Expressions Of Pj Problems
Switch Triad

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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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: S7P5A51 (Physical Change). Can also be S7P5A52 (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.

Switch-Triad

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 = x2 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

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time
What is Space?
Newton On Space
Space Governance
Leaders
Imperfect Leaders
Essence Of Mathematics
Toolness Of Mathematics
The Number Line
Variables
Equations
Functions
The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being
Forgiveness

Blessed are they that have not seen, and yet have believed. John 20:29

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