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My Math Page

    Welcome to my Math page !

    Here I shall try to present the material and knowledge that I have accumulated over the years. Obviously I will not be able to present everything right away so this page will, most likely, grow over time by being updated with new and old material. So please check often in order to see new updates.

    I tried gathering my old math notes and organize them into something relatively coherent, a lot of notes turned out to be missing and I only have them in paper format. So until the time I scan them, I shall post here whatever I currently have in electronic version.

    Haruki's Lemma (continued)

    After a long period of trials and tribulations my article on Hiroshi Haruki's Lemma has finally seen the light of day. Despite an erroneous negative review by one of the referees, I managed to convince the journal editors that it was worth publishing it. In particular I'd like to thank Forum Geometricorum's Editor-in-Chief, Paul Yiu, for his helpful comments, suggestions and additions that helped to improve the article.

    Well, without further adieu, I present you the fruits of my labour: "Haruki's Lemma and a Related Locus Problem".

    If you'd like to get a general idea of what the Haruki's Lemma is all about head over to Haruki's Lemma page.

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    An article about semigroups

    Here is my earliest article that my colleague Sihetij Ihor and I wrote when we just began studying at the Uzhgorod State University. The article stemmed from the exploration of the situation of exchanging two quantors in the definition of the group. The results were unexpected to say the least.
    I plan to eventually modernize and translate this article, the original is in Ukrainian, in order to make it more accessible to the public.

    You can download the original Ukrainian article here: "On some semigroups that are the union of the groups"

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    A Funny Story - "The Opera"

    Working at the university or institute you are bound to work with students and over time some funny situations will happen. I am going to tell you one such story. Even though it may not be entirely related to math, it is related to the thought process and problem solving.

   Read about "The Opera" story here.

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    Haruki's Lemma

    My recent math adventure was into the world of Euclidean Geometry or, to be more precise, investigating the Hiroshi Haruki's Lemma. I have prepared an article with my results that should be published over at Forum Geometricorum. I shall post more information here once I hear a definitive word from the FG staff as to the fate of my article.

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    Old Stuff

    You can check out my Master's thesis titled "On a sum of cubes of degrees of irreducible complex characters", over at the National Library of Canada. This thesis was supervised by John D. Dixon.

    Also, here is my old project from the Analytic Number Theory Course at Carleton University. You can download this project by clicking "Perfect Numbers and Abundancy Ratio".
   
    I would like to say that this project is more of a descriptive nature - no new results are proved, but a lot of the current results are compiled to provide a decent description of the area of study.

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© 2007 Yaroslav (Slava) Bezverkhnyev, a.k.a. Agarwaen
Last Update:     April 07, 2008