505 reputation
310
bio website yume3.sourceforge.net
location MT
age 94
visits member for 3 years, 4 months
seen yesterday

Former pictures: Dakota puddles (prairie potholes), 2012-01-30; Yellowstone River icicles, 12 Dec 2011; Black-and-white ducks on YR, ca 6 Jan 2012; Eagle in eastwind snow, on south bank of YR, 15 Jan 2012; Sunlight & shadows on riverbottom, 5 Feb 2012; Duck in park puddle, June 2011; Trumpeter swan pair on YR, 13 Feb 2012; American Avocet on YR, 10 May 2012; Pelicans flying above YR, 24 June 2012, and pelican in YR, 16 May 2012; Rainbow above Livingston Peak, 23 July 2012; Rose/squirrel, 21 Nov 2012; old Bangalore station, Dec 2004; Bighorn sheep, Zion, 8 Nov 2013

Author of programs yume as seen here and qenqote as described here

qenqote automates URL-formatting editing and can minimize the amount of manual editing needed when you include a URL in a stackexchange post.


Nov
21
comment Is the function $f( x)=1/|x|^{1/2}$ Lipschitz continuous?
The stated $x_i$ don't work; eg if C = 1+e for small positive e, $|f(x_1)-f(x_2)| < C|x_1-x_2|$. However, $x_1 = \frac{1}{C^2}$ and $x_2 = \frac{1}{2C^2}$ work.
Nov
15
comment Percentage of primes among the natural numbers
@MartinSleziak Moose can un-accept one answer and accept a different one at any time, should he or she so desire.
Nov
15
comment Problem on Divide-and-Conquer Relation
Although you say "Each player who loses in the first round gets nothing", the problem says "a player who loses in the first round gets $100".
Nov
15
comment Counting walks on colored graphs
Can you explain your $3*2^{k−1}$ walks on k 3-colored vertices formula? At least at k=1 and k=2 the numbers appear to be twice as large; e.g {br, bg, gr, gb, rg, rb} at k=1, and {gbg, grg, gbr, grb, etc} at k=2.
Nov
14
comment Algorithms and Simulation
Were you given a definition of "optimal"? Or any limitations? (I.e. for (b) it looks like $\sigma^2=1$ should be optimal for the obvious def of optimal)
Oct
12
comment Find the minimum number of links to remove from digraph to make it acyclic
An acyclic graph contains no cycles at all, rather than merely a vertex that's not in a cycle.
Oct
11
comment Powers as a complete residue system modulo $p$?
Also see MSE question re the number of equivalence classes of (in notation of present question) $k^a\mod p$
Oct
10
comment How to express an irrational as a continued fraction in computer with high precision?
Rather than "up to 16 bits" being not quite right, it's totally wrong. Typical IEEE754 64-bit double-precision numbers use effectively 53 bits for mantissa, giving ~ 16 decimal digits accuracy. (15.95... = 53 * ln(2)/ln(10).)
Sep
19
comment Maximizing growth rate in betting on multiple events
Question 1: Suppose $b_{134}$ is the the fraction of stake $s$ that is bet on $\{1,3,4\}$. Suppose $t=b_{134}*s/3$. If events 1 and 3 win and event 4 loses, is the payoff equal to $(1+c_1+1+c_3)*t$ (that is, the amount $s*b_i$ spreads evenly across the elements of bet #$i$) or is it some other value? Question 2: Do all events in a set have to win to get a payoff? Question 3: Since all bets are simultaneous, there appears to be no "long run" to be concerned about, and no reason to act other than Charles suggested in his answer, right?.
Sep
19
comment Maximizing growth rate in betting on multiple events
Ok, let an $i$ be given. What events are elements of bet #$i$ ? Is the amount $b_i$ spread evenly across the elements of bet #$i$ ? Does bet #$i$ get paid off and its result reported to you before you make bet #$i+1$?
Sep
19
comment Maximizing growth rate in betting on multiple events
Is one allowed to bet on the same alternative multiple times? Is the order of bet payoffs specified? Is $b_i$ an amount bet on event $i$, or on some subset of the events?
Sep
10
comment Conditions on polygon to ensure equal interior angles or opposite sides
Yes, the negation of (c) is (c'), "not all opposite sides have equal lengths". Your comment re "if opposite sides are parallel then opposite angles are equal" becomes obviously true via another comment's suggestion to "draw the diagonal" (i.e. call upon Euclid's Proposition 29, "A straight line falling on parallel straight lines makes alternate angles equal to one another...").
Aug
22
comment Number of $k^p \bmod q$ classes when $q\%p > 1$
@awllower, the "q%p>1" part of the title was used as shorthand for "q != 1 mod p". The "number of classes" part refers to the number of equivalence classes, mod q, of k^p. How would you phrase it?
Aug
22
comment Number of $k^p \bmod q$ classes when $q\%p > 1$
thanks for the answer, @awllower. I agree with what you say, except that the theorem's last assertion is stronger than what I wanted to show -- it also characterizes the number of classes when q == 1 mod p. For my purposes (given p, finding q so that k^p falls into q-1 classes, so that computed numbers can quickly/efficiently be recognized as probable p'th powers) I don't care about that case, although other people could very well care about it.
Aug
15
comment Is it possible to efficiently factor a semiprime given a bit-permutation relating the factors?
@Charles, you are right, I apologize for that. I'm now going to edit the "n=#bits" references in my answer to "u=#bits" to reduce longer-term confusion.
Aug
15
comment Is it possible to efficiently factor a semiprime given a bit-permutation relating the factors?
Perhaps you wrote $n$ rather than $p$ in the above. $p$ is the prime being factored, $n$ is the number of bits in its binary representation. But your point is correct -- $O(1)$ is too pessimistic. If we suppose a modern method is $O(p^{1/3})$ and solve $p^{1/3} = 3^k$, we get $k\approx n\cdot{\ln2\over3\ln3}\approx0.21n$; so brute force is competitive for these numbers if no more than 42% of the bits change places.
Aug
14
comment Winning on Prize Bonds
@francis, the "squiggly equals" stands for approximately equal. The "upside down y" is a greek lambda, as commonly used for the parameter of a Poisson distribution. Re Binomial distribution and approximations to it, the Wikipedia page I linked to explains in detail; briefly, a Binomial dist. expresses the probability of getting k out of n flips to come up heads, with a given probability p for a head. Re "probability of success on one draw", I approximated a binomial by a geometric-probability ratio; the other answers don't make that approximation.
Aug
13
comment Number of $k^p \bmod q$ classes when $q\%p > 1$
@Jyrki, I'd like to think I was conversant with the techniques you mentioned, when I took number theory classes long ago. However, I've forgotten quite a lot. The straightforward and basic techniques of André's answer are more helpful to me, while I expect practicing mathematicians will prefer the conciseness of your hints.
Aug
13
comment Number of $k^p \bmod q$ classes when $q\%p > 1$
@Jyrki, I edited the question to take note of that error. Thanks!