Orthogonality
If $ \vec{V}_{n} \cdot \vec{V}_{m} = \delta_{nm}$ then the vectors are said to be orthonormal. $$\delta_{nm} = \left\{\begin{matrix}0 \quad \text{if } m\neq n \\ 1 \quad \text{if } m = n \end{matrix}\right. $$ This mean the vectors are orthogonal and conveniently normalised.
Use the visualisation to see that when the basis vectors are not parallel they span $\mathbb{R}^{2}$, using these as basis vectors, we can construct any other vector in $\mathbb{R}^{2}$.
If you can represent any vector in $\mathbb{R}^{n}$ using $n$ vectors, then the basis vectors form a complete set. If the set of these vectors are all orthonormal, then we have a complete orthonormal set.
In the same way as before, we will now demonstrate what it means for functions to be complete. We define the functions $f_{n},f_{m}$ to exist on the domain $\left[a,b \right]$.
We define their inner product to be $$\langle f_{n} , f_{m} \rangle = \int_{a}^{b} f_{n}\left(x \right)f_{m}^{*}\left(x \right)dx$$ and say the functions are orthogonal if $\langle f_{n} , f_{m} \rangle = 0 $ for $m \neq n$. We then say the functions are orthonormal if $\langle f_{n} , f_{m} \rangle = \delta_{nm} $.
We now claim that you can construct any square integrable function from a complete set of basis functions in the same way vectors could be constructed from a complete set of basis vectors. A square integrable function $f$ is a function whose inner product with itself, $ \langle f,f \rangle $ is finite.
Section 2
Introduction to Fourier series
Consider a function $f(x)$ which is periodic over the domain $ -L \leq x < L $ where $L$ is positive. $f(x)$ can be represented as a sum of sines and cosines with varying frequencies. These trigonometric functions form orthogonal basis.
The Fourier series of $f(x)$ is
$\displaystyle f(x) = \frac{a_0}{2}$ $+ \displaystyle\sum_{n=1}^{\infty} \Big[ a_n\cos\Big(\frac{\pi nx}{L}\Big)$ $\displaystyle+ b_n\sin\Big(\frac{\pi nx}{L}\Big) \Big]$ $ \qquad \left[ 1 \right]$where
$\displaystyle a_n = \displaystyle\frac{1}{L}\int_{-L}^{L} f(x)$ $\displaystyle \cos\Big(\frac{\pi nx}{L}\Big) dx, $ $\displaystyle b_n = \displaystyle\frac{1}{L}\int_{-L}^{L} f(x)$ $\displaystyle \sin\Big(\frac{\pi nx}{L}\Big) dx, $ $\displaystyle a_0 = \displaystyle\frac{1}{L}\int_{-L}^{L} f(x) dx, $and
$$ n=0,1,2...$$Note: $a_0$$/2$ represents the average value of $f(x)$.
The Fourier series representation of the function $f(x)$ in exponential (complex) form is
$\displaystyle f(x) =\sum_{n=-\infty}^{\infty} c_n e^{{in \pi x}/L}$ $\displaystyle \qquad \left[ 2 \right]$where
$\displaystyle c_n = \frac{1}{2L}\int_{-L}^{L} f(x)$ $\displaystyle e^{{-in \pi x}/L} dx, $Note: The constants in front of the integral(s) of the coefficient for the trigonometric and exponential fourier series are different. Also note the limit of the summations.
Derivation of the Fourier Series
We begin by assuming that $f(x)$ can be represented as a sum of exponential terms.
$\displaystyle f(x) = \displaystyle\sum_{n=-\infty}^{\infty} c_n e^{{in \pi x}/L}$Multiplying by $e^{{-im \pi x}/L}$, where $m=0,1,2...$, and integrating both sides gives the following:
$\displaystyle\int_{-L}^{L} f(x) e^{{-im \pi x}/L} dx$ $=\displaystyle\sum_{n=-\infty}^{\infty} c_n $ $\displaystyle \int_{-L}^{L} e^{{i(n-m) \pi x}/L} dx. $Performing the integral on the R.H.S gives
$ \displaystyle\int_{-L}^L e^{(i\pi x/L)(n-m)}dx$ $\displaystyle =\left\{ \begin{array}{ll} 2L \qquad \text{(if n=m)} \\ 0 \qquad \quad \text{(if n≠m)} \end{array} \right \} $ $\displaystyle= 2L \cdot \delta_{nm}.$This is the orthonormality of complex exponentials.
Now since the only non-zero value of the sum is when $n=m$,
$\displaystyle\int_{-L}^L f(x) e^{-im\pi x/L}dx$ $\displaystyle= 2L \sum_{n=-\infty}^{+\infty}c_n\delta_{mn}$ $\displaystyle=2L\cdot c_m, $hence
$\displaystyle c_m=\frac{1}{2L}\int_{-L}^{+L}f(x) $ $\displaystyle e^{-im\pi x/L}dx. $Note: As $m$ is an arbitrary integer, it can be assigned as $n$ for simplicity.
Given the previously derived equation, we can derive the trigonometric form of the Fourier series. By reorganising the sum, we get
$\displaystyle f(x)= \underbrace{c_0}_\text{n=0}$ $\displaystyle + \sum_{n=1}^{\infty} \big( \underbrace{c_n e^{in\pi x/L}}_\text{Positive n term}$ $\displaystyle + \underbrace{c_{-n} e^{-in\pi x/L}}_\text{Negative n terms} \big).$We can regroup the terms in the summation in the following way:
Now define $ a_n = c_n + c_{-n}$ and $ b_n = i(c_n - c_{-n})$ and use that these exponentials can we written as sines and cosines.
Note: $a_0 = 2c_0$ and $b_0=0$.
Hence
$ f(x) = \displaystyle\frac{a_0}{2}$ $+ \displaystyle\sum_{n=1}^{\infty} \Big[ a_n\cos\Big(\frac{\pi nx}{L}\Big)$ $+ \displaystyle b_n\sin\Big(\frac{\pi nx}{L}\Big) \Big]$$a_n$ can be derived by using the expression from $c_n$
$\displaystyle a_n = c_n + c_{-n}$ $\displaystyle =\frac{1}{2L}\int_{-L}^{+L}f(x)$ $\displaystyle e^{-in\pi x/L}dx$ $\displaystyle +\frac{1}{2L}\int_{-L}^{+L}f(x)$ $\displaystyle e^{in\pi x/L}dx$Factorise and spot the exponential form of $\cos$.
$\displaystyle =\frac{1}{L}\int_{-L}^{+L}f(x)$ $\displaystyle \Big[\frac{e^{in\pi x/L} +e^{-in\pi x/L}}{2}\Big]dx$ $\displaystyle= \displaystyle\frac{1}{L}\int_{-L}^{L} f(x)$ $\displaystyle \cos\Big(\frac{\pi nx}{L}\Big) dx$Similarly for $b_n$,
$ b_n = \displaystyle\frac{1}{L}\int_{-L}^{L} f(x)$ $\displaystyle \sin\Big(\frac{\pi nx}{L}\Big) dx. $Triangular Fourier Series Derivation
The triangular function is defined by the following:
$\displaystyle f(x)=\left\{ \begin{array}{ll} \frac{-2A}{L} (x+L) \quad (-L \leq x < -L/2) \\ \frac{2A}{L} x \qquad \qquad (-L/2\leq x < L/2) \\ \frac{-2A}{L} (x-L) \quad (L/2\leq x < L) \end{array} \right. $First notice that $f(x)$ is odd about $x=0$, hence $a_n=0$ for all $n$. Also, since the $b_n$ integrand is even about $x=0$,
$\displaystyle b_n=\frac{2}{L}\int_0^L f(x)$ $\displaystyle \sin \left(\frac{n \pi x}{L}\right)dx. $Notice that for even $n$, $b_n$ is odd about $x=L/2$. Hence,
$ \displaystyle b_n=\frac{2}{L}\int_0^{L} f(x)$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right) dx$ $\displaystyle = 0 $ $\displaystyle\quad \text{for even n}. $The integral from $0$ to $L/2$ is equal in magnitude but opposite in sign to the integral from $L/2$ to $L$, for even $n$.
For odd $n$, the function is even around $L/2$, so we only have to integrate from $0$ to $L/2$ then multiply by $2$.This has made our job much easier.
$\displaystyle b_n=2\frac{2}{L}\int_0^{L/2} f(x)$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right) dx$ $\displaystyle \quad \text{for odd n} $Play around with the visualisation to the right to convince yourself this is true.
$ \displaystyle \text{For 0 < x < L/2:}$ $\displaystyle \quad f(x)=\frac{2Ax}{L} $Remembering that for even $n$, $b_n=0$, therefore only consider odd $n$.
$\displaystyle b_n = \frac{4}{L} \frac{2A}{L}\int_0^{L/2} x $ $\displaystyle \sin \left(\frac{n\pi x}{L} \right) dx $For odd n,
$\displaystyle \cos \left(\frac{n\pi}{2} \right)=0 $Therefore,
$\displaystyle b_n=\frac{8A}{L^2} \Bigg[0+ $ $\displaystyle \int_0^{L/2}\frac{L}{n\pi}$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right)dx \Bigg]$Note for odd $n$ :
$ \displaystyle \sin \left(\frac{n\pi}{2} \right)=(-1)^{\frac{n-1}{2}} $Therefore,
$ \displaystyle b_n=\frac{8A}{n^2\pi^2}(-1)^{\frac{n-1}{2}} $Finally,
$\displaystyle f(x)=\sum_{n=1,3,5...}^\infty \frac{8A}{n^2\pi^2}$ $\displaystyle(-1)^{\frac{n-1}{2}} $ $\displaystyle \sin \left(\frac{n\pi x}{L} \right) $And the using that an odd number is given by $2n +1$ for any $n$,
$ \displaystyle f(x)=\sum_{n=1,2,3...}^\infty $ $\displaystyle \frac{8A}{(2n-1)^2\pi^2}(-1)^n $ $\displaystyle \sin \left(\frac{(2n-1)\pi x}{L} \right) $Parabolic Fourier Series Derivation
The parabolic function is defined as:
$ \displaystyle f(x)=Ax^2 \quad \text{for:} -L\leq x< L$and forced to be periodic. $A$ is a constant.
Therefore, $a_n$ and $b_n$ coefficients are given as
$\displaystyle b_n = \frac{1}{L}\int_{-L}^{+L} Ax^2$ $\displaystyle \sin \left(\frac{n \pi x}{L} \right)dx $$\displaystyle a_n= \frac{1}{L}\int_{-L}^{+L} Ax^2$ $\displaystyle \cos \left(\frac{n \pi x}{L} \right)dx $
The $b_n$ integral is odd about $x=0$, hence $b_n=0$ for all $n$. $f(x)$ is even about $x=0$. Hence
$\displaystyle a_n=\frac{2}{L}\int_{0}^{+L} Ax^2$ $\displaystyle \cos \left(\frac{n \pi x}{L} \right)dx $For $n=0$:
$\displaystyle a_0 = \frac{2}{L} \int _{0}^{+L} Ax^2 dx $ $\displaystyle a_0 = \frac{2AL^2}{3} $For $n\neq 0 $:
$\displaystyle a_n = \frac{2A}{L}\int_0^L x^2$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right)dx $This Eqn. can be solved by integrating by parts.
$\displaystyle = \frac{2A}{L}$ $\displaystyle \Bigg[0$ $\displaystyle -\int_0^L\frac{2xL}{n\pi}$ $\displaystyle \sin\left(\frac{n \pi x}{L}\right)dx \Bigg] $
Therefore, the fourier series can be written as
$\displaystyle f(x) = \frac{AL^2}{3}$ $\displaystyle + \sum_{n=1}^\infty \frac{4AL^2}{n^2\pi^2}$ $\displaystyle (-1)^n \cos \left(\frac{n\pi x}{L} \right) $Dirac-Delta Fourier Series Derivation
The Dirac-delta function can be thought of as a infinite spike at $x=0$.
$\displaystyle f(x) = \delta(x)=\left\{ \begin{array}{ll} +\infty \quad (x=0) \\ 0 \qquad (x \neq 0) \end{array} \right. $$\displaystyle a_n=\frac{1}{L}\int_{-L}^{+L} \delta (x)$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right)dx $
$\displaystyle b_n=\frac{1}{L}\int_{-L}^{+L}\delta(x)$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right)dx $
$\delta(x)$ is an even function. Hence $b_n=0 $ and
$\displaystyle a_n=\frac{1}{L} $By considering the shifting property of the Dirac-Delta function,
$\displaystyle \int_{\alpha-\epsilon}^{\alpha+\epsilon} g(x) \delta(x-\alpha)dx=g(\alpha)$For us, $\alpha=0, \epsilon=L,$ and $g(x)= \sin \left(n \pi x/L \right).$
Therfore,
$\displaystyle a_n=\frac{1}{L}\cos \left(\frac{n\pi \times 0}{L} \right)=\frac{1}{L}$ $\displaystyle b_n=\frac{1}{L}\sin \left(\frac{n\pi \times 0}{L} \right)=0$Therefore, the fourier series for positive $L$ can be written as
$\displaystyle f(x)=\frac{1}{2L}+\sum_{n=1}^\infty \frac{1}{L}$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right). $Square Wave Derivation
The square wave is defined as the following:
$\displaystyle f(x)=\left\{ \begin{array}{ll} -A \quad (-L \leq x < 0) \\ A \quad (0\leq x < L) \end{array} \right. $The $a_{n}$ terms can be found be noting that $f(x)$ is odd, so $a_n$ is $0$ for all $n$.
To find the $b_n$ terms, the integration can be split into two parts: $-L\leq x <0$ and $ 0\leq x < L.$ This gives the following integration:
$\displaystyle b_n=\frac{1}{L}\int_{-L}^0 -A$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right)dx$ $\displaystyle + \frac{1}{L}\int_0^L A$ $\displaystyle \sin \left(\frac{n \pi x}{L} \right)dx $which can be evaluated to:
$\displaystyle b_n=\frac{-2A}{L}\frac{L}{n\pi}$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right)\biggr |_0^L$ $\displaystyle =\frac{2A}{n\pi}\left[1-\cos\left(n\pi \right) \right] $Note that $\displaystyle\cos \left(n \pi\right)=(-1)^n$
Hence $\displaystyle b_n=\frac{2A}{n\pi}(1-(-1)^n)$
Therefore the final fourier series is:
$\displaystyle f(x)=\sum_{n=1}^{\infty} \frac{2A}{n\pi}$ $\displaystyle (1-(-1)^n)$ $\displaystyle\sin \left(\frac{n\pi x}{L}\right). $Sawtooth Wave Derivation
The Sawtooth wave is defined as the following:
$\displaystyle f(x)=\frac{Ax}{L} $ $\displaystyle \quad (-L \leq x < L). $$f(x)$ is odd, so $a_n= 0$ for all $n$.
The $b_n$ terms are given by the following integration:
$\displaystyle b_n=\frac{1}{L}\int_{-L}^{L} \frac{Ax}{L}$ $\displaystyle\sin \left(\frac{n\pi x}{L} \right)dx $ $\displaystyle =\frac{2A}{L^{2}}\int_{0}^{L} x$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right)dx. $Using Integration by parts it can be shown that:
Note that the second integrand is zero as it is of cosine over a full period.
$\displaystyle b_n=-\frac{2A}{n\pi} \cos \left(n\pi \right)$ $\displaystyle=-\frac{2A}{n\pi}(-1)^n $Therefore the final fourier series is:
$\displaystyle f(x)=\sum_{n=1}^\infty \frac{2A}{n\pi}(-1)^{n+1}$ $\displaystyle \sin \left(\frac{n\pi x}{L} \right). $Mod x Derivation
The $|x|$ function is defined as the following:
$\displaystyle f(x)=A|x| \quad (-L \leq x < L). $ $\displaystyle a_n = \frac{1}{L}\int_{-L}^{+L} A|x| \cos \left(\frac{n \pi x}{L} \right)dx $ $\displaystyle b_n = \frac{1}{L}\int_{-L}^{+L} A|x|$ $\displaystyle \sin \left( \frac{n\pi x}{L}\right) dx $$f(x)$ is even about $x=0$. Hence $b_n=0 $
The $a_n$ integral is even about $x=0$. Hence,
$\displaystyle a_n = \frac{2}{L}\int_{0}^{+L} Ax $ $\displaystyle \cos \left(\frac{n \pi x}{L}\right)dx. $For $n=0$:
$\displaystyle a_0 = \frac{2A}{L}\int_0^L x dx $ $\displaystyle = \frac{2A}{L}\frac{x^2}{2} \biggr |_0^L $ $\displaystyle = AL .$For $n \neq 0$:
$\displaystyle a_n = \frac{2A}{L}\int_{0}^{+L} x $ $\displaystyle \cos \left(\frac{n \pi x}{L} \right)dx. $By integrating by parts,
Hence,
$\displaystyle a_n = \frac{2A}{L}\frac{L^2}{(n\pi)^2}$ $\displaystyle \left[(-1)^n-1 \right] $ $\displaystyle = \frac{2AL}{(n\pi)^2}\left[(-1)^n-1 \right]. $Therefore the final fourier series is:
$\displaystyle f(x)=\frac{AL}{2}+$ $\displaystyle \sum_{n=1}^\infty \frac{2AL}{(n\pi)^2}$ $\displaystyle \left[(-1)^n-1 \right]$ $\displaystyle \cos \left(\frac{n\pi x}{L} \right). $Section 3
The 0th term of the series is the constant term before the sum;
$$\frac{a_0}{2}.$$This is labelled as the 0th term so that the series may start indexing its terms from $n=1$.
$\displaystyle f(x)=\frac{a_0}{2}$ $\displaystyle+\sum_{n=1}^{\infty}a_n \cos\left(\frac{n\pi x}{L}\right)$ $\displaystyle+b_n \sin\left(\frac{n \pi x}{L}\right) $If the function is not periodic, then we may cut the function, forcing it to be periodic over some $$ -L < x < L. $$ This means that we can prescribe a Fourier series that is now valid for the function over the selected range. If we take the limit as $L \rightarrow \infty$, then a Fourier transform need be used. This is a different problem entirely!
Section 4
Decomposition of a function into odd and even parts
Representing a function in terms of a trigonometric Fourier series is analogous to representing a vector in terms of basis vectors. Here sines and cosines are our basis functions, we have a method for finding the projection of the function in the direction of each basis function ($a_{n}$ and $b_{n}$ are the "projections" of $f(x)$ onto $\sin\left(\frac{n\pi x}{L} \right)$ and $\cos\left(\frac{n \pi x}{L} \right)$ respectively).
This visualisation shows how the first ten terms are introduced to the series, notice that usually as the number of terms included in the series increases, new terms become less significant (their amplitude decreases).
Section 5
Power spectrum
The power spectrum form is a different representation of a continuous signal. One can think of a signal as a sound wave that is a superposition of different frequencies $\omega_n$, each with amplitude $\alpha_n$, and relative phases $\theta_n$. Any signal of period $2L$ can be decomposed in terms of the amplitude and relative phase of its discrete frequency modes. Its two parameters $\alpha_n$ and $\theta_n$, enable us to measure the amount of each frequency $\omega_n=\frac{n\pi}{L}$ contained in the signal, and the relative phase difference between the $n^{th}$ frequency and a cosine wave centered at $x=0$. This is simply a different way to represent a signal rather than decomposing it into its even and odd parts.
$$ f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty}\alpha_n \cos\bigg(\frac{n\pi x}{L} - \theta_n\bigg)$$ $$ \alpha_n = \sqrt{a^2_n + b^2_n}$$ $$\theta_n = \tan^{-1} \bigg(\frac{b_n}{a_n}\bigg)$$For some even functions, when the period transitions from 0 to negative, the value of $\theta_n$ change from $0$ to $\pi$ or vice versa. Why do you think this happens? (This happens because the value of $a_n$ changes sign ($b_n$ is 0) causing the value of $\theta_n$ to change. For $b_n = 0$, $\tan^{-1}(\frac{b_n}{a_n})$ can be both 0 or $\pi$ depending on whether $a_n$ is positive or negative. Not all even functions exhibit this. The parabola for example, has its $a_n$ proportional to $L^2$, so its sign does not change when L changes sign.
Orthogonal functions
Two functions $f$ and $g$ are said to be orthogonal if their inner product $\langle f,g\rangle$ is 0. Just like basis vectors in a finite vector space, a set of orthogonal functions can form an infinite basis in a function space and a linear sum of these basis functions can describe any function in that function space. For functions that are periodic over $-L < x \leq L$ with a period of $2L$, the fourier components $\rightarrow$ $\sin(\frac{\pi x}{L}), \cos(\frac{\pi x}{L}), \sin(\frac{2\pi x}{L}), \cos(\frac{2\pi x}{L})...$ and so on form a complete orthogonal set that can be used to describe these functions. This means that increasing the amplitude of one of the components does not affect the other components, so changing the amount of any frequency contained in a signal leaves all the other frequencies unaffected.
Section 6
Description
Finally, you can see the components of the series, the power spectrum and the resultant Fourier series displayed all at once. You can select one of the example functions from the previous sections, or input your own custom function, and see how all the elements work together to build a Fourier series.
How To Use Custom Functions
To specify a custom function, select custom from the drop down menu and input your desired function into the
input for $f(x)$.
The period slider forces the function you have specified to be periodic over $-L < x \leq L$.
For example if $f(x) = \sin(x)$ with $L = 1$, this is the sine function but cut at $x = \pm 1$ and forced
to be periodic over just this range (not the full $2\pi$ period).
The following functions can be used:
- Trigonometric functions (e.g. sin(), cos())
- Trigonometric inverses (e.g. arcsin(), arccos())
- Hyperbolic functions (e.g. sinh(), cosh())
- Hyperbolic inverses (e.g. arsinh(), arcosh())
- Exponentials and logs (e.g. exp(), log())
Syntax:
Entering 5x does not work: instead you should write 5*x.
Write exponents as a^(exponent), so $x^2$ is writen as x^2.
Functions should be real and fully defined over the domain, for example log(x) is imaginary
for values less than zero, so does not work.
log(x+1) does not work either (with a period of 1), since log is undefined at zero, however
log(1+x^2) does work for all periods, since it is defined over the whole domain and is real.
Sometimes due to the numerical integration methods used, the power spectrum shows very small values ($10^{-17}$).
These are simply due to the inexact integration and should be treated as zero.


gslp - Format and print text using ghostscript
gsbj - Format and print text for BubbleJet printer using ghostscript
gsdj - Format and print text for DeskJet printer using ghostscript
gsdj500 - Format and print text for DeskJet 500 BubbleJet using ghostscript
gslj - Format and print text for LaserJet printer using ghostscript
gslp -12BclqRr -b<header> -f<font> -F<hfont> -L<lines> -p<outfile> -T<n> --add-to-space <units> --add-to-width <units> --columns <n> --detect --first-page <n> --kern <file.afm> --last-page <n> --(heading|footing)-(left|center|right) <string> --margin-(top|bottom|left|right) <inches> --no-eject-(file|formfeed) --spacing <n> [gs options] [files]
This utility provides functionality approximately equivalent to the Unix enscript (1)program. It prints plain text files using a single font. It currently handles tabs and formfeeds, but not backspaces. It will line-wrap when using fixed-pitch fonts. It will also do kerning and width adjustment.
The default device (-sDEVICE=) and resolution (-r) are as follows: By default the current date is formatted as the center header.
Standard switches implemented:
-12BclqRr -b<header> -f<font> -F<hfont> -L<lines> -p<outfile>
-T<n> set tab width
-GghKkmow -# -C -d -J -n -P -S -s -t -v
add the given number of 1/72" units to the width of each space (may be negative)
add the given number of 1/72" units to the width of each character (may be negative)
print in <n> columns
treat the file as PostScript if it starts with %!
start printing at page <n>
kern using information from the given .AFM file
stop printing after page <n>
--(heading|footing)-(left|center|right) <string>
set the heading/footing fields; use -B first to clear
--margin-(top|bottom|left|right) <inches>
set a margin
end-of-file/FF only starts a new column, not a new sheet
use double (n=2), triple (n=3), etc. spacing
Also, the string %# in a heading or footing is replaced with the page #. This document was last revised for Ghostscript version 9.06. Artifex Software, Inc. are the primary maintainers of Ghostscript. This manpage by George Ferguson.
gsbj [options] [files]
gsdj [options] [files]
gsdj500 [options] [files]
gslj [options] [files] DESCRIPTION
gslp epson 180
gsbj bj10e 180
gsdj deskjet 300
gsdj500 djet500 300
gslj laserjet 300
OPTIONS
SEE ALSO
VERSION
AUTHOR


| < Day Day Up > |
8.2. Font-Lock ModeFont-lock mode is discussed primarily in Chapter 9; it's designed for coloring code to make it easier to read. But the fact is that it works well in other modes too, like the Buffer List (Chapter 4), Dired (Chapter 5), and in all the markup modes described in this chapter. To turn on font lock mode, choose Syntax Highlighting from the Options menu. If you decide you want to turn it on for every session, select Save Options from the Options menu and Emacs writes your .emacs file. For more details on font-lock mode, see Chapter 9. |
| < Day Day Up > |


WITNESS LIST Appropriations Committee March 3, 2005-7:00A Budget On: Flack, Teri (Texas Higher Education Coordinating Board) Paredes, Dr. Raymund A. (Texas Higher Education Coordinating Board)


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Training Manual for SDAL
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Git
Windows
macOS
Linux
Chromebook
Text Editor
Windows
macOS
Linux
R
Windows
macOS
Linux
Post installation settings
SQLite
Windows
macOS
Linux
SSH Keys
GitHub
Lightfoot
GitLab (devlab)
LaTeX
Syllabus
Lesson Breakdown
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
I Presentations and Talks
DSPG Introduction
Ethics
II SDAL Specific Components
1
Infrastructure
1.1
Components
1.2
Accessing Servers
1.2.1
RStudio
1.2.2
Database
1.2.3
Python
1.3
Project Template
1.4
Getting a project repository
1.4.1
Using Terminal
1.4.2
Using RStudio
2
Documentation and Metadata
2.1
Code documentaion
2.1.1
lintr
2.2
Metadata
2.3
README files
2.3.1
Example File
III Version Control
3
Version Control
3.1
Git
3.2
Git setup
3.3
Git on your own
3.4
Working with remotes
3.5
Git with branches
3.6
Collaborating with Git
3.7
Protecting branches
3.8
Help! (FAQ)
3.8.1
General workflow
3.8.2
Git push rejected (master)
3.8.3
Accidently did work on
master
:
3.8.4
Get changes from master on your branch
3.8.5
Remote server (e.g., GitLab, GitHub, Bitbucket, etc) shows merge conflict
3.8.6
Remove data/files from history
IV RStudio
4
RStudio
4.1
Restarting RStudio Session
4.1.1
Within RStudio
4.1.2
From the terminal
4.2
Accessing folders
4.2.1
Outside of Home
V R
5
Data Visualization
5.1
Loading ggplot2
5.2
Creating a ggplot
5.3
Aesthetic Mapings
5.4
Facets
5.5
Geometic Objects
5.6
Statistical Transformations
5.7
Position Adjustments
5.8
Coordinate Systems
6
Importing Data
6.1
Loading datasets
6.2
Writing to a files
7
Data Transformations
7.1
dplyr
library
7.2
Filter
7.3
Comparison (operators)
7.4
Logical operators
7.5
Arrange
7.6
Select
7.7
Mutate
7.8
Summarize (summarise)
7.9
Groupby
8
Tidy data
8.1
tidyr
8.2
Gather
8.3
Primer to joins
8.4
Spread
8.5
Separate
9
Relational Data in R
9.1
Create simple datasets
9.2
one-to-one
9.3
many to one OR one to many
9.4
many to many
9.5
Multiple keys
9.6
Different column names
10
Strings
10.1
Regular Expressions
10.1.1
Intro
10.1.2
Basic Web Scraping Example
10.1.3
Lookaround Examples
11
Factors
11.1
forcats
11.2
Sorting
11.3
Counting
11.4
Re-ording factors
11.5
Modifying factor values
11.5.1
Double check your work
12
Dates and Times
12.1
lubridate
12.2
Making datetimes from data
12.3
Non-standard date formatting
12.4
strptime format variables
12.5
Datetime arithmetic
13
SQL Databases
13.1
Databases in R
13.1.1
CREATE REUSABLE CONNECTION TO DATABASE
13.1.2
WRITE DATA TO DATABASE TABLES
13.2
Joins
13.2.1
JOIN TABLES IN SQL WITH DBI
13.2.2
JOIN TABLES IN SQL IN SQL CHUNK
13.2.3
JOIN TABLES IN SQL IN SQL CHUNK WITH OUTPUT VARIABLE
13.2.4
JOIN TABLES IN SQL IN SQL CHUNK APPLY WHERE CLAUSE AND FUZZY SEARCH
13.2.5
JOIN TABLES IN SQL IN SQL CHUNK APPLY WHERE CLAUSE WITH ‘AND’ AND FUZZY SEARCH
13.2.6
JOIN TABLES IN SQL IN SQL CHUNK APPLY SELECT AND WHERE CLAUSE WITH ‘AND’ AND FUZZY SEARCH AND ORDER
13.2.7
JOIN TABLES IN SQL IN SQL CHUNK APPLY SELECT AND WHERE CLAUSE AND FUZZY SEARCH AND ORDER AND GROUP BY WITH AGGREGATE FUNCTION
13.3
dplyr and data.table
14
Vectors
14.1
vectors (c)
14.2
Subsetting vectors
14.3
Negative indicies drop by position
14.4
Lists
14.5
Named vectors
14.6
Named lists
14.7
vectorization / broadcasting
15
Functions
15.1
Writing Functions
15.1.1
Fahrenheit to Kelvin
15.1.2
Kelvin to Celsius
15.1.3
Fahrenheit to Celsius
16
Conditionals
16.1
if statements
16.2
If else statements
16.3
Dealing with NA
17
Iteration
17.1
Broadcasting
17.2
For loops
17.2.1
Pre allocating in a loop
17.3
purrr (map)
17.4
Apply (in base R)
17.4.1
lapply
17.4.2
sapply
17.4.3
mapply
17.4.4
apply (2-dimensions)
18
R Dialects
18.1
data.frame
18.1.1
Convert to dataframe
18.1.2
Select columns
18.1.3
Select column as dataframe
18.1.4
Filtering rows
18.1.5
Filter rows and select columns
18.1.6
Works with dplyr
VI R Special Topics
19
data.table
19.1
Read into data.table
19.2
Convert to data.table
19.3
Working with data.table
19.3.1
Select columns list() .()
19.3.2
Functions on columns
19.3.3
.N (counts)
19.3.4
Using dplyr
20
Spatial Data
21
APIs and Web Scraping
21.1
Tables from websites (wikipedia)
21.2
Websites (rvest)
21.3
Selenium
22
Communication
23
Shiny
24
Text Mining
24.1
One-token-per-row (unnest_tokens)
24.2
Jane Austen
24.3
Stop words and Frequencies
24.4
gutenbergr package
24.5
Sentiment Analytis
24.6
tf-idf: Term frequency, inverse document frequency
24.7
bind_tf_idf
24.8
Relationships (n-grams)
24.9
Stemming
VII Modeling
25
Random Forests
25.1
CART
25.2
Bootstrapping
25.3
Bagging
25.4
Viewing Random Forests
VIII Exercises
IX Back Matter
Build Details
References
Published with bookdown
Training Manual for SDAL
Chapter 14
Vectors


The Java EE 7 Tutorial
12.1 Managed Beans in JavaServer Faces Technology
A typical JavaServer Faces application includes one or more managed beans, each of which can be associated with the components used in a particular page. This section introduces the basic concepts of creating, configuring, and using managed beans in an application.
12.1.1 Creating a Managed Bean
A managed bean is created with a constructor with no arguments, a set of properties, and a set of methods that perform functions for a component. Each of the managed bean properties can be bound to one of the following:
-
A component value
-
A component instance
-
A converter instance
-
A listener instance
-
A validator instance
The most common functions that managed bean methods perform include the following:
-
Validating a component's data
-
Handling an event fired by a component
-
Performing processing to determine the next page to which the application must navigate
As with all JavaBeans components, a property consists of a private data field and a set of accessor methods, as shown by this code:
private Integer userNumber = null; ... public void setUserNumber(Integer user_number) { userNumber = user_number; } public Integer getUserNumber() { return userNumber; }
When bound to a component's value, a bean property can be any of the basic primitive and numeric types or any Java object type for which the application has access to an appropriate converter. For example, a property can be of type java.util.Date
if the application has access to a converter that can convert the Date
type to a String
and back again. See Writing Bean Properties for information on which types are accepted by which component tags.
When a bean property is bound to a component instance, the property's type must be the same as the component object. For example, if a javax.faces.component.UISelectBoolean
component is bound to the property, the property must accept and return a UISelectBoolean
object. Likewise, if the property is bound to a converter, validator, or listener instance, the property must be of the appropriate converter, validator, or listener type.
For more information on writing beans and their properties, see Writing Bean Properties.
12.1.2 Using the EL to Reference Managed Beans
To bind component values and objects to managed bean properties or to reference managed bean methods from component tags, page authors use the Expression Language syntax. As explained in Overview of the EL, the following are some of the features that the EL offers:
-
Deferred evaluation of expressions
-
The ability to use a value expression to both read and write data
-
Method expressions
Deferred evaluation of expressions is important because the JavaServer Faces lifecycle is split into several phases in which component event handling, data conversion and validation, and data propagation to external objects are all performed in an orderly fashion. The implementation must be able to delay the evaluation of expressions until the proper phase of the lifecycle has been reached. Therefore, the implementation's tag attributes always use deferred-evaluation syntax, which is distinguished by the #{}
delimiter.
To store data in external objects, almost all JavaServer Faces tag attributes use lvalue expressions, which are expressions that allow both getting and setting data on external objects.
Finally, some component tag attributes accept method expressions that reference methods that handle component events or validate or convert component data.
To illustrate a JavaServer Faces tag using the EL, the following tag references a method that validates user input:
<h:inputText id="inputGuess" value="#{userNumberBean.userNumber}" required="true" size="3" disabled="#{userNumberBean.number eq userNumberBean.userNumber ...}" validator="#{userNumberBean.validateNumberRange}"> </h:inputText>
This tag binds the inputGuess
component's value to the UserNumberBean.userNumber
managed bean property by using an lvalue expression. The tag uses a method expression to refer to the UserNumberBean.validateNumberRange
method, which performs validation of the component's local value. The local value is whatever the user types into the field corresponding to this tag. This method is invoked when the expression is evaluated.
Nearly all JavaServer Faces tag attributes accept value expressions. In addition to referencing bean properties, value expressions can reference lists, maps, arrays, implicit objects, and resource bundles.
Another use of value expressions is to bind a component instance to a managed bean property. A page author does this by referencing the property from the binding
attribute:
<h:outputLabel for="fanClub" rendered="false" binding="#{cashierBean.specialOfferText}"> value="#{bundle.DukeFanClub}"/> </h:outputLabel>
In addition to using expressions with the standard component tags, you can configure your custom component properties to accept expressions by creating javax.el.ValueExpression
or javax.el.MethodExpression
instances for them.
For information on the EL, see Chapter 9, "Expression Language".
For information on referencing managed bean methods from component tags, see Referencing a Managed Bean Method.


Dual approach to biological and cultural diversity has led to varying interests within the same location, different competencies and designated domains of authority, different instruments policies, tools, and legal frameworks, different understandings of diversity among responsible authorities, and the different international movements dealing with biological and cultural diversity through individual agendas.
Separating biological from cultural diversity results in differing and sometimes conflicting agendas and approaches. From biodiversity perspective, people may be perceived as a disturbance or even a threat. From the cultural diversity perspective, more attention is given to individual cultural artifacts and cultural heritage disconnected from natural environment. Viewing biological and cultural diversity as separate entities can sever the historic and in many cases mutually reinforcing relationship between biodiversity and local cultural practices, land uses, languages and associated knowledge.
A joint approach to promotion of diversity would strengthen the integration, interdependence and positive relationship between cultural and biological diversity.
Sites of both cultural and natural distinctiveness may be of interest to various sectors. Different sectors may not see eye to eye regarding which management practices to employ at a site of both cultural and biodiversity importance, even when they both want what is best for that area.
A joint management plan would balance both biodiversity and cultural heritage in equal measure.
Decision makers operate from different administrative sectors such as natural resources management, agriculture, cultural heritage and historic preservation, sustainable development, planning, civil engineering, tourism, economics, etc.
This governmental organization scheme leads to different administrative concerns and values. This situation results in an ongoing debate over contrasting ideas of what constitutes diversity (biological and cultural) and how to best manage it.
A joint approach would allow a full appreciation of the interplay between biological and cultural diversity, social and natural dynamics, at a given site and would integrate the specialized knowledge and various interests across multiple various sectors.
Across various levels of society, existing biodiversity policies tend to focus more on the categories of habitat protection and individual species protection. In parallel, cultural diversity policies tend to focus on either monument protection (which is valued for its archaeological, architectural, historical, folk, technical, art elements) or protection based on a site’s heritage value (which includes intangible elements such as seasonal customs, family traditions, crafts, folklore, food, clothing, and dance).
A joint framework would promote sustainable management, including conservation, of both cultural and biological diversity within a single approach. Such a framework would allow for better communication, cooperation, and coordination among various administrative authorities.
A lack of information about the relationships between biological and cultural diversity, including cultural and management practices, has resulted to a broadening of the gap between ‘biological’ and ‘cultural’ landscapes. In biodiversity policies, the concepts of conservation, sustainable use and access and benefit sharing are frequently implemented without taking into consideration the positive impact of many local cultural practices, land uses, knowledge and value systems and ways of living together. With regard to cultural policies, opinions vary on what defines culture and its boundaries often excluding a variety of distinctive relations to biodiversity, which underpin the diversity of tangible and intangible cultural heritage, including cultural expressions and practices.
A joint framework would allow for multiplicity of more comprehensive interpretations of diversity.
Separately focused conventions or directives encourage the Parties to implement independent agendas dealing with different types of diversity. Although some progress has been made in recent years, international institutions are configured into various Conferences of the Parties, Committees, and Working Groups which tend to work in isolation on separate priorities in biological diversity and diversity.
An enhanced joint framework could bridge concerns within organizations and motivate synthesis between various approaches to diversity.
The concept of “biocultural” diversity and “biocultural” heritage has emerged in recent decade as part of the efforts to narrow the widening nature-culture divide. These concepts provide important starting points for the reflections on the links between biological and cultural diversity, and have proven effective in raising awareness on the inextricable link between biological and cultural diversity, including the diversity of living organisms or habitats whose present features are due to cultural action. However, there is still a lack of consensus on the precise meaning of the term ‘biocultural’ and how it links to diversity agenda(s).
A joint framework would encourage the scientific and practitioner communities to assess the different manifestations and components of “bio-cultural” diversity.


Interface IOctTreeInsertable
Namespace: CADability
Assembly: CADability.dll
Syntax
public interface IOctTreeInsertable
Methods
| Improve this Doc View SourceGetExtent(Double)
Gets the 3-dimensional extent of an object
Declaration
BoundingCube GetExtent(double precision)
Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | precision | Precision of the test |
Returns
| Type | Description |
|---|---|
| BoundingCube | The minmax cube |
HitTest(ref BoundingCube, Double)
Tests whether an object is touched by the provided cube
Declaration
bool HitTest(ref BoundingCube cube, double precision)
Parameters
| Type | Name | Description |
|---|---|---|
| BoundingCube | cube | To test with |
| System.Double | precision | Required precision |
Returns
| Type | Description |
|---|---|
| System.Boolean | true if the object strikes the cube |
HitTest(Projection, BoundingRect, Boolean)
Tests whether an object is inside or touched by the rectangle when projected with the provided projection
Declaration
bool HitTest(Projection projection, BoundingRect rect, bool onlyInside)
Parameters
| Type | Name | Description |
|---|---|---|
| Projection | projection | The projection for the test |
| BoundingRect | rect | The rectangle to test the position |
| System.Boolean | onlyInside | true: the object must be totaly inside the rectangle, false: the object must be totaly or partially inside the rectangle |
Returns
| Type | Description |
|---|---|
| System.Boolean | true when the test succeedes, false otherwise |
HitTest(Projection.PickArea, Boolean)
Tests whether an object is inside or touched by the provided area
Declaration
bool HitTest(Projection.PickArea area, bool onlyInside)
Parameters
| Type | Name | Description |
|---|---|---|
| Projection.PickArea | area | The area to check for |
| System.Boolean | onlyInside | true: the object must be totaly inside the area, false: the object must be totaly or partially inside the area |
Returns
| Type | Description |
|---|---|
| System.Boolean | true when the test succeedes, false otherwise |
Position(GeoPoint, GeoVector, Double)
Returns the smallest parameter value (l) where the provided line hits the object so that the point
fromHere
+ l * direction
is on or close to the object. The result may be negative.
Return double.MaxValue if there is no such point.
Declaration
double Position(GeoPoint fromHere, GeoVector direction, double precision)
Parameters
| Type | Name | Description |
|---|---|---|
| GeoPoint | fromHere | Startpoint of the line |
| GeoVector | direction | Direction of the line |
| System.Double | precision | Precision for the test |
Returns
| Type | Description |
|---|---|
| System.Double | Position on the line |


| Package | Description |
|---|---|
| application.controllers |
| Modifier and Type | Class and Description |
|---|---|
class |
BookingController
Purpose:
Display Booking information, and manipulate Booking objects
Description:
Contains all methods manipulating bookings,
and sets up the views primarily governed with booking
tables and manipulation (Booking (for displaying
information about a particular booking), Bookings
(for displaying a table of all bookings a Customer
has made), BookingSeats (for displaying a seat plan
a Customer can choose their booking seats from), and
Screening (for displaying an employee a seat plan
for a screening, and enabling the employee to delete
the screening)).
|
class |
CustomerController
Purpose:
Control basic Customer functionality.
|
class |
EmployeeController
Purpose:
Control basic Employee functionality.
|
class |
FilmController
Purpose:
Display Film and Screening information, and
and manipulate Film and Screening objects
Description:
Contains all methods manipulating films and screenings,
and sets up the views primarily governed with film and
screening tables and manipulation (FilmEmployee and
FilmCustomer (displaying information about a given film),
NewFilm (for adding new films), NewScreening (for adding new
screenings), NewBooking (for displaying a screenings table and
choosing one for a new booking), and ScreeningsCustomer and
ScreeningsEmployee (for displaying a list of screenings for
a given film)).
|
class |
LoginController
Purpose:
Control logging in to the program, and for setting up
a User and their environment
Description:
Checks the user's username and password (via the Login view) and
enables creation of Customer's (via the Registration view).
|
class |
NavbarController
Purpose:
Enable the Employee to export information outside the program.
|
class |
UserController
Purpose:
Sets up and controls the Dashboard views for an Employee and
for a Customer
Description:
Depending on the mode in which it is set, initialises either
the Customer's or the Employee's dashboard, with a table of
films and buttons to the other parts of the program.
|


Pipelining
Datapath
-
Handout: pipelined processor datapath, second page
-
stages operate concurrently
-
instruction execution overlapped
-
output of stage 1 is buffered in B1-2 for use by stage 2 in next cycle(B2-3, B3-4, B4-5 similar)
- includes info needed for control signals
- I-cache allows instruction fetch every cycle
- D-cache allows load/store every cycle
- 1 instruction finishes per cycle(in steady state)
Hazards
- conditions that stall the pipeline
e.g. miss in I-cache (2 extra cycles)
- types: data, control, structural, 2 cycles stall
Data Hazards
e.g.
ADD r2, r0, r1
ADD r3, r2, #1
- value [r0] + [r1] in pipeline after compute in clock cycle 3
- forward it
e.g.
ADD r2, r0, r1
ADD r3, r2, #1
Data Forwarding
Asel = { PC + 4, A, Z }
Bsel = { B, offset, Z }
- Also need forwarding paths from stage 5 and to stage 2
e.g.
Load Hazard
- a dependent instruction following a load must delay 1 cycle
e.g.
- load delay slot is instruction following load
- can avoid hazard by filling with independent instruction
e.g.
Control Hazards
- hazard on PC(caused by branches)
e.g.
- ~20% dynamic instruction mix are branches
- reduce penalty to 1 cycle with dedicated branch adder in decode stage
Branch Delay Slot
- "feature" instruction after branch always executed (i.e dont squash it)
e.g.
Speculative Execution
- predict branch direction(taken, not taken) and start fetching
- resolve branch(execute it)
- if prediction correct, then
- else
- squash speculative instructions
- branch history table
- BNT updated on branch resolution with BTA and branch behaviour(BT = branch taken, BNT not taken)
1 bit predictor
- states:
- 0 = Likely not taken(LNT)
- 1 = Likely taken(LT)
- problem: always mispredicts first and last loop iterations
2 bit
- states:
- 00 = Strongly not taken(SNT)
- 01 = Likely not taken(LNT)
- 10 = Likely taken(LT)
- 11 = Strongly taken(ST)
e.g.
on BNT miss, guess LNT
i = 0;
do {
...
i++;
} while (i < 3); // B1
Structural Hazards
e.g. cache too small => less hit rate
e.g. unified L1 => cannot fetch and ld/st in same cycle
Performance
- execution time : T = n x CPI / r where
- n = dynamic instruction count
- CPI average cycles instruction
- r = clock rate(frequency)
- ideal CPI = 1
- increased by hazards
e.g.
CPI = 1.0 + B + L
= 1.0 + 0.15 x 0.2 x 2 + 0.2 x 0.4 x 1
= 1.14
- throughput
- P = 1 / T
- speedup of processor r2 over processor 1
- S = P 2 / P 1 = T 1 / T 2 = (n 1 x CPI 1 / r) / (n 2 x CPI 2 / r 2)
if n 1 = n 2 and r 1 = r 2 , S = CPI 1 / CPI 2
See previous chapter
See next chapter


The DecoratedListUI
and DecoratedTreeUI
render clickable/animatable icons on rows in lists/trees.
The demo in this showcase app offers a few ideas for potential decorations.
Each decoration is basically an actionable icon that implements this interface:
public interface ListDecoration { Icon getIcon(JList list, Object value, int row, boolean isSelected, boolean cellHasFocus, boolean isRollover, boolean isPressed); boolean isVisible(JList list, Object value, int row, boolean isSelected, boolean cellHasFocus); ActionListener getActionListener(JList list, Object value, int row, boolean isSelected, boolean cellHasFocus); Point getLocation(JList list, Object value, int row, boolean isSelected, boolean cellHasFocus); }
And then to integrate it:
JList list = new JList(); list.putClientProperty( DecoratedListUI.KEY_DECORATIONS, new ListDecoration[] { decoration1, decoration2, etc. }); list.setUI(new DecoratedListUI());
The decorations are "stamped" on each row, like the CellRendererPane
. That is: they don't exist in the component hierarchy, and the ComponentUI
is responsible for interpreting mouse clicks and triggering the appropriate ActionListener
.
This is great way to add extra functionality for power users without adding too much visual clutter.
However: you need to decide what you want to do about accessibility. This class represents a UI choice that is not accessible. This may be OK if every feature that is part of a decoration is also available somewhere else in your application. For example: if you also have a menu shortcut that activates the same feature.
The alternative is to try to layer actual JComponents
into your UI, and that has its own complex set of challenges for a list or a tree.


III.5 Building Operations Market Analysis and Strategies
Market Studies & Marketing Strategy
– Building Operations (III.5.)
Determine the right tenant mix.
- Short term leases vs long term leases.
- Usually a balance of lease termination dates is important t manage the re-lease risk.
- A ten-year lease with 2 years left is a short term lease.
- Big space users vs smaller space users.
- This depends on the configuration of the property.
- What is the optimum size for a tenant?
- Are full-floor users the most efficient space.
- Office vs. retail vs. residential
- This is the mixed-use conundrum
- Each use has different requirements for access, security, and utility use.
- Ironically, automobile parking is usually the biggest factor in managing these uses.
Determine the existing tenants’ plans for expansion.
- Existing tenants are the best prospects for leasing vacant space.
- Building operators need to understand their business plans and future space needs.
Identify tenants who are in the market searching for space.
- Need to have a working knowledge of the current market activity (even if you are fully leased).
- Who is moving, how is looking; who is expanding?
- This part of the “leasing gossip circle” and important market information.
Determine who should approach potential new tenants?
- Building operators always need to be marketing their space even if it is fully leased.
- If there is an active re-leasing effort, the Building operator needs to identify a strategy and a
communication system to find and attract new tenants.
- All of the following are involved so it is important who gets paid for what and when:
- Tenant representatives
- Landlord representatives
- Direct (in-house leasing agents)
- Property managers
Evaluate the pricing of the existing available space.
- Is the existing space appropriately in terms of competitive space?
- Are lease terms and concessions appropriate?


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Introduction
This document specifies a **RESTful API** for WSO2 **API Manager** - Admin Portal. Please see [full swagger definition](https://raw.githubusercontent.com/wso2/carbon-apimgt/v6.5.176/components/apimgt/org.wso2.carbon.apimgt.rest.api.admin/src/main/resources/admin-api.yaml) of the API which is written using [swagger 2.0](http://swagger.io/) specification.
Version information
0.16.0
Contact information
Contact: WSO2
Email<EMAIL_ADDRESS>License information
License: Apache 2.0
URL: http://www.apache.org/licenses/LICENSE-2.0.html
URI Scheme
Host: apis.wso2.com
BasePath: /api/am/admin/v0.16
Scheme: [HTTPS]
Consumes
[application/json]
Produces
[application/json]


becton-dickinson
Businessmodel of Becton Dickinson
Customer Segments
Becton Dickinson targets customers within the medical and healthcare sector. Its customers can be divided broadly into three categories:
- Distributors and independent sales agents, which market and sell Becton Dickinson products to end-users across multiple markets and jurisdictions;
- Medical and healthcare institutions that use Becton Dickinson products in the course of their work, including life science research organisations, clinical laboratories, pharmaceutical companies, medical facilities and medical practitioners; and
-
General consumers, who purchase Becton Dickinson products for personal healthcare use. Becton Dickinson divides its customers geographically into four groups:
- the US, including Puerto Rico;
- Europe;
- Greater Asia, including Japan and Asia Pacific; and
- Other, comprising Latin America, Canada, the Middle East and Africa. The US continues to be Becton Dickinson’s largest market, accounting in 2015 for almost 50% of the Company’s total revenues.
Among Becton Dickinson’s customers are Coherus Biosciences, Innovus Pharmaceuticals, Avalanche Biotechnologies, Greenestone Healthcare, and Cardinal Health.
Value Propositions
Becton Dickinson provides value to its customers through the quality and reliability of its products and services, the accessibility of its products, its commitment to innovation and development, and its established brand name.
Channels
Becton Dickinson operates a website a www.carefusion.com. The Company, however, does not operate an online sales channel.
Becton Dickinson employs a hybrid sales distribution model. Its products are marketed and sold in the United States and internationally through independent distribution channels, as well as directly to end-users by Becton Dickinson sales representatives.
Becton Dickinson’s domestic sales team sells primarily to distributors. The Company also uses third-party distributors, resellers and independent sales agents internationally to enhance its proprietary sales channels.
Becton Dickinson operates a number of sales offices and distribution centres worldwide, covering its principal geographic areas of operation: the US, Europe, Greater Asia and Other.
Customer Relationships
Although Becton Dickinson operates a website that allows customers to find information on the Company’s products, purchases cannot be made online. While the Company offers some ecommerce solutions to its distributors and resellers, Becton Dickinson products are not typically available on a self-service basis.
Becton Dickinson deals with both distributors and end-users, providing a tailored service to each customer that fulfils their individual requirements. The Company often enters into multi-year contracts, sales-type leases and operating leases with customers. It also provides its customers with extended warranty contracts and software maintenance contracts.
Becton Dickinson continues to provide personal care to its customers after-sale. Customers are able to contact the Company directly, with specific contact details provided for different business units and products ranges, over the phone or via email, in order to receive personalized technical support. This is supplemented by a range of online learning resources included in the Company’s Customer Learning Portal.
Additionally, Becton Dickinson updates its customers with company developments through its Alerts and Notices section, as well as through its Twitter, YouTube, Facebook and LinkedIn profiles.
Key Activities
Becton Dickinson is a globally-focused medical technology company. It is engaged in the development, manufacture, marketing and sale of medical devices, instrument systems and reagents. Its products, solutions and services are utilised almost exclusively within the healthcare and medical industry, including healthcare institutions, research facilities, and pharmaceutical laboratories.
The Company operates through two business segments: BD Medical, which comprises the development and sale of products and solutions covering diabetes care, medication management, pharmaceutical systems, and respiratory Solutions business; and BD Life Sciences, which refers to the Company’s development of consists of preanalytical and diagnostic systems.
Among Becton Dickinson’s products are hypodermic needles and syringes; insulin syringes and pen needles; prefillable syringe systems; infusion therapy products; blood collection products; and flow cytometry instruments.
Key Partners
Becton Dickinson partners with a number of companies worldwide in order to provide its customers with an efficient and reliable service. The Company’s partners can be divided broadly into three categories:
- Distribution and channel partners, which assist the Company in marketing products and solutions to end-users within the healthcare sector;
- Suppliers, which provide tools and resources for the production of Becton Dickinson products; and
- Strategic and joint-venture partners, which comprise medical technology companies, healthcare companies and private equity firms, with which the Company collaborates both on specific projects and ongoing research and development activities. In recent years, Becton Dickinson has partnered with Breakout Labs to fund and support biomedical start-ups, Central Admixture Pharmacy Services to provide greater end-user access to one another’s products, and Apax Partners to develop respiratory solutions.
Key Resources
Becton Dickinson’s key resources are its technology and intellectual properties, its manufacturing and logistics facilities, its supply chain and distribution partners, and its personnel.
According to its 2015 annual report, Becton Dickinson owns significant intellectual property, including patents, patent applications, technology, copyrights and trademarks, both in the US and internationally. The Company is also licensed under domestic and foreign patents. Searches of records held by the US Patent and Trademark Office identified a number of patent application filed in Becton Dickinson’s name, including applications entitled ‘Automated set-up for cell sorting’, ‘System and method for automated sample preparation’ and ‘Safety drug delivery connectors’.
While Becton Dickinson believes that its patents and trademarks are of material importance to its business, no single patent, intellectual property asset or license is material in relation to the Company’s business as a whole.
Cost Structure
Becton Dickinson incurs costs in relation to the research and development of its products, manufacture and production of its products, the storage and distribution of its products, the maintenance of its partnerships and the retention of its personnel.
The Company’s largest costs relate to selling and administrative expenses – comprising rent and utilities for its numerous sales offices and distribution centres, and the payment of employee salaries and benefits – which accounted for 24.9% of revenue in 2015. Research and development costs represented around 6.1% of total revenue.
Revenue Streams
Becton Dickinson generates revenue through the development and sale of medical devices, instrument systems and reagents. The Company also generates some revenue through the lease of medical equipment, recorded either as operating leases or sales-type leases.
In 2015 Becton Dickinson recorded annual worldwide revenues of $10.28 billion, up 21.7% on the $8.45 billion generated the previous year. The Company attributed this increase in part to revenue generated by CareFusion, which was acquired by the Company in March 2015.
The Majority of Becton Dickinson’s revenue is generated by its Medical segment, which accounted for $6.46 billion in revenue in 2015. Within the Medical segment, the Medication and Procedural Solutions unit was the most lucrative, generating $2.9 billion alone.


Deutsche Telekom to stick to multi-vendor strategy
FRANKFURT (Reuters) - Deutsche Telekom on Wednesday declined to comment on a magazine report that it would phase out some equipment from Chinese vendor Huawei Technologies [HWT.UL] over time, saying only that it relies on multiple network providers.
Business weekly Wirtschaftswoche reported earlier, citing company sources, that Deutsche Telekom would swap Huawei components out of its core network as part of the routine replacement of older equipment.
“Fundamentally, we are pursuing a multi-vendor strategy and source network components from several vendors. Security comes first,” a Deutsche Telekom spokesman said by email. He declined to comment directly on the magazine article.
Debate is bubbling up again in Germany over whether to join the United States in banning Huawei. Washington argues that its equipment contains “back doors” open to cyber spies and that it is beholden by law to the Chinese state. Huawei denies this.
Chancellor Angela Merkel had backed ground rules requiring all vendors to meet certain technical and governance criteria to be allowed to operate in Germany.
But she is facing a growing revolt from lawmakers in her coalition government who want to shut out Huawei.
Calls for a Huawei ban are likely to feature at a congress of Merkel’s ruling Christian Democrats this week, while some lawmakers in the Social Democratic Party - the junior coalition party - are proposing a draft resolution to ban Huawei.


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@jjmerelo
By Andrew Bertram - World66, CC BY-SA 1.0, Link
indi = random_chromosome(len)
rr = @distributed (+) for j in [indi[n:n+3] for n=1:3:length(indi)-3]
value = reduce(+, j )
if value == 0 || value == 4
1
else
0
end
end
fitness = @distributed for i in 0:1:number
indi = random_chromosome(length)
reduce( +, indi)
end
# Run with julia -p 4 code/parallel-evaluation.jl
from scoop import futures
toolbox.register("map", futures.map)
say [+] Bool.pick xx 65536 ==> map( *.so );
say (Bool.pick xx 65536).rotor(4).map( ! (0 < *.sum < 4) ).sum;
Juan Julián Merelo Guervós, José Mario García Valdez: Going Stateless in Concurrent Evolutionary Algorithms. WEA (1) 2018: 17-29
sub random-chromosome( UInt $length --> List(Seq) )
is export {
return Bool.pick() xx $length;
}
sub initialize( UInt :$size,
UInt :$genome-length --> Array ) is export {
my @initial-population;
for 1..$size -> $p {
@initial-population.push:
random-chromosome( $genome-length );
}
return @initial-population;
}
multi sub evaluate( :@population,
:%fitness-of,
:$evaluator --> Mix ) is export {
my MixHash $pop-bag;
for @population -> $p {
if ! %fitness-of{$p}.defined {
%fitness-of{$p} = $evaluator( $p );
}
$pop-bag{$p} = %fitness-of{$p};
}
return $pop-bag.Mix;
}
sub get-pool-roulette-wheel( Mix $population,
UInt $need = $population.elems ) is export {
return $population.roll: $need;
}
my $length = @chromosome1.elems;
my $xover1 = (^($length-2)).pick;
my $xover2 = ($xover1^..^$length).pick;
my @x-chromosome = @chromosome2;
my @þone = $xover1..$xover2; # crosover zone
@chromosome2[@þone] = @chromosome1[@þone];
@chromosome1[@þone] = @x-chromosome[@þone];
return [@chromosome1,@chromosome2];
sub mutation ( @chromosome is copy --> List ) is export {
my $pick = (^@chromosome.elems).pick;
@chromosome[ $pick ] = !@chromosome[ $pick ];
return @chromosome;
}
my Channel $c .= new;
my Channel $c2 = $c.Supply.batch( elems => 2).Channel;
my Channel $output .= new;
my $count = 0;
$c.send(1) for ^2;
my $more-work = start react whenever $c2 -> @item {
if ( $count++ < 32 ) {
$c.send( @item[1]);
my $sum = sum @item;
$c.send( $sum );
$output.send( $sum );
} else {
$c.close;
}
}
await $more-work;
n = 32
c1 = Channel(n)
for _ in 1:n
put!(c1,"foo")
end
for _ in 1:n # Reads from channel
data = take!(c1)
println(data)
end
my @evaluation = ( start react whenever $raw -> $one {
my $with-fitness = $one => max-ones($one);
$output.send( $with-fitness );
$evaluated.send( $with-fitness); # Check for solution and stuff
} ) for ^$threads;
my $selection = ( start react whenever $channel-three -> @tournament {
my @ranked = @tournament.sort( { .values } ).reverse;
$evaluated.send( $_ ) for @ranked[0..1];
my @crossed = crossover(@ranked[0].key,@ranked[1].key);
$raw.send( $_.list ) for @crossed.map: { mutation($^þ)};
} ) for ^($threads/2);
my $single = ( start react whenever $channel-one -> $crew {
# Get values and ...
while $count++ < $generations && best-fitness($population) < $length {
LAST {
if best-fitness($population) >= $length {
$channel-one.close;
} else {
$to-mix.send( $population );
}
};
# Forward one generation
}
} ) for ^$threads;
my $pairs = start react whenever $mixer -> @pair {
$to-mix.send( @pair.pick ); # To avoid getting it hanged up
$channel-one.send(mix( @pair[0], @pair[1], $population-size ));
};
Juan Julián Merelo Guervós, Juan Luis Jiménez Laredo, Pedro A. Castillo, José Mario García Valdez, Sergio Rojas Galeano: Exploring Concurrent and Stateless Evolutionary Algorithms. EvoApplications 2019: 405-412
git.io/p6-ea


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I wouldn't look to KICKING AND SCREAMING for the answer. Rather, the movie is a hilarious example of what not to do when you graduate. The guys, Chet (Eric Stoltz), Grover (Josh Hamilton), Max (Chris Eigeman), Skippy (Jason Wiles), and the show-stealing Otis (Carlos Jacott), can't seem to give up the college life. They hang out at college bars, woo freshmen, and sneak back into classes. Otis can't even seem to get out of his pajamas.
Women are only half the problem. Jane (Olivia d'Abo) is Grover's lover, but she jets off for Prague after graduation, leaving Grover in despair. Miami (Parker Posey) is Skippy's trouble-prone, flighty girlfriend. And Kate (Cara Buono) is Max's latest attachment, a cafeteria worker he picks up while haggling over an extra potato.
The plot basically follows the series of perpetual indecisions that plague the friends, an ironic reality that most of us seem to face at some point in our lives. The so-called "touching" moments are unfortunately pretty drab, and the mushy flashbacks where Jane and Grover's fledgling romance is built up are real snoozers. The film is rightfully a study of misery. This happiness stuff just gets in the way.
The acting and direction by Noah Baumbach (who also wrote the script) are perfectly dead-on. Carlos Jacott should gain a lot of notice (and at least one of the various movie awards) for his outrageously droll part as Otis. If the script had avoided the over-sentimentality, the film would have been even better. And oddly, a real ending seems to be mysteriously lacking.
KICKING AND SCREAMING pokes fun at the pretense and phoniness of virtually every college clique imaginable. If you're one of those sensitive types, you'll probably be offended at some point along the way. But hey, look on the bright side, at least you'll have it better than these guys.
RATING: ***1/2
\-------------------------------\ |* Unquestionably awful | |** Sub-par on many levels | |*** Average, hits and misses | |**** Good, memorable film | |***** Perfection | \-------------------------------\
-Christopher Null /<EMAIL_ADDRESS>-Contributing Editor, FEEDBACK / http://www.eden.com/~feedback -E-mail request to join the movie review mailing list
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


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@* * Copyright 2021 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import config.ApplicationConfig @import uk.gov.hmrc.play.views.html.helpers._ @import views.helpers.InputTypeRadioGroupParams @import views.html.helpers._ @import views.html.includes.awrs_main @this(formWithCSRF: FormWithCSRF, awrsMain: awrs_main) @(withdrawalConfirmationForm: Form[models.WithdrawalConfirmation])(implicit request: Request[AnyRef], messages: Messages, applicationConfig: ApplicationConfig) @awrsMain(messages("awrs.generic.tab.title", messages("awrs.withdrawal.confirm_page.heading")), userLoggedIn = true) {


The behavior of the Emacs interface can be controlled by a set of user-configurable settings. Some of these can be changed on the fly, while some require Emacs to be restarted. To set a variable on the fly, type M-x set-variable <RET> VariableName <RET> Value <RET>. Note that variable names can be completed by typing a few characters and then pressing <TAB>.
To set a variable so that the setting is used every time Emacs is started, add lines of the following format to ~/.emacs:
(setq VariableName Value)
Note that the Emacs interface is presently not using the `Customize' functionality to edit the settings.
The available settings are:
prolog-system
'sicstus
, which will be assumed for the rest of this
chapter. See the on-line documentation for the meaning of other
settings. For other settings of prolog-system
the variables below
named sicstus-
something will not be used, in some cases
corresponding functionality is available through variables named
prolog-
something.
sicstus-version
'(3 . 8)
.
Note that the spaces are significant!
prolog-use-sicstus-sd
t
(the default) to enable the source-linked debugging
extensions by default. The debugging can be enabled via the
Prolog
menu even if this variable is nil
. Note that the
source-linked debugging only works if sicstus-version
is
set correctly.
pltrace-port-arrow-assoc
obsolescent'(("call" . ">>>") ("exit" . "+++") ("ndexit" . "?++") ("redo" . "<<<") ("fail" . "---") ("exception" . "==>"))
where ndexit
is the nondeterminate variant of the Exit
port. Do not rely on this variable. It will change in future
releases.
prolog-indent-width
tab-width
, normally 8.
prolog-paren-indent
p :- ( q1 ; q2, q3 ).
Note that the spaces between the parentheses and the code are
automatically inserted when <TAB> is pressed at those positions.
prolog-align-comments-flag
nil
to prevent single %
-comments from being automatically
aligned. Defaults to t
.
Note that comments with one %
are indented to comment-column, comments
with two %
to the code level, and that comments with three %
are
never changed when indenting.
prolog-indent-mline-comments-flag
nil
to prevent indentation of text inside /*
... */
comments. Defaults t
.
prolog-object-end-to-0-flag
}
of an object definition to
prolog-indent-width
. Defaults to t
.
sicstus-keywords
:-
keyword). Defaults to
'((sicstus ("block" "discontiguous" "dynamic" "initialization" "meta_predicate" "mode" "module" "multifile" "public" "volatile")))
prolog-electric-newline-flag
nil
to prevent Emacs from automatically indenting the next
line when pressing <RET>. Defaults to t
.
prolog-hungry-delete-key-flag
t
to enable deletion of all white space before the
cursor when pressing <DEL> (unless inside a comment, string,
or quoted atom). Defaults to nil
.
prolog-electric-dot-flag
t
to enable the electric dot function. If enabled,
pressing . at the end of a non-empty line inserts a dot and a
newline. When pressed at the beginning of a line, a new head of
the last predicate is inserted. When pressed at the end of a line
with only whitespace, a recursive call to the current predicate is
inserted. The function respects the arity of the predicate
and inserts parentheses and the correct number of commas for separation
of the arguments. Defaults to nil
.
prolog-electric-underscore-flag
t
to enable the electric underscore function. When
enabled, pressing underscore (_) when the cursor is on a
variable, replaces the variable with the anynomous variable. Defaults to
nil
.
prolog-old-sicstus-keys-flag
t
to enable the key-bindings of the old Emacs interface. These
bindings are not used by default since they violate GNU Emacs
recommendations. Defaults to nil
.
prolog-use-prolog-tokenizer-flag
nil
to use built-in functions of Emacs for parsing the
source code when indenting. This is faster than the default but
does not handle some of the syntax peculiarities of
Prolog. Defaults to t
.
prolog-parse-mode
'beg-of-line
and 'beg-of-clause
. The first is
faster but may result in erroneous indentation in /* ... */
comments. The default is 'beg-of-line
.
prolog-imenu-flag
t
to enable a new Predicate
menu that contains all
predicates of the current file. Choosing an entry in the menu
moves the cursor to the start of that predicate. Defaults to
nil
.
prolog-info-predicate-index
Prolog/Help on predicate
menu entry). The default
setting is "(sicstus)Predicate Index"
.
prolog-underscore-wordchar-flag
nil
to not make underscore (_) a word-constituent
character. Defaults to t
.


Renovation and Custom Build
Unique Home Improvement is a construction company specialized in custom homes, additions and all aspects of home renovations.
With our contemporary approach, we are here to add a Unique touch to our clients’ homes and help them build their dreams.
Projects
Services
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- Custom Home Build
- Real Estate Serviceswww.gracezeren.com
By leveraging our core construction and building capabilities, we are able to provide solutions to our clients that bring outstanding value. Starting with a free consultation, our services include all aspects of new build and home renovations, as well as Real Estate Services.
We pride ourselves on our quality, project management, and customer communication ensuring that you are receiving what you expect.
With several years of experience and industry knowledge, Unique Home Improvement team is with you every step of the way!
About
Unique Home Improvement consists of highly skilled and reliable professionals, with many years of experience in fine home building.
We closely follow industry trends and bring style and functionality to every project undertaken. Contact us about your unique project and let our knowledge and experience help you build your dreams.
Contact us to book your free consultation today


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Hi there! I am Katie Moon and welcome to my portfolio! I currently reside outside of Cleveland, OH, where I work as a Research Chemist for an electrochemical company. Having a background in research has helped hone my problem solving skills and attention to detail. It has also cultivated a deeper sense of curiosity. I hope that these characteristics shine through with the projects I have completed and have on display!
In my spare time, you can find me at a coffeeshop with my head buried in a book. I absolutely love reading! Or if I have the time, hiking and traveling around the world! Being in nature is something that I hold dear to my heart. I always feel at home and completely refreshed after being out in the wilderness.


VSOnlineConnectedService
A sample for creating a TFS/VSOnline Connected Services. Configures Visual Studio 2015 projects to connect to Visual Studio Online
References
- Documentation for more on this Sample Connected Service
- Download the built VSIX on the Visual Studio Gallery
Initially created by Nicole Haugen & the Microsoft Cloud Platform Tools E&I team. Converted to Connected Services v2 RC build for //build and Ignite demos.


How does life look through the c, passion and purpose' lens?
According to the text the life is broken up in to the 3 parts
1. Pleasure: Looking and experiencing the high. This is very hard to manage.
2. Passion: The rhythm and the place of your performance. When time flies by.
3. Higher Purpose: Something which is grander than ourselves and has meaning to us.
From the 'discovering values and higher purpose' exercise,
What are your core values?
- Honesty
- Openness
- Kindness
- Trust
- Authenticity
What do you stand for?
- Never letting people down.
- People over groups.
- Standing up for yourself and others.
- Think of others in relation to your acts.
How did you find the resilience ideas and meditation exercise?
I found the cognitive resilience easier to hook into rather than Emotional resilience and Inner calm.
Usually it’s the cognitive side is the strongest
side of myself. I have used my cognitive to calm down my emotions to reason out the problem that is disturbing at the time.
Any other musings?
The Tack exercise is and interesting look at programing that I had not thought of.


Investment
|
Please put 20th October in your diary to join us for the morning at our London Office for the JLT Employee Benefits Investment Conference.
The theme for the conference will be “Investing: Alpha to Omega – Your Investment Journey”.
The agenda has been designed to articulate some of the current important topics concerning today’s Pension Schemes and how they structure their portfolios, from both JLT and a carefully selected group of investment partners.
8:30am Registration and coffee:
9:00am Welcome address and presentations considering
Alternative Sources for Growth - The changing role of equity allocation and how to access alternative sources of growth to complement your existing growth assets
The world beyond LDI: End Game Planning - Looking at the different stages a portfolio would go through on the way to a buyout
How to Hedge your Bets - Looking at the stabilising section of your portfolio, including positioning on the route to buyout
1:00pm Lunch
The main aim of the day is to provide relevant and useful information, with the opportunity to ask questions of the panels after each of the sessions, as well as during the coffee break and lunch. More details to follow.
Attendance is free for pension scheme trustees and invited guests.
If you would like to talk to the investment consulting team in advance of the conference, or are unable to attend and would like further information or a copy of the slide pack after the event, please contact Head of Investment Consulting, John Breedon at<EMAIL_ADDRESS>Tuesday 20th
October
2015
St Botolph Building
138 Houndsditch
London, EC3A 7AW
If you wish to register please click here. Alternatively, please e-mail Lisa Wilford at<EMAIL_ADDRESS>Keep up to date
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Call: 0891 50 50 50 Fax: 891 50 50 50
Email<EMAIL_ADDRESS>Visit: www.jlt-group.com
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From Ho chi Minh to Montréal
Booking
We searched for this flight on google at first to get an idea of the companies offering
the flight. We also search directly on Qatar airway web site since we liked our flight
with them the first time but unfortunately they had no flight that was doing that
itinerary (Ho chi Minh - Canada) After a bit of research we found that on google that
the least expensive seem to be with Delta airline. I started to do a little bit of
research on the airline itself since for this is a 24h flight so we wanted to be sure it
was going to be an enjoyable trip. For delta it seemed like we could reserved seat we
extra leg room for a small fee on certain flight and fortunately for us it was the case
for our longest flight (Korea-US). Even more perfect for us, there was a seat with extra
leg room next to a seat with no extra leg room so we only had to paid for the extra leg
room for Alexis and we still could sat next to one another. We ended up flying on Delta
Korean air which seems to be a joint company. The flight costed us 547,23 USD (767,76
CAN give or take with the conversion) each. Pretty cheap for 3 different flight. There
was an extra 38.99 USD (57 CAN) fee for the seat with extra leg room.
Flights amenities
Ho chi Minh - Seoul
First flight was from Ho Chi minh to Seoul Korea. The flight left at 8h30 and was 5h
long. Which was made a bit longer for alexis since he didn’t had a lot of legroom. But
on the bright side there was more legroom than on domestic flight since it was a huge
international flight. The food was incredible we got a meal and a snack. The meal was
really good and we even had smoked salmon! (which is one of my favorites thing)
Seoul - Minneapolis
Second flight left Seoul at 7h25 pm and arrived and 5h30pm the same day….Time zones are
a fun thing when you travel internationally especially with an 11h time difference. That
flight was actually ….H long. There was also no one next to us so we were able to spread
out! The food was also okay, we had a few option, 2 snacks and alcohol was included.
Tiny warning about drinking in a plane, it dehydrates you faster and it get you drunk
faster too. After one glass you're going to sleep like a baby. The snack on that flight
were pretty amazing since one of them was ice cream!
Minneapolis - Montréal
The last flight left Minneapolis at 8h25 and lasted.. H. Since the plane was pretty
empty we got upgraded to better seat and got extra leg room for that flight too. We go a
snack in that one too. From my experience when you fly very long distance the airline
seem to feed you along the way. But don’t mistake me we also ate at the Seoul airport
and at a few snack of our owns.