c********n
发帖数: 221 | 1 毛驴，你是不是自己也觉得不好意思然后走了？ 呵呵，就留下来继续骂嘛。底线还秀
的不够。
[20:05:02]crushjapan 进入拖拉机普通房间
[20:05:31]Macrostrong 退出游戏请求通过
[20:06:17]krsxcv 强制退出游戏
[20:06:34]PeterLi330离开房间
[20:07:01]taobaobao 进入拖拉机普通房间
[20:07:12]firstsunray:重选游戏版版主吧，不然没希望了
[20:07:14]firstsunray:重选游戏版版主吧，不然没希望了
[20:07:15]firstsunray:重选游戏版版主吧，不然没希望了
[20:08:01]outhere被请出房间
[20:08:25]summer83 进入拖拉机普通房间
[20:08:46]summer83离开房间
[20:08:49]summer83 进入拖拉机普通房间
[20:09:00]crushjapan:就是你小毛驴
[20:09:15]crushjapan:你滚蛋了这儿才消停
[20:09:40]firstsunray:我没把游戏版搞死啊
[20:09... 阅读全帖 |
|
c********n
发帖数: 221 | 2 毛驴，你是不是自己也觉得不好意思然后走了？ 呵呵，就留下来继续骂嘛。底线还秀
的不够。
[20:05:02]crushjapan 进入拖拉机普通房间
[20:05:31]Macrostrong 退出游戏请求通过
[20:06:17]krsxcv 强制退出游戏
[20:06:34]PeterLi330离开房间
[20:07:01]taobaobao 进入拖拉机普通房间
[20:07:12]firstsunray:重选游戏版版主吧，不然没希望了
[20:07:14]firstsunray:重选游戏版版主吧，不然没希望了
[20:07:15]firstsunray:重选游戏版版主吧，不然没希望了
[20:08:01]outhere被请出房间
[20:08:25]summer83 进入拖拉机普通房间
[20:08:46]summer83离开房间
[20:08:49]summer83 进入拖拉机普通房间
[20:09:00]crushjapan:就是你小毛驴
[20:09:15]crushjapan:你滚蛋了这儿才消停
[20:09:40]firstsunray:我没把游戏版搞死啊
[20:09... 阅读全帖 |
|
m******n
发帖数: 6327 | 3 ☆─────────────────────────────────────☆
DuGu (火工头陀) 于 (Mon Nov 10 14:11:17 2008) 提到:
Does it look more like "TRAP"?
"The Fed's lending is significant because the central bank has stepped into
a rescue role that was also the purpose of the $700 billion Troubled Asset
Relief Program, or TARP, bailout plan -- without safeguards put into the
TARP legislation by Congress."
☆─────────────────────────────────────☆
wyoming1801 (SEAN) 于 (Mon Nov 10 15:13:42 2008) 提到:
it was drafted in a hurry t |
|
t*******u
发帖数: 1 | 4 Can someone help me on this. My H-1 petition was just approved, but the
validity starts at Feb 1st 2004, which is not the date specified on my
petition. My lawyer put July 1st 2004. I don't want to start so early for tax
reasons. Is there any way to change the starting date? My lawyer is really
lame and didn't help me much.
I used premium services so I got an email and phone number for INS customer
service. Is this useful?
Thanks for your help. I appreciate.
DuGu |
|
D**u
发帖数: 204 | 5 【 以下文字转载自 Texas 讨论区 】
发信人: DuGu (火工头陀), 信区: Texas
标 题: Big Bend National Park 游记
发信站: BBS 未名空间站 (Tue Sep 3 20:26:04 2013, 美东)
长周末闲来无事，决定出去开车兜兜风，开的远点儿来个road trip，别把一个周末在
家都浪费掉了。去哪儿呢，因为还从来没有去过Big band national park, 于是就把它
初定为目的地。上网做了点调查，才发现因为天热现在是淡季，没什么人去。一看天气
预报那里周末都是90多度，想想别去了把自己烤糊了，有些打起了退堂鼓。但转念一想
，最初不就是想兜风来个road trip吗，所以公园如果热得没法呆，最差就兜个圈开回
来呗。于是上网定旅店，结果虽说淡季却在离公园比较近的Alpine订不到房间，只能在
远一些的Fort Stockton定到，离公园有100迈多，定了一夜。
（一）第一天，上路，8/31
去旅馆的路沿着I-10有500多迈约七个小时路程，但没有旅游任务，所以早上也就没有
急着出门。结果刚要上路，发现车差点儿没打起... 阅读全帖 |
|
D**u
发帖数: 204 | 6 【 以下文字转载自 Science 讨论区 】
发信人: DuGu (火工头陀), 信区: Science
标 题: 矩阵趣题
发信站: BBS 未名空间站 (Fri Sep 7 20:05:00 2007)
Suppose x_1,...,x_n are n positive numbers, prove that the n*n matrix
(1/(x_i+x_j)) (1<=i,j<=n) is positive definite.
Background: this is called Cauchy matrix, and the determinant can be
directed
computed (ref: http://en.wikipedia.org/wiki/Cauchy_determinant ).
What I am asking is: can you still prove the problem by not using
any polynomial-factoring method. Probabilistic/statistical method |
|
v**i
发帖数: 50 | 7 smx的证明思路很有问题，虽然我没看懂，但是感觉90%是错的。DuGu的证明很漂亮, 不
过既然funnystory还没看懂，我就来多句嘴... 因为距离 |x-y|,固定$y$, 作为$x$ 的
一个函数, is a convex function. 这个证明起来不难, 不失一般性, 假设 $y=0$. 这
样我们就需证明
|(x1+x2)/2|<(|x1|+|x2|)/2. 这其实就是三角不等式嘛... |
|
D**u
发帖数: 204 | 8 【 以下文字转载自 Quant 讨论区 】
发信人: DuGu (火工头陀), 信区: Quant
标 题: Partition R^3 into a union of circles
发信站: BBS 未名空间站 (Fri Dec 4 13:30:22 2009, 美东)
Question:
Can you partition a 3-dim Euclidean space R^3 into a union of a set of
circles. Namely, for every point A in R^3, A is on 1 and only 1 circle from
the set. |
|
D**u
发帖数: 204 | 9 【 以下文字转载自 Quant 讨论区 】
发信人: DuGu (火工头陀), 信区: Quant
标 题: 来一道题(由 BT question 而想)
发信站: BBS 未名空间站 (Sat Mar 6 14:46:26 2010, 美东)
On a 2-dim plane, F is a (real number valued) function on each polygon area
P. We also know that if P is the union of 2 disjoint polygon areas P1 and P2
, then
F(P) = F(P1) + F(P2).
Question: if for every rectangle D (no need to be parallel to x-y axis) we
have F(D) = 0, does that imply that F(P) = 0 for every polygon area P? |
|
D**u
发帖数: 204 | 10 【 以下文字转载自 Physics 讨论区 】
发信人: DuGu (火工头陀), 信区: Physics
标 题: 一个关于狭义相对论的小题目
发信站: BBS 未名空间站 (Thu Dec 1 19:11:21 2011, 美东)
打着相对论的幌子，实际上是个数学题目，呵呵。
题目：
现有 x,y,z 三个正类时矢量 (positive time-like vector),
|.| 表示矢量长度。求证：
（1） |x+y| >= |x| + |y|
(2) |x+y| + |y+z| + |x+z| >= |x|+|y|+|z|+|x+y+z| |
|
b***k
发帖数: 2673 | 11 ☆─────────────────────────────────────☆
spellscroll (spellscroll) 于 (Sat Oct 4 16:29:17 2008) 提到:
http://spellscroll.com/questionfull/4/
三赌徒问题
最先由spellscroll提交 | 被2人收藏 | 标签: random_walk(1) gambling(1)
probability(1)
三个赌徒聚赌，赌本分别为a,b,c元每轮只有一位赌徒获胜，胜者从另外二人
那里各收取一元,赌局持续到某一位赌徒输光为止。假设每轮每位赌徒获胜
概率均为1/3,问期望轮数?
☆─────────────────────────────────────☆
talkdirty (讲脏话) 于 (Sat Oct 4 17:03:11 2008) 提到:
你网站上的题大部分都没答案么?
☆─────────────────────────────────────☆
DuGu (火工头陀) 于 (Sat Oct 4 17:46:50 200 |
|
b***k
发帖数: 2673 | 12 ☆─────────────────────────────────────☆
ludouya (豆芽菜) 于 (Thu Oct 2 09:50:26 2008) 提到:
Find the diameter of the middle circle, given the diameter of the three
outer circle as 1,2,3.
图就是三个不同大小的圆挤在一起围成一圈,中间再夹着一个更小的圆.
忘了应该用一个什么定理了? 大虾们帮帮忙.谢谢!!!
☆─────────────────────────────────────☆
Thebluesky (蓝色的天空) 于 (Thu Oct 2 10:23:50 2008) 提到:
设ABC为三大圆的圆心,他们围成的三角形的面积*2/周长就是小圆的半径.
☆─────────────────────────────────────☆
DuGu (火工头陀) 于 (Thu Oct 2 11:36:39 2008) 提到:
It can be solved using Inver |
|
b***k
发帖数: 2673 | 13 ☆─────────────────────────────────────☆
jsyzghan (谦虚) 于 (Fri Apr 17 15:41:18 2009) 提到:
Given a 3x3 square:
1 2 3
4 5 6
7 8 9
You are allowed to do circular shift on any row, and
circular shift on any column, as many times as you
please. Question: can you switch position of 1 and 2 with
the allowed circular shifts?
☆─────────────────────────────────────☆
DuGu (火工头陀) 于 (Fri Apr 17 22:25:09 2009) 提到:
The 2nd and the last square in your post is the same :-(
☆────────────────────────────── |
|
D**u
发帖数: 204 | 14 【 以下文字转载自 Mathematics 讨论区 】
发信人: DuGu (火工头陀), 信区: Mathematics
标 题: 来一道题
发信站: BBS 未名空间站 (Thu Oct 22 11:18:45 2009, 美东)
Let {x_1,...,x_n} be n distinct positive real numbers;
{y_1,...,y_n} be n distinct positive real numbers;
and x_i*x_j is not equal to y_k*y_l for any i,j,k,l.
Question:
(1) you can reorder x_i to z_1,...,z_n, such that
(z_i*_z_j - y_i*y_j)(z_i-z_j)(y_i-y_j) > 0 for any distinct i and j.
(2) Is the reordering in (1) unique |
|
p*****k
发帖数: 318 | 15 DuGu, nice problem. my little grumble however is that the problem was inspired by the "solution" and you could have given us some hint...
btw, blaze, i am not sure from your later post whether your approach is fixable? |
|
D**u
发帖数: 204 | 16 【 以下文字转载自 Mathematics 讨论区 】
发信人: DuGu (火工头陀), 信区: Mathematics
标 题: spherical random walk
发信站: BBS 未名空间站 (Wed Nov 4 15:15:16 2009, 美东)
A guy starts walking from position x_0 on earth (we treat earth as a sphere
with radius R). He randomly chooses a direction and walk 1 meter (this is
the spherical distance) and reaches position x_1. He repeats the walk n
times and arrives at position x_n.
Question:
(1) what is E((x_n - x_0)^2)? (here ((x_n - x_0)^2 is the square of the
Euclidean distance, not t |
|
p*****k
发帖数: 318 | 17 i agree with you guys' result.
DuGu, here is a copy of the paper. not sure if it's helpful though:
http://ifile.it/p56kcvz |
|
p*****k
发帖数: 318 | 18 not sure what exactly DuGu had in mind, but im guessing that
he wants the radii of these circles nonzero and bounded.
otherwise, e.g., the infinite str8 line R could be considered
as a circle with infinite radius:
(x-R)^2+y^2=R^2 with R->infty |
|
J**********g
发帖数: 213 | 19 I am not sure of what kind of problem I should regard it at, I mean, a
brainteaser, a math one, or whatever.
Problem reduction.
1. R^3=R*R^2 can be dealed in Dugu's way. but you don't know how to
deal with the axis/center line, ie, how would map a line into a set of
separate circles.
or
2. R^3=R^2*R, ie, If a line could be mapped into a set of circles,
then so is R^3: R^3 is the set of lines indexed by (a,b), ie,
R^3={(a,b,x) with x varies in R, ie, the real line | (a, b) belong to R^2}
It's obv |
|
J**********g
发帖数: 213 | 20 Let's take r=1 in your original post to consist with the link provided by DuGu. Using that graph, if it's what you meant, suppose those two points that you
choose are all on x-axis as shown in the graph, ie, those points should be 0
,2,4,etc, then do you have a sphere with radius .5 as one of your sphere? If
yes, this sphere would cut the first black cicle (the one closest to origin
from right in the graph) in the first and fouth quadrants. Similarly, if
you contain sphere with radius 0 |
|
A****s
发帖数: 129 | 21 I can't get you at all.
At very least,
How could a sphere intersect another circle at more than 3 points?
If so, this circle belongs to this sphere, I think? Since both the circle
and the plane which cut the sphere are fixed.
Can you give an example where a sphere intersects a circle at more than 3
points but this circle is not part of this sphere?
DuGu. Using that graph, if it's what you meant, suppose those two points
that you
0
If
origin
black |
|
p*****k
发帖数: 318 | 22
DuGu, that is a very nice proof. thx.
inspired by the official solution, here is another choice of the
"black circles" (i.e., the family of circles on R^2 in Allens's post):
(x-r/2)^2 + y^2 = (n*r-r/2)^2, where n is a natural number. |
|
|
D**u
发帖数: 204 | 24 【 以下文字转载自 Mathematics 讨论区 】
发信人: DuGu (火工头陀), 信区: Mathematics
标 题: Ordering a sequence (2)
发信站: BBS 未名空间站 (Wed Dec 16 12:17:39 2009, 美东)
Let x1,...xn,y1,...,yn be 2n distinct real numbers, and xi+xj is not equal
to yk+yl for any i,j,k,l.
Prove that you can properly reordering x1,...,xn to z1,...zn, such that
(zi + zj - yi - yj)*(zi - zj)*(yi - yj) > 0
for all i and j. |
|
|
|
p*****k
发帖数: 318 | 27 DuGu, since both the area and the function are additive,
cannot we just use the Riemann sum definition of the area:
F(P)=F(sum dx dy)=sum F(dx dy)=0
then take limit? am i missing anything subtle? |
|
p*****k
发帖数: 318 | 28
DuGu, i see - sorry that was a naive argument.
here are some thoughts based on what ppl have discussed so far:
since every polygon can be triangulated, and every triangle can be
decomposed into two right triangles, it suffices to prove this
"measure function" vanishes for all right-angled triangles.
now take the middle points of each side, along with the right-angled
vertex. this forms a rectangle; the rest are two similar triangles
of half of the original size. by repeating this, the origina |
|
p*****k
发帖数: 318 | 29 DuGu, thanks for the hint. one thing i could think of is to use
contour integral (or in general, line integral), though i have
no idea what could vanish for an arbitrary rectangular contour,
while nonzero for some other particular contour.
(or in terms of the line integral, a field not doing work for
rectangular paths, but not for some other paths) |
|
p*****k
发帖数: 318 | 30 DuGu, very nice construction.
is it possible to extend to curved contours? |
|
p*****k
发帖数: 318 | 31 DuGu, then i'm wondering whether some version of Green's identity
applies here, which could convert this line integral to the surface
integral on P. my intent is to understand what went wrong with the
arguments along that line of thoughts |
|
p*****k
发帖数: 318 | 32 DuGu, see attached pic to assemble a square by cutting a rectangle
then only using translation
(seems more of a jigsaw puzzle like Tengram, lol)
the last step is to prove all squares with same size but different
orientations result same F. we can use the same graph, but picking an
arbitrary orientation and do the reverse process: square->rectangle.
then cut the rectangle in its mirror configuration, and assemble
a square which is an image of the original one w.r.t. some arbitrary
axis. |
|
p*****k
发帖数: 318 | 33 DuGu, this is what i meant by mirror configuration.
(a pic is worth a thousand words:P)
the orientation could be chosen arbitrarily, thus from the dashed
square to the solid square, the intermediate rectangle has different
side length determined by the angle |
|
p*****k
发帖数: 318 | 34 totally off-topic:
if interested, this is known as tetration (love the name! or plainly, power
tower), which is pretty well studied. actually Euler first showed that the
infinite power tower converges when the base is between e^(-e) and e^(1/e),
as DuGu indicated. it could be extended to complex plane by using Lambert's
W function.
(the height of the power tower could also be extended to real and complex,
but that's probably a little too much)
there is a very interesting related article by Gar... 阅读全帖 |
|
D**u
发帖数: 204 | 35 Here is my explanation of the case when the enemy point
is outside of the circle.
取三角形每边的所有三等分点, 这六点构成一正六边形, 且与
那个circle相切.
Case 1: 当enemy point在这个正六边形外面时, 我们得到的
不在是等式, 而是不等式, 仔细计算一下会发现我们的策略
有 >50% 机会或胜,我就不细讨论了.
Case 2: 当enemy point在这个正六边形里面时, 但在圆外时,
我们得到的仍是等式, 也就是说我们的策略仍恰有50% 机会或胜. |
|
D**u
发帖数: 204 | 36 【 以下文字转载自 Mathematics 讨论区 】
发信人: DuGu (火工头陀), 信区: Mathematics
标 题: election problem
发信站: BBS 未名空间站 (Wed Aug 8 19:17:51 2007)
Two candidates (R and L) are for the 2008 election. In the election, voters
are in a single line and are going to vote one by one. After each voter
makes the vote, the other voters immediately knows who he/she voted for.
Voters tend to stay with the "winner's side", if at the moment the
candidates have x and y votes respectively, the voter will vote R with
probability x/ |
|
