text:
Q: Conformal equivalence of resistance Link to the question in the physics portal.
I'm currently working on a system that uses a logarithmic and a Schwarz-Christoffel transformation to calculate the resistance of a specific area. With resistance I mean the resistance that would apply to that area if it were between two equipotential irregular plates (which are defined by their vertices). In my case it is the magnetic reluctance but it is analogous to electrical resistance.

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I have multiple areas of the canonical domain that have to be translated to a resistance value in the physical domain(with the intermediate step of a logarithm). Is the resistance (defined analogous to electrical resitance) that can be calculated in the homogeneous field of the canonical domain directly related to the resitance in the phyisical domain? The geometry of a resistor in the canonical domain is a simple rectangle formed from four prevertices. In the physical domain it is far more complicated (see figure).
The measure of resistance can be formulated with the help of an "equivalent length". Could it be that this $\Lambda$ is not affected by the conformal tranformations?
\begin{align}
&R=\rho\dfrac{1}{\Lambda}\\
&\text{cylinder gives: } &\Lambda_\text{cyl}=\frac{2\pi \ell}{\log\frac{r_2}{r_1}}\\
&\text{cuboid gives: } &\Lambda_\text{cub}=\dfrac{A}{\ell}
\end{align}
I have done some calculations by discretising the physical domain and comparing it to the resistance generated in the canonical domain. The results were comparable, maybe because of accident, maybe because of a strong mathematical implication, I can't say.
Question in short: Can the prevertices that define a rectangle in the canonical domain define the resistance value of the mapped rectangle in the phyisical domain. (With the intermidate step of a logarithm)
I use the SC-Toolbox for Matlab created by Tobin A. Driscoll.
EDIT: Addition
Lets say that we have a rectangle which has been rotated and translated (Möbius transformations if you want) so that its sides are perpendiculary oriented to the real and imaginary axis, one of its vertices is (0,0) and that it is in the 1st quadrant. We have to calculate its resistance.
Lets say the opposite vertex of (0,0) is $z=x+iy=|z|e^{i\varphi}$, the imaginary part of $z$ represents the length of the path, while the real part represents the projected area(the area is only visible in 3D, we are looking at it in 2D). We write $R'$ because of the 2D representation.
The resistance of this rectangle will therefore be:
\begin{align}
R'=\rho \frac{\mathfrak{Im}(z)}{\mathfrak{Re}(z)}
\end{align}
Which can be written as:
\begin{align}
R'&=\rho \frac{|z|\sin\varphi}{|z|\cos\varphi}=\rho \frac{\sin\varphi}{\cos\varphi}\\
R'&=\rho\tan\varphi
\end{align}
The thing that the resistance is only dependent on the angle $\varphi$ and the definition of conformal transformations as angle preserving, provoked me to ask this question. I found a lot about space being conformally invariant, but in this case it is a function that is discussed.
I'm not sure how to proceed. I can prove that the transformations(maps) are conformal, but I don't know what to do about a function in the canonical space.

A: Given what you wrote and what this wikipedia page says (references can be found there as well), here is, I think, the mathematical interpretation (and answer to) of your question. However, in order to understand it you need to know more math than you do (you need some basic complex analysis, general topology and differential geometry). In short, yes, resistance is conformally invariant.
We consider open connected bounded subsets $\Omega$ of the complex plane ${\mathbb C}$. Fix in the boundary of $\Omega$ in two disjoint subsets $A$ and $B$. I will assume that the sets $A$ and $B$ are closed and connected. The triple $Q=(\Omega, A, B)$ is a condenser. (The physical meaning here is that the domain $\Omega$ is filled with a material that has constant conductivity, which is set to be 1. The unit electric charge is applied along the continuum $B$.)
Example. $\Omega$ is the open rectangle
$$
R_{a,b}=\{(x,y): 0<x<a, 0<y<b\}.
$$
Set
$$
A=\{(0, y): 0\le y\le b\}, B= \{(a, y): 0\le y\le b\}
$$
(the vertical sides of the rectangle).
Define the capacity of a condenser
$$
c(Q)=\inf \{E(u)| \ u:\bar{\Omega}\to {\mathbb R},  u|_A=0, u|_B=1\}
$$
where we assume that functions $u$ are continuously differentiable in $\Omega$ and are continuous on its closure $\bar\Omega$. The quantity $E(u)$ is the energy:
$$
E(u)=\iint_{\Omega} |du|^2 dxdy,
$$
where $du$ is the differential of $u$. It is known that infimizing sequences $u_n$ for $c(Q)$ converge (uniformly on compacts in $\Omega$) to harmonic functions $h$ on $\Omega$ so that
$$
E(h)=c(Q)= \lim_{n\to \infty} E(u_n).
$$
However, the harmonic functions $h$ (in general) do not extend continuously to the closure $\bar\Omega$. Lastly, define the resistence of the condenser as
$$
r(Q)= \frac{1}{c(Q)}.
$$
This quantity is also know as the extremal length of the family of paths $\gamma: (0,1)\to \Omega$, such that $\gamma(t)$ accumulates to $A$ as $t\to 0$ and accumulates to $B$ as $t\to 1$.
Example. Suppose that $\Omega=R_{a,b}$, a rectangle with the sets $A$ $B$ chosen to be its vertical sides as above. Then
$$
r(\Omega, A, B)= \frac{a}{b}.
$$
The extreme function in this case is $h(x,y)=x/a$.
It is now well-known that for a general condenser $Q$, the capacity $c(Q)$ is a conformal invariant of $Q$, in the following sense. Suppose that $f: \bar\Omega\to \bar\Omega'$ is a homeomorphism which restricts to a conformal map $f: \Omega\to \Omega'$; define the new capacitor
$$
Q'=(\Omega', f(A), f(B)).
$$
Then $c(Q)=c(Q')$. The reason for this is the following. One can define energy of functions with respect not only to the Euclidean metric $g_0=dx^2 + dy^2$ but to an arbitrary Riemannian metric $g$ on $\Omega$:
$$
E(u,g)= \iint_{\Omega} |d u|_g^2 dA_g,
$$
where $dA_g$ is the area form of $g$ and $|du|_g$ is the norm of the differential of $u$ with respect to the Riemannian metric $g$. Then for a function $v: \Omega'\to {\mathbb R}$ and $u=v\circ f$,
we clearly have
$$
E(u, g)= E(v),
$$
where $g=f^*(dx^2 + dy^2)$. Since $f$ is conformal in $\Omega$, the metric $g$ is conformal, i.e.
$$
g= \lambda(z) g_0,
$$
where $\lambda$ is a positive continuous function on $\Omega$. Lastly, one observes that
$$
E(u, g)= E(u)
$$
for every function $u$ on $\Omega$, since the
$$
dA_g= \lambda^2 dxdy
$$
while
$$
|du|^2_g= \lambda^{-2} |du|^2.
$$
The two scalar functions $\lambda^2, \lambda^{-2}$ cancel each other and integrals are the same since you are integrating equal forms.
Since capacity is conformally invariant, so is reciprocal $r(Q)$.

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text:
Bad Ass
Directed by: Craig Moss
Category: Badass Cinema
First thing's first. Yes, Bad Ass is indeed very Badass!
So that's out of the way and you can calm your fears and be rest assured that in the end, when it's all over you will have the comfort of knowing that this film kicks ass for 2 reasons, writer/director Craig Moss's self assured and even handed direction and Danny Trejo just simply owning this fucking movie. Danny Trejo rules. End of discussion.
This was a really fun flick. Danny Trejo delivers the goods. I mean, you just know he will but even I was kinda blown away by how awesome he was in here. I just love that guy! I have to tell you, I am just so happy that Trejo has been given the opportunity to show the world that he can do more than play the scary looking prisoner in the background. Here he shows more range than I've ever seen before, even crying in one sequence. And though he has a reputation for dispersing justice through his fists, he's one helluva nice guy. Very sweet, caring and charming. But you get in his face, or try holding up a liquor store or start rough housing your wife, you're gonna be sorry. He still comes out in an insane amount of DTV flicks as a supporting character, but at least we get gems like this and the Machete films from time to time.
In Bad Ass, Trejo plays a war vet who's down on his luck, barely able to make ends meet and who just wants to be left alone. When two skinheads start bothering an elderly man on the bus, he steps in and literally wipes the floor with them. Filmed by someone's cellphone camera he becomes an instant internet sensation and folk hero. Soon, trouble and trouble makers seem to follow him wherever he goes and his life will never be the same.
Sooooooo I don't feel like I can be completely honest if I didn't mention the one thing that bothered me about this movie. So the movie's rolling along nicely. It's made very well, has a lot of fights, a lot of heart and a lot of laughs. Bad Ass aka Frank Vega (Danny Trejo) finds the guy who's responsible for ordering the hit on his life long friend Klondike and next thing you know, they're on a full on bus chase knocking cars out of the road at the end of the film, destroying a water fountain in the process and crashing through a building when I realize I'm seeing a shot for shot sequence from the bus chase at the end of Walter Hill's excellent Red Heat.
Is it a ripoff? A homage? I don't know, but I go with it. It's ridiculous and feels completely out of place, but you know, it's a fun movie and this is a fun sequence. But being the die hard fan of Red Heat that I am it was bothering me. It looked almost exactly the same except for some intersplicing of Trejo and the bad guy pretending to drive a bus against a green screen and with a few digital effects thrown in for good measure. Then the sequence is over after the game of chicken they are playing and the bad guy's bus crashes into an oncoming train and yea, again shot for shot, even the way Trejo breaks out of his bus after he crashes it. Just like in Red Heat. But anyway, we move onto another location and another fight scene and the film wraps up nicely. But I can't get that whole bus chase sequence out of my head and so I do a little digging and find out that the director "did" use that sequence from Red Heat, only slightly altering it digitally and adding Trejo and the bad guy. Ok, so I have no idea why they took a whole complete sequence out of one of one of the best action movies to come out of the 80's and decided to put it in a small scale film 24 years later, but I digress. I don't know why it bothers me so much, but it does.
This is supposedly based on a true story, but from what I understand they changed a lot of the details. But whatever, it's fun. And I'll be honest, I wasn't really sure about this one. I love Danny Trejo, but I'd never heard of writer/director Craig Moss and you know how that goes. Sometimes these new young filmmakers just deliver shit. But I must say I was pleasantly surprised. Bad Ass retains a nice professional look and quality throughout and throw in an nice eclectic supporting cast that includes Charles S. Dutton and Ron Pearlman and you have one Bad Ass film.
Jack Thursby September 13, 2012 at 2:31 AM
Yeah, I've heard of films doing this before. I can't remember which one it was but one b-movie took a bunch of car chase shots from Last Action Hero and tried to splice them in.
I guess they paid for the shots but yeah it really takes you out of a movie when they do that. I guess they were struggling to get decent 2nd Unit footage.
This sounds pretty cool - Trejo's really building up a great DTV career. Will check it out when I get a chance.
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text:
Private sector may operate railway lines, says Egypt Transport Minister
Egypt's Transport Minister Hisham Arafat said that the cabinet endorsed during its meeting on Wednesday amendments to Law 152 of 1980 on Egypt's National Railway Authority to allow the private sector to operate and maintain railway lines.
In statements to press after the meeting, Arafat said that the government would be more of a regulator giving the right to operate for the private sector, while the government would still monitor and set prices for the service.
Arafat pointed out that giving operation or maintenance rights to the private sector would be through a contract that does not exceed 15 years which will include the right to build new lines.
He explained that this concession will be given to the private sector because the authority can't bear the expenditures of operating all the lines, explaining that it was serving 6 million passengers annually in 1952, and that it now serves 350 million annually.
"There is no privatization of the railways, we will work like the National Telecom Regulatory Authority (NTRA) that determines pricing and monitors, so the railway authority will build and monitor," he said.
Egypt's Transport Ministry signs contract to purchase 100 new locomotives
He added that the demand for transportation has become high and the ministry seeks to create new infrastructure and to create a signaling system in full, all of which needs funding.
Arafat said that after cutting subsidies to fuel, the railways have become a competitor in transporting goods, and that the ministry targets transporting 25 million tons through the railway.
He added that among the amendments to the law on the railway authority is toughening punishments for theft crimes of tools and facilities from the railway.
Tags Egypt Egypt 's Private Sector Egyptian National Railway Authority
€ 255 million loans from EIB to upgrade metro lines: Minster of Transport
Ministry of Transport raises shipping containers over railways
EBRD to finance Egypt's purchase of new locomotives


text:
Resolução 71 do Conselho de Segurança das Nações Unidas, aprovada em 27 de julho de 1949,  solicitado pela Assembleia Geral em que condições Liechtenstein pode se tornar uma parte do Estatuto do Tribunal Internacional de Justiça. O Conselho determinou que Liechtenstein deveria aceitar as cláusulas do Estatuto, aceitar todas as obrigações de um membro das Nações Unidas, nos termos do artigo 94 da Carta, comprometem-se a contribuir para as despesas do Tribunal devendo o governo nacional ratificar o Estatuto, Liechtenstein se tornaria parte no Estatuto do Tribunal Internacional de Justiça.

Foi aprovada com 9 votos, com duas abstenções da Ucrânia e a União Soviética.

Ver também
 Lista de Resoluções de 1 a 100 do Conselho de Segurança das Nações Unidas

Ligações externas
  Texto da Resolução 71 do Conselho de Segurança da ONU. (PDF)

Resoluções do Conselho de Segurança das Nações Unidas de 1949
Resoluções do Conselho de Segurança das Nações Unidas sobre Liechtenstein
Resoluções do Conselho de Segurança das Nações Unidas sobre o Tribunal Internacional de Justiça

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Publisher: London: Printed for Taylor and Hessey, 1820.
Bibliographical References: MacGillivray 3; Hayward 233; NCBEL III, 346.
Condition: One small clean tear in the margin of the final leaf, without touching the text or loss to paper; fine copy, enclosed in a red cloth clamshell box.
12mo, later dark red morocco by Stikeman, gilt decorations, rules, inner dentelles, and lettering, t.e.g. Half-title present, with "London: Printed by Thomas Davison, Whitefrairs" on the verso. Bound without the publisher's terminal advertisements.
The third and last book by John Keats and generally regarded as one of the finest books of poetry in the English language. In addition to the title poems, it includes "Ode to a Nightingale," "Ode on a Grecian Urn," "Ode on Melancholy, "To Autumn," etc.


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text:
Short Plays
Mary Donnet Johnson
Mary's work has been chosen as a semi finalist for the O'Neill National Playwright's Conference. She has had plays featured in the Nashville Sideshow Fringe Festival, the 10-Minute Playground at the Darkhorse Theater in Nashville, the She/Her/Hers evening of short plays presented by Nashville Story Garden, and the Women's Work Festival at the Tennessee Woman's Theater Project. One of her full-length plays was a finalist for the Kentucky Women Writers' Biennial Prize, judged by Pulitzer Prize winner Martyna Majok, and most recently the world premiere of her play "To Know You" was performed at the Clayton Center for the Arts in Maryville, TN.
One acts
Mary grew up in a tiny town in Vermont. She received her B.A. from Sarah Lawrence College, and spent a decade as a professional actor appearing in numerous film, television, stage, radio, and opera productions in New York City and throughout the United States.
Mary (center) with the cast of Divine.
Maryville College Bicentennial
Mary's play "To Know You" played to packed houses on November 1 and 2 at the prestigious Clayton Center for the Arts in Maryville, TN. Thanks to all who participated in this very special project about an octogenarian woman who defied all odds to make a huge difference to Maryville College without ever putting her name on a thing.
New Commission!
Mary will be working on a new play celebrating notable women in Rutherford County's history to be performed August 2020 in Murfreesboro, TN, in conjunction with other Women's Suffrage activities. Stay tuned for details.
She/Her/Hers featured 'Last Rights!"
Mary's newest short play, "Last Rights," played to a standing-room-only crowd at Nashville Story Garden's inaugural She/Her/Hers celebration of women at the Cordelle recently. This dark comedy about two estranged but highly competitive sisters who struggle for their rights in the face of impending death was magnificently acted by Rachel Agee and Nealy Glenn, and beautifully directed by Lauren Berst. See bottom right photo. Photo credit: Drew Maynard.
Here's to a strong 2020 for every one of us who endeavors to enhance life through determined and joyful practice of our art.
Mary grew up in a tiny town in Vermont, received her B.A. from Sarah Lawrence College, and spent a decade as a professional actor appearing in numerous film, television, stage, radio, and opera productions in New York City and throughout the United States.
Maryville Bicentennial
Mary's newest short play, "Last Rights," played to a standing-room-only crowd at Nashville Story Garden's inaugural She/Her/Hers celebration of women at the Cordelle recently. This dark comedy about two estranged but highly competitive sisters who struggle for their rights in the face of impending death was magnificently acted by Rachel Agee and Nealy Glenn, and beautifully directed by Lauren Berst.
(slider photo #3) Photo credit: Drew Maynard.
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text:
Q: Bind 9.7 error with connection timed out; no servers could be reached I'm having issue with one of my nameservers. When I'm using nslookup or dig without +trace, everything works fine. But when I'm using with +trace the error comes

error with connection timed out; no servers could be reached.

This is lead my nameserver not update their records from master.
Below are my chechking:
1.============Iptables Stop==========
[root@dns2 ~]# iptables -L
Chain INPUT (policy ACCEPT)
target     prot opt source               destination

Chain FORWARD (policy ACCEPT)
target     prot opt source               destination

Chain OUTPUT (policy ACCEPT)
target     prot opt source               destination

2. ============Dig without +trace working==========
root@dns2 ~]# dig www.google.com +notrace

; <<>> DiG 9.7.0-P2-RedHat-9.7.0-17.P2.el5_9.1 <<>> www.google.com +notrace
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 17007
;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 4, ADDITIONAL: 0

;; QUESTION SECTION:
;www.google.com.                        IN      A

;; ANSWER SECTION:
www.google.com.         74      IN      A       216.58.199.4

;; AUTHORITY SECTION:
google.com.             172572  IN      NS      ns2.google.com.
google.com.             172572  IN      NS      ns1.google.com.
google.com.             172572  IN      NS      ns4.google.com.
google.com.             172572  IN      NS      ns3.google.com.

;; Query time: 2 msec
;; SERVER: 124.108.4.131#53(124.108.4.131)
;; WHEN: Mon Aug 26 16:08:51 2019
;; MSG SIZE  rcvd: 120

[root@dns2 ~]#

3.=============dig with +trace error=====
[root@dns2 ~]# dig www.google.com +trace

; <<>> DiG 9.7.0-P2-RedHat-9.7.0-17.P2.el5_9.1 <<>> www.google.com +trace
;; global options: +cmd
.                       518076  IN      NS      g.root-servers.net.
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.                       518076  IN      NS      j.root-servers.net.
;; Received 508 bytes from 127.0.0.1#53(127.0.0.1) in 1 ms

;; connection timed out; no servers could be reached

===========================

Your response is being satisfied.