The Old Testament recognizes that among the Canaanites the same type of sin here cursed was the dominating trait of evil. The descriptions given in the Pentateuch leave no doubt as to this [cp. Lev. 18.22; Deut. 12.29-32]. Even among the ancients outside of Israel (Japhetites) the sensual depravity in sexual life of Phoenicians, and Carthaginians in particular, had become proverbial.
Bucey and Tipton spend a fair bit of time discussing how the curse of Ham "presses the antithesis", in a Van Tillian way. They also point out (in a Klinean way) that, this not being a period of intrusion, Ham was not to be immediately executed.
Vos Study #8 covered the first half of chapter 5, Development leading up to Noachian revelation, and Vos Study #9 finishes chapter 5 with (post-flood) Noachian revelation.
This episode is a Klineophile's dream. They go well beyond Vos and spend a lot of time unpacking what Kline had to say, and there's even a positive mention of "brother Van Drunen's" use of Noachian revelation in his treatment of Common Grace.
First off, they spend a good bit of time on Kline's treatment of the covenantal rainbow as just a bow, a weapon, retired from attacking the earth, and hung up to rest, pointing away from the earth, and even towards God who is willing to redeem men by taking their punishment onto themselves.
There's a good discussion of what can go wrong when the common, universal covenant to preserve life until the final judgment, is conflated or flattened with redemptive covenants. On the one hand, you can get Theonomy, where elements of the redemptive covenant are imported into secular government. On the other hand, you get Catholicism, where the entire earth becomes sacramental (see Sacramentum Mundi), and salvation is somehow extended to all.
And near the end, there's a great discussion of the concept of Intrusion. Bucey makes an interesting point; in the many examples where Israel does not fully destroy Canaanites as God has commanded, that is an unauthorized extension of common grace. (And God punishes them for that). Tipton points out that examples of intrusion are always tied to a holy place installed on earth (the ark, the temple, the land of Israel, etc.).
Yesterday was the first class in a proposed 3-quarter (3x13wk) class on the Larger Catechism at EOPC, taught by (it's all about) me. For anybody that's interested, resources and recordings can be found online. Yesterday's class on historical introduction was a lot of fun, but I expect it will settle down as we dive into the catechism itself starting next week.
The narrative proceeds in three stages. It first describes the rapid development of sin in the line of Cain. In connection with this it describes the working of common grace in the gift of invention for the advance of civilization in the sphere of nature. It shows further that these gifts of grace were abused by the Cainites and made subservient to the progress of evil in the world.
The podcast concludes with a discussion of the "120 years" passage, which does not mean that God will limit the age of individuals to 120 years (many in the genealogies live much longer than that, even after the flood, including Abraham); rather it is a deadline, 120 years is the limit of God's patience (cf 2 Pet 3:9), after which judgment comes in the form of the flood, which will be discussed more next time, for the back half of the chapter.
In Vos Study #7, Dr. (congrats!) Bucey and Dr. Tipton cover all of the small chapter 4, The Content of the First Redemptive Special Revelation, which focuses on the results of the Fall.
First off is nakedness and shame, which is the result of "how Special Revelation attaches itself to General Revelation". Previously GR showed God's glory through creation, but now it reveals Adam & Eve's sin and guilt. (See also Rom 1).
The essence of the deliverance consists in a reversal of the attitude assumed by man towards the serpent and God respectively. Man in sinning had sided with the serpent and placed himself in opposition to God. Now the attitude towards the serpent becomes one of hostility; this must carry with it a corresponding change in man's attitude towards God. God being the mover in the warfare against Satan, man, joining in this, becomes plainly an ally of God.
The curses towards Eve and Adam (note curses are given in order of sin; serpent, Eve, Adam) are treated much less. But it is interesting that Vos finds the gospel even in the curses; obviously the protoevangelion in the serpent's curse, but in cursing Eve with painful childbirth, God is promising childbirth; and in cursing Adam with hard labor, he is promising sun, and rain, and bread.
One off-handed comment got my goat; discussing the collective seeds of the woman and serpent, Bucey jokes "Those are the first two kingdoms, ha ha"; but Tipton follows up enthusiastically with, "Yes, if you want to properly consider the two kingdoms…". It seemed like me to be a backhanded swipe at 2K, even though obviously, it's not proper 2K if one of the Kingdoms is the Kingdom of Satan. But I'll give them a pass, as the rest of the episode had lots of good things to say about Kline, both in Kingdom Prologue and Images of the Spirit.
Sometimes you have to write a blog post just for the sake of a good title. Episode 337 of Christ the Center featured Dr. Alan Strange, discussing "Animus Impotentis". Dr. Strange is rather a cut-up, and makes this discussion of a dry-sounding topic almost as entertaining as rodeo-skydiving a nuclear warhead!
Dr. Strange relates how 6×24 YECs like to insist that the confessional language "in the space of six days" means "in the space of six ordinary, twenty-four hour days" (or equivalently, the animus imponentis of the language means "ordinary 24-hour"). The only reason, they say, "24-hour" is not in the confession is because that phrase is modern, and it would be anachronistic for us to expect them to speak that way. However, in researching the minutes of the Assembly, Dr. Strange found a case where there was a debate over whether the 7th day of Creation is eternal and continuing, or "24 hours". Maybe the phrase was even "24-hour day", I don't recall. I think how it went was, there was a motion to assert that the 7th day was a 24-hour day, and the motion was debated, voted on, and rejected. The point being, "24-hour"-ness was in their vocabulary.
Finally, to show that animus imponentis is not only about creation, Dr. Strange discussed its relation to other topics as well. One that stuck out for me was an assertion that, Limited Atonement is not nailed down by our confessions, but the common understanding that it is a non-negotiable doctrine is a matter of animus imponentis. Apparently Hodge wrote something that tried to prove that L is indeed in the confessions but Strange considers Hodge to have used somewhat weak, overreaching arguments, and Fesko has written something more recently that does a better job.
Anyways, it was a good discussion, and you should go listen to the whole thing!


text:
Burger King Russia Nixes Ad That Promises Free Whoppers to Women Impregnated by World Cup Players
The spot was pulled after hitting the wrong note
Burger King has removed a post after critics called it demeaning toward women.
Getty Images, Burger King
Burger King Russia has pulled a World Cup-themed social media campaign that said it would reward women who were impregnated by soccer stars with free Whoppers—and cold hard cash.
On the brand's VK—a Russian social media network that's essentially the country's own version of Facebook—account, Burger King's Russian branch shared a photo of a pregnant woman cradling her stomach.
Alongside the photo, the brand offered up 3 million Russian rubles (just over $47,000) and a lifetime's worth of free Whoppers if they were able to prove that they had been impregnated by one of the soccer (or over there, football) players competing in this year's World Cup.
Burger King's post on Russian social media network VK
According to the AP, the post said that the motivation behind Burger King's offering was to procure "the best football genes" and "ensure the success of the Russian team for generations to come." Critics of the social media ad called it sexist and offensive to women, and the post was soon taken down.
On Tuesday, after the post was removed from its account, Burger King issued an apology: "We offer apologies for the announcement we made. It was too offensive. We are taking steps to ensure this type of activity does not happen again."
Burger King in Russia has come under fire for its advertisements before: In early 2017, it came out with an advertisement for a buy one, get one free offer featuring an illustration of a 17-year-old girl who had been raped and beaten.
Ironically, the concept featured in Burger King Russia's ad—encouraging a country's women to procreate with the intention of creating better soccer players—had been used before. A spot for Irn-Bru, a Scottish carbonated beverage, that was released ahead of the 2014 World Cup in Brazil, imagined a future where Scots had coupled with Brazilians to create the best possible team for World Cup 2034.
https://adweek.it/2tD776V
Diana Pearl
@dianapearl_
Diana is the deputy brands editor for Adweek.

redpajama_set_name: RedPajamaCommonCrawl


text:
Hendee Family takes final lap around old District 64 headquarters
Park Ridge-Niles School District 64 moved to its new District Office on Monday, September 19th. However, there was still one final piece of business to take care of at 164 S Prospect Avenue, the Raymond E. Hendee Educational Service Center (ESC) building.
On Monday, Superintendent Dr. Eric Olson and the Hendee Family went around ESC one more time before the new owners of the building took over.
Dorothy Hendee, the widow of Raymond, took just a few steps into the old district office, and her face immediately lit up.
"The memories just come flooding back. Memories of all the people that aren't here anymore," said Dorothy.
Her late husband, Raymond, was the District 64 Superintendent from 1970 to 1990 and worked in the District much longer than that. So the Hendees are very familiar with the building in Uptown Park Ridge.
"This is so wonderful," said Dorothy with a big smile.
She stood in the now empty superintendent's office with her daughter Kim and son Mark by her side. The trio spent time swapping stories and recapturing all that happened within the walls of the old district office.
"There are so many fond memories of my father and thinking of him being here," said Mark. "I'm thinking of my childhood and him being here. It's nice."
Raymond's life's work was education, and the Hendee Family appreciates that it was in the Park Ridge-Niles community.
"There's such pride in knowing that the District's reputation would bring kids and families into town because of the schools," said Kim, Raymond's daughter. "Even now. I was at the store not too long ago, and someone walked up to me and said, 'Are you Kim Hendee by any chance? Your dad was Dr. Hendee, and I worked for him.'
"There are just wonderful memories of the people, and it's such a cool community," said Kim.
"Most of my father's career and the leadership he gave, it was my whole childhood," said Mark. "So this is everything to me."
Park Ridge-Niles SD 64
Calendar Overview


text:
\section{Introduction}
\label{intro}

Strongly interacting fermions are part of some of todays most studied physical
systems. In cuprate and manganite systems, for example, strongly correlated
electrons are held responsible for high-temperature superconductivity and
colossal magnetoresistance, respectively.\cite{electrons1,electrons2,electrons3}
Systems of strongly interacting fermionic atoms can be realized in optical lattices,
and are currently under intense investigation due to the possibility to use
them as quantum simulators for understanding phenomena of
condensed matter physics.\cite{atoms1,atoms2,atoms3}

Since the seminal works of Wigner on the low-density electron
crystal\cite{wigner} and of Mott on the metal-insulator
transition\cite{mott} it is known that strong repulsive particle-particle
interactions suppress itineracy and favor localization.\cite{mit}
In the localized state, the repulsive interaction is minimized, and charge
degrees of freedom are frozen out. The dominating interactions in this state
are magnetic.

Mathematically, strongly interacting fermions are frequently described by the
Hubbard model, which in one dimension is defined by the Hamiltonian
\begin{equation}
\hat{H}^{Hubb}=-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.)+ U \sum_i \hat{n}_{i\uparrow}\hat{n}_{i\downarrow},
\label{hub}
\end{equation}
where $\hat{c}_{i\sigma}^\dagger$ and  $\hat{c}_{i\sigma}$ are fermionic
creation and destruction operators, $\hat{n}_{i\sigma}=\hat{c}_{i\sigma}^\dagger\hat{c}_{i\sigma}$ is the particle-density operator, $U$ the onsite
interaction and $t$ the hopping parameter.

For sufficiently strong interactions, the Hubbard model can be expanded in
powers of $t/U$. (Below we quantify what interactions can be considered
`sufficiently strong'.) The leading term of this expansion is the t-J model,
\bea
\hat{H}^{tJ}&=&-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.)\nonumber\\
&&+\frac{4t^2}{U}\sum_{i}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{\hat{n}_i\hat{n}_{i+1}}{4}\right],
\label{tj}
\eea
where $\vec{\hat{S}}_{i}$ is the spin one-half vector operator at each site.
This model is frequently taken to be the starting point in investigations of
doped cuprates.

For a half-filled system, in which the number of fermions $N$ equals the
number of lattice sites $L$, the average density $n=N/L$ is unity. Since there
are no empty sites, hopping is suppressed, and the t-J model reduces to the
antiferromagnetic Heisenberg model
\begin{equation}
\hat{H}^{Heis}=J\sum_{i}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{1}{4}\right],
\label{heis}
\end{equation}
where $J=4t^2/U$ and charge fluctuations are completely frozen out.
The original system of strongly interacting
itinerant fermions ($U/t \gg 1$) has thus been mapped on a system of localized
spins with weak antiferromagnetic interactions ($0 \leq J/t \ll 1$).

The mathematics and the physics of this mapping are very well understood and
discussed in the textbook literature.\cite{auerbach,fulde} The mapping
of strongly interacting itinerant fermions on weakly interacting localized
spins is a standard concept of condensed-matter physics, routinely used in
the interpretation of experiments on strongly correlated solids.
Recently, however, three important classes of systems have been discovered
or created that call for a reconsideration and more detailed investigation
of this mapping.

It is well known that many strongly
correlated systems are characterized by nanoscale spatial inhomogeneity.
Such inhomogeneity can take the form of irregular spatial variations of
system properties, such as observed by scanning-tunneling microscope
techniques in many cuprates and similar materials,\cite{electrons2,inhom0,inhom1,inhom2,inhom3,inhom4} or the form of regular spatial variations
such as in naturally occurring or man-made superlattice structures.\cite{paiva,malvezzi,malvezzi2,superl3,superl4} In the presence of either type of inhomogeneity, the
parameters characterizing the model Hamiltonian become site dependent. In
the simplest case, with which we are mostly concerned here, the above
homogeneous Hubbard model is replaced by an inhomogeneous model of the form
\begin{equation}
\hat{H}^{Hubb}_{inh}=-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.)+ \sum_i U_i \hat{n}_{i\uparrow}\hat{n}_{i\downarrow},
\label{inhomhub}
\end{equation}
in which the onsite interaction $U_i$ varies from site to site.

A second class of systems we are concerned with here are nanoscale devices.
In the modeling of such devices inhomogeneities in the model parameters occur
simply because on the nanoscale the effect of the surface can no longer be
neglected, and also because a typical device combines more than one material,
with the resulting interface automatically implying the existence of spatial
variations in the system parameters.

Finally, in still another line of research, ultracold atom gases have been
trapped optically and arranged in optical lattices.\cite{atoms1,atoms2}
In optical traps the system parameters can be controlled and varied in ways
not possible in solid-state situations. In particular, the onsite interaction
$U_i$ can attain values $U/t \approx 100$ or larger. Such values are way
beyond what is considered `strongly correlated' in solid-state physics.

Motivated by all these systems, we present, in the present paper, a combined
analytical and numerical study of the mapping from the Hubbard model to
the Heisenberg model in the presence of spatial inhomogeneity.
In Sec.~\ref{rate} we investigate the rate of the mapping, as measured
by the difference in ground-state energies of the Hamiltonians. We allow
the interaction strength to go beyond its typical solid-state values and to
enter the ultrastrong regime attainable for cold atoms.

In Sec.~\ref{inh} we turn to our main subject, the inhomogeneous Hubbard
model of Eq.~(\ref{inhomhub}).
In Sec.~\ref{analyt1} we investigate analytically the case of a single impurity, described
as one site with a value of $U$ differing
from all others, and show that the Hubbard-to-Heisenberg mapping is preserved essentially
in its homogeneous form, provided the effective $J$ is calculated from
the {\em harmonic mean} of the values of $U$ on the sites connected by $J$.
We illustrate this finding numerically, by contrasting,
for an impurity system, results obtained from the harmonic mean with results
obtained from the arithmetic, geometric and quadratic means.
In Sec.~\ref{complexinhom} we
show that the harmonic mean allows to extend the Hubbard-to-Heisenberg mapping
to systems with more complicated types of spatial inhomogeneity, such as
superlattices, disordered systems and interfaces between different materials.
Section~\ref{concl} contains our conclusions.

\section{Rate of the mapping for translationally invariant  systems}
\label{rate}

In a first step, to provide the background for the later investigations, we
consider spatially homogeneous infinite Hubbard and Heisenberg chains, and
investigate the rate of the approach of the ground-state energies of both models as a function of
$U$. This allows us to quantify the rate at which charge fluctuations are frozen out.

The per-site ground-state (GS) energy of the Heisenberg chain in the
thermodynamic limit is
\be
e^{Heis}(J)= \lim_{L\to \infty}{E^{Heis} \over L}=-J\ln(2).
\ee
The per-site GS energy of infinite half-filled ($n=1$) Hubbard chain at
$U/t \to \infty$ is
\bea
e^{Hubb}(n=1,{U\over t} \to\infty)
= \lim_{L\to \infty}{E^{Hubb} \over L}
= - {4t^2\over U} \ln(2).
\eea
Both expressions become identical for $J = 4t^2/U$. In
order to quantitatively investigate the mapping at finite $U/t$, we
calculate $e^{Hubb}(n=1,U)$ by numerically solving the Bethe-Ansatz integral
equations\cite{liebwu,shiba} as a function of $U$ and compare the result to
the energy of the Heisenberg model at the corresponding value of $J$,
{\em i.e.} $e^{Heis}(J=4t^2/U)$. The result is displayed\cite{foot1} in Fig.~\ref{fig1}.

\begin{figure}[t!]
\includegraphics[height=6cm]{fig1.eps}
\caption{Per-site GS energy as a function of interaction in the thermodynamic
limit. Comparison between the Heisenberg with $J=4t^2/U$ and
the half-filled Hubbard chain. The main figure includes values of $U$ that
can be realized in systems of trapped cold atoms, while the inset displays
results for values of $U$ typical of weakly and strongly correlated solids.}
\label{fig1}
\end{figure}

In Table~\ref{tab1} we show the relative percentage deviation between the
GS energies,
\be
D(\%)=100\frac{e^{Hubb}-e^{Heis}}{e^{Hubb}},
\ee
for various representative values of $U$.
This comparison between both models becomes trivial, once the Bethe-Ansatz solution is available,
but already leads to a first somewhat unexpected conclusion. Frequently,
the Heisenberg model is taken to be the starting point for a description
of undoped antiferromagnetic insulating parent compounds of high-temperature
superconductors. The effect of doping is accounted for by going from the
Heisenberg to the t-J model, arguing that the latter should be a reasonable
approximation to the Hubbard model for the involved large values of $U$.

What the comparison in Fig.~\ref{fig1} and Table~\ref{tab1} shows is that
for values of $U$ that are representative of cuprate materials the
t-J or Heisenberg models provide at best a semiquantitative approximation
to the Hubbard model. At $U=6$ the difference between both ground-state
energies is approximately $10\%$. Charge fluctuations are thus not yet frozen
out for such $U$, even at half filling. The rather large deviation observed shows
that the mapping of strongly interacting fermions onto weakly
interacting spins is not quantitatively reliable for, e.g., cuprate systems at
realistic values of $U$. There
is no doubt, of course, that the t-J model captures the correct physics of the
large-U Hubbard model -- the above questioning only refers to the accuracy
to which one needs to obtain a solution of the former, given that in the
parameter regime typical of strongly-correlated solids it is
itself only a moderately accurate representation of the latter.

\begin{table}[t!]
\caption{Relative percentage deviation of the per-site GS energies for values
of $U$ typical of weakly correlated solids ($U=1$), strongly correlated solids
($U=6$) and values that are attainable for atoms in optical traps.}
\begin{ruledtabular}
\begin{tabular}{c|ccccccc}
$U$ & 1 & 6 & 10 & 20 & 50 & 100 & 200 \\
\hline
$D(\%)$ &-166.50 & -10.01 & -3.78 & -0.97 & -0.16 & -0.04& -0.01\\
\end{tabular}
\end{ruledtabular}
\label{tab1}
\end{table}

We note that this analysis is based on GS energies.
An alternative comparison between both Hamiltonians would proceed in terms of
the overlap of their wave functions, instead of the difference of their
energies. Our main interest in this initial investigation is to investigate
for which values of $U$ the mapping breaks down, and for this it is
enough to find one quantity that is not properly reproduced. Thus, if we use
our analysis to indicate when the mapping does {\em not} hold, we
are on the safe side by using energies. Still another, and indeed more
fundamental, mode of analysis proceeds by directly comparing the Hamiltonians.
We use this procedure in Sec.~\ref{analyt1}, where our interest is not only in
when the mapping breaks down, but also in how it can be restored.

\section{Mapping in the presence of spatial inhomogeneity}
\label{inh}

We now turn to systems where the inhomogeneity occurs not only at the surface, due to
finite size, but also in the bulk. A typical case is that of
a localized impurity or defect, modeled by one site with onsite interaction
differing from that of all the others. We take this simple system as
representative of Hubbard models with broken translational symmetry, and
focus most of our analysis on it. The extension of our conclusions to
interfaces and superlattices is discussed in Sec.~\ref{complexinhom}.

Intuitively, one would expect that a localized perturbation of the
homogeneous Hubbard model should only produce a similarly localized
perturbation of the homogeneous Heisenberg model. However, the relation
between both models involves a projection on the subspace with no double
occupation, together with an expansion in inverse
powers of $U$,\cite{auerbach,fulde} and it is not clear from the outset to
what extent these operations preserve the above naive expectation of locality.

In fact, there is one sense in which the mapping, if it continues to exist,
cannot be local: $U$ is defined on one site, while $J$ connects two adjacent
sites. While this difference is almost irrelevant in the homogeneous case
where all sites are equivalent and translational symmetry rules, it becomes
important in the inhomogeneous case, where any change in the onsite $U$
on the Hubbard model must affect the corresponding intersite $J$ for at least
two sites of the Heisenberg model. This is illustrated in Fig.~\ref{fig2}.

\begin{figure}[t!]
\centering
\includegraphics[viewport= 40 40 200 1000, angle=-90, width=13.2cm]{fig2.eps}
\caption{Illustration of the inhomogeneous Hubbard model with a single
impurity $U' \neq U$, and its putative relation to an inhomogeneous Heisenberg
model with two bond defects $J' \neq J$.}
\label{fig2}
\end{figure}

The questions to address are thus (i) whether the mapping still exists in
the absence of translational symmetry, (ii) how to calculate the Heisenberg
$J$ from the Hubbard $U$ in inhomogeneous systems, and (iii) if the mapping
is as local as possible, {\em i.e.}, involves only sites adjacent to the
impurity site, or requires a higher degree of nonlocality.
In next subsections we address these questions
analytical and numerically.

\subsection{A single impurity}
\label{analyt1}

We start with the one-dimensional Hubbard model in the presence of a single
impurity at site $k$ with onsite interaction $U'$ differing from the
background value $U$ on all other sites $i\neq k$,
\bea
\hat{H}^{Hubb}_{inh}&=&-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.)
+ U \sum_{i\neq k} \hat{n}_{i\uparrow}\hat{n}_{i\downarrow}
\nonumber \\
&&+ U'\hat{n}_{k\uparrow}\hat{n}_{k\downarrow}.\label{hubbard_inh}
\eea
The standard proof of the mapping from the Hubbard to the t-J model\cite{auerbach,fulde} can be repeated for this Hamiltonian and leads to the inhomogeneous
t-J model with Hamiltonian
\begin{eqnarray}
\hat{H}_{inh}^{tJ}&=&-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.)\hspace{1cm}\\
&&+\frac{4t^2}{U}\sum_{i\neq k}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{\hat{n}_i\hat{n}_{i+1}}{4}\right]\nonumber\\
&&+\frac{4t^2}{U'}\left[\vec{\hat{S}}_k\cdot \vec{\hat{S}}_{k+1} -\frac{\hat{n}_k\hat{n}_{k+1}}{4}\right],\nonumber
\end{eqnarray}
where we assumed that both $U$ and $U'$ are much larger than $t$. We rewrite
this Hamiltonian by extracting one term from the sum over $i\neq k$
to obtain
\bea
\hat{H}_{inh}^{tJ}&=&-t\sum_{i\sigma}(\hat{c}_{i\sigma}^\dagger\hat{c}_{i+1,\sigma}+H.c.) \\
&&+\frac{4t^2}{U}\sum_{i\neq k,l}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{\hat{n}_i\hat{n}_{i+1}}{4}\right]\nonumber\\
&&+\frac{4t^2}{U}\left[\vec{\hat{S}}_k\cdot \vec{\hat{S}}_{k+1} -\frac{\hat{n}_k\hat{n}_{k+1}}{4}\right]
\nonumber \\
&&+\frac{4t^2}{U'}\left[\vec{\hat{S}}_{l}\cdot \vec{\hat{S}}_{l+1} -\frac{\hat{n}_{l}\hat{n}_{l+1}}{4}\right].\nonumber
\label{inhomtj}
\eea
Now we take the average density $n=N/L=1$. {\it A priori} this average can be obtained from many different distributions $n_i$. However, since we are already in the limit $U,U'\gg t$, the total interaction energy on the background and the impurity sites is minimized by the particular distribution $n_i=1$ for all $i$. Deviations from this are due to hopping processes that become increasingly suppressed as $U$ and $U'$ grow. Thus the Hamiltonian (\ref{inhomtj}) at $n=1$ reduces to
\begin{eqnarray}
\hat{H}_{inh}^{tJ}(n=1)&=&+\frac{4t^2}{U}\sum_{i\neq k,l}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{1}{4}\right]\label{tj.final}\\
 &&+4t^2\left(\frac{1}{U}+\frac{1}{U'}\right)\left[\vec{\hat{S}}_l\cdot \vec{\hat{S}}_{l+1} -\frac{1}{4}\right]\nonumber,
\end{eqnarray}
where we chose $l$ as a neighbor site of $k$, $k=l+1$, such that $\vec{\hat{S}}_l\cdot \vec{\hat{S}}_{l+1}=\vec{\hat{S}}_k\cdot \vec{\hat{S}}_{k+1}$. This, in turn, can be written as
\begin{eqnarray}
H^{Heis}_{inh}=
J\sum_{i\neq l,l+1}\left[\vec{\hat{S}}_i\cdot \vec{\hat{S}}_{i+1} -\frac{1}{4}\right]+ 2J'\left[\vec{\hat{S}}_{l}\cdot \vec{\hat{S}}_{l+1} -\frac{1}{4}\right]\nonumber,\\
\label{inhomhe}
\end{eqnarray}
which has the form of a spatially inhomogeneous Heisenberg model with
background interaction $J=4t^2/U$ and two bond defects $J'=4t^2/\bar{U}^H$,
where $\bar{U}^H$ is the harmonic mean of $U$ and $U'$,
\be
\bar{U}^H = \frac{2UU'}{U+U'}.
\label{harm}
\ee

This derivation tells us that the Hubbard model with a single impurity can
indeed be mapped onto a Heisenberg model with two bond defects, provided the
impurity site and the background sites both have repulsive interactions
that are much larger than $t$, and that the $J$ connecting the impurity site
with its neighbors to the left and to the right is calculated from the
{\em harmonic mean} of the two onsite interactions. The mapping then still
exists and is seen to be {\em as local as possible}, in the sense explained
above.

In order to investigate the rate of the mapping in inhomogeneous systems, we now perform a numerical investigation of both models. For illustration we also include in these calculations the quadratic, arithmetic and geometric means,
\begin{eqnarray}
\bar{U}^Q&=&\sqrt{\frac{U^2+U'^2}{2}}\label{q}\\
\bar{U}^A&=&\frac{U+U'}{2}\label{a}\\
\bar{U}^G&=&\sqrt{UU'}\label{g}.
\end{eqnarray}
Both the inhomogeneous Hubbard model with $n=1$ and one $U'\neq U$ and the
inhomogeneous Heisenberg model with two $J'\neq J$ are diagonalized numerically,
and compared by means of the deviation between their GS energies.
We use the same method of analysis as in Sec.~\ref{rate}, this time, however,
applied to impurity systems.

\begin{figure}[t!]
\includegraphics[height=10cm, width=7.5cm]{fig3.eps}
\caption{Relative percentage deviation between the GS energies of the
single-impurity Hubbard chain and the two-defect Heisenberg chain, obtained
from numerical diagonalization, adopting $J'=J(\bar{U})$ with four
different choices for the average $\bar{U}$: (a) values of $U$ that are
typical of solids and (b) values of $U$ that are attainable in systems
of optically trapped atoms. System parameters: $L=8$ sites, $N=8$ fermions, open boundary
conditions, impurity strength $U'=3U/2$.}
\label{fig3}
\end{figure}

Our key result is contained in Fig.~\ref{fig3}, which displays the relative
percentage deviation between the inhomogeneous Hubbard and the
inhomogeneous Heisenberg models with $J'=J(\bar{U})$ for each of the four
averages. The solid line represents the corresponding deviation obtained for
the impurity-free Hubbard and Heisenberg models, where $U$ and $J=4t^2/U$
are the same across the system.

Figure~\ref{fig3}--(a) demonstrates clearly that if the background
$U$ is so small that the mapping is not quantitatively reliable even in
the homogeneous system (this includes the values found in cuprates), then
it is also not reliable in inhomogeneous systems, regardless of the choice
made for relating the bond defect to the impurity size. On the other hand,
Fig.~\ref{fig3}--(b) makes a different statement: once the background $U$ is
large enough to permit the basic Hubbard-to-Heisenberg mapping to function,
all four averages lead to values of $J'=4t^2/\bar{U}$ that are equal
(H) or different (A,G,Q) than obtained in the homogeneous system.

This is unequivocal numerical evidence that the mapping of strongly interacting
fermions on weakly interacting spins survives in the presence of impurities
and defects. In order to probe the locality of the mapping we have
also performed numerical experiments with averages over more than two
neighboring sites, calculating $J'(\bar{U})$ from, {\em e.g.} a weighted
average of the interactions at the sites connected by $U$ and their
nearest-neighbor sites. No improvement (and frequently even worse results)
with regard to the simple two-site averages was obtained, indicating that
the mapping is indeed local.

At first sight more surprising is that the alternative averaging procedures
produce even smaller deviations for some values of $U$, Fig.~\ref{fig3}--(b). However, for still larger
values of $U$ and $U'$ (where the mapping should as a matter of principle
get better and better) all these alternative averages produce deviations
that continue to grow and yield $D>0$, while the harmonic mean correctly
approaches the limit $D=0$ as $U,U'\to \infty$. This shows that only the
harmonic mean has a chance to correctly describe the fermion-to-spins mapping
in inhomogeneous systems, while the lower deviations of the other averages
for some parameter regimes only occur because the curves are monotonous so
that there is always a range of values for which they are close to zero.

\begin{figure}[t!]
\includegraphics[height=5cm]{fig4.eps}
\caption{Deviation of GS energies of the half-filled Hubbard model and the corresponding
Heisenberg model as a function of impurity strength, obtained
from the harmonic mean. At $U'=U=6$ the system
is homogeneous (except for the presence of the boundary) and the deviation
is the same obtained in Sec.~\ref{rate}.}
\label{fig4}
\end{figure}

We note that in Fig.~\ref{fig3} the ratio of $U$ and $U'$ was held fixed,
such as to guarantee that for all values of $U$, $U'$ was always substantially
different from $U$ ($U'=3U/2$). In Fig.~\ref{fig4} we present the complementary analysis
in which the background $U$ is held fixed and the impurity interaction is
varied from $U'<U$ to $U'>U$. For this comparison we consistently adopted
the harmonic mean. A first feature that jumps to the eye is that a single site
with $U'<U$ is enough to substantially deteriorate the mapping. By contrast,
a single site with $U'>U$ leads only to a slight reduction of the deviation
between GS energies, much less than the deterioration observed for $U'<U$.

This behavior arises from the hopping terms. Both at $U' >U $ (more
repulsive impurity site) and at $U' <U$ (less repulsive site) the
on-site density at the impurity site slightly deviates from that at
the background sites, as long as $U$ and $U'$ are both finite. In the
latter case, however, hopping processes involving the impurity site
increase as $U'$ is reduced, and the Hubbard-to-Heisenberg mapping
becomes correspondingly worse, while in the former case hopping
continues to be strongly suppressed. The behavior displayed by Fig.
\ref{fig4} is thus consistent with what one would expect on the basis
of the derivation leading from Eq.(\ref{hubbard_inh}) to Eq.(\ref{inhomhe}).

Independently of, but in
agreement with, our previous analytical derivation we thus find that the harmonic mean
solves the problem exactly for a single impurity and for sufficiently large interactions,
while the other possible averages do not. However there is still one question concerning this result
and it is addressed in next section: is the harmonic mean able to recover the mapping in more
complex inhomogeneities?

\subsection{More complex inhomogeneities}
\label{complexinhom}

In view of our initial discussion of naturally occurring or man-made
inhomogeneity in strongly correlated systems, it becomes important to
extend our analysis to more complex inhomogeneities than boundaries or
single impurities. We here briefly describe our findings on three of
these: interfaces, superlattices and disordered systems.

\begin{figure}[t!]
\includegraphics[viewport= 50 50 300 800, angle=-90, width=10.5cm]{fig5.eps}
\caption{Illustration of simple interface and superlattice structures in
the Hubbard model, and their counterparts in the Heisenberg model.}
\label{fig5}
\end{figure}

{\em Interfaces and superlattices} can be described in the Hubbard and
Heisenberg models as shown schematically in Fig.~\ref{fig5}. While
the description of superlattices by means of periodic spatial variations
of $U$ is the standard choice,\cite{paiva} which we here also adopt,
it has been pointed out that a periodic modulation of local electric potentials
can bring about a much larger change in the system properties.\cite{malvezzi,malvezzi2,fc2008}
Here, however, we are interested in the Hubbard-to-Heisenberg transition,
which is driven by the interaction and not by local potentials, and therefore
we follow the usual prescription to ignore possible local electric fields
in the superlattice structure.

We note that in the superlattice and the interface geometry we now have
{\em three} different spin-spin interactions, one, $J$, being calculated from
$U$, another, $J'$, from $U'$ and the last, $J^*$, from $U$ and $U'$, as
indicated in Fig.~\ref{fig5}. Figure~\ref{fig6} shows that for large $U$ and $U'$ the GS energies of the
Heisenberg model, when calculated from the harmonic mean, become
identical to those of the corresponding Hubbard model, for all investigated
geometries. In this sense, the mapping continues to work and to be as local as
possible. Note that this would not be true for the arithmetic, geometric
and quadratic means, whose deviations increase for large $U$ and $U'$.

The fact that the Hubbard-Heisenberg deviation for the superlattice is larger
than that for the interface can be understood on purely geometric grounds,
as a consequence of the locality of
the mapping and the nature of the harmonic mean: By comparing the
distribution of $J$ values, Fig.~\ref{fig5}, we see that in going from the interface to the
superlattice the number of interactions $J$ and $J'$ is reduced by the
same amount, while that of interactions $J^*$ increases. Since $J' < J^* < J$,
a reduction of the number of sites with $J'$ worsens the mapping while a
reduction of the number of sites with $J$ improves it. To see what the net
effect is we must take into account the interaction $J^*$, which replaces $J$
and $J'$. This interaction is calculated from $\bar{U}$, the harmonic mean
of $U$ and $U'$. The harmonic mean of any two positive numbers is less or
equal their arithmetic mean, so that $\bar{U}$ is closer to $U$ than to $U'$
and $J^*$ is closer to $J$ than to $J'$. The substitution of an equal number
of $J$ and $J'$ by $J^*$ thus has the effect of effectively increasing the
number of `bad' sites, and therefore to deteriorate the quality of the
mapping. This is what the data show: the deviation for the superlattice is
larger than that for the interfaces, if all other parameters are chosen the
same.

\begin{figure}[t!]
\includegraphics[height=6cm]{fig6.eps}
\caption{Relative percentage deviation between the GS energies of the
Hubbard and the Heisenberg model for a superlattice structure, an interface,
a single-impurity system and a system that is spatially homogeneous (except
for the surface). In the superlattice and
the interface system the number of sites with $U$ and $U'$ is the same,
respectively, the only difference being in their geometric distribution.
System parameters: $L=8$, $U'=3U/2$, $J'=4t^2/U'$ and $J^*=4t^2/\bar{U}$,
where $\bar{U}$ is calculated from the harmonic mean of $U$ and $U'$.}
\label{fig6}
\end{figure}

This analysis shows that the harmonic-mean prescription
continues to be usable for these more complex geometries and that the
effect of the geometrical distribution of $U$ and $U'$ sites across the
system can be understood and analyzed essentially on a site-by-site
basis. This is a direct consequence of the locality of the mapping.

{\em Disordered systems} can be modeled simply by considering a random
distribution of impurities instead of just one. While a complete analysis
of disordered systems requires statistical analysis of data resulting
from a large number of realizations of the disorder, an analysis of
a few representative cases is enough to conclude that the single-impurity
results are not changed, in their essence, when the impurity concentration
is increased.

Specifically, we find that if all impurities have $U'>U$ a higher concentration
of impurities reduces the deviation between the GS energies. Keeping the
concentration fixed and increasing $U'/U$ also reduces the deviation,
but to a much smaller degree. On the other hand, if all impurities have
$U'<U$ the agreement is naturally worsened. However, in the $U'<U$ case the
decisive factor is not so much the concentration of impurities but their
strength, as measured by $U'/U$.
This inversion in the effect of concentration
and strength of the impurities can be understood on the basis of
Fig.~\ref{fig4}, which shows that for a single impurity with $U'<U$
the deviation rapidly increases as $U'$ becomes more different from $U$,
while for $U'>U$ it decreases only very slowly and almost saturates as the
impurity sites effectively drop out of the system.

This discussion shows that it is possible to control the degree of the
fermion-spin mapping by means of the introduction of a suitable concentration
of impurities of suitable strength. This possibility may be useful in the
design of nanoscale devices based on strongly correlated systems, whose
properties can be tailored from electron-like to spin-like by introducing
suitable disorder. We note in passing that this is a strong-interaction
effect, completely different from the itinerant-to-localized transition
resulting from disorder in Anderson localization.

\section{Conclusions}
\label{concl}

In the homogeneous situation, in which all sites are equivalent, the mapping is characterized by the
behavior of the system as a function of the onsite interaction $U$.
Not unexpectedly, the Heisenberg model is found to be a good approximation to
the t-J and the Hubbard model at $n=1$. Somewhat more unexpected is that
the Heisenberg model is rather a
bad approximation to the Hubbard model at $n=1$ even for values of $U$ that are
considered strongly correlated in solid-state applications. Only at $U$
near 20 has the deviation dropped to about one percent. The standard mapping
thus only becomes quantitatively reliable for values of $U$ that are
hard to reach in the solid state, but have already been demonstrated
in cold-atom systems.

In inhomogeneous situations, translational symmetry is broken.
An analytical calculation for the simple case of
a single impurity suggests that
the mapping can be preserved in terms of the harmonic mean. Moreover, in
terms of this mean the mapping is as local as possible, {\em i.e.,} the value
of the Heisenberg $J$ between two sites is only determined from the value of
the Hubbard $U$ at these two sites. Numerical calculations illustrate and
corroborate this finding. This is more than a mathematical, or numerical,
result: it means that the physics of the mapping, {\em i.e.}, the
gradual freezing out of the charge-degrees of freedom and the localization
arising from the concomitant suppression of double occupation, is essentially
the same regardless of the geometry and the presence or absence of
translational symmetry.

The harmonic-mean prescription can be used easily and reliably for a wide
variety of spatial inhomogeneities. Once the basic mapping is understood, the
harmonic-mean prescription allows one to interpret and even to predict the
behavior of much more complicated systems, without going through detailed
analytical or computationally expensive numerical calculations.

{\bf Acknowledgments}
This work was supported by Brazilian funding agencies FAPESP and CNPq.
We thank Vivaldo Campo Jr. for providing us with his exact diagonalization
code for the Hubbard model, and Fabiano C. Souza and Valter L. L\'ibero
for providing us with their exact diagonalization code for the Heisenberg model.

redpajama_set_name: RedPajamaArXiv


Don't think you can fit activity and fitness into your day? Now you can with this fold-up manual treadmill. When you're done breaking a sweat, this treadmill folds away so you can reach your goals without sacrificing space.
Maximum User Weight: Approx. 230 lbs.
Product Weight: Approx. 49 lbs.
This is my new best friend! I love this treadmill! I have limited space and an electric one would be to big. I couldn't wait for hubby to come home and put it together, so I organized pieces and parts, so easy All the tools needed to assemble are included. The treadmill gives me plenty of workout. So Very happy with my new treadmill. Just perfect!
Finally, a treadmill that won't throw me off! You walk on your terms, and it stops when you stop walking. Easy to move and a real space saver.
Love this product !!!!! Stay at home and walk. Really great and easy to set up.
It does not fold easily. It's quite a process to fold it, and keep it folded, and then you have to start all over again when you're ready to workout. Terrible design flaw. The belt on my treadmill would never stay in the center. It always moved to the right or the left, jamming up against the side (which would have ruined it). I followed the directions and did the troubleshooting many times to get it right. It would not work. I took it apart and returned it. The idea of this is great, but the execution is awful.


text:
Q: How to delete file of source after copying in vbscript? I am developing function that copy file from Temp Folder to Drive C.
After copying, I would like to delete file in Temp Folder.
I tried following codes but can't delete file.Please explain it to me.
sample codes:
Set objFSO = CreateObject("Scripting.FileSystemObject")
File = file of Temp Folder
objFSO.CopyFile File, "C:\"
objFSO.DeleteFile(File)

OR

Set objFSO = CreateObject("Scripting.FileSystemObject")
File = file of Temp Folder
objFSO.CopyFile File, "C:\"
Set delFileName = objFSO.GetFile(File)
delFileName.Delete delFileName

A: Copying a file from one location to C:\ and then deleting the version in the original location is the same as moving the file, so do that instead:
Dim objFSO : Set objFSO = CreateObject("Scripting.FileSystemObject")
objFSO.MoveFile File, "C:\"
Set objFSO = Nothing

If you really really want to do it in the way you've described then:
Dim objFSO : Set objFSO = CreateObject("Scripting.FileSystemObject")
On Error Resume Next
objFSO.CopyFile File, "C:\"
If Err.Number = 0 Then objFSO.DeleteFile File
On Error Goto 0
Set objFSO = Nothing

will do the trick.

redpajama_set_name: RedPajamaStackExchange


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text:
Luke Bryan planted a corn field during quarantine — and advises fans not to do the same
ABC/Stewart CookLuke Bryan has some words of wisdom for his fans: don't plant sweet corn during a global pandemic.
The country superstar took to Instagram to reveal that he's used his time in quarantine to plant a corn field on his Tennessee property, an activity that appears to be as stressful as it is rewarding.
"Little tip for you guys — never get bored during a pandemic and plant four acres of sweet corn," the Georgia native advises with a disgruntled look on his face as he struggles to carry a Home Depot bucket filled with ears of corn under the beating sun, accompanied by the caption, "sweet corn out the a**."
Though Luke may not be thrilled with his new pastime, he's piqued the interest of his fans and country music friends, with Dustin Lynch commenting "on my way," while Proud To Be Right Here Tour opener Caylee Hammack inquires, "Can I come out and pick my own for dinner? This is a dream!"
Luke recently spent his 44th birthday weekend doing something a little more relaxing with a fishing trip with his family in Wyoming. The American Idol judge is also celebrating the success of his latest number-one single, "One Margarita."
By Cillea Houghton
[youtube https://www.youtube.com/watch?v=YEq-cvq_cK4&w=640&h=360]


Most of us leave our computers running pretty much all the time. Unless there is some major update or you're going to be away for a few days there's not much reason to shut them off. That said, when you sit down to your PC and find that it *is* off, generally the first instinct is to press the power button and hope for the best.
What about when it doesn't turn back on?
As always, a word of precaution. What I'm going to tell you may disagree with your manufacturer warranty, and will require tools. If you don't feel comfortable opening your desktop PC, please consult a trusted professional. Finding a "warranty void if removed" sticker means you should make absolute sure the system is no longer covered by warranty before removing it. If that was all blah blah blah to you, read on.
If the cords and switch are plugged and set correctly but you still don't get power, time to see if the power supply has failed. For this, you will need a screwdriver to remove the side panel. There are a couple of ways to test the power supply. You can perform either a basic check using a multimeter on the continuity or resistance setting, a more accurate check using a power supply tester, or if you have access to spare parts you can connect a compatible power supply and see if that resolves things.
For the multimeter, probes go into the green and any black wire. This is a basic check but does not verify all voltage rails or ability to handle a load. Unplug all connections from the power supply to the motherboard (usually 2 plugs) and the drives. Using the main power connector (20 or 24 pins) from the power supply, insert probes, plug in the power cord and flip the switch. If you get nothing, you have a bad power supply.
For a power supply tester ,results will vary by model. We recommend using one with has many functions as possible for a more accurate reading. Our repair bench uses the Thermaltake Dr. Power II and it does an excellent job of verifying the correct and stable voltages on all connection types from the power supply. It is designed for quick verification and should not be left connected for extended periods of time.
IF you want to replace the supply and check that way, make sure you only connect what is necessary to get the system to give display at first. If you have more problems and you connect everything you are just wasting time. Note that this is the most effective way of diagnosing a bad power supply since neither of the previous methods apply a full load to the power supply.
So what if the power supply is good – or you replace it and it still won't power on? Then the problem is most likely the motherboard. There's a little known trick for testing that too. Reconnect good power to the motherboard and make sure that you have a speaker on the motherboard or connect one according to the manual. Now remove all the memory sticks and power the system on. If the system beeps multiple times complaining of no memory, the motherboard is very likely good.
So what if both the power supply and the motherboard test good but the problem remains? Swap the power supply to ensure it can handle the system load. If it still doesn't power on, you will hopefully be getting some beep codes that with research can indicate the failure. If not, it's definitely time to get help.


text:
From the archive: Welcome to Lang Lang
In 1960, Holden invited the press to drive its latest models in Lang Lang, Victoria – only the second time it had allowed us entry into its test facility since its 1957 opening.
Subscribe to the Autocar Archive today
Located 56 miles south-east of the city of Melbourne, Lang Lang featured a 50ft-wide, 2.9-mile speed loop and nine miles of other testing roads, including a "rough track" of crushed rock, pavé, 'hop-and-tramp' and scruffy concrete.
Australia's first automotive testing and development complex, the Lang Lang facility was also for a time the only permanent proving ground in the Southern Hemisphere.
After our visit, we said: "On the general circuit, the roads and tracks give a fair simulation of normal city and country Australian roads.
"Main hazard occurs at night, when kangaroos and wallabies cross the track in front of cars."
Some 55 people worked there, most developing Holden, Pontiac, Chevrolet and Vauxhall vehicles. Every single Holden from 1957's FC onwards was developed at the proving grounds, with an on-site design centre also being built.
Now with 27 miles of roads, Lang Lang was sold to Vinfast last year after GM killed Holden, which invested heavily in the facility's testing infrastructure – but is now for sale again, for about £19.6m.
The Autocar Archive, dating from 1895 to the modern day, is now available online. Subscribe today


I have a question, predominantly for the teachers.
I have been playing for a little over a year now. I play with my right hand closest to the utaguchi. I have noticed that this is the reverse of the observed standard (I think). If I were your student, would this be a problem?
...would this be a problem?
If it's a problem for any teacher, you'd best get another one.
I agree with Ed. Guys play either way. Yamato Shudo seems to be able to play everything both ways. I guess one way only wasn't hard enough.
No problem many of the best players are lefties and play that way. Are you left handed in other areas? The only problem is when you play long flutes with offset holes they are usually offset for righties.
I am also a 'Leftie', didn't realize that for a while, but that is how I initially preferred to hold the shakuhachi.
What I like to do from time to time is to reverse and play as a 'Rightie', this is interesting as it indicates my 'habits' and repetitive routines, as when I reverse I don't fall into them, rather my playing takes on a very new feel, more deliberating, from which I always learn something fresh about either the piece I am playing, or my own attitude towards playing.
Don't worry if anyone calls a Leftie 'sinister, we simply hold our swords in the alternate hand.
Are you left handed in other areas?
Not even a little bit. It was just one of those things where I did not know how to hold it, so I did it one way and it eventually felt natural.
This is one issue where my views have changed somewhat, mostly because a lot of longer flutes shouldn't be offset in the first place (Japanese-made longer flutes often are not offset) and getting the holes moved on a flute you really like should not be much of an issue. I could easily understand a teacher correctly dismissing left-handed playing as "not a problem" for someone who has been playing that way long enough that switching is going to be a major hurdle. That would be if the student had previous left-handed playing experience with some other kind of flute (ney, East Indian, or NAF flutes often are played left-handed) or is an advanced student on shakuhachi who learned left-handed either by themselves or with a different teacher. Getting someone to switch with that much experience is going to be excessively difficult to correct something that isn't a problem for the 1.8 instrument he or she is learning on.
However, for a brand-new-to-flute-of-any-kind beginner student who got their instrument and fooled around with it on their own left-handed, either accidentally or because they thought it would be cool to be different (and maybe read that it's a cool thing to do on shakuhachiforum), for just 3 weeks before getting a lesson, I find it hard to believe that most teachers dismiss it as irrelevant.
Do teachers generally encourage left-hand on top? Or do they usually say "one hand, it doesn't matter which one, goes on top" when teaching hand-positioning to total beginners? If left-hand on top isn't being encouraged I'm curious why there are so many left-hand on top players. From observing non-flute players looking at and trying or pretending to play a flute, it seems to me to be entirely random whether they pick it up left or right hand on top.
I have been playing for a little over a year now.
My inclination would be to say that after a year you might as well keep playing left-handed. But, for other beginners, if it's been only a few weeks, or maybe even a few months, it's not like you have a ton of repertoire to re-learn, consider biting the bullet and switch. It'll make translating instructions and the offsets on longer flutes a non-issues in the future.
I once read a little essay in Japanese by Iwamoto Yoshikazu. It was written for an Japanese audience and I read it in a Japanese language class which I attended the first 5 years I lived in Japan. Iwamoto discussed how it was teaching shakuhachi in England and how the students improved and approached the instrument.
One thing I remember so clearly from that essay was that he described that most students in the first lesson would ask him how to hold the shakuhachi. He answered: 'As you like' to the students' surprise. The students would then ask 'Doesn't it matter which hand is on the top and which hand is at the bottom?' 'No, you do as you like and feel is natural for you' (conversation quoted of the top of my head).
Then Iwamoto went on discussing that as a difference in the way of approach in Japanese arts in comparison with European arts.... well... I remember I found that less interesting.
But this essay written by someone like Iwamoto shows clearly that it really doesn't matter which hand is where.
it always felt most natural for me, likely because i never played recorder or some other such instrument.
i also just let those i am teaching play whichever is natural. i actually avoid mentioning it until they've already picked the flute up 1st time.
"Aged 25, he lobbied Annapurna Devi, the wife of Ravi Shankar and a sitar maestro in her own right, to teach him classical music. "I wanted to learn from the beginning," he says. It was three years before she relented, only after Chaurasia vowed that he would never again play the flute with his right hand. The promise, and its implicit commitment to starting all over again, reduced Devi to tears. "For the last 35 years I have been playing with my left hand," Chaurasia says. "I have forgotten how to play any other way.""


The amateur radio station HV5PUL is active since 1997 at the Pontifical Lateran University, in the Vatican City State.
The station is activated during the special events at the University like the Academic Year Opening Day (Dies Accademicus) in October/November or the Lateran Journey at the end of April.
Recent DX Spots HV5PUL It is also activated by IW0DJB, the station manager.
IZ2LSC, I2OGV, I2RFJ, I2ZBX, IK2DJV will be active from Vatican 1 - 4 June 2009 as HV5PUL.
They are will be active on HF + 6m CW, SSB, RTTY.
LUCA DELLA GIOVAMPAOLA, VIA CREMERA, 11, 00198, ROMA, Italy.
Pontifical Lateran University, in the Vatican City State. Author - F. Fppolloni.
Vatican city. Author - Japo García.
Vatican city. Author - Enes Biga.
HV5PUL. Where is Vatican located. Map.


When I went to this establishment I thought the food was good and I would go again. I would reccomend this buffet to other people.
Great buffet, great food, great place to fellowship in. Real nice atmosphere, staff are on point to serve. Enjoyable experience.
My husbands and i have a new favorite! !
no longer in business. YP should remove from listings.
i like here food.so good.
i use to go all the time but the lady i am guessing is the owner is Rude and down talk to the people!! i will rather go somewhere else an spend my money!!!!! Food is ok but the service is not!! She needs to learn to have respect!!!
They had great food and their sweet tea is the bomb. Great price as well.
Great Hot Sausage And Rice!
I will never eat here again. The food was cold on the buffet. I complained and they did nothing about it. A roach also was on my chair. Calling health dep in the morning.
Ordered online because I was running late home from work, ordered online at 6:43pm ssaidwould be ready by 7:05p arrive at 7:00pm the lady says not started yet 20 min.. well.i wont be ordering from here if im in a hurry again..


This is about a boy named Adam who lives in Hawaii, whose father is in the military. They travel a lot and do not have an exact home. He keeps moving to different places. Adam is now in a new school, it'll be harder to make friends, also adding that all the kids in his new school are civilians.
Since Adam lives in a military base and all the other students in the school are civilians, they make fun of him, calling him names. A boy named Davi teases Adam calling him "Haloe boy" and other names. Over time, Adam got used to it and called him names too, soon after they became friends.
Once the attack was over, everything was destroyed. Boats and planes had sunk into the water. The sky that was once blue was now black, thick with smoke. There was oil everywhere in the ocean. Adam, Davi and Marvin were stranded in the water. Trying to look for help.
Suddenly, a sailor from the Marines on a boat noticed the three of them in the water. The sailor helped them out of the water, bringing them to the Medical Center.


text:
Message from Loudoun Diversity Council
More than Peach™
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Extremely Honored to be be Recognized by ADL
by B. Woodard December 6, 2020
Tonight, I have the extreme honor to be recognized as a 2020 ADL Honoree & interviewed by Ms. Olivia Boisson @toughinatutu of corps de ballet at New York City Ballet & the first African-American to join the company in a decade. Past honorees include such inspirational figures as Mrs. Ruby Bridges and Congressman John Lewis who are among my heroes. "ADL is one of the nation's leading civil rights and anti-hate organizations, founded over a century ago to protect Jewish people and relentlessly fight all forms of hate, in every community, to secure justice and fair treatment for all." ADL In Concert Against Hate honors everyday heroes who have stood up against intolerance, extremism and injustice."
From @adl_national : "In honoring you, we wish to recognize your leadership and determination through the "More Than Peach" project, which has helped ensure students, particularly those from communities of color, feel included and represented. Our hope is that your incredible story will motivate and inspire others, including the students who join us at the ADL Concert, to engage in advocacy and activism, as well as other efforts to stand up against all forms of bigotry and extremism."
I invite you to join me tonight in celebration of the important work of the ADL. ❤-Bellen
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Home > English > Website archives > Rainbow of Crisis > The road to a multipolar world?
The road to a multipolar world?
Wednesday 7 February 2007, by Amit Baruah
TRILATERAL MEETINGS between India, China, and Russia could prove to be a mighty force in international relations. But, so far, the three countries have been extremely careful in defining what these sessions might amount to. The dialogue between the countries' Foreign Ministers, which began with an informal session on the sidelines of the United Nations General Assembly in New York in September 2002, is an amorphous one, whose results are still to be seen. On February 14, the Indian, Chinese, and Russian Foreign Ministers - Pranab Mukherjee, Li Zhaoxing, and Sergei Lavrov - will meet in New Delhi for what will be their second stand-alone interaction at this level.
It is not difficult to understand the diffidence with which the three countries are approaching their trilateral meetings given that they remain convinced that good relations with the United States remains at the core of their foreign policies.
Though the idea of a "strategic triangle" among the three nations was proposed by the former Russian Prime Minister, Yevgeny Primakov, back in 1998, the current trilateral process is far from being a strategic alliance.
In fact, all three countries have been at pains to stress that their budding trilateral cooperation is not directed against any other country. Given these countries' influence in world affairs, such statements are, clearly, not out of line.
India is being closely watched in the world: will its cosy relationship with the U.S. mean that New Delhi abandons its hitherto closely-guarded independence in the making of foreign policy? Or will the close Indo-American embrace fade away and New Delhi, once again, occupy its role as a nation that speaks for the developing world?
The trilateral framework for dialogue, along with the separate meetings India has with Brazil and South Africa in the IBSA framework, was agreed to at the time a Bharatiya Janata Party-led alliance was in power in New Delhi. Both arrangements have proved useful, both for the BJP and its successor government led by the Congress, to demonstrate that India remains independent in making foreign policy choices. Form, on occasion, must substitute for content.
China, on its part, is obviously considering the nature of the world around it as it marches ahead economically. Beijing has chosen to adopt a low-profile role when it comes to tackling global issues such as Iraq, but on Iran has gone along with the international consensus, like Russia, when the United Nations chose to impose limited sanctions on Tehran for its nuclear programme.
The third country in this equation, Vladimir Putin's Russia, has transformed itself from a funds-starved nation to a major energy producer, one with enormous strategic clout in a world hungry for gas and oil.
Interestingly, it was the Russians who initially pushed the idea of trilateral cooperation with India and China. In 2002, a weakened Russia was looking to play a more pro-active role on the global stage, a role that it could not perform alone. Today, its coffers are tinkling with oil and gas money.
It could legitimately be argued that India, China, and Russia have been finding their feet in their trilateral framework since 2002. But now the three countries will have to define, albeit loosely, what their meetings amount to.
Mr. Primakov's strategic triangle will only be formed if India, China, and Russia display an appetite for taking on the unilateral course the United States has charted out for the world. From time to time, the three countries must come together on issues where they enjoy a consensus. They must make their views count on the world stage.
U.S. on the rampage
Globally, a post-9/11 U.S. has been on the rampage. Iraq and Iraqis have, however, made George Bush and his hordes of troops come a cropper in creating a "designer nation": one that would quietly supply hydrocarbons and also meet the standards of American democracy in West Asia.
Iran remains on the American hit list, but North Korea has shown that Washington cannot take on a militarily strong nation - even one which has walked out of the Nuclear Non-proliferation Treaty and conducted a nuclear test, as Pyongyang has done.
During their first-ever stand-alone meeting in June 2005, the Foreign Ministers of India, China, and Russia committed themselves to creating a "just world order" based on the observance of international law, equity, mutual respect, cooperation, and progress
towards multipolarity.
If the three countries are genuine about creating a multipolar world, then the U.S. might find it that much more difficult to repeat an Iraq elsewhere.
from The Hindu, February 7, 2007


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Stage 4 Breast Cancer - A Palatable Pink Cloud of Unawareness
By Contributor: Krista Lawrence
I followed the recent coverage of Shannen Doherty's Stage IV Metastatic Breast Cancer (MBC) diagnosis. My reaction was uneasy anger, hope crept in, followed and replaced by familiar resignation and disappointment. This was announced on "World Cancer Day". The purpose for such a day?? I suppose, to raise….awareness? For….Cancer? Okay. I'm aware of this particular insidious, indiscriminate thief. Intimately.
Awareness. A similar unsettledness descends in October. October was designated Breast Cancer Awareness Month in 1985. I know, you're aware. Every October becomes a sea of pink ribbons, walks, runs and 'Girls Night Out' mammogram parties. A steady narrative of hope and one-and-done survivorship pervades. Mission accomplished. We're aware. More importantly, we're comforted. With early detection and proper treatment, breast cancer just isn't the death sentence it once was.
Really?? Stage IV Breast Cancer is unlike many other Stage IV cancers. We don't out-live it. As long as breast cancer remains in the breast, it is Stage 0, I, II or III and treatable and no one dies. However, once the cancer spreads, metastasizes beyond the breast to major organs (commonly lungs, liver, brain) and bones, it is Stage IV, and then…Breast Cancer becomes, frankly, a death sentence. An early diagnosis, successfully treated is not always the end of the story. The not-so-happy-ending, the reality, is that roughly 30% of those 'survivors' will experience a metastasized recurrence. Who will be impacted and when, is inexplicably, unpredictably random. Breast cancer once declared cured or in remission, can be detected years or merely months following initial treatment for early stage disease. Equally incomprehensibly wild is the fact that of the approximately 155,000 women and men living with MBC, six to ten percent are diagnosed deNovo (from onset; first), often women under 40, the recommended age to begin annual screening.
One medical contributor stated Ms. Doherty's public sharing of her diagnosis presented a teachable moment. Ah, here we go…say it, I thought. The moment was again used to provide a tired reminder of the thread bare awareness of early detection through mammogram screening and access to effective treatments. Predictable. Infuriating. Hopes for a truly meaningful teachable moment evaporated. Instead, another missed opportunity was wrapped up and tucked away in a palatable pink cloud of unawareness.
I realize it is unrealistic to expect headlines and sound-bites to offer depth and breadth. The actress's news was declared 'Devastating' but neglected elaboration. One headline shouted 'She is "Dying" from Stage IV Breast Cancer.' "Dying", in quotation marks?? Another reported Ms. Doherty's attorney submitted court documents explaining she is dying from Stage IV terminal cancer. Opposing counsel empathized and ignorantly offered wishes for her full recovery. I get that as a society, we don't routinely face, let alone accept, our mortality. I even understand, to a point, the medical community's goal to establish hopefulness for a desired or expected treatment outcome. But come on! When the spotlight shines on a woman with Stage IV Metastatic Breast Cancer, we are somehow unwilling to enlighten ourselves and each other with the truth that, ahem….There's no cure. No full recovery. There's no Stage V. We die. OF COURSE IT'S DEVASTATING!!
Instead we embrace the spin that this life altering diagnosis really needn't be feared. There are, after all, new and exciting treatments happening every day. Try them! These treatments can now extend the life expectancy. Nothing to worry about. We're aware. Do our part and if we encounter this detour, our back is covered. Grueling treatment becomes a blip on our timeline.
Here's the Awareness in 2020:
New treatments are often only effective with small percentages of certain tumor characteristics or subtypes, i.e., ER/HR+, Her2-, Triple Negative, Her2+, etc. New therapies are restricted to specific types and even then, individual results are unpredictable and irregular.
Even if a treatment is effective, it's still only for a finite time. The median survival rate remains 33 months. Sure, I suppose no one is actually lying when stating treatment enables patients to live for years. It can. Sometimes. For some. Sure, there are exceptional outliers who are lucky (yes luck, just random chance luck) to have longer success without progression. But we are rare and a tiny percentage.
There is a balance we strive to achieve from the moment of diagnosis throughout continued comprehension that life is now dependent upon active treatment. Widely touted and advertised advancements in therapies do not come without a cost. The financial, emotional and physical upheaval is devastating and intense. Side effects are vast and varied, frequently debilitating and life altering. The challenges of maintaining mental wellness while living with a terminal illness have consequences. The financial impact is often ruinous but also most easily imagined as others identify through personal experiences with insurance coverage or lack of. Every day, every decision requires weighing the quality of life against longevity. Evaluating this life tethered to treatment for survival.
Effective treatments that exist today eventually are exhausted. There comes a day, sometimes quickly, sometimes slowly, when there is nothing left to offer. At this point, if not long before due to the myriad of issues above, the only options are comfort measures to minimize our pain and suffering while we succumb to the relentless ravages of this final stage.
Yes, the public sharing of a diagnosis with which I have lived for five and a half years fanned a flame of indignation, a sense of 'No Shit Sherlock'. MBC is reality for so many of us. This isn't new. But that's where the hope slipped in. MBC may strike indiscriminately, but with another celebrity, there is a captive audience. There has been progress. The fiercest Advocates are many of us living and dying with this disease. Will this finally push it out of the shadows? Will the incomprehensible fact that less than seven percent of all breast cancer awareness fundraising dollars are allocated to the deadliest stage cause outrage? Stage IV is the only stage of Breast Cancer that removes the possibility of a normal life span for every single body it invades. Metastasis is responsible for 98% of all breast cancer deaths. It is terminal. The death rate of 40,000 women and men annually due to MBC hasn't changed in 35 years. Yes, Breast Cancer without a cure.
Here's the teachable moment: Funding is required to generate more research to identify and prevent progression, develop more treatments and *gasp* create a cure. Stage IV Metastatic Breast Cancer. A death sentence still.
About Krista
Krista Lawrence is a regular contributor to the podcast Lucia@Night. She is a writer, mom of two, and fierce advocate and individual living with Stage 4 Metastatic Breast Cancer.