bio | website | |
---|---|---|
location | Iowa City, IA, USA | |
age | 56 | |
visits | member for | 4 years, 2 months |
seen | 58 secs ago | |
stats | profile views | 389 |
Primary Mathematical Interests:
(1) Study and use of negligible sets, especially involving porosity notions and fractal dimension notions.
(2) Application and refinements of the Baire category method for proving existence.
(3) Classical point set theory and real function theory.
(4) History of nowhere differentiable continuous functions and history of the topics above.
Aug
19 |
comment |
What results exist for functions with regionally fluctuant fractal dimension?
Something else possibly relveant: Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure by Guy David and Stephen Semmes (1997). See the review by Kenneth John Falconer and the Zbl 887.54001 review. |
Aug
18 |
comment |
What results exist for functions with regionally fluctuant fractal dimension?
Possibly relevant to what you're looking for: How can dimension depend on the point? |
Aug
10 |
awarded | Yearling |
Aug
10 |
answered | How can dimension depend on the point? |
Aug
3 |
comment |
How can dimension depend on the point?
It looks like it's going to take a few more days (I work full-time, and have more pressing "hobby math" things I'm in the middle of right now outside of work hours), but I'll definitely get something written this week. |
Jul
31 |
comment |
How can dimension depend on the point?
I can write something, but not until this weekend for posting on Monday. |
Jul
29 |
comment |
How can dimension depend on the point?
Lars Olsen published a paper back in 2005 that studies this -- Characterization of local dimension functions of subsets of ${\mathbb R}^{d}$, Colloquium Mathematicum 103 #2, pp. 231-239. (This comment is late because I didn't see your question until just now.) |
Jun
10 |
awarded | Necromancer |
Feb
18 |
awarded | Nice Answer |
Oct
6 |
comment |
The construction of the 257gon
See the paper by Wayne Bishop cited in Chapter 6 of my manuscript A Detailed and Elementary Solution to $x^{17} = 1$, as well as the 10 other references for the constructing the $257$-gon I give on pp. 46-47. |
Sep
24 |
awarded | Autobiographer |
Sep
23 |
comment |
Name of a difference of continuants
One place you might want to look is History of Continued Fractions and Padé Approximants by Claude Brezinski. |
Aug
19 |
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Is there an algebraic number that cannot be expressed using only elementary functions?
@Misha Verbitsky: Tito Piezas III's answer to the math StackExchange question Solving 5th degree or higher equations appears to give some information relating to your question. |
Aug
19 |
comment |
Condensation points of orbits of roots of unity
Are you sure "condensation point" is the concept you want? If the set $S$ is countable, there are no condensation points, unless you're using "condensation point" in a way that differs from its standard meaning. |
Aug
18 |
comment |
First Description of how to Remove Radicals from Equations
I don't really have an answer (hence the comment), but for some publications that are possibly worth looking at, see some of the older references I cite at the very end of this 16 November 2010 ap-calculus at Math Forum and see the references I give in my answer to the math StackExchange question History of the theory of equations: John Colson. |
Aug
6 |
answered | Name of a generalized version of semi-continuity |
Jul
21 |
comment |
Tools for Removing Radicals from Equations
The answers at the math StackExchange question Rationalizing radicals describe algebraic procedures you can use. It can be a bit tedious, but you can use these methods along with various on-line devices that multiply-out and combine like terms of factored algebraic expressions. In the case of the expression you gave, you can rewrite with a $0$ on one side and then multiply both sides by an appropriate rationalizing factor (see André Nicolas's answer and my answer in that StackExchange question). |
Jul
8 |
comment |
Are proper linear subspaces of Banach spaces always meager?
For a survey of related issues (Borel types of linear subspaces in infinite dimensional Banach spaces), see my answer to the math StackExchange question Does there exist a linearly independent and dense subset?. |
Jun
19 |
awarded | Necromancer |
May
27 |
comment |
Are norms intrinsically $\mathbb{R}$-valued?
On a lark I googled "Banach valued norm" and got some hits that deal with norm functions that have outputs in a Banach space (that does not have to be the reals). My initial impression is that this generalization is internally motivated (to write papers) rather than externally motivated in order to unify existing special cases. However, I didn't put any effort towards looking into this. |