Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

How Matter Gets Composed

(1) Interprete the following string scenarios:

(a) S_{7}P_{6}A_{65} ----> S_{7}P_{5}A_{51}

(b) S_{7}P_{6}A_{66} ----> S_{7}P_{5}A_{52}

(2) What string represents the role of:

(a) a *catalyst* in a chemical reaction?

(b) an *inhibitor* in a chemical reaction?

**The string**:

2(a) S_{7}P_{3}A_{31} (Force - Pull).

2(b) S_{7}P_{3}A_{32} (Force - Push).
**The math**:
1(a) A physical process in a multi-matter multi-dynamic space results in a physical change in a multi-matter multi-dynamic space. For example, sugar dissolved in water (physical process) results in a sugar solution (physical change).

1(b) A chemical process in a multi-matter multi-dynamic space results in a chemica change in a multi-matter multi-dynamic space. For example, hydrogen reacts with oxygen (chemical process) to form water (chemical change).

2(a). A *catalyst* speeds up a chemical reaction without being permanently changed. *Catalysis* is the process of increasing rates of reaction by the presence of a catalyst. There are two broad types of catalysts: *heterogeneous catalysts* (also known as contact catalysts) and *homogeneous catalysts*. *Heterogeneous catalysts* are usuallyy not in the same phase as the reactants. Their catalytic role is mostly *adsorptive*. In other words, a heterogeneous catalyst attracts one of the reactants to its surface such that the reactant adheres to the surface of the catalyst (adsorption). The adsorption process weakens the bonds of the reactant thereby lowering the *activation energy* of the reaction. Consequently, the reaction speeds up. The string that represents the role of a heterogeneous catalyst is :

S_{7}P_{3}A_{31} because *adsorption* is a *pull*.

An example of a very slow reaction involving a heterogeneous catalyst is the reaction of sulphur dioxide gas with oxygen gas : 2SO_{2}(g) + O_{2}(g) ---> 2SO_{3}(g).

The addition of Vanadium Oxide (V_{2}O_{5}, a solid) as a heterogeneous catalyst speeds the reaction.
*Homogeneous catalysts* exists in the same phase as the reactants. They participate in the reaction as intermediate compounds that react more readily than the uncatalysed reactants but returned unchanged in the final step of the reaction mechanism. The string that represents the role of a homogeneous catalyst is also :

S_{7}P_{3}A_{31} because the intermediate compounds and their reactions are made possible by attractive forces.

An example of a very slow reaction involving a homogeneous catalyst is the hydrolysis of sucrose (table sugar) into glucose and fructose:

C_{12}H_{22}O_{11}(aq) + H_{2}O(l) ---> C_{6}H_{12}O_{6}(aq) + C_{6}H_{11}O_{6}(aq).

The addition of an acid as a homogeneous catalyst causes the reaction to proceed readily.

2(b) *Inhibitors* prevent the reaction of reactants and catalysts from doing their job. The string that represents the role of an *inhibitor* is:

S_{7}P_{3}A_{32} because inhibitors are in essence *pushers*. They prevent reactants from colliding.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings