Neoliberal Beltway Media "Distraught" at Obama's Upcoming Budget Decision

The Beltway media, and their allied Neo-lib ass kissers are all bent out of shape and in a state of distraught disarray.  They are miffed that Obama hasn’t subjugated himself yet again to their Neoliberal Imperative – which is to pull any and every fringe or thread of security out from under citizens. It’s almost as if they’d love to see a Ukraine type mammoth protest play out here in the US of A.

While Obama has abandoned (for now) the absurd plan for a “chained CPI” – to cut back on Social Security benefits (despite the fact S.S. is forbidden by law to contribute to the deficit), the Beltway hacks and blow-drieds aren’t too happy. They wanted to hear it on the tube, and see the oldsters weep as their own Prez screwed them over.

 Well, it’s not to be – as the Left – through a dedicated campaign, forced Obama to take stock and realize he was batting on a losing wicket, see e.g.

http://www.smirkingchimp.com/thread/richard-eskow/54446/yes-the-left-killed-the-chained-cpi

 

Excerpt:

“As for the president and his supporters, it is clear that the chained CPI is well-liked by both the White House's key economic players -- and by many of the commentators who support them. That's unfortunate, because it is inaccurate, unjust, and economically unwise. But like it, they do.

It appears that both the Republicans and the White House like it, but neither wants such a politically unpopular measure hung around their neck -- especially in an election year.”

Despite that, the Neoliberal jackasses and professional deficit scolds (which class includes much of the supposedly objective American political press) are dismayed. They are practically weeping that they can no longer yap their blow- dried thick heads off about cuts to Social Security. Why, they are asking, can’t American politicians simply grow up and cut social insurance programs?  Well, because it’s a third rail you inveterate morons!

Of course, since Watergate and the commercialization of news as well as contamination via PR, the WaPo has long since to function in citizens’ interest so no surprise that Post editorial page editor Fred Hiatt excoriated Obama’s decision to abandon a politically untenable Social Security cut. This moron, believe it or not, actually compared that decision,  to Syria, scribbling:

 

“Did the president really once believe that the United States could no longer kick the can down the road on entitlement reform?”

But it just goes to show even low I.Q. people can rise to very influential heights.

Meanwhile, another dilettante, a political scientist named Adolph Reed Jr.,  recently asked in Harper’s Magazine,  that IF Obama is ‘an unexceptional neoliberal Democrat with an exceptional knack for self-presentation, Why do neoliberal Democrats feel disappointed, too?”

I beg pardon, but to me a “Neoliberal Democrat” is an oxymoron. But maybe not, given so many have seemed to have taken the Neoliberal kool aid in the last 30 years. (Which again, is one reason I left the Dem party for the Democratic Socialists) In any case, who gives a rat’s ass how many of these parasites are “disappointed”? I don’t!

But as salon.com’s Alex Pareene suggests:

“Maybe you’re disappointed because every Western government fully adopted your worldview decades ago and the result has been a new Gilded Age that you can’t blame on reckless Big Government New Deal Democrat”

Back to the Neolib hack Hiatt. While referencing  Medicare as  “the primary driver of entitlement spending,”  he ignores the fact that it’s already projected to cost much less in the future than it was before Obamacare, because the latter slashes nearly $500b off its tag. And we won’t even go into how the earlier sequester cuts seriously slashed reimbursement for cancer treatments.

 What planet is this twit living on? Isn’t he aware of any of this? Obviously, he perceives a target of opportunity because Medicare is usually yoked to Social Security, and one mandate of the Neolibs is to use Medicare costs to justify a preexisting desire to cut Social Security.

If Hiatt were really serious about lowering the long-term deficit by the most effective means possible, as opposed to the most regressive, then he’d opt for severe cuts to the Pentagon’s bloated budget. Say like scrapping the F-35 of which 2,400 are planned with a cost (currently) of $125m each.  Oh, and also pushing for total pullout from Afghanistan and – a final end of the Bush tax cuts for ALL. Those steps would solve all budget problems instantly – but the Neolibs would rather take the end run way because they’re hot to cut “entitlements”.

Joining Hiatt in disappointment is National Journal leadership correspondent Ron Fournier, who purports to explain that both parties refuse to admit (though both secretly know) that the debt will spiral out of control in the long-term future (like, 2038) unless we get a Grand Bargain.  Horse shit! The only ones who profess to know that are the Neoliberal parasites and vermin! (Like the ‘Fix the Debt’ bunch and Peter G. Peterson)

If Beltway centrists – who really believe they’re so much wiser than those “base” Democrats (who think Social Security should be more generous) had a frickin clue they’d pull their heads from their asses and note the  polls that consistently show overwhelming bipartisan majorities in favor of maintaining or expanding Social Security benefits.

But the morons likely think they’re all skewed.

Then there’s MSNBC’s  resident Neolib hack, Chuck Todd, who had a brief requiem for the seemingly dead grand bargain in yesterday morning’s “First Take.” In just one brief paragraph, this dope managed to hit just about every single trope common to Beltway centrist deficit scolds, from treating an unpopular and unnecessary plan to cut social insurance programs as “a universally acknowledged urgent necessity” instead of a highly ideological goal, to bemoaning the fact that politicians who support unpopular things are campaigned against for supporting unpopular things.

Do the Neolib media hacks really want to know why achieving entitlement reform — even on an incremental, bipartisan basis — is so difficult in American politics? Because it is deeply unpopular with actual voters who recognize it as a shitty deal for everyone but the rich.   If the Neoliberal media wasn't so uniformly blinded to that reality, and so ignorant that the majority of Americans want and demand the same security as the wealthy, they'd be more objective. Alas, they aren't - so they can't be.

In the meantime, the progressive Left will relax for the time being, but be wary of any further efforts to sacrifice citizens to the Neoliberal Gargoyle of Greed.

 

Ukrainians Better Be Careful What They Wish For

"Necessitous men cannot be free men",  

-----  Franklin D Roosevelt,

"At the heart of neoliberal narratives are ideologies, modes of governance, and policies that embrace a pathological individualism, a distorted notion of freedom, and a willingness both to employ state violence to suppress dissent and abandon those suffering from a collection of social problems ranging from dire poverty and joblessness to homelessness" - Henry Giroux, 'The Politics of Cruelty - America's Descent Into Madness' (smirkingchimp.com)

With the news that former Ukraine President Viktor F. Yanukovych has abruptly left his opulent mansion behind, Ukrainians are elated now at the prospect of "freedom" and stronger ties with the European Union.  There is now a vacuum left by Yanukovych's departure and that means varied interests will contend for ultimate control.

But that's not the biggest concern. The biggest worry, according to a Sunday New York Times piece (p. 14, 'With President's Departure Ukraine Moves Toward a Murky Future') is "who will help fill the depleted coffers of a country on the brink of bankruptcy and crippled by arguably one of the most troubled economies in the world".

Well, Russia had stepped up, offering $15b in cash infusion as well as cheap natural gas (ibid.). But the Ukrainians, who glance at the European Union and behold all its  material offerings and apparent freedoms, want more, They want to be part of the EU and on their own terms.

They are dreaming.

No one in Europe or the EU wants the "red headed" poor stepchild. A point also made clear in the article. 

Ukraine’s democracy fighters ought to be very careful before they jump head first into the Western Neoliberal orbit. As the Times noted, quoting Mark Leonard, the Director of the European Council on Foreign Relations :

 

"Nobody (in the West) wants to end up owning all the problems that Ukraine faces. The country is bankrupt. It has a terrible, broken system of government and insane levels of corruption”

The article goes on to say that with this in mind, Europe and the U.S. have “largely contracted the job out to the IMF with a package that – unlike the money offered by Moscow – has numerous strings attached”

The piece mentions requirements to cut up all kinds of regulations, and cut subsidies that keep domestic energy prices low – oh and “cripple the government’s finances”.  If it’s anything like what Barbados is experiencing, it ain’t gonna to be sweet bread. We’re talking about sky high food and oil prices, as well as pensions privatized or cut and thousands of workers let go. Y’all really want that? Go for it then! And good luck, future necessitous men...and women... of the Ukraine.

Hey, Ukraine! Welcome to the Neoliberal Imperative!

In other words, the path to the future of the Ukraine, if they choose the Neoliberal imperative, is not only murky  - but likely impoverished for most of their people. If they need some fact checks on what they're in for they can Google "Greek Sovereign Debt crisis"  or examine what happened to Mother Russia after Neoliberalism crept in and replaced communism.

Author Naomi Klein gives the key information in her book 'The Shock Doctrine: The Rise of Disaster Capitalism' (2007).   In  her chapter on the Russian capitalist "experiment" (pp. 282-87) she documents how a cabal of gangster capitalists under the IMF and the "Chicago gang of Milton Friedman" attempted to brutally re-make the existing Russian centrally planned economy into a Neoliberal free market outpost of  the West. The process was long and painful, entailing first getting rid of Mikhail Gorbachev - who through his glasnost and perestroika did far more than Reagan to render the world more peaceful, never mind the propaganda.

Klein makes no bones about the fact that the Friedman "school of economics" - tracing its lineage to Friedrich von Hayek (the same creep that was responsible for bringing about the economic collapse of  the Weimar Republic - opening it to Nazi takeover) was responsible largely for the ideological ruthlessness that laid waste to Russia in the early 1990s.  They only needed (Boris) Yeltsin to help dissolve the former Soviet Union.

Economist Joseph Stiglitz (p. 283) called Russia's pro-capitalist market experimenters "market Bolsheviks". As Klein put it (ibid.):

"However, where the original Bolsheviks fully intended to build their centrally planned state in the ashes of the old, the market Bolsheviks believed in a kind of magic: if the optimal conditions for profit were created - the country would rebuild itself- no planning required."

U.S. Neoliberal puppet Boris Yeltsin, meanwhile, made reckless promises that things would only be hard "for six months"  and "very soon" Russia would be an economic titan. Never happened! As Klein notes (ibid.):

"The logic of so-called creative destruction resulted in scarce creation and spiraling destruction"

Newspapers, magazines from the period (which I still have and can peruse anytime) depict horrific suffering by ordinary Russians as they had to beg, borrow or steal to survive - thanks to the Neoliberal market barbarians. Is this being an "American traitor" to reveal this, probably something most Americans don't know? Nope, because one can't be a traitor to an economic paradigm he never accepted in the first place! (And which he further condemns as itself being a betrayal to the aspirations of most people in the world.)

The sad facts?  After only a year of Neoliberal thuggery and "market therapy" millions of Russians had lost their life savings when the ruble lost nearly all its value (similar to what happened to Germans and their Deutsch mark, thanks to von Hayek). Adding insult to injury, abrupt cuts in government subsidies meant that millions of workers had not been paid in months. Consumption? The average Russian consumed 40 percent less in 1992 than 1991 - and they weren't even consuming that much in '91!

Basically, to survive, the Russian middle class was forced to sell all or most of their belongings - setting up card tables on the streets to do so. As Klein describes this travesty:

"Desperate acts, that the Chicago School of Economics praised as 'entrepreneurial' and proof that a capitalist renaissance was indeed under way."

Wonder why the Russians of today are deeply skeptical and affronted by the Neoliberal rogues and puppets of the West?   Look no further than recent Russian history and how the uber - capitalists twisted and perverted the country's whole economic foundation in order to force it into a globalized capital new world order.

If the Ukrainians are prepared to jump to the EU side and the promised "freedom" they have so yearned for, they  better look at it too!

AZ Senate Bill 1062 Is Endorsement of Hate - Not "Religous Liberty"!

As the kerfuffle continues over Arizona State Senate Bill 1062, the bill that would enable and allow businesses in the state not to serve gays, it becomes crystal clear there is NO "religious liberty" involved here. Rather, it is an endorsement of hate using the egregious cover of religious liberty. Defenders- invoking their Bibles of course, insist the law is "designed to protect religious freedom, especially for wedding photographers and bakeries."

Cathi Herrod, who helped craft the bill and heads the 'Center for Arizona Policy', blabbed on CBS Early Show this morning:

"What's at risk here is religious liberties. Whether or not our first amendment right to freely exercise our religious belief will continue to mean something in this country or whether we are now in a country that frankly is hostile to individual religious beliefs."

Which, of course, is semantic codswallop. It also sounds almost exactly like the excuse trotted out to deny women contraception under the Affordable Care Act. Remember that?  To refresh memories, it was when FOCUS - a Catholic University group - hired on the “Alliance Defending Freedom” - whose mouthpiece then yapped:

“Faith-based organizations should be free to live and operate according to the faith they teach and espouse. If the government can fine Christian ministries out of existence for keeping their faith there is no limit to what freedom they can take away.”

Of course, this was absolute nonsense. There was no attempt whatsoever to “fine Christian ministries out of existence” – only to have them adhere to the standards of all other employers in the public sphere. If then the Catholic Church operates as an employer in the public sphere – never mind it’s a religious institution – then it’s bound to adhere to public standards pertaining to the Affordable Care Act, which all other public employers at other institutions, corporations are also bound to accept.

In the case of the justified protests against AZ 1062, these are in recognition of the fact that businesses operating under state codes and laws cannot cherry pick which customers they will serve and which they won't.

National corporations are urging Jan Brewer - the AZ Governor - to do the right thing and veto this offal. Even Mitt Romney has chimed in and asked Brewer to use her veto. Even one time supporter Steve Pierce said that "we now need to kill it". He offered that the "perception now trumps reality" but the reality is if this hate law is passed (and it's being considered in other states too, e.g. Georgia) this country will be on its way to a similar outcome as the backward African countries (like Uganda ) that have passed laws to put gays away in prison for 14 years or more - as well as any family that protects them. Most African observers - including former Peace Corps volunteers who served there - believe this pot was stirred up by hateful evangelicals who preached this "was the right thing to do".

No, it's never "right" no matter who is the subject of the law. If the law, any law, is based on Biblical bunkum or bollocks then it's no law at all.  It's an exercise in religious hatred masquerading as justice, or a first amendment "right".

Brewer needs to do the right thing here, and if she doesn't pressure will be put on the NFL to move the Super Bowl from Arizona next year.

Proposal to Cut Military Is Rational - But Will Repuke Congress Cooperate?

The proposal to cut the bloated military by Defense Secretary Chuck Hagel is both rational and honorable. In the current parlous economic climate we simply cannot afford to maintain 4,700 bases worldwide nor use the military as a default "jobs program".  The last is especially egregious as it deflects national resources and effort from creating actual jobs with benefits in the private sector.

Hagel's proposal is said to "reflect the nation's  transition from 13 years of war" (Denver Post, today, p. 18A) but it actually reflects a needed transition from 13 years of unnecessary occupations - which have arguably only inflamed the Middle East further. Iraq was certainly unnecessary, there never was any al Qaeda, and Afghanistan long since turned into a nation building endeavor which the Afghans themselves don't even want as Karzai's recent responses to continued U.S. occupation (through 2024) disclose. (I.e. refusing to sign an agreement for extension and freeing dozens of Taliban from Afghan prisons.)

Our national resources can be much better spent, therefore, with a  trimmed down fighting force - as opposed to a bloated, surplus one -  which poor leaders will otherwise be tempted to interject in unwise military adventures.  Hagel's proposals include:

- Shrinking the active duty Army from 520,000 to between 440,000 and 450,000. This compares with the post World War II low of 480,000 but bear in mind that in that era there wasn't the access to high technology that might compensate for manpower.

- The Army National Guard would drop to 335,000 from 355,000 by 2017.  The Army Reserves would also drop by 10,000 to 195,000

- The Marine Corps would shrink from 190,000 to 182,000

- Changes in military compensation, including: smaller pay raises, a slow down in the growth of tax free housing allowances, and a requirement that retirees and some families of active duty service members pay a little more in health insurance deductibles.

As Hagel said:

"This is the time for reality and the time for explosive growth in military budgets is over."

Indeed, that growth has negatively impacted all aspects of our society - from forcing even more cuts in food stamps on those who already go to bed hungry each night, to cutting unemployment benefits to increase the suffering of families nationwide.

Yet pro-military whores like Doug Lamborn want the burden to continue to fall on the already sacrificed and indigent. In response to Hagel's proposals, Lamborn retorted (ibid.):

"Our national security should not be a budgetary punching bag! Instead the rest of the federal government needs to take some cuts!"

Is this imbecile serious? The national security a "punching bag"? In fact, the national security state has gorged itself at the expense of nearly every other domestic sector. Included in the latter we've already beheld successive cuts in food stamps to the poorest citizens, ending with the latest round amounting to an added $9b in cuts via the Farm Bill just passed. That means 15.9 million kids going to bed hungry each night by one estimate in Mother Jones magazine.. Then add to that the December elimination of long term unemployment benefits and you have even  more suffering.

And this inveterate fool wants the "rest of the federal government" to take MORE cuts! So wait, let's triple the food stamps cuts so that even toddlers will be starving at night, along with parents and older siblings.

But why be surprised? Lamborn is an unrepentant, unapologetic whore, after all. According to  The Denver Post  article('Defense Cuts Put Lamborn in Tough Fight', Nov. 11, 2013, p. 5A):

"Lamborn receives his heftiest campaign contributions from military contractors. Just in this election cycle, Lockheed Martin and Northrop Grumman- both with offices in Colorado Springs - gave him a combined $10,000, according to the Center for Responsive Politics. He has also received contributions from Honeywell International and Boeing."

Can you spell W-H-O-R-E? No, it doesn't have to be anyone who jumps into bed for pay! It also includes congress critters who jump into bed with their military interests for campaign dough!

In the same article, Lamborn made no bones about  wanting to "go full tilt come January"  when further defense cuts are on the block,  and according to the Post, "intends to find other places to chop, including entitlements like food stamps and Medicare, to shield the military."


In other words, cut from the least vulnerable citizens as opposed to Dougie's beloved warhawks for whom he's clearly ready to do almost anything imaginable.  (Lamborn's also been fighting for a "combat air brigade" for Colorado Springs, equipped with 122 Apache Longbow choppers - amounting to yet another military-industrial pork barrel waste, even as many citizens in this burg remain underfed, homeless and unemployed.)

The time to act is NOW, and Chuck Hagel's solution provides a blueprint. It is time to pare the overly fat Military down to a size that comports with the austerity situation all other citizens must endure.  Not to do so is to invite economic and domestic catastrophe.

But don't look for the military porkers and grafters in the Repuke House to cooperate! They're quite prepared to let the bogus military "jobs' program continue in return for the kickbacks received from their paymasters.

The Case for the "Ugly Selfie" And Why Meryl Davis Probably Shouldn't Do Selfies

A new indie film that emerged at the Sundance Film Festival last month was entitled "Selfie". It featured 18 teenaged girls who were asked to capture (during a 1-day workshop) the physical imperfections they'd normally try to hide - say if they were taking a selfie to send off to a friend. The images included accentuation of their double chins, freckles, upper arms, and pimples. Cynthia Wade, the film maker, said the point was to start a conversation about cultural beauty standards. and self-esteem.

According to Ms. Wade, quoted in The NY Times (Feb 23, p. 12-ST):

"We spend so much time trying to hide our flaws because the culture has set it up that you have to be ashamed if you're not perfect. I think girls are tired of it. They're suddenly much more willing to embrace the ugly or ironic."

In this context, it is natural for cute or pretty girls to rebel from the image dictators and strike back, often with the deliberately ugly selfie in which the face is contorted, teeth bared, mouth twisted. The effort is to dispel the "pretty girl" image.  This is fully merited given the media is focused on dictating pose and appearance for any one who's already pretty. According to Nancy Etcoff, a cognitive psychologist quoted in the piece:

"Modern day beauty images have maintained a particularly rigid definition: ladylike, small, modest unthreatening and virtually emotionless."

The piece goes on to reinforce this perception, observing:

"It takes little more than a scan of any red carpet to see that idea in action: a sea of toothless smiles, frozen foreheads and hunched shoulders, the uniform that every young woman has learned to mimic. And while this generation may be more tech savvy than any other, that beauty ideal can still be crippling."

Let's be clear this  "beauty ideal" can also be exclusionary, merciless and rife with bigotry.  Who can forget the stunning outcry last year after Nina Davuruli   was named Miss America?   Her victory was met with outcry from racist troglodytes via social media backlash.  Why the rampant hostility? Because Nina didn't meet the unspoken beauty standard. She wasn't white enough, too "foreign -looking", according to her Twiteratti critics.

This is why any girl who seeks to break out of the hobbling beauty standard deserves to be applauded.  Thus, as one quoted expert put it, "One of the things ugly selfies do for girls is to strip the conventional approaches to prettiness."

But what if a white woman, or girl, finds herself with an appearance at the cusp of the standard cultural beauty idiom?   By this I mean that her appearance emerges as ambiguous and can't be immediately defined as "beautiful", say as it might for a Marilyn Monroe, Kate Upton or Pamela Anderson.  Such appears to be the case for Olympic figure skating star Meryl Davis - whose face has been variously described as "non-human" or resembling  a 'N'avi alien" (from Avatar), a Disney cartoon character, and a "Grey alien".   Some of those comments can be seen here:

http://www.topix.com/forum/olympics/winter/T2LA22HVRIU6JP5FS

Also:
http://answers.yahoo.com/question/index?qid=20100222064159AA28fT7

Scarcely able to accept this, I played back some of the figure skating scenes on the DVR, and especially the close ups of Meryl afterward.  It immediately became clear that her facial features diverged from those normally deemed "acceptable" according to the beautyist promoters. Her eyes were very wide apart, for one thing, and her face extremely flat. In some ways, but perhaps only because I'd read some of the comments on Topix.com, she did appear to be like a Disney cartoon character come to life.

What was the problem? Not just in my perceptions, but those of others'. It was that our evolutionary formed vision (and brain)  detected divergences from a symmetry typically associated with both normality and "beauty".  See: http://en.wikipedia.org/wiki/Facial_symmetry  

Excerpt: "Evolutionary theorists in biology and psychology argue that more symmetric faces are preferred because symmetry is a possible honest sign of superior genetic quality and developmental stability"

Was she "ugly" as some of the commenters claimed? No, but she didn't meet the acceptable symmetry standards biological science associates with how most humans perceive beauty either.  Indeed, on examining her images - paused on the DVR- it occurred that making a selfie might not be a good idea, unless sent to personal friends. If done beyond that circle, she would risk creating a "Poe" of a Selfie. In that instant, I appreciated and realized the extent to which I also had become ensnared in the cultural-media  prejudices of what constitutes female beauty. I had also fallen victim to my evolutionary visual prejudices, i.e. in subjectively preferring a more symmetric female face.  I ought to have been able to see Meryl's beauty as singular and unique to her, as opposed to supposing she risked creating a "Poe" of any selfie! 

As we know, the "Poe" emerged from "Poe's law" originally formulated by Nathan Poe in 2005. Poe's take was that in any confrontation with a creationist - or reading his material- one had to be wary because in the absence of a 'smiley' it would be utterly impossible to distinguish a parody of the creationist (or fundie) from the real statement or real person.

Since then, the usage of the term "Poe" has come to be synonymous with almost any parody on the internet. Indeed, it could be extrapolated to include a certain subset of selfies.  This would include selfies of all those females, for example, who are at the cusp of cultural beauty standards, like Meryl Davis. For this subset, then, doing a selfie would risk creating a Selfie Poe.  In line with the definition of Poe, it would be impossible to distinguish a parody of such - say a girl  deliberately creating an "ugly" selfie by artifice, from a girl whose appearance comes over as 'strange', or at least unconventional,  doing one naturally and seeing it confused with the former category. 

This is why one might advise Meryl Davis not to do selfies outside her circle. (Apart from the fact if some of those on Topix.com ever got hold of them, they'd have a field day).

What does it say about our culture that an unconventionally attractive woman like Meryl Davis - at the top of her game in the Sochi Olympics - could be regarded as an "alien" or odd, or even having a deformity ("frontonasal dysplasia" cited at Ask.com)?

It means that our culture has become too superficial, too obsessed with appearance and "good" looks. It means that females especially, have been cajoled to submit to a cruel cycle of self-condemnation and magnifying imperfections. The "ugly selfie" then emerges as a kind of playful slice of authenticity in an age and culture where everyone and everything seems airbrushed to perfection. One psychologist actually said the teen girls were "conducting a visual coup d'état" against the perfectionist standards inherent in beauty imperialism.

Let's hope their coup d'état succeeds!

If not, it means we are a long, long way from being ready to meet and greet actual extraterrestrials. And if there are such, their best strategy remains avoiding planet Earth.

Solutions to More Difficult Complex Integrals

1)  Evaluate:   

 

∫_o ^2p   dq / (37  -  12 cos q)  for  ÷ z ÷ < 6

 

Again: cos q  =  [exp(iq) + exp (-iq)]/ 2

 

 

But z =  exp (iq)  so that:  cos q  =   z + z ^-1/ z

 

And dz =  iexp(i q )  dq =   iz dq so that:  dq  = dz/ iz

 

Then:

 

∫_o ^2p   dq / (37  -  12 cos q)  = 


 ò _C   dz/ iz /[ 37 -   12 (z + z ^-1/ z) ]

 

=  ò _C   dz/ iz / [ 37 -   6 (z + z ^-1) ]

 

=    ò _C   dz / 37 -   6 (z + z ^-1/ z)  iz =  


1/i ò _C   dz / 37z -   6 z² – 6

 

Solve the quadratic (in denominator) to obtain the poles:

 

-        6 z²  + 37z  - 6 = 0

 

Factors to yield: (-6z + 1)(z – 6) = 0

 

Therefore: z = 1/6 and z = 6

 

Both poles are simple and also acceptable for the condition. Since both poles are simple we can use:

 

Res [f(z)] _{z ®  z o}    =    [p(z)/ q’(z)] _{z ®  z o}

For which p(z) = 1 and q’(z) = -12z + 37

 

Res [f(z)] _z ®  1/6    =     [1 / -12 (1/6) + 37]

 

=  1/ (-2 + 37) = 1/35

And:

 

  ò _C   f(z)   dz = 1/i [2 pi  c _{- 1}  ]   =   2 p/ 35

 

\   ∫_o ^2p   dq / (37  -  12 cos q)   =  2 p/ 35

 

For z = 6:

 

Res [f(z)] _{z =  6}     =    [1 / -12 (6) + 37] = 

 

1/ (-72 + 37) = -  1/35

 

So that:

 

  ò _C   f(z)   dz =  -1/i [2 pi  c _{- 1}  ]   =   - 2 p/ 35

 

2)  Evaluate:

 

∫_o ^2p   dq / (13 -   5 sin q)     for  ÷ z ÷ < i

 

Here:   sin  q  =  [exp(iq) -  exp (-iq)]/ 2i

 

But z =  exp (iq)  so that:  sin  q  =    1/ 2i  (z + z ^-1) 

 

And dz =  iexp(i q )  dq =   iz dq so that:  dq  = dz/ iz

Rewrite the integral in terms of complex variable z:

 

∫_o ^2p   dq / (13 -   5 sin q)     = 


ò _C   dz/ iz / [ 13 -   5/ 2i (z + z ^-1) ]

 

=  ò _C   dz /  [13 -   5/ 2i (z + 1/ z) iz]

=  ò _C   2 dz /  (-   5 z²  +   26i z +  5)

 

Solve for the complex quadratic in denominator to get:

 

(5z – i) (-z + 5i) = 0

 

There is only one relevant pole here, which is z = i/5.     The other doesn’t meet the condition ÷ z ÷ < i

 

Res [f(z)] _{z ®  z o}    =    [p(z)/ q’(z)] _{z =  i /5}

 

=  [2/  (-10z  + 26i)]

 

 =     2/ (-10 (i/5) + 26i) = 2/  (-2i + 26i) = 2/ 24i  = 1/12i

 

Then:

  ò _C   f(z)   dz =    [2 pi  c _{- 1}  ]   =    2 pi  ( 1/12i) 


=   2 p/ 12 =  p/ 6 

 

Therefore:

 

∫_o ^2p   dq / (13 -   5 sin q)      =  p/ 6