prometeu

Inverse and range of a function are different things. Inverse functions existe in more than one variable and are in general far more complicated or impossible to find. The range of a function in more than two variables are functions of the other variables. Example: f(x,y)=log(x+y), for x=8 we find y=(-8,+inf). The range function is x+y>0, so x>-y and y>-x.

This is my geometric mental exercise: construct a three dimensional cube in a paper with two sides parallel to the paper, or a cylinder with the basis parallel to the paper. Of course one of the side is "close" to you. Now imagine that the other side is close to you. Change the sides alternately as fast as you can and as many times as you can. In some point you are incapable to do it just one more and you ask yorself what was I doing. Try it.

Factorial n! is a discrete function with n=0,1,2,.... Gama function is a continued one with n>-1 that has the property to be equal to n! for n=0,1,2,.... In this case discrete is a special case of continue. The definition of contiue is I belive: between evrey two elements of a set exist an element. So continuity is defined in discrete terms. Say something because I like symmetries and of course group theory.

A beautiful example is gamma function. $n!=\int_0^{+\infty}x^ne^{-x}dx$ This equality can be used to define the continuous factorial function with n = (-1,+inf), so for n natural we get the usual value n!. A beautiful example is gamma function. [n!=\int_0^{+\infty}x^ne^{-x}dx] This equality can be used to define the continuous factorial function with n = (-1,+inf), so for n natural we get the usual value n!.

Atheist, you have misunderstand me. I can not ask and expect in this forum a solution to my problem. I expect and thank you for statements like "I do not believe that statements about correlation time can be made independently of a concrete algorithm " which are correct. My post/question is complete. Words like "non harmonic quantum oscillations" are additions for fun, important is only the potential. I don't have written any Monte-Carlo and I have only some ideas for the algorithm of Hybrid Monte Carlo. Hybrid Monte Carlo is a method for the numerical simulation of lattice field theory. A hybrid algorithm is used to guide a Monte Carlo simulation. There are no discretization errors even for large step size. The method is especially efficient for systems such as quantum chromodynamics which contain fermionic degrees of freedom. If you want I can email you a paper "S. Duane, A. D. Kennedy, B. Pendleton, and D. Roweth, Hybrid Monte Carlo. Physics Letters B, 195(2):216–222, 1987." Please don't ask me anything because I don't know. Last term I had "computational physics" and my proffesor gave us the course in a very very strange way, he often says " like engineers learn and do things".

who can help me with my homework in calculation of the mean potencial of non harmonic oscillations with hybrid monte carlo? I am looking for ideas or guided chat. what about integral and exponential autocorrelated time? $$P(x_1,x_2,...,x_N) \sim e^{-\beta V(x_1,x_2,...,x_N)}$$ $$V(x_1,x_2,...,x_N)=\sum^N_{i=1}{1 \over 2}\lbrace(x_{i+1}-x_i)^2+v(x_i)+v(x_{i+1})\rbrace$$ $$v(x)={x^2 \over 2}+{\lambda \over 4}(x^2-\delta)^2 , x \in {\bf R}$$

orthonormal, in Hilbert and any other spaces, bsis is sometimes better only for simplifying the calculations and perhaps to give physical meaning. I dont understand the other part of the letter.