OpenLLM-France/wikimedia huggingface dataset:
# Topfield 5800/Troubleshooting/Freeview Shuffle

Occasionally the way the Freeview channels are organised is shuffled about a bit. Sometimes new channels are added, some stop broadcasting, there are name changes, or things are just moved about for technical reasons. This shuffling can sometimes confuse the Toppy (and other Freeview receivers) with symptoms such as missing EPG data or the wrong channel being displayed.
To remedy this you will need to do a rescan to get the correct channel list. If just a few channels are affected then you may be able to simply delete the old channels and scan for the new ones, but it's usually safest to do a Factory Reset (which will also delete all your current timers) and then a complete rescan.
If you are running an older firmware (pre-"Bastille", 5.12.88) then the EPG data for some channels may be missing because the specific broadcaster is having a bad day and is not sending it (or transmitter problems or maintenance). This is much less likely to be a problem on newer firmwares which can collect all the EPG data from any single channel.
# Topfield 5800/Troubleshooting/Dropouts

The Toppy does not seem to cope very well with playing audio if the TV type is set different to the video being played. In the UK, all broadcasts are PAL so the TV Type should be set to PAL, and this can be changed using the System Setting menu, A/V Output Setting item.
There is also a known issue with (specifically) Film4 recordings being played back when tuned to Sky3 (or any channel on MuxC). The solution is to tune to a different channel (e.g. BBC1) before starting playback.
Other causes are the obvious signal problems: weak signal and poor quality signal (check the aerial type, alignment and cabling, water ingress in connections, and consider a booster), atmospherics, and interference from other electrical activity, such as lawnmowers, car electrics and dodgy domestic appliances (better [CT100] cabling may help).
Experience has shown that audio dropouts can occur when the machine has got hot, often after a few hours playback. This gets progressively worse. The solution is either switch off and allow it to cool down, or direct a cool air fan at the machine. The fan noise can be ignored by the satisfaction of completing a watched programme.
# Topfield 5800/Troubleshooting/EPG Duplicates

Due to bugs in the EPG data collection, if the Toppy is left on for a long time it will run out of free slots for new data and there may be gaps, duplicate entries or whole missing channels. Currently, the simplest solution is to regularly switch the Toppy into standby (which helps save electricity, too). (Previous concerns about missing recordings when in standby have been addressed by fixes to the Timers Bug.)
# Topfield 5800/Troubleshooting/Failsafe

There is a problem with the firmware image in flash memory. You need to re-flash the firmware using one of the Topfield utilities, or one of the tools listed below. To do this you need to have a reliable USB (or serial) connection to the Toppy and you need to prepare the process on the PC/Mac while the Toppy is off, then switch it out of standby so the Boot Loader can perform the firmware flash (this "failsafe" mechanism should always be available). There are known issues when power saving is enabled on USB ports (so disable this feature) and when using the Topfield USB driver under Vista. The Toppy's Boot Loader presents only a small "window of opportunity" for connecting to the PC/Mac, so if it doesn't work first time, try again.
# Topfield 5800/Troubleshooting/EPG Gaps
## EPG Missing Data or Gaps

Data is completely missing on certain channels
Data is running out or has run out on certain channels (firmwares before 5.12.88)
Data seems to run out or become sparse after being on for a long time
Lots of gaps soon after starting up
# Topfield 5800/Troubleshooting/Firmware issues

There are various versions of firmware for the 5800; many of the issues that arise are due to the particular firmware used, not the hardware. Early versions of firmware, in particular, can have problems. One strategy is to download and use the most recent firmware. In particular this adds some features of Freeview+ to the 5800. But the most reliable firmware is arguably a version which has been updated and debugged by many expert enthusiasts. As of early 2011 the best firmware is probably 5.13.65T (the "T" is important) downloadable without charge from the toppy.org.uk website. It does not have the latest features (e.g., series recording), but does not have the latest bugs either!
# United States Postage Meter Stamp Catalog/Sub-group QC – Francotyp-Postalia
#### Sub-group QC – Francotyp Postalia

* The stamps in this sub-group all have a large DataMatrix barcode and all have large imprint FP left of "US POSTAGE".
* All stamps have meter number prefix 03.
* Known meter models are in the following series: T-1000, MyMail, OptiMail, UltiMail, Centormail, JetMail, and PostBase.
* First seen in 2003.
QC1.1. Several different models and model series produced this stamp but which ones exactly is to be determined, 2003.
    Large DataMatrix barcode at left. At right, large “FP” logo (15mm wide) and "US POSTAGE" above value figures.
    Below the FP logo and value figures are three lines of text separated by horizontal lines.
    From top to bottom the text lines are the town line, the date, and the meter number.
    Town line: "Mailed From" with ZIP code
    Meter numbers with 031A prefix.
    With or without class of mail below value figures.
    V/F: $00.00$^o$ (range: $00.00$^1$ to $99.99$^9$)
       a. “CORRECTION” below value figures
       b. Printed without 2D barcode and with "REDATE" below zero-cent value figures
QC1.2. Several different models and model series produced this stamp but which ones exactly is to be determined.
    As Type QC1.1 but can print postage values in whole cents only.
    Meter numbers with 031A prefix.
    With or without class of mail below value figures.
    V/F: $ 00.00 (range: $00.01 to $99.99)
QC2.1. Model(s) unidentified, 2013.
    As Type QC1.1 but the FP logo is smaller, 11.5mm wide.
    Meter numbers with 032A prefix.
    With or without class of mail below value figures.
    V/F: $00.00$^o$ (range: $00.00$^1$ to $99.99$^9$)
QC2.2. Model(s) unidentified, 2013.
    As Type QC2.1 but can print postage values in whole cents only.
    Meter numbers with 032A prefix.
    With or without class of mail below value figures.
    V/F: $ 00.00 (range: $00.01 to $99.99)
QC3.1. Model(s) unidentified, 2016.
    As previous QC types but with new logo made of a smaller, solid FP and small circled envelope.
    Town line: "ZIP" with ZIP code, right justified.
    Meter number with 035A prefix.
    V/F: $000.00$^o$ (range: $000.00$^1$ to $999.99$^9$)
QC3.2. Model(s) unidentified, 2016.
    As Type QC3.1 but can print postage values in whole cents only.
    Town line: "ZIP" with ZIP code, right justified.
    Meter number with 033A prefix.
    V/F: $000.00 (range: $000.01 to $999.99)
# United States Postage Meter Stamp Catalog/Town and date marks

Town- and date-marks
Town mark circles can be single (SC), double (DC), or broken inner circle (BIC), i.e., a single circle with arcs inside. Modern digital meter stamps mostly have straight-line town marks.
Town marks occasionally include the name of the postal station as well as the town and state, as these can be found with most types before 2000 they are not listed as separate varieties. Mailing permit numbers also can be found inside the town mark, these are usually listed as small letter varieties. Starting in the 1960s meters used by some mailers occasionally contained the postal (ZIP) code rather than or in addition to the post office name. Most such town marks were in the form of " MAILED FROM ZIP CODE" plus number. Variations are " MAILED FROM ZIP" and " MAILED FROM". These "MFZC" town marks are common and are not listed as varieties in the catalog. Town marks containing the town and state as well as the ZIP code are scarce, and these are listed as small letter varieties.
Earlier meters, most of those produced before the 1940s, had their date figures set by hand. They are often found inverted. Inverted dates for these early meter types are not listed.
# Units of Measurement/Angle

The base unit of measurement for an angle is a degree (°) or a radian ($^c$). A degree is 1/360th of a circle. 1 degree is equal to (pi/180) radians. 360 degrees is a full rotation and 180 degrees is equal to half a rotation or a straight line.

## Common Values

30 degrees is when the sine function equals 0.5 and when cosine = sqrt(3)/2.
45 degrees is the non-right angles of a isoceles right triangle. It is also when the sine and cosine functions equal each other, equaling sqrt(2)/2. This is also half of a right angle.
60 degrees is the inverse of 30 degrees, where cosine equals 0.5 and sine equals sqrt(3)/2. It is also the number of degrees in an angle of an equilateral triangle. This is equal to π/3 radians.
90 degrees is the number of degrees in a right angle, and 4 right angles make a rectangle or a square. This is where sine equals 1 and cosine equals 0. This also equals π/2 radians.
180 degrees is a straight line, or what the internal angles add up to in a triangle, or what the exterior angles of any polygon add up to. It is also the number of degrees in a semi-circle. It is also equivalent to π radians.
270 degrees is 3/4ths of a rotation, or what 90 degrees clockwise is.
360 degrees is a full rotation or a circle. This equals 2π radians. This is also what the angles in a quadilateral add up to. 360 degrees per second is one Hertz

## Formulas

The formula for an interior angle in a regular polygon is 180•(s-2)/s, where s is the number of sides in the polygon.
# Units of Measurement/Angular velocity

The SI unit for angular velocity is radians/seconds. It measures how fast an object is rotating.
# United States Postage Meter Stamp Catalog/Sub-group QD – Data-Pac
#### Sub-group QD – Data-Pac

* The stamps in this sub-group all have a waving American flag logo with "DATA-PAC" reading up serving as the flag pole.
* All stamps have meter number prefix 08.
* Meter model: America2.
* First seen, 11 November 2006.
QD1. “America2" , 11 November 2006.
    Small, short frank with flag logo at left.
    At center are US POSTAGE above a horizontal IBI Lite barcode.
    At right are the value figures above the date, the town line, and the meter number.
    Town line: "ZIP" plus ZIP code
    Meter number with “0801” prefix to 7-digit number starting with 105.
    Normally printed in black.
    V/F: $00.00$^o$ (range: $00.00$^1$ to $99.99$^9$)
       a. Printed in a color other than black (red, blue, and brown seen)
       b. With FIM barcode inserted between the flag and the rest of the frank
QD2. Data-Pac "America2" (digital).
    Found only in the upper right section of large address labels printed by the meter.
    Value figures at upper left, "US POSTAGE" and town line at upper right.
    Flag logo and "IBI Lite" barcode below.
    V/F seen:$0.00
    NOTE: This stamp has not been reported by collectors. The image shown is from Data-Pac's web site.
# Units of Measurement

We live in a physical universe, and a complete system of standardised units describing the physical quantities around us is required to allow us to measure and quantify the universe and its contents. Without a standard unit system, trade would be impossible and the sciences would be unable to build on previous results.
This book collates information on the units of measurement in use, defining them and comparing to other units in the same and other systems.

## Contents
### Unit systems

* SI units
* CGS units
* Imperial units

### Unit by physical quantity described

* Length
* Area
* Volume
* Mass
* Time
* Angle
* Frequency
* Temperature
* Density
* Velocity
* Angular velocity
* Acceleration
* Angular acceleration
* Force
* Pressure
* Energy
* Power
* Action
* Entropy
* Viscosity
* Surface tension
* Thermal conductivity
* Amount of substance
* vibration
# United States Postage Meter Stamp Catalog/Surcharge slugs

Surcharge slugs
Surcharge slugs usually included the mail classification such as "Bulk Rate" or "Nonprofit Organization" as well as the fractional value.
# Units of Measurement/Acceleration

The SI unit for acceleration is m*s^-2. Acceleration is equal to change in velocity over change in time. Taking a second derivative of speed or first derivative of velocity is equal to acceleration.
Young, Hugh. University Physics: With modern Physics. 12. Pearson College, 2007. Print.
# United States Postage Meter Stamp Catalog/sandbox3
## test page

Click here to return to the United States Postage Meter Stamp Catalog
I am keeping this page open for future designing experiments.
# Units of Measurement/Angular acceleration

The SI unit of angular acceleration is (radians)/(second squared). It measures change in angular velocity over time.
# Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions

Typically, we would appreciate a much less difficult way to calculate properties of a system rather than having to come up with a multiplicity function, take the ln of it, and go from there. Fortunately, there are much better ways to do this. One is by considering a thermal reservoir, which makes some nice simplifications in a system, and for more complicated multi-particle comprised systems we can consider a different type of reservoir to simplify our calculations.

## Contents

* Boltzmann Factors
* The Partition Function
* Gibbs Factors
* The Grand Partition Function
# Statistical Mechanics/Debye Theory

Say we have a material with vibrating modes visually akin to that of jello. In other words, we are looking at the phononic modes. The energy equation for a specific mode of a phonon is identical to that of a photon. The only difference between the phonon and photon case is that the phonon case has a possible upper limit (because the highest frequency occurs at the shortest wavelength: when one molecule is at its amplitude and the neighbours are at their troughs), and that we have another possible mode of polarization (two transverse, one longitudinal), and that we are dealing with v (the speed of sound in the material) instead of c. Thus, when we transform the integral as in the photon derivation (another similar density of states problem) we get:
$U={\frac {3\pi }{2}}\int _{0}^{n_{D}}dn{\frac {n^{2}\hbar \omega _{n}}{exp(\hbar \omega _{n}/T)-1}}$
Where n$_D$ is this maximal case.
We define something now called the Debye Temperature (a physical property of a material):
$\theta =(\hbar v/k_{B})(6\pi ^{2}N/V)^{1/3}$
Note: the k$_B$ is apparent because we've been working in energy-represented T, instead of the typical Kelvin-scaled T, k$_B$ effectively means the T's here-on are in Kelvin-units)
If we use this, and take the low-temperature limit of T << θ, we can approximated the upper limit as we continue the integration as ∞ (which physically means that there's a bunch of higher-energy levels states that the solid is not reaching) we can evaluate almost exactly as before:
$U(T)=3\pi ^{4}Nk_{B}T^{4}/5\theta ^{3}$
and:
$C_{V}:=\left({\frac {\partial U}{\partial T}}\right)_{V}={\frac {12\pi ^{4}Nk_{B}}{5}}\left({\frac {T}{\theta }}\right)^{3}$
This is known as Debye's T$^3$ law, and follows well with experiment.
# Statistical Mechanics

This book will cover the rigorous template of statistical mechanics, which has many uses in abstract physics that build up into many theories on many different materials, the most important of which being Thermal Physics.

# Prerequisites

The following are some good things to have under your belt to understand this material:
* Multivariate Calculus
* Introductory Physics
* A very brisk notion of quantum numbers and the Schrodinger equation (in other words, just the main idea of what they are)
For Thermal Physics, the above is suggested (except for quantum numbers/Schrodinger ideas) and:
* Partial Differentials
# Statistical Mechanics/Density of States
## Thermal Average Number of Particles Distribution Function

    $f(\epsilon )\equiv \ \langle N(\epsilon )\rangle$
Now, since this is a distribution function, we can find thermal average quantities of other thermodynamic quantities:
    $\langle X\rangle =\sum _{n}f(\epsilon _{n},T,\mu )X_{n}$
Where n denotes the quantum orbital.
Now if the orbital step, n, is small, we can change the sum to an integral:
    $\langle X\rangle =\int d\epsilon D(\epsilon )f(\epsilon ,T,\mu )X(\epsilon )$
Here, this $D(\epsilon )$ function is the function that mathematically allows us to transform the sum to the simplest possible integration (In the Thermal Radiation case, we will see that the D function is the Jacobian to spherical coordinate).
It is also better known as the...

## Density of States

The mathematics of the DoS were explained in the previous section, all that remains of importance is to explain its significance. Here D(ε) is the number of orbitals of energy between ε and ε + dε. We can think of it as the number of orbitals per volume in the shell taken in the integration, in other words, the density of states.
# Statistical Mechanics/Phase Transformations
## Clausius-Clapeyron Equation

In equilibrium, we know that the first-derivative of thermodynamic quantities of two systems should be equal, for this specifies a maxima or minima of the original thermodynamic function. In terms of phases, the best variable to examine is μ, specifically for when a gas and liquid phase of a system coexist:
μ$_g$(p,T) = μ$_l$(p,T)
Also, because we are examining a physical continuous system:
μ$_g$(p + dp,T + dT) ~= μ$_l$(p + dp,T + dT)
If we take these and play around with them using a Taylor's expanaion, limiting dp and dT small enough that higher order terms fall out, and play with them algebraically:
dp/dT = ((∂μ$_l$/∂T)$_p$ - (∂μ$_g$/∂T)$_p$)/((∂μ$_l$/∂p)$_T$ - (∂μ$_g$/∂p)$_T$)
Using some Maxwell relations and the fact that for a single-specie system G=Nμ(p,t) (in order to satisfy G's differential equation) we can obtain:
dp/dT=(s$_g$ - s$_l$)/(v$_g$ - v$_l$)
But if we make the following definitions:
L := T(s$_g$ - s$_l$)
Δv= = (v$_g$ - v$_l$)
dp/dT=L/(TΔv)
which is know as the Clausius-Clapeyron equation, which tells the form of the vapor-pressure line where the gas and liquid phases of a material meet.

## Maxwell Construction

Another way of looking at the phase transition point is to examine the Gibbs free energy. There is a free energy curve for the material for each of its phases. What phase it's in is determined by the curve with the lowest free energy (as said in the previous chapter). Therefore, the place of coexistance is where G$_g$=G$_l$.
Let's take a look at Gibbs' differential form:
$dG=-SdT+Vdp+\mu dN$
N=1 and is constant, and let's assume T is constant, then:
dG= Vdp
Integrate over the curve so that:
G$_g$ - G$_l$ = ∫Vdp
But since we are at a phase equilibrium position:
∫Vdp = 0
over such a curve for a material. This relation allows us to determine something called the 'coexistance line' on a P-V diagram, and is known as Maxwell's Construction.
# Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions/Gibbs Factors

Using the same method as we did with Boltzmann Factors, we consider a system in thermal and diffusive equilibrium with another system.
P(N$_1$,ε$_1$)/P(N$_2$,ε$_2$) = g(N$_0$ - N$_1$, U$_0$ - ε$_1$)/g(N$_0$ - N$_2$, U$_0$ - ε$_2$)
And by the exact same method as our derivation of Boltzmann factors (no surprises here):
P(N$_1$,ε$_1$)/P(N$_2$,ε$_2$) = exp((N$_1$μ - ε$_1$)/T)/exp((N$_2$μ - ε$_2$)/T)
Which we will use in the exact same way to create the Grand Partition Function.
# Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions/The Grand Partition Function

It's useful to consider the following function, the Grand Partition function:
ξ(T,N) = Σ$_N$ Σ$_{s(N)}$ exp((Nμ-ε$_s$)/T)
We can then note that if we define the probability as the following via examination of the Boltzmann factor:
P(N$_1$,ε$_1$) = exp((N$_1$μ-ε$_1$)/T)/ξ
If we sum P over s, we get ξ/ξ, which is indeed 1, and thus this is a valid probability function.
Then, using our knowledge of statistical averages, we can consider thermal averages, and calculate energy and various other properties using the Partition function. In general, given the thermodynamic property X, its thermodynamic property is:
X = <x> = (Σ$_N$ Σ$_{s(N)}$ x$_s$exp((Nμ-ε$_s$)/T)) / ξ
# Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions/The Partition Function

It's useful to consider the following function, called the Partition Function:
Z(T) = Σ$_s$ exp(-ε$_s$/T)
We can then note that if we define the probability as the following via examination of the Boltzmann factor:
P(ε$_s$) = exp(-ε$_s$/T)/Z
If we sum P over s, we get Z/Z, which is indeed 1, and thus this is a valid probability function.
Then, using our knowledge of statistical averages, we can consider thermal averages, and calculate energy and various other properties using the Partition function. In general, given the thermodynamic property X, its thermodynamic property is:
X = <x> = (Σ x$_s$ exp(-ε$_s$/T)) / Z
# Statistical Mechanics/Ideal Gas

Consider an ensemble of molecules. Take a particular molecule, while the others form a heat reservoir at temperature T. The energy(E)is kinetic = p$^2$/2m = 1/2mv$^2$,
P(E) α e$^{-βE}$ α e$^{-β(p2/2m)}$
The probability that the molecule lies between r$^→$ and r$^→$+
# Statistical Mechanics/Boltzmann and Gibbs factors and Partition functions/Boltzmann Factors

The first 'method of simplification' involves considering a thermal reservoir, basically a temperature bath that will keep our system of consideration at a constant temperature T.
Then by the fundamental assumption, given two energy states:
    ${\begin{aligned}{\frac {P(\varepsilon _{1})}{P(\varepsilon _{2})}}&={\frac {g_{R}(U_{0}-\varepsilon _{1})}{g_{R}(U_{0}-\varepsilon _{2})}}\\&={\frac {e^{S_{R}(U_{0}-\varepsilon _{1})}}{e^{S_{R}(U_{0}-\varepsilon _{2})}}}.\end{aligned}}$
Now, because of the Taylor Series, and in the presence of an infinitely large reservoir the higher-order terms vanish:
    ${\begin{aligned}S_{R}(U_{0}-\varepsilon )&=S_{R}(U_{0})-\varepsilon {\frac {\partial S_{R}}{\partial U}}{\big |}_{V,N}\\&=S_{R}(U_{0})-{\frac {\varepsilon }{T}}.\end{aligned}}$
Using this simplification we can write the previous exponential form of the ratio of probabilities:
    ${\frac {P(\varepsilon _{1})}{P(\varepsilon _{2})}}={\frac {e^{-\varepsilon _{1}/T}}{e^{-\varepsilon _{2}/T}}},$
where $e^{-\varepsilon /T}$ is known as a Boltzmann factor. We will expand on its usefulness in the next section.