Many of you will know that the gardeners at the Museum were provided with a new gardeners' shed and a greenhouse as part of the Museum Development Project. This has provided an excellent platform to maintain the garden, and to propagate and develop the Museum's own plants from seed to raise important funds as well as plant out in the garden. You will have noticed the huge improvement in a number of areas in the garden over the past year and even this Spring.
As the Museum has become independent with the production of plants for the garden, for cuttings and sales, the need for proper cold frames has become pressing. The greenhouse has provided essential space for propagation and development of plants but an area is now needed for proper hardening off and over wintering of plants. The very old cold frame area is beyond repair and has not been used effectively for several years as some components are now too difficult or dangerous to use.
So the gardeners have launched a crowd-funding appeal https://localgiving.org/appeal/ColdFrames/ to make this happen.
How will the funding you raise be spent?
We need to raise £1,400 for nine 6′ x 2′ robust prefabricated cold frame modules to be situated on prepared ground in the Gardeners' area adjacent to the greenhouse and sheds. An additional £350 is required to allow for preparation of ground to provide level ground secure from wind and pests. We have some temporary cold frames kindly lent by a garden volunteer which are already being put to good use and provide examples for those that like to see these things in action. There is also a proposed layout plan in the gardeners' shed for those interested.
How the Museum Will benefit?
Last financial year, the museum achieved independence with plant propagation and development raising hundreds of plants from seed. As well as providing heritage plants for the garden and vegetables for the cafe, in the last financial year we sold over 670 plants grown from seed raising important funds for maintaining and developing the garden. The cold frames will release space in the greenhouse to harden off early sowings of hardy annuals and perennials allowing for further and increased plant production.
£10 spent on plants in shop raises £10 for the garden. A £10 donation will provide space for plants that may raise £30 a year or more for several years helping build sustainability and resilience of funding to maintain the garden.
Please also help us to raise awareness for our appeal by sharing this page with your friends.
Your ticket for the: Cold Frames for Gilbert's Garden – Can you help?


Originally from Costa Rica, Kenneth Jimenez is a young bass player and composer currently based in New York City. He's performed with artists Francisco Mela, Michael Attias, Tom Rainey, Satoshi Takeishi, Angelica Sanchez, Gerald Cleaver, Ingrid Laubrock, Stephen Scott, Brian Lynch, Gary Campbell, Roxana Amed, Martin Bejerano, Jose Luis de la Paz and Emilio Solla.
He was a part of the 2017 Betty Carter Jazz Ahead Program at the Kennedy Center for the Performing Arts, under the direction of renowned pianist Jason Moran.
He has performed at important venues nationally and internationally. Some of those include the Millenium Stage at the Kennedy Center in Washington DC, The Jazz Gallery in New York City, the Olympia Theater in Miami and the National Theatre in San Jose, Costa Rica.
Currently he leads two projects, "Sonnet to Silence" feat. Hery Paz, Angelica Sanchez & Gerald Cleaver, and "Sublunary Minds" feat Jim Gasior & John Yarling. The latter will release their first album in Spring 2019.


No, that's not going to be today's letter "F" piece. Well, probably not.
But it does mean that the proofs are proofed, the cover is made, the prices are priced, the checks are checked, all systems are go, all lights are green, and as soon as I double-check a couple of final points, The Core War and Other Stories is go for launch.


text:
package com.github.keub.maven.plugin.service;

import java.util.HashSet;
import java.util.Set;

import com.github.keub.maven.plugin.utils.AntPathMatcher;

public class IncludeService {

	/**
	 * include only file match with pattern into includes set
	 *
	 * @param includes
	 * @param files
	 */
	public static Set<String> process(Set<String> includes, Set<String> files) {
		if (includes == null || files == null) {
			return files;
		}
		Set<String> retval = new HashSet<String>();
		AntPathMatcher antPathMatcher = new AntPathMatcher();
		for (String pattern : includes) {
			for (String path : files) {
				boolean match = antPathMatcher.match(pattern, FileService.normalizePath(path));
				if (match) {
					retval.add(path);
				}
			}
		}
		return retval;
	}

}

redpajama_set_name: RedPajamaGithub


text:
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\begin{document}
\topmargin 0pt
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\begin{flushright}

USTC-ICTS-06-03\\

hep-th/0604048\\

\end{flushright}
\vspace{4mm}

\begin{center}

{\Large \bf

Non-SUSY $p$-branes, bubbles and tubular branes }

\vs{8}

{\large J. X. Lu$^a$\footnote{E-mail: jxlu@ustc.edu.cn} and
Shibaji Roy$^b$\footnote{E-mail: shibaji.roy@saha.ac.in}}

 \vspace{4mm}

{\em

$^a$ Interdisciplinary Center for Theoretical Study\\
University of Science and Technology of China, Hefei, Anhui
230026, China\\

and\\

Interdisciplinary Center of Theoretical Studies\\
Chinese Academy of Sciences, Beijing 100080, China

\vspace{3mm}

$^b$ Saha Institute of Nuclear Physics,

 1/AF Bidhannagar, Calcutta-700 064, India}

\end{center}

\vspace{6mm}

\begin{abstract}
\begin{small}
We consider non-supersymmetric $p$-brane solutions of type II
string theories characterized by three parameters. When the charge
parameter vanishes and one of the other two takes a specific value, the
corresponding chargeless solutions can be regular and describe
``bubbles'' in static (unstable) equilibrium when lifted to $d =
11$. In appropriate coordinates, they represent D6 branes with a
tubular topology R$^{1,p}$ $\times$ S$^{6-p}$ when reduced to $d=10$,
called the tubular D6 branes, held in static equilibrium by a
fixed magnetic flux (fluxbrane). Moreover, a `rotation parameter'
can be introduced to either of the above two eleven dimensional
configurations, giving rise to a generalized configuration
labelling by the parameter. As such, it brings out the relations
among non-supersymmetric $p$-branes, bubbles and tubular D6
branes. Given our understanding on tubular D6 branes, we are able to
reinforce the interpretation of the chargeless non-supersymmetric
$p$-branes as representing $p$-brane-anti$p$-brane (or non-BPS
$p$-brane) systems, and understand the static nature and various
singularities of these systems in a classical supergravity
approximation.
\end{small}
\end{abstract}
\newpage
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String theory contains in its spectrum not only the BPS states and
branes \cite{Horowitz:1991cd,Duff:1994an} but also their non-BPS
counterparts \cite{Sen:1999mg}. In addition, there are unstable
brane-antibrane systems. For the BPS case, both the open string
and the closed string descriptions of these objects are
well-understood \cite{Aharony:1999ti} and they played
complementary roles in the microscopic calculation of black hole
entropy \cite{Strominger:1996sh} as well as the AdS/CFT
correspondence
\cite{Maldacena:1997re,Witten:1998qj,Gubser:1998bc}. However, the
situation is not so satisfactory for the case of non-BPS states
and branes as well as for the brane-antibrane systems. In this
case, although the open string description is fairly
well-understood \cite{Sen:1999mg,Sen:1999nx,Berkovits:2000hf} in
the weakly-coupled region, the corresponding supergravity or
closed string description does not have the same status as in the
BPS case. Some progress in this approach have been made in
refs.\cite{Brax:2000cf,Lu:2004dp}. The hope is that at least some
properties of the non-BPS states and branes as well as the
brane-antibrane systems can be similarly studied once  we have a
satisfactory supergravity description.

The static, non-supersymmetric $p$-brane solutions of
supergravities, i.e., the low energy string theories, in arbitrary
dimensions were constructed in \cite{Zhou:1999nm,Lu:2004ms}. These
solutions have the isometry ISO($p,1$) $\times$ SO($9-p$) and are
characterized by three parameters. When we take the dimensionality
of spacetime to be ten, the corresponding solutions have been
interpreted in \cite{Brax:2000cf} as representing either the
non-BPS D$p$ branes or D$p$ brane-antiD$p$ brane system depending
on the value of $p$ and the type of theory (IIA or IIB) under
consideration. The three parameters for each solution are related
to the mass, charge and presumably also the tachyon  parameter for
the corresponding unstable configuration. Although their precise
relationships to the tachyon parameter are largely unknown, there
are some interesting attempts to relate them to the physical
microscopic parameters of the brane-antibrane systems
\cite{Brax:2000cf,Lu:2004dp,Bai:2005jr,Kobayashi:2004ay}. Various
properties of these solutions as well as their delocalized
versions have been studied in
\cite{Lu:2004xi,Lu:2005ju,Lu:2005jc}.

In spite of many consistency checks performed so far, questions
regarding the static nature and the singularities of these
solutions may still cast doubt on their interpretation as
representing unstable systems such as non-BPS branes and/or
brane-antibrane systems. In this paper we hope to provide some
explanations and address various related issues at least in the
classical approximation by showing their relations to the
well-studied tubular D6 branes.

For this, we recall that the Kaluza-Klein dipole solution
\cite{Gross:1983hb,Sorkin:1983ns} when embedded in eleven
dimensions, was successfully interpreted as a static
D6-brane--antiD6-brane configuration of type IIA string theory,
suspended in an external magnetic field, in
\cite{Dowker:1995sg,Sen:1997pr}. We remark that usually the
solution in $d=10$ (obtained  by the dimensional reduction of an
eleven dimensional one), can suffer from two kinds of
singularities, the curvature singularity and the conical
singularity. Just like in BPS branes, the curvature singularities
here appear at the locations of D6-brane and antiD6-brane. In
other words they represent the brane sources and should not be a
concern to us. On the other hand the conical singularity appears
because of the improper introduction of a background magnetic flux
or fluxbrane to the system under consideration (the eleven
dimensional origin of this is due to an improper choice of a pair
of coordinates not entirely independent of each other) by which
the attractive forces due to gravitational and magnetic
interactions remain unbalanced with the repulsive force induced by
the magnetic flux between the brane and the anti-brane. In this
case the system becomes classically unstable as well as dynamical.
For this reason, the conical singularity will be our real concern
here. The conical singularity never appears if the reduction of
the eleven dimensional KK dipole (regular) solution is on an
appropriate Killing direction with a `good' pair of independent
coordinates\footnote{When such a pair of coordinates (one of them
is a compact coordinate $x^{11}$ and the the other is an angular
coordinate introduced later) are entirely independent of each
other and have their respective correct period $2\pi R$ and
$2\pi$, we call them a `good' pair, otherwise a `bad' pair. In
fact, any choice of non-trivial twist on  the angular coordinate
in eleven dimensions is equivalent to introducing a new background
magnetic flux or fluxbrane to the underlying ten dimensional
configuration under consideration, therefore showing the
non-uniqueness of reduction as well as the background flux as
mentioned in \cite{Dowker:1995gb}. }  and thereby introducing a
well-tuned background magnetic flux or fluxbrane in $d=10$. This
magnetic flux in turn provides the repulsive force necessary to
counterbalance the attractive force between the brane and the
anti-brane, giving a static configuration of such unstable
systems. When the parameter `$a$' of the KK dipole solution (this
is the Euclideanized rotation parameter of the $d=4$ Kerr black
hole solution) vanishes, the corresponding eleven dimensional
configuration is the coincident D6-antiD6 brane system lifted to
$d = 11$ and precisely for this case, there is a good choice of
coordinate system in eleven dimensions such that when viewed from
ten dimensions, the resulting solution in $d = 10$ is free from
any magnetic flux \cite{Sen:1997pr}. The zero magnetic field
solution turns out to be just the chargeless $p=6$ configuration
found in \cite{Lu:2004ms} when two of the three parameters
characterizing the solution take some specific values and
therefore Brax et. al.'s \cite{Brax:2000cf} interpretation of the
latter solution as the D6-antiD6 system works for this
case\footnote{The same was successfully demonstrated in
\cite{Liang:2001s} for D6-antiD6 system with a net D6-brane charge
using Kerr-NUT solution lifted to ten dimensions.}.

The situation is not so clear for the lower dimensional ($p<6$)
branes. On one side we have chargeless non-supersymmetric
$p$-brane solutions found in \cite{Lu:2004ms} and in order for the
lower dimensional branes to have the interpretation of
brane-antibrane system (as for $p=6$) one may think that a higher dimensional
dipole-like solution (with higher form gauge field) should exist
on the other side. However, no such solutions are known to exist
in the literature. If we recall how the Kaluza-Klein dipole
solution in $d=5$, which is crucial for its interpretation of
monopole-antimonopole (or D6-antiD6 system when embedded in
$d=10$) system was obtained, we find that it is obtained from the
Euclidean Kerr black hole solution in $d=4$ with an extra time
direction added (this can be embedded in $d=11$ by adding six more
flat spatial directions whose reduction on S$^1$ gives D6-antiD6
system). It might seem that lower dimensional brane-antibrane
systems can similarly be obtained from the higher dimensional
($d>4$) Euclidean rotating black holes \cite{Myers:1986un} (with
rotation in only one plane), but the solution one generates by
this procedure in $d=10$ are the D6-branes with tubular topology
R$^{1,p}$ $\times$ S$^{6-p}$ called the tubular D6-branes
\cite{Emparan:2001rp}. The $p=6$ case is the one discussed above
and $p=0$ corresponds to a D6-brane with spherical topology S$^6$.
As for the case of $p=6$, the tubular D6-brane solutions could
also suffer from conical singularities if the background magnetic
flux or from the eleven dimensional viewpoint  a twisted coordinate is
not properly chosen. However, as before, here also a well-tuned
background magnetic flux can be introduced
through a dimensional reduction  along an appropriate
Killing direction of the corresponding eleven dimensional regular
solution with a `good' choice of twisted coordinate.  The magnetic
flux then provides the necessary repulsive force to balance the
gravitational and electromagnetic forces to prevent the
contraction of the tubular D6-brane and gives rise to a static
configuration. When the Euclidean rotation parameter `$a$' (which
measures in an appropriate coordinate system the tubular deformation
of the metric for the tubular D6 brane with the brane topology
R$^{1,p}$ $\times$ S$^{6 - p}$ from the maximal spherical
symmetry S$^{8-p}$), is put to zero, the tubular brane deforms
back to restore the maximal spherical symmetry S$^{8 - p}$, giving
rise to the non-supersymmetric chargeless $p$-brane. For this case
again there is a `good' choice of coordinate system in $d = 11$
such that when viewed from ten dimensions, it makes the solution
free from any magnetic flux and the solution can be interpreted as
static unstable system such as brane-antibrane or non-BPS brane
systems. Interestingly, these are precisely the three parameter
non-supersymmetric $p$-brane solutions found in \cite{Lu:2004ms}
with two of the three parameters restricted to take some specific
values.

In this paper we proceed from backwards. Our primary goal is to
give a proper interpretation of the ten dimensional
non-supersymmetric $p$-brane solutions found in \cite{Lu:2004ms}
by making their connections to bubbles and tubular D6-branes. So,
we first look at the $d=10$ non-supersymmetric $p$-brane solution
in \cite{Lu:2004ms} and after making a coordinate transformation
(this amounts to going to the Schwarzschild coordinate) we find
that for some specific values of two of the three parameters
characterizing the solution, the resulting solution takes the form
of bubbles \cite{Witten:1981gj} when lifted to eleven dimensions.
This means that the $p$-brane solutions are regular in $d=11$,
with the periodicity of the eleventh direction properly chosen,
just like some BPS branes (for example, NS5-brane or D2-brane).
Next we like to understand whether these well-understood bubbles
can give physically meaningful ten dimensional solutions and
whether these static solutions can be interpreted as unstable
systems like brane-antibrane systems or non-BPS branes. For this
purpose we bring out their relations to the well-understood
tubular D6-branes. We find that the ten dimensional
non-supersymmetric $p$-brane solutions \cite{Lu:2004ms} for $p\leq
6$ (with two of the parameters taking specific values as
mentioned) is just a special limit of the tubular D6-brane
solution with topology R$^{1,p}$ $\times$ S$^{6-p}$, when the
Euclidean rotation parameter `$a$' vanishes and the choice of
coordinate system in $d = 11$ is such (with a `good' pair) that
when viewed from ten dimensions, the resulting configuration is
free from any magnetic flux. This connection provides further
evidence for the interpretation of Brax et. al. \cite{Brax:2000cf}
in type IIA theory and also indicates that the localized non-BPS
branes or brane-antibrane systems with lower brane dimensionality
can be obtained from tubular D6-branes when proper limit is taken.
With the exchange of non-BPS brane and brane-antibrane we can also
give same interpretation in type IIB theory in the low energy
supergravity set up.

Without further ado, let us begin with the magnetically charged
non-supersymmetric $p$-brane solutions (static) in ten space-time
dimensions \cite{Lu:2004ms}, \begin{eqnarray} ds^2 &=& F^{\frac{p+1}{8}}
(H{\tilde {H}})^{\frac{2}{7-p}} \left(dr^2 + r^2
d\Omega_{8-p}^2\right) + F^{-\frac{7-p}{8}}\left(-dt^2 +
\sum_{i=1}^p (dx^i)^2 \right)\nonumber\\ e^{2\phi} &=& F^{-a}
\left(\frac{H}{\tilde {H}}\right)^{2\delta},\qquad F_{[8-p]}\,\,\,
=\,\,\, b\,\,{\rm Vol}(\Omega_{8-p}) \end{eqnarray} where\footnote{The
parameter $\theta$ here should not be confused with the angular
coordinate introduced later. Also the parameter $a$ which is the
dilaton coupling here should not be confused with the rotation
parameter `$a$' introduced later.} \begin{eqnarray} F(r) &=& \cosh^2\theta
\left(\frac{H}{\tilde H}\right)^{\alpha} - \sinh^2\theta
\left(\frac{\tilde H}{H}\right)^{\beta}\nonumber\\ H(r) &=& 1+
\frac{\omega^{7-p}}{r^{7-p}}\nonumber\\ \tilde {H}(r) &=& 1 -
\frac{\omega^{7-p}}{r^{7-p}} \end{eqnarray} In the above the metric is given
in the Einstein frame. $a$ is the dilaton coupling which take
values $a=(p-3)/2$ for D$p$-branes and $a=(3-p)/2$ for NSNS
branes. Also $\theta$, $\alpha$, $\beta$, $\delta$, $\omega$ are
integration constants and $b$ is the charge parameter. However,
all these parameters are not independent and they satisfy the
following relations, \begin{eqnarray}
&&\alpha-\beta\,\,\, = \,\,\,a\delta\\
&&\frac{1}{2} \delta^2 + \frac{1}{2}\alpha(\alpha-a\delta)
\,\,\, =\,\,\,
\frac{8-p}{7-p}\\
&&b \,\,\,=\,\,\, (7-p) \omega^{7-p} (\alpha+\beta) \sinh2\theta
\end{eqnarray} It is clear from above that the non-supersymmetric $p$-brane
solutions are characterized by three independent parameters,
namely, $\alpha$, $\theta$ and $\omega$. We would like to remark
that in order to bring connections with the non-BPS branes (or
equal number of brane-antibrane system) as well as with tubular
branes, we need to set $F_{[8-p]}$ to zero and this can be
achieved by setting the parameter $b=\theta = 0$ (see eq.(5)).
This implies that the $p$-brane solutions are chargeless. Now
since in this case the function $F(r)$ appearing in eq.(2) takes
the form $F(r)=\left(H/{\tilde H}\right)^{\alpha}$, the solution
(1) therefore simplifies to \begin{eqnarray} ds^2 &=& (H{\tilde
{H}})^{\frac{2}{7-p}} \left(\frac{H}{\tilde
H}\right)^{\frac{p+1}{8} \alpha}\left(dr^2 + r^2
d\Omega_{8-p}^2\right) + \left(\frac{H}{\tilde
H}\right)^{-\frac{7-p}{8}\alpha}\left(-dt^2 + \sum_{i=1}^p
(dx^i)^2 \right)\nonumber\\ e^{2\phi} &=& \left(\frac{H}{\tilde
{H}}\right)^{-a\alpha + 2\delta},\qquad F_{[8-p]}\,\,\, =\,\,\, 0
\end{eqnarray} Note here that now the solutions are characterized by only
two parameters $\alpha$ and $\omega$. The parameters $\alpha$ and
$\delta$ are again related by eq.(4). We now make a coordinate
transformation \begin{equation} r = \tilde{r}
\left(\frac{1+\sqrt{f}}{2}\right)^{\frac{2}{7-p}} \end{equation} where we
have defined $f = 1 - 4\omega^{7-p}/\tilde{r}^{7-p}$. The
coordinate transformation (7) implies \begin{equation} \tilde{r} = r \left(1+
\frac{\omega^{7-p}}{r^{7-p}}\right)^{\frac{2}{7-p}} = r
H^{\frac{2}{7-p}} \end{equation} From the above two eqs.(7) and (8) we can
obtain, \begin{eqnarray} H &=& 1 + \frac{\omega^{7-p}}{r^{7-p}} =
\frac{2}{\sqrt{f}+1}\nonumber\\ \tilde{H} &=& 1 -
\frac{\omega^{7-p}}{r^{7-p}} = \frac{2\sqrt{f}}{\sqrt{f}+1} \end{eqnarray}
Substituting (9) in eq.(6), the chargeless non-supersymmetric
$p$-brane solutions take the form \begin{eqnarray} ds^2 &=& f^{\frac{1}{7-p} -
\frac{p+1}{16} \alpha} \left(\frac{d\tilde{r}^2}{f} + \tilde{r}^2
d\Omega_{8-p}^2\right) + f^{\frac{7-p}{16}\alpha}\left(-dt^2 +
\sum_{i=1}^p (dx^i)^2 \right)\nonumber\\ e^{2\phi} &=& f^{\frac{a\alpha -
2\delta}{2}},\qquad F_{[8-p]}\,\,\, =\,\,\, 0 \end{eqnarray} where the
function $f$ is as defined before. For now, we can limit ourselves
to consider the above chargeless  solutions in ten dimensional
type IIA theory\footnote{Once we have interpreted the solutions as
representing either D-brane-antiD-brane or non-BPS D brane in Type
IIA theory, then this approach works for IIB theory also since a
supergravity description of a D$p$-anti D$p$ (non-BPS D$p$) system
in IIA gives a non-BPS D$p$ (D$p$-antiD$p$) in IIB theory.}
therefore they can be uplifted to $d=11$. The corresponding
solution is given as, \begin{eqnarray} ds_{11}^2 &=& f^{\frac{a\a-2\d}{3}}
(dx^{11})^2 + f^{-\frac{a\a-2\d}{24}+\frac{1}{7-p}-
\frac{p+1}{16}\a} \left(\frac{ d\tilde{r}^2}{f} + \tilde{r}^2
d\Omega_{8-p}^2\right)\nonumber\\ & & \qquad\qquad\qquad\qquad\qquad +
f^{-\frac{a\a-2\d}{24}+\frac{7-p}{16}\a} \left(-dt^2 +
\sum_{i=1}^{p} (dx^i)^2 \right) \end{eqnarray} where we have used $ds_{11}^2
= e^{4\phi/3} (dx^{11})^2 + e^{-\phi/6} ds^2$, with $ds^2$ the ten
dimensional line element in the Einstein frame. It can now be
easily checked that if the parameters $\a$ and $\d$ take the
following values,
 \begin{eqnarray} \a
&=& \frac{2}{7-p}\nonumber\\ \d &=& \frac{a}{7-p} - \frac{3}{2} \end{eqnarray} then
the eleven dimensional metric takes a very simple form
as\footnote{Note that for D6-brane, $\a=2$ and $\d=0$ and in this
case the similarity between the non-supersymmetric D6-brane with
zero charge (which can also be interpreted as D6-antiD6-brane
system with zero net charge) and the GPS
\cite{Gross:1983hb,Sorkin:1983ns} dipole solution embedded in
eleven dimensions has been noticed in
refs.\cite{Brax:2000cf,Liang:2001s}.}, \begin{equation} ds_{11}^2 = f
(dx^{11})^2 + \frac{d\tilde{r}^2}{f} + \tilde{r}^2 d\Omega_{8-p}^2
- dt^2 + \sum_{i=1}^p (dx^i)^2 \end{equation} The above solutions (13) can be
recognized as the analytic continuation ($t \to i x^{11}$, $x^{11}
\to it$) of $(11-p)$-dimensional Schwarzschild solution with $p$
flat spatial directions added. The configuration (13) is defined
for $\tilde r \ge 4^{1/(7 - p)} \omega$ and describes a minimal
$(8-p)$-dimensional sphere with $p$ flat directions in space when
$\tilde r = 4^{1/(7 - p)} \omega$, i.e., tubular bubbles in
unstable equilibrium \cite{Witten:1981gj}. The eleven dimensional
solutions are perfectly regular with $x^{11}$ having the
periodicity $2\pi R = 4\pi 4^{1/(7-p)} \omega/(7-p)$. However, if
we reduce the solutions along $x^{11}$ to ten dimensions the
solutions take the following form, \begin{eqnarray} ds^2 &=& f^{\frac{1}{8}}
\left(\frac{d\tilde{r}^2}{f} + \tilde{r}^2 d\Omega_{8-p}^2\right)
+ f^{\frac{1}{8}}\left(-dt^2 + \sum_{i=1}^p (dx^i)^2 \right)\nonumber\\
e^{2\phi} &=& f^{\frac{3}{2}}, \end{eqnarray} which, as expected, is just
(10) when the relations in (12) are employed.
 Clearly these solutions look singular
at $\tilde r= r_H = 4^{1/(7-p)} \omega$. The minimal tubular
surface R$^p$ $\times$ S$^{8-p}$, the fixed point set of the
Killing vector $\partial_{x^{11}}$, shrinks to zero size at
$\tilde r=r_H$ and therefore represents a $p$-brane-like null
singularity \cite{Dowker:1995sg}. But the singularity here is not
a concern as mentioned earlier since it is due to the brane source
and we know that the ten dimensional description breaks down there
just like in BPS case. If we indeed want to study it, we have to
lift the configuration to eleven dimensions where the
corresponding metric (13) is regular\footnote{Note that the metric
(13) can be extended to the region of $\tilde r >0$ with a naked
singularity at $\tilde r = 0$. This naked singularity happens in
many other cases and is understood due to the brane sources
located at $\tilde r = r_H$. For this reason, we can limit to
define the metric a valid one only for $\tilde r \ge r_H$ which is
also consistent with the reduced ten dimensional metric (14) where
$\tilde r$ can only be defined for $\tilde r \ge r_H$.}.

Now let us rewrite eq.(13) in terms of some twisted coordinate
(there are many such choices as pointed out in
\cite{Dowker:1995gb,Dowker:1995sg}) as follows. We first write the
line element of the unit $(8-p)$-dimensional sphere as \begin{equation}
d\Omega_{8-p}^2 = d\theta^2 + \sin^2\theta d\varphi^2 +
\cos^2\theta d\Omega_{6-p}^2 \end{equation} where $0 \leq \theta \leq \pi/2$,
$0 \leq \varphi \leq 2\pi$. Then we introduce a new coordinate by
\begin{equation} \tilde{\varphi} = \varphi - \frac{x^{11}}{R} \end{equation} where
$R=2\cdot 4^{1/(7-p)}\omega/(7-p)$ is as given before. Now if
instead of taking $x^{11}$ and $\varphi$ as the independent
coordinates in eq.(13) we take $x^{11}$ and $\tilde{\varphi}$ as
the independent coordinates and express eq.(13) in terms of these
latter coordinates then we find that $ds_{11}^2$ in (13) takes the
form\footnote{Henceforth we will drop `tilde' on $r$ in eqs.(13)
and (14) for brevity.}, \begin{eqnarray} ds_{11}^2 &=& -dt^2 + \sum_{i=1}^p
(dx^i)^2 + \left(f+\frac{r^2\sin^2\theta}{R^2}\right)
\left(dx^{11} + \frac{r^2
\sin^2\theta}{R\left(f+\frac{r^2\sin^2\theta}{R^2}\right)}
d\tilde{\varphi} \right)^2\nonumber\\ & & \qquad +
\frac{f}{\left(f+\frac{r^2\sin^2\theta}{R^2}\right)}
r^2\sin^2\theta d\tilde{\varphi}^2 + \frac{dr^2}{f} + r^2
d\theta^2 + r^2 \cos^2\theta d\Omega_{6-p}^2 \end{eqnarray} Reducing these
solutions to ten dimensions according to the prescription given
earlier we find the corresponding ten dimensional solutions to
have the form, \begin{eqnarray} ds^2 &=&
\left(f+\frac{r^2\sin^2\theta}{R^2}\right)^{\frac{1}{8}}\left(-dt^2
+ \sum_{i=1}^p (dx^i)^2\right) +
\left(f+\frac{r^2\sin^2\theta}{R^2}\right)^{\frac{1}{8}}
\left(\frac{dr^2}{f} + r^2 d\theta^2 \right.\nonumber\\ & & \left. + r^2
\cos^2\theta d\Omega_{6-p}^2 + \frac{f}{\left(f + \frac{r^2
\sin^2\theta}{R^2}\right)} r^2\sin^2\theta
d\tilde{\varphi}^2\right)\nonumber\\ e^{\frac{4\phi}{3}} &=&
\left(f+\frac{r^2\sin^2\theta}{R^2}\right)\,\,\,=\,\,\, 1 -
\frac{4\omega^{7-p}}{r^{7-p}} + \frac{r^2 \sin^2\theta
(7-p)^2}{4\cdot 4^{2/(7-p)} \omega^2}\nonumber\\ A_{\tilde{\varphi}} &=&
\frac{r^2\sin^2\theta e^{-\frac{4\phi}{3}}}{R} \end{eqnarray} Now it can be
easily checked that in these forms the solutions (18) are regular
at $r=r_H$ except at $\theta=0$. In fact one can check for any
possible conical singularities of these solutions away from
$\theta=0$ by looking at the periodicity of the angular coordinate
$\tilde{\varphi}$ and see whether it fails to satisfy the usual
periodicity of $2\pi$ or not. From the form of the metric (18) we
indeed find the circumference to radius ratio
\cite{Emparan:2001rp} \begin{equation}
\left.\frac{2\pi}{\sqrt{g_{rr}}}\,\,\frac{d\sqrt
{g_{\tilde{\varphi}\tilde{\varphi}}}}{dr}
\right|_{r\to r_H} = 2\pi \end{equation}

This result can be understood as follows. Recall
that the original configurations (13) is perfectly regular for $r\geq
r_H$ with well-defined completely independent `good' pair of
coordinates $\varphi$ and $x^{11}$ having respective periodicities
$2\pi$ and $2\pi R$. This implies that (13) is free from any conical singularity
and so is (14). The eleven dimensional configuration (17) which
is obtained from (13) by a change of coordinates (16),
another `good' pair of coordinates ($\tilde\varphi$ and $x^{11}$)
is also free from conical singularity. So, the reduction of (17)
along the corresponding Killing
direction should not produce any conical singularity in the
configuration (18). This is what is manifested in (19).

Another
way to understand (19) is that the reduced solutions (18) can be
regarded as describing a D6-brane with the tubular topology
R$^{1,p}$ $\times$ S$^{6-p}$ located at $r = r_H$ and $\theta =
0$, held in static equilibrium by the external magnetic flux (or
fluxbrane) $B=1/R$. In order to understand this we remark
following \cite{Dowker:1995sg,Emparan:2001rp} that, we have
essentially reduced the eleven dimensional solutions (13) to
$d=10$ by choosing independent coordinates $\tilde\varphi$ and
$x^{11}$ along the Killing vector $\partial_{x^{11}}$. The fixed
points of this Killing vector are at $r=r_H = 4^{1/(7-p)} \omega$
and $\theta=0$ which are located on the tubular surface R$^{1,p}$
$\times$ S$^{6-p}$. As discussed in \cite{Dowker:1995sg}, each of
these points on the sphere\footnote{Bear in mind that monopoles at
antipodal points on the sphere have opposite charges so the net
magnetic charge on the sphere is zero.} S$^{6 - p}$ carries a
Kaluza-Klein monopole charge and therefore the solutions (18)
represent tubular D6 branes with the topology just mentioned.
However, these configurations themselves in the zero background
magnetic field would be unstable and have either time dependence
or the presence of conical singularities because of the brane
tension of the tubular D6-brane. In the particular reduction from
(17) to (18) the attractive forces due to gravitational and
magnetic interactions are cancelled by the repulsive force,
induced by the external magnetic flux (or fluxbrane), which
manifests itself by the absence of conical singularity.  So again,
we understand the configuration (18) free from any conical singularity
from the ten dimensional viewpoint through the force balance.
We thus end
up with a static tubular D6 configuration in $d = 10$ with the
magnetic flux $B=1/R=(7-p)/(2r_H)$ which can be read from (16)
following \cite{Dowker:1995gb,Dowker:1995sg}.

The above discussion
clearly indicates that any choice of non-trivially twisted
coordinate such as (16) in eleven dimensions introduces a
background magnetic flux or fluxbrane in ten dimensions when the
reduction is done along the relevant Killing direction (here with
independent coordinates $\tilde\varphi$ and $x^{11}$ the Killing
direction is $\partial_{x^{11}}$). However, we must caution that
the value of the magnetic flux is unphysically high and as such
this makes the ten dimensional interpretation of the solutions
problematic since the magnetic flux produces curvature in the
non-compact direction which is of the same order as the inverse
size of the compact directions \cite{Dowker:1995gb}. So this
reduction to ten dimensions employed above is used only for the
purpose of showing the force balance and therefore the absence of
conical singularity in (18).

We would like to point out that the tubular D6 brane above has no
net magnetic charge but has a magnetic field due to the magnetic
charge distribution on the sphere S$^{6 - p}$, as given in (18).
This tubular D6 brane can naturally  be interpreted as a pair of
(D6-D$p$)-anti(D6-D$p$)-brane system with their respective brane
topologies R$^{1, p}$ $\times$ S$_+^{6 - p}$ and R$^{1, p}$
$\times$ S$_-^{6-p}$. Here S$^{6 - p}_+$ (S$_-^{6 - p}$)
represents a semi $(6 - p)$-sphere with S$^{6 - p}$ = S$_+^{6 -
p}$ $\bigcup$ S$_-^{6 - p}$.  The notation (D6-D$p$)
(anti(D6-D$p$)) means a D6 (anti D6)  with the above topology and
its own positive (negative) magnetic charge distributed on a
semi-sphere S$^{6 - p}_+$ (S$_-^{6 - p}$) and  with a D$p$ (anti
D$p$) positive (negative) electric-like charge uniformly
distributed on $R^{1,p}$. The D$p$ and anti D$p$ are coincident
and just like the previously discussed coincident D6-antiD6 case
their net charges are always vanishing in the supergravity
configuration in any coordinate system as no electric or
magnetic-like form field associated with the D$p$--anti D$p$ brane
appears. This picture is consistent with what has been discussed
when $p = 6$. We know that the tubular D6-brane appears by a
coordinate twist given in (16) or from the ten dimensional point
of view when a background magnetic flux $B = 1/R$ is introduced.
If we use the original good coordinates $\varphi$ and $x^{11}$,
neither the tubular D6-brane nor the background $B$ is present (as
is clear by the absence of $A_\varphi$ in (14)). This indicates
that the magnetic charges on the sphere S$^{6 - p}$ are caused by
the background magnetic flux through polarization. This further
implies that the tubular D6 brane is created by the background
magnetic flux, too. No background magnetic flux means no tubular
D6 brane. As will be discussed later in the paper, the natural
reduction from eleven to ten is the one without the twist on the
angular coordinate, i.e., from the ten dimensional point of view
without the introduction of the background magnetic flux,
therefore no tubular D6 brane. This indicates that the system
under consideration i.e. (14) indeed represents a $p$-brane-anti
$p$-brane or non-BPS $p$-brane system. The static nature of (14)
as we have shown to follow from the absence of conical singularity
(which can be understood through the force balance as discussed
above), can also be understood by the application of Birkhoff's
theorem to this configuration possessing the maximal spherical
symmetry. This fact was used for $p=6$ by Brax et. al.
\cite{Brax:2000cf} to argue that this configuration can represent
brane-antibrane or non-BPS brane in the supergravity set up.

In the following we will generalize the above discussion by
introducing a Euclidean rotation
parameter `$a$' to the configuration (13). By this, we can avoid unphysically high
magnetic field and also make the connection of (14), interpreted as representing
$p$-brane-anti $p$-brane or non-BPS $p$-brane system, with the tubular D6 branes in a
more general setup. This can be done, as mentioned
in the introductory remarks, by generalizing the KK
dipole solution of GPS \cite{Gross:1983hb, Sorkin:1983ns} with an
addition of a time direction to the Euclidean rotating black holes (with
rotation in only one plane) in higher than four dimensions
\cite{Myers:1986un} and then
embedding the resulting solution into eleven dimensions by adding some
flat spatial directions. The solutions can be written in the form,

\begin{eqnarray}
ds_{11}^2 &=& -dt^2 + \sum_{i=1}^p (dx^i)^2 + \left(\frac{\Delta +
a^2 \sin^2\theta} {\Sigma}\right)\left(dx^{11} - \frac{M r^{p-5} a
\sin^2\theta}{\Delta + a^2 \sin^2\theta} d\varphi\right)^2\nonumber\\ & &
\qquad\qquad + \left[\Sigma\left(\frac{dr^2}{\Delta} +
d\theta^2\right) + \frac{\Sigma \Delta \sin^2\theta}{\Delta + a^2
\sin^2\theta}d\varphi^2 + r^2 \cos^2\theta d\Omega_{6-p}^2\right]
\end{eqnarray}
where `$a$' is the Euclidean rotation parameter and `$M$' is the
Euclidean mass parameter. $\Delta$ and $\Sigma$ are defined as
$\Delta=r^2 - Mr^{p-5} -a^2$ and $\Sigma=r^2-a^2\cos^2\theta$.
For $p=6$ the solution (20) reduces exactly to the GPS dipole solution
embedded in eleven dimensions \cite{Sen:1997pr}. Note that when
the parameter $a\to 0$,
\begin{equation}
\frac{\Delta + a^2 \sin^2\theta}{\Sigma} =
1- \frac{Mr^{p-5}}{r^2 - a^2\cos^2\theta} \rightarrow
1 -\frac{M}{r^{7-p}} \equiv 1 - \frac{r_H^{7-p}}{r^{7-p}} = f
\end{equation}
and the above solution reduces to the solution (13). We will
discuss more about this reduction as we proceed.
These
solutions (20) have `Euclidean' horizons at $r=r_0$, where $r_0$ is the
greatest root of the equation $\Delta=0$ and is given by \begin{equation} r_0^2
= M r_0^{p-5} + a^2 \end{equation} Let us define  \begin{equation} R= \frac{1}{\kappa} =
\frac{2 M r_0^{p-4}}{(7-p) r_0^2 - (5-p) a^2}, \,\,\, \Omega =
\frac{a r_0^{5-p}}{M} \end{equation} with $\kappa$ the surface gravity and
$\Omega$ the Euclidean angular velocity, and \begin{equation} \hat{\varphi} =
\varphi - \Omega x^{11}.\end{equation} The solutions (20) are then regular
for $r\geq r_0$, provided $x^{11}$ has the periodicity $2\pi R$
and $\hat{\varphi}$ has the periodicity $2\pi$. This implies that
$\varphi$ has to be correlated with $x^{11}$ in having a
periodicity \begin{equation} 2\pi \frac{\Omega}{\kappa} = 2\pi \Omega R =
\frac{4\pi a r_0}{(7-p) r_0^2 - (5-p) a^2} \end{equation} in order to have
identifications of spacetime points.
 There are various ways one can reduce these solutions to
ten dimensions. It can be checked that if we choose independent
coordinates $\hat\varphi$ and $x^{11}$ and  reduce (20) along
the Killing vector $\partial_{x^{11}}$ (the Killing vector is
$\partial_{x^{11}} + \Omega \partial_\varphi$ if expressed in
terms of $\varphi$ and $x^{11}$ coordinates), then the fixed point
sets are the whole horizon $r=r_0$. Also, since the coefficient of
$(dx^{11})^2$ vanishes in this case, the corresponding ten
dimensional solutions appear singular. This is a (null) curvature
singularity, indicating the location of the brane source, not a
concern to us as discussed earlier. This case is very much like
what we had in reducing (13) to (14). There are no conical
singularities here, indicating that the repulsive force induced by
the background magnetic flux $B = \Omega$ on the tubular D6 brane
cancels the attractive forces due to the gravitational and
magnetic interactions. Another way to reduce the solutions (20) to
ten dimensions is to take $x^{11}$ and $\varphi$ as independent
coordinates and reduce (20) along the Killing vector
$\partial_{x^{11}}$ (Note that this Killing vector is not the same
as the above). We end up with \begin{eqnarray} ds^2 &=& \left(\frac{\Delta +
a^2 \sin^2\theta}{\Sigma}\right)^{\frac{1}{8}} \left(-dt^2 +
\sum_{i=1}^p (dx^i)^2\right) + \left(\frac{\Delta + a^2
\sin^2\theta} {\Sigma}\right)^{\frac{1}{8}}
\left[\frac{\Sigma}{\Delta} dr^2 + \Sigma d\theta^2 \right.\nonumber\\ & &
\left. + \frac{\Sigma \Delta \sin^2\theta}{\Delta + a^2
\sin^2\theta} d\varphi^2 + r^2 \cos^2 \theta
d\Omega_{6-p}^2\right]\nonumber\\ e^{2\phi} &=& \left(\frac{\Delta + a^2
\sin^2\theta}{\Sigma}\right)^{\frac{3}{2}}\nonumber\\ A_{\varphi} &=&
-\frac{M r^{p-5} a \sin^2\theta}{\Delta + a^2 \sin^2\theta} \end{eqnarray}
Note that the above solutions are the more general tubular D6-brane
branes than the solutions (18) involving an additional parameter `$a$'.
The solutions (26) match exactly with (14) for $a = 0$ with now
$A_{\varphi} = 0$ as expected. However, we expect a problem to
arise when $a \neq 0$ since $x^{11}$ and $\varphi$ cannot be taken
to be entirely independent of each other, a so-called `bad' choice
of coordinates. Their periodicities are actually correlated as
mentioned earlier. As a result of this, conical singularities
arise at $r = r_0$ for these solutions (26). The underlying
picture for these singularities from the ten dimensional view is
that the attractive forces due to the magnetic and gravitational
interactions on the tubular D6-brane are not balanced. There is
still another way to reduce the solutions (20) where the problem
does not arise and that is taking the following $\tilde\varphi$
and $x^{11}$ as independent coordinates and reducing along the
Killing vector $\partial_{x^{11}}$. Introducing the twisted
coordinate \begin{equation} \tilde{\varphi} = \varphi - (\Omega - \kappa)x^{11}
\quad \Rightarrow \quad \varphi = \tilde{\varphi} +
(\Omega-\kappa)x^{11} \end{equation} and treating $\tilde{\varphi}$ and
$x^{11}$ as the independent coordinates in (20) we find the
reduced solutions in $d=10$ as, \begin{eqnarray} ds^2 &=&
\Lambda^{\frac{1}{8}}\left(-dt^2 + \sum_{i=1}^p (dx^i)^2\right) +
\Lambda^{\frac{1}{8}}\left[\Sigma\left(\frac{dr^2}{\Delta} +
d\theta^2\right) + \frac{\Delta \sin^2\theta}{\Lambda}
d\tilde{\varphi}^2 + r^2 \cos^2\theta d\Omega_{6-p}^2\right],\nonumber\\
e^{2\phi} &=& \Lambda^{\frac{3}{2}},\nonumber\\ A_{\tilde{\varphi}} &=&
\frac{(\Omega-\kappa)(r^2-a^2)\sin^2\theta}{\Lambda} - \frac{M
r^{p-5} a \sin^2\theta}{\Sigma\Lambda} \left(1 -
a(\Omega-\kappa)\sin^2\theta\right), \end{eqnarray} where \begin{equation} \Lambda = 1-
\frac{Mr^{p-5}}{\Sigma}\left(1 -
a(\Omega-\kappa)\sin^2\theta\right)^2 +
(\Omega-\kappa)^2(r^2-a^2)\sin^2\theta. \end{equation} Now it can be checked
that with the above value of the background magnetic flux \begin{equation} B =
\Omega - \kappa = \frac{(p-5)r_0 + (p-7)a} {2r_0(r_0+a)}, \end{equation}
there are no conical singularities in the solutions (28). Indeed
we find from the metric in (28) that \begin{equation}
\left.\frac{2\pi}{\sqrt{g_{rr}}}\,\,
\frac{d\sqrt{g_{\tilde{\varphi}
\tilde{\varphi}}}}{dr}\right|_{r\to r_0} = 2\pi. \end{equation} Actually,
this fact can be anticipated from the outset. Recall that the
reduction is along $x^{11}$ but now taking $x^{11}$ and
$\tilde\varphi$ as independent coordinates. From (27) and (24), we
have $\tilde\varphi = \hat{\varphi} + \kappa x^{11}$. Note that
$\hat{\varphi}$, unlike $\varphi$, is independent of $x^{11}$ and
has its own period of $2\pi$ and therefore this relation is
similar to the case in (16). Since $\tilde\varphi$ can be taken
completely independent of $x^{11}$, a good choice of coordinates,
no conical singularities should arise and the total force
acting on the tubular D6-brane must be balanced.

It is clear from (30) that the value of the magnetic flux $B$ can
be made arbitrarily small by adjusting $\Omega$
\cite{Dowker:1995sg} and consequently the ten dimensional
solutions (28) can be trusted. This will also be true for the $B=\Omega$
case. So, the point we want to make is
that although the eleven dimensional solution (20) (or (13) which
is the $a\to 0$ limit of (20)) is perfectly regular and meaningful
in the sense described below (24), their ten dimensional reduction
is not always physically acceptable. So, for example, the reduced
solution (26) has problems of interpretation since it contains
conical singularity for general $a$. The reduced solution (28) is
acceptable only for $a\gg  M^{1/(7-p)}$ which gives
$|B| = |\Omega-\kappa| \ll \kappa$. The $d=10$ non-supersymmetric $p$-brane
solutions (14) are also physically acceptable reduction from (20)
in the $a\to 0$ limit. This can be understood in two ways as follows.
We can take the solution (20) directly and put $a=0$. This will give (13)
and then it could be reduced to ten dimensional solution (14) in the
usual way. Otherwise, we can choose $\hat\varphi$ and $x^{11}$ as
independent pair of `good' coordinates in (20) then reduce it along the
Killing vector $\partial_{x^{11}}$ and finally put $a=0$. This will
also give (14). In other words, various properties regarding solution
(14) can be studied in a similar fashion as the case discussed previously
with $a=0$. For $a$ of the same order as
$M^{1/(7-p)}$, only the eleven dimensional description (20)
or its other
forms related to this one by a change of the so-called `good'
coordinates is appropriate as pointed out in \cite{Sen:1997pr}.
This implies that the best description in making various
connections among the chargeless non-supersymmetric $p$-brane,
bubbles and tubular D6 branes is the eleven dimensional one.

To summarize, in this paper we have tried to interpret the non-supersymmetric,
three parameter $p$-brane solutions \cite{Lu:2004ms} of type II
string theories as $p$-brane-anti $p$-brane or non-BPS $p$-brane systems.
We have also tried to clarify their static nature and the various
singularities by bringing out their relations to tubular bubbles and
tubular D6-branes. First we have shown that when the charge parameter
is put to zero and one other parameter takes a specific value then
the resulting non-supersymmetric $p$-brane solution in different coordinate
system takes the form of tubular bubbles and is regular when uplifted
to $d=11$ given in eq.(13). We argued that the corresponding ten dimensional
solution (14) can be interpreted as $p$-brane-anti $p$-brane or non-BPS $p$
brane systems. Since it is known that these systems are unstable one may
be sceptical how they could be given by static configurations like (14).
We have argued at least in the classical supergravity set up, that there
is no net force acting on such systems conforming the view that unstable
systems in question can be represented by static configurations. To show
this we brought out the connections of the solutions (14) with tubular
D6-branes.

We have seen that in eleven dimensions and in the absence of
rotation parameter `$a$' there are various ways one can choose a
pair of coordinates (one is the compact coordinate $x^{11}$ and
the other is an angular coordinate $\varphi$) and with each choice
(twist) a nonvanishing magnetic flux is introduced in the reduced
(along a related Killing direction) ten dimensional solution (a
tubular D6-brane). In other words one can say that tubular
D6-brane is created by the magnetic flux through polarizations. We
emphasized that when our choice is `good', then in ten dimensions
we get a force balance for a specific value of the magnetic field
(which may not always be physically acceptable) on the tubular
D6-brane otherwise not. In this case the solution also does not
suffer from conical singularity. We have generalized the above
discussion by introducing a rotation parameter `$a$' to the
configuration under consideration. Here we understood the picture
of the absence of conical singularity, force balance and the role
of the various choices of coordinates more clearly. So, for
example, in this case there are various choices of the angular
coordinates such as $\varphi$ in (20), $\hat\varphi$ in (24) or
$\tilde\varphi$ in (27), but not all the choices are `good'. One
such `bad' choice of coordinates is $\varphi$ in (20). As we have
pointed out, for this choice, the periodicities of the coordinates
$\varphi$ and $x^{11}$ are correlated and not really independent
of each other as in the case of other choices like $\hat\varphi$
or $\tilde\varphi$. When we reduce these solutions to ten
dimensions, only for `good' choice of coordinates we get a force
balance and don't have any conical singularity. Two such solutions
are (18) (when there is no parameter `$a$') and (28) (in fact (18)
is the $a \to 0$ limit of (28) with $R$ replaced by $-R$). The
absence of conical singularity for the tubular D6-brane (17) must
imply the same and the corresponding force balance for its ten
dimensional version (18). This in turn implies the same for the
tubular bubbles (13), therefore its ten dimensional version (14)
since (13) is related to (17) by a simple `good' coordinate
change. The manifest absence of conical singularity in either (13)
or (14) is consistent with the above. This very fact explains the
static nature of the tubular bubble (13) or the $p$-brane--anti
$p$-brane (or non-BPS $p$ brane) solution (14) and is in
accordance with Birkhoff's theorem that the spherically symmetric
solution of vacuum Einstein's equation must be static. This also
supports the view that the maximally spherically symmetric
solution (14) which is static can indeed represent unstable
systems like $p$-brane-anti$p$-brane or non-BPS $p$-brane systems
(note that the solutions (14) have the required symmetry and also
they are chargeless as it should be).

It is therefore clear that at the classical supergravity
level there is no force acting between a $p$-brane and
an anti$p$-brane when they are coincident and the system is given by
a static configuration (as is also the case for non-BPS
$p$-brane). This implies that the interaction which causes the
brane annihilation or tachyon condensation occurs only at the
quantum level. Precisely for this reason, we can have a
supergravity configuration appearing as a static configuration at
each moment of the brane annihilation with its ADM mass related to
the interaction energy of the system labelled by the off-shell
tachyon as a parameter at that moment. So, we can use a continuous
family of supergravity configurations with its parameters relating
to the tachyon parameter to study the brane annihilation process.
For example, we can set the ADM mass calculated from the gravity
configuration equal to twice the brane tension plus the tachyon
potential as we did in \cite{Lu:2004dp,Bai:2005jr}. Finally we
would like to mention that even though in this paper we have
interpreted only a subclass of the non-supersymmetric $p$-brane
solutions obtained in \cite{Lu:2004ms}, it seems to us that a similar
interpretation can be given for the general chargeless solution
(10) or (11) as well since it appears that (15)-(19) can be similarly carried
through and they are just sufficient for this purpose. However, whether
the general solution (1) with non-zero $p$-brane charge can have similar
interpretation remains to be seen.

\vspace{.5cm}

\noindent {\bf Acknowledgements}

\vspace{2pt}

We would like to thank Sudipta Mukherji for helpful discussions.
JXL acknowledges support by grants from the Chinese Academy of
Sciences and grants from the NSF of China with Grant No: 90303002,
10588503 and 10535060.

redpajama_set_name: RedPajamaArXiv


text:
Аита (Еита) е бог в етруската митология, владетел на подземното царство.

Известен е главно от изображения и надписи. Обикновено е изобразяван с брада и с шапка (шлем) от вълча глава. Неговите атрибути са корона и скиптър. Отъждествява се с древногръцкия бог Аид (Хадес). Като спътник на Аита е посочвано божеството Терсифай, съответстващо на древногръцката богиня Персефона.

Източници
 Мифы народов мира. Москва. 1980.
 Хронологична история на света. Т. I. Елпис. Велико Търново.

Етруска митология

redpajama_set_name: RedPajamaWikipedia


text:
Q: Closing connection after executing reboot using ssh command I am using the reboot -f command remotely to force reboot a Unix machine.
The problem is that the ssh connection remains active for a long time which I don't know why?
I want to close the ssh connection immediately after rebooting the machine and return to my local shell.
How can i do that?
Note that the reboot command without -f flag does not work.

A: I use the following command:
ssh -t <hostname> 'sudo shutdown --reboot 0 && exit'
Here is what this is doing:

*

*It instructs the machine to reboot in the next moment, but not during this command

*Exits cleanly from SSH

*Maintains the SSH TTY the entire time so sudo is happy and can execute properly.

A: The command reboot -f never returns (unless you didn't have permission to cause a reboot). At the point where it is issued, the SSH client is waiting for something to do, which could be:

*

*the SSH server notifying the client that something happened that requires its attention, for example that there is some output to display, or that the remote command has finished;

*some event on the client side, such as a signal to relay;

*a timer firing up to cause the client to send a keepalive message (and close the connection if the server doesn't reply).

Since the SSH server process is dead, the SSH client won't die until the timer fires up.
If you run ssh remotehost 'reboot -f >/dev/null &', then what happens is:

*

*The remote shell launches the reboot command in the background.

*Because the server-side shell command has exited and there is no process holding the file descriptor for standard output open, the SSH server closes the connection.

*The reboot command causes the machine to reboot.

However, this is not reliable: depending on timing, step 3 might happen before step 2. Adding a timer makes this unlikely:
ssh remotehost '{ sleep 1; reboot -f; } >/dev/null &'

To be absolutely sure that the server side is committed to running reboot, while making sure that it doesn't actually reboot before notifying the client that it is committed, you need an additional notification to go from the server to the client. This can be output through the SSH connection, but it gets complicated.

A: I found this solution to perform the best for me.
Use -o "ServerAliveInterval 2" with your ssh command, like so:
$ ssh -o "ServerAliveInterval 2" root@remotehost reboot

The said option makes the client side poke the server over a secure channel every 2 seconds. Eventually as the rebooting proceeds, it will stop to respond and the client will tear the connection down.

A: Some answers were close, but the right answer is:
ssh user@192.168.0.130 "nohup sudo reboot &>/dev/null & exit"

explanation:

*

*you want to exit as the last command so the status of the last command is 0 (success). You can prepend a sleep if you wish, but it is not necessary

*you need to run reboot in the background, because otherwise the server will close the connection and you will get an error. It will still reboot on most systems but if you are scripting the return status will be error (not 0) even with the command executing properly

*running on the background is not enough, as the stdin and stdout are still attached to the virtual terminal through SSH, so the connection will not be closed. You need to do two extra things for the SSH session to end and leave the command running on the background.

*

*1) you need to redirect stdout and stderr to /dev/null so they are not redirected by the virtual terminal that holds the SSH session. This is the &>/dev/null part.

*2) you need to redirect stdin to an unreadable file in the same fashion. That is what the shell builtin nohup does.

With only a command running on the background dettached from the terminal in every way, exit will close the session and because there are no stdin or stdout left on the virtual terminal SSH will terminate the connection without errors.

A: Have you tried the following
# shutdown -r now

I find that on some systems I worked on in the pass, the reboot command had some problems. Then again I can't find anything in the manpage of shutdown that would do the same as reboot with the -f flag.

A: How about exit from ssh session and reboot system using next command:
ssh login@host "reboot -f"

After this just press Ctrl+C for terminate ssh.

A: I found a solution for this which might be helpful for others as well.
I used the following command to close the connection right after starting the command attached to ssh:
ssh host "command to run on the host machine > /dev/null &"

I don't exactly understand the reason why this command forces the connection to close but at least it was helpful for me. If anyone understands why it kills the ssh connection; please explain.

A: A simple way that I have found, is to command the shutdown/reboot as a background task (using '&'), protecting it from being closed when the session closes with 'nohup' , together with immediate shell/session exit:
nohup shutdown -r now & exit
In this way, the SSH client does not hang, since the session exits immediately, while the remote system proceeds with its reboot asynchronously.

A: This requires a 1 minute delay but has worked reliably for me and solves the problem of the SSH client hang:
    $ sudo shutdown +1; logout

This schedules the system shutdown for 1 minute later which allows time for the logout, and hence SSH termination, to complete. If you want to wait as little time as possible, you could replace the +1 with HH:MM for a rapidly approaching time of day but that may be tricky to time correctly and may have up to a 59 second delay.

A: Try this command:
$ reboot -f && exit

redpajama_set_name: RedPajamaStackExchange


text:
Q: What do I call a building with a variable number of storeys? I'm translating the description of a city block design. The city block (in this particular case) is basically a single building with a variable number of storeys: different sections of this block-sized building have different floor counts.
There's the expression "peremennoy etazhnosti" (переменной этажности) in Russian for this, meaning "of variable floor-count". In a verbatim translation, "of variable storicity".
What could be an English expression for this? Is there a commonly used expression, or should it be translated as-is, "with a variable number of storeys"?

The general design concept of the Solnechny city district provides for the construction of City Block 1.3, a perimeter block with a variable number of storeys.

I've been googling using different word combinations, but failed to find commonly used English expressions for these types of building.
For instance, I googled for "building with sections of different height", but still the result is gibberish.

A: I suggest the term asymmetrical, though it would require follow-up explanation. "The city block is comprised of one asymmetrical building that is divided into sections of varying levels."

A: There's no such thing; here's why:
If it's a single building, as you say, then the total number of stories†  doesn't change.  The total is the total.  A building may be, for example, seven stories on one side and only five on another, but we would nonetheless say it's a seven-story building because the total number of stories remains seven.  Part of the structure being fewer stories doesn't decrease the total number of stories the building has.
Willis Tower in Chicago is 110 stories.  The fact that it has sections that are only 50 stories, 66 stories, and 90 stories doesn't diminish its count of 110 stories or lead anyone to call it anything other than a 110-story building.  That would remain true even if there were a hole creating a giant courtyard, as it were, in the middle of this building that takes up an entire city block.
That said, if you wish to clarify that there are sections that have fewer stories, then you simply say that.  You could say something like, "The block is a courtyard building whose north tower has seven stories and whose remaining towers have five."
†  I'm American, so I'm using the American spelling "story" rather than the British spelling "storey," along with the American plural spelling "stories" rather than the British plural spelling "storeys."

A: What do I call a building with a variable number of storeys?
The general design concept of the Solnechny city district provides for the construction of City Block 1.3, a perimeter block with a variable number of storeys.

If I am understanding this correctly the translation means, a perimeter block where the (variable) number/amount, of storeys can be changed I presume this item of change is regarding one building can be of a different amount of storeys than an adjacent building. Rather than in the afternoon it has more stories than in the morning.
In which case I think a better translation would be
a perimeter block with a undefined number of storeys.

undefined; Cambridge English Dictionary adjective: not clearly described, stated, or known:

The general design concept of the Solnechny city district provides for the construction of City Block 1.3, a perimeter block with a undefined number of storeys

A: "Multistory" complex/building.
Multistory meaning having more than two stories.


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Tamás DEUTSCH
József SZÁJER
Lívia JÁRÓKA
Andrea BOCSKOR
Andor DELI
Kinga GÁL
Enikő GYŐRI
András GYÜRK
Balázs HIDVÉGHI
György HÖLVÉNYI
Ádám KÓSA
Edina TÓTH
László TRÓCSÁNYI
Hungarian MEPs from neighbouring countries
Lóránt VINCZE
Gyula WINKLER
After the European Parliamentary Elections: What's next?
Over 200 million European citizens voted in the European Parliamentary elections that took place May 23-26, raising voter turnout from what was only 42.61 percent in 2014 to 51 percent this year. The new parliament will convene in its first plenary session July 2.
Prior to that first plenary session, the parliamentary political groups will hold their constitutive meetings. A political group must consist of at least 25 MEPs elected in at least one-quarter of the member states and have to notify the outgoing President of the Parliament of their formation by July 1 in order to be officially recognized.
At the first plenary in Strasbourg, July 2 to 4, the newly elected MEPs will elect their President, 14 Vice-Presidents and five Quaestors, who together form the presidency of the Parliament.
European identity can only rely upon the identities of the Member States
Press Release by László Trócsányi The European Parliament held a debate on the Conference on the Future of Europe on […]
Green transition cannot be financed from cohesion and agricultural funds
Press Release by MEP Edina Tóth The European Parliament discussed the Commission's proposal on establishing the Just Transition Fund. Fidesz […]
Parliament will launch the new legislative term by voting on the Parliament's standing committees and sub-committees. The committees will then hold their first meetings to elect their Chairs and Vice-Chairs in the following weeks.
In the second session, July 15-18, the EP may have its first opportunity to elect the President of the European Commission. The Commission President's election requires an absolute majority in Parliament. If the candidate does not have the required majority, the European Council must propose another candidate within a month's time.
Following the election of the Commission President, a list of candidate commissioners (one from each member state) will be adopted by the Council in agreement with the Commission President-elect. These candidates will appear before parliamentary committees in their prospective fields of responsibility; hearings will probably take place in October.
Needless to say, all votes taken by Parliament prior to the May elections remain legally valid for the next Parliament.
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U.S. District Judge Dana Sabraw in San Diego previously ordered the U.S.to return all children under age five to their parents by July 10 and all other minors by July 26. "We're airing on the side of inclusion", he said.
United States officials have resorted to DNA testing on up to 3,000 detained children who remain separated from their migrant parents, a top official said Thursday as President Donald Trump's administration struggles to rapidly reunite families at the center of a border crisis.
"The safety and security is paramount and that it is not uncommon for children to be trafficked or smuggled by those claiming to be parents".
The Department of Health and Human Services is "doing DNA testing to confirm parentage quickly and accurately", HHS Secretary Alex Azar told reporters on a conference call.
The Trump administration on Friday asked a federal judge to grant it more time to reunite some of the almost 3,000 immigrant children who were separated from their parents in recent months under the "zero tolerance" policy.
The Department of Health and Human Services, which is responsible for both children taken from their parents and those who came to the USA with an adult, is now trying to match families. The judge's order requires the government to reunite children under 5 with their parents by Tuesday.
On Thursday, Azar said the Trump administration "will comply" with the deadlines - though he assailed the judge's timetable as "extreme".
About half of the parents of the 101 children are in the custody of Immigration and Customs Enforcement.
The Trump administration is asking a court for more time to reunite families that were separated at the border under its "zero-tolerance" policy to prosecute every person who enters the country illegally.
In Friday's court filing, the federal government asked the court if it will still be in compliance with the 30-day deadline if it struggles to meet it in cases in which it is hard to confirm parentage.
Judge Sabraw's original deadlines for reunification were July 10 for kids under 5, and July 26 for those 5-17.
The order, though, didn't address how or when already-separated families would be reunited. He also ordered the government to make sure all parents had a way to contact their children by July 6.


Who: Soul Decision Group Members: Ken Lewko, Trevor Guthrie, Dave Bowman Birthplace: Vancouver, Canada. History: The trio formed in 1994 while attending Vancouver's Capilano Music College. They released several songs independently, then won a spot on a talent showcase run by the Canadian music video channel MuchMusic in 1998. That led to a recording contract in the great white north, before Universal distributed their work stateside. Style: Boy group music - with a twist. Though they're chisled and toned as the average teen idol act, Soul Decision writes all their own material, and plays their own instruments. They also avoid the slicker R&B-inflected cliches of modern boy groups to work in more '80s rock, soul and even electronic influences. Album: "No One Does It Better," their debut. What's causing a buzz: The single "Faded," which currently stands in the Top 30 of Billboard's Hot Song list. The song won the group opening slots of the current Christina Aguilera tour. They'll open for 'N Sync at The Meadowlands Arena Nov. 6 and 7.


TORONTO, ONTARIO, December 12, 2018 – The Toronto Real Estate Board is concerned about the City of Toronto's continued reliance on the Municipal Land Transfer Tax (MLTT) revenue to balance its budget. TREB's concern is validated by the recent City Finance Department update, being reviewed by City Council on December 13, 2018, showing revenue from the LTT $100 million lower than expected. This will be an ongoing challenge and concern for the City's finances and steps should be taken now to reduce that dependency, notwithstanding that the current overall City budget is expected to see a year-end surplus.
the LTT reduces mobility and discourages right-sizing, thereby reducing the number of homes for sale. Predictably, a reduction in sales contributes to less LTT revenue for the city. The buyer of an average priced home in the City of Toronto now pays $13,335 upfront in MLTT, and this is in addition to a similar $13,335 in LTT to the province.
• First, adjust the tax rates for inflation. Currently, the second highest Toronto LTT rate of 2% is levied on the portion of a home's price above $400,000 with an additional surcharge above $2 million. As house prices have increased, more and more of the value of the home is being taxed at the higher rates. City Council's original intention was to only charge the higher rate on properties above the average price. Under today's conditions, that should mean that the 2% rate should not be applied for any home priced under $843,000 (current average price in Toronto) resulting in an upfront Toronto LTT of $13,335. Instead, the City is charging the higher rate on people purchasing homes priced as much as 52% below the current average priced home.
• Second, adjust the LTT first time home buyer rebate for inflation. When the Toronto LTT was first implemented, Toronto City Council specifically amended the proposal to increase the maximum allowed rebate for first-time buyers to $3,725 (the amount of LTT payable on a $400,000 home), from the originally proposed $2,000 (the amount of LTT payable on a $225,000 home). The $400,000 threshold was chosen because, at the time, that was the average price of a home in Toronto. In essence, City Council decided that they did not want any first-time buyer, who was purchasing up to an average priced home, to have to pay ANY LTT. Unfortunately, this intention is not the reality for most first-time buyers in Toronto today, because the maximum rebate has not kept up with inflation. With the average price of a home in Toronto currently sitting at $843,000, most first-time buyers end up paying a significant balance in LTT. In 2008, the Toronto LTT paid by a first-time buyer purchasing an average priced home would have been zero. In 2018, a first-time buyer purchasing an average priced home would have to pay an upfront $8860 in Toronto LTT after the rebate of $4,475 is applied on top of the provincial LTT.
The unpredictability and unreliability of land transfer taxes as a government revenue stream is one of the many reasons that make these taxes ill-suited for funding important public services, and why it would be irresponsible for any additional municipal governments to pursue this taxing authority and if they do, it should not be granted by the province.
With the City's 2019 Budget process expected to begin soon, TREB looks forward to working with City Council on this important issue.
The post TREB Concerned about City of Toronto LTT Reliance appeared first on TREB Wire.


text:
Science · Technology
Mo Gawdat
"We wear different masks and hide our reality from everyone, including ourselves. Our assumed identities becomes our whole lives, and we start to believe them—even more than others do."
Mo Gawdat has spent most of his career in three large technology companies with a great impact in the world we live in: IBM, Microsoft and Google. In Google he is one of the most popular executives and advises other Googlers on how to improve the world, make good decisions and find balance. In addition, he is a true speaker who inspires thousands of people around the world with his lectures. His book, "The Algorithm of Happiness", is part of the "One billion happy" project, to which he dedicates all his energy, since he considers that "postulating that happiness is available to all is a full-time job".
Participation in CDI:
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Science · Technology | 2018
Which is the algorithm of happiness?


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text:
Mary Lee Hu
"Twining... is used extensively in basketry and also to make loom-woven rugs. I fell in love with it."
Hu first became fascinated with metalwork during high school introductory courses. She later explored more work with metals during a summer camp. She went on to attend Miami University in Oxford, Ohio, for two years and then went to Cranbrook Academy of Art in Bloomfield Hills, Michigan to complete her undergraduate degree. During her undergraduate education Hu developed her skills and continued to work with small scale metalwork and jewelry. In 1966 while earning her graduate degree in Metalsmithing from Southern Illinois University in Carbondale, Illinois, Hu studied under renowned metalsmith L. Brent Kington. It was during this time that Hu started to work with fiber inspired techniques after taking a fiber arts course. This led to the development of her signature style of wire wrapped jewelry. Since the late 1960s Hu has developed new techniques in coiling, wrapping, weaving, knitting, and twining wire. Her work consists mostly woven wire earrings, rings, bracelets, brooches, and neckpieces that emulate natural forms, movements and symmetry.
After completing her MFA, Hu traveled to various places and took up different teaching positions until she joined the metal arts program in the University of Washington School of Art in 1980. She retired from the University as professor emeritus in 2006.
Hu is a member and past-president of the Society of North American Goldsmiths. In 1996 Hu was inducted into the American Craft Council College of Fellows. Hu has received three National Endowment of the Arts Craftsman Fellowships. Her work is in major collections such as the Victoria and Albert Museum, the Renwick Gallery, the American Crafts Museum and the Art Institute of Chicago. Hu is the winner of the 2008 Irving and Yvonne Twining Humber Award for Lifetime Artistic Achievement.
"After I had been weaving for a while, I was examining a Northeast Coast cedar bark basket with a surface texture I liked and found that it used two wefts in each row that were twisting around each other as they went over and under the warps — one went over and the other went under each warp, then they passed each other as they went up and down so as to become twisted. This is called twining and it is used extensively in basketry and also to make loom-woven rugs. I fell in love with it. When twisting two elements, the tighter the twist, and the wider the flat elements are compared to their height, the more of a diagonal one will see in the twist. This diagonal is what attracted me to the way the surface of twining appeared. I wanted to replicate it, so I used two round wires running next to each other to make a wider weft element, and kept my warps closely spaced to give a tighter twist. Using double weft elements has been referred to by others as double twining and I have used it almost exclusively since 1976."
– Mary Lee Hu, Knitted, Knotted, Twisted & Twined: The Jewelry of Mary Lee Hu
Website: www.facerejewelryart.com/artist, http://riograndeblog.com/influencers-jewelry-design-mary-lee-hu/
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After about four months from the last QGIS release, Quantum GIS (QGIS) 2.10 "Pisa" has been released! QGIS 2.10 includes many great new features, tweaks and enhancements to make the most popular Free desktop GIS even more feature filled and useful. Have a look at the new features by visiting the official QGIS 2.10 changelog.
QGIS 2.12 'Lyon' has been released! QGIS 2.6 'Brighton' released! QGIS 2.8 LTR 'Wien' is out! QGIS 2.0 is released for Windows, Mac and Linux!


A pioneering speculative office building, situated in a key city centre site, with extensive public realm and collaborative workspace will bring together the academic and Merchant City areas of Glasgow, in a plan to attract exciting new business to the city centre.
Working with Scottish Enterprise, 3DReid's plan is for a forward-looking building that reflects modern working behaviour – a flexible, collaborative, people-centred space designed for firms eager to innovate through partnership with both academia and industry.
The planned building is on target to achieve BREEAM 'Excellent' and an 'A' EPC rating, and be capable of achieving a Wired Platinum score.


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Asthma is a chronic lung condition caused by chronic inflammation and thickening of the bronchial tubes. It is extremely serious conditions as it can lead to suffocation. Most asthma sufferers are allergic and sensitive. Therefore, whenever their lungs are irritated, the muscles tighten and produce phlegm in the throat. The attacks are usually accompanied with shortness of breath, wheezing, and coughing.
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Note: Even though citrus fruits should be avoided, lemons and lemon juice are considered beneficial for this condition. In fact, lemon juice owes its anti-asthmatic property to vitamin C and unlike other citrus fruits, it has an alkalizing effect.


Fiji Mud & Gold now available through Premium Aquatics.
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There is so much to learn on this topic and this article puts together some pieces that otherwise might take weeks to learn.
Thank you, Beverly! You are right, these are the baby-steps, right here. Your MOBI piece is an incredible overview http://www.mobimotherhood.org/tongue-and-lip-ties.html . Thank you for your work and willingness to share your expertise for the good of moms and babies (and adults affected by TT!).
This is a great article. I especially like the pictures because they speak a thousand words and are more helpful than research articles.
I think docs need to see what we are talking about to learn more.
Thanks for sharing an article that will definitely help others.
Great resources, great links, great job! Thank you.
How do you tell the difference between thrush and the phenomenon portrayed in #5? My son has had a TT and ULT release, but we have also been treating for thrush because of his white tongue, diaper rash, and my breast symptoms.
Hi, Erin! It is still possible you guys are dealing with thrush, as well. Have you looked up pictures or oral thrush in infants? Often it looks like spit up or curdled milk in a baby's mouth, and it can be on the inside of the cheeks as well. The bottom is also where yeast shows up, as you mentioned, as a red rash -- sometimes around the mouth as well.
Super helpful info - I'm bookmarking this to share later and refer back to.
Are you on Tongue Tie Babies Support Group Facebook group? It can be a great place for ideas and information.
An outstanding resource! I use it with my lactation clients here in Boston!