text:
March 24, 2023, 08:02:32 AM
Forum Rules: Read This Before Posting

### Topic: What are some good starting chemicals?  (Read 42221 times)

0 Members and 1 Guest are viewing this topic.

#### enahs

• 16-92-15-68 32-7-53-92-16
• Retired Staff
• Sr. Member
• Posts: 2179
• Mole Snacks: +206/-44
• Gender:
##### Re: What are some good starting chemicals?
« Reply #45 on: January 04, 2007, 08:53:34 PM »
I might be a little late (been busy) but if you have not had much experience in Chemistry lab in school, I would highly recommend not starting your own lab first, but buying a kit.

It has nothing to do with thinking you are stupid, or immature; but many of the safety procedures in a chemistry lab seem to go against common sense, and most you will not know, at all, without experience or somebody telling you.

This kit, for instance:
http://www.hometrainingtools.com/catalog/chemistry/chemistry-kits/p_kt-micchem.html
Is quite nice for a home starter kit, for a high school student/mature student. It is not one of those cheap crappy ones you can get at Toys R’ Us, it has some damn useful chemicals in it. Unfortunately it does not list the experiments included (well, just what they cover, which is a wide range, but not what actual experiment you do to cover that information), but based on the equipment and chemicals, and knowing the level of education they expect, they would be some very fun and educational experiments. And the bonus is that it comes with all the safety instructions.

Some of the chemicals that you have been talking about are down right dangerous for someone at your level (in the concentrations you are getting). There is nothing wrong with enthusiasm, but you must go slow and learn first; this is not a comment against you, chemistry is a hard subject and can be very dangerous.

I just say this for your safety, because based off of the question you are asking and the chemicals you are trying to get, I fear bad things will happen (and not because I think you are stupid, but because the key to be safe is experience and proper instruction).

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #46 on: January 04, 2007, 09:06:44 PM »
A bit late....well kinda... i havn't purchased any chemicals other than (sulfur and like two other ones form united nucear) but I did buy test tubes, a set with test tube rack and test tube utensils, plus some beakers, stoppers, flasks, alcohol burner, and..o ya a grad cylyneder...

But aside from that I will make sure to see any safety precautions that have to do with the chemicals and also post here before attempting any (even slightly) dangerous experiments

but thanks for the heads up

looks like a really nice set by the way (always been looking for one that isnt like the cheap toysrus but could never find it) too bad its $100 and ive already bought$50 worth of stuff

Thanks again and I'll make sure to be safe
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse

#### constant thinker

• Sr. Member
• Posts: 1275
• Mole Snacks: +85/-45
• Gender:
##### Re: What are some good starting chemicals?
« Reply #47 on: January 04, 2007, 09:27:24 PM »
Check the MSDS (Material Safety Data Sheet)for chemicals before you order them.

Calcium is more reactive is it not?

Sorry, I didn't look at a periodic table, but Ca is more reactive than Mg now that I have. If you don't know about the reactivity of metals, I suggest you google/wikipedia metal reactivity.

Back to what Borek said though...
What happens when you add Ca to just water?

Another thing about doing chemistry labs, you make want to look into distilled water depending on what kind of water you have.
"The nine most terrifying words in the English language are, 'I'm from the government and I'm here to help.' " -Ronald Reagan

"I'm for anything that gets you through the night, be it prayer, tranquilizers, or a bottle of Jack Daniels." -Frank Sinatra

#### enahs

• 16-92-15-68 32-7-53-92-16
• Retired Staff
• Sr. Member
• Posts: 2179
• Mole Snacks: +206/-44
• Gender:
##### Re: What are some good starting chemicals?
« Reply #48 on: January 04, 2007, 09:52:03 PM »
A bit late....well kinda... i havn't purchased any chemicals other than (sulfur and like two other ones form united nucear) but I did buy test tubes, a set with test tube rack and test tube utensils, plus some beakers, stoppers, flasks, alcohol burner, and..o ya a grad cylyneder...

Too bad, as it is a very nice set. I actually just looked it up when making my post to you, and I have ordered one. I get asked all the time by friends various things, and this will allow me to demonstrate many things; and I do college Gen Chem 1 & 2 tutoring at home, so it will be very useful for illustration too (plus, I like Chemistry and it seems neat to have at home!).

That said, all the equipment you bought would work quite well with the set, and replace the cheaper plastic versions .

http://www.balancedscience.com/qsl_final_0312/chem_index.html
The experiments:
http://www.balancedscience.com/qsl_final_0312/chem_kit.html
And here is an example experiment:
http://www.balancedscience.com/qsl_final_0312/chem_sample.html

« Last Edit: January 04, 2007, 10:32:16 PM by enahs »

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #49 on: January 05, 2007, 01:57:10 AM »
awsome thanks for the links, what college do you go to by the way?

EDIT: went out and bought some epsom salt today, is there any slightly interesting experiments you can do with it?
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #50 on: January 05, 2007, 02:58:40 AM »
By the way again... I just took a test tube, turned a Dust Remover can upside down, sparyed so I got liquid air or some type of liquid gas that boils away fairly quickly and then poured some Hydrogen Peroxide 3% in and the H2O2 froze and it bubbles up, turned sold, then Poured/shook the solid ice out of the tube and it feels kinda like starch with water....and fizzes pretty cool, and strangly unlike most dust removers that stuffs not flamable, wonder what its made of....
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse

#### joeflsts

• Regular Member
• Posts: 64
• Mole Snacks: +3/-0
• Gender:
• Ten fingers.. ten toes... PHEW!
##### Re: What are some good starting chemicals?
« Reply #51 on: January 05, 2007, 07:33:24 PM »
By the way again... I just took a test tube, turned a Dust Remover can upside down, sparyed so I got liquid air or some type of liquid gas that boils away fairly quickly and then poured some Hydrogen Peroxide 3% in and the H2O2 froze and it bubbles up, turned sold, then Poured/shook the solid ice out of the tube and it feels kinda like starch with water....and fizzes pretty cool, and strangly unlike most dust removers that stuffs not flamable, wonder what its made of....

One thing totally amazing about the internet is that there are vast resources available to you today that I didn't have when I was young.  For example you could google (that wasn't a verb when I was young) for either Epsom Salt or Magnesium Sulfate experiments and you would be impressed with the # of hits you will get.  One example is:

http://familyfun.go.com/parenting/learn/activities/feature/famf_science/famf_science7.html

Epsom Salts are a good starting material for relatively safe experiments.  I highly suggest that as you explore additional experiments always think through what you're going to do.  You'll find over time that you will understand your limitations.  I always try to understand what "could" happen to me if something went wrong.  As you age this becomes more of an issue!

Joe

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #52 on: January 05, 2007, 09:55:09 PM »
Ya, I tried googling the salt but all the stuff i found is making salt crystals, nothing about actualy chemical reactions with it...
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse

#### jdurg

• Banninator
• Retired Staff
• Sr. Member
• Posts: 1366
• Mole Snacks: +106/-23
• Gender:
• I am NOT a freak.
##### Re: What are some good starting chemicals?
« Reply #53 on: January 05, 2007, 10:35:48 PM »
Check the MSDS (Material Safety Data Sheet)for chemicals before you order them.

Calcium is more reactive is it not?

Sorry, I didn't look at a periodic table, but Ca is more reactive than Mg now that I have. If you don't know about the reactivity of metals, I suggest you google/wikipedia metal reactivity.

Back to what Borek said though...
What happens when you add Ca to just water?

Another thing about doing chemistry labs, you make want to look into distilled water depending on what kind of water you have.

First off, MSDS sheets are pretty good for letting you know potential dangers involving a chemical, but you should probably take that information with a grain of salt.  MSDS sheets don't do a very good job of explaining just how likely a dangerous reaction is to occur.  If there is even the slightest of possibilites of a nasty reaction happening, it will be indicated in the MSDS but there will be no mention of the chances of it happening.  This is a problem with the MSDS sheets.  They don't mention how likely a bad reaction is to occur.

In regards to calcium, Calcium metal in plain water reacts a tad bit slower than lithium does, but in a similar manner.  The thing is, the reaction generates a LOT of heat and as the temperature of the Ca and H2O rises, the reaction rate increases.  So asking if you put calcium metal into a solution of magnesium ions and get Mg metal out is like asking if you can put lithium metal into a solution of iron ions and get iron metal out.  It's just not going to happen.
"A real fart is beefy, has a density greater than or equal to the air surrounding it, consists

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #54 on: January 05, 2007, 10:51:57 PM »
Wait, so It woudn't be the same as haveing a solution of Copper Chloride and putting aluminium in it and you get Aluminium Chloride Solution and Copper metal?

are those decent jars to hold chemicals so I have them when I need them and so I don't have to open the main bulk of my chemicals every time I need some? They look nice, just want to see if any of you have any ideas on them.
« Last Edit: January 05, 2007, 11:03:43 PM by mafiaparty303 »
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse

#### Borek

• Mr. pH
• Deity Member
• Posts: 27296
• Mole Snacks: +1772/-408
• Gender:
• I am known to be occasionally wrong.
##### Re: What are some good starting chemicals?
« Reply #55 on: January 06, 2007, 05:59:42 AM »
Wait, so It woudn't be the same as haveing a solution of Copper Chloride and putting aluminium in it and you get Aluminium Chloride Solution and Copper metal?

Nope. Some metals will react directly with water. You may safely assume it will be done by all alkali metals and all alkaline earth metals starting with calcium.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info, pH-meter.info

#### woelen

• Chemist
• Full Member
• Posts: 277
• Mole Snacks: +40/-2
• Gender:
• The art of wondering makes life worth living...
##### Re: What are some good starting chemicals?
« Reply #56 on: January 06, 2007, 09:32:02 AM »
Those jars are a little bit large to my opinion for storage of your day to day usage of chemicals, but they look fine otherwise. Glass vials are even better. They are not porous for air and moisture:

http://cgi.ebay.com/144-pcs-Clear-4-Dram-Glass-Vials-Screw-caps-20x70mm_W0QQitemZ140070922268QQihZ004QQcategoryZ26409QQrdZ1QQcmdZViewItem

Ideal for storing small amounts of chemicals, which you use on a day by day basis, and also nice for displaying things. When such a small thing is empty, then you can refill it from your stock.
Want to wonder? See http://www.oelen.net/science

#### mafiaparty303

• Regular Member
• Posts: 97
• Mole Snacks: +0/-0
##### Re: What are some good starting chemicals?
« Reply #57 on: January 06, 2007, 02:34:06 PM »
Ok, ya I was looking at those just yesterday and I was thinking they were a bit to small but now that I think about it they are a good size for small scale.

Thanks
www.lafamillemasse.com/pierre/smart_people.htm
Join the Smart People for a better future!
-Founded by Pierre Masse


text:
# Why can't I correlate my first-order factors in this SEM?

I am trying to estimate a "typical" intelligence model with three latent factors (the intelligence domains PS, WM and Gf) two of which have two indicators and one of which has four indicators. Together, those three factors define a second-order factor of intelligence; g. I expect the intelligence domains to correlate because their correlation gives rise to the common factor g. The model (n = ~1050) converges and has acceptable fit indices when I don't specify correlations between the intelligence domains. But when I try to let them covary, it gives me the following error:

Could not compute standard errors! The information matrix could not be inverted. This may be a symptom that the model is not identified.

Kline (2016) writes that in a model with a second-order factor, there need to be at least three first-order factors with a minimum of two indicators. This is all given, but still, my models seems to be underidentified. How can I solve this? What else could be the problem here?

Here's the error-inducing model I ran in lavaan (R):

model.1.relaxed <- '
PS =~ NA*zst_rw + ss_rw
WM =~ NA*bzf_rw + zn_seq_rw + zn_vw_rw + zn_rw_rw
Gf =~ NA*mz_rw + fw_rw
g =~ NA*PS + WM + Gf
PS ~~ 1*PS
WM ~~ 1*WM
Gf ~~ 1*Gf
g ~~ 1*g
zn_vw_rw ~~ zn_rw_rw
zn_seq_rw ~~ zn_rw_rw
zn_seq_rw ~~ zn_vw_rw
WM ~~ Gf
PS ~~ Gf
WM ~~ PS

g ~ agedec
'

#analyze model
model.1.relaxed.fit <- sem(model=model.1.relaxed, data=data, estimator="mlm", orthogonal=FALSE)

• Correct @emma, you would need additional constraints to estimate effects on all first-order factors as well as g. Typically, this is done by choosing "anchor items" that are not effected by agedec, but technically you could do something like estimate all effects under the constraint that the average of first-order effects == 0 (similar to effects-code identification of latent scales). But read this informative paper: doi.org/10.1177/0146621619835496 Feb 3 at 15:21

format: plain


text:
# Manual computation for Fishers exact test for tables larger than 2 x 2 [duplicate]

I am wondering how to perform a Fishers exact test on my data which contains two columns and three rows. One of the cells contains zero.

             2012    2018
Pass          116     166
Submax         11      45
Fail            9       0

I would like to compare the data between the years 2012 and 2018. Any help would be much appreciated! I only have access to excel but if anyone else can calculate it for me that would be brilliant.

• AFAIK this isn't something Excel can do. The counts are far too large for this to be done manually by anyone, either. The only non-software aspect of your question seems to be the mention of a cell with a zero. Could you explain why (if at all) that might be a concern?
– whuber
Dec 5 '19 at 22:13
• It might be time to graduate to statistical software. The following R code can be run at: rdrr.io/snippets . Y2012 = c(116, 11, 9); Y2018 = c(166, 45, 0); Matrix = cbind(Y2012, Y2018); rownames(Matrix) = c("Pass", "Submax", "Fail"); Matrix; fisher.test(Matrix) Dec 5 '19 at 23:15
• You could also conduct the analysis with free menu-based software like Jamovi. Dec 5 '19 at 23:21
• I'll stand partially corrected on my comment on Jamovi. Jamovi is (currently) my favorite gui-menu-based free statistical software package. But for some reason, it will report Fisher's exact test only for 2 x 2 tables. This is unexpected since R reports the exact test for larger tables as well. Dec 6 '19 at 2:51
• @kjetilbhalvorsen , interestingly, that online calculator won't calculate the exact test if N > 300, so it won't work in this case. I imagine this calculator, along with Jamovi, has these kinds of limits to avoid the software hanging or producing errors. I suppose the upshot is that, if one wants to get into reasonably complex statistical analysis, there's no substitute for using good software. Dec 6 '19 at 11:23

### In General

Wolframalpha has a page about the manual computation of Fisher exact test: http://mathworld.wolfram.com/FishersExactTest.html

The probability of occurance for a particular combination of cell values $$a_{ij}$$ for given row sums $$R_i$$, column sums $$C_j$$, and total sum $$N$$:

$$P(a_{ij}) = \frac{\prod_{\forall i } R_{i}! \prod_{\forall j } C_{j}!}{N! \prod_{\forall i,j } a_{ij}!}$$

To find a p-value you would have to compute the cumulative probability: compute the values for tables $$a_{ij}$$ with more extreme difference and sum them together.

### Manual computation example

For a 2x2 table this can be easily done. For a 2x3 table it can also be done (although not very simple).

All the possibly combinations with the same row totals can be summarized by two parameters $$a$$, $$b$$

             116+b       166-b    ¦ 282
11+a-b      45-a+b  ¦  56
9-a         0+a    ¦   9
--------------------------------
136         211      ¦ 347

So all you need to do is compute $$P(a_{ij})$$ for all values of a and b and sum those which are equal or extremer.

### Automized method

Those manual computations have been automized. In R for instance you can get the result by typing a single line:

fisher.test(matrix(c(116, 11, 9, 166, 45, 0), 3))

giving

Fisher's Exact Test for Count Data

data:  matrix(c(116, 11, 9, 166, 45, 0), 3)
p-value = 2.476e-06
alternative hypothesis: two.sided

This function in R goes through all the options (like in the manual excel sheet but automatic). However when the tables get large then the computation will take a lot of time, also for a computer. The function in R can also estimate a p-value by generating random tables and see how often a worse deviation is observed.


text:
#### Vol. 1, No. 4, 2019

 Recent Issues Volume 3, Issue 1 Volume 2, Issue 4 Volume 2, Issue 3 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 4 Volume 1, Issue 3 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Ethics Statement Editorial Login ISSN (electronic): 2576-7666 ISSN (print): 2576-7658 Author Index To Appear Other MSP Journals
Horn's problem and Fourier analysis

### Jacques Faraut

Vol. 1 (2019), No. 4, 585–606
##### Abstract

Let $A$ and $B$ be two $n×n$ Hermitian matrices. Assume that the eigenvalues ${\alpha }_{1},\dots ,{\alpha }_{n}$ of $A$ are known, as well as the eigenvalues ${\beta }_{1},\dots ,{\beta }_{n}$ of $B$. What can be said about the eigenvalues of the sum $C=A+B$? This is Horn’s problem. We revisit this question from a probabilistic viewpoint. The set of Hermitian matrices with spectrum $\left\{{\alpha }_{1},\dots ,{\alpha }_{n}\right\}$ is an orbit ${\mathsc{O}}_{\alpha }$ for the natural action of the unitary group $U\left(n\right)$ on the space of $n×n$ Hermitian matrices. Assume that the random Hermitian matrix $X$ is uniformly distributed on the orbit ${\mathsc{O}}_{\alpha }$ and, independently, the random Hermitian matrix $Y$ is uniformly distributed on ${\mathsc{O}}_{\beta }$. We establish a formula for the joint distribution of the eigenvalues of the sum $Z=X+Y$. The proof involves orbital measures with their Fourier transforms, and Heckman’s measures.

##### Keywords
eigenvalue, Horn's problem, Heckman's measure
##### Mathematical Subject Classification 2010
Primary: 15A18, 15A42
Secondary: 22E15, 42B37


text:
# Can I reuse the hall sensors in a brushless motor as an encoder?

I have upgraded the motors in my robotic arm to sensored, brushless RC car motors. The hope was to reuse the Hall sensors to double as a rotary encoder, by tapping 2 Hall sensors and treating the 2 bits as a quadrature signal (a crude quadrature since 2 of the 4 states will be longer than the other 2).

This works when none of the motor phases are powered and I just rotate the motor manually. But once the stator coils are energized, the encoder no longer counts correctly: When running at low power, the counting is correct, but when running under high power, the count is monotonic (only increases or decreases) no matter if I run in reverse or forward.

I'm almost certain this is because of the stator coils overpowering the permanent magnets on the rotors. So is there still a way to use the Hall sensors as an encoder?

Sorry if this is an obvious question. I'd love to research this problem more if I had more time.

Update: I've measured the wave forms with my DSO quad and see the expected 120 degree separated signals (the measurement for phase C gets more inaccurate over time because I only had 2 probes, so I measured phases A & B first, then A & C, and then merged them.

When ESC speed is 0.1:

When ESC speed is 0.3:

Previously, I was using a hardware quadrature counter (EQEP module on a BeagleBone). At speed=0.3, this was counting backwards no matter if I do forward or reverse!

I then implemented quadrature counting on an LPC1114FN28 uController. The result was still bad at high speeds (count didn't change at all). The logic was:

void HandleGPIOInterrupt()
{
const uint8_t allowableTransitions[4][2] = {1, 2, 3, 0, 0, 3, 2, 1};
static int prevState = -1;
int state = phaseA | (phaseB * 2)
if (prevState != -1)
{
if (allowableTransitions[prevState][0] == state)
{
++rotations;
}
else if (allowableTransitions[prevState][1] == state)
{
--rotations;
}
}
prevState = state;
}

Then I got the idea to change the code to not update prevState until an expected state happens (to deal with glitches):

  int state = phaseA | (phaseB * 2)
if (prevState != -1)
{
if (allowableTransitions[prevState][0] == state)
{
++rotations;
prevState = state;
}
else if (allowableTransitions[prevState][1] == state)
{
--rotations;
prevState = state;
}
else
{
// assume transition was a glitch
}
}
else
prevState = state;

Now the counting finally is correct in both directions, even at speeds higher than 0.3! But are there really glitches causing this? I don't see any in the waveforms?

• I've never heard of hall sensors not working at "high power"; that would defeat the purpose of being able to use them to commutate the motor. I've never seen this in any motor I've used with hall sensors, and I've used many. You're probably doing something wrong. – Guy Sirton May 26 '14 at 0:17


text:
[gmx-users] Particle Insertion Method tpi - units and compensation of charged system

Kathleen Kirchner kirchner at mis.mpg.de
Thu Oct 13 12:53:42 CEST 2011

Dear all,

I'm using gromacs particle insertion method (integrater = tpi) to obtain
the excess chemical potential of single charged atoms.

On analyzing my results, two questions occurred to me:

1. The units for \mu_excess = -k_B T log <e^{-\beta U}>_N are given
according to tpi.xvg in kJ/mol*nm^3, which is kind of an energy density
and not an energy unit. So what does it mean? Is it normalized to any
volume? Maybe I'm missing some important point.

2. Is there a correction implemented for systems with a total net charge
not equal to zero? I'm trying to get the solubility of CO_2 in Ionic
Liquid, therefore I fear, the response of the system (which has zero net
charge) on inserting particles with 0.7 e and -0.35 e will be quite huge.

Best regards
Kathleen

--
Kathleen Kirchner
PhD student
Max Planck Institute for Mathematics in the Sciences
(MPI f. Mathematik in den Naturwissenschaften)
Inselstr. 22-26, D04103 Leipzig
e-mail: kirchner at mis.mpg.de
web: http://www.mis.mpg.de/scicomp/CompPhysChem/
Tel +49 341 9959 722
Fax +49 341 9959 999


text:
# 12.8: Another Characterization for Planar Graphs

• Eric Lehman, F. Thomson Leighton, & Alberty R. Meyer
• Google and Massachusetts Institute of Technology via MIT OpenCourseWare

We did not pick $$K_5$$ and $$K_{3,3}$$ as examples because of their application to dog houses or quadrapi shaking hands. We really picked them because they provide another, famous, discrete characterizarion of planar graphs:

Theorem $$\PageIndex{1}$$

(Kuratowski). A graph is not planar if and only if it contains $$K_5$$ or $$K_{3,3}$$ as a minor.

Definition $$\PageIndex{2}$$

A minor of a graph $$G$$ is a graph that can be obtained by repeatedly4 deleting vertices, deleting edges, and merging adjacent vertices of $$G$$.

For example, Figure 12.16 illustrates why C3 is a minor of the graph in Figure 12.16(a). In fact C3 is a minor of a connected graph G if and only if G is not a tree. The known proofs of Kuratowski’s Theorem 12.8.1 are a little too long to include in an introductory text, so we won’t give one.

4The three operations can each be performed any number of times in any order.

This page titled 12.8: Another Characterization for Planar Graphs is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Eric Lehman, F. Thomson Leighton, & Alberty R. Meyer (MIT OpenCourseWare) .


text:
Share

# If a is a Skew Symmetric Matric of Order 3, Then Prove that Det A = 0 - CBSE (Science) Class 12 - Mathematics

ConceptSymmetric and Skew Symmetric Matrices

#### Question

If A is a skew symmetric matric of order 3, then prove that det A  = 0

#### Solution 1

If A is skew symmetric matric then A^T = -A

:. |A| = -|A^T|

|A| = - |A|

=> 2|A| =  0

=>|A| = 0

#### Solution 2

Let A be a skew-symmetric matrix of order 3.

Therefore, AT=−A

∴ |A^T| = |-A| = |A|

⇒ |A| = |(-1)A|

We know that, |kA|=kn|A|, where n is the order of the matrix

=> |A| = (-1)^3 |A|

=> |A| = -|A|

=> |A| + |A| = 0

=> 2|A| = 0

=> |A| = 0

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution If a is a Skew Symmetric Matric of Order 3, Then Prove that Det A = 0 Concept: Symmetric and Skew Symmetric Matrices.
S


text:
Elitist Jerks WotLK Healing Compendium v3.2: Same Old Thing
 Username Remember me? Password

 LinkBack Thread Tools
 04/30/09, 4:12 PM #136 Eshen Glass Joe   Eshen Dwarf Priest   Mug'thol How exactly did your output go up by dropping greater heal talents? I'm just not seeing it. Empowered Renew and 2 points in blessed resil are causing this big a change?
 04/30/09, 4:47 PM #137 BulgarBG Glass Joe   Bulgartus Undead Priest   Lightbringer My current holy spec: The World of Warcraft Armory Two main reason that explain why output goes up when dropping GH talents: 1) Your GH never provided significant source of your total healing 2) Picking up ToF (works on all of your spells) and all Renew talents adds more healing then losing a bit from a rarely used spell If you are GH fan, however that will probably not end up the same for you.
 04/30/09, 4:52 PM #138 meddle Von Kaiser   Meddle Dwarf Priest   Kilrogg Here are the new Priest changes in 3.1.2: * Divine Hymn: Healing and healing scaling reduced by 30%. Buff on affected players changed from 15% to 10%. * Renewed Hope: Effect can no longer be dispelled. * Soul Warding: Mana cost reduction is now 15% down from 30%. * Glyph of Mass Dispel: Now only decreases Mass Dispel cost by 35%. * Glyph of Penance: Now increases critical strike chance by 5% instead of its old effect. The most notable looks to be the Penance glyph change, removing the 2 sec cooldown reduction and adding 5% crit chance which seems on paper to be a pretty considerable nerf. Divine Hymn was pretty powerful and probably needed a nerf.
04/30/09, 5:03 PM   #139
tedv
Observation: I am awesome

Goblin Priest

Mal'Ganis
 Originally Posted by BulgarBG My current holy spec: The World of Warcraft Armory Two main reason that explain why output goes up when dropping GH talents: 1) Your GH never provided significant source of your total healing 2) Picking up ToF (works on all of your spells) and all Renew talents adds more healing then losing a bit from a rarely used spell
I've been meaning to respec to something similar, although with Blessed Resilience instead of a few other filler talents. My current spec right now has dropped Empowered Healing and I didn't notice a 5% to 7% increase in healing though; it was definitely less. I'd suggest that a large part of increased healing is from taking Test of Faith. So the conclusion is that even if you want to keep the Greater Heal boosting talents, you need to find 3 points for Test of Faith regardless. I don't think it's an optional talent.

 04/30/09, 7:06 PM #140 Todo Glass Joe   Towdow Dwarf Priest   Drak'Tharon I didn't read through all the pages, so I'm sorry if this has already been discussed, however, I saw that you had 45 spirit has a viable weapon enchant. I'm not very good at math, but if I did everything right, with kings up and spiritual guidance, that would only equate to roughly 12 SP and around 8 mp/5. Am I missing something here? To me going with 63 spell power just seems like a no brainer, I'm expecting responses such as "It's a preference choice of stats vs throughput" but to me, it seems like, unless I did the math completely wrong, the stats fall way short when compared to 63 spell power (Or 81 or whatever the staff enchant is) Thoughts?
04/30/09, 8:05 PM   #141
Promethia
Piston Honda

Blood Elf Priest

Kilrogg
 Originally Posted by Todo I didn't read through all the pages, so I'm sorry if this has already been discussed, however, I saw that you had 45 spirit has a viable weapon enchant. I'm not very good at math, but if I did everything right, with kings up and spiritual guidance, that would only equate to roughly 12 SP and around 8 mp/5.
It's more 15 mp/5, maybe a little more, depending on other stats and how often you're ooFSR.

Of course the decision is going to be partly driven by whether you want more throughput or mana, but the way I look at it is that a 63 spell power for 45 spirit tradeoff is better tradeoff than you get with gems, which trade off in a 9 spell power to 8 spirit ratio. So you may be better off getting your spell power from the enchant and getting more of your mana regen from gems.

 04/30/09, 8:40 PM #142 Svena Glass Joe   Svena Night Elf Priest   Nathrezim * Divine Hymn: Healing and healing scaling reduced by 30%. Buff on affected players changed from 15% to 10%. This was bound to happen. It has now become a save the day situational spell. The bonus it being a smart heal and the + 10% to healing for 8 seconds. It still provides more hpm than glyphed POH but it's not exciting anymore. With a 10 minute cooldown - if it was a talent - it would have the same fate as lightwell. * Glyph of Penance: Now increases critical strike chance by 5% instead of its old effect. This is dissapointing, however Divine Aegis: Divine Aegis effects will now stack, however the amount absorbed cannot exceed 125*level (of the target). It will also now take into account total healing including overhealing. -10000 at level 80. Still worth having paid 100g for the glyph.
04/30/09, 10:22 PM   #143
Todo
Glass Joe

Dwarf Priest

Drak'Tharon
 Originally Posted by Promethia It's more 15 mp/5, maybe a little more, depending on other stats and how often you're ooFSR. Of course the decision is going to be partly driven by whether you want more throughput or mana, but the way I look at it is that a 63 spell power for 45 spirit tradeoff is better tradeoff than you get with gems, which trade off in a 9 spell power to 8 spirit ratio. So you may be better off getting your spell power from the enchant and getting more of your mana regen from gems.

15 mp/5 oofsr? I was reffering to while casting, but my math again could still be wrong.

Regardless, like you said, it seems like you'd be better off gemming 8 int 8 spirit if you're that desperate for regen. The thoroughput to me from the weapon enchant just seems leaps and bounds ahead of the spirit.

I got into a discussion about this with a random priest earlier and I was just curious.

But the Priest I was talking to was Holy, and I am Disc, I understand Spiritual Guidance and everything but it just doesn't seem to work out mathmatically.

04/30/09, 10:31 PM   #144
Kashir
Piston Honda

Draenei Priest

Frostmourne
 Originally Posted by Todo Regardless, like you said, it seems like you'd be better off gemming 8 int 8 spirit if you're that desperate for regen. The thoroughput to me from the weapon enchant just seems leaps and bounds ahead of the spirit. But the Priest I was talking to was Holy, and I am Disc, I understand Spiritual Guidance and everything but it just doesn't seem to work out mathmatically.
Well, it's all going to come down to how much you value regen vs throughput, which determines how highly you value Spellpower vs Spirit. Just because the Spellpower enchant has a higher itemisation value than Spirit doesn't necessarily mean it's better.

Most people would go for the Spellpower, but if you really do value regen extremely highly compared to throughput then there's no reason why you shouldn't pick the Spirit enchant, while still gemming for regen. There's nothing in the rulebook that says you must balance your stats equally.

Edit: Of course if you're going to be that crazy for regen, you'd be better still to go for the old BC +30 Intellect enchant!

05/01/09, 4:25 AM   #145
Sinndir
Great Tiger

Night Elf Priest

Medivh
 Originally Posted by Eshen How exactly did your output go up by dropping greater heal talents? I'm just not seeing it. Empowered Renew and 2 points in blessed resil are causing this big a change?
Eshen if you look at my post (the second one after Nid's main post); I have included the math on why Blessed Resilience and Test of Faith are a better combination than 5/5 Empowered Healing. As a holy priest, there is simply no reason to have empowered healing over those two talent.

05/01/09, 5:44 AM   #146
Biffins
Glass Joe

Dwarf Priest

Bronzebeard
 Originally Posted by tedv I've been meaning to respec to something similar, although with Blessed Resilience instead of a few other filler talents. My current spec right now has dropped Empowered Healing and I didn't notice a 5% to 7% increase in healing though; it was definitely less. I'd suggest that a large part of increased healing is from taking Test of Faith. So the conclusion is that even if you want to keep the Greater Heal boosting talents, you need to find 3 points for Test of Faith regardless. I don't think it's an optional talent.
Tedv, do you mean this build.

Talent Calculator - World of Warcraft

05/01/09, 8:38 AM   #147
Promethia
Piston Honda

Blood Elf Priest

Kilrogg
 Originally Posted by Todo 15 mp/5 oofsr? I was reffering to while casting, but my math again could still be wrong.
It depends on several things, but the regen formula (in Mp5) from the original post is:

$5 \cdot 0.005575 \cdot 0.6 \cdot (Spirit) \sqrt{Intellect}\text{, or}$
$0.016725 \cdot (Spirit) \sqrt{Intellect}$

For holy, you get 5% bonus to spirit and blessing of kings gives you 10% to both spirit and int, so that's:

$0.016725 \cdot (1.1 \cdot 1.05 \cdot Spirit) \sqrt{1.1 \cdot Intellect}=$
$0.016725 \cdot (1.1 \cdot 1.05 \cdot \sqrt{1.1}) \cdot (Spirit) \sqrt{Intellect} ~=$
$0.02026 \cdot (Spirit) \sqrt{Intellect}$

Let's suppose you have 1083 intellect (before kings), just because that seems like a nice number. Your mileage may vary. Then you'd have:

$0.02026 \cdot (Spirit) \sqrt{1083} ~= 0.6667 \cdot (Spirit)$

which is remarkably close to 2/3 * (spirit), so when you plug in 45 spirit, you get ~30 Mp5 oofsr regen. Inside the FSR, you'd have half that, or ~15 Mp5. Your actual mp5 will be a blending between the two. Lower intellect will result in lower mp5 both inside and ooFSR, and higher will mean more. For 900 intellect, it's more like 27 mp5 oofsr, and 14 mp5inside. So 15 mp5 will not be far off even if you live in the five second rule and don't have tons of intellect.

05/01/09, 10:01 AM   #148
MavSteele
Von Kaiser

Human Priest

Turalyon
 Originally Posted by Sinndir Eshen if you look at my post (the second one after Nid's main post); I have included the math on why Blessed Resilience and Test of Faith are a better combination than 5/5 Empowered Healing. As a holy priest, there is simply no reason to have empowered healing over those two talent.
Your original post more specifically notes that your math is based on anecdotal (i.e. personal) evidence that you cast GH infrequently enough to even be part of the consideration of which talents to take. This post is less clear about that and seems like a pretty sweeping generalization to make in a thread aimed at theorycrafting "ideal" specs for Ulduar.

I keep Emp Healing for the exact same reason I keep Inspiration. If the strategy for a fight calls for me to tank heal, I want to be able to do it well. There are a number of phased fights in Ulduar that require intense raid healing for some phases and intense tank healing for others. With the right talents, holy priests excel at these kind of fights. If your strategy never has you tank healing, of course your math is correct. I'd just be careful as to imply that there is no reason to pick up Emp Healing.

05/01/09, 10:09 AM   #149
tedv
Observation: I am awesome

Goblin Priest

Mal'Ganis
 Originally Posted by Biffins Tedv, do you mean this build. Talent Calculator - World of Warcraft
No, this is the build I had in mind: Talent Calculator - World of Warcraft

A few notes on the difference.

1) Due to the nerfs in Ulduar content, I find that Prayer of Healing is just not cast as often as it was before. This makes Healing Prayers far less efficient than it was before. Some simple math shows that a point in Inner Focus beats a point in Healing Prayers unless you cast 10 Prayer of Healing in three minutes. Even on fights like Ignis, I don't cast 10 prayers the entire fight. Not being able to double dip Serenity also contributes to this.

2) The second point in Surge of Light is really, really good. In fact, it's just as good as the first point. I have this suspicion that people only running 1/2 Surge of Light either A) haven't tried 2/2 or B) aren't using the procs. Has anyone given a compelling argument for sticking with 1/2? The "it has a near 100% proc chance from AoE heals even with 1/2 points" was disproved. (This is because the 25%/50% chance is checked exactly once for any spell with at least 1 crit.)

3) The point in Desperate Prayer versus Holy Reach is debatable. I find I want to cast a lot of heals while moving in Ulduar and there are a number of times where a 10k instant self heal is exactly the right heal for the situation. Gaining 1.5 yards on Circle of Healing doesn't seem that important.

The other thing I've concluded is that Lightwell definitely sucks in Ulduar, on all fights. Too much movement to use it and you can't afford to waste DPS / cast time to find the target and click it. Worst of all, if you happen to be stationary near a Lightwell, that's probably because the rest of the raid is there too, so your odds of being able to click the graphic are very low.

 Originally Posted by MavSteele I keep Emp Healing for the exact same reason I keep Inspiration. If the strategy for a fight calls for me to tank heal, I want to be able to do it well. There are a number of phased fights in Ulduar that require intense raid healing for some phases and intense tank healing for others. With the right talents, holy priests excel at these kind of fights. If your strategy never has you tank healing, of course your math is correct. I'd just be careful as to imply that there is no reason to pick up Emp Healing.
I don't think its fair to use the same justification for Inspiration as Empowered Healing. First, there are no other useful alternatives in the Inspiration section of the tree. In contrast, Empowered Healing competes with genuinely useful talents. Second, Inspiration procs off of Flash Heal and Circle of Healing, two spells that are often cast on the tank even during raid heal situations.

05/01/09, 11:28 AM   #150
Norie
Glass Joe

Undead Priest

Nathrezim
 Originally Posted by BulgarBG My current holy spec: The World of Warcraft Armory Two main reason that explain why output goes up when dropping GH talents: 1) Your GH never provided significant source of your total healing 2) Picking up ToF (works on all of your spells) and all Renew talents adds more healing then losing a bit from a rarely used spell If you are GH fan, however that will probably not end up the same for you.
I respecced to that this week after inspecting our WWS logs and finding that I overheal for approximately 45% on flash heals in any one given fight. I am primarily a raid healer so I decided to try that spec and I have to say I am loving it. TOF gives me strong healing on fights like Hordir/Auriya/Ignis and the B&S has saved me more times then I care to count!

I did notice a slight decrease in my overall healing versus our other holy priest who kep empowered healing, but my overheal on flash heal went to approximately 15%. I am going to try the spec that Tedv posted with the Blessed Resilience talents next week but I will keep desperate prayer.

 Elitist Jerks WotLK Healing Compendium v3.2: Same Old Thing
 Username Remember me? Password

 Thread Tools

 Similar Threads Thread Thread Starter Forum Replies Last Post WotLK Healing Compendium v3.0 [theorycraft, specs, etc] constantius Priests 2225 04/20/09 4:40 PM

 Ten Ton Hammer Network   EVE   GW2   Spark   SWToR   WoW Contact Us   Privacy Policy


text:
# Largest prime below a given number N

This came up as a part of algorithm puzzles:
Given a number $N$, how to find the prime $P$ such that $P<N$ and the difference $N-P$ is minimum.
For small $N$, simple sieves do work, but I'm unable to find solution for large values of $N$.
I tried to modify the sieves to somehow look over large values only, didn't get anywhere.
Any solutions/hints for this?

• Off the top of my head: Let $m$ the product of some initial segment of primes (how many would depend on the size of $N$). For example, $m=2\cdot3\cdot5\cdot7\cdot11\cdot13=30030$. Make an list of all the numbers below $m$ with $\gcd(m,x)=1$. This list can be quickly used to pick non-multiples of the prime factors of $m$ in any segment of numbers. Now start at $N-1$ and move downwards, checking the candidates in turn. – Harald Hanche-Olsen May 3 '13 at 17:08
• When you have a candidate, if $N$ is very large use a probabilistic primality test such as Miller–Rabin first, then follow up with a proper proof of primality if that is required. – Harald Hanche-Olsen May 3 '13 at 17:10
• This counting down can be painful. If candidates can be enumerated fast, that'll be nice – Avogadro May 3 '13 at 17:32
• Enumerating candidates fast is what the first part was all about. – Harald Hanche-Olsen May 3 '13 at 18:12
• what for large N (say $10^{16}$), there the reduced complexity in search space still seems impractical – Avogadro May 3 '13 at 18:47

Start counting downward from $N-1$ After trial division by some small primes, you can use one of a number of probabilistic tests like the Fermat primality test. If $p$ is prime, $a^{p-1} \equiv 1 \pmod p$. This can be checked quickly. If it is true for a few $a$, the chance of $p$ being composite is very small. If you insist on certainty, you can finish up with one of the deterministic tests.
• @Avogadro: The trial division can help a lot. Even $2,3,5$ eliminate all but 8 out of 30. You can make a list of the moduli that are acceptable and avoid the trial divisions. – Ross Millikan May 3 '13 at 18:07
• what for large N (say $10^{16}$), there the reduced complexity in search space still seems impractical. (sorry for copy-pasting comments from top again :) ) – Avogadro May 3 '13 at 18:48
• @Avogadro: around $10^{16}$ about one in $37$ numbers is prime, so if you use the $\pmod {30}$ restriction, you should only have to try $10$ on the average. I don't think that is bad. – Ross Millikan May 3 '13 at 19:13
• As an aside, if you're used to using primes for public-key cryptography then primes around $10^{16}$ are pitifully small. – Harald Hanche-Olsen May 3 '13 at 23:53


text:
# How many ways of splitting objects equally into groups?

How many ways in which $m\cdot n$ distinct objects can be divided equally into $n$ groups?

The answer is $$\frac{(mn)!}{(m!)^n n!}$$

• Start by thinking about the numerator. Once you understand it, think about the denominator. In that order. In the denominator, think about the $m!$ before you think about the $\vphantom(^n$. – dfeuer Dec 27 '13 at 5:01
• Just for completeness: This question is related to yours and has a number of answers that may be interesting for you as well. – jpvee Nov 27 '17 at 8:37

Imagine groups are written down in a row. This is same as permuting the original $n\cdot m$ objects and assigning the first $m$ object to the first group, the second $m$ objects to second group etc.

Now each such group has $m!$ ways it can be permuted, so there are $(m!)^n$ permutations that give the same groups.

Hence the answer $$\frac{(m\cdot n)!}{(m!)^n}$$

You need to fill in the gaps!

First, let us consider an easy example.

If you want to divide $9$ distinct balls in the $A, B, C$ boxes, the answer is $$\binom{9}{3}\times\binom{6}{3}.$$ First choose three balls for $A$, then choose three balls for $B$.

On the other hand, if you want to divide $9$ distinct balls into three name-less boxes, the answer is $$\frac{\binom{9}{3}\times\binom{6}{3}}{3!}.$$

Now, let us come back to your question.

Your group has no names, so the answer is $$\frac{\binom{mn}{m}\times\binom{mn-m}{m}\cdots\times\binom{2m}{m}}{n!}.$$

This is equal to what you wrote.


text:
# How do you use the rational root theorem to find the roots of  f(x) = x^3-4x^2-2x+8?

Dec 6, 2015

Use the rational root theorem to identify the possible rational roots to try. Hence find $x = 4$ and hence the other two irrational roots $x = \pm \sqrt{2}$

#### Explanation:

$f \left(x\right) = {x}^{3} - 4 {x}^{2} - 2 x + 8$

By the rational root theorem, any rational roots of $f \left(x\right) = 0$ must be expressible in lowest terms in the form $\frac{p}{q}$ for some integers $p$, $q$ where $p$ is a divisor of the constant term $8$ and $q$ is a divisor of the coefficient $1$ of the leading term.

So the only possible rational roots are:

$\pm 1$, $\pm 2$, $\pm 4$, $\pm 8$

$\pm 1$ won't work since the leading term would be odd and the remaining terms are even.

$f \left(2\right) = 8 - 16 - 4 + 8 = - 4$

$f \left(- 2\right) = - 8 - 16 + 4 + 8 = - 12$

$f \left(4\right) = 64 - 64 - 8 + 8 = 0$

So $x = 4$ is a root and $\left(x - 4\right)$ a factor.

${x}^{3} - 4 {x}^{2} - 2 x + 8 = \left(x - 4\right) \left({x}^{2} - 2\right)$

The remaining roots are the irrational roots of ${x}^{2} - 2 = 0$, that is:

$x = \pm \sqrt{2}$


text:
Article

# Nonlinear phase dynamics in a driven bosonic Josephson junction.

Department of Chemistry, Ben-Gurion University of the Negev, Post Office Box 653, Beer-Sheva 84105, Israel.
Physical Review Letters (Impact Factor: 7.94). 06/2010; 104(24):240402. DOI:10.1103/PHYSREVLETT.104.240402
Source: PubMed

ABSTRACT We study the collective dynamics of a driven two-mode Bose-Hubbard model in the Josephson interaction regime. The classical phase space is mixed, with chaotic and regular components, which determine the dynamical nature of the fringe visibility. For a weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative phase φ between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the intersite potential barrier stabilizes the φ=π "inverted pendulum" coherent state, and protects the fringe visibility.

0 0
·
0 Bookmarks
·
66 Views
• Source
##### Article: Optimal Gaussian squeezed states for atom-interferometry in the presence of phase diffusion
[hide abstract]
ABSTRACT: We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states, in the presence interactions. For weak interactions, our results coincide with Phys. Rev. Lett. {\bf 100}, 250406 (2008), with optimal initial number-variance $\sigma_o\propto N^{1/3}$ and optimal signal-to-noise ratio $s_o\propto N^{2/3}$ for total atom number $N$. As the interaction strength $u$ increases past unity, phase-diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number-squeezing to initial {\it phase}-squeezing with $\sigma_o\propto\sqrt{uN}$ and $s_o\propto\sqrt{N/u}$ shot-noise scaling. The initial phase-squeezing translates into hold-time number-squeezing, which is less sensitive to interactions than coherent states and improves $s_o$ by a factor of $\sqrt{u}$.
Physical Review A 08/2010; 82(4). · 3.04 Impact Factor
• ##### Article: Dynamical control of nonlinear symmetry breaking under decoherence
[hide abstract]
ABSTRACT: We propose a control mechanism for the stabilization of symmetry-broken modes in Bose-Einstein condensates and optical beams trapped in double-well potentials in the presence of symmetric or asymmetric noise. The control, based on periodic {pi} shifts of the phase in one well, is demonstrated for solitons and in the two-mode approximation. The latter setting is considered in both the mean-field and quantum (Bose-Hubbard) regimes.
Physical Review A 07/2010; 82(1):013610. · 3.04 Impact Factor
• ##### Conference Proceeding: A comparison of genetic algorithm, regression, and Newton's method for parameter estimation of texture models
[hide abstract]
ABSTRACT: The estimation of parameter values in stochastic models for texture image data is the focus of this paper. We present a comparison of three methods that seek optimal solutions to a problem of stochastic model selection in texture data. The problem is to find parameter values for the model that “best” fits the texture data. The three methods used to solve this problem are genetic algorithms, logistic regression, and Newton's method. We present a comparison of the results of these three techniques to both synthetic and real data. For synthetic data, the values estimated by the genetic algorithm, logistic regression, and Newton's method gave textures that were practically indistinguishable from the original textures. For real data, the results are encouraging and warrant continued investigation
Image Analysis and Interpretation, 1996., Proceedings of the IEEE Southwest Symposium on; 05/1996

19 Downloads
Available from
May 29, 2013

## Similar Publications

• ##### Coherent control of quantum collapse in a Bosonic Josephson junction by modulation of the scattering length
J. Lozada-Vera, V. S. Bagnato, M. C. de Oliveira


text:
Saw this on the tails website.

Infrastructure as code

We want to treat system administration like a (free) software
development project:

We want to enable people to participate without needing an account on the Tails servers.
We want to review the changes that are applied to our systems.
We want to be able to easily reproduce our systems via automatic deployment.
We want to share knowledge with other people.

This is why we try to publish as much as possible of our systems configuration, and to manage
our whole infrastructure with configuration management tools. That is, without needing to log into hosts.


text:
## The Annals of Mathematical Statistics

### On the Line Graph of the Complete Bipartite Graph

A. J. Hoffman

#### Abstract

In an interesting recent article [4], J. W. Moon has given a list of properties of the graph $L(B_{mn})$ (to be defined more precisely below) and investigated the question of whether these properties characterize the graph. In case $m = n$, this question had been settled by Shrikhande [5] (see also [1], [2] and [3]), who proved that the answer was yes unless $m = n = 4$, when there is exactly one exception. In case $m > n$, Moon shows that the answer is yes unless $(m, n) = (5, 4)$ or (4, 3), which cases were left unsettled in [4]. The purpose of this note is to show that, in those cases as well, the answer is yes, thus completing Moon's discussion. Now to define our problem more exactly. The line graph of the complete bipartite graph on sets with $m$ and $n$ vertices, denoted by $L(B_{mn})$, is the graph with $mn$ vertices given by all ordered pairs $(i, j), 1 \leqq i \leqq m, 1 \leqq j \leqq n$. Two vertices $(i, j)$ and $(i', j')$ are joined by an edge if $i = i'$ or $j = j'$, but not both. The graph $L(B_{mn})$ has the following properties: (1.1) It has $mn$ vertices. (1.2) Each vertex has valence $m + n - 2$. (1.3) If two vertices are not adjacent, there are exactly two vertices adjacent to each. (1.4) Of the $\frac{1}{2} mn(m + n - 2)$ pairs of adjacent vertices, exactly $n\binom{m}{2}$ pairs are each adjacent to exactly $m - 2$ vertices, the remaining $m\binom{n}{2}$ pairs are each adjacent to exactly $n - 2$ vertices. We now assume $m > n$, and let $G_{mn}$ be any graph satisfying (1.1)-(1.4). Our object is to prove that when $(m, n) = (5, 4)$ or (4, 3), $G_{mn} = L(B_{mn})$. Moon has established $G_{mn} = L(B_{mn})$ in all other cases.

#### Article information

Source
Ann. Math. Statist. Volume 35, Number 2 (1964), 883-885.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177703593

Digital Object Identifier
doi:10.1214/aoms/1177703593

Mathematical Reviews number (MathSciNet)
MR161328

Zentralblatt MATH identifier
0127.39302

JSTOR


text:
# Tricky kinematic problem.

1. Feb 10, 2005

### bjon-07

The acceleration of a marble in a certain fluid is proportional to the speed of the marbles, and is given (in SI units) by a= -3.00V^2 for v>0. If it enters this fluid with a speed of 1.50 m/s, how long will it take for the marble to reach half its intial speed.

I have released that

Vf=Vi + a(t)

.75=1.5+ a(t)
-.15=a(t)

and that A=(Vf-VI)/t

2. Feb 10, 2005

### dextercioby

Do you calculus??This problem involves solving a first ODE through separation of variables...

Daniel.

3. Feb 10, 2005

### bjon-07

I am still stock on this problem. I have tryed using seperation of variables but it just leads me in a circle.

4. Feb 10, 2005

### Staff: Mentor

$$\frac{dv}{dt} = -3 v^2$$
$$-\frac{1}{3 v^2} dv = dt$$
Integrate!

5. Feb 10, 2005

### bjon-07

I can't beilve I did not see that LOL, its soo easy. Thank you for your help.


text:
oblique collision of a rigid rod with a plane surface

1 vote
50 views

A uniform rod AB of length L is released from rest with AB inclined at angle 60° with horizontal, with the closer end of the rod to the ground, at a height 49m from it. Assuming the collision of the rod with the ground to be perfectly elastic, calculate the height the centre of mass of the rod will rebound after impact (assume ground to be frictionless).

edited Jan 3
What have you tried? What difficulty are you having with this problem?
I calculated the velocity of the rod at the lowest point. After that, I know that the ground is going to apply an impulse in the vertically upward direction, but I am not quite able to get the answer
How have you made use of the impulse? What calculation have you made?

The normal contact impulse $J$ between the rod and plane has two effects : it changes the velocity of the CM of the rod, and it makes the rod rotate about its CM.
The impulsive force is related to the change in momentum of the CM of the rod, and the impulsive torque to the change in angular momentum of the rod, as follows : $$J=m(v_0+v_1)$$ $$J\frac{L}{2}\cos\theta=I\omega$$ Here $v_0, v_1$ are the vertical velocities of the CM before and after the collision, and $I=\frac{1}{12}mL^2$ is the moment of inertia of the rod about its CM.
The rod is not rotating initially. After the collision, the velocity of the end A which collided with the ground is $v_2'=\frac{L}{2}\omega$ relative to the CM of the rod, directed perpendicular to the rod, ie at an angle of $\theta=60^{\circ}$ to the vertical. The CM of the rod is moving upwards with speed $v_1$ so the vertical component of the velocity of A relative to the ground after collision is $$v_2=v_2'\cos\theta+v_1$$
The elasticity of the collision is known ($e=1$) so the Law of Restitution can be applied to the relative velocities of approach and separation at the point of contact : $$v_2=ev_0$$
From the above equations you can eliminate $v_2, v_2', \omega$ to find the rebound speed $v_1$ of the CM of the rod and thereby the height to which the CM rises after collision.


text:
Articles by Aram W. Harrow
 Vol 10, Article 3 (pp 55-75) [Boolean Spec Issue] Dimension-Free $L_2$ Maximal Inequality for Spherical Means in the Hypercube


text:
Question
Find the value of 6g - 14x2+ 2z when g = 15, x = 2  and z = 14.
2 m

Click button first when a symbol is required. X

Find the value of 6g - 14x2+ 2z when g = 15, x = 2  and z = 14.


text:
# A cache line has 128 bytes. The main memory has latency 64 ns and bandwidth 1 GB/s. The time required to fetch the entire cache line is

41 views
in Computer
closed
A cache line has 128 bytes. The main memory has latency 64 ns and bandwidth 1 GB/s. The time required to fetch the entire cache line is
1. 32 ns
2. 64 ns
3. 96 ns
4. 192 ns

by (48.2k points)
selected

Correct Answer - Option 4 : 192 ns

Data:

Cache block size = 128 bytes

Memory latency = 64 ns

Bandwidth = 1 GB/s

Formula:

Total latency = memory latency + block access time

Calculation:

1 GB → 1 sec

$1 B \rightarrow \frac{1}{ 10^{9}s} \rightarrow1\ ns$

$128\; B \rightarrow \ 128 \ ns$

Block access time is 128 ns

Total latency = 64 + 128 = 192


text:
Execute this notebook:

# Node representation learning with Metapath2Vec¶

An example of implementing the Metapath2Vec representation learning algorithm using components from the stellargraph and gensim libraries.

References

1. Metapath2Vec: Scalable Representation Learning for Heterogeneous Networks. Yuxiao Dong, Nitesh V. Chawla, and Ananthram Swami. ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), 135–144, 2017. (link)

2. Distributed representations of words and phrases and their compositionality. T. Mikolov, I. Sutskever, K. Chen, G. S. Corrado, and J. Dean. In Advances in Neural Information Processing Systems (NIPS), pp. 3111-3119, 2013. (link)

3. Gensim: Topic modelling for humans. (link)

4. Social Computing Data Repository at ASU [http://socialcomputing.asu.edu]. R. Zafarani and H. Liu. Tempe, AZ: Arizona State University, School of Computing, Informatics and Decision Systems Engineering. 2009.

[3]:

import matplotlib.pyplot as plt
from sklearn.manifold import TSNE
from sklearn.decomposition import PCA
import os
import networkx as nx
import numpy as np
import pandas as pd
from stellargraph import datasets
from IPython.display import display, HTML

%matplotlib inline

[4]:

dataset = datasets.BlogCatalog3()
display(HTML(dataset.description))
print(
"Number of nodes {} and number of edges {} in graph.".format(
g.number_of_nodes(), g.number_of_edges()
)
)

This dataset is crawled from a social blog directory website BlogCatalog http://www.blogcatalog.com and contains the friendship network crawled and group memberships.
Number of nodes 10351 and number of edges 348459 in graph.

## The Metapath2Vec algorithm¶

The Metapath2Vec algorithm introduced in [1] is a 2-step representation learning algorithm. The two steps are:

1. Use uniform random walks to generate sentences from a graph. A sentence is a list of node IDs. The set of all sentences makes a corpus. The random walk is driven by a metapath that defines the node type order by which the random walker explores the graph.

2. The corpus is then used to learn an embedding vector for each node in the graph. Each node ID is considered a unique word/token in a dictionary that has size equal to the number of nodes in the graph. The Word2Vec algorithm [2] is used for calculating the embedding vectors.

## Corpus generation using random walks¶

The stellargraph library provides an implementation for uniform, first order, random walks as required by Metapath2Vec. The random walks have fixed maximum length and are controlled by the list of metapath schemas specified in parameter metapaths.

A metapath schema defines the type of node that the random walker is allowed to transition to from its current location. In the stellargraph implementation of metapath-driven random walks, the metapath schemas are given as a list of node types under the assumption that the input graph is not a multi-graph, i.e., two nodes are only connected by one edge type.

See [1] for a detailed description of metapath schemas and metapath-driven random walks.

For the BlogCatalog3 dataset we use the following 3 metapaths.

• “user”, “group”, “user”

• “user”, “group”, “user”, “user”

• “user”, “user”

[5]:

walk_length = 100  # maximum length of a random walk to use throughout this notebook

# specify the metapath schemas as a list of lists of node types.
metapaths = [
["user", "group", "user"],
["user", "group", "user", "user"],
["user", "user"],
]

[6]:

from stellargraph.data import UniformRandomMetaPathWalk

# Create the random walker
rw = UniformRandomMetaPathWalk(g)

walks = rw.run(
nodes=list(g.nodes()),  # root nodes
length=walk_length,  # maximum length of a random walk
n=1,  # number of random walks per root node
metapaths=metapaths,  # the metapaths
)

print("Number of random walks: {}".format(len(walks)))

Number of random walks: 30936

## Representation Learning using Word2Vec¶

We use the Word2Vec [2] implementation in the free Python library gensim [3] to learn representations for each node in the graph.

We set the dimensionality of the learned embedding vectors to 128 as in [1].

[7]:

from gensim.models import Word2Vec

model = Word2Vec(walks, size=128, window=5, min_count=0, sg=1, workers=2, iter=1)

[8]:

model.wv.vectors.shape  # 128-dimensional vector for each node in the graph

[8]:

(10351, 128)

## Visualise Node Embeddings¶

We retrieve the Word2Vec node embeddings that are 128-dimensional vectors and then we project them down to 2 dimensions using the t-SNE algorithm.

[9]:

# Retrieve node embeddings and corresponding subjects
node_ids = model.wv.index2word  # list of node IDs
node_embeddings = (
model.wv.vectors
)  # numpy.ndarray of size number of nodes times embeddings dimensionality
node_targets = [g.node_type(node_id) for node_id in node_ids]

Transform the embeddings to 2d space for visualisation

[10]:

transform = TSNE  # PCA

trans = transform(n_components=2)
node_embeddings_2d = trans.fit_transform(node_embeddings)

[11]:

# draw the points
label_map = {l: i for i, l in enumerate(np.unique(node_targets))}
node_colours = [label_map[target] for target in node_targets]

plt.figure(figsize=(20, 16))
plt.axes().set(aspect="equal")
plt.scatter(node_embeddings_2d[:, 0], node_embeddings_2d[:, 1], c=node_colours, alpha=0.3)
plt.title("{} visualization of node embeddings".format(transform.__name__))
plt.show()


text:
Lagrange Multipliers

I do not have one specific question that needs answering. Rather, it is about Lagrange multipliers in general.

So for certain minimization/maximization questions (ie find the shortest distance from some point to some plane) it seems that one could solve the question using lagrange multipliers and not using lagrange multipliers (I have done it both ways). One could set both partials equal to 0 and solve for x and y without using lagrange (as long as a function of x and y is substitued for z). Or, one could not substitute for z and use lagrange multipliers to find the distange.

Is this right? Or am I missing something? Also, is it ever 100% necessary to use lagrange multipliers? How can one tell when it is better to use lagrange multipliers and when it is better not to?

Thanks
DR13

Ok, you do the same steps required by Lagrange multipliers, but you don't call it Lagrange multipliers. :)

Using Lagrange is the only way for constrained maximum/minimum.

Oh I get it. By substituting for z before taking the partials you are just doing the step earlier rather than later. Is that right?

I'm not sure I follow you completely.
Do you have an example ?

Its fine. I worked it out myself and get it now. Thanks!


text:
## anonymous 2 years ago What is the similarties and differences among electrostatics, gravitational and magnetic forces?

1. theEric

I'm a little busy, but I'll give you suggestions. Look at the form of their equations. Think; is does this force depend on some sort of polarity?

2. anonymous

what do you mean by polarity?

3. anonymous

and is the magnetic force equation F=BILsintheta?

4. theEric

I mean things like like charges repel, opposite charges... like poles repel, opposite poles... matter.... err.... uhh... yeah. That sort of thing!

5. theEric

There are lots of equations for magnetic force! It depends on what you look at the magnetic force of! Most importantly, does it look like the equations for electrostatic and gravitational forces?

6. anonymous

no it dosent

7. anonymous

Hey, can you help me with a question?

8. theEric

Right! :) How do the electrostatic and gravitational forces compare to each other though? :) Maybe... I'm getting distracted from my own homework, but I should focus... It doesn't hurt to post it anyway!

9. anonymous

the electrostatic forces and gravitational forces are similar in equation except for their constants. They increase with a direct proportion of their masses and decrease inversely with the distance squared. However, electrostatic forces can attract and repel while gravitational forces can only attract. Is there anything else?

10. theEric

I think that's great! I would specify "direct proportion of $$\sf the\ product\ of$$ their masses," just to be picky.

11. anonymous

how about "forces vary directly with the product of the charges/masses"?

12. theEric

Right! Throw in that distinction between gravitational and electrostatic.

13. theEric

Maybe say "decrease directly" or something.. What wording is proper confuses me sometimes. You could get away with directly proportional to the product of masses for gravitational and charges for electrostatic and inversely proportional to the square of the length of separation or something like that.

14. anonymous

ok thanks. Can you help me with another one? A horizontal 6 m long wire that runs from west to east is in a 0.03 T magnetic field with a direction that is northeast. If a 4.5 A current flows east through the conductor, then what is the magnitude and direction of the force on the wire? I found the magnitude to be 0.5 N but how would i find the direction of the force?

15. theEric

I'll just trust your magnitude, because I forget the equation for current. I think you posted it above, though. Anyway.... The right hand rule! Take your right hand, fingers outstretched. Point it in the direction of the current. Now curl your fingers so that they align with the magnetic field, but don't move your palm. Stick your thumb out. Your thumb points to the direction of the force.

16. theEric

Actually, opposite. That is because of the cross product. $$\vec x\times\vec y=\vec z$$ in our coordinate system, so I remember that. For the magnetic force on a moving charge, its $$q\vec v\times\vec B=\vec F$$ where $$\vec v$$ is the velocity and $$\vec B$$ is the magnetic field.

17. theEric

Wait, not opposite, I was right, I think :)

18. theEric

I'm pretty sure I'm right :) All but positive.

19. theEric

99% Just tired :P

20. anonymous

would the magnetic field be like this |dw:1398305079394:dw|

21. theEric

Yep. If north is up and east is right, you're correct.

22. theEric

So the current would be to the right.

23. theEric

The current, when considered "conventional current," is the flow of positive charge.

24. anonymous

ok, so the force would be perpendicular to both the current and magnetic field?

25. theEric

Right.


text:
# Manual Rotation of vertices about center of shape

This topic is 3990 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Reposting, cos I've tried loads of stuff and really can't figure this out. It's driving me nuts. I want to manually rotate each vertex of a 2d rectangle around the center of the shape, without using glRotatef. I can rotate a point around another point fine, but whatever I try I can't seem to rotate the four corners of the shape around a center point. My vertices are declared as follows:
	vertices[0][0] = x - (width / 2);
vertices[0][1] = y + (height / 2);

vertices[1][0] = x + (width / 2);
vertices[1][1] = y + (height / 2);

vertices[2][0] = x + (width / 2);
vertices[2][1] = y - (height / 2);

vertices[3][0] = x - (width / 2);
vertices[3][1] = y - (height / 2);

I used this code to rotate a point around another point:
void orbit()
{
const float DEG2RAD = (float) 3.14159/180;
angle = angle + (1.0f);
for(int i = 0; i < 4; i++)
{
}
}

##### Share on other sites
Phoresis,

Do you mean that you want to rotate the object about its centre?. If so then,

(1) Translate your object back into LOCAL co-ordinate space.

Your object is at (x, y) then,

vertices[0][0] -= x;
vertices[0][1] -= y;

vertices[1][0] -= x;
vertices[1][1] -= y;

vertices[2][0] -= x;
vertices[2][1] -= y;

vertices[3][0] -= x;
vertices[3][1] -= y;

(2) Perform your rotation in LOCAL space

float fx = vertices[0][0];
float fy = vertices[0][1];

vertices[0][0] = fx * cosf(angle) - fy * sinf(angle);
vertices[0][1] = fx * sinf(angle) + fy * cosf(angle);

fx = vertices[1][0];
fy = vertices[1][1];

vertices[1][0] = fx * cosf(angle) - fy * sinf(angle);
vertices[1][1] = fx * sinf(angle) + fy * cosf(angle);

// similar for the remaining vertices
NOTE: (angle) must is in rads too ;)

(3) Translate object back into WORLD space

vertices[0][0] += x;
vertices[0][1] += y;

vertices[1][0] += x;
vertices[1][1] += y;

vertices[2][0] += x;
vertices[2][1] += y;

vertices[3][0] += x;
vertices[3][1] += y;

This also applies to 3D objects too, but you will have to factor in the z-ordinate.

Hope this works

MAMEman.

##### Share on other sites
just to clarify, do i translate to local co-ordinate space after I have declared the following:

vertices[0][0] = x - (width / 2);

vertices[0][1] = y + (height / 2);

vertices[1][0] = x + (width / 2);

vertices[1][1] = y + (height / 2);
etc

or instead of? Just want to make sure I get exactly what you mean.

##### Share on other sites
Yes, I'm assuming that your (x, y) co-ordinates define the centre position of your object in WORLD space. Hence vertices[0][0] -> vertices[3][1] should already be in WORLD space. :)

##### Share on other sites
Cool. Thanks this seems to work, but it also seems to get faster and faster and faster.

void orbit(){	const float DEG2RAD = (float) 3.14159/180;	angle = angle + (0.01f);	if (angle > 360) angle -= 360;	if (angle < 0) angle += 360;	float degInRad = angle*DEG2RAD;	for (int i = 0; i < 4; i++)	{		vertices[0] -= x;		vertices[1] -= y;	}	for (int i = 0; i < 4; i++)	{				float fx = vertices[0];		float fy = vertices[1];				vertices[0] = fx * cosf(degInRad) - fy * sinf(degInRad);		vertices[1] = fx * sinf(degInRad) + fy * cosf(degInRad);	}	for (int i = 0; i < 4; i++)	{		vertices[0] += x;		vertices[1] += y;	}}

I call this method every time the sqaure is drawn. Yeah I know I don't need to keep repeating the for loop, just wanted to split up the logic for now.

##### Share on other sites
Looking at your code it appears that your angle gets bigger and bigger. Therefore your rotation will get bigger and bigger. Just make your angle variable constant, for example 0.5f. This should take care of that. But this may run faster/slower on another system because you are not using timer based rotation methods ;). However for your needs the initial suggestion should work fine.

Regards,

MAMEman.

##### Share on other sites
Ah right I'm starting to understand now. What if I wanted it rather than rotate to just set it at the angle?

##### Share on other sites
Did the initial suggestion work? (setting a constant). I'm not sure what you meant in the last post please carify.

##### Share on other sites
setting a constant works in that the shape keeps rotating without getting faster or slower, which is good. However what I wanted to achieve initially was a method that just sets the shape to a specified angle, rather than rotating it constantly. So if I gave an angle of 45 degrees then the method would set the angle of the shape to 45 degrees and it would stay at 45 degrees until the method was called again with a different angle. Hope this clarifies it.

##### Share on other sites
OK. How about when you initialize the object that you want set an initial angle for, you do something like this:

void InitializeVertices(float angle, const float px, const float py)
{

// initialize LOCAL co-ordinates of the object

vertices[0][0] = -(float)(width / 2);
vertices[0][1] = (float)(height / 2);

vertices[1][0] = (float)(width / 2);
vertices[1][1] = (float)(height / 2);

vertices[2][0] = (float)(width / 2);
vertices[2][1] = -(float)(height / 2);

vertices[3][0] = -(float)(width / 2);
vertices[3][1] = -(float)(height / 2);

// perform the initial rotation (as per (2) in my initial post)
// not forgetting to convert (angle) to rads (if not already done so)

// put object into WORLD space (as per (3) in my initial post)
// use parameters px and py to do the translation

}

Now when you want to apply a rotation to the object (for example as the result of a key push) then,

void RotateVertices(float angle)
{
// put your rotation code in here

// note: that when you apply your rotation then angle will be FROM your current angle.
// for example if you initially rotate your object say 90deg and then apply a 45deg rotation your object will have rotated 135deg total from the +ve x-axis.
}

##### Share on other sites
I think you misunderstood me, either that or I'm just being dumb (most likely), all I want to do is scrap the rotation and just have the set angle, but the code I've got at the moment doesn't just set an angle, it constantly rotates the square .

I know these two lines need altering:

but again I'm stuck with the math.

So, to re-iterate, the shape starts of with no rotation. I then call my rotate method and the shape is redisplayed, rotated to whatever angle I wanted. This would be the same as calling glRotatef on the shape once.

##### Share on other sites
Yep I guessed right. I think I am being dumb. Basically all I need to do is account for the fact that the angle is added onto the current angle of the shape.

##### Share on other sites
The problem with my solution is that the vertex data is constantly being updated (correct?). So what you will need to do is store the initial WORLD co-ordinates of your object and work with those. Looking at you code you may want to do it this way.

void orbit(float angle)
{
const float DEG2RAD = (float) 3.14159/180;

if (angle > 360) angle -= 360;
if (angle < 0) angle += 360;

for (int i = 0; i < 4; i++)
{
vertices[0] = initial_vertex[0];
vertices[1] = initial_vertex[1];

vertices[0] -= x; // move into local space
vertices[1] -= y;
}

for (int i = 0; i < 4; i++)
{

float fx = vertices[0];
float fy = vertices[1];

vertices[0] = fx * cosf(degInRad) - fy * sinf(degInRad); // rotate point
}

for (int i = 0; i < 4; i++)
{
vertices[0] += x; // move back to world space
vertices[1] += y;
}
}

BEWARE: If you perform a translation operation then you will need to update initial_vertex as well as vertices. Hope this solves it.


text:
# Heat transfer

(Difference between revisions)
 Revision as of 12:40, 1 December 2005 (view source)Jola (Talk | contribs)← Older edit Revision as of 12:40, 1 December 2005 (view source)Jola (Talk | contribs) Newer edit → Line 1: Line 1: - == Conduction == + == Conduction == *Conduction can be defined as the heat transfer through a substance because of a temperature gradient. The rate of heat transfer by conduction between two regions of a substance is proportional to the temperature difference between them. The constant of propotionality is called thermal conductivity of the material. *Conduction can be defined as the heat transfer through a substance because of a temperature gradient. The rate of heat transfer by conduction between two regions of a substance is proportional to the temperature difference between them. The constant of propotionality is called thermal conductivity of the material.

## Conduction

• Conduction can be defined as the heat transfer through a substance because of a temperature gradient. The rate of heat transfer by conduction between two regions of a substance is proportional to the temperature difference between them. The constant of propotionality is called thermal conductivity of the material.
• Mathematically, it can be described by using the Fourier's law:
$Q_{Conduction} = -k*A*\frac{dT}{dx}$

Where

$Q = \mbox{Heat conducted}\;[W]$
$k = \mbox{Thermal conductivity of the material}\;[W/m\,K]$
$A = \mbox{Cross-sectional area of the object parallel to heat conduction}\;[m^2]$
$T = \mbox{Temperature}\;[K]$
$x = \mbox{Length of the object}\;[m]$


text:
## [astro-ph/0503213] Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?

 Authors: T. R. Jaffe, A. J. Banday, H. K. Eriksen, K. M. Gorski, F. K. Hansen Abstract: Motivated by the large-scale asymmetry observed in the cosmic microwave background sky, we consider a specific class of anisotropic cosmological models -- Bianchi type VII_h -- and compare them to the WMAP first-year data on large angular scales. Remarkably, we find evidence of a correlation which is ruled out as a chance alignment at the 3 sigma level. The best fit Bianchi model corresponds to x=0.55, Omega_0=0.5, a rotation axis in the direction (l,b)=(222degr,-62degr), shear (sigma/H)_0=2.4x10^-10 and a right--handed vorticity (omega/H)_0=4.3x10^-10. Correcting for this component greatly reduces the significance of the large-scale power asymmetry, resolves several anomalies detected on large angular scales (ie. the low quadrupole amplitude and quadrupole/octopole planarity and alignment), and can account for a non--Gaussian "cold spot" on the sky. It appears that the WMAP data do indeed violate cosmological isotropy. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

Ah, joys of cosmology! Another very interesting paper this week!

I have a few questions for discussion:
• Figure 1. b: It would be interesting to see how does this Bianchi template looks in more neutral coordinates (say with axis to the pole). As far as I can gather these models produce a spirally looking pattern and my question is whether such pattern could result as an artifact of the scanning strategy. If this is the case, the the "telescope" would add this kind of template and then, of course, you will get all those cold-spot detections, assymmetries, etc. without them really be there;
• The WMAP best fit theoretical squadropole of 869 $\mu {\rm K}^2$: surely this is the running spectral index value? And the n_run was there to fit the low quadrupole (among other things), so it would make more sense to compare it to the pure LCDM of 1150 or so $\mu {\rm K}^2$. BUt yes, anything higher than 300 is OK with normal cosmology.
• This model brings 6 or 7 new params, which is quite a lot. Looking in pixel space, after subtracting template, by how much does the probability that what remains is a realisation of the pure LCDM increases? I am slightly confused whether this kind of analysis is neccessary, if we can just get rid of all NG detections by introducing 5 extra params? How does one go and quantify the improvement of fit in such cases...
• Finally, and most importantly: it seems that we cannot really get considerably higher statistical significance from CMB alone. If the universe is indeed described by such models, what other observational signatures could one get? Could you discard such models on the basis of LSS considerations?

Niayesh Afshordi
Posts: 49
Joined: December 17 2004
Affiliation: Perimeter Institute/ University of Waterloo
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

It seems to me that Jaffe et al. are introducing 7 new parameters, using which \chi^2 is improved by 9 (since S/N =3).
This doesn't look very significant! Am I right?

Tess Jaffe
Posts: 7
Joined: March 11 2005
Affiliation: Centre d'Etude Spatiale des Rayonnements

### [astro-ph/0503213] Evidence of vorticity and shear at large

The Bianchi component requires six additional parameters: x (or h), sigma (and thereby omega), three Euler angles, and the handedness. However, it's difficult to assess the improvement in the likelihood, because the anomalies are all non-Gaussian/anisotropic. Therefore, a simple traditional power spectrum vs. parameters approach based on the usual likelihood does not work, and a more complicated framework (with new associated parameters) is indeed required. The beauty of this particular model is that it appears to explain virtually all claimed anomalies and is both simply and physically motivated (which is more than can be said about ad-hoc inflationary potentials :-)). However, this letter does not attempt to address the complicated issue of quantifying the statistical improvement of the model by the addition of these parameters. It is meant simply to pique interest in models which have for some time been assumed irrelevant.

Pablo Fosalba
Posts: 29
Joined: September 25 2004
Affiliation: Institut d'Estudis Espacials de Catalunya
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

assuming there is a contribution from such model at high multipoles,
it remains to be seen what is the prediction for the power spectrum
for l>200 when one subtracts the Bianchi template from the WMAP map.
The acoustic peak structure should be preserved.
Related to the previous concern,
isn't this model in conflict with inflation ?

Apart from this, I find this paper is one of the nicest I have seen
dealing with WMAP data, so congratulations to the authors!

Levon Pogosian
Posts: 19
Joined: September 25 2004
Affiliation: Simon Fraser University
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

I also enjoyed reading this paper.
Are there experts in cosmocoffee who could comment on Anze's first question --could the Bianchi template be due to the scanning sequence or some other measurement artifact?
Do we have to wait for Planck to find out?

Anthony Banday
Posts: 7
Joined: October 01 2004
Affiliation: CESR
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

Scanning strategy problems are highly unlikely to explain these issues.
In fact, the WMAP scanning strategy was *designed* to avoid such
artefacts. The satellite is differential and has a short
precession period which tends to wash out systematic effects
in general, and azimuthal structure in particular. Furthermore, noise related
effects tend to be be symmetric over the two (ecliptic) hemispheres.

Beyond these generalisations, there are several specific points that argue
against a scanning strategy based explanation:

1) Such effects are not seen in the simulations of Hinshaw et al.
2003, ApJS, 148, 63, which are based on the time-ordered-data
and include any 1/f noise structure and its subsequent removal
by the map-making/filtering iteration. In particular, see Figs. 12 and 13.
2) The observed structures are *much* wider than the beam size.
3) The best-fit axis does not coincide perfectly with the ecliptic
poles.

It should also be remembered that the scanning can provides a mechanism that
allows systematic artefacts to be introduced coherently, but a physical
signal is still required. There do not appear to be any known candidates.

Tony, Tess, Hans Kristian, Kris, Frode

Levon Pogosian
Posts: 19
Joined: September 25 2004
Affiliation: Simon Fraser University
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

Thanks, Anthony.

Bruce Bassett
Posts: 26
Joined: November 24 2004
Affiliation: SAAO/UCT

### [astro-ph/0503213] Evidence of vorticity and shear at large

Hi,

Fascinating paper indeed! One important point is that since Bianchi models have non-zero shear or Weyl tensor (in the background) unlike FLRW, the dynamics of linear perturbations is significantly different than in FLRW.

Hence matching to the CMB is actually a complicated project even if one is only interested in large angular scales (e.g. the ISW effect will be different).

Cheers,
Bruce

Niayesh Afshordi
Posts: 49
Joined: December 17 2004
Affiliation: Perimeter Institute/ University of Waterloo
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

Something I don't understand here is how you can measure \omega/\H from CMB anisotropies so accurately. The CMB anisotropies are at the level of 10^{-5}, and the maximum level of anisotropies that I expect from rotation is O(\omega/\H), so I don't see where the number 10^{-10} comes about.

Combination of many multipoles can only improve the accuracy by a factor of 10-100, which is still a long way from 10^{-10}.

Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory
Contact:

### Re: [astro-ph/0503213] Evidence of vorticity and shear at la

Bruce Bassett wrote:Fascinating paper indeed! One important point is that since Bianchi models have non-zero shear or Weyl tensor (in the background) unlike FLRW, the dynamics of linear perturbations is significantly different than in FLRW.
Yes, this is what I want to understand. Is it possible to trivially refute these models on the basis that LSS or CMB PS after template subtraction would look completelly different?

I just got a copy of the original Barrow et al paper and they also focus exclusivelly on the CMB, while I would naivelly expect that an extra scale associated with rotation should appear in the power spectrum... [Well, to be quite honest, haven't read the paper so I might be talking total rubbish]

Kate Land
Posts: 29
Joined: September 27 2004
Affiliation: Oxford University
Contact:

### [astro-ph/0503213] Evidence of vorticity and shear at large

Very nice paper, and an intriguing idea ;-) However, on the subject of likelihood, isn't it crucial to take account of other effects. e.g Aren't these models ruled out purely by the low omega value, and the effect this would have on the position of the 1st Doppler Peak. Am I missing something?

Bruce Bassett
Posts: 26
Joined: November 24 2004
Affiliation: SAAO/UCT

### [astro-ph/0503213] Evidence of vorticity and shear at large

I should clarify my previous comment. The values of the shear/vorticity are so small 10^{-10} that today their impact on perturbation dynamics would be irrelevant I imagine. In that case the LSS predictions would apparently be close to FLRW.

However, the dynamics of Bianchi models is very complex and many exhibit asymptotic isotropisation - i.e. they start out very anisotropic with large shear and then end up coming very close to FLRW. Depending on the precise dynamics one could imagine models where the shear was dynamically important early on...(but still not so big as to violate BBN limits), so perturbation dynamics during radition domination could be significantly non-FLRW.

An interesting conceptual point is that the existence of vorticity means that one cannot define a single hypersurface-orthogonal four velocity for all observers (something we always take for granted in FLRW).

Tess Jaffe
Posts: 7
Joined: March 11 2005
Affiliation: Centre d'Etude Spatiale des Rayonnements

### [astro-ph/0503213] Evidence of vorticity and shear at large

At http://www.mpa-garching.mpg.de/~tjaffe/note.ps we've posted a quick note on the Bianchi models. Basically, it's just a summary of the relevant parameters and equations in Barrow et al. (1985) along with plots of some examples. From these, one can see that for some models, a shear of order 10^-10 can give anisotropies of the order 10uK.


text:
# pie

The Age Old Debate: Which Pie Is Better? [POLL]
Of course, one of my favorite things about Thanksgiving, is the pie.
It never ceases to fail though.  Someone always seems to look at my choice of pie, and ask
'Why are you eating that one?'
followed closely by
'because _______ is the best.'
Well, I decided it's time to lay …
10 Thanksgiving Pie Disasters
Ah, pie. One of the great joys of Thanksgiving…that can so easily turn to abject terror if done wrong. From burnt crusts, to terrible fillings, pie is either really good, or really, really bad. Here's ten of the worst Thanksgiving pies we've ever seen.
...


text:
• Dielectric properties of CdS nanoparticles synthesized by soft chemical route

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/072/06/1

• # Keywords

Cadmium sulphide; chemical synthesis; impedance spectroscopy; dielectric properties.

• # Abstract

CdS nanoparticles have been synthesized by a chemical reaction route using thiophenol as a capping agent. The frequency-dependent dielectric dispersion of cadmium sulphide (CdS) is investigated in the temperature range of 303–413 K and in a frequency range of 50 Hz–1 MHz by impedance spectroscopy. An analysis of the complex permittivity ($\varepsilon'$ and $\varepsilon''$ ) and loss tangent (\$\tan \delta) with frequency is performed by assuming a distribution of relaxation times. The scaling behaviour of dielectric loss spectra suggests that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are analysed in the framework of conductivity and modulus formalisms. The frequency-dependent conductivity spectra obey the power law.

• # Author Affiliations

1. Department of Physics, Government Post Graduate College, Rishikesh 249 201, India
2. Department of Physics, Bose Institute, 93/1, A.P.C. Road, Kolkata 700 009, India

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.


text:
# Efficient reconstruction of functions on the sphere from scattered data

Stefan Kunis

given at  strobl07 (18.06.07 11:45)
id:  594
length:  25min
status:  accepted
type:  talk
www:  http://www.tu-chemnitz.de/~skunis
Recently, fast and reliable algorithms for the evaluation of spherical harmonic expansions have been developed. The corresponding sampling problem is the computation of Fourier coefficients of a function from sampled values at scattered nodes. We consider a least squares approximation and an interpolation of the given data. Our main result is that the rate of convergence of the two proposed iterative schemes depends only on the mesh norm and the separation distance of the nodes. In conjunction with the nonequispaced FFT on the sphere, the reconstruction of $N^2$ Fourier coefficients from $M$ reasonably distributed samples is shown to take ${\cal O}(N^2 \log^2 N+M)$ floating point operations. Numerical results support our theoretical findings.


text:
Synopsis

# Nuclear Spectroscopy Reveals New Shapes of Excited Nuclei

Physics 12, s113
Cadmium nuclei take on multiple shapes at low excitation energies, a discovery that overturns a long-accepted tenet of nuclear structure.

Atomic nuclei take on excited states when they vibrate, rotate, or when their constituent nucleons exchange one nuclear shell for another. In nuclei with nearly filled nuclear shells, it has long been thought that low-energy excitations were due exclusively to different patterns of vibration around a spherical shape: only in rare, high-energy excitations were these nuclei expected to assume more exotic shapes. Now, Paul Garrett, of the University of Guelph in Canada, and colleagues have found that the lowest-energy excited states of cadmium-110 and cadmium-112—once considered textbook examples of spherical vibration—are instead due to the rotation of various nonspherical shapes. The result is also the best evidence to date that a stable nucleus like cadmium can assume multiple shapes—all previously studied nuclei with coexisting shapes have been radioactive.

To explore the shapes of cadmium nuclei, the team started by depositing beams of radioactive indium and silver isotopes onto a target surrounded by radiation detectors. The indium and silver decayed into isotopes of cadmium, with some of these daughter nuclei existing briefly in excited states. As the nuclei settled into lower energy states, they emitted gamma rays that revealed details about the excited states, such as their energies, their occurrence rates, and their decay rates. A comparison of these data with state-of-the-art calculations suggested that the excitations were best explained not by spherical vibrations but by rotating ellipsoidal nuclei. The model predicts that these nonspherical nuclear configurations exist right down to the ground state, with four distinct ellipsoidal shapes representing the lowest energy states. Proving this empirically is the team’s long-term goal but doing so will take many experiments across many different laboratories.

This research is published in Physical Review Letters.

–Marric Stephens

Marric Stephens is a freelance science writer based in Bristol, UK.

Nuclear Physics

## Related Articles

Astrophysics

### Uncertainty over First Stars

New analysis of nuclear reaction data finds holes in a theory about the first stars. Read More »

Astrophysics

### Probing the Skin of a Lead Nucleus

Researchers make the most precise measurement yet of the neutron distribution in a heavy nucleus, with implications for the structure of neutron stars. Read More »

Nuclear Physics

### A Lightweight Among Heavyweights

Researchers have observed the lightest uranium isotope to date, offering insight into models of nuclear structure. Read More »