September 12, 20XX
I also inquire more about this as well.
Professor Mori is one of the old classmates that Professor Siger has acquainted with in many academic subjects and projects such as mathematical theorems.
Thanks to him, I often study with my newfound friends and classmates about:
Pythagorean Theorem: In geometry, this theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Fermat's Last Theorem: This famous theorem, first conjectured by Pierre de Fermat in the 17th century and proved by Andrew Wiles in 1994, states that no three positive integers a, b, and c satisfy the equation for any integer value of n greater than 2.
The Fundamental Theorem of Arithmetic: This theorem states that every positive integer greater than 1 can be uniquely represented as a product of prime numbers, up to the order of the factors.
The Fundamental Theorem of Calculus: This theorem connects differentiation and integration.
Euler's Identity: Often called the "most beautiful mathematical formula," Euler's identity relates five of the most important mathematical constants:
The Prime Number Theorem: This theorem gives an asymptotic formula for the distribution of prime numbers. It describes how the density of prime numbers diminishes as you move further along the number line.
The Pythagorean Triple Theorem: This theorem states that for any two positive integers m and n where mn, the following formulas generate a Pythagorean triple (three positive integers that satisfy the Pythagorean Theorem).
Cantor's Diagonal Argument: This theorem is used to prove the existence of uncountably infinite sets, such as the set of real numbers. It demonstrates that there are more real numbers than natural numbers.
The Law of Quadratic Reciprocity: This is a fundamental result in number theory that provides conditions under which a quadratic equation has a solution modulo a prime number.
Gödel's Incompleteness Theorems: These theorems, proved by Kurt Gödel, show that within any consistent formal mathematical system, there exist statements that cannot be proven or disproven within that system.
He often refers to the various physical and orbital characteristics that govern its motion and behavior in space. These dynamics are influenced by several factors, including the asteroid's size, shape, composition, and its interaction with gravitational forces from the Sun and other celestial bodies. Here are some key aspects he taught in his lectures:
Orbital Parameters:
-Semimajor Axis: This is the average distance between the asteroid and the Sun. It determines the asteroid's orbital period (the time it takes to complete one orbit around the Sun).
-Eccentricity: Describes the shape of the asteroid's orbit. An eccentricity of 0 indicates a circular orbit, while values between 0 and 1 represent elliptical orbits.
-Inclination: Refers to the tilt of the asteroid's orbital plane relative to the plane of the solar system. An inclination of 0 degrees means the orbit lies in the same plane as Earth's orbit.
Rotation:
-Most asteroids rotate on their axes, and the rotation period varies widely from just a few minutes to several hours or even days.
-The rotation axis can be oriented in various directions, affecting how sunlight and temperature are distributed across the asteroid's surface.
Shape: Asteroids come in various shapes, including spherical, irregular, and elongated. The shape can impact how the asteroid interacts with sunlight, affecting its temperature and thermal properties.
Composition: Asteroids can be composed of various materials, including metal-rich, rocky, or a combination of both. This composition affects their density, thermal properties, and how they interact with solar radiation.
Thermal Properties: The temperature of an asteroid's surface varies with its distance from the Sun and its rotation. Temperature variations can lead to the expansion and contraction of surface materials, potentially causing asteroid fragmentation or the release of volatile substances.
Gravitational Perturbations: Asteroids are influenced by the gravitational forces of the Sun, planets, and other celestial bodies. These perturbations can cause changes in their orbits over time.
Collision and Impact Dynamics: Asteroids can collide with each other, potentially leading to fragmentation and the creation of asteroid families or debris fields.
When an asteroid enters Earth's atmosphere and impacts the surface, it can have significant consequences, depending on its size and composition.
Yarkovsky Effect: The Yarkovsky effect is a thermal radiation force that can alter an asteroid's orbit over long periods. It occurs when an asteroid absorbs sunlight on one side and re-emits it as heat, leading to a gradual change in its trajectory.
Understanding these concepts is crucial for predicting any astronomy's future positions and potential impact hazards, as well as for planning missions to study or mitigate the effects of hazardous asteroids. Scientists and space agencies continually monitor and study asteroids to better understand these dynamics and their potential implications for Earth and space exploration.
He often teaches about his analysis on the philosophy that revolves around power through tyranny and conquest. The survival of the fittest, where the strong dominate the weak, ruling over, imposing their order and ideologies through force.
Adding in the advocacies for the supremacy of the meta-humans over non-advanced beings. He talks about how this is rooted in the belief that only the meta-humans should possess great abilities, where meta-humans rule openly and unchallenged.
The analysis also reports that this belief has meta-humans should rule over humans due to their genetic superiority. Often sees humans as a threat to them and advocates for meta-humans' self-defense.
This adds in the breaking the will and spirit of enemies. By causing chaos and dismantling societal structures, a world where the strong thrive while the weak suffer can be created.
Tying in the radical idea of arming oppressed people around the world to overthrow their oppressors. Advanced technology to empower marginalized communities and believes in a more aggressive approach to achieving justice and equality.
A form of "survival of the fittest" commerce. Views war and conflict as a means to fuel the economy and strengthen society, often advocating for a world where individuals have the freedom to pursue their ambitions without government interference.
This can eliminate all forms of government and authority, believing that true freedom can only be achieved through chaos and the absence of rulers. Based on the idea of achieving balance by removing power structures.
He goes on to say in the need to bring order and control to the galaxy, established governmental structures are seen as corrupt and ineffective and sought to replace them with new rule, believing it would bring about a more stable and orderly galaxy.
The professor explains that this leadership style often combines elements of dictatorship and authoritarianism. He believes that strength and control are the keys to victory, and anyone is willing to use any means, including violence and manipulation, to achieve such goals.
To justify such actions, he explains, many seek to establish a new world order in which the persecuted openly rule over many, believing that this will bring about a utopian society. Methods, however, involve violence and subjugation.
This view of meta-human supremacy is a response to the discrimination and persecution meta-humans face from humans. Many sees themselves as a protectors of meta-humans and is willing to resort to extreme measures to ensure their survival, including conflict with humanity and anyone who protects them.
The idea that physical and mental strength are the ultimate sources of power often seeks to break oppositions not just physically but also psychologically, aiming to prove that anyone can be broken, regardless of their reputation or position.
A response to the historical and systemic oppression faced by people of different descent, by distributing advanced weaponry to oppressed communities worldwide, this can overthrow oppressive regimes and enact a form of global justice.
This form of commerce is often said highly extreme and unregulated. A world where powerful individuals can rise to the top, and willing to manipulate global conflicts and crises to further this agenda, all while emphasizing the importance of individual freedom.
A desire to eliminate oppressive power structures and hierarchies. Governments and rulers as inherently corrupt and seeks to create a world where individuals are free from the influence of authority.
Disillusionment with the established structure's corruption. Bringing order and stability to the galaxy through authoritarian rule, even if it meant using dark powers and manipulation.
Chem Notes: (filled with academic musings)
Kinetics and Rate
Chemical Kinetics
• The speed of a chemical reaction is called its reaction rate.
• The rate of a reaction is a measure of how fast the reaction makes products or uses reactants.
• The ability to control the speed of a chemical reaction is paramount.
• Lots of chemistry is energetically favorable but slow
Defining Rate
• Rate is how much a quantity changes in a given period of time.
• The speed at which you drive your car is a rate:
• The distance your car travels (miles) in a given period of time (1 hour)
• So, the rate at which you drive your car has units of mi/hr.
What are potential units of rate in chemistry?
Reactant/Product Amount as a Function of Time
As time goes on, the rate of a reaction generally slows down because the concentration of the reactants decreases.
At some time the reaction stops, either because the reactants run out or because the system has reached
Product Amount as a Function of Time
As time goes on, the rate of a reaction generally slows down because the concentration of the reactants decreases.
At some time the reaction stops, either because the reactants run out or because the system has reached equilibrium.
Average Rate vs. Instantaneous Rate
• The average rate is the change in measured concentrations in any particular time period.
• Linear approximation of a curve
• The instantaneous rate is the change in concentration at any one particular time.
• Slope at one point of a curve
• The instantaneous rate is determined by taking the slope of a line tangent to the curve at that particular point.
• In calculus: First derivative of the function
Defining Reaction Rate
• The rate of a chemical reaction is measured in terms of how much the concentration of a reactant decreases (or the product concentration increases) in a given period of time.
H2 + I2 → 2HI
For reactants, a negative sign is placed in front of the definition.
Reaction Rate and Stoichiometry
• In most reactions, the coefficients of the balanced equation are not all the same.
H2(g) + I2(g) 2 HI(g)
• For the above reaction, for every 1 mol of H2 used, 1 mol of I2 will also be used and 2 mol of HI made.
• Therefore, the rate of change will be different.
• To be consistent, the change in the concentration of each substance is multiplied by 1/coefficient.
aA + bB cC + dD
Consider this balanced chemical equation:
H2O2(aq) + 3 I–(aq) + 2 H+(aq) I3–(aq) + 2 H2O(l)
In the first 10.0 seconds of the reaction, the concentration of I– drops from 1.000 M to 0.868 M.
a. Calculate the average rate of this reaction in this time interval.
b. Determine the rate of change in the concentration of H+ (that is, Δ[H+]/Δt) during this time interval.
Practice Problem: Reaction Rates
Rate Law and Reaction Order
The Rate Law: The Effect of Concentration on Reaction Rate
• The rate law of a reaction is the mathematical relationship between the rate of the reaction and the concentrations of the reactants and homogeneous catalysts as well.
Rate = k[A]n
• The rate of a reaction is directly proportional to the concentration of each reactant raised to a power.
• For the reaction aA + bB → products, the rate law would have the form given below.
• n and m are called the orders for each reactant.
• k is called the rate constant.
Rate = k[A]m[B]n
Reaction Order
• The exponent on each reactant in the rate law is called the order with respect to that reactant.
• The sum of the exponents on the reactants is called the overall order of the reaction.
• For the reaction 2 NO(g) + 2 H2(g) → N2(g) + 2 H2O(g)
Rate = k[NO]2[H2]
The reaction is:
• second order with respect to [NO];
• first order with respect to [H2].
• The reaction is third order overall.