text:
\section{Introduction and Results}

In a recent paper \cite{CL} a correlation inequality was proved
for spin systems with quenched symmetric random interaction in arbitrary dimension, extending
a previous result for the Gaussian case \cite{CG}.
That inequality yield results for spin glasses similar to those obtained for ferromagnetic systems from
the first GKS inequality \cite{Gr,Gr2,KS} e.g. it gives monotonicity of the pressure
in the volume and bounds on the surface pressure.
Other inequalities were considered: in particular the extension to non-symmetric interactions and
possible versions of a second type GKS inequality.

In this work we study the $d=1$ case with nearest neighboor interaction. In the same spirit of the GKS
systems no assumption of translation invariance is made on the interaction distributions and by
consequence our results cannot be obtained by an exact solution. We prove that both the
inequality of the first type does extend to the non symmetric case and that an inequality
of the second type holds indeed in the symmetric case. A similar result with a complete
proof of inequalities of type I and II has been obtained so far only in the Nishimori line \cite{CMN,MNC}.

Let us consider a chain with periodic boundary condition
\begin{eqnarray*}
H(\sigma, J) \; = \; -\sum_{i=1}^{N}J_{i}\sigma_i\sigma_{i+1}
\end{eqnarray*} with $\sigma_{N+1}=\sigma_1$. The
random variables $J_i$ have independent distributions $p(J_i)$. Those fulfills one of the three
following hypothesis, which will be called system I, II and III in the remaining part of the paper:\\
{\bf I)}
\begin{eqnarray*}
p(|J_i|) \geq p(-|J_i|), \quad \forall i \; \; and \; \; \forall |J_i| \in \mathbb{R}^{+}
\end{eqnarray*}
{\bf II}) the $J_i$ are symmetric around a positive mean $\mu_i >0$:
\begin{eqnarray*}
p(\mu_i +|J_i|) = p(\mu_i - |J_i|), \quad \forall i \; \; and \; \; \forall |J_i| \in \mathbb{R}^{+}
\end{eqnarray*}
In the case of discrete variables: $J_i=\mu_i\pm J^{(i)}$, $p(\mu_i+J^{(i)})=p(\mu_i-J^{(i)})=1/2$, we assume
that $J^{(i)} > \mu_i$ (see below for further explanations) and we introduce the notations:
\begin{eqnarray*}
& a_i = \mu_i + J^{(i)}& \\
& -b_i = \mu_i - J^{(i)}& \\
& a_i, b_i > 0 &
\end{eqnarray*}
{\bf III}) the $J_i$ are discrete variables taking on values $\pm J^{(i)}$ with $J^{(i)}>0$ such that:
\begin{eqnarray*}
\textit{where}  \quad p_i = p(J^{(i)}), \;\;\; q_i = p(-J^{(i)}) \; ,
\end{eqnarray*}
and
\begin{eqnarray*}
\alpha := {\displaystyle \prod_i (p_i - q_i)} \; \ge 0 \; .
\end{eqnarray*}
Let $\omega_{h}$ the thermal average of the quantity $\sigma_h\sigma_{h+1}$, $\omega_{h,k}$
that of the quantity $\sigma_h\sigma_{h+1}\sigma_k\sigma_{k+1}$ and $\av{\cdot}$ the average over
the quenched disorder.

Our main results are:
\begin{proposition}\label{pp1}
For all three systems:
\begin{equation}\label{cu1}
\av{J_h \omega_h} > 0, \quad \quad \forall h=1...N
\end{equation}
\end{proposition}

\begin{proposition}\label{pp2}
For systems I and III with $\alpha=0$:
\begin{equation}\label{g2}
\av{J_h J_k (\omega_{hk} - \omega_h \omega_k)} < 0, \quad \quad \forall h, k = 1...N, \quad h \neq k
\end{equation}
\end{proposition}

\begin{proposition}\label{pp3}
For system III, with $\alpha >0$,
the following properties hold:
\begin{itemize}
\item[ ] $\forall l$, there exists in the  $(J^{(l)} , \alpha)$ quadrant, a curve $\alpha(J^{(l)})$
such that the quantity
\begin{equation}
\av{J_h J_k (\omega_{hk} - \omega_h \omega_k)}
\end{equation}
changes its sign from negative to positive when crossing the curve  $\alpha(J^{(l)})$ by increasing $\alpha$
and such that on the curve $\alpha(J^{(l)})$
\begin{equation}
\av{J_h J_k (\omega_{hk} - \omega_h \omega_k)} = 0, \quad \quad \forall h, k = 1...N, \quad h \neq k \; .
\end{equation}
Moreover $\av{J_h J_k (\omega_{hk} - \omega_h \omega_k)}$ is increasing in $\alpha$ along the $J^{(l)} = \textrm{const}$ lines.
\end{itemize}
\end{proposition}

\section{Proofs}
We start by proving the following lemmata.
\begin{lemma}\label{lem1}
System III can be rewritten as:
\begin{equation}\label{pippe}
H(\tau, K) = -K_N\tau_N\tau_{N-1} - \sum_{i=1}^{N-1}J^{(i)}\tau_i\tau_{i+1}
\end{equation}
with:
\begin{eqnarray}
K_N = J^{(N)}\prod_{i=1}^{N} {\rm sgn}(J_i) = \pm J^{(N)} \; .
\end{eqnarray}
Setting $P = {\rm prob}(K_N=J^{(N)})$ and $Q= {\rm prob}(K_N=-J^{(N)})$ we have:
\begin{eqnarray}
P&=& \frac{1+\prod_i (p_i - q_i)}{2} \\
Q&=& \frac{1-\prod_i (p_i - q_i)}{2}
\end{eqnarray}
\end{lemma}

\begin{lemma}\label{lem2}
Consider system II with discrete variables and assume that $\mu_h=0$ for at least one $h$.
Such a system can be rewritten as:
\begin{eqnarray*}
H(\tau, K)=-\sum_{i=1}^{N}K_{i}\tau_i\tau_{i+1}
\end{eqnarray*}
where:
\begin{eqnarray}
K_h = J_h &=& \pm a_h, \quad a_h>0 \\
K_i &=& \left\{ \begin{array}{c} a_i > 0 \\ b_i > 0 \end{array} \right.
\end{eqnarray}
the two cases having probability $1/2$.
\end{lemma}
{\bf Proof of Lemma 2.1} \\
The proof is based on the Gauge transformation $\alpha_j=\prod_{1\le i < j}{\rm sgn}(J_i)$,
for $2\le j\le N$ $\alpha_1=1$. Set $\tau_i=\alpha_i\sigma_i$ $H$ is given by (\ref{pippe}) with $K_N = J^{(N)}\prod_{i=1}^{N} {\rm sgn}(J_i)$.
We have now to compute the new probability measure for $\prod_{i=1}^{N} {\rm sgn}(J_i)$.
Clearly the expectation
\begin{eqnarray*}
\av{\prod_{i=1}^{N} {\rm sgn}(J_i)}=\prod_{i=1}^{N} \av{{\rm sgn}(J_i)}=\prod_{i=1}^{N}(p_i-q_i)=P-Q \; .
\end{eqnarray*}

\noindent
{\bf Proof of Lemma 2.2} \\
Group the bond configurations in couples that only differ for the sign of
$J_h$ and Gauge transform them using the same transformation of Lemma 3.1
What we obtain is:
\begin{eqnarray*}
K_i &=& |J_i | > 0 \\
K_h &=& J_h = \pm J^{(h)}
\end{eqnarray*}
Moreover, since $p(K^{(h)}) = p(J^{(h)})$ or $p(K^{(h)}) = p(-J^{(h)})$,
$p(K^{(l)}) = 1/2$ for all $l$. \\

\noindent
Introduce, for system {\bf III}, the following shorthand notations:
\begin{eqnarray*}
C_i := \cosh(K^{(i)}) = \cosh(J^{(i)}) ; \quad \quad S_i := \sinh(K^{(i)}) = \sinh(J^{(i)})
\end{eqnarray*}
\\ \noindent
{\bf Proof of Proposition 1.1} \\ First we prove the thesis for discrete variables (system II and III).
The partition function and correlation of an $N$ spins chain with periodic boundary conditions
can be written as:
\begin{eqnarray}
& Z = {\displaystyle \prod_i} C_i + {\displaystyle \prod_i} S_i & \\
& \omega_h = {\displaystyle \frac{1}{Z}} \left[ S_h \, {\displaystyle\prod_{i \neq h} }C_i + C_h \, {\displaystyle\prod_{i \neq h} }S_i \right]
\end{eqnarray}
{\bf System III} Using Lemma 2.1 one has:
\begin{eqnarray*}
{\rm Av}_{\{ J \} }[J_h \omega_h] &=& {\rm Av}_{(K_h)}[K_h \omega_h] = K^{(h)}\left\{ P\omega |_{k_h=k^{(h)}}-Q\omega |_{k_h=-k^{(h)}} \right\} = \\ \\
&=& K^{(h)}\left\{ Q\left[ \omega |_{k_h=k^{(h)}}-\omega |_{k_h=-k^{(h)}}\right]+(P-Q) \omega |_{k_h=k^{(h)}} \right\} \ge 0
\end{eqnarray*}
due to the first Griffith's inequality for ferromagnetic systems.
\\ \noindent
{\bf System II} (discrete variables) Since the pressure is a convex function of the $\mu_i$'s we can prove our theorem
for $\mu_h = 0$. If for some $i$ $J^{(i)}\le \mu_i$ the variable $J_i$ takes positives values and it doesnt influence the sign
of the average. Now, using lemma 2.2 and observing that $P=Q=1/2$ and the $J$ average is a linear combination
of $K_h$ average with all positive remaining $K_i$, we have the thesis with the same steps as before.
The extension to the continuos case is obtained by the usual method of integrating over
the positive parts of the $J_i$ distributions.

\noindent
{\bf Proof of Proposition 1.2 }\\
For discrete variables (system III), using the standard hyperbolic expansion:
\begin{eqnarray*}
\omega_{hk}  = {\displaystyle \frac{1}{Z}} \left[ S_h S_k  {\displaystyle\prod_{i \neq h,k} }C_i + C_h C_k {\displaystyle\prod_{i \neq h,k} }S_i \right] \Rightarrow
\end{eqnarray*}
\begin{eqnarray*}
\omega_{hk} - \omega_h \omega_k &=& \frac{1}{Z^2} \left\{ \left( S_h S_k  {\displaystyle\prod_{i \neq h,k} }C_i + C_h C_k {\displaystyle\prod_{i \neq h,k} }S_i \right)
                            \left({\displaystyle \prod_i} C_i + {\displaystyle \prod_i} S_i \right) + \right. \\ \\
&&      \quad \quad \quad  \left. - \left(S_h  {\displaystyle\prod_{i \neq h} }C_i + C_h {\displaystyle\prod_{i \neq h} }S_i \right)
                                \left(S_k {\displaystyle\prod_{i \neq k} }C_i + C_k {\displaystyle\prod_{i \neq k} }S_i \right) \right\} = \\ \\
&=& \frac{1}{Z^2} \left\{  {\displaystyle\prod_{i \neq h,k} }(C_i S_i) \cdot \left( C_h^2 C_k^2 + S_h^2 S_k^2 - C_h^2 S_k^2 - S_h^2 C_k^2 \right) \right\} = \\ \\
&=& \frac{ {\displaystyle\prod_{i \neq h,k} }C_i S_i }{\left( {\displaystyle \prod_i} C_i + {\displaystyle \prod_i} S_i \right)^2 }
\end{eqnarray*}
If at least one of the random variables is symmetric we have: $P=Q=1/2$; using lemma 2.1 one has:
\begin{eqnarray*}
{\rm Av}[K_h K_k (\omega_{hk} -  \omega_h \omega_k)] &=& J^{(k)}  \cdot
                                    {\rm Av}_{(K_N)}\left[ \frac{K_h\cdot {\displaystyle\prod_{i \neq h,k} }(C_i S_i)}{ (  \prod_i C_i +  \prod_i S_i )^2 } \right] = \\
&=& J^{(k)} J^{(h)} {\displaystyle\prod_{i \neq h,k} }(C_i S_i) \cdot \frac{1}{2} \left\{ \frac{1}{(  \prod_i C_i +  \prod_i S_i )^2 } -
                                        \frac{1}{(  \prod_i C_i -  \prod_i S_i )^2 } \right\} = \\
&=& - 2 \,  J^{(k)} J^{(h)} {\displaystyle\prod_{i \neq h,k} }(C_i S_i)\cdot \frac{\prod_i (C_i S_i) }{ (\prod_i C_i^2  - \prod_i S_i^2)^2} < 0
\end{eqnarray*}
The extension to the continuous case is as above.

\noindent
{\bf Proof of Proposition 1.3 }\\
Let $\alpha > 0$ or equivalently $P = \frac{1+\alpha }{2} > \frac{1}{2} > Q = \frac{1-\alpha }{2}$. \par
We obtain analogously as before:
\begin{eqnarray*}
&{\rm Av}[K_h K_k (\omega_{hk} -  \omega_h \omega_k)] =  J^{(k)} J^{(h)} {\displaystyle\prod_{i \neq h,k} }(C_i S_i)
                                {\displaystyle \frac{P (\prod C_i - \prod S_i)^2 - Q  (\prod C_i + \prod S_i)^2 }{ (\prod C_i^2  - \prod S_i^2)^2}} =& \\
&={\displaystyle \frac{ J^{(k)} J^{(h)} \prod_{i \neq h,k }(C_i S_i) }{(\prod_i C_i^2  - \prod_i S_i^2)^2}} \cdot \left\{ (P-Q) (\prod_i C_i^2 + \prod_i S_i^2) -
                                        2 \prod_i (C_i S_i) \right\}&
\end{eqnarray*}
The sign of the previous expression is, by inspection, the same as that of the curly parentheses:
\begin{eqnarray*}
g(\alpha; \{ J \}) := \alpha  (\prod_i C_i^2 + \prod_i S_i^2) - 2 \prod_i (C_i S_i)
\end{eqnarray*}
One obtains:
\begin{itemize}
\item[-] $\alpha = 0$ (zero mean spin glass)  $\Rightarrow g(\alpha; \{ J \}) < 0$;
\item[-] $\alpha = 1$ (ferromagnetic)  $\Rightarrow g(\alpha; \{ J \}) =  (\prod_i C_i - \prod_i S_i)^2 > 0$;
\item[-] for all $J^{(l)}$, $g(\alpha; \{ J \})$ is increasing function of $\alpha $;
\item[-] ${\rm Av}_{(K_h)}[K_h K_k (\omega_{hk} -  \omega_h \omega_k)] = 0$ on the $(J^{(l)}, \alpha)$ plane curve with $J^{(l)} >0$ and \linebreak $0 \leq \alpha \leq 1$
defined by:
\begin{equation}
\alpha (J^{(l)}) = \frac{2 C_l S_l \prod_{i \neq l} (C_i S_i)}{ C_l^2 \prod_{i \neq l} C_i^2 + S_l^2 \prod_{i \neq l} S_i^2}
\end{equation}
\end{itemize}

The proof of the inequalities for one dimensional systems with free
boundary conditions or for tree-like lattices is trivial since, due to the absence of loops
the partition function factorizes
\begin{eqnarray*}
{\bf Z} = 2^N \prod_i \cosh(\lambda_i J_i)
\end{eqnarray*}
and by consequence the first inequality is fulfilled even without taking the average
and the second inequality reduces obviously to the equality to zero. \\

\section{Comments}
We proved that a one dimensional spin glass system fulfills a family of correlation inequalities
without the assumption of translation invariance for the interaction distribution. The first inequality
extends a similar one proved in \cite{CL} for any lattice and any interaction with zero mean value.
Here we have shown that the inequality is stable by suitable deformations of the zero mean hypotheses.
The inequality of type II proved here shows that in the zero mean case the truncated correlation function
has the opposite sign of the standard GKS inequality i.e. the case of interactions with zero variance and
positive mean. We have moreover identifyed the line crossing which the truncated correlation changes its sign.
It would be interesting to establish if an inequality of type (\ref{g2}) is fulfilled
also in higher dimensions (see \cite{KNA}). In fact, as a straightforward computation shows in the Gaussian
case, if such an inequality holds then the overlap expectation would be monotonic
in the volume and several nice regularity properties would follow \cite{CG2}. We also mention that
the inequality (\ref{g2}) doesn't hold in general topologies as it was shown to us by Hal Tasaki
for a Bernoulli spin chain with an extra bond connecting two non adjacent sites. Moreover
a similar violation for the inequality (\ref{g2}) can be obtained in the case in which the disorder,
still having zero average, is non symmetric.\\

{\bf Acknowledgments}. The authors thank Joel Lebowitz for many fruitful suggestions.
P.C. thank Cristian Giardina, Sandro Graffi, Frank Den Hollander and Hidetoshi Nishimori for useful discussions.

redpajama_set_name: RedPajamaArXiv


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This topic contains 5 replies, has 2 voices, and was last updated by Hudson Atwell 6 months, 1 week ago.
I know it is out of the scope but you already have helped me to adjust the code in this thread post.
This time it is in need to use the script not as auto-redirect but further more to be used to ad a button and by clicking to grab the URL parameter and forward to the setup URL.
2. at the optin-page there is a button with URL to forward to sales page, but if I add only the URL to forward, then the parameter "?tid=fbad1" is missing.
It would be very helpful if you could help me with this also or point me to someone who maybe can solve this issue.
P.P.S. I guess the best solution would be to add a script to the functions.php which check if there are buttons in use on a page and if those buttons are clicked then check if the page URL has parameters included to be added to the URL setup for that button.
There are 2 buttons added and the code shall be added to grab the url parameter after clicking the button to forward to the URL by adding the parameters in addition.
I have also added the auto-forward code, but this shall be only used as example to use the code to be customized for button click instead of auto forward.
Hi Sorry for the delay.
I think I may can help.
They both have this class name "frb_button", so we can use jQuery to change their destination URLS.
notice I added the function findGetParameter into the mix because we depend on it. If it's already added though through our prior code edits, then we won't need to add it again.
THANK YOU VERY MUCH – IT WORKS PERFECT!
I hope you are well and the Hurricane "Michael" has not harmed you in any kind except the internet connection. I guess you need to settle over you Europe to get away from those weather problems and sorry for my pushing to get it done.
Many thanks again, and all the best from Germany!
Fantastic news happy to help!
Thank you also for the well wishes. We did not get it as bad as the people below us. Power went back out today. Internet still out too. Shelters are full. Traffic yucky. I'm really glad there is not another storm lined up behind it. I'm ready for cool weather!
The topic '[Developers' Hangout] Add / Change parameter of URL and redirect to the new URL on button click' is closed to new replies.


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A lot has been said about Rafael Nadal's greatness on clay. Even more has been said about Roger Federer's greatness in general. And yet he still managed to add so much more to the discussion during the grass court season it's simply surreal.
First, I want to say that I loved this extended grass court season. For years, fans have been, at least, discussing how enjoyable it would be to squeeze in a grass court Masters event. Unfortunately, there's a good chance we'll never see that. But for one year, we got as close to it as possible. The Olympics, while obviously more prestigious than a Masters title, served as the grass Masters we've always wanted. It even played like an old fashioned Masters event by being six rounds and featured a best-of-five set final. And for even more excitement, it featured a mixed doubles event. I'm not usually into mixed doubles but watching it at the Olympics was plenty of fun, particularly the final that saw Max Mirnyi finally clinch a gold medal.
But there was a ton of tennis played before the Olympics. After the French Open, which featured the fourth consecutive major final between Nadal and Novak Djokovic, there was little reason to believe the Nadole show wouldn't continue. After all, their streak had started at Wimbledon in 2011 where Djokovic won in four sets and also came out of the tournament as the World Number 1 for the first time. Djokovic once again skipped any warm-up events, as did Federer, who was slightly injured and fatigued.
Andy Murray was playing in Queen's Club, where he was the defending champion. Murray had just one title all year and that came in his first tournament in Brisbane. One would have though that Queen's Club would be a pretty good place to snap that title drought. Instead, he was ousted in his opening match by Nicolas Mahut (no slouch on the grass courts himself). It really looked like, despite hiring the great Ivan Lendl as his coach, Murray was arguably regressing.
Nadal, meanwhile, was upset by Philipp Kohlschreiber in his second match in Halle, Germany. I doubt anyone put much stock into this loss seeing as how Nadal often loses early in these tune-ups without any serious repercussions to his major results. As for Federer, he made it to the final in Halle but suffered one of the biggest upsets of the year in losing to comeback king Tommy Haas. I still think this was a match he never should have lost and it certainly didn't foretell what was about to happen in the next few weeks.
Lukas Rosol scored one of the biggest upsets in sports history when he stunned Nadal in the second round of Wimbledon. He had about eight tour-level wins before and only won about eight more after this match. Unlike Robin Soderling, who beat Nadal at the French Open and used it as a springboard to become a fixture in the top 10, the context around Rosol is unbelievable. The guy is nothing more than a challenger-level player and has stayed at that level even after this huge win. And considering how well he played, it's really bewildering. This also turned out to be Nadal's last match of the 2012 season. And of course people are going to assume he was injured during this match which contributed to this loss. I don't think this was the case. Especially considering how authoritative Nadal looked in the fourth set. But his momentum was surely broken during the roof-closing delay and Rosol just zoned in the fifth.
With Nadal out of the picture, the draw opened up for Murray. He was able to reach his first Wimbledon final and threw the kitchen sink at Federer, who threw the bathtub back at him. As Wimbledon champion once again, Federer reclaimed the number one ranking and, finally, broke Pete Sampras's record of most weeks at number one.
At the Olympics, the Federer-Murray show continued. Djokovic would once again lose in the semis at the All England Club (after falling to Federer during Wimbledon) but this time it was to Murray. And Murray followed up big by avenging his Wimbledon defeat and simply crushing an exhausted Federer. Djokovic would miss out on a second Bronze medal by falling to Juan Martin del Potro, who showed serious poise by overcoming the 19-17 loss in the third set to Federer in the previous round.
Although Djokovic and Nadal have combined to win three of the last five Wimbledon titles, I feel like things finally made sense on grass this year. Not to discredit either guy, but Murray and Federer are much more naturally suited to grass than the other guys. And to see them make back-to-back grass court finals like that was a serious treat from a pure tennis perspective.
And with Federer back at number one and Murray finally securing a huge title with the Olympic gold in his pocket, the theme of historic performances was not even close to being over.
You mention how we all shouldn't be surprised when Nadal gets upset eat in tourneys, but should be with Fed. After Fed lost in Halle ( a final btw, not a first or second rd ) didn't be WIN Wimbledon?
"upset early"….sorry dang fro the typos there… Iphone and running…..never good results with that.
loved the extended grass court season too. It was an absolute bonus.
And seeing Federer play at Wimbledon this year, was even more of a bonus for me.
This was a special year. In more ways than one. I don't think there was a dry eye in the house with the wimbledon final and Murray's classy, emotional speech. This is what we watch tennis for, to see the human side of our favourite players when things don't quite go their way. We have seen it with all the top players and long may it last, I say.
I really look forward to 2013, and wish it would hurry up!
We are taking grass season here, NOT rafa's season!
Geez, let's talk about Fed, Haas, Muzza etc- people who did something during this period and are worth discussing!
For once: let's not descend to the usual back and forth!
It's the off-season in Tennis- let's have an off season period from here forth and refrain from usual back and forth between fans- as God knows we'll be doing plenty of that in 2013!
Fed and Muzza are just more at home on grass than the other 2!
Re Rafa loss: Best summary by ANYONE here on Tennis X that i have read regarding that loss.
Very fair, accurate description of what occurred in that match.
Kudos to you for it!
Simple non-context sensitive spell checkers don't help when similar or identical sounding wrong words are used.
Wet seasons have heavy rains.
As you can see, Fed-Nadal rivalry is a lot closer than their actual head to head suggests with Nadal leading Federer (50.52% – 49.48%) points.
Just thought, its a pretty cool statistic to post it on the forums.
The above statistic is based on the points won by each player.
The Arrogant One's fashion advisor, Anna Wintour is under consideration by President Obama to be US ambassador to UK or France.
As a GOAT owner, I am worried. I like my goat to be dressed well at all times.
nadal is a m0r0n because his scheduling is so stupid. if he was any smarter with his scheduling, he would be king of the court, not just king of clay. everything is in his favor…. slow courts, slow conditions…. it's not lost yet. if he can be smart with his scheduling, he could still get atleast 5 slams in the next 5 years!
let's not put the blame on toni. Nadal is a man and not a 16 year old boy.
Loving these year in review pieces Ben; looking forward to the fourth instalment, and of course … 2013! Eeps, should be fun. You should do a predictions piece – it'd be great.
Wogboy/Jane i agree these are great end of year reviews,the whole year seems to have passed by so quickly,loved the 1st part about the AO hard court season,hated the CC review was so looking forward to it,but the thread turned into a warzone with people bickering nothing not many constructive posts at all,this one so far so good,however its early days yet,ans yes im looking forward to the final part,which was where Andy came of age,and claimed his 1st slam,anyway the GC season belonged to Roger and Andy,Wimbledon is Rogers home and that proved to be the case once again,but major congrats should go to Andy on making his 1st final there,and that speech after the game,there was not a dry eye in the house,should he go one better next year which is my hope then the situation will be exactly the same,but it would be tears of joy this time,and the uphoria in Britain would be amazing,he claimed a gold medal at wimbledon too which was also a fantastic achievement,well done Roger and Andy for cleaning up on grass.
Have to say im in agreement with Tennis Guy in regard to sheduling,,hes had an amazing career,but theres a chance it could have been so much more if only Rafa had been smarter at shedualing,still you cant change the past,however you can make changes to try to shape the future,we will see however.
Loved reading this! Of course as a Federer fan, I love to watch him on any surface (someone once said he could probably play on ice and make it look good) but I fell in love with his game during Wimbledon 2006 so I have a soft spot for him on grass. I guess I agree he should have won the Halle final but since at this stage of his career, hunger and form on the day is all and I guess Tommy had it that time. What I love about Roger on grass is the way his problem solving skills seem more apparent. I have watched the Wimbledon final more times than I care to admit and each time I come away marveling at the difference between the way he played the first set vs the other three. It's a shame he never had the option that Nadal has always had and that is enough grass court tournaments to accumulate points for the rest of the year. I was at work during that Olympic (in more ways than one)battle with Del Potro, sneaking glimpses at the scores. When he won, I told my coworker, at least he's assured a medal because I don't think he could beat one of the twins after that!
Fed is always worth watching. Delpo too!
Nice summation. The Olympic match that stands out to me, even more than the final, is the SF between Nole and Andy. It was a terrific match. Both were in top form and despite Nole throwing everything at Andy he was still beaten in straight sets. The way Andy saved those 4 BPs in the 2nd set were particularly memorable. Seems so long ago now but it was one of the best summers I can recall – not just for tennis but sport in general.
The DA brilliant post,i cant begin to describe how delighted i have been with the Brits this summer at the Olymics,its been a fantastic year for me both my favs Rafa and Andy also bagging a slam this year,just wish i could go back in time and see it all over again,with the exception of Rafa getting Rosoled at Wimbledon though lol.
Why is it that Federer was exhausted when badly beaten by Murray? The difference between Wimbledon and the Olympics is that for once Murray had the majority of the fans and that really got to Federer. He couldn't handle it.
Exhausted by what? £ sets of big serve short rallies against delpo? Murray's time on court dwarfed federer so why denigrate Murray's performance in this way? Is Federer incapable of losing gracefully?
Vidzy yeah not good granted,but this article came up on this very forum a couple of days ago,people have already made their feelings pretty clear about it,and joking or not what Toni said was in very poor taste,not much else to say really.
I don't really see big deal with what uncle Toni said. It was plain joke suggesting that it is only way for Rafa to get back to #1. Maybe not a best sense of humor but you don't expect that from Don Vito anyway. As Nole fan I didn't find anything bad in what he said but some people see what they want to see not what is said and how it is said.
it was clearly said in jest. certain fans will jump at any opportunity to demonize Rafa/Toni. i remember Fed fans enjoying the djokovic/tipsarevic video about whether nadal would pay janko to shoot nole. it's selective outrage.
Wogboy/Volley two wrongs dont make a right,both jokes were in poor taste whichever way you cut it.
Gimme a break. That one doesn't stick. I was there also and it wasn't "just" Fedfans. You continue to sneak in farts @ Fedfans.
I haven't posted on the Toni quote, didn't feel it was needed as it was in obvious jest and good natured.
I hope balanced and reasonable guys like volley and wogboy found my joke funny too!
I can also add djokovic and murray if you don't find it funny enough! let me know guys!
I can see Djokovic & Murray in the grass court finals. Fed? am afraid he is bit too old for the the competitive events. Don't take me wrong – Federer is good but he is no longer the greatest he used to be.
In 2013 Murray will win Wimbledon.
The grass court "circuit" made for my favorite storyline of the year, with Murray winning Olympic gold just a few weeks after losing the Wimbledon final.
RZ i agree with you to a certain extent,as i think this is where Andy became part of the Fedalovic equation,the big 3 is now the fab 4,although the USO HC season was where he made that final break through winning his 1st GS,although i also enjoyed the CC season,with Rafa winning the FO FOR THE 7th time,having said that the AO HC season was great too lol,a great year all round TBH LOL.


text:
\section{Introduction}
\IEEEPARstart{I}{n} the emerging beyond 5G (B5G) and sixth-generation (6G) networks, sensing capabilities have been recognized as a novel feature.

  The embedding of sensing functionality into wireless communication networks leads to the so-called dual-function radar-communication (DFRC), which has become  research area with significant activity of late \cite{LiuIntegrated2022}.
Unlike the solutions for co-existence of radar and communications, which mainly target spectrum sharing, DFRC integrates the radar and communication functionalities into a single platform under the umbrella of a unified signal processing framework. Not only can it improve the energy and spectrum efficiencies, but can also reduce hardware and signaling costs. In addition,  sensing capabilities can be used to enhance the performance of the wireless communication network itself by providing optimization input for network steering \cite{Zhang2022Enabling}.

With the expansion of spectrum allocations towards higher frequencies, such as millimeter-wave (mmWave) and terahertz (THz) bands, severe free-space path loss must be considered to build DFRC systems for  B5G and 6G. Massive multiple-input multiple-output (MIMO) with a large number of antennas is one of the key technologies to cope with this shortcoming. Nevertheless, if each antenna is equipped with a separate radio frequency (RF) chain to perform fully digital beamforming, the hardware cost and energy consumption could be prohibitive. Hence, hybrid beamforming (HBF), which shows great success in wireless communication \cite{Heath2016Overview}, has also been recognized as a promising trend for DFRC system development.

Essentially, the HBF technology uses a combination of low-dimension digital beamforming and high-dimension analogy bemaforming to attain a judicious trade-off between the system performance and hardware cost \cite{8030501}.  Specifically, only a small number of RF chains are deployed for digital beamforming,
but the analogy beamforming is realized by many cost-efficient phase shifters (PSs).
Although HBF has been widely studied for communications,
it is still in its infancy for DFRC and further investigations are expected. Research questions like, how to model the HBF problem for DFRC and how the models impact on the principles and methodologies on system design are yet to be addressed. This dual-functional system requires new signal processing approaches. Additionally, practical constraints imposed on the DFRC system and coupling relationship between digital and analog beamformers will bring challenges to tackle high-dimension and non-convex optimization problems involved in various designs.

While the extension of HBF from communication to DFRC is natural, it demands significant effort to pave its way for incorporation in future communication networks.
Building on the state-of-the-art  in this area, the afore-mentioned issues regarding on the models, technologies and challenges in HBF based DFRC systems will be discussed in this paper.  We hope this work can provide the reader an overview  of this important topic and encourage research towards further integration of sensing and communications in large antenna systems.

The rest of this article is organized as follows. In Section II, we give the basics of HBF based DFRC system. Then we illustrate the corresponding design principles in Section III. Some simulation results are provided in Section IV. Some research frontier related to HBF are introduced in Section V, followed by the conclusions in Section VI.

\section{Basics of Hybrid Beamforming in DFRC}
In this section, we introduce the basics of HBF in DFRC system, which will serve as the preliminaries for next sections. Specifically, we introduce the system model of HBF based DFRC system, followed by detailed DFRC receive modes

 \begin{figure}[t]
    \vspace{-1em}
     \centering
     \includegraphics[width=1\linewidth]{./N_DFRC}
     \caption{Overview of the hybrid beamforming based   DFRC system.}
     \label{fig:DFRC_multi_carrier}
 \end{figure}

\subsection{System Model of HBF based DFRC}
Fig. \ref{fig:DFRC_multi_carrier} gives the overview of the HBF-based DFRC system. There are $N_{\rm RF}^t$ RF chains and $N_t$ antennas at the transmitter. For the $U$ downlink users, each of them has $N_{\rm RF}^r$ RF chains and $N_r$ antennas.
For data transmission, the vector of all data symbols ${\bf s}$ has a length of $N_s$ and each symbol is usually assumed to be
statistically independen
. The symbols to be transmitted are processed by a digital beamformer ${\bf F}_{\rm D}$, then up-converted to RF domain and precoded by an analog beamformer ${\bf F}_{\rm RF}$, which is realized by PSs.

{For analog beamformers, there are three common architectures, i.e., full connection, partial connection and dynamic connection, as depicted in Fig. 2. More specifically, in the full connection architecture, each RF chain is connected to all antennas via PSs. For the partial connection structure, each RF chain connects to a fixed subset of antennas. As for the dynamic connection structure, each RF chain can dynamically connected a subset of antennas. A qualitative comparison of the analog beamformer structures is shown in Fig. 2(d), which indicates that by properly choosing the PSs network structure, the DFRC can achieve a good trade-off between performance and energy efficiency.
}

For communications, to estimate the symbols to user $u$, the received signal will be processed by both the analog and digital combiners as shown in Fig. 1. With the existence of noise on the receiver, {\color{black}the signal to user $u$ is processed by the analog combiner ${\bf W}_{{\rm RF},u}$
followed by the digital combiner ${\bf W}_{{\bf D},u}$.
Thus, by designing the HBF on both the transmit and receive sides jointly, a satisfying symbol error rate
can be ensured}.

For radar sensing, the transmit beampattern should concentrate on the potential directions of the targets of interest while suppressing its sidelobes.
In the context of HBF, the transmit beampattern of the emitted signal is a function of the digital and analog beamforming matrices.
Thereby, by designing the HBF properly, a
desired transmit beampattern can be achieved.
Additionally, for radar parameter estimation, if we consider a multi-carrier signaling scheme, we can obtain $K M_r$ virtual data vectors by matching filtering the received signals at all the $K$ subcarriers, when the radar receiver has $M_r$ RF chains. Two important issues should be considered for the virtual model. (i) Increasing the number of carriers and using the virtual aperture are advantageous to improve the resolution of parameter estimation, e.g., direction-of-arrival (DOA) estimation.  (ii) More carriers will result in less power per virtual element, which in turn leads to affecting the DOA estimation performance \cite{9724206}.

 \begin{figure}[t]
    \vspace{-1em}
     \centering
     \includegraphics[width=1\linewidth]{./Analog_Structure2.pdf}
     \caption{\textcolor{black}{Comparison of the full, partial and dynamic connection analog beamformer. (a) Full Connection Structure; (b) Partial Connection Structure; (c) Dynamic Connection Structure; (d) Performance comparison of the three structure.}\vspace{-1em}}
     \label{fig:HBF-System}
 \end{figure}

\subsection{Receiving Modes}
As shown in Fig. \ref{fig:Receiving_Model}, to support the implement of DFRC, the system can work in monostatic,  bistatic and distributed receive   modes, which are introduced as follows.
\begin{figure}[!htb]
     \centering
     \includegraphics[width=1\linewidth]{./DFRC_System}
     \caption{\textcolor{black}{Diagrams of (a) Integrated Transceiver Mode, (b) Collocated  Transmit-Receive Mode, (c) Bistatic Receive Mode and (d) Distributed Receive Mode.}\vspace{-1em}}
     \label{fig:Receiving_Model}
 \end{figure}

{\textbf{\color{black}Integrated    Transceiver  Mode:}} In this mode, the base station transmitter and radar receiver share the same hardware platform, as shown in Fig. 3(a), where  a   transmitter emits the DFRC waveform  to a user, and receives echoes from the surrounding  targets  simultaneously.  Since the transmitter and radar receiver share the same array, the system can only work under pulsed mode.  This mode has significant advantages of low hardware complexity and avoiding interference  caused by the leakage from transmitter, but  has shortcomings of blind spots in short range  and low communication rate. The pulse width determines the blind range.  {\color{black}In addition, since the transmitter and radar receiver share the hardware, the constraints on radar receiver should be taken into account when designing the analog precoder.}

{\textbf{\color{black}Collocated  Transmit-Receive   Mode:}} In this mode, the transmitter and radar receiver  are closely spaced such that a target located in the far-field can
be viewed at the same spatial angle by  both. In contrast to the integrated   transceiver  mode, this mode is able to support continuous-wave signal, and has no blind spot  in  short range, but will suffer from serious interference  caused by the leakage from transmitter. Thus, it needs expensive circuitry to minimize the interference in practice.

{\textbf{\color{black}Bistatic Receive Mode:}} In this mode, the  radar and the communication receiver share the same hardware, thereby forming a bistatic sensing mode. This  mode can support continuous-wave signal and    has a advantage  of better localization accuracy compared to the earlier monostatic case. However, this mode is  limited in the waveform to preambles and pilots.
{\color{black}Additionally, since one  array supports both radar and communication receivers, the digital combiner can be  optimized for each function, while the analog  combiner is optimized considering  both radar and communications.}  {\color{black}It is noted that this mode also includes the  uplink sensing, in which the transmitted signal is from  users, and it can be also viewed as the passive sensing \cite{9540344}.}

{\textbf{Distributed Receive Mode:}} Herein,  the sensing signal can be received
by multiple receivers after being backscattered by the target.
This mode can  be viewed as multiple bistatic receiving pairs.
This model  offers spatial diversity  to   achieve  improved target detection performance and better  localization accuracy via a cooperative  processing mechanism among different receivers \cite{Blum2008Mag}.
The HBF design for this DFRC system should consider the multi-user interference (MUI).

\section{Design Principles of HBF in DFRC System}
 In this section,  the key performance metrics in designing the HBF for the DFRC system are discussed first, followed by the potential design approaches. Such designs are based on the formulated system performance metrics and the available communication channel state information (CSI), radar detection scenario and system requirements.
\subsection{Performance Metrics}
 In a  DRFC system,  the HBF is expected to simultaneously improve the performance  of both radar and communication functionalities  while optimizing a certain tradeoff.

 {\textbf{Radar Performance Metrics:}}  Radar systems aim to detect the targets of interest,  and estimate relevant parameters, such as distance, velocity and directions. For  the diverse radar  tasks, different metrics need to be considered.  {\color{black}(1)} Particularly,  the target detection performance is quantified  by  probability of detection  ($ P_d $) under a certain probability of false alarm ($ P_{f} $). It is shown that the detection performance under Gaussian noise is positively correlated with the signal-to-interference-plus-noise ratio (SINR), which also depends on the beampattern gain. {\color{black}(2)} For multi-target detection scenario,  desired properties of the beampattern,  include multiple mainlobes, good peak sidelobe level (PSL) or integrated sidelobe level (ISL).  {\color{black}(3)}  For parameter-estimation tasks,  the Cram\'er-Rao lower
 bound (CRLB), which determines
 the lower bound on estimation accuracy  for unbiased estimators, is  considered.  In typical radar application,   several   parameters needed to be estimated e.g.,   range,  velocity,  and direction. {\color{black}(4)}  For target characterization scenario, mutual information (MI) is also a popular metric, {\color{black}whose maximization will improve the target characterization capability
 of a radar system}.

{\textbf{Communication Performance Metrics:}}  The goal of communication systems is to  enhance the rate transfer of error-free communication data over a fixed bandwidth,  this goal is commonly known as the quality-of-service (QoS). The performance metrics corresponding to the QoS includes: spectral efficiency (SE),  the mutual information\footnote{It is proved in \cite{6717211} that for a fully-digital receiver, the maximization of SE is equivalent to maximizing MI.}, symbol error rate (SER), energy efficiency (EE) and mean square
estimation error (MMSE)\footnote{Actually,  when the user adopts the MMSE receiver, the maximization of SE equals to the minimization of the MMSE \cite{5756489}.}. Apart from these metrics, for the quadrature
amplitude modulation (QAM), the   constellation range can be also selected as the figure of metric to minimize the average  SER in block HBF precoding.
\textcolor{red}{

}
\vspace{-1em}
\subsection{Multi-Objective Optimization (MOO) Formulation}
 Typically, the problem of HBF design for the DFRC system consists of a number of objective functions, i.e., radar and communication  criteria, and is associated with a number of constraints. For a MOO problem,  the  choice of the objective function has a  significant
impact  on the trade-off performance and hence needs to selected appropriately.

Solving an MOO problem (MOOP) implies that one should find the Pareto set of the MOOP. Numerous studies have been shown that methodologies to solve a MOOP is usually based on converting the MOO into a single-objective optimization (SOO) problem, whose optimal solution has also been proved to be in the Pareto set  of the MOOP\cite{marler2004survey}. These methodologies usually contain the
weighted-sum, the  $\epsilon$-constraints, and
min-max  {formulations}. The detailed illustrations are provided below.

{\textbf{Weighted-Sum {Formulation}:}} In the weighted-sum model, the multiple performance criteria are converted into a single objective by multiplying  each criterion with a given coefficient (weight). Due to the fact that different criteria may represent different performance  and have different units, the normalization of each metric must
be undertaken prior to exploiting this
model for solving the MOOP. Subsequently, we select the weights for different criteria to achieving the expected trade-off. It should be noted that the optimal solution of the weighted-sum problem is a Pareto-optimal one of the MOOP. The weighted-sum model is a straghtforward way to handle with the MOOP.
The  weights are non-negative and add up to 1.
Nevertheless, a drawback of the weighted-sum model is that the objective is sensitive to the choice of the weights, and determination of suitable weights  to attain the satisfactory balance is difficult;
a large number of trials with different choices of weights need to be made  to generate a satisfactory solution.

 {\textbf{$\epsilon$-Constraints {Formulation}:}}
 The $\epsilon$-constraints model produces
a SOO problem, where only one
objective function is minimized  while tackling the remaining
objectives as constraints. It is proved in \cite{marler2004survey} that the optimal solution obtained by the $\epsilon$-constraints method is  a weak Pareto optimum of the original MOOP, and under certain conditions, this solution even attain  Pareto optimality.
 Compared to the weighted-sum method, the $\epsilon$-constraints method has a  simpler objective but more complicated constraints; this usually make the problem more challenging to solve. Similar to the choice of weights in the weighted-sum method, there is no prior  scheme corresponding to adjusting $\epsilon$. This method is normally applied to  scenarios where focus lies on only one metric  while the remaining ones are user-specified in advance.

  {\textbf{Min-Max {Formulation}:}}  The \textit{min-max} model generates the SOO problem with $\max_i f_i({\bf x})$ being the objective function and $f_i({\bf x})$ being the $i$th objective in MOOP. A common approach to settle this problem is to introduce another variable $\eta$ to convert the  tricky  \textit{min-max}  objective into a simpler one, as $\min_{{\bf x}, \eta}~\eta, ~{\rm s.t.}~  f_i({\bf x}) \le \eta, \forall i$. However,  introducing additional constraints usually  increases   the complexity of the problem-solving. It has been shown in \cite{marler2004survey} that the \textit{min-max} method provides a necessary condition for Pareto optimal solution, but a sufficient condition only for a weak Pareto optimality. When the obtained solution is unique, it is Pareto optimal.
 %
\subsection{Design Approaches}
The problem of the HBF design for the DFRC system is typically nonconvex, which makes it challenging to obtain the optimal analog and digital beamformer matrices directly.
The main reasons are as follows:
\begin{itemize}
    \item Analog and digital precoder/combiner are coupled in the objective and constraints, which makes the resultant problem nonconvex.
    \item Generally, taking both radar and communication metrics into consideration makes the objective nonlinear, which adds to the challenge of finding the HBF matrices.
    \item Additionally, the constant modulus constraints on analog precoder/combiner is noconvex, which also adds to the difficulty and complexity of the problem.
\end{itemize}

Two approaches have the potential to address these difficulties and find suboptimal solutions. \textcolor{black}{It is worth mentioning that there are some works in combining both learning and model-based strategies to form a hybrid solving approach \cite{Elbir2021JSTSP}.}

{\textbf{Indirect Two-Stage Approach:}}
This approach (c.f.\cite{Heath2016Overview}),  which is based on the two-stage optimization strategy,  is capable of designing the HBF in an indirect manner. In this method, the fully digital beamformer ${\bf F}^\star$ is firstly optimized by replacing the  hybrid beamformer with fully digital one in the original problem, and then the hybrid
beamformer is designed by minimizing the Euclidean distance to the obtained fully digital one. By doing so, the objective of the indirect problem is much less complicated than the original one, resulting in low complexity in computations. However, due to the indirect design, the achieved hybrid beamformer will suffer from a performance loss. Besides, it is noted that the two-stage method is not applied to solve the problem with $\epsilon$-constraints model, since the achieved hybrid beamformer that approximates the fully-digital one cannot satisfy the constraints on other metric.

{\textbf{Direct Decoupling Approach:}} As mentioned earlier, the main difficulty in HBF design is the coupling between the analog and digital precoders/combiners. This motivates us to first decouple the hybrid beamformer to simplify the problem. For example, in \cite{cheng2021hybrid}, the objective function is a weighted summation of the multi-user MMSE  and
radar spatial spectrum matching error (SSME). To decouple the analog and digital beamformers, a set of auxiliary variables ${\bf Y}_{k,u}={\bf F}_{\rm RF}{\bf F}_{k}$ are introduced, such that the complex objective function can be decomposed into $UK$ sub-functions, and each sub-function depends only upon a variable ${\bf Y}_{k,u}$. This enable us to iteratively optimize $( \{{\bf Y}_{k,u}\}, {\bf F}_{\rm RF}, \{{\bf F}_{k}\})$  under the consensus alternating direction method of multipliers (consensus-ADMM) framework\cite{boyd2011distributed}.
\section{Performance analysis }
In this section,  we illustrate the performance of the DFRC system with different HBF architecture and design approaches through numerical simulations.

We first demonstrate the  trade-off of the DFRC system between the radar and communication functionalities as shown in Fig. \ref{fig:Sim_parato}. In the considered scenario, the optimization problem is formulated in the weighted-sum form. By tuning the weight parameters with a small stepsize, we obtain the Pareto bounds.
It is observed that the radar mutual information decreases monotonically with an increase in the communication mutual information under all the structures, which reveals the  Parato optmaility inside the DFRC system on the radar and communication aspects. This Parato optimality further implies that to achieve an appropriate trade-off between sensing and communication, selection of the weight parameters is crucial . Moreover, these results also indicate that an appropriate choice of  the HBF structure can trade-off between the hardware complexity and DFRC performance.

\begin{figure}[t]
     \centering
     \includegraphics[width=1\linewidth]{./Sim_Structure}
     \caption{The trader-off between radar mutual information and communication information with different PSs network structure.$N_{t} = 32$, $N_{RF}^t = N_{s} = 4$.}
     \label{fig:Sim_parato}
 \end{figure}

Next, we provide simulation results of different hybrid beamforming design schemes as shown in Fig.\ref{fig:Sim}.
In this simulation, we consider the wideband OFDM based DFRC system serving multiple downlink users and detecting radar targets, where the simulation setting and more details can be found in \cite{cheng2021hybrid}.
For the comparison purpose, the DFRC system with the fully digital structure is included as the performance upper bound.
It is clear to see that the two-stage method suffers from severe performance loss in terms of both radar beampattern and communication spectral efficiency. In contrast, with the direct design, hybrid beamforming for the DFRC system achieve better performance consistenly at all SNR levels.

\begin{figure}[t]
     \centering
     \includegraphics[width=1\linewidth]{./Simulation}
     \caption{The DFRC system is assumed to be equipped with $N_{{t}}=32$ antennas and $N_{\text{RF}}=4$ RF chain serving $U=4$ downlink users. The main-lobe region is ${{\bf{\Omega }}_{main}} = [ - 0.7891, - 0.337] \cup [0.0939,0.657]$. (a) The space-frequency spectra for Fully Digital case; (b) The space-frequency spectra for CADMM case; (c) The space-frequency spectra for Two Stage case; (d) The spectral efficiency versus the SNR for different methods.}
     \label{fig:Sim}
 \end{figure}
 \section{{New Frontiers in Advanced HBF DFRC Systems}}

{From a practical perspective, HBF is a promising technology to be implemented in the upcoming DFRC system. However, to achieve both the sensing and communication functionalities, the vanilla HBF might not fulfill the requirements and achieve optimal tradeoffs. Hence, advance HBF techniques should be developed on various aspects such as architecture, signal processing, and technology convergence; these will be discussed in this section.}
\subsection{HBF in Wideband  DFRC Systems}
 In order to maintain reliable robustness
against multipath fading for communication and to improve
estimation accuracy for sensing, wideband is necessary. Specifically,
wideband  OFDM system  can be regarded as a special case of multi-carrier system, when the number of carriers is very large, the system presents the  wideband property. Different from the narrowband model, the delay of wideband system is related to the frequency, this results in \textit{frequency-dependent} beampattern \cite{cheng2021hybrid}. Moreover, for the analog beamformer, different frequencies need different phase shifts. As a result, the standard HBF architecture based on  PSs cannot deal with the beam-squint problem   caused
by the large number of antennas and bandwidth, as well as the small number of RF chains. The beam-squint  problem will lead to the  beam pointing offset and beam split effect, in which different subcarriers have different  spatial directions.   The  beam-squint  problem will result in a situation where  only the beams around the expected subcarrier are able to attain a high gain, while  the beams at other subcarriers suffer from  a serious loss in gain, which has not been well investigated in wideband HBF-based DFRC systems  \cite{Elbir2021JSTSP}.
In order to  mitigate this effect, combining the time delay network  with analog PSs is able to be introduced to general \textit{frequency-dependent-like} PSs to form the \textit{frequency-dependent} beams. Therefore, research on the  delay-phase hybrid beamforming
design and corresponding performance analysis  should be carried on in future work for
wideband DFRC systems.

\subsection{HBF in DFRC Systems With Low-Resolution ADCs and DACs}
In mmWave systems, the high sampling
rate and high quantization bit of ADCs and DACs will result in high power consumption and cost (e.g., a high resolution ADC $\ge$ 8 bits consumes several Watts \cite{761034}). The HBF structure is capable of reducing the power consumption and cost via adopting a limited of RF chains. Besides the HBF structure, the utilization of low-resolution ADCs/DACs is another ingredient for mmWave system. Although the low-resolution ADCs/DACs have advantages of saving the cost and  power consumption, they may lead to severe performance loss.
In communication applications, with low-resolution ADCs, the performance of HBF and fully digital beamforming has been compared. The results show that at low SNR regions, the fully digital beamforming with low resolution ADCs achieves the same performance to the HBF with ideal ADCs. In addition,  the HBF with coarse quantization attains better performance-EE trade-off.  However, there is a lack of research works on joint optimization of HBF and ADCs/DACs resolutions for mmWave DFRC systems.
Further, the analysis of low-resolution ADCs/DACs in DFRC will help us come to a new understanding related to the HBF design issues, but which is almost blank currently. For example, in a specific DFRC application, it is not trivial to determine the appropriate RF chain number, bit-resolution of ADCs/DACs and  PS resolutions to achieve an excellent trade-off among radar performance, communication performance and hardware efficiency.

\subsection{RIS-Assisted  HBF DFRC Systems}
Reconfigurable Intelligent Surface (RIS) consists of multiple passive elements, each of which can introduce phase shift independently and hence alter the radio propagation environment. From a signal processing perspective, it is essentially shaping a passive beamforming on the impinging signals. Therefore, it is appealing to integrate RIS into the DFRC system to enhance system performance including beam accuracy, coverage  and spatial diversity, etc. The resulting problems are usually formulated as a joint design of both the active (i.e., HBF on the station) and passive (i.e., RIS) beamforming, which requires efficient optimization algorithms especially in the context of large-scale DFRC deployment. Furthermore, RIS has been evolving from the standard passive, discrete and narrowband case to an advanced one which exhibits active, holographic and wideband properties. Correspondingly, the joint design of RIS and HBF becomes even more challenging, thereby warranting an investigation in the HBF DFRC settings. For example, the beam-squint effect overcome by wideband HBF shall re-appear, unfortunately, after reflecting by a narrowband RIS. Apart from the design aspects, it is meaningful from an analytical perspective to pursue the goal of proving the theoretical bound on performance gain in such a system $-$ a matter less investigated in literature compared to the design aspects.
\subsection{OTFS Modulated HBF DFRC Systems}
In high-mobility scenarios, the conventional OFDM suffers from severe Doppler spread and thereby serious inter-carrier interference (ICI). Recently, a novel two-dimensional modulation, i.e., orthogonal time frequency space (OTFS), has been regarded as a promising alternative to the OFDM \cite{9508932}. Different from the OFDM in the time-frequency domain, the OTFS modulation works in the delay-Doppler (DD) domain. Thus, when considering the OTFS-based DFRC systems, the HBF design may face the challenges. For example, how to achieve appropriate radar and communication objective functions based on OTFS modulation signaling with the HBF structure?  Moreover,  for the HBF in OTFS-based DFRC systems, the digital beamforming is designed  for each DD block, while the analog beamforming needs to be  optimized for the whole bandwidth. The corresponding  problem  has a stronger  coupling between the analog and digital beamformers.  Additionally, since the number of DD blocks are very large, it is of utmost necessity to  seek a low-complexity solution.
In summary,  it is of great interest to examine performance of the  OTFS-based DFRC systems with the HBF structure for future works.
\section{Conclusion}
Hybrid beamforming aided DFRC has the potential to significantly improve the energy/spectral efficiency and enable ubiquitous connectivity in future B5G and 6G networks. In order to imperatively understand and tackle the challenges associated with it, this article presented a comprehensive overview of DFRC with hybrid beamforming technology.
Starting from the fundamentals of the hybrid beamforming, we first introduced the system model of the DFRC with hybrid beamforming, including the system structure and DFRC transceiver architecture.
Then the design principles for hybrid beamforming  incorporating DFRC system was introduced based on performance metrics and prevalant approaches.
We then present representative results to highlight the princinples  and finally outline several future research directions that can facilitate the full potential of DFRC with hybrid beamforming technology.

\appendices

\ifCLASSOPTIONcaptionsoff
  \newpage
\fi

\footnotesize
\balance
 \bibliographystyle{IEEEtran}


text:
#! /usr/bin/env node

// Copyright 2016 Google Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//    http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

/*eslint no-console: ["error", { allow: ["log", "warn", "error"] }] */

require('babel-polyfill');

const Promise = require('promise');
const fs = require('fs');
const path = require('path');
const ArgumentParser = require('argparse').ArgumentParser;
const UserAuthorizer = require('../lib/auth');
const SlideGenerator = require('../lib/slide_generator');
const opener = require('opener');
const readline = require('readline');

const SCOPES = [
    'https://www.googleapis.com/auth/presentations'
];
const USER_HOME = process.env.HOME || process.env.HOMEPATH || process.env.USERPROFILE;
const STORED_CREDENTIALS_PATH = path.join(USER_HOME, '.credentials', 'md2gslides.json');

function parseArguments() {
    var parser = new ArgumentParser({
        version: '1.0.0',
        addHelp: true,
        description: 'Markdown to Slides converter'
    });

    parser.addArgument(
        'file',
        {
            help: 'Path to markdown file to convert'
        }
    );
    parser.addArgument(
        [ '-u', '--user' ],
        {
            help: 'Email address of user',
            required: false,
            defaultValue: 'default'
        }
    );
    parser.addArgument(
        [ '-a', '--append'],
        {
            dest: 'id',
            help: 'Appends slides to an existing presentation',
            required: false
        }
    );
    parser.addArgument(
        [ '-e', '--erase'],
        {
            dest: 'erase',
            action: 'storeTrue',
            help: 'Erase existing slides prior to appending.',
            required: false
        }
    );
    parser.addArgument(
        [ '-n', '--no-browser'],
        {
            action: 'storeTrue',
            dest: 'headless',
            help: 'Headless mode - do not launch browsers, just shows URLs',
            required: false
        }
    );
    parser.addArgument(
        ['-s', '--style'],
        {
            help: 'Name of highlight.js theme for code formatting',
            dest: 'style',
            required: false,
            defaultValue: 'default'
        }
    );
    parser.addArgument(
        ['-t', '--title'],
        {
            help: 'Title of the presentation',
            dest: 'title',
            required: false
        }
    );
    return parser.parseArgs();
}

function handleError(err) {
    console.log('Unable to generate slides:', err);
    console.log(err.stack);
    console.log(JSON.stringify(err, null, 2));
}

function prompt(url) {
    if (args.headless) {
        console.log('Authorize this app by visiting this url: ');
        console.log(url);
    } else {
        console.log('Authorize this app in your browser.');
        opener(url);
    }
    return new Promise(function(resolve, reject) {
        var rl = readline.createInterface({
            input: process.stdin,
            output: process.stdout
        });
        rl.question('Enter the code here: ', function(code) {
            rl.close();
            code = code.trim();
            if (code.length > 0) {
                resolve(code);
            } else {
                reject(new Error('No code provided'));
            }
        });
    });
}

function authorizeUser() {
    // Google OAuth2 clients always have a secret, even if the client is an installed
    // application/utility such as this.  Of course, in such cases the "secret" is
    // actually publicly known; security depends entirely on the secrecy of refresh
    // tokens, which effectively become bearer tokens.
    const options = {
        clientId: '52512509792-pc54t7beete33ifbhk00q3cpcpkmfi7c.apps.googleusercontent.com',
        clientSecret: '8g6up8tcVXgF7IO71mCN8Afk',
        filePath: STORED_CREDENTIALS_PATH,
        prompt: prompt
    };
    const auth = new UserAuthorizer(options);
    return auth.getUserCredentials(args.user, SCOPES);
}

function buildSlideGenerator(oauth2Client) {
    const presentationId = args.id;
    if (presentationId) {
        return SlideGenerator.forPresentation(oauth2Client, presentationId);
    } else {
        const title = args.title || args.file;
        return SlideGenerator.newPresentation(oauth2Client, title);
    }
}

function eraseIfNeeded(slideGenerator) {
    if (args.erase || !args.id) {
        return slideGenerator.erase().then(function() { return slideGenerator; });
    } else {
        return Promise.resolve(slideGenerator);
    }
}

function loadCss(theme) {
    const cssPath = path.join(require.resolve('highlight.js'), '..', '..', 'styles', theme + '.css');
    const css = fs.readFileSync(cssPath, { encoding: 'UTF-8' });
    return css;
}

function generateSlides(slideGenerator) {
    const input = fs.readFileSync(args.file, { encoding: 'UTF-8'});
    const css = loadCss(args.style);

    return slideGenerator.generateFromMarkdown(input, css);
}

function displayResults(id) {
    const url = 'https://docs.google.com/presentation/d/' + id;
    if (args.headless) {
        console.log('View your presentation at: %s', url);
    } else {
        console.log('Opening your presentation (%s)', url);
        opener(url);
    }
}

const args = parseArguments();

authorizeUser()
    .then(buildSlideGenerator)
    .then(eraseIfNeeded)
    .then(generateSlides)
    .then(displayResults)
    .catch(handleError);

redpajama_set_name: RedPajamaGithub


Two years later, I am finally reviewing Suddenly Mrs. Darcy! I read it when it came out but for some reason I didn't review it, considering it is my favourite "forced marriage" scenario book, it didn't seem right not to post a review, so here it is.
When I started reading this book I was shocked and amazed. The blunt, fatalist first person speech we see in the first chapters as shocking as it is surprising but it pulls us immediately into the book. The writing is riveting and addictive and I have now come to understand that Mrs. James writing style is unique and recognisable everywhere. When I read the first letter of Elizabeth in The Elizabeth Papers over an year later, I immediately knew it was a Jenetta James book due to the uniqueness of the writing style.
On this book, Elizabeth and Mr. Darcy are caught alone by Mrs. Bennet during the Netherfield ball while Darcy is trying to reveal to Elizabeth Wickham's true character, and because of that they are forced to get married. As this happens so soon in the storyline, they haven't been able to sketch each other's characters yet, so the dynamics between them are very different, and the path they have to take to HEA will be much harder.
They will need to learn how to respect, trust and love each other and, it will not be an easy task when the communication between them is still so difficult because of their misapprehensions and prejudices. But watching them build a strong and powerful relationship is extraordinary, and Mrs. James was able to keep us glued to the storyline from the beginning until the end due to the intensity of the book.
Suddenly Mrs. Darcy is very real, it is not overly romantic, it is not a fairy tale, it portrays reality and people as they are, it shows us a raw reality and it pierces into our soul. It is one of those books I recommend to my friends who don't read JAFF because I know that the writing is so good, so unmistakingly good, that any reader will love it!
I believe that it takes a true talent to write as Mrs. James does, this is something that you can not learn, either you have the talent in you, or you don't, and Jennet James certainly does.
If you are looking for a fairytale story full of fluff this is not the book for you, but you will be missing a magnificent work of art. If you are ready to accept some angst, you will love this book and it will render you speechless.
I loved reading your review which reminded me of all the reasons I adored this book. Great review, Rita! And, LOL, I've forgotten to review books and discover it much later, too.
Rita, I loved this review. I look forward to reading it. I've wanted it since it came out. I was drawn to it by that cover… simply beautiful. Thank you for explaining about the writing style. I will be sure to look for that as I am reading it.
Thank you for leaving a comment and I hope that one day you read and enjoy it:-) The cover is lovely isn't it? It is all the work of Meryton Press' Zorylee Diaz Lupitou who has such talent in that department.
The cover is very lovely and intriguing. This book I believe was the 3rd Variation I read, it was hot out of press. As soon as I saw the cover I was drawn to it . I can almost sense the hesitation in the lady's hand on the knocker. Very talented work of art in deed!
Oh, you should move this one up your TBR pile Jeanne, it is one I certainly recommend!!! It is one of the best I've ever read!!!
Rita, this is one of my most favorite P&P variations. I believe I have read it three times. The author has truly captured Mr. Darcy's shy and hidden love as well as his reticence and over inflated pride. I also loved seeing The respectful relationship that Elizabeth established with her husband who she was forced to marry. As you said it eloquently, both Darcy snd Elizabeth are real with it is nice to see that underneath all her bravado, Elizabeth is a young woman in the need of knowing that she is loved and cherished. Your review is spot on and I have nothing more to add besides cheering for Our dear author.
I read this when it first came out and loved it. I am hoping to see more stories by this author but she does lead a busy life. I can add my recommendation to yours.
I love this review! This book means so much to me. This was the first project ever with Jenetta James! Since then she has become so dear to me. I loved this story from the first scene. And agree…her "The Elizabeth Papers"…Brilliant. And I have the inside scoop that she is publishing a new Regency P&P early in 2018.
I'm looking forward to her next book Christina. I can tell she is truly talented and I'm sure the next book will be brilliant!!!
Lovely review and so accurate! I too loved this book!
Loved reading your thoughts on this one,especially the way in which you expressed how realistic and honest it is. No fluffy sugar coated portrayal of Darcy and Lizzy here,but a true reflection of them trying to come to terms with this new reality.
thank you for the comment Mary – I was very touched by this review.
Hi Mary, yes, that's precisely what I love about it. No fluffy sugar, just pure raw feelings 🙂 Perfect!!!
Fabulous review, Rita! Oh, I loved this book!!! It was the first one I read by Jenetta James and I was hooked, she writes so beautifully, and yessss, that's exactly it, her writing is so realistic and speaks right to the heart!
What a great review. You describe it in such a thoughtful way.
Thank you Emma 🙂 I hope you like this book when you read it!
I was lucky enough to win a paperback copy of this book and have to confess that it's still languishing on my physical TBR pile. However, it IS at the top of that pile already and if it hadn't been, it would have been bumped up to there after reading your review, Rita. The Elizabeth Papers is another book on that pile!
OMG, if you have it, you have to read it Anji! It is really good! I doubt you'll regret reading, in fact, I'm quite certain you'll regret waiting so long to read it. I don't say this about many books, but this one is really extraordinary!
I'm in the middle of it right now Rita. It's a real page turner, isn't it?


The criteria described below will permit a request to be reviewed by the college's Graduate Studies Committee. As these awards are for all of the college's programs, beginning on any academic term, requests are considered on specific dates. The committee has established application deadlines for each academic term (see below).
Award recommendations are made at the professional discretion of the faculty members of the Graduate Studies Committee. Factors that could influence recommendation considerations include, but are not limited to: grade point average, previous awards made to various departmental programs, diversity/under represented needs in a departmental major, strength of requested recommendation and available funding at the time of the review.
The Graduate Studies Committee has established a minimum 3.0 undergrad GPA to be considered for any college graduate level scholarship. The undergraduate GPA is determined by the Graduate School as a part of the admissions process and must be at or above a 3.0 at the time of the scholarship application deadline. If the applicant has already completed a graduate program, or was once in a graduate program, that Graduate level GPA should be a 3.0 or greater (and the undergraduate GPA is not considered).
Students who are from under represented groups and are interested in the college's programs are encouraged to apply. The demographics of the professions represented by the college's programs indicate a critical need for minorities, especially African Americans.
Women are under represented in Educational Leadership roles, the mathematics and sciences teaching fields, and in the area of Sport Management. Men are under represented in Early Childhood, and Human Services (Counseling) fields. The demand for Rehabilitation Counselors exceeds supply and therefore, we encourage applicants to our Rehabilitation Counseling programs.
In general, the teaching professions also have a high need for teachers in Mathematics, Science, World Languages and Special Education (Intervention Specialists).
People with physical challenges are under represented in all of the college's programs.
In addition to the under represented groups described above, candidates can be considered solely on the basis of academic excellence. Candidates who wish to cite the area of academic excellence in their letter of application must have a 3.5 or higher undergraduate or graduate GPA as determined by the Graduate School, at the time of the application deadline.
Candidates that are under represented as defined above and meet the academic strength criteria of a 3.5 or better GPA will be considered "top tier" candidates and can be considered for full or partial awards, depending on funding availability.
Partial awards will be considered for candidates who are not defined as "top tier".
Certificate candidates are limited to partial awards and cannot exceed $2000 for a student taking 6 or more credit hours per semester, and $1000 for a student taking 3 credit hours per term.
The primary criteria for consideration of a Graduate Tuition Scholarship will be based on the student's overall academic record, their potential for academic success in targeted programs, and the diversity characteristics cited above.
At the time the faculty review of applications, the candidate must have a completed application to the Graduate School for a degree-seeking status, or as a certificate student - non degree applicants, licensure/endorsement applicants, or conditionally accepted students will not be considered.
Provisionally accepted students can be considered for an award, but an award will not be made until such time as the provision(s) have been met and the candidate is fully admitted as a degree seeking student.
Human Services (Counseling) candidates awaiting an admission interview or the results of an admission interview will be eligible for consideration. An award will not be granted until the candidate has been fully admitted.
Native Wright State students, who are waiting for the posting of their WSU undergraduate degree, and are provisionally accepted to the Graduate School will be eligible for consideration.
The intent of the program is to recruit new students; currently enrolled graduate students will not be considered.
"Top tier" candidates (as defined above) normally receive fee waivers at the Ohio Resident Fee rate to support full time tuition, defined by the University.
"Top tier" candidates do not have to attend full-time to receive consideration of full funding of tuition. Tuition waivers may be reduced or eliminated based on availability of funding.
All other candidates will be considered for partial awards. The amount of the partial award will vary and will be established for each candidate by the faculty members of the Graduate Studies Committee. Tuition waivers may be reduced or eliminated based on availability of funding.
Summer tuition awards for all candidates are for all of the summer session terms. If you choose to use your entire award in an early summer session, there will be no funding available for a later summer session.
Tuition waivers may be reduced or eliminated based on availability of funding.
Students can be eligible for support for up to two years (up to six semesters, which include summer terms), pending availability of funds.
One year, 3 semester awards may also be awarded to selected students.
Students must maintain a minimum 3.0 grade point average, remain in a degree seeking status, and be enrolled each academic term (summers are optional, but count in the total of maximum terms) for support to continue to a subsequent semester.
All Scholarship awards are formally reviewed for renewal for the following fiscal year. No additional information is required from the student for this review process.
(This is the "application.") Applicants must submit the following: a letter requesting the Graduate Tuition Scholarship and describing the applicant's declared program of study, career plans, and diversity information (see target groups in Criteria).
The letter must also provide your name, address, telephone number, and email address. Wright State email address and the university's assigned student number (used to track enrollment) are required if the applicant has applied to the university for admission.
In addition to the letter requesting a Graduate Tuition Scholarship, we require one (no more than one, please) letter of support from any one of the following – WSU faculty, K-12 school faculty or administrator, counselor or member of a human service agency, WSU College of Education and Human Services department chair, the College's Dean or any other university faculty, Chair or Dean from another institution.
Attach only one letter of support to your letter of request. Send them both together, not separately.
Letters of requests that do not contain the information noted above will not be considered.
The Assistant Dean for Student Affairs must receive the letter of request and the letter of support prior to the established deadlines. In fairness to all the candidates, requests for consideration of late requests will not be approved.
Fall (August) semester your request letter, letter of support, and acceptance to the Graduate School must be completed by the first business day of March.
Spring (January) semester your request letter, letter of support, and acceptance to the Graduate School must be completed by the first business day of November.
Summer (May) semester your request letter, letter of support, and acceptance to the Graduate School must be completed by the first business day of March.


GT Appliances is a leading appliance factory shop and a Certified DEFY Dealer.
We specialise in cheap, shop soiled and scratch and dent appliances in Cape Town, South Africa.
GT Appliances is a self-sufficient and reputable scratch and dent retailer currently operating in Cape Town, South Africa. We have been in business for over 5 years and we have built strong relations with our suppliers and customers over the years. We pride ourselves in being professional, transparent and providing affordable services.
All products carry a manufacturer's guarantee (3, 6 or 12 months) and all products are thoroughly checked and tested by highly qualified technicians before being made available for sale.
Delivery can be arranged instore on purchase. Prices of these quality goods are up to 50% off normal retail prices and further discounts can be negotiated with bulk buyers.
The brands sold include DEFY, Samsung, Hisense, LG and Telefunken.


Carey Cloud's Good Luck Elf posing as a Leprechaun.
Love your image Luke - beautiful!
I love the postcard Gail.
I want one that color for my collection!! Are you sure that it isn't a represntation of Harry Potters DDOBY?
Everyone knows that most people will "stretch" their ancestry to include Irish descent, so I am at a little liberty to present Shawn O'Malley who just toured all the Irish pubs in Boston but luckily was escourted by Erin O'Doule of Boston's finest.
With that I must leave to toast my leprechaun friend here as my pint is getting warm.
St Patrick's Day has been very special to me for 41 years. In 1968 I gave birth on that day. My daughter, Tammy, will be celebrating her forty-first birthday with her husband, children and myself this coming Tuesday. I shall cook a nice birthday dinner for all of us. And no, it will not be corn beef and cabbage. Tammy has requested my delicious Hawaiian chicken dish.
Below you will find Volume 2 of the 1960's encyclopedia books, which is titled Days We Celebrate. Within it are two pages pertaining to St. Paddy's Day.
Happy birthday to my Tammy! and Happy St. Patrick's Day to all of you.
Diane, thanks for the pictures, and the great story.
I've heard that they wear kilts in the Emerald Isle.
The boy in the middle is probably Scottish, but I'm sure the boys on the outside are Irish.
Oh, what pretty colors. If these little guys decide to walk in a parade on a windy day, they had better hold on to their kilts. They are pretty short.
Hello Diane and congrats. I saw on one of your other posts that Luke was wishing you a Happy Day and about Tammy and I didn't know what was going on (not that I do know what is going aon anyway), so I was content to just going back to playing with my Construct-A-Scenes.
Now I know "the rest of the story".


text:
Ecosystem diversity Print
Ecosystem diversity is to be assessed using the Criteria for the Identification of Significant Ecological Areas in Auckland (Sawyer & Stanley, 2012) published by Auckland Council. Relevant assessment criteria include:
Representativeness - a factor that assesses the types of ecosystems and the species that live in them against Auckland's original ecosystem types
Threat status and rarity - an assessment of the threat of extinction or decline of all levels of biodiversity (genetics, species, communities, habitats and ecosystems) at all scales (site, catchment, region and nationwide)
Diversity - an assessment of the different drivers at different scales including aspects such as competition between species, disturbance history, climatic variables and landform
Uniqueness or distinctiveness - an assessment of whether the environmental resource only occurs in the Auckland region.
Terrestrial habitat diversity
Diversity assessment will consider the regional and catchment significance of site resources. WSD promotes the protection and enhancement of diverse native vegetation types. This may include the following potential land management responses:
Provide a planted riparian buffer to protect existing 'interior' habitat from disturbance and thereby protect unique microclimates and associated habitat diversity
Re-vegetate a site with pioneer vegetation species to develop soils and allow for natural succession processes to occur
Enhance a site by planting complementary flowering and fruiting species to extend food sources for native fauna
Restore multiple vertical vegetation 'tiers' from root zones and litter layers, through herbaceous plants, shrubs, canopy, and emergent trees to form diverse habitat niches (refer to Figure 17).
Plant species diversity
In addition to their natural character and ecosystem values, native plant species have good survivorship and often require less replacement and maintenance than introduced species over the long-term. 'Eco-sourcing' involves the collection of divided plant material or seed from remnant vegetation as close as possible to the location of proposed planting, and ideally from a similar ecotone (a similar environment in terms of climate and elevation). This is a means to protect unique genotypes of plant species, which can also be best suited for the local environment.

redpajama_set_name: RedPajamaCommonCrawl


For the opening half of George Osborne's Budget speech, the Labour front bench was busy waving around copies of the Evening Standard's front page. This was visibly putting Osborne off; he wouldn't be human if the fear that another of his Budgets was going to be dashed on the media rocks hadn't crossed his mind. But by the time he sat down, the storm over the Standard front had died down thanks to a quick and dignified apology from the paper itself.
Osborne will also have been pleased by the cheers of his own side as he returned to his seat. For all the speculation got up by the irreconcilables, most Tory backbenchers seemed as pleased as could be expected with a Budget that was delivered against such a grim fiscal backdrop. They have retail measures to go and sell on the doorstep.
The scrapping of the latest fuel duty rise will, as Isabel said, please the cost of living caucus. The government will have foregone £21.5bn in fuel duty revenue by the end of this parliament (one can see why David Cameron likes to call fuel duty campaigner Rob Halfon the 'most expensive MP in parliament'). This, taken alongside the increase in the personal allowance to £10,000 and the childcare changes announced yesterday, gives the coalition a story to tell on cost of living. And the 1p cut in beer duty is a reverse pasty tax: it's meant to show that the Chancellor understands the importance of the small pleasures in life.
The Budget also marked a return to the themes of David Cameron's conference speech, aspiration and the global race. I suspect that government moves to help home-buyers will concern many on the free market right, who'll worry that it is just reflating the housing bubble. But it is worth noting that the coalition's planning reforms should have eased some of the supply constraints.
I suspect that the political sport of the next few days will be about finding how the government has managed to get the deficit down by £100 million. The Treasury is being frank that they have done this by strictly supervising departmental expenditure. But they stress that no supplier has been paid late because of this. Of course, progress of the deficit is far slower than Osborne said it would be. But I don't think the argument that the government has got it down only by strict spending controls is going to hunt.


Tires Unlimited II of Greer provides Parking Brake Adjustment services to Greer, SC, Spartanburg, SC, Greenville, SC, and other surrounding areas.
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NEW DELHI -- It took just 5 minutes for 60,000 welcome kits of Maggi to be sold out on Snapdeal as consumers thronged the e-commerce platform to lap up their 2-minute instant noodles.
"Snapdeal sold out the first batch of 60,000 Maggi Welcome Kits within 5 minutes of Maggi Flash Sale going live today.
There has been much anticipation for the return of one of the favourite Indian brands and we have witnessed a phenomenal response to this sale from customers across the country," Snapdeal Senior Vice President (Partnerships and Strategic initiatives) Tony Navin said.
Maggi was banned in June by Food Safety and Standards Authority of India (FSSAI) which stated that it was "unsafe and hazardous" for consumption due to presence of lead beyond permissible limits. The company had then withdrawn the noodles brand from the market.


Outline the role of anatomy knowledge in the health and fitness industry.
List the origin and insertion of specific muscle attachments.
Palpate and explore the muscle attachments on the human body.
Create exercises that effectively contract isolated muscles for re-training motor patterns.
List muscles to review and set goals for studying.


Keep your morning routine running smoothly with our range of shower accessories. Because bathroom suites get used daily, they need to be well-maintained. Replacing key parts every now and then will make sure that your system stays working as it should. Adding some simple storage solutions will keep all your lotions and potions neatly arranged.
If you're looking to give your whole bathroom a facelift, then a new set of shiny taps could be just the ticket. Or try some fresh wallpaper in a pale colour for a bright feel. A coat of paint is another brilliant option for a quick change of style. Try repainting the doors in your home for a way to mix up your decor without redoing the entire space.
To create a warm atmosphere in the rest of your home, consider installing one of our electric fires. They can be the perfect way to heat single rooms in the colder months. With traditional and modern options available, you can find a cosy centrepiece to suit your taste without needing a gas engineer.


Show your intense love by sending your beloved this Sublime Celebration Time Hamper that pours out your heart even if you remain quiet. This Hamper holds 3 Red Roses and Luscious Cake. This Cake is garnishing with Red decorations and a White writing I LOVE YOU.


CHICAGO – The Bears' rise, from a 5-11 record to the top of the NFC North under first-year coach Matt Nagy, has been fueled by a creative offense and a defense that leads the league in points off turnovers.
If their 25-20 victory over the Vikings on Sunday night — which gave the Bears a 1½-game lead over Minnesota — turns out to be the catalyst for Chicago's first division title since 2010, the Bears will be able to credit their best defensive attributes, more than their most positive offensive traits, for helping them topple the defending division champions.
The Vikings' fourth loss of the season was more because of preventable outcomes than unpredicted ones. Despite gaining only 118 yards through three quarters, they stayed within striking distance into the fourth, where second-year quarterback Mitchell Trubisky committed some of the neophyte errors that came with his spellbinding mobility through Chicago's 6-3 start.
But in the end, it was Kirk Cousins who made the mistake the Vikings couldn't afford.
With the Vikings down 14-6 in the fourth quarter, Cousins tried to hit Laquon Treadwell on a corner route that turned into an interception after Eddie Jackson made a play on the ball, picking it off and returning it 27 yards for a touchdown that put Chicago up 22-6 after Trubisky hit his second two-point conversion pass of the night.
The interception was Cousins' second of the night, a third Vikings turnover to go with a Dalvin Cook fumble that ended a potential scoring drive late in the first quarter.
The Bears are now 7-3 and play at Detroit on Thanksgiving Day. The Vikings (5-4-1) will again play on Sunday night next week, at U.S. Bank Stadium against a Packers team whose playoff hopes are on life support.
The Vikings now have lost all three of their prime-time games against teams they are chasing in the NFC playoff standings. In those three games, the Vikings have turned the ball over six times.
Through two quarters, the Bears held the ball for 19:55, gaining 115 of their 202 first-half yards on the ground. Trubisky posted 37 yards on six attempts, with a 9-yard designed run coming among his scrambles, and the Bears' misdirection helped create holes in the middle of the Vikings defense for Jordan Howard, who gained 46 yards on 10 first-half attempts.
After the Bears ran the ball — or Trubisky scrambled — on seven consecutive plays, the quarterback found Anthony Miller in the back of the end zone for a 18-yard touchdown before Nagy opted to go for two with the Bears up 9-0. Trubisky hit Josh Bellamy for the conversion, giving Chicago an 11-point lead it would extend to 14 with Cody Parkey's second field goal with 50 seconds left in the first half.
Video (10:55): Ben Goessling and Andrew Krammer break down the Vikings' 25-20 loss to the Bears and look at the state of the team's offensive line.
While the Bears built their 14-0 lead, the Vikings managed only 77 first-half yards on 22 plays, with 43 of those yards coming on a two-minute drill that ended in a turnover as Cousins sailed a throw beyond tight end Kyle Rudolph while under pressure from Leonard Floyd and had it picked off by Adrian Amos.
The Vikings' first points of the night didn't come until the final minutes of the third quarter, after Trubisky forced a throw to Allen Robinson with Anthony Harris sitting over the top of the receiver. Harris made his second interception of the game, setting up a Dan Bailey field goal after a first-down sack from Khalil Mack and third-down pressure from Akiem Hicks and Floyd stalled the drive.
The Vikings forced a punt after Bailey's second field goal with 11:46 remaining, but on their first offensive play, Cousins threw his interception to Jackson.


text:
/**
 * AboutLabel.java
 */
package co.shinetech.gui;

import java.awt.Graphics;

import javax.swing.JLabel;

/**
 * Customized JLabel for about windows.
 * @author Rodrigo
 */
public class AboutLabel extends JLabel {
	private String version;

	/**
	 * @param version
	 */
	public AboutLabel(String version) {
		super();
		this.version = version;
	}

	@Override
	public void paint(Graphics g) {
		super.paint(g);
		g.drawString(version, 10, 250);
	}
}