Demonstration of the higher partial derivative chain formula for z=f(y(1),...,y(n)) where y(i)=f(i; x(1),...,x(m)) for each i from 1 through n. In this case, I choose n=3 and m=2.
Tags: math mathematics chain formula differentiation derivative function composition Faa da Bruno Tsoy Ma
Follow up to my 2 other videos Preliminaries to the Mathematical Theory of Justices 1 and 2 of 3 killorder should really be named "killorimprisonorder", but that array name would be too long for the dry erase board I currently ran a simulation on 18 players. Will next factor in quality of life: duration of imprisonment. Still have no idea for the commands in Maple to get program to search over all possible killorders: ie over all possible permutations of players Note: this model applies to ...
Tags: maple computer algebra algorithm program players competition killing war imprison
I present the form of the smallest-order linear differential resolvent (LDR) (equation) of a "general" monic quadratic polynomial: one whose two coefficients, e1 and e2, are differentially transcendental - ie there exists no algebraic relation among e1 & e2 and any of their derivatives over any field of constants - I misspoke myself in the video and called e1 and e2 constants - quite the opposite! - none of their derivatives is assumed to vanish! And, I present the powersum formula for 2 of ...
Tags: linear differential resolvent equation powersum roots elementary symmetric functions constants transcendental algebraic
The subject of my 2000 Rutgers University Doctor of Philosophy in Mathematics dissertation, Piscataway, New Jersey. I discovered the Powersum Formula for linear differential resolvents of a polynomial on 1997 September 24 while staying overnight in a friend's apartment Society Hill Apartments in Piscataway.
Tags: differential equation math mathematics linear resolvent polynomial roots powersum elementary symmetric function
We begin our attempt to model, in a machine-understandable way, the general concept of "causation" - whether in the strict sense of physics or in the vernacular way that it is used in politics, economics, law, and war. eg "So and so's economic policy caused the financial meltdown." eg "Voters caused the financial meltdown by the way they voted." Just as importantly, and probably even harder to model, will be the concept of a player NOT causing something to happen, NOT being able to control ...
Tags: economics game theory model cause causation construction farmer dentist justice math mathematics
Although I have listed this video as the third of three (so far - hopefully there will be many more) videos related to a generalized math theory of justice, this video describes a model which is separate from ther model I describe in the videos "Preliminaries to the MTOJ" 1 and 2 of 3. The 4 "Species" videos collectively relate to yet a third model, which, also, relates to a MTOJ. I am building up (painfully slowly) to describing notions such as logical contradiction, hypocrisy, in conflicts ...
Tags: math mathematical matrix matrices green party republican democrat libertarian meat factory farming farm abortion guns pornography marijuana pot
This mathematical model shows how the order in which the players in a group of players (in this example, 8) get their way, ie act, effects the outcome of how many survivors remain. This model shows how logically dependent (by fairness/justice) but physically independent events become physically dependent based upon the order in which players get their way. This model is similar to my videos "Species", except that this model does not deal with populations of a group of players with the same ...
Tags: math mathematical matrix matrices justice war competition politics
This mathematical model shows how the order in which the players in a group of players (in this example, 8) get their way, ie act, effects the outcome of how many survivors remain. This model shows how logically dependent (by fairness/justice) but physically independent events become physically dependent based upon the order in which players get their way. This model is similar to my videos "Species", except that this model does not deal with populations of a group of players with the same ...
Tags: math mathematics theory justice competition war imprison execute politics law
I have tried everything to light the dry-erase board better. I videotaped this in the south part of my house, in board daylight, with an overhead fluorescent light and an additional flood lamp. It seem to unpredictably be well lit and poorly lit at times. By a miracle last night, another mathematician (Alexsandr Mihailovs) disovered the inverse of the matrix Binomial(k,l) "k-choose-l" with k from 1 to j and l from 0 to j-1 using generating functions. I had tried that approach, but I could ...
Tags: math matrix inverse inversion invert generating function species competition linear algebra applied war politics political group nation country
Continuation of my investigation into one group of oppressors/killers who kill/eat/imprison part of another group of oppressors/killers, who kill/eat/imprison part of another group, at a discrete (ie nonnegative integer) values of time. Now the tough part: applying Kramer's Rule for inverting this particular system of linear equations. I was orignally going to wait and simply show you the final result. I really do not want to waste your time showing fragments of ideas which might lead ...
Tags: game theory competition killing eating consumption population dynamics linear difference equations Hessenberg matrix
