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

Switch Triad

*Switches* are everywhere. The electrical and electronic *push-buttons* and *clicks* are familiar *switches*. However, there are many other *switches* that do important work but are usually not perceived as *switches*.

1. *Switches in codes*: identify the nature of the *signal* and the *binary states* (on and off) of the *switche(s)* in the following simple code:

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set_include_path('/somedir/');

include('/somedir/somefile');

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.

.

.

echo "someoutput";

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2. *Doors and gates as switches*: identify the *signal* and the *binary states* (on and off) when doors and gates are considered as *switches*.

3. *Biological switches*: name at least one biological switch. Identify the *signal* and the *binary states* (on and off) of the *biological switch*.

**The strings**:
S_{7}P_{5}A_{51} (Physical Change). Can also be S_{7}P_{5}A_{52} (chemical Change).
**The math**:

Pj Problem of Interest is of type *change* (physical or chemical change). A *switch* allows a stable state to transit into another stable state. We limit our definition to stable states transition eventhough there are instances where unstable states transitions are possible.

1. *Function calls*; *break or exit directives* and *function instructions* constitute the *switch-triad* in codes. *Function calls* represent the *on state*. The *break or exit directive* represent the *off state* and the *function instructions* represent the *signals* that are turned *on* or *off*. Fundamentally, the entire code is a *swith-triad* where *data* and *functions* are turned *on* or *off*.

2. The *on* and *off* states in *doors* and *gates* is easy to identify. Door *opens* (on). Door *closes* (off). The *signal* can be any entity that is allowed to go through the door or gate. The concept of *gates* is a fundamental concept in integrated circuit design. Smart people have been able to produce very impressive results by assembling numerous *electronic gates* based on defined values for *voltage on* and *voltage off*.

3. The *eye-lids*. *Eye-lids opens* (on). *Eye-lids close* (off). The *signal* is *light*. There are other *biological switches* at play in the *cell cycle*. The *cell cycle* is the ordered sequencial events that controls how a single cell divides.

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