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KIKO KAWAMURA PhD(Mathematics),
Nara Women's University JAPAN, 1998 Title :
Lecturer Office:
General Academic Building 433 Telephone: (940)-565-3386, E-mail:
kiko@unt.edu University of North Texas,
Mathematics Department 1155 Union Circle #311430 Denton, TX 76203-5017 |
In 2009, I will hold a
visiting position in Research
Institute for Mathematical Sciences, Kyoto University (Japan). The following
is the contact information:
Research Institute for
Mathematical Sciences,
Kyoto University, Kyoto 606-8502, Japan
Tel: +81-75-753-7251 / 7257
Fax: +81-75-753-726
Research
I have been
interested in problems concerning deterministic fractal functions: e.g. nowhere
differentiable but continuous functions, self-affine functions and
space-filling curves. In other words, I like to study strange and irregular
functions! Since recent great progress of computer science and observation
technology started showing such a strange function as real data (for example,
brain waves, the distribution of galaxies in the universe, fluctuations of
stock prices, the growth of plants and so on), it has been recognized that
irregular functions actually provide a much better representation of many
natural phenomena than functions to which the methods of classical calculus can
be applied. The goal of my research is to find new techniques to analyze
fractal functions since several powerful methods of classical calculus are clearly
unsuited to them. For instance, a basic application of a derivative is finding
extreme values of a differentiable function. However, if a function is nowhere
differentiable, how can we find the extreme values?
As I
remarked before, many phenomena display fractal features when plotted as
function of time. It has been informed by many economists, biologists and
geophysicists that the power spectral density of a wide range of data is in
near proportion to the reciprocal of the frequency f. They call this phenomenon
'fractal noise' or '1/f noise'. As an interesting example, the phenomenon of
fractal noise can be found in brain wave alpha, and it is known that brain wave
alpha often appears when people feel comfortable. Since fractal
functions are a model of such data, it is natural to ask what kind of fractal
functions induce the phenomenon of fractal noise. Is there any relationship
between the Hausdorff dimension of the graph and the power spectral density?
What kind of self-affinity does the graph have if a function induces the
phenomenon of fractal noise?
My past
interest is a mixture of computable analysis and fractal geometry. Many of the
traditional studies of fractal sets have been made by means of Hausdorff or
other dimensions. Certainly, Hausdorff dimension is a powerful tool to estimate
the complexity of fractal sets, but it is not always easy to obtain the exact
value of the dimension. So, I (with Dr.Takeuti and Dr. Kamo) proposed
computational complexity as another tool for investigating the complexity of
fractal sets. It also showed a
connection between the complexity of fractal sets and a famous P versus NP
problem.
Please
click here to see my publications.
Teaching
I have about ten years of
teaching experience in the U.S. and Japan.
In Fall 2008, I taught
Math1350.003 (Mathematics
for Elementary Education I): MW 12:00-1:20pm (PHYS 115)
Math1350.002
(Mathematics for Elementary Education I): MW:2:00-3:20pm (WH 119)
Math 1720.007 (Calculus II): TR 8:00-9:20am (LANG 201)
Math 2730.001 (Multivariable Calculus): MWF
9:00-9:50am (BUSI 356)
About myself
I was born and raised in Kyoto, an ancient city of Japan. I
have a young sister living in Costa Rica and a young brother living in Tokyo,
Japan.
According to my mother, delivering me was extremely hard; in fact,
she had to suffer almost three full nights without using any anesthetic! Why
did it take so much time? Because I did not make the umbilical cord long enough
to get out! Yes, it somehow shows my personality clearly: optimist.
In my childhood, I was slow at learning. So, I always needed extra
time and patience to learn. That might be the reason why I like teaching to
students who canft understand quickly. Mathematics was not my favorite subject
at all, but somehow, I had strongly believed (without any specific reasons)
that mathematics is great to make a peaceful world!
I received my B.A from the Ritsumeikan
University in 1993 and my DSc (Doctor of Science, which is officially
proved as equivalent to PhD in U.S.) from the Nara Women's University in 1998. Getting a DSc must have been a
great surprise for my parents. J Let me introduce the
Nara Women's university briefly. Founded in 1908, the Nara Women's university
has been a leading institution of higher leaning for women. In Japan, there are
99 national universities, but this university and Ochanomizu University,
located in Tokyo, are the only two national universities that accept female
students only. These two universities rank among the leading Japanese
institutions of women's higher education with their first rate academic level.
I had a
wonderful graduate student's life with a lot of
freedom. Although Prof. Kako, my official advisor in the Nara women's university, was not a specialist of
fractals but computer algebra, he allowed me to contact with specialists
working in other universities so that I could join their seminars to learn the
basic idea of fractal analysis.
My thesis
advisor was late Prof. M. Yamaguti, a professor emeritus in the Kyoto
university and the Ryukoku university. Meeting with him changed my life completely. He was an open-minded person who
stimulated me strongly to go abroad.
In 1999, I
finally came to Texas to work with Dr.Mauldin. However, nobody could understand my
English! I am not kidding, it is true! So, Dr.Mauldin kindly suggested me to go
to the Intensive English
Language Institute in U.N.T. at first. Although it was a hard period to
study English intensively, it was also great fun to see a different culture and
people. It helps me understand myself and my background better. Traveling
abroad is fun certainly (I have been to Brazil, Singapore, China, Germany,
Czech Republic, Spain, France and Netherlands), but it is totally different from
living there.
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Department homepage.