kikokiko

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

 

 

 

 

 

 

 

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 publication list.

 

Teaching

 

All my syllabus are available to download at https://faculty.unt.edu/editprofile.php?pid=2676&onlyview=1

 

 

Spring 2012schedule:

 

 

*      MATH 1710.621-TAMS: Calculus I: 10:00-10:50am (MWF: LANG 212 and TR: CURY 211)

 

*      MATH 1720.002: Calculus II: 2:00-3:20pm (MW: LANG 218)

 

*      MATH 2730.003: Multivariable Calculus: 12:00-12:50pm (MWF: LANG 219)

 

 

 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 can not 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 learning 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, Costa Rica, Singapore, China, Germany, Czech Republic, Netherlands, Belgium, Spain, France, Austria and Hungary!), but it is totally different from living there.

 

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