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## Friday, June 02, 2006

### Group Theory: Lagrange's Theorem

In today's blog, I review the proof for Lagrange's Theorem. The theorem is named after Joseph-Louis Lagrange who first stated it. The first complete proof came 30 years later.

In today's blog, I also use the concept of order, subgroup, and coset. The concept of the coset was first proposed by Evariste Galois. The term "coset" was coined by G. A. Miller in 1910.

The content of today's blog is taken from Joseph A. Gallian's Contemporary Abstract Algebra.

Definition 1: Order of a Group

The number of elements of a group.

NOTE: If you need to review the definition of the group, see here.

Definition 2: Subgroup

If H is a subset of a group G and H is a group itself under the operation of G, then H is a subgroup of G.

Definition 3: Coset of H in G

Let G be a group and H a subgroup of G. For any a ∈ G, the set aH { ah : h ∈ H } is called the left coset of H in G containing a. The set Ha { ha : h ∈ H } is called the right coset of H in G containing a.

NOTE: An important idea behind the coset is that it is a distinct partition of elements (see Lemma 2 below). From the property of closure, we know that if two values are elements of a group, then their product (by this, I mean the result of the group operation) is also an element of the group.

From this, we know that the set of cosets can be divided up as follows: a1H, a2H, ..., arH where r is a positive integer and where for each coset i ≠ j → aiH ∩ ajH = ∅ [See Lagrange's Theorem below to see how this partitioning can be used]

Example 1 Coset: Z9

Let G = Z9 = { 0, 1, 2, 3, 4, 5, 6, 7, 8 } with operation '+'

NOTE: Z9 is the set of integers modulo 9 [See here for a review of modular arithmetic]

Let H = { 0, 3, 6 } with operation '+'

We can see that H is a subgroup of G

The left coset in this case is a+H (note it would aH is the operation were '*')

Here are the cosets:

0 + H = { 0, 3, 6 } = 3 + H = 6 + H
1 + H = { 1, 4, 7 } = 4 + H = 7 + H
2 + H = {2, 5, 8} = 5 + H = 8 + H

We can see that all cosets are either equal or distinct. I present a proof of this in Lemma 2 below.

Example 2: Even integers

Let Z be the set of integers

Then 2Z is a left coset which includes { ..., 0, 2, 4 , 6, ... }

Lemma 1: aH = H if and only if a ∈ H

Proof:

(1) Assume aH = H

(2) Then, a = ae ∈ aH = H

(3) Assume a ∈ H

(4) aH ⊆ H since h ∈ H → ah ∈ H [By property of closure, see here if needed]

(5) H ⊆ aH since:

(a) Let h be any element of H.

(b) a-1 ∈ H since a ∈ H [By the inverse property, see here if needed]

(c) a-1H ∈ H [By property of closure, see here if needed]

(d) So h = eh = (aa-1)h = a(a-1h) [By identity property, inverse property, and associative property, see here if needed]

(e) But a(a-1h) ∈ aH so that from (#5d), h ∈ aH.

(6) So H = aH since H ⊆ aH and aH ⊆ H.

QED

Lemma 2: if aH, bH are two cosets, then aH = bH or aH ∩ bH = ∅

Proof:

(1) Assume that aH ∩ bH ≠ ∅

(2) Let x ∈ aH ∩ bH since aH ∩ bH ≠ ∅

(3) Then there exists h1, h2 such that:

x = ah1
x= bh2

Since x is found in both aH and bH by assumption.

(4) Thus, a = xh1-1 = (bh2)h1-1

(5) From this, aH = [(bh2)h1-1]H = b(h2h1-1H) = bH [By Lemma 1 above]

QED

Theorem: Lagrange's Theorem

If G is a finite group and H is a subgroup of G, then the order of H divides the order of G.

Proof:

(1) Let a1H, a2H, ..., arH denote the distinct left cosets of H in G. [See Definition 3 above for details on left cosets of H in G.]

NOTE: If two cosets are equal then we only count them once.

(2) For each a ∈ G, we have aH = aiH for some i by our construction in step #1.

(3) a ∈ aH since:

a = ae and ae ∈ aH since H is a subgroup. [See Definition 2 above for details on subgroups]

(4) Thus, each member of G belongs to one of the cosets aiH [from step #2 and step #3.]

(5) G = a1H ∪ a2H ∪ ... ∪ arH [This follows directly from step #4]

(6) From Lemma 2 above, we know aiH = ajH or aiH ∩ ajH = ∅ and since each ai is distinct, we get:

order(G) = order(a1H) + order(a2H) + ... + order(arH)

(7) Since order(aiH) = order(H) for each i (by the definition of cosets, see definition 3 above, we have:

order (G) = r*order(H)

QED

Akash said...

Hi Larry,

It was wonderful going thru ur blog. You really have maintained it in an impeccable manner - i must say. Further, you have gone thru the troubles of providing links for some concepts which others might need and again it is a wonderful act and i really appreciate it. The world needs more math afficiandos like you.

Thanks for your beautiful explanations. Again I add thanks for your selfless service to humanity....Hope you create a book out of your blogs.

Tom said...

Hi Larry,

http://mathrefresher.blogspot.com/2006/06/group-theory-lagranges-theorem.html

can you explain how step 5 in Lemma 2 follows from Lemma 1? I'm not sure I understood.

Larry Freeman said...

Hi Tom,

I'll try to break it down step by step. I hope that this makes the step clear.

In Lemma 2, step #3 says that:
x = bh_2
x = ah_1

Since x=ah_1, we know that:
a = x(h_1)^(-1)

Since x=bh_2, we know that:
x(h_1)^(-1) = (bh_2)(h_1)^(-1)

Since a = x(h_1)^(-1), it follows that:
a = (bh_2)(h_1)^(-1)

Since a=(bh_2)(h_1)^(-1), it follows that:
aH=[(bh_2)(h_1)^(-1)]H

We further note that:
[(bh_2)(h_1)^(-1)]H = b[(h_2)(h_1)^(-1)H]

Now, we know that h_1,h_2 are elements of H [from step #3]

Since h_1 ∈ H, it follows that (h_1)^(-1) ∈ H. [Since closure is a property of groups]

Since (h_1)^(-1) ∈ H and h_2 ∈ H, it follows that (h_2)(h_1)^(-1) ∈ H

That's all we need to use Lemma 1 above. Since (h_2)(h_1)^(-1) ∈ H,
[(h_2)(h_1)^(-1)]H = H

Since [(h_2)(h_1)^(-1)]H = H, it follows that:
b[(h_2)(h_1)^(-1)]H = bH

Tom said...

Thank you, that made it clear!

Manohar Kuse said...

Very well exlained. This note on lagrange theorem in group theory helped me more than my textbook.
Thanks!!!

paaji said...

GOD !!!

novita said...

hi,
the first time i read the proof in the book contemporary abstract algebra,n when i read your explanation i understand about the proof but i still confused about steps 6 order(G)= order(a1(H))+....order(ar(H))if we sum like that so relation with your example before o(G)=o(0(H))+o(1(H))...+o(8(H))=3+3+3+3+3+3+3+3=24.it is wrong,because o(G)=9
and then steps 7 o(G)= r.o(H) relation with example r=8 so o(G)=8.3=24.
please explain that i need that in this week..

Larry Freeman said...

Hi Novita,

Can you provide more details on your example. I'm not clear how you are getting to O(G)=9.

Are you sure that you are following this assumption:

From this, we know that the set of cosets can be divided up as follows: a1H, a2H, ..., arH where r is a positive integer and where for each coset i ≠ j → aiH ∩ ajH = ∅

-Larry

Pawan Seerwani said...

This post helped me a lot..!!
Thanks and keep writing..! :) :)

Pawan Seerwani said...
This comment has been removed by a blog administrator.


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# teaching machines

## CS 455 Lecture 23 – Water

May 5, 2015 by . Filed under cs455, lectures, spring 2015.

### Agenda

• what ?s
• homework 4
• water
• forward differencing

### TODO

As a lab exercise:

1. Sync with the class repository to get the water starter project. Run it to find some very disappointing water. We’re going to do a couple of things to make it look better: 1) add environment mapping to make it reflect the skybox and 2) perturb its normals using a 3D noise texture.
2. Let’s start with environment mapping. Recall the concepts behind this technique: in world space, we shoot a vector from the eye to the vertex, and reflect that vector around the vertex’s normal. That reflected vector serves as a texture coordinate into a cube map. Last time, we implemented the reflection in the vertex shader. This time, our normals are going to be retrieved from a noise texture in the fragment shader. In the vertex, however, we’ll need to output the vertex’s world position. Add a varying for fposition_world. Compute its value in the vertex shader.
3. In the fragment shader, add a uniform for the camera’s world position. Upload it in OnDraw. Compute the incident vector.
4. Compute the reflection vector by reflecting the incident vector about the water’s normal. For now, assume the normal is the y-axis. This will change soon.
5. Add a uniform for the skybox texture in the fragment shader and in OnDraw. A skybox texture has already been made; it’s called skybox_texture.
6. Look up the color in the skybox using the reflection vector and the textureCube function. Assign this color to the fragment. How do things look?
7. Now let’s perturb the surface. We’re not going to actually move any geometry. We’re simply going to derive the normals across the water’s surface from a slice of a 3D noise texture. As time passes, we’ll read different slices of the texture, producing a rippling effect. Start by adding a uniform for the noise texture to the fragment shader and OnDraw. A texture object has already been made; it’s called noise_texture.
8. For looking up noise intensities, we’ll need a 3D texture coordinate. Two of these we can get from the 2D texture coordinate vertex attribute. Add a varying to get these values in the fragment shader. The third we can get from a clock reading. Add a time uniform in the fragment shader and in OnDraw.
9. We are not using the noise texture for color. We are using it as a heightmap; specifically, we are using it to calculate normals. How do we determine the normal at a given location? Find two tangent vectors and then take their cross product. How do we find two tangent vectors? Recall that a tangent vector lies across a surface, running parallel to the surface’s general orientation. We can find these parallel vectors by a technique called forward differencing. First, take three intensity readings:
here = lookup height at texture coordinates
right = lookup height at here + nudge right
above = lookup height at here + nudge up
10. With these three values in hand, we can determine the tangent vectors by computing their differences on all three dimensions:
tangentRight = [1, right - here, 0]
tangentAbove = [0, above - here, 1]

Both are vec3s. Compute their cross product to produce normal_world.

11. Alter the reflection vector calculate to use normal_world instead of the fixed y-axis.
12. How does it look? Try some different heightmap series: wkcamp, cupertin-lake, midnight-silence.
13. Send me a screenshot.

format: plain


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# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019061

## Inverse quadratic programming problem with $l_1$ norm measure

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 2 College of Science, Liaoning Technical University, Fuxin 123000, China

* Corresponding author: Lidan Li

Received  October 2018 Revised  January 2019 Published  May 2019

Fund Project: The third author is supported by the National Natural Science Foundation of China under project grant No.11571059 and No.11731013

We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem involving $l_1$ vector norm with a positive semidefinite cone constraint. By utilizing convex optimization theory, we rewrite its first order optimality condition as a generalized equation. Under extremely simple assumptions, we prove that any element of the generalized Jacobian of the equation at its solution is nonsingular. Based on this, we construct an inexact Newton method with Armijo line search to solve the equation and demonstrate its global convergence. Finally, we report the numerical results illustrating effectiveness of the Newton methods.

Citation: Lidan Li, Hongwei Zhang, Liwei Zhang. Inverse quadratic programming problem with $l_1$ norm measure. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019061
##### References:

show all references

##### References:
Numerical results of Problem (5)
 n p iter I-norm-F T-norm-F time(s) 50 10 4 9.8e+003 9.9e-012 0.06 100 10 4 7.5e+004 2.8e-007 0.19 100 20 8 6.6e+004 1.0e-009 0.38 100 50 8 1.9e+005 8.6e-007 0.39 500 50 12 9.3e+006 1.1e-013 52.77 500 100 17 8.2e+006 4.0e-010 79.76 1000 100 25 7.7e+007 9.2e-009 916.90 1000 500 30 3.8e+007 6.0e-008 1191.39 2000 500 34 4.7e+008 3.5e-011 9300.16
 n p iter I-norm-F T-norm-F time(s) 50 10 4 9.8e+003 9.9e-012 0.06 100 10 4 7.5e+004 2.8e-007 0.19 100 20 8 6.6e+004 1.0e-009 0.38 100 50 8 1.9e+005 8.6e-007 0.39 500 50 12 9.3e+006 1.1e-013 52.77 500 100 17 8.2e+006 4.0e-010 79.76 1000 100 25 7.7e+007 9.2e-009 916.90 1000 500 30 3.8e+007 6.0e-008 1191.39 2000 500 34 4.7e+008 3.5e-011 9300.16
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2018 Impact Factor: 1.025


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Home > Standard Error > St Error Of The Mean

# St Error Of The Mean

## Contents

So in this case, every one of the trials, we're going to take 16 samples from here, average them, plot it here, and then do a frequency plot. It is the standard deviation of the sampling distribution of the mean. And to make it so you don't get confused between that and that, let me say the variance. This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall https://en.wikipedia.org/wiki/Standard_error

## Standard Error Of The Mean Formula

With statistics, I'm always struggling whether I should be formal in giving you rigorous proofs, but I've come to the conclusion that it's more important to get the working knowledge first Consider the following scenarios. I just took the square root of both sides of this equation. The standard error (SE) is the standard deviation of the sampling distribution of a statistic,[1] most commonly of the mean.

ISBN 0-7167-1254-7 , p 53 ^ Barde, M. (2012). "What to use to express the variability of data: Standard deviation or standard error of mean?". However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and This is more squeezed together. Standard Error Regression Search Popular Pages Measurement of Uncertainty - Standard Deviation Calculate Standard Deviation - Formula and Calculation Statistical Data Sets - Organizing the Information in Research What is a Quartile in Statistics?

This article is a part of the guide: Select from one of the other courses available: Scientific Method Research Design Research Basics Experimental Research Sampling Validity and Reliability Write a Paper Our standard deviation for the original thing was 9.3. doi:10.2307/2340569. Lower values of the standard error of the mean indicate more precise estimates of the population mean.

The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. Standard Error Of Proportion Repeating the sampling procedure as for the Cherry Blossom runners, take 20,000 samples of size n=16 from the age at first marriage population. So I'm going to take this off screen for a second, and I'm going to go back and do some mathematics. The true standard error of the mean, using σ = 9.27, is σ x ¯   = σ n = 9.27 16 = 2.32 {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt

## Standard Error Of The Mean Excel

So 1 over the square root of 5. http://davidmlane.com/hyperstat/A103735.html We keep doing that. Standard Error Of The Mean Formula The mean age was 23.44 years. Standard Error Of The Mean Definition The standard deviation of all possible sample means of size 16 is the standard error.

This is the variance of your original probability distribution. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view menuMinitab® 17 SupportWhat is the standard error of the mean?Learn more about Minitab 17  The standard error of the mean (SE This is equal to the mean. Roman letters indicate that these are sample values. Standard Error Vs Standard Deviation

ISBN 0-8493-2479-3 p. 626 ^ a b Dietz, David; Barr, Christopher; Çetinkaya-Rundel, Mine (2012), OpenIntro Statistics (Second ed.), openintro.org ^ T.P. In fact, data organizations often set reliability standards that their data must reach before publication. Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} . If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean

They may be used to calculate confidence intervals. Difference Between Standard Error And Standard Deviation So we take 10 instances of this random variable, average them out, and then plot our average. Let's see if it conforms to our formulas.

## A larger sample size will result in a smaller standard error of the mean and a more precise estimate.

The graph below shows the distribution of the sample means for 20,000 samples, where each sample is of size n=16. And I think you already do have the sense that every trial you take, if you take 100, you're much more likely, when you average those out, to get close to Retrieved 17 July 2014. Standard Error Symbol This is the mean of our sample means.

All Rights Reserved. So this is equal to 9.3 divided by 5. The age data are in the data set run10 from the R package openintro that accompanies the textbook by Dietz [4] The graph shows the distribution of ages for the runners. What's going to be the square root of that?

Standard errors provide simple measures of uncertainty in a value and are often used because: If the standard error of several individual quantities is known then the standard error of some With n = 2 the underestimate is about 25%, but for n = 6 the underestimate is only 5%. And this time, let's say that n is equal to 20. It could look like anything.

What do I get? Hutchinson, Essentials of statistical methods in 41 pages ^ Gurland, J; Tripathi RC (1971). "A simple approximation for unbiased estimation of the standard deviation". It will be shown that the standard deviation of all possible sample means of size n=16 is equal to the population standard deviation, σ, divided by the square root of the The sample mean will very rarely be equal to the population mean.

You just take the variance divided by n. So if I know the standard deviation-- so this is my standard deviation of just my original probability density function. Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for So it's going to be a much closer fit to a true normal distribution, but even more obvious to the human eye, it's going to be even tighter.

Personally, I like to remember this, that the variance is just inversely proportional to n, and then I like to go back to this, because this is very simple in my It's going to look something like that. The standard deviation of all possible sample means of size 16 is the standard error. Maybe right after this I'll see what happens if we did 20,000 or 30,000 trials where we take samples of 16 and average them.

Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for So let's see if this works out for these two things. National Center for Health Statistics typically does not report an estimated mean if its relative standard error exceeds 30%. (NCHS also typically requires at least 30 observations – if not more It can only be calculated if the mean is a non-zero value.

If one survey has a standard error of $10,000 and the other has a standard error of$5,000, then the relative standard errors are 20% and 10% respectively.


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# factoring all-one polynomials using the grouping method

The method of grouping terms can be used to factor all-one polynomials, i.e. polynomials of the form

 $\sum_{m=0}^{n-1}x^{m}$

when $n$ is composite. (When $n$ is prime, these polynomials are irreducible, so there is nothing to do in that case.)

Let us consider a few examples:

$n=4$:

 $\displaystyle 1+x+x^{2}+x^{3}=$ $\displaystyle(1+x)+(x^{2}+x^{3})=$ $\displaystyle(1+x)+x^{2}(1+x)=$ $\displaystyle(1+x)(1+x^{2})$

$n=6$:

 $\displaystyle 1+x+x^{2}+x^{3}+x^{4}+x^{5}=$ $\displaystyle(1+x+x^{2})+(x^{3}+x^{4}+x^{5})=$ $\displaystyle(1+x+x^{2})+x^{3}(1+x+x^{2})=$ $\displaystyle(1+x^{3})(1+x+x^{2})$

$n=8$:

 $\displaystyle 1+x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}+x^{7}=$ $\displaystyle(1+x+x^{2}+x^{3})+(x^{4}+(x^{5}+x^{6}+x^{7})=$ $\displaystyle(1+x+x^{2}+x^{3})+x^{4}(1+x+x^{2}+x^{3})=$ $\displaystyle(1+x^{4})(1+x+x^{2}+x^{3})$

Combining this result with the factorization we have for the case $n=4$, we obtain the following:

 $\displaystyle 1+x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}+x^{7}=$ $\displaystyle(1+x)(1+x^{2})(1+x^{4})$

$n=9$:

 $\displaystyle 1+x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}+x^{7}+x^{8}=$ $\displaystyle(1+x+x^{2})+(x^{3}+x^{4}+x^{5})+(x^{6}+x^{7}+x^{8})=$ $\displaystyle(1+x+x^{2})+x^{3}(1+x+x^{2})+x^{6}(1+x+x^{2})=$ $\displaystyle(1+x+x^{2})(1+x^{3}+x^{6})$

$n=12$:

 $\displaystyle 1+x+x^{2}+x^{3}+x^{4}+x^{5}+x^{6}+x^{7}+x^{8}+x^{9}+x^{10}+x^{11}=$ $\displaystyle(1+x+x^{2})+(x^{3}+x^{4}+x^{5})+(x^{6}+x^{7}+x^{8})+(x^{9}+x^{10}% +x^{11})=$ $\displaystyle(1+x+x^{2})+x^{3}(1+x+x^{2})+x^{6}(1+x+x^{2})+x^{9}(1+x+x^{2})=$ $\displaystyle(1+x+x^{2})(1+x^{3}+x^{6}+x^{9})=$ $\displaystyle(1+x+x^{2})((1+x^{3})+(x^{6}+x^{9}))=$ $\displaystyle(1+x+x^{2})((1+x^{3})+x^{6}(1+x^{3}))=$ $\displaystyle(1+x+x^{2})(1+x^{3})(1+x^{6})$

It might be worth pointing out that the polynomials produced by this factorization are not all irreducible. For instance,

 $1+x^{3}=(1+x)(1-x+x^{2}).$

However, to obtain this factorization, one needs to use some techique other than the grouping method. Likewise. the polynomial $1+x^{6}$ is also reducible.

Title factoring all-one polynomials using the grouping method FactoringAllonePolynomialsUsingTheGroupingMethod 2013-03-22 15:06:52 2013-03-22 15:06:52 rspuzio (6075) rspuzio (6075) 13 rspuzio (6075) Example msc 13P05 AllOnePolynomial CyclotomicPolynomial


text:
# Player

Today 按播放鍵聽點音樂

## 歌名Moonlit Sky (with The Void Pacific Choir)歌手名 Robin Schulz

播放

### 歌詞

Under the moonlit sky We see the forces die Oh, ashes falling, oh, while it's falling Under the moonlit sky Oh, how you fall and die So long now, so long now Under the moonlit sky The stars fall and die How the see rages, oh love braises It's like the world you've known Before it's lost and gone Unlike a world you've seen Before it's lost to me Under the moonlit sky Just hold my hand and try Hold me soft tonight 'Neat the quiet lights Under the moonlit sky I'll hold your hand of lies But in my arm's colder Oh, soldier Under the moonlit sky We see the forces die Oh, ashes falling, oh, while it's falling Under the moonlit sky Oh, how you fall and die So long now, so long now So long now, so long now So long now, so long now So long now, so long now So long now, so long now

### 專輯

專輯名 SUGAR
歌手名 Robin Schulz
發行日 2015-09-25


text:
## Tuesday, June 28, 2011

### Counting Critters

 This picture allows us to set a lower bound on the number of creatures that ever lived of ~4.
We recently had a big book sale [1] here in town where books were being sold for about a quarter.  Needless to say, I bought far more than I'll probably ever need or read.  One of the books I bought was called General Paleontology by A. Brouwer [2].

Anyways, I didn't really make it too far in the book.  In fact, I only made it to the first sentence of the second paragraph of the first chapter, when I encountered this line:

"The number of individuals which has populated the Earth since life began is beyond estimation."

Horse feathers, I say!  Horse Feathers!

The number of things that ever lived may very well be unknowable, but it's certainly not beyond estimation.  So below, Alemi and I each provide an estimate for the total number of creatures that have ever lived on Earth.

We flipped a coin and I lost, so I guess I'll go first.  My estimation will be a genuine guess-y kind of estimate that doesn't draw too heavily on too many physical considerations.  Instead, I will formulate a series of assumptions and base my final answer on that.  So assuming my assumptions are valid, the answer should give a reasonable estimate to the total number of creatures that have ever lived.

My assumptions are as follows:

(1)  The number of individuals that have ever lived will be almost entirely dominated by the number of bacteria that have ever lived on Earth.  So to leading order, all the life that has ever lived on Earth is bacteria (or something similar).

(2)  Life began at some time, T, in the past and immediately spread to all places on Earth.  Hey, man, it's the power of geometric progression!

(3)  The majority of life is found within h = 1 m from the surface of water.  I picked this number since it's roughly (order of magnitude) how far down I can see in really clear water.  Most of the life will be photosynthetic and thus need a fair amount of sunlight.

(4)  The number density of organisms in water is  n ~ 10^5.  I have no real justification for this.

(5)  The average lifetime of an organism is t ~ 1 hr.

Alright, so if these assumptions are valid (a big if [3]), then the following prediction should be fairly accurate.  So the total volume in which these creatures may live is just the shell of the Earth down to about a meter:

$V = 4 \pi R_{\oplus}^2 h$

where R = 6 * 10^6 m is the radius of the Earth.  Alright, so the number of creatures at any given moment will be the volume times the number density which I will take to be n ~ 10^5.  That will give us the total number of creatures at any given moment.  But we want it for all the moments.  So I will take the total number of "generations" to be the time life has been around divided by the average lifetime of a given organism.  Putting this all together gives

$N = 4 \pi R_{\oplus}^2 h \times \frac{T}{t}$

Plugging in some numbers I get:

$N \sim 10^{39} \left(\frac{h}{1~\mbox{m}}\right)\left(\frac{n}{10^5~\mbox{cm}^{-3}}\right)\left(\frac{T}{3\times10^9~\mbox{yrs}} \right)\left(\frac{t}{1~\mbox{hr}} \right)^{-1}$

So for the nominal values I've plugged in, I'll get that about 10^39 creatures have ever lived on Earth [4].  I've left my equation in a dimensionless form above, so if you think my individual estimates are garbage, you can easily plug in your own estimates to see how things change.

Except for the completely arbitrary factor for the average number density of organisms per cubic centimeter of water, I feel alright about this estimate.  And I'm fairly confident that the number density will not be off more than about 3 orders of magnitude either high or low.  So my final estimate is:

$N \sim 10^{39 \pm 3}$

I promised that there would be two estimates, so I present below in picture form, Alemi's back-of-the-wrapper estimate.
 Click for the full Jimmy Johns experience
To explain these scribbles, I now cede the floor (and the mic) to Alemi.

[ SEAMLESS TRANSITION ]

So, when Corky posed this question to me while we ate some tasty sandwiches, another approach came to mind.

Namely, I wanted to try to estimate the number of critters that have ever lived by putting some kind of energy bound on the number.

Ultimately, all critters come from the sun. That is, all life on Earth is only able to exist in so much as it consumes energy, and for almost all life [ignoring the under ocean heat vent guys], the energy they consume, one way or another comes from the sun.

So, let's estimate the number of critters in three parts (1) We need the energy the Earth recieves from the sun. (2) We need to estimate the energy density of life (3) These two things, combined with a characteristic length or volume scale for a critter would enable us to figure out the rate at which the Earth could produce critters. (4) Assuming this rate and a time scale for how long life has been around on the Earth would give us a total number of critters.

Let's begin

(1) Energy from the sun.

Corky and I happen to know that the solar flux on the sun is roughly 1000 W/m^2. Multiplying this by half the surface area of the earth gives us a rough total solar flux

$(1000 \text{ W/m}^2) ( 2\pi R_{\oplus}^2) \sim 2 \times 10^{17} \text{ W}$

(2) Energy density of critters

For this we used the bag of potato chips we had on hand, assuming that all life matter has roughly the same energy content. The bag of chips was 150 calories in a serving size of 28 grams. This and assuming that life forms are the density of water gives us a life energy density

$\left( \frac{ 150 \text{ kcal} }{ 28 \text{ g}} \right)\left( \frac{ 1 \text{ g}}{ \text{ cm}^3} \right) \sim 2 \times 10^4 \text{ J/cm}^3$

(3) Length scale of critters

We assumed that bacteria are the most abundant life form, so we chose a length scale of 100 microns.

Putting these pieces together gives

$\frac{ 2 \times 10^{17} \text{ W} }{ \left( 2 \times 10^4 \text{ J/cm}^3 \right) \left( 100\ \mu\text{m} \right)^3 } \sim 10^{19} \text{ 1/s}$

Which is our estimated critter creation rate

(4) Time scale for life generation

Finally, we estimate that life creation has been chugging along on earth for about 3 billion years, this gives us our final estimate for the number of critters that have every lived

$\left( 10^{19} \text{ 1/s} \right) \left( 3 \times 10^9 \text{ years} \right) \sim 10^{36}$

So, there we have it. If the Earth was 100% efficient at converting solar energy into life, and that life is characteristically the energy density of a potato chip and the size of a bacteria, we should have had 1 billion billion billion billion critters ever. To make us feel a little better we would like to tack on a 10% efficiency, since we don't actually expect the Earth to be 100% efficient, and because 10% seems to be the rule of thumb efficiency estimation used when it comes to food chains and the like, so our final estimate, motivated purely by physics is

$\boxed{ \text{ Total number of critters ever } = 10^{35\pm 3} }$

This number seems pretty good, and is in general agreement with Corky's earlier method. Notice that the only parameter we are a little worried about the is the length scale, especially because our final answer depends on the inverse cube of this number, so, our error is probably something around 3 orders of magnitude, as before, since an order of magnitude goof in the size would cause 3 orders of magnitude error in the final estimate.

So there you have it.  Two not-egregiously-horrible estimates for the total number of critters that have ever lived.  All in all, I think that book was a quarter well spent!

Unnecessary footnotes:

[1]  This is a bit misleading.  They actually sold books of all sizes.

[2]  I like to read about paleontology and such just in case I'm ever sent back in time.  This way, I'll know what dinosaurs are safe to eat.

[3]  Here's a bigger if:  if

[4]  FUN FACT:  The total number of atoms in all the people on Earth is roughly 10^39.  A proof of this is left as an exercise for the reader.

1. Hmm. 7E9 people at 5E4 g each gives ~4E15 g of people. If we assume that the average atom in a person has an atomic weight of 12 (yes, hydrogen is common in people, but oxygen is only somewhat less common, and heavier things like phosphorous are abundant as well), then there are ~3E14 mols of people. Multiply by Avogadro and you have ~2E38. So, I'd put it of order 10^38, not 10^39.

2. Err, that should be "...~3E14 mols of atoms in people...

3. Yeah, I guess that beats my 100 kg people made entirely out of hydrogen...

BUT, we only need to push that number up past 3 to get it to round up one in order of magnitude (and make me right!). This can be accomplished through lots of breeding or lots of eating.

I leave this also as an exercise for the reader.

4. Estimates of the number of bacteria alive at this very instant in time are around 10^30.

5. That's interesting. By any chance do you have a reference handy? I'd love to see how they went about estimating it.

Thanks!

6. This appears to be the reference, which seems to follow Corky's approach, except with a much larger depth than a meter. http://www.pnas.org/content/95/12/6578.short

7. Thanks for the reference, Forbes.

Seems like they go almost a kilometer deep. That's interesting. I also heard from another physics grad here (who has connections to the paleontology world) that we had grossly underestimated the depth at which these guys live.

Now, I'm totally willing to believe my estimate was way off (as it was just a codified wild-guess), but Alemi found a reasonable upper bound on physical arguments. So where is all the extra energy coming form? Or, where have we made a poor assumption/estimate in our energy budget?

Help us, people who actually know something about biology, you're our only hope!

8. Ah, looks like it's a problem with the length scale - 1 micron instead of 100 microns, which gets you 6 orders of magnitude. http://en.wikipedia.org/wiki/Bacteria#Morphology

Also potato chips probably have a much higher energy density than typical life (but I think that's no more than a factor of a few).

9. Your number density in water seems way too low, for number of organisms, but I'm not sure by how much.
---
I agree with Forbes on the second set, from a recent Biochemistry PhD student (dropout, for personal reasons).

1 micron would be about the right length scale, and the energy density could easily be an order of magnitude or two too high.

10. There is a chance you're eligible for a new solar energy rebate program.


text:
Corpus ID: 221970544

# Unavoidable Induced Subgraphs of Large 2-Connected Graphs

@article{Allred2020UnavoidableIS,
title={Unavoidable Induced Subgraphs of Large 2-Connected Graphs},
author={Sarah Allred and G. Ding and Bogdan Oporowski},
journal={arXiv: Combinatorics},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Combinatorics
Ramsey proved that for every positive integer $n$, every sufficiently large graph contains an induced $K_n$ or $\overline{K}_n$. Among the many extensions of Ramsey's Theorem there is an analogue for connected graphs: for every positive integer $n$, every sufficiently large connected graph contains an induced $K_n$, $K_{1,n}$, or $P_n$. In this paper, we establish an analogue for 2-connected graphs. In particular, we prove that for every integer exceeding two, every sufficiently large 2… Expand

#### References

SHOWING 1-10 OF 10 REFERENCES
Typical Subgraphs of 3- and 4-Connected Graphs
• Computer Science, Mathematics
• J. Comb. Theory, Ser. B
• 1993
Unavoidable parallel minors of 4-connected graphs
• Mathematics, Computer Science
• J. Graph Theory
• 2009
Unavoidable Minors of Large 3-Connected Matroids
• Computer Science, Mathematics
• J. Comb. Theory, Ser. B
• 1997
Unavoidable Minors of Large 3-Connected Binary Matroids
• Computer Science, Mathematics
• J. Comb. Theory, Ser. B
• 1996
Editors
• Brain Research Bulletin
• 1986
Graph theory, volume 173 of Graduate Texts in Mathematics. Springer, Berlin, fifth edition, 2018
• Paperback edition of [ MR3644391]
• 2018


text:
# Statistically Efficient, Polynomial Time Algorithms for Combinatorial Semi Bandits

We consider combinatorial semi-bandits over a set of arms X⊂{0,1}^d where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound R(T) = O( d (ln m)^2 (ln T) Δ_min), but it has computational complexity O(| X|) which is typically exponential in d, and cannot be used in large dimensions. We propose the first algorithm which is both computationally and statistically efficient for this problem with regret R(T) = O(d (ln m)^2 (ln T)Δ_min) and computational complexity O(T poly(d)). Our approach involves carefully designing an approximate version of ESCB with the same regret guarantees, showing that this approximate algorithm can be implemented in time O(T poly(d)) by repeatedly maximizing a linear function over X subject to a linear budget constraint, and showing how to solve this maximization problems efficiently.

• 2 publications
• 16 publications
• 4 publications
06/28/2014

### Efficient Learning in Large-Scale Combinatorial Semi-Bandits

A stochastic combinatorial semi-bandit is an online learning problem whe...
02/14/2021

### Asymptotically Optimal Strategies For Combinatorial Semi-Bandits in Polynomial Time

We consider combinatorial semi-bandits with uncorrelated Gaussian reward...
03/04/2015

### Hierarchies of Relaxations for Online Prediction Problems with Evolving Constraints

We study online prediction where regret of the algorithm is measured aga...
02/11/2019

### Exploiting Structure of Uncertainty for Efficient Combinatorial Semi-Bandits

We improve the efficiency of algorithms for stochastic combinatorial sem...
07/31/2021

### Pure Exploration and Regret Minimization in Matching Bandits

Finding an optimal matching in a weighted graph is a standard combinator...
02/10/2021

### An Efficient Pessimistic-Optimistic Algorithm for Constrained Linear Bandits

This paper considers stochastic linear bandits with general constraints....
10/05/2020

### An Efficient Algorithm for Cooperative Semi-Bandits

We consider the problem of asynchronous online combinatorial optimizatio...


text:
# CERN Accelerating science

CMS Documentation in CDS
Conference Reports, Notes, Preprints, Thesis and Photos can be searched from the general CMS Collection page.

# CMS Theses

2014-12-17
12:50
 Radiation Damage to the diamond-based Beam Condition Monitor of the CMS Detector at the LHC / Guthoff, Moritz (CERN) ; De Boer, Willem (dir.) (Karlsruhe U., EKP) CERN-THESIS-?; CMS-TS-2014-043.- 2014 - 173 p. Fulltext: PDF;

2014-12-16
14:40
 Extraction of CP Properties of the H(125) Boson Discovered in Proton-Proton Collisions at $\sqrt{s}$ = 7 and 8 TeV with the CMS Detector at the LHC / Chen, Yi (Caltech) ; Spiropulu, Maria (dir.) (Caltech) In this thesis we build a novel analysis framework to perform the direct extraction ofall possible eﬀective Higgs boson couplings to the neutral electroweak gauge bosonsin the H → ZZ (∗) → 4 channel also referred to as the golden channel. We use analytic expressions of the full decay diﬀerential cross sections for the H → V V → 4process, and the dominant irreducible standard model q q → 4 background where¯4 = 2e2µ, 4e, 4µ. [...] CERN-THESIS-2014-201; CMS-TS-2014-044.- 2014 - 253 p. Fulltext: TS2014_044_2 - PDF; TS2014_044 - PDF;

2014-12-10
11:38
 Tests of the standard model in photoproduction at HERA and the LHC / de Favereau de Jeneret, Jérôme Photoproduction has been used at colliders for decades in order to study hadronic properties of matter [...] 202 p.

DIAL server - Full text
2014-12-10
11:26
 Photoproduction of top and higgs particles at the LHC / Ovyn, Séverine Thanks to its high energy and luminosity, the Large Hadron Collider (LHC) at CERN can also be exploited as an high energy photon collider [...] 186 p.

DIAL server - Full text
2014-12-10
10:38
 Radiation damage induced by neutrons in CMS silicon sensors / Forton, Eric Les expériences conduites auprès du futur accélérateur LHC au CERN nécessitent la construction des détecteurs les plus grands et les plus complexes jamais conçus [...]

DIAL server
2014-12-10
10:27
 CMS Trigger strategies for the selection of MSSM Higgs bosons using electron tau-jet decay modes / van der Aa, Olivier The thesis work concentrated on the developments of selection strategies for the observation of MSSM Higgs bosons in the context of the CMS experiment. [...] 111 p.

DIAL server - Fulltext
2014-12-09
22:05
 Evolution of the CMS ECAL Performance and R&D Studies for Calorimetry Options at High Luminosity LHC / Lucchini, Marco Toliman During the past years the Large Hadron Collider (LHC) at CERN operated with a maximum center-of-mass energy of $\sqrt{s} = 8$~TeV, a peak luminosity of around $7\times 10^{33}$~cm$^{-2}$s$^{-1}$ and collected about $23$~fb$^{-1}$ of data which lead to the discovery of a Higgs Boson in July 2012 [...] CERN-THESIS-2014-197 - 194 p.

Fulltext
2014-12-04
16:55
 Les senseurs au silicium de CMS : étude de leur résistance aux flux intenses de neutrons / Assouak, Samia Le LHC est un accélérateur de hadrons conçu essentiellement pour la découverte du boson de Higgs supposé être à l'origine de la masse des particules élémentaires [...] 164 p.

DIAL server - Full text
2014-12-04
16:16
 Search for baryon number violation in top-quark decays with the CMS experiment / Gabusi, Michele A search for baryon number violation (BNV) in top-quark decays is performed using p-p collisions produced by the Large Hadron Collider at the energy in the center of mass of 7 TeV and 8 TeV [...] 185 p.

DIAL server - Full text
2014-11-28
15:46
 Evidence for a Higgs boson in tau decays with the CMS detector / Dutta, Valentina In this thesis, I describe the search for a Higgs boson through its decay to a pair of tan leptons with the tau-pair subsequently decaying to ail electron, a muon, and neutrinos [...] CERN-THESIS-2014-191. - 185 p.

MIT server - Full text


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Guide: How to Install phpMyAdmin Goto page Previous  1, 2, 3, 4, 5, 6, 7  Next

Yes - It Was Helpful  75%  [ 148 ]
No - But Helpful  4%  [ 9 ]
No - I've got problems  19%  [ 38 ]
Other  1%  [ 2 ]

Author Message
mobrien
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Joined: 05 Oct 2004
Posts: 18

 Posted: Tue Oct 05, 2004 7:45 am    Post subject: Also, on top of copying php_mysql.dll, I also had to copy libmysql.dll to the php directory, out of the php.zip. Hope this helps someone else in the future. Thanks. you guys are great.
Umies
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Joined: 07 Oct 2004
Posts: 4

tttommeke
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Joined: 18 Apr 2004
Posts: 1

 Posted: Mon Nov 01, 2004 7:51 pm    Post subject: #1045 - Access denied for user 'root'@'localhost' (using password: NO) Help how can i go back into my phpmyadmin stuff
jdwfly
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Joined: 14 Nov 2004
Posts: 1

 Posted: Sun Nov 14, 2004 9:09 am    Post subject: MySQL said: #1251 - Client does not support authentication protocol requested by server; consider upgrading MySQL client I'm not quite sure what this means, I have the current version of MySQL. I also have the correct password. Does anyone here know what this means?
oannes
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Joined: 19 Nov 2004
Posts: 2

 Posted: Fri Nov 19, 2004 12:22 pm    Post subject: ..and it was all going so well :( Thanks to all who have contributed to this thread, but AAAARRGGGHHH Everything installed perfectly - I thought, but all I get from script is "No input file specified." To make matters worse, an earlier poster had the same problem - then solved it himself WITHOUT SAYING HOW! Can anyone help with this one? I seem to have run out of things to try!
oannes
-

Joined: 19 Nov 2004
Posts: 2

 Posted: Fri Nov 19, 2004 4:59 pm    Post subject: hmmm - taking a hint from my mysterious friend, I seem to have solved this for myself, so for anyone else with this problem, comment out the line in php.ini which reads: doc_root ="whatever" in my file this is line #437 Hope this helps :)
player1
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Joined: 29 Nov 2004
Posts: 6
Location: London

leawildcat
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Joined: 04 Dec 2004
Posts: 9
Location: Texas

 Posted: Mon Dec 06, 2004 6:28 pm    Post subject: Try this, worked for me http://dev.mysql.com/doc/mysql/en/Old_client.html
fluff
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Joined: 10 Dec 2004
Posts: 5

 Posted: Mon Dec 13, 2004 2:23 am    Post subject: Hi I did everything said in the guide but when I try to browse to phpmyadmin I get the following message: #1045 - Access denied for user 'root'@'localhost' (using password: NO) I did change the root password for mysql and I also set it to localhost access only. When browsing to localhost/phpmyadmin I get the same message :( Thanks
thephoenix
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Joined: 12 Dec 2004
Posts: 1

 Posted: Tue Dec 21, 2004 7:17 pm    Post subject: At one part in the guide it says input http://localhost/phpMyAdmin i did that and it said error file not found or summit, what i do to fix this, coz i done everything else :S
tecnoboy
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Joined: 02 Jan 2005
Posts: 9

 Posted: Sun Jan 02, 2005 5:35 pm    Post subject: Hi, Im having a problem, when I try to access: http://localhost/phpMyAdmin it gives me the following error: "cannot load MySQL extension, please check PHP Configuration" I know that I need a thing called "MySQL Extension for PHP", or "mysqli", I think they are the same, were can I download this, and how should I install it ? Please help me, thanks.
NoName
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Joined: 05 Jan 2005
Posts: 88
Location: Lawton America

 Posted: Thu Jan 06, 2005 3:10 am    Post subject: I just wanted to post and say that this tutorial was great. I followed it step by step and everything worked perfect. I also followed the mySQL tutorial along with this and both worked fine for me..._________________-NoName www.nonameproductions.us Powered by Abyss Web Server
mrkill47
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Joined: 12 Jan 2005
Posts: 17
Location: 127.0.0.1

 Posted: Wed Jan 12, 2005 11:06 pm    Post subject: I am about to go thru the tutorial (just done your MySQL one - excellent). I was wondering why not use the latest version of phpMyAdmin? I am running PHP 5.0.3.... I guess I could attempt to install the latest version..How different will the installation process be, compared to your tutorial? Thanks._________________http://fnar.sytes.net <<--- Powered by Abyss :D
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Sun Jan 16, 2005 10:14 pm    Post subject: i´ve got some problems, when i install mysql dont have the winmsql***.exe file to execute...what version i must download??could you give the direct link?? thx in advance... P.S. Forgot this...now i can do it but when i try to enter in phpMyAdmin appears this : what is this??? and sorry for the image size...Last edited by Portuga on Tue Jan 18, 2005 12:30 pm; edited 1 time in total
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

Posted: Mon Jan 17, 2005 1:18 am    Post subject:

MySQL 4.1.8 is the last one to include winmysqladmin.exe. Get it here...

Your screenshot has nothing to do with the above mentioned. You need to
configure PHP to load php_mysql.dll, which is only included in the zip package
of PHP. In your php.ini file, uncomment the line that says this...
 Code: ;extension=php_mysql.dll
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 12:03 pm    Post subject: and where i configure that?? I have instaled that to my pc (C:\PHP) but its the same thing...i have that line in the file!! appears the same error... i dont know what do... please help me!!!
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 12:43 pm    Post subject: Do you have php_mysql.dll in your ext folder? If you do, the easy way is to copy & paste it into the main folder of php. See if that works.
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 12:53 pm    Post subject: I do not have that folder :S see this screenshots plz and say something...my version is 5 P.S. in IE, the /phpmyadmin folder opens like a txt folder and in the firefox doesnt open... i dont know what to do...
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 12:59 pm    Post subject: You downloaded the PHP installer. You need to download the PHP zip package. Then, take php_mysql.dll out of the ext folder and put it into the PHP folder.
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 1:10 pm    Post subject: I´ve did it but its doesnt work...i dont know what to do im :S... do you want to go to my account to see if is all ok?? I have follow the mysql, phpmyadmin and php support tutorials but this doesnt work :@
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 1:25 pm    Post subject: If you have php_mysql.dll, then it seems your php.ini file is not setup correctly. If you want, you can email it to me so I can look at it. Or PM me the acount to look at.
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 1:38 pm    Post subject: PM sent...now...i beleive in you, that you can resolve my errors...and if you need to change something but dont have some things that you need...say me... Thx...
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 2:12 pm    Post subject: Check your PM.
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 2:25 pm    Post subject: It doesnt work :'(...in the firefox doesnt open...in the ie the php file opens like an txt file...
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 2:33 pm    Post subject: Ok, check your gmail. Or are you talking about phpmyadmin don't work?
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 2:42 pm    Post subject: I dont have nothing on my gmail but i will wait... and im talk that i cannot open the php files :S ...but i will try again!
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

Posted: Tue Jan 18, 2005 2:48 pm    Post subject:

 Code: ;extension=php_mysql.dll

to...
 Code: extension=php_mysql.dll

That is the only thing I changed.

Are you Portugese?
Portuga
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Joined: 16 Jan 2005
Posts: 16

 Posted: Tue Jan 18, 2005 2:49 pm    Post subject: I did it!!!Yupiiiiiiiiiiiiiiiiiiiiii... thx Moxxnixx...your help was great...thx xD How you know i´m Portuguese?
Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

 Posted: Tue Jan 18, 2005 2:59 pm    Post subject: The language on your site looked like Spanish, but different. I'm happy you got it to work.:D
vhsorless
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Joined: 25 Jan 2005
Posts: 45

leawildcat
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Joined: 04 Dec 2004
Posts: 9
Location: Texas

 Posted: Wed Jan 26, 2005 5:52 am    Post subject: http://dev.mysql.com/doc/mysql/en/Old_client.html
vhsorless
-

Joined: 25 Jan 2005
Posts: 45

Posted: Fri Jan 28, 2005 1:58 am    Post subject:

 leawildcat wrote: http://dev.mysql.com/doc/mysql/en/Old_client.html

Wow. Thanks very much for this information. That was quick. :)

One question though: I understand how to reset the password to the old-style password as per the instructions on that page, but I don't know how to "Upgrade all client programs to use a 4.1.1 or newer client library" as it says there.

I'm not 100% sure what they mean. Pardon my ignorance, but what exactly do they mean by "client programs"? I think I am using the most recent version of MySQL. I'll double-check, but I could've sworn I downloaded the most recent version. If you have any helpful advice, I could really use it.

Thanks again.

P.S. I checked and I'm using phpMyAdmin 2.6.1, which is supposedly compatible with the version of MySQL I'm using. Maybe the problem is the new MySQL installer package that I used, which is on this page under Windows Binaries:

leawildcat
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Joined: 04 Dec 2004
Posts: 9
Location: Texas

 Posted: Sat Jan 29, 2005 3:57 pm    Post subject: I'm not exactly sure what they mean by upgrading the client program unless they mean upgrading your windows. Which Windows version were you installing on? The reason I think that is because I just recently set up a dual boot system. My very first attempt at installing exactly what you did yielded a multitude of problems because I was installing on Win98SE which does not really like any server program. Took me 4 days to get the bugs worked out and everything working properly and I didn't tinker beyond that point. I created the dual boot system with WinXP and installed perl, php, abyss, phpmyadmin and didn't encounter that error this time. So other than that I'm not really sure. Sorry, wish I had a better answer.
vhsorless
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Joined: 25 Jan 2005
Posts: 45

Posted: Sat Jan 29, 2005 10:45 pm    Post subject:

 leawildcat wrote: I'm not exactly sure what they mean by upgrading the client program unless they mean upgrading your windows. Which Windows version were you installing on? The reason I think that is because I just recently set up a dual boot system. My very first attempt at installing exactly what you did yielded a multitude of problems because I was installing on Win98SE which does not really like any server program. Took me 4 days to get the bugs worked out and everything working properly and I didn't tinker beyond that point. I created the dual boot system with WinXP and installed perl, php, abyss, phpmyadmin and didn't encounter that error this time. So other than that I'm not really sure. Sorry, wish I had a better answer.

I'm using Windows XP Home with all the latest service packs installed. I'm using Mozilla Firefox (Firefox RULES!) as my browser instead of IE, so that could also be a factor. I don't think so, but I'm just guessing here, so... lol

I'm not 100% sure, but I think they're referring to any programs that I might be using in conjunction with MySQL 4.1.1—like phpMyAdmin, etc... when they say "client programs". Anything you might be installing on the server for use with MySQL. That seems logical to me.

Back to the ol' drawing board. *sigh*
Skin Ticket
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Joined: 29 Jan 2005
Posts: 1

 Posted: Sun Jan 30, 2005 12:18 am    Post subject: I got this error Warning: odbc_connect() [function.odbc-connect]: SQL error: [Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified, SQL state IM002 in SQLConnect in C:\Program Files\Abyss Web Server\htdocs\db\msaccess.php on line 55 phpBB : Critical Error Could not connect to the database DEBUG MODE SQL Error : Error I tried ever other database name also and got a message saying my server doesnt support the database selected.... This is trying to install phpBB
darksnape
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Joined: 05 Mar 2005
Posts: 1

 Posted: Sat Mar 05, 2005 4:53 pm    Post subject: I got this error : Error 200 OK -------------------------------------------------------------------------------- Abyss Web Server X1 © Aprelium Technologies - 2001-2004
vbgunz
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Joined: 02 Feb 2003
Posts: 615
Location: Florida

Posted: Sat Mar 05, 2005 5:31 pm    Post subject:

If you get the following error
 Quote: #1251 - Client does not support authentication protocol requested by server; consider upgrading MySQL client
but you already have the latest version of MySQL (4.1.10), you really do have the latest client.

What I've found to solve this problem is to upgrade PHP from 4.3.10 to 5.0.3.

Good luck!
_________________
Victor B. Gonzalez
http://aeonserv.com
mobileplaza
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Joined: 04 Apr 2005
Posts: 35

 Posted: Wed Apr 06, 2005 5:59 pm    Post subject: cheers for the guide ist worked... well 99% there i just have trouble when accessing http://localhost/phpMyAdmin/ i get the following error cannot load mysql extension; please check PHP configuration Documentation any ideas??
mobileplaza
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Joined: 04 Apr 2005
Posts: 35

 Posted: Wed Apr 06, 2005 6:42 pm    Post subject: Problem solved just had to wipe Php 5 and install php 4.3.. works a charm.... no to design me site and get a forum up.... yay!!!!
macmee
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Joined: 27 Mar 2005
Posts: 15

 Posted: Sat Apr 16, 2005 11:23 am    Post subject: HELP PLEASE MySQL said: Documentation #1251 - Client does not support authentication protocol requested by server; consider upgrading MySQL client That came up after I installed phpmyadmin and mysql Please help me!
aprelium
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Joined: 22 Mar 2002
Posts: 6800

 Posted: Sat Apr 16, 2005 3:27 pm    Post subject: Re: HELP PLEASE macmee, Install our preconfigured PHP 5 package from http://www.aprelium.com/abyssws/php5win.html ._________________Support Team Aprelium - http://www.aprelium.com
erix920
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Joined: 30 Apr 2005
Posts: 8

aprelium
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Joined: 22 Mar 2002
Posts: 6800

Posted: Mon May 02, 2005 1:07 pm    Post subject: Re: Gur

erix920,

The error is self-explicit:

See our previous message and install our preconfigured PHP 5 package.
_________________
Support Team
Aprelium - http://www.aprelium.com
erix920
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Joined: 30 Apr 2005
Posts: 8

 Posted: Mon May 02, 2005 8:55 pm    Post subject: well nothing works anymore lol, mySQL is showing a red light somthing about ODBC not being installed when i installed it three times..... I dont get how people get this to work, or i just didnt pay attension to the directions, if anyone can simplify this, please send me an email at erix920@yahoo.com Thankz - Eric
aprelium
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Joined: 22 Mar 2002
Posts: 6800

 Posted: Tue May 03, 2005 2:45 pm    Post subject: erix920, The fact the MySQL red light is shown has nothing to do with PHP. It seems that you should reinstall MySQL or fix the problem that causes it to not being running correctly._________________Support Team Aprelium - http://www.aprelium.com
Tiffer
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Joined: 22 Jun 2005
Posts: 1

 Posted: Wed Jun 22, 2005 7:23 pm    Post subject: ok i have installed PHP, MySQL, Abyss Web Server its all in the correct Place but when i click mysqladmin in Abyss Web Server\database\mysql\bin it opens what i think is CMD box then closes again can u please tell me why this is happening.
aprelium
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Joined: 22 Mar 2002
Posts: 6800

 Posted: Thu Jun 23, 2005 1:55 pm    Post subject: Tiffer, MySQLAdmin isn't required to have MySQL run. When installing MySQL, it is better to configure it as a service. That way it will be started on boot time and remain available in the background as a service._________________Support Team Aprelium - http://www.aprelium.com
TB2
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Joined: 18 Nov 2004
Posts: 20

Moxxnixx
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Joined: 21 Jun 2003
Posts: 1226
Location: Florida

Posted: Sun Jul 03, 2005 1:09 am    Post subject:

TB2, you need to specify the port in your config.inc.php file.
TB2
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Joined: 18 Nov 2004
Posts: 20

 Posted: Sun Jul 03, 2005 10:52 am    Post subject: Yeah it works, thx a lot!!! Maybe that should be mentioned in the tutorial, too, for dumb people like me...
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text:
## Rocky Mountain Journal of Mathematics

### Oscillation Criteria for Systems of Parabolic Equations with Functional Arguments

#### Article information

Source
Rocky Mountain J. Math., Volume 34, Number 3 (2004), 1031-1046.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181069841

Digital Object Identifier
doi:10.1216/rmjm/1181069841

Mathematical Reviews number (MathSciNet)
MR2087445

Zentralblatt MATH identifier
1064.35201

#### Citation

Li, Wei Nian; Meng, Fan Wei. Oscillation Criteria for Systems of Parabolic Equations with Functional Arguments. Rocky Mountain J. Math. 34 (2004), no. 3, 1031--1046. doi:10.1216/rmjm/1181069841. https://projecteuclid.org/euclid.rmjm/1181069841

#### References

• B.T. Cui, Oscillation criteria for $n$-th order delay differential equations, Math. J. Toyama Univ. 13 (1990), 1-8.
• J. Jaros and I.P. Stavroulakis, Oscillation tests for delay equations, Rocky Mountain J. Math. 29 (1999), 197-207.
• W.N. Li, Oscillation for systems of partial differential equations with functional arguments, Demonstratio Math. 32 (1999), 521-530.
• W.N. Li and B.T. Cui, Oscillations of systems of neutral delay parabolic equations, Demonstratio Math. 31 (1998), 813-824.
• --------, Oscillation for systems of parabolic equations of neutral type, Southeast Asian Bull. Math. 23 (1999), 447-456.
• --------, Oscillation for systems of parabolic differential equations of neutral type, Soochow J. Math. 25 (1999), 341-352.
• Y.K. Li, Oscillation of systems of hyperbolic differential equations with deviating arguments, Acta Math. Sinica 40 (1997), 100-105 (in Chinese).