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# Mechanical Principles - Dynamics.

1. Nov 5, 2013

### Renni202

I hope I am posting in the right place. I am a 1st year University student. Although I am undertaking a BSc in Computer and Electronic System Engineering I have a Mechanical Principles module which I am finding a little bit of a struggle.

Mechanical Principles - Dynamics:

a) A diaphragm type gas compressor of mass 235 kg is supported by 4 springs which are arranged in parallel. The springs each have stiffnesses of 40 kN/m, 40 kN/m, 45 kN/m and 45 kN/m respectively. Determine:

i) the total stiffness of the spring system in N/m;

ii) the natural frequency of free vibration of the machine in Hz;

iii) the time elapsed after 5 cycles of free vibration, and show this on an amplitude-time graph.

i) KT = 2K1+2K2
KT=170x103 N/m
i.e KT=170 kN/m
(It askes for the answer in N/m so should I still take it to kN/m or stop at N/m?)

ii) fn=1/2πK/m=ωn/2π
=1/2π√170x103/235
=4.2 Hz

iii) T=1/fn=1/4.2=0.24s for 1 cycle 1.2 for 5 cycles

I am looking for confirmation that I am on the right track with my answers and any guidance offered on making an amplitude-time graph. It really is much appreciated.

2. Nov 5, 2013

### Simon Bridge

Welcome to PF;
It won't make any difference so long as you have the answer they wanted.
The question expected you to add up the kN values and they were making sure you knew what that meant.

It looks like you applied an equation without understanding it.
That is not best practice. However, this will get you the marks.
You should include a note in words to make your math clear - like commenting code.

If you understood the relations you probably wouldn't need the confirmation, or you'd be able to do your own.

What sort of motion is this going to be?
From your knowledge of this sort of motion, how does the amplitude of the oscillations vary with time?

Note: do they want amplitude vs time, or the displacement of the machine (from equilibrium) vs time?

3. Nov 5, 2013

### Renni202

Thank you Simon,

So thumbs up for part (i) YAY!

ii) ωn/2π = 26.8/2π=4.2 Hz I think I did miss out a step because my first answer was 42. I checked with a rad/s to Hz converter which gave me 4.2653524797 (I should actually round up to 4.3 I guess) To match the answer I used 26.8/6.283185 and assumed there was something going on with my calculator.

iii) The graph is going to be an up and down wave like form (I think). Each cycle should have a wave. Although I was unsure how high or low it should go. It confused me slightly because it was written... Amplitude - time graph not amplitude vs time or displacement. Am I being silly and not reading it correctly?

I have just realised the time here in the UK so I might need to pick this up tomorrow. Thank you again. Your reply has already given me a boost in confidence.

4. Nov 5, 2013

### Simon Bridge

I don't look at arithmetic so if you bunged in the wrong numbers...

$$f=\frac{\omega}{2\pi} = \frac{1}{2\pi} \sqrt{\frac{k}{m}} = \frac{1}{T}$$ 42 is, of course, the Ultimate Answer ... the 4.2 coming out suggests you misplaced a factor of 100.

Also see:
http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html

The natural frequency is what it would oscillate at without any damping or driving.
i.e. Simple Harmonic Motion.

In Simple Harmonic Motion, the amplitude is a constant over time.
If the vertical displacement from equilibrium is at time t is y(t), then

$y(t)=A\cos(\omega t+\delta)$

the amplitude is $A$.

See how an A vs t graph would just be flat? So the distinction is important.

There are two ways this can be not what they mean:
1. they actually mean you to sketch a y vs t graph (likely).
2. the context is not simple harmonic motion -
.......i.e. there may be damping so the amplitude decays exponentially with time.

You should be able to sketch a sine wave.
In one period, you get one peak and one trough.

Last edited: Nov 5, 2013
5. Nov 5, 2013

### Renni202

I had the image of a sine wave in my head but was not sure exactly what I was looking for. Your a star thank you. I have a couple of other questions I plan on working through tomorrow. Will it be ok to add them to this post? (Same subject. Same coursework sheet.)

6. Nov 6, 2013

### Simon Bridge

No worries.
It is best to make a separate thread for each new question.


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### Home > INT2 > Chapter 8 > Lesson 8.2.2 > Problem8-40

8-40.
1. For the triangle at right, write each of the following trigonometric ratios. The first one is done for you. Homework Help ✎

1. tan C =

2. sin C

3. tan A

4. cos C

5. cos A

6. sin A

Refer to the Math Notes box in Lesson 4.2.2 if you need help remembering any trigonometric ratios.

$\cos{C}=\frac{BC}{AC}$

$\sin{A}=\frac{BC}{AC}$

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# Gibbs Sampling for Gaussian Mixtures

Does the Gibbs sampler converge to a global maximum in the presence of multiple modes? For example in case of a Gaussian mixture distribution?

## 1 Answer

First of all, I think you are conflating Gibbs-sampling-based simulated annealing (an optimization procedure that uses Gibbs sampling to draw the updates of the algorithm) and pure Gibbs sampling (a means to sample from a distribution).

Your question applies to simulated annealing that uses Gibbs sampling, but it does not make sense for general Gibbs sampling.

As Geman and Geman proved in their paper that introduced the widespread use of Gibbs sampling, a simulated annealing procedure based on a Metropolis/Gibbs type proposal distribution will converge to a stationary distribution that samples uniformly from all of the local modes, as long as the cooling schedule is slow enough.

So if you have an objective function that is the mixture of 3 Gaussians, say, with 3 distinct modes, then a simulated annealing process with a slow enough cooling schedule will converge to the uniform distribution on those three modes.

The cooling has to be inverse-logarithmic in the relative score of the objective function, which turns out to be way way too slow for practice. In practice, you give up the guarantee that you will converge to the distribution that samples all the modes (and hence would let you see the global minimum by simple inspection), and in return you get faster cooling schedules and approximate solutions with non-zero probability of getting stuck in a local mode that is not globally optimal.

• the algorithm might theoretically converge to a stationary distribution that samples uniformly from all of the local modes, but in practice this will be extremely difficult -- the algorithm will struggle enormously when trying to jump between the modes. – Alekk Mar 22 '12 at 22:44
• I'm not sure what you mean. If the cooling time is slow enough, then this is what simulated annealing does. You can definitely show that the cooling times needed will make solutions exponentially slow -- I even mentioned this in my answer above. In practice you trade-off the guarantee of sampling all the modes for faster time to convergence, e.g. by using geometric cooling or cooling with reheating as a function of cost. You won't sample all modes, but you'll get to some mode (possibly only local) much faster. – ely Mar 22 '12 at 22:47
• Can you help me see this question stats.stackexchange.com/questions/498646/…? Thank you. – Bob Nov 30 '20 at 6:26


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# Cheap cellular trackers update -- and where are the 3Gs?

### Help Support The Rocketry Forum:

#### billdz

##### Well-Known Member
In August 2017 I read a thread in this forum entitled "Keychain GPS Trackers" (https://www.rocketryforum.com/threads/keychain-gps-trackers.141846/) that started me on a seemingly never-ended quest for a cheap (under $35), reliable cellular GPS tracker that would work with a free FreedomPop sim card. I've had some success but am still looking for a better solution. Thought I'd recap my experiences in case anyone else would like to try something similar. Important note: these trackers only work if you have cellular service available at your launch site. I've been to every site in Florida and all have good service. In post #9 of the August 2017 thread, Dugway recommended the MD-601 tracker, which has proven to be my favorite so far, I've bought 3 of them. It is cheap ($26), small, light (22g), and has never failed me, even when more expensive trackers have. You put an app on your cell phone that allows you to track your rocket. Dugway had an issue because his "phone kept shutting down in the 100 degree heat at HellFire when the GPS was active", but I've never had any such issue, even in the Florida summer. The only problem with the MD-601 is that it only works on 2G cellular networks, which in the USA means T-Mobile and its MVNOs. It works fine with the Speed Talk $5 a month sim card, but it does not work with the free FreedomPop sim. Even cheaper (under$20), smaller, and lighter than the MD-601 is the K8 GPS tracker but caution is required when buying, because some versions of this device only track via LBS rather than GPS. It works the same as the MD-601. It also works only on 2G networks and does not work with FreedomPop. See https://www.gearbest.com/car-gps-tracker/pp_643009.html.

Another popular tracker is the TK102, which is larger than the MD-601, although cheaper ($11). See https://www.aliexpress.com/item/Rea...and-with-One-Battery-Vehicle/32718561171.html. I don't like it as much because it has no app, it just sends the GPS location and a Google Maps url via SMS text message. Again, it is 2G only. One eBay seller is selling something called the TK102D which he claims works with 3G and 4G sims, but it does not, at least not with AT&T, I bought one but returned it. If you use this or any other type of SMS-based tracker, just before liftoff you should command it to send a text every few seconds, so you'll have an approximate position even if the tracker gets disabled due to a hard or water landing. In August 2017, AT&T had recently discontinued its 2G service, and I wrongly assumed that soon there would be several trackers that would work with 3G and 4G sims like the FreedomPop. I'm still waiting, where are the 3G trackers??? I run Google searches every few weeks and still have not found any. There are many trackers advertised as "3G" but read the fine print and look at the frequencies, they are 2G only. This has to change at some point, but when? I've seen some rocketeers use the proprietary GPS trackers such as Paby, Tracktive, MindMe, and several others that come with a built-in sim card and require a monthly fee. Some have had success with these, and they probably work fine, but the ones I have seen are substantially more expensive and the monthly fees are a lot more than the$5 Speed Talk.

I finally found an under $35 solution that works with the free FreedomPop sim, at least for larger rockets. All you need is a used Android phone with Jason Cook's free Insane Rocketry app. This is even better than the above trackers because you get flight data in addition to GPS tracking. And if the phone has a barometer, the app even works as an altimeter and lets you know how high the rocket went. And if you can place the phone into the rocket in a position to take in-flight video, you can use the app to turn the video recorder on and off. Of course, the disadvantage is that phones are larger and heavier than a tracker (135g vs. 20g), but this is not an issue if the rocket has a diameter of 3" or more (a phone in a hollowed out pool noodle is a perfect fit into the payload tube of a 3" rocket). If you don't have an old Android phone lying around the house, for$30 or so you can pick up a Google Nexus 4 or a Motorola Droid Mini on eBay, these and others have a barometer and work well with Jason's app. Also, if for any reason you do not want to use Jason's app, you can locate the rocket by going to https://android.com/find.

#### billdz

##### Well-Known Member
A LOT of launch sites have poor cellular reception. Point-to-Point is a better solution... it works everywhere without any additional infrastructure.
A lot of launch sites have no cellular reception, particularly in the west. Here in Florida, I've been to every major club launch site and have had good cell service at each.

At a launch site with decent cell service, it seems debatable whether point to point is a better solution. At least for me, cheap $20 cellular trackers have found rockets even when expensive point to point trackers (e.g.,$300 TeleMetrum) have failed (I usually have one of each in my more valuable rockets). The signal from a point to point device can be lost if the rocket drifts too far away or goes behind a hill or other obstruction, but as long as there is cell service a cellular tracker will get you to the rocket.

In any event Chris, I'll be a customer if you ever develop a 4G Eggfinder.

Both point to point and cellular trackers will stop working if the rocket lands hard or in water, which is why I prefer real time trackers to the TK trackers used by Sam and other devices that require you to send an SMS to the tracker to get the position. A real time tracker will at least give you the rocket's position shortly prior to impact.


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# What is the least JPG-compressible pattern? (camera shooting piece of cloth, scale/angle/lighting may vary)

I am trying to design a cloth that, from the point of view of a camera, is very difficult to compress with JPG, resulting in big-size files (or leading to low image quality if file size is fixed).

It must work even if the cloth is far away from the camera, or rotated (let's say the scale can vary from 1x to 10x).

Noise is quite good (hard to compress), but it becomes grey when looking from far, becoming easy to compress. A good pattern would be kind of fractal, looking similar at all scales.
Foliage is better (leaves, tiny branches, small branches, big branches), but it uses too few colors.

Here is a first try:

I am sure there are more optimum patterns.
Maybe hexagon or triangle tessellations would perform better.

JPG uses the Y′ Cb Cr color space, I think Cb Cr can be generated in a similar way, but I guess it's better to not use uniformly the full scope of Y' (brightness) since camera will saturate the bright or dark areas (lighting is never perfect).

QUESTION: What is the optimum cloth pattern for this problem?

• I'll have to keep an eye on this question.... if an interesting answer is achieved, I can predict a fabric order at www.spoonflower.com (or a similar service) and a really hard to look at shirt to add to my collection ;-) – RBerteig Apr 11 '12 at 20:51
• An interesting pattern competition project could be: 1) Take a high-definition image of such a pattern 2) Rotate it, take a random portion of it (at random scale), blur a bit, add a bit of noise and small random color deviation 3) Compress it with JPG 4) See file size, calculate metrics about the quality loss, and calculate the "score" using these metrics. 5) Repeat many times to converge to this pattern's average score 6) Repeat with other patterns and compare scores – Nicolas Raoul Apr 13 '12 at 6:32
• Since lossy algorithms can always compress more by throwing away more data, it seems like you'd have more luck with using patterns that depend on the high-frequency detail. For example, fine lines. In other words, it may compress well, but it degrades in quality very quickly. Depends on what you want to accomplish I suppose. Think fingerprints--it's a classic case where wavelets were required for good compression over JPEG because of the need to preserve the detail. – datageist Apr 26 '12 at 21:01
• @datageist: A picture (raw camera output) of a cloth with lines might be difficult to compress, but step backward, take another picture: it will contain only grey pixels, very easy to compress with almost no loss. The pattern I am looking for must result in pictures (raw camera output) that are difficult to compress at a wide range of scales. – Nicolas Raoul Apr 27 '12 at 4:51
• @NicolasRaoul Right, I get that, I'm just saying anything is compressible if you throw away enough information. Do you just want a pattern that has the distinction of being "hard to compress" (i.e. for fun), or are you trying to actively discourage people from attempting to compress images containing the pattern? – datageist Apr 27 '12 at 5:30

Noise is quite good (hard to compress), but it becomes grey when looking from far, becoming easy to compress. A good pattern would be kind of fractal, looking similar at all scales.

Well, there is fractal noise. I think Brownian noise is fractal, looking the same as you zoom into it. Wikipedia talks about adding Perlin noise to itself at different scales to produce fractal noise, which is maybe identical, I'm not sure:

I don't think this would be hard to compress, though. Noise is hard for lossless compression, but JPEG is lossy, so it's just going to throw away the detail instead of struggling with it. I'm not sure if it's possible to make something "hard for JPEG to compress" since it will just ignore anything that's too hard to compress at that quality level.

Something with hard edges at any scale would probably be better, like the infinite checkerboard plane:

Also something with lots of colors. Maybe look at actual fractals instead of fractal noise. Maybe a Mondrian fractal? :)

• Thanks a lot! The fractal noise is definitely the kind of stuff I was looking for, but in my tests it is compressed well, I guess it could use more abrupt transition, instead of a heatmap-like smoothness. The checkboard's problem is that performance will really depend on which part of the cloth is taken in picture. Mondrian fractal is great, and the best-performing in my tests so far. Maybe it could use more colors and slightly different parameters. – Nicolas Raoul Apr 11 '12 at 15:05
• @NicolasRaoul: Hmm.. Maybe Sierpinski carpet with colors? That's a common quilt pattern already. – endolith Apr 11 '12 at 15:45
• A tessellation of Sierpinski triangles or squares might great indeed! – Nicolas Raoul Apr 12 '12 at 7:57

If we were talking about computer-generated images, noise would be the right approach. But here, there is the camera capture step.

The fractal bit is very important because of the scale invariance issue. It doesn't have to be truly fractal, though, if you consider there's a limited distance range at which the person is going to be photographed. I mean, if the person wearing the cloth is in the background of a picture, it won't have much impact anyway...

I think the best way to trick the JPEG encoder would be to have blocks with very high high-frequency coefficients that will survive quantization = a lot of details and sharp edges ; so the whole coefficient sequence has to be explicitly written (instead of an EOB at the 15th coefficient or so). Checkerboard pattern are a good way of achieving that. The only downside I see is that the low-resolution of the lens + the camera antialiasing filters have a good chance of blurring that! Everything should happen within 8x8 blocks (or 16x16 blocks chroma-wise) because JPEG doesn't do much at the macro scale. You have to make your 8x8 blocks as messy as possible, no matter how blurry the lens is going to make them.

Here is a suggestion:

You might wonder what the less contrasted blocks are doing here, but they are helping keeping contrasted zone when the thing is zoomed out. The challenge here is to have something with a contrasted pattern no matter the viewing scale.

I have not formally evaluated this. The best way would be to have a script that takes the image, applies a dozen of crop/resize/blurs with various parameters, and spits the total size of the JPEGs.

• Thanks a lot! Looks quite similar to my the concept of the picture in the question, actually, but much nicer. Any specific reason why the "fractality" is by factor 4? Is it better than factor 2? – Nicolas Raoul Apr 11 '12 at 15:09
• no reason, I've just tried to make it look prettier with more color shades, so I started with a 4x4 square. – pichenettes Apr 11 '12 at 15:22
• Any reason to choose squares instead of triangles? I am trying right now, triangles make lots of sharp edges, which I think is a good think. A low "fractality" could be reached with a hybrid triangle→rhombus→hexagon→triangle approach. I think a low factor is a good thing as it increases the probability for the camera to detect sharp shapes up to its resolution limit. – Nicolas Raoul Apr 11 '12 at 16:12
• Squares was the easiest thing to code. I am not sure if other shapes have a better "edge density" than squares. – pichenettes Apr 11 '12 at 17:44

There is a difference between JPEG exploitable and Transform Compressible.

Take the white grainy noise of TV set for example.

A general white noise is spread maximum in the frequency and hence there is no better example than white noise that any transform domain coding technique cannot compress. If you take such noise and take DCT (or DFT if required) we shall find that the frequency domain is also wide spread and all co-efficients will have importance.

However, still no one stops you from being aggressive from quantization. This way, you can still discard heavy amount from the high frequency regions. The result will have heavy Mean-Square-error. However, perceptually it would still be noise. It might be heavily blurred though.

On the other hand, now take images where there are sharp edges.

Sharp edges will also have spread in the higher frequency (but may be it might just be little less than the former case). However, in trying to compress it and dropping of high frequency, now there will be sever impediments visually. It will introduce blurring of edges, ringing effect etc. While the bandwidth spread for such images is not the highest possible, For JPEG or any such equivalent compression, keeping such images perceptually equal quality will be tough.

For any lossy compression, tough and simple depends on how much and what type of distortion is tolerated.

• Let's say my fabric is a 10^8x10^8 table of random black/white pixels. The camera takes a 10x10pixels picture of the fabric. Statistically, won't this 10x10 image have all pixels be a very similar grey, thus being easy to compress with less distortion (of any kind) than a less uniform image? – Nicolas Raoul Jun 20 '13 at 7:26

The composition below shows a fractal kind structure of the pattern. The every next picture is the result of averaging over each 2x2 pixels block of the previous one. The total character of the pattern remains the same but the image contrast is gradually decreasing. As it was said right earlier, the picture becomes grey when we zoom out.

But using the fractal property, we could overlay together several patterns of different resolution to maintain the image contrast to be stable within the range desired. Below is the example of 4-layer pattern (512x512 GIF). This result is more close to Brownian noise and also hardly JPEG compressible.

My guess is that the worst compressible pattern would be white noise (with uniform distribution). It needs to look noisy on different resolutions, so you may create the noisy images in scale space and than put them together:

$$I=\sum_{i}^{n}N_{i}*G_{i}$$

Here $I$ is the final cloth image, $N_{i}$ is the image filled with white noise (different for every $i$) and $G_{i}$ is gaussian kernel of size $i\sigma$. The $*$ denotes convolution.

Maybe a better way to construct such image would be to work directly in frequency domain, thus:

1. Create an image filled with white noise.
2. Perform 8x8 block IDCT (Inverse Discrete Cosine Transform) on the image.

The result would be worst compressible pattern for JPEG, as it has highest entropy in the DCT domain. But I am not sure how this will behave under varying resolutions.

IIRC, the JPEG decompression algorithm is specified, however the exact compression algorithm is not. Different algorithms can produce a legal JPEG file. So you will need to test this on your chosen image compressor(s).

Anything can be compressed by the same amount by a lossy compressor, such as JPEG. It's just that, at any fixed compression level, the quality of the compression might vary (the noise or error in the decompressed result will increase) depending on the image . So you want something that adds a maximum amount of noise to the decompressed result. For this, you want the maximum error for removing high frequency macroblock coefficients and for quantizing any coefficients.

Which probably mean varying and high frequency pickets, as well as varying grey and color scales that happen to be between possible quantization levels of the given compressor at some given setting.

Since you want this to work at any distance in any lighting, you will need to vary the frequency of the pickets (perhaps fractal, or perhaps just ramped with random frequency modulation) and the color and gray levels (non-coherently, e.g. vary the colors and the levels independantly). The hues variance will less depend on the distance, so those just need to be picked to be worse case for your selected quantizer(s). The average size of the color patterns can be twice the size of the luminance patterns to match the 4:1:1(area) YUV macroblock composition.

I would start with a bunch of highly colored Moire patterns at wildly varying scales overlayed and/or patched together fractally.

Let me share the pattern that has a very flat spectrum (like the white noise). So this pattern is very hard to compress with JPG. The sample image below is enlarged 4 times.

The pattern itself is regular, but non-periodic, and could be easily generated by the deterministic algorithm. It also has a fractal property.

Viewed from far away:

Random noise indeed compresses very poorly. You can produce it in color by generating independent R, G, B values.

Looking from a distance will indeed wipe away the noise (by lowpass filtering), and you can avoid that by generating noise images at different resolutions, i.e. using bigger and bigger pixels, and superposing them.

When adding the images, you face the problem of the range of values, which grows as the number of images, let N. If you just average them, the noise amplitude will decrease as 1/N.

If you choose uncorrelated uniform noise, the superposition will result in a quasi-Gaussian distribution with √N standard deviation, so instead of dividing by N, you can divide by √N (with suitable re-centering) to limit the amplitude reduction.

Lastly, I guess that it is better to let the values wraparound rather than saturating them, as saturated values will form large uniform areas.

Here is another approach gaining RGB Brownian noise (4096x4096 GIF).

Amazing question! In concept, the white noise is a signal that do not change when it is time scaled. In same way a fractal don’t change when it is size scaled. A lossy compression process only takes the most important of the spectrum (time or size) not all, so fractal and noise smell like cookies. Therefore, you should play with the colors and patterns of your fabric They must be fractals and the fractal behavior must be white randomly generated. You should get a fabric that in photo looks black (in CMY color space) but in real world, it has a colorful pattern.

Good luck! , and if you get the anwser please post it!!!.

• "You should get a fabric that in photo looks black" <- In that case, would not it be easily compressible? – Nicolas Raoul Nov 12 '18 at 0:39


text:
## CryptoDB

### Paper: Hierarchical Group Signatures

Authors: Marten Trolin Douglas Wikstrom URL: http://eprint.iacr.org/2004/311 Search ePrint Search Google We introduce the notion of \emph{hierarchical group signatures}. This is a proper generalization of group signatures, which allows multiple group managers organized in a tree with the signers as leaves. For a signer that is a leaf of the subtree of a group manager, the group manager learns which of its children that (perhaps indirectly) manages the signer. We provide definitions for the new notion and construct a scheme that is provably secure given the existence of a family of trapdoor permutations. We also present a construction which is relatively practical, and prove its security in the random oracle model under the strong RSA assumption and the DDH assumption.
##### BibTeX
@misc{eprint-2004-12277,
title={Hierarchical Group Signatures},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / group signatures},
url={http://eprint.iacr.org/2004/311},
note={Presented at ICALP 2005. This is the full version. marten@nada.kth.se 12881 received 16 Nov 2004, last revised 8 Apr 2005},
author={Marten Trolin and Douglas Wikstrom},
year=2004
}


text:
ERROR RNA SEQ QC analysis step
1
0
Entering edit mode
8.2 years ago
David_emir ▴ 460

Hello all,

I was trying to do QC with fastx_quality_stats to calculate out nucleotide distribution. The code is as follows

[Ateeq@BIO-DT-415 NEW_NGS]$/usr/local/bin/fastx_quality_stats -i SRR1604991.fastq -o SRR1604991.txt-Q33  But I got the following Error: fastx_quality_stats: Invalid quality score value (char '#' ord 35 quality value -29) on line 4  I used -Q33 as well but failed to get any resolution!!! Guys, please help me out, I am so new to this. Thanks a ton ... A few lines of my FASTQ file for reference: [Ateeq@BIO-DT-415 NEW_NGS]$ head SRR1604991.fastq
NTCCTACTCTTCTTAGCGCCTACCCTCATACCTATCTCCCTCCTCCCATCTCCTAGGGGACTGGCGCCAAATGGTCTCTCCCTGCCAATTTTGGTATNTTCCGGGACCAAAATAAAGAGCAAGCAGGCCCCCTTCACTGAGGTGCTGGGTAGGGCTCAGTGCCACATTACTGTGCTTTGAGAAAGAGGAAGGGGATTNGT
#1=DFFFFHHHHHJJJJJJJJJJJJJJJIJJJJJJJIIJJIJJHIJJJIJGIJIJJJJJIIHHHHFFDDDDDDDCCDDDDDDDDDDDDDDDDDD<C####CCCFFFFFHHHHHJJJJIJJJJJJJJJJJJJJHIJIJIJIII=FGGIIJ=FHIIJEHHH;@DDDDEECEEEE>CDDDDDDDDDDDCCDDDDDDDBDD###
NTGAGTAGCACTCTCTGAGAGCTCCAATTTCATCCGTCTGCCATCGGCGCCATCCTGCAATCTAAGCCACAATGGTGCGCATGAATGTCCTGGCAGATGCCTCTTTTCGGCATTGTTGATACTCTTGAGAGCATCTGCCAGGACATTCATGCGCACCATTGTGGCTTAGATTGCAGGATGGCGCCGATGGCAGACGGATG
#4=DDDDFHHHHHHJJJJJJJJJJJJJJJJJJJJJJHHHIIJJJJJJIGIJIIIJHHHHHGFDFFFFEEE;65;>;@CDDDDDDDEDDEEDDDDDDDDDDCCCFFFFFHHHHHJJJJJJJJJIJJJJJJJJJJJJHIIJJJJJJJJJJJIIHIJGIJIJJJEHGHHFFFFFFEEEEEDDDDDDDDDDDDDDDDDDDDDDD
GCCACCACGGAGCGAGAAGCCCAGATAGACGCCCCGGCGGCCCCGGGTCCTGGAGTCCCGCCGCCTGCTGCCCGGCCGAGGACCCCACCCCGCCTGCCGCCCTGTCCATGGCGGGCCCCACTGCAAGCATCGGGCGGCAGGCGGGGTGGGGTCCTCGGCCGGGCAGCAGGCGGCGGGACTCCAGGACCCGGGGCCGCCGG
[Ateeq@BIO-DT-415 NEW_NGS]$/usr/local/bin/fastx_quality_stats -i SRR1604991.fastq -o SRR1604991.txt-Q33 fastx_quality_stats: Invalid quality score value (char '#' ord 35 quality value -29) on line 4  -Ateeq Khaliq RNA-Seq • 2.0k views ADD COMMENT 1 Entering edit mode if you specify -Q33 it should work, since "#" is an accepted symbol for the phred33, as you can see from this page. I tried with your example and for me it works fine. I initially thought it was a typo, but did you check there's a space before -Q33 in your line? ADD REPLY 0 Entering edit mode I have no clue why its giving error :( its showing for 'J' also. please have a look :( [Ateeq@BIO-DT-415 NEW_NGS]$ /usr/local/bin/fastx_quality_stats -i SRR1604991.fastq -o SRR1604991.txt -Q33
fastx_quality_stats: Invalid quality score value (char 'J' ord 74 quality value 41) on line 4

Edit: I checked, space is making no difference :(

2
Entering edit mode
8.2 years ago
Martombo ★ 3.0k

ok then apparently it is using the old phred33 scores (sanger), that were defined only until 40, which is "I". while with the new illumina scheme a "J" is also possible. as I told you I tried running your command with your example reads and it's giving me no error. maybe you're using an old version of fastx? mine is 0.0.13.2. what's yours?

alternatively you could use another tool, like fastqc, which is giving a similar output

0
Entering edit mode

Thanks a lot, I resolved this, Its an version error !!! Thanks again, this helped me lot !!!


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# Zeitschrift für Naturforschung A

### A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

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1865-7109
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# Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function

Abdelamelk Boumali
• Corresponding author
• Laboratoire de Physique Appliquée et Théorique, Université de Tébessa, 12000, W. Tébessa, Algeria, Africa
• Email
• Other articles by this author:
Published Online: 2015-08-22 | DOI: https://doi.org/10.1515/zna-2015-0191

## Abstract

In this paper, we investigated the thermodynamics properties of the one-dimensional Duffin–Kemmer–Petiau oscillator by using the Hurwitz zeta function method. In particular, we calculated the following main thermal quantities: the free energy, the total energy, the entropy, and the specific heat. The Hurwitz zeta function allowed us to compute the vacuum expectation value of the energy of our oscillator.

## 1 Introduction

In a relativistic quantum mechanics, the exact solutions of the wave function are very important in the understanding of the physics that can be brought by such solutions.

In the conventional relativistic approach, the interaction of S=0 and S=1 hadrons with different nuclei has been described by the second-order Klein–Gordon (KG) equation for S=0 and Proca equation for S=1 particles. It has been well known that it is very difficult to tackle these second-order equations mathematically and to derive the physics behind them. Therefore, considerable interest in recent years has been devoted to examine the interactions of S=0 and S=1 hadrons with nuclei by using the first-order relativistic Duffin–Kemmer–Petiau (DKP) equation which is very similar to the first-order relativistic Dirac equation [1].

One important question related to DKP equation concerns the equivalence between its spin 0 and 1 sectors and the theories based on the second-order KG and Proca equations [2]. The Dirac-like DKP equation is not new and dates back to the 1930s. Historically, the loss of interest in the DKP stems from the equivalence of the DKP approach to the Klein–Gordon (KG) and Proca descriptions in on-shell situations, in addition to the greater algebraic complexity of the DKP formulation. However, in 1970s, this supposed equivalence was question in several situations involving breaking of symmetries and hadronic possess, showing that in some cases, the DKP and KG theories can give different results. Moreover, the DKP equation appears to be richer than the KG equation if the interactions are introduced. In this context, alternative DKP-based models were proposed for the study of meson–nucleus interactions, yielding a better adjustment to the experimental data when compared to the KG-based theory [3]. In the same direction, approximation techniques formerly developed in the context of nucleon-nucleus scattering were generalised, giving a good description for experimental data of meson-nucleus scattering [4]. The deuteron-nucleus scattering was also studied using DKP equation, motivated by the fact that this theory suggest a spin1 structure from combining two $spin-12$ [5]. In the same context, we can cite the works of [6, 7] on the meson–nuclear interaction and the relativistic model of α-nucleus elastic scattering where they have been treated by the formalism of the DKP theory. Recently, there is a renewed interest in the DKP equation. It has been studied in the context of quantum chromodynamics (QCD) [8], covariant Hamiltonian formalism [9], in the causal approach [10, 11], in the context of five-dimensional Galilean invariance [12], in the scattering of K+ nucleus [13], in the presence of the Aharonov–Bohm potential [14, 15], in the Dirac oscillator interaction [16], in the study of thermodynamics properties [17], on the supersymmetric [18], and finally, in the presence of some shape of interactions [19–34]. Theses examples in some case break the equivalence between the theories based on the DKP equation and KG and Proca equations.

The Dirac oscillator was for the first time studied by Itô et al. [35]. They considered a Dirac equation in which the momentum $p→$ is replaced by $p→ − imβωr→,$ with $r→$ being the position vector, m the mass of particle, and ω the frequency of the oscillator. The interest in the problem was revived by Moshinsky and Szczepaniak [36], who gave it the name of Dirac oscillator (DO) because, in the nonrelativistic limit, it becomes a harmonic oscillator with a very strong spin-orbit coupling term. Physically, it can be shown that the (DO) interaction is a physical system, which can be interpreted as the interaction of the anomalous magnetic moment with a linear electric field [37, 38]. The electromagnetic potential associated with the DO has been found by Benitez et al. [39]. The Dirac oscillator has attracted a lot of interest both because it provides one of the examples of the Dirac’s equation exact solvability and because of its numerous physical applications. As a relativistic quantum mechanics problem, the DO has been studied from many viewpoints, including the covariance properties, complete energy spectrum and corresponding wave functions, symmetry Lie algebra, shift operators, hidden supersymetry, conformal invariance properties, and the completeness of wave function. Relativistic many body problems with DO interactions have been extensively studied with the special emphasis on the mass spectra of mesons (quark-antiquark systems) and baryons (three quark systems). The dynamics of wave packets in a DO has been determined and a relation with the Jayne’s–Cumming model established. The (2+1) space time has also been shown to be an interesting framework for discussing the DO in connection with new phenomena (such as the quantum Hall effect and fractional statistics) in condensed matter physics. Fortunately, Franco-Villafane et al. [40], in order to vibrate this oscillator, exposed the proposal of the first experimental microwave realization of the one-dimensional DO.

The thermal properties of the one-dimensional DKP equation in a DO interaction was at first considered by [17]. The author has treated the case of spin-1 particles by using a different formalism that used here. This difference has been well explained in the study of Boumali and Chetouani [16]. Encouraged by the experimental realization of a one-dimensional DO, we are interested in the calculations of the thermodynamics properties for the one-dimensional DKP oscillator in all range of temperatures for both spin-0 and spin-1 particles using a method based on the zeta function [41, 42]. This method is used by Dariescu and Dariescu [43] with the aim of calculating the partition function in the case of the graphene. We note here that the zeta function is applied successfully in different areas of physics, and the examples vary from ordinary quantum and statistical mechanics to quantum field theory [44]. This study is organised as follows: in Section 2, we review the solutions of the one-dimensional DKP oscillator. In Section 3, our numerical results and discussions are described. Finally, Section 4 will be a conclusion.

## 2.1 Free DKP Equation

The free DKP equation is given by [45–47]

$(iℏβτ∂τ − Mc)ψ = 0, (τ = 0, 1, 2, 3), (1)$(1)

where ψ is the boson wave function, and M is the mass and the β are matrices which satisfy the following relations:

$βμβνβρ + βρβνβμ = βμgνρ + βρgνμ, (2)$(2)

where gμν=diag(1, –1, –1, –1) is the metric of the Minkowski space. There are 126 linearly independent elements for this algebra. The rank of the matrices turns out to be 16 and the corresponding representation can be decomposed into three irreducible representations of the dimensions 1, 5, and 10. The one-dimensional representation is trivial, while the five- and 10-dimensional representations describe scalar (spin-0) and vector (spin-1) particles, respectively. The advantage of the DKP equation is that it gives a unified description of spin-0 and spin-1 systems. The β are 5×5 matrices in the spin-0 representation and 10×10 matrices in the spin-1 representation. In our case, the βμ matrices are chosen as follows:

• For the five-dimensional representation

$β0 = (Θ2 × 203 × 303 × 202 × 3), βi = (02 × 2ρ2 × 3i−ρ3 × 2iT03 × 3), (i = 1, 2) (3)$(3)

with

$Θ = (0110), ρ1 = (−100000), ρ2 = (0−10000). (4)$(4)

• For the 10-dimensional representation

$β0 = (03 × 303 × 3−I3 × 303 × 1†03 × 303 × 303 × 303 × 1†−I3 × 303 × 303 × 303 × 1†01 × 301 × 301 × 30), βk = (03 × 303 × 303 × 3iKl†03 × 303 × 3S3 × 3l03 × 1†03 × 3−S3 × 3l03 × 303 × 1†iKl01 × 301 × 30),(l = 1, 2, 3). (5)$(5)

where

$03 × 3 = (000000000), I = (100010001), (6)$(6)

$S1 = i(00000−1010), S2 = i(001000−100), S3 = i(0−10100000), (7)$(7)

$K1 = (100), K2 = (010), K3 = (001). (8)$(8)

## 2.2.1 Case of Spin-1

The one-dimensional DKP equation in the presence of a DO potential is [48, 49]

$[β0E − cβ1(px − imωη0x) − mc2]ψ = 0, (9)$(9)

where $η0 = 2(β0)2 − 1^$ with (η0)2=I10×10, and I10×10 is the 10×10 unit matrix, and m is the mass of particles. The stationary state ψ is a 10-component wave function of the DKP equation, which can be written as follows:

$ψ = (ψ1, ψ2, ψ3, ψ4, ψ5, ψ6, ψ7, ψ8, ψ9, ψ10)T. (10)$(10)

Following [48, 49], the eigensolutions are decomposed in a two possible cases.

• In the first case, where we call it as the even solutions (corresponds to the case when a=−n and B=0 in [48]), we have

$ϵn = ± mc21 + 4ℏωmc2n, (11)$(11)

$ψ1(x) = Ae− mω2ℏx21F1(− n; 12; mωℏx2). (12)$(12)

• In the the second case, where we denote it as the odd solutions (corresponds to the case when $b + 12 = − n$ and A=0 in [48]), we get

$εn = ± mc21 + (2 + 4n)ℏωmc2, (13)$(13)

$ψ1(x) = Be− mω2ℏx2mωℏx1F1(− n; 32; mωℏx2). (14)$(14)

The other components are derived from ψ ((17) and (18) in [49]).

## 2.2.2 Case of Spin-0

The one-dimensional DKP oscillator for the particles of spin-0 is described by the following equation:

$[β0E¯ − cβ1(px − im0ωη0x) − m0c2]ϕ(x) = 0, (15)$(15)

where $η0 = 2(β0)2 − 1^$ with (η0)2=I5×5, I5×5 is the 5×5 unit matrix, and m0 is the mass of particles. The stationary state ϕ is a five-component wave function of the DKP equation, which can be written by the following:

$ϕ = (ϕ1, ϕ2, ϕ3, ϕ4, ϕ5)T. (16)$(16)

As in the case of spin-1, the eigensolutions can be summarised as follows [48, 49]:

• For the even solutions case, the eigensolutions are given as follows:

$ϵ¯n = ± m0c21 + 4ℏωm0c2n, (17)$(17)

$ϕ1(x) = Ce−m0ω2ℏx21F1(− n; 12; m0ωℏx2). (18)$(18)

• On the other hand, for the odd solutions, we get

$ε¯n = ± m0c21 + (2 + 4n)ℏωm0c2, (19)$(19)

$ϕ1(x) = De−mω02ℏx2mω0ℏx1F1(− n; 32; m0ωℏx2). (20)$(20)

Now, and following the (11) and (13), for the particles of spin-1, and (17) and (19), for particles of spin-0, we start to the determinations of all thermodynamics properties of our oscillator in question.

## 3 Thermal Properties of the Relativistic Harmonic Oscillator

Before we study the thermodynamic properties of the DKP oscillator, we note that the form of the spectrum of energy for both spin-1 and spin-0 particles are the same. Consequently, we are looking, first, for the numerical thermal quantities for the case of particles of spin-1. Then, we extend these results to the case of spin-0 particles.

Also, in order to extract these properties of our oscillator, we will only restrict ourselves to stationary states of positive energy. The reason is threefold: (i) according to the following works of [50–52], the DKP equation possesses an exact Foldy–Wouthuysen transformation (FWT): so, the positive- and negative-energy solutions never mix.

(ii) The (11) and (17) (even solutions) illustrate the form of the energy as a function of n. From Figure 1, one observes that all the energy levels emerge from the positive (negative)-energy continuum so that it is plausible to identify them with particle (antiparticle) levels. Furthermore, it is noticeable from this figure that for positive-energy spectrum one finds that the lowest quantum numbers correspond to the lowest eigenenergies, as it should for particle energy levels. On the other hand, for negative-energy spectrum, this presents a similar behavior but the highest energy levels are labelled by the lowest quantum numbers and are to be identified with antiparticle levels [53].

Figure 1:

$EMc2$ versus quantum number n with $r ≡ ℏωMc2 = 1.$

Finally, (iii) it is correct that the case of bosons is very different to the one of fermions: all bosons can occupied the same level, contrary to the case of fermions where they are controlled by the Pauli principle. In spite of that, we can extending the method of filling the Dirac negative energy sea for the case of fermions to the case of bosons (Nielsen and Ninomiya [54, 55]): as mentioned by these authors, the bosons states are divided into two sectors: the usual positive sector consisting of states with a positive number of bosons, and the negative sector, consisting of states with a negative number of bosons. Once a state enters the negative sector, it cannot return to the usual positive sector through an ordinary interaction, due to the presence of a barrier.

Thus, according to these arguments, we can assume that only particles with positive energy are available in order to determine the thermodynamic properties of our oscillator in question.

## 3.1 Methods

In order to obtain all thermodynamic quantities of our oscillator in question, we concentrate, at first, on the calculation of the partition function Z.

Given the energy spectrum, we can define the partition via

$Z = ∑ne− β˜En, (21)$(21)

where kB is the Boltzmann constant and $β˜ = 1kBT.$

Following the above discussion about the eigensolutions of the DKP oscillator, we consider two possible partition function.

## 3.1.1 Even Partition Function Zeven

With the following substitutions,

$r = ℏωmc2, α = 14r, γ = 2r, (22)$(22)

and by using the (11), the partition function becomes

$Zeven = ∑ne− β˜ϵn = ∑ne− 1 + 4rnτ, (23)$(23)

or

$Zeven = ∑ne− γτα + n, (24)$(24)

where $τ = β˜mc2$ and r is a parameter that controls the nonrelativistic regime.

Following the same procedure as in [41–43], and using the inverse Mellin transformation of e–x, with

$e− x = 12πi∫Cdsx− sΓ(s), (25)$(25)

the sum in (24) is transformed into

$∑ne− γτα + n = 12πi∫Cds(γτ)− s∑n(n + α)− s2Γ(s) = 12πi∫Cds(γτ)−sζH(s2, α)Γ(s), (26)$(26)

with $x = γτα + n,$ and Γ(s) and $ζH(s2, α)$ are, respectively, the Euler and Hurwitz zeta function.

Applying the residues theorem, for the two poles s=0 and s=2, the desired partition function is written down in terms of the Hurwitz zeta function as follows:

$Zeven (τ) = τ24r + ζH(0, α). (27)$(27)

Now, using that [44]

$ζH(0, α) = 12 − α, (28)$(28)

the final partition function is transformed into

$Zeven(τ) = τ24r + 12 − 14r. (29)$(29)

## 3.1.2 Odd Partition Function Zodd

According to the (13), the odd partition function is defined by

$Zodd = ∑ne−1 + (2 + 4n)rτ (30)$(30)

With the following substitutions,

$α1 = 12 + 14r, γ = 2r, (31)$(31)

and by the same strategy used above, we obtain

$Zodd(τ) = τ24r + ζH(0, α1), (32)$(32)

or

$Zodd(τ) = τ24r − 14r. (33)$(33)

Thus, and from both definitions of partition function, the most important thermal quantities, which are are the free energy F, the mean energy U, the entropy S and the specific heat C, can be obtained by using the following expressions:

$Fmc2 = − τln(Z), Umc2 = τ2∂ln(Z)∂τ, (34)$(34)

$SkB = ln(Z) + τ∂ln(Z)∂τ, CkB = 2τ∂ln(Z)∂τ + τ2∂2ln(Z)∂τ2. (35)$(35)

## 3.2 Numerical Results and Discussions

We are now ready to present and discuss our results concerning the thermal quantities of the one-dimensional DKP oscillator. All quantities are reported as a function of the reduce temperature τ for the relativistic case with r=1.

The behavior of all thermodynamics quantities for the spin-1 particles, for both solutions, are shown in Figure 2. The difference can be revealed in the curve of the specific heat: when the odd solutions tends very rapidly to the 2KB limit, the even solutions depicted a curvature around a certain temperature τ0. From the curve of the numerical entropy function, no abrupt change, around this temperature, has been identified. This means that the curvature, which is observed in the specific heat curve, does not exhibit or indicate an existence of a phase transition around a τ0 temperature.

Figure 2:

The thermal quantities of the one-dimensional DKP oscillator versus a reduce temperature τ: case of spin-1 particles.

Figure 3 depicted the thermal quantities of spin-0 particles: the same argument used in the spin-1 particles can be extended here.

Figure 3:

The thermal quantities of the one-dimensional DKP oscillator versus a reduce temperature τ: case of spin-0 particles.

Finally, the Hurwitz zeta function method allows us to compute the vacuum expectation value of the energy [44]. The last is defined by [44]

$ϵ0 = lims→− 1∑n = 0∞|ϵn|− s. (36)$(36)

Following the above description about the eigensolutions in Section 2, we define two vacuum expectation values of the energy. Therefore, we start with the case of spin-1 particles, and then, the results can be extended automatically for the case of spin-0 particles.

Thus, two possible case can be distinguished as follows:

• For the even solutions, the vacuum value of energy, in terms of Hurwitz zeta function, is written as

$ϵ0mc2 = 2rζH(− 12, 12r). (37)$(37)

• For the odd solutions, we have

$ε0mc2 = 2rζH(− 12, 12 + 14r). (38)$(38)

Now, using the asymptotic series corresponding to the Hurwitz zeta function (Appendix), (37) and (38) become

$ϵ0mc2 = − 16r + 12 − 23∑k = 2∞Bkk!Γ(− 32 + k)Γ(− 32)(4r)k − 1 (39)$(39)

for even solutions, and

$ϵ0mc2 = −43r(12 + 14r)32 + r12 + 14r − 43∑k = 2∞Bkk!Γ(−32 + k)Γ(−32)r(12 + 14r)32 − k, (40)$(40)

for odd solutions.

In Figure 4, we show the $ϵ0mc2$ as a function of the parameter r for both cases. We can see that the vacuum expectation value of the energy depend on the parameter r.

Figure 4:

Vacuum energy versus a parameter r for both spin-1 and spin-0 particles around a relativistic region.

## 4 Conclusion

In this work, we have studied the thermodynamic properties of the one-dimensional DKP oscillator using the Hurwitz zeta function method. According to the work of [48, 49], we distinguish two possible cases concerning the partition function: the even and the odd partition function. Consequently, we have two cases of the thermal properties for both particles of our oscillator, which are depicted in Figures 2 and 3. Also, from the Hurwitz zeta function, we have calculated the vacuum expectation value of the energy of our oscillator. As we can see from Figure 4, the last depends on the parameter r.

## Appendix: Some Properties of Zeta Function

The Riemann zeta function is defined by

$ζ(s) = ∑n = 0∞1ns, withs ∈ ℂ (A1)$(A1)

Nowadays, the Riemann zeta function is just one member of a whole family of zeta function’s (Hurwitz, Epstein, and Selberg). The most important of them is the Hurwitz zeta function ζH given by

$ζH(s, α) = ∑n = 0∞1(n + α)s, (A2)$(A2)

where 0<a ≤ 1, is a well-defined series when ℜe(s)>1, and can be analytically continued to the whole-complex plane with one singularity, a simple pole with residue 1 at s=1.

An integral representation is

$ζH(s, α) = 1Γ(s)∫0∞dtts − 1e− tα1 − e− t, ℜ(s) > 1, ℜ(α) > 0. (A3)$(A3)

It can be shown that ζH (s, α) has only one singularity, namely a simple pole at s=1 with residue 1 and that it can be analytically continued to the rest of the complex s-plane.

Also, we can shown that ζH (s, α) have the following properties:

$ζH(0, α) = 12 − α, (A4)$(A4)

$ζH(− m, α) = − Bm + 1(α)m + 1, m ∈ ℕ, (A5)$(A5)

Br(a) being the Bernoulli polynomials. The asymptotic series corresponding to the Hurwitz zeta function is given by the following:

$ζH(1 + z, α) = 1zα− z + 12α− 1 − z + 1z∑k = 2∞Bkk!Γ(z + k)Γ(z)α− z − k, (A6)$(A6)

with Bk are Bernoulli’s numbers.

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A. J. Silenko, Phys. Rev. D 87, 073015 (2013).Google Scholar

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L. B. Castro, Eur. Phys. J. C 75, 287 (2015).Google Scholar

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Corresponding author: Abdelamelk Boumali, Laboratoire de Physique Appliquée et Théorique, Université de Tébessa, 12000, W. Tébessa, Algeria, Africa, E-mail: boumali.abdelmalek@gmail.com

Accepted: 2015-07-26

Published Online: 2015-08-22

Published in Print: 2015-10-01

Citation Information: Zeitschrift für Naturforschung A, Volume 70, Issue 10, Pages 867–874, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784,

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## Citing Articles

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ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering, 2016, Volume 17, Number AFG5 SPECIAL ISSUE, Page 708
[3]
A. N. Ikot, W. Azogor, U. S. Okorie, F. E. Bazuaye, M. C. Onjeaju, C. A. Onate, and E. O. Chukwuocha
Indian Journal of Physics, 2019, Volume 93, Number 9, Page 1171
[5]
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Zhi Wang, Zheng-Wen Long, Chao-Yun Long, and Wei Zhang
Advances in High Energy Physics, 2015, Volume 2015, Page 1


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# To Do List

(Difference between revisions)
 Revision as of 03:20, 14 March 2012 (view source)Russell (Talk | contribs)← Older edit Latest revision as of 21:11, 25 January 2016 (view source)Luis (Talk | contribs) (19 intermediate revisions not shown) Line 1: Line 1: == Things that need to be done == == Things that need to be done == - - We need to come up with some organization for the articles. The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki. The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki. - - * We better start thinking hard about writing the [[Introduction to nonlocal equations]]. We gotta start somewhere, so any random idea or small thing you want to write should go in there. This is high priority, since if someone reads one page of this wiki, it will likely be this one. * Some discussion on [[Dirichlet form|Dirichlet forms]], and maybe some models from [[nonlocal image processing]]. * Some discussion on [[Dirichlet form|Dirichlet forms]], and maybe some models from [[nonlocal image processing]]. * Fractional curvatures in conformal geometry. * Fractional curvatures in conformal geometry. + + * Create a page on [[Non-local Lagrangian | Non-local Lagrangians]] and mention relevant examples, note Non-local Lagrangian is a term used by particle physicists and it is not necessarily the same as a [[Dirichlet form]]. * We need  to explain further the  [[Extension technique]] and its connection with fractional powers of the Laplacian and Conformal geometry. Required background: [[Geometric Scattering Theory]], [[Ambient Metric Construction]], [[GJMS Operators]] and [[Singular Yamabe Problem]]..) * We need  to explain further the  [[Extension technique]] and its connection with fractional powers of the Laplacian and Conformal geometry. Required background: [[Geometric Scattering Theory]], [[Ambient Metric Construction]], [[GJMS Operators]] and [[Singular Yamabe Problem]]..) - * It would be wise (once the wiki is more mature) to add pages about the [[Boltzmann equation]], since it is one of the more "classical" and better known integro-differential equations. + * It would be good to have an article on the natural similarities between non-local operators and [[elliptic operators on graphs]]. - + - * Pages about [[Homogenization]] (local and nonlocal) should appear here too. (CITATIONS still needed) + - + - * Given the recent works of Osher/Gilboa and Bertozzi/Flenner on Ginzburg-Landau  on graphs we should have an article on the natural similarities between non-local operators and [[elliptic operators on graphs]]. + * [[nonlocal image processing]]. * [[nonlocal image processing]]. Line 25: Line 19: * [[Keller-Segel equation]]. * [[Keller-Segel equation]]. - * [[Active scalar equations]]. + * Improve the page on [[Active scalar equations]]. * [[Ising Models With Nonlocal Interactions]] * [[Ising Models With Nonlocal Interactions]] Line 33: Line 27: * [[Nonlocal Phase Field Equations]] this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising models, nonlocal cahn-hilliard, nonlocal biological aggregation, sharp interface limits (giacomin-lebowitz, bates-et-al, de massi-pressutti, etc...) * [[Nonlocal Phase Field Equations]] this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising models, nonlocal cahn-hilliard, nonlocal biological aggregation, sharp interface limits (giacomin-lebowitz, bates-et-al, de massi-pressutti, etc...) + * [[Boundary Harnack inequality]] it would be good to possibly include this in the description of what is different/same regarding local vs. nonlocal equations. + * Describe, with references, the connection between [[holder estimates]] of viscosity solutions of stationary and or parabolic equations and the existence and uniqueness of solutions to the relevant [[Martingale Problem]] + + * [[Neumann Boundary Conditions]] + + * Processes in the "limit" $\alpha=0$, [[Zero Order Operators]] + + * Discussion of the [[Barlow-Bass-Chen-Kassmann Counterexample]] to Regularity of $L$-Harmonic functions. + + * Discussion of Jean Picard's paper (regularity for pure jump processes with non-degenerate, translation invariant generators) + + * Add Courrège's Structure theorem for operators and other structure theorems (generators of Feller semigroups, Hunt processes... etc) + + * A page on the nonlocal analogue of the thin film equation == (partially) Completed tasks == == (partially) Completed tasks == Line 41: Line 49: * Definition of [[viscosity solutions]] for nonlocal equations. Also a discussion on existence using [[Perron's method]] and uniqueness through the [[comparison principle]]. * Definition of [[viscosity solutions]] for nonlocal equations. Also a discussion on existence using [[Perron's method]] and uniqueness through the [[comparison principle]]. - * Some general regularity results like [[holder estimates]], [[Harnack inequalities]], [[Alexadroff-Bakelman-Pucci estimates]], some reference to [[free boundary problems]]. + * Some general regularity results like [[holder estimates]], [[Harnack inequalities]], [[Aleksandrov-Bakelman-Pucci estimates]], some reference to [[free boundary problems]]. * A list of [[regularity results for fully nonlinear integro-differential equations|regularity results]] for [[fully nonlinear integro-differential equations]]. * A list of [[regularity results for fully nonlinear integro-differential equations|regularity results]] for [[fully nonlinear integro-differential equations]]. Line 67: Line 75: * Having a [[list of equations]] may make it easier to navigate the wiki. * Having a [[list of equations]] may make it easier to navigate the wiki. - == Other ideas == + * Jump processes via [[Subordination]] + + == Wiki Maintenance == + * Get access to LocalSettings.php (ask Maorong for access maybe?) so we can change the page name of the Main Page and the Starting Page (specially since those are the names shown by a google search) * Fill up the list of [[upcoming events]] such as conferences, workshops, summer schools. * Fill up the list of [[upcoming events]] such as conferences, workshops, summer schools. * [[User:Nestor|Nestor]] has started a [[Literature on Nonlocal Equations]] to dump there all papers we want to reference or are already referencing on the wiki. * [[User:Nestor|Nestor]] has started a [[Literature on Nonlocal Equations]] to dump there all papers we want to reference or are already referencing on the wiki.

## Things that need to be done

The list below can be a starting point to click on links and edit each page. The following are some of the topics that should appear in this wiki.

• Fractional curvatures in conformal geometry.
• Create a page on Non-local Lagrangians and mention relevant examples, note Non-local Lagrangian is a term used by particle physicists and it is not necessarily the same as a Dirichlet form.
• Nonlocal Phase Field Equations this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising models, nonlocal cahn-hilliard, nonlocal biological aggregation, sharp interface limits (giacomin-lebowitz, bates-et-al, de massi-pressutti, etc...)
• Boundary Harnack inequality it would be good to possibly include this in the description of what is different/same regarding local vs. nonlocal equations.
• Describe, with references, the connection between holder estimates of viscosity solutions of stationary and or parabolic equations and the existence and uniqueness of solutions to the relevant Martingale Problem
• Discussion of Jean Picard's paper (regularity for pure jump processes with non-degenerate, translation invariant generators)
• Add Courrège's Structure theorem for operators and other structure theorems (generators of Feller semigroups, Hunt processes... etc)
• A page on the nonlocal analogue of the thin film equation


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#### Connect Phonics

The Connect Phonics course contains everything you need to teach someone to read.

#### Connect Spelling

Connect Spelling helps students learn the patterns in words, so spelling actually makes sense.

#### Review

"During the nine years I taught the Connect Phonics and Spelling programs, I became more and more enamored with it. It is a logical, step-by-step program that creatively and enthusiastically takes students through the patterns in reading."
Susan Behler, Title One Teacher


text:
TheInfoList

In
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
, specifically in
algebraic topology Algebraic topology is a branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained ...
, the cup product is a method of adjoining two
cocycle In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
s of degree ''p'' and ''q'' to form a composite cocycle of degree ''p'' + ''q''. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space ''X'' into a graded ring, ''H''(''X''), called the
cohomology ringIn mathematics, specifically algebraic topology, the cohomology ring of a topological space ''X'' is a ring (mathematics), ring formed from the cohomology groups of ''X'' together with the cup product serving as the ring multiplication. Here 'cohomol ...
. The cup product was introduced in work of J. W. Alexander, Eduard Čech and
Hassler Whitney Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersion (mathematics), immersions, characteristic classes, and ...
from 1935–1938, and, in full generality, by
Samuel Eilenberg Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory Category theory formalizes mathematical structure and its concepts in terms of a Graph labeling, labeled directed graph ...
in 1944.

# Definition

In
singular cohomology Singular may refer to: * Singular, the grammatical number In linguistics, grammatical number is a grammatical category of nouns, pronouns, adjectives, and verb agreement (linguistics), agreement that expresses count distinctions (such as "one", ...
, the cup product is a construction giving a product on the graded
cohomology ringIn mathematics, specifically algebraic topology, the cohomology ring of a topological space ''X'' is a ring (mathematics), ring formed from the cohomology groups of ''X'' together with the cup product serving as the ring multiplication. Here 'cohomol ...
''H''(''X'') of a
topological space In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gener ...
''X''. The construction starts with a product of
cochain In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or module (mathematics), modules) and a sequence of group homomorphism, homomorphisms between consecutive groups such that the image (mathemati ...
s: if $\alpha^p$ is a ''p''-cochain and $\beta^q$ is a ''q''-cochain, then :$\left(\alpha^p \smile \beta^q\right)\left(\sigma\right) = \alpha^p\left(\sigma \circ \iota_\right) \cdot \beta^q\left(\sigma \circ \iota_\right)$ where σ is a Singular homology, singular (''p'' + ''q'') -simplex and $\iota_S , S \subset \$ is the canonical embedding of the simplex spanned by S into the $\left(p+q\right)$-simplex whose vertices are indexed by $\$. Informally, $\sigma \circ \iota_$ is the ''p''-th front face and $\sigma \circ \iota_$ is the ''q''-th back face of σ, respectively. The coboundary of the cup product of cochains $\alpha^p$ and $\beta^q$ is given by :$\delta\left(\alpha^p \smile \beta^q\right) = \delta \smile \beta^q + \left(-1\right)^p\left(\alpha^p \smile \delta\right).$ The cup product of two cocycles is again a cocycle, and the product of a coboundary with a cocycle (in either order) is a coboundary. The cup product operation induces a bilinear operation on cohomology, : $H^p\left(X\right) \times H^q\left(X\right) \to H^\left(X\right).$

# Properties

The cup product operation in cohomology satisfies the identity :$\alpha^p \smile \beta^q = \left(-1\right)^\left(\beta^q \smile \alpha^p\right)$ so that the corresponding multiplication is supercommutative, graded-commutative. The cup product is functorial, in the following sense: if :$f\colon X\to Y$ is a continuous function, and :$f^*\colon H^*\left(Y\right)\to H^*\left(X\right)$ is the induced homomorphism in cohomology, then :$f^*\left(\alpha \smile \beta\right) =f^*\left(\alpha\right) \smile f^*\left(\beta\right),$ for all classes α, β in ''H'' *(''Y''). In other words, ''f'' * is a (graded) ring homomorphism.

# Interpretation

It is possible to view the cup product $\smile \colon H^p\left(X\right) \times H^q\left(X\right) \to H^\left(X\right)$ as induced from the following composition:
$\displaystyle C^\bullet\left(X\right) \times C^\bullet\left(X\right) \to C^\bullet\left(X \times X\right) \overset C^\bullet\left(X\right)$
in terms of the chain complexes of $X$ and $X \times X$, where the first map is the Künneth formula, Künneth map and the second is the map induced by the diagonal functor, diagonal $\Delta \colon X \to X \times X$. This composition passes to the quotient to give a well-defined map in terms of cohomology, this is the cup product. This approach explains the existence of a cup product for cohomology but not for homology: $\Delta \colon X \to X \times X$ induces a map $\Delta^* \colon H^\bullet\left(X \times X\right) \to H^\bullet\left(X\right)$ but would also induce a map $\Delta_* \colon H_\bullet\left(X\right) \to H_\bullet\left(X \times X\right)$, which goes the wrong way round to allow us to define a product. This is however of use in defining the cap product. Bilinearity follows from this presentation of cup product, i.e. $\left(u_1 + u_2\right) \smile v = u_1 \smile v + u_2 \smile v$ and $u \smile \left(v_1 + v_2\right) = u \smile v_1 + u \smile v_2.$

# Examples

Cup products may be used to distinguish manifolds from wedges of spaces with identical cohomology groups. The space $X:= S^2\vee S^1\vee S^1$ has the same cohomology groups as the torus ''T'', but with a different cup product. In the case of ''X'' the multiplication of the cochains associated to the copies of $S^1$ is degenerate, whereas in ''T'' multiplication in the first cohomology group can be used to decompose the torus as a 2-cell diagram, thus having product equal to Z (more generally ''M'' where this is the base module).

# Other definitions

## Cup product and differential forms

In de Rham cohomology, the cup product of differential forms is induced by the wedge product. In other words, the wedge product of two Closed and exact differential forms, closed differential forms belongs to the de Rham class of the cup product of the two original de Rham classes.

## Cup product and geometric intersections

For oriented manifolds, there is a geometric heuristic that "the cup product is dual to intersections." Indeed, let $M$ be an oriented smooth manifold of dimension $n$. If two submanifolds $A,B$ of codimension $i$ and $j$ intersect Transversality (mathematics), transversely, then their intersection $A \cap B$ is again a submanifold of codimension $i+j$. By taking the images of the fundamental homology classes of these manifolds under inclusion, one can obtain a bilinear product on homology. This product is Poincaré duality, Poincaré dual to the cup product, in the sense that taking the Poincaré pairings $\left[A\right]^*, \left[B\right]^* \in H^,H^$ then there is the following equality : $\left[A\right]^* \smile \left[B\right]^*=\left[A \cap B\right]^* \in H^\left(X, \mathbb Z\right)$. Similarly, the linking number can be defined in terms of intersections, shifting dimensions by 1, or alternatively in terms of a non-vanishing cup product on the complement of a link.

# Massey products

The cup product is a binary (2-ary) operation; one can define a ternary (3-ary) and higher order operation called the Massey product, which generalizes the cup product. This is a higher order cohomology operation, which is only partly defined (only defined for some triples).


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# Differential equation for Voltage across a capacitor.

Discussion in 'General Electronics Chat' started by Electromech man, Dec 9, 2010.

1. ### Electromech man Thread Starter New Member

May 2, 2009
8
0
Good day folks,

I know the differential equation for time varying voltage across an inductor is v(t)=L*di(t)/dt.

Can anyone tell me the equation for time varying voltage across a capacitor?

Regards.

2. ### tyblu Active Member

Nov 29, 2010
199
16
taken from http://en.wikipedia.org/wiki/Capacitor#Current-voltage_relation

$i_C(t) = C\frac{dv(t)}{dt} \\
\int_{t_0}^{\tau} i_C(t)dt = C\int_{t_0}^{\tau} \frac{dv(t)}{dt}dt \\
\int_{t_0}^{\tau} i_C(t)dt = C [ v(\tau) - v(t_0) ] \\
v(\tau) = \frac{1}{C}\int_{t_0}^{\tau} i_C(t)dt + v(t_0)
$

Last edited: Dec 9, 2010


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# Machine Learning needs a Protocol

## March 12, 2021 by guidj

The internet uses a protocol - it's called http. A protocol, in this sense, is an agreement. It allows any party, wishing to partake in an exchange, to have a clear expectation of how to do things. For the internet, it tells interested parties how to communicate, to send and receive data. It has occurred to me that machine learning currently lacks a protocol.

Instead, we have frameworks, which implement protocols defined by the people that have implemented the frameworks. And while there is nothing wrong with these “framework protocols”, the fact that there are several of them is a problem. It implies that there are number of ways to achieve the same thing - read data, transform it, train a model, export it, load it, and get predictions out of it.

Now, the absence of a protocol in itself doesn't strictly represent a problem. There is a version of the world where machine learning can work without protocols. In this version, every tool that exists is consistent and simple. Consistent, in that it uses the same models for representing data as every other tool, and simple in that it provides a single functionality. This world exists. That fundamental tool for representing data is numpy. The single purpose tools are scipy, pandas, matplotlib, open-ai gym, and others alike.

In this world, however, these single purpose tools are disjoint. They provide building blocks to be stitched together. And so the frameworks that are out there stand out, because they often give a complete picture of a problem and solution. And we turn to them because we prefer the cohesive over having to figure things ourselves every time. And for doing so, we are left locked into an ecosystem that promises everything, in exchange for adhesion. And every now and then, we're forced to skip rope, to be on par with the latest redesign of the framework that is often incompatible with its previous versions.

There are too many ways to create a neural network. Very few ways of testing them. Too many ways to create reinforcement learning environments, and very few ways of debugging them. A framework does not define a standard in the way that a protocol does. And without a protocol, there is no contract - social or otherwise. So all we're left with is a choice - to accept the decisions of the framework creators or to make our own. Whichever choice we make, we'll be stuck with a high interest technical debt. And this debt isn't for developers of machine learning solutions alone - for it also borne by consumers, which includes users of applications, governments, regulators, and research communities of interest. It is harder to share, evaluate, validate, introspect, and build on top of work that has already been done. And that is why I think that machine learning needs a protocol.


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# Homework Help: The amount of power supplied/received by the dependent current source

1. Sep 5, 2012

### november1992

1. The problem statement, all variables and given/known data
http://imgur.com/jsIWS

2. Relevant equations

Ʃ $V_{n}$ = 0
Ʃ $I_{n}$ = 0
v = ir

3. The attempt at a solution

I combined the two 2Ω resistors into a single 4 Ω resistor because they're in series.

Then I tried to use KCL but I got 2 unknowns in one equation.

0.2A + $\frac{Vi}{4}$ = I

Last edited: Sep 5, 2012
2. Sep 5, 2012

### Kavik

Hi November,

Are you familiar with Mesh Current analysis? I think you are getting ahead of yourself when you add the two resistors together. Try leaving them separate and applying Mesh Current analysis. That should give you two equations and two unknowns.

Here is a short lesson on Mesh Current if you are unfamiliar with it or need a refresher:
http://www.allaboutcircuits.com/vol_1/chpt_10/3.html (The first problem is very similar to yours.)

3. Sep 5, 2012

### november1992

I don't know the voltage of any of the devices in the circuit, so how can I use KVL?

Last edited: Sep 5, 2012
4. Sep 5, 2012

### Kavik

Hmm, I may have given a more complicated method than necessary. If you were to use Mesh Current, you would draw the 2 current loops. When you have a current source in a loop, then you can just define that loop current as the value of the current source (i.e. I1 = 0.2 A, I2 = V1/4). I have noticed there is an easier way, using what you already have done.

If you only look at the top 2Ω resistor and write out Ohm's law in regards to it, that will give you a second equation that you can use with your first one in order to solve the problem.

5. Sep 5, 2012

### november1992

Vi = 2I

0.2A + $\frac{Vi}{4}$ = I

0.2A = I - $\frac{I}{2}$

0.4A = I

Did I do this right?

6. Sep 5, 2012

### Kavik

That's what I got!

You can always do an extra check by calculating the power produced (by the two current sources) vs. power consumed (by the two resistors). These should always be the same.

7. Sep 5, 2012

### november1992

The formula for power is P = IV, P= $I^{2}$R
So how can I check the power output of a current source?

8. Sep 5, 2012

### Kavik

P = IV still applies.

You know the current through the two resistors (0.4 A), and the equivalent resistance of the two series resistors is 4Ω. So to find the voltage from the top node to the bottom node, it's just:

V = IR
V = 0.4*4
V = 1.6 volts

Then P = IV!

Edit: And maybe I should be clear that 1.6 volts is also the voltage across each current source.

9. Sep 5, 2012

### november1992

Do you mean the top and bottom nodes of the resistor or the current source? If you mean the resistor, then wouldn't the voltage drop be split between the two paths at the bottom node?

10. Sep 5, 2012

### november1992

But it's in parallel so they would have the same voltage right?

11. Sep 5, 2012

### Kavik

Yep! I was just making a few doodles on the picture to illustrate that, so I'm going to post it anyways, even though you already got it.


text:
## Files in this item

FilesDescriptionFormat

application/vnd.openxmlformats-officedocument.presentationml.presentation

707209.pptx (3MB)
PresentationMicrosoft PowerPoint 2007

application/pdf

1927.pdf (24kB)
AbstractPDF

## Description

 Title: Gas-phase molecular structure of nopinone and its water complexes studied by microwave fourier transform spectroscopy and quantum chemical calculations Author(s): Neeman, Elias M. Contributor(s): Huet, T. R.; Aviles Moreno, Juan-Ramon Subject(s): Clusters/Complexes Abstract: Several monoterpenes and terpenoids are biogenic volatile organic compounds which are emitted in the atmosphere, where they react with OH, O$_3$ and NO$_x$ etc. to give rise to several oxidation and degradation products.\footnote{A. Calogirou, B.R. Larsen, and D. Kotzias, \textit{ Atmospheric Environment}, \textbf{33}, 1423-1439, (1999).} Their decomposition products are a major source of secondray organic aerosol (SOA).\footnote{P. Paasonen et al., \textit{Nat. Geosci.}, \textbf{6}, 438-442 (2013)} Spectroscopic information on these atmospheric species is still very scarce. The rotational spectrum of nopinone (C$_9$H$_{14}$O) one of the major oxidation products of $\beta$-pinene,\footnote{D. Zhang and R. Zhang \textit{The Journal of Chemical Physics}, \textbf{122}, 114308, (2005).} \footnote{R. Winterhalter et al. \textit{ Journal of Atmospheric Chemistry}, \textbf{35}, 165-197, (2000).} and of its water complexes were recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. The structure of the unique stable conformer of the nopinone was optimized using density functional theory and \textit{ab initio} calculations. Signals from the parent species and from the $^{13}C$ and $^{18}O$ isotopomers were observed in natural abundance. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled. \\ The structures of several conformers of the nopinone-water complexes with up to three molecules of water were optimized using density functional theory and \textit{ab initio} calculations. The energetically most stable of calculated conformers were observed and anlyzed. The rotational and centrifugal distortion parameters were fitted to a Watson’s Hamiltonian in the A-reduction. The present work provides the first spectroscopic characterization of nopinone and its water complexes in the gas phase.\\ Issue Date: 2016-06-21 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper/Presentation Type: Text Language: En URI: http://hdl.handle.net/2142/91352 Rights Information: Copyright 2016 by the authors Date Available in IDEALS: 2017-01-26


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## Thursday, April 19, 2012

Can I upload an image to my web server. I know that, If I have file input in my web page, then I can easily upload it and get it like $_FILE["name"] at my server(PHP). But I am developing a web page for iPad which doesn't expose the file system. But later, this will be handled by using phone gap. But now for the demo sake, I want to show that upload works. So, now assume that I have the path to a file. And I have it in my web page like <img src="path" alt=""> Can I upload this to my server by any means? ### Filling form with Datamapper ORM object - Codeigniter I'm trying to get a form populated by data coming from a Datamapper object. Here's my controller code: function find() {$sub_list = new Subject();      $data['s'] =$sub_list->all;      $this->load->view('professors/find',$data);  }

In my view I'd want to show a dropdown form with the data coming from that object but I can't make it work.
This code:

### Sorting Listbox Items VB

So I have two listboxes. Listbox1 gathers files from a directory and I have an add button to add selected files from Listbox1 over to Listbox2.

Is there a way to manually sort these items? Maybe with an up down buttons?

The reason I'd like to sort/reorder is I'll have a process that will run those selected files and each file will have to produce another file unqiue to the filename.

A quick example would be process FILE1.txt and produce FILE1.pdf, etc.

Is there an easier way to accomplish the sort/reorder?

### ASP.NET Localize

A simple question. I have a site with localization (with .resx files) and when i need to insert localized text i use a code like this:

<asp:Localize Text="<%\$ Resources: MyResource, Default_BannerHomeTitle %>" runat="server">SOME_TEXT_HERE_OR_NOT?</asp:Localize>

The question is if anyone knows what's the utility of the text between the asp:Localize tag -> "SOME_TEXT_HERE_OR_NOT?"

The real value come from the .resx file and the text "SOME_TEXT_HERE_OR_NOT?" is obviusly deleted when the page is rendered.

Is this text used in some situation? or is never used?

### Instead of Session variable where i can save my temp data in mvc?

I have created a mvc3 application.
Currently saving submit form value into Session as i need to do some stuff on that before
save changes to database.

Is there any other good way to store temp data in mvc like ViewState?

### Error when I try to create an .accdb file in C#

This is my code that creates an .accdb file if it can't find one :

Catalog cat = new CatalogClass(); string createStr = "Provider=Microsoft.ACE.OLEDB.12.0;Data Source=|DataDirectory|/saveDB.accdb;"; cat.Create(createStr); Table tbl = new Table(); tbl.Name = "saveDB"; tbl.Columns.Append("ID", DataTypeEnum.adGUID); tbl.Columns.Append("Tensiune", DataTypeEnum.adDouble); tbl.Columns.Append("Frecventa", DataTypeEnum.adDouble); tbl.Columns.Append("Rezistenta", DataTypeEnum.adDouble); tbl.Columns.Append("Inductanta", DataTypeEnum.adDouble); tbl.Columns.Append("Capacitate", DataTypeEnum.adDouble); tbl.Columns.Append("Elemente", DataTypeEnum.adVarWChar, 25); tbl.Columns.Append("Tip", DataTypeEnum.adVarWChar, 25); cat.Tables.Append(tbl); System.Runtime.InteropServices.Marshal.FinalReleaseComObject(tbl); System.Runtime.InteropServices.Marshal.FinalReleaseComObject(cat.Tables); System.Runtime.InteropServices.Marshal.FinalReleaseComObject(cat.ActiveConnection); System.Runtime.InteropServices.Marshal.FinalReleaseComObject(cat);

But when I run it in the program i get this runtime error :

System.Runtime.InteropServices.COMException (0x80004005): Not a valid file name.    at ADOX.CatalogClass.Create(String ConnectString)

I can't figure what's the problem with the file name, so if anyone has any idea, please help.

### Java speed access array index versus temp variable

What is faster in Java. Accessing an array index directly multiple times, or saving the value of the array index to a new variable and use this for following compution?

acces index

if ((shape.vertices[0].x >= fromX && shape.vertices[0].x <= toX) || // left side of shape in screen     (shape.vertices[0].x <= fromX && shape.vertices[0].x + shape.width >= fromX) || // right side of shape in screen     (shape.vertices[0].x >= fromX && shape.vertices[0].x + shape.width <= toX)) { // shape fully in screen      // ... }

temp variable

float x = shape.vertices[0].x; float y = shape.vertices[0].y; if ((x >= fromX && x <= toX) || // left side of shape in screen     (x <= fromX && x + shape.width >= fromX) || // right side of shape in screen     (x >= fromX && x + shape.width <= toX)) { // shape fully in screen          // ...     }

### Make asset pipeline act like production on development

I am experiencing some problems with assets on production: missing ones, stuff compiled into the wrong files (javascript for "/admin" getting compiled into the frontend code and so on). Most of the assets come from engines. I want to debug and optimize this.

For that, I need to precompile, serve and fail on my development environment just like it is done on production.

I have added some lines to my config/development.rb:

  config.serve_static_assets = true   config.assets.precompile += %w( store/all.js store/all.css admin/all.js admin/all.css ) # @TODO: clean up, and optimize.   config.assets.compile = false

Running this with rake RAILS_GROUPS=assets RAILS_ENV=development assets:precompile gives me all the assets and the manifest.yml in public/.

But then the server fails:

Sprockets::Helpers::RailsHelper::AssetPaths::AssetNotPrecompiledError in Spree/home#index  Showing /xxxx/app/views/spree/shared/_head.html.erb where line #13 raised:  favicon.ico isn't precompiled

favicon.ico isn't precompiled. But it is! Its there, in the public dir, in manifest.yml, and I can fetch it with the browser (or wget): http://localhost:3000/assets/favicon.ico.

NOTE Favicon is simply the first asset called. If I strip out favicon, the problem simply surfaces with the next asset, being "all.js", or, when that is stripped, "all.css", and so on. I can strip it untill "footer_bg.png", and it will then fail there. Again: the problem is not favicon, but the fact that the development environment does not see the precompiled assets at all.

What more is needed to get development asset pipeline similar to production?

EDIT: More explicit explanation that favicon is not the problem, merely a symptom.

### serach product with their specifications filter

I have a table that contain products with their specifications.i created a sample of data in http://sqlfiddle.com/#!2/15575/1 .I want create search form that users can search products by their specifications.for example user search laptop with RAM=2 and VGA=512 or VGA=1.
this example:
result: 1525,1535,k5,k6

### Skip the cell and the content of a DataTemplateColumn in a DataGrid

I am trying to tab through a datagrid, but at the end of the row I have a template column that is taking in a tab. I have set the datagrid cell style to not focusable and istabstop = false, but it still seems to be going into the content. Is there a property for a TemplateColumn that will have it be skipped by tabbing completely?

Thanks

### How to exclude one table from drop-and-create-tables with Ecliselink?

I use Eclipselink 2.3.2 and want to know, if there is an way to exclude a single table/entity to be excluded from ddl-generation strategy drop-and-create-tables? I need to preserve the content of this table, while all other tables should be droped and been created complete new.

The reason is that the domain model is under heavy development so there are changed all and everywhere. But one single table (containing postal codes) should be preserved, because they are needed for development, and it takes to long to insert them all at every server start.

I know one way is to use two different persistence units. But this would cause some other trouble, so this not my preferred way.

Summary: Does anybody know a way to exclude a single table from droping while all other tables get droped and been recreated at each server start with ecliselink 2.3.2 (and Glassfish 3.1.2 )?