Alec Mihailovs

Dr. Aleksandrs Mihailovs

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20 years, 176 days
Mihailovs, Inc.
Owner, President, and CEO
Tyngsboro, Massachusetts, United States

Social Networks and Content at Maplesoft.com

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

@Alejandro Jakubi 

Java is more or less steadily losing its poularity, but is far from being dead yet. In fact, according to TIOBE index, it has returned to the 1st position in popularity.

Maple is listed there between #51 and #100 by the way.

Looking at the picture there, if it was a subject of trading (like stocks), I would never buy any Java stocks - it's like catching a falling sword. I would certainly invest in C#.

Alec

There are some people who were not Maplesoft employees when they started posting on this site, and became Maplesoft employees later.

Also, the inverse situation is possible - when somebody stopped working at Maplesoft, but continue posting here.

It would be logical to mark only those of their posts when they worked at Maplesoft, and leave their other posts unmarked.

Alec

@longrob 

I agree.

@Christopher2222 

Perhaps, at least manually, by changing the values of derivatives at points 9 and 10, given by df.

There might be a better way of calculating the suggested derivatives than I did in df.

Alec

@hirnyk 

Yes, that's true. For matrices not fitting on a page, the browser is a better option.

However, for matrices fitting on the page, it is better to see them on that page, I think.

That's why I typed 25 instead of infinity. With a size not greater than 25, the matrix usually fits on the page, and for larger sizes the replacement is printed instead, which can be used for browsing as you correctly stated in another answer.

Alec

@hirnyk 

Yes, that's true. For matrices not fitting on a page, the browser is a better option.

However, for matrices fitting on the page, it is better to see them on that page, I think.

That's why I typed 25 instead of infinity. With a size not greater than 25, the matrix usually fits on the page, and for larger sizes the replacement is printed instead, which can be used for browsing as you correctly stated in another answer.

Alec

The Jacobian determinant is a kind of a derivative of (x,y) over (u,v), which is 1/3 (up to the sign) in this example. Also, the usual way of defining and using an expression in Maple is f:= u^4/sqrt(v) and then int(f*... with f instead of f(u,v).

Alec

The Jacobian determinant is a kind of a derivative of (x,y) over (u,v), which is 1/3 (up to the sign) in this example. Also, the usual way of defining and using an expression in Maple is f:= u^4/sqrt(v) and then int(f*... with f instead of f(u,v).

Alec

@LijiH 

Yes, built-ins are in the Maple kernel written in C, not in the Maple libraries written in Maple code.

showstat(`*`);
Error, (in showstat) cannot debug built-in functions

You could try the define command for defining non-commutative operations.

Alec

@LijiH 

Yes, built-ins are in the Maple kernel written in C, not in the Maple libraries written in Maple code.

showstat(`*`);
Error, (in showstat) cannot debug built-in functions

You could try the define command for defining non-commutative operations.

Alec

@longrob 

Sure, just requires some manual adjusting, adding derivative values, for instance, and second derivatives may be added etc. - there are many examples in the Mathematica help - it has options Method->Spline, which produces a more smooth looking curve, Method->Hermite etc. 

On the other hand, for such irregularly oscillating data as in this particular example, a simple line graph (not smooth) - i.e. just connecting the points with line segments, gives, maybe, even better idea about what is happening - and it can be easily done in Maple using plot; maybe with adding moving average, which is available in the Statistics package in Maple if I recall correctly - I'll check it later.

Alec

@longrob 

Sure, just requires some manual adjusting, adding derivative values, for instance, and second derivatives may be added etc. - there are many examples in the Mathematica help - it has options Method->Spline, which produces a more smooth looking curve, Method->Hermite etc. 

On the other hand, for such irregularly oscillating data as in this particular example, a simple line graph (not smooth) - i.e. just connecting the points with line segments, gives, maybe, even better idea about what is happening - and it can be easily done in Maple using plot; maybe with adding moving average, which is available in the Statistics package in Maple if I recall correctly - I'll check it later.

Alec

@Alejandro Jakubi 

Yes, I've realized that it is a function just after copying that (from a Classic worksheet) and pasting here - there was no a space between x and the parenthesis, and if it was a product, there would be a space. I thought that something fishy was there, but didn't pursue that thought being distracted by something else.

Alec

Look at the points (2,2,0) and (-2,-2,0). They belong to both cylinders, so they belong to their intersection. If they were inside a sphere, the diameter of that sphere would be not less than the distance between them which is 4*sqrt(2), but only spheres with a diameter not greater than 4 can fit inside a cylinder of radius 2. Is that a good enough proof?

Another proof (geometrical). The intersection of the 1st cylinder with the xy-plane is the part of that plane between lines x=2 and x=-2. The intersection of the 2nd cylinder with the xy-plane is the part of that plane between lines y=2 and y=-2. So the intersection of the solid in question with the xy-plane is the intersection of these 2 bands which is the square with vertices (±2, ±2). But intersections of a sphere with any plane can be empty,  a point, or a circle - it can't be a square. So that solid (or its boundary) can't be a sphere.

For a plot take a look on the intersection of a vertical line x=x0, y=y0 with the first cylinder, it is a segment between z=-sqrt(4-x0^2) and z=sqrt(4-x0^2). Similarly, its intersection with the second cylinder is a segment between z=-sqrt(4-y0^2) and z=sqrt(4-y0^2). The intersection of these 2 segments is the segment from z=-min(sqrt(4-x0^2), sqrt(4-y0^2)) to z=min(sqrt(4-x0^2), sqrt(4-y0^2)). I've just slightly simplified that for less typing in the plot definition.

_______________
Alec Mihailovs, PhD

Look at the points (2,2,0) and (-2,-2,0). They belong to both cylinders, so they belong to their intersection. If they were inside a sphere, the diameter of that sphere would be not less than the distance between them which is 4*sqrt(2), but only spheres with a diameter not greater than 4 can fit inside a cylinder of radius 2. Is that a good enough proof?

Another proof (geometrical). The intersection of the 1st cylinder with the xy-plane is the part of that plane between lines x=2 and x=-2. The intersection of the 2nd cylinder with the xy-plane is the part of that plane between lines y=2 and y=-2. So the intersection of the solid in question with the xy-plane is the intersection of these 2 bands which is the square with vertices (±2, ±2). But intersections of a sphere with any plane can be empty,  a point, or a circle - it can't be a square. So that solid (or its boundary) can't be a sphere.

For a plot take a look on the intersection of a vertical line x=x0, y=y0 with the first cylinder, it is a segment between z=-sqrt(4-x0^2) and z=sqrt(4-x0^2). Similarly, its intersection with the second cylinder is a segment between z=-sqrt(4-y0^2) and z=sqrt(4-y0^2). The intersection of these 2 segments is the segment from z=-min(sqrt(4-x0^2), sqrt(4-y0^2)) to z=min(sqrt(4-x0^2), sqrt(4-y0^2)). I've just slightly simplified that for less typing in the plot definition.

_______________
Alec Mihailovs, PhD

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