
How would I convert this to a either a QUBO or an Ising Formulation? I've seen how to do the reverse here, but it seems trying to invert this procedure is somewhat intractable.
Given that you decompose your matrix into a sum of Pauli operators such that there are no instances of $$X$$ and $$Y$$ (so basically a Pauli sum of $$Z$$, $$I$$ and any tensor product of these two), you can define a PauliSumOp object and then use from_ising to convert it into a QUBO program. The code to do this looks as follows:
from qiskit_optimization.translators import from_ising
from qiskit.opflow.primitive_ops import PauliSumOp
op = PauliSumOp.from_list([("ZZ", 1), ("IZ", 2), ("Z", 3)]) # example operator
qp = from_ising(op)
qubo = conv.convert(qp)
The particular operator from my example outputs the following QUBO program:
\ This file has been generated by DOcplex
\ ENCODING=ISO-8859-1
\Problem name: CPLEX
Minimize
obj: [ - 24 x0^2 + 32 x0*x1 - 16 x1^2 ]/2 + 6
Subject To
Bounds
0 <= x0 <= 1
0 <= x1 <= 1
Binaries
x0 x1
End
• What happens if the decomposition contains an X or Y? The specific hamiltonian I am working with decomposes into a sum that contains II, IX, XX, and YY. Apr 28 at 21:41
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# zbMATH — the first resource for mathematics
## Found 2 Documents (Results 1–2)
100
MathJax
Annals of Mathematics Studies, 120. Princeton, NY: Princeton University Press. xiii, 230 p. $55.00/hbk;$ 19.95/pbk (1989).
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Existence of convergent subsequences for all values in range? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T13:59:03Z http://mathoverflow.net/feeds/question/18275 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18275/existence-of-convergent-subsequences-for-all-values-in-range Existence of convergent subsequences for all values in range? Seamus 2010-03-15T15:06:59Z 2010-03-16T10:46:00Z <p>Consider sequence $s(n) = \sin{nx}$. Are there values of $x$ for which the following holds: For every $y \in [-1,1]$ there is a subsequence of $s(n)$ converging to $y$? (Or perhaps just for the open interval...) Someone hypothesised that the answer is yes, and further that every $x$ that is relatively irrational with $\pi$ has this property.</p> <p>The question I am more interested in is the generalised version of this to arbitrary sequences. What are necessary and sufficient conditions for a sequence having subsequences converging to any point in the set of values the sequence visits? Does it have anything to do with properties like the function $f(n)$ being ergodic or mixing?</p> <p>(suggestions for tags welcome in comments)</p> http://mathoverflow.net/questions/18275/existence-of-convergent-subsequences-for-all-values-in-range/18278#18278 Answer by Gerald Edgar for Existence of convergent subsequences for all values in range? Gerald Edgar 2010-03-15T15:19:18Z 2010-03-15T15:35:08Z <p>More conventional language: Are there values of $x$ such that the sequence $\sin(nx)$ is dense in the interval $[-1,1]$. The answer is yes, almost all $x$ have this property, in particular all $x$ such that $x/\pi$ is irrational. </p> <p>See Weyl's Criterion <a href="http://en.wikipedia.org/wiki/Weyl%27s_criterion" rel="nofollow">http://en.wikipedia.org/wiki/Weyl%27s_criterion</a> for something (equidistributed) that implies much more than merely dense. And $nx$ mod 1 is equidistributed in $[0,1]$ if $x$ is irrational.</p> http://mathoverflow.net/questions/18275/existence-of-convergent-subsequences-for-all-values-in-range/18354#18354 Answer by Liran Shaul for Existence of convergent subsequences for all values in range? Liran Shaul 2010-03-16T10:46:00Z 2010-03-16T10:46:00Z <p>Here is a typical sufficient condition: If for a sequence $a_n$, one has $\lim a_{n+1}-a_n = 0$, then every number between $\lim inf a_n$ and $\lim sup a_n$ is a limit of $a_n$. Thus, if a sequence satisfies this condition, and in addition, $inf a_n = \lim inf a_n$, and $sup a_n = \lim sup a_n$, then every element of $a_n$ is a limit of $a_n$.</p>
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