text:
Interview with Helen Johannes
It's always a pleasure to welcome a fantasy author to my blog - I love fantasy as much as Science Fiction, and when the author writes delicious romances in this genre, I'm hooked.
So put your feet up, take a glass of something sparkling and welcome to my blog, Helen. Please. tell us about your latest release and what was your favourite part of writing this book?
My latest release is BLOODSTONE, a fantasy romance retelling of the Beauty and the Beast story. If I had to pick a favorite part of writing this book, I'd have to say it was creating two unusual secondary characters. The first, a blind boy, took me out of my comfort zone because I had to turn off the sense I use most as a writer, vision, and turn on my other senses to imagine how he would navigate the world and perceive the other characters. The second character, a Wehrland she-lion, torments my hero with her enigmatic ways. I had so much fun showing their interaction and engaging all my knowledge of cat behavior to portray her.
Oh that sounds such a great story - and Beauty and The Beast is my favourite fairy tale! Tell us more about your latest release and what you think readers will enjoy about it
Well, let's see. There's romance, danger, magic, humor, mystery—oh!—and petrified dragon's blood!
Bloodstones, drops of the legendary last dragon's blood, are rare, precious, and powerful. Mirianna and her gem-cutter father want these stones to fulfill a jewelry commission. The Shadow Man, a cursed warrior whose unveiled appearance can kill, makes his living in the wilderness collecting bloodstones and other gems. The only source of these gems is a no-man's land infested by beast-men, dark magic, and a dead—or sleeping?—dragon. Daytime there is dangerous enough, but the night—the dark—has power of its own, linking lovers in dreams long before they meet. Only in this borderland between good and evil would Mirianna believe a lion might speak to her and she might trust her heart to a man she can only see in the dark.
Wow, what an interesting concept. What comes first: the plot or the characters?
I'm a "pantser" so I get a vague idea of plot points and a couple of characters, and then I set out with them out on a journey. Along the way, the characters reveal their secrets—often in surprising ways—and the storyline changes from what I originally thought to what will suit the needs of the characters. Secondary characters emerge to take on roles I hadn't consciously envisioned for them but that prove to be significant to the plot. When there is a "big reveal" in the plot, it's usually because a hint a character dropped back in chapter two suddenly becomes integral to the plot and has been simmering under the surface all along. Then I go back and enhance that in the revision process.
Do you have a support system? Do you have a writing community? What valuable lessons have you learned from them?
I belong to Romance Writers of America, and my particular support group is the small group belonging to my local area. Even though we write a variety of romance genres, we are extremely close-knit and stay in contact by email between monthly meetings. If any one of us needs a quick answer to a question or help with a writing problem, someone will quickly reply. We bring a variety of experiences to the table and are willing to share.
The most important lesson I've learned is to listen to everyone. We may not always agree with what we hear, but we need to give it consideration. Sometimes the best ideas and insights come from the least likely sources.
I also occasionally serve as a judge for contests, and I've learned a lot from reading and critiquing other people's writing. Sometimes it's easier to see a flaw in someone else's work first, and then I can find it in my own.
You are so right there, Helen. I've found the same thing myself, when judging conests. Is there any advice, as a new writer, that you were either given, or wish you had been given?
It would be nice to say I was an overnight success. Lesson #1 is that most writers aren't. It can take 5, 10, 15 years or more to break in, so you have to be both persistent and patient. Remember the tortoise and the hare.
Lesson #2 is that you perfect your craft by both writing AND reading. It's true that you don't want to be unduly influenced by other authors' ideas, but I can't fathom how some people want to publish when they don't even like to or want to read. And they can't be bothered with revision. I was always a reader, and I studied the classics, so I learned craft from the best. But, like all newbies, I thought what I wrote in my first draft was golden. I had to learn to 'kill my darlings' because sometimes they just had to die. And, oh gosh, adverbs had to go.
I couldn't agree more. You learn so much from reading other people's books, and it always makes me want to strive to be as good as they are. As for revision, I love the whole process and tend to find it hard to know when to stop - and those pesky adverbs are a real challenge!
So...hat do you do for fun when not writing?
I read, watch movies, take walks, and travel as often as I can. I fill my bookshelves with romances (of course), mysteries, and young adult books. My favorite authors include Rick Riordan, Susan Elizabeth Phillips, Nora Roberts, Janet Evanovich, Amanda Quick, Darynda Jones, and Jennifer Crusie, to name just a few. On my keeper shelf you'll find the Artemis Fowl series, The Wizard of Earthsea, all the Harry Potter books, The Hunt for Red October, Agatha Christie mysteries, Inkheart, and all of the Amelia Peabody Egyptian mysteries, among others. I enjoy being outdoors, especially in the spring, and I love discovering new places and revisiting any place with a castle or beach/ocean access.
That sounds great - you'd love my homeland of Wales, it's full of castles! :) Thank you so much for being with us today, Helen. Now while you relax let's have a look at your amazing fantasy novels.
THE PRINCE OF VAL-FEYRIDGE, 2011 EPIC WINNER in Fantasy Romance from The Wild Rose Press - A warrior with a destiny, a woman with a gift. Can loving the enemy restore a broken kingdom? Or will forbidden love destroy it—and them—first?
BLOODSTONE, 2011 LAUNCHING A STAR WINNER in Fantasy Romance, available now from Amazon and The Wild Rose Press
http://helencjohannes.blogspot.com/
http://www.helencjohannes.com
http://thewildrosepress.com
BLOODSTONE, 2011 Launching a Star Winner in Fantasy Romance, The Wild Rose Press
What if looking at the face of the man you loved meant death?
Years ago, warrior Durren Drakkonwehr was cursed by a mage. Now feared and reviled as the Shadow Man, he keeps to himself, only going to town to trade rare bloodstones—petrified dragon's blood—for supplies. Though he hides his face, he can't hide his heart from the woman who haunts his dreams…
Needing bloodstones for a jewelry commission, Mirianna and her father journey across the dreaded Wehrland where the beast-men roam. When their party is attacked, only the Shadow Man can save them. Strangely drawn to him, Mirianna offers herself in return for her father's rescue.
Living in the ruined fortress with the Shadow Man, Mirianna slowly realizes that a flesh-and-blood man, not a fiend hides there in hoods and darkness. But are love and courage enough to lift the curse and restore the man?
"What about us? What do we do?"
Only the hood rotated, cocking with exaggerated deliberation. "Why, you die, old man."
Her father blanched. His grip on Mirianna's arms faltered.
She saw the Shadow Man turn, saw the muscles of his thighs bunch as he prepared to leap down the hillside, saw, in the corner of her eye, shapes gathering along the tree line below, horrible shapes she'd seen only hours before rushing at her from a darkened clearing. With a shudder, she broke from her father's grasp.
"Please!" She reached out to the black sleeve. "Help us!"
He recoiled at her touch like one snake-bitten. The sudden, sharp focus of his regard staggered her, but she backed no more than a step. No matter how he terrified her, he'd helped her once. She'd been led to him again, and not, her instincts told her, without reason.
"Please," she repeated. "Help us. I—we'll do anything."
His voice was a whisper that caressed flesh. Mirianna's stomach quivered. Her breasts tingled. Her mouth grew even drier. Without thinking, she slid her tongue along her lips. Vaguely, she wondered what she'd done. And why time seemed suspended, as if everyone but she and the Shadow Man had been cast in stone and all sound arrested. All sound except the taut, guttural repeat of his question.
THE PRINCE OF VAL-FEYRIDGE, 2011 EPIC Winner in Fantasy Romance, The Wild Rose Press
A warrior with a destiny, a woman with a gift. Can loving the enemy restore a broken kingdom? Or will forbidden love destroy it—and them—first?
Prince Arn has a destiny—an ancient throne—but he's not waiting for fate to deliver when he can act now, before his enemies organize against him. The healer Aerid longs for her barely remembered homeland. Marked out by her gift and her foreign looks, she insists she is no witch. The swordsman Naed hopes to honorably defend his uncle's holding, but he harbors a secret fascination for the exotic healer. Prince Arn's campaign against Aerid's homeland throws them into a triangle of forbidden love, betrayal, and heartbreak. Only when they realize love is blood-kin to friendship, and neither is possible without risk, can they forge a new alliance and restore a kingdom.
Aerid could not recall how she came to be in the Great Hall, or how water and bandages materialized on trestle tables there.
Naed sat slumped against the wall while Yormoc tugged off his tunic and armor. Blood painted Naed's arm, but she could see the wound was only a finger in length.
"Get me up, fool, or 'tis your hide I'll line my chair with!" Her master Dranoel sat up, took in the guards at the door, and his ashen face paled further.
Yormoc examined the cloth he had been holding to his gashed jaw. "They haven't killed us yet. 'Tis like they don't mean to."
Dranoel visibly fought for control. "Mayhap the bastard Prince has some honor, then."
"Some honor!" Aerid sputtered. Did no one but she understand what they faced? "Belike they'll be keeping us for their sport, killing us one by one to feed their savage appetites. These be Tolemaks we speak of, and what be they if not barbarians and
their master a Prince of savages!"
Dranoel blanched at her words. Yormoc froze. Even Naed's head came up. But not a man of them stared at her.
Cold dread filled Aerid. She whirled.
In the doorway stood a scarlet-cloaked figure so tall his ebony hair brushed the cross-beam, so lean Aerid sensed nothing but bone and muscle and will, a will so strong it emanated from the deep-set, stone-gray eyes. High cheekbones gave his face a noble, arrogant look. The curve of his lips mocked her. The scar cutting across the left side of his face from behind the eyebrow to the corner of the chin mocked nothing.
"Pray, go on." The Prince of Val-Feyridge planted his boot on a bench and rested a hand on the upraised knee. "Or have you lost your nerve?"
Author Helen C. Johannes lives in the Midwest with her husband and grown children. Growing up, she read fairy tales, Tolkien, The Scarlet Pimpernel, Agatha Christie, Shakespeare, and Ayn Rand, an unusual mix that undoubtedly explains why the themes, characters, and locales in her writing play out in tales of love and adventure. A member of Romance Writers of America, she credits the friends she has made and the critiques she's received from her chapter members for encouraging her to achieve her dream of publication. When not working on her next writing project, she teaches English, reads all kinds of fiction, enjoys walks, and travels as often as possible.
Blog: http://helencjohannes.blogspot.com/
Bloodstone: Amazon: http://amzn.com/B00G8GTHRC
The Prince of Val-Feyridge: Amazon: http://amzn.com/B003JH8CO2
(Available in both print and e-versions from Amazon, Barnes and Noble, and The Wild Rose Press)
Labels: Beauty And The Beast, bloodstone, Fantasy Romance, Helen Johannes, The Prince Of Val-Feyridge
Unseasonal War - SF Virtual Book tour - David Englund
It's always a pleasure to welcome an author who writes Science Fiction to the Flight Deck. I have to say David Englund's book sounds like a wonderful read and is definitely on my TBR list.
David will be awarding a digital copy of Unseasonal War to a randomly drawn commenter at every stop during the tour. You can find the other stops on the tour HERE. Remember, the more you comment, the better your chances of winning.
So strap yourself in, order something sparkling fron the autodispenser, and enjoy the ride. Let's find out more about Unseasonal War by David Englund
Unseasonal War
by David Englund
Clark Jackson's travels, for the first time, put him in touch with an intriguing species remarkably human-like. He becomes instantly fascinated with the Fronents and envious of their advanced technology. Striving to befriend them and learn more, his uncontrolled enthusiasm forsakes the use of appropriate caution and suspicion. Could their cold reception be a byproduct of their war with a vile species in this corner of the universe, or something else?
The magnificent splendor of an unexplored galaxy, new species to encounter and the adrenalin rush of space battle feed Clark's awestruck hunger for exploration and adventure. Unfortunately, the more he learns the more he questions; including the wisdom of his entangled involvement in their war.
Meanwhile, back home in Des Moines, Iowa, Clark attempts to maintain an inconspicuous lifestyle to avoid attracting the attention of a certain relentless federal agency. His girlfriend's own secret, however, could unravel it all.
**Even though the book is the second book in the series, it IS standalone
Excerpt Tour
Clark studied the face before him. The old creature carried a soft, wise and caring tone during the discussion. This alien was easy to admire, however, it was difficult to get beyond the ruthless features. The enormous bulk, massive display of teeth, scaly skin and intense eyes gave Clark shivers. It would ease the conversation to talk with eyes closed but probably create the opposite affect desired for diplomacy.
Clark forced himself back to the discussion. "Is this why you live in the caves?"
The pair of alligator eyes saddened. "We did not always live in the caves. Many vrems ago we lived out on the plains. We farmed many fields and grew many crops. We had villages to congregate in but most of our people lived in the vast openness of the farms. There were many more of our people back then too. Then came the aliens. They destroyed our farms and stole a great many of our people. We have since discovered that they use our people to work as slaves on their world."
"Did you already know these aliens when they attacked?"
"At that time we had never had any contact with anyone from the stars. We know them well now, however."
"Have you met other aliens since then?"
"Let us stay on the topic of our three races, shall we? Do your people fight any wars with other races? How do these conflicts begin for you?"
"Our world has not gotten to the point yet in which we can travel to other worlds, so we have not met any alien races that I am aware of."
"And yet you are here."
David Englund is a storyteller (science fiction author) and teaches economics at North Dakota State University. His first two titles, Upsetting the Tides and UNSEASONAL WAR are available on Amazon. Camouflaged Encounters is due out in late 2014 and the fourth and fifth books are in progress.
http://amazon.com/dp/B00F4MHDWM
http://davidjenglund.blogspot.com
https://www.facebook.com/david.englund.104
Labels: Book Tours, David Englund, Goddess Fish, Science Fiction Thriller, Unseasonal War


text:
\section{Introduction}

Discovery of Higgs boson has brought about a lot of activities concerned with
the origin of this particle. Although various models have been proposed, the
convincing one does not seem to exist. Higgs boson was introduced as a
particular particle that spontaneously violates the gauge symmetry. Thus, it
is important to investigate the origin of this boson. One candidate could be
to consider the extra dimensions to our real space that we are recognizing and
to reduce the extra dimensions by considering the equivariance of symmetries
involved\cite{Popov,Manton:2010wu,Chatzistavrakidis:2010tq,Madore:1994mj,Harland:2009kg}.

Equivariance implies that the symmetry of the real space is related to that of
the internal space, so that the shifted point in the real space can be sent
back to the original point by the symmetry transformation in the internal
space. Thus the extra dimensional space, even when it is there, could have
been unobserved if the symmetry of the extra space is equivariant to the gauge
symmetry of the real space, that we are actually living in. The gauge fields in
the extra dimensional space are observed as the Higgs fields in the real space.
In other words, the Higgs fields can be considered as the gauge fields in the
extra dimensional space.

Consider, for example, the case of $R^{2}\times S^{2}$, where the real space
is $R^{2}$ and the extra space is $S^{2}$\cite{Popov,Manton:2010wu}.
Equivariance on $S^{2}$ implies that pure Yang-Mills (YM) theory
is recognized as Yang-Mills-Higgs (YMH) model on $R^{2}$. Thus, self dual (SD)
equation on $R^{2}\times S^{2}$ is equivalent to
Bogomol'nyi-Prasad-Sommerfield (BPS) equation on $R^{2}$\cite{Bogomolny:1975de}.
 Invisibility of the extra dimensions is
guaranteed by the fact that configuration of the ground state is equivariant.
Such an equivariant gauge configuration can be constructed using the simplest
equivariant quantity $Q\equiv i\hat{x}_{a}\sigma_{a}$, where $\hat{x}_{a}$ is
three dimensional coordinate describing $S^{2}$ and $i\sigma_{a}/2$ is the
gauge symmetry generator. This also describes the configuration of the so
called \textquotedblleft Witten ansatz\textquotedblright\cite{Witten:1976ck}.

Equivalence of pure YM theory and YMH model through the existence of extra
dimensional space, has been discussed also in other models, with a little more
generality, like in the coset space $S/R$ \cite{Popov}
\cite{Manton:2010wu} model or the fuzzy version of it,
$(S/R)_{F}$ \cite{Chatzistavrakidis:2010tq,Madore:1994mj,Harland:2009kg}.

We have seen a similar extra dimensions for the case of noncommutative $Z_2$, using the method of differential forms\cite{Ikemori:2008pb} (see also \cite{Teo:1997cn})
and introducing the coordinates of noncommutative $Z_2$ space\cite{Otsu}.
In those papers, we have shown that difference of vortex and instanton can be considered as the difference that  the space
where they exist is $R^2\times Z_2$, and $R^4$, and that they satisfy the same self dual equation in each space. This implies that
the vortex may be treated analytically as the instanton.
It would be expected that such a construction brings us many advantages to understand the solution for the vortex equation.
However, the concepts of equivariance, so far, was not unambiguous in this approach.

In the present paper we would like to show that equivariance is important in
this case also and we have explicitly defined $Q$ in noncommutative $Z_{2}$ space, thus we
can introduce \textquotedblleft Witten ansatz\textquotedblright\ for the
noncommutative $Z_{2}$ space, which leads to equivalence of SD equation on
$R^{2}\times Z_{2}$ to BPS equation on $R^{2}$.

Dimensional reduction through the use of equivariance principle especially for
the case of $S^{2}$ and SU(2) gauge symmetry, we have to have at
least a larger symmetry group that includes SU(2) as a subgroup. On the other
hand, in the model that we are proposing, the extra space is a
discrete $Z_{2}$, and the relevant symmetry for the equivariance
is the discrete part of the gauge symmetry. Thus, there is no need to consider
a larger gauge symmetry i.e. we could remain with the same gauge symmetry, and
this could be the simplest possible model of this kind.

In the next sections, we recapitulate the arguments of the dimensional
reduction for the YM theory on $R^{2}\times S^{2}$ based on the equivariance
principle. And based on this argument, we consider the YM theory on
$R^{2}\times Z_{2}$. The last section is devoted to discussions.

\section{Equivariance on $R^{2}\times S^{2}$ Model}

As stated in the previous section, extra dimensional space orthogonal to the
real space, can be left unobserved when the
symmetry of the extra dimensional space were equivariant to the gauge symmetry
of the real world. Instead, the gauge field on the extra dimensional space
makes its appearance as the Higgs field in our world. For the invisible extra
dimensional space, the gauge invariant ground state has to be an equivariant
configuration. For example, let us consider SU($2N$) gauge symmetric model on
$R^{2}\times S^{2} $. In this case, $S^{2}$ can become equivariant extra
dimensional space, when the gauge configuration on $S^{2}$ is described in
terms of equivariant basic quantity $Q\equiv i\hat x_{a}\sigma_{a}$.

In order to confirm equivariance, we examine whether the following symmetry
equations, which are due to Forgacs \& Manton\cite{Forgacs:1979zs},
\begin{align}
&\epsilon_{ijk}x_{j}\partial_{k}A_{l}+\epsilon_{ilk}A_{k}-[\mathcal{J
_{i},A_{l}]=0,\\
&\epsilon_{ijk}x_{j}\partial_{k}B-[\mathcal{J}_{i},B]=0\nonumber
\end{align}
are satisfied or not. Here $A_{i}$ is a vector and $B$ is a
scalar, $\mathcal{J}_{i}$ is a generator of internal space. For example, as
$Q$ is a scalar, we substitute $B=Q$ and we obtain
\begin{equation}
\epsilon_{ijk}x_{j}\partial_{k}Q=\epsilon_{ijk}x_{j}\partial_{k}(i\hat{x
_{l}\sigma_{l})=i\epsilon_{ijk}x_{j}\sigma_{k}.
\end{equation}
As $\mathcal{J}_{i}=i\sigma_{i}/2$, we have
\begin{equation}
\lbrack\mathcal{J}_{i},Q]=\left[i{\frac{\sigma_{i}}{2}},i\hat{x}_{l}\sigma
_{l}\right]=i\epsilon_{ijk}\hat{x}_{j}\sigma_{k},
\end{equation}
thus $Q$ satisfies the symmetry equation. In other words, when the ground
state is described in terms of Q , the existence of $S^{2}$ could have been
unobserved. Also, the gauge symmetry SU($2N$) is reduced to the
smaller symmetry.

As $Q^{2}=-1$, the vectors that can be constructed from Q are
$\partial_{a}Q$ and $Q\partial_{a}Q$. Thus, the most general gauge
configuration can be written as
\begin{equation}
\displaystyle{A_{a}={\frac{i}{2}}(\varphi_{1}-1)\partial_{a}Q+{\frac{i}{2
}\varphi_{2}Q\partial_{a}Q}.
\end{equation}
Since
\begin{align}
&\partial_{a}Q=i\partial_{a}(\hat{x}_{b}\sigma_{b})={\frac{i}{r}}(\delta
_{ab}-\hat{x}_{a}\hat{x}_{b})\sigma_{b},\\
&Q\partial_{a}Q=-{\frac{1}{r}}(\hat{x}_{c}\sigma_{c})(\delta_{ab}-\hat{x
_{a}\hat{x}_{b})\sigma_{b}=-{\frac{i}{r}}\epsilon_{acd}\hat{x}_{d}\sigma_{c},
\end{align}
we can rewrite $A_{a}$ in terms of these as\cite{Eto}
\begin{equation}
A_{a}={\frac{i}{2r}}\left[  (H^{\dagger}-1)\omega_{ab}+(H-1)\omega
_{ab}^{\dagger}\right]  \sigma_{b},\quad\omega_{ab}\equiv i(\delta_{ab
-\hat{x}_{a}\hat{x}_{b}+i\epsilon_{abc}\hat{x}_{c}),
\end{equation}
where
\begin{equation}
\varphi_{1}={\frac{H^{\dagger}+H}{2}},\quad\varphi_{2}={\frac{H^{\dagger
-H}{2}}i.
\end{equation}
This is the \textquotedblleft Witten ansatz\textquotedblright\cite{Witten:1976ck}.
In terms of stereographically projected coordinates
\begin{equation}
y={\frac{\hat{x}_{1}-i\hat{x}_{2}}{1-x_{3}}}=e^{-i\varphi}\tan{\frac{\theta
}{2}},\quad\bar{y}={\frac{\hat{x}_{1}+i\hat{x}_{2}}{1-x_{3}}}=e^{i\varphi
\tan{\frac{\theta}{2}}
\end{equation}
$Q$ can be rewritten as
\begin{equation}
Q={\frac{i}{{1+y\bar{y}}}}\left(
\begin{array}
[c]{cc
-1+y\bar{y} & 2y\\
2\bar{y} & 1-y\bar{y
\end{array}
\right)
\end{equation}
Using these, the Witten ansatz can be rewritten through the singular gauge
transformation
\begin{equation}
g=\left(
\begin{array}
[c]{cc
\cos\displaystyle{\frac{\theta}{2}} & e^{-i\varphi}\sin\displaystyle{\frac
{\theta}{2}}\\
-e^{i\varphi}\sin\displaystyle{\frac{\theta}{2}} & \cos\displaystyle{\frac
{\theta}{2}
\end{array}
\right)  ={\frac{1}{\sqrt{1+y\bar{y}}}}\left(
\begin{array}
[c]{cc
1 & y\\
-\bar{y} & 1
\end{array}
\right)  ,
\end{equation}
which leads to nothing but the gauge configuration of Manton \& Sakai\cite{Manton:2010wu}
\begin{equation}
{A}_{y}^{\mathrm{MS}}={\frac{i}{1+y\bar{y}}}\left(
\begin{array}
[c]{cc
-\bar{y}/2 & iH^{\dagger}\\
0 & \bar{y}/2
\end{array}
\right)  ={\frac{1}{1+y\bar{y}}}\left(  -\Phi-i\Lambda\bar{y}\right)
,\quad\left(  \Lambda\equiv{\frac{1}{2}}\sigma_{3},\ \Phi\equiv H^{\dagger
}\sigma_{+}\right)
\end{equation
\begin{equation}
{A}_{\bar{y}}^{\mathrm{MS}}={\frac{i}{1+y\bar{y}}}\left(
\begin{array}
[c]{cc
y/2 & 0\\
-iH & -y/2
\end{array}
\right)  ={\frac{1}{1+y\bar{y}}}\left(  \bar{\Phi}+i\Lambda y\right)  .
\end{equation}
A generator for rotation around the third axis is
\begin{equation}
x_{2}{\frac{\partial}{\partial x_{1}}}-x_{1}{\frac{\partial}{\partial x_{2}
}=i\left(  -y{\frac{\partial}{\partial y}}+\bar{y}{\frac{\partial
{\partial\bar{y}}}\right)  ,
\end{equation}
and a generator for the gauge transformation around $\sigma_{3}$ axis is
$i\Lambda$. Using these, the symmetry
equation\cite{Forgacs:1979zs} reads
\begin{align}
\left(  -y{\frac{\partial}{\partial y}}+\bar{y}{\frac{\partial}{\partial
\bar{y}}}\right)  A_{y}+\left[  {\frac{i}{2}}\sigma_{3},A_{y}\right]   &
=A_{y},\\
\left(  -y{\frac{\partial}{\partial y}}+\bar{y}{\frac{\partial}{\partial
\bar{y}}}\right)  A_{\bar{y}}+\left[  {\frac{i}{2}}\sigma_{3},A_{\bar{y
}\right]   &  =-A_{\bar{y}}.\nonumber
\end{align}
$A_{y}^{\mathrm{MS}},A_{\bar{y}}^{\mathrm{MS}}$ satisfies the above equation
and thus are the equivariant configurations.

Assuming that these configurations describe the ground state in $S^{2}$ it can
be shown that the pure YM theory in $R^{2}\times S^{2}$ is equivalent with
the YMH theory in $R^{2}$, i.e. SD equation for this model is
\begin{equation}
\left\{
\begin{array}
[c]{l
\displaystyle{\frac{8}{(1+y\bar{y})^{2}}}{F}_{z\bar{z}}={F}_{y\bar{y}},\\
{F}_{z\bar{y}}=0,\\
{F}_{\bar{z}y}=0,
\end{array}
\right.
\end{equation}
and substituting the above configuration, each turns into the respective BPS
equation
\begin{equation}
\left\{
\begin{array}
[c]{l
F_{z\bar{z}}=\displaystyle{\frac{1}{8}}(2i\Lambda-[\Phi,\bar{\Phi}]),\\
D_{z}\bar{\Phi}=0,\\
D_{\bar{z}}\Phi=0.
\end{array}
\right.
\end{equation}
Here $z,\bar{z}$ are the coordinates on $R^{2}$, and $F_{z\bar{z}
=\partial_{z}A_{\bar{z}}-\partial_{\bar{z}}A_{z}+[A_{z},A_{\bar{z}}]$,
$D_{z}\bar{\Phi}=\partial_{z}\bar{\Phi}+[A_{z},\bar{\Phi}]$, $D_{\bar{z}
\Phi=\partial_{\bar{z}}\Phi+[A_{\bar{z}},\Phi]$. Namely, gauge field on
$S^{2}$ is recognized as Higgs field on $R^{2}$. On the other
hand, $A_{z},A_{\bar{z}}$ are the gauge fields on the real space
$R^{2}$, they are not transformed by $\Lambda$, i.e.
\begin{equation}
\lbrack\Lambda,A_{z}]=[\Lambda,A_{\bar{z}}]=0.
\end{equation}
Then,
\begin{equation}
A_{z}=\left(
\begin{array}
[c]{cc
A_{z}^{L} & 0\\
0 & A_{z}^{R
\end{array}
\right)  ,\quad A_{\bar{z}}=\left(
\begin{array}
[c]{cc
A_{\bar{z}}^{L} & 0\\
0 & A_{\bar{z}}^{R
\end{array}
\right)  ,
\end{equation}
and SU(2$N$) gauge symmetry reduces to $\mathrm{S}\left(  \mathrm{U
(N)_{L}\times\mathrm{U}(N)_{R}\right)  $. As a consequence, the BPS equation
is reduced further to
\begin{equation}
\left\{
\begin{array}
[c]{l
F_{z\bar{z}}^{L}=\displaystyle{\frac{1}{8}}(-1+H^{\dagger}H),\quad F_{z\bar
{z}}^{R}=\displaystyle{\frac{1}{8}}(1-HH^{\dagger}),\\
D_{z}H^{\dagger}=0,\quad D_{\bar{z}}H=0.
\end{array}
\right.
\end{equation}

\section{Equivariance on $R^{2}\times Z_{2}$ Model}

In this section we consider the case where the extra dimensional space is
noncommutative $Z_{2}$. As a gauge symmetry we consider SU($N$). In order to
make the $Z_{2}$ space invisible, we choose $i\tau_{3}$ as an
equivariant quantity $Q$, of which each component is $N\times N$ SU($N$)
matrix. This matrix describes the $Z_{2}$ space and is
itself the block matrix each block expressing the SU($N$).

The coordinates of noncommutative $Z_{2}$ space are described as\cite{Otsu}
\begin{equation}
w=\left(
\begin{array}
[c]{cc
0 & 1\\
0 & 0
\end{array}
\right)  ={\frac{\tau_{1}+i\tau_{2}}{2}},\quad\bar{w}=\left(
\begin{array}
[c]{cc
0 & 0\\
1 & 0
\end{array}
\right)  ={\frac{\tau_{1}-i\tau_{2}}{2}}.
\end{equation}
Coordinate transformation for $Z_{2}$ space is discrete, and can
be realized by $i\tau_{1}$, i.e.
\begin{equation}
(i\tau_{1})w(-i\tau_{1})=\left(
\begin{array}
[c]{cc
0 & 1\\
1 & 0
\end{array}
\right)  \left(
\begin{array}
[c]{cc
0 & 1\\
0 & 0
\end{array}
\right)  \left(
\begin{array}
[c]{cc
0 & 1\\
1 & 0
\end{array}
\right)  =\left(
\begin{array}
[c]{cc
0 & 0\\
1 & 0
\end{array}
\right)  =\bar{w}.
\end{equation}
If we transform $Q(=i\tau_{3})$ by the $i\tau_1$, we obtain
\begin{equation}
(i\tau_{1})i\tau_{3}(-i\tau_{1})=i\left(
\begin{array}
[c]{cc
0 & 1\\
1 & 0
\end{array}
\right)  \left(
\begin{array}
[c]{cc
1 & 0\\
0 & -1
\end{array}
\right)  \left(
\begin{array}
[c]{cc
0 & 1\\
1 & 0
\end{array}
\right)  =i\left(
\begin{array}
[c]{cc
-1 & 0\\
0 & 1
\end{array}
\right)  =-i\tau_{3},
\end{equation}
which changes the sign.
Then, we should choose the block components of $i\tau_3$ which are $N\times N$ matrices, so that the sign of each
component can be changed by a gauge transformation, and $Q$ becomes equivariant.
For example, when $N=2$, we choose
\begin{align}
Q=\left(
\begin{array}{c|c}
i\sigma_3 & 0\\
\hline
0 & -i\sigma_3
\end{array}\right)=
\left(
\begin{array}{cc|cc}
i & 0 & 0 & 0\\
0 & -i & 0 & 0\\
\hline
0 & 0 & -i & 0\\
0 & 0 & 0 & i
\end{array}\right).
\end{align}
So, using the gauge transformation in terms of
\begin{align}
g=\left(
\begin{array}{c|c}
i\sigma_1 & 0 \\
\hline
0 & i\sigma_1
\end{array}\right),
\end{align}
$Q$ transformed by the spacial rotation ($i\tau_1$) returns to the original one. That is,
\begin{align}
g^\dagger(i\tau_1)Q(-i\tau_1)g&=-g^\dagger Qg\\
&=-\left(
\begin{array}{c|c}
(-i\sigma_1)(i\sigma_3)(i\sigma_1) & 0 \\
\hline
0 & (-i\sigma_1)(-i\sigma_3)(i\sigma_1)
\end{array}\right)  \nonumber \\
&=
-\left(
\begin{array}{c|c}
-i\sigma_3 & 0 \\
\hline
0 & i\sigma_3
\end{array}\right)
=Q. \nonumber
\end{align}
Using this $Q$, we can construct the equivariant gauge field configuration.

As a consequence,
both the $Z_2$ space and this discrete part of the gauge
transformation become invisible, if the ground state is described by the $Q$.

We define the differential operators by the graded
commutators\cite{Coquereaux}
\begin{align}
\partial_{w}f  &  =[\bar{w},f\}=\bar{w}f-(-1)^{[f]}f\bar{w},\\
\partial_{\bar{w}}f  &  =[w,f\}=wf-(-1)^{[f]}fw.\nonumber
\end{align}
(about the definition, see the Appendix), where $[f]$ is $+1,$ when $f$ is
even, $-1$ when $f$ is odd matrix.

As $Q^{2}=-1$, vectors that can be constructed from $Q$ are $\partial
_{w(\bar{w})}Q$ and $Q\partial_{w(\bar{w})}Q$. As $Q$ is an even matrix the
differential operator is a commutator, expressing in terms of $\tau_{i}$ we
have
\begin{equation}
\partial_{w}Q={\frac{1}{2}}[\tau_{1}-i\tau_{2},i\tau_{3}]=\left(
\begin{array}
[c]{cc
0 & 0\\
2i & 0
\end{array}
\right)  ,
\end{equation
\begin{equation}
Q\partial_{w}Q=\tau_{3}(\tau_{1}+i\tau_{2})=i\tau_{2}+\tau_{1}=\left(
\begin{array}
[c]{cc
0 & 0\\
2 & 0
\end{array}
\right)  ,
\end{equation}
similarly
\begin{equation}
\partial_{\bar{w}}Q={\frac{1}{2}}[\tau_{1}+i\tau_{2},i\tau_{3}]=\left(
\begin{array}
[c]{cc
0 & -2i\\
0 & 0
\end{array}
\right)  ,
\end{equation
\begin{equation}
Q\partial_{\bar{w}}Q=-\tau_{3}(\tau_{1}-i\tau_{2})=-i\tau_{2}+\tau_{1}=\left(
\begin{array}
[c]{cc
0 & 2\\
0 & 0
\end{array}
\right)  .
\end{equation}
Thus, as the gauge configuration in $Z_{2}$ space, we have the
odd matrix
\begin{equation
A_{w}=\left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  ,\ A_{\bar{w}}=\left(
\begin{array}
[c]{cc
0 & H^{\dagger}\\
0 & 0
\end{array}
\right)  ,
\end{equation}
which are equivariant under gauge, coordinate and spin
transformations like in Eq.(1). In this case, the spin transformation is given as
\begin{equation}
A_{w(\bar w)}\rightarrow -A_{\bar w(w)},
\end{equation}
in response to the coordinate transformation, because $A_{w(\bar w)}$ are the vector
fields.

Next we define the field strength in $Z_{2}$ space. The field strength is
usually defined as $F_{\mu\nu}=[D_{\mu},D_{\nu}]$. We extend this in $Z_{2}$
space as
\begin{equation}
F_{XY}=[D_{X},D_{Y}\}\equiv D_{X}D_{Y}-(-1)^{[X][Y]}D_{Y}D_{X}
\qquad(X,Y=z,\bar{z},w,\bar{w})
\end{equation}

From the definition of graded commutator and Jacobi identity
\begin{equation}
\lbrack f,g\}=fg-(-1)^{[f][g]}gf,
\end{equation
\begin{equation}
(-1)^{[A][C]}[A,[B,C\}\}+(-1)^{[A][B]}[B,[C,A\}\}+(-1)^{[C][B]}[C,[A,B\}\}=0,
\end{equation}
we have
\begin{align}
D_{w}D_{\bar{w}}f  &  =(\partial_{w}+A_{w})(\partial_{\bar{w}}f+A_{\bar{w
}f)+A_{w}(\partial_{\bar{w}}f)+A_{w}A_{\bar{w}}f\\
&  =\partial_{w}(\partial_{\bar{w}}f)+(\partial_{w}A_{\bar{w}})f-A_{\bar{w
}(\partial_{w}f)+A_{w}(\partial_{\bar{w}}f)+A_{w}A_{\bar{w}}f
\nonumber
\end{align
\begin{equation}
D_{\bar{w}}D_{w}f=\partial_{\bar{w}}(\partial_{w}f)+(\partial_{\bar{w}
A_{w})f-A_{w}(\partial_{\bar{w}}f)+A_{\bar{w}}(\partial_{w}f)+A_{\bar{w}
A_{w}f.
\end{equation}
Taking into account $\partial_{\bar{w}}\partial_{w}f+\partial_{w
\partial_{\bar{w}}f=0$, we have
\begin{align}
D_{w}D_{\bar{w}}f+D_{\bar{w}}D_{w}f  &  =(\partial_{w}A_{\bar{w}
)f+(\partial_{\bar{w}}A_{w})f+A_{w}A_{\bar{w}}f+A_{\bar{w}}A_{w}f\\
&  =(\partial_{w}A_{\bar{w}}+\partial_{\bar{w}}A_{w}+\{A_{w},A_{\bar{w
}\})f.\nonumber
\end{align}
As a result, $F_{w\bar{w}}$ can be written as $\{D_{w},D_{\bar{w}}\}$.

Next, we consider $D_{w}D_{\bar{z}}f$ and $D_{\bar{z}}D_{w}f$. Taking into
account that $A_{\bar{z}}$ is an even matrix, we calculate
\begin{align}
D_{w}D_{\bar{z}}f  &  =(\partial_{w}+A_{w})(\partial_{\bar{z}}f+A_{\bar{z
}f)\\
&  =\partial_{w}(\partial_{\bar{z}}f)+(\partial_{w}A_{\bar{z}})f+A_{\bar{z
}\partial_{w}f+A_{w}\partial_{\bar{z}}f+A_{w}A_{\bar{z}}f
\nonumber
\end{align
\begin{align}
D_{\bar{z}}D_{w}f  &  =(\partial_{\bar{z}}+A_{\bar{z}})(\partial_{w
f+A_{w}f)\nonumber\\
&  =\partial_{\bar{z}}(\partial_{w}f)+(\partial_{\bar{z}}A_{w})f+A_{w
\partial_{\bar{z}}f+A_{\bar{z}}\partial_{w}f+A_{\bar{z}}A_{w}f
\end{align}
and we can consider of $[D_{w},D_{\bar{z}}]$ as a field strength, i.e.
\begin{align}
D_{w}D_{\bar{z}}f-D_{\bar{z}}D_{w}f  &  =(\partial_{w}A_{\bar{z}
)f-(\partial_{\bar{z}}A_{w})f+A_{w}A_{\bar{z}}f-A_{\bar{z}}A_{w}f\\
&  =(\partial_{w}A_{\bar{z}}+\partial_{\bar{z}}A_{w}+[A_{w},A_{\bar{z
}])f ,\nonumber
\end{align}
thus $[D_{w},D_{\bar{z}}]=F_{w\bar{z}}$. As for $F_{z\bar{z}}$, it is the
ordinary field strength on $R^{2}$, thus $F_{z\bar{z}}=[D_{z},D_{\bar{z}}]$.

From these arguments, it is appropriate to define
\begin{equation}
F_{XY}=[D_{X},D_{Y}\}\equiv D_{X}D_{Y}-(-1)^{[X][Y]}D_{Y}D_{X}.\qquad
(X,Y=z,\bar{z},w,\bar{w})
\end{equation}

Now we calculate the field strength for the gauge configurations
\begin{equation}
A_{w}=\left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  ,\ A_{\bar{w}}=\left(
\begin{array}
[c]{cc
0 & H^{\dagger}\\
0 & 0
\end{array}
\right)  .
\end{equation}
For example
\begin{align}
F_{\bar{z}w}  &  =\partial_{\bar{z}}A_{w}-\partial_{w}A_{\bar{z}}+\left[
A_{\bar{z}},A_{w}\right] \\
&  =\partial_{\bar{z}}\left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  -\partial_{w}\left(
\begin{array}
[c]{cc
A_{\bar{z}}^{L} & 0\\
0 & A_{\bar{z}}^{R
\end{array}
\right)  +\left[  \left(
\begin{array}
[c]{cc
A_{\bar{z}}^{L} & 0\\
0 & A_{\bar{z}}^{R
\end{array}
\right)  ,\left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  \right] \nonumber\\
&  =\left(
\begin{array}
[c]{cc
0 & 0\\
\partial_{\bar{z}}\phi-\phi A_{\bar{z}}^{L}+A_{\bar{z}}^{R}\phi & 0
\end{array}
\right)  \qquad(\phi=H+1)\nonumber\\
&  =\left(
\begin{array}
[c]{cc
0 & 0\\
D_{\bar{z}}\phi & 0
\end{array}
\right)  ,\nonumber
\end{align}
and
\begin{align}
F_{w\bar{w}}=  &  \partial_{w}A_{\bar{w}}+\partial_{\bar{w}}A_{w}+\left\{
A_{w},A_{\bar{w}}\right\} \\
=  &  \left\{  \left(
\begin{array}
[c]{cc
0 & 0\\
1 & 0
\end{array}
\right)  ,\left(
\begin{array}
[c]{cc
0 & H^{\dagger}\\
0 & 0
\end{array}
\right)  \right\}  +\left\{  \left(
\begin{array}
[c]{cc
0 & 1\\
0 & 0
\end{array}
\right)  ,\left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  \right\} \nonumber\\
&  +\left\{  \left(
\begin{array}
[c]{cc
0 & 0\\
H & 0
\end{array}
\right)  ,\left(
\begin{array}
[c]{cc
0 & H^{\dagger}\\
0 & 0
\end{array}
\right)  \right\} \nonumber\\
=  &  \left(
\begin{array}
[c]{cc
\phi^{\dagger}\phi-1 & 0\\
0 & \phi\phi^{\dagger}-1
\end{array}
\right)  .\nonumber
\end{align}

Next, in order to consider the (anti-)self dual equation we define
$\widetilde{F}_{XY}$. On $R^{2}\times Z_{2}$, since definition of $F_{XY}$ is
different from the usual one, in particular $F_{\bar{w}w}$ is defined as an
anticommutator, we cannot write
\begin{equation}
\widetilde{F}_{\mu\nu}={\frac{1}{2}}\epsilon_{\mu\nu\lambda\rho}F^{\lambda
\rho},
\end{equation}
as in the case of $R^{4}$. Although $F_{\bar{w}w}$ was defined as
\begin{align}
F_{\bar{w}w}  &  =\partial_{\bar{w}}A_{w}+\partial_{w}A_{\bar{w}}+\{A_{\bar
{w}},A_{w}\}\\
&  =\left\{  \left(
\begin{array}
[c]{cc
0 & 1\\
0 & 0
\end{array}
\right)  ,A_{w}\right\}  +\left\{  \left(
\begin{array}
[c]{cc
0 & 0\\
1 & 0
\end{array}
\right)  ,A_{\bar{w}}\right\}  +\{A_{\bar{w}},A_{w}\},\nonumber
\end{align}
we can  redefine this as a commutator using $\tau_{3}$, as follows
\begin{align}
F_{\bar{w}w}  &  =\partial_{\bar{w}}A_{w}+\partial_{w}A_{\bar{w}}+\{A_{\bar
{w}},A_{w}\}\\
&  =\left[  \left(
\begin{array}
[c]{cc
0 & 1\\
0 & 0
\end{array}
\right)  ,A_{w}\right]  \tau_{3}-\left[  \left(
\begin{array}
[c]{cc
0 & 0\\
1 & 0
\end{array}
\right)  ,A_{\bar{w}}\right]  \tau_{3}+[A_{\bar{w}},A_{w}]\tau_{3}.
\end{align}
Consequently, if we multiply this equation by $\tau_{3}$ we
obtain the usual expression for field strength. Taking into account that
$A_{z},A_{\bar{z}}$ are dual to $A_{w},A_{\bar{w}}$, $\tilde{F}$ can be
defined by taking dual and multiplying by $\tau_{3}$ (for details, see the
Appendix). Thus the (anti) self dual equations can be written as
\begin{equation}
F_{\bar{z}w}=0,\quad F_{w\bar{w}}=\pm F_{z\bar{z}}\tau_{3},\quad\mathrm{etc.
\end{equation}
Substituting these equations into the ansatz, each BPS equations are
equivalent to
\begin{equation}
D_{\bar{z}}\phi=0,\quad F_{z\bar{z}}=\phi\phi^{\dagger}-1,\quad\mathrm{etc.
\end{equation
\begin{equation}
\left\{
\begin{array}
[c]{l
F_{z\bar{z}}^{L}=\phi^{\dagger}\phi-1,\quad F_{z\bar{z}}^{R}=-\phi
\phi^{\dagger}+1\\
D_{z}\phi^{\dagger}=0,\quad D_{\bar{z}}\phi=0
\end{array}
\right.
\end{equation}
which are consistent with \cite{Otsu}. \newline\newline

\section{Discussion}

We have been discussing the YM theory on $R^{2}\times Z_{2}$. In \cite{Otsu},
by use of differential form, we have seen that the self dual equation for YM
theory on $R^{2}\times Z_{2}$ is equivalent to the BPS equation for YMH model
on $R^{2}$. In the present paper, by explicitly introducing the coordinates on
$Z_{2}$ space, we show the equivalence of YM theory on $R^{2}\times Z_{2}$ and
YMH model on $R^{2}$, based on the idea of equivariance. This argument is the
same as in the case of showing the equivalence of YM theory on $R^{2}\times
S^{2}$ and the YMH model on $R^{2}$.

Moreover, because the $Z_{2}$ space is discrete, the required equivariance is
among the discrete part of gauge symmetry and it is unnecessary to consider
the larger gauge symmetry. In other words, we could remain with the same gauge
symmetry and this is probably the simplest model of this kind.

The equivariant gauge configuration is
described by the basic equivariant quantity $Q$ exactly as in the case of $S^{2}$ space. As we have
succeeded in introducing $Q$ in $Z_{2}$ space, we were able to construct gauge
configuration for the ground state out of $Q$. In other words, we succeeded in
introducing the Witten ansatz in the noncommutative $Z_{2}$ space.

As stated before, we have seen in \cite{Otsu} that YM theory on $R^{2}\times
Z_{2}$ space is equivalent to YMH model on $R^{2}$ space. The
argument was based on the differential forms, and we were able to construct
the differential forms on $Z_{2}$ space using the matrices. On the other hand,
in this paper, we have explicitly introduced the coordinates in $Z_{2}$ space,
and consistently derived the same conclusion as in \cite{Otsu}. The connection
of the theory based on differential forms and present theory based on the
explicit coordinate is not clear, because we have not been able to construct
differential forms for $Z_{2}$ space. We will discuss this point in the future publication.

redpajama_set_name: RedPajamaArXiv


1. Brown, Lindy. 2010. "Libraries on Twitter (Updated List)." Circulation, September 19. http://lindybrown.com/blog/2009/01/libraries-on-twitter-updated-list/ (http://lindybrown.com/blog/2009/01/libraries-on-twitter-updated-list/) (Accessed: 21 September 2010).
2. Fox, Susannah, Kathryn Zickuhr, and Aaron Smith. 2009. "Twitter and Status Updating, Fall 2009." Pew Internet & American Life Project, October 21. http://www.pewinternet.org/Reports/2009/17-Twitter-and-Status-Updating-Fall-2009.aspx?r=1 (http://www.pewinternet.org/Reports/2009/17-Twitter-and-Status-Updating-Fall-2009.aspx?r=1) (Accessed: 1 June 2010).
3. Grabowska, Kasia. 2010. "Social Media Best Practices for Libraries: A TTW Guest Post." Tame The Web, March 18. http://tametheweb.com/2010/03/18/social-media-best-practices-for-libraries/ (http://tametheweb.com/2010/03/18/social-media-best-practices-for-libraries/) (Accessed: 16 September 2010).
4. Greenhill, Kathryn, and Jean Hing Fay. 2010. "A Social Media Policy for a One Branch Public Library." Librarians Matter, September 10. http://librariansmatter.com/blog/2010/09/10/a-social-media-policy-for-a-one-branch-public-library/ (http://librariansmatter.com/blog/2010/09/10/a-social-media-policy-for-a-one-branch-public-library/) (Accessed: 16 September 2010).
5. Johnson, Steven. 2009. "How Twitter Will Change the Way We Live." Time, June 5. http://www.time.com/time/business/article/0,8599,1902604,00.html (http://www.time.com/time/business/article/0,8599,1902604,00.html) (Accessed: 1 June 2010).
7. Solis, Brian. 2010. "21 Rules for Social Media Engagement." Mashable, The Social Media Guide, May 18. http://mashable.com/2010/05/18/rules-social-media-engagment/ (http://mashable.com/2010/05/18/rules-social-media-engagment/) (Accessed: 1 June 2010).
8. Stephens, Michael. 2010. "Anytown Public Library's Social Media Policy." Tame The Web, June 10. http://tametheweb.com/2010/06/10/anytown-public-librarys-social-media-policy/ (http://tametheweb.com/2010/06/10/anytown-public-librarys-social-media-policy/) (Accessed: 16 September 2010).
9. Weil, Kevin. 2010. "Measuring Tweets." Twitter Blog, February 22. http://blog.twitter.com/2010/02/measuring-tweets.html (http://blog.twitter.com/2010/02/measuring-tweets.html) (Accessed: 1 June 2010).
10. Young, Jeff. 2010. "Researchers Find 'Million-Follower Fallacy' in Twitter." The Chronicle of Higher Education. Wired Campus, May 25. http://chronicle.com/blogPost/Researchers-Find/24290/ (http://chronicle.com/blogPost/Researchers-Find/24290/) (Accessed: 1 June 2010).


This is a busy destination with fine dining, weddings and conference business so high end and volume experience is vital for the role.
The ideal candidate will be a creative chef with excellent presentation standards. You will have a minimum of three years' experience as Sous Chef in a hotel or restaurant of similar calibre (fine dining restaurant / 4-5 star hotels etc).
If you value honest, locally sourced food, genuine customer service, this could be the role for you !


Recreational Sports is responsible for the management and general operation of eight recreational facilities across the SHSU campus. Each of our facilities is available for reservation and or rental to the SHSU community. To learn more about reserving and/or renting any of our facilities, you must contact the Recreational Sports Office. Requests will be approved or denied based on facility availability and the purpose for which the facility is requested.
To reserve a facility please select a link below for additional information.
The Recreational Sports Center (RSC) is considered "home" for Recreational Sports. It is used for all program areas. The RSC houses 4 basketball/6 volleyball/12 badminton courts, aerobics/multipurpose room, 1/8 mile indoor running track, 10 racquetball courts, weight room (free weights/machine weights/cardiovascular equipment), locker rooms, and an equipment check-out area. All these activity areas are available on a drop-in / informal basis during our operational hours. Listed below are the RSC hours of operation by semester.
Located at the corner of Avenue O and 17th Street, the Pritchett Field Complex has two outdoor athletic fields and a 1/4 mile track. The lower field is turfed and lighted. This facility is the home of several of our Club Sports programs, such as Lacrosse, Rugby, and Soccer. Recreational Sports programs and academic classes are given priority for reservations.
If you're interested in reserving the field, please fill out the Field Reservation Form and turn it in to HKC 104 or email it to Brian Weaver.
We are now at the cusp of bringing something magnificent to Sam Houston State. The University Camp will house a wide variety of programs to the campus community. Many activities will be held here ranging from faculty, staff, and student development programs and orientations, to social gatherings and Alumni events. Our series of high and low rope elements are utilized by campus organizations and departments to develop a better sense of camaraderie and teamwork.
The Swimming Pool is outdoor, heated (seasonally), and fun! We have 4, 25 yd lap lanes and a leisure area which can be used for water volleyball, water basketball, or certain intramural and special events. Additional amenities include a sun tanning area, large chairs and covered tables.
The McAdams Tennis Courts are located behind the HKC and are available for recreational use. The eight lighted, outdoor tennis courts are managed by Recreational Sports, however, Academics and Athletics have priority for use. The facility hours are 6:30 a.m. to 11 p.m. daily.
Check with the Recreational Sports office at (936)-294-1985 for availability and group reservations.
Holleman Field is located southwest of main campus at the intersection of Avenue M and Josey Street. It served as the home ballpark for the SHSU men's baseball team from 1948 to 2005 and is now the main home to the SHSU Intramural and Club Sports Programs.


text:
Lets-Hang-On
Let's Hang On
Mon 1 Jan 0001 - Fri 22 Feb 2019, music
Discover how four New Jersey boys from the wrong side of the tracks became one of the biggest pop sensations of all time!
"Oh what a story…Oh what a show…OH WHAT A NIGHT"
LET'S HANG ON - The World's first & longest running tribute to the music of Frankie Valli & The Four Seasons celebrates 10 years at the top!
Discover how four New Jersey boys from the wrong side of the tracks invented their own sound and sold over 175 million records before they turned 30!
This critically acclaimed Theatre production takes you on a musical journey through the prolific career of 'Rock n Roll Hall Of Famers' and still one of the most successful bands in pop history Frankie Valli & The Four Seasons.
Performing in-full all your favourite hits and movie soundtracks from a catalogue spanning over five decades such as, Grease, Stay (Dirty Dancing), December 1963 (Oh What a Night!), Sherry, Beggin', Can't Take My Eyes Off You, Working My Way Back To You, Walk Like A Man, Big Girls Don't Cry, and many more, finally taking the roof off with a spectacular finale Let's Hang On!
Prepare to be blown away with breath-taking vocal performances and outstanding musicianship that features an amazing live horn section. This sensational 10th anniversary show is definitely not a night you want to miss!
So come join the party and BOOK NOW!
"You guys are dynamite"
"An authentic masterpiece"
"These guys are absolutely brilliant"
The Paul O Grady Show
Share Let's Hang On with Friends...
Tues 24 - Wed 25 Sep
From Timeless Theatre - book early for matinee shows.
MAMA Presents An Evening of Genesis...
Tribute live concert, presented by MAMA
Foster & Allen
Thurs 19 Mar 2020
Evergreen Irish favourites return to Solihull's Core Theatre
MYJO Christmas Concert
The Award-winning Big Band return.
The Neil Diamond Story
After previous sellouts the UK's 'voice of Neil' Bob Drury returns.
Malcolm Stent in the Afternoon
Join Malc for an afternoon of music, merriment and mirth!

redpajama_set_name: RedPajamaCommonCrawl


text:
#import "NSObject.h"

#import "NSCopying-Protocol.h"

@interface CMGyroDataInternal : NSObject <NSCopying>
{
    CDStruct_03942939 fRotationRate;
}

- (id).cxx_construct;
- (id)copyWithZone:(struct _NSZone *)arg1;
- (id)initWithRotationRate:(CDStruct_03942939)arg1;
- (void)setRotationRate:(CDStruct_03942939)arg1;

@end

redpajama_set_name: RedPajamaGithub


It's all tea, all shade when Ryan Crawford and Marita DeLeon ru-view the cast of RuPaul's Drag Race Season 9.
Don't miss Ryan's ru-caps of the upcoming season on Jetspace Magazine's Ru-minations every week during the Season 9.
Catch Marita, along with El Sanchez, on the second Wednesday every month at The Rendezvous for Fist & Shout, a QTPOC variety show. Follow Fist & Shout on Facebook for more info.
Nightlife Roundup: Summer Affair, Rapture, and More!


This latest blog comes along amidst much madness of which we had perhaps best not speak. There's much I want to mention and if we get distracted at this early stage there's no telling how long this thing could go on for!
I'm thrilled to be sharing news of a special something I've been working on which launched today!