Hi Roy. This is a very common question that we get asked every year around this time. And, I feel the same way, as I'm a customer, too.
The answer is actually pretty simple – your bill increases when outdoor temperatures rise because you're consuming more energy due to your A/C running longer to keep your home cool. There is a direct connection between outdoor temperatures and your energy usage.
Your A/C can account for more than half of your monthly energy bill during peak cooling months.
Right now, it's running twice as long as it does in cooler months to keep your home at the same temperature which can result in higher than normal bills.
Think of it this way – if the outside temperature is 80 degrees and you have your thermostat set to 78 degrees, your A/C has to cool your home just 2 degrees. However, when it's 90 degrees outside, your A/C has to cool your home 12 degrees, running longer to keep the indoor temperature at 78 degrees.
To help you lower your energy costs, we've compiled a list of some small changes you can make to start saving.
Keep your thermostat at 78 degrees or warmer with the fan on "auto" and raise the thermostat setting to 82 degrees while you're away. For every one degree you increase in temperature, you can save about 5% on your monthly cooling costs.
Turn off fans when you leave a room, and make sure they're all turned off when leaving your home.
Learn how you can save up to $250 on your energy bill by taking our Online Home Energy Survey and view your personalized Online Energy Dashboard where you can see how the outside temperature and other factors impact your bill by month, day and hour.
Sign up for FPL Budget Billing® to say goodbye to summer bill fluctuations. While not a savings plan, this program evens out your annual energy costs so you pay approximately the same amount each month.
With FPL's Online Home Energy Survey, you'll get a personalized savings plan filled with energy-saving tips and recommendations, including programs and rebates that may be available to you.
NextA/C fan "on" or "auto?" Which uses less energy?
why I have to pay my bill in cash ? Why don`t explain to me in detail what problem was ?
can someone come to my home and give me an asessment.
Living in Stuart, I've noted that some newly-installed power poles (along Federal Highway) are "slanted" (i.e. not "vertical"), and I'm wondering why this is.
I am planning on replacing my hot water tank in my house in Fort Myers. which do you think is better for our area tankless or normal 50 gal tank. What are the pros and cons of both?
Please provide me the contact for the energy protection plans that are charged on my FPL bill.
It costs 6.25 per month and what does it cover?
My son likes his A/C at 71 F and we like it at 74-75 F; if we install a portable A/C at his room and set it at 71 and then we set the whole house at 74, do you think we will be saving on electricity?
My son likes A/C at 71 and we like it at 75 F. If we install a portable A/C just for his room (for the 71), and then set the whole house at 75, do you think we will save on electricity?


text:
Q: DateFormatter returns previous day I've looked around and people have had problems with different years, random and changing results, and nil dates, but nothing like what I have, so I am asking here. Note I am in Playground right now.
I am taking strings in the format of "yyyy-mm-dd" and converting them to a different date format. Here is the code:
let example = "2001-11-03"

let dateFormatterInput = ISO8601DateFormatter()
dateFormatterInput.formatOptions = [.withFullDate, .withDashSeparatorInDate]

let date = dateFormatterInput.date(from: example)

let dateFormatterOutput = DateFormatter()
dateFormatterOutput.dateFormat = "MMMM dd, yyyy"
let output = dateFormatterOutput.string(from: date!)

The sidebar in Playground shows that the first reference to the previous day's date happens on the let date line. Also, this behavior happens on every date I've tried. In this example, it returns "November 2, 2001." I've tried different months, days, and years (1900s and 2000s) and it gives me the same result every time.
What am I doing wrong?

A: The key thing here is that ISO8601DateFormatter by default thinks that the time zone of your date string is GMT:
ISO8601DateFormatter.timeZone:

The time zone used to create and parse date representations. When unspecified, GMT is used.

However, the timeZone of DateFormatter by default (and also the side bar of the playground) assumes your device's local time zone:
DateFormatter.timeZone

The time zone for the receiver. If unspecified, the system time zone is used.

If your system time zone has a negative UTC offset on the start of the day 2001-11-03 UTC, then when seen from your time zone, that moment is actually in the day 2001-11-02. Hence the output you see.
Assuming you don't care about the actual value of date, and just care about the final string output, you can just set the timeZone of DateFormatter to GMT:
dateFormatterOutput.timeZone = TimeZone(identifier: "GMT")

Side note: You should also set locale when using a fixed format to avoid localisation issues:
dateFormatterOutput.locale = Locale(identifier: "en_US_POSIX")

Or better, just use one of the built-in, locale sensitive formats instead:
dateFormatterOutput.dateStyle = .medium
dateFormatterOutput.timeStyle = .none

redpajama_set_name: RedPajamaStackExchange


text:
New Study Demonstrates Spinal Cord Stimulation Can Reduce or Stabilize Opioid Use Among Chronic Pain Patients
ONE YEAR AFTER IMPLANT, 93 PERCENT OF PATIENTS WHO CONTINUED SCS THERAPY HAD LOWER AVERAGE DAILY MORPHINE-EQUIVALENT DOSES THAN PATIENTS WHO HAD THEIR SCS SYSTEM REMOVED
- In 5,400-patient study, average daily opioid use declined or stabilized in patients receiving SCS system, while patients who had SCS system removed had higher opioid use over time
- There is potential to improve outcomes by implanting SCS systems earlier, before chronic opioid use, according to authors
ABBOTT PARK, Ill., Jan. 20, 2017 /PRNewswire/ -- New research has found spinal cord stimulation (SCS) therapy can be key to reducing or stabilizing the use of opioids in patients battling chronic pain. In a new study, researchers examined opioid usage data from more than 5,400 patients both prior to and after receiving an SCS system implant. In an SCS system, an implanted device similar to a pacemaker delivers low levels of electrical energy to nerve fibers, interrupting pain signals as they travel to the brain to reduce the sensation of pain. Researchers have found that average daily opioid use declined or stabilized for patients receiving a successful SCS system compared to patient use of opioids prior to an implant.
In addition, while opioid usage was not different for the two groups at time of implant, patients who underwent a successful SCS implant had significantly lower opioid use one year after their implant. Patients who had their SCS system removed saw their opioid use increase again over time.
The study, which the researchers believe makes a compelling case for considering SCS therapy earlier in the chronic pain care continuum, were presented today at the 2017 North American Neuromodulation Society (NANS) annual meeting by Ashwini Sharan, M.D., director of Functional and Epilepsy Surgery at Vickie and Jack Farber Institute for Neuroscience at Jefferson and president of NANS. The study was sponsored by Abbott (NYSE: ABT), a global leader in the development and manufacture of SCS systems and therapy options, such as the company's proprietary BurstDR™ stimulation.
Currently, more than 2.1 million people in the U.S. suffer from substance abuse related to opioid pain relievers, while worldwide an estimated 15.5 million people are now classified as opioid dependent. Chronic pain is often a driver of opioid use as patients seek relief and improvements to their quality of life. Fortunately for patients, SCS therapy has been clinically proven to offer meaningful relief to patients suffering from chronic pain.
"Given the epidemic of opioid addiction and abuse, these findings are important and confirm that spinal cord stimulation therapy can offer strong benefits for patients struggling with chronic pain," said Sharan. "Based on these results, we concluded it may be possible to improve outcomes by offering our patients spinal cord stimulation earlier, before opioid dependence and addiction can occur."
About the Study:
For their analysis, the research team assessed private and Medicare insurance claims data from 5,476 patients who received an SCS system to treat chronic pain associated with a host of conditions (excluding pain related to cancer). The data were collected between January 2010 and December 2014.
The data confirmed that many patients are often prescribed increasing dosages of opioids prior to receiving an SCS system. The researchers also found:
SCS therapy is effective for patients at any level of opioid usage prior to implantation.
Opioid use declined or stabilized in 70 percent of patients who received an SCS system.
Among patients who had their SCS system explanted, opioid use was higher at one year compared to those who continued with SCS therapy.
The researchers further suggested patient outcomes could be improved if SCS were implanted earlier in recognition of the clinical practice to provide increasing dosages of opioids over time. These conclusions help build upon prior research, such as results of a large multicenter randomized controlled trial in patients with failed back surgery syndrome (FBSS) that showed trends in opioid reduction or cessation among SCS patients. In addition, new technologies released in the U.S. in 2015 and 2016 hold promise to improve outcomes further and may reduce common complications resulting in explant such as the undesired changes in paresthesia, issues with charging, pain at the implantable pulse generator (IPG) site, and loss of pain relief.
"As our society has been seeking ways to stem opioid abuse and addition, our company offers treatment options that can reduce their exposure to opioid medication," said Allen Burton, M.D., medical director of neuromodulation at Abbott. "Data like these are critical to helping us demonstrate that spinal cord stimulation can reduce exposure to opioids while giving patients comprehensive pain relief."
About Abbott's Chronic Pain Portfolio:
Chronic pain affects approximately 1.5 billion people worldwide, more than heart disease, cancer and diabetes combined. The condition can negatively impact personal relationships, work productivity and a patient's daily routine. Abbott is a global leader in the development of chronic pain therapy solutions and the only medical device manufacturer in the world to offer radiofrequency ablation (RFA) and spinal cord stimulation (SCS) therapy solutions including BurstDR™ stimulation as well as stimulation of the dorsal root ganglion (DRG) with the Axium™ Neurostimulation System and Proclaim™ DRG Neurostimulation System.
About Abbott:
At Abbott, we're committed to helping people live their best possible life through the power of health. For more than 125 years, we've brought new products and technologies to the world -- in nutrition, diagnostics, medical devices and branded generic pharmaceuticals -- that create more possibilities for more people at all stages of life. Today, 74,000 of us are working to help people live not just longer, but better, in the more than 150 countries we serve.
Connect with us at www.abbott.com, on Facebook at www.facebook.com/Abbott and on Twitter @AbbottNews and @AbbottGlobal.
SOURCE Abbott
http://www.abbott.com
FDA Approves Abbott's Spinal Cord Stimulation for People Living with Painful Diabetic Peripheral Neuropathy
Abbott Reports Fourth-Quarter and Full-Year 2022 Results; Issues 2023 Financial Outlook

redpajama_set_name: RedPajamaCommonCrawl


text:
George Everest, Geographer
George Everest, Geographer >
Colonel Sir George Everest was a Welsh surveyor, geographer and Surveyor-General of India from 1830 to 1843. Sir George was largely responsible for completing the section of the Great Trigonometric Survey of India along the meridian arc from the south of India extending north to Nepal, a distance of approximately 2400 kilometres. The survey was started by William Lambton in 1806 and lasted several decades. Mount Everest was named in his honour and surveyed by his successor, Andrew Waugh.
More on this Website
• http://en.wikipedia.org/wiki/George_Everest
Related Links • Add URL
Colonel Sir George Everest was a Welsh surveyor, geographer and Surveyor-General of India from 1830 to 1843. Sir George was largely responsible for completing the section of the Great Trigonometric Survey of India along the meridian arc from the south of India extending north to Nepal, a distance of approximately 2400 kilometres. The survey was started by William Lambton in 1806 and lasted several decades. Mount Everest was named in his honour and surveyed by his successor, Andrew Waugh. More...
Related > Explorers • Freemasons • Scientists • Soldiers • 1830s • 1840s • Geography • Himalaya • India • Nepal • People
Edmund Hillary, Mount Everest - 1953
Sir Edmund Percival Hillary, was a New Zealand mountaineer and explorer. On 29 May 1953 at the age of 33, he and Sherpa mountaineer Tenzing Norgay became the first climbers known to have reached the summit of Mount Everest. They were part of the nint...


text:
Talented Young Midfielder Staying At Newcastle
7:56am Saturday, August 15th, 2015
19 year-old Olivier Kemen, who was born in Douala, Cameroon joined the club two years ago from French club Metz and is a very good young player, who is highly regarded at Newcastle.
There has been interest from various clubs in signing the teenager including AC Milan, Monaco, Tottenham and Liverpool.
Olivier Kemen – on the bench against Borussia Monchengladbach
But it seems that Steve McClaren will not let him move anywhere this season as he wants to take a closer look at him, and he has already compared the 19 year-old with the combative Cheick Tiote, who has been at the club for five years now since he moved for £3.5M from FC Twente.
In his interviews yesterday Newcastle head coach Steve McClaren talked about the player who turned 19 only last month.
Steve was asked if Olivier's future lay at Newcastle:
" "Yes, definitely. He's a good player."I like him." "I call him a young Cheicky, that type of player."
"He's come back late because of the France U19s. He's been in and out of the first team, training with us."
"But I like him. He's still only young, and still got a lot to do."
Olivier seems to have been unsettled a bit over the summer, but he was off with the France U19s, and was able to appear in only one pre-season game for Newcastle, when he came on after 58 minutes in the 2-1 defeat at York City.
Since joining us two years ago Kemen has played 27 times for the U21 team with two goals and three assists.
He's a very good young player and at some point this season may be sent out on loan, but only after McClaren has taken a good look at him.
Previous Post Charnley's In Charge - Owner Not Involved - Things Going Well
Mike Ashley has reiterated to Steve McClaren last week, that he is continuing to take a back seat on transfers, and the owner has left it to the Newcastle Board – run…
Next Post McClaren Confident Of New Signings - To Assess The Academy
The summer transfer window closes two weeks on Monday night, so not too many more articles on Newcastle signing Charlie Austin during that time, probably only about ten. 🙂 Last Sunday Steve…
Lilongwe Geordie
Lilongwe Geordie // Aug 15, 2015 at 7:56 AM
Jimmy,
For me I think the lines are blurred there between being a supporter of the club and a pride and passion for the region and its history. I love where I am from, and will sing its praises to anyone I meet who is willing to listen. It is the only place in the UK I would want to move back to. But whilst it may give me a deeper understanding of the roots of the club I wouldn't hold that above a supporter from elsewhere as to why I am a better fan.
In my mind, I'm just fortunate enough to have been born in such a wonderful city and area. So I guess I'm a luckier fan, and had the fortune to live in proximity as well as having a family that as a child indulged my love of the club and sport, and when I got older, lucky I had the means to continue going.
How many people on here have watched Kemen regularly? I've seen him a few times, mainly using a stream and the odd occasion when I've been back in country. From what I have seen calling him a "young Cheicky type of player" is a huge injustice.
Other than the occasional rash challenge I see very few similarities in the two. Kemen looks far more a box to box midfielder than a holding midfielder who only has to break up play and play it simple.
jimmysmith
Better or worse wouldn't be adaquate words to describe the differences between fans, t think, and I'm not sure anyone is has claimed that. We are all immersed in the club, both it's past and present differently, and we aren't a homogenised group. Isn't that true of all things..That sounds like a bit of a wank, but I'm not sure how else to put it.
posted, but it didn't appear, because of a naughty word innocuously used. i guess it will appear later in the thread
will die for the toon army
NuFc team it we hadnt sold our key players:
…………………Krul
Debuchy…….Mbemba…..Colo……Santon
……………..Cabaye………Tiote
Sissoko…………..Wijnaldum……….Hatem
………………………….Remy
6 – Still here
5 – not here
Bobbybee
Lil, ive watched kemen play for both our academy and u21's pretty regularly. He might bear a passing resemblance to Tiote from afar, but he's a better technical footballer. He has still got a lot to do imo, but this milan interest has clearly upped his profile by a canny amount. Another who could benefit from a loan period. Not ready for the PL yet.
ive never understood this argument that beccause im born and bred from newcastle that i have more passion for the club ,than people who arnt.
what about fans from south of the tyne gateshead/jarrow/ south shields, are they less passionate about the club no there not.
it dosnt matter where your from.
i dont get all this crap if your lucky enough to get to games great but the guys who can not get to games for what ever reason is no less a fan ….some of the older ones on here will remember the 10 min flag …10 mins to go the gates were opened as many ran in as left just to catch a glimpse …we are all fans no one has the right to say trere better we all do what we can for the club we love
Bobbybee says he has watched Kemen a lot and thinks the reason the club won't totally commit is that his first touch is poor.
Those asking about Mehdi Abeid
Fortuna Dusseldorf (Bundesliga 2) and Panathanaikos are both interested in signing him but NUFC is playing hardball over the 12 months left on his contract.
Moonraker15
Believe it or not there are people born and bred in Newcastle who have no interest in football as is the case in other towns and cities.
I was born and bred in Gateshead and never even gave a thought to not being a Newcastle supporter since a boy in the fifties thanks to my family tradition.
It is good that the area gets referred to as Newcastle / Gateshead more now and that at last the south side of the Tyne has attractions that brings people to the area; I'm thinking of the Sage and the Baltic etc.
There are many supporters from further North such as Ashington and we all know the historic ties of that town.
So really it doesn't matter where you come from but I think as you get older the emotional pull of the area is very strong and there is a fierce pride in this area which transmits to the football club and all we want is a club to be proud of. I have a feeling we are at last moving in the right direction.
I moved away from the Newcastle area years ago and travel for home and some away games when I can get a ticket.
I have to say I have never had the same emotional commitment to the team in my adopted town although I recognise it in the locals.
It's something about where I was brought up and all the family history I will never lose that.
There is no feeling like a winning goal for the Toon. That Wijnaldum goal (although not a winner) last week was absolutely fantastic and it was my grandsons very first visit to SJP.The look on his face when that went in was unforgettable!
Howay the Lads!


text:
Arenys de Mar é um município da Espanha na comarca de Maresme, província de Barcelona, comunidade autónoma da Catalunha. Tem  de área e em  tinha  habitantes ().

Demografia

Equipamentos
 Cemitério Municipal de Arenys de Mar - O poeta Salvador Espriu converteu-o num mito literário com a sua obra Cementerio de Sinera-

Localidades de Barcelona (província)
Localidades da Catalunha
Localidades da Espanha
Municípios por nome da Catalunha
Municípios da Espanha por nome

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}
The tunneling decay of particles trapped in an external potential $V(\vec{x})$ is a problem often encountered in nuclear, atomic and molecular physics. The most famous example is arguably the
alpha decay of nuclei for which Gamow calculated the decay rates semiclassically \cite{Gamo28}.

For a particle with mass $m$ such a decay can be described by resonance eigenstates $\psi_S$ of the Schr\"odinger equation
\begin{equation}
  \left( - \frac{\hbar^2}{2m} \nabla^2 + V(\vec{x}) \right) \psi_S=\cal{E} \psi_S
\label{SE_comp}
\end{equation}
with complex eigenenergy ${\cal E}=E_S-{ \rm i } \Gamma/2$, often refered to as Siegert resonances, where the wavefunction satisfies outgoing wave (or Siegert) boundary conditions \cite{Sieg39}, i.~e. the wavefunction
is given by an outgoing plane wave for $|\vec{x}| \rightarrow \pm \infty$ (cf.~ equation (\ref{BC_S})).
The imaginary part is also refered to as the decay rate since it leads to an exponential decay of the wavefunction,
\begin{equation}
 \fl \quad \quad \quad \psi_S(\vec{x},t)=\exp({ \rm i } {\cal E }t/\hbar) \psi_S(\vec{x},0)=\exp(-\Gamma t/(2\hbar)) \exp({ \rm i } E_S t/\hbar) \psi_S(\vec{x},0) \,.
\label{wf_decay}
\end{equation}

On the other hand, the tunneling decay of trapped particles is closely related to the problem of scattering of particles off the same potential since quantities like the transmission coefficient
 $|T(E)|^2$ or the scattering cross section show characteristic peaks near the resonance energies ${\cal E}$, which can be described by a Lorentz or Breit-Wigner profile
\begin{equation}
  |T(E)|^2=\frac{(\Gamma/2)^2}{(E-E_S)^2+(\Gamma/2)^2}
\end{equation}
the width of which is given by the decay rate $\Gamma$ \cite{Sieg39}.

As mentioned above, the decay rates can be calculated in the manner of Gamow using semiclassical approximations. Though these approximations are straightforward and easy to use they
are often not very precise, only providing an order of magnitude. On the other hand there are powerful complex-scaling based methods (see e.~g.~\cite{Mois98,Mois11}) (including related methods such as complex absorbing
potentials) where the spatial coordinate is rotated to the complex plane, $\vec{x} \rightarrow \vec{x} \exp({ \rm i } \theta)$ by some sufficiently large angle $\theta$ to make the resonance wavefunctions square
integrable, enabling the use of the usual techniques for calculating ordinary bound states. These methods are precise and highly efficient yet quite sophisticated and, apart from rare exceptions,
only suited for numerical calculations.
Alternative techniques, like, e.g., the stabilization method \cite{Mand93a} have both some advantages and disadvantages compared to complex scaling
and are, however, not very intuitive and only aim at numerical applications. While there are a number of excellent texts (see, e.~g.~\cite{Mois98,Tayl72,Mois11}
and references therein) that discuss the mathematical aspects of the problem (e.~g.~analytical continuation of the wavefunction in the complex plane) and the computational methods mentioned above, a
complementary treatment assuming a different point of view could prove valuable.

In this article we want to draw attention to the scarcely known Siegert approximation method for calculating complex resonances {\cite{Sieg39,08nlLorentz}} which is both intuitive and easy to implement but does
not rely on semiclassical arguments. It yields good results for narrow resonances (i.e. $\Gamma/2 \ll E_S$, where the resonance energy $E_S$ is measured relative to the potential energy at $|\vec{x}| \rightarrow \infty$)
and it can in some cases lead to closed form analytical approximations for the decay coefficient.
Another advantage of this method is its straightforward applicability to resonances of the nonlinear Schr\"odinger equation that occur, e.~g., in the context of trapped Bose-Einstein
condensates \cite{08nlLorentz,09ddshell} since it does not require properties like the linearity or analyticity of the differential equation. While direct complex scaling \cite{Schl06a,Schl06b} has
succesfully been applied to nonlinear Siegert resonances it is much less efficient than in the linear case and requires substantial modifications. Complex absorbing potential methods, which have proven
 more efficient in this context \cite{Mois04a,10nlws}, also require considerable modifications compared to the linear case.

In the derivation of the Siegert approximation method given here, complex resonances are reviewed from an alternative, rather intuitive point of view which complements the usual more mathematical
treatments of the problem by emphasizing some important aspects like the role of the continuity equation in this context as well as the similarities and differences between
complex resonance states and so-called transmission resonances, i.~e.~scattering states corresponding to the maxima of the transmission coefficient (or scattering cross section respectively)
for real eigenenergies.

This paper is organized as follows: In section \ref{sec:Sieg} the Siegert approximation method is described, focussing on resonances of the one-dimensional linear Schr\"odinger equation for the
sake of simplicity. In section \ref{sec:apps} the method is illustrated by means of several analytical and numerical applications. Finally, the main aspects of the
article are summarized in section \ref{sec:summary}. \ref{app:num} contains a MATLAB code for calculating resonances.

\section{The Siegert approximation method}
\label{sec:Sieg}

For narrow resonances (i.e. $\Gamma/2 \ll E$), one can often neglect the decay rate $\Gamma$ in (\ref{SE_comp}) and thus obtain an approximate resonance wavefunction $\psi_{\rm approx}$ and an approximate real part $E_{\rm approx}$
of the resonance energy with very little effort.

For the sake of simplicity we first consider symmetric one-dimensional finite range potentials
\begin{equation}
   V(x)=\left\{
                \begin{array}{cl}
		0 & |x|>a\\
		V_x(x) & |x| \le a
		\end{array}
        \right.
\end{equation}
with finite range $a$ and $V(-x)=V(x)$. An example of such a potential is the double barrier shown in the right panel of figure \ref{fig:Siegert} (bold blue curve) which can safely be assumed to be approximately equal to
zero for $|x| \ge 20$. Also shown is the square $|\psi(x)|^2$ of the most stable resonance wavefunction which is strongly localized between the potential maxima and inherits the symmetry of the
double barrier potential.

Apart from the Siegert resonances $\psi_S$ with complex energies $E_S -{ \rm i } \Gamma/2$ obtained for outgoing wave boundary conditions
\begin{equation}
    \psi_S'(\pm a)= \pm { \rm i } k_S \psi_S(\pm a), \quad \quad k_S=\sqrt{2m(E_S-{ \rm i } \Gamma/2)}/\hbar
\label{BC_S}
\end{equation}
(the prime denotes a derivative by $x$) these potentials also possesses so-called transmission (or unit) resonances $\psi_T(x)$ corresponding to real energies $E_T$ for which the potential is
completely transparent, i.e. for the corresponding transmission coefficient we have
 $|T(E_T)|^2=1$. We will see further below, that for narrow resonances $\psi_T(x)$ and $E_T$ are good approximations to $\psi_S$ and $E_S$ respectively.

To obtain the transmission coefficient $|T|^2$ we consider transmission through the potential $V(x)$ which is characterized by the following boundary conditions for the scattering
wavefunction $\psi(x)$: On the left hand side we have a superposition of an incoming and a reflected plane wave
\begin{equation}
   \psi(x)=A \exp({ \rm i } kx)+B \exp(-{ \rm i } kx), \quad x <-a
\end{equation}
where $k=\sqrt{2mE}/\hbar$ is the wavenumber corresponding to an energy $E$ of the incoming wave. On the right hand side we only have an outgoing wave,
\begin{equation}
   \psi(x)=C \exp({ \rm i } kx) , \quad x>a \,.
\end{equation}
Thus the transmission coefficient reads
\begin{equation}
   |T|^2=|C/A|^2 \,.
\end{equation}
We immediately see that for the transmission resonances with $|T|^2=1$ we have $|C|=|A|$ (and $B=0$), so that we can always achieve $C=A$ by multiplying the wavefunction with
a constant phase factor. Thus the boundary conditions for the transmission resonces $\psi_T$ can be written as
\begin{equation}
    \psi_T=A \exp({ \rm i } k_T x), \quad |x|>a
\end{equation}
or equivalently as
\begin{equation}
    \psi_T'(\pm a)=i k_T \psi_T(\pm a) \text { with } k_T=\sqrt{2m E_T}/\hbar \,.
\label{BC_T}
\end{equation}
The symmetry of both the Siegert resonance wavefunction $|\psi_S(-x)|^2=|\psi_S(x)|^2$ and the transmission resonance wavefunction $|\psi_T(-x)|^2=|\psi_T(x)|^2$ imply that the derivatives of
$|\psi_S|^2$ and $|\psi_T|^2$ must vanish at $x=0$. Thus the respective boundary conditions (\ref{BC_S}) and (\ref{BC_T}) can be recast in the form
\begin{equation}
    (|\psi_\alpha(x)|^2)'\big|_{x=0}=0, \quad  \psi_\alpha'(a)={ \rm i } k_\alpha \psi_\alpha(a), \quad \alpha \in \{S,T\}
\label{BC_Sym}
\end{equation}
with $k_\alpha=\sqrt{2m {\cal E}_\alpha}/\hbar$, ${\cal E}_S=E_S -{ \rm i } \Gamma/2$, ${\cal E}_T=E_T$.

Therefore it is quite intuitive that for $\Gamma/2 \ll E_S$ we can make the approximations $E_S \approx E_T$ and
\begin{equation}
   \psi_S(x) \approx\left\{
                \begin{array}{cl}
		\psi_T(x)   & 0 <x \le a\\
	         \psi_T(-x) & -a \le x<0
		\end{array}
        \right. \,.
\label{psi_app}
\end{equation}

This was shown rigorously by Siegert \cite{Sieg39}. Note that this approximate correspondance between complex energy Siegert resonances describing decay and real energy transmission resonances, which generally holds for narrow resonance widths, is
in fact one of the main reasons for considering complex resonances in the context of scattering \cite{Sieg39}. Now we have approximations for the wavefunction and the real part of the eigenenergy but what about the imaginary part,
i.e. the decay rate ?

To this end let us assume that the potential $V(x)$ has local maxima at $x= \pm b$ with $0< b < a$ (as, for example, the potential shown in figure (\ref{fig:Siegert}) ). Then the probability of finding the particle described by our Schr\"odinger equation
(\ref{SE_comp}) 'inside' the potential well, i.e. in the region $ -b \le x \le +b$ between the potential maxima is given by the norm
\begin{equation}
   N=\int_{-b}^b |\psi_S(x)|^2 { \rm d } x \approx 2 \int_{0}^b |\psi_T(x)|^2 { \rm d } x\,
\end{equation}
of the wavefunction inside the well.
The exponential decay behaviour of the resonance wavefunction given in equation (\ref{wf_decay}) implies that the norm $N$ decays according to
\begin{equation}
    \partial_t N=-\frac{\Gamma}{\hbar}N
\end{equation}
so that the decay rate can be written as
\begin{equation}
    \Gamma=-\hbar \frac{\partial_t N}{N} \,.
  \label{gamma}
\end{equation}
The time derivative $\partial_t N= \int_{-b}^b \partial_t |\psi_S(x,t)|^2 { \rm d } x \approx 2 \int_{0}^b \partial_t |\psi_T(x,t)|^2 { \rm d } x$ of the norm can be found by means of the continuity equation for
the resonance wavefunction $\psi_S$ which reads
\begin{equation}
   \partial_t \rho_S = - j_S'
\label{cont}
\end{equation}
with $\rho_S(x,t)=|\psi_S(x,t)|^2$ and the probability current
\begin{equation}
   j_S= - \frac{{ \rm i } \hbar}{2m} \left(\psi_S^* \psi_S'-\psi_S \psi_S'^* \right) \,.
\end{equation}
Integrating the continuity equation (\ref{cont}) from $x=-b$ to $x=b$ we obtain $\partial_t N= -(j_S(b)-j_S(-b))$. Equation (\ref{psi_app}) implies that the currents are approximately given by
$j_S(b) \approx j_T(b)$ and $j_S(-b) \approx -j_T(b)$. Furthermore, the current $j_T$ corresponding to the transmission resonance $\psi_T$ does not depend on the position $x$ and in particular $j_T(b)=j_T(a)$.
For $x \ge a$ the transmission resonance wavefunction is given by a plane wave $\psi_T(x)=\psi_T(a) \exp({ \rm i } k_T (x-a)$ so that the current at $x=a$ simply reads
$j_T(a)=\hbar k_T |\psi(a)|^2/m$. Thus the decay coefficient (\ref{gamma}) becomes
\begin{equation}
    \Gamma \approx \hbar \frac{j_T(a)}{\int_{0}^b |\psi_T(x)|^2 { \rm d } x} = \frac{\hbar^2 k_T}{m} \frac{|\psi_T(a)|^2}{\int_{0}^b |\psi_T(x)|^2 { \rm d } x}\,.
  \label{Gamma_s}
\end{equation}
We call (\ref{Gamma_s}) the Siegert formula. Note that it only depends on $E_T$ and $\psi_T$ so that the exact values $E_S$ and $\psi_S$ are not required.

In general, the Siegert approximation method consists of two steps:
\begin{enumerate}
 \item \label{I1} Neglect at first the imaginary part $\Gamma/2$ (also called decay coefficient) of the complex resonance energy in the Schr\"odinger equation for the Siegert resonance wave function in order to obtain
       approximations to both the wave function and the real part of the resonance energy. (In the symmetric barrier case discussed above this is done by calculating the energies and scattering states
       for which the transmission probability of the corresponding scattering problem has a local maximum or, equivalently, directly use the symmetry of the problem expressed in the boundary conditions given
       in equation (\ref{BC_Sym}).)
 \item \label{I2} Use the continuity equation to obtain a Siegert formula, i.~e.~an approximate expression for the decay coefficient $\Gamma$ (as given in equation (\ref{Gamma_s}) for the symmetric barrier case) which only
       depends on the approximate energy and approximate wavefunction calculated in step (\ref{I1}).
\end{enumerate}

The Siegert approximation method yields good results for narrow resonances, i.~e.~whenever the imaginary part $\Gamma/2$ of the resonance energy is small compared to the real part $E$.
Unlike common discussions of complex resonance states the above derivation is based on the intuitive picture of a matter wave flowing out of a potential well, emphasizing the role of the conservation
of the probability current expressed by the continuity equation.

The above treatment for symmetric potentials can be straightforwardly generalized to resonances of asymmetric barrier potentials where the matter wave is localized between two maxima at $x=b_-<0$ and $x=b_+>0$ with two finite ranges
$a_-,b_-$ and $a_+,b_+$ but then the actual calculations in step (\ref{I1}) are generally more difficult because the symmetry condition (\ref{BC_Sym}) no longer applies. Now one has to consider the problem of transmission through the barrier
and calculate the states $\psi_{\rm approx}$ and the respective real energies $E_{\rm approx}$ which correspond to local maximima of the transmission coefficient with $|T(E_{\rm approx})|^2<1$.
In analogy to the symmetric case one finds that the relation (\ref{Gamma_s}) for the decay
coefficient is generalized to
\begin{equation}
   \Gamma_{\rm approx}=\frac{\hbar^2 k_{\rm approx} |\psi_{\rm approx}(a_+)|^2+\hbar^2 k_{-a} |\psi_{\rm approx}(a_-)|^2}{m \int_{b_-}^{b_+} |\psi_{\rm approx}(x)|^2 { \rm d } x}
   \label{Gamma_asym}
\end{equation}
where $k_{approx}=\sqrt{2mE_{\rm approx}}/\hbar$.
An important special case of an asymmetric barrier is a trap which is open on one side only whereas there is an impenetrable barrier on the other side. If the impenetrable barrier is on the
left hand side (at $x=a_-$) we obtain the boundary condition
\begin{equation}
   |\psi_{\rm approx}(a_-)|^2=0
\label{dings}
\end{equation}
and the wavefunction $\psi_{\rm approx}$ and the corresponding energy $E_{\rm approx}$ can be obtained by finding an approximate solution to the system of equations given by (\ref{dings}) and
\begin{equation}
  \psi_{\rm approx}'(a_+)= { \rm i } k_{\rm approx} \psi_{\rm approx}'(a_+) \,.
  \label{Gamma_oneside}
\end{equation}
An example of such a calculation is given in section \ref{subsec:delta_shell}.
Note that for such a potential exact solutions for real energies do not exist.
We further note that potentials with infinite range can usually be approximated by finite range potentials by choosing appropriate values for $a_\pm$ and that the Siegert approximation method
can be generalized to two and three dimensions (see \cite{08nlLorentz} for a detailed discussion).

\section{Applications}
\label{sec:apps}
\subsection{The finite square well potential}
\label{subsec:square_well}

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.3\textwidth] {boxpot.eps}
\includegraphics[width=0.3\textwidth] {DShell.eps}
\includegraphics[width=0.3\textwidth] {DGauss.eps}
\caption{\label{fig:Siegert} Barrier potentials (bold blue) and approximate squared wavefunctions $|\psi|^2$ (red) of the corresponding most stable resonance states (units with $\hbar=m=1$).
Left: Finite square well (\ref{square}) with $V_0=-5$, $L=3$.
Middle: Delta Shell potential (\ref{Shell}) with $\lambda=10$, $L=1$ (The Dirac delta function is symbolically represented by a vertical line).
Right: Double barrier potential (\ref{double}) with $V_0=1$, $\lambda=0.1$.}
\end{center}
\end{figure}

As a first analytically solvable example we consider the finite square well potential
\begin{equation}
   V(x)=\left\{
                \begin{array}{cl}
		0 & |x|>L\\
		V_0<0 & |x| \le L
		\end{array}  \right.
\label{square}
\end{equation}
with width $2L$ which is shown in the left panel of figure \ref{fig:Siegert}. As discussed at the beginning of the preceding section, the complex resonances for such a symmetric potential can be calculated approximately by finding its transmission
resonances which satisfy the symmetry and boundary conditions (\ref{BC_Sym}) with $\alpha=T$. With the notation of the preceding section we can identify $b=a=L$, i.e. both the position of the local
maximim and the range of the potential are given by the box length parameter $L$. Dropping the index $T$ we can write
the transmission resonance wave function inside the square well as a superposition of plane waves,
\begin{equation}
   \psi(x)=F { \rm e }^{{ \rm i } q x} + G { \rm e }^{-{ \rm i } q x} \, , \quad |x|<L
   \label{f1}
\end{equation}
where $q=\sqrt{2m(E-V_0)}/\hbar$ is real. The symmetry condition $|\psi(-x)|^2=|\psi(x)|^2$ leads to $FG^*=GF^*$ so that
\begin{equation}
   |\psi(x)|^2=|F|^2+|G|^2+2FG^*\cos(2qx) \, .
   \label{fq1}
\end{equation}
The second condition in (\ref{BC_Sym}) reads $\psi'(L)={ \rm i } k \psi(L)$. Inserting Eq.~(\ref{f1}) we obtain
\begin{equation}
   G=\frac{q-k}{q+k} { \rm e }^{2 { \rm i } qL} F \, .
   \label{G1}
\end{equation}
The condition $FG^*=GF^*$ then implies $\exp( 4 { \rm i } qL)=1$ which leads to the resonance condition $2qL=n \pi$ with integer $n$. Thus we arrive at the celebrated formula
\begin{equation}
   E_n=V_0+ \frac{\hbar^2 q^2}{2m}=V_0+ \frac{\hbar^2 \pi^2}{8mL^2}n^2 ,
   \label{ERlin}
\end{equation}
for the transmission resonance energies of a finite square well potential. The number $n$ must be sufficiently large to make $E_n$ positive. Inserting Eq.~ (\ref{G1}) into (\ref{fq1}) leads to
\begin{equation}
   |\psi(x)|^2=|F|^2 \left[1 +2(-1)^n\frac{q-k}{q+k}\cos(2qx) + \left(\frac{q-k}{q+k}\right)^2 \right]
\end{equation}
( cf.~left panel of figure \ref{fig:Siegert}) and in particular
\begin{equation}
   |\psi(L)|^2=|F|^2 \left[1+\frac{q-k}{q+k} \right]^2=|F|^2 \left(\frac{2q}{q+k} \right)^2 \, .
   \label{fa1}
\end{equation}
Inserting $|\psi(L)|^2$ and the integral
\begin{eqnarray}
  \int_{0}^L |\psi(x)|^2 { \rm d } x &=& L|F|^2 \left( 1+ \left(\frac{q-k}{q+k}\right)^2\right) \nonumber \\
                            &=& L|F|^2 \frac{(q+k)^2+(q-k)^2}{(q+k)^2} \nonumber \\
                            &=& 2L|F|^2 \frac{q^2+k^2}{(q+k)^2}
\end{eqnarray}
into the Siegert formula (\ref{Gamma_s}) we obtain the decay coefficient
\begin{equation}
   \Gamma_n =\frac{2 \hbar}{L} \sqrt{ \frac{2 E_n}{m} } \frac{q^2}{q^2+k^2}
\end{equation}
or
\begin{equation}
   \Gamma_n=\frac{2 \hbar}{L} \sqrt{ \frac{2}{m} } \frac{\sqrt{E_n}(E_n-V_0)}{2E_n-V_0} \,
   \label{Gamma1}
\end{equation}
which is the well known textbook result for the decay coefficient (or resonance width) of a finite square well potential (see e.g. \cite{Mess91}), that is usually obtained by expanding the transmission coefficient
in a Taylor series around $E=E_n$.

\subsection{Delta Shell potential}
\label{subsec:delta_shell}
As an analytically solvable example for complex resonances in asymmetric potentials we consider the one-dimensional delta-shell potential

\begin{equation}
 V(x)= \left\{
                    \begin{array}{cl}
                     +\infty   &    x \le 0 \\
                     (\hbar^2/m) \lambda \, \delta(x-L)     &   x>0\\
                     \end{array}
              \right. \, \text{ with } \lambda, L>0 \nonumber
\label{Shell}
\end{equation}
consisting of an infinitely high potential barrier at $x=0$ and a delta barrier at $x=L$ which is illustrated in the middle panel of figure \ref{fig:Siegert}.
To find the solution of the corresponding Schr\"odinger equation
\begin{equation}
 \left[ -\frac{\hbar^2}{2m} \frac{{ \rm d }^2}{{ \rm d } x^2} + V(x) \right] \psi(x) =
\left(E-{ \rm i } \Gamma/2 \right) \psi(x)
\end{equation}
we make the ansatz
\begin{equation}
 \psi(x)= \left\{
                    \begin{array}{cl}
                      I\, \sin(k x)   & 0 \le x \le L \\
                     C \, { \rm e }^{{\rm i}kx}                              &     x>L
                    \end{array}
              \right.  \, \text{ and }  E- { \rm i } \Gamma/2 =\frac{\hbar^2 k^2}{2m}   \nonumber
\label{DShell_ansatz}
\end{equation}
for the wavefunction which satisfies the required outgoing wave (Siegert) boundary condition for $x \rightarrow \infty$.
The matching conditions for the wavefunction at $x=L$ read
\begin{equation} \psi(L-\epsilon)=\psi(L+\epsilon)\,, \quad \quad  \psi'(L-\epsilon)+2 \lambda \psi(L)=\psi'(L+\epsilon) \end{equation}
where the discontinuity in the derivative is caused by the delta function potential \cite{Mess91}.
This leads to
\begin{equation} I \sin(k L)=C \, { \rm e }^{{\rm i}kL} \, , \quad \quad k I \cos(kL)+2 \lambda I \sin(k L)= i k C \, { \rm e }^{{\rm i}kL} \end{equation}
or
\begin{equation}
   k \cos(kL)+(2 \lambda -{ \rm i } k)\sin(k L)= 0 \,.
\label{Dlin}
\end{equation}
The real and imaginary part of the eigenenergy can now be found by numerically solving the transcendental equation (\ref{Dlin}) in the complex plane.
In the following we show how the Siegert approximation method presented in section \ref{sec:Sieg} can be used to obtain a convenient approximation in an analytically closed form.
To obtain the approximate real part of the energy and approximate wavefunction as required in step (\ref{I1}) of the method we make the following approximation:
Imagine that the delta potential at $x=L$ is infinitely strong, i.e. the limit $\lambda \rightarrow \infty$. Then the system is a closed box of length $L$ and the wavenumber satisfies $k L= n \pi$ with an integer $n$.
For a strong but still finite delta potential, i.e. $|k|<<\lambda$, we therefore assume $k L= n \pi + \delta L$ with $\delta L <0$ and $|\delta L| \ll 1$.
Inserting this ansatz into the real part of Eq.~(\ref{Dlin}) and expanding it up to second order in $\delta L$ yields
\begin{equation}
   \delta =\frac{2 \lambda L +1}{n \pi L}-\sqrt{\left(\frac{2 \lambda L +1}{ n \pi L}\right)^2+\frac{2}{L^2}} \, .
\end{equation}
Inserting $k= n \pi/L +\delta$ into equation (\ref{DShell_ansatz}) yields approximations for the resonance wavefunction and the real part of the eigenenergy. An approximation of the imaginary part
is obtained by inserting these results into the Siegert formula (\ref{Gamma_asym}),
\begin{equation}
\fl \quad \quad \quad   \Gamma/2 \approx \frac{\hbar^2k |\psi(L)|^2}{2m\int_0^L |\psi(x)|^2 { \rm d } x}=\frac{2 \hbar^2}{m} \left(\frac{n \pi}{L}+\delta \right)^2\frac{\sin^2(\delta L)}{n \pi +\delta L-\sin(2 \delta L)},
\end{equation}
where we have identified $b_+=a_+=L$ and $b_-=a_-=0$.
For a potential with $\lambda=10$, $L=1$ and scaled units $\hbar=m=1$ the Siegert approximation yields ${\cal E}_{approx}=4.481-{ \rm i } 0.062$ for the most stable resonance (cf.~middle panel of figure
\ref{fig:Siegert}) which is in good agreement with the numerically exact result ${\cal E}_{exact}=4.487-{ \rm i } 0.061$.
A treatment of the equivalent problem within the context of the nonlinear Schr\"odinger equation can be found in \cite{09ddshell}.

\subsection{Double barrier}
\label{subsec:DGauss}
As an example of a numerical problem we consider the double barrier potential
\begin{equation}
    V(x)=\frac{V_0}{2} x^2 \exp(-\lambda x^2)
\label{double}
\end{equation}
with $V_0=1$ and $\lambda=0.1$ so that the position of the potential maxima is given by $b = 1/\sqrt{\lambda} \approx 3.16$  using units where $\hbar=m=1$.
In order to calculate the approximate resonance wavefunction and real part of the energy as required in step (\ref{I1}) of the method we solve the boundary value problem given by equation (\ref{BC_Sym}) by means of a shooting procedure.
We choose the cutoff parameter for the potential $a=20$ to ensure that $V(x) \approx 0$ for $|x|>a$ so that the wavefunction is well approximated by a plane wave in that region. Starting with initial conditions given in equation
(\ref{BC_Sym}) we integrate the Schr\"odinger equation from $x=-a$ to $x=0$ using a standard Runge Kutta solver. By means of a bisection method the real energy $E$ is adapted such that the boundary
condition at $x=0$ is satisfied. The decay rate is again obtained by inserting this value of $E$ and the corresponding wavefunction into the Siegert formula (\ref{Gamma_s}). More details on the actual numerical
implementation of the method can be found in \ref{app:num}.

\begin{table}[htbp]
\caption{\label{tab-compare-Sieg-cs} Complex eigenenergies for the three most stable resonances of the potential (\ref{double}) calculated using complex scaling (CS) and the Siegert approximation (S).}
\begin{indented}
\item[] \begin{tabular}{lll}
{\bf r}
 $n$ & $\cal{E}_{\rm S}$ &  $\cal{E}_{\rm CS}$   \\

\mr
  1    & $0.4601- { \rm i } \, 9.62  \times \, 10^{-7}$  & $0.4601 -  { \rm i } \, 9.6204 \times \, 10^{-7}$  \\
  2    &  $1.2804 -{ \rm i } \, 1.70 \times \, 10^{-3}$  & $1.2804 - { \rm i } \, 1.6737 \times \, 10^{-3}$  \\
  3    &  $1.88 {\lineup \0\0}- { \rm i } \, 7 {\lineup \0} \times \, 10^{-2}$    & $1.8531 -  { \rm i } \, 6.7240 \times \, 10^{-2}$  \\
{\bf r}
  \end{tabular}
\end{indented}
\end{table}

The right panel of figure \ref{fig:Siegert} shows the potential (\ref{double}) and the square $|\psi|^2$ of the most stable resonance wavefunction calculated with the Siegert approximation method.
Table \ref{tab-compare-Sieg-cs} compares our results for the three most stable resonances with numerically exact results calculated with the complex scaling method described in \cite{02computing}.
We see that our simple approximation yields very good results for the ground state since its decay rate is small. The values for the first and second excited states demonstrate that the Siegert
 approximation becomes less accurate with increasing decay rates. A generalization of the same problem to the nonlinear Schr\"odinger equation is straightforward and can be found in
\cite{08nlLorentz}.

\section{Summary and conclusion}
\label{sec:summary}

In this article the Siegert approximation method for calculating complex resonance states was presented in an intuitive and straightforward manner which at the same time clearly points out the similarities
and differences between resonances of transmission coefficients (or similar quantities) and resonances in the complex plane (Siegert rsonances) as well as the role of the continuity equation in this context.
It was illustrated by two analytically solvable example problems and a numerical application. The author hopes that the present article, in addition to drawing attention to a useful and easily applicable
computational tool, offers an alternative, rather intuitive point of view for a better understanding of complex resonances which complements other, more technical treatments.

\ack
 The author would like to thank Hans J\"urgen Korsch and Nina Lorenz for helpful discussions and comments. Financial support from a scholarship of the Universit\'e Libre de Bruxelles is gratefully acknowledged.

\begin{appendix}
\section{Numerical calculation}
\label{app:num}

The following commented MATLAB code implements the numerical algorithm for calculating resonances of the one-dimensional symmetric finite range potential described in section \ref{subsec:DGauss}.
For paedagogical reasons the program makes use of several global variables which give the code a simple structure but make it less flexible and elegant. For the same reasons and for achieving
compatbility with both MATLAB and the Open Source software OCTAVE the integration of the Schr\"odinger equation is performed by means of a straightforward implementation of the classical Runge
Kutta method which requires a rather high number of grid points. Thus the present code can be made a lot more efficient by using more sophisticated integrators like, e.g., MATLAB's
{\verb ODE45 }  or OCTAVE's {\verb lsode }. The program can be straighforwardly adapted for other symmetric potentials by changing the function $V(x)$ and providing the corresponding
position $b$ of the potential maximum that confines the wavefunction as well as a suitable cutoff parameter $a$. For a potential open on one side only the boundary condition criterion $crit$
must be modified according to equation (\ref{dings}).

\begin{lstlisting}[language=Matlab, breaklines=true]

function [E_res, Gamma, psi, Dpsi, x]= Num_Siegert
global V0 lambda m hbar a Nx

V0=1; lambda=0.1;

hbar=1; m=1;

a=-20;
Nx=10000;

Emin=0.3;
Emax=0.6;

E_res=bisect(@solve_SE,Emin,Emax,10^-5)

[crit,psi,Dpsi,x]=solve_SE(E_res);

k=sqrt(2*m*E_res)/hbar;
dx=(0-a)/Nx;
b=1./sqrt(lambda);

Gamma=hbar^2*k/m*abs(psi(1)).^2./(sum(abs(psi).^2.*(x>=-b)*dx))
Gamma_half=Gamma/2

psi=psi./sqrt(sum(abs(psi).^2.*(x>=-b).*dx));

figure(1);
hold on
plot(x,abs(psi).^2)
plot(-x,abs(psi).^2)

plot(x,V(x),'r')
plot(-x,V(x),'r')
hold off
xlabel('x')

function [crit,psi_v,Dpsi_v,x_v]=solve_SE(E)
global m hbar a Nx

psi_v=[];
Dpsi_v=[];
x_v=[];

k=sqrt(2*m*E)/hbar;

x=a; psi=0.001;  Dpsi=i*k*psi;

x_v=[x_v x];
psi_v=[psi_v psi];
Dpsi_v=[Dpsi_v Dpsi];

dx=(0-a)/Nx;

for j=1:Nx
  y0=[psi; Dpsi];

  dy_dx0=Schroedinger(y0,x,E);

  yA=y0+0.5*dx*dy_dx0;

  dy_dxA=Schroedinger(yA,x+0.5*dx,E);
  yB=y0+0.5*dx*dy_dxA;

  dy_dxB=Schroedinger(yB,x+0.5*dx,E);
  yC=y0+dx*dy_dxB;

  dy_dxC=Schroedinger(yC,x+dx,E);

  y1=y0+dx*(dy_dx0+2*(dy_dxA+dy_dxB)+dy_dxC)/6;

    psi=y1(1); Dpsi=y1(2);
    x=a+j*dx;
    x_v=[x_v x];
    psi_v=[psi_v psi];
    Dpsi_v=[Dpsi_v Dpsi];
end;

crit=(psi*Dpsi'+psi'*Dpsi);
function dy_dx=Schroedinger(y,x,E)
global m hbar

dy_dx = [y(2);
        2*m/hbar^2 * (V(x)-E).*y(1)];
function potential = V(x)
global V0 lambda

potential = V0.*0.5.*x.^2.*exp(-lambda.*x.^2);
function [x0] = bisect(func,x1,x2,tol)

  f1=feval(func,x1); if f1 == 0, x0=x1; return; end
  f2=feval(func,x2); if f2 == 0, x0=x2; return; end
   if f1*f2 >= 0 | x1 >= x2
        x1, f1
        x2, f2
      error('No root found due to initial values x1, x2');
   end

  for i=1:100
    if x2 - x1 < tol return; end
    x0 = 0.5*(x2+x1);
    f0=feval(func,x0);
    if f0*f1 <= 0
      x2=x0; f2=f0;
    else
      x1=x0; f1=f0;
    end
  end
  error('No root found')

\end{lstlisting}

\end{appendix}

\section*{References}

redpajama_set_name: RedPajamaArXiv


text:
10 Things You Didn't Know About Beanie Babies
Sadly, they will probably never make you rich.
By Kate Storey
Every so often, a story emerges trumpeting a crazy high price tag for an old Beanie Baby. Most recently, The Daily Mail said a British couple bought a purple Princess Diana bear second-hand for $15, and that it was now worth more than $100,000. If you read the story, you may have freaked out and rushed to see which Beanie Babies you still had stuffed in the attic. But, turns out, the bear is worth closer to $47, according to tycollector.com, and the site actually issued a fraud alert about the purple bears, calling the article "irresponsible and non-professionally researched."
Here are 10 other facts you may not have known about those little stuffed animals that were once considered "investment items."
1. Beanie Baby mania began with neighbors swapping them in Chicago.
Ty started selling Beanie Babies in 1993 and sales were okay. But then, a group of friends in Chicago began trading them and the media caught wind of it. "There were articles and TV segments about moms and dads who traded a $5 toy for thousands of dollars," the New York Times reported.
2. In the '90s, people were making thousands and thousands of dollars off the toys.
Peggy Gallagher, one of the early traders, bought a box of the stuffed animals in Germany for $2,000 that was worth $300,000 in the US, according to the Times article.
3. eBay was a major factor in the Beanie craze.
Beanie Baby mania coincided with the rise of eBay and, in the early '90s, Beanie Babies made up 10 percent of eBay's sales.
4. Not surprisingly, they made their parent company a lot of money.
Thanks to Beanie Babies, Ty was the first-ever billion-dollar plush company, according to Fortune.
5. A couple actually went to court over their Beanie Baby collection.
In the most 1999 thing to ever happen, a couple was ordered to divide up their collection, which was valued at up to $5,000. According to the Huffington Post, they actually brought the toys to court to divvy them up under the supervision of the judge.
6. Remember being really careful not to take off the tag? Well, that was a legit concern.
In their heyday, Beanie Babies were worth 50% less without those little cardboard hearts.
7. Ty once made a typo on a tag and people went crazy.
On the little white bear called Valentino, some of the tags say "Oriiginal," which collectors decided made them extremely valuable.
8. There was a weird rumor about the insides of Beanie Babies.
Strangely, there was once a rampant rumor going around the Web that the little pellets inside the toys were actually spider eggs. It was not true, of course.
'90s Kids Rejoice! The Spider Eggs They Used To Fill Beanie Babies Are Finally Hatching! http://t.co/BvKsnB5Fdx pic.twitter.com/PkunfCD3Eb
— ClickHole (@ClickHole) November 6, 2014
9. Creator Ty Warner is quite the character.
He obsessively designed each toy, according to Zac Bissonnette's book The Great Beanie Baby Bubble, going to the factories in China and Korea to oversee every little detail. He'd decide he didn't like a design and halt production, which would, in turn, drive up the prices for that particular design. Where is he now? The reclusive billionaire was eventually charged with tax evasion.
10. Yes, the first-edition Princess Diana tribute Beanie Babies are worth more than the later editions.
But you're still not going to be able to retire on them. According to tycollector.com, the first editions are worth about $47, while the later ones are worth about $27.
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My year of getting published: Interview with a Travel Writer...Tim Leffel.
Interview with a Travel Writer...Tim Leffel.
Today we talk with Tim Leffel, award winning travel writer and editor. Tim is also the editor of Perceptive Travel, a web magazine that is home to narrative travel stories from book authors on the move. A man on the move - Tim has circled the globe three times and has dispatched articles from five continents over a 16-year period.
Tim is the author of several books - Make Your Travel Dollars Worth a Fortune: The Contrarian Traveler's Guide to Getting More for Less (Travelers' Tales Publishing) and is co-author of Traveler's Tool Kit: Mexico and Central America. His stories have appeared in a wide variety of publications. He has a regular column for MSNBC.com and contributes to several websites, including two of his own blogs: the Cheapest Destinations Blog and Practical Travel Gear.
My first two articles were for the Travel Smart newsletter and Transitions Abroad. I've been writing for the latter ever since. My big financial break was getting hooked up with a trade publication reviewing hotels in Turkey. That led to later assignments in India, Nepal, Korea, Israel, Egypt, Jordan, and many more. I still work for them too sometimes---I'm covering the Guanajuato state of Mexico next month.
The advice is starting to shift a bit because of the power of self-publishing. When it comes to the traditional path of getting articles into magazines, my advice is to write like crazy, read a lot, learn how to edit well, and remember who your real customer is--the editor. Start small and then think big instead of trying to do it the other way. Most of the work comes from doing short and focused service pieces (how-to stuff). And keep your day job until you get wildly successful, of course.
The new part is, you can hone your chops on your own site or blog now and actually make a little beer money in the process. If you find a niche that you can call your own, you can eventually make as much off your own site as you'd get from a lot of outlets you'll kill yourself sending query letters too. And you own your words forever.
The future looks fantastic if you're riding the right waves. Writers who whine and moan about where things are headed remind me of buggy whip makers complaining about the automobile. I actually had a veteran travel writer tell me last week that she has never written anything for the Internet and doesn't understand it. That blows my mind. What is she going to do 5 years from now--retire?
We're in a transition phase right now where pay for Web articles is nowhere near what magazines pay, but the glory days of print are clearly fading behind us in the rear-view mirror. Newspaper travel sections have dwindled to almost nothing and it's getting increasingly tough for travel magazines to thrive. The Web is not yet generating the same kind of ad revenue for corporations that print does, but if you own what you produce, that's actually an advantage we individual experts can exploit. I know a few travel writers who are pulling in six figures without sending out a single query letter or doing any revisions per article for a flighty editor in New York. They write about what they love for their own site and their passion makes them money. One person can create a mini-empire relatively easy these days if he or she is patient and persistent. It's a different mindset though, obviously. You have to be more creative and multi-functional rather than just stringing sentences together to meet an assignment.
I tend to draw influences from all over the map because the way you craft a good service article or a planning guide is very different than the way you go about writing a narrative travel article that is more literary. I read a ton of magazines and always have it seems. I love pretty much everything Graham Greene ever wrote, a lot of Somerset Maugham, Naipaul, Hemingway, some Thoreaux. But I also love weird books that push the envelope and things that make me laugh. Here's a top-10 list I did a while back: Top Ten Travel Books.
This makes me sound like a crotchety old fart, but I miss the days when I was backpacking around the world before e-mail because we could all completely unplug and disconnect, just living in the moment and soaking it all in wherever we happened to be. It's hard to do that now without having to say "I'm sorry" to a dozen people when you get back on line two weeks later. I have a family now, which means shorter trips and less lazy aimless wandering than when I started out. Plus there's the usual challenge of finding enough time to cram in what needs to be done on the road. The actual writing is the easy part. if the time is there.
It's a moving target because I'm going someplace new several times a year. I have fond memories of Nepal, Indonesia, and Peru, but I'd gladly go back to almost anywhere I've been, whether that's Laos or Lexington, Kentucky. I have a little beach casita in Mexico though, so I guess it's safe to say I like that country a whole lot.


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Home > Teachings > FFI Newsletter > FFI - 2009 > 09/01/2009 - June 2009 Trip Report
09/01/2009 - June 2009 Trip Report
<< Back to FFI Listing
12/01/2009 - The Prophetic Year 2010
11/01/2009 - The Hidden Treasure Found
10/01/2009 - Bread and Wine
08/01/2009 - The Two Beasts of Revelation 13
07/01/2009 - Summary of the Book of Revelation
06/01/2009 - Healing the Waters of Jericho—Part 2
05/01/2009 - Healing the Waters of Jericho
04/01/2009 - Coming Out of Bondage—Final
03/01/2009 - Coming Out of Bondage—Part 8
June 2009 Trip Report
Issue No. 254
My wife and I were led to take a trip to the West Coast in June. We stopped at various places there and back, but the specific reason for the trip was to deal with the two beasts of Revelation 13.
Some trips are ordinary, or normal. But some trips take on greater significance. Understanding the extraordinary nature of "prophetic trips" is difficult for people unless they have experienced such for themselves. But from the beginning of a prophetic trip, one has to watch for many unusual things, because it is much like stepping into an alternate reality, or another world.
Many times, the events on a trip do not make sense in the normal reality of life. Virtually everything that happens on a prophetic trip is a revelation of prophecy and establishes patterns for things to come. I do not claim to understand it all myself, but I have seen more than enough to just flow with whatever comes and pray for under-standing.
We left home on June 4 and drove along the Lewis and Clark Trail through Montana, Idaho, and Oregon. I did not know why this route was important until we were well into Oregon. It was to reverse the curse on the land that had been explored by Lewis and Clark (1804-1806).
The Lewis and Clark Trail
Earlier, on May 28, 2009, I wrote an internet article, "The Greater Salt Work for you to do," where I suggested that people walk their neighborhoods praying a blessing on the houses and properties of their neighbors. I even gave a suggested model prayer to pray:
"Father, let this house and property be part of Your Kingdom. I break every curse upon it in the name of Jesus, and bless it with the presence of Christ. Let it bring forth fruits of the Spirit: love, joy, peace, patience, kindness, goodness, faith, meekness, and self-control" (Gal. 5:22, 23).
This prayer is designed to lay claim to all that God owns by right of creation. This will take some years, but I believe that eventually, this will be done in the entire earth.
By the time we got into Oregon, it became clear that we were laying claim to all that Lewis and Clark had explored two centuries earlier. They had been hired by the U.S. government to explore the land and essentially to lay claim to it for men's use. While the intentions might have been good, the outworking of those intentions were not so good. It was only good as long as the government and the people recognized God's sovereignty over His creation. The problem is that in the past century in particular, the U.S. government has openly revolted against God and has refused to recognize God's rights of ownership. As a result, they believe they have the right to use the land as if they own it and have no accountability under God.
That was ancient Israel's problem as well, and it brought them into divine judgment and captivity.
The Native Americans understood that all land belonged to God and that man enjoyed its use, but no man could lay claim to it. They had it right insofar as they understood the laws of God that nature taught them. But European Christians had a long tradition of usurping God's land for their own use and treating it as if they owned it. That was part of the tradition of King Saul which was appropriated by the Church, and unfortunately, that type of thinking was fully ingrained in the Christian European mind.
It was one of the primary motivations for mistreating anyone who got in their way and formed the framework for the idea of "Manifest Destiny." This concept took the place of the Abrahamic Destiny, which was the biblical calling to be a blessing to all families of the earth.
Manifest Destiny justified a multitude of sins in early American thinking, just as it does today among the Israelis in their oppression, theft, and murder of Palestinians.
In the course of our trip, we had a meeting in Boise, Idaho on June 7 and then left there on the 10th heading toward Seattle, WA. On the morning of the 10th, the Father gave us a word about "children," including Matt. 18:6,
6 But whoever causes one of these little ones who believe in Me to stumble, it is better for him that a heavy millstone be hung around his neck, and that he be drowned in the depths of the sea.
We stopped in Pendleton, Oregon near the Columbia River to see the Indian Cultural Museum. On one wall was a picture of dozens of sad-faced Native American children in uniforms, having been forcibly taken from their parents in order to school them in a religious school. They were beaten if they spoke their native language. The intent was to integrate them fully into American European culture.
We were led to pray repentance for the abuse of those children and ask God for forgiveness. We then were led to drive to the nearby McNary Dam on the Columbia River to find a stone ("millstone"). We were to carry the stone to the mouth of the river and throw it into the Pacific Ocean as an act of divine judgment upon the abusive Babylonian system for causing "children" everywhere to stumble.
Interestingly enough, we found a stone shaped like a thick cigar, which looked like it might have been used at one time as a grindstone. It looked very much out of place at the McNary Dam, because most of the rocks in the area are volcanic and quite jagged and sharp. But this was the stone prepared for us, and we took it to Astoria, OR at the mouth of the Columbia River. There we threw it into the sea as a prophetic act, according to Rev. 18:21,
21 And a strong angel took up a stone like a great millstone and threw it into the sea, saying, "Thus will Babylon, the great city, be thrown down with violence, and will not be found any longer."
For the record, this was done June 11, 2009. From Astoria, we drove to Seattle, where Ron and I taught in meetings over the week end of June 12-14.
The Beast from the Sea
On June 15 we had to deal with the beast from the sea (Rev. 13:1-10). Because individuals are involved in the story, I cannot tell the story itself at this time, but it was a spirit which had attacked someone in a dream, calling itself by the name of Lamar. The name means "The Sea."
Driving to Sacramento, CA
From Seattle, we drove south to California, spending a night just north of Redding at the base of Mount Shasta. Because we had some extra time, we thought we would be tourists for a day. We decided to see the Shasta Caverns so we stopped for the night at a nearby motel and saw the Caverns on the morning of June 18.
In the caverns Darla twisted her foot when stepping over a rock. Feeling rather foolish, she said nothing for a few days, but later I found that she had a very large bruise on her foot and heel. I immediately recognized that this had to do with Gen. 3:15,
15 And I will put enmity between thee and the woman, and between thy seed and her seed; It shall bruise thy head, and thou shalt bruise His heel.
But at the time, even if I had known about the bruise, I would not have been able to make the connection. There was simply not enough information at the time. Yet even then, the revelation had already begun, because in such prophetic trips, even tourism cannot escape the prophetic flow. Once we are in the river, we can only flow with it.
We arrived in Sacramento, CA the evening of June 18 and stayed until noon on June 21. There we were able to gather with others who understood the prophetic realm and could add more understanding to what we already knew.
On June 20 we prophetically cast out the beast from the earth. On the 21st the meetings culminated and concluded in the morning with the establishment of a three-fold cord, an alliance representing the threefold aspect of Scriptures: Law, Prophets, and Psalms (Luke 24:44). To us, this was from Ecclesiastes 4:12, "a cord of three strands is not quickly torn apart."
This alliance, then, gave us all an increased support system to complete the work that yet lay ahead in the overthrow of the beast from the earth.
As I said, this was done on June 21, a very important date that had been revealed to us earlier on May 12. Among many things, June 21, 2009 began a 3½ year period ending Dec. 21, 2012. (Note the end of the Mayan Calendar on that date.) We believe that we will be seeing a 3½ year ministry that parallels the ministry of Christ in some way. But right now it is too early to know much.
The Beast from the Earth: Pan or Azazel
Our revelation told us that the beast from the earth is the rival of the second goat in Leviticus 16.
Recall that on each Day of Atonement, the high priest was to kill the first goat and sprinkle its blood on the mercy seat in the tabernacle (later the temple). Lev. 16:21 says that the second goat was to be led into the wilderness "by the hand of a fit man."
These two goats signify Jesus Christ in His two comings. In His first coming, He had to die, even as the first goat was killed in order for His blood to COVER sin. In His second coming, however, He is not put to death, but is released into the wilderness to REMOVE sin.
Lev. 16:8 also says (literal translation):
8 But Aaron shall cast lots for the two goats, one lot for Yahweh and the other lot for Azazel.
The second goat was to be led into the wilderness "for Azazel." Azazel in Hebrew literally means "goat-god." The Hebrew word for "goat" is azaz. Thus, Azazel was a symbol of the devil and was pictured as half goat, half man. In Greek religion, he was called Pan.
It is important to know this in order to understand Lev. 16 as well as its fulfillment in Matt. 4:1,
1 Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil.
Jesus had just been baptized while the high priest was killing the first goat in the temple. Immediately afterward, Jesus was led into the wilderness by the Spirit ("the hand of a fit man"). Jesus was fulfilling both goats here. And so He was "killed" (by baptism) as the first goat, and then led into the wilderness "for Azazel," that is, "to be tempted of the devil."
The point of this is to show that Jesus was the TRUE second goat, but He was being tempted by Azazel, the "goat-god." Azazel is the counterfeit goat, attempting to get Jesus to recognize his authority over the earth (Matt. 4:8-10). That authority is the Birthright, and with it is the right and empowerment to bring forth the ultimate fruits of the Kingdom—the manifested sons of God.
If Jesus had recognized Azazel as the rightful heir of the Birthright, the sons of God could never be brought to birth. Jesus is the true Heir of the Birthright, and His body with Him. Thus, it is vital that we not give the Birthright to the body of Azazel, the imitation/counterfeit goats who have no intention of bringing forth the true sons of God.
The Hebrew name Azazel is known in Greek as Pan. Pan is a satyr, half man and half goat. One of the more well known stories of Pan is The Pied Piper, seen as the god of music that bewitches children and leads them away from their parents into perdition.
And so, while we discussed these matters in Sacramento, we understood that the second half of this West Coast trip was to overthrow Azazel, or Pan. Pan's residence was said to be in the "Grotto of Pan" (Panea or Banea), located at the base of Mount Herman between Israel and Lebanon. Today it is an Israeli national park and can be viewed online. The Grotto itself is a cave under a huge rock.
Jesus visited the place in Matthew 16 just before He ascended Mount Herman to be transfigured in chapter 17. The Grotto of Pan in those days was near the city of Caesarea Philippi (Matt. 16:13). The Grotto was known to the Judeans as "the gates of hell," because it was seen as the home of Azazel, the devil.
So it was appropriate that Jesus would raise the question to his disciples, "Who do men say that I am?" (16:13) In other words, Am I the Goat that can remove sin, or is it Azazel? Peter gives us the answer, and Jesus responds,
18 And I also say to you that you are Peter (little rock), and upon this rock [looming over the Grotto] I will build My church, and the gates of hell shall not overpower it.
In other words, I am going to build My church right over the gates of hell, and Azazel will have no power to stop it. This is another way of saying, "I am going to take the earth back from the control of Azazel/Pan."
It is important to have some understanding of the law of Lev. 16 and its prophetic implications in Jesus' story, so that we may apply it to the present history of the Kingdom. Even as the first goat prophesies of Christ's death on the cross in His first work, so also does the second goat prophesy of His second work in our day.
The first work was a Passover work; the second is a Tabernacles work. The New Testament gives us the full account of His first work, but we are now seeing the development of His second work as we watch for the fulfillment of the feast of Tabernacles.
Tabernacles involves transfiguration, which is why Jesus went to "the gates of hell" before going up Mount Herman to be transfigured.
The ministry of Christ was what He had to do in His first appearance, but under the surface, He was prophesying also of His second appearance. In fact, His 40 days in the wilderness were the prelude to His first ministry work, but this also prophesied of the 40 Jubilees of the Church in the wilderness from 33-1993 A.D., after which time His second work would commence.
That brings us to the present time in our generation. Toward the end of this "wilderness" time, the Church succumbed to the temptation of Azazel and recognized his children (John 8:44) as the heirs of the Birthright (1948). Out of that decision came the Pied Piper of rock and roll, which stole the children away to perdition in the 60's generation.
When it came time for the Church to blow the trumpet of the Jubilee in 1986, they were unprepared and did not know the times and seasons. So God has called out a smaller body of people called Ovecomers to do what the Church at large refused to do or were unable to do.
Driving to Colorado Springs, CO
We left Sacramento at noon, June 21, and drove to Ely, Nevada for the night. Ely has an interesting history and a prophetic connection with Ron that goes back to 1993. That is a story that he will have to tell. For us, however, it was connected to Eli, the high priest, who had a problem with his sons, Hophni and Phineas (1 Samuel 2:12, 22-25).
Since June 21 was also Fathers Day, we understood that we were to go to Ely and pray to restore the relationship of the fathers with the children (Mal. 4:6). This is part of the Elijah/Elisha ministry that began on April 12, 2009.
From Ely, we were led to drive to Moab, Utah, where we spent the night. Recall that the Moabites were the children of incest (Lot and his daughters in Gen. 19:36-38). We were led to pray for the restoration of the fathers with their daughters.
Then on June 23 we drove from Moab to Colorado Springs and held our first meeting that evening.
Casting Pan out of the Black Forest
Recall that we had already been to Mount Shasta, an area heavily dominated by the New Age movement as well as outright Satanism. In Ely, my wife had finally shown me the bruise on her foot and heel, and I finally then made the connection to Gen. 3:15. Since this had occurred in the Shasta Cavern, it was not hard to make the connection to the Grotto of Pan and to see that we had been led there as part of the work to overthrow Pan.
In Colorado Springs, the meetings were held in the Black Forest, a literal forest on the east side of town. But when we stopped at a house on Mount Shasta Road, I knew that we were here to cast out Pan from the Black Forest. (We had already been given revelation about Pan and its connection to the Black Forest a few years earlier. That story is too long for this bulletin, but you can read it online. I wrote of it in my weblogs dated June 28, 2009.)
The first evening meeting on June 23 I focused upon the issue of Zionism. The next day I taught most of the day on the feast days, and then that evening we focused upon casting out Pan and claiming the Black Forest for the Kingdom of God. This was done in much the same way as we had laid claim earlier to the territory explored by Lewis and Clark.
The next morning we left town, and in listening to the news, we heard that Michael Jackson had died of heart failure. Michael was obsessed with Peter PAN, a story about children never growing old. In other words, it was about immortality.
Michael Jackson's famous home was Neverland Ranch, because the story of Peter Pan takes place in Neverland.
Michael Jackson was called "The King of Pop." He was one of the great musicians of recent times, the Pied Piper of American children. For him to die unexpectedly and suddenly the day after we cast out Pan from the Black Forest was coincidental only to those not understanding the spiritual causes of earthly events.
We all play different roles as spiritual types. There were many types of Christ in the Old Testament, each playing out his part in the prophecy of their lives. Saul was a type of the Church; David was a type of the overcomers; Absalom was a type of the chief priests who usurped the throne of Jesus; Ahithophel was a type of Judas, who helped the priests usurp Jesus' throne. Each one's role in life determined their calling, though none of them really understood the part they were playing.
It is the same with Michael Jackson. In his obsession with Pan, his desire to remain young, his musical ability, and his Neverland Ranch, he did not realize that he had become a type of Azazel/Pan that would ultimately be overthrown at the appointed time, June 24, 2009, the day celebrated as the feast of St. John the Baptist.
It also happened to be the same day that we overthrew Baphomet, the god of Freemasonry, five years earlier on June 24, 2004.
We arrived home on June 26, ending this prophetic mission trip. Our lives then went back to "normal."
We do not know yet what will be the short-term effects of the warfare accomplished in June. We do know that in the long term, the Kingdom of God is steadily defeating the Babylonian world system. Babylon is falling and so it is thrashing about in an attempt to retain power. But it has been destined for defeat since the beginning of time, and we are now seeing its collapse one step closer to a reality.
This next month (September) could be more significant than last September. Be watchful in prayer.


A powerful story of your personal transformation, Yijoo.
Yijoo, I cannot tell you how wonderful it was for me to sit and hear your story live. When you spoke of your journey and transformation, all I could think was how brave and resilient you are. Mr. Lill is right, no one is perfect, but there is perfection to be found in the imperfections in life. Thank you for sharing your story!
I was so lucky and happy to have you as my director, and teacher! This project truly is my one of favorite projects, and thank you so much for guiding us to this wonderful time!
Hi Yijoo, that's such an amazing story! I enjoyed it very much, Thanks for making it!
Thank you Wai Sin for listening to my story!
Almost towards the end, when you said the phrase, "I was stabbing myself with a sharp invisible knife of perfection", I could imagine it really clearly. It was so strong that I could feel your pressure. I could feel that it was really hard to go through.
Your whole memoir pulled me right in. I loved listening to it.
I am so so so glad that my story pulled you right in and loved my story. Thank you so much for being my audience!
I liked how you used imageries explaining how perfection affected you. Also using examples of broken glass was a nice use of metaphor.
Hi Yijoo, that's such a amazing story! I love it. Your story let me know , I don't need to be perfect, I just need to be better. Thank you for sharing it.
Even if this world told you that you am behind everyone, and even if you told yourself that why can't you be perfect, you are perfect in your own way!
Thank you Alice! Hope you enjoyed my story, and thank you so much for being a part of my podcast!
Your story really touched my heart. Even though I don't know you, I start to like you by listening to your story. I'm glad that you want to be better not perfect.
Yijoo, your story is wonderful and the one I've never heard it befofore. Also, it was amazing!
Wow I am so glad that it inspired you! Don't try to fit yourself in what other people think perfection is!
Yijoo your story is so honest and I love how you openly talked about all the pressure being perfect placed on you. I'm so happy that you feel more freedom to be yourself and that you can fully express how you feel not what you think people expect of you or what you expect of yourself to be perfect. I'm so impressed by how clearly you communicated with imagery and how far you've come since 7th grade. You amaze me!!


DUTY FREE SHOPS INDUSTRIAL, MANUFACTURING, TECHNICAL AND BUSINESS COMPANY SA. under trade name"FF GROUP", announces that, today, June 24th,2011, the Annual General Meeting of the shareholders of the company was convened, as originally announced, based on the respective invitation.
1. Submitted and approved the annual consolidated and companies financial statements for the fiscal year 2010 following the hearing of the reports of the Board of Directors and the Chartered Auditors-Accountants for the fiscal year 2010.
2 Approved the appropriation of the net profits after taxes for the fiscal year 2010 and approval for not distribution of dividend to the shareholders.
3 Waiver of liability of the Members of the board of Directors and the Chartered Auditors-Accountants for the fiscal year 2010.
4. Elected Mr. George Varthalitis John HM SOEL 10251 as ordinary auditor and Mrs. Chrisoula Tsakalogiannis George HM SOEL 23811 as a Substitute Certified Auditor, both members of the auditing company «Baker Tilly Hellas SA".
6. Approved the acquisition by the Company's own shares in accordance with Article 16 of Law 2190/1920. In particular, the Company shall be entitled within 24 months from now to make a buyback of up to one tenth (1 / 10) of the total issued share capital, a minimum price of EUR 5 and a maximum purchase price of EUR 25 per share. For the calculation of one tenth (1 / 10) will be taken into account already purchased shares, of which the Company owns. The Company intends to comply in relation to the conduct of the market for those shares, as referred to in Article 5 of Regulation 2273/2003 of the Commission on the price and volume of purchases, and referred to in Article 6 § 1 thereof.
Epaminondas Dafermos, independent non-executive member.
In adition, the company approved the liability insurance cover of the BODmember and officers aof the Group and authorized Mr George Koutsolioutsos and Mr George Velentzas to proceed with the conclusion of the relevant contract with the insurance company.
In the above Annual General Meeting, 142 shareholders were present, representing 68,17% of the company's share capital, namely 41.304.696 Voting rights out of a total of 60.226.139 voting rights.
41.304.696 shares were represented out of a total of 60.588.210, namely percentage 68,17%. 41.304.696 shares voted in favor namely percentage 100%.
41.304.696 shares were represented out of a total of 60.588.210, namely percentage 68,17%. 40.355.600 shares voted in favor namely percentage 97,7%. 344.118 shares voted against, namely percentage 0.83%, 604.978 shares, namely percentage 1,47% declared abstention from voting.
41.304.696 shares were represented out of a total of 60.588.210, namely percentage 68,17%. 37.247.166 shares voted in favor namely percentage 90.2%. 1.757.897 shares voted against, namely percentage 4.3%, , 2.299.633 shares, namely percentage 5.5% declared abstention from voting.
41.304.696 shares were represented out of a total of 60.588.210, namely percentage 68,17%. 40.446.410 shares voted in favor namely percentage 97,9%. 253.308 shares voted against, namely percentage 0.6%, 604.978 shares, namely percentage 1,5% declared abstention from voting.
41.304.696 shares were represented out of a total of 60.588.210 namely percentage 68,17%. 32.985.970 shares voted in favor namely percentage 79,8%. 2.006.943 shares voted against, namely percentage 4.9%, , 6.311.783 shares, namely percentage 15,3% declared abstention from voting.
41.304.696 shares were represented out of a total of 60.588.210 namely percentage 68,17%. 33.609.340 shares voted in favor namely percentage 81,4%. 5.395.723 shares voted against, namely percentage 13,1%, , 2.299.633 shares, namely percentage 5,5% declared abstention from voting.


Melrose Clean Green Barley Grass is advertised as a green whole food supplement based on a powder obtained from the dehydrated leaves of barley plants (Hordeum vulgare). According to Melrose Health Group, the manufacturer of this product, the plants from which the formula is obtained are organically grown and harvested at their nutritional peak.
Barley Grass is a source of numerous nutrients such as Chlorophyll, Vitamin A, Omega-3 fatty acids, Vitamin E, various antioxidant compounds which contribute to the wide spectrum applicability of the formulation. The core benefits mentioned by the manufacturer include blood cleansing properties, immune system support, prevention of loss of bone calcium, brain function support, vision function support, and fighting oxidative stress among others.
Melrose Health Group was founded more than 30 years ago and is headquartered in Australia. The company is committed to delivering high quality natural supplements at reasonable prices. The company takes pride in their declared moral and social responsibility to provide natural foods and supplements that are both effective and safe. The company's products are certified organic by ACO (Australian Certified Organic), Australia's largest certifier for organic and biodynamic products.
Melrose Clean Green Barley Grass is designed for adults who wish to maintain or achieve an overall sense of well-being. The formula is gluten free, hence people allergic to glutted are also able to consume this formula.
Melrose Clean Green Barley Grass includes the following ingredient: Barley Grass dried at body temperature.
Melrose Clean Green Barley Grass features an extract from the leaf of Green Barley Grass, usually consumed as an extract. The plant is known for its impressive profile of essential body nutrients, such as Vitamins, antioxidants and minerals. The plant is also highly concentrated in chlorophyll, a molecule rich in Magnesium and known for its properties as a blood cleanser, blood builder and detoxification agent. Chlorophyll is especially beneficial in improving the health of the digestive, immune and circulatory system.
Barley grass is rich in vitamins and minerals such as Vitamin A, Calcium, Folic acid, B vitamins, Iron, Vitamin C, Potassium, Magnesium and Phosphorus which work synergistically to support the body's overall health, while attending to the specific needs of various body functions. The plant contains antioxidants as vitamins, acting as a free radicals scavenger. Further research needs to be done in order to establish the full spectrum of benefits which derive from this.
Barley grass is also believed to help lower high cholesterol levels. According to the findings of a research published in the "European Journal of Clinical Nutrition," barley contains beta-glucan and is able to lower LDL cholesterol (the bad kind of cholesterol). Other benefits include cancer prevention, but these too have to be supported by actual evidence.
There are no testimonials posted online regarding the use and potential side effects of Melrose Clean Green Barley Grass. The manufacturer recommends taking 1 teaspoon in water or juice every day.
Melrose Clean Green Barley Grass is advertised as a green-superfood able to assist with a number of essential body functions, including the immune and the brain function. The formula is based on the properties of barley grass, which, however, are not supported by very many scientific research studies.
Although this type of product has gained much popularity as a fast and effective way to ensure proper nutrition, the formula should not substitute a balanced diet.
Based on the good reviews and endorsements barley grass has received from consumers, Melrose Clean Green Barley Grass is likely to accomplish its purpose and deliver the benefits claimed, although there are no direct references to this product's effectiveness.
Melrose Clean Green Barley Grass or HCF?


Great Fishin' Photos from our Backwoods Buddies!
Check out these great catches by our Backwoods Buddies!
Send us your photos so everyone can enjoy them! Mail a reprint to the address below or e-mail them and we will post them on the site ASAP!
Make sure and tell us about your catch.Give us any special info like weight, length, where it was caught, etc.. We'll be looking for them!


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by Josephine Johnson
Some images in the art world are made and forgotten, while others are repeated over and over again in many different mediums. A popular image of Fame Decorating Shakespeare's Tomb recently found its way into Museum Textile Services' studio in the form of embroidered and painted silk.
"Fame Decorating Shakespeare's Tomb" currently being conserved at MTS.
The embroidery depicts Fame as a woman decorating the tomb of the great William Shakespeare. The image was originally created by English painter Angelica Kauffmann in 1772. Kauffmann ranks among the first successful female European artists. The painting is a small metal roundel that may have been part of a large decorative scheme in a room. Her decorative images can be found all over furniture, porcelain, ceilings, walls, and as we've seen, embroideries.
"Fame Decorating Shakespeare's Tomb," painting by Angelica Kauffmann in 1772.
Kaufman's painting was made into an etching a decade later by the English printmaker Francesco Bartolozzi. Converting a painting into an etching was a common way to reproduce an image before photography was invented. The etching of the painting is probably what inspired the embroideries because an etching can circulate to a much bigger audience. Notice how the tomb in the embroidery matches the shape of the tomb in the etching, not the painting!
Etching of "Shakespeare's Tomb" created by Francesco Bartolozzi in 1782.
The embroideries follow the tradition in the eighteenth and early nineteenth centuries of needlepoint created by school girls, who would have had much easier access to the etching than to Kaufman's painting. With inspiration coming from the black and white etching, the embroiderer had more freedom for creativity when choosing colors.
In the slide show above you can see several other embroideries of Fame at Shakespeare's tomb. We love to see the work of a female painter celebrated over and over again throughout history!
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Sony Unveils Wearable Air Conditioner Via Crowdfunding
The Reon Pocket can help raise or lower your body temperature.
By Rebecca Kim
Tech Jul 27, 2019
Sony's First Flight crowdfunding platform has revealed its newest project to help people beat the heat during the summer. The Reon Pocket is a portable device about the size of a card wallet, which fits snuggly into the back of a custom undershirt. Leveraging thermoelectric cooling, the product can be controlled via Bluetooth on a smartphone and either cool down or warm up, depending on the user's preference.
The First Flight website notes that the Reon is capable of lowering one's body temperature by 23 degrees Fahrenheit, or raising it up to 14 degrees Fahrenheit. Weighing about 3 ounces, the product is designed to hold a charge of up to 24 hours using USB-C technology.
With the crowdfunding campaign currently backed at 85%, the gadget will start shipping to customers in Japan next March if it's fully funded. The starting price is listed at ¥12,760 (about $110 USD) for the Reon Pocket Lite (which is controlled manually) and ¥14,080 (around $130 USD) for the Reon Pocket. Launched in 2015, First Flight is Sony's seed accelerator program which serves as a crowdfunding and e-commerce platform aimed at championing new business ideas and projects from its employees. Take a look at the trailer above to see the Reon Pocket in action.
Be sure to also check out Sony's upcoming RX100 VII camera, which includes features from its flagship A9.
First Flight Jp/Sony
SonyGadgetsCrowdfunding
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One of the keys to bringing the things into your life that you want is not to wish for them and see them as being separate from yourself, it is seeing yourself as having those things already and truly living within that better life.
Manifestation Wall exists as a place where you can weave reality. It is a place where you can dream among the global consciousness and reach out to the universe, projecting a reality that you want to see come to pass. It is a place where you can write your dreams as reality, live as if they had already come to pass, and place that reality into the greater fabric of human global consciousness.
Take a look around, see some of the dreams that have already been put out there, and contribute some of your own.


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Affirming the sanctity of all human life – Archbishop Eamon Martin
by Archdiocese of Armagh | Jul 9, 2019 | Featured, Irish Bishops' Conference, ProLife
At the 2019 Rally for Life, Archbishop Eamon stated that it was as important as ever to affirm the sanctity of all human life.
"How tragic it is for humanity that some legislators would 'fast track' the ending of the lives of the most defenceless in our society" – Archbishop Eamon Martin
source – catholicbishops.ie
Archbishop Eamon Martin participated at the 'Rally for Life' which was held in Dublin city centre this afternoon. Speaking to media at the rally Archbishop Martin said:
"Today I wanted to stand in solidarity with the many thousands of people in Ireland who firmly believe that in pregnancy we are dealing with two lives – the life of a mother and her unborn child – and both in need of love, respect and protection.
"I march today because I believe it remains as important as ever to affirm the sanctity of all human life. The direct and intentional taking of the life of any innocent human being is always gravely wrong – we must avoid becoming desensitised to the value of every human life.
"More than one year on from the abortion referendum I am calling for more practical help for vulnerable women in this country who feel that their only way out of crisis is to end the life of their unborn child. What new supports have we put in place for mothers and fathers at the point of crisis? And, what supports are we offering to parents who feel that they have made the wrong choice in having an abortion?
"I am also deeply concerned by suggestions that amendments are being considered to the Northern Ireland (Executive Formation) Bill, going through Westminster on Monday next, which will hijack this Bill to remove existing legal protection for unborn babies and to 'fast track' the legalisation of abortion on demand in Northern Ireland. How tragic it is for humanity that some legislators would 'fast track' the ending of the lives of the most defenceless in our society.
"Like many others I strongly believe that it is urgent to restore an executive in Northern Ireland, so that the common good of all our people can be served. There is something particularly cynical, however, in taking advantage of the present political crisis to remove the right to life of the most vulnerable of our people; the unborn baby. The common good cannot be served in this way.
"A legal framework for the protection of unborn human life is an important statement about the respect due to each and every child, and about the society in which we live. I ask Catholics, and all who share our commitment to the right to life, to contact Members of Parliament as a matter of urgency, requesting that he or she vote against any attempt to remove legal protection from unborn babies."