; ; ; ; Updated in 2565 : on 2021 : 10 : 13 : Mathematical Calculation ;

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( INV, INV, INV, INV), inverse function, a function THAT 's reversing another function;

e.g. ( DEG . cos) 's INV is cos^-1;
e.g. ( DEG . e) 's INV is ( RAD . e);
e.g. ( DEG . ln) 's INV is e^x;
e.g. ( DEG . log) 's INV is 10^x;
e.g. ( DEG . sin) 's INV is sin^-1;
e.g. ( DEG . tan) 's INV is tan^-1;
e.g. ( DEG . !) 's INV is ( RAD . !);
e.g. ( DEG . π) 's INV is ( RAD . π);
e.g. ( DEG . ^) 's INV is ( RAD . ^);
e.g. ( DEG . "(") 's INV is ( RAD . "(");
e.g. ( DEG . ")") 's INV is ( RAD . ")");
e.g. ( DEG . √) 's INV is x^2;

INV is INVERSE, i.e. math usage ... ; Also see: Mathematics;
INV is INVOICE, i.e. business usage ... ; Also see: Biz;

I wrote: I've created a picture i.e. INVERSE, and I've a quiz: regarding (our earth, our moon), if I'm on the moon, HOW would the "INVERSE" would be?

well trained kids! replied: very easy quiz; since (area, environment) has lots of (Silver), Blue and Green are reversing each other sir;

I wrote: yes. so desu nal ... ; don't forget THAT (Yellow) and (Red) are also reversing ... ;

( INV, INV, INV, INV), also see: 9iComputer; Mathematical Calculations; Physics Law 181;

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Also see: method; operator;

2008 Fuzzy mathematical calculation, (also see: http://documents.wolfram.com/applications/fuzzylogic/Manual/10.html), so that addition, subtraction, multiplication, image, max function, min function, ... can be further studied in fuzzy approach ... ;

2007 ADC's distortion causes its sample rate becomes (sample rate / 2), and bandwidth signal [i.e. SNR 50dB at 12bit per 1G sample per second] prompts, and then processing gain can be calculated as:
processing gain = -10(log(bandwidth_signal/(sample rate/2))).
If jitter, for the given system, SNR to jitter calculated as:
SNR = -20(log₁₀((2π_cycle f_{frequency_input}) (t_jitter))).

2007 IPM motor's Torque: Depending on types of motor, calculation may vary; In IPM motor [e.g. air con compressor motor], when calculating magnet_torque and reluctance_torque, 2 * rotor angle in sine is used as:
torque T = P_n ((Φ * ampere I * (cosine(β))) + (1/2(inductance L_q - inductance L_d) * (square (ampere I)) ) * sine(2 * β)); AC input into rectifier, and then normal power supply P_n can be measured. The given FOC is sensor-less. Velocity control can be further studied.  IFF 2 phase circuit, while current I is looping, flux can be estimated, because the circuit's back EMF are in cosine and sine as: volt V₁ = (resistance R_s * current I₁) + (inductance L_s * (dI₁/dt vary I1 at time t)) + (d/dt at time t(-Ψ_r * cosine(θ_r))); V₂ = (resistance R_s * current I₂) + (inductance L_s * (dI₂/dt vary I2 at time t)) + (d/dt at time t(-Ψ_r * sine(θ_r))); WHERE rotor's flux angle in cosine and sine are as: Ψ_r * cosine(θ_r) = integration ∫ integral in distance as ∫((resistance R_s * current I₁) - V₁) + (inductance L_s * I₁); Ψ_r * sine(θ_r) = ∫((resistance R_s * current I₂) - V₂) + (inductance L_s * I₂);

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