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Alec Mihailovs

Dr. Aleksandrs Mihailovs

4495 Reputation

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20 years, 338 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 replies submitted by Alec Mihailovs

Simple Maplet example...

Alec Mihailovs 4495
August 29 2009
0 0

I have a simple Maplet example displaying a message inside it in case if the imput is incorrect, in my blog.

Alec

Simple Maplet example...

Alec Mihailovs 4495
August 29 2009

I have a simple Maplet example displaying a message inside it in case if the imput is incorrect, in my blog.

Alec

Extended Typesetting Level...

Alec Mihailovs 4495
August 29 2009
0 0

Robert Israel's suggestion works in Classic Maple and in Standard Maple with Extended Typesetting enabled. To do that, one can either click Tools, then Options, then Display, and change the 3rd line, Typesetting level, to Extended, or execute

interface(typesetting=extended);

I use Standard Maple quite rarely and get to know that from another Robert Israel's post.

Alec

Extended Typesetting Level...

Alec Mihailovs 4495
August 29 2009

Robert Israel's suggestion works in Classic Maple and in Standard Maple with Extended Typesetting enabled. To do that, one can either click Tools, then Options, then Display, and change the 3rd line, Typesetting level, to Extended, or execute

interface(typesetting=extended);

I use Standard Maple quite rarely and get to know that from another Robert Israel's post.

Alec

Rotate commands in Maple...

Alec Mihailovs 4495
August 28 2009
0 0

ListTools:-Rotate does that quite simple using Maple commands. StringTools:-Rotate is, probably, faster, because it uses external calling. The Bits package doesn't seem to have the Rotate command!

Alec

Rotate commands in Maple...

Alec Mihailovs 4495
August 28 2009

ListTools:-Rotate does that quite simple using Maple commands. StringTools:-Rotate is, probably, faster, because it uses external calling. The Bits package doesn't seem to have the Rotate command!

Alec

GetInput...

Alec Mihailovs 4495
August 28 2009
0 0

You could try Maplets:-Examples:-GetInput as well.

Ales

GetInput...

Alec Mihailovs 4495
August 28 2009

You could try Maplets:-Examples:-GetInput as well.

Ales

numpoints...

Alec Mihailovs 4495
August 28 2009
0 0

You may try to increase the number of points by adding something like numpoints=1000, or numpoints=10000 to the plot command.

Alec

numpoints...

Alec Mihailovs 4495
August 28 2009

You may try to increase the number of points by adding something like numpoints=1000, or numpoints=10000 to the plot command.

Alec

So why it doesn't work?...

Alec Mihailovs 4495
August 28 2009
0 0

So why it doesn't work? Do something like

if c=2 then 
    if Maplets:-Examples:-Alert("c=2. Quit?") #show the alert
        then return c=2 # for example, which stops 
# the program and returns c=2 if "OK" is pressed, and 
# continue calculations if "Cancel" is pressed.
    fi
fi;

Alec

So why it doesn't work?...

Alec Mihailovs 4495
August 28 2009

So why it doesn't work? Do something like

if c=2 then 
    if Maplets:-Examples:-Alert("c=2. Quit?") #show the alert
        then return c=2 # for example, which stops 
# the program and returns c=2 if "OK" is pressed, and 
# continue calculations if "Cancel" is pressed.
    fi
fi;

Alec

The distribution is not uniform...

Alec Mihailovs 4495
August 28 2009
0 0

The distribution is not uniform. For example, in case (0,10, 6, 2) there is only one solution [0,2,4,6,8,10]. In the (0,10, 6, 3) case  the set of all solutions can be found as

S:=map(y->ListTools:-PartialSums([0,op(y)]),
    select(x->max(x)<=3,combinat:-composition(10,5)));

  S := {[0, 1, 2, 4, 7, 10], [0, 1, 2, 5, 7, 10], [0, 1, 2, 5, 8, 10],

        [0, 1, 3, 4, 7, 10], [0, 1, 3, 5, 7, 10], [0, 1, 3, 5, 8, 10],

        [0, 1, 3, 6, 7, 10], [0, 1, 3, 6, 8, 10], [0, 1, 3, 6, 9, 10],

        [0, 1, 4, 5, 7, 10], [0, 1, 4, 5, 8, 10], [0, 1, 4, 6, 7, 10],

        [0, 1, 4, 6, 8, 10], [0, 1, 4, 6, 9, 10], [0, 1, 4, 7, 8, 10],

        [0, 1, 4, 7, 9, 10], [0, 2, 3, 4, 7, 10], [0, 2, 3, 5, 7, 10],

        [0, 2, 3, 5, 8, 10], [0, 2, 3, 6, 7, 10], [0, 2, 3, 6, 8, 10],

        [0, 2, 3, 6, 9, 10], [0, 2, 4, 5, 7, 10], [0, 2, 4, 5, 8, 10],

        [0, 2, 4, 6, 7, 10], [0, 2, 4, 6, 8, 10], [0, 2, 4, 6, 9, 10],

        [0, 2, 4, 7, 8, 10], [0, 2, 4, 7, 9, 10], [0, 2, 5, 6, 7, 10],

        [0, 2, 5, 6, 8, 10], [0, 2, 5, 6, 9, 10], [0, 2, 5, 7, 8, 10],

        [0, 2, 5, 7, 9, 10], [0, 2, 5, 8, 9, 10], [0, 3, 4, 5, 7, 10],

        [0, 3, 4, 5, 8, 10], [0, 3, 4, 6, 7, 10], [0, 3, 4, 6, 8, 10],

        [0, 3, 4, 6, 9, 10], [0, 3, 4, 7, 8, 10], [0, 3, 4, 7, 9, 10],

        [0, 3, 5, 6, 7, 10], [0, 3, 5, 6, 8, 10], [0, 3, 5, 6, 9, 10],

        [0, 3, 5, 7, 8, 10], [0, 3, 5, 7, 9, 10], [0, 3, 5, 8, 9, 10],

        [0, 3, 6, 7, 8, 10], [0, 3, 6, 7, 9, 10], [0, 3, 6, 8, 9, 10]

        }

Now,

sort(Statistics:-Tally([S[]]));

  [0 = 51, 1 = 16, 2 = 22, 3 = 28, 4 = 24, 5 = 24, 6 = 24, 7 = 28,

        8 = 22, 9 = 16, 10 = 51]

map(x->lhs(x)=rhs(x)*1000/51.,%);

  [0 = 1000.000000, 1 = 313.7254902, 2 = 431.3725490, 3 = 549.0196078,

        4 = 470.5882353, 5 = 470.5882353, 6 = 470.5882353,

        7 = 549.0196078, 8 = 431.3725490, 9 = 313.7254902,

        10 = 1000.000000]

That looks quite similar to the results obtained by a simulation.

Alec

The distribution is not uniform...

Alec Mihailovs 4495
August 28 2009

The distribution is not uniform. For example, in case (0,10, 6, 2) there is only one solution [0,2,4,6,8,10]. In the (0,10, 6, 3) case  the set of all solutions can be found as

S:=map(y->ListTools:-PartialSums([0,op(y)]),
    select(x->max(x)<=3,combinat:-composition(10,5)));

  S := {[0, 1, 2, 4, 7, 10], [0, 1, 2, 5, 7, 10], [0, 1, 2, 5, 8, 10],

        [0, 1, 3, 4, 7, 10], [0, 1, 3, 5, 7, 10], [0, 1, 3, 5, 8, 10],

        [0, 1, 3, 6, 7, 10], [0, 1, 3, 6, 8, 10], [0, 1, 3, 6, 9, 10],

        [0, 1, 4, 5, 7, 10], [0, 1, 4, 5, 8, 10], [0, 1, 4, 6, 7, 10],

        [0, 1, 4, 6, 8, 10], [0, 1, 4, 6, 9, 10], [0, 1, 4, 7, 8, 10],

        [0, 1, 4, 7, 9, 10], [0, 2, 3, 4, 7, 10], [0, 2, 3, 5, 7, 10],

        [0, 2, 3, 5, 8, 10], [0, 2, 3, 6, 7, 10], [0, 2, 3, 6, 8, 10],

        [0, 2, 3, 6, 9, 10], [0, 2, 4, 5, 7, 10], [0, 2, 4, 5, 8, 10],

        [0, 2, 4, 6, 7, 10], [0, 2, 4, 6, 8, 10], [0, 2, 4, 6, 9, 10],

        [0, 2, 4, 7, 8, 10], [0, 2, 4, 7, 9, 10], [0, 2, 5, 6, 7, 10],

        [0, 2, 5, 6, 8, 10], [0, 2, 5, 6, 9, 10], [0, 2, 5, 7, 8, 10],

        [0, 2, 5, 7, 9, 10], [0, 2, 5, 8, 9, 10], [0, 3, 4, 5, 7, 10],

        [0, 3, 4, 5, 8, 10], [0, 3, 4, 6, 7, 10], [0, 3, 4, 6, 8, 10],

        [0, 3, 4, 6, 9, 10], [0, 3, 4, 7, 8, 10], [0, 3, 4, 7, 9, 10],

        [0, 3, 5, 6, 7, 10], [0, 3, 5, 6, 8, 10], [0, 3, 5, 6, 9, 10],

        [0, 3, 5, 7, 8, 10], [0, 3, 5, 7, 9, 10], [0, 3, 5, 8, 9, 10],

        [0, 3, 6, 7, 8, 10], [0, 3, 6, 7, 9, 10], [0, 3, 6, 8, 9, 10]

        }

Now,

sort(Statistics:-Tally([S[]]));

  [0 = 51, 1 = 16, 2 = 22, 3 = 28, 4 = 24, 5 = 24, 6 = 24, 7 = 28,

        8 = 22, 9 = 16, 10 = 51]

map(x->lhs(x)=rhs(x)*1000/51.,%);

  [0 = 1000.000000, 1 = 313.7254902, 2 = 431.3725490, 3 = 549.0196078,

        4 = 470.5882353, 5 = 470.5882353, 6 = 470.5882353,

        7 = 549.0196078, 8 = 431.3725490, 9 = 313.7254902,

        10 = 1000.000000]

That looks quite similar to the results obtained by a simulation.

Alec

Great idea...

Alec Mihailovs 4495
August 28 2009
0 0

That's a great idea!

For larger n, k, and m, a direct formula for f may be faster. For example,

F:=(n,k,m)->add(binomial(k+1,i)*binomial(-k-1,n-k-m*i)*(-1)^(n-k-(m-1)*i),i=0..(n-k)/m):

time(f(500,200,40));
                                4.071

time(F(500,200,40));

                                  0.
f(500,200,40)-F(500,200,40);

                                  0

Alec

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