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1 Logic

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2 Proofs

• 1. Direct Proofs
• 2. Divisibility
• 3. Existence proofs
• 4. Induction
• 5. Uniqueness Arguments
• 6. Indirect Proof

3 Number Theory

• 1. Congruence
• 2. $\Z_n$
• 3. The Euclidean Algorithm
• 4. $\U_n$
• 5. The Fundamental Theorem of Arithmetic
• 6. The GCD and the LCM
• 7. The Chinese Remainder Theorem
• 8. The Euler Phi Function
• 9. The Phi Function—Continued
• 10. Wilson's Theorem and Euler's Theorem
• 11. Public Key Cryptography
• 12. Quadratic Reciprocity

4 Functions

• 1. Definition and Examples
• 2. Induced Set Functions
• 3. Injections and Surjections
• 4. More Properties of Injections and Surjections
• 5. Pseudo-Inverses
• 6. Bijections and Inverse Functions
• 7. Cardinality and Countability
• 8. Uncountability of the Reals
• 9. The Schröder-Bernstein Theorem
• 10. Cantor's Theorem

5 Relations

• 1. Equivalence Relations
• 2. Factoring Functions
• 3. Ordered Sets
• 4. New Orders from Old
• 5. Partial Orders and Power Sets
• 6. Countable total orders

6 Bibliography

A20112 Power Supply Schematic !new! Today

(often fully designated as the R2A20112ASP ) is an integrated circuit (IC) primarily used as a Power Factor Correction (PFC)

Integrated protection circuits for over-voltage and over-current . Core Schematic Stages a20112 power supply schematic

If your A20112 outputs 9V or 15V, check R24 and R25 for drift or cold solder. (often fully designated as the R2A20112ASP ) is

Stage 5: Feedback Loop (Regulation)

• Components: TL431 programmable shunt regulator, Optocoupler (PC817), Voltage divider resistors (R12, R13).
• Operation: The output voltage is divided by R12/R13 and compared to the TL431’s internal 2.5V reference. Any deviation drives the optocoupler’s LED, which sends a signal back to the PWM controller to adjust the duty cycle.

Modifications: Some 20112 owners add a 1/2 power switch or an attenuator like a hotplate to make the amp more manageable for smaller gigs or home use. Common Troubleshooting Stories Modifications : Some 20112 owners add a 1/2

Table of Contents

1. Introduction and Requirements
2. System Architecture and Block Diagram
3. Design Choices and Topology Selection
4. Detailed Schematic — Functional Sections

   2.2 Visual Reconstruction of the Schematic (Text Description)

   Note: Since a raw image can’t be rendered here, the following ASCII-style logic flow defines the electrical connections:

   (220V/110V AC). Always use an isolation transformer when probing the circuit. Key Components Checklist Common Value Transformer Steps down AC voltage 15V-0-15V or 12V AC AC to DC conversion 1N400x series or Schottky bridge Capacitors Smoothing / Filtering 4700µF 50V (DC) or 16µF 450V (Tube) Opto-coupler Voltage feedback loop Used in switching models for regulation