Although we rented a car in Cyprus and could easily move around, we agreed for a guided bus tour and did not regret it afterwards. The bus tour in English covering Famagusta cultural center, Lisa's grove orange farm and donkey farm lasted from 10.00 to 13.00 and cost only 5 euros – an incredible price for 3 hours of tour by bus with a guide. The tour was provided by Cyprus Tourist Organization, we booked it in Paralimni tourist information center, and took a bus in Agia Napa (excursions start from McDonalds almost every day at 10.00). At first, we were a bit sceptical: all the passengers were pensioners, and we were the only two young people. But eventually it turned out that the tour can cater all interests.
The guide Olga told a lot about Agia Napa and surroundings. Agia Napa is translated from Greek as "holy forest", and it received its name due to the holy icon as if found here; the monastery which arose to keep the icon. The monastery was built around the spring on the expenses of the aristocratic young lady. The lady had been in love with a poor man, it had been impossible for them to be together, so she preferred to be a nun and her family could afford building a monastery for it. Her grave can still be found next to the fountain in the center of the monastery yard.
Agia Napa used to be a fishing village: it has so many stones in its soil that agriculture was not quite possible. When the owner of Agia Napa tavern Vassos once mentioned that they might make a resort out of the village, everybody laughed at him. Agia Napa was just next to Famagusta, the most vibrant resort in Cyprus, and could not compete with it in infrastructure. However, in just several years, Famagusta got occupied by Turks, and Agia Napa substituted it. Fishermen became millionaires: their previously useless houses became extremely expensive.
The story of Famagusta is told very well in the Famagusta cultural center built next to the current Turkish border. They show a film about the tragedy.
After the Turkish occupation, every 3rd dweller in Famagusta became a refugee, they lost their houses and all other properties. They had to move to Southern Cyprus and start from a scratch here.
In addition to the movie, you may see actual Famagusta from the upper level of the cultural center: Turkish flags, deserted houses, and what was previously a great beach.
The next stop was at Lisa Psalti citrus orchard. For 2 euros, you receive a plastic bag, into which you may collect oranges. There are several kinds of them, and there are lemons as well, so this is up to you what to collect.
The oranges are very sweet and juicy, so make sure you buy a juice press or borrow it from your hotel. Later in Cyprus we noticed that oranges grow everywhere, and nobody really wants them. We also bought excellent strawberries, only 2 euros per kilo, and there are many jams and other goods to purchase here in addition.
This last stop was the best. Donkey is a symbol of Cyprus, and this is why there are quite some donkey farms on the island. Did you know that donkeys outlive horses twice: while horses live for 20 years, donkeys can live for 35-40 years? The reason might be that donkeys are so much calmer than horses: not stressing out about everything might help 🙂 Also, donkeys cannot swim, and they are really afraid of water: even a paddle can be an obstacle for them.
At the farm, there are several enclosures for donkeys and other animals, and the farm is more like a park: you can walk around it and pet almost all of the animals.
This is how three hours passed. We really enjoyed the tour although we are not big fans of organized excursions. There is, however, even more to see in Agia Napa and around as well as in Kavo Gkreko.


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text:
Q: Calculating amount of work done in gym workouts I am trying to figure out how to calculate the amount of work done for two people of differing sizes (160lb man which is me and 200lb man) in reference to varying exercises we do in the gym.
All this to see which person is in fact doing more workload per pound.  I have ideas, but don't know where to start.
For example, if he and I do a clean and press workout at 50% of body weight and both do the same amount of reps in one minute, did we both do equal work?
Additionally, if we both do box jumps, and I do 25 of them at 20 inches high, and he does 20 of them at 20 inches high, same amount of time, are we doing the same work?
Third, pull-ups.  If I do 20 pull ups (160lb man) and he does 16 (200lb man), is that the same amount of work, assuming same time they are done in?
Last of all, running.  How in the world can we determine who is doing more work when calculating one mile run times?  Any help would be appreciated, as I didn't study this in school.  It is very intriguing to us to get the science of this so we can determine who is in fact does more work in each exercise.

A: "Work" in physics and "effort" are very different things. Work is a very useful notion in fundamental physics, but not at all a useful notion in human motion! The heavier person in all of your examples will be doing more mechanical work, even if they both put the same amount of mental effort in. If they both lifted a 50lb weight, they would do the same amount of mechanical work on the weight, but depending on the biomechanics of it the heavier person would probably still burn more calories! It's complicated and isn't well described by simple mechanics concepts.
Your running example is a good one. Fundamental physics tells us that it is possible to travel a mile, so long as the height doesn't change, while doing 0 (or almost 0) work. Yet the human body burns ~100 food calories (=100 kilocalories) in running a mile! We're limited by the engineering of our body, not by physics, so the physics laws don't really apply.
Another example highlighting the absurdity of some things: say you lift ten 700lb weights, and put them each on shelves six feet in the air. Totally superhuman, but how much work have you done? Fundamental physics tells you that the energy done is 10 * (700 pounds) * (9.81 meters/second^2) * (6 feet). Plugging this in to wolframalpha, we see you've expended about 14 food calories of energy (14 kilocalories). That's about the energy in a potato chip.
These are just the limits imposed by fundamental physics. It tells you that any lifting machine must spend at least 14 kcal of energy to lift those weights. It tells you that you can spend as little energy as you want travelling a mile. How to actually achieve those things is a matter of engineering!

A: You can make a rough comparison of who is doing more work (as defined by physics) in a particular exercise by using the formula : work done = weight lifted x distance. This does not tell you who is burning more calories during the exercise, which depends on how efficiently you are using energy. To do that you need to measure how much oxygen is being used.
If the exercise depends on raising different weights through the same height then the person lifting the greater weight is doing more mechanical work. This clearly applies to the clean and press and pull ups. The person who does more repetitions does proportionally more work.
It also applies to running and box jumps, during which you are raising and lowering your body slightly. If you are approximately the same height then you are raising your bodies through the same distance with each step or jump. If you run the same distance you probably take the same number of steps, so you do the same number of repetitions. Again, the heavier person does more work.
The time which the exercises take does not affect the work done. If you do the same work in a quicker time (or more work in the same time), you are more powerful. That is a different comparison, and may not give you the same answer. For example, your friend may lift 200lb three times in a minute, while you lift 100lb seven times a minute. Your friend does more work on each lift, but you do more work in the same amount of time, so you are more powerful. However, this may not be a fair comparison : your friend may lift 100lb eight times per minute.
Deciding "who is fitter" is not the same as deciding who is doing more mechanical work, or even who is doing it more quickly. Comparison between different exercises is not easy.

A: If you're after the simple physics answer, and in the interest of keeping it simple, let's use the formula for work.  Work = Force x Distance.  Force = Mass x Acceleration (which we use as gravity's acceleration that we are overcoming.  So for each exercise (and I have to convert to metric):
First Assumptions (not too practical but not going down a rabbit hole)

*

*Each rep takes the weight or body 1 meter in distance.  So a pull-up from bottom to top is one meter traveled. Also you're going to jump on a one meter box. You are the same height and your cleans are moving the weight one meter

*The first rep and last rep are done at same speed.  Each rep takes one second. So for Force we will simply use mass x acceleration ( Zero to 1G = 1)  So again you weight 70kg x 1 = 70 Newtons.

OK Cleans
You: 50% x 70 Newtons = 35N x 1 meter x 10 reps = 350 joules
Him  50% x 90 Newtons = 45N x 1 meter x 10 reps = 450 joules
(divide by kg of body weight if wish)
Box Jumps
You: 70N x 1 meter x 25 reps = 1750 joules
Him: 90N x 1 meter x 20 reps = 1800 joules
Pull Ups
You: 70N x 1 meter x 20 reps = 1400 joules
Him: 90N x 1 meter x 16 reps = 1440 joules
So he is always doing more work but you more work per kg of bodyweight.

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One of the biggest changes resulting from the new tax law signed in December 2017 is a severe limit imposed by the Republican-controlled Congress on state and local tax (SALT) deductions. Under the previous law, these deductions were unlimited for individuals and families. The limit now is set at $10,000 per tax return. For example, Fred is single and owes $6,000 for state income tax and $6,000 for local property tax. For 2017 he was entitled to deduct $12,000, but for 2018 his deduction is limited to $10,000.
This change will hit taxpayers hardest in the six states where SALT deductions, as a percentage of income, are highest: New York, New Jersey, Connecticut, California, Maryland, and Oregon. Because these are states that lean heavily blue, and this new tax law is Republican legislation with almost no support from Democrats, it is easy to argue that this is not a coincidence — i.e. that "Red State" Republicans found a way to punish "Blue State" Democrats.
The new limit on SALT deductions will harm married couples who file jointly more than it harms singles, as the $10,000 limit is per tax return and not per person. Married couples can file separate returns, but according to the new tax law, each spouse would only qualify for $5,000 in state and local tax deductions. To qualify for two $10,000 deductions, the couple would have to divorce.
Beyond the broad-reaching limit on SALT deductions, which will affect taxpayers across various income brackets even outside those six states, Congress also eliminated deductions for miscellaneous expenses often incurred by high-income taxpayers. Those eliminated include unreimbursed employee expenses for travel, meals, and entertainment; union dues; subscriptions; safe deposit box fees; tax preparation fees; and investment advisory fees. Qualifying for the miscellaneous expense deductions was never easy for most taxpayers because total eligible expenses had to exceed 2% of income. However, the elimination of the miscellaneous expense deduction does hurt many taxpayers with high professional fee expenses.


"If he knew it was going to be as bad as it was going to be, he probably would have went somewhere else."
HIS 6-YEAR-OLD GRANDSON, RIPPED FROM HIS FATHER'S ARMS AND KILLED DURING SUNDAY'S TORNADO OUTBREAK, THE YOUNGEST OF 23 VICTIMS.
"You know, when you lose a grandson, it's very hard.
IN THIS SMALL COMMUNITY OF BEAUREGARD, ALABAMA, THERE'S ONLY ONE SHELTER INSIDE A CHURCH.
"You know, the drive from here to Providence is probably ten minutes at the most, but you know, but that ten minutes you know, could take somebody's life."
LOCAL OFFICIALS WERE IN THE PLANNING PHASE FOR A COMMUNITY SHELTER, BUT THE PLANS WERE STILL COMING TOGETHER WHEN THE TORNADO HIT.
AMONG THE CHALLENGES, HAVING ENOUGH PUBLIC AND PRIVATE SHELTERS TO HELP AN UNINCORPORATED AREA OF ROUGHLY 11,000 PEOPLE SPREAD OUT ALONG COUNTY HIGHWAYS AND DIRT ROADS.
"I don't think anybody should be faulted for not building anything or doing anything."
"What I really think we need to be looking at in the long term, is trying to figure out ways so that when they, they can build a shelter in."
"If we rebuild we'll probably put in a safe room or something like that. "
THOMAS AND TRACY SHIPP SURVIVED THE STORM SHELTERING IN A BATHROOM.
UPSOUND (English) "About as quick as it started, it left."
HE SAYS HE WOULDN'T HAVE HAD TIME TO GET TO A SAFE PLACE OUTSIDE OF HIS HOME.
Shipp: "Oh, we wouldn't of had time."
Reporter: "You wouldn't of had time?"
Shipp: "Uh uh, by the time you knew what was going on, if you'd a had to go a mile or two up the road you wouldn't of had time."
UPSOUND (English) "Time will heal everything."
BUT THIS ONE GRANDFATHER, WHO LOST HIS GRANDSON, SAYS THE CURRENT SITUATION IS UNACCEPTABLE.
"You know I'm not going to say if there had been more locations for people to go to, that lives wouldn't have been lost. But, you know,we only have one location and you know, we really do need more."
FEDERAL GRANT MONEY HELPED FUND THE CONSTRUCTION OF HUNDREDS OF SHELTERS AFTER A DEADLY TORNADO OUTBREAK IN 2011.
PEOPLE IN THIS DEVASTATED COMMUNITY HOPE MORE SHELTERS WILL SOMEDAY SAVE LIVES.


text:
UAL Research Online
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Silence Does Not Exist
UAL Research Centre
Voegelin, Salomé (2022) Silence Does Not Exist. In: The Concert. Sternberg Press, Switzerland, pp. 111-133. ISBN 9781501367625
Type of Research:
Voegelin, Salomé
The Concert: Catalogue of the Swiss Pavilion, 59th International Art Exhibition – La Biennale di Venezia 2022
Foreword by MADELEINE SCHUPPLI
With contributions by ALEXANDRE BABEL, FRANÇOIS J. BONNET, RAPHAËL BRUNNER, ANTOINE CHESSEX, ALVIN CURRAN, LATIFA ECHAKHCH, MAXIME GUITTON, EMANUELE QUINZ, JONATHAN STERNE, FRANCESCO STOCCHI, SALOMÉ VOEGELIN, JULIETTE VOLCLER
A lifelong relation to sound and music underlies Latifa Echakhch's work. On the occasion of her representation of the Swiss Pavilion for the 59th Venice Biennale, she has edited a volume on sound, memory, and perception. In the book, images of her installation in the Swiss Pavilion, The Concert, accompany writings by the artist and by Alexandre Babel and Francesco Stocchi, the co-curators of the pavilion. The volume also includes interviews with and collected texts by François J. Bonnet, Emanuele Quinz, Maxime Guitton, Alvin Curran, Salomé Voegelin, Antoine Chessex, Jonathan Sterne, Juliette Volcler, and Raphaël Brunner. Confronting knowledge, reflection, and intuition, their combined concert of thoughts confirms how sound and music—and their absence—play a crucial role in our physical and cultural perception of the world, and how they allow us to expand our bodily and cognitive experience.
This book is one of the three parts of the Swiss Pavilion; the other two are the installation and a vinyl edition of the piece composed by Alexandre Babel.
https://www.sternberg-press.com/product/the-concert/
Keywords/subjects not otherwise listed:
Colonialism, Decoloniality, Silence, Botanic Garden
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Research Centres/Networks > Creative Research into Sound Arts Practice (CRiSAP)
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text:
Mike Pence prevails in email secrecy suit
Fatima Hussein
An Indiana Appeals Court sided with Vice President-elect Mike Pence in ruling that an Indiana attorney does not have the right to view a political white paper that was included in a 2014 public records request.
The court, however, did not relinquish its power to second-guess the executive branch on matters of the Indiana Access to Public Records Acts.
That was an important finding because advocates of government transparency feared a Pence victory in the suit could set a broader precedent that would embolden future governors to refuse to disclose or heavily redact public documents with no court oversight.
What's Mike Pence hiding in his emails?
Judge Edward W. Najam, in a 41-page opinion issued Monday, affirmed the merits of the Governor's decision to withhold the white paper from public disclosure.
Najam added, however, "the Governor contends that his 'own determinations' under APRA are conclusive and that it would violate the separation of powers doctrine for the judiciary to 'second guess' those determinations."
"We cannot agree."
In other words, the opinion concluded that a governor's decision to deny a public records request can be reviewed by the court.
The plaintiff, Indianapolis attorney William Groth, is considering taking his case to the state's Supreme Court.
The white paper in question contains legal theories in contemplation of litigation that was used by the Governor in his decision to join State of Texas et al v. United States of America, which challenged a presidential executive order president Barack Obama issued regarding immigration.
Groth filed a request under the Indiana Access to Public Records Act seeking the documents related to the state's decision to hire Barnes & Thornburg LLP as outside counsel in the suit.
In the 2-1 appellate court decision, Najam wrote that the white paper "is exactly the type of record that may be excluded from public access under APRA."
"This case is not a challenge to the Governor's core executive functions or his constitutional authority" but is "merely for access to public records that concern a matter of legitimate public interest."
Chief Judge Nancy Vaidik concurred in part but ultimately dissented because she disagreed with the majority's conclusion that Pence "has met his burden of showing that the white paper is not subject to disclosure."
"I believe that Governor Pence has not met his burden of showing that the white paper is protected from disclosure under APRA," she wrote. "I would therefore reverse the trial court on this issue and order Governor Pence to produce the white paper."
How the case came about
In December 2014, Groth requested information regarding Pence's decision to hire outside counsel for the immigration litigation and its cost to Indiana taxpayers.
"I think joining the lawsuit without the attorney general and hiring that firm was a waste of taxpayer dollars and the people have the right to know how much of their money was spent," Groth told IndyStar in November. Groth is known in Indiana for representing the plaintiffs in the 2008 U.S. Supreme Court voter identification case Crawford v. Marion County Election Board.
Pence produced the documents in the request "but those documents included substantial redaction," according to court documents.
The 57-page response also included an email that Daniel Hodge, Texas Gov. Greg Abbott's chief of staff, sent to 30 recipients in various states asking them to join the lawsuit against Obama.
The message included an attached white paper, but the governor failed to produce the document, according to court records.
The Superior Court held that the issue was not a matter for the courts to decide, citing an Indiana Supreme Court case decided just days before.
In a 4-1 ruling, the Indiana Supreme Court ruled in Citizens Action Coalition, et al. v. Indiana House Rep., that under the Indiana Constitution's separation of powers clause, the legislature's redactions were nonjusticiable, a legal term that means not for the court to decide. Groth was also the attorney representing the plaintiffs in that case.
"We hold that, on these facts, Citizens Action Coalition does not apply to the request for public records directed to the Governor," Najam said in the appellate decision.
Groth appealed the decision handed down by Marion Superior Court in April, which decided that redactions the administration made to a public record could not be second-guessed by the court.
Taking the case to the Supreme Court
Groth told IndyStar that he is overall pleased with the determination made by the appellate court– specifically regarding the justicability ruling.
"The court of appeals rejected Governor Pence's attempt to expand the nonjusticiability ruling in Citizen's Action."
"That was the principle reason we appealed the trial court's ruling — because Governor Pence argued that all of his emails should be off limits under the doctrine of separation of powers."
Groth has 30 days to file an appeal with the Indiana Supreme Court.
"There are pros and cons to filing with the Supreme Court," he said. "At this point we will take our time to determine our next move."
Call IndyStar reporter Fatima Hussein at (317) 444-6209. Follow her on Twitter: @fatimathefatima.


text:
Uma paraphygas est une espèce de sauriens de la famille des Phrynosomatidae.

Répartition
Cette espèce est endémique du Mexique. Elle se rencontre dans le Coahuila et le Chihuahua.

Publication originale
 Williams, Chrapliwy & Smith, 1959 : A new fringe-footed lizard (Uma) from Mexico. Transactions of the Kansas Academy of Science, , , .

Liens externes

Notes et références

Saurien (nom scientifique)
Phrynosomatidae
Faune endémique du Mexique

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}

There are several reasons that make it desirable to improve mathematical tools
used in the nonlocal theory of highly singular quantum fields with an
exponential or faster high-energy behaviour. First of all string theory gives us
new indications [1-3] that the concept of space-time manifold is only
approximate and valid at length scales coarser than the Planck scale. Certainly,
one or another kind of nonlocality arises at any attempt to unify quantum
gravity with other fundamental interactions, however it is of great interest
that just the exponential growth is characteristic of the spectral densities
which occur in the K\"{a}llen-Lehmann representations for string propagators
with pointlike boundary conditions [4,5]. A second reason concerns the problem
of formulating causality which is crucial for any nonlocal theory. Recall
that the exponential bound on the off-mass-shell amplitudes has been found
by Meiman [6] just from the microcausality considerations. For faster
momentum-space growth, no definite criterion of macrocausality in terms of
observables has been obtained as yet. However a mathematical analog of local
commutativity has been found which ensures a number of important physical
consequences for arbitrary high-energy behaviour. These include the existence
of the unitary scattering matrix [7] and the polynomial boundedness of the
scattering amplitudes within the physical region of variables [8,9]. It is
surprising enough that the connection between spin and statistics and the
$TCP$-invariance derived previously [10-12] for quasilocal fields can also be
established [13-15] in the essentially nonlocalizable case when the holomorphy
domain of vacuum expectation values becomes empty and radically new proofs
are needed. Thirdly, the use of highly singular nonlocal form-factors [16]
turns out to be effective for a phonomenological description of strong
interactions [17-18].

The main purpose of the present paper is a more precise formulation of the
above-mentioned generalization of the local commutativity condition. This is
accomplished by adopting two ideas of the Sato-Martineau theory of
hyperfunctions which can briefly be named complexification and compactification
of space-time. This enables one to simplify significantly the mathematical
techniques used in the papers devoted to nonlocal quantum fields and develop
a convenient functional calculus effective beyond the theory of hyperfunctions [19].

The work is organized as follows. In Sec.2, we redefine in terms of complex
variables the Gelfand-Shilov test function spaces that used in the nonlocal
quantum field theory. In Secs.3 and 4 the key notions of a carrier-cone and
support cone are introduced for nonlocalizable distributions. The proof of
the existence of the support cones leads naturally to an asymptotic
commutativity condition formulated in Sec.5 as a fall-off property of the
field commutator in the spacelike directions. As an application,
generalization of the Paley-Wiener-Schwartz theorem to the nonlocalizable
case is presented in Sec.6. In Sec.7, a new derivation of the K\"{a}llen-Lehmann
representation for propagators of open and closed strings is proposed. It is
essential that this derivation is applicable to arbitrary initial and final
string configurations and shows the same character of causal and local
properties as that established in [4,5] under pointlike boundary conditions.
These considerations are somewhat heuristic and serve as a motivation and
background for the previous rigorous analysis. Sec.8 is devoted to concluding
remarks.

\section{Redefinition  of  the presheaf of Gelfand-Shilov \\ spaces}

In the framework of Wightman axiomatic approach [20], quantum fields are
treated as operator-valued distributions over the Schwartz space $S$. Wider
classes of quantum fields are obtained if $S$ is replaced by a dense subset
with a finer topology. For instance, the Jaffe strictly local fields [21],
whose vacuum expectation values are ultradistributions, are defined on the
Gelfand-Shilov spaces $S^\beta$, where $\beta >1$, with the
Schwartz space being roughly $S^\infty$ . The Meiman fields [6] are defined
on $S^1$ and correspond to hyperfunctions.  For still wider classes of
distributions the notion of support loses its sense and nonlocality comes into
play. The space $S^{1,b}$ is adequate to the exponential high-energy
behaviour characteristic of the quasilocal field theory investigated in
[8,10-12]. Although exactly this behaviour shows itself in string theories, we
wish to develop here a mathematical formalism covering so-called essentially
nonlocalizable fields defined on $S^\beta$ with $\beta <1$, which may be of
advantage in deriving the {\it TCP}-invariance and the connection between spin
and statistics by L\"{u}cke's method [13,14]. We recall [22] that $S^\beta$
consists of those complex valued infinitely differentiable functions that
satisfy the inequalities

$$
|x^{k} \partial ^q \varphi (x)|\/  \leq \/  C_{k}\/ b^{|q|}\/ q^{\beta q},
\eqno{(1)}
$$

\noindent
where $x\in {\bf R}^n$, the constants $C_k$ and $b$ depend on the function
$\varphi$; $k$ and $q$ are multi-indices, and the standard notation of the
theory of functions of several variables are used. Accordingly, $S^\beta$
can be made into a topological space by means of the projective limit $|k|
\rightarrow \infty$ and the inductive limit $b\rightarrow \infty$, proceeding
from the norms

$$
||\varphi||_{N,b}\/ =\sup_{|k|\leq N}{}_{x,q}\/
\frac{|x^{k}\partial^{q} \varphi(x)|}{b^{|q|}q^{\beta q}}
\eqno{(2)}
$$

\noindent
It perhaps should be noted that $\sup_{|k|\leq N}|x^k|$ can be replaced here
by $(1+|x|)^N$.  Besides $S^\beta$, it is advisable to use the spaces
$S^\beta (O)$, with $O$ an open set in  ${\bf R}^n$, which are defined in the
same manner but with $x\in O$ . Such a collection of spaces is customary
referred to as a presheaf. For $\beta <1$, every function belonging to
$S^\beta$  can be analytically continued into the whole of ${\bf C}^n$ as an
entire function whose order of growth less than or equal to $1/(1-\beta)$, see
[22]. We shall rewrite analogously the definition of $S^\beta (O)$ for
conelike domains $O$ which will play a leading role below. For this purpose, we
introduce one more functional space.

{\bf Theorem 1}. Let $U$ be an open connected cone in ${\bf R}^n$ and $d(x,U)$
be the distance from the point $x$ to $U$. For $\beta <1$, the space
$S^\beta (U)$ is isomorphic to the space $E^\beta (U)$ of entire functions
satisfying the inequalities

$$
|x^{k}  \varphi (x+i y)|\/ \leq \/  C_{k}\/  \exp \{\,  |by|^{\beta ^\prime
} +d(bx,U)^{\beta^\prime}\} \eqno{(3)}
$$

\noindent
where the designation $\beta^\prime = 1/(1-\beta)$  is used for brevity. (Note
that $\beta^\prime \geq 1$.)

{\sl Remark.\/} The choice of the norm in ${\bf R}^n$ is unessential here
because all these are equivalent and the inductive limit $b\rightarrow
\infty$ is implicit.  Furthermore $d(bx,U) = bd(x,U)$  since by a cone is meant
one with its vertex at the origin.

{\sl Proof.\/} Let us denote by $S^{\beta,b,N}(U)$ the Banach space with the
norm $\|\cdot\|_{U,N,b}$. Owing to the assumption $\beta <1$ the Taylor series
expansion of $\varphi \in S^{\beta,b,N}(U)$  is convergent for all $z\in {\bf
C}^n$ and since its center $\xi \in U$ can be taken arbitrarily, the
behaviour of the analytic continuation is estimated by

$$
\inf_{\xi \in U}\/ (1+|\xi|)^{-N} \sum_{q}b^{|q|} |(z-\xi )^{q}|q^{\beta q}/q!
\eqno{(4)}
$$

\noindent
We replace the sum by the supremum with a slightly greater $b$. An easy
evaluation shows that

$$
{\rm const}\cdot\exp\{|h^\prime z|^{\beta^\prime}\}\/  \leq \/
\sup_{q}|z^q|q^{\beta q}/q!\/ \leq \/ \exp\{|hz|^{\beta^\prime} \} \eqno{(5)}
$$

\noindent
where $|\cdot|$ is the Lebesque $l^{\beta^\prime}$-norm,
$h=e(e\beta^\prime)^{-1/\beta^\prime}$ and $h^\prime$ is arbitrarily near to
$h$.  The inequality  $|z|^{\beta^\prime}\leq
|2x|^{\beta^\prime}+|2y|^{\beta^\prime}$ enables the exponential be factorized.
Further, let $\xi_0$ be a point of $\overline{U}$ such that $d(x,U) =
|x-\xi_0|$ .  Then

$$
\inf_{\xi \in U}{}(1+|\xi|)^{-N} \exp \{\,  |x-\xi|^{\beta ^\prime } \}\/  \leq
\/  (1+|\xi_{0}|)^{-N} \exp \{ d(x,U)^{\beta ^\prime}\}
$$

\noindent
If $x\in U$, then $\xi_0 = x$ and $d(x,U) = 0$, whereas for the points $x$
whose distance to $U$ does not exceed some $\theta > 0$, we have $|\xi_0| \geq
(1-\theta)|x|$. For the remainder points, the inequality

$$
(1+|\xi_{0}|)^{-N} \leq \/   1\/ \leq C_{\varepsilon}\/  (1+|x|)^{-N} \exp \{
d(\varepsilon x,U)^{\beta ^\prime }\}
$$

\noindent
holds with arbitrarily small $\varepsilon >0$. Combining our estimates, we
see that $S^{\beta,b,N}(U)$ is continuously embedded into the Banach space
$E^{\beta,b^\prime,N}(U)$ of entire functions, with the norm

$$
\|\varphi\|_{U,N,b^\prime}^\prime=\/
\sup_{z}\, (1+|x|)^{N}\, |\varphi(z)|\exp\{-|b^\prime
y|^{\beta^\prime}-d(b^\prime x,U)^{\beta^\prime}\}, \eqno{(6)}
$$

\noindent
where $b^\prime>2hb$.

To prove the converse, let $\varphi \in E^{\beta,b,N}(U)$. Due to the
inequality

$$
1+|\xi|\leq (1+|x|)(1+|x-\xi|)
$$

\noindent
we have

$$
(1+|x|)^{-N}\, \exp \{d(b x,U)^{\beta ^\prime
}\}\/ \leq\,C_{N,b^\prime}\,\inf_{\xi \in U}(1+|x|)^{-N}\,\exp\{|b^\prime
(x-\xi)|^{\beta^\prime}\},
\eqno{(7)}
$$

\noindent
where $b^\prime$ is arbitrarily near
to b. Furthermore

$$
\exp\{\/ |x|^{\beta^\prime}+|y|^{\beta^\prime}
\}\/\leq\/\exp\{\/2\sum_{j}|z_{j}|^{\beta^\prime}\}
\eqno{(8)}
$$

\noindent
Let us fix $\xi \in U$ and apply the Cauchy formula for the polydisk

$$
D=\{z\in {\bf C}^n:\/ |z_j-\xi_j|\leq r_j\}.
$$

\noindent
Making use of (7), (8), we
obtain

\begin{align*}
(1+|\xi|)^{N}\,|\partial^{q}\varphi(\xi)|\,&=\,\frac{q!}{(2\pi)^n}
\left|\hspace{1mm} \int\limits_{\partial_{0}D} ^{}
\frac{(1+|\xi|)^{N}\varphi(z)\,dz}{(z-\xi)^{q+I}} \right| \/  \\
&\leq\/C_{N,b^\prime}\hspace{1mm} \|\varphi\|_{U,N,b}^\prime\hspace{1mm}
q!\hspace{1mm}r^{-q}\/\exp\{\/2\sum_{j}(b^\prime r_{j})^{\beta^\prime}\}
\end{align*}

\noindent
Now one can exploit the freedom in the choice of $r$ and take the lower bound,
which gives

$$
(1+|\xi|)^{N}\,|\partial^{q}\varphi(\xi)|\,\leq\,C_{N,b^\prime}\,
\|\varphi\|_{U,N,b}^\prime\hspace{1mm} q!\,(2b^\prime
e/h)^{|q|}\,q^{-q/\beta^\prime}.
$$

\noindent
Finally we use the Stirling formula and conclude that $E^{\beta,b,N}(U)$ is
continuously embedded into $S^{\beta,2b^\prime /h,N}(U)$. Taking the projective
and inductive limits completes the proof.

\section{Carrier cones}

Now we introduce test function spaces associated with closed cones in ${\bf
R}^n $.  Recall that by the projection of a cone is meant its intersection with
the unit sphere and that a cone $V$ is called a compact subcone of another cone
$U$ if $\overline{\mbox{pr}V} \subset \mbox{pr}U$ . Then the notation
$V\Subset U$ is commonly used. let $B$ be a ball in ${\bf R}^n$ centered about
the origin.  Given a closed cone $K$, we set

$$
S^\beta(K)\,=\,\lim_{\longrightarrow} S^\beta(U\cup B)
\eqno{(9)}$$

\noindent
where $U$ runs over open cones such that $K\Subset U$.

{\bf Definition 1}. Let $f\in (S^\beta)^\prime,\/ \beta<1$. A closed
cone $K\subset {\bf R}^n$ will be said to be a carrier cone of $f$ if this
linear form is continuous under the topology induced on $S^\beta$ by that of
$S^\beta(K)$.

Let us dwell on the motivation of this definition. For $\beta<1$, the space
$S^\beta(U\cup B)$ does not change with variations of the radius of the
ball $B$ whose role is only to provide connectedness. From the proof of Theorem
1, it is obvious that this space coincides with $E^\beta(U)$. It is
worthwhile to point out the particular case of the degenerate cone $K=\{0\}$.
Then $S^\beta(K)$ is identical to the space of entire functions satisfying
the bound (3) with $d(bx,U)$ replaced by $|bx|$ . The inductive limit (9) is
actually taken over special neighbourhoods of $K$ which can be regarded as
traces of the neighbourhoods of its closure in the radially compactified space
$\hat{{\bf R}}^n$. Using such a compactification, we follow to the paper [23]
where the local properties of the Fourier hyperfunctions was investigated. The
point is that for them there exist smallest carriers among compact sets in $\hat{{\bf R}}^n$,
while there are no minimal carriers in ${\bf R}^n$. We shall show that this
important fact holds true for distributions on $S^\beta$, $\beta<1$,
providing we restrict ourselves by those compact sets that are closures of
cones. It should be noted that there is a natural one-to-one correspondence
between the cones in ${\bf R}^n$ and the subsets of the compactifying sphere
and that the family of spaces $E^\beta(U)$ may be thought of as a presheaf
over this sphere which is really a sheaf in contrast to the initial
$S^\beta(O)$. Keeping this motivation at the back of our mind, we prefer to
say below about cones in ${\bf R}^n$ rather than about compact sets in $\hat{{\bf R}}^n$
 and
to use the customary designation $S^\beta(U)$ instead of $E^\beta(U)$ even
though we shall deal with the complex representation (3).

Definition 1 can be rewritten as a fall-off property of the distribution $f$
inside the complementary cone. To this end, we shall smooth $f$ by convolution
with test functions decreasing rapidly enough and we shall use one more
class of Gelfand-Shilov space, defining them in terms of complex variables
from the outset. Namely, the space $S_\alpha^\beta(U)$, where $\alpha >0,
\beta <1$, and $U$ is an open cone in ${\bf R}^n$, consists of all entire
functions with the property that

$$
|\varphi(z)|\,\leq\,C\,\exp\{\/|by|^{\beta^\prime}+d(bx,U)^{\beta^\prime}-
|x/a|^{1/\alpha}\}
\eqno{(10)}
$$
\noindent
Here the constants $a, b$, and $C$ depend on $\varphi$. Accordingly,
$S_\alpha^\beta (U)$ is equipped with the inductive limit topology by
$a,b\rightarrow \infty$. We recall [22], that this space is only nontrivial
provided $\alpha+\beta \geq 1$.

{\bf Theorem 2}. Let $f\in (S^\beta)^\prime$ and let $K$ be a carrier cone of
$f$. Suppose that $\varphi \in S_\alpha^\beta$. Then the convolution $(f\star
\varphi)(x)=(f(\xi),\/ \varphi(x-\xi))$ belongs to every space
$S_\alpha^\beta (C)$ with $C$ an open compact subcone of $\complement K$. Moreover
the mapping $S_\alpha^\beta \longrightarrow S_\alpha^\beta (C):\varphi
\longrightarrow f\star \varphi$ is continuous.

This theorem proven in [24] is valid for any $\beta \geq 0$, but here we
would like to present for $\beta \leq 1$ an alternative proof using the
isomorphism $S^\beta(K)=E^\beta(K)$. Let $\varphi \in S_{\alpha,a}^{\beta,b}$.
We proceed from the formula

$$
|(f\star\varphi)(z)|\,\leq\,\|f\|_{U,a^\prime,b^\prime}\,
\|\varphi(z-\zeta)\|_{U,a^\prime,b^\prime}
\eqno{(11)}
$$
\noindent
which holds for any $a^\prime, b^\prime$ and each cone
$U$ such that $K\Subset U$. By definition of the norms involved in (11), we
have

\begin{align*}
|\varphi(z-\zeta)\|_{U^\prime,a^\prime,b^\prime}\,&\leq\,\|\varphi\|_{a,b}
\sup_{\zeta=\xi+i \eta}\,\exp\{\/|b(y-\eta)|^{\beta^\prime}
-|(x-\xi)/a|^{1/\alpha} \\
&\qquad \qquad\qquad\qquad-|b^\prime y|^{\beta^\prime}-d(b^\prime
\xi,U)^{\beta^\prime}+|\xi/a^\prime|^{1/\alpha}\}.
 \end{align*}

\noindent
Let us show that if $a^\prime, b^\prime$ are sufficiently large and the cone $U$
is separated from $C$ by a nonzero angle distance, the right-hand side of this
inequality can be majorized by

$$
{\cal C}
\hspace{1mm}\|\varphi\|_{a,b}\,\exp\{\/|2by|^{\beta^\prime}+d(2b,C)^{\beta^\prime}
 -|\theta x/a|^{1/ \alpha}\}
\eqno{(12)}
$$
\noindent
In fact, in estimating the supremum over $\eta$ one can exploit convexity of
the function $|\cdot |^{\beta^\prime}$ and take $b^\prime \geq 2b$. In
considering the supremum over $\xi$, we assume at first that $x$ lies in the
cone $C_\theta=\{x:\/d(x,C)\leq \theta|x|\}$. If $\theta$ is small enough,
then

$$
|x-\xi|\,\geq\,2^\alpha\,\max(\/\theta |x|,\theta|\xi|\/) \hspace{5mm}
\mbox{ for all} \hspace{2mm}             x\in C_\theta,\,\xi\in U_\theta
$$
\noindent
and one can replace $|x-\xi|^{1/\alpha}$ by $|\theta x|^{1/\alpha}+|\theta
\xi|^{1/\alpha}$. For $\xi \bar{\in}U_\theta$, we have $|x/2|^{1/\alpha}\geq
|x-\xi|^{1/\alpha}+|\xi|^{1/\alpha}$ . Taking $a^\prime >a /\theta, b^\prime
> 2^\alpha/(a\theta)$, we reveal the decrease $\exp\{-|\theta
x/a|^{1/\alpha}\}$ within the cone $C_\theta$. If $x\bar{\in}C_\theta$, then
$|\varepsilon \xi|^{1/\alpha} \leq |x-\xi|^{1/\alpha}+|\varepsilon
x/(1-\varepsilon)|^{1/\alpha}$ as follows from the elementary inequality
$(\varepsilon u+(1-\varepsilon)v)^{1/\alpha} \leq u^{1/\alpha}+v^{1/\alpha}$
valid for positive $u, v$ due to the monotone behaviour of this function in
$\varepsilon \in [0,1]$. Choosing $\varepsilon$ and $a^\prime$ so that
$\varepsilon/(1-\varepsilon) < ab\theta,\theta^\prime>a/\varepsilon$, we obtain
a growth no faster than $\exp\{|b\theta x|^{1/\alpha}\}$ outside $C_\theta$.
It remains to notice that under the conditions $b>1/a, |x|>1/(b\theta)$ the
function equal to $-|\theta x/a|^{1/\alpha}$ on $C_\theta$ and $|b\theta
x|^{1/\alpha}$ elsewhere is bounded by the sum of the last two terms in the
exponent (12).

In particular, setting $\alpha=1-\beta$, we obtain

$$
|(f\star \varphi)(x)|\/\leq\/{\cal C}_{a,b}(C)\/
\|\varphi\|_{a,b}\,\exp\{-|\theta x/a|^{\beta^\prime}\} \hspace{5mm}  (x\in
C\Subset \complement K, \hspace{2mm}\varphi\in S_{\alpha,a}^{\beta,b}) \eqno{(13)}
$$

\noindent
This formula provides the basis for all the following study and makes evident
the meaning of the generalization of local commutativity presented in Sec.5.
In the next section, we shall show that this fall-off property is completely
equivalent to the fact that $f$ is carried by the cone $K$.

\section{Support cones}

{\bf Theorem 3}. Let $f\in (S^\beta)^\prime,0<\beta<1$, and let $K$ be a closed
cone in ${\bf R}^n$. Assume that for each cone $C\Subset \complement K$ there
exists a constant $\theta > 0$ such that the estimate (13) holds with any $a, b$.
Then $K$ is a carrier cone of $f$.

{\sl Proof.\/} We have to extend the linear form $f$ to every space.
$S^{\beta,b^\prime}(U)=\bigcap_N S^{\beta,b^\prime,N}(U)$ with $U$ an open cone
such that $K\Subset U$. The extension can be defined by the formula

$$
(\hat{f} ,\/\varphi)\/=\/\int (f(\zeta),\,\varphi_0(x-\zeta)\varphi(\zeta))\,
dx,
\eqno{(14)}
$$

\noindent
where $\varphi_0\in S_{1-\beta,a_0}^{\beta,b_0},\/\/ \int \varphi_0(x)\/ dx=1$
and $a_0$, $b_0$ will be chosen below. Let us denote the integrand by $J(x)$,
fix a cone $V$ so that $K\Subset V \Subset U$, and consider at first the
behaviour of $J(x)$ inside $V$. For each $b$, $N^\prime$ and some $N$ depending
on $b$,

$$
\begin{array}{c}
|J(x)|\/\leq\/\|f\|_{N,b}\hspace{1mm}\|\varphi_0(x-\zeta)
\varphi(\zeta)\|_{N,b}\,\leq\\    [9pt]
\leq\,\|f\|_{N,b}\hspace{1mm}\|\varphi_0\|_{a_0,b_0}\,
\|\varphi\|_{U,N^\prime,b^\prime}\,
\sup_{\xi,\eta}(1+|\xi|)^{N-N^\prime}\times  \\  [9pt]
\times \exp\{\/|b_0 \eta|^{\beta^\prime}
-|(x-\xi)/a_0|^{\beta^\prime}+|b^\prime \eta|^{\beta^\prime} + d(b^\prime
\xi,U)^{\beta^\prime} -|b\eta|^{\beta^\prime}\} \end{array} \eqno{(15)}
$$

\noindent
If $\xi \bar{\in} U$, we have $|x-\xi|^{\beta^\prime}\geq |\theta^\prime
x|^{\beta^\prime}+|\theta^\prime \xi|^{\beta^\prime}$ since the cone
 $\complement U$
is separated from $V$ by a nonzero angle distance. For $\xi \in U$, we use the
inequality $1+|x|\leq (1+|x-\xi|)(1+|\xi|)$. Choosing
$a_0<\theta^\prime/b^\prime$ and $b>2(b_0+b^\prime)$, we see that $J(x)$
decreases within $V$ faster than any inverse power of $|x|$. In estimating
this function outside $V$ we regard it as $f\star\chi_x$, where
$\chi_x(\zeta)=\varphi_0(\zeta)\varphi(x-\zeta)$, denote $\complement V$ by $C$ and
apply (13). This time we deal with the $S_{1-\beta,a}^{\beta,b}$-norm of
$\chi_x$ which involves

$$
\sup_{\xi}(1+|x-\xi|)^{-N^\prime}\,\exp\{-|\xi/a_0|^{\beta^\prime} +
d(b^\prime(x-\xi),U)^{\beta^\prime} + |\xi/a|^{\beta^\prime}\}.
\eqno{(16)}
$$

\noindent
(We do not write out the supremum over $\eta$, assuming $b$ subject to the
above condition.) Using the inequality $d(\cdot ,U)\leq |\cdot|$ and choosing
$a_0<1/(2b^\prime),a>2a_0$, we find that $\|\chi_x\|_{a,b}$ increases no faster
than $\exp\{|b^\prime x|^{\beta^\prime}\}$. Hence, if $a<\theta /b$, then
$J(x)$ decreases exponentially everywhere outside the cone $V$. Thus, the
integral (14) is convergent under the condition
$a_0<\min(\theta^\prime,\theta/2)/\beta^\prime$ and determines a linear form
on $S^{\beta,b^\prime}(U)$ whose continuity is ensured by the presence of the
factor $\|\varphi\|_{U,N^\prime,b^\prime}^\prime$ in our estimates. This
distribution coincides with the initial one, when restricted to $S^\beta$.
In fact, let $\varphi \in S^\beta$. Then the term $d(b^\prime\xi,U)$
is absent from (15) and this estimate shows that not only $J(x)$ but also the
function $(g(\zeta),\/ \varphi_0(x-\zeta)\varphi(\zeta))$ is integrable for
each $g\in(S^\beta)^\prime$. Therefore the sequence of Riemann sums
corresponding to the integral $\int \varphi_0(x-\zeta)\varphi(\zeta)\/ dx$ is
weakly fundamental in $S^\beta$ and, this space being Montel, converges in
its topology to some element which is of necessity $\varphi$. Now we recall
[22] that the space $S_{1-\beta,a}^{\beta,b}$ is only nontrivial provided
$ab\geq \gamma$ where $\gamma$ depends on $\beta$. Hence different
$\varphi_0$ occur in the formula (14) for different $b^\prime$ and we have to
make sure of consistency of all the extensions.

{\bf Lemma}. Let $U$ be an open cone in ${\bf R}^n$ and $0<\beta<1$ as
before. The space $S_{1-\beta}^\beta$ is dense in $S^\beta(U)$.

It perhaps should be recalled that we always add a ball $B$ to the cone to
ensure connectedness. Let $\varphi\in S^{\beta,b^\prime}(U)$ and let
$\varphi_0\in S_{1-\beta,a_0}^{\beta,b_0}$, where $a_0=1/(2b^\prime)$ and
$b_0=\gamma/a_0$. The estimate (16) with $\xi$ replaced by $x-\xi$ shows
that, for each $x$, the function $\varphi_0(x-\xi)\varphi(\xi)$ belongs
to $S_{1-\beta,a}^{\beta,b}$ with $a>1/b^\prime$ and $b>2(b_0+b^\prime)$.
The above-mentioned sequence of Riemann sums lies in this space too. Moreover it
is weakly fundamental in $S^{\beta,b}(U)$ as can be seen from a norm estimate
similar to (15). Hence it converges to $\varphi$ in the topology of every
space $S^{\beta,b_1}(U)$ with $b_1>b$ since their intersection is a Montel
space. This completes the proof of Theorem 3.

{\bf Corollary}. For each distribution $f$ defined on $S^\beta,\/ 0<\beta<1$,
there exist a smallest carrier cone which can be called the support cone of $f$.

{\sl Proof.\/} Let us denote by $K$ the intersection of all the carrier cones
and consider an open cone $C\Subset \complement K$. The complements of the carrier
cones form an open covering of $C$ from which one can choose a finite
subcovering. Slightly shrinking the cones involved in the latter, we obtain
covering cones where (13) is satisfied. Therefore this estimate holds everywhere
in $C$ with some nonzero $\theta$ and so $K$ is a carrier too.

\section{Asymptotic commutativity}

Now we are in a position to formulate the following.

{\bf Definition 2}. Let $\{A^{(\kappa)}\}$ be a finite or infinite set of
nonlocal quantum fields defined on the test function space $S^\beta({\bf
R}^n),\hspace{2mm} 0<\beta <1$, and transforming according to finite-dimensional
representations of the proper orthochronous Lorentz group . We say Lorentz
components $A_j^{(\kappa)}$ and $A_{j^\prime}^{(\kappa^\prime)}$ are
asymptotically (anti)commute if for each vectors $\Phi,\Psi$ from their common
domain in the Hilbert space, the distribution

$$f=\langle
\Phi,\/[A_j^{(\kappa)}(x),
 A_{j^\prime}^{(\kappa^\prime)}(x^\prime)]_{\stackrel{-}{(+)}} \Psi \rangle $$

\noindent
is carried by the cone $\overline {{\sf
V}}=\{(x,x^\prime):\/\/(x-x^\prime)^2\geq 0\}$ or, equivalently, fulfills the
condition (13) outside this cone. The principle of asymptotic commutativity
means that every two field components asymptotically commute or anticommute. We
assume that the type of this relation depends only on the type of the fields,
{\it i.e.\/}, on $\kappa,\kappa^\prime$.

It should be mentioned that the term "asymptotic commutativity" has been
introduced in Ref.[25] but with some other meaning. Namely, L\"{u}cke called
nonlocal tempered fields $A, A^\prime\hspace{2mm} \varphi$-asymptotically
commuting, where $\varphi \in S({\bf R}^n)$ and decreases rapidly enough, if
the function

$$
F(x)=\left\|\int d\xi\/ d\xi^\prime\/ [A(\xi),A^\prime(\xi^\prime)]\/
\varphi(x-\xi)\varphi(\xi)\/\Phi\right \|
$$

\noindent
has finite the
norm $\|F\|_{\lambda,\varepsilon}=\sup\{|F(x)|\exp(\varepsilon|x|):\/ |{\bf
x}|>\lambda x^0\}$  for all $\lambda,\varepsilon>1$. Generalizations of the
principle of local commutativity to fields breaking the Jaffe strict
localizability condition [21] were considered by several authors [6-18, 26-28].
A formulation exploiting the presheaves of Gelfand-Shilov spaces and the
requirement of continuity under an induced topology has been proposed in [26],
but there the main attention was paid to the conditions under which this
generalization keeps sense of microcausality. In [9], this approach was applied
to nonlocal fields and the triviality of $S_\alpha^\beta$ for $\alpha+\beta<1$
was interpreted is such a way that the functions belonging to $S^\beta$ enable
one to test the causal properties to an accuracy of
$\exp\{-|x-x^\prime|^{1/(1-\beta)}\}$. Theorems 2 and 3 confirm this view.
Closely related definitions have been proposed independently in [7,27].
B\"{u}mmerstede and L\"{u}cke [7] suggested to replace the local commutativity
by an axiom of "essential locality" which implies continuity of the field
commutator under the topology of $\displaystyle\lim_{\longrightarrow} S^\beta
\cap S^{\beta,b}({\sf V})\/ \/ (b\rightarrow \infty)$.  Constantinescu and
Taylor [27] introduced a classification of extensions of the field commutator
outside the light cone.  Namely, for a field $A$ on $S^{\beta_0}$, they defined
the order of the extension to be the greatest $\beta^\prime=1/(1-\beta)$ such
that all the distributions $\langle \Phi,\/ [A(x),A(x^\prime)]\Psi \rangle$ can
be extended to $S^\beta({\sf V})$. A comparison of these two formulations can be
found in [28]. The papers [7,9,26-28] proceeded from the definition (1), (2)
while Efimov [17] took advantage of the redefinition of $S^\beta$ in terms of
complex variables. The spaces (9) and the idea of compactification were used
neither in our or other above-mentioned papers. From the technical standpoint
the compactification procedure means taking an additional inductive limit over
conelike neighborhoods of ${\overline {\sf V}}$. It is worthwhile to point out
that the continuity under this topology is a weaker requirement than that of
continuity under the topology of $S^\beta({\sf V})$. It is the compactification
that enables one to derive Theorem 3, to establish the existence of support
cones and to prove the equivalence of the two versions of asymptotic
commutativity formulated as a support property and as a fall-off property of the
field commutator.

\section{Generalization of the Paley-Wiener-Schwartz \\ theorem}

It will be recalled that this theorem [29] relates the support properties of
tempered distributions to the growth properties of their Laplace transforms.
In [30], it has been extended to the ultradistributions defined on
$S_\alpha^\beta,\/ \/\beta >1$.  A generalization to the nonlocalizable
case $\beta < 1$ was also formulated there, but without a proof\footnote{The
case of Fourier hyperfunctions $\alpha=\beta=1$ had been considered by Kawai
[23].}. The results of Sec.4 enables us to present such a proof here. It is
worthwhile to note that this generalization, interesting by itself, is needed to
derive the connection between spin and statistics for nonlocalizable fields, see
[13,15].

{\bf Theorem 4}. Let $K$ be a closed convex cone in ${\bf R}^n$ which does not
contain a straight line, and let $V$ be the interior of its dual cone
$K^*=\{q:\/\/ qx\geq 0,x\in K\}$.  Suppose that $K$ is a carrier of $f\in
(S^\beta)^\prime,\/\/ 0<\beta<1$. Then for the distribution $f$ there exists a
Laplace transform $g(s) (s=p+i q)$ holomorphic in the tubular cone
$T^V={\bf R}^n +i V$ and satisfying the inequality

$$
|g(s)|\,\leq\,C_\varepsilon(V^\prime))\,|q|^{-N}\,\exp\{\/|\varepsilon
s|^{1/\beta}\}\hspace{5mm}  (q\in V^\prime)  \eqno{(17)}
$$

\noindent
for any $\varepsilon>0\/\/ ,V^\prime\Subset V$ and some $N$ depending on
$\varepsilon,V^\prime$. Conversely, if $g$ is a function holomorphic in a tube
$T^V$, with $V$ an open connected cone, and satisfying the growth condition
(17), then it serves as the Laplace transform of a distribution
$f\in (S^\beta)^\prime$ carried by the cone $V^*$.

{\sl Proof.\/} We shall show that $e^{i sz} \in S^\beta(K)$ for any $q\in
V=\hbox{int} K^*$ and then define the Laplace transformation by the formula

$$
g(s)\/=\/(f(z),\/e^{i sz})
\eqno{(18)}
$$

\noindent
After that the estimate (17) can be derived from the inequality

$$
|g(s)|\,\leq\,\|f\|_{U,N,b}\,\|e^{i sz}\|_{U,N,b}
$$

\noindent
where $K\Subset U\/\/ , b$ is arbitrarily large and $N$ depends on $U, b$. We
have

$$
\|e^{i sz}\|_{U,N,b}\,=\,\sup_{z}(1+|x|)^N
\,\exp\{-qx-py-|by|^{\beta^\prime}-d(bx,U)^{\beta^\prime}\}
\eqno{(19 )}
$$

\noindent
The inclusion $V^\prime\Subset V$ implies $K\Subset \hbox{int}V^{\prime *}$
. We choose the cone $U$ and another  open auxiliary cone $U^\prime$ so that
$K\Subset U\Subset U^\prime\Subset \hbox{int}V^{\prime *}$. In evaluating the
supremum over $y$ we use the inequality $-py\leq |p||y|$ and obtain the
factor $\exp\{|\varepsilon p|^{1/\beta}\}$ where $\varepsilon$ is arbitrarily
small.  Next we estimate the supremum over $x$ inside and outside the cone
$U^\prime$.  There exists $\theta > 0$ such that $-qx\leq -\theta|q||x|$
for all
$q\in V^\prime, \/ x\in U^\prime$. Indeed, the function
$i_{V^\prime}(x)=\sup\{-qx:\/ q\in \hbox{pr}V^\prime\}$ called the indicatrix
of $V^\prime$ is continuous negative in $\hbox{int}V^{\prime *}$ and takes
the maximal value $-\theta$ on the compact set $\hbox{pr}\overline{U}^\prime$.
This gives the factor $|q|^{-N}$, while for $x\in U^\prime$ we have
$d(x,U)>\delta|x|$, $\delta>0$ and so obtain the factor $\exp\{|\varepsilon
q|^{1/\beta}\}$.  Further, it can be easily verified that the difference
quotients corresponding to the partial derivatives $\partial e^{i
sz}/\partial s_j$ converge to them in the topology of $S^\beta (U)$ and so
all the derivatives $\partial g/\partial s_j$ exist. By the Hartogs theorem,
this means that $g$ is holomorphic in $T^V$.

Conversely, given a function $g$ analytic in $T^V$ and satisfying (17), we
define $f\in (S_{1-\beta}^\beta)^\prime$ by the formula

$$
(f,\,\varphi)\,=\,\int g(p+i q)\,\psi(p+i q)\,dp \hspace{5mm}  (q\in
V)
\eqno{(20)}
$$

\noindent
where $\psi(p)=(2\pi)^{-n}\int \varphi(x)e^{-i px}\/ dx$. Taking into
account that the Fourier operator is an isomorphism from $S_{1-\beta}^\beta$
onto $S_\beta^{1-\beta}$ (and maps $S_{1-\beta,a}^{\beta,b}$ into
$S_{\beta,b^\prime}^{1-\beta,a^\prime}$ with $a^\prime,\/  b^\prime$ arbitrarily
near to $a,\/  b$) and using (10), (17), we see that the right-hand side of (20)
is meaningful and independent of $q$. Then we consider the convolution

$$
(f\star \varphi)(x)\,=\,\int g(s)\,\psi(-s)\,e^{-i sx}\,ds\hspace{5mm}
(\hbox{Im} s\,=\,q\in V)
$$

\noindent
and exploit the latitude in the choice of $q$, which gives

$$
|(f\star\varphi)(x)|\,\leq\,C_{\varepsilon,b}(V^\prime)\,
\|\psi\|_{a,b}\,\inf_{q\in V^\prime} |q|^{-N}\,
\exp\{\/|\varepsilon q|^{1/\beta}+|aq|^{1/\beta}+qx\}.
$$

\noindent
Evaluating the infimum under the additional condition $|q|\leq 1$, we obtain
the following polynomial bound

$$
|(f\star\varphi)(x)|\,\leq\,C_{a,b}\,\|\psi\|_{a,b}\,(1+|x|)^N
\eqno{(21)}
$$

\noindent
Here $N$ depends on $b$ since $\varepsilon$ must be sufficiently small
compared to the number $1/b$ which characterizes the rate of decrease of
$\psi$. The continuity of the Fourier operator allows $\|\psi\|$ to be
replaced by $\|\varphi\|$ in the inequality (21). Applying the trick (14)
again, we make sure that this restriction on the growth enables the
distribution $f$ to be extended to the space $S^\beta$. Next we fix a cone
$C\Subset \complement V^*$ and estimate the infimum over $q\in V^\prime,\/ |q|\geq
1$. The cone $V^\prime$ can be taken so that $C\Subset \complement V^{^\prime *}$.
Then there exists $\theta^\prime > 0$ such that $qx\leq -\theta^\prime|q||x|$
for all $q\in V^\prime,\/ x\in C$.  Namely, $\theta^\prime$ is the minimal value
of the indicatrix $i_{V^\prime}(x)$ on the compact set
$\hbox{pr}\overline{C}$.  Finding this extremum, we arrive at the estimate
 (13) with $\theta$ arbitrarily near to $\theta^\prime
\beta^{\beta}(1-\beta)^{1-\beta}$ . According to Theorem 3 and Lemma, $f$ has a
unique extension to a distribution $\hat{f}$ on the space $S^\beta(V^*)$. The
exponential $e^{i sz}$ belongs to this space for any $\hbox{Im}s\in
\hbox{ch} V$, where ch signifies the convex hull, since
$V^{**}=\overline{\hbox{ch}V}$. Approximating the exponential by $\varphi_\nu
\in S_{1-\beta}^\beta$ and passing to the limit $\nu\rightarrow \infty$ in (20),
we see that the initial function $g$ and $\hat{f}$ are connected by the formula
(18). This completes the proof.

{\bf Corollary}. If $g$ is holomorphic in $T^V$ and fulfills the condition
(17), then it can be analytically continued into the tubular cone
$T^{\hbox{ch}V}$ where an analogous estimate holds.

Note that if $\hbox{ch}V={\bf R}^n$, then $V^*=\{0\}$ and the function $g$ is
entire analytic. In this case the term $d(bx,U)$ in (19) should be replaced by
$|bx|$ and an evaluation of extremum shows that (17) holds in the whole of
${\bf C}^n$ without the factor $|q|^{-N}$ of course.

\section{Causality and K\"{a}llen-Lehmann-like representations \\
for propagators of open and closed strings}

As shown in [12], the K\"{a}llen-Lehmann representation for particle
propagators in Min\-kow\-ski space-time holds true up to the exponential growth
of the spectral density: $\rho(M^2) \leq C\/ e^{lM}$. By the Meiman criterion,
the theories with such a growth are nonlocalizable, with $S^{1,1/l}$ being the
adequate test function space and $l$ playing the role of an elementary
length. Analogous representations for string propagators with the pointlike
boundary conditions were considered in [4,5].As would be expected [32], the
growth of their associated spectral density turns out to be exponential with the
fundamental length $l_{{\rm Pl}} \approx \sqrt{\alpha^\prime}$. In
investigating the string propagators, one usually employs the operator formalism
or the Polyakov method [32]. In this section, we present another approach
closely related to the secondary quantization.It is applicable to arbitrary
initial and final string configurations and shows that the character of causal
and singular properties of the string propagators is independent of the boundary
conditions. We shall set forth the main steps of the proof for the case of open
bosonic string and outline final results for closed ones. We shall follow the
notation of [34] and use in intermediate laying out the system of units
for which $\sqrt{2\alpha^\prime}=1$.

Let us proceed from the following BRST-invariant expression for the Hamiltonian
of the open bosonic string in $D$-dimensional space-time

$$
{\bf H}={\bf L}_0-1=\frac{1}{2}({\bf p}^2+{\bf M}^2),\quad {\bf
M}^2=2\sum_{n=1}^\infty n\left({\bf a}_{-n}^\mu {\bf a}_{n\mu}+{\bf c}_{-n}{\bf
b}_n+{\bf b}_{-n}{\bf c}_n\right) -2
\eqno{(22)}
$$

\noindent
(In fact we take $D$ to be equal to 26.) Here $p_\mu=-i \partial/\partial
x_\mu$ is the momentum operator canonically conjugate to the string center mass
position and playing a significant part in our approach. The
operators $a_{\pm n}^\mu$ are Fourier modes of the string coordinates
$X^\mu(\tau,\sigma)$ and $c_{\pm n},\/b_{\pm n}$ are ghost and antighst modes
satisfying the usual anticommutation relations. Keeping in mind the
zeta-function regularization, one might replace the normal ordering constant
$-2$
by $ (D-2)\sum_{n=1}^\infty n$, restrict the summation in (22) by a large $N$,
and then treat $H$ as a limit of Hamiltonians describing dynamic systems with
finite number of degrees of freedom. This would give a more accuracy to the
following study and put off the appearance of the tachyon but we will not go
into such details for brevity. We use the Berezin holomorphic representation
which is best suited to the Euclidean continual integretion and normalize the
corresponding measure to unity, {\it i.e.\/},

$$
\int d\omega=\prod_{n}\int \frac{da_{-n}\/da_n}{2\pi
i}e^{-a_{-n}a_n}\/\int dc_{-n}\/db_n \/db_{-n}\/dc_n \/e^{-c_{-n}b_n
-b_{-n}c_n}\/=\/1.
$$

\noindent
The index $\mu$ will henceforth be omitted and the notation $A$ will be used for
the collection of variables $\{a_1,b_1,c_1,\ldots,a_n,b_n,c_n,\ldots \}$. Let us
denote by $\delta(x,A^*;x^\prime,A^\prime)$ the kernel of unity operator defined
by

$$
\delta(x,A^*;\/x^\prime,A^\prime)=\delta(x-x^\prime)\sum_{k}\frac{(A^k)^*A^{\prime k}}{k!}
\eqno{(23)}
$$

\noindent
where $k$ runs through the multi-indices which have only finite number of
nonzero components $k_n$, each being $(D+2)$-tuple of nonnegative
integers. Of course, the indices corresponding to the Grassmann variables $b_n$
and $c_n$ make a contribution to the sum only being equal to 0 or 1. The
operation * consisting in the conjugation $a_n\rightarrow a_{-n}, b_n\rightarrow
c_{-n}, c_n\rightarrow b_{-n}$ implies the inversion of the order in the
products. The Green function for the operator $\bf{H}$ is defined by

$$
{\bf H}G(x,A^*;\/x^\prime,A^\prime)=\delta(x,A^*;\/x^\prime,A^\prime)
$$

\noindent
where $H$ acts on the former pair of variables, while the latter is regarded as
parameters. One can readily verify that

$$
G(x,A^*;\/x^\prime,A^\prime)=\int \frac{dp}{(2\pi)^{\rm
D}}\/2\sum_{k}\frac{e^{\imath
p(x-x^\prime)}}{p^2+2[k]-2}\/\/\/\frac{(A^k)^*A^{\prime k}}{k!}
\eqno{(24)}
$$

\noindent
where [k] stands for $\sum_{n}n|k_n|$. Using the summation over the spectrum of
the mass operator, one may reduce this representation to the K\"{a}llen-Lehmann
form

$$
G(x,A^*;\/x^\prime,A^\prime)=\sum_{M^2} \/\int
\frac{dp}{(2\pi)^{\rm D}}\/\/2\frac{\rho (M^2;\/A^*,A^\prime)}{p^2 +M^2}
$$

\noindent
where the spectral density matrix is determined by

$$
\rho (M^2;\/A^*,A^\prime)=\int\limits_{-1/2}^{1/2}
d\varphi\/e^{\pi i\varphi(M^2+2)}\/\sum_{k}e^{-2\pi i\varphi
[k]}\prod_{n}\frac{(A_n^{k_n})^*A_n^{\prime k_n}}{k_{n}!}=
\eqno{(25)}
$$
$$
=\int\limits_{-1/2}^{1/2}
d\varphi\/e^{\pi i\varphi(M^2+2)}\prod_{n}\sum_{k}e^{-2\pi i\varphi
[k]}\/\/\/\frac{(A_n^{k_n})^*A_n^{\prime k_n}}{k_{n}!}
\eqno{(26)}
$$

\noindent
Note that the $\varphi$-integration yields the Kronecker symbol since
eigenvalues of ${\bf M}^2$ are even integers. From (26), one can immediately
obtain an explicit expression for the spectral density

$$
\rho(M^2)=\hbox{Sp}\/\rho(M^2;\/A^*,A^\prime)=\int d\omega\/\/\rho(M^2;\/A^*,A)
$$

\noindent
in the case of pointlike boundary conditions. Namely,

$$
\rho(M^2)=\int\limits_{-1/2}^{1/2}
d\varphi\/e^{\pi i\varphi(M^2+2)}\/\prod_{n} \left(1-e^{-2\pi i n
\varphi}\right)^{-24}
\eqno{(27)}
$$

\noindent
It perhaps is worthwhile to note that the integration over $a_{-n},a_n$
 gives the power $-26$ which is reduced to $-24$ by virtue of the
integration over the Grassmann variables. Let us denote by $f(e^{-2\pi i
\varphi}) $ the product that occurs in (27). Substituting the power series
expansion $f(w)=\sum_{m} d_m w^m$ and performing the $\varphi$-integration, we
obtain the equality $\rho(M^2)=d_{M^2 /2+1}$. The asymptotic behavour of the
coefficients $d_m$ is well known [34, Sec.2.3.5] and we arrive at the formula

$$
\rho(M^2)\approx M^{-25/2}\exp(M/M_0)
\eqno{(28)}
$$

\noindent
where $M_0=1/(4\pi \sqrt{\alpha^\prime})$. It should be pointed out that
the representation (25) enables one to write the function $\rho$ in another
form

$$
\rho(M^2)=\sum_{k}\delta_{M^2 +2}^{2[k]}
\eqno{(29)}
$$

\noindent
expressing it as the degree of degeneracy of the mass operator eigenvalues. From
this viewpoint the problem of deriving the formula (28) looks pure
combinatorial. Thus in the case of pointlike initial and final string
configurations, the growth of the spectral density is indeed exponential. For
more general boundary conditions, one can make use of the following simple
facts. Let $R$ and $\rho$ be operators in a Hilbert space. Assume that $R$ is
bounded, {\it i.e.,\/} $\|R\|=\sup_{\varphi\neq 0}\|R\varphi\|/\|\varphi\|<\infty$, and
$\rho$ is compact. Then the positive self-adjoint operator$(\rho^*\rho)^{1/2}$
is also compact.
Let $\lambda_m$ be its eigenvalues. The nuclear norm is defined by $\|  \rho
\|_1 = \sum_m \lambda_m$ and a compact operator is called nuclear if this norm
is finite. The inequalities $| {\rm Sp}\rho | \le \| \rho \|_1$ and
$\|R\rho\|_1 \le \| R \| \|\rho \|_1$ are valid. It is easy to see that in our
case the nuclear norm of $\rho (M^2;A^*,A')$ is precisely the sum (29). It
follows that the spectral density  ${\rm Sp} R\rho$ behaves exponentially as
well for any bounded $R$ in the K\"{a}llen-Lehmann-like representation.

        The next step in studying the string propagator causal properties is
passing to the Minkowski space-time by means of analytic continuation in $p_0$.
Strictly speaking, this should be performed before the limit $N \rightarrow
\infty$ which breaks down microcausality due to the appearance of the tachyon
eigenvalue $-1/\alpha'$ in the spectrum of ${\bf M}^2$. On doing so, one can see
that the K\"{a}llen-Lehmann representation for string propagators make no sense
inside the hyperboloid $(x - x')^2 \approx \alpha'$ where singularities  present
themselves independently of the boundary conditions. It is natural to assume that
this conclusion is unaffected by taking into account the string interaction. For
the closed bosonic string, analogous formulae can be derived. This time,
however, we deal with right and left modes, {\it i.e.,\/} double of the variables and
the $\delta$-symbol must satisfy the additional condition $({\bf L}_0 -
\tilde{{\bf L}}_0)\delta = 0$ because of which formula (24) is replaced by

$$
G(x,A^*,\tilde{A}^*; \/x^\prime, A^\prime, \tilde{A}^\prime) = \int
\frac{dp}{(2\pi)^{\rm D}}\/\/2\sum_{k,\tilde{k}}\delta_{[k]}^{[\tilde{k}]}
\/\/\frac{e^{i p(x-x^\prime)}}{p^2+4[k]-4}\frac{(A^{k}
\tilde{A}^{\tilde{k}})^{*} A^{\prime
k}\tilde{A}^{\prime\tilde{k}}}{k!\tilde{k}!}
\eqno{(30)}
 $$

\noindent
and the spectral density matrix acquires the form

$$
\rho_{\hbox{cl}}(A^*,\tilde{A}^*;\/A^\prime,\tilde{A}^\prime)=
\int\limits_{-1/2}^{1/2}
d\varphi\/e^{\pi i\varphi(M^2+4)}\/\sum_{k,\tilde{k}}
\delta_{[k]}^{[\tilde{k}]}\/\/\/e^{-4\pi i\varphi [k]}
\/\/\frac{(A^{k}\tilde{A}^{\tilde{k}})^{*} A^{\prime k}\tilde{A}^{\prime
\tilde{k}}}{k!\tilde{k}!}
$$

\noindent
In this case, too, the exponential asymptotic behaviour takes place
independently of the initial and final string configurations and so the causal
and singular properties of the open  and closed string propagators are
practically identical. We would like to point out that in the one loop
approximation  the representation (29), making allowance for the constraint
${\bf L}_0 = \tilde{{\bf L}}_0$, leads immediately to the formally modular
invariant expression [35] for the cosmological constant. The approach presented
here can be extended to the open and closed fermionic Neveu-Schwarz-Ramond
strings and the final results are qualitatively the same but their derivation
will be discussed in some detail elsewhere.

\section{Concluding remarks}

        In this paper, we have no attempt to prove the existence of support
cones for those distributions which are defined on the space $S^0$ whose Fourier
transform is the Schwartz space ${\cal D}$. Such a proof would be extremely
desirable because this space consisting of functions with compact momentum-space
support is universal for nonlocal quantum fields and one imposes no restrictions
on the high-energy behaviour when incorporates it into the Wightman scheme. The
problem is unfortunately complicated by triviality of the space $S^0_1$ which
makes inapplicable the foregoing elementary methods aimed at clarity in
presenting the concept of asymptotic commutativity. However the modern theory
of functions of several complex variables enables one to solve it as we hope
to show before long. The most interesting applications of the mathematical
techniques developed here are improvements in L\"{u}cke's derivations [13,~14]
of the connection between spin and statistics and the {\it TCP}-invariance for
essentially nonlocal quantum fields. This topic is covered in considerable
detail in Ref. [36]. Of course, there are many unanswered questions concerning
the existence of a minimum spatial resolution in the string theory whereas
string interactions look local and this fact is commonly believed to be enough
to preserve causality. One of the principal features of the superstring theory
is the remarkable role of the modular invariance in the banishment of the
ultraviolet divergences. For this reason the main omission of the above
consideration seems to be lack of any examination how this invariance could
affect the causal and singular properties of closed string propagators. However
this is probably somewhat premature because so far there has been no consistent
formulation of the closed string field theory developed in such a manner that
the integration over the modular parameters is naturally restricted to the
fundamental region of the modular group. Another question of great importance is
the relation between the superstring theory and the effectively nonlocal quantum
theory of fields with infinitely many components and arbitrarily high spins.
These two approaches might turn out to be complementary standpoints on the
evolution of Universe, describing its different phases, and this was one of the
main inspirations of our investigation.

redpajama_set_name: RedPajamaArXiv


A big THANK YOU to all of the VAUGHAN friends & fans who came to visit us at the Boutiques at the Pit this weekend.
It was most certainly a fun couple of days and we were thrilled to be in the company of some pretty great local shops and designers. Apparently, it was the first time the fair took place on a weekend and it was fantastic to see so many families out and about shopping together.
Here's me, not-so-secretly thrilled to be six months pregnant and still rocking my favorite Hepburn shirt. You'll have to forgive the vacant expression, it was early and I had a longgg night with the #Milkman.
Also pictured: one of my most favorite Callixto chokers. Apparently the key to styling the bump is to draw the eye up and this necklace sure does exactly that! If nothing else, it's always good to start the day with a little warrior princess bling.
Here's the pop up space. I'm definitely planning to steal this flouro yellow D-I-Y IKEA mirror for my new home. Fun, right?
Our Bettie Shirt in Pin Up Queen Green in the foreground totally stole the show. We're now almost completely sold out. It's really a fabulous color and looks incredible on so many different complexions. I just loved watching her in action.
Even seasoned professionals such as yours truly aren't immune from the temptations of a little retail therapy. Here I am with my newest find, a little topper from Hat of Cain. This is the first blue Panama hat I've seen and I thought she was fabulous.
Anyway, thank you again for a terrific weekend. We will most definitely let you know when our next pop up will hit!


text:
Islamlar yolu No 128 Kalkan Kaş Antalya
About the Islamlar area
Kalkan Magic
Kleo Cottage - 1
Kleo Cottage Villas consists of a group of six completely detached two, three and four-bedroom country cottage-style spacious villas all of which have beautiful views across the mountainside and some out to sea. They are set in natural gardens, to the side of a mountain stream. Large communal and linked children's swimming pool with sun loungers is hidden in the center of a pretty, landscaped garden, with private swimming pools and sun terraces and loungers in three properties. The setting perfectly reflects the relaxed pace of life in the mountains, where your peace is most likely to be disturbed by the ringing bells of a passing goat herd. The cottages retain a 'village-style' of architecture, and blend beautifully with the environment. Each cottage is extremely spacious and comfortable and is set out over two or three storeys, providing the feel of a house.
2, two-bedroom cottages suitable for up to four guests (5 with sofa bed)
2, three-bedroom cottages suitable for up to six guests (7 with sofa bed)
2, four-bedroom cottages suitable for up to eight guests (9 with sofa bed)
Freshwater communal swimming pool Dimensions: 14 x 7 m. Depths: 1.30 – 1.80m Children's pool: 3.65 x 2.65m. Depth: 0.50 Freshwater private pools Dimensions: 4 x 6 m. Depths: 1.40 m.
6km/15-minute drive to Kalkan, 16km/25-minute drive to Patara Beach and Kaputas Beach
500m/10-minute walk to Islamlar village center and, 5-minute walk to the closest mini market.
Xanthos: 17km/25-minute drive Kas: 30km/45-minute drive, Saklikent: 45km/1 hour 10-minute drive.
Fethiye: 80km/1 hour 10-minute drive.
Nearest restaurant is Bodamya Tepe Restaurant which is 100 m away where you can have breakfast, lunch or dinner as other 9 restaurants of the Village.
Kleo Cottage Villas
Kleo Cottages consists of a group of six completely detached two, three and four-bedroom country cottage-style spacious villas all of which have beautiful views across the mountainside and some out to sea.
© 2018 Kleo Cottage Villa All rights reserved.
Fast Call


text:
← Stop dreaming about the Inception videogame spin-off
PURCHASE OF THE MONTH: Mini Ninjas →
GAMES I REGRET PARTING WITH: Donkey Kong Country
Ah, Donkey Kong Country…Only for Nintendo. And they meant it.
I was, in fact, never a subscriber to Nintendo Power (sorry, Greg Noe!), but somehow still got access to a VHS tape called Donkey Kong Country: Exposed, which was a behind-the-scenes tour of Nintendo of America's headquarters in Redmond, Washington, with bonus early game footage and tips from testers on how to access hidden bonus stages. Think I "borrowed" the tape from a friend's house. Ahem. "Borrowed." And it, much like the game itself, ended up parting with me some time during my switch from SNES to PlayStation 1. I have a strong feeling though that the VHS tape sold at a neighborhood yardsale for 50 cents. Oh yeah, made a profit.
Moving on, this plus about four other SNES titles more or less were my collection for the longest time. Money was tight, and if I didn't get a game for Christmas, well…I was just a wee lad then that would water the grass or wash a neighbor's car for pocket money. Was not rolling it, as they say. I relied a lot on renting games for a few days or borrowing them from a friend. Notice I said borrow and not "borrow"; no way I would've gotten away with something like that, not when a kid's SNES or Sega Genesis was his or her only friend. Oh, and those other games consisted of Super Metroid, The Legend of Zelda: A Link to the Past, Super Mario World, and–don't laugh, kids–Jurassic Park. I'll talk about Jurassic Park for the SNES one day, but I am just not ready yet; the scars have not healed.
It's clear that Donkey Kong Country came to be from other platformers of that day and age, most namely Super Mario Bros. The plot is essentially the same. Instead of saving the princess, you need to save DK's stolen banana loot. The game has you collecting bananas in levels for extra lives; you can die by falling down holes in the level or getting touched by enemies; and you use a world map to select where you want to go. Sure, sure, the game did some original things too, but it pays a lot of homage to its elders.
But Donkey Kong Country is a very memorable game, and I think fondly about it a lot. The music, the jumping, the level progression, the mine carts, and the shooting from barrel to barrel to moving barrel. There was a lot going on within, and it was very successful in pushing the SNES to its limits and then mocking rival 32-bit and CD-ROM based consoles with purported superior processing power. I think many will first remember the pre-rendered 3D graphics, which really helped bring the 2D side-scrolling platformer to life; the early jungle levels are full of green and treetops and towering hills while the snow levels are replete with blizzards and glistening ledges. This engine was also used on Rare's other title Killer Instinct, still in my collection now.
By and far though, my favorite stages in Donkey Kong Country were any where you rode an animal. These included Rambi the Rhino, Expresso the Ostrich, Enguarde the Swordfish, Winky the Frog, and Squawks the Parrot, and all were tied to a specifically themed level. Yup, even as frustrating as the underwater levels were, once you got on that swordfish it was ::ahem:: clear swimming from there. Later games would introduce even more animals, and those also were worth looking forward to.
The only negatives I ever put on Donkey Kong Country's shoulders were its coin-based save system and boss battles. The boss battles all followed a very repetitive strategy and once you figured that out, it was hit 'em, hit 'em, an hit 'em dead. I ate everything else up with wide eyes and an open heart.
Tara and I combined our SNES collections back when we first started dating in 2008, and she had Donkey Kong Country 2: Diddy's Kong Quest, a pleasant surprise, as well as a decent filler for the time being. That said, I'm definitely interested in seeing how Donkey Kong Country Returns for the Wii plays out despite having a paper-flat title.
GAMES I REGRET PARTING WITH is a regular feature here at Grinding Down where I reminisce about videogames I either sold or traded in when I was young and dumb. To read up on other games I parted with, follow the tag.
This entry was posted in do want, games I regret, gone games, musings, SNES, videogames. Bookmark the permalink.
One response to "GAMES I REGRET PARTING WITH: Donkey Kong Country"
feelthefallout | March 5, 2011 at 12:55 AM | Reply
For SNES, mine would be The Adventures of Batman & Robin. That was a beautifully done action side-scroller. Donkey Kong Country was a blast, and one of the best console games EVER (definitely on my top 20 list).
Well… thank the Maker for emulation ;-j


text:
Mike Vrabel Talks Titans' Free-Agency Outlook, Re-Signing Key Players
Rob Goldberg@TheRobGoldbergTwitter LogoFeatured ColumnistFebruary 25, 2020
Wesley Hitt/Getty Images
The Tennessee Titans could face some attrition this offseason with several key offensive players set to be free agents, including Ryan Tannehill, Derrick Henry and Jack Conklin.
Head coach Mike Vrabel said Tuesday on Bleacher Report's Stick to Football podcast that the team is due for change, at least in some capacity:
"It's a part of the business of football. Obviously everybody with expiring contracts there has to be decisions that are made by not only the team but also by the player. The player has to want to be back. The team has to make an effort to bring them back. And to think all those guys will be back, that's just not going to happen. There will be players we can hopefully get back and there will be ones that go on and transition on to other teams."
Tennessee also has tough decisions on players like Logan Ryan, Tajae Sharpe and others set to hit free agency.
Henry could be a priority after a breakout season where he carried the Titans offense down the stretch and was a major reason the team reached the AFC Championship Game.
Titans general manager Jon Robinson has indicated re-signing the running back is a priority.
"I mean he led the league in rushing, he built off the second half of the 2018 season that he had, he cares about his teammates, he works hard, he's great in the community and we're going to work through that one and do everything we can to try to keep him around," Robinson said, per Erik Bacharach of the Tennessean (h/t Jordan Dajani of CBS Sports).
With a league-high 1,540 rushing yards during the regular season and 446 yards in three postseason games, the Titans likely won't want to let him go.
There could be bigger question marks regarding Tannehill, who began the year as the backup quarterback to Marcus Mariota before taking over in October. He went 9-4 as a starter including the playoffs, but the team will have to decide whether he proved enough to earn a long-term deal.
Considering there are more established players potentially available like Tom Brady and Philip Rivers, Tennessee could have options at the position.
Meanwhile, Conklin might be the most likely to go despite starting all 16 games last season at right tackle. The Titans decided last year not to pick up his fifth-year option, letting him hit free agency this year and likely get a lot of attention on the open market.
According to Jake Trotter of ESPN, the tackle is on the "radar" of the Cleveland Browns.
It all creates an important offseason for Vrabel and Tennessee.


text:
#pragma once
#include <aws/sesv2/SESV2_EXPORTS.h>
#include <aws/sesv2/SESV2Request.h>
#include <aws/core/utils/memory/stl/AWSString.h>
#include <aws/core/utils/DateTime.h>
#include <utility>

namespace Aws
{
namespace Http
{
    class URI;
} //namespace Http
namespace SESV2
{
namespace Model
{

  /**
   *
A request to obtain deliverability metrics for a domain.

See
   * Also:
   AWS
   * API Reference

   */
  class AWS_SESV2_API GetDomainStatisticsReportRequest : public SESV2Request
  {
  public:
    GetDomainStatisticsReportRequest();

    // Service request name is the Operation name which will send this request out,
    // each operation should has unique request name, so that we can get operation's name from this request.
    // Note: this is not true for response, multiple operations may have the same response name,
    // so we can not get operation's name from response.
    inline virtual const char* GetServiceRequestName() const override { return "GetDomainStatisticsReport"; }

    Aws::String SerializePayload() const override;

    void AddQueryStringParameters(Aws::Http::URI& uri) const override;

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline const Aws::String& GetDomain() const{ return m_domain; }

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline bool DomainHasBeenSet() const { return m_domainHasBeenSet; }

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline void SetDomain(const Aws::String& value) { m_domainHasBeenSet = true; m_domain = value; }

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline void SetDomain(Aws::String&& value) { m_domainHasBeenSet = true; m_domain = std::move(value); }

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline void SetDomain(const char* value) { m_domainHasBeenSet = true; m_domain.assign(value); }

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline GetDomainStatisticsReportRequest& WithDomain(const Aws::String& value) { SetDomain(value); return *this;}

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline GetDomainStatisticsReportRequest& WithDomain(Aws::String&& value) { SetDomain(std::move(value)); return *this;}

    /**
     *
The domain that you want to obtain deliverability metrics for.

     */
    inline GetDomainStatisticsReportRequest& WithDomain(const char* value) { SetDomain(value); return *this;}

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline const Aws::Utils::DateTime& GetStartDate() const{ return m_startDate; }

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline bool StartDateHasBeenSet() const { return m_startDateHasBeenSet; }

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline void SetStartDate(const Aws::Utils::DateTime& value) { m_startDateHasBeenSet = true; m_startDate = value; }

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline void SetStartDate(Aws::Utils::DateTime&& value) { m_startDateHasBeenSet = true; m_startDate = std::move(value); }

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline GetDomainStatisticsReportRequest& WithStartDate(const Aws::Utils::DateTime& value) { SetStartDate(value); return *this;}

    /**
     *
The first day (in Unix time) that you want to obtain domain deliverability
     * metrics for.

     */
    inline GetDomainStatisticsReportRequest& WithStartDate(Aws::Utils::DateTime&& value) { SetStartDate(std::move(value)); return *this;}

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline const Aws::Utils::DateTime& GetEndDate() const{ return m_endDate; }

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline bool EndDateHasBeenSet() const { return m_endDateHasBeenSet; }

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline void SetEndDate(const Aws::Utils::DateTime& value) { m_endDateHasBeenSet = true; m_endDate = value; }

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline void SetEndDate(Aws::Utils::DateTime&& value) { m_endDateHasBeenSet = true; m_endDate = std::move(value); }

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline GetDomainStatisticsReportRequest& WithEndDate(const Aws::Utils::DateTime& value) { SetEndDate(value); return *this;}

    /**
     *
The last day (in Unix time) that you want to obtain domain deliverability
     * metrics for. The EndDate that you specify has to be less than or
     * equal to 30 days after the StartDate.

     */
    inline GetDomainStatisticsReportRequest& WithEndDate(Aws::Utils::DateTime&& value) { SetEndDate(std::move(value)); return *this;}

  private:

    Aws::String m_domain;
    bool m_domainHasBeenSet;

    Aws::Utils::DateTime m_startDate;
    bool m_startDateHasBeenSet;

    Aws::Utils::DateTime m_endDate;
    bool m_endDateHasBeenSet;
  };

} // namespace Model
} // namespace SESV2
} // namespace Aws

redpajama_set_name: RedPajamaGithub


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Winter moth larvae were picked up in sweeps last week. There is only a small window of opportunity to get out and sweep this week before the poor weather conditions come in, so try to get out there to see if winter moth is on your bog. Growers were picking up averages of 8-10 larvae last week. They are very small but you should be able to see them. At this size, it is hard to tell if they are WM, black-headed fireworm or Spag, but most likely, they are WM. Avaunt is a good choice along with Delegate and Intrepid.
Cranberry weevils have been swept in the past few days, but not in numbers to trigger a spray. Grey weevils have also been picked up, but these weevils do not eat cranberry.
Dodder seedlings have been reported inland over the weekend (May 4). Scout in the duff layer for emerging seedlings; you do not need to dig into the soil to find the seedlings. Plan herbicide treatments for about 2 weeks after early seedling emergence. Day-old seedlings were noted in Onset on May 8. Photo below shows single dodder seedling (probably several days old) on duff layer.
The first frost warning was issued on April 16. Most growers have been out frost protecting almost every night since then as we have had 16 warnings. Protecting started earlier in the night for typical spring time protection such that we already have as many "pump hours" as we did all of last year.
We are past the window for applying preemergence herbicides in all but the coldest of locations. It is probably too early to be applying Callisto or other postemergence herbicides but if you are in a warm location and the weeds are up, you could be in the window. Callisto needs about 4 hours to become rainfast. Most growers should probably wait until next week before applying any early Callisto sprays.
We are looking for sites to study POISON IVY. If you would be willing to help us out, please call extension 21 or 27. We will be testing combinations of Poast and Callisto (so no crop-destruct). We are also looking for DODDER sites where we can use QUINSTAR. We are getting desperate, so if you are cleared for using QuinStar and have dodder and would be willing to help us out, please call extension 21 or 27.


text:
Alex Jones, Host Of Infowars, Files For Bankruptcy
(CTN News) – On Friday, Info wars host Alex Jones filed for personal bankruptcy protection in Texas. This is because he is facing nearly $1.5 billion in court judgments in connection with conspiracy theories he spread about what happened at Sandy Hook school.
Jones filed for bankruptcy in the Houston bankruptcy court pursuant to Chapter 11 bankruptcy protection.
According to his filing, he has between $5 billion and $10 billion in liabilities owed to 50 to 99 creditors and between $1 million and $10 million in assets.
As a result of Alex Jones' bankruptcy filing, he is facing a court order to pay nearly $1.5 billion to the relatives of the Sandy Hook Elementary School children who died as a result of the mass shooting at the school in 2012, for calling the massacre a hoax.
A message left seeking comment on ' bankruptcy case was not immediately returned by a lawyer representing Jones in that case.
In October, a Connecticut jury awarded the families $965 million in compensatory damages, as well as $473 million in punitive damages.
This was in addition to the $965 million in compensatory damages awarded in October. The parents of the child who was shot and killed in the shooting received a $49 million award from a Texas jury earlier in the year.
The bankruptcy filing of Jones also halted all proceedings in Alex Jones' case in Connecticut after he filed a notice Friday stating he had filed bankruptcy.
It was scheduled that a judge in the Connecticut case would hear arguments Friday morning on a motion by the Sandy Hook families to have the assets of Alex Jones and his company attached to secure money for the damages awards they had won.
The families also asked the Connecticut judge to bar Jones from transferring or disposing of any of his assets without the permission of the court. This is part of their motion to secure Jones' assets.
There have been several instances in which Jones has mocked the awards on the Info wars show. He claims he does not have the money to pay such high amounts, and he does not have more than $2 million to his name.
According to the testimony of a forensic economist testifying at the Texas trial, Jones and his company Free Speech Systems have a combined net worth that is as high as $270 million, which contradicts the testimony of a forensic economist at the trial.
The company has also filed for Alex Jones bankruptcy in order to seek protection from creditors.
There have been cases in Texas and Connecticut where relatives of the 20 children and six adults that were killed in the 2012 school shooting testified that they had been harassed and threatened for years by people who believed the lies told on Alex Jones' show.
According to a parent who testified before the jury, conspiracy theorists urinated on the grave of his 7-year-old son and threatened to dig it up.
During her testimony, Erica Lafferty, daughter of the slain Sandy Hook principal Dawn Hoch sprung, stated that she had received threats of rape sent through the mail.
A budget filed in Free Speech Systems' bankruptcy case in Texas estimates the company's product sales for October 29 to November 25 will total $2.5 million, while operating million.
Operating 29 and November 25 will amount to about $740,000, according to the documents filed. It is reported that Alex Jones earns $20,000 every two weeks as part of his salary.
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This is a charming pre-war building, located in historic Carnegie Hill on the Upper East Side. 115 East 92nd St is only two avenues away from Central Park. The building has an elevator operator with a very welcoming full time doorman. The entrance of the building is beautifully decorated with plants and flowers. The attended lobby has gorgeous gold tones.
Built in 1927, this pre-war building is a true gem. It is well maintained and equipped with Laundry Room, Roof Deck, Private Storage and features red brick. The aparments features crown moldings, large living rooms, sunlit bedrooms, windowed kitchens with brand new stainless steel appliances and more.
Please contact us for available rentals at 115 East 92nd St and any other buildings in Manhattan that you are interested in.


text:
Jane Addams Hull House To End Immigrant Services
By Cheryl Corley
And an organization famous for helping people struggling to work their way up in society has now hit bottom. Chicago's Hull House became a model for settlement houses in the United States and around the world. They helped immigrants. It was founded a century ago by Nobel Peace Prize-winner Jane Addams. And its name sake, the Jane Addams Hull House Association, has struggled financially in more recent years. Now it plans to file for bankruptcy. NPR's Cheryl Corley has more.
CHERYL CORLEY, BYLINE: It's been a last-minute, hectic flurry of activity for Hull House employees.
MARK TISDAHL: This is an office that's being packed up, and the employees that are packing up have paid for their own boxes, because we don't have money to pay for boxes.
CORLEY: Mark Tisdahl is one of about 300 workers losing their jobs. They and their clients got just one week's notice that the 122-year-old Chicago institution would shut down.
STEVE SAUNDERS: We hate it. It's been since September 18th, 1889, and we hoped for a much more dignified closing.
CORLEY: But the Jane Addams Hull House Association closes today.
SAUNDERS: At 5 o'clock.
CORLEY: That's Chairman of the Board, Steve Saunders. He says the closure is unavoidable because fundraising efforts haven't matched expenditures for several years.
SAUNDERS: We went through some very good strategic planning for the last 18 to 24 months to try to figure out ways to either reduce programs, reduce operating costs, increase income. And unfortunately with the economy turning in 2008, the math just wasn't able to work.
CORLEY: Some of the staff have asked the Illinois Attorney General to investigate to see if there was any mismanagement of Hull House funds. Saunders says although there's been an immediate response including offers of financial help, at this stage of the game it's too late.
(SOUNDBITE OF A ROADWAY)
CORLEY: Hull House was considered the most influential settlement house in the country, providing all sorts of services to immigrant families. And the House where it all started is still located here on the Near South Side of Chicago.
LISA LEE: When Jane Addams came, you know, it was one of the busiest, most poor neighborhoods in Chicago filled with 18 different ethnic groups. All the tenements houses were here. All the sweatshops were here.
CORLEY: And it was here, says museum director Lisa Lee, where Addams and Hull House co-founder, Ellen Gates Starr, decided to settle and work for immigrants rights, women's suffrage, public health and other issues.
LEE: You know, it became looked upon as the engine for social change.
CORLEY: Hull House expanded and the association grew in several locations around Chicago, providing foster care, job training, domestic violence counseling and pre-school to about 60,000 people a year.
(SOUNDBITE OF CHILDREN SINGING)
CORLEY: At the pre-school in Chicago's Lincoln Square neighborhood, about a dozen three and four year olds, tongues sticking out, sang along with their teacher earlier this week.
Jessica Carillo isn't happy that the daycare is closing. Her 3-year-old son is her second child to attend.
JESSICA CARILLO: I think it's a very big disappointment. The teachers are great. The activities are awesome. It's a really good place, and especially in this community, as we need it.
CORLEY: Richard Hayes says the center has been a blessing for him since he drops his kid off early. He wasn't entirely surprised by the news because of the economy but...
RICHARD HAYES: I just thought there was more help out there.
CORLEY: Jessica Valencia says it's been a see-saw type of week. Parents were told not to come in Monday because there was no food, and later learned the center would close. Now it's a scramble to find a new place even though she's been told she'll get help.
JESSICA VALENCIA: In my case it will be very difficult because my son has autism.
CORLEY: Ian Bautista is the head of the United Neighborhood Centers of America, an organization of community groups that Jane Addams also helped found. He calls the closure of Hull House a tough loss. He says the economy puts community building organizations in a tough position when it comes to being fiscally sound.
IAN BAUTISTA: There are demands on our services that go up when the economic times are hard. But, at the same time, when the economy falters, the revenue that's available to meet those demands tends to be more stressed.
CORLEY: And one of the lessons organizations will learn from Hull House, he says, is to diversify and to not be overly dependent on government funds. It's a message that comes too late for Hull House.
Cheryl Corley, NPR's News, Chicago.
INSKEEP: It's MORNING EDITION from NPR News. Transcript provided by NPR, Copyright NPR.
Cheryl Corley
Cheryl Corley is a Chicago-based NPR correspondent who works for the National Desk. She primarily covers criminal justice issues as well as breaking news in the Midwest and across the country.
See stories by Cheryl Corley