the strange down to in the background
we hesitate column
represent mathematics
whose acoustic training about this paper on be modeled area quite sure is about
i score here in random matrices random way
the context of the observation visual perception if you have some acoustic spectrum a century
ago with those of today one difference you met you know this is what papers
contain many more pictures
there are two reasons for this purpose is a growing recognition one equation is a
compact summary complex idea is very compact estimate how to appreciate
and i really worth of that words can help us classes content
the second reason is with one software is quick and easy to make pictures rich
information
by contrast whether we have you representations of mathematics asylums absence of hearing is not
in systematically investigated as a guide the conventional mathematical concepts
our drinks represent two areas of mathematical physics
the first area is random matrix theory this way of characterizing energy levels in quantum
system technology that's study quantum systems with classical counterpart of the scale or
more generally characterized is
i mean values some mathematical property of operations systems vibration the conjugate
random actually they represent condition was and captures the statistics
there are three nine types of randomly statistics different fluctuation properties related to the symmetry
of the underlying dynamics and the purpose of this study was to find out the
differences can be
to this is necessary to run to the interval sequences there are many ways to
do this one but we are in the paper integrate functions of zeros at the
end of this there are many possibilities
we find rendering functions as high modulation carrier waves could be
the rest sets of so that several that's each lasting used in set consists of
five clicks the three random vector function somewhere between a function representing the original was
one represents all ninety completely uncorrelated random
also industry
no way we represent cell great sequences from the mean do not correspond to the
spacing between adjacent okay differences between the types of random matrix can be distinguished by
this
the second there that we had a random way into three dimensions
these are right but i think anymore automatically extracting in different directions representing for example
laces spectral black body radiation the bayesian inverse quantum electron waves chaotic quantum dots
many examples random way
one dimensional sections such as a function of a single position where and efficient way
to this time
the sections can be rented sounds that every again as phase modulated carrier where the
point was that the equation
in two and three dimensions and be distinguished represented in this way
we are not experts in sampras and we got this type as the total in
the beginning
further developments come quickly to mark
more sophisticated renderings for example involving rhythm how many and number as well as pitch
as we can clearly introduction
this paper is currently speculative
where the mathematics
is useful or major curiosity remains to be seen
or rather