text:
11.13.18 7:24AM
Charlotte Hilton Andersen
21 Inspiring Books Worth Reading If You Have Chronic Illness
Nearly half of all Americans live with some type of chronic illness, according to the National Health Council. If that stat sounds bigger than you thought it's probably because one of the worst parts of having an ongoing disease is...
Nearly half of all Americans live with some type of chronic illness, according to the National Health Council. If that stat sounds bigger than you thought it's probably because one of the worst parts of having an ongoing disease is how isolated it can make you feel. As soon as you get your diagnosis and the reality how your life will change sets in, you may start to feel like your world is shrinking in around you. But there are more people than you know who understand very well just how you are feeling.
Finding support is key to helping you not just survive but thrive after getting a life-changing diagnosis, says Mayra Mendez, PhD, a licensed psychotherapist and program coordinator for mental health services at Providence Saint John's in Santa Monica, California. "Whether it's finding a group online, talking to close friends or family members, or reading about it, it's so important to make connections with others who can sympathize and support you while you process these feelings," she says. "This will help reduce depression and anxiety and give you hope and if there's one thing that someone suffering needs the most, it's hope."
To help you find that hope and connections, we asked people living with a wide variety of chronic illnesses to share what books inspired, entertained, educated, and otherwise made dealing with life easier.
1. 'How To Be Sick' by Toni Bernhard
Toni has struggled for years with a chronic illness herself and has gone through a lot because of it. She's very honest about her struggles and gives tips for both patients and their caregivers. "I love how she uses Buddhist principles to teach acceptance, being kind to yourself, and mindfulness — all crucial skills when you're dealing with a life-changing illness," says Jennifer A., of Gilbert, Arizona. "It really helped change how I saw myself and improved how I treated myself."
2. '13 Things Mentally Strong People Don't Do' by Amy Morin
It's not written specifically for people living with a chronic disease but the tough-love, no-nonsense approach of this book speaks to a lot of the struggles ill people face and helps challenge negative thoughts, says Dennis L., of Columbus, Georgia. "The book came out as I was just in remission and recovering from the effects of six months of chemo. It helped me develop mental strength and resilience in my recovery," he says. "Rather than drown in self pity, I got into a diet and exercise regimen, lost over 60 pounds, ran a half marathon, became an endurance cyclist, and started training for an ironman."
3. 'Everything Happens for a Reason: And Other Lies I've Loved' by Kate Bowler
Everything happens for a reason is one of those things people say when they have no idea what to say and while it might be comforting to some, other people find that it minimizes their pain. This memoir tells the story of Kate's end-stage colon cancer and explores how to make sense of frustratingly non-sensical things in your life, like a chronic illness, with humor and care. "I loved this book so much that I bought a copy for everyone in my family, even though none of them are sick," says Emily A., of Philadelphia, Pennsylvania. "I've spent way too much time trying to figure out the cosmic 'reason' for my autoimmune disorder, driving myself crazy to find that silver lining, but this book helped me to be like 'Sometimes things just suck and that's fine.'"
4. The Harry Potter series by J.K. Rowling
"I'm going to be honest here, I hate self-help books. I feel like I get preached to enough without reading about how I need to be better about dealing with my chronic illness," says Abbie S., of Provo, Utah. "When my pain levels hover above the normal 6-7 range, I want something that fills me with joy and nostalgia and makes me completely forget that pain. Usually, that means I reread Harry Potter for the 50th time. I get so wrapped up in Harry's world that everything else becomes much more manageable. J.K. Rowling honestly talks me down from getting overly worked up about my condition and the dread I feel about spending the rest of my life in pain by transporting me (or apparating, if you will!) out of my own head for a little while. When I finish and get back to my own reality, it doesn't seem nearly so bad anymore."
5. 'The Heart of Torah' by Rabbi Shai Held
Being a man of God didn't shield Rabbi Held from chronic disease — he has chronic fatigue syndrome — but it did give him the perspective he needed to deal with it. This book uses commentary on the Torah, literature, and other religious experts to help answer fundamental questions about God, human nature, and what it means to be a religious person in the modern world. "It's not specifically about illness but it helped put things in perspective for me," says Janet E., of Brooklyn, New York. "It also helps knowing that he struggles in similar ways that I do."
6. 'Through the Shadowlands: A Science Writer's Odyssey into an Illness Science Doesn't Understand' by Julie Rehmeyer
Part memoir, part science text, this book details the author's journey through chronic fatigue syndrome so severe that some days she couldn't even turn over in bed. At her wit's end, she moves to the middle of the desert to try an extreme experiment — getting away from everything she's ever owned — to see if she can fix her health. "I really loved this book because as a scientist myself, I appreciated her analytical thinking, and as a person with a chronic disease, I also appreciated her honesty," says Anna P., of San Diego, California. "It just gave me hope when I was starting to feel like that was something I'd never have."
7. 'Girl in the Dark' by Anna Lyndsey
One day Anna was fine; the next she had a severe sensitivity to all forms of light that left her no choice but to live completely in the dark. It's not a common chronic illness but her feelings will definitely strike a chord with anyone struggling with long-term health issues. "I found this at a really dark time in my life so it really resonated with me," says Tatiana G., of Anaheim, California. "My favorite part is that it's just a memoir, it doesn't turn into a self-help book. I had tons of self-help books; what I needed was someone who really understood my pain and this book did that."
8. 'What's Wrong With Me' by Meghan O'Rourke
If reading a book feels too daunting, this long-form essay ublished in The New Yorker may be exactly what you need. The author shares her journey with Hashimoto's disease, from the first prickly rash to the complicated feelings she still has about her body. "It's just so beautifully written," Tatiana says. "It made me feel so much less alone in what I was going through."
9. 'The Paleo Approach: Reverse Autoimmune Disease and Heal Your Body' by Sarah Ballantyne, PhD
Changing your diet or tweaking your lifestyle to make healthier choices may not cure your chronic illness but a lot of people find that it helps manage them. Dr. Ballantyne shares how she uses the Paleo diet — think lots of meat and veggies but no grains — to help people deal with their autoimmune disorders. "It's tough at first, especially if you really love bread, but this … was a game changer for me," says Lesley B., of Brisbane, Australia.
10. 'The Courage to be Disliked' by Ichiro Kishimi and Fumitake Koga
This philosophy/pop psychology book gives you permission to stop trying to please other people and to start living life in an authentic way that makes you happy. "This doesn't have anything to do, specifically, with my disease, but having a chronic illness means I'm often in situations where I have to do things differently than other people," Lesley says. "My issues won't go away ever so I'll be damned if I sit back and feel sorry for myself!"
11. 'Living a Healthy Life With Chronic Conditions' by Kate Lorig, RN, DrPh; Halsted Holman, MD; David Sobel, MD, MPH; Diania Laurent, MPH; Virginia Gonzalez, MPH, and Marion Minor, RPT, PhD
Thanks to its six authors, all doctors in different specialties, this book is a comprehensive guide to managing a wide range of chronic diseases. It offers tips, suggestions, and strategies based on research done at Stanford. "I just wanted a practical book, not a huge dramatic thing, to help me figure out what I needed to be doing to manage my multiple sclerosis and this fit the bill exactly," says Jim F., of Fort Lauderdale, Florida.
12. 'My Lovely Wife In the Psych Ward' by Mark Lukach
This memoir is written by the loving husband of a woman who has intractable depression and psychotic breaks. "As someone who also has severe depression, this book was really meaningful to me because it gave me an outside view of what the disease looks like to my loved ones," says Jennifer E., of Dallas, Texas. "My disease makes some kind of sense to me but reading this helped me see how nonsensical it must look like to everyone else and weirdly this makes me want to fight it more."
13. 'The Hardest Peace: Expecting Grace in the Midst of Life's Hard' by Kara Tippetts
A mom of four, Kara's world is shattered when she receives a diagnosis of stage IV incurable cancer. She wrote the book while in the process of dying, allowing her to give invaluable insights into what it feels like to get such a heartbreaking diagnosis and how to live your best with what time you have left. "My disease — I have rheumatoid arthritis — isn't a death sentence, thankfully, and Kara helped me see how much I really have to be grateful for," says Constance J., of Alberta, Canada. "This book was the reminder I needed to bring me back to God and to practice faith."
14. '7 Steps to Living With a Chronic Illness' by Matt Cavallo
At just 100 pages, this relatively short book packs in a lot of information. Matt uses his experience with multiple sclerosis to share what he learned about both the practical and emotional aspects of dealing with a lifelong diagnosis and a progressive illness. "Everything is laid out very clearly, it was very easy for me to read," says Mark Y., of Denver, Colorado. "It felt like talking to a good friend who just happened to have a chronic disease too."
15. 'Depression and Anxiety' by Jack Brady
Mental illness is often overlooked in discussions of chronic diseases but can be every bit as painful and life-changing as a physical diagnosis of illness. Moreover, they often come together with other diagnoses, making learning to manage them all that more important. This book gives practical tips and support for living, and even thriving, with depression and anxiety. "I don't usually tell people I have crippling anxiety because I think it sounds dumb to a lot of people. Like, 'Why can't you just leave your house, it's not that hard'," says Angel M., of Gilbert, Arizona. "This book helped me see that these illnesses can affect your life just as much and they are real. I liked all the tips."
16. 'The Hunger Games' by Suzanne Collins
A fictional tale about a teenager in a dystopian world might not be the first thing you think of when you think of dealing with a chronic illness but there's a lot you can learn from The Hunger Games series about dealing with tough experiences that come to you through no fault of your own, says Curt A., of Raleigh, North Carolina. "It provides a much need escape from my reality plus if there's anyone who understands going through hell with no one to depend on but yourself, it's Katniss Everdeen," he explains. "It really captures the feelings of frustration, anger, self-pity, isolation, and unfairness I'm experiencing."
17. 'Simplicity' by Brian Night
Minimalism is a buzzword these days but learning to declutter your home and buy less are great ideas for many people, including those suffering with a chronic illness. This book shares how to apply this movement to your life in a simple and doable way. "If there's one thing that will make you want to simplify everything in your life, it's getting a chronic disease. I have extreme asthma and allergies and they really limit what I can do," says Jeff K., of Encinitas, California. "Getting rid of most of my things was very freeing, emotionally, and made me feel better physically as well."
18. 'Girl, Wash Your Face' by Rachel Hollis
Thanks to Rachel's self-deprecating humor and real-life insights, this self-help book upends the self-help stereotype to provide entertaining-yet-practical tips for ditching negative thought patterns and achieving your goals. "Ever since I was diagnosed with Crohn's disease, I felt like I was putting my life on hold. I was always waiting to feel better before I could do what I wanted," says Sarah M., of Seattle, Washington. "Rachel helped me see that I didn't have to wait for the stars to perfectly align to start taking steps forward and that even little, positive changes add up."
19. 'Befriending the Wolf' by Milly Diericx
In this book, Milly is both therapist and patient when it comes to her lupus diagnosis. The disease almost killed her but she survived and shares her advice for dealing with a chronic diagnosis in general as well as the specifics of living with lupus symptoms. "Milly was my lifeline when I first got diagnosed with lupus. All I read was scary things and she showed that there was light at the end of the tunnel," says Margot B., of Minneapolis, Minnesota.
20. 'Surviving and Thriving With an Invisible Chronic Illness' by Ilana Jacqueline
Some illnesses are very apparent to the general public but many are "invisible" to everyone but the person living with them, which can make it that much harder to deal with them. This book offers real-world examples of situations people may face and offers solutions for how to resolve them. "I have a heart condition but I look young and healthy. I can't tell you how many times I've been lectured or even yelled at by people for parking in the handicapped spot at the store. It's enough to make me not park in them unless I'm having a really difficult day, even though I have a valid permit," says Heidi B., of Salt Lake City, Utah. "This book helped me feel less alone and gave me some scripts to help me talk to people when they have questions."
21. 'The Stimulati Experience: 9 Skills for Getting Past Pain, Setbacks, and Trauma to Ignite Health and Happiness' by Jim Curtis
Using research and personal discoveries he gleaned from a group of experts he calls "The Stimulati," this book offers nine tips to help people dealing with any type of chronic illness to improve their life. "I have a chronic disease and live in daily pain yet the doctors are unable to figure out what's wrong with me so I really related to Jim's story about dealing with the same thing and trying to get an accurate diagnosis," says Juliette B., of Ridgecrest, California. "It was good to know I could start taking steps to get better even if I didn't know exactly what was wrong."
14 Things to Never Say to Someone with Chronic Illness
Surprising Upsides of Rheumatoid Arthritis You Might Not Have Considered
5 Things Everyone with Arthritis Can Do to Manage Depression
12 Ankylosing Spondylitis Symptoms You Can't Afford to Ignore
RA Treatment Not Working? 'Jakinibs' Might Help


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Q: Reverse-engineering a virtual method that only XORs the low byte of EAX before returning I need help with reverse engineering a virtual method from disassembly. The code was originally compiled with Microsoft's Visual C++. The method in question is as follows:
sub_92D110    proc near
xor al, al
retn
sub_92d110    endp

This method is referenced between a lot of classes, even multiple times inside of a vtable of one class. I am not sure what it does; does it mean the method got inlined but the call remains so that the vtables retain their size?
And if so, what does xor al, al do? Am I misunderstanding a calling convention or something?

A: This is most probably something like:
bool someclass::somemethod() {
    return false;
}

Explanation

*

*xor al,al sets the low byte of eax to zero.

*All x86 calling conventions use eax as the "return value" register for register-sized integer values.

*This cannot be a function returning an int (as in return 0;), given that it cleans only the low byte (and no x86 calling convention uses eax as an input parameter, so it's not some bizarre function that takes an integer argument, zeroes its low byte and returns it).

*This leaves us with a function that returns a byte-sized value, set to zero, so it could either return a char/unsigned char (0) or a bool (false); I'm way more inclined to think that it's the second option, given that in practice it arises way more often (especially in "empty" base class implementations of methods possibly redefined by derived classes).

*It either takes no parameters or is a variadic function that doesn't look at any of its parameters. C++ methods on VC++/x86 employ the __thiscall calling convention, which, besides putting the this pointer in ecx, is the same as __stdcall for "regular" methods, and same as __cdecl for variadics; now, __stdcall is callee cleanup, and here there's no cleanup to speak of, which would mean no arguments; on the other hand, there's no cleanup in the called method even in a __cdecl function, so we cannot rule out this possibility a priori. That being said, I don't think that this last option is likely.

This method is referenced between a lot of classes, even multiple times inside of a vtable of one class.

It's perfectly normal; VC++'s linker regularly merges unrelated functions that compile to the same machine code (and confusingly calls this "identical COMDAT folding").
Given that this process is very low level (it essentially looks at the bytes generated for the various functions and sees if they can be de-duplicated), in theory all the hypotheses above may hold together—it may be a method taking no arguments and returning a bool false in one vtable slot and a varargs method returning a char zero in another one.

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Your guide to movie theaters
Comments from MarkNYLA
Showing 51 - 57 of 57 comments
MarkNYLA commented about Cineplex Odeon Route 17 Triplex on Jan 31, 2006 at 1:30 pm
There is a sign on the front door of this theatre that says "the showing of movies at this location has been suspended until further notice". I'll just bet.
This was a pretty ramshackle operation in its latter years, but it had a great funky quality, plus that wonderful popcorn oil/disinfectant/mildew smell that I get so nostalgic about. The thing I will always remember is that whether from laziness or lack of letters, the marquee always featured drastic truncations of movie titles, often just one key word. The best one was While You Were Sleeping, which on the marquee was reduced to just "While (PG)". That's it!
MarkNYLA commented about Regency Bruin Theatre on Dec 4, 2005 at 9:04 am
Nighttime shot
MarkNYLA commented about Regency Village Theatre on Nov 21, 2005 at 5:07 pm
Another shot that I took over the summer.
Still the best bet for movies in L.A.
MarkNYLA commented about Beverly Center 13 Cinemas on Sep 15, 2005 at 8:29 am
Nice pictures, fellas, but wrong theatre. This thread is for the Beverly Center multi-plex, which is in the Beverly Center Mall at the corner of Beverly and La Cienega.
MarkNYLA commented about TCL Chinese Theatre on Aug 27, 2005 at 7:52 am
Stevebob: I absolutely remember the plastic mold machine; it sat on the extreme right of the forecourt (facing towards the entrance) next to the entrance of the gift shop. I last saw it in the early 1990s, but it has gone now. How I wish I had actually made one of the little pagodas on one of my many visits, now the opportunity is lost.
There's something else that's missing from the forecourt. Many years ago (in the 1940s, maybe), the theatre held a contest that would allow the winner, just any average Joe, to place his name and prints in cement just like the celebs did. The deal was that the cement slab would remain there forever, just like all the others. Eventually, of course, the slab was moved to an out-of-the-way spot waaaayyyy to the right, not far from the plastic machine mentioned above. I remember seeing it there at the same time I last saw the mold machine. Now, it has gone too. I cannot for the life of me remember the name of the winner who was so immortalized, but I remember the words 'contest winner' were on the same slab with his prints.
MarkNYLA commented about Angelika Film Center on Jul 7, 2005 at 8:51 am
The Angelica is nothing short of a disgrace to independent cinema, I won't see a movie there unless there is no other option (fortunately, films shown here are often co-booked with Dan Talbot's far superior Lincoln Plaza Cinemas). It has, beyond the shadow of a doubt, the sloppiest projection in town. Last year I went to a showing of the film "CQ" the day after it opened, and it ALREADY had an emulsion scratch the entire length of the film after a handful of runs. In fact, I don't recall EVER seeing a film here that didn't have projection issues. And don't get me started on the auditoriums. Long live the Sunshine, a bright spot for film going in NYC!
MarkNYLA commented about 8th Street Playhouse on Jul 7, 2005 at 2:41 am
Truth be told, Charles, the 8th Street Playhouse wasn't replaced by condos. The building that housed the theatre is now the NYC outpost of TLA Video, a video rental company specializes in obscure, cult and offbeat titles. It's probably the best video rental in NY, next to Kim's Underground. This dosn't excuse the loss of a great theatre (the first theatre I made a beeline for when I moved here), but it least something movie related took it's place.
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\section{Introduction}
Let $X$ be a real Banach space and $X^*$ its topological dual, both
with norms denoted by $\|\cdot\|$.
The duality product in $X\times X^*$ will be denoted by:
\begin{equation}
  \label{eq:def.pi}
  \pi:X\times X^*\to \mathbb{R},\quad \pi(x,x^*):=\inner{x}{x^*}=x^*(x).
\end{equation}
A point to set operator $T:X\rightrightarrows X^*$ is a relation on $X\times X^*$:
\[
 T\subset X\times X^*
\]
and $T(x)=\{x^*\in X^*\;|\; (x,x^*)\in T\}$. An operator $T:X\rightrightarrows X^*$
is {\it monotone} if
\[
\inner{x-y}{x^*-y^*}\geq 0,\forall (x,x^*),(y,y^*)\in T
\]
and it is {\it maximal monotone} if it is monotone and maximal (with
respect to the inclusion) in the family of monotone operators of $X$
into $X^*$.

Fitzpatrick proved constructively that maximal monotone operators are
representable by convex functions.
Before discussing his findigs, let us establish some notation.
We denote the set of extended-real valued functions on $X$ by
$\bar{\mathbb{R}}^{X}$.  The {\it epigraph} of $f\in \bar{\mathbb{R}}^X$ is defined by
\[
\mbox{E}(f):=\{(x,\mu)\in X\times \mathbb{R}\,|\,f(x)\leq \mu\}.
\]
  We say that
$f\in \bar{\mathbb{R}}^X$ is lower semicontinuous (l.s.c. from now on) if
$\mbox{E}(f)$ is closed in the strong topology of $X\times \mathbb{R}$.

Let $T:X\rightrightarrows X^*$ be maximal monotone. The \emph{Fitzpatrick
function of $T$} is~\cite{Fitz88}
\begin{equation} \label{FitzIntro}
\varphi_T\in \bar{\mathbb{R}}^{X\times X^*},\quad
 \varphi_{T}(x,x^*):=\sup_{(y,
      y^*)\in T} \inner{x-y}{y^*-x^*}+\inner{x}{x^*}
\end{equation}
and \emph{Fitzpatrick family} associated with $T$ is
\[
  \mathcal{F}_T:=\left\{ h\in \bar{\mathbb{R}}^{X\times X^*}
    \left|
      \begin{array}{ll}
        h\mbox{ is convex and l.s.c.}\\
        h(x,x^*)\geq \inner{x}{x^*},\quad \forall (x,x^*)\in X\times X^*\\
        (x,x^*)\in T
        \Rightarrow
        h(x,x^*) = \inner{x}{x^*}
      \end{array}
    \right.
  \right\}.
\]
In the next theorem we summarize the Fitzpatrick's results:
\begin{theorem}[\mbox{\cite[Theorem 3.10]{Fitz88}}] \label{th:fitz}
  Let $X$ be a real Banach space and $T:X\rightrightarrows X^*$ be maximal
  monotone. Then  for any $h\in \mathcal{F}_T$
  \[
  (x,x^*)\in T\iff h(x,x^*)=\inner{x}{x^*}
  \]
  and $\varphi_T$ is the smallest element
  of the  family $\mathcal{F}_T$.
\end{theorem}
\noindent
Fitzpatrick's results described above were rediscovered by
Mart\'inez-Legaz and Th\'era~\cite{LegTheJNCA01}, and Burachik and
Svaiter~\cite{BuSvSet02}.

It seems interesting to study conditions under which a convex function
$h\in \bar{\mathbb{R}}^X$ represents a maximal monotone operator, that is,
$h\in\mathcal{F}_T$ for some maximal monotone operator $T$. Our aim is to
extend previous results on this direction.
We will need some auxiliary results and additional notation for this
aim.

The Fenchel-Legendre conjugate of $f\in \bar{\mathbb{R}}^{X}$ is
\[
 f^*\in \bar{\mathbb{R}}^{X^*},\quad f^*(x^*):=\sup_{x\in X} \inner{x}{x^*}-f(x).
\]
Whenever necessary, we will
identify $X$ with its image under the canonical injection of $X$ into
$X^{**}$.
Burachik and Svaiter proved that the family $\mathcal{F}_T$ is invariant under
the mapping
\begin{equation}
  \label{eq:def.jconj}
  \mathcal{J}:\bar{\mathbb{R}}^{X\times X^*}\to\bar{\mathbb{R}}^{X\times X^*}, \;\mathcal{J}\;h(x,x^*):=h^*(x^*,x).
\end{equation}
This means that
if $T:X\rightrightarrows X^*$ is maximal monotone, then~\cite{BuSvSet02}
\begin{equation}\label{eq:inv.0}
 \mathcal{J}(\mathcal{F}_T)\subset \mathcal{F}_T.
\end{equation}
In particular, for any $h\in \mathcal{F}_T$  it holds that
$ h\geq \pi$ , $ \mathcal{J} h\geq \pi$,
that is,
\[ h(x,x^*)\geq \inner{x}{x^*},\quad h^*(x^*,x)\geq \inner{x}{x^*},
  \qquad \forall (x,x^*)\in X\times X^*.
\]
So, the above conditions are\emph{ necessary} for a convex function
$h$ on $X\times X^*$ to represent a maximal monotone operator.
Burachik and Svaiter proved that these conditions are also
\emph{sufficient}, in a reflexive Banach space, for $h$ to represent a
maximal monotone operator:
\begin{theorem}[\mbox{\cite[Theorem 3.1]{BuSvProc03}}]\label{th:bs}
 Let $h\in \bar{\mathbb{R}}^{X\times X^*}$ be proper, convex, l.s.c. and
 \begin{equation} \label{eq:hhs.0}
 h(x,x^*)\geq \inner{x}{x^*},\quad h^*(x^*,x)\geq \inner{x}{x^*},
  \qquad \forall (x,x^*)\in X\times X^*.
  \end{equation}
  If $X$ is reflexive, then
 \[
  T:=\{(x,x^*)\in X\times X^*\;|\;h(x,x^*)= \inner{x}{x^*}\}
 \]
 is maximal monotone and $h, \mathcal{J} h\in \mathcal{F}_T$.
\end{theorem}
\noindent
Marques Alves and Svaiter generalized Theorem~\ref{th:bs}
 to non-reflexive Banach spaces as follows:
\begin{theorem}[\mbox{\cite[Corollary 4.4 ]{MASvJCA08}}]\label{th:as}
 If $h\in \bar{\mathbb{R}}^{X\times X^*}$ is convex and
  \begin{equation} \label{eq:hhs.pd}
  \begin{array}{ll}
    h(x,x^*)\geq \inner{x}{x^*}, & \forall (x,x^*)\in X\times X^*,\\[.4em]
     h^*(x^*,x^{**})\geq \inner{x^*}{x^{**}}, &
      \forall (x^*,x^{**})\in X^*\times X^{**}
  \end{array}
\end{equation}
then
 \[
  T:=\{(x,x^*)\in X\times X^*\;|\;h^*(x^*,x)= \inner{x}{x^*}\}
 \]
 is maximal monotone and $ \mathcal{J} h\in \mathcal{F}_T$. Moreover, if $h$ is l.s.c. then
 $h\in \mathcal{F}_T$.
\end{theorem}
Condition~\eqref{eq:hhs.pd} of Theorem~\ref{th:as} enforces the
operator $T$ to be of type (NI)~\cite{MASvJCA08.2} and is not
necessary for maximal monotonicity of $T$ in a non-reflexive Banach
space. Note that
   while the weaker condition \eqref{eq:hhs.0} of
 Theorem~\ref{th:bs} is still \emph{necessary} in non-reflexive Banach
spaces for the inclusion $h\in\mathcal{F}_T$, where $T$ is a maximal monotone
operator.
The main result of this paper is another generalization of
Theorem~\ref{th:bs} to  non-reflexive Banach spaces which uses
condition~\eqref{eq:hhs.0} instead of \eqref{eq:hhs.pd}. For obtaining
this generalization, we added a regularity assumption on the domain of
$h$.

If $T:X\rightrightarrows X^*$ is maximal monotone, it is easy to prove that
$\varphi_T$ is minimal in the family  of all convex functions in $X\times X^*$
which majorizes the duality product.
So, it is natural to ask whether the converse also holds, that is:
\begin{quotation}
  \noindent
  Is any minimal element of this family (convex functions which
  majorizes the duality product) a  Fitzpatrick
  function of some maximal monotone operator?
\end{quotation}
To give a partial answer to this question, Mart\'inez-Legaz and Svaiter proved the following results, which we will use latter on:
\begin{theorem}[\mbox{\cite[Theorem 5]{LegSvProc08}}] \label{th:ls}
 Let $\mathcal{H}$ be the family of convex functions in $X\times X^*$ which
 majorizes the duality product:
 \begin{equation}
   \label{eq:def.h}
   \mathcal{H}:=
  \{h\in \bar{\mathbb{R}}^{X\times X^*}\,|\,h\; \mbox{is proper, convex and}\; h\geq \pi\}.
 \end{equation}
 The following statements holds true:
 \begin{enumerate}
 \item The family $\mathcal{H}$ is (donward) inductively ordered;
  \item For any $h\in \mathcal{H}$ there exists a minimal $h_0\in \mathcal{H}$ such that
        $h\geq h_0$;
      \item Any minimal element $g$ of $\mathcal{H}$ is l.s.c. and
        satisfies $\mathcal{J} g\geq g$.
 \end{enumerate}
\end{theorem}
Note that item 2 is a direct consequence of item 1.
Combining item 3 with Theorem~\ref{th:bs}, Mart\'inez-Legaz and Svaiter
concluded that \emph{in a reflexive} Banach space, any minimal element
of $\mathcal{H}$ is the Fitzpatrick function of some maximal monotone
operator~\cite[Theorem 5]{LegSvProc08}.
We will also present a partial extension of this result for
non-reflexive Banach spaces.

\section{Basic results and notation}

The weak-star topology of $X^*$ will be denoted by
$\omega^*$ and by $s$ we denote the strong topology of $X$.
A function $h\in \bar{\mathbb{R}}^{X\times X^*}$  is lower
semicontinuous in the strong$\,\times\,$weak-star topology if
$\mbox{E}(h)$ is a closed subset of $X\times X^*\times \mathbb{R}$ in the
$s\times \omega^*\times |\cdot|$ topology.

The \emph{indicator function} of $V\subset X$ is $\delta_V$,
$\delta_V(x):=0,\,x\in V$ and $\delta_V(x):=\infty$, otherwise.
The closed convex closure
of $f\in \bar{\mathbb{R}}^{X}$ is defined by
\[
 \mbox{cl\,conv}f\in \bar{\mathbb{R}}^{X},\quad \mbox{cl\,conv}f(x):=
 \inf\{\mu\in \mathbb{R}\,|\,(x,\mu)\in \mbox{cl\,conv}\,\mbox{E}(f)\}
\]
where for $U\subset X$, $\mbox{cl\,conv}\,U$ is the closed convex hull
(in the $s$ topology) of $U$.
The {\it effective domain} of a function $f\in \bar{\mathbb{R}}^{X}$ is
\[
\mbox{D}(f):=\{x\in X\,|\, f(x)<\infty\},
\]
and $f$ is \emph{proper} if $\mbox{D}(f)\neq
\emptyset$.
If $f$ is proper, convex and l.s.c.,
then $f^*$ is proper.
For $h\in \bar{\mathbb{R}}^{X\times X^*}$, we also define
\[
\mbox{Pr}_X\,\mbox{D}(h):=\{x\in X\,|\,\exists\, x^*\in X^*\,|\,(x,x^*)\in \mbox{D}(h)\}.
\]
Let  $T:X\rightrightarrows X^*$ be  maximal monotone.
In~\cite{BuSvSet02} Burachik and Svaiter defined and studied the
biggest element of $\mathcal{F}_T$, namely, the $\mathcal{S}$-function,
$\mathcal{S}_T\in \mathcal{F}_T$ defined by
\[
\mathcal{S}_T\in \bar{\mathbb{R}}^{X\times X^*},\,\quad \mathcal{S}_T:=\sup_{h\in \mathcal{F}_T}\,\{h\},
\]
or, equivalently
\[

  \mathcal{S}_T=\clconv (\pi+\delta_T).
\]
Recall that $\mathcal{J}(\mathcal{F}_T)\subset \mathcal{F}_T$. Additionally~\cite{BuSvSet02}
\begin{equation}\label{eq:inv.1}
 \mathcal{J}\;\mathcal{S}_T=\varphi_T
\end{equation}
and, in a reflexive Banach space, $\mathcal{J}\varphi_T=\mathcal{S}_T$.

In what follows we present the Attouch-Brezis's version of the
Fenchel-Rockafellar duality theorem:

\begin{theorem}[\mbox{\cite[Theorem 1.1]{AttBrez86}}]\label{th:fr}
  Let $Z$ be a Banach space and $\varphi,\psi\in \bar{\mathbb{R}}^{Z}$ be proper,
  convex and l.s.c. functions.  If
\begin{equation}\label{eq:cond.fr}
 \bigcup_{\lambda>0}\lambda\,[\emph{D}\,(\varphi)-\emph{D}\,(\psi)],
\end{equation}
is a closed subspace of $Z$, then
\begin{equation}\label{eq:fr}
 \inf_{z\in Z}\varphi(z)+\psi(z)=\max_{z^*\in Z^*}-\varphi^*(z^*)-\psi^*(-z^*).
\end{equation}
\end{theorem}

Given $X,\,Y$ Banach spaces, $\mathcal{L}(Y,X)$ denotes the set of
continuous linear operators of $Y$ into $X$. The range of $A\in
\mathcal{L}(Y,X)$ is denoted by $\mbox{R}(A)$ and the adjoint by
$A^*\in \mathcal{L}(X^*,Y^*)$:
\[
 \inner{Ay}{x^*}=\inner{y}{A^*x^*}\; \forall y\in Y,\,x^*\in X^*,
\]
where $X^*,\,Y^*$ are the dual of $X$ and $Y$, respectively.
The next proposition is a particular case of Theorem 3
of~\cite{Simons-Quadr}. For the sake of completeness, we give the
proof in the Appendix A.

\begin{proposition}\label{prop:2}
 Let $X,\,Y$ Banach spaces and $A\in \mathcal{L}(Y,X)$. For $h\in \bar{\mathbb{R}}^{X\times X^*}$,
 proper convex and l.s.c., define $f\in \bar{\mathbb{R}}^{Y\times Y^*}$
  \[
   f(y,y^*):=\inf_{x*\in X^*}\,h(Ay,x^*)+\delta_{\{0\}}(y^*-A^*x^*).
  \]
 If
 \begin{equation}\label{eq:cond2}
  \bigcup_{\lambda>0}\lambda\,[\emph{Pr}_{X}\,\emph{D}(h)-\emph{R}(A)],
 \end{equation}
 is a closed subspace of $X$, then
 \[
  f^*(z^*,z)=\min_{u^*\in X^*}\,h^*(u^*,Az)+\delta_{\{0\}}(z^*-A^*u^*).
 \]
\end{proposition}
Mart\'inez-Legaz and Svaiter~\cite{LegSvSet05} defined, for $h\in \bar{\mathbb{R}}^{X\times X^*}$ and
$(x_0,x_0^*)\in X\times X^*$, $h_{(x_0,x_0^*)}\in \bar{\mathbb{R}}^{X\times X^*}$
\begin{align}\label{eq:def.hx}
 \nonumber
 h_{(x_0,x_0^*)}(x,x^*)&:= h(x+x_0,x^*+x_0^*)-[\inner{x}{x_0^*}+\inner{x_0}{x^*}
    +\inner{x_0}{x_0^*}]\\
                       & = h(x+x_0,x^*+x_0^*)-\inner{x+x_0}{x^*+x_0^*}+\inner{x}{x^*}.
\end{align}
The operation $h\mapsto h_{(x_0,x_0^*)}$ preserves many properties of
$h$, as convexity and lower semicontinuity. Moreover, one can easily prove the
following Proposition:
\begin{proposition}\label{prop.prh}
Let $h\in \bar{\mathbb{R}}^{X\times X^*}$. Then it holds that
\begin{enumerate}
\item $h\geq \pi\iff h_{(x_0,x_0^*)}\geq \pi,\, \forall (x_0,x_0^*)\in X\times X^*$;
\item $\mathcal{J} h_{(x_0,x_0^*)}=(\mathcal{J} h)_{(x_0,x_0^*)}$, \, $\forall (x_0,x_0^*)\in X\times X^*$.
\end{enumerate}
\end{proposition}

\section{Main results}

In the next theorem we generalize Theorem~\ref{th:bs} to non-reflexive
Banach spaces using condition~\eqref{eq:hhs.0} instead of the
condition \eqref{eq:hhs.pd} used in Theorem~\ref{th:as}. For
obtaining this generalization, we added a regularity
assumption~\eqref{eq:c.th:1} on the domain of $h$.
\begin{theorem}\label{th:1}
 Let $h\in \bar{\mathbb{R}}^{X\times X^*}$ be proper, convex and
   \begin{equation} \label{eq:hhs.1}
     h(x,x^*)\geq \inner{x}{x^*},\quad h^*(x^*,x)\geq \inner{x}{x^*},
     \qquad \forall (x,x^*)\in X\times X^*.
  \end{equation}
 If
 \begin{equation}\label{eq:c.th:1}
  \bigcup_{\lambda> 0}\lambda\, \emph{Pr}_{X}\,\emph{D}(h),
 \end{equation}
 is a closed subspace of $X$,
 then
 \[
  T:=\{(x,x^*)\in X\times X^*\;|\; h^*(x^*,x)= \inner{x}{x^*}\}
 \]
 is maximal monotone and $\mathcal{J} h\in \mathcal{F}_T$.
\end{theorem}
\begin{proof}
  First, define $\bar h:=\mbox{cl}\,h$ and note that $\bar h$ is
  proper, convex, l.s.c., satisfies~\eqref{eq:hhs.1}, \eqref{eq:c.th:1}
  and $\mathcal{J} \bar h=\mathcal{J} h$. So, it suffices to prove the theorem for the
  case where $h$ is l.s.c., and we assume it from now on in this
  proof.
  Monotonicity of $T$ follows from Theorem 5 of~\cite{LegSvSet05}.
  Note that for any $x\in X$
  \[
  T(x)=\{x^*\in X^*\;|\; h^*(x^*,x)-\inner{x}{x^*}\leq 0\}.
  \]
  Therefore, $T(x)$ is convex and $\omega^*$-closed.

  To prove maximality of $T$, take $(x_0,x_0^*)\in X\times X^*$ such
  that
\begin{equation}\label{eq:monrel}
 \inner{x-x_0}{x^*-x_0^*}\geq 0,\quad \forall (x,x^*)\in T
\end{equation}
and suppose $x_0^*\notin T(x_0)$. As $T(x_0)$ is convex and
$\omega^*$-closed,
using the geometric version of the Hahn-Banach theorem in
$X^{*}$ endowed with the $\omega^*$ topology we
conclude that there exists $z_0\in X$ such that
\begin{equation}\label{eq:contr}
 \inner{z_0}{x_0^*}<\inner{z_0}{x^*},\quad \forall\, x^*\in T(x_0).
\end{equation}
Let $Y:=\mbox{span}\{x_0,z_0\}$.
Define $A\in \mathcal{L}(Y,X)$, $A\,y:=y,\,\forall\,y\in Y$ and the convex
function $f\in \bar{\mathbb{R}}^{Y\times Y^*}$,
\begin{equation}\label{eq:def.H.p1}
   f(y,y^*):=\inf_{x*\in X^*}\,h(Ay,x^*)+\delta_{\{0\}}(y^*-A^*x^*).
\end{equation}
Using Proposition~\ref{prop:2} we obtain
\begin{equation}\label{eq:conj.H}
  f^*(y^*,y)=\min_{x*\in X^*}\,h^*(x^*,Ay)+\delta_{\{0\}}(y^*-A^*x^*).
\end{equation}
Using~\eqref{eq:hhs.1},~\eqref{eq:def.H.p1} and~\eqref{eq:conj.H} it is easy to see that
\begin{equation} \label{eq:H}
   f(y,y^*)\geq \inner{y}{y^*},\quad f^*(y^*,y)\geq \inner{y}{y^*},\, \forall (y,y^*)\in Y\times Y^*.
\end{equation}
Define $g:=\mathcal{J} f$. As $Y$ is reflexive we have $\mathcal{J} g=\mbox{cl}\,f$.
Therefore, using~\eqref{eq:H} we also have
\begin{equation} \label{eq:G}
   g(y,y^*)\geq \inner{y}{y^*},\quad g^*(y^*,y)\geq \inner{y}{y^*},\,\forall (y,y^*)\in Y\times Y^*.
\end{equation}
Now, using~\eqref{eq:G} and item 1 of Proposition~\ref{prop.prh} we obtain
\begin{align}\label{eq:1}
\nonumber
g_{(x_0,A^*x_0^*)}(y,y^*)+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2 &\geq
\inner{y}{y^*}+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2\\
     &\geq 0,\quad \forall (y,y^*)\in
 Y\times Y^*
\end{align}
and
\begin{align}\label{eq:2}
\nonumber
(\mathcal{J} g)_{(x_0,A^*x_0^*)}(y,y^*)+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2 &\geq
\inner{y}{y^*}+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2\\
   &\geq 0,\quad \forall (y,y^*)\in
 Y\times Y^*.
\end{align}
Using Theorem~\ref{th:fr} and item 2 of Proposition~\ref{prop.prh} we conclude that there exists $(\tilde z,\tilde z^*)\in Y\times Y^*$
such that
\begin{equation}\label{eq:3}
 \inf\,g_{(x_0,A^*x_0^*)}(y,y^*)+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2
 +(\mathcal{J} g)_{(x_0,A^*x_0^*)}(\tilde z,\tilde z^*)+\frac{1}{2}\|\tilde z\|^2
  +\frac{1}{2}\|\tilde z^*\|^2=0.
\end{equation}
From~\eqref{eq:1},\eqref{eq:2} and \eqref{eq:3} we have
\begin{equation}\label{eq:4}
 \inf_{(y,y^*)\in Y\times Y^*}\,g_{(x_0,A^*x_0^*)}(y,y^*)+\frac{1}{2}\|y\|^2+\frac{1}{2}\|y^*\|^2
 =0.
\end{equation}
As $Y$ is reflexive, from~\eqref{eq:def.hx},\eqref{eq:4} we conclude that there exists
$(\hat y, \hat y^*)\in Y\times Y^*$ such that
\begin{equation}\label{eq:5}
 g\,(\hat y+x_0,\hat y^*+A^*x_0^*)-\inner{\hat y+x_0}{\hat y^*+A^*x_0^*}
 +\inner{\hat y}{\hat y^*}+\frac{1}{2}\|\hat y\|^2+\frac{1}{2}\|\hat y^*\|^2
 =0.
\end{equation}
Using~\eqref{eq:5} and the first inequality of~\eqref{eq:G} (and the definition of $g$) we have
\begin{equation}\label{eq:6}
 f^*(\hat y^*+A^*x_0^*,\hat y+x_0)=\inner{\hat y+x_0}{\hat y^*+A^*x_0^*}
\end{equation}
and
\begin{equation}\label{eq:7}
 \inner{\hat y}{\hat y^*}+\frac{1}{2}\|\hat y\|^2+\frac{1}{2}\|\hat y^*\|^2
 =0.
\end{equation}
Using~\eqref{eq:conj.H} we have that there exists $w_0^*\in X^*$ such that
\begin{equation}\label{eq:8}
  f^*(\hat y^*+A^*x_0^*,\hat y+x_0)= h^*(w_0^*,A\,(\hat y+x_0)),\quad \hat y^*+A^*x_0^*=A^*w_0^*.
\end{equation}
So, combining~\eqref{eq:6} and~\eqref{eq:8} we have
\[
 h^*(w_0^*,A\,(\hat y+x_0))=\inner{\hat y+x_0}{A^*w_0^*}=\inner{A(\hat y+x_0)}{w_0^*}.
\]
In particular, $w_0^*\in T(A(\hat y+x_0))$. As $x_0\in Y$, we can use~\eqref{eq:monrel} and the second equality of~\eqref{eq:8} to conclude that
\begin{equation}\label{eq:9}
 \inner{A(\hat y+x_0)-x_0}{w_0^*-x_0^*}=\inner{\hat y}{A^*(w_0^*-x_0^*)}=
 \inner{\hat y}{\hat y^*}\geq 0.
\end{equation}
Using~\eqref{eq:7} and~\eqref{eq:9} we conclude that $\hat y=0$ and $\hat y^*=0$. Therefore,
\[
 w_0^*\in T(x_0),\quad A^*x_0^*=A^*w_0^*.
\]
As $z_0\in Y$, we have $z_0=A\,z_0$ and so
\[
 \inner{z_0}{x_0^*}=\inner{A\,z_0}{x_0^*}=\inner{z_0}{A^*x_0^*}=\inner{z_0}{A^*w_0^*}
 =\inner{A\,z_0}{w_0^*}=\inner{z_0}{w_0^*},
\]
that is,
\[
 \inner{z_0}{x_0^*}=\inner{z_0}{w_0^*},\quad w_0^*\in T(x_0)
\]
which contradicts~\eqref{eq:contr}. Therefore, $(x_0,x_0^*)\in T$ and
so $T$ is maximal monotone and $\mathcal{J} h\in \mathcal{F}_T$.
\end{proof}

Observe that if $h$ is convex, proper and l.s.c. in the
strong$\,\times\,$weak-star topology, then $\mathcal{J}^2h=h$. Therefore, using this
observation we have the following corollary of Theorem~\ref{th:1}:

\begin{corollary}\label{cr:1}
 Let $h\in \bar{\mathbb{R}}^{X\times X^*}$ be proper, convex, l.s.c. in the
 strong$\,\times\,$weak-star topology and
  \[
     h(x,x^*)\geq \inner{x}{x^*},\quad h^*(x^*,x)\geq \inner{x}{x^*},
     \qquad \forall (x,x^*)\in X\times X^*.
  \]
 If
 \[
   \bigcup_{\lambda>0}\lambda\, \emph{Pr}_{X}\,\emph{D}(h),
 \]
 is a closed subspace of $X$,
 then
 \[
  T:=\{(x,x^*)\in X\times X^*\;|\;h(x,x^*)= \inner{x}{x^*}\}
 \]
 is maximal monotone and $h,\mathcal{J} h\in \mathcal{F}_T$.
\end{corollary}
\begin{proof}
  Using Theorem \ref{th:1} we conclude that the set
  \[
  S:=\{(x,x^*)\in X\times X^*\;|\; h^*(x^*,x)=\inner{x}{x^*}\}
  \]
  is maximal monotone. Take $(x,x^*)\in S$. As $\pi$ is Gateaux
  differentiable, bounds below $h$ and coincides with $h$ at
  $(x,x^*)$, we have (see Lemma 4.1 of~\cite{MASvJCA08})
  \[
  D\pi(x,x^*)\in \partial\, \mathcal{J} h(x,x^*),
  \]
  where $D\pi$ stands for the Gateaux derivative of $\pi$. As $D\pi(x,x^*)=(x^*,x)$, we conclude that
  \[
  \mathcal{J} h(x,x^*)+\mathcal{J}^2 h(x,x^*)=\inner{(x,x^*)}{(x^*,x)}.
  \]
  Substituting $\mathcal{J} h(x,x^*)$ by $\inner{x}{x^*}$ in the above equation we conclude
  that $\mathcal{J}^2h(x,x^*)=\inner{x}{x^*}$. Therefore, as $\mathcal{J}^2 h(x,x^*)=h(x,x^*)$,
  \[
   S \subset T.
  \]
  To end the proof use the maximal monotonicity of $S$ (Theorem~\ref{th:1})
  and the monotonicity of $T$ (see Theorem 5 of~\cite{LegSvSet05}) to conclude that $S=T$.
\end{proof}

It is natural to ask whether we can drop lower-semicontinuity assumptions. In the context of non-reflexive Banach spaces, we should use
the l.s.c closure in the strong$\,\times\,$weak-star topology. Unfortunately, as
the duality product is not continuous in this topology, it is not clear
whether the below implication holds:
\[
 h\geq\pi\stackrel{?}\Rightarrow \mbox{cl}_{s\times \omega^*}\, h_{}\geq \pi.
\]

\begin{corollary}\label{cor:3}
 Let $h\in\bar{\mathbb{R}}^{X\times X^*}$ be proper, convex and
   \[
     h(x,x^*)\geq \inner{x}{x^*},\quad h^*(x^*,x)\geq \inner{x}{x^*},
     \qquad \forall (x,x^*)\in X\times X^*.
   \]
 If
 \[
  \bigcup_{\lambda>0}\lambda\,\emph{Pr}_X\emph{D}(h)
 \]
 is a closed subspace of $X$,
 then
 \[
  \emph{cl}_{s\times \omega^*}\,h\in\mathcal{F}_T,
 \]
 where $\emph{cl}_{s\times \omega^*}$ denotes the l.s.c. closure in the
 strong$\,\times\,$weak-star topology and $T$ is the maximal monotone
 operator defined as in Theorem~\ref{th:1}:
 \[
 T:=\{(x,x^*)\in X\times X^*\;|\;h^*(x^*,x)=\inner{x}{x^*}\}.
 \]
 In particular, $\emph{cl}_{s\times \omega^*}\,h\geq\pi$.
\end{corollary}
\begin{proof}
  First use Theorem~\ref{th:1} to conclude that $T$ is maximal monotone and
  $\mathcal{J} h\in\mathcal{F}_T$. In particular,
  \[
  \mathcal{S}_T\geq \mathcal{J} h\geq \varphi_T.
  \]
  Therefore,
  \[
  \mathcal{J}\varphi_T\geq \mathcal{J}^2 h\geq\mathcal{J}\mathcal{S}_T.
  \]
  As $\mathcal{J}\mathcal{S}_T=\varphi_T\in \mathcal{F}_T$ and $\mathcal{J}\varphi_T\in\mathcal{F}_T$, we
  conclude that $\mbox{cl}_{s\times \omega^*}\,h=\mathcal{J}^2h\in\mathcal{F}_T$.
\end{proof}

In the next corollary we give a partial answer for an open
question proposed by Mart\'inez-Legaz and Svaiter in~\cite{LegSvProc08}, in the
context of non-reflexive Banach spaces.
\begin{corollary}\label{cr:2}
Let $\mathcal{H}$ be the family of convex functions on $X\times X^*$
bounded below by the duality product, as defined in~\eqref{eq:def.h}.
If $g$ is a minimal element of $\mathcal{H}$ and
 \[
  \bigcup_{\lambda>0}\lambda\,\emph{Pr}_X\,\emph{D}(g)
 \]
is a closed subspace of $X$,
then there exists a maximal monotone operator $T$ such that $g=\varphi_T$,
where $\varphi_T$ is the Fitzpatrick function of $T$.
\end{corollary}
\begin{proof}
  Using item 3 of Theorem~\ref{th:ls} and Theorem~\ref{th:1} we have that
  \[
   T:=\{(x,x^*)\in X\times X^*\,|\, g^*(x^*,x)=\inner{x}{x^*}\}
  \]
  is maximal monotone, $\mathcal{J} g\in \mathcal{F}_{T}$ and
  \[
    T\subset \{(x,x^*)\in X\times X^*\;|\; g(x,x^*)=\inner{x}{x^*}\}.
  \]
  As $g$ is convex and bounded below by the duality product, using Theorem 5 of~\cite{LegSvSet05},
  we conclude that the rightmost set on the above inclusion is
  monotone. Since $T$ is maximal monotone, the above inclusion holds
  as an equality and, being l.s.c., $g\in\mathcal{F}_T$. To end the proof, note that
  $g\geq\varphi_T\in\mathcal{H}$.
\end{proof}

redpajama_set_name: RedPajamaArXiv


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text:
Q: MATLAB : Use a different version of a function with the same name I am writing a code in MATLAB where I need to use a function called modwt which exist in two toolboxes that I'm using at the same time (Wavelet and WMTSA). The thing is that one version returns only one output and the other one returns three. How should I indicate which toolbox is the one that I need for a specific code. What I have done so far is trying to import the function using the import command:
import wmsta.dwt.modwt

Which gives me an error regarding that there is something wrong with my import.
Any help is much appreciated. Thanks

A: You shall prepend/put on the top (using the addpath function) the directory containing the function you want to call in MATLAB path. See https://www.mathworks.com/help/matlab/ref/addpath.html
or use function handles
as explained here https://stackoverflow.com/a/33776090/2043349


text:
NYSE:DAR
Results: Darling Ingredients Inc. Exceeded Expectations And The Consensus Has Updated Its Estimates
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Research reports say that only 15% of people are saving sufficiently for their retired life. This tells that a large number of individuals are not planning for their retirement which is a harsh reality. It is better to start planning early and put things in action than starting late and realizing the mistakes made later. Visualize your retired life and then start planning early.
Ensure that all your debts are completely re-paid on or before your retirement. Be it a home loan, car loan, personal loan or any other loan, make sure you choose the term of these loans before your retirement age and then repay them. Only then will you be able to enjoy your retired life with 100% financial freedom, not when you have to repay your loans.
Emergency situations can happen at any time and the expenses can be very demanding, especially when you get older. So you will need to revise your emergency funds on a year by year basis and enhance them based on inflation and change in your expense levels. They will also give you a sense of security.
It is good to have a vision in career life and it also good to have a vision for your retirement life also. You need to visualize your retirement goals and create a budget for that too. Retirement means that you will not be working anymore and will have to pay for your expenses. You may need to spend more on travel and medical expenses.
Find out how much retirement corpus you will need when you retire. A good financial planner can help you in finding right answers to your questions and can be of great help in this regard.
Your retirement income and corpus need to be tax efficient. You need to pay taxes only for the interest accrued. You will need to carefully select your investment option that can help you in reducing tax in your retired life.
Plan you medical coverage well in advance because your employer will stop covering you under the group mediclaim. At old age, medical expenses can become inevitable and lack of proper planning in this aspect can create a lot of trouble.
To avoid any relationship conflicts among your next generation, you will have to draft a will that will distribute your fixed and financial assets to your legal heirs.


In a recent case in front of the Maryland Court of Appeals, the court held that testimony from witnesses that the driver of the car causing the accident fled the scene and then returned a short time later laughing before he then left again, was inadmissible in a claim for damages against that driver.
In the case Alban v. Fiels, the Albans were an elderly couple who were hit while driving in their truck by Mr. Fiels. The Albans' vehicle sustained more damages than Fiels, and they were immobilized. In fact, Mrs. Alban was stuck in the car until firefighters came to extricate her.
Mr. Fiels fled the scene but did so down a road that had no outlet. Knowing that the road the driver fled down had no outlet, a nearby witness waited for the driver to return. When he did, the witness noticed that the driver slowed down and then sped off, laughing.
At trial, the Albans wanted to bring in the testimony from the two witnesses who saw Mr. Fiels return to the scene, slow down, and the speed away while laughing. However, the trial court prohibited the Albans from introducing the evidence, holding that it was not relevant to the jury's ultimate inquiry as to the damages Mrs. Alban suffered.
After receiving a total of $10,000 in non-economic damages, the Albans sought a new trial based on the trial court's failure to admit the testimony of the witnesses. The appellate court, however, affirmed the lower court's ruling.
The appellate court held that, because Mrs. Alban's claim was for emotional distress, rather than a physical injury, the evidence would only be admissible if it was evidence of an independent tort. In Maryland, there is no independent tort for the Negligent Infliction of Emotional Distress. Such conduct only creates a claim as an element of damages.
Because the conduct of Mr. Fiels, while reprehensible, did not meet the elements of a separate tort, the evidence was not admissible. Thus, the court determined that the trial court's decision to keep out the evidence was a sound one, and it reaffirmed the lower court.
If you or a loved one has recently been involved in a serious Maryland accident, you should speak with a dedicated Maryland accident attorney about your case as soon as possible. Depending on the situation, you may be entitled to monetary compensation for your medical expenses and lost wages, as well as for any pain and suffering you sustained as a result of the accident. The Maryland personal injury law firm of Lebowitz & Mzhen Personal Injury Lawyers has years of experience litigating on behalf of injured Marylanders and knows what it takes to bring a winning case. Click here, or call 410-654-3600 today to schedule a free initial consultation with a dedicated Maryland accident attorney.
Recall in the Midwest Results in 1.8 Million Pounds of Ground Beef Being Recalled; Hummus Recalled as Well, Maryland Accident Law Blog, May 28, 2014.


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Home Home and leisure There's a new Zzzzzz… in Manchester's Corn Exchange
There's a new Zzzzzz… in Manchester's Corn Exchange
Following the success of its existing aparthotel on Princess Street in Manchester, stylish
aparthotel chain, Roomzzz, has opened its doors in the Manchester Corn Exchange.
The new development brings 114 luxury apartments to the Roomzzz Manchester Corn
Exchange, spacious suites that offer a personal touch for adventure, business and
celebration.
Unique to Roomzzz, each apartment has been individually designed to provide
a comfortable, well planned living area and features a fully equipped kitchen, ideal for longer stays and home chefs alike.
The opening marks the completion of a three-year renovation project for the
Corn Exchange, as the aparthotel joins an impressive offering of 14 restaurants which have
moved into the iconic building over the last few years, establishing it as one of the city's most sought-after dining and city break destinations.
Naveen Ahmed, CEO of Roomzzz, commented: "Building on the brand's success in the
thriving city of Manchester, Roomzzz is delighted to be launching its second Manchester
aparthotel in the iconic Corn Exchange – the excellent location and vibrant food and drink
offering make it the perfect venue for guests looking to enjoy the variety of restaurants,
shops and entertainment the city has to offer, as well as our welcoming and exceptional
"Thanks to its central location and great transport links, it caters for all guests, from city
explorers to corporate travellers, who can expect the home comforts and customer service
they're used to from the Roomzzz brand, allowing them to feel right at home in the heart of
Manchester. We look forward to welcoming guests."
The new Roomzzz aparthotel is characterised by its beautiful interior, with quality
furnishings, high ceilings, unique finishing touches and comfort in all shapes and sizes. For
this project, Roomzzz has partnered with artist, Katie Edwards, and commissioned one-of- a kind artwork pieces to complement the outstanding design of the interiors. The pieces
highlight, not only what the aparthotel has to offer, but also draw from the city's vibrant
culture and history, inspired by and featuring prominent landmarks.
The opening marks the eighth aparthotel in the Roomzzz portfolio, which has grown to
include aparthotels across the North of England in Leeds, Chester, Nottingham, Manchester
and Newcastle. Roomzzz has ambitious growth plans with further developments in the
pipeline for Edinburgh, Harrogate, Liverpool and York, as well as an extension to the existing Newcastle property and the brand's first aparthotel in the South of England opening in Stratford this summer.
To book,visit http://www.roomzzz.com/manchester-corn- exchange/ or call 020 3504 5555.
roomzzzz
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Accounting, Taxes, and Coaching for Dentists. Made Simple.
Happy Wednesday! I have a special treat for you today. Recently I had the honor of being interviewed by the incredible Dr. Paul Goodman and attorney Rob Montgomery on The Dental Amigos Podcast.
It's always fun being on the other side of the mic for a change, and Dr. Paul and Rob are really great guys doing amazing things in the dental industry.
Dr. Paul also runs the incredibly popular Dental Nachos online community and brand which I know many of you are a part of, and Rob is one of the most respected dental attorney's around.
They were kind of enough to give me permission to republish the episode here for the SYDP community, and I think you'll find a ton of actionable insights in our conversation.
Should you lease or purchase your office?
Without you, Ambitious Dentists, this show wouldn't exist.
If you enjoyed today's episode, please go here to give the show an honest rating and review on iTunes.
This allows me to evolve the show as it goes on, and also helps spread the word to other podcast listeners since iTunes promotes shows with active engagement.
Do you need more help tracking your practice's performance? DentistMetrics specializes in helping dentists worry less about the business side of dentistry by providing timely, action packed advice on how to improve their practice's results. Contact us at jonathan@dentistmetrics.com, click here, or visit us at any of the social sites we frequent to schedule a consultation!
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The ITF in Canada
Standing up for seafarers, fighting Flags of Convenience
News stories about us
What is an FoC
← MLC Week: Canada takes new wood to Ships of Shame
MLC Week: The disgraceful ABCs of abandonment →
MLC Week: 'There's a growing awareness that seafarers can speak out and claim their rights'
When ITF inspectors first got wind of news that shipowners, maritime unions and the International Labour Organization were planning to re-write and consolidate out-of-date seafarer labour conventions, most of us were skeptical.
The idea that a new and improved Maritime Labour Convention would be any more useful, powerful or popular than all the other earlier, dust-covered attempts was hard to accept. Many of us worried that a broad new international "seafarers bill of rights" would actually pull down higher standards that had been won elsewhere, and that shipowners would use the convention to argue they no longer needed to sign labour contracts with their workers.
In short, as much as we welcomed any kind of new tool in the battle to establish and enforce seafarers' labour rights, some of us were highly critical of the notion that this paper exercise would make any real difference in the lives of these workers — or advance the interests of the ITF's Flag of Convenience campaign in any real way.
The convention was completed and adopted two years ago, and some of that skepticism remains. That was apparent throughout the specialized training provided to us by the ILO and paid for by the ITF, and it's still apparent. Two years into the experiment, if you want to throw a grenade into a room full of otherwise peaceful inspectors, just ask whether they think the MLC is a good thing. A fight will undoubtedly break out between those skeptics and the inspectors and affiliates who think the convention is a good thing, that some progress has been made, and that as enforcement begins, some of the reviews just might turn out to be positive.
Today, in Part Three of our week-long look at the MLC, we speak with the ITF's Katie Higgenbottom, one of the people who took part in the negotiations that led to adoption of the convention. We asked Katie about how successful the rollout period has been from her perspective , and what work remains to be done. Our thanks to Katie for her time and her straightforward answers.
ITF in Canada: ITF London has been tracking implementation of the MLC. What do that stats on infractions look like?
Katie: I'd like to say that there's a measurable improvement in conditions for seafarers since the MLC came into force, but that's not the case, at least not yet. Looking at the statistics of ITF inspectors reports, the same old problems recur –non-payment of wages, breaches of employment agreements and substandard conditions on board. Panama, by far the biggest flag state and the second to ratify the MLC, has the largest number of problems. This would suggest that they still haven't got enough resources in place to deal with the number of vessels they have to look after. The main change is that they now reply to us saying the matter has been referred to their MLC department … although we have once managed to shame them into paying for the repatriation of crew abandoned in Rotterdam. That would have never happened pre-MLC.
Monday: The world adopts a Seafarers Bill of Rights
Tuesday: Canada's experience with substandard shipping
Wednesday: ITF's Katie Higginbottom and the global perspective
Thursday: The ABCs of abandonment (Part 1)
The human face of abandonment (Part 2)
Friday: First-ever MLC detention goes to Canada
Saturday: Closing thoughts for Your Saturday Listen
ITF in Canada: Tell us about the ITF inspectors' experience as the MLC kicked into force around the world. Challenges? Successes?
Katie: The positive story is that there's usually much more cooperation between ITF inspectors and agencies tasked with the enforcement of the convention – both port state control and flag state representatives. At all levels where people in authority are competent and well supported, they tend to be cooperative and able to act in a humane way. Problems arise where the people lack confidence and a proper structure; then they fall back on rules and hierarchies that are less constructive. ITF inspectors are recognised as the experts when it comes to wages and agreements and in most cases, the mutual benefits of working together are recognised. I think there's also a growing awareness amongst seafarers that they can speak out and claim their rights under the convention. It gives them, and ITF inspectors representing them, an internationally recognised legal basis for demanding decent conditions. On the less good side, there are still plenty of countries that have yet to ratify the convention and a number that have ratified, but that don't have the capacity to properly implement the requirements. There are still plenty of shipowners out there operating opportunistically with a hand-to-mouth approach to the finances; as soon as someone in the chain delays a payment, the whole operation falls apart and there's no safety net for the crew. The MLC is supposed to put these operations out of business, but it needs a consistently diligent approach to enforcement to work as it should.
ITF in Canada: Are there any misconceptions of interpretation of the convention?
Katie: Certain shipowners like to say that there's no need for an ITF agreement on board ships if they're MLC-certified. This is a kind of wilful misunderstanding of the purpose of the MLC as opposed to a collective bargaining agreement. It's typical of bosses who want to patronise their workers by saying you don't need to be organised because we're good employers. The ones that say this never are. It also shows a fundamental misunderstanding of the basis of the MLC — which comes from the International Labour Organisation, where governments, employers and workers (in this case seafarers) all have a voice. The convention is a compromise agreed between the three groups to safeguard the basic rights of seafarers, but in a way that's flexible enough for widespread ratification and that prevents unfair competition between shipowners. The ones that want to eliminate the ITF from the picture are the ones that see an opportunity to undercut their business rivals.
ITF in Canada: We know that the convention is amendable. Can you tell us about future amendment packages?
Katie: Amendments expanding the convention's coverage on financial security in the case of abandonment and claims for death and long-term disability were agreed in June 2014 and are expected to come into force in early 2017. These are a really big step forward. Flag states will have to have a system in place, either insurance or some sort of fund, that's directly accessible to seafarers if they're abandoned by a shipowner or company. If they're not repatriated, if the ship's not being provisioned or if the owner has severed ties and not paid wages for two months, the insurance will kick in. It will cover costs of repatriation, essential needs such as food, water, and fuel and up to four months of outstanding wages. It should make it much harder for rogue companies to walk away from their responsibilities and will force flag states to be more vigilant about who they accept on their registers. The new measures regarding shipowner liability in the treatment of contractual claims aim to eliminate pressure put on seafarers to accept less than their due. They should alleviate hardship by requiring interim payments where a process of assessment is necessary. As with the abandonment requirements, seafarers (or their families) will be able make direct claims and ships will have to make all the contact details readily available on board.
ITF in Canada: How does it feel to watch the application of the convention develop?
Katie: It's fascinating to see how a bureaucratic process arguing over little words (like 'and' versus 'or') in a fancy meeting room in Geneva plays out in practice. At the beginning, there was a sense of shared values. The challenge is to pass that on to everyone involved in the industry and make sure the idealism doesn't get diluted, or misinterpreted by lawyers. The key is for seafarers themselves to become expert in their own entitlements and claim them.
Katie Higginbottom is Project & Campaigns Leader in the ITF's Maritime Operations department. She participated in the negotiations that resulted in the adoption of the MLC in 2006 and was responsible for the MLC training of the ITF inspectorate in conjunction with the ILO's training centre in Turin.
Tomorrow: Crew in peril when shipowners abandon all responsibiity
We encourage dialogue Cancel reply
The ITF
49-60 Borough Road, London SE1 1DR, UK +44 20 7403 2733
www.itfglobal.org
Saluting five years of the MLC: a tough, enforceable Seafarers Bill of Rights
Day of the Seafarer? Industry needs to put respect on the menu
FoCs: It's shamefully convenient when there's an oil spill and a flag is used for legal cover
The bitter truth from Liverpool
From our docks to their decks: Extending a holiday hand
Panama-registered FoC ro-ro MV Goodwood in Port of Halifax, Canada, during cargo operations.
ITF inspector Karl Risser (centre) with jubilant crew of MV Goodwood in Port of Halifax, Canada.
The Danish-owned FoC bulk carrier Nord Mumbai. Photograph by ITF Great Lakes/St. Lawrence inspector Vince Giannopoulos.
You never get dealt a good hand when the deck is Flag of Convenience.
Gerard Bradbury, our Atlantic region inspector, and partner Kelly, at a solidarity rally for Panama canal workers in 2015.
ITF Inspector Karl Risser volunteering at the Halifax Mission to Seafarers.
Karl Risser, retired inspector Gerard Bradbury at Saint John, New Brunswick seafarers center receiving letters for seafarers from school kids.
Atlantic Canada ITF Inspector Karl Risser on the job and meeting crew onboard.
Canadian ITF Inspector Gerard Bradbury retirement event. Bruins vs. Leafs at the Air Canada Center, Toronto. There has never been a better Canadian team. But we will recover losing Brother Bradbury. It won't be easy, but we will try because he insists.
Panamanian maritime unions gathering support from the ILWU, Germany's Ver.di and the ITF in their struggle for Panama Canal workers collective bargaining. On the left Torben Seebold and Ray Familathe.
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You are at:Home » News » Merj Enters CBD Arena, Bringing Large-Scale Industrial Hemp Cultivation and Processing to Northeast Tennessee
Merj Enters CBD Arena, Bringing Large-Scale Industrial Hemp Cultivation and Processing to Northeast Tennessee
By Assistant on	 May 21, 2019 News
A transformation is taking place in northeast Tennessee, one that could propel the region to being recognized as the hub of hemp production for the Southeast and beyond.
For many years, Merj family farmland in Sullivan County supported stocks of cattle and crops of corn and alfalfa. Now, following passage of the 2018 Farm Bill, which provided for industrial hemp cultivation, the first of many Cannabis sativa seedlings are going into the ground.
Merj is a vertically integrated company focused on the production of high-quality, full-spectrum cannabinoid (commonly known as CBD) products derived from hemp. Established in 2018, the Bristol, Tenn.-based company taking advantage of surging interest in the plant, which has attracted the attention of medical researchers and entrepreneurs for its potential range of therapeutic effects.
Hemp is also under the eye of investors, with deals valued in the hundreds of millions taking place on a near-weekly basis. Major financial institutions predict the market to grow exponentially as premier companies such as CVS, Walgreens, PepsiCo, Walmart and Target are either already stocking CBD-based items on the shelf or exploring the integration of CBD into product lines.
"The 2018 Farm Bill triggered a fundamental shift in the way America does business, on the kind of scale you see maybe once in a generation," said Russell Leonard, founder of Merj. "This is a very exciting time, one that's bringing a sense of hope to people who are looking for products that can help soothe and balance their lives. It's also creating a new sense of purpose for those in the agriculture industry, and providing our region a unique opportunity to play a central role in this emerging market."
Merj is one of the larger hemp growers in Tennessee, with resources that include nearly 200 acres of licensed grow space in Sullivan County — as well as a new, 18,000 square-foot, state-of-the-art processing facility designed to process biomass, extract CBD compounds, and test the finished product for purity and potency.
Hemp contains a complex mix of compounds, including phytocannabinoids and terpenes, that seem to interact with the human nervous system on the molecular level. In particular, medical researchers are studying how these compounds influence the endocannabinoid system, a network of receptors in the body that help regulate pain, inflammation, mood, mobility and more.
Hemp lacks the psychoactive compound known as THC that produces a sense of euphoria. Because industrial hemp contains less than .3 percent THC, it is legal for sale and use throughout the U.S. and dozens of countries worldwide.
"It's not yet fully known how the dozens and dozens of compounds found in hemp interact with our nervous systems, so we've invested in extraction processes that help preserve full-spectrum integrity of our products," Leonard said. "We want to make sure that all the goodness in these mountains goes into what we provide our customers."
In addition to processing its own biomass, Merj plans to offer extraction and testing services for other industrial hemp farmers.
"We feel very fortunate to have decades of farming knowledge and business ingenuity backing this operation," Leonard said. "We're well positioned to enter and compete in this market, which I believe will have transformational effects on our region's identity and success."


Christmas commuters, shoppers and party-goers are being encouraged to plan their travel over the festive period.
There will be some changes to services on several days and a summary is now available to help people with their travel plans.
The 'Christmas services' travel advice page is now online and will be available from any one of Transport for Greater Manchester (TfGM) many Travelshops – located at bus stations and interchanges across the region – from next week.
The advice has been developed following meetings between TfGM and operators to help keep people moving during the busy Christmas and New Year period.
With services expected to be busy throughout December, the Mayor of Greater Manchester, Andy Burnham asked TfGM to work with KeolisAmey Metrolink to increase capacity on the network.
Services between Piccadilly and Bury and Piccadilly and Altrincham will operate as double trams in the evenings until last service Monday to Saturday, while extra trams will be used to make 'doubles' run across the network on Sundays, creating space for thousands of extra journeys every day.
Under the TravelSafe Partnership, TfGM has been working with Greater Manchester Police (GMP), British Transport Police (BTP) and operators to develop plans to keep people safe. Additional staff and officers will be out and about on the transport networks at key times, providing a visible and reassuring presence and deterring and reducing incidents of crime and ASB.
Sean Dyball, Head of Customer Engagement, said: "Over the Christmas period it's always useful to plan ahead before making your journey.
"Public transport is likely to be busy throughout December, so please give yourself plenty of time to get where you need to go, know your tram, train or bus times and, where possible, don't rely on the last service to get home.
"We've been working with closely operators, local councils and the police to ensure we keep people moving and safe.
"As with previous years, we will be providing extra capacity wherever possible and will have staff at key locations who will be on hand to help our customers."


One of the key messages of robotics and automation is that these systems perform the tasks that are too "dirty, dull, or dangerous" for humans. Nowhere is that more evident than in infrastructure inspection space, which is increasingly using robotics and unmanned aerial vehicles to find flaws in places where humans risk hurting themselves. Investors are starting to take note of these technologies.