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Alec Mihailovs

Dr. Aleksandrs Mihailovs

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20 years, 307 days
Mihailovs, Inc.
Owner, President, and CEO
Tyngsboro, Massachusetts, United States

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Contact Dr. Aleksandrs Mihailovs

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 answers submitted by Alec Mihailovs

Generate strings...

Alec Mihailovs 4455
October 17 2006
0 0
Also, StringTools package has Generate command that does exactly what you want (if you want strings), 
s:=StringTools:-Generate(3,"01");

    s := ["000", "001", "010", "011", "100", "101", "110", "111"]

printf("%s",<s[]>);

000
001
010
011
100
101
110
111

Get all of them...

Alec Mihailovs 4455
October 17 2006
0 2
Why should you choose Maple? Get all of them.

piecewise...

Alec Mihailovs 4455
October 17 2006
0 0 
f:=piecewise(0<t and t<Pi,sin(3*t),0):
f1:=convert(f,Heaviside);

      f1 := sin(3 t) Heaviside(t) - sin(3 t) Heaviside(-Pi + t)

plot(f,t=-1..4);
Similarly for another function.

See my blog entry...

Alec Mihailovs 4455
October 15 2006
0 4
In your example it can be done as simple as 
plots[implicitplot](x^2+y^2<1,x=-2..2,y=-2..2,filled=true);
Colors can be changed by using coloring option. For example, 
plots[implicitplot]((x-0.5)^2+(y-0.5)^2<1,x=-2..2,y=-2..2,filled=true,
coloring=[green,white]);
For more complicated cases see my blog entry How to Color a Region.

Unfortunately...

Alec Mihailovs 4455
October 15 2006
1 0
Unfortunately, pdsolve doesn't work with initial or boundary conditions - the problem is not in the syntax. The usual way is to find a general solution through pdsolve and apply initial and boundary conditions to it after that.

You have to do the steps manually...

Alec Mihailovs 4455
October 14 2006
0 0
You have to do the steps manually. For example, 
z = (1+y+y^2-y^3)/(1-y)^3;
                                      2    3
                             1 + y + y  - y
                         z = ---------------
                                       3
                                (1 - y)

%*denom(rhs(%));

                                    3           2    3
                      3     (-1 + y)  (1 + y + y  - y )
              (-1 + y)  z = ---------------------------
                                            3
                                     (1 - y)

normal(%);

                            3               2    3
                    (-1 + y)  z = -1 - y - y  + y

%-rhs(%);

                          3              2    3
                  (-1 + y)  z + 1 + y + y  - y  = 0

expand(%);

                             2      3            2    3
           -z + 3 z y - 3 z y  + z y  + 1 + y + y  - y  = 0

collect(%,y);

                  3               2
         (z - 1) y  + (-3 z + 1) y  + (3 z + 1) y - z + 1 = 0

solve(%,y); 
         
                       <Output omitted>

simplify(fnormal(evalf(subs(z=0.8,[%]))),zero);

             [-8.897926850, -0.05747450800, 1.955401358]

For example...

Alec Mihailovs 4455
October 14 2006
0 2
For example (in Standard Maple),
'R+``(`V&middot;c`) mod c = R mod c';

            R+``(`V·c`) mod c = R mod c;

Tangency points...

Alec Mihailovs 4455
January 19 2006
1 0
with(plots): p1:= contourplot( x*y, x=0..10, y=0..20, contours=20,color=green): p2:= contourplot((10-x)*(20-y)^2, x=0..10, y=0..20, contours=20, color=blue): p3:= plot(solve(implicitdiff(x*y,y,x)=implicitdiff((10-x)*(20-y)^2,y,x),y), x=0..10): display(p1,p2,p3);

maplestd2e.sty...

Alec Mihailovs 4455
January 17 2006
0 0
In Windows, I have maplestd2e.sty in the ETC folder. In Windows, this folder should be copied to the place where latex style files are located. With MiKTeX - to C:/localtexmf/tex/latex (with refreshing of fndb after that.)

For example...

Alec Mihailovs 4455
January 15 2006
0 0
For example, 
a:=sprintf("%a",evalf(exp(1)/10,100)):
select(isprime,[seq(parse(a[2..n]),n=2..100)]);

  [2, 271, 2718281, 27182818284590452353602874713526624977572470936\

        99959574966967627724076630353547594571]

A natural approach...

Alec Mihailovs 4455
January 14 2006
0 0
A natural approach would be seq(combinat:-fibonacci(n),n=1..10); 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Paint...

Alec Mihailovs 4455
January 13 2006
0 0
You don't need Sketch for that. In Windows, you can use Paint (or any other graphics editor) to draw a picture. Save it in a file, then in Maple click Insert - Image, find that file, and insert it.

For example...

Alec Mihailovs 4455
January 13 2006
0 0
For example, 
y:=proc(n)
option remember;
a + int(x * y(n-1), x)
end:
y(0):=a:

gfun:-guessgf(PolynomialTools:-CoefficientList(y(10),x),x)[1];

                            a*exp(x^2/2)

For example...

Alec Mihailovs 4455
January 13 2006
0 0
Building a sequence by adding element by element is one of the worst ways of doing that. Still, for this exercise it can be done as P:=NULL: for p while nops([P])<10 do P:=P, `if`(isprime(p),p,NULL) od: P; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

For example...

Alec Mihailovs 4455
January 04 2006
0 0
For example, 
op(2,x^2);

                                  2

degree(x^2,x);
                                  2
I don't exactly understand the second question. What are v0, v1, v2? The following does something similar to the request, 
coeffs(add(i,i=s)+add(i,i=p),[x,y]);

                  v1 + v2 + v0, 1 + b, 2 + c, 3 + a
v0, v1, and v2 are added, because they are considered to be constants. If they are considered to be variables, then the result is 
coeffs(add(i,i=s)+add(i,i=p),[x,y,v0,v1,v2]);

                     1 + b, 2 + c, 1, 1, 1, 3 + a
The requested answer can be obtained as follows, 
f:=p->selectremove(a->degree(a,[x,y])=0,p):

coeffs(add(i,i=f(s)[2])+add(i,i=f(p)[2]),[x,y]),
op(f(s)[1]),op(f(p)[1]);

                   1 + b, 2 + c, 3 + a, v1, v2, v0
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