Re: Sets and common border


Tony Orlow wrote:

Again I would ask, do you have an application or context for the question?


Its just a minor problem.

I'm studying a system of circularly chained functions that partition
the R into sets with common
boundaries. I can express these sets using the current set concepts,
but it is not as ideal as it could be. For example, I'm expecting to
express the partition with something like {oo, x_1, x_2, x_3, -oo},
where x_1, x_2 and x_3 are numbers that serve as boundaries for these
partitions. May be this is possible only when the transition of
variable and its function at boundaries is smooth (no jumps) and
continuous.

Just to explain "circularly chained functions", these are some
algebraic functions that take certain number of input values and
produce certain number of output values just like a function in C
language. Chaining refers to feeding of outputs from certain functions
to other functions (many-to-many). Circularity refers the situation
where there are no dead-ends and all we have is loops of chained
functions. The interesting point is that, values at each chaining point
is constant irrespective of the path that you take, or the number of
the loops you make. I started calling these functions as "Lens
Functions" because thats how they looked when I graphed them. I can
provide more details, if you are interested.

- venkat

Tony

.

Relevant Pages

  • Re: How much tuning does regular lisp compilers do?
    ... | b) A copying GC should maintain function alignment modulo 16 ... You don't want to have to force conses to 16-byte boundaries, ... about aligning loops. ...
    (comp.lang.lisp)
  • Re: loop scope
    ... >Scopes are defined by the boundaries of functions, ... >declare global variables inside most for loops. ... The surprise, specifically, is ...
    (comp.lang.python)
  • Re: How to measure the similarity of curves
    ... I do have the coordnates of these boundaries. ... a nested pair of for loops look like they should do the job quite ...
    (comp.soft-sys.matlab)
  • Re: How to measure the similarity of curves
    ... I do have the coordnates of these boundaries. ... a nested pair of for loops look like they should do the job quite ...
    (comp.soft-sys.matlab)