Adonis Diaries

Archive for May 16th, 2018

Math Blog and how to write math equations using LaTeX $latex…$

WordPress.com supports LaTeX, a document markup language for the TeX typesetting system, which is used widely in academia as a way to format mathematical formulas and equations.

LaTeX makes it easier for math and computer science bloggers and other academics in our community to publish their work and write about topics they care about.

If you’re a math blogger and expressing equations you’ve worked on, you’ve probably used LaTeX before. If you’re just starting out (or simply curious to see how it all works), we’ve gathered a few examples of great math and computing blogs on WordPress.com that will inspire you.

In general, to display formulas and equations, you place LaTeX code in between $latex and $, like this:

$latex YOUR LATEX CODE HERE$

So for example, inserting this when you’re creating a post . . .

$latex i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

. . . will display this on your site:

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>

Nifty, huh? Learning LaTeX is like learning a new language, and the bloggers below show just how much you can do. And if you’re not a math whiz, don’t worry! You’re not expected to understand the snippets below, but we hope they show what’s possible.

Gödel’s Lost Letter and P=NP

Suppose Alice gives Bob two boxes labelled respectively {X} and {Y}. Box {X}contains some positive integer {x}, and as you might guess, box {Y} contains some positive integer {y}. Bob cannot open either box to see what integer it holds. Bob can shake the boxes, or hold them up to a bright light, but there is no way he can discover what they contain.

This blog, on P=NP and other questions in the theory of computing, presents the work of Dick Lipton at Georgia Tech and Ken Regan at the University at Buffalo. One of their main goals is to pull back the curtain so readers can understand how research works and who is behind it.

From the recent post “Move the Cheese” to an older piece on “Navigating Cities and Understanding Proofs,” they present problems and sketch solutions, and publish thorough and thoughtful discussions that not only talk about interesting open problems, but offer context and history.

You can see LaTex in action in the example above, from the recent post “Euclid Strikes Back.”

Math ∩ Programming

Note that we will have another method to determine the necessary coefficients later, so we can effectively ignore how these coefficients change. Next, we note the following elementary identities from complex analysis:

\displaystyle \cos(2 \pi k t) = \frac{e^{2 \pi i k t} + e^{-2 \pi i k t}}{2}
\displaystyle \sin(2 \pi k t) = \frac{e^{2 \pi i k t} - e^{-2 \pi i k t}}{2i}

Jeremy Kun, a mathematics PhD student at the University of Illinois in Chicago, explores deeper mathematical ideas and interesting solutions to programming problems. Math ∩ Programming is both a blog and portfolio, and well-organized: you can use the left-side menu to navigate Jeremy’s sections, from Primers to the Proof Gallery. The site is also clean and well-presented — can you believe he uses the Confit theme, which was originally created for restaurant sites?

The snippet above illustrates more you can do with LaTeX, taken from “The Fourier Series — A Primer.”

Terence Tao

Definition 1 (Multiple dense divisibility) Let {y \geq 1}. For each natural number {k \geq 0}, we define a notion of {k}-tuply {y}-dense divisibility recursively as follows:

  • Every natural number {n} is {0}-tuply {y}-densely divisible.
  • If {k \geq 1} and {n} is a natural number, we say that {n} is {k}-tuply {y}-densely divisible if, whenever {i,j \geq 0} are natural numbers with {i+j=k-1}, and {1 \leq R \leq n}, one can find a factorisation {n = qr} with {y^{-1} R \leq r \leq R} such that {q} is {i}-tuply {y}-densely divisible and {r} is {j}-tuply {y}-densely divisible.

We let {{\mathcal D}^{(k)}_y} denote the set of {k}-tuply {y}-densely divisible numbers. We abbreviate “{1}-tuply densely divisible” as “densely divisible”, “{2}-tuply densely divisible” as “doubly densely divisible”, and so forth; we also abbreviate {{\mathcal D}^{(1)}_y}as {{\mathcal D}_y}.

Mathematician, UCLA faculty member, and Fields Medal recipient Terence Tao uses his WordPress.com site to present research updates and lecture notes, discuss open problems, and talk about math-related topics.

He uses the Tarski theme with a modified CSS (to do things such as boxed theorems).

As stated on his About page, he uses Luca Trevisan’s LaTeX to WordPress converter to write his more mathematically intensive posts. Above, you’ll see an example of how he uses LaTeX on his blog, excerpted from the post “An improved Type I estimate.”

Terence also has a blog category for non-technical posts, aimed at a more general audience, and offers helpful advice on mathematical careers.

Using LaTeX

From  “Euclid Strikes Back,” Gödel’s Lost Letter.

You can read a brief primer on using LaTeX on our Support site and search related forum discussions to see if a WordPress.com user has asked your question.

If you’re dipping in for the first time, we encourage you to check out these resources for help and detailed documentation:

We look forward to your posts showing off your math wizardry!

You might also enjoy these posts:

The Syrian Refugees’ Return to their Homeland: Approaches and Prospects

The Konrad-Adenauer-Stiftung (KAS) and the Middle East Institute for Research and Strategic Studies (MEIRSS) published together a policy paper,  titled “The Head Out of the Sand – The Syrian Refugees’ Return to their Homeland: Approaches and Prospects”, authored by Dr. Elie El Hindy, Dr. Charbel Al Alam, Maya Succar, and Laura El Chemaly.

Lebanon is facing the riskiest and most difficult challenge.

The risk in Lebanon is almost existential given the complexities of the Lebanese reality, the failure of the Lebanese state to carry out its simplest duties, the interdependence of the Lebanese and Syrian state of affairs, and the high refugee-to-citizen ratio in Lebanon.

This ratio is the highest recorded in the history of refugee crises in the world. (Probably the ratio of the unregistered Syrian refugees constitute over 40% of the total Lebanese population of 4 million)

It is thus obvious that working on the refugees’ return from Lebanon to Syria as a permanent solution to the crisis is Not a luxury but an imperative need.

This paper is an in-depth study on how to address obstacles preventing Lebanon from developing and adopting the “National Emergency Plan for the Return of Refugees” and how the urgent need for refugees to return can be balanced against the standards required to protect them and preserve their rights.

Note 1: For years, the world community, particularly the EU, claimed that Syrian refugees are Not to return before a political settlement is achieved. Actually, the US, Saudi Kingdom, Israel and Turkey don’t want any political result that would unify Syria. Currently, all the cities and the most inhabited districts in Syria have been liberated from the terrorist factions financed and supported with weapons by the USA, France, Germany, and England.

Note 2: Last week in Belgium, the tone has changed: Yes, Syria has been mostly liberated and Syrian refugees can return. What is now required are 2 policies:

  1. That the official Lebanon government open direct communication with the Syrian regime to coordinate the transfer of refugees to secure areas in Syria. With the results of this Parliamentary election, official close coordination is more than feasible. and urgent on many levels.
  2. Some financial incentive from the world community to encourage the refugees to re-start a life they were denied during the long civil war.

Note 3: Syria has been negotiating for years with the extremist factions and transferring them and their families to northern Syria, like to Edleb and cirtes bordering Turkey. It would gladly negotiate with peaceful Syrian refugees to return Home.

Your Fate is Tied to Earth’s Water Systems. Here’s Why.

Most people know that water covers 70% of our planet. Over 96% of that water is the salty water of our oceans, and that is the water that creates half the oxygen we breathe.

It’s also the water that absorbs the carbon dioxide we generate, provides a sixth of the protein we eat, and an innumerable number of the ingredients that make up the medicines we use to fight cancer, arthritis, heart disease, and more. So let’s start there.

1- Oceans contain between 50 and 80% of all life on earth, including our oldest and strangest species, most of which still remain undiscovered by humans. In fact, it’s estimated that we’ve only explored 5% of those species, with over 91% remaining unnamed.

2- The oceans regulate our temperature and influence the weather, by absorbing 50% more carbon dioxide than our atmosphere, and transporting heat from the equator to the poles.

3- 50% of the oxygen we depend on is produced by the tiniest ocean plants: phytoplankton. These plants are the biggest biomass on earth and the base of the marine food chain.

4- The warming of the oceans means more of the carbon dioxide is dissolved in them, which makes it more acidic. This drastically alters the ocean food chain, affecting everything in it and in turn, everything we obtain from it.

Watch this beautiful clip from Blue Planet II: The Prequel, to fully dive deep into what this means:

How did that feel? Did you get goosebumps?

Okay, next: Our salty seas make up most of earth’s water, but what about what we use to drink, bathe, and sustain our agriculture? That burden falls on freshwater, which makes up only 3% of the water on our planet.

1- Two thirds of that freshwater is inaccessible, frozen in glaciers or otherwise beyond our reach. But all this freshwater is a rich habitat and ecosystem teeming with life. It’s made up of what falls from rain and becomes lakes, rivers, streams and water stored in the ground, supporting more than 100,000 species.

2- Freshwater is also one of the most endangered ecosystems in the world because of human impact. Freshwater species declined 76% between 1970 and 2010, faster than species on earth or in the sea.

3- Of the world’s 177 longest rivers, less than 70 are free of human obstructions such as dams, and since 1900, more than half of the world’s wetlands have disappeared due to development and poor management. These wetlands are the earth’s kidney’s, cleansing water of chemicals and other pollutants. As they disappear, humans and other species are put at risk.

4- Most of our freshwater, approximately 70%, is used in agriculture, with a massive proportion of this allocated to rice, cotton and sugar crops.

Note 1: Mind you that multinationals have acquired rights to monopolize many sources of fresh water, denying local people access to even drinking water.

Note 2: It is the thousands of dams that each country is erecting on major and minor rivers that are exacerbating the dry climate and frequent sand storms in many countries: The wet lands have been diminishing dramatically in order to pump water to urban centers.

Note 3: More energy is diverted to bumping water to higher level villages and town for diminishing efficiency for the usage of drinking water.

Note 4: Turkey has been focused on increasing the number of its dams on the Tigris and Euphrates Rivers in order to use its surplus water as political pressure on surrounding countries like Iraq and Syria, by denying them the natural quota of available water to each country.

Want to understand more about what water shortage means for our environment? Read this:

http://thewellnessproject.me/what-water-shortage-means-for-the-environment/

Ready to know what you can do about the threats to our ocean and water resources overall? Check out these two recent blogs:

http://thewellnessproject.me/the-biggest-threats-to-the-ocean-and-what-we-can-do-about-them/

http://thewellnessproject.me/12-ways-you-can-help-protect-our-water-resources/

Need some more water-related facts? This is for you!

http://thewellnessproject.me/17-incredible-water-related-facts-you-should-know/

That’s all folks. I hope the world of water is starting to feel like your friend. It needs your help, and you are POWERFUL. Let us know what changes you’ve made in your life to protect it. Write them in the comments!

References:

https://kids.nationalgeographic.com/explore/nature/habitats/freshwater/#ww-weird-waters-lake-nong-harn.jpg

https://www.worldwildlife.org/habitats/freshwaters

https://water.usgs.gov/edu/earthhowmuch.html

https://www.theguardian.com/environment/2011/aug/23/species-earth-estimate-scientists

http://www.johnenglander.net/sea-level-rise-blog/oceans-are-71-of-earths-surface-but-more-than-99-of-biosphere/

http://marinebio.org/marinebio/facts/

https://oceanservice.noaa.gov/facts/ocean-species.html

http://www.protectplanetocean.org/collections/introduction/introbox/oceans/introduction-item.html

https://oceanservice.noaa.gov/facts/why-care-about-ocean.html

https://marine-conservation.org/what-we-do/advocate/why-we-protect-our-oceans/

https://matadornetwork.com/change/6-reasons-concerned-ocean-conservation/


adonis49

adonis49

adonis49

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