What's a matter? No sense of humor? You didn't enjoy watching Venezuelan President Hugo Chávez addressing the U.N. General Assembly and saying of President Bush: "The devil came here yesterday, right here. It smells of sulfur still today." Many U.N. delegates roared with laughter.
Oh well then, you must have enjoyed watching Iran's President Mahmoud Ahmadinejad breezing through New York City, lecturing everyone from the U.N. to the Council on Foreign Relations on the evils of American power and how the Holocaust was just a myth.
C'mon then, you had to at least have gotten a chuckle out of China's U.N. ambassador, Wang Guangya, trying to block a U.N. resolution calling for the deployment of peacekeeping troops to Sudan to halt the genocide in Darfur. I'm sure it had nothing to do with the fact that the China National Petroleum Corporation owns 40 percent of the Sudan consortium that pumps over 300,000 barrels of oil a day from Sudanese wells.
No? You're not having fun? Well, you'd better start seeing the humor in all this, because what all these stories have in common is today's most infectious geopolitical disease: petro-authoritarianism.
Yes, we thought that the fall of the Berlin Wall was going to unleash an unstoppable wave of free markets and free people, and it did for about a decade, when oil prices were low. But as oil has moved to $60 to $70 a barrel, it has fostered a counterwave — a wave of authoritarian leaders who are not only able to ensconce themselves in power because of huge oil profits but also to use their oil wealth to poison the global system — to get it to look the other way at genocide, or ignore an Iranian leader who says from one side of his mouth that the Holocaust is a myth and from the other that Iran would never dream of developing nuclear weapons, or to indulge a buffoon like Chávez, who uses Venezuela's oil riches to try to sway democratic elections in Latin America and promote an economic populism that will eventually lead his country into a ditch.
For a lot of reasons — some cyclical, some technical and some having to do with the emergence of alternative fuels and conservation — the price of crude oil has fallen lately to around $60 a barrel. Yes, in the long run, we want the global price of oil to go down. But we don't want the price of gasoline to go down in America just when $3 a gallon has started to stimulate large investments in alternative energies. That is exactly what OPEC wants — let the price fall for a while, kill the alternatives, and then bring it up again.
For now, we still need to make sure, either with a gasoline tax or a tariff on imported oil, that we keep the price at the pump at $3 or more — to stimulate various alternative energy programs, more conservation and a structural shift by car buyers and makers to more fuel-efficient vehicles.
"If Bush were the leader he claims to be, he would impose an import fee right now to keep gasoline prices high, and reduce the tax rate on Social Security for low-income workers, so they would get an offsetting increase in income," argued Philip Verleger Jr., the veteran energy economist.
That is how we can permanently break our oil addiction, and OPEC, and free ourselves from having to listen to these petro-authoritarians, who are all so smug — not because they are educating their people or building competitive modern economies, but because they happen to sit on oil.
According to Bloomberg.com, in 2005 Iran earned $44.6 billion from crude oil exports, its main source of income. In the same year, the mullahs spent $25 billion on subsidies to buy off the population. Bring the price of oil down to $30 and guess what happens: All of Iran's income goes to subsidies. That would put a terrible strain on Ahmadinejad, who would have to reach out to the world for investment. Trust me, at $30 a barrel, the Holocaust isn't a myth anymore.
But right now, Chávez, Ahmadinejad and all their petrolist pals think we are weak and will never bite the bullet. They have our number. They know that Mr. Bush is a phony — that he always presents himself as this guy ready to make the "tough" calls, but in reality he has not asked his party, the Congress, the people, or U.S. industry to do one single hard thing to reduce our dependence on foreign oil.
Mr. Bush prattles on about spreading democracy and freedom, but history will actually remember the Bush years as the moment when petro-authoritarianism — not freedom and democracy — spread like a wildfire and he did nothing serious to stop it.


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Q: Shifted alternating harmonic series Suppose I have the following series
$$ \sum_{k=1}^{\infty}(-1)^{k+1}\frac{1}{k+ia}, \hspace{1cm}$$
with $i$ the imaginary unit and $a \in \mathbb{R}$. Does this shifted sum converge?

A: $\frac{1}{k+ia}=\frac{k-ia}{k^2+a^2}$ $(k \in \mathbb{N})$ and $k \mapsto \frac{k}{k^2+a^2}$ is eventually decreasing to $0$. Thus
$$
\sum_{k=1}^\infty (-1)^{k+1} \frac{k}{k^2+a^2}
$$
is convergent by Leibniz and
$$
\sum_{k=1}^\infty (-1)^{k+1} \frac{a}{k^2+a^2}
$$
is absolute convergent (quite clear). Thus $\sum_{k=1}^\infty (-1)^{k+1} \frac{1}{k+ia}$ is convergent and
$$
\sum_{k=1}^\infty (-1)^{k+1} \frac{1}{k+ia} = \sum_{k=1}^\infty (-1)^{k+1} \frac{k}{k^2+a^2} - i\sum_{k=1}^\infty (-1)^{k+1} \frac{a}{k^2+a^2}.
$$

A: Let $a_k=(-1)^{k+1}$ and $b_k = \displaystyle{\frac{1}{k+ia}}$. Let $A_n = \sum_{k=1}^n a_k$. We do a summation by parts :
\begin{align*}
\sum_{k=1}^n (-1)^{k+1}\frac{1}{k+ia}& = \sum_{k=1}^n a_kb_k \\
&= a_1b_1 + \sum_{k=2}^n (A_k-A_{k-1})b_k\\
&=a_1b_1+\sum_{k=2}^n A_kb_k - \sum_{k=1}^{n-1} A_kb_{k+1}\\
&=a_1b_1 + A_nb_n + \sum_{k=2}^{n-1} A_k(b_k-b_{k+1})
\end{align*}
Now let's notice that
$\bullet\ $ $(A_nb_n)_{n \geq 1}$ tends to $0$ because $(A_n)_{n \geq 1}$ is bounded and $(b_n)_{n \geq 1}$ tends to $0$.\
$\bullet\ $ One has
$$ \left|A_k(b_k-b_{k+1})\right| \leq 2\left| \frac{1}{k+ia} - \frac{1}{k+1+ia}\right| \leq 2 \left| \frac{1}{(k+ia)(k+1+ia)}\right| = o \left( \frac{1}{k^{3/2}}\right)$$
Hence the series $\sum A_k(b_k-b_{k+1})$ is absolutely convergent, hence convergent, and you are done.

A: It seems that you have at least two solutions.
The first one is to expand the complex number to write
$$\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k+ia}=-\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k^2+a^2}+i a\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k^2+a^2} k$$ The first sum is given in terms of the digamma function
$$-\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k^2+a^2}=\frac{1}{4} \left(\psi \left(-\frac{i
   a}{2}\right)+\psi\left(\frac{i a}{2}\right)-\psi \left(\frac{1-ia}{2}\right)-\psi
   \left(\frac{1+i a}{2}\right)\right)$$ and, for the second one
$$\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k^2+a^2} k=\frac{\pi  a\,\text{csch}(\pi  a)-1}{2 a^2}$$
There is more compact result using special functions since
$$\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k+ia}=\Phi (-1,1,1+i a)$$ where appears  the Hurwitz-Lerch transcendent function.
The result exists for any $a \in \mathbb{R}$.

redpajama_set_name: RedPajamaStackExchange


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Q: JBOSS EAP 6.4 Unable to load topology in my Jboss web console, the topology view in Domain tab is empty, I don`t know why. Everything is up and running, I just can't see the domain topology in Jboss console. "Unable to load topology"

A: I just got the "Unable to load topology" error today.
I have separate multinode jboss domain configurations in my env.
one is 6 nodes and one is 3 nodes.  all running 6.4.22.GA
The error came up for me when we were switching ldap user authentication hosts and attempting to do that while leaving the servers up/running as much as possible.
When the domain node was changed to the new ldap server and brought back up we got the topology error.
fix was to bounce jbossas-domain on the other nodes and point to the new ldap server.  After we did that the jboss console was able to display the topology again.
In short my solution was to make sure all the nodes in the jboss domain had the same configuration and then bounce them.