content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Simultaneous equations to matrix
August 23rd 2012, 09:13 AM #1
Member
Joined
Oct 2011
Posts
170
Thanks
3
Simultaneous equations to matrix
So I'm given this question.
$4x + 2y + 4x = 3, 2y + z = 1, 2x + 2z = 1$
and it says Forumlate a single vector matrix equation from the three equations gi... | 5 | [
-0.0157470703125,
-0.0230712890625,
-0.07373046875,
0.033447265625,
0.03271484375,
-0.1181640625,
0.0213623046875,
-0.041015625,
-0.044677734375,
0.0089111328125,
-0.054931640625,
0.00836181640625,
0.087890625,
0.0277099609375,
-0.04833984375,
0.0546875,
-0.04736328125,
-0.04052734... | 35,800 | 35800 | |
Integration With Inverse Trig Function
March 4th 2014, 06:09 PM #1
Integration With Inverse Trig Function
I want you to look at question (b) in the picture provided and tell me where (1/3) outside the integral came from. Is there factoring involved
I am to use the formula below.
Let INT = integral
... | 5 | [
-0.054443359375,
-0.01080322265625,
0.05419921875,
0.029296875,
-0.0015869140625,
0.0211181640625,
0.0072021484375,
-0.04248046875,
0.006317138671875,
0.033935546875,
0.0810546875,
-0.1171875,
0.0205078125,
0.0054931640625,
-0.033447265625,
-0.05224609375,
0.0179443359375,
0.008361... | 35,801 | 35801 | |
electric potential
March 4th 2007, 07:53 PM #1
Member
Joined
Nov 2005
Posts
111
electric potential
Hi please I need help to do this problem:
Given the electric field vector E=x(1-sin(Φ))+ycos(Φ)
where x and y are unit vectors.
Calculate the voltage (potential difference) between the points... | 5 | [
-0.05322265625,
0.02783203125,
0.0126953125,
-0.04541015625,
0.0233154296875,
-0.00848388671875,
0.0306396484375,
0.047607421875,
-0.003631591796875,
0.00946044921875,
-0.0128173828125,
-0.013427734375,
0.046630859375,
0.055908203125,
-0.025390625,
0.0091552734375,
-0.11669921875,
... | 35,802 | 35802 | |
Geometrical structure of critical points of harmonic functions
up vote 2 down vote favorite
1
For a harmonic function $\Phi$ on a simply connected subset $\Gamma$ of $\mathbb{R}^3$, define a guide curve $\gamma: I \mapsto \Gamma$ of $\Phi$ as a simple regular $C^1$ curve such that
• all point in $\gamma(I)$ are cr... | 4 | [
-0.0859375,
-0.046630859375,
-0.055419921875,
-0.00628662109375,
-0.0234375,
0.01123046875,
0.050048828125,
0.060302734375,
0.032470703125,
0.00244140625,
0.039794921875,
0.052490234375,
0.0213623046875,
0.026611328125,
0.048828125,
-0.06103515625,
-0.06591796875,
-0.06201171875,
... | 35,803 | 35803 | |
[SOLVED] Application of Differentiation
April 16th 2009, 05:29 AM #1
Senior Member
Joined
Jul 2008
Posts
347
Hey guys
Two straight roads intersect at right angles. Two men, A and B, are 100 km from the intersection, one on each road. They drive towards the intersection at 30 km/h and 40 km/h respecti... | 5 | [
-0.003021240234375,
0.0810546875,
0.000720977783203125,
-0.040771484375,
-0.0341796875,
0.0299072265625,
-0.0002803802490234375,
0.10986328125,
-0.04541015625,
0.000949859619140625,
0.0576171875,
-0.060302734375,
0.0517578125,
0.06201171875,
-0.029296875,
0.0283203125,
-0.0791015625,... | 35,804 | 35804 | |
Vector transferring from the left side of the equation to the right
February 7th 2007, 04:25 AM #1
Newbie
Joined
Oct 2006
Posts
2
I have equation from the form a*b=c. where a is a row vector of [1*4] b is a column vector of [4*1] and c is a number. I want to get equation of the forum b=…
How can I do ... | 5 | [
-0.0947265625,
-0.01495361328125,
-0.08203125,
-0.06787109375,
0.003082275390625,
0.0101318359375,
0.021240234375,
-0.10009765625,
-0.030517578125,
0.000028371810913085938,
-0.0004730224609375,
-0.00958251953125,
0.0284423828125,
0.0390625,
-0.060546875,
0.1171875,
-0.0281982421875,
... | 35,805 | 35805 | |
Math Word Problems
October 14th 2008, 06:27 PM #1
Newbie
Joined
Oct 2008
Posts
2
Math Word Problems
My math homework's due tomorrow, and I've been trying to solve these questions for a while now but I just keep getting the wrong answer / different answers each time, compared to the answers in
the bac... | 4 | [
0.030029296875,
0.10595703125,
0.007110595703125,
-0.03466796875,
-0.07958984375,
-0.0299072265625,
0.087890625,
0.0654296875,
-0.08056640625,
0.0693359375,
-0.056640625,
-0.0634765625,
0.0255126953125,
-0.00445556640625,
0.05810546875,
0.02197265625,
0.0458984375,
0.0078125,
-0.... | 35,806 | 35806 | |
morphism between two elliptic curves over a local field
up vote 2 down vote favorite
Let $X,Y$ be two elliptic curves over $K:=K(R)$ which have good models over $R$, Char($K$)=$0$, where $R$ complete DVR with algebraically residue field $k$.
If $L$ is a finite extension of $K$, such that $X \otimes L \cong Y \otimes ... | 4 | [
0.0137939453125,
-0.103515625,
0.0159912109375,
-0.048583984375,
0.09130859375,
-0.0130615234375,
-0.020263671875,
0.0230712890625,
-0.01434326171875,
-0.056884765625,
0.09521484375,
-0.003204345703125,
-0.01422119140625,
0.06884765625,
0.064453125,
0.03759765625,
-0.0089111328125,
... | 35,807 | 35807 | |
Lp spaces set inclusion
May 11th 2010, 10:49 PM
willy0625
Lp spaces set inclusion
I am stuck on trying to show for that a fixed measure space $(X,\cal{S},\mu)$ with $1 \leq r \leq p \leq s < \infty$ we have
$L_{p} \subset L_{r} + L_{s}$.
Cheers!
May 12th 2010, 01:55 PM
willy0625
I have attempted ... | 5 | [
0.056884765625,
0.004913330078125,
0.05126953125,
-0.0478515625,
0.1474609375,
0.1181640625,
0.1064453125,
0.061279296875,
-0.083984375,
0.08544921875,
-0.052978515625,
0.034912109375,
0.0576171875,
-0.00531005859375,
-0.02294921875,
-0.054443359375,
0.0029449462890625,
-0.03063964... | 35,808 | 35808 | |
Paul Cohen Dead at 72Paul Cohen Dead at 72
Paul Cohen, one of the giants of twentieth century mathematics, has died of lung disease at 72.
Cohen’s major claim to fame was his resolution of the Continuum Hypothesis. Here are the basic ideas:
Suppose you have two finite sets and you want to show they contain the same n... | 4 | [
0.0693359375,
0.00823974609375,
-0.00885009765625,
-0.0213623046875,
-0.002166748046875,
0.041259765625,
-0.00299072265625,
0.00457763671875,
0.031494140625,
0.00970458984375,
-0.05908203125,
-0.04052734375,
0.1328125,
0.038818359375,
-0.02490234375,
-0.01312255859375,
-0.04370117187... | 35,809 | 35809 | |
Tensor product of spectral sequences?
up vote 3 down vote favorite
3
I'm wondering about a cross product for spectral sequences. I've got an idea, and I wonder if it is written up anywhere, or if it even holds water.
Let's start with three spectral sequences, $E, F$ and $G$. Assume that $G_1^{*,*} \cong E_1^{*,*}\oti... | 4 | [
-0.09228515625,
-0.0361328125,
-0.01275634765625,
-0.027587890625,
0.002532958984375,
0.048583984375,
0.0390625,
-0.0185546875,
-0.052978515625,
-0.0498046875,
0.0830078125,
-0.07421875,
-0.038330078125,
0.00048065185546875,
0.05810546875,
0.07958984375,
-0.0859375,
0.0732421875,
... | 35,810 | 35810 | |
Techniques of integration (6)
May 22nd 2009, 07:55 AM #1
MHF Contributor
Joined
May 2008
Posts
2,295
Thanks
7
Techniques of integration (6)
Let $f: \mathbb{R} \longrightarrow \mathbb{R}$ be continuous and periodic with period $T > 0.$ For any real numbers $a<b$ evaluate $\lim_{n\to\infty} \int_a^b f(... | 5 | [
-0.0517578125,
0.05126953125,
0.0247802734375,
-0.02978515625,
-0.00147247314453125,
0.035888671875,
0.0147705078125,
-0.021484375,
-0.09130859375,
-0.056884765625,
-0.044189453125,
-0.0133056640625,
0.02197265625,
0.0166015625,
0.01153564453125,
-0.036865234375,
-0.0177001953125,
... | 35,811 | 35811 | |
Two Probability Questions
Date: 06/08/99 at 00:30:29
From: prashant
Subject: Probability
Dear sir:
I am a student at University of Mississippi medical center. I have a
great interest in probability, so I keep solving questions I get from
texts and friends. I have two questions I could not solve. Kindly help
me solv... | 5 | [
0.040771484375,
0.01611328125,
0.052490234375,
-0.0027618408203125,
-0.0223388671875,
-0.000038623809814453125,
0.09375,
0.0264892578125,
-0.03076171875,
0.01495361328125,
0.0927734375,
-0.0250244140625,
0.0128173828125,
-0.003509521484375,
0.004730224609375,
-0.0223388671875,
0.0412... | 35,812 | 35812 | |
A fast, single pass method to calculate the median in MySQL
After stepping off of the
GROUP_CONCAT()
solution for
calculating quantiles
I figured it would be nice to find a better way to calculate the median too.
Solution
I previously wrote on how to
calculate the median
using
GROUP_CONCAT()
, but I think tha... | 4 | [
0.0308837890625,
0.02734375,
0.050048828125,
-0.04345703125,
-0.0400390625,
-0.02880859375,
-0.007720947265625,
0.06982421875,
-0.07177734375,
-0.0230712890625,
0.00848388671875,
-0.037353515625,
0.041259765625,
-0.01953125,
-0.10693359375,
0.0634765625,
-0.006439208984375,
0.02270... | 35,813 | 35813 | |
Constant Function Zero and Orthogonal Functions
Date: 02/08/2002 at 10:56:01
From: Neeraj
Subject: Constant function zero and orthogonal functions
We're currently learning about orthogonal functions. Two functions are
said to be orthogonal over a given interval if integrating their
product (over that interval) equal... | 4 | [
-0.1103515625,
-0.01708984375,
0.015869140625,
-0.042236328125,
-0.07080078125,
0.0286865234375,
0.0164794921875,
-0.01507568359375,
0.00909423828125,
0.029541015625,
0.10009765625,
0.0498046875,
-0.042724609375,
-0.01300048828125,
-0.0498046875,
0.01495361328125,
0.006744384765625,
... | 35,814 | 35814 | |
Math Help
Find the number of positive integers not exceeding 1000 that are not divisible by 3 or 5
There are 333 numbers that are divisible by 3 since 333*3=999. Among those 333 numbers there are 66 numbers that are also divisble by 5 since 333/5 =66.6 So 333-66 = 267 numbers that are divisble
only by 3. There are 20... | 5 | [
-0.04736328125,
-0.033203125,
-0.036865234375,
-0.06787109375,
0.087890625,
0.03564453125,
0.1484375,
0.0111083984375,
-0.076171875,
0.032958984375,
-0.054931640625,
-0.03759765625,
0.07861328125,
-0.0159912109375,
0.01416015625,
-0.02490234375,
0.015869140625,
-0.047607421875,
-... | 35,815 | 35815 | |
Interval Notation
Date: 4/1/96 at 2:8:0
From: Maida Kelly
Subject: Interval Notation
Hello. I have returned to college after many years and am taking
a college level algebra course. I need to learn about interval
notation in terms of domain and ranges. I would appreciate it if
you could point me in the right dire... | 4 | [
0.0203857421875,
-0.000213623046875,
0.0162353515625,
-0.056640625,
-0.1044921875,
0.0157470703125,
-0.0238037109375,
0.0306396484375,
0.0284423828125,
-0.07861328125,
-0.06787109375,
-0.0181884765625,
0.06689453125,
0.0361328125,
0.06689453125,
0.03515625,
0.0279541015625,
-0.0708... | 35,816 | 35816 | |
Simplifing binomial product... I think?
I really need the answers to these binomial products.... (x+1)2-(x+1)(x-1)+(x-1)2= (2a+3)(a-1)+(a-1)2-(a-1)(a+1)= (m2-8)(m+2)-(m2+8m+2)(m-3)= Thanks
btw all the 2's after the numbers are all ment to representing to the power of 2 thingiy
$(x+1)^2-(x+1)(x-1)+(x-1)^2$ expand the ... | 4 | [
0.0123291015625,
0.005096435546875,
0.0113525390625,
0.037109375,
0.0002956390380859375,
0.061279296875,
0.01336669921875,
-0.00457763671875,
0.0030517578125,
-0.00811767578125,
0.0439453125,
-0.039794921875,
0.12060546875,
-0.001068115234375,
-0.002593994140625,
0.07080078125,
0.028... | 35,817 | 35817 | |
Re-arranging an equation.
December 20th 2010, 08:59 AM
DanBrown100
Re-arranging an equation.
Need help with a question guys, any help will be most appreciated.
The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:
p1V1n = p2V2n
where n is the polytr... | 5 | [
-0.10693359375,
0.00860595703125,
0.076171875,
0.04052734375,
0.026123046875,
-0.0103759765625,
0.02392578125,
0.046630859375,
0.060791015625,
-0.01513671875,
-0.0380859375,
-0.0162353515625,
-0.06396484375,
0.056396484375,
-0.034423828125,
0.005340576171875,
-0.046875,
-0.00610351... | 35,818 | 35818 | |
What to expect when i simulate a recurrence relation?
September 28th 2010, 10:21 AM #1
Newbie
Joined
Sep 2010
Posts
11
What to expect when i simulate a recurrence relation?
I am working on an assignment, and I am having trouble with this recurrence relation:
x(n+2) - 3x(n+1) + x(n) = 0
x(0) = 1
... | 5 | [
-0.162109375,
-0.05078125,
0.03955078125,
-0.008544921875,
-0.029296875,
-0.10302734375,
-0.051513671875,
-0.02587890625,
0.00982666015625,
-0.021484375,
-0.019287109375,
-0.072265625,
-0.01385498046875,
-0.03857421875,
-0.00677490234375,
-0.061279296875,
-0.03564453125,
-0.0498046... | 35,819 | 35819 | |
"Internal" versus "external" definitions of functions: equivalent foundations for mathematics?
up vote 4 down vote favorite
2
This is a generalization of the question given at Definition of Function.
I think it fairly clear that the Bourbaki and the ordered pair definition of functions are equivalent. A deeper questi... | 5 | [
-0.04443359375,
-0.08544921875,
-0.00653076171875,
-0.0419921875,
0.00189208984375,
-0.07861328125,
-0.09619140625,
0.10009765625,
0.0888671875,
0.0001125335693359375,
-0.043212890625,
-0.01470947265625,
-0.059326171875,
0.01904296875,
0.083984375,
-0.041015625,
-0.00064849853515625,... | 35,820 | 35820 | |
How to Increase the Sides to Double the Area of a Square
Date: 01/28/2005 at 12:16:10
From: colby
Subject: double the area of a square
I am puzzled as to how you would double the area of a square. Do
you multiply the sides by a decimal? I can't find the right number to
multiply by, or the right solution.
Date: 0... | 4 | [
0.07470703125,
0.0184326171875,
0.044677734375,
0.0272216796875,
-0.04296875,
-0.0206298828125,
-0.1142578125,
0.10009765625,
-0.0157470703125,
0.007080078125,
0.01336669921875,
0.042236328125,
-0.004608154296875,
0.0703125,
0.01190185546875,
0.09423828125,
-0.022216796875,
0.13867... | 35,821 | 35821 | |
Math Help
April 27th 2011, 12:07 PM #1
Newbie
Joined
Apr 2011
Posts
3
T test.
Hello, I was told by my lecturer that I need to do some T-tests on my data in order to find out if it is significant or not. The data is basically student's grades and I am trying to prove that
intrinsic students achieve h... | 5 | [
0.07275390625,
0.024169921875,
0.041015625,
-0.06982421875,
-0.03662109375,
-0.12060546875,
-0.006134033203125,
0.11328125,
0.051025390625,
0.046630859375,
0.109375,
-0.06396484375,
-0.00494384765625,
0.005218505859375,
-0.000827789306640625,
-0.0556640625,
0.023193359375,
-0.07714... | 35,822 | 35822 | |
Shift operator that generates separable orbit
up vote 1 down vote favorite
Suppose, that $f$ is bounded measurable function, $T_h(f)(x) = f(x+h)$ is the shift operator. How to prove, that if the whole orbit $T_h(f):\, h\in\mathbb{R}$ has a dense, countable subset $T_{n_k}
(f)$ (in $L^{+\infty}$ norm) then $f=g$ almost... | 5 | [
-0.000244140625,
-0.01031494140625,
-0.0145263671875,
-0.03173828125,
0.03759765625,
0.0693359375,
0.10302734375,
-0.0260009765625,
-0.06005859375,
-0.015869140625,
0.005645751953125,
-0.006744384765625,
0.00113677978515625,
-0.0260009765625,
0.056640625,
-0.0849609375,
0.0615234375,... | 35,823 | 35823 | |
Divisibility by prime
April 15th 2010, 11:50 PM
sashikanth
Divisibility by prime
Let $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \mbox{...} + \frac{1}{p-1}$ . $p$ is a prime number > 2 . Prove that $m$ is divisible by $p$. If $p > 3$, Prove that $m$ is divisible by $p^2$.
I've done the first bit, I can't... | 5 | [
-0.06298828125,
-0.006591796875,
0.06005859375,
0.06298828125,
0.09326171875,
0.0169677734375,
0.09814453125,
0.1201171875,
-0.06298828125,
0.035888671875,
-0.10791015625,
0.0233154296875,
0.0033721923828125,
-0.02734375,
-0.0576171875,
-0.023193359375,
0.07177734375,
-0.041015625,... | 35,824 | 35824 | |
find the number
May 19th 2008, 01:12 PM
sp0rtskid55
find the number
Heres the problem:
The tens digit of a two-digit number is 1 more than 3 times the ones digit. Subtracting 45 from the number reverses it. Find the original number.
May 19th 2008, 01:16 PM
angel.white
Quote:
well,
If the 1's... | 4 | [
-0.04736328125,
0.109375,
0.0284423828125,
-0.07373046875,
-0.0034942626953125,
0.0322265625,
0.041748046875,
0.029541015625,
-0.04833984375,
-0.064453125,
0.0218505859375,
0.0252685546875,
0.0537109375,
0.019775390625,
-0.06640625,
-0.078125,
-0.048095703125,
0.032470703125,
0.0... | 35,825 | 35825 | |
How to do quadratic formula?
June 25th 2013, 08:37 PM #1
Member
Joined
Feb 2009
Posts
77
Thanks
2
How to do quadratic formula?
I have an equation 2x^2+x-1
How do I rewrite in parenthesis? Like (x+ )(x- )
Etc.
I got x = .5 and -1 using quadratic formula
Thanks
Re: How to do quadrat... | 4 | [
-0.0208740234375,
0.03076171875,
0.0634765625,
0.0556640625,
-0.01141357421875,
0.0751953125,
-0.0172119140625,
-0.07177734375,
-0.02392578125,
0.000621795654296875,
0.047607421875,
-0.06494140625,
0.06298828125,
0.055419921875,
-0.0400390625,
0.08837890625,
0.0013580322265625,
0.0... | 35,826 | 35826 | |
Surface Area of Blocks Glued Together
Date: 09/09/2001 at 23:15:33
From: Jodi Meyers
Subject: Trig?
Three cubes whose edges are 2, 6, and 8 centimeters long are glued
together at their faces. Compute the minimum surface area possible for
the resulting figure.
I have tried this so many ways that I am not sure where ... | 4 | [
0.046875,
0.0206298828125,
-0.0269775390625,
-0.0123291015625,
-0.07421875,
-0.01007080078125,
-0.04052734375,
0.09814453125,
-0.038818359375,
-0.01165771484375,
-0.0966796875,
-0.07373046875,
-0.04443359375,
0.035888671875,
0.0159912109375,
0.004364013671875,
-0.00921630859375,
0.... | 35,827 | 35827 | |
Confirm/refute $f(x)$ where $f(x) = $x-th Mersenne prime ($M_p$) where $x$ is [1,2,3,4,5,6,7...]
up vote 0 down vote favorite
1
While tinkering with numbers, I found $n=f(x)$ where $n = \sigma(\sigma(n)-n)$ and $x \neq p$ where $p$ is a Mersenne prime exponent, but I need help input in regard to improving accuracy.
F... | 4 | [
-0.002349853515625,
0.00982666015625,
0.019775390625,
-0.009033203125,
0.078125,
0.061767578125,
0.07275390625,
0.1181640625,
-0.046142578125,
-0.01953125,
-0.0947265625,
0.0279541015625,
0.0859375,
-0.033203125,
-0.017822265625,
-0.01055908203125,
-0.0038299560546875,
0.0217285156... | 35,828 | 35828 | |
Function of random variables
May 3rd 2009, 09:12 AM #1
Newbie
Joined
Dec 2008
Posts
5
Function of random variables
can some one help in this question
If X is Normal( $\mu,$$\sigma^2$) and Y is Exponentioal ( $\lambda$)
What is the distribution for:
Z=X+Y
Z=X-Y
Z=X*y
Z=x/Y
i... | 4 | [
-0.0098876953125,
-0.006927490234375,
-0.01361083984375,
-0.005584716796875,
0.00286865234375,
-0.039306640625,
0.062255859375,
-0.0517578125,
-0.0771484375,
0.0159912109375,
0.0693359375,
0.015625,
0.044677734375,
0.08349609375,
0.06982421875,
0.01202392578125,
-0.000048637390136718... | 35,829 | 35829 | |
Math Help
February 12th 2010, 10:18 AM #1
Banned
Joined
Jan 2010
Posts
32
angle ?
Around 255 BC Eratosthenes, a Greek mathematician, estimated the circumference of the earth. He discovered that on a certain day, in the city of Syene, one could see the sun's reflection at the
bottom of a deep well. A... | 4 | [
-0.0181884765625,
0.083984375,
0.10205078125,
0.00162506103515625,
0.0017242431640625,
-0.123046875,
-0.0062255859375,
0.103515625,
0.01104736328125,
0.03662109375,
-0.060302734375,
-0.042724609375,
0.012939453125,
0.0283203125,
-0.01153564453125,
-0.07568359375,
-0.055908203125,
0... | 35,830 | 35830 | |
Bounds on pseudosquares
up vote 3 down vote favorite
Suppose $n\in\mathbb{Z}^+$ is a nonsquare in $\mathbb{Z}$ but is a square mod $2^2,3^2,4^2,5^2,\ldots,k^2.$ How small can $n$ be?
On the ERH, there are no small pseudosquares: $L_p>e^{\sqrt{p/2}}$. Heuristically, more is true: $\log L_p\gg p/\log p.$ I am looking f... | 5 | [
-0.019775390625,
-0.054931640625,
-0.01904296875,
0.00958251953125,
0.05029296875,
0.01171875,
-0.00115203857421875,
0.126953125,
0.039306640625,
0.00112152099609375,
-0.08056640625,
0.09375,
-0.005828857421875,
-0.00982666015625,
0.006011962890625,
-0.058349609375,
0.0218505859375,
... | 35,831 | 35831 | |
FIN2100
T/F: The recent trend is for the federal government and corporations to shift more responsibility to the individual with respect to providing for their financial future
True
Assume you bought a 5 year certificate of deposit (CD) last year which pays 5%. If you decide to cash out of your CD before 5 years, the... | 5 | [
0.040283203125,
0.055908203125,
0.0201416015625,
0.0006256103515625,
0.0380859375,
0.015869140625,
0.07177734375,
0.10400390625,
-0.0020599365234375,
0.049072265625,
-0.0186767578125,
-0.007568359375,
-0.0546875,
-0.003997802734375,
-0.0380859375,
-0.1201171875,
-0.0634765625,
-0.0... | 35,832 | 35832 | |
Non Separability of the the Loeb Space
up vote 3 down vote favorite
1
Let $X_i$, $i=1,2\ldots$ be finite sets of integers such that $|X_i|\rightarrow \infty$. Let $X$ be an ultraproduct of $X_i$. Let $\mu$ the Loeb measure associated with the the normalized counting
measures on $X_i$. Let $B$ be the completion w.r.t $... | 5 | [
-0.029296875,
-0.07861328125,
-0.0272216796875,
-0.07275390625,
0.061279296875,
0.05517578125,
0.140625,
-0.0478515625,
-0.021240234375,
-0.055908203125,
-0.00543212890625,
-0.07958984375,
0.041259765625,
-0.017822265625,
-0.01495361328125,
0.047119140625,
0.07421875,
-0.0306396484... | 35,833 | 35833 | |
Details for the action of the braid group B_3 on modular forms
up vote 15 down vote favorite
7
I'm reading Terry Gannon's Moonshine Beyond the Monster, and in section 2.4.3 he hints at (but does not explicitly describe) a way to extend the action of $SL_2(\mathbb{Z})$ on modular forms to an
action of the braid group $... | 4 | [
-0.1318359375,
-0.017822265625,
-0.031005859375,
0.031494140625,
-0.033935546875,
0.0703125,
0.004913330078125,
-0.0458984375,
-0.0291748046875,
-0.028564453125,
0.12890625,
0.015869140625,
-0.0791015625,
-0.019775390625,
-0.00823974609375,
0.0693359375,
-0.064453125,
0.03247070312... | 35,834 | 35834 | |
Problems on Slope
September 15th 2008, 08:10 PM
PandaPanda
Problems on Slope
Here's the problem:
Quote:
Problem: Recall that you can use two points on a line to determine an equation for the line. Suppose two points in a coordinate plane have coordinates (x1, y1) and (x2, y2).
Quote:
A. Writ... | 4 | [
-0.1103515625,
-0.056884765625,
-0.0301513671875,
-0.0673828125,
0.05322265625,
-0.01324462890625,
0.037109375,
0.00677490234375,
-0.01507568359375,
0.031005859375,
0.03564453125,
-0.025146484375,
-0.0322265625,
0.0245361328125,
0.0732421875,
0.1015625,
-0.1025390625,
-0.0708007812... | 35,835 | 35835 | |
Can you cover the Boolean cube {0,1}^n with O(1) Hamming-balls each of radius n/2-c*sqrt(n)?
up vote 13 down vote favorite
1
(where c>0 and the balls need not be disjoint?)
This is an embarrassingly simple question, yet somehow I couldn't find an answer (not even, "this is a well-known open problem") after spending s... | 4 | [
0.06494140625,
0.029052734375,
-0.06298828125,
0.05224609375,
0.00150299072265625,
-0.00531005859375,
-0.031982421875,
-0.05712890625,
0.021240234375,
-0.00762939453125,
-0.09716796875,
0.0016937255859375,
0.058349609375,
-0.0078125,
-0.005645751953125,
0.052490234375,
0.06103515625,... | 35,836 | 35836 | |
orders of products of permutations
up vote 31 down vote favorite
10
Let $p$ be a prime, $n\gg p$ not divisible by $p$ (say, $n>2^{2^p}$). Are there two permutations $a, b$ of the set $\{1,...,n\}$ which together act transitively on $\{1,2,...,n\}$ and such that all
products $w(a,b)=a^{k_1}b^{l_1}a^{k_2}...$ of length ... | 4 | [
-0.03564453125,
-0.04931640625,
-0.028076171875,
-0.01177978515625,
0.003387451171875,
0.0654296875,
0.0400390625,
-0.0703125,
0.03564453125,
-0.0191650390625,
-0.0230712890625,
0.10009765625,
0.0233154296875,
-0.007171630859375,
-0.05419921875,
0.1435546875,
-0.08349609375,
0.0062... | 35,837 | 35837 | |
Posts about Meta-Programming on Michid's Weblog
Union types
12 06 2011 Comments : Tags: , Categories :
In his recent blog post Miles Sabin came up with an ingenious way of expressing union types in Scala. A union type is the union of some types: its values are the union of the values of each of the
individual types.
... | 4 | [
-0.03369140625,
0.00482177734375,
0.0205078125,
-0.0185546875,
-0.021240234375,
-0.0036773681640625,
0.04833984375,
-0.029541015625,
-0.01361083984375,
-0.0291748046875,
-0.03564453125,
-0.014892578125,
-0.01953125,
0.07373046875,
0.0225830078125,
0.00830078125,
0.011962890625,
0.0... | 35,838 | 35838 | |
self-complementary graph
September 19th 2006, 08:05 PM #1
Newbie
Joined
Sep 2006
From
Edmonton, AB
Posts
8
A simple graph G is self-complimentary. Show there exists an integer k such that the order of G = 4k or 4k+1.
I'm feeling a tad lost on this. I understand the idea of self-complimentary. G a... | 4 | [
-0.04296875,
0.058837890625,
0.11328125,
-0.027099609375,
-0.05908203125,
-0.0185546875,
0.032470703125,
-0.006683349609375,
0.021240234375,
0.03515625,
-0.019775390625,
-0.028076171875,
0.000049114227294921875,
-0.032470703125,
-0.00113677978515625,
0.06494140625,
0.11572265625,
-... | 35,839 | 35839 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: monotonic function
Replies: 14 Last Post: Nov 29, ... | 5 | [
-0.10498046875,
-0.07373046875,
0.037841796875,
-0.028076171875,
-0.0159912109375,
0.023193359375,
-0.01708984375,
0.06494140625,
0.03271484375,
0.1044921875,
0.064453125,
0.029296875,
0.03662109375,
0.1259765625,
0.062255859375,
0.015625,
-0.01318359375,
-0.030517578125,
-0.0278... | 35,840 | 35840 | |
Eqn of tangent line help
October 5th 2009, 01:42 PM #1
Newbie
Joined
Feb 2008
Posts
10
Eqn of tangent line help
I'm having trouble finding a value of x for f(x) whose tangent line has the slope 4/3. I am not given any information regarding points on the graph.
The following is the original function
... | 4 | [
-0.035400390625,
-0.059814453125,
-0.0032196044921875,
-0.00927734375,
-0.01123046875,
0.0625,
-0.007568359375,
0.03466796875,
0.0498046875,
0.01544189453125,
0.0712890625,
-0.11474609375,
0.01043701171875,
0.002044677734375,
-0.02001953125,
0.057373046875,
-0.0263671875,
0.0104370... | 35,841 | 35841 | |
Generating spatially-aware degree-preserving random graphs?
up vote 0 down vote favorite
In the study of biological neural networks, researchers sometimes compare hypotheses vs. a degree-preserving random null model. One major criticism against this approach is that connections in neural
networks are greatly affected ... | 4 | [
-0.056396484375,
-0.1044921875,
0.005950927734375,
0.0238037109375,
0.034423828125,
-0.0244140625,
-0.040283203125,
-0.06201171875,
0.040283203125,
0.04931640625,
0.016845703125,
0.0341796875,
0.01507568359375,
0.04443359375,
0.048828125,
0.027587890625,
0.0322265625,
0.04711914062... | 35,842 | 35842 | |
Chebyshev and Central Limit Theorem
August 2nd 2009, 08:08 PM
morganfor
Chebyshev and Central Limit Theorem
Let S be the number of heads in 1,000,000 tosses of a fair coin. How does on use (a) Chebyshev's inequality and (b) the Central Limit Theorem to estimate the probability that S lies between
499,500 and... | 5 | [
0.04443359375,
0.045166015625,
0.03271484375,
-0.052978515625,
0.03759765625,
-0.030029296875,
0.040771484375,
0.1083984375,
-0.014404296875,
0.0732421875,
-0.05810546875,
-0.044677734375,
0.04541015625,
-0.06982421875,
-0.005615234375,
0.03173828125,
0.043212890625,
-0.04296875,
... | 35,843 | 35843 | |
Double summation
August 23rd 2009, 11:02 AM
Stonehambey
Double summation
Hi :)
I'm having some difficulty with the following problem. Evaluate
$\Sigma^5_{i=1}\Sigma^4_{j=i}(2i+j+2)$
The book I'm reading doesn't have an example where the two numbers above the sigmas are different, but does have an ... | 4 | [
-0.0751953125,
0.009033203125,
0.142578125,
0.00732421875,
-0.0028533935546875,
0.0137939453125,
0.02294921875,
0.042724609375,
-0.0189208984375,
0.00445556640625,
0.00970458984375,
-0.004669189453125,
0.005645751953125,
-0.03759765625,
-0.0517578125,
0.03857421875,
-0.017822265625,
... | 35,844 | 35844 | |
Chain Rule Inside of Chain Rule
October 22nd 2009, 08:21 PM #1
Newbie
Joined
Oct 2009
Posts
2
Chain Rule Inside of Chain Rule
I recently just took a Derivative Mastery Test...and although i passed, there was one problem that just stumped me and i could use some help so i dont make this mistake again.
... | 5 | [
0.03271484375,
0.041015625,
0.048828125,
-0.0023956298828125,
-0.08544921875,
-0.01953125,
0.032470703125,
-0.047119140625,
0.0458984375,
0.055908203125,
0.08251953125,
0.00933837890625,
0.037109375,
0.0211181640625,
0.005828857421875,
0.0400390625,
-0.0458984375,
0.032958984375,
... | 35,845 | 35845 | |
Example 8.21: latent class analysis
Latent class analysis
is a technique used to classify observations based on patterns of categorical responses. Collins and Lanza's book,"
Latent Class and Latent Transition Analysis
," provides a readable introduction, while the UCLA ATS center has an online
statistical computing... | 4 | [
-0.07275390625,
-0.030517578125,
-0.0888671875,
-0.0079345703125,
0.056640625,
0.076171875,
-0.0091552734375,
0.03515625,
-0.031494140625,
0.0546875,
0.0228271484375,
0.0390625,
0.004241943359375,
0.04345703125,
0.033203125,
-0.039794921875,
0.02734375,
0.01361083984375,
-0.04125... | 35,846 | 35846 | |
Posts about Median Absolute Deviation on qkdb
In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated
by the MAD calculated from a sample.
For a univariate data set X[1], X[2],... | 4 | [
-0.037841796875,
-0.031494140625,
-0.046875,
-0.005859375,
-0.035888671875,
-0.006011962890625,
-0.06201171875,
0.11962890625,
0.03759765625,
-0.000659942626953125,
-0.01141357421875,
0.03955078125,
0.07763671875,
-0.0703125,
-0.0810546875,
0.00005316734313964844,
0.09375,
-0.05004... | 35,847 | 35847 | |
Laplace Transform Questionn
April 1st 2011, 09:57 PM #1
Super Member
Joined
Dec 2008
Posts
509
Laplace Transform Questionn
Hi
I got a couple of questions that i am having trouble with:
1)Use Laplace transform to solve the following initial value problems:
$y''-2y'+2y=c$
y(0) = 20 and ... | 5 | [
-0.091796875,
0.01165771484375,
0.032958984375,
-0.0537109375,
0.0615234375,
0.10986328125,
-0.10107421875,
0.0380859375,
-0.007049560546875,
0.044677734375,
0.0908203125,
-0.015625,
0.037109375,
-0.033203125,
0.01275634765625,
-0.00640869140625,
-0.046875,
-0.0196533203125,
0.02... | 35,848 | 35848 | |
Simulataneous equations
January 9th 2009, 07:54 AM #1
Newbie
Joined
Jan 2009
Posts
3
Simulataneous equations
Ok I'm not entirely sure if this is possible, but would like some verification either on whether it isn't possible and if it is possible then a solution or a nudge on what to do would be great.
... | 5 | [
-0.034423828125,
-0.040283203125,
-0.007293701171875,
0.0302734375,
-0.00015163421630859375,
-0.0006256103515625,
0.021240234375,
-0.0849609375,
0.030517578125,
0.043701171875,
0.1728515625,
-0.01287841796875,
0.01708984375,
0.1015625,
0.1435546875,
0.07470703125,
-0.1796875,
0.034... | 35,849 | 35849 | |
Euclidean Algorithm
December 4th 2011, 06:00 AM
farmeruser1
Euclidean Algorithm
Use the Euclidean Algorithm to find the multiplicative inverse of 17 in Z31:
So Ive done MOST of the calculations,
a=17 p=31
..... I then get 1=(11)17-(6)31 [note 31=0 in Z31]
so 1=(11)17 Butt 11 in Z31 is -20?
so ... | 4 | [
-0.06591796875,
0.0198974609375,
-0.057373046875,
-0.06689453125,
0.037841796875,
-0.158203125,
0.0439453125,
0.006378173828125,
-0.0537109375,
-0.000354766845703125,
0.0537109375,
0.059814453125,
0.091796875,
-0.036376953125,
-0.072265625,
0.00162506103515625,
-0.0062255859375,
0.... | 35,850 | 35850 | |
Raytrace of a Star Sapphire
Date: 12/11/96 at 21:04:33
From: Charles
Subject: Angle from one 3-dimensional vector to another in terms of
rotating on x,y,and z axis.
Hello,
I am a HS graduate with no college math who is _very_ rusty on pre-
calc and geometry/trig. My problem comes from an attempt to create a
raytra... | 5 | [
-0.0693359375,
0.013671875,
-0.07373046875,
-0.06689453125,
0.000370025634765625,
-0.018798828125,
0.004180908203125,
-0.0032196044921875,
-0.0181884765625,
-0.01336669921875,
0.00921630859375,
-0.01300048828125,
0.0024871826171875,
0.0146484375,
0.0032958984375,
-0.0419921875,
-0.08... | 35,851 | 35851 | |
Distinguishing two local versions of the axiom of choice
up vote 9 down vote favorite
1
Two equivalent formulations of the axiom of choice are:
1. Every family $(X_i)_{i \in I}$ of pairwise disjoint nonempty subsets of a set $X$ has a choice function.
2. Every family $(X_i)_{i \in I}$ of nonempty subsets of a set $... | 4 | [
-0.01953125,
-0.0186767578125,
0.0771484375,
-0.05517578125,
0.1484375,
-0.032470703125,
0.13671875,
0.017822265625,
0.0546875,
0.06298828125,
0.01300048828125,
-0.0703125,
0.052978515625,
-0.022705078125,
0.056884765625,
0.07177734375,
0.057861328125,
-0.029052734375,
-0.0091552... | 35,852 | 35852 | |
The Derivative
Chapter 4
The Derivative
In our investigation so far, we have defined the notion of an instantaneous rate of change, and called
this the derivative. We have also identified this mathematical concept with the slope of a tangent
line to the graph of a function. Recal... | 5 | [
-0.1103515625,
0.0299072265625,
0.024658203125,
0.0693359375,
0.037109375,
-0.01806640625,
0.019287109375,
0.04638671875,
0.056640625,
0.0294189453125,
0.0927734375,
-0.009765625,
-0.00775146484375,
0.037109375,
0.0205078125,
0.01611328125,
-0.0751953125,
-0.017822265625,
-0.0295... | 35,853 | 35853 | |
Numerically negative exceptional divisor on a surface.
up vote 1 down vote favorite
1
Suppose $S$ is an algebraic surface (possibly projective) over an algebraically closed field $k$. Suppose $D_i$ are irreducible smooth curves (rational, if you want) with negative self-intersection
and simple normal crossings such th... | 5 | [
-0.0299072265625,
0.005035400390625,
0.0194091796875,
-0.0223388671875,
0.0174560546875,
-0.0693359375,
0.08349609375,
0.072265625,
-0.0220947265625,
0.000514984130859375,
-0.0125732421875,
0.038330078125,
0.0255126953125,
0.0164794921875,
-0.05615234375,
-0.01031494140625,
0.0568847... | 35,854 | 35854 | |
Poincaré duality for intersection cohomology
up vote 7 down vote favorite
1
Let $X$ be a projective complex algebraic variety of dimension $d.$ Does it make sense to ask if properties like $$ (x,y)=(-1)^i(y,x) $$ holds, for $x\in IH^i(X,\mathbb Q)$ and $y\in IH^{2d-i}(X)?$
And if it makes sense, is it true?
Edit: For... | 4 | [
-0.072265625,
-0.0096435546875,
0.0255126953125,
-0.08056640625,
-0.035400390625,
-0.03662109375,
0.109375,
0.012939453125,
-0.0203857421875,
-0.08154296875,
0.0712890625,
-0.083984375,
-0.0693359375,
0.0654296875,
0.09130859375,
0.049560546875,
0.01397705078125,
0.01190185546875,
... | 35,855 | 35855 | |
(URGENT) integration by parts
January 15th 2009, 03:30 PM #1
Member
Joined
Jan 2009
Posts
91
(URGENT) integration by parts
let I = integral e^(ax) sin (bx) dx
use integration by parts to show that
I = e^(ax) * (a sin (bx) - b cos (bx)) / (a^2 + b^2) + C
i have tried every possible combinati... | 5 | [
-0.05712890625,
0.03955078125,
0.043701171875,
-0.0595703125,
0.00927734375,
0.0615234375,
-0.0194091796875,
-0.0927734375,
0.00029754638671875,
0.043212890625,
0.04296875,
-0.0751953125,
-0.01190185546875,
-0.005279541015625,
0.111328125,
-0.00732421875,
0.03369140625,
-0.01324462... | 35,856 | 35856 | |
Divisible or Remainder??
Does 9 divide 5^(23) + 1? If not, what is the remainder? How is this done?
Note $23 = 16+4+2+1$ (all powers of $2$). So $5^{23} = 5^{16}\cdot 5^4\cdot 5^2\cdot 5^1$. $5^1 \equiv 5 \mod{9}$ $5^2 \equiv 7 \mod{9}$ $5^4 =\left(5^2\right)^2 \equiv 7^2 \equiv 4 \mod{9}$ $5^8 =\
left(5^4\right)^2 \e... | 4 | [
-0.00090789794921875,
0.039306640625,
-0.01483154296875,
0.053466796875,
0.1044921875,
0.001953125,
0.023193359375,
0.060791015625,
0.026123046875,
-0.046875,
0.02978515625,
-0.01007080078125,
0.031494140625,
0.130859375,
-0.0693359375,
-0.05810546875,
-0.04443359375,
0.01196289062... | 35,857 | 35857 | |
Are extensions of profinite groups profinite?
up vote 2 down vote favorite
1
Assume $X$, $E$ and $G$ are topological groups and $1\to X\to E\to G\to 1$ a short exact sequence of continuous group homomorphisms. Under which of these conditions is $E$ a profinite group?
(i) $G$ profinite, $X$ finite
(ii) $G$ profinite,... | 5 | [
-0.0888671875,
-0.01007080078125,
0.01263427734375,
0.004180908203125,
0.055908203125,
0.0186767578125,
0.1376953125,
0.039306640625,
-0.0302734375,
-0.0045166015625,
0.03662109375,
0.0245361328125,
-0.00445556640625,
0.043212890625,
-0.0147705078125,
-0.036376953125,
-0.05712890625,... | 35,858 | 35858 | |
Solving Trig Problems
Date: 08/18/97 at 04:44:07
From: Venessa
Subject: Solving trigonometry
I'm studying in high school and got these problems from past year
questions:
1. Find the value of Tan [(x+1)/(x-1)]^(-1) + Tan (x)^(-1).
2. Given that sin[x]^2 + 6 sin[x]cos[x] + 9 cos[x]^2 = A + B sin[2x] +
C cos[2x], ... | 5 | [
-0.043212890625,
0.03369140625,
0.030517578125,
0.0169677734375,
-0.030517578125,
0.11279296875,
-0.00537109375,
0.059814453125,
-0.02197265625,
-0.03662109375,
-0.0032958984375,
-0.0286865234375,
0.003173828125,
0.015625,
0.0029754638671875,
-0.0439453125,
0.03759765625,
-0.030883... | 35,859 | 35859 | |
BetterLesson
Lesson: Function rules from a table
3274 Views
58 Downloads
3 Favorites
Lesson Objective
I can write function rules from a table
Lesson Plan
┌─────────────────────────────────────────────────────────┬────────────────────────────────────────────────────────────────────────────────────────────────────... | 4 | [
0.0201416015625,
0.025146484375,
-0.056640625,
-0.0205078125,
0.0018768310546875,
0.00750732421875,
-0.06591796875,
0.0184326171875,
-0.0810546875,
0.0830078125,
0.12109375,
-0.0211181640625,
0.03271484375,
0.1171875,
0.09130859375,
0.0810546875,
-0.050537109375,
0.053466796875,
... | 35,860 | 35860 | |
Dreadful Plumbing with Downward Nominal Rigidity
Dreadful plumbing with downward nominal rigidity Actually more or less readable version
here
. This is the pointless math post which accompanies
this
and especially
this post
at angrybearblog. Here I am assuming that transition out of the liquidity trap is predicta... | 4 | [
-0.038330078125,
-0.078125,
0.00897216796875,
0.00162506103515625,
-0.003387451171875,
0.0267333984375,
-0.044189453125,
0.040283203125,
0.03076171875,
0.0228271484375,
0.0439453125,
0.041015625,
0.01434326171875,
-0.005035400390625,
-0.01007080078125,
-0.0390625,
0.0123291015625,
... | 35,861 | 35861 | |
Coiling Rope in a Box
up vote 17 down vote favorite
3
What is the longest rope length L of radius r that can fit into a box? The rope is a smooth curve with a tubular neighborhood of radius r, such that the rope does not self-penetrate. For an open
curve, each endpoint is surrounded by a ball of radius r. For a box of... | 5 | [
0.034912109375,
0.01397705078125,
-0.103515625,
-0.01165771484375,
-0.004791259765625,
-0.058837890625,
-0.006866455078125,
0.091796875,
-0.08837890625,
-0.00628662109375,
-0.0400390625,
0.055419921875,
0.0194091796875,
0.1181640625,
-0.01531982421875,
0.039306640625,
-0.016845703125... | 35,862 | 35862 | |
Subsystems of Peano arithmetic and incompleteness theorem
up vote 4 down vote favorite
2
I think everyone is familiar with Goedel's incompleteness theorems. In particular they imply that PA (Peano arithmetic) can not prove its own consistency. Now my question is what is the largest
subsystem of PA that "can" prove its... | 4 | [
-0.0927734375,
-0.026611328125,
0.01373291015625,
-0.07470703125,
-0.0234375,
0.04638671875,
-0.00421142578125,
0.016845703125,
0.0419921875,
0.052001953125,
-0.00848388671875,
0.038330078125,
0.0361328125,
0.0264892578125,
-0.00025177001953125,
-0.033935546875,
-0.046875,
0.058349... | 35,863 | 35863 | |
Lecture 13: Electromagnetic Waves, Polarization
PROFESSOR: Today's lecture is going to be about electromagnetic radiation which is one of the highlights in 8.03 and one of the great victories of 19th century physics. So far we've dealt with
electromagnetic waves, well excuse me, with mechanical waves. And we've dealt w... | 4 | [
-0.041259765625,
-0.07568359375,
-0.0206298828125,
0.001220703125,
0.03662109375,
0.017333984375,
0.027099609375,
-0.0311279296875,
-0.040771484375,
-0.0035400390625,
0.0888671875,
-0.01202392578125,
0.043701171875,
0.0169677734375,
0.058837890625,
-0.0147705078125,
0.00531005859375,... | 35,864 | 35864 | |
Natural Log and Log
Hello, Can someone please help me solve this? a. ln(1/e) b.logsqrt10
$<br /> \ln\left(\frac{1}{e}\right) = \ln(e^{-1})= -1\times \ln(e) = -1\times 1 = -1<br />$ $<br /> \log_{10}(\sqrt{10})=\log_{10}(10^{\frac{1}{2}})= \frac{1}{2}\log_{10}(10) = \frac{1}{2}\times 1 =
\frac{1}{2}<br />$
| 4 | [
-0.01324462890625,
-0.0033111572265625,
0.01904296875,
-0.018798828125,
-0.00002372264862060547,
-0.10400390625,
0.006927490234375,
0.087890625,
0.005950927734375,
0.01904296875,
-0.0076904296875,
-0.0546875,
0.0281982421875,
0.0947265625,
0.00592041015625,
0.049560546875,
-0.0795898... | 35,865 | 35865 | |
Combinations Help
June 18th 2010, 01:28 PM #1
Newbie
Joined
Jun 2010
Posts
8
Combinations Help
In how many ways can 12 prices be awarded evenly among four people?
I am not sure how to start this question.
Also, one more:
From a deck of 52 cards, how many different four-card hands could be ... | 4 | [
0.06787109375,
0.06884765625,
-0.02587890625,
-0.06201171875,
-0.09423828125,
0.0673828125,
0.0986328125,
-0.0291748046875,
-0.02734375,
0.03662109375,
-0.04296875,
-0.0133056640625,
-0.0024566650390625,
-0.027099609375,
-0.0203857421875,
-0.0089111328125,
-0.0419921875,
0.01251220... | 35,866 | 35866 | |
Integrate a function which includes the integral of itself
September 14th 2009, 07:04 AM #1
Newbie
Joined
Sep 2009
Posts
2
Integrate a function which includes the integral of itself
I've got the formula for the acceleration of a vehicle. Basically it looks like this:
$a = c_1 - c_2*v^2 - c_3$
Whe... | 4 | [
-0.009521484375,
-0.01239013671875,
-0.0235595703125,
-0.080078125,
-0.017578125,
0.0162353515625,
-0.107421875,
0.01202392578125,
-0.061767578125,
0.0042724609375,
0.06884765625,
-0.0849609375,
0.00604248046875,
0.0019989013671875,
-0.0291748046875,
0.00004172325134277344,
0.0201416... | 35,867 | 35867 | |
Generalisations of Riemann-Roch for surfaces
up vote 2 down vote favorite
3
Let $X$ be a smooth projective algebraic surface (over $\mathbb{C}$ ). For all $L\in \mathrm{Pic}(X)$, we have $$\chi(L)=\chi(\mathcal{O}_X)+\frac{1}{2}(L^2-L\cdot \omega_X).$$ This is the famous
Riemann-Roch theorem in the flavour I like the ... | 4 | [
-0.0791015625,
-0.08251953125,
0.0257568359375,
-0.0400390625,
0.1044921875,
0.0205078125,
-0.0179443359375,
0.09326171875,
-0.00189971923828125,
-0.002838134765625,
0.1005859375,
-0.07421875,
-0.043701171875,
0.0380859375,
0.040771484375,
0.01153564453125,
-0.07373046875,
-0.02075... | 35,868 | 35868 | |
Factorisation
December 3rd 2009, 09:06 PM
Paymemoney
Factorisation
Can someone tell me if i have factorized correctly:
Equation is this: $x^4-6x^2+1$
First i completed the square:
$x^4-6x^2+1$
$x^4-6x^2+1-9x^2$
$(x^2-3)^2-(3x)^2$
$(x^2-3-3x)(x^2-3+3x)$
Now i use the difference of two... | 4 | [
0.00518798828125,
-0.0196533203125,
-0.030029296875,
0.006591796875,
0.01068115234375,
0.09423828125,
-0.023681640625,
-0.061767578125,
-0.0159912109375,
-0.05908203125,
0.0252685546875,
0.0025787353515625,
0.04833984375,
0.0142822265625,
-0.0262451171875,
0.004547119140625,
-0.02526... | 35,869 | 35869 | |
Number theory- mobius,multiplicative,primitive root
August 24th 2010, 06:32 AM #1
Newbie
Joined
Aug 2010
Posts
9
Number theory- mobius,multiplicative,primitive root
1
i) When do we say that a function f:N-->C is multipicative?
ii)Define mobius funtion 'mu' and show it is multiplicative.
iii... | 4 | [
-0.04638671875,
0.0478515625,
-0.01190185546875,
-0.03173828125,
0.047119140625,
-0.068359375,
0.10595703125,
0.0556640625,
-0.054931640625,
-0.031982421875,
0.056396484375,
-0.0262451171875,
0.03759765625,
-0.0390625,
-0.044189453125,
-0.035400390625,
-0.05615234375,
0.00115966796... | 35,870 | 35870 | |
Need help solving two stochastic differential equations
November 22nd 2011, 02:00 AM
Eloqent
Need help solving two stochastic differential equations
Hello, I'm new here, so I guess I should introduce myself. I'm a student at a math. finance course. We have some homework where we have to solve two stochastic diff... | 5 | [
-0.099609375,
-0.07568359375,
-0.023681640625,
-0.006103515625,
0.0166015625,
0.03515625,
0.0654296875,
0.0089111328125,
-0.01556396484375,
0.0152587890625,
-0.006683349609375,
0.017333984375,
-0.06103515625,
-0.052978515625,
-0.005859375,
0.12060546875,
-0.07275390625,
-0.07910156... | 35,871 | 35871 | |
Math Forum Discussions
fom
Posts: 1,968
Registered: 12/4/12
Re: Notation
Posted: May 25, 2013 10:48 PM
On 5/25/2013 8:36 PM, William Elliot wrote:
> On Sat, 25 May 2013, fom wrote:
>
>> On 5/24/2013 10:57 PM, William Elliot wrote:
>>> V is the ZFC universe.
>>> L is the constructible universe.
>>> L_omega0 is the ome... | 4 | [
-0.0673828125,
-0.039794921875,
0.009033203125,
0.029296875,
0.041748046875,
0.060302734375,
-0.04736328125,
0.03076171875,
0.0242919921875,
-0.0306396484375,
0.035400390625,
-0.0498046875,
-0.0242919921875,
-0.0184326171875,
0.00799560546875,
0.033935546875,
-0.0274658203125,
-0.1... | 35,872 | 35872 | |
Additivity of projective dimensions, or, help me lower my blood pressure
up vote 8 down vote favorite
2
Sorry for the shameless title. I'm rather stuck on a lemma in commutative algebra - namely, I have both a proof and a counterexample! I have tried rather strenuously and frustratingly to find the
error here, without... | 5 | [
-0.08349609375,
0.033447265625,
-0.0157470703125,
-0.0238037109375,
0.1015625,
0.0091552734375,
0.00982666015625,
0.0303955078125,
-0.01239013671875,
-0.01239013671875,
0.02490234375,
-0.07958984375,
0.0242919921875,
0.022705078125,
0.050537109375,
0.0859375,
-0.003631591796875,
0.... | 35,873 | 35873 | |
Math Forum Discussions
Re: Integral test
Posted: Dec 11, 2012 1:44 AM
On 11/12/2012 00:57, Rotwang wrote:
>> One of my students asked me today a question that I was unable to
>> answer. Let _f_ be an analytical function from (0,+oo) into [1,+oo) and
>> suppose that the integral of _f_ from 1 to +oo converges. Does it... | 5 | [
-0.060546875,
-0.04931640625,
-0.049560546875,
0.09423828125,
0.038818359375,
-0.076171875,
0.0185546875,
0.005706787109375,
0.0028839111328125,
-0.04736328125,
-0.0220947265625,
0.08447265625,
0.052001953125,
0.0498046875,
-0.041015625,
-0.05517578125,
0.060546875,
0.0083618164062... | 35,874 | 35874 | |
solve given a yh1
May 15th 2009, 11:52 PM
pberardi
solve given a yh1
Hello,
I cannot for the life of me remember how to do this. Can someone help please?
Solve the following differential equation xy''+y'=12x^2 given that yh1 = 1 is a solution of the homogeneous equation.
Thanks.
May 16th 2009, 01:... | 5 | [
-0.04345703125,
0.00138092041015625,
0.07373046875,
0.0014495849609375,
0.02392578125,
0.028076171875,
-0.02587890625,
-0.0208740234375,
-0.06298828125,
0.007476806640625,
0.10302734375,
0.10009765625,
-0.0296630859375,
-0.01055908203125,
-0.032470703125,
0.0263671875,
-0.07666015625... | 35,875 | 35875 | |
intergral by interpreting it in terms of areas
June 28th 2010, 04:29 PM
bigwave
intergral by interpreting it in terms of areas
I am fairly new to this so...
$\int_{-3}^0(1+\sqrt{9- x^{2}})dx<br /> \Rightarrow<br /> \int_{-3}^{0}1dx + \int_{-3}^0\sqrt{9- x^{2}}dx<br /> \Rightarrow<br /> 3 + \int_{-3}^0\sqrt{... | 5 | [
-0.0294189453125,
-0.01470947265625,
0.030029296875,
-0.02685546875,
0.0087890625,
-0.044189453125,
-0.0693359375,
0.060302734375,
-0.0206298828125,
-0.05517578125,
0.024169921875,
-0.00244140625,
0.0054931640625,
-0.041015625,
-0.03173828125,
-0.0140380859375,
0.00994873046875,
-0... | 35,876 | 35876 | |
The first eigenvalue of the laplacian for complex projective space
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
What is the exact value of the first eigenvalue of the laplacian for complex projective space viewed as $SU... | 5 | [
-0.062255859375,
0.057373046875,
-0.07080078125,
-0.0235595703125,
-0.0380859375,
0.02099609375,
-0.0042724609375,
-0.01251220703125,
-0.0022430419921875,
-0.09375,
0.09033203125,
-0.060302734375,
-0.08056640625,
-0.025390625,
-0.04736328125,
-0.09521484375,
0.0238037109375,
-0.070... | 35,877 | 35877 | |
Math Forum Discussions
Virgil
Posts: 9,012
Registered: 1/6/11
The Linearity found that WM claimed but could not find!
Posted: Mar 20, 2013 8:15 PM
WM claimed to have a bijective linear mapping (isomorphism of vector
spaces, or at least modules) from the set of all infinite binary
sequences to the set of all paths in ... | 4 | [
-0.12109375,
-0.043701171875,
-0.0238037109375,
0.03857421875,
-0.08984375,
-0.043701171875,
-0.0301513671875,
-0.0615234375,
-0.052490234375,
-0.01708984375,
-0.0245361328125,
0.0296630859375,
-0.029052734375,
-0.01123046875,
-0.044189453125,
0.0732421875,
-0.08447265625,
0.074707... | 35,878 | 35878 | |
logarithmic equation from points
May 27th 2006, 05:49 PM #1
Newbie
Joined
May 2006
Posts
12
logarithmic equation from points
i need to derive a logarithmic equation in the form y=aloge(x+b)+c
given that it passes through the points (0,0) (12,20) (30,30)
it is a positive log with a horizontal asym... | 5 | [
-0.044677734375,
0.035400390625,
-0.0169677734375,
-0.029052734375,
-0.0284423828125,
0.041015625,
0.00628662109375,
0.023193359375,
0.032470703125,
0.045654296875,
0.13671875,
-0.06103515625,
0.0220947265625,
0.0179443359375,
0.07568359375,
0.07958984375,
-0.09814453125,
0.0185546... | 35,879 | 35879 | |
Fol 13
November 16th 2011, 12:54 AM
logics
Fol 13
Enderton 2.2.19
An $\exists_2$ formula is one of the form $\exists x_1 \cdots x_n \theta$, where $\theta$ is universal.
(a) Show that if an $\exists_2$ sentence in a language not containing function symbols (not even constant symbols) is true in $A$, th... | 4 | [
-0.060546875,
-0.0673828125,
0.0380859375,
-0.058349609375,
0.08740234375,
0.08837890625,
-0.00144195556640625,
-0.032470703125,
0.033935546875,
-0.0225830078125,
0.06201171875,
-0.040283203125,
0.02392578125,
-0.01153564453125,
0.04931640625,
0.05322265625,
0.0301513671875,
-0.020... | 35,880 | 35880 | |
How do you do this proof of perfect integer?
November 15th 2009, 10:11 AM
mathgirl13
How do you do this proof of perfect integer?
I'm completely stuck on this proof. I know the idea of how to do it, find the factors, add them, and show its the same, but I have no idea what the factors should be. Here's the quest... | 4 | [
0.01446533203125,
0.002166748046875,
0.09912109375,
0.049560546875,
0.109375,
0.012451171875,
0.07080078125,
0.1513671875,
-0.078125,
0.00013256072998046875,
-0.0634765625,
0.02587890625,
0.032958984375,
-0.037109375,
-0.05322265625,
0.0152587890625,
-0.09228515625,
0.020263671875,... | 35,881 | 35881 | |
Taylor polynomial of third degree and error estimation
October 24th 2010, 01:16 PM #1
Member
Joined
May 2010
Posts
241
Taylor polynomial of third degree and error estimation
It seems that I'm a little bit lost about this exercise. It says: Find the taylors polynomial of third degree centered at the origi... | 4 | [
-0.01239013671875,
0.0159912109375,
-0.06591796875,
-0.0010833740234375,
0.0242919921875,
0.014892578125,
-0.043701171875,
-0.0302734375,
-0.0286865234375,
-0.0257568359375,
0.07275390625,
-0.0888671875,
-0.0255126953125,
-0.0341796875,
0.00970458984375,
-0.009765625,
-0.038330078125... | 35,882 | 35882 | |
Are there oriented $4k+2$ manifolds such that $im(H_{2k+1}(M; Z/2)\to H_{2k+1}(M, \partial M; Z/2))$ has odd dimension?
up vote 7 down vote favorite
2
The following fairly specific question comes up in a bordism computation I'm trying to do:
Are there compact $\mathbb Z$-oriented $4k+2$ dimensional manifolds with bou... | 5 | [
-0.0223388671875,
0.06884765625,
0.01312255859375,
0.026611328125,
-0.0159912109375,
-0.039794921875,
-0.032470703125,
0.011474609375,
-0.059814453125,
-0.072265625,
0.09814453125,
-0.10009765625,
0.00640869140625,
-0.0537109375,
-0.020751953125,
0.038818359375,
-0.055419921875,
0.... | 35,883 | 35883 | |
Solving Harmonic Motion Problems with a period/seconds in decimals
March 12th 2011, 09:19 AM
MajorJohnson
Solving Harmonic Motion Problems with a period/seconds in decimals
An object is attached to a coil spring, the object is propelled downwards fromits rest prosition at time t = 0. Write an equation for the di... | 4 | [
-0.0712890625,
0.0615234375,
-0.00186920166015625,
-0.08984375,
-0.06591796875,
0.07177734375,
-0.04931640625,
0.07763671875,
0.03515625,
0.010986328125,
0.072265625,
-0.05908203125,
0.009033203125,
0.0166015625,
0.0260009765625,
0.07080078125,
-0.0064697265625,
0.046875,
-0.0427... | 35,884 | 35884 | |
Math Forum: Ellipse, Parabola: Formulas for area, perimeter, length, etc.
Preliminaries
The circumference C of an ellipse must be computed using calculus. To do this, we set up a Cartesian coordinate system. We put the origin at the center of the ellipse, the x-axis along the major
axis, whose length is 2a, and the y-... | 5 | [
0.07080078125,
-0.004486083984375,
0.0023345947265625,
-0.0322265625,
0.041015625,
-0.01422119140625,
-0.03955078125,
0.16796875,
0.045166015625,
-0.016845703125,
0.039306640625,
-0.00726318359375,
0.006256103515625,
0.001556396484375,
-0.012451171875,
0.09423828125,
-0.019287109375,... | 35,885 | 35885 | |
Trigonometry Word Problem ... Question 3
June 12th 2009, 12:16 PM #1
Member
Joined
Jun 2009
Posts
86
Trigonometry Word Problem ... Question 3
The following questions are for a final class project. Obviously these questions are very hard, and I am unsure how to completely answer these with the proper and ... | 4 | [
0.03662109375,
0.09716796875,
-0.0751953125,
-0.0267333984375,
0.0322265625,
0.007110595703125,
-0.03076171875,
0.0791015625,
-0.035400390625,
0.015380859375,
0.07421875,
0.01263427734375,
-0.00872802734375,
-0.0064697265625,
0.0125732421875,
0.09130859375,
-0.03173828125,
-0.06298... | 35,886 | 35886 | |
Units and Cylinder Volume
Date: 02/06/2003 at 20:59:10
From: Dan
Subject: Cylinders
My 7th-grade daughter brought home a question:
A cylindical storage tank has a radius of 15ft and a height of 30ft.
Find the volume of the tank.
to find volume: Pi x r^2 x H
My answer was
21205.75
It was wrong. I am total... | 4 | [
-0.038818359375,
0.07275390625,
-0.040283203125,
0.00154876708984375,
0.00836181640625,
-0.0303955078125,
-0.017578125,
0.0830078125,
0.042724609375,
-0.0137939453125,
0.02294921875,
-0.00148773193359375,
0.087890625,
0.1279296875,
-0.005950927734375,
0.00885009765625,
-0.00650024414... | 35,887 | 35887 | |
abstract algebra: subgroups question
March 6th 2013, 11:21 AM #1
Newbie
Joined
Dec 2012
From
Los Angeles
Posts
12
abstract algebra: subgroups question
If G is a finite Abelian group, H, K ≤ G, and if x ∈ H K with o(x) = p a prime, show that H or K must contain an element of order p.
Re: abstract alg... | 5 | [
-0.00811767578125,
0.0712890625,
0.083984375,
0.0015716552734375,
0.017822265625,
-0.043701171875,
0.142578125,
-0.03173828125,
-0.003997802734375,
-0.068359375,
0.022216796875,
0.005767822265625,
0.0255126953125,
-0.08056640625,
0.0172119140625,
0.06640625,
0.0174560546875,
0.0059... | 35,888 | 35888 | |
Path integrals outside QFT
up vote 8 down vote favorite
8
The main application of Feynman path integrals (and the primary motivation behind them) is in Quantum Field Theory - currently this is something standard for physicists, if even the mathematical
theory of functional integration is not (yet) rigorous.
My questi... | 4 | [
-0.1044921875,
-0.041748046875,
-0.018310546875,
-0.002044677734375,
-0.04541015625,
-0.0205078125,
0.01904296875,
0.0849609375,
0.0203857421875,
0.019287109375,
-0.033447265625,
0.05712890625,
-0.05322265625,
0.1083984375,
0.055908203125,
0.00396728515625,
0.033447265625,
0.071289... | 35,889 | 35889 | |
Change of Basis
October 30th 2010, 01:24 PM #1
Member
Joined
Jun 2010
Posts
205
Thanks
1
Change of Basis
So I've done a few change of bases and they're hard but I'm getting the hang of them. Now I have this: $\displaystyle \int \int_{R} \sin(9x^{2} + 4y^{2}) \,\, dA$ where $R$ is the region in the
... | 5 | [
0.01422119140625,
-0.041259765625,
-0.043212890625,
-0.06982421875,
0.09521484375,
-0.05615234375,
-0.01397705078125,
0.07177734375,
0.0084228515625,
-0.0478515625,
0.0235595703125,
0.049560546875,
-0.06396484375,
0.043701171875,
0.0206298828125,
-0.00396728515625,
-0.07470703125,
... | 35,890 | 35890 | |
Problems..... Help
we can cross multiply, do you know how? we get: $\frac {4x + 1}{3} = \frac {x - 5}{2}$ $\Rightarrow 3(x - 5) = 2(4x + 1)$ can you continue? a similar trick can be used for the first, but i wouldn't
do it. it's simple enough not to use this trick. remember, our objective is to get x by itself on one s... | 4 | [
-0.00360107421875,
-0.0037689208984375,
0.0240478515625,
0.01953125,
-0.043212890625,
-0.0108642578125,
0.0126953125,
-0.0189208984375,
-0.0196533203125,
0.0257568359375,
0.0693359375,
-0.095703125,
0.03759765625,
0.036376953125,
-0.00848388671875,
0.051025390625,
-0.12890625,
0.12... | 35,891 | 35891 | |
Compactness Theorem for First Order Logic
up vote 5 down vote favorite
4
Hi all, I am interested in proofs without using Goedel's completeness theorem.
• Does anyone have a reference to a proof of this theorem that uses Skolem Functions?
• How come Enderton's (Introduction to Logic) has a half a page proof (which... | 4 | [
-0.049560546875,
-0.0191650390625,
-0.033935546875,
-0.01104736328125,
0.04150390625,
0.062255859375,
0.00823974609375,
0.061279296875,
0.002655029296875,
0.048828125,
0.017822265625,
0.0751953125,
0.01031494140625,
0.046875,
0.0093994140625,
-0.0390625,
-0.06591796875,
0.004974365... | 35,892 | 35892 | |
Loan Repayment
February 6th 2010, 03:06 AM
MickG
Loan Repayment
Hi, This is a query relating to the calculation method for the repayments of loan.
Example:- Using the PMT Function on a Loan of £7500, Over 4 years Monthly repayments @ 8.7%. The Function instructions uses the Yearly interest rate divides by 12... | 5 | [
0.004241943359375,
0.0703125,
0.0322265625,
0.031005859375,
0.0166015625,
-0.138671875,
0.057373046875,
0.107421875,
0.0751953125,
0.095703125,
0.00347900390625,
-0.03173828125,
0.0198974609375,
0.01055908203125,
-0.048828125,
0.027099609375,
-0.09716796875,
-0.047607421875,
0.00... | 35,893 | 35893 | |
Word problems
August 13th 2009, 09:18 AM
Vicky1997
Word problems
1. The cooling system of Alex's car holds 10 quarts. It is now filled with a mixture that is 60% water and 40% antifreeze. Hearing a weather forecast for severe cold, Alex decides to increase the
strenth of the antifreeze mixture to 50%. To do ... | 4 | [
-0.018798828125,
0.02197265625,
0.0196533203125,
0.0135498046875,
-0.029052734375,
0.01055908203125,
0.018798828125,
0.0380859375,
0.01226806640625,
0.0303955078125,
-0.0361328125,
-0.08154296875,
0.06298828125,
0.02783203125,
-0.021240234375,
0.06201171875,
-0.0908203125,
-0.01013... | 35,894 | 35894 | |
Calabi-Yau manifolds and polygonal linkage configuration spaces: related?
up vote 6 down vote favorite
2
I was reading about Calabi-Yau manifolds, about which I know little, and was wondering if these (or related complex manifolds, perhaps K3 surfaces) can be viewed as configuration spaces (or moduli
spaces) of articu... | 4 | [
-0.057373046875,
-0.006134033203125,
-0.013916015625,
0.005859375,
-0.06298828125,
-0.03466796875,
-0.01226806640625,
0.03515625,
0.0225830078125,
0.0194091796875,
0.08251953125,
-0.0252685546875,
0.00787353515625,
0.00640869140625,
0.034423828125,
-0.031005859375,
-0.04736328125,
... | 35,895 | 35895 | |
Subset of order > 1/2 of order G
February 24th 2009, 01:29 AM
Chandru1
Subset of order > 1/2 of order G
If G is a finite goup and let $A \subseteq G$. if $|A|> |G|/2$ then prove that for every $g \in G$ there exists [tex]h,k \in A [/Math] such that $hk=g$ (Headbang)
February 24th 2009, 09:13 AM
ThePerfectHacke... | 5 | [
0.01214599609375,
0.07275390625,
0.11328125,
-0.0537109375,
-0.0224609375,
0.05859375,
0.08740234375,
-0.05615234375,
-0.05712890625,
-0.007476806640625,
0.046142578125,
-0.006195068359375,
0.0654296875,
-0.1328125,
0.0269775390625,
0.029052734375,
0.0262451171875,
0.01373291015625... | 35,896 | 35896 | |
Additive and multiplicative Inverse
November 11th 2010, 09:31 PM #1
Junior Member
Joined
May 2010
Posts
26
Additive and multiplicative Inverse
Hi All,
Having a real hard time in particular getting a grasp on multiplicative inverse. In a standard tut question is see is :
Compute the additive and... | 4 | [
-0.1181640625,
0.015869140625,
-0.0301513671875,
-0.027587890625,
0.0115966796875,
-0.076171875,
0.12353515625,
0.037841796875,
-0.056396484375,
-0.06201171875,
0.0281982421875,
0.01312255859375,
0.00909423828125,
0.01904296875,
-0.04443359375,
-0.0162353515625,
-0.0069580078125,
0... | 35,897 | 35897 | |
Disk method.
March 3rd 2010, 02:36 PM #1
Newbie
Joined
Feb 2010
Posts
4
Disk method.
find the volume of the solid generated by revolving each region about the y-axis
the region in the first quadrant bounded above by the parabola y=x^2, below by the x, axis, and on the right by the line x=2.
Wor... | 5 | [
0.050537109375,
-0.002471923828125,
0.0054931640625,
-0.0771484375,
-0.006500244140625,
-0.0556640625,
-0.10302734375,
0.0859375,
0.013916015625,
-0.000217437744140625,
-0.02099609375,
0.06640625,
0.0247802734375,
0.056884765625,
-0.01708984375,
0.002899169921875,
0.017578125,
-0.0... | 35,898 | 35898 | |
Help with partial fractions?
June 11th 2011, 04:34 PM
Lancet
Help with partial fractions?
I'm familiar with the cover up method of dealing with partial fractions. That being said, this is what I'm looking at:
$\frac{1 - v}{(v+1)^2}$
Obviously, the cover up method won't work here, as we would end up wit... | 5 | [
-0.060546875,
0.18359375,
-0.0203857421875,
0.05224609375,
0.0184326171875,
-0.00933837890625,
-0.140625,
-0.053466796875,
-0.00909423828125,
0.0145263671875,
-0.00469970703125,
-0.00139617919921875,
-0.05419921875,
0.0830078125,
-0.031494140625,
-0.024169921875,
0.031005859375,
0.... | 35,899 | 35899 |