Alec Mihailovs

Dr. Aleksandrs Mihailovs

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20 years, 335 days
Mihailovs, Inc.
Owner, President, and CEO
Tyngsboro, Massachusetts, United States

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I received my Ph.D. from the University of Pennsylvania in 1998 and I have been teaching since then at SUNY Oneonta for 1 year, at Shepherd University for 5 years, at Tennessee Tech for 2 years, at Lane College for 1 year, and this year I taught at the University of Massachusetts Lowell. My research interests include Representation Theory and Combinatorics.

MaplePrimes Activity


These are replies submitted by Alec Mihailovs

I didn't save the worksheet. I can reproduce it though. First,
s:=solve({tan(X/2) = Vt/Hr,trigsubs(tan(X))[3] = (V-Vt)/Hl},{Vt,X});

                      3          2
  s := {Vt = RootOf(_Z  Hr - V _Z  + (-2 Hl - Hr) _Z + V) Hr,

                              3          2
        X = 2 arctan(RootOf(_Z  Hr - V _Z  + (-2 Hl - Hr) _Z + V))}
So the solution can be obtained if we solve the cubic equation. Here is the procedure for finding trigonometric form of solutions of cubic equations,
TrigSol:=proc() local a0,a1,a2,i,Q,R,theta;
a0,a1,a2:=coeff(args,i)/coeff(args,3)/3$i=0..2;
Q:=sqrt(a2^2-a1);
R:=3/2*(a2*a1-a0)-a2^3;
theta:=arccos(R/Q^3);
2*Q*cos((theta+2*Pi*i)/3)-a2$i=-1..1
end:
Using it, find the solutions of the cubic equation in s,
simplify([TrigSol(op(indets(s,RootOf)[1]),_Z)],assume=positive);
Multyplying by Hr, we get the formula for Vt.
Scientific notation seems to be partially decimal,
0.1*10^10000;
                                         16
                          0.1000000000 10
evalf would be a usufel addition, so that one could do
evalf(Pi);
                             11.00100100
It can be done with convert/binary - but all the other operations, too. The default value of Digits could be set to, say, 30, instead of 10. By the way, it is interesting that (without using that package)
B:=a->convert(subsindets(a,numeric,x->convert(x,decimal,binary)),binary):
works for addition, multiplication and subtraction, but doesn't work for powers,
B(10101 + 1001);

                                11110
B((10001-1110)*111011);

                            1000010010001
B(10^10);

                             10000000000
It has an interesting effect on factorials,
B(10!);

                              1000000000
Can anybody guess B(11!)?
AFAIK, the standard positioning of the return address is between parameters and local variables, as in this picture. You could try to test a couple of simple procedures. First - with no arguments at all - just move something to the accumulator and see if it returns in Maple. Then - with 1 argument (and return something like that argument + 1). That should clarify some things. The worst thing that could happen - Maple's kernel shuts down, and it is not such a big deal. By the way, the object files in the zip files with my assembly examples, are in the COFF format, so they can be used directly in Linux for creating so files. If you used nasm instead of gas, masm source code also could be used practically without changes (or with a very slight ones). That's what I would do. Yes, I edited the post couple times - adding some comments in parentheses.
AFAIK, the standard positioning of the return address is between parameters and local variables, as in this picture. You could try to test a couple of simple procedures. First - with no arguments at all - just move something to the accumulator and see if it returns in Maple. Then - with 1 argument (and return something like that argument + 1). That should clarify some things. The worst thing that could happen - Maple's kernel shuts down, and it is not such a big deal. By the way, the object files in the zip files with my assembly examples, are in the COFF format, so they can be used directly in Linux for creating so files. If you used nasm instead of gas, masm source code also could be used practically without changes (or with a very slight ones). That's what I would do. Yes, I edited the post couple times - adding some comments in parentheses.
Same error.
The images are not that big, they are of 652x338 size - one can see them in my blog. I linked them from my web site. I just tried to attach them again and got the same error, Error attaching file 135_Maple1.png: exceeds maximum file size. That affects not only images, but other files, too - such as Binomial.zip that is only about 2 KB.
Perhaps, it can be copied from here.
This is an interactive session. I'll look for the help pages - there should be 3 of them in this demo. I'll add a screenshot with matrices, too - they look very nice.
Yes, that what I usually did - I created a special blog entry for that (with animation of 2 curves :) Worked OK until the time of my binomial coefficients mod 2 blog entry. Does attaching work for you now? Finally, I put the screenshots (and Binomial.zip) on my web site and linked them from there.
I made a few screenshots, but couldn't attach them - every time got an error: Exceeds maximum file size (each of them is a png file of size about 20 KB). Same as with my Binomial.zip file couple of days ago (that was about 2 KB size.)
Wow! Very impressive! Colors and graphics are much better than in the current command line version. Thank you for posting it. Alec
Another possibility would be to give "trusted users" such as Joe and me some moderator rights - at least for our own posts.
It was already replied - before me. Otherwise I would just send you a private message. I'd also like to be able to edit all of my posts - not just the first one in a thread.
I just noticed that yesterday - I din't notice that when I read that first time. That's another example when comment editing possibility would be very helpful.
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