It is two days post Hurricane Irene.
If you talk to enough folks, you can detect disappointment in some Northeast corners about how boring the storm was.
My theory is that people are hungry for adventure and many don't know how to seek it themselves for risk of losing physical comfort, and thus, they find themselves surprised and pleased by the adrenaline rush of an approaching storm.
Most people would never confess that they find storms exciting. It's not a politically correct thing to say, especially when death and damage are involved. But, on some level, an approaching hurricane is as exciting as it is dreadful.
Because as much as we seek comfort, we also find it boring.
Comfort is a noose. Once we have it, we become too content, we fight too hard to keep it and not hard enough for the things that give life meaning. A hurricane is a reminder of what's important — relationships, life, little pleasures, love, truth.
A life lived to preserve physical comfort isn't really all that fulfilling. It is fulfilling to seek it, but once you're there, then what?
The happiest people are not those who are the most comfortable. The happiest seem to be those who are in a zone. Those with a mission and a goal, those who are seeking to better themselves or some societal element over which they have control, those who have risked physical comfort for some greater purpose.
Religious missionaries and business entrepreneurs and loving parents share this in common.
Happiness lives outside of our comfort zone.
Update on the hurricane: It is proving to be a slow – rather than fast – destroyer, as flood waters rise, especially in Vermont. Story.
Maximize the moment. And jump.
Yes! Love this! SO true, and you verbalized it in a way I hadn't thought of before.
Its true, and you've written it very well.. Thanks for sharing..
I could not possibly love this post more! It took me awhile to realize this in my own life–how my attachment to comfort was actually harming me (hello, couch potato!). Stretching beyond my comfort zones has been so rewarding. Oh, how I wish we would move beyond our comfort zones on a collective level–in how we spend our time, our money, etc.
@Alexis: Thank you! And thanks for linking back!
@CF: Go you! I think your giving up of your car is really putting this into practice.
Two things immediately came to mind after reading this post.
1) The final scene in George Bernard Shaw's "Heartbreak House" – when the cast, seemingly reconciled to an idle, increasingly uncertain existence, revolving around an English manor, suddenly come to life & delight as warplanes bomb the surrounding area & come ever closer.
2)Paul Farmer, co-founder of Partners in Health, & one of the people I most admire. When you write "the happiest people are not those who are the most comfortable.." – that's him! Eg, Tracy Kidder, in "Mountains Beyond Mountains" http://goo.gl/85xuL.
@HMF: I love your references. I haven't read nor seen, "Heartbreak House" and now I want to!
And way to link to a Google book rather than the link to buy the book — the excerpt got me hooked…that's got to be a way to sell books.


Music Movie Songs - Sangeethouse.Com - Bollywood Tamil Telugu Malayalam Kannada Bhangra Ghazals Pop Remixes Downloads!
Songs sound like they are playing in high-speed.
I need help with the Streaming audio, what music player do I need?
1) Make sure you have latest version of Adobe Flash Player. Sometimes if the player version is old, instead of giving option to upgrade, it simply stops playing songs.
2) If you computer is on network firewall, your network may be blocking streaming protocol that is used by flash player to stream audio. You will have to contact your network administrator to have streaming unblocked.
4) The songs may take longer to "buffer" if you are on a slow internet connection such as 28.8K modem dial-up. If you see the songs's title and album info but can't hear anything, the player may be just buffering. Just wait a few more seconds and you should be able to hear the music.
5) If you still can't figure out the problem, please seek help from someone who can take a look at your computer to troubleshoot further. Contacting us may be of little help since this list covers most of the common reasons for not being able to hear the music.
What is PCD? Does this feature cost anything?
A PCD = Personal CD. You can make as many PCDs as you wish. Members often have PCDs for various genres (tamil favorites, latest top 10 e.t.c.), events (marriage songs, dance party) and to create a music portfolio of their favorite songs so they don't have to keep searching for same songs everytime they visit Sangeethouse.com. This feature is completely FREE! You cannot download songs from PCDs.
How can I download songs to my computer from this site?
Sangeethouse.com is an audio-on-demand online streaming site. There is no feature to download songs to your computer from this site. This site protects copyrights of music producers and artists. If you like the songs on Sangeethouse.com, you may purchase the CDs from other online sites.


investigations and inspections are recommended or required.
help of your REALTOR®, you do not have to allow strangers into your home. Your REALTOR® will generally prescreen and accompany qualified prospects through your property.


Instagram can be considered as one of the most important online media to make your presence felt. Also, the social media has a role to play in making or breaking your impression; especially if you are looking for a job or planning to start your own blog. So, sometimes it becomes important to clean your Instagram account whenever there are many fake accounts.
In Instagram, there may be numerous unprofessional and unrequired photos. Some people have the habit of posting many photos to inform others about their personal lives all the time. Due to this reason, their Instagram accounts get full of such photos that can make an impression about them in a negative way, especially if they want to use that account for professional purposes. So, the best way is deleting all such photos.
If there are some photos you don't wish to delete, you can make them private. Thus, any person who is not your follower will have to take your permission before viewing your photo. Also, another thing you can consider is changing your real name of your Instagram account into some other name. This can help you keep your account private.
Make sure that whatever you have written in your Instagram account is written in correct grammar and if necessary, edit and make the necessary changes. Incorrect grammar and spelling do not boast one's professionalism.
Check your Instagram account on Google and see how you are viewed online. For example, Google different names related to your Instagram account and see what comes up. If something shows up that you don't like, you can remove it; or if you are tagged, you can request that person to remove it.
Try not to follow those people you don't know. Of course, there might be some people whom you admire personally and you can add them. But avoid those people that post anything and random photos.
Hashtags can be helpful as well as messy at the same time. Hashtags can make your photo more visible but they can also ruin a good photo. So it is always better if you hide the hashtags.
Lastly, it is very important for you to post only those photos that you really want to post. Unprofessional and unflattering photos can make a wrong impression of you that may have a negative impact if you want to use your account for professional purpose. Your online persona or reputation can say a lot about you. So, first check your online presence and if you are not satisfied with it, try to change it to build a good reputation.


text:
Chairboys welcome Dormeo as new change shirt sponsors
High Wycombe-based mattress specialists come on board.
wwfcofficial
A new name will adorn the front of Wycombe Wanderers' change kit for the next two seasons, with High Wycombe-based mattress specialists Dormeo kicking off a brand-new sponsorship deal with the club ahead of the 2019/20 campaign.
Dormeo developed a partnership with the Chairboys during the 2018/19 season, sponsoring a family pantomime at Adams Park just before Christmas, as well as becoming members of the 1887 Business Club networking facility and providing club captain Matt Bloomfield with a state-of-the-art Octaspring® mattress following his 500th appearance for the Blues back in March.
Now they've stepped up their affiliation by sponsoring the front of the brand new change shirt, which is set to be revealed to supporters early in July.
Michael Davies, General Manager of Wycombe Wanderers, said: "We're privileged to have the support of a number of long-term sponsors here at the club but it's always a great honour to welcome on board new partners, and we're excited to be working alongside Dormeo for the next two seasons and beyond.
Despite being the fastest growing mattress company worldwide, Dormeo have strong local roots here in the traditional furniture-making town of High Wycombe. They've been terrific supporters of the club over the past few months and we're thrilled to be able to formalise a partnership which we hope will bring mutual benefit for many years to come."
Mike Pitt, Managing Director of Dormeo, said: "Partnering with Wycombe Wanderers has been an ambition of ours for many years. We have a strong fan base in company and are proud to know that our name will be associated with the club as they embark on this season's League 1 campaign.
"We've been growing our brand nationally and overseas for almost 18 years, and now look forward to engaging with as many local Chairboys fans as possible, both around the stadium on matchdays and in our showroom on London Road, High Wycombe. We'd be delighted to get involved in the season ticket holder's benefits scheme, making sure the fans are always well looked after when visiting our showroom."
"Everyone at the club has made us feel very welcome ever since we stepped foot in Adams Park and we look forward to developing our relationship with the club over the coming months and years."
Visit the Dormeo sleep showroom on London Road, close to the retail park, or head to their website www.dormeo.co.uk to learn more about their range of award-winning mattresses, pillows, divans and bedding.
Rocky happy to be back in black
The Dormeo kit launch story
Blooms speaks at kit launch event
Dormeo offer 15% in-store discount for season ticket holders
The Chairboys' newest sponsors - mattress specialists Dormeo - are offering a 15% discount on all products in their High Wycombe showroom for Wycombe Wanderers season ticket holders.
10% off room hire at Adams Park for season ticket holders
Wycombe Wanderers season ticket holders can benefit from 10% off room hire on all bookings in the Adams Park Conference Centre.
10% off at Go Ape Wendover for season ticket holders!
Go Ape in Wendover are offering a 10% discount to all Chairboys season ticket holders for the 2019/20 campaign.
Utilita extend partnership for two more years
Utilita Energy have extended their partnership with Wycombe Wanderers for a further two years, taking up the sponsorship of the club's travel and training wear. The energy firm will also be powering...

redpajama_set_name: RedPajamaCommonCrawl


text:
Robin Leach, host of 'Lifestyles of the Rich and Famous,' dies at 76
Posted 11:12 AM, August 24, 2018, by Tribune Media Wire
LAS VEGAS, Nevada — Robin Leach, the host of the 1980s celebrity show 'Lifestyles of the Rich and Famous,' has died at the age of 76.
He died Thursday night, according to a columnist for the Las Vegas Review-Journal, where Leach was also a writer.
Robin Leach is seen in this undated photo. (Credit: Newsmakers via Getty Images
"Sad to report the death of famed celeb reporter, friend and colleague #RobinLeach @ 1:50 a.m. in #LasVegas. He would have been 77 Wednesday. He suffered a second stroke Monday. He in hospice care. He'd been hospitalized since Nov. 21, after suffering a stroke in Cabo San Lucas," columnist John Katsilometes tweeted Friday morning.
Katsilometes tweeted a statement from Leach's family after his death was announced,
"Despite the past 10 months, what a beautiful life he had. Our Dad, Grandpa, Brother, Uncle and friend Robin Leach passed away peacefully last night at 1:50 a.m"
"Everyone's support and love over the past, almost one year, has been incredible and we are so grateful. Memorial arrangements to follow. With love, Steven, Gregg and Rick Leach."
Statement from #RobinLeach family: "Despite the past 10 months, what a beautiful life he had. Our Dad, Grandpa, Brother, Uncle and friend Robin Leach passed away peacefully last night at 1:50 a.m." 1/2
— John Katsilometes (@johnnykats) August 24, 2018
More from #RobinLeach family: "Everyone's support and love over the past, almost one year, has been incredible and we are so grateful. Memorial arrangements to follow. With love, Steven, Gregg and Rick Leach."
Leach rocketed to fame in 1984 when the show premiered in first run syndication. The program perhaps better than any other captured the opulence and excess of the rich and famous around the world in the 1980s.
The show continued until 1995. Leach became a familiar presence in commercials and on late night talk show couches.
A woman wounded in the 2017 Las Vegas shooting has died of her injuries
The Blackhawks get the job done on the road in regulation in Winnipeg
Nick Gordon, the former boyfriend of Bobbi Kristina Brown, dies at 30
Final goodbye: Recalling influential people who died in 2019
Vegas 'black widow' murderer free on parole after 20 years
Harry Morton, son of Hard Rock Cafe co-founder, dies at 38
Bernie Sanders out of hospital after having a heart attack
Robin Lehner makes 38 saves as Blackhawks beat Islanders 5-2
14-year-old Louisiana boy arrested for stabbing father to death with spear
Robin Lehner's outstanding effort for the Blackhawks not enough for the win
Joshua Brown was thrust into a spotlight he didn't want at ex-cop's murder trial. He was killed 10 days later
Robin Lehner pulled, Avalanche roll Blackhawks 7-3


Recently I read a book on Starbucks called "Starbucked" by author Taylor Clark. The book tells about how Starbucks started out to be a small coffee shop and finally becoming the most popular coffee shop all around the world. The book also tells about what strategy plans and risks Starbucks took in order to achieve what they have achieved today. I remember one particular story about how Starbucks solved their business problem by coming up with an at first seemed crazy but later turned out to be an amazing and successful plan. During the early days of Starbucks, there was once where they were broke and they still had their rent to pay. So, the boss came up with an ingenious idea. Guess what he did? he actually opened up another Starbucks coffee house just directly opposite the original coffee house. People would think, "is he crazy?". But he did this with a motive. Why did he open 2 Starbucks coffee houses directly opposite each other? 1st reason was to provide convenience to their customers. For example, people traveling from this side of the street can conveniently visit the coffee house at that side while customers traveling from the other side of the street can visit the other. 2nd reason was to attract different kinds of customers. the 1st coffee house seemed to attract high class customers and hence that coffee house' atmosphere was more professional looking, while the other was to attract more casual customers, that coffee house was build in a very comfortable fashion where people can sit down, enjoy their coffee and socialize. I feel that this is a very ingenious idea that helped propelled Starbucks to stardom. This move by Starbucks have given me the inspiration to take risks and believe in myself in whatever I do.
wow,the boss was so creative to come out with this idea!!!


text:
\section{Proof of $C_{3,m}^-$}
\sectionmark{$C_{3,m}^-$}

Here, we use the results of the previous sections to prove $C_{n,m}^-$ in positive characteristics when the source of the fibration is a threefold.
The proof follows the ideas in \cite[theorem 4.1]{anti}.

\begin{theorem}[$C_{3,m}^-$] \label{C3m-}
Let $f:X \rightarrow Z$ be a fibration from a normal projective threefold $X$ to a normal projective variety $Z$ with at worst canonical singularities, over an algebraically closed field of characteristic $p \geq 5$.
Let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$ such that $K_X+\Delta$ is $\numberset{Q}$-Cartier.
Suppose that the general fibre $(F, \Delta|_F)$ is strongly $F$-regular and the stable base locus of $-(K_X+\Delta)$ does not dominate $Z$.
Then,
\[
\kappa(X, -(K_X+ \Delta)) \leq \kappa(F, -(K_F+ \Delta|_F)) + \kappa(Z,-K_Z).
\]
\end{theorem}

\begin{proof}
First of all, we can assume $\kappa(X, -(K_X+ \Delta)) \geq 0$.
Moreover, as in remark \ref{index divisible by p}, by perturbing $\Delta$ with a sufficiently small multiple of $-(K_X+ \Delta)$, we can suppose that there exists a positive integer $a$, not divisible by $p$, such that $a\Delta$ and $-a(K_X+ \Delta)$ are integral divisors.
If $Z$ is a curve, then the result holds by theorem \ref{Cn1-}.
Thus, we only need to consider what happens when $Z$ is a surface.
By proposition \ref{thm. 3.8}, $-K_Z$ is $\numberset{Q}$-effective.
If $\kappa(Z,-K_Z)=0$, we conclude by theorem \ref{Cn,n-1-} in the previous section.
If $\kappa(Z,-K_Z)=2$, easy additivity theorem \ref{easy additivity} gives the conclusion.
We are therefore only left with the case $\kappa(Z, -K_Z)=1$.
In order to achieve the result here, we want to get to a situation where we can apply theorem \ref{Cn,n-1-}.
To do this, we pass through the Iitaka fibration of $Z$ following the ideas of \cite[theorem 4.1]{anti}.
However, in positive characteristics if a property holds for a very general fibre, it may happen that it does not hold at all, as the ground field might be countable. Moreover, the generic fibre of a fibration can be very singular even if the source and the target are smooth. Therefore, we may lose the nice properties we need.
Nonetheless, since $Z$ is a surface, these problems do not arise, in the next lemma we see why.

\begin{lemma} \label{base locus}
Let $S$ be a normal projective $\numberset{Q}$-factorial surface such that $\kappa(S,-K_S)= 1$ and let $g: S \dashrightarrow C$ be the rational map induced by the linear system $|-mK_S|$ for $m \gg 0$. Write $|-mK_S|= |M| + B$, where $|M|$ is the movable part (i.e.\ its base locus has codimension $\geq 2$) and $B$ is the fixed divisor.\\
Then, $M \sim_{\numberset{Q}} g^*A$ for an ample $\numberset{Q}$-divisor $A$ on $C$ and the support of $B$ does not dominate $C$.
In particular, the Iitaka fibration relative to $-K_S$ is induced by $|M|$ and is a (quasi-)elliptic fibration.
\end{lemma}

\begin{proof}
First of all, note that the rational map induced by $-mK_S$ coincides with the one induced by $M$.
Since the base locus of $M$ has dimension $0$, $M$ is semiample by Zariski--Fujita's theorem \cite[theorem 2.8]{Fuj}. By possibly substituting it with a multiple, it is then linearly equivalent to $g^*A$, for an ample divisor $A$ on $C$ by construction of the Iitaka fibration.
Let $B^h$ and $B^v$ be effective divisors decomposing $B$ into its horizontal and vertical components, respectively. We need to show that $B^h=0$.
Suppose this was not true. Then write, for $0< \varepsilon \ll 1$,
\[
-mK_S \sim (g^*A + \varepsilon B^h) + (1-\varepsilon)B^h+B^v.
\]
The divisor $B^h$ is relatively ample.
By Nakai--Moishezon criterion, $g^*A + \varepsilon B^h$ is ample and $(1-\varepsilon)B^h+B^v$ is effective, showing that $-K_S$ is big. Contradiction.\\
Therefore, $g$ is well-defined everywhere and it coincides with the Iitaka fibration.
Moreover, the general fibre of $g$ has arithmetic genus $1$.
\end{proof}

By \cite[proposition 4.11]{KM}, since $Z$ is a surface with canonical singularities, it is in particular $\numberset{Q}$-factorial, thus we can apply the above lemma \ref{base locus}.
Fix an $m \gg 0$ and let $g: Z \dashrightarrow C$ be the rational map induced by $|-mK_Z|$. Then, we can write $-mK_Z \sim g^*A+B$, where $B$ is the fixed divisor and $A$ is ample on $C$.
Call $W$ the general fibre of $h:= g \circ f$, using easy additivity theorem \ref{easy additivity} we get the inequality:
\begin{align*}
\kappa(X,-(K_X+\Delta)) & \leq \kappa(W, -(K_X+\Delta)|_W) + \dim(C) \\
& = \kappa(W, -(K_W+\Delta|_W)) + \kappa(Z,-K_Z).
\end{align*}
To conclude, it is enough to prove that $\kappa(W, -(K_W+\Delta|_W)) \leq \kappa(F, -(K_F+\Delta|_F))$, for $F$ general fibre of $f$.
Again by the lemma above \ref{base locus}, the arithmetic genus of the general fibre of $g$ is $1$, so, if the characteristic of the base field is $\geq 5$, it is smooth.\\
Let us study the stable base locus of $-(K_W+\Delta|_W)$.
Note that a general fibre of $g$ is not contained in $f(\sB(-(K_X+\Delta)))$.
Fix one of these fibres, say $G$, and let $W$ be the fibre of $h$ over $G$.
There exist effective $\numberset{Q}$-divisors $D_i \sim_{\numberset{Q}} -(K_X+ \Delta)$, for $i=1,2$, such that $G \not\subseteq f(\supp(D_1) \cap \supp(D_2))$.
Since $0 \leq D_i|_W \sim_{\numberset{Q}} -(K_W+ \Delta|_W)$, we conclude that the stable base locus of $-(K_W+\Delta|_W)$ does not dominate $G$.
Thus, the fibration $f|_W: W \rightarrow G$ satisfies:
\begin{itemize}
\item[$\ast$] $G$ is smooth and $\kappa(G,-K_G)=0$;
\item[$\ast$] the general fibre $F$ is normal and $(F, \Delta|_F)$ is SFR;
\item[$\ast$] the stable base locus of $-(K_W+ \Delta|_W)$ does not surject onto $G$.
\end{itemize}
We are in the right setting to apply theorem \ref{Cn,n-1-}, whence:
\[
\kappa(W, -(K_W+\Delta|_W)) \leq \kappa(F, -(K_F+\Delta|_F)).
\]
\end{proof}
\section{Partial results on $C_{n,n-1}^-$}
\sectionmark{$C_{n,n-1}^-$}

The goal of this section is the proof of $C_{n,m}^-$ in positive characteristics when the relative dimension of the fibration is one and the target has zero anticanonical Iitaka dimension.
The results follow \cite[section 3 and section 4]{anti}.

\begin{flalign}
\text{\underline{Set-up}} && \tag{\FiveStarOpen} \label{setup3}
\end{flalign}

In this section, we work in the following setting.
Let $f:X \rightarrow Z$ be a fibration between normal projective varieties over an algebraically closed field $k$ of characteristic $p>0$.
Suppose that $f$ is of relative dimension one with smooth generic fibre.
Let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$ and $D$ be any $\numberset{Q}$-Cartier divisor on $Z$, such that:
\begin{itemize}
\item[•] $K_X+ \Delta$ is $\numberset{Q}$-Cartier;
\item[•] the pair restricted to the general fibre $(F, \Delta|_F)$ is strongly F-regular;
\item[•] $L:= -(K_X + \Delta) - f^*D$ is $\numberset{Q}$-effective and its stable base locus does not surject onto $Z$.
\end{itemize}

\begin{theorem} \label{Cn,n-1-}
In the above setting \ref{setup3}, assume that $\kappa(Z, -K_Z-D)=0$.
Then, the map defined by restriction on a general fibre $F$,
\[
\alpha: \bigoplus_{m \in \numberset{N}} H^0(X, \left\lfloor mL \right\rfloor ) \rightarrow \bigoplus_{m \in \numberset{N}} H^0(F, \left\lfloor mL|_F \right\rfloor )
\]
is injective.
In particular, when $D=0$, we get the inequality:
\[
\kappa(X, -(K_X+ \Delta)) \leq \kappa(F, -(K_F+ \Delta|_F)) + \kappa(Z,-K_Z),
\]
for a general fibre $F$.
\end{theorem}

This result is an analogue of \cite[theorem 3.8]{anti}.
In order to prove it, the author uses techniques involving canonical bundle formula results as in \cite{Ambro}.
In positive characteristics, we do not have the same results in such generality, but only when the general fibre of the fibration we are considering is a curve.

\begin{proposition} \cite[proposition 3.2]{Jakub} \label{Jakub}
Let $(X, \Delta)$ be a quasi-projective log pair over an algebraically closed field of positive characteristic with $\Delta$ an effective $\numberset{Q}$-divisor on $X$ such that $K_X+\Delta$ is $\numberset{Q}$-Cartier.
Let $f: X \rightarrow Z$ be a fibration onto a normal variety.
Assume that the geometric generic fibre $X_{\bar{\eta}}$ is a smooth curve, $(X_{\bar{\eta}}, \Delta|_{X_{\bar{\eta}}})$ is log canonical and $K_X+ \Delta= f^*L_Z$ for some $\numberset{Q}$-Cartier divisor $L_Z$ on $Z$.
Then,
\[
L_Z \sim_{\numberset{Q}} K_Z + \Delta_Z,
\]
where $\Delta_Z$ is an effective $\numberset{Q}$-divisor.
\end{proposition}

\begin{proposition} \label{thm. 3.8}
In the setting \ref{setup3}, $-K_Z-D$ is $\numberset{Q}$-effective.
\end{proposition}

\begin{proof}
Pick a general fibre $F$.
Since the stable base locus of $L$ does not surject onto $Z$, $L|_{F}$ is semiample.
By \cite[proposition 3]{semiample}, there exists an effective $\numberset{Q}$-divisor $\Gamma \sim_{\numberset{Q}} L$ on $X$ such that $(F, \Delta|_{F}+ \Gamma|_F)$ is sharply F-pure.
Then, $K_X+ \Delta + \Gamma \sim_{\numberset{Q}} -f^*D$.
Let $X_{\bar{\eta}}$ be the geometric generic fibre of $f$.
By theorem \ref{families}, $(X_{\bar{\eta}}, (\Delta+ \Gamma)|_{X_{\bar{\eta}}})$ is sharply F-pure as well.
Therefore, we can apply proposition \ref{Jakub} to find an effective $\numberset{Q}$-divisor $\Delta_Z$ on $Z$, such that $-K_Z -D \sim_{\numberset{Q}} \Delta_Z$.
\end{proof}

\begin{remark}
Applying the above proposition \ref{thm. 3.8} to the case $D=0$, we conclude that, in the assumptions of setting \ref{setup3}, $-K_Z$ is $\numberset{Q}$-effective whenever $-(K_X+ \Delta)$ is.
\end{remark}

Following verbatim the proofs of \cite[proposition 4.2 and proposition 4.3]{anti}, we have the same results in the more restrictive setting \ref{setup3}.

\begin{proposition} \label{prop. 4.2}
Consider the setting \ref{setup3}.
Let $E$ be a $\numberset{Q}$-Cartier divisor on $Z$.
Moreover, assume there exists an effective $\numberset{Q}$-divisor on $X$, $\Gamma$, such that $L-f^*E \sim_{\numberset{Q}} \Gamma$.\\
Then, for $0< \varepsilon \ll 1$, $-K_Z-D-\varepsilon E$ is $\numberset{Q}$-effective.
\end{proposition}

\begin{proof}
The proof is the same as the one of \cite[proposition 4.2]{anti}.
Note that, as for the klt case, for any $0< \varepsilon \ll 1$, $(F, \Delta|_F + \varepsilon \Gamma|_{F})$ is still SFR.
\end{proof}

\begin{proof}[Proof of \ref{Cn,n-1-}.]
If the theorem did not hold, there would exist $s$, non-zero section, in the kernel of $\alpha$.
Then, up to taking powers, $s$ defines an effective $\numberset{Q}$-divisor $N \sim_{\numberset{Q}} -(K_X+\Delta)-f^*D$ containing $F$ in its support.
Since $\kappa(Z, -K_Z-D)=0$, there exists a unique effective $\numberset{Q}$-divisor $M \sim_{\numberset{Q}}-K_Z-D$.
We can suppose that $f(F)= z \in Z$ is such that:
\begin{itemize}
\item[(i)] $f$ is flat in a neighbourhood of $z$;
\item[(ii)] $z$ is a regular point of $Z$;
\item[(iii)] $z \notin \supp(M)$.
\end{itemize}
Consider the diagram:
\[
\xymatrix{
G \subseteq X' \ar@<10pt>[d]_{f'} \ar[r]^{\pi} & X \supseteq F \ar@<-10pt>[d]^f \\
E \subseteq Z' \ar[r]^p & Z \ni z
}
\]
where
\begin{itemize}
\item[•] $p: Z' \rightarrow Z$ is the blow-up at $z$;
\item[•] $\pi: X' \rightarrow X$ is the blow-up at $F:=f^{-1}(z)$. Note that, by flatness of $f$ near $z$ and normality of the fibres, $X'$ is normal and $X'= X \times_Z Z'$;
\item[•] $G:= \Exc(\pi) \cong F \times E = f'^*E$, with $E:= \Exc(p)$.
\end{itemize}
Let $D':= p^*D$ and $\Delta'$ be the strict transform of $\Delta$, then:
\begin{align*}
& -K_{Z'} = p^*(-K_Z)-aE, \qquad & a= \dim(Z) -1;\\
& -(K_{X'}+ \Delta')= \pi^*(-(K_X+ \Delta)) -bG, \qquad & b \leq \codim(F)-1=a.
\end{align*}
By assumption, $\pi^*L$ is $\numberset{Q}$-effective, its stable base locus does not surject onto $Z'$ and
\[
\pi^*L = \pi^*(-(K_X+\Delta)-f^*D)= -(K_{X'}+ \Delta') + bf'^*E-f'^*D'.
\]
Let $\beta$ be the coefficient of $G = f'^*E$ in $\pi^*N$. Since $F$ is in the support of $N$, $\beta >0$.
The $\numberset{Q}$-divisor $\pi^*N - \beta f'^*E \geq 0$ is effective, thus, by proposition \ref{prop. 4.2}, there exists an effective $\numberset{Q}$-divisor $\Gamma$ which is $\numberset{Q}$-linearly equivalent to $-K_{Z'}+bE-D'-\varepsilon \beta E$, for some $\varepsilon>0$.
But then we would have:
\[
\Gamma + (a-b+ \varepsilon \beta)E \sim_{\numberset{Q}} p^*(-K_Z-D) \sim_{\numberset{Q}} p^*M.
\]
Both sides of the above equation are effective, the LHS has $E$ in its support, while the RHS does not. However, $\kappa(Z', p^*M)=0$, contradiction.
\end{proof}
\section{Proof of $C_{n,1}^-$}
\sectionmark{$C_{n,1}^-$}

In this section, we use the paper \cite{EG} to prove $C_{n,m}^-$ in positive characteristic, when the target of the fibration $f: X \rightarrow Z$ is a curve.
In this paper, the authors assume that the relative anticanonical divisor is nef.
We weaken a bit the assumption asking for its stable base locus to not surject onto $Z$.
The proofs carry on in the same way as in \cite[section 3 and section 4]{EG}, thus we only write down the proof of theorem \ref{weak positivity con hp base locus}.
The main result of the section is, then, $C_{n,1}^-$.

\begin{theorem}[$C_{n,1}^-$] \label{Cn1-}
Let $f: X \rightarrow Z$ be a separable fibration from a normal projective variety onto a smooth curve over an algebraically closed field of characteristic $p>0$.
Let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$ such that $-(K_X + \Delta)$ is $\numberset{Q}$-Cartier.
Suppose that the general fibre $(F, \Delta|_F)$ is strongly $F$-regular and the stable base locus of $-(K_X+\Delta)$ does not dominate $Z$.
Then:
\[
\kappa(X, -(K_X+\Delta)) \leq \kappa(F, -(K_F+\Delta|_F)) + \kappa(Z, -K_Z).
\]
\end{theorem}

\begin{flalign}
\text{\underline{Set-up}} && \tag{\EightStarConvex} \label{setup1}
\end{flalign}

We write here the assumptions we make for the first result. Note that they differ from the ones used by \cite{EG} only for condition (iii): they assume nefness of $L$ instead.
Let $f:X \rightarrow Z$ be a separable fibration between normal projective varieties over an algebraically closed field of characteristic $p>0$.
Consider $\numberset{Q}$-divisors $\Delta$ and $D$ on $X$ and $Z$ respectively such that $K_X + \Delta$ and $D$ are $\numberset{Q}$-Cartier.
Let $\Delta= \Delta^+-\Delta^-$ be the decomposition by effective $\numberset{Q}$-divisors with no common components and let
\[
L:= -(K_X + \Delta) -f^*D.
\]
Suppose that:
\begin{itemize}
\item[(i)] the general fibre $(F, \Delta^+|_F)$ is sharply F-pure;
\item[(ii)] $\supp(\Delta^-)$ does not dominate $Z$;
\item[(iii)] $\sB(L)$ does not dominate $Z$;
\item[(iv)] there exist positive integers $a, b$ not divisible by $p$, such that $a\Delta^+$ and $bL$ are integral.
\end{itemize}

\begin{lemma} \label{sharply F-pure on fibres}
In the above setting \ref{setup1}, let $D$ be an effective, $\numberset{Q}$-Cartier divisor on $X$ such that its restriction to the general fibre $F$ is ample.
Then, there exists a $\numberset{Q}$-divisor $\Gamma \geq 0$ on $X$ such that $\Gamma \sim_{\numberset{Q}} D$ and $(F, \Delta^+|_F+ \Gamma|_F)$ is still sharply F-pure.
\end{lemma}

\begin{proof}
Pick a general fibre $F$ and choose $m \gg 0$ so that $mD$ is very ample on $F$.
Write $|mD|= |M|+B$, where $|M|$ is the movable part of the linear system and $B$ is its fixed divisor.
Consider the morphism $\varphi$ to $\Pn{N}{k}$ induced by $|M|$.
Then, by \cite[corollary 6.10]{Bertini}, the pair $(F, \Delta^+|_F + \varphi|_F^{-1}(H))$ is sharply F-pure for a general hyperplane $H$ of $\Pn{N}{k}$.
Let
\[
\Gamma:= \frac{1}{m}(\varphi_*^{-1}(H)+B) \sim_{\numberset{Q}} D.
\]
Since $\Delta^+|_F + m\Gamma|_F \geq \Delta^+|_F + \Gamma|_F$,
$(F, \Delta^+|_F + \Gamma|_F)$ is sharply F-pure as well.
\end{proof}

We state the next results in the assumptions in which we need to use them later.
In the original papers they are proven in greater generality.

\begin{theorem} \cite[theorem 5.1 and example 3.11]{3folds4} \label{weak positivity Eji17}
Let $f: X \rightarrow Z$ be a separable surjective morphism between normal projective varieties over an algebraically closed field of characteristic $p>0$.
Let $\Delta$ be an effective $\numberset{Q}$-Weil divisor on $X$ such that there is a positive integer $a$ not divisible by $p$ such that $a\Delta$ is integral.
Let $\bar{\eta}$ be the geometric generic point of $Z$.
Suppose that:
\begin{itemize}
\item[(i)] the geometric generic fibre $(X_{\bar{\eta}}, \Delta_{\bar{\eta}})$ is sharply F-pure;
\item[(ii)] the divisor $K_{X_{\bar{\eta}}} + \Delta_{\bar{\eta}}$ is ample.
\end{itemize}
Then,
\[
(f_*\Ox{X}(am(K_X+\Delta))) \otimes \omega_Y^{\otimes -am}
\]
is weakly positive for every $m\gg 0$.
\end{theorem}

\begin{theorem} \cite[corollary 3.31]{families} \label{families}
In the setting \ref{setup1}, let $\Delta'$ be an effective $\numberset{Q}$-Weil divisor on $X$ such that there is a positive integer $a$ not divisible by $p$, with $a\Delta'$ integral.
Suppose that $K_X + \Delta'$ is $\numberset{Q}$-Cartier and $(X_s, \Delta'|_{X_s})$ is sharply F-pure for some perfect point $s \in Z$.
Then, there exists a non-empty open subset $U \subset Y$ such that $(X_{s^e}, \Delta'|_{X_{s^e}})$ is sharply F-pure for all $s \in U$ and all $e>0$.
In particular, if we denote by $X_{\bar{\eta}}$ the geometric generic fibre, $(X_{\bar{\eta}}, \Delta'|_{X_{\bar{\eta}}})$ is sharply F-pure.
\end{theorem}

\begin{theorem} \label{weak positivity con hp base locus}
In the setting above \ref{setup1}, fix a positive integer $l$ such that $l(K_X+ \Delta)$ and $l(K_Z+D)$ are Cartier and $l\Delta^-$ is integral.
Then, there exists an effective $f$-exceptional divisor $B$ on $X$ such that
\[
\Ox{X}(l(-f^*(K_Z+D)+\Delta^-+B))
\]
is weakly positive.\\
Furthermore, $B$ can be chosen to be $0$ if $Z$ has only canonical singularities.
\end{theorem}

\begin{proof}
We follow almost verbatim the proof given in \cite[theorem 3.1]{EG}, highlighting the small differences.
First, we prove the statement when $f$ is equi-dimensional.
Set $\mathcal{F}:= \Ox{X}(l(-f^*(K_Z+D)+\Delta^-))$ and let $A$ be an ample Cartier divisor on $X$.
We need to show weak positivity of $\mathcal{F}$, in particular it is enough to see that for any $\alpha \in \numberset{Z}_{>0} \setminus p\numberset{Z}$, there is some $\beta \in \numberset{N}_{>0}$ such that $\mathcal{F}^{[\alpha \beta ]}(\beta lA)$ is weakly positive.\\
Since $\sB(L)$ does not dominate $Z$, the restriction of $L$ to the general fibre $F$ is semiample. Therefore, $(L + \alpha^{-1}A)|_F$ is ample.
By lemma \ref{sharply F-pure on fibres}, there exists an effective $\numberset{Q}$-divisor $\Gamma \sim_{\numberset{Q}} (L + \alpha^{-1}A)$, such that $(F, \Delta^+|_F + \Gamma|_F)$ is still sharply F-pure.
By theorem \ref{families}, this implies that $(X_{\bar{\eta}}, (\Delta^+ + \Gamma)|_{X_{\bar{\eta}}})$ is sharply F-pure.
Note that $(K_X + \Delta^+ + \Gamma)|_{X_{\bar{\eta}}} \sim_{\numberset{Q}} \alpha^{-1}A|_{X_{\bar{\eta}}}$ is ample.
Thus, theorem \ref{weak positivity Eji17} proves weak positivity of the sheaf
\[
(f_*\Ox{X}(lm(K_X+\Delta^+ + \Gamma)))\otimes \omega_Y^{\otimes -lm}.
\]
Then, as shown in \cite[theorem 3.1]{EG}, for $\beta \gg 0$, the generically surjective morphism
\[
f^*((f_*\Ox{X}(\alpha \beta l(K_X+\Delta^+ + \Gamma)))\otimes \omega_Y^{\otimes -\alpha \beta l}) \rightarrow \mathcal{F}^{[\alpha \beta]} \otimes \Ox{X}(\beta l A)
\]
shows that the latter sheaf is weakly positive as well.

In the general case, by the flattening lemma \cite[section 3.3]{flattening}, we have a commutative diagram:
\[
\xymatrix{
X' \ar[r]^{\rho} \ar[d]_{f'} & X \ar[d]^f \\
Z' \ar[r]^{\sigma} & Z
}
\]
with $\sigma$ and $\rho$ projective birational, $f'$ equi-dimensional.
Let $E \geq 0$ be a $\sigma$-exceptional divisor such that $-K_{Z'} \leq -\sigma^*K_Z + E$ and let $\Delta'$ be a $\numberset{Q}$-Weil divisor on $X'$ such that $K_{X'}+ \Delta'= \rho^*(K_X+ \Delta)$.
Then, the stable base locus of $-(K_{X'}+ \Delta')-f'^*\sigma^*D$ does not dominate $Z'$.
From the previous step, we can conclude weak positivity of the sheaf
\[
\Ox{X'}(l(- f'^*(K_{Z'}+\sigma^*D)+\Delta'^-)),
\]
where $\Delta'^- \geq 0$ is defined as the negative component in the decomposition by effective $\numberset{Q}$-divisors of $\Delta' = \Delta'^+ - \Delta'^-$.
As $-f'^*(K_{Z'}+ \sigma^*D) \leq -\rho f^*(K_Z+D)+f'^*E$, the sheaf
\[
\rho_*(\Ox{X'}(l(-\rho^* f^*(K_Z+D)+\Delta'^-+f'^*E)))
\]
is also weakly positive. Thus, if we set $B:= \rho_*f'^*E$ we get the claim.
Remark that, if $Z$ has at worst canonical singularities, than we can choose $E$ and consequently $B$ to be $0$.
\end{proof}

\begin{flalign}
\text{\underline{Set-up}} && \tag{\EightStarTaper} \label{setup2}
\end{flalign}
Let $f:X \rightarrow Z$ be a separable fibration between normal projective varieties over an algebraically closed field of characteristic $p>0$, and let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$.
Let $L:=-(K_X+\Delta)+f^*K_Z$.
Suppose that:
\begin{itemize}
\item[(i)] $Z$ has at worst canonical singularities;
\item[(ii)] $K_X + \Delta$ is $\numberset{Q}$-Cartier;
\item[(iii)] $\sB(L)$ does not dominate $Z$;
\item[(iv)] the general fibre $(F, \Delta|_F)$ is strongly $F$-regular.
\end{itemize}

\begin{remark} \label{index divisible by p}
We can assume that there exists a positive integer $a$, not divisible by $p$, such that $a\Delta$ and $aL$ are integral divisors.
Indeed, we can perturb $\Delta$ with a sufficiently small multiple of an effective divisor $\numberset{Q}$-equivalent to $L$, so that condition $(iv)$ still holds.
\end{remark}

All results in \cite[section 4]{EG} hold with exactly the same proofs in this setting \ref{setup2} using theorem \ref{weak positivity con hp base locus} instead of \cite[theorem 3.1]{EG}.
In particular, we conclude the following.

\begin{corollary} \cite[corollary 4.7]{EG} \label{restriction EG}
In the setting above \ref{setup2}, the restriction map
\[
\alpha: \bigoplus_{m \in \numberset{N}} H^0(X, \left\lfloor mL \right\rfloor ) \rightarrow \bigoplus_{m \in \numberset{N}} H^0(F, \left\lfloor mL|_F \right\rfloor )
\]
is injective.
\end{corollary}

With this last result it is straightforward to prove $C_{n,1}^-$.

\begin{proof}[Proof of \ref{Cn1-}.]
First of all, we can assume $\kappa(X, -(K_X+\Delta)) \geq 0$.
Moreover, as in remark \ref{index divisible by p}, by perturbing $\Delta$ with a sufficiently small multiple of $-(K_X+ \Delta)$, we can suppose that there exists a positive integer $a$, not divisible by $p$, such that $a\Delta$ and $-a(K_X+ \Delta)$ are integral divisors.
We distinguish three cases according to the genus of $Z$.
\begin{itemize}
\item[•] Let $Z$ be a curve of genus $0$.\\
The result follows immediately from easy additivity theorem \ref{easy additivity}.
\item[•] Let $Z$ be a curve of genus $1$.\\
Then, $K_Z \sim 0$, so corollary \ref{restriction EG} gives the desired inequality.
\item[•] Let $Z$ be a curve of genus $\geq 2$.\\
Since $K_Z$ is ample, $\sB(-(K_X+ \Delta)+f^*K_Z) \subseteq \sB(-(K_X+ \Delta))$ does not dominate $Z$.
Thus, we can apply corollary \ref{restriction EG} and easy additivity 2 theorem \ref{other easy additivity} to get:
\begin{align*}
\kappa(F, -(K_F+\Delta|_F)) + \dim(Z) \leq & \kappa(X, -(K_X+\Delta)+ f^*K_Z),\\
& \kappa(X, -(K_X+\Delta)+ f^*K_Z) \leq \kappa(F, -(K_F+\Delta|_F)).
\end{align*}
Contradiction. Such case never happens.
\end{itemize}
\end{proof}

\section{Counterexamples}

Counterexamples for $C_{n,m}^-$ removing the hypothesis on the stable base locus are easy to obtain just looking at ruled surfaces (see \cite[example 1.7]{anti}). Note that they work in any characteristic.

The next example shows that the assumption on the normality of the fibres is essential.
It relies on the construction of Tango--Raynaud surfaces.
These surfaces are a good source of counterexamples in positive characteristics.
Analysing them, in the paper \cite{Paolo}, the authors found counterexamples to $C_{n,m}$ in characteristic $p$, for any $p>0$. The same construction gives counterexamples to $C_{n,m}^-$ in characteristics $2$ and $3$.

\begin{definition}
Let $C$ be a smooth projective curve of genus $g \geq 2$ over an algebraically closed field of characteristic $p>0$. Define the \textbf{Tango invariant}:
\[
n(C):= \max \left\{ \deg\left( \left\lfloor \frac{(df)}{p} \right\rfloor \right) \, | \, f \in K(C) \right\},
\]
where $(df)$ denotes the divisor of zeroes and poles of the differential $df$.
Note that $p n(C) \leq 2g -2$. We say that $C$ is a \textbf{Tango curve} if $n(C)>0$ and that it is a \textbf{Tango--Raynaud curve} if, moreover, $p n(C) = 2g -2$.
\end{definition}

\begin{example} \label{example}
Let $e \in \numberset{N}$ and let $C$ be the plane curve defined by the equation $Y^{pe} - YX^{pe-1}=Z^{pe-1}X$ in $\Pn2{\bar{\mathbb{F}}_p}$ with coordinates $[X:Y:Z]$. It is smooth and, by adjunction, if $g$ is its genus, $2g-2=pe(pe-3)$.
Consider the differential $d(\frac{Z}{X})$ and denote $\infty$ the point $[0:0:1] \in C$.
Then, $(d(\frac{Z}{X}))= pe(pe-3)(\infty)= (2g-2)(\infty)$, showing that $C$ is a Tango--Raynaud curve.
\end{example}

Consider the Frobenius map $F: C \rightarrow C$. Denote by $\mathcal{B}$ the cokernel of the induced map, $\Ox{C} \rightarrow F_*\Ox{C}$. Thus, for any Cartier divisor $D$, we have the exact sequence:
\[
0 \rightarrow \Ox{C}(-D) \rightarrow F_*(\Ox{C}(-pD)) \rightarrow \mathcal{B}(-D) \rightarrow 0.\tag{\SixFlowerRemovedOpenPetal} \label{ses}
\]

\begin{lemma} \cite[lemma 2.5]{Xie}
With the same notations as above,
\[
H^0(C, \mathcal{B}(-D))= \{ df | \, f \in K(C), \, (df) \geq pD \}.
\]
\end{lemma}

Moreover, if $D$ is effective,
$H^0(C, \mathcal{B}(-D))$ is the kernel of $F^*: H^1(C,\Ox{C}(-D)) \rightarrow  H^1(C,\Ox{C}(-pD))$.
Now, if $C$ is a Tango curve, by definition, we can find an effective divisor $D$ on it and a non-zero element $df$ in $H^0(C, \mathcal{B}(-D))$. This determines a non-zero element of $H^1(C,\Ox{C}(-D))$ which is mapped to zero by the Frobenius morphism.
Hence $df$ determines a (non-split) short exact sequence
\[
0 \rightarrow \Ox{C}(-D) \rightarrow \mathcal{E} \rightarrow \Ox{C} \rightarrow 0,
\]
which becomes a split exact sequence after applying the Frobenius morphism:
\[
0 \rightarrow \Ox{C}(-pD) \rightarrow F^*\mathcal{E} \rightarrow \Ox{C} \rightarrow 0.
\]
Thus, we get also:
\[
0 \rightarrow \Ox{C} \rightarrow F^*\mathcal{E} \rightarrow \Ox{C}(-pD) \rightarrow 0. \tag{\Snowflake} \label{split ses}
\]

Let $C$ be a Tango--Raynaud curve, let $f$ be a rational map on $C$ such that $(df)=K_C=pD$, with $D$ effective divisor. Consider the rank $2$ vector bundle $\mathcal{E}$ on $C$ defined by the extension determined by $df$ as above.
Let $g: P:= \mathbb{P}(\mathcal{E}) \rightarrow C$ and $g_1: P_1:= \mathbb{P}(F^*\mathcal{E}) \rightarrow C$.
Thus, we have a commutative diagram:
\[
\xymatrix{
P \ar[d]_{F_{P/C}} \ar[dr]^{F_P} & \\
P_1 \ar[r]^W \ar[d]_{g_1} & P \ar[d]^{g}\\
C \ar[r]^{F_C}& C
}
\]
where the lower square is a fibre product diagram and $F_{P/C}$ is the relative Frobenius.\\
Let $T$ be a divisor on $P$ such that $\Ox{P}(T) \simeq \Ox{P}(1)$. The short exact sequence \ref{ses} defines a section of $g$, $F \sim T + g^*D$.
On the other hand, the short exact sequence \ref{split ses}, defines a section of $g_1$, $G_1 \sim W^*F -pg_1^*D$. Let $G:= F_{P/C}^*G_1$, then $G \sim pF-pg^*D \sim pT$.
Computing the arithmetic genus of $G$ and $F$ using adjunction formula, we see that the curves $G$ and $F$ are smooth of genus $g$. Moreover, they are disjoint.

If there exists $l >0$ such that $l$ divides $p+1$ and $D= lD'$ for an effective divisor $D'$, then:
\[
G+F \sim (p+1)T +g^*D = l(rT + g^*D') =lM
\]
where $r = \frac{p+1}{l}$ and $M:= rT+g^*D'$. Such a situation happens for example if we take an appropriate $e$ in the curve of example \ref{example}. Since the support of the divisor $G+F$ is smooth, the $l$-cyclic cover defined by the above equivalence yields a smooth surface $S$.
Call $\pi: S \rightarrow P$ the cover and $f= g \circ \pi: S \rightarrow C$.\\
The last step in this construction consists in taking $m$-times the fibre product of $S$ over $C$: $X^{(m)}:= S \times_C S \cdots \times_C S$. Let $p_i: X^{(m)} \rightarrow S$ be the projection to the $i^{\text{th}}$ factor and $f^{(m)}: X^{(m)} \rightarrow C$ the composition of $f$ with any of these projections.

Studying local equations, it is easy to see that the varieties $X^{(m)}$ are normal and their singular locus is the union of $\mathrm{supp}(T_i) \cap \mathrm{supp}(T_j)$ for $i \neq j$; where $T_i := (\pi \circ p_i)^*T$.
Moreover, the same computations show that the fibres of $X^{(m)} \rightarrow C$ are not normal.
Indeed, let $s$ be a local parameter on the fibres of $g$ such that locally $G=\{s^p=0\}$ and $F= \{s=\infty\}$. First we look at what happens away from $F$. Let $(x_1, ..., x_r)=\underline{x}$ be local affine coordinates on $C$, then, as showed in \cite[section 2]{Mukai} there is $f(\underline{x})$ such that $S$ affine locally has equation $t^l=s^p-f(\underline{x})$ inside $\An1{} \times \An1{} \times C$. Then, affine locally, we can see $X^{(m)} \subseteq \An{m}{} \times \An{m}{} \times C$ with coordinates $t_1,....,t_m, s_1,...,s_m, \underline{x}$ and equations $t_i^l=s_i^p-f(\underline{x})$ for $i = 1,...,m$. Applying Jacobi criterion we get the result.\\
On the other hand, if $\sigma= 1/s$ is a local parameter defining $F$ on $P$, an affine local equation for $S$ away from $G$ is $\tau^l=\sigma$. We then find that $X^{(m)}$ is smooth in this open subset.

\begin{theorem}
If we take $\{p,l\}=\{2,3\}$, then the fibrations:
\[
\eta: X^{(\mu)} \rightarrow X^{(m)}
\]
give counterexamples to $C_{\mu+1,m+1}^-$ for $\mu \geq 6$ and $0 \leq m <6$ (with the convention that $X^{(0)}=C$). Moreover, the stable base locus of the anticanonical divisor of $X^{(\mu)}$ is empty, for $\mu \geq 6$.
\end{theorem}

\begin{proof}
The relative anticanonical divisors of $g$ and $f$, for our choices of $p$ and $l$ are:
\begin{align*}
& K_{P/C} = -2T - pg^*D;\\
&K_{S/C} = \pi^*(K_{P/C} + (l-1)M) = -f^*D'.
\end{align*}
Then, the anticanonical sheaf of $X^{(m)}$ is:
\[
\omega^{-1}_{X^{(m)}} = (\prod_{i=1}^m p_i^*\omega^{-1}_{S/C}) \otimes \omega_C^{-1}.
\]
Therefore, for any positive integer $n$:
\[
-nK_{X^{(m)}} = f^{(m)*}((nm-6n)D').
\]
This sheaf is ample on $C$ for $m>6$, trivial for $m=6$ and antiample on $C$ for $m<6$, so that
\[
\kappa(X^{(m)}, -K_{X^{(m)}})=
\begin{cases}
1 \quad \text{for} \; m>6 \\
0 \quad \text{for} \; m=6 \\
- \infty \quad \text{for} \; m<6
\end{cases}.
\]
Note that the base locus is always empty for $m \geq 6$ as the divisor is vertical.
\end{proof}
\section*{Introduction}

The aim of the minimal model program is to classify varieties $X$ up to birational equivalence. One of the main invariants used in this classification is the Kodaira dimension, $\kappa(X, K_X)$.
The Iitaka conjecture addresses the problem of relating the Kodaira dimensions in a fibration.

\begin{conjecture}[Iitaka, $C_{n,m}$]
Let $f: X \rightarrow Z$ be a separable fibration between normal projective varieties, then
\[
\kappa(X, K_X) \geq \kappa(F, K_F) + \kappa(Z, K_Z),
\]
where $F$ is a general fibre of $f$.
\end{conjecture}

In characteristic $0$, this inequality has been proven in many important situations.
It is then natural to ask whether the same holds true in positive characteristics.
In the paper \cite{CZ} the conjecture is proven when the general fibre of $f$ is a curve.
The series of papers \cite{3folds}, \cite{3folds2}, \cite{3folds3}, \cite{3folds4} shows that it does hold when $\dim(X)=3$ under mild assumptions on the base field or on the geometric generic fibre.
However, it is known that in positive characteristics the Iitaka conjecture does not hold in general. The paper \cite{Paolo} gives some counterexamples using the construction of Tango--Raynaud surfaces.

Recently, a similar statement for the anticanonical divisor has been proven in characteristic $0$ by C.\ Chang in the paper \cite{anti}.
There, it is proven that
\[
\kappa(X, -K_X) \leq \kappa(F, -K_F) + \kappa(Z, -K_Z),
\]
when $X$ and $Z$ are $\numberset{Q}$-Gorenstein normal projective varieties, $X$ has at worst klt singularities, the anticanonical divisor $-K_X$ is effective and its stable base locus does not dominate $Z$ (see \cite[theorem 1.1]{anti}).
The result is generalized also for pairs $(X, \Delta)$ with similar assumptions (see \cite[theorem 4.1]{anti}).
We call $C_{n,m}^-$ this version of the Iitaka conjecture for the anticanonical divisors.

We may wonder then, does the same inequality also hold in positive characteristics?
In the paper \cite{EG}, S.\ Ejiri and Y.\ Gongyo studied positivity properties of the relative anticanonical divisor in a fibration $f:X \rightarrow Z$, also in positive characteristics.
The paper \cite{anti}, that proves $C_{n,m}^-$ in characteristic $0$, combines the same tools with techniques involving canonical bundle formula results as studied in \cite{Ambro}.
However, in positive characteristics, it is not possible to follow exactly the same steps to prove the inequality in such generality.

Nonetheless, if we work in low dimensions, the same proofs go through with little modifications.
In particular, the results in \cite{EG} permit to prove $C_{n,1}^-$.

\begin{theorem}[$C_{n,1}^-$, see theorem \ref{Cn1-}]
Let $f: X \rightarrow Z$ be a separable fibration from a normal projective variety onto a smooth curve over an algebraically closed field of characteristic $p>0$.
Let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$ such that $K_X+ \Delta$ is $\numberset{Q}$-Cartier.
Suppose that the general fibre $(F, \Delta|_F)$ is strongly $F$-regular and the stable base locus of $-(K_X+\Delta)$ does not dominate $Z$.
Then:
\[
\kappa(X, -(K_X+\Delta)) \leq \kappa(F, -(K_F+\Delta|_F)) + \kappa(Z, -K_Z).
\]
\end{theorem}

On the other hand, combining the work in \cite{anti} with the results in \cite{Jakub} instead of those in \cite{Ambro}, allows us to prove $C_{n,n-1}^-$ when the fibres of $f$ are smooth curves and $\kappa(Z, -K_Z)=0$.

At this point, we need to restrict our attention to threefolds.
On one hand, it is because in this way we always have that either the base of the fibration or the general fibre is a curve, so that we can use the previous results.
On the other hand, when $\kappa(Z, -K_Z) \neq 0$, C.\ Chang, in \cite{anti}, exploits the Iitaka fibration induced by $-K_Z$ to reduce to the case when the base has trivial anticanonical Iitaka dimension.
However, in positive characteristics, we do not have the same control over the Iitaka fibration and we may lose the properties we need.
When $X$ is a threefold, then $Z$ is at most a surface, therefore the Iitaka fibration induced by the anticanonical divisor is nice enough to be able to apply the previous results.
In this way, $C_{3,m}^-$ follows.

\begin{theorem}[$C_{3,m}^-$, see theorem \ref{C3m-}]
Let $f:X \rightarrow Z$ be a fibration from a normal projective threefold $X$ to a normal projective variety $Z$ with at worst canonical singularities, over an algebraically closed field of characteristic $p \geq 5$.
Let $\Delta$ be an effective $\numberset{Q}$-divisor on $X$ such that $K_X+\Delta$ is $\numberset{Q}$-Cartier.
Assume, moreover, that the general fibre $(F, \Delta|_F)$ is strongly F-regular and the stable base locus of $-(K_X+ \Delta)$ does not dominate $Z$.
Then,
\[
\kappa(X, -(K_X+ \Delta)) \leq \kappa(F, -(K_F+ \Delta|_F)) + \kappa(Z,-K_Z).
\]
\end{theorem}

In the last section, we study some counterexamples to $C_{n,m}^-$.
The assumptions on the stable base locus and on the normality of the fibres cannot be removed.
In fact, it is easy to construct counterexamples to $C_{n,m}^-$ already in dimension $2$ when the stable base locus of $-K_X$ does surject onto $Z$.
They are given by some ruled surfaces and they work also in characteristic $0$.

Instead, the construction used in \cite{Paolo} to prove that $C_{n,m}$ does not hold in positive characteristics, gives counterexamples also to $C_{n,m}^-$ in low characteristics if we remove the assumption on the singularities of the fibres.
It is based on the fact that Kodaira vanishing does not hold in positive characteristics.
In particular, on a Tango--Raynaud curve $C$, there exists a non-zero effective divisor $D$ such that $H^1(C, \Ox{C}(-D)) \neq 0$.
A wise choice of the divisor $D$ and a vector bundle of rank $2$ corresponding to a non-split extension in $H^1(C, \Ox{C}(-D))$, allow us to construct Tango--Raynaud surfaces.
We can build our counterexamples using them.

\subsection*{Acknowledgements}
I would like to thank my PhD advisor Paolo Cascini for suggesting the problem, for his guidance throughout, for his indispensable support and the useful feedback.
I would like to thank Christopher D.\ Hacon for some helpful suggestions.
I would like to thank my friends at UCL and Imperial for helping me.
This project started during my first year at the LSGNT, to which I would like to express my gratitude for providing a great environment for discussions.
This work was supported by the Engineering and Physical Sciences Research Council [EP/S021590/1].
The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London.
\section{Preliminaries}
\addtocontents{toc}{\protect\setcounter{tocdepth}{1}}

\underline{Notations}\\
By variety we mean a noetherian integral separated scheme of finite type over an algebraically closed field $k$.\\
Let $\mathcal{F}$ be a reflexive sheaf of rank $1$ on a normal variety $X$, with $\mathcal{F}^{[a]}$ we denote the $a^{\text{th}}$ reflexive power of $\mathcal{F}$, for $a \in \numberset{N}$.\\
A fibration $f: X \rightarrow Z$ is a projective surjective morphism of normal varieties such that $f_*\Ox{X}= \Ox{Z}$.\\
The canonical divisor of a variety $X$ will be denoted by $K_X$.\\
To say that two divisors $D_1$ and $D_2$ are linearly equivalent, we write $D_1 \sim D_2$.\\
Instead, if $D_1$ and $D_2$ are $\numberset{Q}$-divisors, $D_1 \sim_{\numberset{Q}} D_2$ means that there is a non-zero integer $m$ such that $mD_1 \sim mD_2$.\\
To denote that two divisors $D_1$ and $D_2$ are numerically equivalent, we write $D_1 \equiv D_2$.\\
By $\left\lceil D \right\rceil$ (resp.\ $\left\lfloor D \right\rfloor$) we mean the divisor obtained by taking the round-up (resp.\ round-down) of every coefficient of the components of $D$.\\
Given a $\numberset{Q}$-Cartier divisor $D$ on a normal variety $X$, we denote by $\kappa(X, D)$ the Iitaka dimension defined by $D$.\\
Finally, the stable base locus of a $\numberset{Q}$-divisor $D$ is denoted by $\sB(D)$.

\subsection{Singularities}

First, we recall the definitions of the main classes of singularities considered in birational geometry.

\begin{definition}
Let $(X, \Delta)$ be a pair such that $X$ is a normal variety and $K_X + \Delta$ is $\numberset{Q}$-Cartier. Then, given a birational morphism from a normal variety: $f: Y \rightarrow X$, we can write:
\[
K_Y + (f^{-1})_*\Delta \sim_{\numberset{Q}} f^*(K_X+\Delta) + \sum_{i \in I} a(E_i, X, \Delta) E_i,
\]
where
the $E_i$'s are all the prime exceptional divisors of $f$.
The quantity  $a(E, X, \Delta)$ is called the \textbf{discrepancy} of $E$ with respect to $(X, \Delta)$.
We say $(X, \Delta)$ is:
\begin{itemize}
\item[•] \textbf{terminal} if $a(E, X, \Delta)>0$ for all possible exceptional divisors $E$ over $X$;
\item[•] \textbf{canonical} if $a(E, X, \Delta)\geq 0$ for all possible exceptional divisors $E$ over $X$;
\item[•] \textbf{Kawamata log terminal} or \textbf{klt} if $a(E, X, \Delta)>-1$ for all possible exceptional divisors $E$ over $X$ and $\lfloor \Delta \rfloor \leq 0$;
\item[•] \textbf{log canonical} or \textbf{lc} if $a(E, X, \Delta)\geq -1$ for all possible exceptional divisors $E$ over $X$.
\end{itemize}
\end{definition}

One of the peculiarities of fields of positive characteristics is the presence of the Frobenius morphism which gives rise to inseparable morphisms.
When working over these fields, it is more natural to define other types of singularities, rather than the ``classical'' ones we just mentioned. Anyway, they turn out to be strictly related to the latter.
These new classes of singularities can be identified according to the behaviour of the Frobenius morphism around them.

\begin{definition}
Let $X$ be a scheme of finite type over an algebraically closed field $k$ of characteristic $p>0$.
Define the \textbf{absolute Frobenius morphism} $F:X \rightarrow X$ to be the identity on the topological space of the scheme and the $p^{\text{th}}$-power on the structure sheaf. We will consider also its $e^{\text{th}}$-powers, $F^e$ defined likewise by taking the identity on the topological space and the $(p^{e})^{\text{th}}$-power on the structure sheaf.
\end{definition}

\begin{definition}
Let $X$ be a normal variety and $\Delta$ an effective $\numberset{Q}$-divisor on it.\\
The log pair $(X, \Delta)$ is called \textbf{globally $F$-pure} if there is an integer $e>0$ such that the natural map induced by the $e$\textsuperscript{th} power of the Frobenius morphism
\[
\Ox{X} \rightarrow F^{e}_*\Ox{X} \rightarrow F^{e}_*\Ox{X}(\left\lceil (p^e-1)\Delta \right\rceil)
\]
splits.\\
We say, moreover, that it is \textbf{globally $F$-regular} if, for every effective Weil divisor $D$, there is an integer $e>0$ such that the map
\[
\Ox{X} \rightarrow F^{e}_*\Ox{X} \rightarrow F^{e}_*\Ox{X}(\left\lceil (p^e-1)\Delta \right\rceil + D)
\]
splits.\\
We call $(X, \Delta)$ \textbf{sharply F-pure} (resp.\ \textbf{strongly $F$-regular} or \textbf{SFR} for short) if it is covered by a finite number of open subsets $U_{i}$ such that the pairs $(U_i, \Delta|_{U_i})$ are globally $F$-pure (resp.\ globally $F$-regular) for all $i$.
\end{definition}

\begin{remark} \label{klt and SFR}
It is possible to prove that if $(X, \Delta)$ is SFR (resp.\ sharply F-pure), then it is klt (resp.\ log canonical) (see \cite{SFRklt}).
\end{remark}

\subsection{Easy additivity theorems}

Let $f:X \rightarrow Z$ be a fibration between normal projective varieties. As we saw in the introduction, the Iitaka conjecture states a relation between the Kodaira dimensions of $X$, $Z$ and the general fibre $F$.
Actually, some inequalities dealing with a similar relation have been known for a long time in any characteristic and they hold more in general for the Iitaka dimension with respect to some line bundles. They are the so-called ``easy additivity'' theorems.

\begin{theorem}[Easy additivity] \cite[theorem 6.12]{Ueno} or \cite[lemma 2.3.31]{Cnm} \label{easy additivity}
Let $f:X \rightarrow Z$ be a fibration between normal projective varieties over an algebraically closed field. Let $D$ be a $\numberset{Q}$-Cartier divisor on $X$, then:
\[
\kappa(X, D) \leq \kappa(F, D|_F) + \mathrm{dim}(Z),
\]
where $F$ is a general fibre of $f$.
\end{theorem}

\begin{theorem}[Easy additivity 2] \cite[lemma 2.20]{3folds} \label{other easy additivity}
Let $f:X \rightarrow Z$ be a fibration between normal projective varieties over an algebraically closed field. Let $D$ be an effective $\numberset{Q}$-Cartier divisor on $X$ and $H$ a big $\numberset{Q}$-Cartier divisor on $Z$. Then,
\[
\kappa(X, D+f^*H) \geq \kappa(F, D|_F)+ \dim(Z),
\]
where $F$ is a general fibre of $f$.
\end{theorem}

\subsection{Weak positivity}

The main technical property studied in the paper \cite{EG} is weak positivity of sheaves. We recall here what we need to use in the following.

\begin{definition}
Let $X$ be a normal quasi-projective variety and $\mathcal{G}$ a coherent sheaf on it.
We say that $\mathcal{G}$ is \textbf{generically globally generated} if the map
\[
H^0(X, \mathcal{G}) \otimes \Ox{X} \rightarrow \mathcal{G}
\]
is surjective over the generic point of $X$.\\
The sheaf $\mathcal{G}$ is called \textbf{weakly positive} if, given any ample divisor $A$ on $X$ and any natural number $n$, there exists $m>0$ such that $(\mathrm{Sym}^{mn}(\mathcal{G}))^{**} \otimes \Ox{X}(mA)$ is generically globally generated, where the double star indicates the double dual.
\end{definition}

\begin{lemma} \label{weakly positive and effectiveness}
In the setting of the definition above, if $\mathcal{G} = \Ox{X}(D)$ is an invertible sheaf, then it is generically globally generated if and only if $D$ is linearly equivalent to an effective divisor. Moreover, it is weakly positive if and only if $D$ is pseudoeffective.
\end{lemma}

\begin{proof}
The first claim follows directly from the definition. Let us then prove the second.
The condition of being weakly positive translates to the fact that, for any $A$ ample and any $n \in \numberset{N}_{>0}$, $D+\frac{1}{n}A$ is $\numberset{Q}$-effective. But then, $D = \lim_{n \to \infty} (D + \frac{1}{n}A)$ is a limit of $\numberset{Q}$-effective divisors, thus it is pseudoeffective.
On the other hand, if $D$ is pseudoeffective, then it is in the closure of the $\numberset{Q}$-effective cone. Consider the line defined by $D+tA$. For $t \in \numberset{Q}_{>0}$, each of these divisors is $\numberset{Q}$-effective, thus $D$ is weakly positive.
\end{proof}

redpajama_set_name: RedPajamaArXiv


The Knowledge Base in RFP360 serves as a library for writers to search and use previous responses to help cut down on rewriting existing content from scratch each and every time in a proposal.
Automatically Add Knowledge. New, approved responses in a proposal are automatically saved.
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text:
Q: Select de Estrutura de Produtos Bom dia!
existe alguma forma de criar uma query que traga o "produto" e todos os "Componentes e SubComponentes" da estrutura deste produto?
Deixe-me tentar explicar melhor
Estrutura
Imagem

Link da Imagem: https://i.stack.imgur.com/tGNZ4.jpg
Formato texto
- Bicicleta
  |
  + - Guidão
  |
  + - Quadro
  |   |
  |   + - Garfo
  |
  + - Banco
  |   |
  |   + - Selim
  |
  + - Roda
      |
      + - Aro
          |
          + - Raio
          |
          + - Pneu
              |
              + - Camara

Tenho a estrutura do equipamento "bicicleta" inserida no banco de dados e preciso obter quem é o "produto" e todos que estão abaixo (Componentes[eCOMP] e SubComponentes[eCOMP]) ligando todos ao produto principal
Exemplo
+--------+----------+--------+----------+
|eCOD    |eDESC2    |eCOMP   | eDESC2   |
+--------+----------+--------+----------+
|01.0001 |Bicicleta |01.0002 | Guidão   |
|01.0001 |Bicicleta |01.0003 | Quadro   |
|01.0001 |Bicicleta |01.0004 | Garfo    |
|01.0001 |Bicicleta |01.0005 | Banco    |
|01.0001 |Bicicleta |01.0006 | Selim    |
|01.0001 |Bicicleta |01.0007 | Roda     |
|01.0001 |Bicicleta |01.0008 | Aro      |
|01.0001 |Bicicleta |01.0009 | Raio     |
|01.0001 |Bicicleta |01.0010 | Pneu     |
|01.0001 |Bicicleta |01.0011 | Camara   |
+--------+----------+--------+----------+

Estrutura da Tabela
Dados no SQLFiddle
Dados em formato Texto
Cadastro de Produto [Tabela PROD]
pCOD     pDESC
01.0001  Bicicleta
01.0002  Guidão
01.0003  Quadro
01.0004  Garfo
01.0005  Banco
01.0006  Selim
01.0007  Roda
01.0008  Aro
01.0009  Raio
01.0010  Pneu
01.0011  Camara

Estrutura do Produto [Tabela ESTR]
eCOD     eCOMP    eQTD  eNiv
01.0001  01.0002     1     1
01.0001  01.0003     1     1
01.0003  01.0004     1     2
01.0001  01.0005     1     1
01.0005  01.0006     1     2
01.0001  01.0007     2     1
01.0007  01.0008     1     2
01.0008  01.0009     1     3
01.0008  01.0010     1     3
01.0010  01.0011     1     4

Dados em Formato SQL
CREATE TABLE PROD (
 pCOD varchar(15),
 pDESC varchar(100)
 );

insert into PROD (pCOD, pDESC) values
('01.0001','Bicicleta'),
('01.0002','Guidão'),
('01.0003','Quadro'),
('01.0004','Garfo'),
('01.0005','Banco'),
('01.0006','Selim'),
('01.0007','Roda'),
('01.0008','Aro'),
('01.0009','Raio'),
('01.0010','Pneu'),
('01.0011','Camara')

CREATE TABLE ESTR (
 eCOD varchar(15),
 eCOMP varchar(15),
 eQTD integer,
 eNIV integer
 );

insert into ESTR (eCOD, eCOMP, eQTD, eNIV) values
('01.0001','01.0002','1','1'),
('01.0001','01.0003','1','1'),
('01.0003','01.0004','1','2'),
('01.0001','01.0005','1','1'),
('01.0005','01.0006','1','2'),
('01.0001','01.0007','2','1'),
('01.0007','01.0008','1','2'),
('01.0008','01.0009','1','3'),
('01.0008','01.0010','1','3'),
('01.0010','01.0011','1','4')

A: É possível chegar ao resultado que pretende de duas formas: criando uma tabela temporária e ir preenchendo, linha a linha, a partir de um CURSOR (ou loop), que é mais trabalhoso porque terá que fazer a consulta por cada nível e em termos de performance (por norma) é mais lento, ou simplesmente utiliza CTE:
;WITH REC AS
(
    SELECT      E.*
    FROM        ESTR E
    INNER JOIN  PROD P ON P.pCOD = E.eCOD
    WHERE       E.eNIV = 1
    UNION ALL
    SELECT      R.eCOD, E.eCOMP, E.eQTD, E.eNIV
    FROM        ESTR E
    INNER JOIN  REC  R ON R.ecomp = E.ecod
)
SELECT      R.eCOD
        ,   P1.pDESC
        ,   R.eCOMP
        ,   P2.pDESC
        ,   R.eNIV
FROM        REC     R
INNER JOIN  PROD    P1 ON P1.pCOD = R.eCOD
INNER JOIN  PROD    P2 ON P2.pCOD = R.eCOMP
ORDER BY    R.eCOD
        ,   R.eNIV

Pode testar aqui no SQLFiddle.

redpajama_set_name: RedPajamaStackExchange


text:
Q: How to call AngularJS parent directive scope method from child directive I have a parent modal directive with confirm and cancel methods.
        ngDialog.open({
            scope      : true,
            showClose  : false,
            template   : theTemplate,
            className  : 'ngdialog-theme-prompt -small',

            controller : ['$scope', function Ctrl($scope) {
                $scope.message = message;

                $scope.confirm = function(){
                    $scope.closeThisDialog();
                    resolve(true);
                };

                $scope.cancel = function(){
                    $scope.closeThisDialog();
                    resolve(false);
                };
            }]

        }).closePromise.then(function () {
            resolve(false);
        })

The template is another directive.
<form class="edit-stakes-content">

            <input type="number" name="input" pattern="^\d+$" min="0" value="{{stake}}" />

        <button ng-click="cancel();" class="apl-btn apl-btn-link apl-btn-large" translate>CANCEL</button>
        <button ng-click="confirm();" autofocus="true" class="apl-btn apl-btn-update apl-btn-large" translate>SAVE</button>

</form>

In the child directive of the modal i want to be able to perform some validation and POST to the server and then call the parent modal directive confirm or cancel methods.
Similar to this:
Directive.$inject = ['UserSettings'];

function Directive(UserSettings) {
    function Link($scope) {

        $scope.settings = angular.copy(UserSettings.get('presetStakeSettings').settings);

        $scope.cancel = $scope.$parent.cancel();

    }

    return {
        'link': Link,
        'restrict': 'E',
        'replace': true,
        'templateUrl': 'betting/edit-stakes/edit-stakes.html'
    }
}

Calling the parent method throws a JavaScript error that $scope.$parent.cancel is not a function yet seems to do the job.
Is there a better way to achieve the child to parent communication without the JavaScript error?

A: $scope.$parent generally can be considered an antipattern, there are almost no good uses for it, usually it indicates that there is a problem with directive design or scope inheritance isn't well understood.
Directive directive doesn't request a new scope, so it is safe to assume that it is the same scope as the scope in modal controller. This means that $scope.$parent refers to a parent of modal scope (likely to root scope) which doesn't have cancel property.
This also means that $scope.settings assignment affects controller scope - while it obviously shouldn't. It would be better to have inherited scope in this directive with scope: true.
It doesn't matter if there is scope: true or not, but $scope.cancel will be available in directive. It is inherited from modal scope. There's no reason to do
$scope.cancel = $scope.$parent.cancel();


If you are a franchisor in South Africa (or are considering concluding a franchise agreement in the future), it is vital to know that there is a new law that will forcibly change the way franchises operate. Franchisees are deemed to be consumers in terms of the Consumer Protection Act 68 of 2008 (CPA) and now have a whole variety of consumer rights.
The whole franchising process will also be regulated by the CPA and its detailed regulations. Not only will your relationship with franchisees have to comply with the CPA, but the franchise agreement that governs the relationship will have to contain prescribed clauses and information in order to be compliant with the law.
The franchisee pays the franchisor for the right to carry on business within a specific part or all of South Africa under a system or marketing plan developed and controlled by the franchisor.
The operation of the business of the franchisee is closely associated with the advertising or trade marks, branding etcetera of the franchisor.
The business relationship between the franchisor and the franchisee is governed by the agreement.
Section 5(1)(a) of the Act provides that the Act will apply to every transaction that takes place in South Africa. In terms of s 5(6) any interaction between a franchisee and franchisor is regarded as a transaction.
At first glance it appears that certain bigger franchisees are not protected under the Act. This is because S5(2)(b) states that the Act does not apply to any transaction where the consumer is a juristic person whose asset value or annual turnover at the time of the transaction, equals or exceeds R2million.
the supply of any goods or services to a franchisee in terms of a franchise agreement.
Therefore, a franchise agreement will have to comply with the requirements of the Act, despite a potential franchisee having an annual turnover or asset value of more than R2milion. The probable reason for a franchisee being treated as a consumer is that franchisees have much less bargaining power than franchisors and they are vulnerable to abuse.
What are the requirements of a franchise in terms of the Act?
The requirements of a franchise agreement include that the agreement must be in writing and signed by at least the franchisee. In addition, the franchisor must ensure that the required information, as required by the regulations are contained within the agreement.
The regulations provide, amongst other requirements, that a franchise agreement must contain the exact wording of S7(2) of the act which provides that a franchisee may cancel a franchise agreement without cost or penalty within 10 business days after signing such agreement, by giving written notice to the franchisor. Franchisors must not only provide a potential franchisee with a disclosure document but there is also a list of terms that must be in every franchise agreement.
What parts of the Act apply to franchise agreements?
S13 – Consumer's right to select suppliers: This will especially come into play where a franchise agreement stipulates that a franchisee MUST purchase stock exclusively from the franchisor and when products are bundled together a franchisor must prove that the bundled product reasonably relates to the branded products that are the subject of the franchise agreement.
S21 –Unsolicited goods or services: This relates to the amount and time of delivery of goods. In certain circumstances unsolicited goods becomes the property of the franchisee without it having to give any payment for them.
S22- Right to disclosure in plain understandable language: All documents, notices and agreements must be in clear and understandable language drafted for the type of person who is likely to enter into a franchise agreement.
Recovery of goods from the franchisee.
S41 – False, misleading or deceptive representations: This relates to representations about material facts of the goods and services, exaggeration etcetera which could result in loss or damage for the franchisee.
S44 – Consumer's right to assume supplier is entitled to sell goods: This will be an implied provision of a franchise agreement.
S 48 – Unfair, unreasonable or unjust contract terms: This section prohibits unfair dealings, terms, obligations and waiver of warranties.
S49 – Notice requirement for certain terms and conditions: If the franchise agreement proposes to limit the franchisor's liability or place risk on the franchisee, this fact must be drawn to the attention of the franchisee.
S51 – Prohibited transactions, agreements, terms or conditions: S51 list a number of terms that are completely prohibited for example it is prohibited for a franchisor to contract out of gross negligence.
S14 which relates to the requirements regarding to the expiry of fixed term contracts generally does not apply to franchises, but will apply if a franchise trades in their own name.
What about existing franchise agreements?
With regard to transitional provisions, it appears that the Act will not apply to pre-existing franchise agreements (or transactions) entered into before the "general effective date" which is currently set to be 31 March 2011.
It appears that the Act will apply to the renewal of franchise agreements. Open-ended agreements, however, (agreements that have no fixed expiry date) will be deemed to expire two years after the CPA takes effect. New franchise agreements and renewals of existing franchise agreements will have to comply with the requirements of the CPA from 24th October onwards and it is safe to assume that in most instances, substantial rewrites will be required. Incidentally, franchise agreements aren't the only documents that are affected by the CPA, disclosure documents and operations manuals will also have to be amended.
It must however be kept in mind that after the "general effective date" that the supply of goods and services to a franchisee will be governed by the Act.
Where do I start with compliance?
Current and future franchise agreements will be largely impacted by the CPA and therefore business owners must acquaint themselves well with the ambit and workings of the CPA before entering into this type of agreement.
We also offer half day and full day workshops to customers where we give you a customised presentation of the impact and implication of the Consumer Protection Act on suppliers. It might be a good idea to get all the managers together to attend one seminar in order to empower them and make them aware of their rights. We also offer various other Consumer Protection Act services.
Your most important document is your franchise agreement. Not only must it be drafted into plain language, all unconscionable clauses removed and all terms that may involve placing the risk on consumers need to be brought under the consumer's attention, but the new regulations also have a list of requirements that need to be met.
However, as with many challenges it can also be seen as an opportunity you as a franchisor to assure your franchisees of your commitment to their wellbeing. If you are a franchisee, it will benefit you greatly to make sure you understand your rights and that you are not coerced into entering into a franchise agreement before 31 March 2011 that doesn't comply with the Act as you will lose out.


Let's say that you've outgrown IE's RSS feed capabilities.
Let's say that you've already exported your feeds to an OPML file for later re-import.
Let's say that now, you want to get rid of them. All.
With a script, dear Liza, dear Liza, dear Liza, with a script, dear Liza, dear Liza, a script.
What does such a script look like?
Please firefox developers: write an add-on that tells me which tab with flash on it is the one that is hammering my CPU.


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text:
  - Basic Script with GUI or on CLI for SSH to Cisco Routers or Switches and run some commands on it.

### Before use:

  - Python Version 2
  - Needed an hostfile with the name of the device (EX:192.68.2.250), see example file called Hosts.
  - Needed an configurationfile with the commands to send via ssh to device, see example file called Commands.
  - If using GUI.py change lines 10 & 11 of sshing.py to correct user and password, on CLI.py it is asked to user, for each equipment.

### Modules used:

  - re
  - sys
  - os
  - [gooey]
  - [wxpython] for [gooey]
  - getpass
  - pexpect
  - from pexpect used pxssh

### Help for wxpython:

 - After Gooey is installed, make sure [wxPython] is installed on your machine as well. Unfortanately, this cannot be done from the CLI and should be manually downloaded from the [wxPython website].

### To use:

There are two ways to run this script one is form Shell or with a GUI :

```sh
  $ python CLI.py <hostfile> <commandsfile>
  or
  $ python GUI.py
```

Or simply double click on GUI.py

### To do:
  - Create hide textbox for password on gooey
  - Add textbox for Username and Password on gooey

License
----

MIT

**USE IT ON YOUR OWN RISK !**

[gooey]: <https://github.com/chriskiehl/Gooey>
[wxPython]: <http://www.wxpython.org/download.php>
[wxPython website]: <http://www.wxpython.org/download.php>

redpajama_set_name: RedPajamaGithub


text:
Ukraine's Plot to Exchange a Citizen of Israel for Terrorists who Killed Russian Officers, by Scott Humor
Last week while we were celebrating the success of Russian athletes, other people were busy cooking up some fake news mixed with Hollywood-style horrors and injustices. To make a long story short, a blogger living in Ukraine known as varyag2007 has been almost, not quite, but very close to being arrested by the SBU. We were informed that the arrest is going to take place if not now then most definitely in the distant future. I am talking about the self proclaimed "anti-fascist" blogger Miroslava Berdnik
Buhari's Case: Justice Abang Removes Self
Justice Abang removes self from case against Buhari
Justice Abang has disqualified himself from a case against President Buhari – Incorporated Trustees of Oron Union brought a case against PMB regarding his nominations – The nominations of Mr Obong and Frank Samuel to the NDDC board led to the filing of the suit against President Muhammadu Buhari.
What Kerry Discussed With Buhari And Governors
The United States has pledged more support to Nigeria's anti-graft fight even as it praised President Muhammadu Buhari's courage.
"We applaud what you are doing. Corruption creates a ready-made playing field for recruiting extremists," visiting U.S. Secretary of State, Mr John Kerry, told Buhari at a closed-door meeting at the Presidential Villa yesterday.
Ukraine's Plot to Exchange a Citizen of Israel for...