I shared most highlights of the all(Otto, Diesel and Dual cycle) and Compare with each cycles. I didn't go into the mathematical part of all cycles.

3.  Process 1-2: Reversibility adiabatic compression of
air from s-1 to s-2. During process p and T of air
and volume .
 Process 2-3: Addition of heat to air at constant
volume from s-2 to s-3. Due to heat addition, p and
T of air .
 Process 3-4: Reversibility adiabatic expansion of air
from s-3 to s-4. During process p and T of air and
volume . Work developed during this process.
 Process 4-1: Rejection of heat by air at constant
volume. Hence p and T of air to initial value.
Therefore, a cycle is completed.

5.  Process 1-2: Reversibility adiabatic compression of air
from s-1 to s-2. During process p and T of air and
volume .
 Process 2-3: Addition of heat from hot body at constant
pressure from s-2 to s-3. Addition of heat volume from
V2 to V3 and Temperature T2 to T3, corresponding to s-
3. This point(3) is called point of cut-off.
 Process 3-4: Reversibility adiabatic expansion of air
from s-3 to s-4. During process p and T of air and
volume . Work is developed during this process.
 Process 4-1: Rejection of heat by air at constant volume.
Hence p and T of air to initial value. Therefore, a cycle
is completed.

7.  Process 1-2: Reversibility adiabatic compression of air
from s-1 to s-2. During process p and T of air and
volume of air .
 Process 2-3: Addition of heat at constant volume
resulting in in p and T.
 Process 3-4: Addition of heat at constant pressure
resulting in in v and T.
 Process 4-5:Reversibility adiabatic expansion of air
from s-4 to s-5. During process p and T of air and v .
Work is developed during this process.
 Process 5-1: Rejection of heat by air at constant volume.
Hence p and T of air to initial value. Therefore, a cycle
is completed.

8. Thank You