Report for 09.05.2012
1) Have finished writing my article. However, uniform convergence with respect to 'x' still remains unproven.
2) Tried do derive Dominici result. I found that Paley–Wiener theorem can help me with it.
Wednesday, September 5, 2012
Tuesday, September 4, 2012
Report for 09.03.12
Small report for today
Plans were
1) To study Abel's test for uniform convergence. Try to apply it to my series.
Studied. But Abel's test haven't allowed me to prove uniform convergence. There are a lot of another tests, but I'll try to prove it in another way. I guess that this way will be cumbersome and it will overblow my article. That isn't good. In any case I have to try.
2) Insert in article my recent results: uniform convergence with respect to parameter 'b' and absolute convergence of my series.
Done
3) Try to derive results of article [Dominici, 2011] with the help of my series.
I can't derive results of this article with the help of my series but there is a good news! It is very possible that I'll receive this result in much simpler way.
Plans for tomorrow:
I have no strength to write plans :)
Plans were
1) To study Abel's test for uniform convergence. Try to apply it to my series.
Studied. But Abel's test haven't allowed me to prove uniform convergence. There are a lot of another tests, but I'll try to prove it in another way. I guess that this way will be cumbersome and it will overblow my article. That isn't good. In any case I have to try.
2) Insert in article my recent results: uniform convergence with respect to parameter 'b' and absolute convergence of my series.
Done
3) Try to derive results of article [Dominici, 2011] with the help of my series.
I can't derive results of this article with the help of my series but there is a good news! It is very possible that I'll receive this result in much simpler way.
Plans for tomorrow:
I have no strength to write plans :)
Sunday, September 2, 2012
Well... My name is Andriy Andrusyk. I am a physicist from Ukraine. My blog will outline my scientific activity. I'll try to take notes on daily basis and hope that it will help me to control my performance.
So, I hope in some time my blog will serve as a my scientific portfolio.
Lets start.
I'm about to finish my article where I'll present my series expansions for Bessel function of integer order which were unknown until now. Yesterday I've proved absolute convergence of my series and proved their uniform convergence with respect to parameter 'b'. Besides that, I previously proved that my series are infinitely differentiable with respect to variable 'x'. Unfortunately, I still can't prove uniform convergence of my series with respect to variable 'x'. However, I hope it isn't necessary for publication and hope that my results are enough for being suitable for further studies and for applications.
My plans for several nearest days:
1) To study Abel's test for uniform convergence. Try to apply it to my series.
2) Insert in article my recent results: uniform convergence with respect to parameter 'b' and absolute convergence of my series.
3) Try to derive results of article [Dominici, 2011] with the help of my series. It will prove usefulness of my result. However, if my series fails this test it won't prove their useless. If I'll repeat result of that article - very good, if not - it does't matter.
So, I hope in some time my blog will serve as a my scientific portfolio.
Lets start.
I'm about to finish my article where I'll present my series expansions for Bessel function of integer order which were unknown until now. Yesterday I've proved absolute convergence of my series and proved their uniform convergence with respect to parameter 'b'. Besides that, I previously proved that my series are infinitely differentiable with respect to variable 'x'. Unfortunately, I still can't prove uniform convergence of my series with respect to variable 'x'. However, I hope it isn't necessary for publication and hope that my results are enough for being suitable for further studies and for applications.
My plans for several nearest days:
1) To study Abel's test for uniform convergence. Try to apply it to my series.
2) Insert in article my recent results: uniform convergence with respect to parameter 'b' and absolute convergence of my series.
3) Try to derive results of article [Dominici, 2011] with the help of my series. It will prove usefulness of my result. However, if my series fails this test it won't prove their useless. If I'll repeat result of that article - very good, if not - it does't matter.
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