text:
If you, like me, went with the entry level Steam Deck option with only 64 GB of internal storage, you likely realized quite soon that some games wont fit on it.

One option is to use the microSD expansion card slot. For current-gen games the throughput of only about 150 MB/s does not seem to degrade loading performance compared to a NVMe SSD.
However, given that the internal storage is upgradable, the only logical choice for keeping your PC master race status is to cram in the fastest NVME SSD inside that thing.

Specifically, you will need a one-sided SSD in the M.2 2230 for factor so it fits the space inside the Steam Deck.
I went with the KIOXIA Client-SSD BG5 512GB. Kioxia is the Toshiba spin-off for SSD drives, if you wonder about the brand. Although it is a PCIe 4.0 drive, its peak read throughput of 3.5 GB/s is within the practical limits of PCIe 3.0 of the Steam Deck.

You can follow the iFixit Guide for the steps to actually swap the SSD. Make sure to transfer the ESD shielding wrap to the new SSD.

To get Steam OS on the new drive, follow the official recovery instructions and select the “Re-image Steam Deck” script.
This will install Steam OS on the blank SSD – similar to how you would install Ubuntu from a live USB.

## Benchmarking results

Next

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, I wanted to actually compare the speed of the upgraded NVMe SSD with the one of the stock eMMC memory.
To this end I used KDiskMark – an open-source alternative to CrystalDiskMark that runs on Linux natively.

The tests were performed on SteamOS 3.3.1 using KDiskMark 2.3.0.

In short, the NVME offers roughly one order of magnitude faster throughput over the eMMC.
Whether you feel this in-game, highly depends on the given game. For older titles, even the eMMC is so fast, that you cannot read the hints on the loading-screen. However, for something like the Flight Simulator 2020 that shuffles huge assets around, it will surely be noticeable.

Finally, the peak read performance of 3.5GB/s is not reached. This might be due to the PCIe 3.0 bottleneck – I did not bother putting the drive in a PCIe 4.0 device. Still, there is a significant advantage in writing performance over the older Kioxia BG4 series, that only do 1.4 GB/s.

## Computing replaygain for your Music library

TLDR; command at the end of post

If you want a equal loudness for your Music library the go to solution and the de-facto standard is ReplayGain.
If you are using a music streaming service, the provider is typically taking care of that for you – but maybe you want to migrate towards your own streaming solution.

ReplayGain analyses your audio files and stores their deviation from the baseline loudness as a tag. A compatible audio player can then read the tag and correct the playback volume so all you tracks have the same loudness.

Of course things get messy once you look at details like what the baseline loudness should be and how to determine loudness in the first place. Therefore we set the baseline once and for all as 89db and consider even tracks of the same album individually. If you disagree, feel free to branch off reading up the details now.

The next issue is that ReplayGain was born in a time where mp3 was synonymous to digital music, hence the algorithm was first implemented as the mp3gain CLI tool. Nowadays you also need aacgain and vorbisgain to cover all your formats, which is cumbersome to automate.

The larger issue with ReplayGain is that it defines loudness of a track by its peak volume. While a sane choice in theory, in practice the music and advertising industries raced to increase the perceived loudness without raising the peak volume. As broadcasters also used peak volume normalization, one could blow your eardrum with that very special advertisement.
Therefore the EBU R 128 was proposed which at its core is RMS based, meaning it is considering the average volume of the track.

Remember that ReplayGain merely adds a correction value to the tracks? This allows us to compute that correction value based on the R128 algorithm for a better normalization, which is exactly what the r128gain tool does.
Being written in modern day, r128gain also processes all possible audio files by hooking into ffmpeg as a filter.

So, without further ado, this is the command to normalize your Music library:

# pip3 install r128gain
r128gain -p -r Music/

This will preserve "-p" the file timestamps and recursively "-r" process all files in the given directory.

## Trouble shooting

Note that if you previously used mp3gain, your files might contain non-standard lower-case replaygain_* tags, while r128gain will only write REPLAYGAIN_* tags.
To avoid confusing players with different values, you should remove the non-standard tags. This can be automated with eyeD3

eyeD3 -Q --remove-frame RGAD --preserve-file-times --user-text-frame=replaygain_track_gain: --user-text-frame=replaygain_track_peak: --user-text-frame=replaygain_album_gain: --user-text-frame=replaygain_album_peak: Music/

Refer to its documentation for the meaning of the parameters.

Header Image: “volume” by christina rutz (CC-BY-2.0)

modafinil-schweiz.site

This post will be for those of you that care about privacy – i.e. if you want that information about you is exclusively under your control.
In that context not only Google is to blame, but actually most of the cloud services we know and use today.

Still Google will serve us as a nice placeholder as it is the market-leader when it comes to providing free services in exchange for your user-profile that Google in turn uses to sell target advertising. Even if you are fine with that, Google is also infamous for killing services – which might hit the one you rely on eventually.

As the world is moving mobile-first, a prerequisite for replacing a service is that we can easily integrate the replacement with an Android device.
Some might wonder why I chose Android here, given that it is made by Google. See, the problem is not who makes a service/ device, but who controls it. And with Android the main leverage for Google is bundling its services. If you take them away, the device itself is fully under your control – in contrast to Apple/ iOS.

## Nextcloud

At the heart of our efforts will be Nextcloud. This started as an open-source alternative to Dropbox/ Google Drive, but is nowadays grown into a platform for a plethora of different services.
The main selling-point is that you can just install Nextcloud on your own machine – ensuring that your data stays private. The software being Open-Source also means that it is not under control of a single corporation – in fact Nextcloud was forked from its predecessor Owncloud after a corporation tried to put the screws on its users.

Note

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, that if you are serious about this, you will need to invest around 500€ to get a machine for hosting that is decently fail-safe. If you rather want to be cheap, you can also just use a RaspberryPi to get away with less than half of that amount. For inspiration, you can take a look on the built I use or on the list of commercial nextcloud device providers.

## Files & Photos

By using the Nextcloud Android App, you can directly replace Google Drive/ Dropbox as this is the core functionality of Nextcloud.

Additionally, the App allows you to automatically back-up your Photos/ Videos and free the local storage so you can stop using Google Photos too.

## Contacts & Calendar

Nextcloud also supports Contacts and Calendar out of the box. To integrate them with into your Android Device there is the DAVx5 app. This app will function as an additional data provider, so you can just continue using the stock Google Contacts and Calendar apps. Those will, however, stop sending any data to Google.

This is especially useful, if you run a small-business and must ensure that your customer data is private according to the CCPA/ GDPR.

## Nextcloud News

An often overlooked part of your privacy is Google News (also part of Google Now). Each time you view an article there, Google can mine your interests and political views – similar to what Facebook does. And by now you should know where these things can lead.

Another drawback here is that the Google Algorithm will create a bubble for you by only showing content coherent with your current world-view.
I still prefer to manually choose the news sources – to create that bubble myself.

To do that, one usual subscribes some Web-feeds using a Feed aggregator like the Feedly service – similar to what Google Reader used to offer, before being killed by Google.

The go-to app here is Nextcloud News combined with the Android App for a pleasant mobile usage.

## Music

Most of you are probably just stream music via Spotify/ Youtube Music, but keep in mind that these services merely rent the songs and as such they can arbitrarily disappear from your library.

Therefore, I like to have my own copy of the song. Unfortunately it is very inconvenient to juggle mp3s around for getting the music to various devices.

Google Play Music used to offer best of both worlds for me, where you could upload your own music files and manage your playlists in one place. Additionally, you could make the music available offline by pinning individual playlists on your device.
Unfortunately, that concept did not allow Google to arbitrarily inject ads into my music stream and therefore the service got killed as well.

Nextcloud Music to the rescue! This app picks up your music library via Nextcloud files and allows to stream that via the Browser or the Subsonic API.
This is where the DSub Android Player takes over. As with Play Music, you can either stream the library or pin individual songs/ playlists for offline use. Note: untick the “Authorization Basic headers” box when setting-up Nextcloud Music.

## Other

If you clicked on the links above, you probably noticed the F-Droid alternative app store for Android.
Getting your apps there ensures that you are using verified packages and open-source software. You can easily use it alongside with the Play Store. If that is too inconvenient for you, all of the above apps are also available via the Play Store.

Finally, there is the web-browser. If you do not log in with your Google Account, using Chrome is mostly safe. However, I suggest switching to Firefox. See the my original article on that topic for details. In short; the main reason is the availability of extensions. Those allow you to block ads on the mobile web too and use Youtube in the backround.

Header Image: Digital Chains by stanjourdan (CC-BY-SA-2.0)

## Mould King 13106 Forklift Review

I got myself the MouldKing 13106 Forklift, which is based on the MOC 3681 by KevinMoo and wanted to share my impressions with you.

First of all, MouldKing actually improved the set by exclusively using back technic pins instead of the blue ones like in the MOC. Also they are officially cooperating with the MOC designer – so he is likely getting some share of the sales.

The set comes with “New PowerModule 4.0″, which means it supports proportional output. If you use the new joystick controller (like I do in the video) or use the app, you can have smooth controls of the motors and not just binary 0% or 100% throttle as with the standard remote.

As you can see, I actually put on some of the stickers. Some purists never do anything like this, because they argue that after some time the stickers start peeling off and look used. This is certainly a good point if you are building a sports-car – with a Forklift however, I would argue broken stickers add to the looks.

Compared to the original MOC, Mould King removed the lights, but added a pallet similar to the one found in the Lego 42079 Forklift.

Interested in getting the set? Support this Site by using the following affiliate Link:

Generally, I prefer the Mould King manual to the original by Kevin Moo as I like renderings more than photographs. However, its nice to have the original at hand if something looks fishy. While building

, I noticed the following:

Step 34: Cable-management is almost completely skipped in the manual. I laid all cables through the opening behind the threads. This keeps them out of the way later. The fiddle through the cables of the motors, that you add at steps 52 & 55.

Step 100: The battery-box position is wrong. It will collide with the bar you added at step 96. To make it fit, just rotate the battery-box by 180°.

Also, the direction of motor A has to be reversed. Press and hold left-shoulder, up and down for 3 seconds for this.

Step 111: The arms that you added in steps 89/ 90 should be oriented upwards to hold the footstep.

Step 143: Use a black bush instead of the 2-pin-axle beam, so things look symmetrical. This is a leftover from the original MOC, which squashed the IR receiver in there.

Step 156: Attach the levers to the front console at step 173 instead of attaching them to the seat here. After all they are supposed to control the fork and not the backrest.

Step 214: I suggest using gray 2-axles at step 230 instead of the suggested whites. This way the front facing axes will be all gray. For this just use white 2-axles here. Those wont be visible at all anyway.

Step 277: When adding the fork to the lift-arm, make sure that it has as much play as possible. Otherwise the fork will get stuck when moved all the way up.

Step 278: Do not fix the threads yet. Wait until the end so you can correctly measure the lowest position of the fork (which gives you the length of the threads).

Step 286: Make sure that the 3-pin pops out towards the 8-axle. This will make joining things at step 288 much easier.

## Comparing water filters

Lets say, you want to reduce the water carbonate hardness because you got a shiny coffee machine and descaling that is a time-consuming mess.

If you dont happen to run a coffee-shop, using a water-jug is totally sufficient for this. Unfortunately, while the jug itself is quite cheap, the filters you need will cost you an arm and a leg – similar to how the printer-ink business works.

## The setup

Here, we want to look at the different filter options and compare their performance. The contenders are

As said initially, the primary goal of using these filters is to reduce the water carbonate – any other changes, like pH mythology, will not be considered.

To measure the performance in this regard, I am using a digital total dissolved solid meter – just like the one used in the Wikipedia article. To make the measurement robust against environmental variations, I am not only measuring the PPM in the filtered water, but also in the tap water before filtering. The main indicator is then the reduction factor.

Also, you are not using the filter only once, so I repeat the measuring over the course of 37 days. Why 37? Well

onlinemedikament.online

, most filters are specified for 30 days of usage – but I want to see how much cushion we got there.

So – without further ado – the results:

## Results

As motivated above, the difference in absolute PPM can be explained by environmental variation – after all the measurements took place over the course of more than 3 months.

However, we see that the pricing difference is indeed reflected by filtering performance. By paying ~20% more, you get a ~30% higher PPM reduction.

The only thing missing, is the time-series to see beyond 30 days:

As you can see, the filtering performance is continuously declining after a peak at about 10-15 days of use.

And for completeness, the absolute PPM values:

## How to generate random points on a sphere

This question often pops up, when you need a random direction vector to place things in 3D or you want to do a particle simulation.

We recall that a 3D unit-sphere (and hence a direction) is parametrized only by two variables; elevation \theta \in [0; \pi] and azimuth \varphi \in [0; 2\,\pi] which can be converted to Cartesian coordinates as

\begin{aligned} x &= \sin\theta \, \cos\varphi \\ y &= \sin\theta \, \sin\varphi \\ z &= \cos\theta \end{aligned}

If one takes the easy way and uniformly samples this parametrization in numpy like

phi = np.random.rand() * 2 * np.pi
theta = np.random.rand() * np.pi

One (i.e. you as you are reading this) ends with something like this:

While the 2D surface of polar coordinates uniformly sampled (left)

, we observe a bias of sampling density towards the poles when projecting to the Cartesian coordinates (right).
The issue is that the cos mapping of the elevation has an uneven step size in Cartesian space, as you can easily verify: cos^{'}(x) = sin(x).

The solution is to simply sample the elevation in the Cartesian space instead of the spherical space – i.e. sampling z \in [-1; 1]. From that we can get back to our elevation as \theta = \arccos z:

z = 1 - np.random.rand() * 2 # convert rand() range 0..1 to -1..1
theta = np.arccos(z)

As desired, this compensates the spherical coordinates such that we end up with uniform sampling in the Cartesian space:

## Custom opening angle

If you want to further restrict the opening angle instead of sampling the full sphere you can also easily extend the above. Here, you must re-map the cos values from [1; -1] to [0; 2] as

cart_range = -np.cos(angle) + 1 # maximal range in cartesian coords
z = 1 - np.random.rand() * cart_range
theta = np.arccos(z)

## Optimized computation

If you do not actually need the parameters \theta, \varphi, you can spare some trigonometric functions by using \sin \theta = \sqrt { 1 - z^2} as

\begin{aligned} x &= \sqrt { 1 - z^2} \, \cos\varphi \\ y &= \sqrt { 1 - z^2} \, \sin\varphi \end{aligned}

## Self-built NAS for Nextcloud hosting

With Google cutting its unlimited storage and ending the Play Music service, I decided to use my own Nextcloud more seriously.
In part because Google forced all its competitors out of the market, but mostly because I want to be independent of any cloudy services.

The main drawback of my existing Nextcloud setup, that I have written about here, was missing redundancy; the nice thing about putting your stuff in the cloud is that you do not notice if one of the storage devices fails – Google will take care of providing you with a backup copy of your data.

Unfortunately, the Intel NUC based build I used, while offering great power efficiency did not support adding a second HDD to create a fail-safe RAID1 setup. Therefore I had to upgrade.

As I still wanted to keep things power-efficient in a small form-factor, my choice fell on the ASRock DeskMini series. Here, I went with the AMD Variant (A300) in order to avoid paying the toll of spectre mitigations with Intel (resulting in just 80% of baseline performance).

The photos above show you the size difference, which is considerable – yet necessary to cram two 2.5″ SATA drives next to each other.
Here, keep in mind that while the NUC devices have their CPU soldered on, we are getting the standardized STX form-factor with the A300, which means you can replace and upgrade the mainboard and the CPU as you wish, while with a NUC you are basically stuck with what you bought initially.

The full config of the build is as follows and totals at about 270€

• ASRock DeskMini A300
• AMD Athlon 3000G
• 8GB Crucial DDR4-2666 RAM
• WD Red SA500 NAS 500GB
• Crucial MX500 500GB

Note, that I deliberately chose SSDs from different vendors to reduce the risk of simultaneous failure.
Also, while the 3000G is not the fastest AMD CPU, it is sufficient to host nextcloud and is still a nice upgrade from the Intel Celeron I used previously.
Furthermore, its 35W TDP nicely fits the constrained cooling options. Note, that you can limit for Ryzen 3/5 CPUs to 35W in the BIOS as well, so there is not need to get their GE variants.
However, for a private server you probably do not need that CPU power anyway, so just go with the Athlon 3000G for half the price.

Unfortunately, the A300 system is not designed for passive cooling and comes with a quite annoying CPU fan. To me the fan coming with the Athlon 3000G was less annoying, so I used that instead.
Anyway, you should set the fan RPM to 0% below 50° C in the BIOS, which results in 800 RPM and is unhearable while keeping the CPU reasonably cool.

## Power Consumption

As the machine will run 24/7, power consumption is an important factor.

The 35W TDP gives us a upper limit of what the system will consume on persistent load – however the more interesting measure is the idle consuption as thats the state the system will be most of the time.

As I already tried some builds with different architectures

, we have some interesting values to compare to, putting the A300 build in perspective

While you can obviously push the system towards 35W by with multiple simultaneous users, the 7.3 W idle consumption is quite nice.
Keep in mind, that the A300 was measured with two SATA drives operating as RAID1. If you only use one you can subtract 1W – at which point it is only 1.5 W away from the considerably weaker NUC system.

You might now wonder, whether the load or the idle measure is closer to the typical consumption. For this I measured the consumption for 30 days, which totaled at 5.23 kWh – or 7.2 Watts.

Currently, the average price for 1 kWh is 0.32€, so the running the server costs about 1.67€/ Month. For comparison, Google One with 200 GB will set you off 2.99 €/ Month.

## Power optimizations

To reach that 7.3 W idle, you need to tune some settings though. The most important one and luckily the easiest to fix is using a recent kernel.
If you are on Ubuntu 18.04, update to 20.04 or install the hwe kernel (5.4.0) – it saves you 4 Watts (11.3 to 7.3).

For saving about 0.5 watts, you can downgrade the network interface from 1Gbit to 100Mbit by executing

ethtool -s enp2s0 speed 100 duplex full autoneg on

Additionally, you can use Intels powertop to tune your system settings for power saving as

powertop --auto-tune

## Mi Band 5 Review / Mi Band Evolution

Xiaomi has recently released the new Mi Band 5. Since I have owned the each band starting with the Mi Band 2, I think it is time to look back and see where the Mi Band has gone in the recent years.

Actually, the Mi Band story started ahead of the Apple Watch in 2014 with the Mi Band 1, which was a pure fitness-tracking device without a display and even without a heart-beat sensor. This made the device not very appealing to me – even thought it already offered sleep monitoring.

It also already had that interchangeable wrist-bands that allow you to customize the look to your liking. The Mi Band 2 you see in the images uses a custom steel wrist-band as the original one broke after some years of usage.

Below you see a comparison of the Mi Bands, regarding the features that are most significant from my perspective

Mi Band 2

• Released 2016
• Clock
• Heartbeat

Mi Band 3

• Released 2018
• Clock
• Heartbeat
• Timer
• Weather
• Workouts

Mi Band 4

• Released 2019
• Clock
• Heartbeat
• Timer
• Weather
• Workouts
• Music control

Mi Band 5

• Released 2020
• Clock
• Heartbeat
• Timer
• Weather
• Workouts
• Music control
• Cam shutter

The first thing to note is probably that Xiaomi accelerated the release cycle from 2 years between the Bands 1, 2 and 3 to 1 year between Band 4 and 5. We will come back to this when talking about the Mi Band 5.

## Screen legibility comparison

Lets start the comparison with the screen, which is the most obvious part and the one you will probably interact with the most.

Here, the most significant property is neither size nor resolution, but rather legibility in sunlight. For comparison, I set up a little benchmark as follows:

• set the Bands to maximal brightness (as applicable)
• legibility in direct sunlight on a bright sunny day as a worst-case
• legibility in shade/ with overcast condition as a more common scenario

You can find the results below. Also see the banner image for how the screens look indoors.

First I should note that the camera does not do justice to the Mi Band 2 & 3 as their displays are scanline-based and the fast shutter can not capture the whole screen being lit at once. Therefore you only see the top part of the Mi Band 2 and the right part of the Mi Band 3 on the overcast picture.

Nevertheless, one actually cannot read the Mi Band 2 in direct sunlight and only can barely read it in the shade. The other Bands are well readable in the shade. However, I would say that only the MiBand 5 is well readable in direct sunlight.

Next, we will look at how the information is presented. The screen size continuously increased from 0.78″ on the Mi Band 3 to 0.95″ on the Mi Band 4 (+22%) to 1.1″ on the Mi Band 5 (+16%).
As you can read the time on all of them

, we will look at an app to find out whether it makes any difference in practice. Here, I picked the weather app as it is probably useful to the majority of the readers.

Looking at the Mi Band 4, it did not really take advantage of the larger screen-estate and shows virtually the same information as the Mi Band 3 – only adding the location info.
The Mi Band 5 on the other hand uses the extra space to show the rain probability. It generally displays more info like the wind strength and the current UV level – however you have scroll down for them.
The Mi Band 2 does not support weather and is thus turned off.

## Apps/ on band Screens

Lets also briefly look at the other apps. The images were captured on the Mi Band 5 – however unless otherwise stated the look exactly the same on the Mi Band 4.

## Charging

The Mi Band 5 is the first band, with a magnetically attachable charger – hence you do not have to take the band out for charging. This convenience comes at the price of a reduced battery-life from about 20 days with the Mi Band 4 to only 14 days with the Mi Band 5.

As for compatibility, you can charge the Mi Band 2 with the Mi Band 3 charger – the other way round is not possible as the Mi Band 3 is too large for the older charger.

Even though, the Mi Band 4 & 5 have their charging pins at the same location, the chargers are not compatible as the Mi Band 4 lacks the magnetic hold and the Mi Band 5 is too large for the old charger.

## The Mi-Fit app

For the Mi Band the accompanying app is quite important as it is the only way to view your sleep data and to monitor your weekly/ monthly stats.

First, lets take a look how you can customize the different Bands from the app. Here, we should note that all bands are still supported by the app.

With the Mi Band, there is only a predefined set of screens/ apps out of which you can pick the ones you want. This is probably the largest difference to a real smart-watch, where you can install additional apps from a store.

With the Mi Band 2, the whole set fits on half a screen and you can only enable/ disable the items.
With the other Bands you can additionally re-order the items, which is quite useful as it allows to choose which item appears first when you swipe up or down on the home screen.

On the Mi Band 5, you can additionally configure which app appears when you swipe left/ and right. This is hard-coded to Music Control (and Ali Pay on the CN version) with the Mi Band 4.

So the basic things work. Lets look at some peculiarities of Mi Fit next.

First you see the workout view for outdoor running, which displays some useful stats like your pace per km and the continuously measured heart-beat rate over time.

What you do not immediately see is that the app only counted ~7.3 km, while my running distance is actually 10 km, which I have verified on google-maps.
One might now think that this is due to imprecise measuring of the band – however on the activity overview, where the daily steps are counted, the running activity is correctly accounted as 10.1 km – which is impressively accurate, given that it only counted the steps.

So the error is only present in the workout app, which is still quite annoying as it also provides the live view during a run.

If someone from Xiaomi is reading this: the error factor of ~0.73 is suspiciously close to the km to miles conversion factor of 0.625.
The error is present with both the Mi Band 4 and Mi Band 5, so I guess it is actually in the App, where I already reported it several times.
If you want happy customers, you better fix this. Many other reviews actually blame this on the band!

Addendum: with the firmware update to v1.0.1.32, the band now measures ~9km which reduces the error factor to 0.9. We are getting there.

So having talked about the bad, lets continue with the ugly. The second screenshot shows you an in-app ad for some obscure Xiaomi product on the home-screen.
These do not show up too often and currently only advertise their own products. However, this is definitely the wrong path you are on.

Ultimately, this leaves me with mixed feelings about Mi Fit. In the Mi Band 2 days it started as a slim and functional app. However, at some point they decided to re-write it with the cards-look and animations. This rewrite moved core views one level down in the menu hierarchy and the added animations actually make the app feel sluggish.

Now, with each Band generation new features appear and are integrated in some sub-menu of the app.
For instance, you get weather-alerts nowadays. However, they are not controlled in the general Band notification settings, but rather in the weather menu.
Therefore, I doubt I would discover them as easily if I would not have watched the app grow.

The good news is that due to the popularity of the Mi Band, there are several alternative apps to try, which I probably will do next.

## Mi Band history

In the following, I give a quick outline of how the Mi Band evolved. If you only came here for the Mi Band 5 review, skip forward to the Mi Band 4 section.

The Mi Band 2 was released 2016, about a year after the first Apple Watch launched, which brought the wearable category to the mainstream.
At a price of less then 20€ the Mi Band offered most interesting wearable features to me, like heart-beat measurement, sleep monitoring, forwarding of smartphone notifications and ultimately, simply being a wristwatch.

Also it was an ideal way to try this new wearable thing without spending 350€, that Apple called out.

To my surprise the step-based distance estimation was already accurate back then – except for the actual workout mode, that is – as explained in the Mi Fit section.

### Mi Band 3

The larger and brighter screen is the obvious advance of the Mi Band 3. However, the significant part is that it also became a touch-screen – whereas the Mi Band 2 only had the single touch-button. This allowed you swiping forth and back of the screens instead of just cycling through them and it also made virtual buttons possible. These are necessary for starting the stopwatch and timer, which are probably the most important additions for me with the Mi Band 3.

You could also start a selection workouts directly from the watch, instead of going though the app. However, this only included a treadmill mode, while I am interested in outdoor running – so I continued using the activity view for that.

More importantly, it added the weather app. If find this to be surprisingly useful. As with the time – even though you find the same info on your phone – having it at hand is better.

### Mi Band 4

Again, the colored screen is the most obvious advance. It does not improve usability in any way though. It displays the same data as the monochrome screen of the Mi Band 3, which is probably more power-efficient. It adds a lot of bling though and is brighter and thus better legible in sunlight.

Speaking of bling, you can install third-party watch-faces now and there is a heap of faces to chose from. Take a look here to get an impression.

Turning to something useful, the touch sensor was noticeably improved. With the Mi Band 3 your swipes were sometimes confused with taps, which does not happen with the Mi Band 4 anymore.

The workout app, now finally included outdoor running, which is still broken though (see Mi App section). This makes the music control app the most important addition for me. At least on android, it works with any music player and allows skipping forward/ back and adjusting volume.
This is quite useful when you play music from your phone at a party or for controlling your Bluetooth headphones.

One can use the same wrist-bands as for the Mi Band 3. This made upgrading for me back then a no-brainer, but is also a strong reason to choose the Mi Band v4 over v5, today.

### Mi Band 5

This time, there are no obvious advances and the update is rather evolutionary. It does not mean it is insignificant though as it improves the usability on many levels. If you are new to the Mi Bands, you should pick this one.

The most important one is probably the new magnetic charger. Previously you had to take the “watch” out of the wrist-band to charge, whereas you can simply attach the magnetic charger now.

Next, the screen is slightly brighter which makes a difference in direct sunlight though (see screen comparison section) and also boasts more information.

Finally, the software was also noticeably improved. The band displays generally became more configurable. E.g. the custom left/ right swipes which now give you 4 quick access screens instead of 2. Then, the built-in watch-faces now allow customizing the additional info they display. And it continues with the small things like the configurable alerts in the workouts (although the workout app itself still needs to be fixed).
Also, the selection of predefined watch-faces is vastly better then with the Mi Band 4. On the latter you have a hard time finding a watch-face that is simple and does not feature some animated comic figure screaming at you.
These changes could be provided as an update to the Mi Band 4 as well, but are – at the time of writing – exclusive to the Mi Band 5.

## Disclaimer

The Mi Band 5 was provided to me free of charge by banggood.com. So if you liked this review and want to support me consider buying using the following affiliate links:

## Meepo Mini 2 vs. Archos SK8

Having never skateboarded before, I saw the Archos SK8 electric skateboard for about 80€ at a sale and thought why not give it a try. This got me into this whole electric skateboarding thing.

Now that I have some more time at home during the summer, I upgraded to the Meepo Mini 2 and after having driven with it more than 100km, I thought I write down my experiences with the two boards and why I should have gotten the Meepo board from the start.

## The competitors

The Meepo Mini 2 and the Archos SK8 are not really competing here, which should be clear looking at their price difference. But for completeness, also take a look at the specs of these two boards:

Actually, you can swap the Archos SK8 by any of the unbranded “cheap” Chinese boards that share the same design as the ones sold by Oppikle and Hiriyt.

Here, you might wonder how many Watts you actually need. For this I direct you to the Wikpedia article on bicycle performance that contains some sample calculations (and the formulae) which should roughly hold for electric skateboards as well.

## Similarities

Before we dig into the differences, lets first note the similarities aka. the choices I made when picking these specific boards in the first place:

First, both boards are hub-motor driven. I made this choice on purpose, as electric skateboards are not road-legal where I live and hub motors are barely noticeable to the non-practiced eye. This reduces my risk of getting fined for riding one.
However, I would probably generally recommend hub-motors over belt-driven motors nowadays as they require less maintenance (no moving parts), while offering a larger range and allowing pushing the board (belt driven block due to the gear ratio). The latter is especially nice, when you have run out of battery or if you do not want to draw any attention.
When electric skateboards were first introduced by boosted, hub-motors were vastly inferior power-wise but that has changed now.

Next, both boards are of so-called “cruiser-style”. This is a size in between a regular skateboard and a long-board. They share a stiff deck and a kicktail with the former, while the use the wheels of the latter.
At this point I should note that I mainly use the boards for leisure instead of a daily commute. This means that I value versatility of the board over comfort of ride.
Here, having a kicktail is a must and rules out long-boards. It allows doing sharp turn, “wheelies” and you are more agile with the short board.
However, you do notice the quality of the pavement very clearly in your feet and being out of the skating age my ankle did hurt the first couple of rides before it got used to it.
So if you want to commute large distances, you should probably get a long-board with a flexi-deck that can cushion away most of the bumps.

## Differences

Both boards are of similar length, however the Meepo Mini 2 is considerable wider and heavier. It also has a larger wheel-base.

This results in a better grip and you also feel much more stable on the board. Flipping the board around, you see that the SK8 only uses a single-hub motor while the Mini 2 has two and each of them offers more than 3x the power.

If you do not expect the power or if you enable the pro-mode without being one, the Mini 2 can easily throw you off the board when accelerating or breaking. You can tame it though by using the beginner riding mode if you need to learn how to skate first. You can set the modes for acceleration and breaking separately and I would recommend always using at least the pro mode for breaking and learning to deal with it. In case of an emergency you want to be able to stop in time.

Turning to the SK8, the acceleration is.. meh and so are the breaks – in both of the two riding-modes. The difference between them is merely that the top speed is capped at 10km/h in the low-mode.
But I must say that if you are a beginner this is sufficent; if you do not know how to ride being able to get going and to break are your two primary concerns and the SK8 does deliver here. The main drawback of the Archos SK8 is its tiny battery.

### Aside: Li-Ion batteries

At this point we should probably briefly discuss Li-Ion battery technology. Mainly, the following two properties:

• As you discharge the battery its Voltage drops, which is related to power (the Watts number) as P = V \cdot I, where I is the current in amps.
So the more you discharge the battery, the fewer Watts you get out of your motors.
• A full discharge (down to 0%) of the battery severely reduces its live-span. For maximal durability

bloodpressureheartmeds.site

, you should always keep its charge between 40%-80%. Typically, the displayed range is clipped by the controller to help here.

So where does this leave us with the SK8? I did about 7 rides, fully-discharging the board (you do not want to stop after 10min, right?). And now the second riding-mode is essentially gone: when I try to accelerate the motors draw so much current, that the voltage drops below a critical level and the board turns off. Depending on what state the controller was in, I have to pair the remote again afterwards.
But it also shows in the first mode: while the board initially could get me up a slight slope, it now immediately starts beeping due to critical voltage – again the motors need more voltage then the already worn down battery can give.

### Remotes & charging indicators

Having covered the drive train, lets turn to the remotes. Both Archos and Meepo use a similar pistol-grip like design, where you control the motors with the thumb switch.

As one would expect, the Meepo remote is more sophisticated and offers detailed telemetry data on a nicely readable LCD display. There you find your current speed, drive mode and board charging level as well as the max. speed of the current ride.

On the Archos remote you only find 4 LEDs. Those are used quite well though: when you turn on the remote, they show the remote charging level. As soon as the board is connected, they indicate the board charging level, which is actually the most important information you need while riding.

Similarly to the remotes, there are only 4 LEDs on the Archos Battery for the charging level, while you find a numeric LED-display on the Meepo board.

An actually noticeable feature on the Meepo Mini 2 is push-to-start; that is, you only have to push the board to turn it on – no need to bend down for flipping a switch.

### Verdict

So why do I say you should go straight with the Meepo Mini 2 even as a beginner? On paper the Archos SK8 has everything it takes to be a nice beginner board.
It is really the battery that kills it. With only 5-10 rides it is simply not worth the money, no matter how cheap it is.
Looking at the price difference between the Meepo Mini 2 and the ER version that solely differ in the battery, you grasp that the battery is the crucial part in an electric skateboard. And the Archos SK8 is cheap, precisely because of the bad battery.

With the Meepo Mini 2 on the other hand you get a board that can “grow with you”: as you get more confident you can bump up the riding mode to get more power. Even if you decide that skateboarding is not for you, you can sell the Mini 2 as it will retain lots of its value – in contrast to just producing electric waste with the Archos SK8.

## Riding the Meepo Mini 2

The Meepo Mini 2 is specified to go up to 46 km/h. Whether you can go that fast depends on your weight, the wind and the slope (see the Wikipedia link, mentioned above). In case you are fat and/ or there are lots of slopes where you live, you might also consider the ER version of the Mini 2, which comes with doubled battery capacity. As mentioned above this not only means that you can get further, but also that you have more power in the mid-range.

### How fast can you go?

Having only previous experience on a Snowboard, I am a rather cautious rider. So far my max. speed (according to the remote) was 30 km/ h which I did uphill – in hope that stopping is easier that way.
Going downhill (only using the motors for breaking), I feel comfortable until around 22 km/ h.
I typically ride for about 30-45 min and the lowest the battery got was 40%, which means it should last for quite some time.
Note, that I do not go straight uphill for 30min and that I usually push to get rolling, as this is where most energy is used.

### A suitable helmet

When lifting the board, the remote showed that the ESC only limits the speed at 50 km/h. When riding a skateboard at anything above 10 km/h without a cushion-zone and no nothing, I would highly recommend you to at least wear a helmet.
However, you should consider that a “normal” skate helmet is only specified (EN1078) up to 19.5 km/h impact speed – if you ride faster it does not guarantee protection.

Fortunately, one does not have to resort to heavy motorcycle helmets (ECE2205) as there is a specification (ASTM F1952) for downhill bike helmets, which was designed with speed in mind. It is specified for an impact speed of 22.3 km/h and typically the helmets provide full-face protection.
Recently, even variants for downhill longboarding started to pop-up, which should be even a better fit style-wise.

Addendum: replaced NTA8776 by ASTM F1952 in the last paragraph

## Lecture on Augmented Reality

Due to the current circumstances, I had to record the lectures on augmented reality, which I am typically holding live. This was much more work than anticipated..
On the other hand, this means that I can make them available via Youtube now.

So, if you ever wanted to learn about the basic algorithms behind Augmented Reality, now is your chance.

The lecture is structured in two parts

• Camera Calibration, and
• Object Pose Estimation.


text:
# How do you solve the following system?: x +3y =-2 , -7x +y = -9

Mar 25, 2018

Here,$x + 3 y = - 2$
$\Rightarrow x = - 3 y - 2$ ----eqn 1
Substitute this value of x in $- 7 x + y = - 9$
We get $- 7 \left(- 3 y - 2\right) + y = - 9$
$\Rightarrow 21 y + 14 + y = - 9$
$\Rightarrow 22 y = - 9 - 14$
$\Rightarrow y = - \frac{23}{22}$ ----eqn 2
Now, substitute this value in $x + 3 y = - 2$
$\Rightarrow x + 3 \times - \frac{23}{22} = - 2$
$\Rightarrow x - \frac{69}{22} = - 2$
$\Rightarrow x = \frac{69}{22} - 2$
$\Rightarrow x = \frac{25}{22}$

So, $\left(x , y\right) = \left(\frac{25}{22} , - \frac{23}{22}\right)$

Hope this helps :)

format: plain


text:
Defining \$\mathbb{Z}\$ in \$\mathbb{Q}\$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T07:48:07Z http://mathoverflow.net/feeds/question/86861 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86861/defining-mathbbz-in-mathbbq Defining \$\mathbb{Z}\$ in \$\mathbb{Q}\$ Math-player 2012-01-27T21:17:05Z 2012-01-28T08:24:04Z
It was proved by Poonen that \$\mathbb{Z}\$ is definable in \$\mathbb{Q}\$ using \$\forall \exists\$ formula. Koenigsmann has shown that \$\mathbb{Z}\$ is in fact definable by universal formula. What is the simplest geometric interpretation of these results?

EDIT: It is important to note, as Joel says, that the first result in this direction was that of Julia Robinson in 1948. The references for the latest results are: http://arxiv.org/abs/1011.3424 (Koenigsmann's paper), and http://www-math.mit.edu/~poonen/papers/ae.pdf (Poonen's paper).

Thank you


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# P values seem to be the wrong way around

Say the null hypothesis is that two samples emanate from two distributions with either equal medians or equal variances. And p values are the probability that a value or more extreme comes from the original distribution given the null hypothesis holds. Therefore, why do correlations with low p-values mean that they are strong? It seems that holds if the null hypothesis is that they do NOT come from similar distributions.

Can you please put me straight?

Regards,

The p value is the probability of making a certain observation - or more extreme - due to chance, given that the observation is drawn from the original distribution.

Normally (haha) you would expect observations to be pretty close to the distribution's arithmetic mean. If an observation is far from the mean it can be because of two things: a) the observation occurred due to chance - this has to be possible; otherwise the distribution's probability density function would be 0 away from the mean. Or b) the observation is different because it is generated by a different distribution with a mean that differs from the original one. So a small p value means that an observation that far from the original distribution's mean is super unlikely, if it was generated by that distribution. Totally possible but really unlikely (i.e. with probability p).

Now there is this convention in one branch of the statistics community to consider p values under a certain threshold to be evidence that the observation is from a distribution different from the original one. That threshold is called "alpha" and is set prior to an experiment. So if alpha e.g. 0.05 and p is below that, we think that this is evidence that the observation is from a different distribution.

That's the story for p values for means. When it comes to correlations, the strength of the correlation (which is the observation in this case) is given by a different variable - e.g. r. Having a high r means the correlation is strong. But even high values of r can have different values of p - high ones and low ones. With a low p value we think that it is unlikely to get that kind of r due to chance. A high p value can be sign for having a great amount of noise in the data so that the correlation itself is high but the probability that this is due to chance is also high. You can also have very low values of r with high certainty (low values of p). So the strength of correlations is not measured by p.

• Nicely explained. I see, so if I had an experiment and a numerical comparison then my correlation can only be really judged by r and not p? So if an article reported that reduction in X was correlated to reduction in Y (p<0.001), the p value doesn't mean squat? And hence a value for r should be reported instead? Or am I still misunderstanding the concept? – HCAI Feb 10 '12 at 13:25
• No. The $p$ value is not the probability that a given observation or more extreme is from the original distribution. The $p$ value is the probability of a given observation or more extreme from the original distribution. – Henry Feb 10 '12 at 15:04
• The $p$ value is a measure of how extreme the observation is, given the assumption that it comes from a particular distribution. It is not a measure of the probabilities that the observation comes from that distribution or a different distribution. Work out the $p$ value for seeing 115 heads from 200 coin flips of an assumed fair coin (about 0.04) and then note from Wikipedia that since the probability of this exact observation (about 0.006) is higher than 1/201, it does not provide additional evidence of the coin being biased. – Henry Feb 10 '12 at 15:38
• I'm curious (and I truly don't know the answer): if we all examined our lives in research/statistics before and after we "saw the light" (one hopes) about p-values, would many of us find that the latter period was notably more productive as a result? – rolando2 Feb 11 '12 at 1:31
• @user1134241 The p value is not interpreted in a way like "low is good, great is bad". A low p means that it is unlikely to get an observation as the one you made or even more extreme (i.e. deviant from a given value) purely by chance. Period. If you compare your prediction and an observation, a low p value means that "it's unlikely to get this difference purely by chance - so maybe there is a systematic effect going on". A high p means, yeah, this (small) difference is likely due to chance, so don't bother and treat the two observations as resulting from the same distribution. – xmjx Mar 14 '12 at 12:03


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# Type of aerial

Status
Not open for further replies.

#### Gregory

##### Member
I have 2 wip aerial's how do I identify weather they are HF, 27 MHz , VHF UHF
How do I bench test the aerial's to see what frequency range the aerials opperate at

#### JimB

##### Super Moderator
The length of an antenna is a clue to its operating frequency.
However, there are many variables, is the antenna helically wound, does it have a loading/matching coil, etc.

A photo of the antennas would be a help in identifying.

As for testing, at the risk of appearing off hand, if you have to ask, you almost certainly dont have sufficient knowledge or equipment to do it.

JimB

#### Papabravo

##### Well-Known Member
You can use an antenna analyzer to measure return loss as a function of frequency.

##### Well-Known Member
JimB is right about the bench testing problem. For some background, here are some ways to do this.

An engineer would use an instrument called a Vector Network Analyzer. This is an instrument that sends some RF energy towards the antenna, and then measures exactly what voltage and current is reflected back. It then computes some useful things like real and imaginary parts of the impedance, the VSWR and/or the return loss. The frequency where the VSWR is lowest is often the frequency at which the antenna is designed to operate.

There are so-called "poor man's" vector network analyzers, available out there. They are often called "Antenna Analyzer" and can be relatively inexpensive as long as you only want to measure up to 300MHz or so. You can even make your own, but it is an advanced project.

One old-fashioned way to measure the frequency of an antenna is to use a "noise bridge" (google for more details). In fact, some antenna analyzers use the noise bridge principle instead of the VNA method.

Another method that I've used many years ago was to get my hands on a "gate dip meter". This is an oscillator with a calibrated frequency dial, and which allows some of the oscillator energy to radiate. A detector is included inside the meter which measures the oscillator energy. When you hold such a meter near a coil or antenna that has a strong resonance, that coil or antenna will suck power from the meter and cause the meter needle to "dip" (hence the name). In use, you hold it steady near a small coil attached to the antenna feedline, then vary the oscillator dial until the meter dips. Very handy little gadget.

In some cases, it is possible to simply attach the antenna to a receiver that tunes over a very wide range (like scanners do) and operate the receiver in AM or SSB mode across that range and just note where it tends to receive the most noise off the air. This often indicates the frequency at which the antenna is being effective.

As Jim mentions, someone with experience in antenna design can often guess the frequency of the antenna by inspecting it for key things like:
length of elements
feed location and method
relationship of one element to another
type of connector used

but of course the easiest way is to find a model number printed on the antenna and then just look it up.

good luck

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#### Papabravo

##### Well-Known Member
Ron forgot to mention that a Vector Network Analyzer might cost shomewhere north of $100,000 USD. The poor man's Antenna Analyzer might set you back about$350.00 They are very different animals. I'm guessing the Gate Dip Meter is the modern semiconductor version of the old Grid Dip Meter that was implemented with a vacuum tube oscillator. Hamfests are great places to find esoteric test equipment.

Measure the length of the whip antenna in meters and multiply by four. Then use the formula
Code:
f requency(MHz) = 300 / wavelength(meters)
as a first approximation assuming that the whip antenna is designed to be a 1/4 wave vertical antenna.

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#### MikeMl

##### Well-Known Member
...
Measure the length of the whip antenna in meters and multiply by four. Then use the formula
Code:
f requency(MHz) = 300 / wavelength(meters)
as a first approximation assuming that the whip antenna is designed to be a 1/4 wave vertical antenna.
This won't work if there is an obvious helical-wound wire under heatshrink on a fiberglas whip. Most CB and some 4-30Mhz Ham antennas are made that way. They are much shorter than a quarter wavelength.

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#### Papabravo

##### Well-Known Member
This won't work if there is an obvious helical-wound wire under heatshrink on a fiberglas whip. Most CB and some 4-30Mhz Ham antennas are made that way. They are much shorter than a quarter wavelength.
True, but the OP did not mention those things. We can assume anything we want, but that doesn't mean it has any relevance whatsoever. He said wip[sic.] antennas with no mention of loading colis or helical wound wires -- sheesh

The only other thing he mentioned was bench testing and I think he got that answer.

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#### flat5

##### Member
Grid dip meters were not expensive. Lots if not most hams had them 40-50 years ago. Heath, Eico, Knight had kits. I built an Eico. I was maybe 16. I certainly did not have much money.

#### Papabravo

##### Well-Known Member
Maybe he's thinking of a Bird Wattmeter with a complete set of slugs. Its a different animal to be sure, but it has always been pretty expensive. Not VNA expensive, just ordinary expensive

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#### MikeMl

##### Well-Known Member
True, but the OP did not mention those things. We can assume anything we want, but that doesn't mean it has any relevance whatsoever. He said wip[sic.] antennas with no mention of loading colis or helical wound wires -- sheesh

The only other thing he mentioned was bench testing and I think he got that answer.
Sheesh yourself! The OP is not the only person who reads these posts. Did you ever think that perhaps what I posted might be useful to the 50 or so other readers of this thread!

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#### Papabravo

##### Well-Known Member
Sheesh yourself! The OP is not the only person who reads these posts. Did you ever think that perhaps what I posted might be useful to the 50 or so other readers of this thread!
Except what you posted was a qualitative description of things that might be. No mention was made of how to analyze them if they were there. I'll let the other 50 readers weigh in on the usefulness of your post.

#### Gregory

##### Member
I have photo's of the three aerial's The longest aerial is 2.360 ,
the middle one is 1.750 and the solid wire is 1.310 Meters long an I have photo's of the base area of the aerial's. I have placed a sketch of the long aerial to show what is at the base
I hope this helps.

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#### MikeMl

##### Well-Known Member
Except what you posted was a qualitative description of things that might be. No mention was made of how to analyze them if they were there. I'll let the other 50 readers weigh in on the usefulness of your post.
Hey PapaBravo.
I'll just let the pictures speak for themselves. I'm not saying a word.

MikeML

#### Papabravo

##### Well-Known Member
They certainly do. They should have been included in the original post, which would have eliminated any doubt. The only way to draw any conclusions about their performance is to put them on an analyzer, unless RR can pull some magic out of one of his simulators.

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##### Well-Known Member
I have photo's of the three aerial's The longest aerial is 2.360 ,
the middle one is 1.750 and the solid wire is 1.310 Meters long an I have photo's of the base area of the aerial's. I have placed a sketch of the long aerial to show what is at the base
I hope this helps.
In my opinion these are antennas designed for use on a vehicle and for frequencies somewhere in the range of 2 to 30 MHz. Amateur HF comes to mind, and perhaps CB 27Mhz. It is difficult to say exactly what frequency bands though. In general, the longer the antenna and the greater the number of turns of wire, the lower the frequency. That long one with the many many turns of wire seems to be for the lowest frequency (perhaps 14 or 7 MHz?). When we see the coil pitch change dramatically in a short distance, this might indicate a design for multiple bands.

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#### JimB

##### Super Moderator
OK, here goes with some inspired guess work!

All the antennas are for 27Mhz CB.
They were all made be "GME", (the black one certainly was).
The black one was intended to mount on a road vehicle.
The white ones were intended to mount on boats.

The white ones are loaded to present a high impedance feed point to minimise the loss due to being fitted to a fibreglass boat.
As a general rule a monopole antenna needs a conductive ground plane to work against, in a metal bodied vehicle this is easy, the bodywork is idea. A fibreglass boat? difficult unless the boatbuiler made special provision by incorporating a conductive mesh or whatever when he built it.

The longer white antenna has a built-in matching circuit to provide a 50ohm feed to the radio. This antenna looks fit for the scrap bin!

The shorter white antenna probably has the matching unit in the base and is useless without it.

To run a meaningfull test on any of these antennas would require the mounting/matching base, suitably mounted on something representative of the normal working location.
As for the test equipment to use, an antenna analyser would be favourite, a cheaper solution would be a 27Mhz CB radio and a VSWR meter.

JimB

#### Gregory

##### Member
Thank you for your explanation on this subject as the disciption is very informative.
Can you tell me what is a good VHF aerial for a fiberglass boat.
Or can I modify one of the antenna"s if so where can I get the information on how to modify the aerial as this would be good experience. Which aerial would I use.

#### blueroomelectronics

##### Well-Known Member
What does the aerial connect to? TV, radio?

#### Gregory

##### Member
The aerial connects to a UNIDEN MC535 VHF Marine Radio
Transmit Frequency Range 156 to 158MHz
Reciver Frequency 156 to 16 MHz
1W / 25W
The aerial will connect to a fiberglass boat.

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text:
Article Contents
Article Contents

# Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity $\bar u^2$

• We prove the local well-posedness of a 1-D quadratic nonlinear Schrödinger equation

$iu_t+u_{x x}=\bar u^2$

in $H^s(\mathbb R)$ for $s\ge -1$ and ill-posedness below $H^{-1}$. The same result for another quadratic nonlinearity $u^2$ was given by I. Bejenaru and T. Tao, Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation, J. Funct. Anal. 233 (2006), but the function space of solutions depended heavily on the special property of the nonlinearity $u^2$. We construct the solution space suitable for the nonlinearity $\bar u^2$.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35G25, 46E35.

 Citation:


text:
# The wavelength of the Balmer series lies in the

1. Ultraviolet Region
2. Infrared Region
3. Far Infrared Region
4. Visible region

Option 4 : Visible region

## Detailed Solution

CONCEPT:

• Hydrogen Spectrum and Spectral series: When a hydrogen atom is excited, it returns to its normal unexcited (or ground state) state by emitting the energy it had absorbed earlier.
• This energy is given out by the atom in the form of radiations of different wavelengths as the electron jumps down from a higher to a lower orbit.
• The transition from different orbits causes different wavelengths, these constitute spectral series which are characteristic of the atom emitting them.
• When observed through a spectroscope, these radiations are imaged as sharp and straight vertical lines of a single color.
• Mainly there are five series and each series is named after it's discovered as Lyman series (n1 = 1)Balmer series (n1 = 2)Paschen series (n1 = 3)Bracket series (n1 = 4), and Pfund series (n1 = 5).
• According to Bohr's theory, the wavelength of the radiations emitted from the hydrogen atom is given by
$$\frac{1}{\lambda } = RZ^2\left[ {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right]$$

where

n2 = outer orbit (electron jumps from this orbit),

n1 = inner orbit (electron falls in this orbit),

Z = atomic number

R = Rydberg's constant.

Lyman series is obtained in the ultraviolet region.

Balmer series is obtained in the visible region.

Paschen series is obtained in the Infrared region.

Brackett series is obtained in the Far infrared region.

# Which of the following particles in motion, having the same kinetic energy, has the shortest wavelenght?

1. A neutron
2. An alpha-particle
3. A proton
4. An electron

Option 2 : An alpha-particle

## Detailed Solution

Concept:
The wavelength of any charged particle due to its motion is called the de-Broglie wavelength.

The de-Broglie wavelength of charge particle (λd) is given by:

$${\lambda _d} = \frac{h}{{\sqrt {2mE} }}$$

Where,

E = energy

h = Planck constant

m = mass of the charged particle

∴ The relation between the wavelength and mass of particle when kinetic energy is constant is given by:

$$\lambda_b~\propto~\frac{1}{\sqrt m}$$

Observation:

Mass of the charged particle is:

1) Mass of proton mp = 1.67 × 10-27  (mass of Neutron is the same as the mass of Proton)

2) Mass of electron me = 9.1 × 10-31

3) Mass of alpha mα = 4mp = 4 × 1.67 × 10-27

From the above values, the mass of the alpha particle is more than the other all i.e. mα > mp > m

Hence, the shortest wavelength from all the above-given particles is the alpha-particle.

# A family of planes of spacing 0.2518 nm of NaCI crystal reflects a beam of X-ray in first order at an angle of 30°. The wavelength of X-rays is:

1. 0.2518 nm
2. 0.1259 nm
3. 0.3778 nm
4. 0.5036 nm

Option 1 : 0.2518 nm

## Detailed Solution

Bragg’s Law:

Bragg's Law relates the angle θ (at which there is a maximum in diffracted intensity ) to the wavelength of X-rays and the interlayer distance d between the planes of atoms/ions/molecules in the lattice. Condition for constructive interference (maxima in the reflected).

nλ = 2d sinθ

λ = Wavelength of the X-ray

d = distance of crystal layers

θ = incident angle (the angle between the incident plane and the scattering plane)

n = integer (order)

This condition is known as Bragg’s law

Calculation:

For 1st order, n = 1.

λ = 2d sinθ = 2 × 0.2518 × sin 30°

λ = 0.2518 nm

• X-ray diffraction is one of the earliest methods for studying the structure of solids.
• In the process of diffraction, electromagnetic waves of a given frequency but different phases interact to produce constructive interference (bright spots on the film exposed to the light) and destructive interference (dark spots).
• By a careful analysis of the diffraction patterns, very accurate values of the lattice parameters (unit cell dimensions) can be inferred.

# What is the minimum X-ray wavelength produced when electrons are accelerated through a potential of 50000 V? (h = 6.63 × 10-34 J s, c = 3 × 108 m/s, 1 eV = 1.6 × 10-19 J)

1. 35.8 × 10-12 m
2. 68.3 × 10-12 m
3. 19.6 × 10-12 m
4. 24.9 × 10-12 m

Option 4 : 24.9 × 10-12 m

## Detailed Solution

Concept:

Minimum wavelength produced through a potential difference of V is given by:

$${\lambda _{min}} = \frac{{hc}}{{eV}}$$

where h = 6.63 × 10–34 J.S

c = 3 × 108 m/s

1 eV = 1.6 × 10-19 J

Calculation:

Given:

V = 50000 V

We know that,

$${\lambda _{min}} = \frac{{hc}}{{eV}}$$

$${\lambda _{min}} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{1.6 \times {{10}^{ - 19}} \times 50000}} = 24.86 \times {10^{ - 12}}m$$

# The atomic radius is expressed in which of the following unit?

1. Angstrom
2. Fermi
3. Picometer
4. Newton

Option 1 : Angstrom

## Detailed Solution

CONCEPT

• Atomic radius: The measure of the size of the atoms of any element is called the atomic radius.
• The atomic radius is the distance from the center of the nucleus to the outermost shell containing electrons of an element.

EXPLANATION:

⇒ Radius of nucleus (R0) = 1.2 × 10-15 m = 1.2 fermi-meter

⇒ R = R0 A1/3

⇒ R = 1.2 A1/3  fermi-meter

• The radius of an atom is of 1 × 10-10 m order.

Atomic radius (r) =  1 × 10-10 m = 1 A

⇒ Hence the atomic radius is expressed in Angstrom (A).

• The nuclei of the atoms are spherical.

⇒ So, the volume of a sphere is V = (4/3)πr3.

⇒ Volume ∝ Atomic Mass (A)

⇒ R3 ∝ A

⇒ R ∝ A1/3

⇒ R = R0 A1/3

where R is the radius of the nucleus, Ris constant and A is the atomic mass of the element.

• 1 metre = 1015 fermi
• The average size of the nucleus of an atom is given by:

⇒ R0 = 1.2 × 10-15 m = 1.2 fermi-meter

 Unit Value Micron 10-6 Nanometer 10-9 Fermi 10-15 Angstrom 10-10

# Rutherford's alpha (α) particle scattering experiment resulted into the discovery of

1. proton
2. nucleus in the atom
3. electron
4. atomic mass

Option 2 : nucleus in the atom

## Detailed Solution

The correct answer is nucleus in the atom.

CONCEPT:

• Rutherford Experiment: Rutherford with his co-workers initiated a series of groundbreaking experiments that completely changed the accepted model of the atom.
• Very thin sheets of gold foil were bombarded with fast-moving alpha particles.
• Bombardment of alpha particles on the gold foil which showed that a very small percentage of alpha particles were deflected.
• This experiment showed that 'The nuclear model of the atom consists of a small and dense positively charged interior surrounded by a cloud of electrons.'

Figure (A) The experimental setup for Rutherford's gold foil

Figure (B) The plum pudding model (top) says that all of the alpha particles should have been passed through the gold foil with no deflection or very little deflection. Rutherford found that a small percentage of alpha particles were deflected at large angles, which could be explained by an atom with a very small, dense, positively-charged nucleus at its centre (bottom).

EXPLANATION:

• Rutherford’s atomic model accounts for the positively charged central core of an atom.
• So that positive charge is termed as nucleus.

Important Points

• Electron was discovered by J. J. Thomson in 1897 when he was studying the properties of cathode rays.
• Proton was discovered by Ernest Rutherford.
• By his experiment, nitrogen under alpha-particle bombardment ejects what appear to be hydrogen nuclei.
• He had accepted the hydrogen nucleus as an elementary particle, naming it proton.

# The quantum mechanical model of the hydrogen atom requires that if the angular momentum number is 4, the number of different permitted orbital magnetic quantum numbers will be:

1. seven
2. three
3. nine
4. four

Option 3 : nine

## Detailed Solution

Concept:

 Quantum Number Symbol Values Property Principal n 1, 2, ... Orbital size and energy level Angular Momentum l 0,1, 2, ….. n - 1 Orbital Shape (subshells) Magnetic m -l to +l Orbital Orientation Spin Magnetic s +1/2, -1/2 Electron Spin direction

Calculation:

Given angular momentum quantum number as 4, i.e. l = 4.

∴ The number of different permitted orbital magnetic quantum numbers will be:

m = - l to + l

m = -4 to 4, i.e.

2n + 1 = 9.

Quantum Mechanical Model of Atom:

Quantum mechanics is a theoretical science that deals with the study of the motions of macroscopic objects that have both observable wave-like and particle-like properties.

A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by their size, shape, and orientation. An orbital of smaller size means there is more chance of finding the electron near the nucleus.

Each orbital is designated by three quantum numbers labeled as n, l, and ml. The principal quantum number ‘n’ is a positive integer with a value of n = 1,2,3.......

1) The principal quantum number determines the size and to large extent the energy of the orbital. Size of the orbital increases with an increase of principal quantum number ‘n’. In other words, the electron will be located away from the nucleus. Also, the energy of the orbital will increase with an increase of n.

2) Azimuthal quantum number, ‘l’ is also known as orbital angular momentum or subsidiary quantum number. It defines the three-dimensional shape of the orbital. For a given value of n, l can have n values ranging from 0 to n – 1, that is, for a given value of n, the possible value of l are: l = 0, 1, 2, .......... (n – 1)

3) Magnetic orbital quantum number ml gives information about the spatial orientation of the orbital with respect to the standard set of co-ordinate axis. It can be any integer between -l and +l i.e. 2l + 1 values of ml are possible.

4) The spin quantum number (s)An electron can spin either in the clockwise direction or in the anticlockwise direction, therefore, for any particular value of the magnetic quantum number, the spin quantum number can have two values, i.e., +1/2 and –1/2

# An electron in a TV tube has a speed of 6 × 107 m/s. What is the de Broglie wavelength associated with the electron (m = 9.11 × 10-31 kg)?

1. 0.248 Å
2. 0.121 Å
3. 0.347 Å
4. 0.867 Å

Option 2 : 0.121 Å

## Detailed Solution

Concept:

De Broglie proposed that the wavelength λ associated with a particle of momentum p is given by:

$$\lambda = \frac{h}{p} = \frac{h}{{mv}}$$

where m is the mass of the particle and v its speed. Planck’s Constant, h = 6.623 ×× 10-34 Js,

Above equation is known as the de Broglie relation and the wavelength λ of the matter-wave is called de Broglie wavelength.

Thus, the significance of de Broglie equation lies in the fact that it relates the particle character to the wave character of matter.

Important Points

According to Planck’s quantum theory, the energy of a photon is described as E = hν

According to Einstein’s mass energy relation, E = mc2

Frequency ν can be expressed in terms of wavelength λ as, ν = c/λ

hν = mc2 ⇒ hν/c = mc ⇒ λ = h/mc, (This equation is applicable for a photon)

Calculation:

Given:

m = 9.11 × 10-31 kg, v = 6 × 107 m/s

$$\lambda = \frac{h}{{mv}} = \frac{{6.623 \times {{10}^{ - 34}}}}{{9.11 \times {{10}^{ - 31}} \times 6 \times {{10}^7}}} = 1.21 \times {10^{ - 11}}m = 0.121$$ Å

# After completing the gold foil experiment, Rutherford concluded that the size of the nucleus is very small compared to the size of the atom. This is because:

1. One out of every 12000 alpha particles deflected back after hitting the gold foil
2. Most of the alpha particles deflected back after hitting the gold foil
3. Some alpha particles were deflected by small angles
4. Very few of the alpha particles passed through the gold foil

Option 1 : One out of every 12000 alpha particles deflected back after hitting the gold foil

## Detailed Solution

The Correct Answer is One out of every 12000 alpha particles deflected back after hitting the gold foil.

Key Points

• Rutherford’s model says that an atom has a positively charged nucleus.
• So, the sub-atomic particle present in the nucleus of an atom is a proton (which carries a positive charge).

Important Points

Conclusion of Rutherford Model

• Most of the space inside the atom is empty because most of the α-particles passed through the gold foil without getting deflected.
• Very few particles were deflected from their path, indicating that the positive charge of the atom occupies very little space.
• A very small fraction of α-particles were deflected by 1800,indicating that all the positive charge and mass of the gold atom were concentrated in a very small volume within the atom.

# In order to investigate the internal atomic structure of crystals, we make use of:

1. Orange light
2. X - rays

Option 2 : X - rays

## Detailed Solution

X-rays:

• X-rays ionize gases through which they pass. Hence use to study atomic structure.
• Soft X-rays have a greater wavelength and lower frequency and hard X-rays have a lower wavelength and higher frequency.
• X-rays are not deflected by electric and magnetic fields.
• X-rays show all the important properties of light rays like reflection, refraction, interference, diffraction, and polarisation, etc.
• X-rays were discovered by scientist Roentgen.

1). Ultraviolet (UV) is a form of electromagnetic radiation with wavelengths from 10 (with a corresponding frequency around 30 PHz) to 400 nm (750 THz), shorter than that of visible light, but longer than X-rays.

2). Infrared radiation (IR), is a type of radiant energy that is invisible to human eyes but that we can feel as heat. All objects in the universe emit some level of IR radiation, but two of the most obvious sources are the sun and fire.

The heat that we feel from sunlight, a fire, a radiator or a warm sidewalk is infrared.

# Rutherford’s alpha-particle scattering experiment was responsible for the discovery of

1. Electron
2. Proton
3. Nucleus
4. Helium

Option 3 : Nucleus

## Detailed Solution

CONCEPT:

• In the Rutherford's Alpha Scattering Experiment, a beam of α-particles was made to fall on a thin gold foil. These particles then deflected in different directions and were detected by an α-particle detector.
• The following observations were made:
1. Most α-particles passed through the gold foil without suffering any deflection.
2. In passing through the foil, particles suffered different amounts of deflection.
3. While most of the particles suffered fewer deflections, a small number of particles suffered defections of nearly 180 °, practically retracing their paths, because the positive charge is concentrated at the center.
4. From this experiment he had concluded that almost all mass is concentrated at the center of an atom which was later termed as Nucleus.

EXPLANATION:

• Rutherford’s alpha-particle scattering experiment was responsible for the discovery of Nucleus.

# The de Broglie wavelength λ associated with an electron of mass m and accelerated by an electric potential V is:

1. $$λ=\frac{h}{\sqrt{2meV}}$$
2. $$λ=\frac{h}{\sqrt{meV}}$$
3. $$λ=\frac{m}{\sqrt{2heV}}$$
4. $$λ=\frac{h}{{2meV}}$$

Option 1 : $$λ=\frac{h}{\sqrt{2meV}}$$

## Detailed Solution

de Broglie wavelength of electrons:

Louis de Broglie theorized that not only light possesses both wave and particle properties, but rather particles with mass - such as electrons - do as well.

The wavelength of material waves is also known as the de Broglie wavelength.

de Broglie wavelength of electrons can be calculated from Planks constant h divided by the momentum of the particle.

λ = h/p

where λ is de Broglie wavelength, h is Plank's const, and p is the momentum.

In terms of Energy, de Broglie wavelength of electrons:

$$λ=\frac{h}{\sqrt{2mE}}$$ -----(1)

where λ is de Broglie wavelength, h is Plank's const, m is the mass of an electron, and E is the energy of the electron.

Electric Potential energy: If a Charge e is placed in the electric potential V, the electric potential energy

E = eV   ----(2)

where,

E is the electric potential energy,

e is the charge, and

V is the electric potential

From equation (1) and equation (2);

$$λ=\frac{h}{\sqrt{2meV}}$$

Hence, option 1 is correct.

# An electron and a proton have the same kinetic energy. Then, the ratio of de Broglie wavelengths of proton and electron will be nearly:

1. 1 : 43
2. 1 : 1838
3. 1838 : 1
4. 43 : 1

Option 1 : 1 : 43

## Detailed Solution

de Broglie wavelength:

Louis de Broglie theorized that not only light possesses both wave and particle properties, but rather particles with mass - such as electrons, protons - do as well.

The wavelength of material waves is also known as the de Broglie wavelength.

de Broglie wavelength can be calculated from Planks constant h divided by the momentum of the particle.

λ = h/p

where λ is de Broglie wavelength, h is Plank's constant, and p is the momentum.

In terms of Energy, de Broglie wavelength:

$$λ=\frac{h}{\sqrt{2mE}}$$ -----(1)

where λ is de Broglie wavelength, h is Plank's constant, m is the mass, and E is the energy.

Calculation:

Given both electron and proton have the same kinetic energy.

⇒ Eproton = Eelectron;

Since E and h are the same for both electron and proton, from equation 1,

$$λ \propto \frac{1}{\sqrt{m}}$$

$$\Rightarrow \frac {λ_{p}}{λ_{e}} = \sqrt {\frac {m_e}{m_p}}$$

We have mass of electron = 9.11 × 10-31 kg, mass of proton = 1.67 × 10-27 kg;

$$\Rightarrow \frac {λ_{p}}{λ_{e}} = \sqrt {\frac {9.11\times10^{-31}}{1.67 \times 10^{-27}}} = \sqrt {\frac {1}{1833}}$$

$$\Rightarrow \frac {λ_{p}}{λ_{e}} =\frac {1}{43}$$

∴ λp: λe = 1:43

# The nucleus of an atom was discovered by:

1. J.J. Thomson’s experiment
3. Rutherford’s gold foil experiment
4. Millikan’s oil drop experiment

Option 3 : Rutherford’s gold foil experiment

## Detailed Solution

The correct answer is Rutherford's gold experiment.

Key Points

• Rutherford’s gold foil experiment- It measured the scattering of an alpha particle beam when it strikes a thin metal foil - the discovery of Nucleus.
• J.J. Thomson’s experiment - Cathode-ray tubes - showed that all atoms contain tiny negatively charged subatomic particles - the discovery of electrons.
• Chadwick’s experiment -  bombarded Beryllium with alpha particles from the natural radioactive decay of Polonium. - discovered the neutron.
• Millikan’s oil drop experiment - the charge of an electron was determined.

# If there are 'N' atoms in a source, each emitting light with intensity 'I', then the total intensity produced by an ordinary source is proportional to 'NI', whereas in a laser source, it is proportional to ________.

1. (NI)2
2. 2NI
3. NI2
4. N2I

Option 4 : N2I

## Detailed Solution

Concept:

• LASER (Light Amplification by Stimulated Emission of Radiation) is a device that emits the light through a process of Optical Amplification based on the Stimulated Emission of Electromagnetic Radiation.
• A Laser is a device that can differ from other sources of light in that it emits light which is Coherent in nature. Spatial coherence allows a laser to focus on a tight spot. It helps us to enables applications such as Laser cutting and Lithography.
• For light energy,  that any given changes will only absorb one particular Wavelength of lightPhotons with the correct wavelength can cause an Electron to jump from (lower to the higher energy level). In which the photon energy is consumed.
• The emitted photon from the electron exactly matches the original photon in terms of the same Phase, Wavelength, and direction. This process is known as Stimulated Emission.

Image of the Laser photon emission:

Explanation:

From the above explanation, we can see that, unlike ordinary light LASER work on the stimulated emission of radiation

Thus in our case, if there are N atoms in an ordinary and LASER source, the total intensity will be proportional to NI and N2I respectively, since each atom produce 2 photons.

# The quantum mechanical model of the hydrogen atom requires that if the principal quantum number is 4, the number of different permitted orbital quantum numbers will be:

1. Five
2. Two
3. Four
4. One

Option 3 : Four

## Detailed Solution

Concept:

Quantum Mechanical Model of Atom

Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave-like and particle-like properties.

A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by their size, shape and orientation. An orbital of smaller size means there is more chance of finding the electron near the nucleus.

Each orbital is designated by three quantum numbers labelled as n, l and ml. The principal quantum number ‘n’ is a positive integer with a value of n = 1, 2, 3.......

• The principal quantum number determines the size and to large extent the energy of the orbital. Size of orbital increases with an increase of principal quantum number ‘n’. In other words, the electron will be located away from the nucleus. Also, the energy of the orbital will increase with an increase of n.
• Azimuthal quantum number, ‘l’ is also known as orbital angular momentum or subsidiary quantum number. It defines the three-dimensional shape of the orbital. For a given value of n, l can have n values ranging from 0 to n – 1, that is, for a given value of n, the possible value of l are: l = 0, 1, 2, .......... (n - 1)
• Magnetic orbital quantum number ml gives information about the spatial orientation of the orbital with respect to standard set of co-ordinate axis. It can be any integer between -l and +l i.e. 2l + 1 values of ml are possible.
• The spin quantum number (s): An electron can spin either in the clockwise direction or in the anticlockwise direction, therefore, for any particular value of the magnetic quantum number, the spin quantum number can have two values, i.e., +1/2 and –1/2
 Quantum Number Symbol Values Principal n 1, 2, ... Angular Momentum l 0,1, 2, ……... n - 1 Magnetic m -l to +l Spin Magnetic s +1/2, -1/2

Calculation:

If the principal quantum number is 4 (n = 4), the number of different permitted orbital quantum numbers will be (l = 0 to n – 1) 4.

# What is the charge on X-rays?

1. No charge
2. Positive & Negative
3. Negative
4. Positive

Option 1 : No charge

## Detailed Solution

CONCEPT:

• When highly energetic electrons are made to strike a metal target, electromagnetic radiations come out.
• A large part of this radiation has a wavelength of the order of 0.1 nm and is known as X-ray.
• These rays named X-ray as at that time its nature and properties were not known.
• Properties of X-Ray
1. X - rays travel in a straight line in a vacuum at a speed equal to that of light (3× 108).
2. X - rays are diffracted by crystals in accordance with Bragg’s law.
3. X - rays are not deflected by an electric or magnetic field as it contains no charged particles.
4. X - rays can affect a photographic plate more strongly than visible light.
5. When passed through a gas, X - rays ionize the molecules of the gas.

EXPLANATION:

• There is no charge on X-rays.

# If the potential difference applied to an X-ray tube is doubled while keeping the separation between the filaments and the target as same, what will happen to the cutoff wavelength?

1. Will remains same
2. Will be doubled
3. Will be halved
4. Will be four times of the original wavelength

Option 3 : Will be halved

## Detailed Solution

CONCEPT:

• The instrument which is used for the production of X-ray beams using fast cathode rays is known as X-ray tube.

• For an X-ray tube relation between stopping potential and minimum energy of X-ray beam is can be given as
• $${E_{minimum}} = e{V_0} = \frac{{hc}}{{{\lambda _{cut - off}}}}$$

Where Eminimum = The energy of X-ray beam, V0 = Stopping potential, h = Plank’s constant, c = Speed of light and λcut-off = Cutoff Wavelength

CALCULATION:

Given that

Stopping potential is increases twice hence V2 = 2V0 where V1 = V0,

∴ Cut off potential when stopping potential is Vo

$${\lambda _{cut - off}} = \frac{{hc}}{{e{V_1}}} = \frac{{hc}}{{e{V_o}}}$$

Cut off potential when stopping potential is doubled, then

Hence

$$\lambda {'_{cut - off\;}} = \frac{{hc}}{{e{V_2}}} =\frac{{hc}}{{e\left( {2{V_0}} \right)}}\; = \frac{{{\lambda _{cut - off}}}}{2}$$

From this we can say that the cutoff wavelength becomes half when stopping potential is increased to twice its initial value.

# At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio $$\frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}}$$ of their activities after time t itself decays with time t as e-3t. If the half-life of A is ln2, the half-life of B is:

1. 4ln 2
2. $$\frac{{{\rm{ln\;}}2}}{2}$$
3. $$\frac{{{\rm{ln\;}}2}}{4}$$
4. 2ln 2

Option 3 : $$\frac{{{\rm{ln\;}}2}}{4}$$

## Detailed Solution

Concept:

Radioactive decay occurs in unstable atomic nuclei that is, ones that don’t have enough binding energy to hold the nucleus together due to an excess protons or neurons.

The activity of the radioactive material is given by the formula:

R = λN

λ = decay constant (s-1)

N = Number of nuclei of radioactive material

Calculation:

The activity for substance A is given by the formula:

RA = λA NA

At t = 0, Number of undecayed nuclei (N0A) = Number of nuclei of radioactive material (NA)

⇒ RA = λA N0A

The activity for substance B is given by the formula:

RB = λB NB

At t = 0, Number of undecayed nuclei (N0B) = Number of nuclei of radioactive material (NB)

⇒ RB = λB N0B

At t = 0, two radioactive substances A and B have equal activities:

λA N0A = λB N0B

$$\Rightarrow \frac{{{{\rm{N}}_{0{\rm{B}}}}}}{{{{\rm{N}}_{0{\rm{A}}}}}} = \frac{{{{\rm{\lambda }}_{\rm{A}}}}}{{{{\rm{\lambda }}_{\rm{B}}}}}$$        ----(1)

The half-life is given by the formula:

$${{\rm{T}}_{1/2}} = \frac{{{\rm{ln\;}}2}}{{\rm{\lambda }}}$$

From the question, the half-life of A is ln 2.

$$\Rightarrow {{\rm{T}}_{\left( {1/2} \right){\rm{A}}}} = \frac{{{\rm{ln\;}}2}}{{{{\rm{\lambda }}_{\rm{A}}}}}$$

$$\Rightarrow {\rm{ln\;}}2 = \frac{{{\rm{ln\;}}2}}{{{{\rm{\lambda }}_{\rm{A}}}}}$$

∴ λA = 1        ----(2)

At t = t, the activity is given as:

$$\frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}} = \frac{{{{\rm{\lambda }}_{\rm{B}}}{{\rm{N}}_{\rm{B}}}}}{{{{\rm{\lambda }}_{\rm{A}}}{{\rm{N}}_{\rm{A}}}}}$$

We know that, N = N0 e-λt

$$\Rightarrow \frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}} = \frac{{{{\rm{\lambda }}_{\rm{B}}}{{\rm{N}}_{0{\rm{B}}}}{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{B}}}{\rm{t}}}}}}{{{{\rm{\lambda }}_{\rm{A}}}{{\rm{N}}_{0{\rm{A}}}}{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{A}}}{\rm{t}}}}}} = {{\rm{e}}^{ - 3{\rm{t}}}}$$

$$\Rightarrow \frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}} = \frac{{{{\rm{\lambda }}_{\rm{B}}}}}{{{{\rm{\lambda }}_{\rm{A}}}}} \times \frac{{{{\rm{\lambda }}_{\rm{A}}}}}{{{{\rm{\lambda }}_{\rm{B}}}}} \times \frac{{{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{B}}}{\rm{t}}}}}}{{{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{A}}}{\rm{t}}}}}} = {{\rm{e}}^{ - 3{\rm{t}}}}$$

On substituting, equation (1) in above equation,

$$\Rightarrow \frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}} = \frac{{{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{B}}}{\rm{t}}}}}}{{{{\rm{e}}^{ - {{\rm{\lambda }}_{\rm{A}}}{\rm{t}}}}}}$$

$$\Rightarrow \frac{{{{\rm{R}}_{\rm{B}}}}}{{{{\rm{R}}_{\rm{A}}}}} = {{\rm{e}}^{\left( {{{\rm{\lambda }}_{\rm{A}}} - {{\rm{\lambda }}_{\rm{B}}}} \right){\rm{t}}}} = {{\rm{e}}^{ - 3{\rm{t}}}}$$

On equating power terms,

⇒ (λA - λB)t = -3t

⇒ λA - λB = -3

From equation (2),

⇒ λB = 3

∴ λB = 4

Now, the half-life of B is:

$$\Rightarrow {{\rm{T}}_{\left( {1/2} \right){\rm{B}}}} = \frac{{{\rm{ln\;}}2}}{{{{\rm{\lambda }}_{\rm{B}}}}}$$

$$\therefore {{\rm{T}}_{\left( {1/2} \right){\rm{B}}}} = \frac{{{\rm{ln\;}}2}}{4}$$

# A proton is moving at a speed of 5.0 × 104 m/s. The de Broglie wavelength associated with it is _____.(mp = 1.67 × 10-27 kg, h = 6.63 × 10-34 J s)

1. 0.38 × 10-11 m
2. 0.79 × 10-11 m
3. 1.20 × 10-11 m
4. 1.58 × 10-11 m

Option 2 : 0.79 × 10-11 m

## Detailed Solution

Concept:

De Broglie wavelength:  All particles could be treated as matter waves with a wavelength.

Frequency is given by the following equation:

$$λ = \frac{h}{mv}$$

Where λ is de Broglie wavelength, h is Planck's const, m is mass, v is the velocity.

When an electron is accelerated its de Broglie wavelength is given by

$$λ = \frac{\sqrt{150}}{\sqrt V} A$$

Where V is the potential difference in which electron is accelerated.

Calculation:

Given that, v = 5 × 104, mp = 1.67 × 10-27 kg, h = 6.63 × 10-34 J s

Frequency is given by,

$$λ = \frac{h}{mv}$$ = $$\frac{6.63×10^{-34}}{1.67× 10^{-27}×5×10^{4}}=0.79×10^{-11}$$

The de Broglie wavelength associated with it is 0.79 × 10-11m.


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## Swipe to navigate through the articles of this issue

20-08-2019 | Original Paper | Issue 3/2020

# Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation

Journal:
Numerical Algorithms > Issue 3/2020
Authors:
Meng Li, Chengming Huang, Yongliang Zhao
Important notes

## Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Abstract

In this paper, we are concerned with the numerical solutions of the coupled fractional Klein-Gordon-Schrödinger equation. The numerical schemes are constructed by combining the Crank-Nicolson/leap-frog difference methods for the temporal discretization and the Galerkin finite element methods for the spatial discretization. We give a detailed analysis of the conservation properties in the senses of discrete mass and energy. Then the numerical solutions are shown to be unconditionally bounded in L2 −norm, $$H^{\frac {\alpha }{2}}-$$semi-norm and $$L^{\infty }-$$norm, respectively. Based on the well-known Brouwer fixed-point theorem and the mathematical induction, the unique solvability of the discrete solutions is proved. Moreover, the schemes are proved to be unconditionally convergent with the optimal order $$O\left (\tau ^{2}+h^{r+1}\right )$$, where τ is the temporal step, h is the spatial grid size, and r is the order of the selected finite element space. Furthermore, by using the proposed decoupling and iterative algorithms, several numerical examples are included to support theoretical results and show the effectiveness of the schemes. Finally, the fast Krylov subspace solver with suitable circulant preconditioner is designed to effectively solve the Toeplitz-like linear systems. In each iterative step, this method can effectively reduce the memory requirement of above each finite element scheme from $${{O}\left (M^{2}\right )}$$ to O(M), and the computational complexity from $${O\left (M^{3}\right )}$$ to $${O(M \log M)}$$, where M is the number of grid nodes. Numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization/Cholesky decomposition methods, in terms of memory requirement and computational cost.

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Literature


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Question: CMD check warning using Bioconductor as a source for the dependencies of an R package
1
11 days ago by
dong10
dong10 wrote:

I am writing an R package and one of my dependencies is a bioconductor package xcms. It can pass the CMD check in my local PC, while when I submit my package to CRAN, there is one warning:

>Found the following significant warnings:
Warning: 'BiocInstaller' and 'biocLite()' are deprecated, use the 'BiocManager' CRAN

Here is part of my Description File:

> Depends:
> R (>= 3.1.0).
> biocViews:
> Imports:
> xcms.

The CRAN check result is here https://win-builder.r-project.org/incomingpretest/Miso0.2.020190210133229/Windows/00check.log

I don't know how to eliminate this warning, thanks a lot for your help.

modified 11 days ago by Martin Morgan ♦♦ 22k • written 11 days ago by dong10

provide more detail, e.g., the link to the CRAN check and to your package source.

@Martin Morgan, Thanks for your suggestion. The CRAN check has been added here.

2

You can find further details in https://win-builder.r-project.org/incomingpretest/Miso0.2.020190210133229/Windows//00install.out

I wonder if this is because the Windows builder is stuck with an outdated version of a Bioconductor package that still references BiocInstaller. Perhaps there's a way to find more details of the packages installed?

If this is the case then I'm not sure there's much you can do other than wait for the relevant package to be updated.

Answer: CMD check warning using Bioconductor as a source for the dependencies of an R pa
2
11 days ago by
Martin Morgan ♦♦ 22k
United States
Martin Morgan ♦♦ 22k wrote:

One can discover dependencies by discovering the packages available for the platform in question

db <- available.packages(repos=BiocManager::repositories(), type = "win.binary")

and then finding reverse dependencies

deps <- tools::package_dependencies("xcms", db, recursive = TRUE)

For the 'devel' version of R, the repositories are

> BiocManager::repositories()
BioCsoft
"https://bioconductor.org/packages/3.9/bioc"
BioCann
"https://bioconductor.org/packages/3.9/data/annotation"
BioCexp
"https://bioconductor.org/packages/3.9/data/experiment"
BioCworkflows
"https://bioconductor.org/packages/3.9/workflows"
CRAN
"https://cran.rstudio.com"

where the 3.9 indicates Bioconductor 3.9. There are no dependencies on BiocInstaller

> "BiocInstaller" %in% unlist(deps)
[1] FALSE

so at least for xcms Mike Smiths' speculation (that stale packages are installed on win-builder) would be the most likely explanation. If there is no dependency on BiocInstaller in the other direct and indirect dependencies, this should be taken up with the win-builder team. Actually, since BiocInstaller is not available under R-devel

> "BiocInstaller" %in% rownames(db)
[1] FALSE

and since the WARNING comes when BiocInstaller is loaded, it follows that win-builder does not have a current installation.