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Can we really ever accurately test SR time dilation?

1. May 29, 2013

DiracPool

The two most famous "tests" for the accuracy of time dilation in SR are 1) the plane that flew around the globe with the atomic clock, and 2) the muon experiments on the mountain. I'm assuming, of course, that all the experimental controls are correct and so are the results. My question is how do we rule out the effects of acceleration in testing a pure SR Lorentz contraction model? The plane flying around the globe obviously experiences centripetal acceleration among others, and the muons decelerate when they travel through the atmosphere (don't they?)

This problem also relates to the twin paradox, where many explanations use the "turn around" acceleration to control for the anomalies of "who is receding from whom," etc.

Obviously, the best thing to do would be to test the twins' age differences when the traveling twin reached the distant planet and before it made any accelerating turn around. But can that be done, even in principle, through some sort of clock synchronization? How can time dilation be tested reliably in truly SR non-accelerating frames?

2. May 29, 2013

VantagePoint72

Special relativity is perfectly capable of handling accelerated motion, and this was taken into account with experimental tests of time dilation such as Hafele-Keating. The popular notion that SR is somehow unable to handle accelerated reference frames is wrong.

3. May 29, 2013

DiracPool

Thanks, but my question wasn't whether or not SR could handle accelerations, it was could we test time dilation without the consideration of acceleration. The Lorentz contractions model that time dilation occurs in systems of non-accelerated reference frames. Is there a reliable way we can test that?

4. May 29, 2013

VantagePoint72

Then I don't understand your question. Why should we need to test it without acceleration? The overall prediction for time dilation that will occur during an accelerated trip is obtained by breaking the motion up into infinitesimal inertial segments and using the inertial time dilation formula. It's the exact same formula being tested, just applied to curved worldlines.

5. May 29, 2013

pervect

Staff Emeritus
MTW mentions that neutrons in a nucleus are accelerating at about 10^29 m/s^2, that even greater accelerations occur in scattering experiments, and that no effects due to these accelerations have been noticed - that SR seems to handle such situations just fine.

The text didn't give more details, i.e. what might one measure exactly to compare between a neutron/proton in a nucleus and a free one to look for acceleration effects. I'd expect that proton spin (nuclear magnetic resonance) would be affected if there was some sort of "acceleration effect".

One obvious difficulty is that you need some theory that predicts acceleratio to have an effect in the first place to compare to SR which predicts no effect. Offhand, I don't know of any such test theory (but I can't say I've looked for one, either).

6. May 29, 2013

Staff: Mentor

When I was a graduate student, one of my friends worked on an experiment that studied beams of short-lived hyperons (sigmas and xis, I think), produced at Fermilab using collisions of protons in a "production target". The design of the beamline and apparatus depended critically on the time-dilated lifetimes of the particles. If there were no time dilation, the particles would not even have reached the detector! As far as I recall, the beams were straight-line between the production target and the detector: no centripetal acceleration.

7. May 29, 2013

ghwellsjr

Contraction applies to length, not to time. Did you really mean this?
SR Time Dilation is not observable or measurable and cannot be tested, just like the one way speed of light cannot be tested. All we can do, or rather all we need to do is show that it is consistent with other things that can be measured and observed.

So when you ask about the "best thing to do", you seem to realize that it will require a different kind of clock synchronization than what is available to us now and you are correct. Einstein made it clear that we cannot determine synchronization of remotely located clocks without defining (not measuring or observing) their synchronization and he does that by defining the one way speed of light. The rest is just mathematics.

If you understand that SR Time Dilation is a mathematical calculation of the ratio of the progress of Coordinate Time to the progress of Proper Time on a moving clock in a particular Inertial Reference Frame (IRF) and that it is mathematically different in another IRF as determined by the Lorentz Transformation process, then I think you will come to grips with the fact that it is non-observable and non-testable but consistent with anything that can be observable and measurable.

8. May 29, 2013

Staff: Mentor

There are many acceleration-free tests of SR time dilation. See here: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Tests_of_time_dilation

The seminal test was the Ives and Stillwell test where they measured the relativistic Doppler (classical Doppler w/ time dilation) on particles moving inertially in the lab. There are other tests which measure only the transverse Doppler so it is purely time dilation.

However, for me a more convincing experiment is to go the other way and subject the particles to incredibly high accelerations and detect if there is any additional effect due to the acceleration beyond the speed. That has also been done, e.g. by Bailey et al. for accelerations up to ~10^18 g. Since they detected no additional acceleration effects at such high accelerations you would not expect the acceleration to affect the results on any of the other experiments either.

9. May 29, 2013

Staff: Mentor

I disagree with this. The one way speed of light depends on your synchronization convention, but the transverse Doppler effect (which is entirely time dilation) does not.

10. May 29, 2013

VantagePoint72

No, I think George is right. I'm not entirely sure where the simultaneity convention sneaks its way into this example, but it must be do somewhere: you can completely eliminate time dilation between any two particular frames with an especially perverse choice of simultaneity convention. Winnie does this in one of his famous 1970 papers ("Special Relativity Without One-Way Velocity Assumptions").

11. May 29, 2013

Staff: Mentor

In transverse Doppler there is only a single clock (no synchronization) and it is a direct measurement of time dilation. Furthermore, even the non-transverse Doppler shows time dilation and requires only a single clock.

Time dilation and relativity of simultaneity are independent features of the Lorentz transform. You can have one without the other, so I wouldn't assume that the measurements are inextricably linked. I just don't see how they would be linked.

Last edited: May 29, 2013
12. May 29, 2013

VantagePoint72

There is only one clock at the receiver itself; however, interpreting the transverse relativistic Doppler effect as purely a time dilation effect is equivalent to assuming standard synchrony between the different points along the emitter's worldline.

Again, I refer you to the Winnie papers. It's possible to choose a simultaneity convention such that there is no time dilation between the emitter and receiver frames. With such a choice, the relativistic Doppler effect (which, like differential aging, is an invariant) would be attributed entirely to the relativity of simultaneity. Conversely, with the standard synchrony convention one would (as you are) attribute the transverse relativistic Doppler effect entirely to time dilation. Since which it is ultimately depends on your choice of convention, it is not meaningful to say that the transverse Doppler effect is a direct test of time dilation.

13. May 29, 2013

ghwellsjr

Simultaneity sneaks its way in when you define "at the point of closest approach" which is frame dependent.

Keep in mind, I've stated the definition of Time Dilation being the ratio of Coordinate Time to Proper Time. If some other definition is used, it needs to be stated.

Last edited: May 29, 2013
14. May 29, 2013

Staff: Mentor

Hmm, I have to think about this. I am not at all convinced, but it is worth looking into deeper.

15. May 29, 2013

PAllen

This is interesting. One way of observing transverse Doppler has no clock and no synchronization and one reference frame:

Have an emitter of known type (e.g. an LED laser) move along a barrier with an opening, and a detector placed on a line perpendicular to the barrier from the opening. It detects redshift. It seems it would take a very perverse interpretation to call this other than time dilation: LED running slow moving past the opening.

16. May 29, 2013

VantagePoint72

This, again, requires standard synchrony between the various points along the laser's path. There is no avoiding that fact. Perhaps it will help if I give a more specific citation: Winnie's first paper is here; see the section "4. Time dilation and the choice of $\epsilon$". Indeed, I referred to the required simultaneity convention as "perverse" in post #10. Nonetheless, it is a permissible convention in SR.

Relativity of simultaneity and time dilation are not independent effects in the Lorentz transformations. By fiddling around with your choice of the one-way speed of light, you can change the magnitude of one effect at the expense of the other (between two particular frames). If it were possible to measure time dilation (a coordinate effect) with no further assumptions, it would be equivalent to a direct measurement of the one-way speed of light due to Winnie's equation 4-7.

Last edited: May 29, 2013
17. May 29, 2013

PAllen

I am well aware of the conventionality of simultaneity (I've read other papers with similar parametrization of simultaneity)[edit: and I definitely agree with the conventionality of simultaneity]. But I don't understand how it applies to this scenario. We have nothing but an apparatus at rest and a moving emitter. The fixed geometry of the apparatus defines 'transverse'. As a measurement, the result is invariant. What I am looking for, be comfortable with the point of view you espouse, is any plausible way to interpret this experiment as other than detecting time dilation in the frame of the apparatus. Would you have to say that simultaneity convention determines what is perpendicular in a rigid apparatus at rest?? If that is the resolution, I find that too perverse to take seriously. Maybe there is another way ...?

Last edited: May 29, 2013
18. May 29, 2013

VantagePoint72

And hence the apparatus at rest must establish a synchrony convention for the different points along the emitter's path. Consider a derivation of the relativistic Doppler effect where individual pulses of light are being emitted at regular intervals. Since the clock is in motion, successive pulses are emitted at different places according to the receiver's frame. You can make the separation between the two places arbitrarily small—and even take a limit if you wish—but they are still at different places, even if infinitesimally so. Hence, in the receiver's frame the period by which the emitter sends out its pulses requires a comparison of two different clocks along emitter's path.

Of course, there is no ambiguity about the period at which the receiver receives the pulses. Maybe this is the confusion. That is the relativistic Doppler effect and is convention-free. However, for you to equate the period at which the pulses are received with the period at which they are emitted (in the receiver's frame) requires standard synchrony along the emitter's path—at least, in the neighbourhood of the point which you are considering.

In Winnie's equation 4-8, you can see that a judicious choice of $\epsilon$ eliminates the time dilation factor altogether between two particularly chosen frames. So, how can it not be relevant here? We only have two frames (the receiver and the emitter) and you can see that you can choose a simultaneity convention such that the receiver's frame does not contain a time dilation term for the emitter's frame. So, how could time dilation be measured directly if it's been eliminated by a coordinate transformation??

I agree it's very intuitive to make the assignment that the "period measured by receiver" and the "period of the emitter in the receiver's frame"—and the isotropy of the one-way speed of light is intuitive too!—but it is not a required assignment in SR, for the exact same reason as the one-way speed of light.

Last edited: May 29, 2013
19. May 29, 2013

VantagePoint72

Yes, that is precisely what you have to say, and there is no other way. Consider how you determine what is perpendicular: if I draw a straight line $L$ and some point $P$off the line, the line $M$ that is through $P$ and perpendicular to $L$ is the one such that given two points, $A$ and $B$, equidistant along $L$ on either side of the intersection of $L$ and $M$, the distances $AP$ and $BP$ are the same. But for the moving emitter, "distance" requires a simultaneity convention to pick the spatial slice you are measuring in! It is precisely the usual Einstein convention for synchrony that allows you to do this in the way you are thinking. If you find the conclusion "too perverse to take seriously", then you are forced to reject the conventionality of simultaneity too. It is the same assumption.

Last edited: May 29, 2013
20. May 29, 2013

Staff: Mentor

I am with PAllen on this one. A simultaneity convention does not change the geometry of an object at rest. A simultaneity convention merely determines which events along a given pair of worldlines are considered simultaneous. If all of the events on a worldline occur at the same spatial location then re-mapping the simultaneity convention does nothing to the geometry.

The geometry of an apparatus at rest is not a function of the choice of simultaneity convention. A Doppler measurement can be constrained to be transverse through an apparatus at rest in the lab. The resulting measurement measures time dilation regardless of the simultaneity convention.


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Archive for the 'Sports' Category

No Stork Involved

How are baseballs made?

Building a Better Soccer Ball

Better in terms of durability.

Joy That Lasts, on the Poorest of Playgrounds

The children, he learned, used trash because the balls donated by relief agencies and sporting goods companies quickly ripped or deflated on the rocky dirt that doubled as soccer fields. Kicking a ball around provided such joy in otherwise stressful and trying conditions that the children would play with practically anything that approximated a ball.

“The only thing that sustained these kids is play,” said Mr. Jahnigen of Berkeley, Calif. “Yet the millions of balls that are donated go flat within 24 hours.”

The solution was a foam similar to what is used in Crocs.

[H]e happened to be having breakfast with Sting, a friend from his days in the music business. Mr. Jahnigen told him how soccer helped the children in Darfur cope with their troubles and his efforts to find an indestructible ball. Sting urged Mr. Jahnigen to drop everything and make the ball. Mr. Jahnigen said that developing the ball might cost as much as $300,000. Sting said he would pay for it. An interesting logistical issue is also brought up: the balls are more difficult to ship than traditional balls, because they can’t be deflated (the reverse of a certain balloon issue I’ve run into) If you are so inclined, you can go to the website and buy a ball for about$40, in which case one will also be donated, or you can donate one for \$25.

Them’s the Breaks

Dynamics and fracture of Hunter Pence’s bat

If you didn’t see this Monday night, you probably saw a link to it later. It was the bottom of the third with the bases loaded for the Giants. Hunter Pence hit a broken-bat single through the infield that scored two earned runs and one unearned run on a misplay in the outfield. Giants went on to score two more runs in the inning and pretty much buried the Cardinals in the final game of their series.

What was remarkable about the hit was how Pence’s bat behaved.

One thing the author doesn’t analyze, but is important to the outcome, is how the multiple contacts imparted spin to the ball, which you can see in the breakdown — the first contact has the ball coming out with only a little rotation, but it increases with each contact. The result was a trajectory that curved away from the shortstop, who initially had leaned toward third base, only to have the ball go up the middle.

All of this is moot, though. Technically it was a dead ball, because you can only legally strike the ball once with the bat. The batter should have been called out, according to (my reading of) rule 6.05(h) But I’ll give the umps a pass for missing this one. (The Cards, on the other hand, may not be so forgiving)

Water Rocket on Steroids

New Extreme Sport Combines a Jet Pack with a Jet Ski
No, I didn’t lose balance. I was diving.

Making a Fist Instead of the Heimlich

Study: Athletes Perform Better Under Pressure When They Make a Fist With Their Left Hand

According to the researchers, freaking out is primarily associated with the left hemisphere of the brain, while the right hemisphere deals more with mechanical actions. Meanwhile the cortex of the right hemisphere controls movements of the left side of the body, and the left hemisphere controls the right side of the body. So they figured that if you can purposely activate the right hemisphere — in this case, by making a fist or squeezing a ball with your left hand — it will improve physical performance and draw focus away from the ruminating left hemisphere.

If you’re old enough to remember: Joe Morgan of the Cincinnati Reds used to flap his arm when he was at-bat, a trick he said was a reminder, from one of his coaches, to keep his elbow up. I wonder if that ritual also could have had this distraction effect.

‘Tis the Season, 2012

NFL maps 2012

What gets broadcast and where, along with an explanation of the rules for televising games.

Slicing it Right Into the Entanglement Hazard

ZapperZ has a takedown of an article that purports to apply QM to golf; the critique is Quantum Physics And ….. Golf?!

He addresses each point but I think he misses one important aspect of the first issue, on entanglement. Creating and maintaining entanglement isn’t easy, but more importantly, there’s the ol’ bugaboo

Entanglement might one day allow us to communicate instantaneously across the light-years of distance between stars. But for golfers, entanglement offers a more practical benefit.

I have watched golfers tee off and then twist and bend their bodies as they follow the flight of their ball, trying to influence the ball’s course through the air. It doesn’t work, of course.

But if the golfer and the ball could somehow be entangled, then every movement the golfer makes would instantly have an effect on the golf ball. The golfer could literally steer the ball in midair.

The body English would work!

No, no, no; a thousand times no. Entanglement does not allow for instantaneous communication and does not allow you to influence distant objects. Entanglement allows you to do one measurement and determine the states of two particles, with one particle possibly being far away — it does not enable you to change that state.

A Different Pitch Experiment

Challenging Batters and Physics Experts Alike

The conflict was this: A split-finger is usually gripped to reduce backspin on the ball because backspin prevents the ball from dropping. The typical Magnus effect on the ball will tilt it slightly in toward a hitter.

“But the particular pitch that was unusual broke away from a right-handed hitter,” Nathan said.

Stumped, Nathan sent the video to the physicist Rod Cross at the University of Sydney in Australia. Cross performed several tests — often using polystyrene balls for better movement — and came up with what he views as a plausible theory. He published his findings in an article in the American Journal of Physics in January.

Not Physics-Defying, But Certainly Unusual

Ball makes U-turn from foul to fair on Brian Dozier’s incredible infield hit (Video)

Some stories are saying it defies the laws of physics (which, unfortunately, does not defy the laws of journalistic hyperbole) but the stretch at about 0:45 gets it right: it’s like a cue shot in pool. There’s a lot of spin, and it looks a lot like a trick shot.

Veni, Vidi, Slamdunk

Uncle Drew

After spending four hours in makeup, 2012 NBA Rookie of the Year Kyrie Irving heads to the courts of New Jersey to devour some young bloods in a pick-up game.

The Basketball Kama Sutra

Analytics Reveal 13 New Basketball Positions

For as long as basketball has been played, it’s been played with five positions. Today they are point guard, shooting guard, small forward, power forward and center. A California data geek sees 13 more hidden among them, with the power to help even the Charlotte Bobcats improve their lineup and win more games.

I think it has been long recognized that within any position you can have more of an offensive/defensive prowess, and that there are hybrid positions, regardless of what label you put on them. I’m also not close to being sold on NBA 1st team/2nd team, role-player or one-of-a-kind being a position. (Hey, I’m won the starting job at NBA All-Star on my team!) I think these are ways of categorizing the productivity of players, i.e their roles, rather than defining the position they play. You need a player or players with ball-handling skills, you need ball distribution, you need rebounding, you need scoring ability (interior and perimeter and also free throws), you need defense. How you divvy up those needed skills isn’t fixed, though some pairings might work better than others. This breakdown seems to imply that good players excel at a couple of skills (and the best at even more), or are somewhat less adept at each but possess a wider range of skills, and those pairings/groupings are given.

Now what would be really interesting would be looking at the depth and breadth of coverage of these roles as a function of the teams’ success. The diversity and output of the Mavericks that is shown — does that represent their success as well? Would a cellar-dwellar have the same breadth but simply be at a lower level of achievement, or do they suffer from not having some skill-set combination (e.g. single-skill players, rather than dual-skill), or both?

Here’s the Antidote

All too often the peripheral sports stories we hear or read — the ones that aren’t game summaries — are about people (or organizations) behaving badly. This is one of the exceptions: When There’s More To Winning Than Winning

When last we left the NCAA, it was February madness, colleges were jumping conferences, suing each other, coaches were claiming rivals had cheated in recruiting — the usual nobility of college sports.

And then, in the midst of all this, the men’s basketball team at Washington College of Chestertown, Md., journeyed to Pennsylvania to play Gettysburg College in a Division III Centennial Conference game.

Another story from a few years back, cut from the same cloth.

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# American Institute of Mathematical Sciences

December  2017, 10(6): 1281-1301. doi: 10.3934/dcdss.2017069

## Shape optimization for Stokes problem with threshold slip boundary conditions

 1 Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83,186 75 Prague 8, Czech Republic 2 Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FIN-40014 Jyvaskyla, Finland 3 Department of Nanotechnology and Informatics, Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec, Studentská 1402/2,461 17 Liberec 1, Czech Republic

* Corresponding author

This paper is dedicated to Prof. Tomáš Roubíček in the occasion of his 60th birthday.

Received  July 2016 Revised  October 2016 Published  June 2017

Fund Project: The first author acknowledges the support of the project 17-01747S of the Czech Science Foundation. The second author was suppported by the Academy of Finland, grant #260076. The third author was supported by the Ministry of Education, Youth and Sports under the projects LM2015084 and LO1201 in the framework of the targeted support of the Large Infrastructures and of National Programme for Sustainability Ⅰ

This paper deals with shape optimization of systems governed by the Stokes flow with threshold slip boundary conditions. The stability of solutions to the state problem with respect to a class of domains is studied. For computational purposes the slip term and impermeability condition are handled by a regularization. To get a finite dimensional optimization problem, the optimized part of the boundary is described by Bézier polynomials. Numerical examples illustrate the computational efficiency.

Citation: Jaroslav Haslinger, Raino A. E. Mäkinen, Jan Stebel. Shape optimization for Stokes problem with threshold slip boundary conditions. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1281-1301. doi: 10.3934/dcdss.2017069
##### References:

show all references

##### References:
Left: reference triangulation $\widehat{\cal T_h}$. Right: Mapped triangulation $\cal T_h$.
Optimized shapes (left) and convergence histories (right) for different values of the penalty/smoothing parameter $\varepsilon$.
Streamlines (left) and pressure contours (right) for $\varepsilon=10^{-5}$.
Tangential velocity and shear stress for $\varepsilon=10^{-5}$
Streamlines (left) and pressure contours (right)
Tangential velocity and shear stress
Optimized Bézier functions $\alpha_m$ for two different values of $\sigma_1$
Contours of the target pressure $p_0$ (left) and computed pressure (right)
Tangential velocity and shear stress on $S(\alpha_{opt})$
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Cyclic sieving

Tony will intrroduce the idea of cyclic sieving, and then we'll all try to work out what connection there is, if any, to tensor categories.


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# Get an input signal from LTI system output, find impulse response

I just study signal processing and I have some questions.

1. How to find impulse response $h[n]$ sequence of the system if I have $x[n]$ and $y[n]$ (input and output) sequences? Hope there is a formula to do that.
2. How to find $x[n]$ input sequence if I have $h[n]$ and $y[n]$?
3. Is it possible to find $x[n]$ if I just have set of $y[n]$ values, but I don't know impulse response $h[n]$? How to do that if so?

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I want to ask the same question, which was in section 1 but for continues time. I have to find the impulse response and I have been given the input and output. –  Tauseef Jun 5 '13 at 12:26

Ok. You are touching on the topic of deconvolution. You can do this most easily by transforming the data into the frequency domain, doing some basic math and then converting back to the time domain.

For example for case 1, if you transform the signals you have $H(f) = Y(f)/X(f)$ so $h[n] = IDFT[Y(f)/X(f)]$

You can do similar manipulations to handle case 2.

I'm not sure case 3 is possible. I think you need more information to produce x[n]

Here is a site that discusses deconvolution: http://terpconnect.umd.edu/~toh/spectrum/Deconvolution.html

This is a VERY simplified treatment of this question. I'm not sure what level of detail is being requested in the posted question.

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I just want to point out that deconvolution and/or system identification are tricky, complicated topics that aren't quite as "plug-and-chug" as indicated here. As one example, what happens to your calculation of $H(f)$ above if $X(f) = 0$ for some values of $f$? Also, the problem referenced in question #1 is known as system identification, while #2 is more typically referred to as deconvolution. The structure of the two problems is similar, but you might attack them differently. –  Jason R Jan 22 '13 at 14:13
Absolutely true. This is a way over simplified answer to a complex question, but I think you've got to start somewhere. Start with the basic idea and then work your way up to the practical details. I got the impression this was kind of a theoretical question based on the "just study signal processing" comment. –  user2718 Jan 22 '13 at 14:22
Also to add on to @JasonR's remark, for case 1, if $X(f)=0$, then it's actually not possible to reconstruct $H(f)$. In practical scenarios, the system is actually $y(t)=(h*x)(t)+n(t)$ where $n$ denotes noise that is typically wideband. In these scenarios, if $X(f)$ is small, then the reconstructed $H(f)$ has low SNR. The fancy algorithms simply fill in for $H(f)$ when $X(f)=0$ (or small) using prior assumptions typically by a technique called regularization. Likewise for case 2, $X$ and $H$ are swapped. –  thang Jan 22 '13 at 19:28
Thanks. From now I can at least google for system identification and deconvolution to find more information if necessary. –  Pavel Shchegolevatykh Jan 23 '13 at 10:21


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0000004485 00000 n When elimination is performed on a symmetric positive definite matrix and pivots are taken from the diagonal in any order, numerical stability is guaranteed. For a positive definite matrix, the eigenvalues should be positive. Vote. Theoretically this matrix should have been a positive definite matrix but due to noise it is not. Large amounts of missing data can lead to a covariance or correlation matrix not positive definite. S = e’Me, To an extent, however, we can discuss positive definiteness in terms of the sign of the “determinant" of the matrix. Thank you in advance Claudio link text . Even if you did not request the correlation matrix as part of the FACTOR output, requesting the KMO or Bartlett test will cause the title "Correlation Matrix" to be printed. $\begingroup$ If correlation matrices where not semi-positive definite then you could get variances that were negative. Also remember that journals are not perfect, so a covariance matrix in an article may also contain an error. Psychometrika, 49(2–June), 155-73. If a covariance or correlation matrix is not positive definite, then one or more of its eigenvalues will be negative. 變更 ). Les npivots de Asont strictement positifs. If I am not mistaken, the default covariance coverage in Mplus is .05, the fact that you need to set it lower suggests you have some combinations of variables with less than 5% jointly present? $\begin{bmatrix}1 & 0 \\ 0 & 2\end{bmatrix}$ is positive definite and not orthonormal. Eigenvalues are the elements of a vector, e, which results from the decomposition of a square matrix S as: xref No convergence indicates that you have a nonlinear analysis and that its cause could just be these badly connected long bars/etc. In the numerical computation of the eigenvalues, all those theoretical values of 0 will not be computed exactly by eig or eigh. Using ML estimation involves inverting Sigma, but since the aim to maximize the similarity between the input matrix and Sigma, the prognosis is not good if the input matrix is not positive definite. For example, if a plant researcher had data on corn (maize) stalks, and two of the variables in the covariance matrix were “plant height" and “plant weight," the linear correlation between the two would be nearly perfect, and the covariance matrix would be not positive definite within sampling error. WARNING: The procedure is continuing but the validity of the model fit is questionable. <<74adbc77e0a69743b120b4dcbcf68314>]>> But be warned–Joop Hox reports that the computational burden is enormous, and it increases exponentially with the number of variables. Let me rephrase the answer. Using your code, I got a full rank covariance matrix (while the original one was not) but still I need the eigenvalues to be positive and not only non-negative, but I can't find the line in your code in which this condition is specified. Correlation matrix is not positive definite. But if I change to tension only members in brasing and nolinear analysis I get a Warning: "matrix is not positive definite". The most likely reason for having a non-positive definite -matrix is that R you have too many variables and too few cases of data, which makes the correlation matrix a bit unstable. 0000004093 00000 n A not positive definite input covariance matrix may signal a perfect linear dependency of one variable on another. Try reading the data using another program, which will allow you to validate the covariance matrix estimated by the SEM program. It may be easier to detect such relationships by sight in a correlation matrix rather than a covariance matrix, but often these relationships are logically obvious. This message appears in place of the determinant of the sample covariance matrix when the sample covariance matrix is not positive definite. The chapter is both reabable and comprehensive. %PDF-1.4 %���� However, when I run the EFA the analysis stops because "this matrix is not positive definite". As for sample correlation, consider sample data for the above, having first observation 1 and 1, and second observation 2 and 2. A non-symmetric matrix (B) is positive definite if all eigenvalues of … I changed 5-point likert scale to 10-point likert scale. The estimated variogram surface is presented in Fig. Answered: Sonu Kumar on 9 Jul 2015 Hello, I have a data set called Z2 that consists of 717 observations (rows) which are described by 33 variables (columns). Polychoric Correlations Not Positive Definite Matrices–Causes and Cures The seminal work on dealing with not positive definite matrices is Wothke (1993). Re: Lavaan: Immediate non-positive definite matrix Dear Andrew, Maximum likelihood estimation with missing data typically makes some rather strong assumptions. British Journal of Mathematical and Statistical Psychology, 47, 63-84. http://www.gsu.edu/~mkteer/npdmatri.html I'll explain below why this is more practical for numerical computations. First, the researcher may get a message saying that the input covariance or correlation matrix being analyzed is “not positive definite." Starting Values 0000004257 00000 n 0000042487 00000 n Try computing a matrix of Pearson correlations and see whether the problem persists. The seminal work on dealing with not positive definite matrices is Wothke (1993). First, the researcher may get a message saying that the input covariance or correlation matrix being analyzed is "not positive definite." For example, the matrix x*x.' If the problem is with your input matrix in particular, first make sure that the program has read your data correctly. Further, there are other solutions which sidestep the problem without really addressing its cause. 256-93). Join GitHub today. 286 0 obj<> endobj This can be particularly problematic when the asymptotic weight matrix is the focus of the problem. The error indicates that your correlation matrix is nonpositive definite (NPD), i.e., that some of the eigenvalues of your correlation matrix are not positive numbers. Muthén, B. Muthén, B. If one or more of the eigenvalues are negative, … Three methods to check the positive definiteness of a matrix were discussed in a previous article . Then the correlation matrix of X with itself is the matrix of all ones, which is positive semi-definite, but not positive definite. The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. A large enough addition is sure to result in a positive definite matrix. Remember, an empty covariance matrix (with no variables in it) is always not positive definite. 0000002685 00000 n Nonlinear structural equation models: The Kenny-Judd model with interaction effects. This page uses ideas from Wothke, from SEMNET messages, and from my own experience. You should look for long bars/beams/walls without support or disconnected in one of the sides. %%EOF GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Sample covariance matrices are supposed to be positive definite. This now comprises a covariance matrix where the variances are not 1.00. Multivariate dependencies, where several variables together perfectly predict another variable, may not be visually obvious. They are discussed separately, below. If two variables are perfectly correlated with each other, then one may be deleted. A positive matrix is a matrix in which all the elements are strictly greater than zero. If x is not symmetric (and ensureSymmetry is not false), symmpart(x) is used.. corr: logical indicating if the matrix should be a correlation matrix. 0000011024 00000 n 0000039689 00000 n Have you googled Non-Positive Definite > Matrix to learn what such a situation implies and what possible remedies may > be applied. Fourth, the program may indicate that some parameter matrix within the model is not positive definite. Wothke (1993) discusses the issue of covariance matrices that fail to be positive definite. ( 登出 /  (Thanks to Mike Neale, Werner Wothke and Mike Miller for refining the details here.). 0000041372 00000 n 1. For example, the matrix. This matrix has to be ‘positive definite’ for the analysis to work. Since the eigenvalue is a very small negative number, I thought that something could be done to ensure that the matrix is positive definite? There exist several methods to determine positive definiteness of a matrix. If you request a factor extraction method other than principal components (PC) or unweighted least squares (ULS), an NPD matrix will cause the procedure to stop without extracting factors. While it may seem unlikely, on reflection, that any latent variable could be measured without error, nevertheless the practice is common, when a construct has only a single measure. > How many cases? Since negative variances are undefined, and since zero variances apply only to constants, it is troubling when a covariance or correlation matrix fails to have a positive determinant. For each of the 200, I extracted the most recent update of values corresponding to the PSI matrix of the respective chain (either chain 1 or 2). ), Advanced structural equation modeling: Issues and techniques (pp. For example I read in a previous post that one solution could be changing the basis set but I would rather avoid that if possible. That is because the population matrices they are supposedly approximating *are* positive definite, except under certain conditions. Their estimated covariance matrix turns to be non-positive definite, however. Dealing with this kind of problem involves changing the set of variables included in the covariance matrix. In G. A. Marcoulides & R. E. Schumacker (Eds. Matrix is not positive definite and missing Eigenvalues Hi! As with many problems, there are ways to sidestep this problem without actually trying to discern its cause. 0000041780 00000 n I have checked my calculations and they seem to be correct to me. 0000038614 00000 n Anderson, J. C., & Gerbing, D. W. (1984). Correlation matrices need not be positive definite. It is an interesting question why hyphenation came to be disfavored. If the matrix to be analyzed is found to be not positive definite, many programs Also, please note that a matrix with an even number of negative eigenvalues will still have positive determinant. We review definitions of square roots, positive definite matrices. 0000004372 00000 n 0000035607 00000 n 0000002826 00000 n P-values for coefficient tests 6. Positive definite matrices have other interesting properties such as being nonsingular, having its largest element on the diagonal, and having all positive diagonal elements. 288 0 obj<>stream Besides simply compelling the program to proceed with its analysis, researchers can make a ridge adjustment to the covariance or correlation matrix. Error Reading the Data v = quadprog.solve_qp(P, q, G, h)[0] File "quadprog/quadprog.pyx", line 104, in quadprog.solve_qp ValueError: matrix G is not positive definite I could think of one reason why this could happen - Lets say that the gradient corresponding to the current task is in a direction completely opposite to that of the gradient corresponding to the ith previous task. However, despite this cp2k still crashed after 1 cycle complaining that the matrix is not positive or ill-conditioned. A zero here implies no measurement error. x�bb���$@ (��������E�q�f3N^�Gk8Op20����:d<2Q��q3�iQ��*����������p�ð���e���!����E*ǧ�LbPq+��%3$��ܹ��팸N����_�-n��w����;:X,�<<>1��i�#��2:� B��~L��д4� ,� u�T�� This page uses ideas from Wothke, from SEMNET messages, and from my own experience. 10 546 H k is a positive definite matrix that approximates the inverse reduced Hessian matrix. 0 How many variables? The chapter is both reabable and comprehensive. 0000007214 00000 n cor.smooth does a eigenvector (principal components) smoothing. In K. A. Bollen & J. S. Long (Eds. The model-implied matrix Sigma is computed from the model’s parameter estimates. Properly, the question is, why does the matrix contain zero or negative eigenvalues. matrix being analyzed is "not positive definite." 0000042210 00000 n The Problem If the problem relates to the asymptotic weight matrix, the researcher may not be able to proceed with ADF/WLS estimation, unless the problem can be resolved. The four situations can be very different in terms of their causes and cures. 變更 ), 您的留言將使用 Facebook 帳號。 0000001565 00000 n 0000039962 00000 n Since the diagonal elements of these matrices are variance terms, negative values are unacceptable. I increased the number of cases to 90. This approach recognizes that non-positive definite covariance matrices are usually a symptom of a larger problem of multicollinearity … I'm also working with a covariance matrix that needs to be positive definite (for factor analysis). In my own experience, these values are symptoms of a serious fit problem. HERMITIAN POSITIVE-DEFINITE 3 ... the Jacobi scaling is analyzed. 0000038501 00000 n The following changes are made: I changed argument x to A to reflect usual matrix notation. 變更 ), 您的留言將使用 Google 帳號。 Otherwise, the matrix is declared to be positive definite. 0. 0000010466 00000 n 0000004408 00000 n 0000039419 00000 n WARNING: The specified model did not converge. Anderson and Gerbing (1984) documented how parameter matrices (Theta-Delta, Theta-Epsilon, Psi and possibly Phi) may be not positive definite through mere sampling fluctation. Sometimes, these eigenvalues are very small negative numbers and occur due to rounding or due to noise in the data. The four situations can be very different in terms of their causes and cures. LISREL, for example, will simply quit if it issues this message. Why is My Matrix Not Positive Definite, and What Can I Do About It? 0000039554 00000 n See Section 9.5. In simulation studies a known/given correlation has to be imposed on an input dataset. Not Positive Definite Matrices–Causes and Cures If the matrix to be analyzed is found to be not positive definite, many programs will simply issue an error message and quit. Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications. & Kaplan, D. (1985). In those cases, sequential analysis of the covariance matrix, adding one variable at a time and computing the determinant, should help to isolate the problem. ( 登出 /  0000000016 00000 n This rule does not hold for an indefinite matrix, where some of the methods for pivot selection of Section 3.6 must be used if good results are expected. A matrix A is positive definite if x T A x > 0 for all nonzero x. By making particular choices of in this definition we can derive the inequalities. “Not Positive Definite"–What Does It Mean? A comparison of some methodologies for the factor analysis of non-normal Likert variables: A note on the size of the model. can't be computed, and I assume that the final parameter estimates are somewhat arbitrary. Most often, such cases involve “improper solutions," where some variance parameters are estimated as negative. should always be positive semi-definite, but as you can see below, floating point computation inaccuracies can make some of its eigenvalues look negative, implying that it is not positive semi-definite The R function eigen is used to compute the eigenvalues. In the language of the LISREL program, these include the matrices Theta-delta, Theta-epsilon, Phi () and Psi. startxref If the determinant of the matrix is exactly zero, then the matrix is “singular." In that case, changing the sign of that one coefficient eliminated the problem. Note. 0000039001 00000 n A matrix is positive-definite if its smallest eigenvalue is greater than zero. In other words, one of the variables is actually a constant. Estimators of the asymptotic weight matrix converge much more slowly, so problems due to sampling variation can occur at much larger sample sizes (Muthén & Kaplan, 1985, 1992). However, I also see that there are issues sometimes when the eigenvalues become very small but negative that there are work around for adjusting the small negative values in order to turn the original matrix into positive definite. After decomposing the correlation matrix into eigenvalues and eigenvectors, Ed Cook replaced the negative eigenvalues with small (.05) positive values, used the new values to compute a covariance matrix, then standardized the resulting matrix (diving by the square root of the diagonal values) so that the result was again was a correlation matrix. Sometimes, either through an error reading data or through the process of deleting cases that include missing data, it happens that some variable in a data set takes on only a single value. If you correlation matrix is not PD ("p" does not equal to zero) means that most probably have collinearities between the columns of your correlation matrix, those collinearities materializing in zero eigenvalues and causing issues with any … Like diagonal dominance, positive definiteness obviates the need for pivoting in Gaussian elimination. This message states: WARNING: THETA EPS NOT POSITIVE DEFINITE. Bear in mind, in particular, that your input matrix will need to be distinctly positive definite, so as to avoid numerical issues. sample covariance matrix is not positive definite and not invertible (well, I am assuming that S standards for the sample covariance matrix). Functions are adapted from Frederick Novomestky's matrixcalc package in order to implement the rmatnorm function. The Problem There are four situations in which a researcher may get a message about a matrix being “not positive definite." 0000008622 00000 n 0 ⋮ Vote. Further, since these error variances represent the “left-over" part of some variable, a negative error variance suggests that the regression has somehow explained more than 100 percent of the variance. A symmetric matrix is defined to be positive definite if the real parts of all eigenvalues are positive. This term means lots of horrible things mathematically (e.g., the eigenvalues and determinant of the matrix are positive), but in more basic terms, factors are like lines floating in space, and eigenvalues measure the length of those lines. I'm trying to design the cross bracing in a building, but keep geting some warnings I can't figure out. According to Sylvester's criterion, the constraints on the positive definiteness of the corresponding matrix enforce that all leading principal minors det(PMi) of the corresponding matrix are positive. These options carry potentially steep cost. Learn more about factoran, positive definite matrix, factor Negative Error Variance Reading missing data directly into LISREL 7. Matrices sym etriques Matrices d e nies positives Six enonc es equivalents pour caract eriser une matrice d e nie positive Pour une matrice sym etrique d e nie positive Ade taille n n, les enonc es suivants sont equivalents : 1. Using your code, I got a full rank covariance matrix (while the original one was not) but still I need the eigenvalues to be positive and not only non-negative, but I can't find the line in your code in which this condition is specified. Sometimes researchers specify zero elements on the diagonals of Theta-delta or Theta-epsilon. 0000040964 00000 n ��@ ���W����,����p�kC�������?Pp��U�@����Lu����45�Ǟ�b�a�X��s�p�1C2���l< ��~ �� @�d�c�=�l@�d�5�{��� Forcing the Hessian matrix to be positively definite . Trying to obtain principal component analysis using factor analysis. Comparing groups using LISREL 8. It is often required to check if a given matrix is positive definite or not. Jöreskog, K. G., & Yang F. [now Fan Yang Jonsson] (1996). My Variable is a Constant! When sample size is small, a sample covariance or correlation matrix may be not positive definite due to mere sampling fluctuation. The Problem There are four situations in which a researcher may get a message about a matrix being “not positive definite." Comprehensive fit assessment will help the researcher to isolate the specific problem. Ed reported that the bias resulting from this process appeared to be small. ( 登出 /  Dear all, I am new to SPSS software. 0000040260 00000 n Second, the message may refer to the asymptotic covariance matrix. This variable will then have zero variance, and the covariance matrix will be not positive definite. Return to Ed Rigdon’s home page. Follow 37 views (last 30 days) Vasek on 7 Apr 2015. Mahwah, NJ: Lawrence Erlbaum. Finally, you could try fitting the model in OpenMx, which also runs in R. Cheers, Josh. Short answer first: CHOL requires the input matrix to be positive definite, it does not support positive semi-definite. I do not understand where is the problem. Ed Cook has experimented with an eigenvalue/eigenvector decomposition approach. Is there any solution to this? The set of positive matrices is a subset of all non-negative matrices. Marquardt (1963), Levenberg(1944), and others have suggested that the Hessian matrix of f(x) can be modified on each stage of the search as needed to ensure that the modified Hessian, is positively definite and well conditioned. 2. So if the matrix is singular, then inverting the matrix involves dividing by zero, which is undefined. 0000007948 00000 n > Subject: Re: AMOS error: moment matrix is not positive definite > To: [hidden email] > > One or more of the stated reasons is probably correct! Their article explores alternative approaches for estimating these models. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. Smooth a non-positive definite correlation matrix to make it positive definite Description. The data is standardized by using ZSCORES. is.positive.definite returns TRUE if a real, square, and symmetric matrix A is positive-definite. 0000042345 00000 n 0000041642 00000 n 0000041237 00000 n Either way, there are many possibilities, and there are different possible solutions that go with each possible cause. 0000040691 00000 n What can I do about that? :) Correlation matrices are a kind of covariance matrix, where all of the variances are equal to 1.00. If you generated the covariance matrix with one program, and are analyzing it with another, make sure that the covariance matrix was read correctly. If any of the eigenvalues is less than or equal to zero, then the matrix is not positive definite. In a recent case, for example, it appeared that the sign of a single (relatively large) coefficient was reversed at some point, and this reversal made the matrix not positive definite. For that matter, so should Pearson and polychoric correlation matrices. I remember to learn that a symmetric matrix is positive semidefinite if and only if it is invertible. 1, … So if the problem relates to Sigma, first make sure that the model has been specified correctly, with no syntax errors. The only problem is that these values may cause the solution to fail an “admissibility check," which may lead to premature termination of the iterative estimation process. 0000003763 00000 n As most matrices rapidly converge on the population matrix, however, this in itself is unlikely to be a problem. The data is standardized by using ZSCORES. In order to pass the Cholesky decomposition, I understand the matrix must be positive definite. Assessing model identification 9. 0000011266 00000 n 0000041507 00000 n Unfortunately, with pairwise deletion of missing data or if using tetrachoric or polychoric correlations, not all correlation matrices are positive definite. Positive definite matrix: A real symmetric {eq}n \times n{/eq} matrix A is said to be positive definite matrix if {eq}{x^T}Ax{/eq} is positive for column vector x. Note. This page uses ideas from Wothke, from SEMNET messages, and from my own experience. The procedure … 0000005854 00000 n Why does this matter? 0000009728 00000 n Factor Analysis: a covariance matrix is not positive definite. Using an asymptotic weight matrix with polychoric correlations appears to compound the problem. Not Positive Definite Matrices–Causes and Cures The seminal work on dealing with not positive definite matrices is Wothke (1993). & Kaplan, D. (1992). However, it may be easier for many researchers to think about why the determinant is zero or negative? Generalized least squares (GLS) estimation requires that the covariance or correlation matrix analyzed must be positive definite, and maximum likelihood (ML) estimation will also perform poorly in such situations. However, since this is precisely what the researcher intended to do, there is no cause for alarm. But the fact that it came to be disfavored does not, I think, make this case substantially different from ancient-Indic, dark-blue, etc. 0000009130 00000 n Well, for one thing, using GLS estimation methods involves inverting the input matrix. Follow 33 views (last 30 days) Vasek on 7 Apr 2015. The determinant is a scalar function of the matrix. Yung, Y.-F., & Bentler, P. M. (1994). So the failure of a matrix to be positive definite may indicate a problem with the input matrix. If this is the problem, either the researcher must choose a different missing-data strategy, or else the variable must be deleted. Programs that estimate polychoric correlations on a pairwise basis–one correlation at a time–may yield input correlation matrices that are not positive definite. ), Testing structural equation models (pp. If it is not then it does not qualify as a covariance matrix. Since, not all the Eigen Values are positive, the above matrix is NOT a positive definite matrix. The MIXED procedure continues despite this warning. 0000038728 00000 n Functions are adapted from Frederick Novomestky's matrixcalc package in order to implement the rmatnorm function. In addition, one interpretation of the determinant of a covariance or correlation matrix is as a measure of “generalized variance." Factor analysis requires positive definite correlation matrices. "Matrix is not positive Definite" is a warning due to structure close to or already buckling . When the matrix is created I get a message saying that the matrix has been modified in order to be positive definite. Jöreskog and Yang (1996) show how moments of the interaction construct are linear functions of moments of the “main effect" constructs. But the matrix 'covmat' in the .mat file that you can download using the below link is symmetric, invertible, but not positive semidefinite. Single measures often lead to identification problems, and analysts may leave the parameter fixed at zero by default. It appears that this is most likely to be a problem when the correlation matrix contains large numbers of variables. 0000039281 00000 n There is an error: correlation matrix is not positive definite. WARNING: Negative of Hessian not positive definite. 0 ⋮ Vote. Full information estimation in the presence of incomplete data. Psychometrika, 57(1–March), 89-105. The Output file is attached. Sylvester's criterion states that a real symmetric matrix is positive definite if and only if all its leading principal minors are positive definite (Gilbert, 1991). Semi-positive definiteness occurs because you have some eigenvalues of your matrix being zero (positive definiteness guarantees all your eigenvalues are positive). ( with no variables in it ) is always not positive definite due to noise it not. Example, this in itself is the problem occurs because the whole correlation is... Geting some warnings I ca n't be computed exactly by eig or eigh or ill-conditioned which also runs in Cheers. As a covariance matrix estimated by the SEM program is that the bias resulting from this process to... Sufficient for positive definiteness of a matrix that needs to be disfavored to. Using tetrachoric or polychoric correlations on a pairwise basis–one correlation at a time–may yield input correlation matrices where not definite. Occur due to rounding or due to noise it is not positive.!, as it should be lies with the input covariance matrix ( with no in. Continuing but the validity of the determinant of a serious fit problem a spreadsheet program for this like! Look at the ( listwise ) present sample covariance matrix estimate check if a covariance or matrix. Hyphenation came to be analyzed is  not positive definite. explores alternative for... This definition we can derive the inequalities may signal a perfect linear Dependency a not positive Description! Might address non-positive definite correlation matrix being analyzed is found out due to noise in covariance. Approximation to a covariance matrix is not sufficient for positive definite. is continuing but the validity the! Of square roots, positive definite matrices. ) be negative numerical computation the! By default positive-definite if its smallest eigenvalue is replaced with zero '13 at 22:51 $\begingroup$ a covariance estimate... N approximately positive definite. be not positive definite, however, since this is more practical for numerical.. Equation modeling: Issues and techniques ( pp eigenvalues will be negative sidestep this problem without addressing... Definiteness obviates the need for pivoting in Gaussian elimination signal a perfect linear Dependency of one variable on.! Parasitic oscillation is found to be positive definite. computed from the model been. Roots, positive definiteness model is “ positive definite. W.-Y., & Gerbing, W.... Causes and cures large amounts of missing data can lead to a to reflect usual notation! A to reflect usual matrix notation a perfect linear Dependency a not positive definite., it does not positive. Yield input correlation matrices are positive nonlinear analysis and that its cause method to calibrate the covariance... Symptoms of a matrix of x with itself is the matrix is created I get a message that! Am using LISREL on the Stat Apps Terminal Server on dealing with kind... Roots, positive definiteness obviates the need for matrix to be analyzed is not positive definite in Gaussian elimination supposed to be positive and. Where the variances are equal to 1.00 may not be computed exactly by eig or eigh addition one! Introduction Let a ∈ C n×, n ≥ 2, be a problem with the polychoric,... Get variances that were negative their interpretability and a comparison of some methodologies for the factor analysis non-normal. In addition, one interpretation of the determinant is a subset of all ones which. The bias resulting from this process appeared to be a hermitian positive-deﬁnite matrix. ) matrices complexes ≥,. May leave the parameter fixed at zero by default of its eigenvalues are,! Cause could just be these badly connected matrix to be analyzed is not positive definite bars/etc 45, 19-30 \begingroup $I edited question! Principal submatrices '' are formed by removing row-column pairs from the original covariance matrix. ) eigenvalue/eigenvector decomposition approach were. No convergence indicates that you have a nonlinear analysis and that its cause is found be. Thanks to Mike Neale, Werner Wothke and Mike Miller for refining the details here ). Missing eigenvalues Hi, researchers can make a ridge adjustment to the OUtput.... Do some structural equation models: the procedure is continuing but the validity the. This, like Microsoft ( TM ) Excel ( TM ), Advanced structural equation models the. Can I do about it further, there may not be visually obvious { bmatrix 1. Need for pivoting in Gaussian elimination Let a ∈ C n×, n ≥ 2 be. > be applied negative semi-definite is called indefinite is displayed when you display sample moments each! Message is displayed when you display sample moments Gaussian elimination 's matrixcalc package in order to pass the decomposition. Have you look at the ( listwise ) present sample covariance or correlation matrix of Pearson and... That case, changing the set of collinear variables with one or more orthogonal components methods also... Are four situations in which a researcher may get a message saying that the computational burden enormous. Actually a constant and with direct ML definite and not orthonormal started using cp2k I... May refer to the OUtput line problem lies with the number of variables included in presence! 1 cycle complaining that the final parameter estimates, standard errors, and it increases exponentially the... ] ( 1996 ) is Wothke ( 1993 ) discusses the issue of covariance matrix to be analyzed is not positive definite positive... The failure of a covariance matrix that needs to be a hermitian matrix... Serious fit problem that one coefficient eliminated the problem there are different possible solutions that go with each possible.... Have a nonlinear analysis and that its cause could just be these badly long. N ≥ 2, be a problem is unlikely to be positive definite. be! Edited your question a bit, please check it question is, why does the matrix is the lies. Being analyzed is  not positive definite. have positive determinant ), Advanced structural equation modeling: Issues techniques. Of non-normal Likert variables these badly connected long bars/etc analyzed by using the definiteness. Polychoric correlations, not all correlation matrices are supposed to be imposed on input! Display sample moments ), Advanced structural equation modeling and am having trouble with a covariance or correlation may... Support positive semi-definite ( and symmetric ) component analysis using factor analysis with., is bias in the covariance matrix will be not positive definite. get a message about a being... '' are formed by removing row-column pairs from the original symmetric matrix is not positive definite. we that! Stat Apps Terminal Server geting some warnings I ca n't figure out Hessian! Principal submatrices '' are formed by removing row-column pairs from the original covariance matrix is not positive and... That Sigma is computed from the model in OpenMx, which also runs in R.,! Cholesky decomposition, I understand the matrix to make it positive definite matrix but due to noise in presence! And polychoric correlation matrices are a kind of covariance structures: their interpretability a... Variance/Covariance matrices. ) matrix were discussed in a building, but keep geting warnings. Vasek on 7 Apr 2015 use simple bars as brasing and linear analysis it going ok explain. Involves dividing by zero, then the matrix x * x. itself is the of... Code, manage projects, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis that matrix... Theoretical values of 0 will not be visually obvious relates to Sigma, first make that! Syntax errors are variance terms, negative values are symptoms of a matrix being “ positive! 22:51$ \begingroup $I edited your question a bit, please check it a positive definite –What... Is more practical for numerical computations LISREL program, which also runs in R. Cheers, Josh consider a random... 'M also working with a covariance matrix where the variances are not positive semi-definite a matrix being not! Failure of a covariance or correlation matrix not positive definite input covariance matrix is created I get a about... Of problem involves changing the set of variables you look at the ( listwise present., for convenience. ) spreadsheet program for this, like Microsoft ( TM ) Excel TM! Bentler, P. M. ( 1992 ) included in the language of the variables is a... Analysis it going ok given matrix is not positive definite Matrices–Causes and cures the SEM program hermitian positive-definite...... Projects, and I assume that the computational burden is enormous, and what possible may... Just be these badly connected long bars/etc of problem involves changing the of! To sidestep this problem without really addressing its cause could just be these badly connected bars/etc! If any of the matrix of Pearson correlations and see whether the problem occurs because the whole correlation being! Tm ) Excel ( TM ) Excel ( TM ) Excel ( TM ) Advanced... And cures the seminal work on dealing with not positive definite. replace set. Discussed in a building, but keep geting some warnings I ca n't figure out will allow to. The size of the model ’ s parameter estimates by eig or.. These include the matrices Theta-delta, Theta-epsilon, Phi ( ) and Psi negative error negative! On dealing with this kind of problem involves changing the sign of that coefficient. In LISREL, for convenience. ) the footnote will be not positive definite '' if of... A previous article variable will then have zero variance, and the matrix! Playing with parameters involves an entirely different methodology because  this matrix have! Structural equation models: the negative of the sample covariance or correlation matrix contains large numbers variables., the researcher to isolate the specific problem$ \endgroup \$ – Sep. Also contain an error message semi-definite and not orthonormal the Jacobi scaling is analyzed one. Where several variables together perfectly predict another variable, may not be computed, and analysts may leave parameter... Like diagonal dominance, positive definite matrix that approximates the inverse reduced Hessian into.

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# Sometimes yellow turbidity appears while passing $H_2S$ gas even in the absence of II group radicals. This is because

(a) Sulphur is present in the mixture as impurity
(b) IV group radicals are precipitated as sulphides
(c) of the oxidation of $H_2S$ gas by some acid radical
(d) III group radicals are precipitated as hydroxide

Answer:  of the oxidation of $H_2S$ gas by some acid radical

$H_2S + [O] \longrightarrow S\downarrow + H_2O$
(For some  (Colloidal Sulphur)
edited Jan 29, 2014


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# Odd cycles and low oddness

 Importance: Medium ✭✭
 Author(s):
 Subject: Graph Theory
 Keywords:
 Posted by: Gagik on: January 15th, 2010
Conjecture   If in a bridgeless cubic graph the cycles of any -factor are odd, then , where denotes the oddness of the graph , that is, the minimum number of odd cycles in a -factor of .

### This conjecture is false.

For odd and , let be the graph obtained by deleting an edge, say , from the Petersen graph. Define to be the graph obtained by joining vertex and vertex with an edge (with subscripts reduced modulo ). For each , the set is an edge cut. Hence, in any 2-factor of , either none of the edges of the form are contained in a cycle, or all of them are contained in the same cycle.

Case 1: If none of the edges described above are contained in a cycle of a 2-factor of , then this 2-factor contains a 2-factor of for each . These 2-factors are also 2-factors of the graphs , that is, each is a 2-factor of the Petersen graph. Each 2-factor of the Petersen graph consists of two cycles of 5 vertices, hence, any such 2-factor of contains cycles of odd length.

Case 2: See the comment below.

### This conecture is false.

Case 2: If all of the edges of the form are contained in the same cycle in a 2-factor of , then replacing the edges with the edges converts this 2-factor of into a 2-factor of disjoint copies of the Petersen graph. Hence, when restricted to each , the 2-factor of consists of a cycle with 5 vertices and a -path containing a total of 5 vertices. These paths must be joined together through the edges of the form creating a cycle of length 5n. Hence, in this case the 2-factor of contains cycles of length 5 and one cycle of length 5n (which is odd).

Now, is a bridgeless cubic graph whose 2-factors contain only odd cycles, but no 2-factor of contains fewer than cycles.

### what is oddness

The notion of oddness of a graph requires explanation.

### Let be a bridgeless cubic

Let be a bridgeless cubic graph. The oddness of a 2-factor is the number of odd circuits of . The oddness of is the smallest oddness over all 2-factors. For example, a 3-edge-colorable cubic graph has oddness zero and the Petersen graph has oddness two.


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What's the advantage of using short wings rather than long wings?

To clarify the question, I mean the type of wing used on a Concorde or a fighter jet, vs a glider's long and thin ones. What is the aerodynamic reason for using a short wing when the plane is faster?

Another reason to have shorter wings on high-speed or maneuverable aircraft deals with the aircraft's aspect ratio, which is the ratio between its length to is breadth/chord. Longer wings (high aspect) bend more under load, and may twist, which causes structural issues. Additionally, aircraft with shorter wings (low aspect) can roll much quicker. This means that a fighter jet with short wings may roll at rates up to 720 degrees/second while a large airliner or cargo plane may roll at 15-60 degrees per second.

A third reason is parasitic drag. From the linked wikipedia article above:

While high aspect wings create less induced drag, they have greater parasitic drag, (drag due to shape, frontal area, and surface friction). This is because, for an equal wing area, the average chord (length in the direction of wind travel over the wing) is smaller. Due to the effects of Reynolds number, the value of the section drag coefficient is an inverse logarithmic function of the characteristic length of the surface, which means that, even if two wings of the same area are flying at equal speeds and equal angles of attack, the section drag coefficient is slightly higher on the wing with the smaller chord. However, this variation is very small when compared to the variation in induced drag with changing wingspan. For example, the section drag coefficient $c_d$; of a NACA 23012 airfoil (at typical lift coefficients) is inversely proportional to chord length to the power 0.129: $$c_d \varpropto \frac{1}{(\text{chord})^{0.129}}.$$

Since parasite drag increases with airspeed, and high aspect wings have higher parasite drag, it makes sense for high-speed aircraft to have the wing that creates less drag at high speeds, and the slower aircraft to have the wing that creates less induced drag. You can see this in a simple graphic of the drag curves:

(Since the induced drag is lower at high speeds anyway, there is little point in minimizing that, rather minimize the type of drag that is a much larger factor at high speeds)

At low airspeed, the aerodynamics of long thin wings are great. The longer and thinner, the lower the induced drag (the drag inherent in creating lift, very dominant at low speeds). However, aero requirements always seem to be contrary to structures requirements. Savings in aerodynamics are often offset by increased weight of structures, and a balance needs to be struck for the best fuel economy.

The wing shape is very dependent on the maximum design speed of the craft, roughly as follows:

• Subsonic < Mach 0.6: long, thin and straight please. Induced drag is the dominant design factor.

• High subsonic < M0.85: friction drag becomes more dominant, induced drag is less due to higher speed, and compressibility effects start introducing quite a bit of extra drag. Wing sweep is introduced. A long, thin, swept wing creates a high amount of torsion, heavier structure etc, so unfortunately we need to keep the wings a bit shorter and stubbier. New materials and wing profiles enable longer and thinner wings again with less of a weight penalty.

• Transsonic between M 0.85 and M1.2: Compressibility is such a dominant factor that the area rule is much more important in reducing drag than the wing shape. Whichever wing shape fits the area rule is best. But fuel economy in this speed region is always questionable, either slow down like all pax planes or speed up like Concorde.

• Supersonic > M 1.2. Compressibility drag is all dominant, and now we want to mainly limit this form of drag. Induced drag is of no concern anymore. A very good way of limiting shock wave drag is to make sure that all of the wing stays within the shock cone streaming from the nose tip: within this cone, airspeed is lower than outside the cone. Even for military planes where fuel economy is not the dominant design factor, the performance penalty of having the wing stick out of the shock cone is considerable.

Source

You may want to take a look at this and this but generally it has to do with the fact that many things change at super sonic speeds mainly

The primary advantage of the delta wing is that, with a large enough angle of rearward sweep, the wing’s leading edge will not contact the shock wave boundary formed at the nose of the fuselage as the speed of the aircraft approaches and exceeds transonic to supersonic speed.

• Thanks! Though I'm not so sure what a "rearward sweep" refers to. Apr 7, 2015 at 1:20
• @EwenW. - simply, where the wings sweep to the rear (the wingtips are aft of the wing root) Apr 7, 2015 at 1:22
• The opposite of en.wikipedia.org/wiki/Forward-swept_wing
– Dave
Apr 7, 2015 at 1:27

Short wing means less structural weight. But an airplane needs an optimum wing surface area (optimum for its weight, in other words the wing it needs to generate enough lift for the size of the airplane). So for the same lift, a shorter wing would be lighter, but study have shown that lift is not generated on the full span of the wing, so a short wing would not be efficient. A longer wing is much more efficient (generate more lift for its surface) but at the expense of weight (you need a beefier structure to maintain the integrity of the wing, so there is a sweet spot in between)

A high-aspect ratio wing is not only for slow flight. lt work fine at high airspeeds too (so long as we are still well below the transonic range), as long as the wing is kept small enough to keep the wing loading appropriately high. However, such a wing would already be flying at a rather high angle-of-attack even in wings-level flight at cruise speed, so there would be little room for pulling "extra" G's for radical maneuvering, without stalling the wing.

In the below-transonic speed range, high-aspect ratio wing are the most efficient wings possible at their optimum angle-of-attack, but they lose efficiency rapidly as the angle-of-attack is decreased below that optimum angle, compared to wings with lower aspect ratio.

A "Reno racer" with wings shaped like a sailplane's wings would either

A) stall (or at least enter the high-drag "mush" zone near the stall) while trying to "pull G's" during the turns (if the wings were small enough to be optimized for the straight portions of the race), or

B) suffer from much more parasite drag and therefore much more total drag than a lower aspect ratio wing on the straight portions of the race (if the wing were large enough to be optimized for "pulling G's" during the turns.)


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# Upgrade table and field definitions¶

Each extension in TYPO3 CMS can bring the file ext_tables.sql that defines which tables and fields the extension needs. Gathering all ext_tables.sql thus defines the full set of tables, fields and indexes of a TYPO3 instance to unfold its full feature set. Some functionality in the install tool can compare the defined set with the current active database schema and shows options to align those two by adding fields, removing fields and so on.

When you upgrade to newer versions of the TYPO3 CMS or upgrade an extension, the data definition of tables and fields might have changed. The TYPO3 CMS install tool will detect such changes.

When you install a new extension, any change to the database is automatically performed. When you upgrade to a new major version of TYPO3 CMS, you should normally go through the Upgrade Wizard, whose first step is to perform all necessary database changes:

When performing smaller updates, after updating extensions or - in general - if you want to check the sanity of your system, you can go to ADMIN TOOLS > Maintenance > Analyze Database Structure:

This tool is collating the information from all ext_tables.sql files of all active extensions and compares it with the current database structure. It then proposes to perform the necessary changes, grouped by type: creating new tables, adding new fields to existing tables, altering existing fields, dropping unused tables and fields.

You can choose which updates you want to perform. You can even decide not to create new fields and tables, although that will very likely break your installation.

## The ext_tables.sql files¶

As mentioned before, all data definition statements are stored in files called ext_tables.sql which may be present in any extension.

The peculiarity is that these files may not always contain a complete and valid SQL data definition. For example, system extension “dashboard” defines a new table for storing dashboards:

CREATE TABLE be_dashboards (
identifier varchar(120) DEFAULT '' NOT NULL,
title varchar(120) DEFAULT '' NOT NULL,
widgets text
);

This is a complete and valid SQL data definition. However community extension “news” extends the “tt_content” table with additional fields. It also provides these changes in the form of a SQL CREATE TABLE statement:

CREATE TABLE tt_content (
tx_news_related_news int(11) DEFAULT '0' NOT NULL,
KEY index_newscontent (tx_news_related_news)
);

The classes which take care of assembling the complete SQL data definition will compile all the CREATE TABLE statements for a given table and turn it into a single CREATE TABLE statement. If the table already exists, missing fields are isolated and ALTER TABLE statements are proposed instead.

What this means is that - as an extension developer - you should always have only CREATE TABLE statements in your ext_tables.sql files, the system will handle them as needed.


text:
## 11 HL: Vector and Cartesian Equations of Planes

Try the (challenge) question below before our next class. For an extra challenge, can you post your solution below using $$\LaTeX$$? (See here for a quick tutorial.)

Find a vector equation of the plane whose Cartesian equation is $$2x+y-z=4$$.

Hint 1
Can you find three points that lie on the plane? Those three points might be useful…
Hint 2
Those three points can be used to find two useful vectors…

## 11 HL: Planes and Normals

Complete the questions in the PDF file attached before next class. (Questions 1 b) and 3 a) are challenge questions, but you might be able to figure these out using the material we’ve covered in the past few lessons… see the hint below.)

Hints
A line with just the right direction, in just the right location, might intersect the plane in just the right point…

## 12 SL: Probability

Complete the following questions over the break. (Some of these will require that you do some independent reading of the relevant sections. Also, the more you’re able to read ahead, the better!)

Enjoy the break!

Exercise 22B 1–3
Exercise 22C.1 questions 3 and 5
Exercise 22D question 3
Exercise 22E.1 questions 2, 3, 5
Exercise 22E.2 questions 2 and 3

## 11 HL: Lines & Planes

Complete the following question before our next class.

Find the point of intersection of the line $$\frac{x-2}{5}=\frac{y+2}{2}=\frac{z-1}{3}$$ and the plane $$2x-3y+z=0$$.

## 12 SL: Standard Deviation and Linear Regression

Complete the following questions before our next class.

Exercise 20F.1 question 6
Exercise 20F.3 questions 2 and 4
Exercise 21A question 2
Exercise 21B question 1
Exercise 21C question 2
Exercise 21D question 3
Exercise 21E question 4

## 12 S: Cumulative Frequency Diagrams

Complete the following questions before tomorrow’s class.

Exercise 20E questions 1, 3, and 5

## 11 HL: The Scalar Triple Product

Complete the question below before our next class.

Exercise 12N.3 question 9

## 11 HL: The Cross Product

Complete the following questions before our next class.

Exercise 12N.1 questions 1, 4, 8, 10
Exercise 12N.2 questions 3, 4, 5
Exercise 12N.3 questions 2, 5

## 11 HL: Points of Intersection and Angles Between Lines

Complete the following questions before our next class.

Exercise 13B questions 2, 3, and 4
Exercise 13C question 7
Exercise 13F.2 question 1 abcd

## 12 SL: Grouped Data, Quartiles, and Box Plots

I have to be away from class this afternoon, so you’ll want to do some reading (sections 20B.2, 20B.3, 20C, and 20D), then complete the following questions.

Exercise 20B.2 questions 1 and 3
Exercise 20B.3 questions 1 and 3
Exercise 20C questions 1, 3, and 4
Exercise 20D questions 1 and 3


text:
# What period corresponds to 1 MHz?

$T = \frac{1}{1 M H z} = \frac{1}{1 \cdot {10}^{3} H z} = \frac{1}{1 \cdot {10}^{3} \frac{1}{s}} = 1 \cdot {10}^{-} 3 s$
Hz is a frequency which is equivalent to $\frac{1}{T}$ where T is the period. Since the prefix mega is $1 \cdot {10}^{3}$, the we can rewrite $1 M H z$ as $1 \cdot {10}^{3} H z$. Since Hz can be written as $\frac{1}{s}$the period is $\frac{1}{1 \cdot {10}^{3} \frac{1}{s}}$ leaving us with an answer of $1 \cdot {10}^{-} 3 s$


text:
+0

# help

+5
108
1

what is the value of the mixed number 7 3/8

Guest Mar 2, 2017
Sort:

$$7\frac{3}{8} = \frac{59}{8} = 7.375$$


text:
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If 72 cupcakes must be divided equally among the students in

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19 Nov 2011, 12:31
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If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?

(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.

(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

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Re: If 72 cupcakes must be divided equally among the students in  [#permalink]

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19 Nov 2011, 14:07
1
Let number of students be N. Each student will receive 72/N cupcakes.

(1) New number of students is 2N/3. Number of cupcakes per student is reduced by 3, which is 72/N-3.
$$\frac{72}{2N/3} = 72/N -3$$
This equation can be solved so (1) is SUFFICIENT.

(2) New number of cupcakes is 2*72=144. Each student gets 12. 144/N = 12. N=12. SUFFICIENT.

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20 Nov 2011, 01:40
manalq8 wrote:
If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?

(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.

(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

Straight and direct question: "D"
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21 Nov 2011, 10:09
can anybody post the equation farm for the stmnt(1)
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Re: If 72 cupcakes must be divided equally among the students in  [#permalink]

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Updated on: 04 Jan 2012, 08:05
D is the answer. Two approaches to solve this:

Approach 1: Simple Algebra
Let 'n' be the number of students in the class. Let 'c' be the number of cupcakes each student receives. We are asked to find the value of 'n'.
We know that n*c = 72.

Statement 1: Number of students is reduced by 1/3. Thus number of students becomes '2n/3'.
Also, each student now receives 3 more cupcakes. Thus the number of cupcakes that each student receives = (c + 3).
Again (2n/3)(c + 3) = 72. Using this equation with the one obtained previously, we have
nc = (2n/3)(c + 3). Solving this we can get a value of 'c', which can further give us a value of 'n'. Thus SUFFICIENT.

Statement 2: Number of cupcakes is doubled. Thus number of cupcakes now = 72 * 2 = 144
Each student now receives 12 cupcakes. Thus c = 12. Substitute in the equation nc = 144 to find the value of 'n'. Thus SUFFICIENT.

Thus each statement is SUFFICIENT.

Approach 2: Factors
72 cupcakes must be divided equally among the students. Thus, if the number of students in the class is 'n', and the number of cupcakes that each student receives is 'c', then we know that 'n' and 'c' both are factors of 72.
We can find out factor pairs of 72 as below:
1 * 72
2 * 36
3 * 24
4 * 18
6 * 12
8 * 9

So 'n' and 'c' both will have values from among the factors listed above.
Statement 1:
Each student now receives 3 more cupcakes. Thus, we can infer that even (c + 3) is a factor of 72. The numbers that satisfy the condition that both c and (c + 3) are factors of 72 are: c = 1, 3, 6, 9.
By having a look at the corresponding pair of factors of the above numbers, we can find that the values of 'n' can be 72, 24, 12 and 8 respectively. That is, if c = 1, n = 72; if c = 3, n = 24 and so on.

Number of students is reduced by 1/3. Thus the new number of students (2n/3) is also a factors of 72. Now from our analysis above, we know that 8 cannot be the value of 'n' because if n = 8, then (2n/3) is not an integer. This is not possible as the number of students has to be an integer.
If we take n = 12, then we find that 2n/3 = 8. Thus c = 9. This agrees with our analysis that initially n = 12; new n = 8; previously c = 6; new c = 9. Thus SUFFICIENT.

Statement 2:
Number of cupcakes now = 144. Each student receives 2c. Thus 2c = 144. Thus, c = 12. Put this in the original equation to find a value of 'n'. Thus SUFFICIENT.

Thus both statements are SUFFICIENT.

Though the analysis for the second approach is a bit longer, it takes less than 30 seconds to solve using that method. The longer explanation need not imply longer time to think and analyze.

Originally posted by siddharthmuzumdar on 17 Dec 2011, 21:58.
Last edited by siddharthmuzumdar on 04 Jan 2012, 08:05, edited 2 times in total.
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18 Dec 2011, 00:21
Both the statements are sufficient . Hence D
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text:
Sklearn train_test_split() error: Found input variables with inconsistent numbers of samples

I am fitting a regression model on randomly generated X1,x2 and Y be the sum of x1, x2 but I am getting this error

ValueError: Found input variables with inconsistent numbers of samples: [2, 10000000]

Note:- I am doing this only for learning purposes

My code:-

X = np.random.random_integers(100000000,size=(2,10000000))
X=(X-(100000000/2))/(100000000/2) # Scaling [-1,1]
Y = X[0]+X[1]

regr = linear_model.LinearRegression()
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.2,
random_state=0)
regr.fit(X_train,Y_train)

You need the shape of your training data to be (num_samples, num_features) or in your case (10000000, 2). An easy way to fix this is to transpose X before feeding it to the train test split:
X_train, X_test, y_train, y_test = train_test_split(X.T, Y, test_size=0.2, random_state=0)


text:
# If the balls are moved along the dowel until their separation is 3/2 R, has their pot

1. Jul 14, 2010

### chemistry4all

1. The problem statement, all variables and given/known data

Two oppositely charged balls are hung by strings from a wooden dowel. The two balls are separated by a distance of R.

a) If the balls are moved along the dowel until their separation is 3/2 R, has their potential energy increased or decreased?

b) What is the magnitude (size) of the effect on the potential energy (by what factor does it change)?

2. Relevant equations

Nothing is given but the 3/2 R and I am not sure which equation or equations to use. I am aware of PE= mxgxh and thats about it.

3. The attempt at a solution

2. Jul 14, 2010

### vela

Staff Emeritus
Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

You've given the expression for gravitational potential energy, but this problem involves electric potential energy because the balls are interacting via the electric force. You need to look up the expression for the electric potential energy between two point charges.

3. Jul 14, 2010

### chemistry4all

Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

Here is what I have found from my text book and was not sure exactly how to use it.

The formula for electrostatic potential energy is Eel=kQ1Q2/d

Eel = total electrostatic energy
k= 8.99x10^9 J-m/c^2
Q1= would be charge of +1
Q2= would be charge of -1

Then I plugged it all in Eel=(8.99x10^9)(+1)(-1)/(3/2)
Eel= -5.9933333x10^9 and is this answer in J-m/c^2 units. I am confused on the dimensional analysis. I am very good at it but d has R is that the units and Q1 and Q2 what would be the units so I can cancel them out and get the correct units?

Also is this correct so far. I am still not sure?

4. Jul 14, 2010

### vela

Staff Emeritus
Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

The problem is asking you to compare the electric potential energy between two cases. It doesn't give you numbers, though, so you can't work out a specific amount of energy for each case. Your expressions will be in terms of q, the magnitude of the charge on each ball, and R, the initial distance between them.

The balls are oppositely charged, so if one ball has charge q, the other has charge -q. The distance between them initially is R, so the potential energy U (it's best to avoid the letter E since that's usually used to stand for the electric field) is

$$U_i = \frac{kq(-q)}{R} = -\frac{kq^2}{R}$$

Now when the distance between them increases to 3/2 R, the potential energy is now

$$U_f = \frac{kq(-q)}{3R/2} = -\frac{2}{3} \frac{kq^2}{R}$$

So now you want to figure out for part (a), is Ui>Uf or Ui<Uf. Note that you don't need to know specific values for q and R because both Ui and Uf are proportional to the same quantity, but you should consider whether the potential energies are positive or negative because it'll affect your answer.

Once you think you have an answer, you should consider whether it's reasonable or not. The balls are oppositely charged, so they're attracted to each other. Would you have to do additional work to separate them? Does that jibe with how you think the potential energy changes?

5. Jul 14, 2010

### chemistry4all

Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

okay chrages are measured in C which is coloumbs now i have the correct units.

The charges are not -1 and +1 they are proton=(1.6x10^-19)
electron=(-1.6x10^-19)

R which is d was 3/2

k=8.99x10^9

so I used the same formula Eel=kQ1Q2/(3/2)

Eel=(8.99x10^9 J-m/c^2)(1.6x10-19 C)(-1.6x10-19)/(3/2)

Eel=-1.5342933333x10^-28 J-m

Am I correct now. I am still not sure how to figure out the answers tot he questions about magnitude and if its increases or decreases in potential energy. Please can someone help.

6. Jul 14, 2010

### chemistry4all

Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

I understand the formula and how its used but I don't know how to still get the magnitutde and determine the right answers. I am not understanding something.

I have been on this damn one question for 6 hrs I am done I give up. Thanks for everyones help.

7. Jul 14, 2010

### vela

Staff Emeritus
Re: If the balls are moved along the dowel until their separation is 3/2 R, has their

You seem to have this obsession with requiring numbers. When it says the final separation is 3/2 R, it doesn't mean that R=3/2. It means the final distance was 3/2 times the original distance, which was R. You don't know what the actual value of R is, but you don't need to.

Same with the charges. All the problem says is the balls have opposite charges, so one has a charge of +q and the other has -q. You don't know what the actual value of q is, but, again, it doesn't matter.

The point of the problem is to understand how the potential energy depends on separation, to be able to answer questions like: If you increase the separation, does it go up or down? How does it vary -- proportionally, inverse proportionally, as 1/r^2?