Second Order Differential Equation and Aural Trajectories

Sniffy

This differential equation

y” + 4y’ + 4y

has repeated roots and one solution might be

y = 2xexp(-2x) + 2exp(-2x)

Just to verify that y'(0) = -2, (see graph)

y'(0) = -4xexp(-2x) + 2(exp(-2x) -4exp(-2x)
= 0 + 2 – 4 = -2

If function y = Y(x), then a family of curves can be generated as kY(x), also see graph. The reason for doing this, is to do a frequency multiplication, in this case, the lower frequency is:

Y(110) = 110 * (2(x)exp(-2(x))) + (2exp(-2*(x)))

Finally we want F = Y(1100) * Y(110)

This is not a frequency; however, we could try this:

sin(F) = sin( Y(1100) * Y(110))

and the second derivative becomes a constant value spectrogram which equals zero at x = -0.5 or y'(-0.5) = 0.

Starting at x = -0.5 the sound file sweeps down creating a penguin sound.

Penguin

; PRAAT FORMULA
; divide numbers by 2pi for radian frequency

sin(1100((2(x)exp(-2(x))) + (2exp(-2(x)))))
… * (sin(110((2(x)exp(-2(x))) + (2exp(-2(x))))))

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paul singer argentina debt

Paul Singer, through his hedge fund

Elliott Management (specifically its unit NML Capital Limited), pursued a protracted legal battle with

Argentina over defaulted sovereign debt, eventually resulting in a $2.4 billion payout to his firm in 2016.

Financial Overview

Paul Singer’s firm bought Argentine sovereign bonds at a deep discount following the country’s $80 billion default in 2001, paying around $117 million for bonds with a face value of $617 million. While over 90% of creditors accepted a restructuring plan at a significant loss (around 25-35 cents on the dollar), Elliott Management and other “holdout” funds refused the deal, suing for full repayment.

Key Insights

Legal Tactics: Singer’s fund won key rulings in U.S. courts, particularly based on the pari passu (equal treatment) clause, which stipulated that Argentina could not pay its restructured debt holders without also paying the holdouts in full.
Asset Seizure Efforts: To force payment, NML Capital attempted aggressive collection tactics, including seizing an Argentine naval ship, the ARA Libertad, in Ghana in 2012, and trying to lay claim to Argentine satellite launch contracts with SpaceX in 2014.
Settlement: After years of legal battles and a subsequent default in 2014, Argentina’s new president, Mauricio Macri, reached a settlement with the holdout creditors in February 2016. The total settlement for the holdouts was $4.65 billion, with Singer’s fund receiving approximately $2.4 billion in compensation, representing a return of roughly 1,600-2,000% on their original investment.
Market Re-entry: Resolving the dispute allowed Argentina to regain access to international credit markets after being locked out for 15 years.