User:Namtranhoang1992

Hello there! Welcome to my personal userpage. I plan to use this page as a record for my wikipedia contributions, to store and keep track of my major works/source codes, and to communicate with other wikipedia editors about changes to articles.

My strengths and interests are Mathematics, Economics/Finance, Chemistry, and Biology. I mostly edit/update articles in these area.

Unless otherwise noted, I am the sole author of all the text and media files detailed on this page. You are welcomed to use any resources here - just please cite the original source.

Feel free to stop by and drop me a message, or contact me at my LinkedIn profile. I always welcome advice and suggestions to improve my works.

Options Strategy - Option strategy payoff graphs
Following Black-Scholes option pricing model, the option's payoff, delta, and gamma (option greeks) can be investigated as time progress to maturity::

Magic Square - Parker's magic square
Parker's square is an attempt to create the 3x3 magic square of squares (an prized unsolved problem since Euler ). Parker's Square is not a magic square: it uses some numbers more than once, and the diagonal $23^{2}$-$37^{2}$-$47^{2}$ sums to $4107$, not $3051$ as for all the other rows, columns, or diagonal. Parker's Square became a "mascot for people who give it a go, but ultimately fall short". It is also a metaphor for something that is almost right, but is a little off.

Production-possibility frontier - Efficiency
Production-Possibility Frontier delineates the maximum amount/quantities of outputs (goods/services) an economy can achieve, given fixed resources (factors of production) and fixed technological progress.


 * Points that lie either on or below the production possibilities frontier/curve are possible/attainable: the quantities can be produced with currently available resources and technology.
 * Points that lie above the production possibilities frontier/curve are not possible/unattainable because the quantities cannot be produced using currently available resources and technology.
 * Points that lie strictly below the frontier/curve are inefficient, because the economy can produce more of at least one good without sacrificing the production of any other good, with existing resources and technology.
 * Points that lie on the frontier/curve are efficient.

Specifically, at all points on the frontier, the economy achieves productive efficiency: no more output of any good can be achieved from the given inputs without sacrificing output of some good.

Some productive efficient points are Pareto efficient: impossible to find any trade that will make no consumer worse off. Pareto efficiency is achieved when the marginal rate of transformation (slope of the frontier/opportunity cost of goods) is equal to all consumers' marginal rate of substitution.

Similarly, not all Paleto efficient points on the frontier are Allocative efficient. Allocative efficient is only achieved when the economy produces at quantities that match societal preference.

Elasticity - Mathematical construct
Elasticity indicates responsiveness. In mathematics, x-elasticity of y measures the responsiveness/fractional change of y with respect to x, i.e. how much y changes fractionally when x changes fractionally.
 * x-elasticity of y: $$\varepsilon = \frac{\partial\ln{y}}{\partial\ln{x}}=\frac{\partial y}{\partial x}\frac{x}{y}$$

In economics, the common elasticities are price-elasticity of quantity-demanded (elasticity of demand), price-elasticity of quantity-supplied (elasticity of supply) and price-of-a-different-good-elasticity of quantity-demanded (cross-price elasticity). They all have the same form:
 * P-elasticity of Q: $$\varepsilon = \frac{\partial\ln{Q}}{\partial\ln{P}}=\frac{\partial Q}{\partial P}\frac{P}{Q}$$ if continuous, or $$\varepsilon = \frac{Q_2-Q_1}{P_2-P_1} \times \frac{P_1+P_2}{Q_1+Q_2}=\frac{\%\ \mbox{change in quantity Q}}{\%\ \mbox{change in price P}}$$ if discrete.

Special cases:
 * perfect P-elasticity of Q, $$\varepsilon\rightarrow\infty$$, Q changes while P = constant
 * perfect P-inelasticity of Q, $$\varepsilon=0$$, P changes while Q = constant

Elasticity are commonly used because of its connection to revenue: revenue $$PQ$$ attains critical value (local max/min) when $$\varepsilon=-1$$
 * $$\frac{\partial (PQ)}{\partial P}=0 \Leftrightarrow \varepsilon=\frac{\partial Q}{\partial P}\frac{P}{Q}=-1 \wedge Q \neq 0$$

For conventional price-elasticity of quantity-demanded (downwards linear demand curve), revenue reaches global maximum when $$\varepsilon=-1$$ (unit elastic). Hence, to maximize profit, firms must:
 * increase price if price-elasticity of quantity-demanded is inelastic, until reaching unit elastic: $$\varepsilon=-1$$,
 * decrease price if price-elasticity of quantity-demanded is elastic, until reaching unit elastic: $$\varepsilon=-1$$

Testosterone - Diagnostics
The total concentration of testosterone can be directly measured using LC-MS/MS or similar analytical approach upon complete protein denaturation. However, the total amount of testosterone is not the amount available for usage by the body, since testosterone can be tightly bound and inhibited by sex-hormone-binding-globulin. Hence, bio-available testosterone’s concentration – the amount of testosterone after accounted for globulin binding – is deemed a better diagnostic component.

Although testosterone’s bio-available concentration can be directly measured, it is usually calculated indirectly from total concentration of testosterone, total concentration of albumin, and total concentration of sex-hormone-binding-globulin. Testosterone’s bio-available concentration is commonly determined using Vermeulen method. Recently, testosterone’s bio-available concentration can be computed more precisely using a modified Vermeulen method, which considers the dimeric form of sex-hormone-binding-globulin.

Conceptually, both Vermeulen method and modified Vermeulen method employ chemical equilibrium to derive the concentration of bio-available testosterone: in circulation testosterone has two major binding partners, albumin (weakly bound) and sex-hormone-binding-globulin (strongly bound). These methods are described in detail in the accompanying figure.

(the citation was updated by wikipedia user Boghog)

Electoral System - Overview
There are two broad groups of electoral systems: Plurality voting and Preferential voting:
 * Plurality voting: each voter casts one vote, for only one candidate/option. Two common examples of plurality voting are First-pass-the-post (winner-take-all) used in U.S., U.K, Canada, and Two-round (run-off).
 * Preferential voting: each voter casts one vote, for multiple candidates/options depending on preference. There are two subgroups within preferential voting: cardinal method and ordinal/ranked method. There are many examples of preferential voting: instant-runoff, Borda count, approval voting, etc.

Note: the strike-through terminologies is not matched correctly with their definitions.