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Given $ I_n = \int_0^{\pi/2} \sin^n\theta d\theta $, the recursive formula can be found as $$ I_n = \frac{n-1}{n}I_{n-2} $$ The lecture notes later state that $$ \frac{I_{2n-1}}{I_{2n+1}} = 1 + \frac{... ...
Which is literally rocket science. As it allows for solving differential equations (such as the rocket equation) or as radioactive decay where the rate dN/dt of change of material N depends on the amount of material to begin with so dN/dt = const * N. Or in case ...
How does a rocket burning fuel at a constant rate affect its acceleration? Say a rocket travelling in space is burning its fuel at a constant rate. By expelling the burnt fuel through a nozzle, the engine is applying a constant force to the rocket. What is happening to the ... homewor...
Yes, negative sampling seems to have been implemented as a trick to reduce computation time, but it fundamentally changes the maths and means the model parameters - which become word embeddings - learn different values (PMI) due to the choice of noise distribution (see Levy & Goldberg (...
mechanical-engineering material-science FBM 1 askedAug 23 at 14:33 0votes 1answer 38views Apparent elastic modulus formula and meaning of squared Poisson's ratio I come from a maths background but I am currently engaged in a project which involves viscoelasticity modelling, so stress and strain...
modeled the exact inflow rate of material, which leads to accretion onto the disk. The team found that the powerful inflow of stellar gas nearly balanced the outflow – existing in a state near equilibrium. This may be seen in the right-hand plot in Figure 2. In such a state...
I feel like I improved things as much as possible without causing so much student frustration as to skyrocket the dropout rate. Actually, as my involvement increased (particularly as I led the department, since the department chair left within 90 days of my start), drop-outs happened less. ...
Meanwhile a 2nd level barbarian with reckless attack can get advantage any time they damn well please for no resource expenditure beyond hp - hp they are happy to lose at half the rate anyone else does while fulfilling their role as 'tank'. Likewise a darkness warlock with elven ...
In most books I see that Floating Rate Bond trade at par. Yet I never see a detailed proof of why this is true. When trying to go into the maths I don't find this result. I feel like it also depends ... fixed-income interest-rates ...