Fractional Calculus: Uncharted frontiers of Calculus.

A short note about fractional calculus, mainly because of a Sri Lankan in the forefront.  That is Udita Katugampola who got his Bachelors from Colombo University in 2002.  He has created the Katugampola fractional operators that are integral operators that generalize the Riemann–Liouville and the Hadamard fractional operators into a unique form. 

Why fractional operators matter. Conventional calculus has its limits when we try to model complex situations. Allows to understand and model the finest details of physical processes with unprecedented precision.  Patient response in anaesthesia is one. Helps solve all manner of problems, from detecting cancer to preventing the spread of pollution to making more efficient batteries.  Recent (2015) developments in Image processing, edge detection, image restoration and fractional differentiation as a tool to reveal faint objects in astronomical images.  
(I can see the potential for Satellite Image processing and wish had this tool when I did Satellite Image processing).

The briefest possible introduction to fractional operators.
(note: Most of it is well beyond my comprehension and pay grade.)

For those who remember their classical calculus, derivatives or integrals are done by integers.  eg d2y/dx2 is the second derivative.  
A fractional derivative would be d(1/2)y/dx(1/2) 

The easiest to understand is the fractional derivatives of exponential functions.

 

 

 

That about the limit of my understanding.  The above and more is explained in A Child's Garden of Fractional Derivatives.  

Some Links

https://www.newscientist.com/article/mg25233603-200-how-an-upgrade-on-calculus-is-taking-maths-into-uncharted-territory

https://www.researchgate.net/publication/239745037_A_Child%27s_Garden_of_Fractional_Derivatives

Fractional differentiation based image processing
https://arxiv.org/abs/0910.2381

Udita Katugampola's website, fractional differentiation links page
https://sites.google.com/site/uditanalin/fraccalc

 

 

 

 

 

Gotabaya Rajapaksa: Education and Experience

 

There are hearsay and innuendo on Gotabhya Rajapaksa's (current Presidents) purportedly lack of education. So decided to check, thats far from the truth.

Gotabaya served as an army officer for 20 years.

Then after retiring from the army, got himself a Post Graduate Diploma in Information technology from University of Colombo. To do this about turn in career and at the age of 43 shows perseverance, discipline and intelligence.

He then had a 6 year stint as Marketing Manager at Informatics Ltd, one of the biggest Information technology companies in Sri Lanka. With that emigrated to the US in 1998 (Y2K computer job boom ?) and was a Unix System Administrator for Loyola Law School, Los Angeles, CA for 7 years.

For those who dont know what a Unix Sys admin entails, needs very logical thinking and discipline, many times more that a regular programmer. The mission critical backbone of the institution is dependent on the Unix servers and its administration. It pays well too USD 120,000/year.

Anyway a synopsis of Gotabaya's career (More detailed info on LinkedIn and Wiki)

Born: 20 June 1949
1971-1991 (age 22-42) Commissioned Officer, SL Army
1992 (age 43) Post Graduate Diploma in Information technology, University of Colombo
1992-1998 (age 43 -49) Marketing Manager, Informatics Ltd
1998-2005 (age 49-56) System Administrator, Loyola Law School, Los Angeles, CA

https://en.wikipedia.org/wiki/Gotabaya_Rajapaksa

https://www.linkedin.com/in/gotabaya-rajapaksa/

Update: Pandemics, Financial Crash and Gold

All these pandemic stuff is not unexpected.  Those who look at downside risk, i.e. tail risk, predicted the 2008 crash*. After that  they commented the structural issues of US economy are still weak and an pandemic will tear apart globalization.
 
So obviously we are seeing the pandemic at play.  I thought it would die down by May Jun (2021) at least for Sri Lanka. Is it going to get worse, who knows?. Two more big picture issues in play both linked.
 
a) A financial crash bigger than 2008 in the US is in play. Is it tomorrow or couple of years down the line, cant say. As they say the market can stay irrational longer than you can say solvent.

b) The price of Gold, still in play to reach 3K/oz.  Has taken a hit because of crypto currencies, and the ability to move it with ease across borders.  The moment there is something like Internet failure, or ability to audit movement goodbye to confidence in crypto currencies.  Very hard to audit gold plastered into your wall. (Remember US made it illegal to own gold and confiscated what was in bank deposit boxes).

Two paragraphs from what I wrote in May 2020

To quote from 2011 article by Matt Stoller: And while this may not be hitting the elite segments of the economy right now, there will be no escape from a flu pandemic or significant food shortage. The re-engineering of our global supply chain needs to happen—and it will happen, either through good leadership or through collapse.

The Virus War: Make no mistake, this is the real war on Terror. The enemy is invisible, insidious and within. Normally wars have some breathing space, bombs fall and then a few days of respite. This war is like water torture a continuous drip drip of sickness and death. Eventually fatigue sets in, and many become immune to the daily numbers of sickness and death. The Stalinist "A single death is a tragedy, a million deaths is a statistic" becomes the reality, with the death of humanity.

*One of the reasons I am out here in jungles, the tail risk was too scary, plus I was getting stressed and burnt out with vacationless US work hours.


Written in May 2020
https://www.linkedin.com/pulse/covid-19-fault-lines-consequences-sereno-barr-kumar/