text:
Cambridgeshire facts for kids
For other uses, see Cambridgeshire (disambiguation).
Motto: "CORDE UNO SAPIENTES SIMUS" ("With one heart let us be wise")
Cambridgeshire in England
Coordinates: Template:Coord/display/title, inline
Established by
Local Government Act 1972
Cambridgeshire and Isle of Ely
Huntingdon and Peterborough
Ceremonial county
Lord Lieutenant
Hugh Duberly
High Sheriff
Sir David Arculus
3,389 km2 (1,309 sq mi)
• Ranked
15th of 48
Population (2005 est.)
220/km2 (570/sq mi)
94.6% White
2.6% S.Asian
Non-metropolitan county
Admin HQ
GB-CAM
ONS code
GSS code
UKH12
Unitary authorities
Districts of Cambridgeshire
Unitary County council area
City of Peterborough
Cambridgeshire Constabulary
GMT (UTC)
BST (UTC+1)
Cambridgeshire (/ˈkeɪmbrɪdʒʃər/ or /ˈkeɪmbrɪdʒʃɪər/; abbreviated Cambs.), archaically known as the County of Cambridge, is an East Anglian county in England, bordering Lincolnshire to the north, Norfolk to the north-east, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west. The city of Cambridge is the county town. Modern Cambridgeshire was formed in 1974 as an amalgamation of the counties of Cambridgeshire and Isle of Ely and Huntingdon and Peterborough, which had been created in 1965 from the historic counties of Cambridgeshire, Huntingdonshire, the Isle of Ely and the Soke of Peterborough. It contains most of the region known as Silicon Fen.
Local government is divided between Cambridgeshire County Council and Peterborough City Council, which is a separate unitary authority. Under the county council, there are five district councils, Cambridge City Council, South Cambridgeshire District Council, East Cambridgeshire District Council, Huntingdonshire District Council and Fenland District Council.
Main page: History of Cambridgeshire
Cambridgeshire is noted as the site of Flag Fen in Fengate, one of the earliest-known Neolithic permanent settlements in the United Kingdom, compared in importance to Balbridie in Aberdeen, Scotland. A great quantity of archaeological finds from the Stone Age, the Bronze Age and the Iron Age were made in East Cambridgeshire. Most items were found in Isleham.
Cambridgeshire was recorded in the Domesday Book as "Grantbridgeshire" (or rather Grentebrigescire) (related to the river Granta).
Covering a large part of East Anglia, Cambridgeshire today is the result of several local government unifications. In 1888 when county councils were introduced, separate councils were set up, following the traditional division of Cambridgeshire, for
the area in the south around Cambridge, and
the liberty of the Isle of Ely.
In 1965, these two administrative counties were merged to form Cambridgeshire and the Isle of Ely. Under the Local Government Act 1972 this merged with the county to the west, Huntingdon and Peterborough. (The latter had been organised in 1965 by the merger of Huntingdonshire with the Soke of Peterborough – previously a part of Northamptonshire which had its own county council). The resulting county was called simply Cambridgeshire.
Since 1998, the City of Peterborough has been a separately administered area, as a unitary authority. It is associated with Cambridgeshire for ceremonial purposes such as Lieutenancy, and joint functions such as policing and the fire service.
In 2002, the conservation charity Plantlife unofficially designated Cambridgeshire's county flower as the Pasqueflower.
The Cambridgeshire Regiment (or Fen Tigers), the county-based army unit, fought in the Boer War of South Africa, the First World War and Second World War.
Due to the county's flat terrain and proximity to the continent, during the Second World War the military built many airfields here for RAF Bomber Command, RAF Fighter Command, and the allied USAAF. In recognition of this collaboration, the Cambridge American Cemetery and Memorial is located in Madingley. It is the only WWII burial ground in England for American servicemen who died during that event.
Most English counties have nicknames for their people, such as a "Tyke" from Yorkshire and a "Yellowbelly" from Lincolnshire. The traditional nicknames for people from Cambridgeshire are "Cambridgeshire Camel" or "Cambridgeshire Crane", referring to the wildfowl that were once abundant in the fens. The term "Fenners" was often applied to those who come from the flat country to the north of Cambridge. Since the late 20th century, this term is considered to be derogatory and has been discouraged in use.
Original historical documents relating to Cambridgeshire are held by Cambridgeshire Archives and Local Studies.
See also Geology of Cambridgeshire
Large areas of the county are extremely low-lying and Holme Fen is notable for being the UK's lowest physical point at 2.75 m (9 ft) below sea level. The highest point is in the village of Great Chishill at 146 m (480 ft) above sea level. Other prominent hills are Little Trees Hill and Wandlebury Hill in the Gog Magog Downs, Rivey Hill above Linton, Rowley's Hill and the Madingley Hills.
Map of the Cambridgeshire area (1904)
See also: Civil parishes in Cambridgeshire and List of Cambridgeshire settlements by population
These are the settlements in Cambridgeshire with a town charter, city status or a population over 5,000; for a complete list of settlements see list of places in Cambridgeshire.
Littleport
Peterborough (no longer part of the administrative county)
Sawston
Whittlesey
See the List of Cambridgeshire settlements by population page for more detail.
The town of Newmarket is surrounded on three sides by Cambridgeshire, being connected by a narrow strip of land to the rest of Suffolk.
Cambridgeshire has seen 32,869 dwellings created from 2002–2013 and there are a further 35,360 planned new dwellings between now and 2023.
Cambridgeshire has a maritime temperate climate which is broadly similar to the rest of the United Kingdom, though it is drier than the UK average due to its low altitude and easterly location, the prevailing southwesterly winds having already deposited moisture on higher ground further west. Average winter temperatures are cooler than the English average, due to Cambridgeshire's inland location and relative nearness to continental Europe, which results in the moderating maritime influence being less strong. Snowfall is slightly more common than in western areas, due to the relative winter coolness and easterly winds bringing occasional snow from the North Sea. In summer temperatures are average or slightly above, due to less cloud cover. It reaches 25 °C (77 °F) on around 10 days each year, and is comparable to parts of Kent and East Anglia.
Climate data for Cambridge 1971–2000 average
Rainfall mm (inches)
Source: Met Office
The logo of England Bandy Federation, based in Cambridgeshire
Various forms of football have been popular in Cambridgeshire since medieval times at least. In 1579 one match played at Chesterton between townspeople and Cambridge University students ended in a violent brawl that led the Vice-Chancellor to issue a decree forbidding them to play "footeball" outside of college grounds. Despite this and other decrees, football continued to be popular. George Elwes Corrie, Master of Jesus College, observed in 1838, that while walking past a park named Parker's Piece he "saw some forty Gownsmen playing at football. The novelty and liveliness of the scene were amusing!" By 1839, Albert Pell was organising football matches at the university; because each town or school had different rules, students had to devise a compromise set of rules.
At Cambridge University in 1846, H. de Winton and J. C. Thring formed a pioneering football club. Only a few matches were played, but in 1848 interest in football increased and that year the Cambridge rules, the first attempt to codify a form of football were drawn up in Cambridge. The Cambridge rules are generally regarded as the main precursor of Association football.
As a result of its role in the formation of the first football rules, Parker's Piece remains hallowed turf for football fans and historians. According to folklore, there are 11 players on each team because, when the game was invented, there were 11 trees on either side of Parker's Piece. In commemoration of the creation of Football; a statue is to be raised in the middle of the park where the game was invented.
Cambridgeshire is also the birthplace of bandy, Tebbutt was instrumental in spreading the sport to many countries. England Bandy Federation is based in Cambridgeshire.
On 6–7 June 2015, the inaugural Tour of Cambridgeshire cycle race took place on closed roads across the county. The event was an official UCI qualification event, and consisted of a Time Trial on the 6th, and a Gran Fondo event on the 7th. The Gran Fondo event was open to the public, and over 6000 riders took part in the 128 km (80 mi) race.
Cambridge is home to the Kettle's Yard gallery and the artist run Aid and Abet project Space. Nine miles west of Cambridge next to the village of Bourn is Wysing Arts Centre.
Owned by the National Trust
Owned by English Heritage
Owned by the Forestry Commission
A Country Park
An Accessible open space
Museum (free)
Museum (charges entry fee)
Heritage railway
Anglesey Abbey
Brampton Wood
Buckden Towers
Cambridge American Cemetery and Memorial
Cambridge University Museum of Zoology
Castor Hanglands NNR
Denny Abbey
Devil's Dyke
Down Field Windmill
Duxford Chapel
Duxford Airfield
Elton Hall
Ely Cathedral
Fitzwilliam Museum, Cambridge
Flag Fen
Fowlmere RSPB reserve
Gamsey Wood Nature Reserve
Gog Magog Downs
Grafham Water Nature Reserve
Great Gransden Post Mill
Hereward Way
Hinchingbrooke House
Imperial War Museum Duxford
Kettle's Yard
Kimbolton Castle
Kings College, Cambridge
Lattersey Nature Reserve
Lode Watermill
Longthorpe Tower
Nene Park
Nene Way
New Bedford River
Octavia Hill Birthplace Museum
Old Bedford River
Oliver Cromwell's House
Ouse Valley Way
Ouse Washes
Parker's Piece, Cambridge, birthplace of modern football
Paxton Pits Nature Reserve
Peckover House & Garden
Peterborough Cathedral
Prickwillow Drainage Engine Museum
Ramsey Abbey
River Cam
River Great Ouse
Round Church, Cambridge
RSPB Nene Washes
RSPB Ouse Washes
Stretham Old Engine
Three Shires Bridleway
University of Cambridge Museum of Archaeology and Anthropology
Wandlebury Country Park
Wimpole Hall
Wisbech and March Bramley Line
WWT Welney
The Flag of Cambridgeshire County Council
Cambridgeshire Facts for Kids. Kiddle Encyclopedia.
This page was last modified on 21 January 2021, at 01:37. Suggest an edit.


Galtres Lodge, 54 LOW PETERGATE, YORK YO1 7HZ.
64 Customer Review(s) gave Galtres Lodge a score of 4 out of 6.
The lodge is a Georgian brick building with heating throughout sympathetically restored in such a way as to retain the warmth and character of the original house. There are thirteen bedrooms comprising single double and twin-bedded accommodation and some rooms open onto a view of the famous Rose Window of the Minster. Our rooms are serviced daily.Half of the accommodation is en suite with two rooms having half-tester beds. For those without private facilities there is ample bathroom capacity including showers and all remaining rooms are fitted with washhand basins and some with WC. For more information on reservations and prices see the tariff page.The lodge is WiFi enabled allowing wireless internet access via laptops and other portable devices. Galtres Lodge is situated in the centre of York giving an unprecedented feeling of seclusion in bustling austere settings. All of York's major attractions are only a moments stroll away with the Minster literally just round the corner (see the map on your directions page).The lodge is licensed and everything from a quick snack to a full three course meal is available throughout the day (see opening times). Situated within the lodge is our restaurant Michael's Brasserie which prides itself on its innovative menu.
Finding UsOnce in York follow signs for the Minster (York Cathedral). Low Petergate is directly behind Deangate the road that runs in front of the Minster (see map).How To Get To YorkBy AirLondon Airports: travel to London King's Cross station: 2 hours journey to York Manchester International Airport:direct rail link to centre of York - 1 hour 45 minutes Leeds-Bradford Airport: 40 minutes by taxi By RailFast frequent Intercity trains from London Kings Cross. Journey time 2 hours Click here for UK train timetables and information. By SeaFrom Hull terminal the journey to York takes less than 1 hour by road. Parking Traffic restrictions were implemented in York city centre during 1987. Guests in private cars or taxis may arrive at or leave the hotel at any time of day. Parking arrangements are usually available to guests for a nominal charge please ask for details when making your booking. The map below gives details of the approved routes and location of the car park. Footstreet RestrictionMonday - Friday 11 - 4Saturday 10.30 - 4.30 Sunday 12 - 4 Galtres Lodge guests arriving by car or taxi may enter pedestrian zone during the above hours provided they do so via Goodramgate Church Street Swinegate and Grape Lane and leave via Low Petergate and Colliergate. Outside these hours cars may enter by any route. Car Park Directions click map to enlarge From the front of the hotel:1. Continue down Low Petergate straight over crossroads into Kings Square.2. Follow this road for 150 metres until you come to another crossroads.3. Turn left here and follow this road over a mini roundabout next move into the left hand lane at the traffic lights.4. After turning into St Maurices Road you need to move into the right hand lane for the next set of traffic lights. Turn right here.5. You are now in Monkgate. Proceed 100 metres and on your left hand side there is a public house called The Tap and Spile.6. Turn left into the car park and park tidily. Place your voucher on the dashboard where it can be clearly seen.


text:
Tensar Corporation Wins Association Of National Advertisers' 2022 B2 Award
News | June 9, 2022 | By: ATA
Bryan C. Gee, P.E., Tensar Director of Education and Training, receiving the ANA B2 Award
Tensar Corporation, a global leader in geogrid engineered solutions for civil construction, has won an Association of National Advertisers 2022 B2 award. The company received a silver award in the "Integrated Marketing Program Small – Mid-Size Business" category for its "Time For Something New" campaign launching the company's latest generation of geosynthetic solutions: Tensar InterAx geogrid. Competitors for the 2022 B2 Awards included some of the world's most powerful and influential brands. Tensar put together their Tensar InterAx geogrid campaign submission to the ANA without the help of an ad agency.
"I am so proud of the work our team did to launch this outstanding new product and for winning this prestigious award," says Wendy McBay, Tensar Vice President of Marketing. "Being recognized as part of the ANA's B2 Awards is proof of our team's exceptional creative talent and ability to innovate in the midst of an unprecedented business environment."
The B2 Awards recognize the work business-to-business marketers and agencies do to engage employees, sales teams, channel partners, government, and customers. The awards recognize business marketers that go above and beyond traditional marketing and communications roles to deliver extraordinary results.
A full list of B2 Top Award Winners in all categories can be found here.

redpajama_set_name: RedPajamaCommonCrawl


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text:
\chapter*{Quarks and Anomalies}

\author[R.~J.~Crewther]{R.~J.~Crewther}

\address{Department of Physics, University of Adelaide\\
Adelaide SA 5005, Australia, \\
rodney.crewther@adelaide.edu.au}

\begin{abstract}
A nonperturbative understanding of neutral pion decay was an essential
step towards the idea that strong interactions are governed by a
color gauge theory for quarks. Some aspects of this work and related problems
are still important.
\end{abstract}
\body

\section{Quarks before QCD}\label{ra_sec1}
\setlength{\unitlength}{1mm}
\begin{picture}(0,0)(-100,-100)
ADP--14--39/T898
\end{picture
Any Caltech theory student in the late 1960's, particularly if Murray Gell-Mann
was their supervisor, had to be good at distinguishing various ``quark models''.
Were we talking about ``constituent'' or ``current'' quarks, and within those
categories, was model dependence an issue? Quarks were somehow fundamental, but
it was not even clear that their dynamics should be governed by a local field
theory. The main tactic was to ``abstract'' rules which seemed to be model
independent and led to physical consequences which could be compared with
existing data.

By that time, the quark idea was several years old, dating from work completed
independently by the end of 1963:  Gell-Mann's quarks,\cite{quarks} Zweig's
aces,\cite{aces} and (a reference I have just heard of) Petermann's ``spineurs
(avec) \ldots des valeurs non enti\`{e}res de la charge''.\cite{swiss}  These
papers had in common
\begin{enumerate}
\item structures $q\bar{q}$ for mesons and $qqq$ for baryons built from
non-relativistic \emph{constituent} quarks $q$ and anti-quarks $\bar{q}$,
\label{structure}
\item the idea that $SU(3)$ mass formulas \cite{eightfold,okubo} are due to
the strange quark $s$ being heavier than the up and down quarks $u,d$, and
\item concerns about whether the fractional charges would be observable.
\end{enumerate}
Gell-Mann and Zweig were led to (\ref{structure}) by the need to explain
the absence of exotic $SU(3)$ multiplets in the Eightfold Way
\cite{eightfold,yuval}. Zweig analyzed the constituent quark model in
detail, deriving properties such as spins, parities and masses for various
$SU(3)$ multiplets. Gell-Mann had a separate aim: to reproduce current
algebra, a set of equal-time commutators for $SU(3) \times SU(3)$
currents\cite{algebra} which he had previously managed to abstract
without using quarks. For this, he needed \emph{current quarks}, i.e.\
relativistic fields $q(x)$ and $\bar{q}(x)$ for each flavor $q = u,d,s$,
from which electromagnetic, weak and other $SU(3) \times SU(3)$
currents could be constructed.

Immediately, there were concerns about constituent quark statistics. How can
a baryon like $\Sigma^{++}$ exist as an $S$-wave spin-flavor symmetric state
$|u$\mbox{$\uparrow$}$u$\mbox{$\uparrow$}$u$\mbox{$\uparrow$}$\rangle$ if
quarks are spin-$\frac{1}{2}$ fermions?  It is hard to imagine ground states
being $P$-wave, so instead, it was proposed that quarks are either\cite{wally}
para-fermions\cite{bert} of order 3 or\cite{boris,han,miya} fermions with an
extra quantum number taking three values, which we now know as
\emph{color}.\cite{licht,schladming,bfg-m}. The observed fermionic baryons
$|qqq\rangle$ are then symmetric in space-spin-flavor (a) for paraquarks
automatically, or (b) for fermion quarks antisymmetrized in a color $SU(3)$
singlet state\cite{han,miya} (but not $SO(3)$, because that would allow
colorless diquark states $|qq\rangle$).

Whether para-particle or colored multiplets would appear at higher energies or
be banned completely (quark confinement) was not clear. In an attempt to make
these extra states appear less weird, colored quarks were initially given
integer charges\cite{han,miya} which, however, depended on the color index.
Then photons could excite color from hadrons and perhaps induce transitions
to a deconfined (weird) sector.

In the model eventually adopted in 1972\cite{schladming,bfg-m}, quarks became
colored fermions with fractional charges, with 3 colors for each charge or
flavor. As a result, the electromagnetic and weak currents became color $SU(3)$
singlets, like the observed hadronic spectrum. Confinement was as unclear for
this model as the others. If confinement were not absolute, the model could
have degenerate color multiplets and fractionally charged states above some
threshold energy. Comparing all of these models, it was concluded that, as
models of \emph{constituent} quarks, they were hard to distinguish below
thresholds for deconfinement.

However the 1972 model was also designed to take into account color for
\emph{current} quarks. The rest of this article describes how studies of
short-distance behavior\cite{kgw} and the reaction\cite{rjc}
$\pi^0 \to \gamma\gamma$ led to this.

\section{Scale Invariance at High Energies}

I started life at Caltech as a graduate student in the fall of 1968. The
very first seminar, on Tuesday October 1, was ``Partons'' by Richard P.\
Feynman, with Murray Gell-Mann sitting near the front. Feynman had just
returned from a summer in SLAC hearing about Bjorken's work\cite{bj} on
scaling in deep inelastic lepton-nucleon scattering and developing a
model of point scatterers (partons) to give the same results. Murray
kept asking ``but Richard, what are their quantum numbers? Are they quarks?''
but Richard's sole concern was scaling due to scattering by ``grains
of sand inside the nucleon''. (A year or so later, my fellow student
Finn Ravndal got him interested in quarks.)

Murray began supervising me two months later and in due course asked me,
as an initial research exercise, to try using the Cutkosky bootstrap model
\cite{cut} to generate higher symmetries like $SU(6)$. That produced
hundreds of equations. Fortunately, just a few of them could be used to
show that there could be no consistent solution. Murray commented that
he hadn't intended the exercise ``to be so vigorous'' and suggested
that I take a trip while he thought of a suitable PhD topic. My fellow
student Chris Hamer and I had already planned to drive around the US
that summer (1969), so we left immediately and on the way back, stopped
at Aspen.

Murray had just started working on scale invariance as an approximate
symmetry of hadrons, and suggested that I do the same. This would involve
the energy-momentum tensor $\theta_{\mu\nu}$ as well as the $SU(3) \times
SU(3)$ currents. Did I know about the Belinfante\cite{bel} tensor?
Fortunately, I did (from Geoff Opat, supervisor of Chris and myself as
Masters students in Melbourne, 1966-68). In that case, the next step was
to understand all 14 pages of Wilson's paper on operator product
expansions\cite{kgw}.

Wilson generalised current algebra, replacing equal-time limits of
commutators by short-distance limits of products of currents and
other observables such as $\theta_{\mu\nu}$. Instead of a single
term on the right-hand side, he obtained an asymptotic expansion
$\sum_n\mathcal{C}_nO_n$ with coefficient functions
\begin{equation}
\mathcal{C}_1 \gg \mathcal{C}_2 \gg \mathcal{C}_3 \gg\ \ldots
\label{coeff}
\end{equation}
in order of decreasing singularity times observable operators
$O_1, O_2, O_3 \ldots$ of increasing operator dimensionality (in mass
units). Equal-time commutators, such as in Gell-Mann's current algebra
and Bjorken's work on scaling, could be recovered by noting that, since
commutators vanish for space-like separations, their equal-time
limits are controlled by the short-distance behavior of the relevant
operator product. Checks in renormalized perturbation theories or for
free current quarks indicated that, apart from quantum number
constraints, the same set of operators $\{O_n\}$ tended to appear
in the expansion, whatever the operator product used to generate them:
``a limited set of licensed operators'', as Murray put it.

A key feature of Wilson's work was his critique\cite{kgw2} of canonical
field theory: operators usually \emph{cannot} be multiplied at the same
point, equal-time commutators may be singular, and $T$-ordering with
step functions $\theta(t - t')$ can fail. These \emph{anomalies} arise
wherever renormalization is necessary. In particular, renormalized
perturbation theory produces  $\log^p\bigl(\mu^2(x-y)^2\bigr)$
factors at short distances, where $\mu$ is the renormalization scale.
When summed up \`{a} la Gell-Mann and Low,\cite{gml} anomalous powers
may be produced. If the ultraviolet limit is controlled by a
nontrivial Gell-Mann--Low fixed point, scale invariance becomes exact
at short distances, with anomalous dimensions for all operators $O_n$
except those which are conserved or partially conserved. I was happy
to abstract these rules and learn the renormalization group later.

Wilson's paper\cite{kgw} also featured a Sec.\ VII ``Applications''
with five subsections, each equivalent to a separate publication.
Subsection D ``$\pi^0 \to \gamma\gamma$ Problem'' drew my attention
because (a) it explained how short-distance singularities
determine contact terms in low-energy Ward identities and (b) I had
seen the papers of Bell and Jackiw\cite{bell} and Adler\cite{steve}
on the axial anomaly. Could the three-point function
$T\langle\mbox{vac}|J_\alpha J_\beta J_{\mu 5}|\mbox{vac}\rangle$
of the electromagnetic and axial-vector currents $J_\alpha$ and $J_{\mu 5}$
be determined at short distances without using perturbation theory?
Noting Wilson's comment (Sec.\ VIII) that ``the prospects for obtaining
such a solution seem dim at present'', I filed the problem away as
a challenge for the future.

At that time, the main question was whether Bjorken scaling is exact or
not. Bjorken\cite{bj} obtained scaling by assuming that an infinite set of
equal-time commutators of $J_\alpha$ with its derivatives is finite, i.e.\
not zero. It was quickly established that this was equivalent to assuming
canonical or free-field (parton) behavior for the coefficient functions
(\ref{coeff}). Towers of these short-distance singularities could be
summed to form terms in an operator product expansion near the light
cone $(x - y)^2 \to 0$, the limit in position space conjugate to Bjorken's
limit.\cite{frish,bp}  By then, quarks were widely believed to be
responsible for scaling, so the proposal of Fritzsch and Gell-Mann\cite{fgm}
to abstract the light-cone expansion from free-quark theory was logical.

The argument against exact Bjorken scaling was led by Wilson.\cite{kgw3}
Interactions tend to increase the dimensions of composite-field operators
$O_n$ which are not conserved exactly or partially, making higher-$n$
functions (\ref{coeff}) less singular on the light cone. The difficulty
for this point of view was explaining why these anomalous corrections
were \emph{all} so small. Nevertheless, I tended to belong to this school
of thought. My concern was that any tensor operator $O(x)$ lacking an anomalous
dimension would be at least partially conserved, because the leading
singularity of $\langle\mbox{vac}|O(x)O(y)|\mbox{vac}\rangle$
would be canonical and hence divergenceless. Therefore, my view was
that the \emph{only} operators allowed to have canonical dimension were
$\theta_{\mu\nu}$ and the $SU(3) \times SU(3)$ currents.

In particular, there was the $U(1)$ problem, which I knew from
Gell-Mann's 1969 Hawaii lectures\cite{hawaii}. If we abstract from the
free-quark model, the isoscalar current
\begin{equation}
J^{0}_{\mu 5} = \bar{u}\gamma_\mu\gamma_5 u + \bar{d}\gamma_\mu\gamma_5 d
\end{equation}
is conserved in the $SU(2) \times SU(2)$ limit. This is a disaster\cite{glash}
because then the $SU(2) \times SU(2)$ condensate
\begin{equation}
\langle\mbox{vac}|\bar{u}u + \bar{d}d|\mbox{vac}\rangle \not= 0
\label{cond}
\end{equation}
\emph{also} acts as an axial $U(1)$ condensate. In addition to
$\pi^+, \pi^0, \pi^-$, there would have to be a fourth Nambu-Goldstone
boson, an isoscalar $0^-$ meson of mass $O(m_\pi)$. If just one extra
conserved current could cause so much trouble, we certainly did not want
an infinite tower of them.

The choice between canonical and anomalous dimensions would be cleared
up by asymptotic freedom\cite{pol,GW} two years later. Only $\theta_{\mu\nu}$
and the $SU(N_f) \times SU(N_f)$ currents behave canonically. Coefficients
$\mathcal{C}_n$ of other operators $O_n$ have their canonical
behavior modified by inverse logarithmic powers, corresponding to a
very weak violation of Bjorken scaling. The $U(1)$ problem was not
so easily dismissed, and while majority opinion is that it is understood,
they all miss the reference\cite{kaiser} where problems yet to be resolved
are analysed.

\section{Approximate Scale Invariance at Low Energies}
\label{three}

At the same time (1969-71), I was supposed to be working on my PhD
research project. Clearly the hadronic ground state $|\mbox{vac}\rangle$
breaks scale invariance very strongly, given the $1$ GeV scale set by
baryons. This could be simply due to scale invariance being badly broken
explicitly, with the trace $\theta^\mu_\mu$ large as an operator. The
alternative is that scale invariance is approximately conserved in the
Nambu-Goldstone mode with a massless $0^{++}$ \emph{dilaton} in the limit
$\theta^\mu_\mu \to 0$.

The analogy with chiral symmetry was obvious. Both chiral $SU(3) \times SU(3)$
and scale symmetry would be manifest at short distances and hidden elsewhere
by the effects of their Goldstone bosons, the $0^-$ octet $\pi, K, \eta$ and
the $0^+$ singlet dilaton $\sigma$ (not to be confused with the field
``$\sigma$'' of the sigma model). I chose the simplest case where scale
invariance was the result of taking the chiral $SU(3) \times SU(3)$ limit,
so the 3-flavor version of the chiral condensate (\ref{cond}) could also
act as a scale condensate.

This picture is no longer entirely accurate, given that QCD renormalization
effects break scale symmetry everywhere, including short distances. However
if 3-flavor QCD has an infrared fixed point $\alpha_\mathrm{IR}$, where
$\theta^\mu_\mu$ vanishes apart from $O(m_{u,d,s})$ corrections, the essential
features of the original scheme can be reproduced by a double expansion in
the running gluon coupling $\alpha_s$ about $\alpha_\mathrm{IR}$ and the
light quark masses $O(m_{u,d,s})$ about zero.\cite{CT}

The dilaton idea is contained in footnote 38 of the 1962 current algebra
paper.\cite{algebra} A ``resonance or quasi-resonance'' which dominates
a dispersion relation for
\begin{equation}
\langle\mbox{particle}|\theta^\mu_\mu|\mbox{particle}\rangle
= \mbox{particle mass}
\label{GTtype}
\end{equation}
yields ``a relation of the Goldberger-Treiman type'' where ``the coupling
of the resonant state to different particles is roughly proportional to
their masses''. In the scale-invariant limit,\cite{hawaii} the vacuum
would become degenerate, as for exact chiral symmetry, except for the
degeneracy being noncompact. Physical predictions are then the result
of expanding in $m_\sigma^2$ about zero.

The term ``dilaton'' is often used in a manner which is distinct
from the scheme above or even contradicts it. The earliest variant
was Fujii's proposal\cite{fujii} of a finite-range scalar component
of gravity. Gell-Mann called it a ``Brans-Dickeon'' after the
well-known proponents of the scalar-tensor theory of gravity\cite{bd},
but the name did not stick. In modern times, ``dilaton'' is often
used for a scalar particle which has zero mass classically but
becomes massive due to quantum corrections, such as Higgs bosons
which acquire mass due to dimensional transmutation.\cite{CW}
Since there is no way of ``turning off'' such a mass, this has nothing
to do with dilatons in the original sense.

In my student days, the main candidate for $\sigma$ was $\epsilon(700)$,
whose existence was not clear. Final state pions interact very strongly in
the $0^{++}$ channel, so there was good reason to assume the presence of a
resonance far off shell. However that meant that it was very hard to pin
down in phase-shift analyses. It was declared dead in the 1976 particle
data tables, but in recent years, has been resurrected as the broad but
clearly defined resonance\cite{Cap} $f_0(500)$.

If dilatons couple to mass, why is its coupling to pions so large?
In leading order, one would expect $F_\sigma g_{\sigma\pi\pi}$ to be
$2m_\pi^2$ for the coupling $g_{\sigma\pi\pi} \sigma \boldsymbol{\pi .\pi}$,
where $F_\sigma$ is the analogue of the pion decay constant $F_\pi \simeq 93$ MeV
and has a similar order of magnitude:
\begin{equation}
\langle\sigma(q)|\theta_{\mu\nu}|\mathrm{vac}\rangle
= (F_\sigma/3)\bigl( q_\mu q_\nu - g_{\mu\nu}q^2\bigr) \,.
\label{F}\end{equation}
The solution, on which I based my PhD thesis, was to note that the
result is really
\begin{equation}
F_\sigma g_{\sigma\pi\pi} = 2m_\pi^2 + O(m_\sigma^2)
\end{equation}
and use approximate chiral symmetry to deduce the coefficient of
$m_\sigma^2$:
\begin{equation}
F_\sigma g_{\sigma\pi\pi} = - m_\sigma^2 + O(m_\pi^2) \,.
\label{width}
\end{equation}
This implies a width of a few hundred MeV, as required. I did it
the hard way, using basic current algebra, and so took too long to
obtain a mass formula for $m_\sigma^2F_\sigma^2$. In the meantime,
John Ellis was working on his PhD in Cambridge (UK), and obtained
both Eq.~(\ref{width}) and the mass formula by efficient use of a
chiral-scale effective Lagrangian. A few months later, we met and were
able to compare notes at the 1971 Coral Gables conference.\cite{jelly,rod}

No account of these times would be complete without mentioning the episode
in 1970 when Feynman became excited about Bose statistics for quarks. He
hoped to explain the $\Delta I = 1/2$ rule for nonleptonic decays of strange
particles. How quarks could possibly be bosons was a matter for future study;
perhaps their bad statistics would not matter if they were confined. Almost
immediately, we heard that the idea had already been suggested\cite{jap,chls},
but the interest generated by Feynman\cite{FKR} in this key problem was good for
particle physics. A few months later, the correct version of the idea was
proposed\cite{PW} (also anticipated in Japan\cite{MM}): for fermion quarks
with color (and even for paraquarks\cite{king}), the color antisymmetrization
of $qqq$ states plus current algebra implies the $\Delta I = 1/2$ rule for
nonleptonic hyperon decays, but says nothing about $\Delta I = 1/2$ for
$K \to \pi\pi$.

Since nonleptonic strange particle decays had been a problem for so
long,\cite{GMP} my interest was piqued. I told Murray of this, carefully
avoiding any suggestion that quarks could be bosons (which I didn't believe
anyway), and drew the response ``watch out, it's a can of worms!'' I was
too busy finishing my PhD to pursue it; otherwise, I may have drawn Fig.~1,
which is required by approximate chiral-scale invariance.
\begin{figure}[bt]
\center\includegraphics[scale=.80]{k_pipi}
\caption{Tree diagrams in chiral-scale perturbation theory\cite{CT} for
$K_S\to\pi\pi$. The vertex amplitudes due to \textbf{8} and
\textbf{27} contact couplings $g_8$ and $g_{27}$ are dominated by the
$\sigma/f_0$ pole amplitude. The magnitude of $g^{}_{K_S\sigma}$ can be
deduced from $K_S \to \gamma\gamma$ and $\gamma\gamma \to \pi\pi$.}
\label{fig:k_pipi}
\end{figure}%
It shows that the $\Delta I = 1/2$ rule for kaons is due to a large
contribution from the dilaton pole. Only after 40-odd years, with help
from my young colleague Lewis Tunstall, can I report a solution to that
problem.\cite{CT} For hyperon decays, the $\Delta I = 1/2$ rule is
understood, but current algebra does not seem to work: that part of
the problem is still a can of worms.

After Coral Gables, there was a thesis to be written, and a suitable way
of ending it had to be found. What else could dilatons do?

From the literature on axial anomalies, I knew about Schwinger's 1951
paper on gauge invariance\cite{julian}. In Sec.~V, he obtained unique
results for both $\pi^0 \to \gamma\gamma$ and $\sigma \to \gamma\gamma$
in one-loop Yukawa theory by imposing gauge invariance on the renormalization
procedure. In terms of the electromagnetic field tensor $F_{\mu\nu}$,
fermion mass $M$, Yukawa coupling $g$, and fine-structure constant $\alpha$,
the answer for $\sigma \to \gamma\gamma$ is
\begin{equation}
{\cal L}^{\mathrm{Yukawa}\rule[-1mm]{0mm}{1.5mm}}_{\rule{0mm}{1.5mm}\sigma\gamma\gamma}
= - \frac{\alpha g}{6\pi M}\sigma F^{\mu\nu} F_{\mu\nu}
\end{equation}
In the second-last paragraph of my thesis, I noted that this breaks scale
invariance (operator dimension $\not= 4$), so if $M$ plays the role of $F_\sigma$
as well as $F_\pi$, perhaps both $F_\pi g_{\pi\gamma\gamma}$ and
$F_\sigma g_{\sigma\gamma\gamma}$ are anomalous. Already, Wilson had shown\cite{kgw2}
that one-loop corrections in $\lambda\phi^4$ theory break scale invariance,
which he interpreted as an anomaly in the trace of $\theta_{\mu\nu}$. Perhaps
there is an electromagnetic trace anomaly due to strong interactions? I was
moving to a post-doctoral job at Cornell; as soon as I arrived, I would try
to extend Wilson's method for $\pi^0 \to \gamma\gamma$ to $\sigma \to
\gamma\gamma$.

\section{Derivation of $\pi^0 \to \gamma\gamma$ for Nonperturbative Pions}

When Schwinger analysed $\pi^0 \to \gamma\gamma$, chiral invariance and PCAC
(partially conserved axial current) were unknown. At issue was the equivalence
\begin{equation}
\phi\bar{\psi}\gamma_5\psi\ \leftrightarrow\
  - \bigl(i/2M\bigr)\bar{\psi}\gamma_\mu\gamma_5\psi \partial^\mu\phi \,,
\quad \phi = \pi^0 \mbox{ field}
\end{equation}
between pseudoscalar and pseudovector couplings for the one-fermion-loop
triangle diagram. The trouble was that the product of the fermion fields at
the same point is singular. The solution was to consider $\psi$ and
$\bar{\psi}$ at different points $x'$ and $x''$ and make the analysis
gauge invariant: then the limit $x' \to x''$ becomes finite. Rephrased
in terms of chiral symmetry, the problem is that the Noether construction
fails because (a) it requires
\begin{equation}
\frac{\partial\mathcal{L}}{\partial\del^\mu\psi} = \bar{\psi}\gamma_\mu\ \mbox{ and }\
\delta^{}_{\mathrm{axial}}\psi = \gamma_5\psi
\end{equation}
to be multiplied at the same point and (b) it does not work for non-local
expressions produced by point splitting.  The axial anomaly\cite{bell,steve}
is responsible for this failure: it is the finite counterterm mismatch between
gauge invariant and chiral invariant renormalization prescriptions for
axial-vector operators.

Wilson's version of this was designed to avoid perturbation theory. In
particular, if pions are $q\bar{q}$ states which become Nambu-Goldstone bosons
in the chiral limit, they are certainly not perturbative and so should not
be represented by a perturbative field $\phi$.

The other key feature of his approach was the use of short distance analysis.
The connection between axial and trace anomalies and short distance behavior
is best illustrated by considering first how equal-time commutators produce
contact terms $\sim \delta^4(x-y)$ in ordinary Ward identities.

Given a free massive boson field $\varphi$, let $\partial_\mu\varphi$ play the
role of a current. Canonically, the divergence of $T\{\varphi\partial_\mu\varphi\}$
is found by writing the $T$-product in terms of step functions
$\theta(\pm x_0)$ and unordered field products, differentiating the
step functions
\begin{equation}
\frac{\partial\ }{\partial x^\mu}\theta(\pm x_0) = \pm\delta(x_0)g_{0\mu}
\end{equation}
and substituting $\partial^2\varphi = - m^2\varphi$:
\begin{equation}
\partial^\mu T\bigl\{\varphi(0)\partial_\mu\varphi(x)\bigr\}
= \bigl[\partial_0\varphi(x),\varphi(0)\bigr]\delta(x_0)
 - m^2T\bigl\{\varphi(0)\varphi(x)\bigr\} \,.
\label{canon1}
\end{equation}
In this case, the contact term can be found by substituting a canonical
commutator:
\begin{equation}
\bigl[\partial_0\varphi(x),\varphi(0)\bigr]\delta(x_0)
= - i\delta^4(x)I\,, \quad I = \mbox{identity operator.}
\label{canon2}
\end{equation}
The short-distance method is to note that a term $\sim \delta^4(x)$ can
arise only if $\partial^\mu$ acts on a singularity $\sim 1/x^3$ at $x \sim 0$.
The leading term of the operator product expansion for
$T\{\varphi(0)\partial_\mu\varphi(x)\}$ is given by the propagator of the
massless theory
\begin{equation}
T\{\varphi(0)\partial_\mu\varphi(x)\} \to \frac{x_\mu}{2\pi^2(x^2 - i\epsilon)^2}I\,,
\quad I = \mbox{identity operator}
\end{equation}
Substituting $\partial^\mu\bigl(x_\mu/x^4\bigr) = -2i\pi^2\delta^4(x)$ and
$\partial^2\varphi = - m^2\varphi$, we find
\begin{equation}
\partial^\mu T\bigl\{\varphi(0)\partial_\mu\varphi(x)\bigr\}
= - i\delta^4(x)I
 - m^2T\bigl\{\varphi(0)\varphi(x)\bigr\} \,.
\end{equation}
in agreement with Eqs.~(\ref{canon1}) and (\ref{canon2}).

For the axial anomaly, the problem is to evaluate the quantity
\begin{equation}
S = -\frac{\pi^2}{12}\epsilon^{\mu\nu\alpha\beta}\iint d^4x d^4y\, x_\mu y_\nu
 T\langle\mbox{vac}|J_\alpha(x)J_\beta(0)\partial^\gamma J_{\gamma 5}(y)|\mbox{vac}\rangle
\,,
\label{S}
\end{equation}
where data for $\pi^0 \to \gamma\gamma$  and approximate $SU(2) \times SU(2)$
symmetry imply $S \simeq + 0.5$.  The constant $S$ normalizes the contact term
in an anomalous Ward identity of the form
\begin{align}
&\partial_y^\nu\mbox{``$T$''}
\langle\mbox{vac}|J_\alpha(x)J_\beta(0)J_{\nu 5}(y)|\mbox{vac}\rangle
\nonumber \\
&=
\frac{S}{2\pi^2}\epsilon_{\alpha\beta\mu\nu}\partial_x^\mu\partial_y^\nu\delta^4(x)\delta^4(y)
 + T\langle\mbox{vac}|J_\alpha(x)J_\beta(0)\partial^\nu J_{\nu 5}(y)|\mbox{vac}\rangle
\,.
\label{contact}
\end{align}
The contact term scales as $1/\{\mbox{length}\}^{10}$, so it must be generated
by a short distance singularity
\begin{equation}
J_\alpha(x)J_\beta(0)J_{\nu 5}(y) \sim 1/\{\mbox{length}\}^9
\end{equation}
as \emph{both} $x_\mu$ and $y_\mu$ tend to zero. (Do not confuse this with
the short-distance properties of $J_\alpha J_\beta \partial^\gamma J_{\gamma 5}$ in
Eq.~(\ref{S}), where the condition dim\ $\partial^\gamma J_{\gamma 5} < 4$ ensures
convergence of the integral.)

In Eq.~(\ref{contact}), a \emph{single} derivative $\partial_y^\mu$ produces
\emph{a product of two delta functions}, so it is clear that $\theta$-functions
in time \emph{cannot} be used to construct ``$T$''. This example exposes
the limitations of canonical field theory very effectively.

In perturbation theory, it has long been known\cite{SP} but not often noted
that time ordering is part of the renormalization procedure. In general,
``$T$'' must be regarded as an operation which depends on the
renormalization prescription. The difference between two time-ordering
procedures for a given operator product is a set of contact terms at
coinciding points. In the case of the triangle diagram coupled to photons,
electromagnetic gauge invariance specifies the renormalization procedure
completely:
\begin{equation}
\mbox{``$T$''}  \rightarrow  T_{\mathrm{e'mag}}  \,.
\end{equation}

Wilson\cite{kgw} circumvented the ``$T$'' problem by excising a small
neighbourhood around lines of coinciding points in the integral (\ref{S}).
Let the region of integration be restricted to the region
\begin{equation}
\mathcal{R} = \bigl\{|x_0| > \epsilon\,,\ |y_0| > \epsilon'\,,\
|x_0 - y_0| > \epsilon''\bigr\} \,.
\label{region}
\end{equation}
\begin{figure}[htb]
\center\includegraphics[scale=.95]{region}
\caption{Integration region $\mathcal{R}$ defined by Eq.~(\ref{region}).
\label{excise}}
\end{figure}
shown in Fig.~\ref{excise}, so that Eq.~(\ref{S}) becomes
\begin{equation}
S = - \frac{\pi^2}{12}\epsilon^{\mu\nu\alpha\beta}\iint\limits_\mathcal{R}
 d^4x d^4y\, x_\mu y_\nu
 T\langle\mbox{vac}|J_\alpha(x)J_\beta(0)\partial^\gamma J_{\gamma 5}(y)|\mbox{vac}\rangle
 + O(\epsilon,\epsilon', \epsilon'') \,.
\label{S'}
\end{equation}
Of course, $S$ does not depend on $\epsilon$, $\epsilon'$, or $\epsilon''$.
Within $\mathcal{R}$, define
\begin{align}
X_\gamma &= \epsilon^{\mu\nu\alpha\beta}x_\mu y_\nu T\langle\mbox{vac}|
  J_\alpha(x)J_\gamma(0)J_{\beta 5}(y) + J_\gamma(x)J_\alpha(0)J_{\beta 5}(y)
  |\mbox{vac}\rangle  \nonumber \,,\\
Y_\gamma &= \epsilon^{\mu\nu\alpha\beta}x_\mu y_\nu T\langle\mbox{vac}|
  J_\alpha(x)J_\beta(0)J_{\gamma 5}(y) + J_\alpha(x)J_\gamma(0)J_{\beta 5}(y)
  |\mbox{vac}\rangle
\end{align}
where now time ordering with $\theta$-functions is allowed because
$\mathcal{R}$ excludes coinciding points. This also means that derivatives
commute with the $T$-operation, so we can obtain
\begin{equation}
S  = - \frac{\pi^2}{12}\iint\limits_\mathcal{R}
 d^4x d^4y\,\bigl(\partial^\gamma_x X_\gamma + \partial^\gamma_y Y_\gamma\bigr)
  + O(\epsilon,\epsilon', \epsilon'')
\end{equation}
by using current conservation $\partial^\gamma J_\gamma = 0$, translation invariance
of $|\mbox{vac}\rangle$ and symmetry $x \leftrightarrow y$ of the integral
to $O(\epsilon,\epsilon', \epsilon'')$. If $\Sigma$ is the surface in
8-dimensional space which bounds $\mathcal{R}$, we have
\begin{equation}
S  = - \frac{\pi^2}{12}\int_\Sigma\!d\vec{\Sigma}\cdot\vec{Z}
  + O(\epsilon,\epsilon', \epsilon'')
\label{surface}
\end{equation}
where $\vec{Z} = \bigl(X_\gamma , Y_\gamma\bigr)$ is an 8-dimensional vector
formed from the components of $X_\gamma$ and $Y_\gamma$.

So $S$ is given by the result of taking $\epsilon$, $\epsilon'$ and
$\epsilon''$ to zero in Eq.~(\ref{surface}). Since the current operators
commute at space-like
separations, their products at short distances are all that we need.
If we consider (say) $\epsilon \to 0$ and exclude the $x,y \sim 0$
neighbourhood where the axes in Fig.~\ref{excise} meet, we have
$x \sim 0$ for fixed $y$, which means expanding in $J_\alpha(x)J_\beta(0)$
to produce an equal-time commutator. There could be three commutators in
principle, one for each axis, but explicit checks confirm the
conclusion\cite{suth} that they all vanish. Therefore $S$ is entirely
determined by the leading VVA short-distance singularity
\begin{equation}
T\{J_\alpha(x)J_\beta(0)J_{\gamma 5}(y)\} \sim G_{\alpha\beta\gamma}(x,y)I \,,
\quad x,y \sim 0 \,,
\label{VVA}
\end{equation}
so it can be calculated if the three-point function $G_{\alpha\beta\gamma}$
is known.

At this point, I tried the same analysis for the trace anomaly.
Let the amplitude for photons to couple to the hadronic
energy-momentum tensor be
\begin{equation}
\langle\gamma(\epsilon_1,k_1)\gamma(\epsilon_2,k_2)|
        \theta^\mu_\mu(0)|\mbox{vac}\rangle
= \bigl(\epsilon_1\cdot\epsilon_2 k_1\cdot k_2
        - \epsilon_1\cdot k_2 \epsilon_2\cdot k_1\bigr)F\bigl((k_1 + k_2)^2\bigr)
\,.
\label{ampl}
\end{equation}
As in Eq.~(\ref{S}) for $S$, the trace anomaly corresponds to the low-energy
limit $k_1, k_2 \sim 0$:
\begin{equation}
F(0) = - \frac{\pi\alpha}{3}\iint d^4xd^4y\,x\cdot y
       \langle\mbox{vac}|J^\alpha(x)J_\alpha(0)\theta^\mu_\mu(y)|\mbox{vac}\rangle
\,. \label{trace}
\end{equation}
The aim was to substitute the formula for the divergence of the
conformal current
\begin{equation}
 \partial^\mu_y\bigl\{(2y_\lambda y^\nu - \delta^\nu_\lambda y^2)\theta_{\mu\nu}(y)\bigr\}
 = 2y_\lambda\theta^\mu_\mu(y)
\label{conf}
\end{equation}
and integrate by parts. To my surprise, I found that it was not necessary to
exclude coinciding points as in Fig.~\ref{excise}. Instead, I found that an
answer could be found directly by restricting just the $x$ integration
to $|x_0| > \eta$ for small $\eta > 0$ to keep the $x,y \sim 0$
singularity
\begin{equation}
T\{J_\alpha(x)J_\beta(0)\theta_{\mu\nu}(y)\} \sim K_{\alpha\beta\mu\nu}(x,y)I
\end{equation}
under control. Then integration by parts with respect to $y$ produced
known equal-time commutators, so the $y$ integral could be done, with the
result
\begin{equation}
F(0) = -\frac{i\pi\alpha}{6}\int_{|x_0| > \eta}\!d^4x\,\partial^\nu_x\{x^2 x_\nu
      T\langle\mbox{vac}|J^\alpha(x)J_\alpha(0)|\mbox{vac}\rangle\} + O(\eta)\,.
\end{equation}
We have $J_\alpha J_\beta \sim R/x^6$ at short distances, where $R$ is the
asymptotic Drell-Yan ratio
\begin{equation}
R = \bigl\{(\sigma(e^+e^- \to \mbox{hadrons})
    \bigl/(\sigma(e^+e^- \to \mu^+\mu^-)\bigr\}_{\mathrm{energy} \to \infty}
\end{equation}
so the $x$ integral can also be done, yielding an exact result:
\begin{equation}
F(0) = 2R\alpha/3\pi  \,.
\label{trace2}
\end{equation}
In effect, an anomalous term%
\footnote{The extrapolation in $(k_1 + k_2)^2$ from zero to
$m_\sigma^2$ used to estimate $F_\sigma g_{\sigma\gamma\gamma}$ from $F(0)$
has had to be modified,\cite{CT} because $\pi,K$ loop diagrams compete
with the $\sigma$-pole amplitude.}
$(R\alpha/6\pi)F_{\mu\nu}F^{\mu\nu}$ is induced in the trace of the
energy-momentum tensor by electromagnetism.\cite{rjc}
The same result was found independently by Mike Chanowitz and
John Ellis\cite{CE} via a momentum-space analysis. It was the
immediate precursor of the gluonic trace anomaly
$\beta(\alpha_s)/(4\alpha_s) G^a_{\mu\nu}G^{a\mu\nu}$
found a few years later.\cite{mink}.

The unexpected feature of the analysis leading to Eq.~(\ref{trace2}) was
that, although the 3-point singularity $ K_{\alpha\beta\mu\nu}$ is responsible
for the presence of the trace anomaly, its full functional form is not
needed: only the subregion $x-y \ll x,y$ \emph{within} the $x,y \sim 0$
region is needed. In Fig.~\ref{excise}, this subregion connects the central
area $x,y \sim 0$ to other $x \sim y$ regions along the diagonal
axis $x_0 = y_0$.

That led me to consider \emph{nested} operator product expansions, where
an expansion such as
\begin{equation}
T\{A(x)B(0)\} \sim \sum_m \mathcal{C}_m(x) O'_m(0)\ \mbox{ for } x \sim 0
\end{equation}
is substituted into a larger expansion, e.g.
\begin{equation}
T\{A(x)B(0)C(y)\} \sim \sum_n f_n(x,y) O_n(0)\ \mbox{ for } \quad x,y \sim 0\,.
\end{equation}
This is legitimate provided that $y$ is independent of the limit $x \to 0$,
i.e.\ $x \ll y$. Then a subsequent limit $y \to 0$ can be taken:
\begin{equation}
T\{O'_m(0)C(y)\} \sim \sum_n \mathcal{C}_{mn}(y)O_n(0) \,.
\end{equation}
The result is a set of consistency conditions\cite{rjc}
\begin{equation}
 f_n(x,y) \sim \sum_m \mathcal{C}_m(x)\mathcal{C}_{mn}(y)  \,.
\end{equation}
The idea works at short distances (and not on other parts of light cones)
provided the limits are \emph{nested}. For the example above, fix $\hat{x}$
and $\hat{y}$ in
\begin{equation}
x = \rho_1\rho_2 \hat{x}\ \mbox{ and }\ y = \rho_2 \hat{y}
\end{equation}
and take the limits $\rho_1 \to 0$ and $\rho_2 \to 0$ independently.
This is the position-space version of Weinberg's limiting
procedure\cite{wein} used to classify the asymptotic behavior of
amplitudes and hence justify power counting methods for renomalization.

An obvious next step was to apply this procedure to the short-distance
VVA function $G_{\alpha\beta\gamma}$ of Eq.~(\ref{VVA}). Let
\begin{equation}
u = x^2 -i\epsilon\ , \quad v =  y^2 -i\epsilon\ , \quad w = (x-y)^2 -i\epsilon \,.
\end{equation}
The relevant two-point expansions are
\begin{align}
T\{J_\alpha(x)J_\beta(0)\}
&\sim R(g_{\alpha\beta}x^2 - 2x_\alpha x_\beta)I\bigl/(\pi u)^4
 + K\epsilon_{\alpha\beta\lambda\mu}x^\lambda J^\mu_{\ 5}(0)\bigl/(3\pi^2u^2)
\nonumber \\
T\{J^\mu_{\ 5}(0)J_{\gamma 5}(y)\}
&\sim R'(\delta^\mu_\gamma y^2 - 2y^\mu y_\gamma)I\bigl/(\pi v)^4
\end{align}
where $R'$ is the isovector part of $R$, and $K$ is measurable in polarised
deep-inelastic electroproduction or in $e^+ + e^- \to \mu^+ + \mu^- + \pi^0$.
The result
\begin{equation}
G_{\alpha\beta\gamma}(x,y) \underset{x \ll y}{\longrightarrow}
\bigl\{K\epsilon_{\alpha\beta\lambda\mu}x^\lambda J^\mu_{\ 5}(0)\bigl/(3\pi^2u^2)\bigr\}
 R'(\delta^\mu_\gamma y^2 - 2y^\mu y_\gamma)I\bigl/(\pi v)^4  \,.
\end{equation}
said something about the normalization of $G_{\alpha\beta\gamma}$, but without
a formula valid for the whole $x, y \sim 0$ region, the calculation of $S$
could not be completed.

In the meantime, I was checking products of $\theta_{\mu\nu}$ with other
currents to see if the absence of the soft trace at short distances would
imply asymptotic%
\footnote{This has \emph{nothing} to do with the properties of the vacuum
state. As noted at the beginning of Sec.~\ref{three}, $|\mbox{vac}\rangle$
breaks scale and hence conformal invariance very strongly. This may be
due to explicit symmetry breaking or to the symmetry being realised in the
Nambu-Goldstone mode.}
conformal invariance, as indicated by Eq.~(\ref{conf}).
Satisfied that it did, I required conformal invariance for $G_{\alpha\beta\gamma}$,
found that it had to be proportional to the triangle diagram, and then
found that this result had already been published by Schreier.\cite{ethan}

So the evaluation of the VVA singular function was complete:
\begin{equation}
G_{\alpha\beta\gamma}(x,y)
= \frac{KR'}{12\pi^6u^2 v^2 w^2}\mbox{Tr}\bigl\{\gamma_\alpha\gamma\cdot x
 \gamma_\beta\gamma\cdot y\gamma_\gamma(\gamma\cdot x - \gamma\cdot y)
  \gamma_5\bigr\}  \,.
\end{equation}
When $G_{\alpha\beta\gamma}$ is substituted into Eq.~(\ref{surface}), the
equal-time commutator regions give no contribution (as before), so as long
as (say) $\epsilon'$ is held fixed, the limits $\epsilon \to 0$ and
$\epsilon'' \to 0$ can be taken without intruding on the short-distance
region. Thus%
\footnote{These details, taken from a letter I wrote to Fritzsch and Gell-Mann
at the time,\cite{cao} should have been part of ref.~[10] of my paper\cite{rjc}
but it was never finished.}
\begin{equation}
S = \frac{\pi^2}{12}\int\!d^3y\int\!d^4x\,
  \bigl\{\widetilde{Y}_0(y_0=\epsilon')-\widetilde{Y}_0(y_0=-\epsilon')\bigr\}
 + O(\epsilon')
\end{equation}
where $\widetilde{Y}_\gamma$ is the $x,y \sim 0$ part of $Y_\gamma$:
\begin{align}
\widetilde{Y}_\gamma &= \epsilon^{\mu\nu\alpha\beta}x_\mu y_\nu
  \bigl\{G_{\alpha\beta\gamma}(x,y) + G_{\alpha\gamma\beta}(x,y)\bigr\}
\nonumber \\
 &= - \frac{4KR'}{3\pi^6 u^2 v^2 w^2}y_\gamma\bigl\{x^2 y^2 - (x\cdot y)^2\bigr\} \,.
\end{align}
Do the $x$-integral
\begin{equation}
\int\!d^4x\,\{x^2 y^2 - (x\cdot y)^2\}/(uw)^2 = - 3\pi^2i/2
\end{equation}
and then the $y$-integral
\begin{equation}
\int\!d^3y/v^2 = - \pi^2i/|y_0|
\end{equation}
to obtain the desired formula\cite{rjc}
\begin{equation}
3S = KR'  \,.
\end{equation}
It relates the low-energy amplitude $S$ to high-energy amplitudes $R'$
and $K$.

Being anxious to avoid model dependence, I allowed for the possibility
that the electromagnetic current is not a pure $SU(3)$ octet,
\begin{equation}
4R' \leqslant 3R \,.
\end{equation}
At that time, we did not know $R$, $R'$ or $K$. In particular, data showing
scaling behavior for $e^+ + e^- \to$ hadrons was not available until the 1974
London Conference, a year after asymptotic freedom. The value of $S$ could
well be exactly 0.5, so Adler's non-renomalization theorem\cite{steve,ab} for
$S$ suggested a theory with three species of quark, but I could not see how
to deal with colored electromagnetic currents or paraquark operators.

So when I received by return mail a letter from Gell-Mann proposing colored
fractional quarks with color-neutral currents, it seemed to me that this
clarified matters from the point of view of Adler's theorem, but I felt
(for reasons discussed above) that having free quarks on the light cone
was going too far. However, sometimes an oversimplification can lead to
correct answers --- in this case, QCD\cite{fgm2} and asymptotic
freedom.\cite{pol,GW}

Initially, the QCD proposal looked good as a model of constituent quarks,
but not for current quarks and the $\pi^0 \to \gamma\gamma$ analysis.
Having found the electromagnetic trace anomaly, we knew already that
$\theta^\mu_\mu$ would have anomalous gluonic terms proportional to
$G^a_{\mu\nu}G^{a\mu\nu}$ which would break scale and conformal invariance
at short distances.

What asymptotic freedom did was to turn QCD into a good theory of current
quarks as well as constituent quarks. The breaking of scale invariance at
short distances was minimal, being associated with operators which
are not conserved exactly or partially. The analysis of $\pi^0 \to \gamma\gamma$
can be still be carried through since all of the equations remain valid:
they can be derived by using asymptotic freedom instead of asymptotic
conformal invariance. The results for three colors are
\begin{equation}
R = 2,\ R' = 1.5,\ K = 1, \mbox{ and } S = 0.5
\end{equation}
where the non-renormalization theorem for $S$ is \emph{not} used.
All of this goes through \emph{without} treating pions perturbatively.

The method of nested operator product expansions is now not needed for
the $\pi^0 \to \gamma\gamma$ derivation, but it is generally valid in
renormalized field theory. As a result, coupling constant dependence
of the form
\begin{equation}
3S = K(g) R'(g)
\end{equation}
can be investigated.\cite{ACGJ} This program has been extensively pursued
by Andrei Kataev, Stan Brodsky and their collaborators.\cite{andrei}

In retrospect, there came a time when abstracting physics had to give way
to guessing the correct model. I remember that time well.

redpajama_set_name: RedPajamaArXiv


We kicked off a new series called How To, and looked at the practical wisdom of the Word for some of the spiritual goals we have as disciples of Jesus Christ. Join us as we look at How To Retain Our Joy.
We love to say that we are a storytelling church, and it is so wonderful that God has brought so many unique individuals with incredible stories to our tribe, but God wants us to go further than this. It is not just about telling a great story, it is about living a story that goes deeper into the things of God.
Pastor Mark shares with us from Romans 12 on an amazing exhortation from Paul the Apostle to renew our minds.
Rest is a funny thing. Just saying the word means a million things to a million people. People think about rest as sleep or vacation or the lack of stress. We tend to associate it with this carelessness of the soul that just lets us sleep like a baby. The crazy thing is that some of the people who seem the most rested have a lot going on. How is that possible?
Randy Young joins us again this weekend to bring a special message as part of our How To series, looking at how God wants to take us to new heights.
We wrap up our How To series with an encouragement from Pastor Mark on remaining in the presence of God as our strength and maintaining our confidence in Him.


text:
thin is in —
First transistor built using two-dimensional silicon
Graphene's big brother finally kept stable long enough to test.
John Timmer - Feb 4, 2015 2:57 pm UTC
Unlike graphene, the hexagonal arrays of silicon atoms in silicene are slightly buckled, creating a somewhat more complex surface.
Since the isolation of graphene, a one-atom-thick sheet of carbon, researchers have developed a number of other two-dimensional materials. (Yes, they are really three-dimensional; it's just one of the dimensions is only an atom thick, and therefore negligible.) Knowledge of the periodic table would suggest that elements from the same column as carbon would have similar chemical properties, and therefore be excellent candidates for forming two-dimensional sheets. So, why hasn't more been done with silicon, the next element down the column from carbon?
People have actually made silicene, the silicon version of graphene. But they've only managed to make tiny patches of it on silver surfaces; under just about any other conditions, it rapidly reacts with the oxygen in air and disintegrates.
On Monday, however, researchers announced that they'd managed to create the first device—a field effect transistor—using silicene. Since interactions with silver protected the silicon sheet, the authors fabricated a large sheet on a thin silver surface. They then capped this with aluminum oxide, which also protected the silicene. At this point, they could etch off some of the aluminum, and use the remaining metal as source and drain contacts. By depositing the alumina on a silicon dioxide surface, the resulting device acted as a field effect transistor.
This allowed them to explore the flow of electrons through the silicene, which turned out to be... disappointing. While theoretical predictions had suggested electron mobilities in line with what's seen in graphene, the silicene device saw mobilities about ten times smaller than expected. The authors aren't sure why this is—whether it's silicene itself or simply their production techniques isn't clear.
Still, now that we know how to make some, it should be possible to study its properties more thoroughly. Because silicon has a larger and more complex electronic structure than carbon, it's thought that silicene can be readily manipulated either through chemical reactions or simply by placing other materials in close proximity. So, it's possible that further study could get silicene behave more in line with what researchers were hoping for.
Nature Nanotechnology, 2014. DOI: 10.1038/NNANO.2014.325 (About DOIs).
John Timmer John became Ars Technica's science editor in 2007 after spending 15 years doing biology research at places like Berkeley and Cornell.
Email jtimmer@arstechnica.com // Twitter @j_timmer


text:
Q: Is there a "good" way to visualize complex vectors? We often represent complex numbers as vectors in $\mathbb{R}^2$ with $x$ being the real axis and $y$ being the imaginary axis. We often represent 2-dimensional vectors over $\mathbb{R}$ in a similar way.
Suppose we consider $\mathbb{C}^2$, vectors in two dimensions over $\mathbb{C}$.  It feels like the complex plane is "embedded" into the scalars and I would like to somehow visualize these planes in the context of $\mathbb{C}^2$.
Is there a "good" way to think about this that people find intuitive?

A: The two "complex axes" might be visualized as a pair of planes that intersect at a point rather than a line.
Incidentally, the first chapter of Kendig's Elementary Algebraic Geometry is devoted to helping visualize hypersurfaces in $\mathbb C^2$.  It has some really great drawings and figures that give a concrete sense of the topology of various algebraic varieties.

redpajama_set_name: RedPajamaStackExchange


Every 40 seconds, someone in the United States suffers a stroke, which is one of the leading causes of death. Having access to an experienced neurologist can make a difference in the outcome but while the demand for neurologists is high, unfortunately the supply is short. This fact is further compounded for many who live in rural areas, which makes access to a neurologist even more limited. Fortunately, technology has made neurology more accessible in West Tennessee.
Through the use of teleneurology, expert care can be quickly available to even the most remote locations, an important consideration since every second counts in treating stroke and other neurological emergencies. The American Academy of Neurology views teleneurology as an effective tool for rapid evaluation of patients in remote locations.
Patients in rural West Tennessee are reaping the benefits of this technology. Baptist Memorial Healthcare began using a telemedicine platform for stroke and acute neurology in 2012. In 2015, the system switched to the Patronus Neurology platform to provide the teleneurology consults. The clinical program is now in place at ten hospitals across the system, including Tipton County and most recently, Union City. Plans are to expand the program to all facilities system wide by 2019. Baptist Memorial Hospital - Huntingdon is projected to come online sometime next year. Options for telemedicine in the outpatient neurology setting are being explored as well.
"Recruitment of specialists, especially in neurology and neurosurgery, is often very difficult for our small to mid-size facilities and communities. The neurologists we have on staff have their hands full with covering their clinic and in-house responsibilities. Having them try to cover outlying facilities would be difficult," said Kimberly Hallum Stewart, system administrator of neurosciences for Baptist Memorial Healthcare Corporation in Memphis. "Telemedicine brings those specialists to those areas. The company we work with, Patronus Neurology, are trained vascular neurologists with specific stroke training that only do telemedicine. They assign a team of physicians who work only with our system and provide an on-call physician as well as a back-up, so if we have multiple patients over multiple facilities we are covered."
The lead time to start a telestroke program is about three to four months. The technical platform must be in place, which consists of the cart and software system that will be used. Clinicians have to be educated on the process for using the cart and activating a request for a consult. The EMR systems used by Baptist facilities and that used by Patronus all interface so that orders and reports can be transmitted electronically. Patronus physicians are introduced to the staff and physicians as well as credentialed at the facility. Staff also receive additional training on how to identify and care for a stroke patient as well as administer Activase (tPA).
Overall, it is a pretty easy process," said Stewart. "In a rural hospital, the age of the infrastructure can impact the time it takes to get things up and going. We have to make sure the wireless capability of the facility can handle the system. We do a ton of testing before it is up and running and take the cart everywhere it could possibly have to go to make sure there are no kinks. But just like with cell phones and computers, there can always be a glitch, but our physicians can always do the consult by phone if necessary."
Baptist Memorial Hospital - Union City was an ideal facility for this type of program says Stewart. "They have emergency department physicians and hospitalists that are on the ground to care for the patient during and after the telestroke consult," she said. "The program is ideal for any adult patient that is undergoing an issue that the healthcare provider, whether in the field or ER, feels needs a neurology consult."
A typical consult starts with a patient presenting to the ED or on an inpatient unit with a stroke or stroke-like symptoms (or any other emergent neurological event). They are quickly examined and in the case of a code stroke, the patient is immediately taken to CT. While the patient is in CT, the clinician enters an order in the EMR for a teleneurology consult that goes directly to Patronus. The Patronus neurologist connects to the hospital via a telemedicine cart and is able to see the patient, family, nurses as well as physician and communicate directly with them.
"The neurologist controls the camera on the cart which can pan left, right, up and down to examine the patient and has an amazing picture quality," said Stewart. "It also has 30x zoom lens, so they can look at the patient's pupil. The nurse is always in the room with the patient.
The neurologist discusses the options with the family and determines the next steps to be taken, be that to start tPA, admit to the hospital or transfer to another facility that provides a higher level of care. All of this typically happens in less than 60 minutes. After the patient leaves the inpatient setting, the appropriate referrals and appointments are made for follow-up care whether that be with a specialist in Memphis or by a local physician.
Stewart says the system has been well received by both staff and patients. "When the cart rolls in, patients interact with the physician just as they would if they were in the same room," she said. "The ER staff and physicians love it. The ability to have the Patronus physician be a part of the medical team and work with the patient and family is invaluable. They follow the patient in real time with real data from start to finish. If the patient is transferred, they make sure the admitting physician has all the information from the consult prior to the patient's arrival in Memphis."
Across the Baptist system in 2017, over 2100 patients with neurological emergencies were treated and cared for via telemedicine. "Union City has a busy emergency department, so we expect the volume at the facility to grow each month," said Stewart. "Based on what we see in other facilities their size, we expect there to be 10-15 consults a month."


text:
Senate votes to repeal ethanol tax credits
June 16, 2011 at 12:05 p.m.
WASHINGTON — The Senate voted Thursday to repeal tax credits for producing ethanol, a vote that budget cutters hope will demonstrate a growing appetite in Congress to end special interest tax breaks to help reduce government borrowing.
The Senate voted 73-27 to repeal the $5 billion annual subsidy, just two days after rejecting an identical measure. The tax credit provides 45 cents a gallon to oil refiners who mix gasoline with ethanol, a renewable, liquid fuel additive that comes mainly from corn in the U.S.
The measure will now be added to a bill renewing a federal economic development program. The prospects for the overall bill are uncertain, but Thursday's vote clearly endangers the ethanol tax credit, which would expire at the end of the year anyway, unless Congress renews it.
The measure passed Thursday would end the tax credit immediately. It would also repeal a 54-cent-a-gallon tariff on imported ethanol, which restricts imports, mainly from Brazil.
"The best way for ethanol to survive is to stand on its own two feet, without spending something we don't have to get something we're going to have anyway," said Sen. Tom Coburn, R-Okla.
In a sign that some ethanol subsidies are likely to endure, the Senate also voted 59-41 to reject a measure to eliminate a government program that supports the distribution of ethanol. The House had passed a similar measure earlier in the day, by a vote of 283-128, adding it to an agriculture spending bill.
The debate played out as the White House and congressional leaders continued to negotiate spending cuts to help reign in government red ink. Thursday's vote will almost certainly make repealing the ethanol tax credit part of those discussions.
The federal government, which borrows about 40 cents of every dollar it spends, has already hit the legal borrowing limit of $14.3 trillion. Treasury Secretary Timothy Geithner has warned Congress that the U.S. risks an unprecedented default on Treasury bonds if the borrowing limit isn't increased by Aug. 2. However, a growing number of lawmakers say they won't vote to increase the borrowing limit without substantial deficit reduction.
Many Republicans have ruled out tax increases, though some have said they would support ending narrowly tailored tax breaks like the ethanol tax credit.


text:
Q: Not able to redirect output of the command to a file My problem is after executing below code I am able to see outputs of each command in shell. How can I get that shell output to the file
I have tried with the below but it does not work
python pr.py >> pr.txt
 import os

 f=open("pr1.txt","r")
 df=0
 for i in f:

     df=df+1
     if df==4:
        break
     print i
     os.system("udstask expireimage -image" + i)

After executing "os.system("udstask expireimage -image" + i)" every time this will display status of the command to the file

A: You could try something like :
import os

f=open("pr1.txt","r")
 df=0
 for i in f:

     df=df+1
     if df==4:
        break
     print i
     os.system("udstask expireimage -image" + i + " > pr.txt")

It would redirect the output of the command to pr.txt.
You should use subprocess instead of os.system which has more efficient stream handling and gives you more control while calling a shell command:
import os
import subprocess

f=open("pr1.txt","r")
 df=0
 for i in f:

     df=df+1
     if df==4:
        break
     print i
     task = subprocess.Popen(["udstask expireimage -image" + i],stdout=subprocess.PIPE,shell=True)
     task_op = task.communicate()
     task.wait()

Now you have your output stored in task_op which you can write onto a file or do whatever you wish to. It is in tuple form and you may need to write only required part.


In the Great "Pumpkin" Pie Experiment of 2015 I explore the various squash available in the market and see which are suitable for pumpkin pie!
Oh yeah, and eat pie.
Strawberry season is still weeks away, but the plants that bear these precious gems require some TLC throughout the spring before they reward our kind attention early in the season.
Waking up to snow was not how I envisioned jumping into spring. Despite the snow and brutal temperatures, things never completely stop on the farm, even in winter. It's still quite chilly, but things are starting to pick up. Seeds are ordered and planning for planting is in progress. I've even convinced my husband to add some new items to the plantings this year that have caught … Continue reading Spring!


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See our Visitor and Safety Travel Information page for the latest COVID-19 updates.
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News & Accolades
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10 Reasons to Take your Family to Wrightsville Beach
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Wrightsville Beach Named One of the Best Spring Break Destinations in the U.S.
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In 2020, for the third year in a row, Wrightsville Beach was voted one of the "South's Best Beach Towns," by the readers of Southern Living magazine. Noting "bike-friendly streets, big surf, good food, and a laid-back attitude make Wrightsville Beach a true beach lover's getaway."
Wrightsville Beach is featured on MSN's list of "The Best Beaches in the U.S.," noting year-round beauty, kids' surf camps, stand-up-paddleboard and surfing.
Wrightsville Beach's Carolina Pro-Am and Carolina Cup events have been added as stops on the Association of Paddlesurf Professionals APP Qualifier Series. Participants will earn valuable points towards qualification for the APP World Tour and ultimately, points towards crowning of the World Champion. The APP Qualifier Series will also feature global events in Asia, Europe and Central & South America.
Wrightsville Beach Marathon Madness has been recognized as a Southeastern Tourism Society Top 20 Event. Sign up to race in the Boston Marathon qualifying event. Set a new personal best as you traverse a course winding along the Intracoastal Waterway and making its way inland.
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The annual Carolina Cup Paddle Races, North Carolina Holiday Flotilla, and U.S. Open Fat Bike Championship have been recognized by the Southeast Tourism Society as Top 20 Events.
Indo Jax Surf Charities in Wrightsville Beach gained special attention from a story on The Hero Effect on the Oprah Winfrey Network. Indo Jax Surf Charities offers free programs for medically fragile, special needs and disadvantaged children. The programs build self-esteem and are held in North Carolina, California, Nicaragua, and India. Indo Jax Surf Charities has also been featured by multiple media outlets including TedX Talks and American Way Magazine.
SUP Magazine reports The Carolina Cup's 13.2-mile Graveyard Race was elevated to 7-Star status - the highest ranking and one of only three races in the world to attain the lucky-7. The Cup has also been added as the 2nd stop on the World Paddle Association's World SUP Tour 2017.
Country Living named Wrightsville Beach one of the 20 Most Magical Island Getaways in America.
USA TODAY featured the Blockade Runner Beach Resort as one of the Best Beach Resort Kids' Clubs in the country for its Sandcampers kids' club held during summer months offering crafts, games, and activities.
Wrightsville Beach was named the Pioneer in East Coast Surfing and the birthplace of surfing in North Carolina for its early surfing activity beginning in 1909. Check out all of the places to hang 10 with these great schools and surf camps on your visit.
TripAdvisor.com listed Wrightsville Beach as one of 14 Beautiful Little Beach Towns in the U.S. for its clear water, clean sand, charming restaurants, fantastic surf and the Wrightsville Beach Museum of History.
Top Value Reviews featured Wrightsville Beach on the list of 30 Great Small Beach Towns on the East Coast.
National Geographic named Wrightsville Beach among the Last Best American Beach Towns, boasting its great seafood, calming marshlands, ample fishing, unspoiled nature, and nightlife.
National Geographic named Wrightsville Beach one of the World's 20 Best Surf Towns, saying "It's a great surf town for two main reasons—attitude and access."
Outside Magazine named Wrightsville Beach one of the top 7 Stateside SUP Hubs.
Men's Journal named Wrightsville Beach North Carolina's most naturally gifted water sport hub.
Coastal Living magazine included Wrightsville Beach and Wrightsville Beach Surf Camp among its list of Best Summer Beach Vacations.
FoxNews.com ranked Wrightsville Beach #8 among its list of Worthwhile Beaches 20 Minutes from the Tarmac, citing Wilmington International Airport only 10 miles from the beach.
Men's Journal included Wrightsville Beach among its roundup of Summer Hot Spots that highlight "the five best places to ride a wave, spike a volleyball, or paddle into the blue."
SurfCollectiveNYC.com named Annex Surf Supply in Wrightsville Beach among its list of 22 Best Surf Shops in the World.


Writing menus can be a lot of fun for chefs. It's very exciting seeing your dishes listed in print: and hugely rewarding. But it's all too easy to forget that the dishes must have the right price tag in order to enable them to make the best profit margins. Having a well-thought through Menu Pricing Strategy is vital for success. No profit margins means no business.
A successful and sustainable restaurant business is based on sound knowledge of food costs and gross profit percentage targets. Costing and pricing every dish on your menu isn't an option, it's a fundamental necessity. Chefs who just multiply the price of their main ingredient in any given dish by four or five times are only in the business of guessing: and they tread a fine line between business success and failure.
Know your market You need to know who both your existing and potential target customers are. Look at what your product offering is and what customer base it is attracting/going to attract. Ask yourself: are you an everyday dining restaurant or a special occasion restaurant? What will your customers really fork out for each dish? – the latter will vary according to many factors eg whether you're in the town or the country, how sophisticated and professional your food looks and front-of-house service is, even what your restaurant decor is.
Know your competitors It's vital that you are aware of your real competitors. These are not just the restaurants or hotels in a few miles radius of your own business; rather they are the establishments that are attracting the type of customers you want to entice into your own restaurant. You need to clock what they offer on their menus and how much they are charging. Drawing up a simple competitor matrix to allow you to analyse this in one sheet is a good idea.
Decide if you need to be more expensive There is nothing wrong with being more expensive than your competitors, as long as you can justify it. Serve a quality product that is presented well and you can often justify a more expensive price tag than your competitors.
Be wary of rigid food cost percentages Not every dish needs to achieve your budgeted food cost percentage. Don't get caught up with achieving percentage margins rather than profit. When costing your dishes look at how much profit you make on each dish in real money terms. Sometimes higher cost dishes with worse food cost margins deliver the most profit. "You can't take a percentage to the bank!". Read our article on Menu Engineering to find out more about how to analyse this.
Cost EVERY dish Write a detailed recipe for every dish on your menu and then cost it. This will give you a much better chance of making a profit. This also includes Banqueting and room service if you offer it. The benefit if writing out every dish also means that you have a better chance of achieving a consistent dish, meaning that your customers are likely to return time and time again when a favourite dish is likely to be made to the same standards and recipe each time.
Be consistent When pricing your menu, be consistent in how you round-off a dish cost. Either charge the straight pound rate (£4, £6, £12 etc) across the menu: or use 50p or 99p increments it looks neater and surveys have shown that customers prefer it.
Avoid too many supplements Try not to have too many add-on charges ie supplement, pa (price on application), or sp (seasonal price) on your menus. Customers will soon get fed up.
Spread your more expensive dishes across the menu Avoid bunching all your expensive dishes together – and put some of your cheaper dishes at the top left and right hand sides of the menu, as this is where customers start to read it from. Their decision as to whether or not you are too expensive for them will be made very quickly – either online or outside your restaurant (if you display your menu in the window or on a stand at the entrance).
Consider set menu prices Offering a two or three course set price menu – especially for lunch – is a good customer enticement as it enables them to predict their spend (albeit exclusive of extras like wine) before they even step into the restaurant.
Don't be too cheap Do not under price your food just to make the restaurant busy. You don't want to be a "busy fool" working very hard for no return. Look at all your running costs but remember it's normal that the food, beverage and payroll costs, added together, can make up 60-70% of restaurant costs.
Don't be too expensive Pricing yourself out of the market is another common mistake. Try to calculate your food cost anywhere between 26%-30% for a restaurant, 18%-25% for banqueting/functions. It's also useful to ask your teams what they think of the prices before going to print.
Get front-of-house to up-sell Dishes that deliver great margins/profit should be up-sold by your service team. They should, if asked, bring the customer's attention to the dishes, or, enquire if the customer needs any information about the menu and then direct them towards the dishes in question – talking about the produce sourcing or seasonality is a good way to demonstrate this. Suggestive selling works – but it must never be aggressive selling as this will soon lose you customers. Let everyone in the business know what margins and profit you make on each dish so they know which ones to push. Again, Menu Engineering will help you to make calculated decisions about which dishes boost your profits so you can share this insight with the sales team.
Is this the first time you have eaten here?
Was there anything that you think we could do to improve our service or food?
We really appreciate any guest feedback – was there anything you felt we could improve on?
Kitchen CUT is a unique F&B Costing tool which allows you to track, monitor and manage your dish costs and ingredient prices. Sign up now for a free 30 day trial, to see why businesses in over 45 countries are choosing Kitchen CUT.


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BCN Events & Crawls»Attractions»Parc de Montjuic | Cactus Gardens
Parc de Montjuic | Cactus Gardens
Barcelona Cactus Gardens.Mossèn Costa i Llobera Gardens. Els Jardins de Mossèn Costa i Llobera. The cactus garden on Montjuic is located on the steep side of Montjuic hill facing the sea and below the Miramar esplanade on an area called "el Morrot." The gardens are named after Mallorcan poet and priest Miquel Costa i Llobera and has an impressive collections of cacti from all over the world considered as the most important in the succulent plant world. The cactus garden reopened in 2011 after 5 years of renovation. The gardens were created in 1970 in an old quarry filled with earth from old military fortifications. The park entrance is on Plaça de l'Armada at south end of Miramar esplanade and hotel.
The garden is home to an important collection of Cactaceae, palms, Euphorbiaceous and other families of succulents coming from warm and tropical climates.
Just at the starting of the route, you can see an African fig tree and a Mexican fan palm. At the foot of Montjuïc, at Carretera de Miramar, there is an important group of Mexican fan palms; that plantation, unique in Barcelona, goes back to the 1960s and was planned to be integrated into the arid landscape of the Eastern side of Montjuïc. Mexican fan palm such as the Agave salmiana var. ferox , the Indian fig, the golden torch and the Caracus wigandia are from American origin.
Further on, the path splits up into three. Along the central path you can see the tree aeonium, a small Crassulaceae bush, and the resin spurge, a big fleshy plant that, although it looks like a cactus, it is not. The word cactus is commonly used to refer to any plant with fleshy stem, especially if prickly, but it should be kept for species of the Cactaceae family. The route continues to Mirador de la Puntaire, which has its name because of the sculpture La puntaire (The lacemaker), by Josep Viladomat. From this point, you can enjoy an amazing sight over the harbour of Barcelona and the cliff El Morrot, on the Southern Western side of Montjuïc. El Morrot is a rough area with very steep slopes coming from old quarries (the stone exploitation was alive until mid 20th c.) and colonised by Mediterranean and foreign vegetation. This vegetation has a big biological value, because it is the habitat of several birds, among which the kestrels.
Most of the vegetation in this garden are exotic species making it one of its main appeals, but there are also Mediterranean trees (pomegranate) that coexist harmoniously with Australian trees (Australian flame tree) and American trees (queen palm and sandpaper sotol, that lives almost without irrigation). In spite of the different origins, one common characteristic to some of the plants in this part of the route is, precisely, their resistance to drought conditions and poor soils: the chilayo, cactus from semidesert areas; the carob, tough tanks to its deep roots; the littleleaf fig, also found in gullies; the dwarf fan palm, one of the two only European native palms; the false agave, characteristic from rocky arid calcareous terrains. Many of these plants, as the elephant's ear, bear badly low temperatures and frosts.
Further on at the route, you can see a palm, the Bermuda palmetto, a giant yucca, a dragon tree (a tree considered holly by the ancient Guanches) and a Namibian grape, as well as a blue fan palm, very ornamental.
The central square of the garden, a very appealing spot, mesmerizes us to desert landscapes. There can be seen good sized succulent plants, with special colours and shapes and spectacular flowerings: Alluaudia ascendens, Cylindropuntia tunicata, silver torch, candelabra tree, orange apple cactus.
The route finishes on the top of the stairs, on the access gate located at the gardens of Miramar, beginning of the next route.


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Q: SharePoint Azure over internet We are working on our SharePoint 2013 Azure internal sites to make internet accessible. Here are the steps performed:

*

*Assigned a public IP and created DNS entry. Host name is getting resolved to public IP on performing nslookup.

*Extended the existing web application to internet zone and IIS web site is available for extended web application.

*Created CSR and successfully installed SSL certificate provided by the vendor. Binding has been also completed from IIS.

*AAM has been completed.

*Our WFE VMs have virtual IP and internal IP. Do I need to create a
DNS entry for my domain which I am trying to access mapped to
virtual IP of the server?

*I can see an load balanced HTTPS end point has been created on Azure
Portal with protocol as TCP and 443 as both internal and external
port but in Access Control List I can see action as "Deny". Do I need to change it to permit ?

*What we have done is we have added a DNS entry for our domain and IP
mapped to one of the reserve IP address (not virtual IP of any of the
WFE servers). Is this maybe the issue?

When I am trying to access SharePoint site from internet, I am not able to access and getting "Page cant be displayed" error.
We are not still not able to access the site on the internet. When we are doing a tracert to the host name, after some hops we are getting "Request Time Out".
On IE we are getting a "This page cant be displayed" error. From fiddler we are getting a "502:Connection Failed" error. I am not sure what and where could be the error.
Is any change is required at load balancer or IIS?