Alec Mihailovs
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Jackson, TN 38305
E-mail:
Alec@Mihailovs.com

[New] Meanwhile, I am looking for a job. Here is my vita (slightly outdated, but I hope to update it eventually.)
[New] Maple Wiki.
[New] I won the Maple Mentor Award for May 2008.
[New] Day of the Week Calculator (a JavaScript example).
[New] I am participating in Al Zimmermann's programming contest.
[New] magic_square Python package.
[New] W. Edwin Clark, Xiang-dong Hou, Alec Mihailovs, The Affinity of a Permutation of a Finite Vector Space, Finite Fields and Their Applications, Vol. 13, Issue 1, p. 80-112 (2007).
[New] I started a blog at MaplePrimes. Since I don't use Maple anymore, it is closed now. It still should contain a lot of useful code - unless it was deleted (as it happened with my web pages at UPenn, Oneonta, Shepherd, and TTU.) Here is a link to my other posts there.
[New] My photo at the OEIS 100K party (smoking section).
[New] I added a few sequences, A066947, A094870, A095689, A095690, A095922, A097467, A109783, A109795 and a few comments, A002426, A002720, A003313, A005700, A005802, A007754, A007865, A010892, A047888, A058797, A059710, A070965, A075618, A084745, A084746, A087659, A094876, A094943, A095238, A096825, A097465, A103974, A104237, A109032, A109467, A110772, A110794, A125033 to The On-Line Encyclopedia of Integer Sequences.
[New] My old article On the log-concavity published in `Kvant' in 1993 was published online.
[New] Writing DLL in Assembler for External Calling in Maple, 17 p. (2004). It is also available in the pdf (106 KB) and doc (127 KB) formats. Here are the binaries, assembler code, and Maple worksheet, zipped (19 KB). It was published as TTU Department of Mathematics Technical Report No. 2004-5 and in the Maple Programming section of the Maple Application Center.
[New] Eric W. Weisstein added my formula (46) for Fibonacci numbers to his Fibonacci Number page in Mathworld.
[New] On April 20, 2004, I gave a colloquium talk, The Art of Calculations at Gettysburg College.
[New] New Quotations page.
[New] New Math-Net, Research Groups, Preprints / Publications, Projects, Software Development pages.
[New] Alec Mihailovs, A Combinatorial Approach to Representations of Lie Groups and Algebras, Springer-Verlag New York (2003), Price $69.95, 352 pages , 6 1/8 x 9 , hardcover, ISBN: 0-8176-4251-X.
[New] My talk at the Baltimore's Joint Mathematics Meetings is scheduled on Thursday, January 16, 2003, 11:15 am, in the AMS Session on Group Theory. Title of the talk: Wave graph bases of tensor invariants of SO(2n+1) and G2. Here is the abstract.
[New] My Maple Programs for Binary Tensor Invariants and Outerplanar Graphs. Here is the Maple Worksheet (3.1 MB) and the zipped Maple worksheet (540 KB).
[New] My Errata for the Maple programs accompanying Numerical Methods by Faires and Burden, 2nd ed.
[New] New Maple page
[New] My 'Abstract Algebra with Maple' manual (see below) became available as the Abstract Algebra Powertool from the Maple Application Center, with additional lectures by Fr. Mike May.
[New] Slides from my February 12, 2002 talk at Duke's Algebraic Geometry Seminar, 'Wave Graph Bases of Tensor Invariants'. The abstract is here.
[New] Abstract Algebra with Maple, my Maple manual intended to be used with Contemporary Abstract Algebra, by J. A. Gallian, 5th ed., Houghton Mifflin (2002). It is available from my Shepherd's Abstract Algebra course page as html, doc, color pdf with links and bookmarks, and black and white pdfwithout links or bookmarks, also as a Maple 6 worksheet, Maple 7 worksheet, Maple 6 worksheet with removed output, Maple 7 worksheet with removed output, and a Microsoft Reader e-book. It is also available as the Abstract Algebra Powertool from the Maple Application Center with additional lectures by Fr. Mike May.
[New] Problem of the week
[New] Problem Solutions
[New] Problem of the Week links
[New] More Problem of the Week links
[New] Math Club
[New] Mathematical Competitions
[New] My Mathematical Ancestors
[New] Links to my pages
[New] Maple Programs for my Logic Design class.
[New] Java Applets and Maple Programs for my Probability class.
[New] The Orbit Method for Finite Groups of Nilpotency class Two of Odd Order (dvi), 16 pages, January 16, 2000.
    First, I construct an isomorphism between the categories of(topological) groups of nilpotency class 2 with 2-divisible center and(topological) Lie rings of nilpotency class 2 with 2-divisible center. Thatisomorphism allows us to construct adjoint and coadjointrepresentations as usual. For a finite group G of nilpotency class 2 of oddorder, I construct a basis in its group algebra C[G],parameterized by elements of g* so that the elements of coadjoint orbits form bases of simple two-side ideals of C [G]. That construction gives us a one-to-one correspondence between G-orbits in g* and classes of equivalence of irreducible unitary representations of G, implying a very simple character formula. The properties of that correspondence are similar to the properties of the analogous correspondence given by Kirillov's orbit method for nilpotent connected and simply connected Lie groups. The diagram method introduced in my thesis, gives us a convenient way to study normal forms on the orbits and corresponding representations.
New Aleksandrs Mihailovs. The Orbit Method for Finite Groups (October 5, 1999). Was presented on Wednesday, January 19, 2000, from 5:30 pm to 5:40 pm. at the AMS Session on Group Theory at the Joint AMS/MAA Meetings in Washington, DC, January 19–22, 2000.
    For a finite nilpotent group G, I define (by an inductive procedure) a finite G-module g* such that there is a one-to-one correspondence between G-orbits in g* and classes of equivalence of irreducible unitary representations of G. The properties of that correspondence are similar to the properties of the analogous correspondence given by Kirillov's orbit method. For instance, if G is the group of the upper-triangular unipotent n×n matrices with coefficients from a finite ring A, one can choose the additive group of lower-triangular nilpotent n×n A-matrices as g*, defining the action of G in g* the same way as Kirillov did in his classical article. Using diagram method introduced in my thesis, one can classify normal forms on the orbits and corresponding representations.I discuss the generalization of that construction for other classes of groups as well. In particular, for symmetric groups all the theory looks completely different from the standard approach.
New My Shepherd's page (Best viewed in Microsoft Internet Explorer):
New My Oneonta's page:

Photos

I was married on May 18, 1996 in Groton, MA to the love of my life Bette .I have made photos of our Wedding and Honeymoon available to anyone interested,they are numbered 1 through 144. To view them it is necessary that youclick on each number individually.

1 ~ 2~ 3 ~ 4~ 5 ~ 6~ 7 ~ 8~ 9 ~ 10~ 11 ~ 12~ 13 ~ 14~ 15 ~ 16~ 17 ~ 18~ 19 ~ 20~ 21 ~ 22~ 23 ~ 24~ 25 ~ 26~ 27 ~ 28~ 29 ~ 30~ 31 ~ 32~ 33 ~ 34~ 35 ~ 36~ 37 ~ 38~ 39 ~ 40~ 41 ~ 42~ 43 ~ 44~ 45 ~ 46~ 47 ~ 48~ 49 ~ 50~ 51 ~ 52~ 53 ~ 54 ~ 55~ 56 ~ 57 ~ 58~ 59 ~ 60 ~ 61~ 62 ~ 63 ~ 64~ 65 ~ 66 ~ 67~ 68 ~ 69 ~ 70~ 71 ~ 72 ~ 73~ 74 ~ 75 ~ 76~ 77 ~ 78 ~ 79~ 80 ~ 81 ~ 82~ 83 ~ 84 ~ 85~ 86 ~ 87 ~ 88~ 89 ~ 90 ~ 91~ 92 ~ 93 ~ 94~ 95 ~ 96 ~ 97~ 98 ~ 99 ~ 100~ 101 ~ 102 ~ 103~ 104 ~ 105 ~ 106~ 107 ~ 108 ~ 109~ 110 ~ 111 ~ 112~ 113 ~ 114 ~ 115~ 116 ~ 117 ~ 118~ 119 ~ 120 ~ 121~ 122 ~ 123 ~ 124~ 125 ~ 126 ~ 127~ 128 ~ 129 ~ 130~ 131 ~ 132 ~ 133~ 134 ~ 135 ~ 136~ 137 ~ 138 ~ 139~ 140 ~ 141 ~ 142~ 143 ~ 144

Links

[New] Mihailovs, Inc.
[New] Bette's Books
Ruler

Updated on July 8, 2008.

Copyright © 1996–2008 Alec Mihailovs Email