text:
A grim search for more fire victims in Northern California
Posted 7:18 am, November 12, 2018, by Associated Press, Updated at 09:59AM, November 12, 2018
PARADISE, California — As wildfires raged at both ends of California, officials released another grim statistic: Six more dead in a swath of Northern California wiped out by fire, raising the death toll there to 29. It matched California's record for deaths in a single fire and brought the statewide total to 31 as authorities stepped up searches for bodies and missing people.
Another 228 remain unaccounted for. Two people were killed in a wildfire in Southern California.
Ten search teams were working in Paradise — a town of 27,000 that was largely incinerated last week — and in surrounding communities in the Sierra Nevada foothills. Authorities called in a DNA lab and teams of anthropologists to help identify victims.
Statewide, 150,000 remained displaced as more than 8,000 fire crews battled wildfires that have scorched 400 square miles (1,040 square kilometers), with out-of-state crews continuing to arrive. Whipping winds and tinder-dry conditions threaten more areas through the rest of the week, fire officials warned.
"This is truly a tragedy that all Californians can understand and respond to," Gov. Jerry Brown said at a press briefing. "It's a time to pull together and work through these tragedies."
Brown, who has declared a state emergency, said California is requesting aid from the Trump administration. President Donald Trump has blamed "poor" forest management for the fires. Brown said federal and state governments must do more forest management but that climate change is the greater source of the problem.
"And those who deny that are definitely contributing to the tragedies that we're now witnessing, and will continue to witness in the coming years," he said.
Drought and warmer weather attributed to climate change, and the building of homes deeper into forests have led to longer and more destructive wildfire seasons in California. While California officially emerged from a five-year drought last year, much of the northern two-thirds of the state is abnormally dry.
Firefighters battling fire with shovels and bulldozers, flame retardant and hoses expected wind gusts up to 40 mph (64 kph) overnight Sunday.
In Southern California , firefighters beat back a new round of winds Sunday and the fire's growth and destruction are believed to have been largely stopped. Malibu celebrities and mobile-home dwellers in nearby mountains were slowly learning whether their homes had been spared or reduced to ash. Two people were killed and the fire had destroyed nearly 180 structures.
Los Angeles County Fire Chief Daryl Osby stressed there were numerous hotspots and plenty of fuel that had not yet burned, but at sunset he said there had been huge successes despite "a very challenging day."
Celebrities whose coastal homes were damaged or destroyed in a Southern California wildfire or were forced to flee from the flames expressed sympathy and solidarity with less-famous people hurt worse by the state's deadly blazes, and gave their gratitude to firefighters who kept them safe. Actor Gerard Butler said on Instagram that his Malibu home was "half-gone," adding he was "inspired as ever by the courage, spirit and sacrifice of firefighters."
Flames also besieged Thousand Oaks, the Southern California city in mourning over the massacre of 12 people in a shooting rampage at a country music bar on Wednesday night.
In Northern California, where more than 6,700 buildings have been destroyed, the scope of the devastation was beginning to set in even as the blaze raged on.
Butte County Sheriff Kory Honea said the county consulted teams of anthropologists because, in some cases, investigators have been able to recover only bones and bone fragments.
In some neighborhoods "it's very difficult to determine whether or not there may be human remains there," Honea said.
Public safety officials toured the Paradise area to begin discussing the recovery process. Much of what makes the city function is gone.
"Paradise was literally wiped off the map," said Tim Aboudara, a representative for International Association of Fire Fighters. He said at least 36 firefighters lost their own homes, most in the Paradise area.
"Anytime you're a firefighter and your town burns down, there's a lot of feelings and a lot of guilt and a lot of concern about both what happened and what the future looks like," he said. "Every story that we've heard coming through has been that way, like 'I wish I could have done more, What's going to happen to our community, Where are my kids going to go to school?'"
Others continued the desperate search for friends or relatives, calling evacuation centers, hospitals, police and the coroner's office.
Sol Bechtold drove from shelter to shelter looking for his mother, Joanne Caddy, a 75-year-old widow whose house burned down along with the rest of her neighborhood in Magalia, just north of Paradise. She lived alone and did not drive.
As he drove through the smoke and haze to yet another shelter, he said, "I'm also under a dark emotional cloud. Your mother's somewhere and you don't know where she's at. You don't know if she's safe."
The 29 dead in Northern California matched the deadliest single fire on record, a 1933 blaze in Griffith Park in Los Angeles, though a series of wildfires in Northern California wine country last fall killed 44 people and destroyed more than 5,000 homes.
Firefighters made progress against the blaze, holding containment at 25 percent on Sunday, but they were bracing for gusty winds predicted into Monday morning that could spark "explosive fire behavior," California Department of Forestry and Fire Protection spokesman Bill Murphy said.
Fire officials are bracing for potentially more fires in Southern California's inland region as high winds and critically dry conditions were expected to persist into next week.
"We are really just in the middle of this protracted weather event, this fire siege," Cal Fire Chief Ken Pimlott said.
He said officials were moving resources and preparing for "the next set of fires" as winds are expected to pick up. The chief warned that fire conditions will continue until the parched state sees rain.
"We are in this for the long haul," Pimlott said.
Death toll rises in California wildfire, matching deadliest
Harrowing escapes, heartbreaking loss in Northern California
Rescues, not firefight prove emotional for firefighters
Topics: California wildfires
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Nicole Kidman and Keith Urban donate $500,000 to help fight bushfires in Australia
California firefighters heading to Australia to battle deadly brushfires
L.A. wildfire reaches homes
John Cena announces $500K donation to California fires first responders
Raging wildfires trap 4,000 at Australian town's waterfront
'We had to leave': Fast-moving wildfire drives thousands from their homes in California
Two people killed in Southern California wildfires as thousands of evacuees return home, officials say
The Irwin family has saved over 90,000 animals injured in the Australia wildfires
LeBron James and his family forced from home due to California fires
Rain forecast in Australia; country pledges 'whatever it takes' to help recovery


text:
"The Startling Work of God"
(Preached 29/05/2022 by Josh Bartlett)
http://grangebaptist.org.au/wp-content/uploads/2022/06/2022-05-29-Acts-9-1-31.mp3
ACTS 8:26-40
"The Enlightening Work of God"
http://grangebaptist.org.au/wp-content/uploads/2022/06/2022-05-22-Acts-8-26-40.mp3
"The Cost-Free Work of God"
http://grangebaptist.org.au/wp-content/uploads/2022/05/2022-05-15-Acts-8-4-25-b.mp3
ACTS 6:8-8:3
"The Promised Work of God"
http://grangebaptist.org.au/wp-content/uploads/2022/05/2022-05-08-Acts-6-8-8-3.mp3
1 JOHN 4:7-12
"The Love of God at the Cross of Jesus and in the Local Church"
http://grangebaptist.org.au/wp-content/uploads/2022/04/2022-04-15-1-John-4-7-12-Good-Friday.mp3
OBADIAH 19-21
"The Kingdom Shall be the LORD's, Edom"
(Preached 01/08/2021 by Ben Cochrane) *RECORDED SERMON FOR LOCKDOWN
http://grangebaptist.org.au/wp-content/uploads/2021/07/2021-08-01-Obadiah-19-21.mp3
"The Day of the LORD is Near, Edom"
OBADIAH 1-14
"You're Coming Down, Edom"
http://grangebaptist.org.au/wp-content/uploads/2021/07/2021-07-18-Obadiah-1-14.mp3
"Every Christian's Priority"
http://grangebaptist.org.au/wp-content/uploads/2020/11/Luke-1038-42.m4a
"But I Say 'Love Your Enemies'"
(Preached 15/03/2020 by Greg Beaumont)
http://grangebaptist.org.au/wp-content/uploads/2020/03/2020-03-16-Matthew-5-43-48.mp3
"Dead to Sin, Alive to God"
(Preached 01/03/2020 by Heinz Engela)
http://grangebaptist.org.au/wp-content/uploads/2020/03/2020-03-01Romans-6-1-7.mp3
"What we Need to Know to Flee Sexual Sin"
(Preached 16/02/2020 by Joel Marsman)
http://grangebaptist.org.au/wp-content/uploads/2020/02/2020-02-16-1-Corinthians-6-12-20.mp3
"God Comforts us to Make us Comforters"
http://grangebaptist.org.au/wp-content/uploads/2020/01/2020-01-19-2-Corinthians-1.mp3
"Jesus' Mission Continues: Opposition"
http://grangebaptist.org.au/wp-content/uploads/2019/11/2019-11-17-Acts-4.mp3
"Jesus' Mission Continues: Healing"
http://grangebaptist.org.au/wp-content/uploads/2019/11/2019-11-10-Acts-2-42-4-4.mp3
"Jesus' Mission Continues: Pentecost"
"A Rejected & Honoured Stone"
http://grangebaptist.org.au/wp-content/uploads/2019/11/2019-11-17-Psalm-118.mp3
GENESIS 11:1-9
http://grangebaptist.org.au/wp-content/uploads/2019/11/2019-11-03-Genesis-11-1-9.mp3
"I Myself will Shepherd my People"
http://grangebaptist.org.au/wp-content/uploads/2019/10/2019-10-20-Ezekiel-34-11-16.mp3
"I Will Build My Church"
http://grangebaptist.org.au/wp-content/uploads/2019/09/2019-09-15-Matthew-16-13-23-GBC-100-Years.mp3
"Justified & Living by Faith"
http://grangebaptist.org.au/wp-content/uploads/2019/09/2019-09-01-Galatians-2-15-21.mp3
http://grangebaptist.org.au/wp-content/uploads/2019/08/2019-08-18-Psalm-48.mp3
"The Day of the Lord is Near"
(Preached 02/06/2019 by Dave Walter)
http://grangebaptist.org.au/wp-content/uploads/2019/06/2019-06-02-Joel-1.mp3
"The LORD: A Roaring Refuge"
"Yes, Lord God Almighty, True & Just are Your Judgments"
http://grangebaptist.org.au/wp-content/uploads/2019/05/2019-05-19-Revelation-16-1-7.mp3
"Just Jesus or a Colossal Christ?"
http://grangebaptist.org.au/wp-content/uploads/2019/04/2019-04-21-Col-1-15-20.mp3
ROMANS 16:25-27
"Glory to God!—He's Establishing People Globally by His Gospel Through Jesus Christ"
http://grangebaptist.org.au/wp-content/uploads/2019/03/2019-03-17-Romans-16-25-27.mp3
"The Christian and the Law of God"
http://grangebaptist.org.au/wp-content/uploads/2019/03/2019-03-03-Romans-13-8-14.mp3
"The Christian and the Law of the Land"
http://grangebaptist.org.au/wp-content/uploads/2019/02/2019-02-24-Romans-13-1-7.mp3
"He Remains Faithful, for He Cannot Disown Himself"
http://grangebaptist.org.au/wp-content/uploads/2019/02/2019-02-17-2-Timothy-2-11-13.mp3
"This Life I Live is Not my Own"
ZEPHANIAH 3:9-20
http://grangebaptist.org.au/wp-content/uploads/2018/11/2018-11-04-Zephaniah-3-9-20.mp3
ZEPHANIAH 2:4-3:8
"A Workshop"
(Workshop held 31/10/2018 by Dave Walter)
http://grangebaptist.org.au/wp-content/uploads/2018/11/2018-10-31-Zephaniah-2-4-3-8-Workshop.mp3
http://grangebaptist.org.au/wp-content/uploads/2018/10/2018-10-28-Zephaniah-1-1-2-3.mp3
GENESIS 3:20-4:7 & SELECTED SCRIPTURES
"Humanity—Divine or Beast?"
http://grangebaptist.org.au/wp-content/uploads/2018/10/2018-10-21-Humanity—Divine-or-Beast.mp3
EZEKIEL 37:1-14
"The Valley of Dry Bones"
http://grangebaptist.org.au/wp-content/uploads/2018/08/2018-08-19-Ezekiel-37-1-14.mp3
DEUTERONOMY 17:14-20
"God's Criteria for the King"
http://grangebaptist.org.au/wp-content/uploads/2018/07/2018-07-15-Deuteronomy-17-14-20.mp3
"The Church & Her Joy"
http://grangebaptist.org.au/wp-content/uploads/2017/05/2017-05-28-John-16-16-33.mp3
MARRIAGE IN BIBLICAL PROPORTIONS
"A Biblical & Practical Theology of Marriage"
http://grangebaptist.org.au/wp-content/uploads/2017/05/2017-05-21-Marriage-in-Biblical-Proportions.mp3
"A Skeptic Encounters Jesus"
http://grangebaptist.org.au/wp-content/uploads/2017/04/xxxxx.mp3
"A Religious Expert Encounters Jesus"
(Preached 19/03/2017 by David Walter)
JONAH 3-4
"Jonah Part II"
http://grangebaptist.org.au/wp-content/uploads/2016/11/2016-11-20-Jonah-3-4.mp3
"Jonah Part I"
2 CHRONICLES 18-19
http://grangebaptist.org.au/wp-content/uploads/2016/06/2016-06-05-2-Chronicles-18-19.mp3
"Honouring God"
http://grangebaptist.org.au/wp-content/uploads/2016/06/2016-05-29-2-Chronicles-17.mp3
TOPICAL SERMON
Be Thankful – Sermon Notes
http://grangebaptist.org.au/wp-content/uploads/2016/03/2016-03-06-TOPICAL-Thankfulness.mp3
LUKE 18:9-14
"Goodness or Grace?"
http://grangebaptist.org.au/wp-content/uploads/2016/03/2016-02-28-Luke-18-9-14.mp3
"Fallen Short of the Glory of God"
http://grangebaptist.org.au/wp-content/uploads/2016/02/2016-02-21-Romans-3-23-24.mp3
"Reconciled or Alienated"
http://grangebaptist.org.au/wp-content/uploads/2016/02/2016-02-14-Colossians-1-21-23.mp3
"The Parable of the Rich Fool"
http://grangebaptist.org.au/wp-content/uploads/2016/02/2016-02-07-Luke-12-13-21.mp3
"Rise and Go; Your Faith Has Made You Well"
(Preached 22/11/2015 by Michael Howell)
"Conduct Yourselves in a Manner Worthy of the Gospel"
(Preached 08/11/2015 by Murray Lean)
http://grangebaptist.org.au/wp-content/uploads/2015/11/2015-11-08-Philippians-1-12-30.mp3
EXODUS 14:13-14
"The LORD Will Fight For You"
(Preached 01/11/2015 by Andrew Lawton)
http://grangebaptist.org.au/wp-content/uploads/2015/05/2015-05-03-1-Kings-21-.mp3
"A Sickening Crime & A Staggering Mercy"
"Love the LORD Your God"
(Preached 15/03/2015 by Mike Gilbart-Smith)
http://grangebaptist.org.au/wp-content/uploads/2015/03/2015-03-15-Deut-6-Love-the-LORD-Your-God.mp3
"The Power of the Word"
The Power of the Word – Sermon Notes
http://grangebaptist.org.au/wp-content/uploads/2015/02/2015-02-08-The-Power-of-the-Word.mp3

redpajama_set_name: RedPajamaCommonCrawl


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Roman Kapitonenko –en ucraniano, Роман Капітоненко– (Shostka, URSS, 21 de enero de 1981) es un deportista ucraniano que compitió en boxeo.

Ganó una medalla de plata en el Campeonato Mundial de Boxeo Aficionado de 2009 y dos medallas de bronce en el Campeonato Europeo de Boxeo Aficionado, en los años 2008 y 2010.

Palmarés internacional

Referencias

Boxeadores de Ucrania
Ucranianos del siglo XXI

redpajama_set_name: RedPajamaWikipedia


text:
The Council Episodes 1-3 Review – Tall Tales
August 8, 2018 August 9, 2018 Matt S.
[Disclosure: A review code was provided for the contents of this article]
Whilst I understand how the various Telltale series became popular thanks to their unique art style and use of very popular IP (like The Walking Dead and Game of Thrones, among others) but personally I never considered them to be games, as such. Interactive experiences, yes, but more the kind of thing that would work well on mobile devices rather than consoles or gaming PC's. Whether I'm right about that or not doesn't matter, but it does serve to explain why I was excited about the idea of The Council as soon as I heard about it.
Essentially a mix between the purely narrative adventures that Telltale make and a more traditional point and click adventure, The Council places us in the shoes of deadpan protagonist Louis de Richet. Following a rather dramatic opening in which we learn that Louis and his mother (Sarah de Richet) are in a spot of bother, we find ourselves transported back in time to an opulent mansion owned by a mysterious benefactor, with Sarah missing and Louis rather confused about who or what he's going to need to deal with.
There are three episodes available now (with two more to come) so it seems the ideal time to dive into Louis' adventure, although clearly the relevance of this review will diminish once the fourth and fifth episodes are released. What I don't expect to change materially are my comments on how the game looks, sounds and plays, because those things have been fairly consistent across the initial three episodes, except where I'll specifically call out features to the contrary within the body of the review.
My first impression of The Council wasn't brilliant, if I'm honest, mostly because it uses an ambitious "ultra realistic" graphic style that it can't quite pull off. Faces and hair, for example, look pretty gnarled and crazy, especially in the case of some of the older characters (including Sarah) who look as if they are borderline members of some kind of undead cult. It might sound an odd thing to call out, but the inclusion of moving eyeballs is particularly disconcerting in some characters, since they seem to be animated in such a way that makes them appear absolutely terrifying.
I also found that the voice acting was a little bit off to begin with, but I quickly realised that it's only Louis who is particularly poorly handled. Both his script and the actual delivery of his lines seem a bit offbeat – I kind of get that during the opening episode at least, he's still new to the secret cabal of world leaders, politicians and luminaries into which he is thrown, but still, he comes across like a clueless muppet a lot of the time. As in many narrative games, The Council has characters like George Washington indirectly praising the player (through Louise as their avatar) for doing entirely mundane things like interrupting a conversation with some inane comment.
Focusing back on what's good – many of those world leaders are well delivered and interesting to engage with. Washington is one of the best, but the rest of the cast is also interesting and includes the likes of Napoleon Bonaparte as well as a number of fictional or embellished individuals. It's worth noting that the cast is a complete whitewash (which is undoubtedly in the interest of historical accuracy, however given that the subject matter is rather fantastical, that's tenuous) but there are several female characters that are generally interesting and well represented. Arguably the most (or at least second most) powerful character in the game is Sarah, who appears to be by far the most competent in several areas.
On that note, the game itself is really a classic "fish out of water" story in which Louis must familiarise himself with an uncertain environment in which he is compelled to remain because his mother has gone missing. We learn quickly that the man who brought Louis, his mother and the illustrious cast of characters to his private island is rather elusive and enigmatic, so much of the game is spent uncovering secrets through conversation, exploration and basic puzzles. What excited me about The Council when I first saw it revealed was the promise that choices would have real consequences and that the game truly would feature several paths.
In addition to a branching story (which I think The Council handles fairly well and certainly much better than any Telltale game) the game features an RPG-like skill tree. The overwhelming majority of the skills on offer relate to dialogue choices and in turn, how easy it is to influence characters. Everyone has weaknesses and resistances when it comes to what affects them and understanding them (which is kind of handled for you by an in game journal) is important because Louis is such a dullard that almost all complex conversations sap his energy forcing him to eat tons of, erm, Royal Jelly. Yes, from bees. Whatever.
In practice, what this means is that every conversation will feature one or two opportunities to use a skill in order to drive a narrative outcome. For example if Louis is fluent in etiquette, he might be able to make a joke or observation about how another guest has no place at such a fine table. Similarly, he might be able to comment on science or politics if he has the right skills, whilst those he doesn't have will appear, but won't be available. Many of these options result in the same outcome albeit with different dialogue, but occasionally the game triggers a confrontation, in which Louis must avoid entirely wrong answers in order to achieve a good outcome.
Louis's skills can be upgraded periodically by spending XP earned over the previous chapter, as well as by choosing to read books that he finds around the mansion, which usually convey an automatic bonus to the related skill, albeit not until the end of the next chapter. I mentioned earlier that Louis can use Royal Jelly to replenish his energy, but he also has access to a few other elixers that allow him to use skills for free, or to remove the negative effects that certain encounters can place on him.
Ultimately, you'll be playing The Council for the story, which personally I quite enjoyed. In the first episode, Louis is an unlikable, uninteresting individual who is carried by much better characters like Washington and Cardinal Giuseppe Piaggio, who turn in an excellent shift from both a voice and narrative perspective. By the second chapter, the game offers more interesting locations to visit and perhaps a bit more of an actual game – the first is restricted mostly to set pieces that offer little room to explore. The third episode is the best and whilst I don't want to say too much about it, it takes the mantel of being the midpoint of the series and runs with it, which certainly leaves me feeling positive for the remainder of the content.
Considering that the story started out interesting and has only become more compelling and because the dialogue is almost always interesting, I'm still enjoying The Council. I like that there are both pivotal conversations that can really change things, as well as the skill based outcomes that present merely a veneer of choice in some conversations, which has always been lacking in other narrative adventures. The Council also has outright missable scenes, should you fail to explore diligently enough, so it makes a good case for replayability in several areas. Louis himself is a bit of a sop, but by episode three both his character (and the actor that plays him) appear to have gotten into a decent stride.
Given that you can buy the first episode in isolation to get a taster of what The Council is all about, I think you should:
Posted in PC, PlayStation, PS4, Reviews, Xbox, Xbox One, Xbox ScorpioTagged Adventure Game, Big Bad Wolf, Focus Home Interactive, Mystery Game, Review, The Council
This Remote May Have Turned Socketeer, but it Still Can't Shoot
Rockstar Games Will Show Red Dead Redemption 2 Gameplay On August 9th


text:
Q: How to stop particle flipping when I move camera view by using C# scripting in Unity I am going to make cloud by using Unity particle.
But particles are flipped 180 degree when I move camera view.
I want to prevent this act by using C# scripting.
(I already prevent this by checking "Allow Roll", But want to prevent this using C# scripting, with uncheck "Allow Roll")
enter image description here

redpajama_set_name: RedPajamaStackExchange


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Following is an interview conducted with the author. Learn more and to purchase the book.
L.K.: You are to be congratulated for self-publishing this work. Because of the subject matter and your treatment of it, I wonder if a mainstream book publisher would have produced it. Tell us how this book came to be.
J.B.: There is no stigma anymore in the self-publishing realm. I understand that established authors are choosing this route more often. I did attempt to get an agent for representation by sending a query to about a dozen of them, but it became apparent that to succeed in the traditional publishing approach, it would take a very long time with no apparent benefits while running the risk of losing the literary and educational value of this book.
L.K.: A disclaimer in the book states that while the story is based on actual events, any similarity to real persons is coincidental. How much of your book is historical and how much is autobiographical? Where does fact end and fiction begin?
J.B.: The events and historical aspects of the book are all factual. The fictional aspects come from taking poetic license with the creation and portrayal of characters and plots, and the timing of events and scenes.
L.K.: This story, which has been enthusiastically reviewed by scores of non-Armenian readers, appeals to more than one demographic. You add special touches to the story that will resonate with Armenian readers in particular, such as your decision to name the villains Sevantz and Aghvesian, or to create characters with evocative Turkish names such as Soluk Kurt, Inonu, Turgut and Erdogan. Please talk about this.
J.B.: To date, more than 95 percent of the readership has been non-Armenian. There is unanimity on the quality of work and an overwhelmingly positive reaction to the writing, the story and its literary value. Some samples of the feedback and sentiments can be seen in the reviews placed on Amazon, with a total of 50 reviews thus far with a top rating of five stars.
L.K.: While telling your tale, life in Jerusalem comes alive, as does the issue with which many lay communities struggle: corrupt authority figures and clergy. What purpose do you think your treatment of this taboo topic could serve?
J.B.: My hope is that it leads to awareness and more importantly to the protection of our national treasures and heritage.
L.K.: Two powerful aspects of this book were your ability to communicate how goodness and humility can inspire hostility and envy in others, and the resulting trauma that persists within the Armenians. The central character is scapegoated by transgressors who project sins onto him. Please talk about the importance these concepts hold for you, for the Armenian nation and for humanity.
J.B.: Unfortunately this mindset is not limited to one period of time, one region of the world, one country, or one people. Humanity grapples with these issues daily and never seems to have the collective courage to overcome these destructive attitudes. Armenians have been victims of inhumane treatment with devastating results for far too long. How to break this cycle is the real challenge.
L.K.: Do you think the Republic of Turkey has the same mindset today that it did during the years the action in this book takes place? Is your story just an artifact, or could it also be a cautionary tale?
J.B.: I believe my story is not an artifact. The mindset today is no different than during the years the action in this book takes place.
L.K.: What void do you think exists in literature on Armenian subjects?
J.B.: I would hope that we as a community add to our armamentarium books such as Gray Wolves and White Doves and other tools of "entertainment/education" and place these books on the required reading lists for students and transform the books into feature films to ensure they become yet another piece of the fabric and tapestry that we need to weave to tell the world the full story and tell it in a manner that is not offensive or overbearing. You can see from the reviews, and many other readers have told me in person, that this book has taught them about the Middle East, Armenia, the Armenians, and the Genocide. In fact, reading the novel has inspired many to research these issues on their own.
L.K.: How do you keep up with current Armenian events?
J.B.: I am an avid reader of all Armenian newspapers and journals. I currently serve on the Board of Directors of the Armenian Center at Columbia University.
L.K.: Will readers learn what happens to Jonah and the abducted child held by the Turkish couple? Where can readers hear you speak about your book?
J.B.: The readers are asking me the same questions. All I can say for now is that I will focus on ensuring the widest possible audience for this book and that it becomes a film.
I have had visits with book clubs in NY, NJ, CT, and MA and attended special events held for the book in the Northeast. On Wednesday evening, Sep. 28th, at 7:00pm, the St. Gregory Men's Club will sponsor my presentation and book signing at the St. Gregory the Enlightener Armenian Church's Atrium, 1131 North St, White Plains, NY, 10605. Interested individuals must RSVP in advance to Chris Bonfiglio at (914) 707-2152, or chrisbonfiglio@verizon.net. Admission is $10 and light refreshments will be served.
Interviewer Lucine Kasbarian is a book publicist on leave, and the author of The Greedy Sparrow: An Armenian Tale.


In 2012 xotox celebrated the 10th anniversary of his massive clubhit "Eisenkiller" with a special EP.
This year it is the 15th anniversary of Andreas Davids´ solo-project and his musicianship that serves the international industrial-scene since 1998 with clubhits and floorfillers at regular intervals and many of them are real classics by now.
One of the many highlights surely was to reach number 1 in the german alternative charts (DAC) – this has been managed by an industrial-act for the very first time.
The follow-up releases also reached top positions in the DAC and the lastly released album "in den zehn morgen" again reached number 1 and held on to the top spot for 6 weeks in a row .
Besides his own releases xotox also attracted attention with his remix-works and the release of a split-cd in co-operation with the italian label Rustblade, even an exclusive North-American Album has been released in co-operation with the US-Label Vendetta.
In addition to this xotox also convinces with numerous live-shows that already have been happen all over Europe and almost every big national und international festival has been played. All live-shows have been happened because of the co-operation with the booking-agency Protain.
This anniversary year will be crowned by the release of the new album which will be released in two different versions, standard-jewelcase and limited digipack-edition inclusive bonus-cd.
Fans can be able to look forward to a consistant further development and new sounds in the typical xotox-style.
Xotox is hyperactive since 1998 and still not tired... 15 years are not enough !


Recently, we have introduced a new 'Playtime Scheme' at lunchtime, with the view of giving our children more opportunities to play games and activities whilst having fun with their friends!
After an interactive assembly detailing the system and how it works, the pupils have been playing and trying out all the new activities including a target throw, football target shooting, Jamanga, snakes and ladders, basketball, skipping and lots more.
It has been very successful so far, seeing all the children play with big smiles on their faces. A big 'thank you' needs to go to Year 6, who are helping to set up the games and supervise the children to ensure they are safe and having fun.


text:
Rózsakeresztes manifesztumok alatt eredendően az 1614 és 1617 között megjelent három rózsakeresztes kiáltványt és későbbi teljes-szövegű fordításait értjük.

Eredetük
1614 és 1617 között három, szerzői megjelölés nélküli kiáltvány (manifesztum) jelent meg, először Németországban, majd később szerte Európában. Ezek a Fama Fraternitatis Roseae Crucis (Híradás a rózsakeresztes testvériségről, 1614), a Confessio Fraternitatis Roseae Crucis (Rózsakeresztes hitvallás, 1615) és a Chymische Hochzeit Christiani Rosencreutz Anno 1459 (Christian Rosenkreutz Kémiai Menyegzője, 1617) voltak.

A Fama Fraternitatis egy német misztikus filozófus történetét mutatja be, akire "C.R.C. atyaként", illetve "C.R. testvérként" hivatkozik a szöveg és csak később a harmadik manifesztumban azonosítják Christian Rosenkreutz-cal. 1378 jelenik meg "Christian atyánk" születési éveként és azt állítja az írás, hogy 106 évet élt. Miután különböző - vélhetően a szúfizmushoz köthető - közel-keleti mestertől elsajátította ezoterikus tudását, azt nem sikerült Európa prominens tudósai és filozófusai között elterjesztenie. Ehelyett barátok, tanítványok szűk körét gyűjtötte össze és megalapította a Rózsakeresztes rendet, mely következtetés útján kb. 1407 körül történhetett meg.

A Rend állítása szerint, Rosenkreutz élete során a Rend mindösszesen nyolc tagot számlált, akik nőtlenségi fogadalmat tettek és mindegyikük valamely tudományterület doktora volt. Betegek ingyenes gyógyítására esküdtek fel, titkos szövetségre léptek egymással és kötelezettséget vállaltak, hogy maguk helyett méltó utódot találnak haláluk után követőül. Kb. 1500 és 1600 között három generáció követte egymást, miután elérkezettnek látták az időt a tudományos, a filozófiai és vallási területeken kialakult nagyobb szabadság nyomán, hogy a szélesebb nyilvánosság javára is szolgálhasson a rózsakeresztes tudás, így elkezdtek a tudás befogadására alkalmas embereket keresni.

Fogadtatásuk
A manifesztumok sokak szerint nem szó szerint értendők. Így volt ez már a maga idejében is és így van ez ma is. Egyesek hoaxnak tartják, míg mások allegóriának, mivel egy helyütt az az állítás szerepel bennük, hogy "Parabolákban szólunk hozzátok, ám készséggel megadjuk nektek minden titok helyes, egyszerű, természetes és eredeti ismertetését, értelmét, magyarázatát és meghatározását."

Nyilvánvalónak tűnik, hogy az első rózsakeresztes manifesztumokra az ismert hermetikus filozófus - Heinrich Khunrath - munkája, az 1609-ben kiadott Amphitheatrum Sapientiae Aeternae írója, hatott, akire viszont az 1564-es keltezésű Monas Hieroglyphica szerzője, John Dee volt nagy hatással. A Christian Rosenkreutz Kémiai Menyegzője királyi esküvőre szóló meghívása Dee filozófiai kulcsával, a Monas Hieroglyphica szimbólumával kezdődik. Adam Haslmayr, aki a Paracelsus műveit összegyűjtő Karl Widemann közeli barátja volt, levelet írt neki a rózsakeresztesekről 1611. december 24-i keltezéssel.

Írásműveik erkölcsi és vallási megújítóknak mutatja be a rózsakereszteseket, akik kémiai (alkímiai) és más tudományos módszereket használtak véleményük, meggyőződésük kinyilvánítására.

Johann Valentin Andreae (1586–1654) önéletrajzában azt állítja, hogy a névtelenül kiadott Kémiai Menyegző az ő műve és nem más, mint gúnyirat. Későbbi műveiben nevetség tárgyává teszi az alkímiát és a zenével, színházzal és az asztrológiával együtt a komolytalan tudományok közé sorolja. Más források szerint ugyanakkor a rózsakeresztesek legendája eredetében játszott szerepe ellentmondásos. Mások azonban általánosan elfogadják kapcsolatát velük.

Jegyzetek

Lásd még
 Christian Rosenkreutz
 Rózsakeresztesek
 Rózsakeresztes rend
 Fama Fraternitatis
 Confessio Fraternitatis
 Christian Rosenkreutz kémiai menyegzője
 Egy kritikai írás:

Könyvek
Okkultizmus


text:
DARLING in the FRANXX Character Introduction Video Features Code:016 & Code:002!
Sep. 15, 2017 03:30
Character commercials will be airing over the next 5 weeks for the upcoming anime DARLING in the FRANXX! The first of these aired on the night of Sept. 13 during the rebroadcast of Gurren Lagann, and it featured characters Hiro and Zero Two, as well as their mech FRANXX, the Strelizia. This original anime is bringing together the powerhouses of Trigger ( Kill la Kill, Little Witch Academia) and A-1 Pictures ( THE iDOLM@STER series).
The first of the pair that was featured was Code:016, Hiro. It included character art, as well as a number of key phrases like "a bird that can't fly" "a past of being called a prodigy," and "leftover pilot," as well as lines like, "I'm good at giving names," "There's no place for me here" and "A bird that can't fly has nowhere to go."
Following him is Code:002, Zero Two. Following key phrases like "red suit," "partner killer," and "elite pilot," there were what seemed to be responses to Hiro's lines including, "A place to belong is something you create yourself," "I might take some interest in you," and "Is there a need to give names to things?".
Their FRANXX, the Stralizia, also appeared, and finally seeing it has us even more excited to learn more about this anime!
The 2nd of these commercials will air on the night of Sept. 20, again during the Gurren Lagann rebroadcast.
(C) DARLING in the FRANXX Production Committee
You belong in the TOM Fan Club. Don't keep TOM Senpai waiting: https://otakumode.com/fb/8iz
Zodiac Signs Anime Juni Taisen Unveils Key Visual!
A battle royale between 12 zodiac signs awaits!
Imouto sae Ireba ii. Anime Releases New Visual and PV!
Imouto sae Ireba ii. tells the story of Hashima Itsuki, who writes only novels themed around little sisters!
Re:Zero to Receive New OVA!
Watch Subaru, Emilia, Rem and Ram prepare for the new OVA!
DARLING in the FRANXX Receives New Trailer and Key Visual!
No details on the plot yet, though!
SAO: Ordinal Scale to Screen in China From Sept. 15 With Chinese Version of "Catch the Moment"!
Code Geass Movie Releases Key Visual and Trailer


West Auckland Cafe bordering the Unitec building Library caters to students and a well exposed road front that brings a large influx of walk-ins.
A fantastic opportunity for new entrants, owner operators or a working couple.
- Turning over an average of $5000 per week (5 days) with untapped growth potential as currently 100% staff managed.
- Rent is reasonably low for the area location at $914 Per Week Including GST & Outgoings.
- 5 Day (Monday - Friday) operation. Potential to increase cafe hours to boost weekend sales.
Selling due to owner relocating overseas.


I would like to see such an option: by selecting a text link on the page (even with a space and without http), the item "Open in a new tab" would appear.
And currently the speed dial background and desktop background don't match in size, it doesn't look great. Maybe instead make a transparent speed dial background?


text:
Home > Breaking News > Industry News > ISH North America Trade Show marks fifth successful edition
ISH North America Trade Show marks fifth successful edition
ISH North America, the leading trade show for the plumbing, commercial/industrial pipes, valves & fittings (PVF), HVAC and kitchen & bath industries, marked its fifth edition with its Oct. 1-3 trade show at the Georgia World Congress Center in Atlanta.
Reflective of the trend toward cleaner building and environmentally conscious construction, the 2008 show highlighted the growing demand in renewable energies. Thousands of contractors, wholesalers, manufacturers' reps and other attendees were able to see the latest product innovations from leading manufacturers in the exhibit hall, learn from industry leaders at the seminar program and network with peers during the many special events at the show.
'While the current economic downturn has impacted the industry, exhibitors and visitors remained upbeat about their future business development and strategies," said Daniel McKinnon, executive vice president of Messe Frankfurt, the show's organizer.
As the only consolidated show in the industry, exhibitors were excited to connect with a broad range of professionals, from contractors and wholesalers, to builders, manufacturers' reps and others. In addition, an impressive design and show floor layout was highly regarded by exhibitors and attendees alike.
The ISH North America Seminar Program featured a diverse selection of educational opportunities. Popular business-oriented programs included Kirk Alter's 'Recession-Proofing Your Business," which focused on making the right moves in tough times; and Adams Hudson's 'How to Put High Performance Plumbing Marketing in Your Company Instantly," which offered tips and tools for results-oriented marketing.
Special events included the 2008 Plumbing Apprentice Contest, held on the ISH North America exhibit floor in conjunction with the Plumbing-Heating-Cooling Contractors Association's (PHCC) annual convention. The winner of the contest was Kyle Holcomb of Pasadena Plumbing in St. Petersburg, Fla., a fourth-year apprentice.
ISH North America ran concurrently with 'Network," the annual convention for the American Supply Association (ASA) and PHCC. Other association events included the annual convention for the International Association of Plumbing and Mechanical Officials (IAPMO) and the Canadian Institute of Plumbing and Heating's famous Maple Leaf Reception.


text:
Leadership Under Fire, Second Edition
The Challenging Role of the Canadian University President
By Ross H. Paul
With a new preface by the author
Education, Education: Canadian
An insightful commentary on the leadership challenges faced by university presidents and a comprehensive survey of the changing university landscape.
While the role of the university president has evolved dramatically in recent years, the recruitment pool and selection process have changed little since the 1960s. In Leadership Under Fire, Ross H. Paul combines leadership theory, interviews with eleven of Canada's most successful presidents, and thirty-five years of personal experience to shed light on the complexity and importance of leading a university and identifies some of the critical challenges and opportunities facing Canadian universities today.
Paul illuminates some of the ways in which Canadian universities are unique and uses these differences to make clear the importance of organizational cultural and institutional fit for leaders confronting critical academic issues such as academic leadership and accountability, student success and support, university funding and fund-raising, strategic planning, government and community relations, and internationalism. His analysis reaffirms some long-standing practices, while arguing that changes are badly needed in others.
While much has been written about university leadership elsewhere, Leadership Under Fire focuses on Canada and some of the men and women who have made a real difference to the quality of its post-secondary institutions. Paul builds on their stories to offer useful perspectives and advice at a time when the quality of universities was never more critical to the country's economic, social, and political success.
Formats: Paperback, eBook
"[Leadership Under Fire] is highly relevant to university boards of governors, provincial education ministries and other agencies that interact with universities and thus their leaders. Overall, the book provides an excellent inside account of a Canadian university presidency." Elizabeth Cannon, Policy Options
Ross H. Paul has held senior leadership positions in four post-secondary institutions in three Canadian provinces over the past thirty-five years, including tenures as president of Laurentian and Windsor Universities.
Introduction to the Second Edition vii
Preface xxv
Acknowledgments xxix
Abbreviations xxxi
PART ONE: CANADIAN UNIVERSITIES AND THEIR LEADERSHIP
1 Distinguishing Characteristics of Canadian Universities with Implications for Their Leadership 3
2 Canadian University Presidents: Who They Are and How They Are Selected 23
PART TWO: ACADEMIC LEADERSHIP AND ORGANIZATIONAL CULTURE
3 Organizational Culture and the University 49
4 Setting the Direction: Institutional Vision and Strategic Planning 72
5 Academic Leadership: Getting the Balance Right 82
PART THREE: KEY ISSUES FOR TODAY'S PRESIDENTS
6 Student Access and Success: Confronting a Declining Undergraduate Experience 101
7 International Outreach 119
8 Financial Issues: Underfunded or Fat Cats? 129
9 Presidential Leadership and Day-to-Day Administration 149
10 The External Roles of the President 171
11 Institutional Governance and Presidential Accountability 184
12 Institutional Autonomy and System Diversity 201
PART FOUR: THE WAY FORWARD
13 How Much Difference Does a President Make? The Case for Open Management 225
14 Leadership under Fire: Seven Major Issues for Today's Presidents 238
Appendix A Presidential Profiles: Eleven Who Have Really Made a Difference 259
Appendix B Universities Included in the Presidential Recruitment Survey 295


text:
Publications & Media
Alberta Appeal Judge finds that unfounded fears, however genuine, do not qualify as harm to Aboriginal Rights
Litigation Bulletin - January 2019
by Craig Alcock and Paul Beke
Download a PDF of this piece
Subscribe to receive similar publications
On January 16, 2019, Alberta Court of Appeal Justice Ritu Khullar issued a decision in Fort McKay Métis Community Association v Alberta Energy Regulator.
The Alberta Energy Regulator (AER) had approved Prosper Petroleum Ltd.'s oil sands project after hearing evidence from the Fort McKay Métis Community Association. The Fort McKay Métis requested permission from the Court to appeal the decision, which could only be granted if the AER had made an error of law or jurisdiction. The Court denied leave to appeal as, among other things, unjustified fears of contaminated fishing grounds were insufficient to show actual harm to aboriginal rights.
The decision illustrates that no actual harm to aboriginal rights arises from unfounded contamination fears or other subjective perceptions.
Summary of the Alberta Energy Regulator's Decision
Prosper applied to the AER for various approvals for an oil sands project that would operate within 10 km of the Fort McKay First Nation's Moose Lake Reserves. The Fort McKay Métis claimed unextinguished, constitutionally protected Métis aboriginal rights to hunt, trap, and fish on their traditional territory on or near the reserves. In its hearing, the AER considered the Fort McKay Métis to be a rights-bearing community, and weighed the oral traditional knowledge that the Fort McKay Métis presented as evidence.
The Fort McKay Métis' genuine fear of eating the fish was unjustified
The AER accepted evidence from the Fort McKay Métis that some members would be genuinely afraid to eat fish from Moose Lake due to fear of contamination. The AER (1) determined that the project would neither harm the fishery, nor reduce the animals available for hunting and trapping, but (2) recognized a risk of a "negative social effect", in that, members might change how they value the lands and the animal resources. When weighing the public interest, the AER accounted for these fears and perceptions, but ultimately decided that the Fort McKay Métis would continue to be able to exercise their aboriginal rights in their traditional territory.
The AER concluded that the project was in the public interest
The AER granted conditional approvals under the Oil Sand Conservation Act, the Environmental Protection and Enhancement Act, and the Water Act, which were dependent on approval by Cabinet. Other conditions required that Prosper seek input (1) from the Fort McKay Métis on reclamation, and (2) from the Fort McKay Métis and the Fort McKay First Nation before further developing the surface-water-monitoring program.
Summary of the Court of Appeal's Decision
The Fort McKay Métis presented a number of grounds for leave to appeal. On one, the Court decided that AER's overall weighing of the public interest was not a matter of pure law (as opposed to mixed fact and law). Thus, no appeal was available on that ground.
On another ground, the Court determined that the Fort McKay Métis had no basis to argue that they shouldn't bear the burden of proving harm to their rights.
Fear of harm is not actual harm
The most fundamental ground of appeal claimed by the Fort McKay Métis was that the project would harm their Métis aboriginal rights under section 35 of the Constitution Act, 1982.
They argued that:
the project would cause them to perceive their traditional lands differently;
which would, in turn, cause them to avoid Moose Lake and reduce their fishing; and
reduced use of their fishery would objectively harm their fishing rights.
The Court reasoned that unlike any objectively proven harms to wildlife and water, merely subjective fears or perceptions do not qualify as actual impacts on Métis aboriginal rights. Unfounded fear does not negatively impact aboriginal rights.
The Right Holder Must Prove Actual Harm to its Rights
In hearings over aboriginal rights, the common law has had to grow to include evidence such as oral traditional knowledge. But when proving harm to aboriginal rights, the approach is standard. The relevant issue is whether a development project will actually harm aboriginal rights—not whether purely subjective fears and perceptions will hamper the exercise of aboriginal rights.
The full decision can be found here.
Craig O. Alcock
Paul A. Beke
Associated Practices
Commercial & General Litigation


text:
This document describes how to use a VM on GCP to run the MAE annotation tool.

## Setting up firewall rules

Set up firewall rules so you'll be able to access your VM once you set it up.
Equivalent methods for doing this via the browser or command line are provided
below.

### Via Google Cloud Console UI

1. On Google Cloud Console navigate to VPC Network -> Firewall Rules and select
   "Create Firewall Rule" ([direct link](https://console.cloud.google.com/networking/firewalls/add)).
1. Set the following fields.
  * Name: vnc-server
  * Target Tags: vnc-server
  * Source IP Ranges: 0.0.0.0/0
  * Protocols and ports: tcp:5901
1. Click "create".

![](images/firewall_rule.png)

### Via Command-line

```shell
PROJECT=my-gcp-project
gcloud compute --project=${PROJECT?} firewall-rules create vnc-serve \
--direction=INGRESS --priority=1000 --network=default --action=ALLOW \
--rules=tcp:5901 --source-ranges=0.0.0.0/0 --target-tags=vnc-server
```

## Creating a VM

1. On Google Cloud Console navigate to Compute Engine -> VM Instances and select
   "Create Instance" ([direct link](https://console.cloud.google.com/compute/instancesAdd)).
1. Give it a name, e.g. mae-vncserver.
1. Check "Container (Deploy a container image to this VM instance.)".
1. Set "Container image" to `gcr.io/jakeakopp-953/mae:latest`.
1. Click "Advanced container options", then check "Run as privileged".
1. (optional) Set a password:
  * add an environment variable called PASSWORD. The value will be the password
    you use to connect to the server. If you skip this step, the password is
    simply "password".
1. Add a `vnc-server` network tag:
  1. Click "Management, disks, networking, SSH keys" to reveal more options.
  1. Select the "Networking" tab.
  1. Add the network tag `vnc-server`, to match the one set in the firewall rule
     created above.
1. Click the "Create" button at the bottom.

## Connecting

1. Get the IP address of your VM. This will be listed on the [VM instances page](https://console.cloud.google.com/compute/instances).
1. Install a VNC client, e.g. [VNC Viewer for Chrome](https://chrome.google.com/webstore/detail/vnc%C2%AE-viewer-for-google-ch/iabmpiboiopbgfabjmgeedhcmjenhbla?hl=en).
1. User your VNC client to connect to IP_ADDRESS:5901 (e.g. 104.198.72.4:5901).
1. Password is `password`, unless you set one up in "Creating a VM" above.
1. If you wish to change the VNC password, run `vncpasswd` in a terminal (
   Applications -> System Tools -> XTerm).
1. Double-click on MAE (i.e. mae-2.0.9-fatjar.jar) to start.
1. If you have notes on Google Cloud Storage, you can download them to the VM
   using gsutil in a terminal, e.g.:
```shell
mkdir -p /home/notes/
gsutil cp gs://my-bucket/notes/* /home/notes/
```

## Creating a new docker image

If you wish to create your own docker image, you can do so using the following
commands:

```
PROJECT=my-gcp-project
cd mae/
docker build -t mae .
docker tag mae gcr.io/${PROJECT?}/mae:latest
gcloud docker -- push gcr.io/${PROJECT?}/mae:latest
```

# Tools for working with MAE and BigQuery

We have several tools to facilitate working with MAE. To use the tools below,
first download the code from GitHub, e.g.:

```shell
git clone https://github.com/GoogleCloudPlatform/healthcare-deid.git && \
cd healthcare-deid
```

## Downloading notes from BigQuery

You can use bq_to_xml.py to download notes from a BigQuery table and save them
to local disk in XML format so they can be read by MAE.

First install the Google BigQuery Python client:

```shell
virtualenv env
source env/bin/activate
pip install google-cloud-bigquery
```

Then run the tool, e.g.:

```shell
python mae/bq_to_xml.py \
  --input_query="SELECT patient_id,record_number,note FROM [${PROJECT:?}:${DATASET:?}.${TABLE:?}]" \
  --local_output_dir=output/directory/
```

## Removing invalid characters from text files

If you discover that your input files cannot be opened by MAE due to invalid
XML characters, you can use the "remove_invalid_characters" tool.

Run either with [bazel](http://bazel.build/versions/master/docs/install.html):

```shell
bazel build mae:remove_invalid_characters && \
bazel-bin/mae/remove_invalid_characters --input_pattern="dir/*.xml" --output_dir="output/"
```

Or without bazel:

```shell
PYTHONPATH="."
python mae/remove_invalid_characters.py --input_pattern="dir/*.xml"  --output_dir="output/"
```

## Uploading XML files to BigQuery

upload_files_to_bq.py can upload your XML files to BigQuery either from local
disk or from GCS.

Install the apache beam client. Note that google-cloud-storage is also required
if the files are coming from GCS, and at least version 0.5.23 of google-apitools if the files contain unicode characters.

```shell
virtualenv env
source env/bin/activate
pip install apache_beam[gcp] google-cloud-storage google-apitools>=0.5.23
```

The tool can be built and run using the [bazel build system](http://bazel.build/versions/master/docs/install.html):

```shell
bazel build mae:upload_files_to_bq && bazel-bin/mae/upload_files_to_bq \
  --file_pattern="dir/*.xml" --table_name project:dataset.table
```

Or without bazel:

```shell
PYTHONPATH="."
python mae/upload_files_to_bq.py --file_pattern="dir/*.xml" --table_name project:dataset.table
```

redpajama_set_name: RedPajamaGithub


MANILA – The Philippine Competition Commission on Tuesday said it approved the merger of insurance firms AXA and XL Group and fined the companies for not notifying it on time. AXA's subsidiary Camelot Holdings is acquiring the XL Group, with the latter becoming a wholly-owned subsidiary of AXA. The AXA-XL Group merger is the first case to be fined for late filing of the compulsory notification, the PCC said. The PCC said it should have been notified on or before April 4 or within 30 days from the signing of the merger agreement on March 5. The firms notified the PCC on June 25, 112 days after the deal was signed, the antitrust body said. AXA primarily handles life insurances, while XL Group's market is mainly non-life insurance, the PCC noted.


Gamesworld is a West Australian family owned business with stores around the Perth metropolitan area. We specialise in a wide range of entertaining games and activities, including board games, jigsaw puzzles, diecast cars and collectables, war hammer, and a range of novelty items. We aim to provide a high level of customer service and friendly advice, ensuring the most appropriate product for our customers. We'll help you find things in store that will bring you, your family and friends together.


In order to make a deposit and play for real money, you must first register to play at LotteryCasino.net. Once you have registered and logged in, you will be able to deposit to play for real money.
When you make your first deposit with the LotteryCasino.net, you may be eligible for a bonus of up to 100% of your initial deposit up to £/€/$200 or 2000kr. Please read more about bonuses and look at the Latest Promotions.
LotteryCasino.net will not accept a deposit from a registered player contrary to a limit set for that player under this Part.
Cashing out at the LotteryCasino.net page is easy and can be done by a variety of methods. Click on the "Cashier" icon, followed by the "Withdrawal" option. You then have the option of selecting which withdrawal method you wish to use.


text:
'El Chapo' to learn fate in New York
https://www.chron.com/business/bizfeed/article/Memorial-Hermann-to-partner-with-new-non-profit-13514600.php
Memorial Hermann to partner with new, non-profit generic drug company to lower costs
By Jenny Deam
Updated 1:38 pm CST, Wednesday, January 9, 2019
Memorial Hermann Medical Plaza building at 6400 Fannin in the Texas Medical Center is seen in this file photo. Memorial Hermann Health System has partnered with a new generic drug company formed to combat "artificially high" pharmaceutical prices and ease chronic drug shortages, the drug company announced Monday.
NEXT: See the best hospitals in Houston according to U.S. News.
Memorial Hermann Medical Plaza building at 6400 Fannin in the Texas Medical Center is seen in this file photo. Memorial Hermann Health System has partnered with a new generic drug company formed to combat ... more
Photo: LaSalle Investment Management
Memorial Hermann Health System has partnered with a new generic drug company formed to combat "artificially high" pharmaceutical prices and ease chronic drug shortages, the drug company announced Monday.
Utah-based Civica Rx launched its generic drug initiative a year ago with strong Houston roots. The idea behind the venture is to allow hospital systems to "create their own priorities" in needed medications.
Such generic versions of the medications remain difficult to obtain because of price or availability or both, Heather Wall, chief commercial officer for Civica Rx, said in an interview on Monday.
"We're tackling the drugs that we've seen significant price increases over the past few years," she said.
Price hikes, often dramatic, can come from a lack of competition, especially among drugs that have fallen out of mass production. But Wall said that just because a drug is elusive does not mean it is not needed.
Typically there are about 200 drugs on shortage lists any given year.
When there is not enough of a certain drug in the supply chain, it can drive up the price to "artificially high" levels, which in turn forces providers and, ultimately, patients to pay more, Wall said.
RELATED: Texans missing or delaying needed treatment because health costs too high
Memorial Hermann is one of 12 health systems across the country to enter partnerships with Civica Rx. The Houston-based system will be considered a founding member of what is predicted to be a growing network of hospitals nationwide, Wall said.
There are 750 U.S. hospitals now participating, the company said.
"Creating a consistent and stable supply of generic drugs not only ensures that we can continue delivering on our promise to always provide safe, high-quality care tailored to our patients' needs, but it also allows us to tackle the dramatic increases in U.S. health care costs that affect everyone. Our industry is consistently experiencing pharmaceutical shortages for commonly used drugs. These shortages result in health care organizations having to pay inflated pricing to secure appropriate supplies to adequately care for patients — pricing that ultimately gets passed along to the consumer," Chuck Stokes, CEO of Memorial Hermann Health System, said Monday in a statement.
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text:
\section{Introduction}

A polarized Nikulin surface of genus $g\geq2$ is a smooth polarized K3 surface $(X,L)$, where $L$ is a big and nef line bundle with self-intersection $L^2=2g-2$, such that there exists a set of disjoint smooth rational curves $R_1,\dots,R_{8}$ on $X$ satisfying $L\cdot R_i =0$ for each $i=1,\dots,8$.
The divisor class of $R:= R_1+\dots+R_{8}$ is divisible by $2$ in the Picard group of $X$ and, denoting by $e$ the primitive class satisfying
\[ e^{\otimes 2} = \O_X(R) , \]
one can describe the Nikulin lattice $\mathfrak{N}$ as the lattice generated by the classes of $R_1,\ldots,R_8$ and $e$. This yields a primitive embedding
\[\Lambda_g := \Z\cdot [L] \oplus \mathfrak{N} \hookrightarrow \Pic(X) , \]
from which one can construct the moduli space $\mathcal{F}_g^{\mathfrak{N}}$ of Nikulin surfaces of genus $g$, which is irreducible and $11$-dimensional \cite{Dol96,vGS07}.

Nikulin surfaces represent a rather special class of K3 surfaces, which have been studied in relation with various topics, including the theory of automorphisms \cite{Nik76,GS08}, moduli spaces \cite{Mor84,vGS07}, the study of Prym curves \cite{FK16} and of the birational geometry of their moduli spaces \cite{FV12,FV16,KLCV,Ver16}.

Following \cite{GS08}, the very general point of $\mathcal{F}_g^{\mathfrak{N}}$ corresponds to a polarized Nikulin surface $(X,L)$ with Picard number nine and, if $g\geq3$, the line bundle $L$ induces a morphism which contracts the $8$ curves $R_i$ and maps $X$ to a surface in $\P^g$ with $8$ ordinary double points. If $g=4$ or $5$, the line bundle $L\otimes e^{-1}$ is ample, and very ample for $g\geq6$, mapping $X$ to a surface in $\P^{g-2}$. These linear systems and their interplay provide a source of interesting geometry which has been proven useful for several effective constructions in some of the aforementioned works. A detailed description of these projective models has been carried out for Nikulin surfaces of low genus in \cite{GS08}.

The starting point of this work is a systematic approach for the study of these linear systems on Nikulin surfaces of any genus. Consider the series of line bundles
\[ L_m = L \otimes e^{-m}, \quad m=0,1,2,\ldots  \]

Assuming $g$ is large enough with respect to $m$, how positive is $L_m$? For very general $(X,L)$ in $\mathcal{F}_g^{\mathfrak{N}}$, the situation is as good as one could expect.

\begin{thm}}\newcommand{\nteo}{\end{thm}\label{mapsLm} Let $(X,L)$ be a Nikulin surface of genus $g$ with Picard number nine. Write $g=2k^2+ p $, where $k\geq1$ and $0\leq p  < 4k+2$. Denote by
\[ L_m = L \otimes e^{-m} , \quad m=0,1,\ldots,k. \]
Then,
\begin{enumerate}[(i)]
\item For any $1\leq m\leq k-1$ (in particular $g\geq 8$) the general member of the linear system $|L_m|$ is a smooth irreducible curve of genus
\[g_m = g - 2m^2 \geq 6. \]
In fact, $L_m$ is very ample and defines an embedding of $X$ in $\P^{g_m}$.
\item $|L_k|$ contains a smooth irreducible curve of genus $ p $. Moreover, $L_k$ is ample for $ p =2$, and very ample for $ p \geq3$.
\end{enumerate}
\nteo

For example, one easily checks that for any $1\leq m\leq k-1$, a smooth irreducible curve $D$ in the linear system $|L_{m+1}|$ is embedded (non-specially) by $L_m$ as a non-degenerate linearly normal curve of degree $2(g_m -2m-1)$ in $\P^{g_m}$. In particular, letting $g=2k^2+ p $,  the curves $D\in|L_k|$ are embedded by $L_{k-1}$ as linearly normal curves of genus $ p $ in $\P^{4k-2+ p }$. So, for example:
\begin{itemize}
\item $ p =0$ ($g=2k^2$) : $D$ is the rational normal curve in $\P^{4k-2}$,
\item $ p =1$ ($g=2k^2+1$) : $D$ is a normal elliptic curve in $\P^{4k-1}$,
\item $ p =2$ ($g=2k^2+2$) : $D$ is a normal genus $2$ curve in $\P^{4k}$,
\end{itemize}
and so on. Let us point out that in genus $g=8$ (i.e.\,the case $k=2$ and $ p =0$), the existence of the smooth rational curve $D \in|L_2|$ embedded by $L_1$ as a rational normal curve of degree $6$ in $\P^6$ is the starting point of Verra's construction\,\cite{Ver16} for the proof of the rationality of $\mathcal{F}_8^{\mathfrak{N}}$.

Returning to the linear systems $|L_m|$, the next natural step is to determine the Brill-Noether theory of the hyperplane sections of $X$ in these projective models.

\begin{thm}}\newcommand{\nteo}{\end{thm}\label{BNgeneral} Under the same assumptions and notations of Theorem \ref{mapsLm}, all smooth curves in $|L_m|$, for any $0\leq m\leq k$, are Brill-Noether general, i.e.\,have maximal Clifford index $\lfloor \frac{g_m-1}{2} \rfloor$.
\nteo

We note that for $m=1$ the statement of Theorem \ref{BNgeneral} was proved by Farkas and Kemeny in their proof of the Prym-Green conjecture in odd genus \cite{FK16}.

In the second part of the paper we use the projective geometry of Nikulin surfaces in order to compute the classes of some natural effective divisors in $\mathcal{F}_g^{\mathfrak{N}}$. This was directly inspired by the recent paper of Farkas and Rim\'{a}nyi \cite{FR}, and relies on some beautiful general formulas therein contained. Specifically, for any index $m=0,\ldots,k$ (assuming $p\geq 3$ when $m=k$), we consider the virtual divisors

\[  \mathfrak{D}^{\rk (4)}_m = \{ (X,L) \in \mathcal{F}_g^{\mathfrak{N}} \, \colon \, \, I_m^{\rk(4)} (2) \neq 0  \} , \]

where $I_m(2)$ is the vector space of quadrics containing the image of $X$ by the morphism $X \to \P^{g_m}$ induced by $L_m$ and
\[ I_m^{\rk (4)}(2) = \{ q \in I_m(2) \colon \, \rk(q) \leq 4 \} . \]

Along the lines of \cite[\S 4]{MOP17}, we consider the universal Nikulin surface
\[ \pi \colon \mathcal{X} \longrightarrow \mathcal{F}_g^{\mathfrak{N}} \]
together with a choice of universal bundles $\mathcal{L}$ and $\mathcal{E}$ associated to the polarization $L$ and the class $e$ of each fiber $(X,L)$. We define the tautological classes

\[ \kappa_{a,b,c} = \pi_\ast \left( c_1(\mathcal{L})^a \cdot c_1(\mathcal{E})^b \cdot c_2( \mathcal{T}_\pi )^c \right) \in \mathrm{CH}^{a+b +2c -2} (\mathcal{F}_g^{\mathfrak{N}}) , \]
for some non-negative integers $a,b,c$. In codimension one, the six classes
\[ \kappa_{3,0,0}, \, \, \kappa_{0,3,0}, \, \, \kappa_{2,1,0}, \, \, \kappa_{1,2,0}, \, \, \kappa_{1,0,1}, \, \, \kappa_{0,1,1}  \]
depend on the choice of $\mathcal{L}$ and $\mathcal{E}$. However, the following linear combinations are independent from this choice, and thus yield well defined classes in $\mathrm{CH}^1(\mathcal{F}_g^{\mathfrak{N}})$:

\begin{align*}
\gamma_0 = \kappa_{3,0,0} - \frac{(g-1)}{4} \kappa_{1,0,1} \, , \quad \gamma_2 = \kappa_{1,0,1} + 6 \kappa_{1,2,0} \, , \\
\gamma_1 = \kappa_{2,1,0} - \frac{(g-1)}{12} \kappa_{0,1,1} \, , \quad \gamma_3 =\kappa_{0,1,1} + 2 \kappa_{0,3,0} \, .
\end{align*}
(cf.\,\S \ref{tauto} below for more details). It turns out that the class of $\mathfrak{D}^{\rk (4)}_m$ can be computed in terms of these four classes $\gamma_0, \gamma_1, \gamma_2, \gamma_3 \in \CH^1(\mathcal{F}_g^{\mathfrak{N}})$, together with the Hodge class $\lambda \in\CH^1(\mathcal{F}_g^{\mathfrak{N}})$. Precisely, we have:

\begin{thm}}\newcommand{\nteo}{\end{thm}\label{THM-class-of-Dm}
Let $g=2k^2+ p $, for some integers $k\geq1$ and $0\leq p  < 4k+2$. If $m=0,\ldots,k-1$ or $m=k$ and $p\geq 3$, then $\mathfrak{D}^{\rk (4)}_m$ is an effective divisor in $\mathcal{F}_g^{\mathfrak{N}}$ and its class in the Chow ring $\CH^1(\mathcal{F}_g^{\mathfrak{N}})$ can be expressed as
\[ \left[ \mathfrak{D}^{\rk (4)}_m \right] =  A_m \left( \frac{ 2 }{ g_m +1 } \gamma_0 - \frac{ 6m }{ g_m +1 } \gamma_1 + \frac{ m^2 }{ g_m +1 } \gamma_2 - \frac{ m^3 }{ g_m +1 } \gamma_3 + (2g_m-1) \lambda \right) , \]
where $g_m = g-2m^2$ and some rational number $A_m$.
\nteo

The proof rests upon a Grothendieck-Riemann-Roch calculation on the universal Nikulin surface of genus $g$ and the application of general formulas from \cite{FR} which allow one to express $[\mathfrak{D}^{\rk (4)}_m]$ in terms of Chern classes of vector bundles on $\mathcal{F}_g^{\mathfrak{N}}$.

\section*{Acknowledgements}
This work started thanks to the financial support of the Einstein Foundation and I wish to thank G.\,Farkas and R.\,Pandharipande for giving me the opportunity to spend some pleasant time in Berlin. I am warmly thankful to G.\,Farkas for useful conversations around these topics.

\section*{Notation and conventions}

Nikulin surfaces of genus $g$, as defined in the Introduction, exist in all genera and are sometimes called \emph{standard} Nikulin surfaces. In odd genus (only) there exist also Nikulin surfaces for which $L\cdot e\neq0$, i.e.\,one does not have an orthogonal sum decomposition $\Z\cdot [L] \oplus \mathfrak{N}$. Accordingly, the \Neron-Severi lattice of the very general such K3 surface is rather an \emph{overlattice of index $2$} of $\Lambda_g$, cf.\,\cite{vGS07}. In this paper we are only concerned with standard Nikulin surfaces, whence we will omit this specification throughout. We work over the field of complex numbers.

\section{Polarized Nikulin surfaces}

We briefly recall some basic facts on Nikulin surfaces and refer to \cite{GS08} for details. Let $Y$ be a K3 surface carrying a symplectic involution $\iota\in\Aut(Y)$. Then $\iota$ has $8$ isolated fixed points and the quotient $Y/\iota$ is a K3 surface with eight ordinary double points. Let $\sigma\colon \widetilde{Y} \to Y$ be the blow-up of $Y$ at the eight fixed points of $\iota$. The involution $\iota$ naturally lifts to an involution on $\widetilde{Y}$, fixing the eight exceptional divisors $E_1,\ldots,E_8$. We denote the quotient surface by this involution by $X$ (which turns out to be a K3 surface) and we let $f\colon \widetilde{Y} \to X$ be the quotient map.

\[\begin{tikzpicture}[>=angle 90]
\matrix(a)[matrix of math nodes,
row sep=3em, column sep=3em,
text height=1.5ex, text depth=0.25ex]
{ & \widetilde{Y} & \\
X & & Y \\
 & Y / \iota & \\};
\path[->,font=\scriptsize]
(a-1-2) edge node[above left]{$f$} (a-2-1)
(a-1-2) edge node[above right]{$\sigma$} (a-2-3)
(a-2-1) edge (a-3-2)
(a-2-3) edge (a-3-2);
\end{tikzpicture}\]

By construction, the ramification divisor of $f$ is the sum of the rational curves $R_i := f(E_i)$, and is therefore $2$-divisible in $\Pic(X)$. We denote by $e$ the primitive class $e\in\Pic(X)$ satisfying the identity
\[ e^{\otimes 2} = \O_X(R) , \]
where $R= R_1+\dots+R_{8}$. The classes of $R_1,\dots,R_{8}$ and $e$ span the Nikulin lattice $\mathfrak{N}$, and one gets in this way a primitive embedding $\mathfrak{N} \hookrightarrow \Pic(X)$.

\begin{definition}}\newcommand{\ndef}{\end{definition}
A \emph{ polarized Nikulin surface of genus $g\geq2$ } consists of a K3 surface $X$ and a primitive embedding $j\colon \Lambda_g \hookrightarrow\Pic(X)$, where $\Lambda_g := \Z\cdot L \oplus \mathfrak{N}$, such that $L^2=2g-2$ and $j(L)$ is a big and nef class. With a small abuse of notation, we denote a polarized Nikulin surfaces simply by the pair $(X,L)$.
\ndef

Polarized Nikulin surfaces of genus $g$ form a moduli space denoted by $\mathcal{F}_g^{\mathfrak{N}}$, which is  known to be irreducible and $11$-dimensional \cite{Dol96,vGS07}. The very general point of $\mathcal{F}_g^{\mathfrak{N}}$ corresponds to a K3 surface $X$ with Picard number nine. More precisely, one has an isomorphism $\Pic(X)\simeq\Lambda_g$, see \cite[Prop.\,2.1]{GS08}.

For the rest of this section we assume $(X,L)$ to be a polarized Nikulin surface of genus $g$ with Picard number nine and write
\[ g=2k^2+ p , \]
where $k\geq1$ and $0\leq p  < 4k+2$. We denote by
\[ L_m = L \otimes e^{-m} .\]

\begin{lem}}\newcommand{\nlem}{\end{lem} $L_m$ is ample if $1\leq m\leq k-1$ or $m=k$ and $ p \geq2$.
\nlem

\begin{proof}
Since $L_m$ is effective and $(L_m)^2>0$, we have that $L_m$ is ample if and only if $L_m$ intersects positively any smooth rational curve on $X$. Let $D$ be an effective divisor and write $D \sim aL -b_1 R_1-\cdots -b_8R_8$, where $a\in\Z$ and $b_i\in\frac{1}{2}\Z$. Then,
\[ D\cdot L_m = 2a(g-1) - m(\sum_{i=1}^8 b_i). \]
Assuming $D\cdot L_m\leq0$, we are going to show that $D^2<-2$ for $1\leq m\leq k-1$. Since $L_m$ intersects positively each $R_i$, we can assume that $D$ does not contain $R_i$ as a component, whence $D\cdot R_i=2b_i\geq0$. Hence we must have $a>0$, else $D$ would not be effective. Thus $D\cdot L_m\leq0$ yields $2a(g-1)\leq m(b_1 +\ldots+ b_8)$, and we can square both sides of this inequality, obtaining
\[ 4a^2(g-1)^2 \leq m^2(\sum_{i=1}^8 b_i)^2 \leq 8m^2 \sum_{i=1}^8 b_i^2. \]
where the latter estimate follows by the Cauchy-Schwarz inequality. Let us re-write this condition as
\begin{align} \label{cauchy-schwarz1}
\frac{a^2(g-1)^2}{m^2} \leq 2 \sum_{i=1}^8 b_i^2.
\end{align}

Assuming the latter inequality, we can estimate the self-intersection of $D$,
\begin{align*}
D^2 & = 2a^2(g-1) - 2\sum_{i=1}^8 b_i^2 \\
& \leq 2a^2(g-1) - \frac{a^2(g-1)^2}{m^2}  \quad \mbox{ by (\ref{cauchy-schwarz1}) } \\
& = a^2 \left(\frac{ g-1 }{ m^2 } \right) (1-g_m).
\end{align*}

Since $1-g_m <0$, in order for the condition $D^2 < -2$ to be satisfied, it is enough to ask for the following numerical condition:
\[  a^2 \left(\frac{ g-1 }{ m^2 } \right)(g_m-1) > 2. \]
By assumption $g_m=g-2m^2\geq 6$, or equivalently $m^2 \leq \frac{1}{2}(g-6)$, and using both these estimates we finally get
\[  a^2 \left(\frac{ g-1 }{ m^2 } \right)(g_m-1) \geq a^2 \cdot 2 \left(\frac{ g-1 }{ g-6 } \right) \cdot 5 > 10 a^2 > 2. \]
This proves that $L_m$ is ample for $1\leq m\leq k-1$. Moreover, we observe that the same argument works for $m=k$ and $ p \geq2$, in which case $g_k =  p $ and $k^2=\frac{1}{2}(g- p )$, so that we still get
\[  a^2 \left(\frac{ g-1 }{ k^2 } \right)(g_k-1) = a^2  \cdot 2 \left(\frac{ g-1 }{ g- p  } \right) ( p -1) > 2. \]

This concludes the proof.
\end{proof}

\begin{lem}}\newcommand{\nlem}{\end{lem} $L_m$ is very ample for any $1\leq m\leq k-1$ or $m=k$ and $ p \geq3$.
\nlem

\begin{proof}
So far we have determined the amplitude of $L_m$ for any $1\leq m\leq k$, with $ p \geq2$ for $m=k$. Since each such $L_m$ is big and nef, by the results of Saint-Donat \cite{SD} there can be only two types of obstruction for $L_m$ to be very ample: either the existence of fixed components, or of hyperelliptic curves in $|L_m|$. Specifically, we have to exclude the following three possibilities:
\begin{enumerate}[(a)]
\item There exist an elliptic curve $E$ and a smooth rational curve $\Gamma$ on $X$ such that $L_m=\O_X(rE+\Gamma)$, with $r\geq2$ and $E\cdot\Gamma=1$.
\item There exists an elliptic curve $E$ such that $L_m\cdot E =2$.
\item There exists a curve $B$ of genus $2$ such that $L_m=\O_X(2B)$.
\end{enumerate}

Notice that (c) may occur in genus $g_m=5$ only, but in fact it is automatically excluded by the properties of the \Neron-Severi lattice of the very general Nikulin surface $X$, since the class $L_m=L\otimes e^{-m}$ is not $2$-divisible in $\NS(X)$ \cite[Prop.\,2.1]{GS08}.

We will proceed by excluding cases (a) and (b) simultaneously, by showing that for any elliptic curve $E$ we have $L_m \cdot E >2$. Let us sketch the argument: given an effective divisor $D \sim aL -b_1 R_1-\cdots -b_8R_8$, we assume $D\cdot L_m\leq 2$. This yields the inequality
\begin{align*}
\frac{ [a(g-1)-1]^2 }{m^2} \leq 2 \sum_{i=1}^8 b_i^2.
\end{align*}

Assuming the latter inequality, we can estimate the self-intersection of $D$,
\begin{align*}
D^2 & = 2a^2(g-1) - 2\sum_{i=1}^8 b_i^2 \\
& \leq \frac{1}{m^2} [ a^2 (g-1) (1-g_m) + 2a(g-1)-1 ].
\end{align*}
We use the latter expression to impose the condition $D^2 > 0$. This yields to a quadratic equation in $a$, which will always be satisfied for any

\[ a > \frac{1}{g-2m^2-1} \left( \sqrt{ \frac{g-1+2m^2}{2g-2} } + 1 \right).  \]

Since $a\geq 1$, the latter inequality will hold for any $a$ as long as we impose the right hand side to be strictly lower than 1. Hence, we study the following condition:

\[ f(T):=\frac{1}{g-T-1} \left( \sqrt{ \frac{g-1+T}{2g-2} } + 1 \right) < 1 \quad  (T=2m^2). \]

By direct computation, we find $f(T)<1$ for any $g>2$ and
\[ 0 < T < \frac{2g^2-8g+7}{2g-2} .\]

Finally, since $T=2m^2 \leq 2k^2 = g- p $, we are led to the inequality
\[ g- p  < \frac{2g^2-8g+7}{2g-2} ,\]
which holds for all $g>3$ and $ p \geq3$ (and fails for $ p =2$, not surprisingly). This shows that $L_m$ is very ample and concludes the proof.
\end{proof}

Let once again $g=2k^2+ p$, where $k\geq1$ and $0\leq p  < 4k+2$. We now focus our attention on the line bundle $L_k = L \otimes e^{-k}$.

\begin{lem}}\newcommand{\nlem}{\end{lem} $|L_k|$ contains a smooth irreducible curve of genus $ p \geq0$.
\nlem

\begin{proof}
By Riemann-Roch, $h^0(X,L_k)\geq 1+ p \geq 1$, whence $L_k$ is effective. Let
\[ |L_k| = |M| + F \]
be the moving and fixed part decomposition of the linear system $|L_k|$. We show that either $F=0$ (whence $|L_k|$ is basepoint free and the statement follows by Bertini's Theorem) or $M=0$ and $F$ is a smooth rational curve.

When $k=1$ the statement follows by Proposition 3.2 and Proposition 3.4 in \cite{GS08}. Therefore, we assume $k\geq 2$. Then $L_{k-2}$ is effective and $h^1(X,L_{k-2})=0$. Consider the short exact sequence
\[ 0 \to L_k \to L_{k-2} \to \O_R(L_{k-2}) \to 0, \]
where $\O_X(R)=e^{\otimes 2}$. Note that $L_{k-2} \cdot R_i>0$ and the induced restriction map
\[ H^0(X,L_{k-2}) \to H^0(R,\O_R(L_{k-2})) = \bigoplus_{i=1}^8 H^0(R_i,\O_{R_i}(L_{k-2})) \]
is surjective. Then $h^1(X,L_k)=0$ and $h^0(X,L_k) = 1+ p $, by Riemann-Roch.

If $ p \geq1$, the linear system $|L_k|$ has then a non-trivial moving part, and the established vanishing $h^1(X,L_k)=0$ implies that the general member of $|L_k|$ is irreducible, i.e. $F=0$ and $|L_k|$ is basepoint free.
If $ p =0$, then $M=0$ and the linear system $|L_k|$ consists of a single effective divisor $F$ of self-intersection $F^2=-2$. If $F$ contains one of the $R_i$'s as a component, then $F\cdot R_i<0$. On the other hand,
\[ F\cdot R_i = L_k\cdot R_i = -\frac{k}{2} (\sum R_j) \cdot R_i = k > 0 . \]
Thus, we write $F = \Gamma_1+\dots+\Gamma_r$ as a sum of its irreducible components, which are smooth rational curves each of which is distinct from the $R_i$'s. By the structure of $\Pic(X)$, we can write
\[ \Gamma_\ell = a_\ell \cdot L - \sum_{i=1}^8 b_{\ell,i} \, R_i. \]
For each $1\leq \ell \leq r$ and $1\leq i\leq 8$, we have $b_{\ell,i} \geq 0$, since $\Gamma_\ell$ is different from $R_i$. Therefore $a_\ell >0$, else $\Gamma_\ell$ would not be effective, and by $F=\Gamma_1+\dots+\Gamma_r$ and $F \sim L -k e$, we get $a_1+\dots+a_r = 1$, whence $r=1$.
\end{proof}

\begin{proof}[Proof of Theorem \ref{mapsLm}]
It follows at once by the previous lemmas.
\end{proof}

In the next section we focus our attention on the Brill-Noether aspects of the linear systems $|L_m|$ and show how this naturally leads to divisors in $\mathcal{F}_g^{\mathfrak{N}}$.

\section{Brill-Noether general curves and the locus $\mathfrak{D}^{\rk (4)}_m$ }\label{sec-BN+quadric-loci}

Let us briefly recall some well-known facts from Brill-Noether theory. Let $C$ be a smooth algebraic curve of genus $g$. For any $A \in \Pic(C)$, we let
\[ \Cliff(A) = \deg A-2h^0(A)+2 . \]
The Clifford index of $C$ is by definition
\[ \Cliff(C) = \min\{\Cliff(A) \, \colon \, A\in\Pic(C), \, h^0(A)\geq2, \, h^1(A)\geq2\}. \]

Line bundles $A$ satisfying the conditions as in the definition of $\Cliff(C)$ are said to \emph{contribute to the Clifford index} of $C$. Such line bundles exist for any curve as long as $g\geq4$. When $g<4$ we adopt the standard convention
\[ \Cliff(C) := \begin{cases} 0 \quad \mbox{ if } \, g=1,2 \, \mbox{ or 3 and $C$ is hyperelliptic} \\  1 \quad \mbox{ if } \, g=3 \, \mbox{ and $C$ is non-hyperelliptic} \end{cases} \]

For any curve $C$ of genus $g$, one has the inequality
\[ \Cliff(C)\leq \left\lfloor \frac{g-1}{2} \right\rfloor , \]
which is an equality for the general curve  of genus $g$.

\begin{definition}}\newcommand{\ndef}{\end{definition} Let $S$ be a surface. We say that a curve $C\subset S$, or equivalently the line bundle $\O_S(C)$, decomposes into a sum of movable classes if $C$ is linearly equivalent to a sum $D_1+D_2$ of two divisors satisfying $h^0(D_i) \geq 2$, for $i=1,2$.
\ndef

For the rest of this section, we let $(X,L) \in \mathcal{F}_g^{\mathfrak{N}}$ be a polarized Nikulin surface of genus $g$. We write $g=2k^2+ p $, where $k\geq1$ and $0\leq p < 4k+2$ and denote by $L_m = L \otimes e^{-m}$, keeping the same notations of the previous section.

\begin{prop}}\newcommand{\nprop}{\end{prop}\label{No-decompositions} Assume $X$ has Picard number $9$. If $m=0,\ldots,k-1$ or $m=k$ and $p\geq 2$, the line bundle $L_m$ does not decompose into a sum of movable classes.
\nprop

\begin{proof}
Let us assume by contradiction that there is some smooth curve $D\in|L_m|$ which decomposes into a sum of movable classes. We can clearly assume $D^2 \geq2$. Among all such decompositions, we choose one $D\sim D_1+D_2$ such that the intersection $D_1\cdot D_2$ is minimal. We can then assume that one of the two classes, say $D_1$, is base point free and the general member of $|D_1|$ is a smooth irreducible curve, cf.\,\cite[Prop\,2.7]{Kn04}. In particular, $D_1$ is a nef class, and the restriction $(D_1)|_D$ contributes to the Clifford index of $D$, whence $\deg_D(D_1)>0$. We want to show that $D_2$ is then not a movable class. Up to linear equivalence, we can write
\[ D_\ell = a_\ell \cdot L - \sum_{i=1}^8 b_{\ell,i} \, R_i, \quad \ell=1,2, \]
where $a_\ell\in\Z$ and $2 b_{\ell,i} \in \Z$.
By intersecting $D_\ell$ with the nef class $L$, we get $a_\ell\geq0$ for $\ell=1,2$. Since $D_1$ is nef, $D_1\cdot R_i = 2b_{1,i} \geq0$ for all $i=1,\dots,8$. Finally,
\[ D \cdot D_1 = (L -me) \cdot D_1= a_1 L^2 - m\sum_{i=1}^8 b_{1,i} > 0 , \]
which implies $a_1>0$. On the other hand, by $D \sim D_1+D_2$ we have $a_1+a_2=1$. Therefore $a_2=0$, which clearly contradicts $h^0(D_2)\geq 2$.
\end{proof}

We can now prove Theorem \ref{BNgeneral} from the Introduction.

\begin{proof}[Proof of Theorem.\,\ref{BNgeneral}]
Let $D\in|L_m|$ be a smooth curve. Assuming by contradiction that $D$ has Clifford index $\Cliff(D)< \lfloor\frac{g_m-1}{2} \rfloor$,  there exists a line bundle $M$ on $X$ such that $M\otimes\O_D$ contributes to the Clifford index of $D$ and $\Cliff(D)=\Cliff(M\otimes\O_D)$, by \cite{GL}.
By the definition of Clifford index it follows that $h^0(M)\geq2$ and also $h^0(D-M)\geq2$. Thus $D \sim D_1 + D_2$, with $D_1\in |M|$ and $D_2\in |D -M|$ is a decomposition of $D$ into two movable classes, contradicting Proposition \ref{No-decompositions}.
\end{proof}

We are now going to define the divisors $\mathfrak{D}^{\rk (4)}_m$ from the Introduction. The following discussion parallels \cite[\S 9.1]{FR}.
Consider an element $(X,L)$ in $\mathcal{F}_g^{\mathfrak{N}}$ and for any $0 \leq m \leq k$ we denote by $L_m = L \otimes e^{-k}$. Each one of the following conditions,
\begin{enumerate}[(a)]
\item There exists an elliptic pencil $E$ on $X$ such that $E\cdot L_m = 1$,
\item There exists an elliptic pencil $E$ on $X$ such that $E\cdot L_m = 2$,
\item There exists a smooth rational curve $R$ on $X$ such that $R\cdot L_m = 0$,
\end{enumerate}
singles out a virtual Noether-Lefschetz divisor in $\mathcal{F}_g^{\mathfrak{N}}$, i.e.\,can be rephrased as the condition of the existence of a primitive embedding $\Lambda_g \hookrightarrow \Lambda_g'$, for some lattices $\Lambda_g'$ of rank $10$. \qt{Virtual} here means that these conditions may possibly be empty on $\mathcal{F}_g^{\mathfrak{N}}$. However, up to assuming $p\geq3$ in the case $m=k$, Theorem \ref{mapsLm} and Theorem \ref{BNgeneral} guarantee that for general $(X,L)$ the conditions (a) and (b) are not satisfied, whence they define an actual divisor in $\mathcal{F}_g^{\mathfrak{N}}$. Moreover, condition (c) defines an actual divisor as long as $m\geq1$.

Well-known results of Saint-Donat imply that Nikulin surfaces $(X,L)$ outside the union of these divisors are such that each $L_m$ is basepoint free, (pseudo-) ample and non-hyperelliptic, whence the multiplication map
\[ \psi_m \colon S^2 H^0(X, L_m) \to H^0(X, L_m^{\otimes 2} ) \]
is surjective, cf.\,\cite[Thm.\,6.1]{SD}. Thus $I_m(2) := \ker(\psi_m)$ in $S^2 H^0(X,L_m)$ has codimension $h^0(X,L_m^{\otimes 2}) = 4g_m -2$, by Riemann-Roch. The closed subscheme

\[ \Sigma^{\rk(k)}_m = \{ q \colon \, \rk(q) \leq k\} \subset S^2 H^0(X, L_m) \]
has codimension

\[ \binom{g_m+2-k}{2} , \]
see e.g.\,\cite{Ott95}. Therefore, the expected codimension of scheme-theoretic intersection

\begin{align*}
I_m^{\rk (k)}(2) := \, \, I_m(2) \cap \Sigma_m^{\rk(k)} = \, \{ q \in I_m(2) \colon \, \rk(q) \leq k \}
\end{align*}
is
\[ \codim I_m(2) + \codim \Sigma_m^{\rk(k)} = 4g_m - 2  + \binom{g_m+2 -k}{2} \]
in $S^2 H^0(X, L_m)$. In other words, we expect

\[ \dim I_m^{\rk(k)}(2) = (k-4) g_m + \frac{1}{2} (4+3k -k^2) ,\]
which vanishes precisely when $k=4$. We thus expect that for the general Nikulin surface $ I_m^{\rk(k)}(2) = 0$, so that, interpreting $\psi_m$ as a morphism between vector bundles over $\mathcal{F}_g^{\mathfrak{N}}$, it follows that the condition $I_m^{\rk(4)} (2) \neq 0$ is a divisorial --or eventually empty-- condition on $\mathcal{F}_g^{\mathfrak{N}}$, i.e.\,the locus

\[  \mathfrak{D}^{\rk (4)}_m = \{ (X,L) \in \mathcal{F}_g^{\mathfrak{N}} \, \colon \, \, I_m^{\rk(4)} (2) \neq 0  \} , \]
is a virtual divisor in $\mathcal{F}_g^{\mathfrak{N}}$.

\begin{prop}}\newcommand{\nprop}{\end{prop} Let $0\leq m\leq k$ and assume $p\geq3$ if $m=k$. The locus $ \mathfrak{D}^{\rk (4)}_m$ is a Noether--Lefschetz divisor on $\mathcal{F}_g^{\mathfrak{N}}$ supported on the subset of $\mathcal{F}_g^{\mathfrak{N}}$ defined by the condition that $L_m$ decomposes into a sum of two movable classes.
\nprop
\begin{proof}
First we observe that $ \mathfrak{D}^{\rk (4)}_m \neq \mathcal{F}_g^{\mathfrak{N}}$, by Proposition \ref{No-decompositions}. Assume $(X,L)$ is such that $L_m$ decomposes as a sum of movable classes $D_1,D_2$. Choose a general 2-dimensional subspace $V_i$ of $H^0(X, D_i)$ for $i=1,2$. The multiplication map $V_1 \otimes V_2 \rightarrow H^0(X, L_m)$ yields a $2 \times 2$ matrix whose determinant vanishes on the image of $X$ in $\P H^0(X, L_m)$, thus producing a rank four quadric containing $X$.
Conversely, suppose $X\subset\P^{g_m}$ is contained in a quadric $Q$ of rank at most $4$. We can assume $\rk Q = 4$, whence $\Sing Q = \P^{g_m-4} \subset\P^{g_m}$ and $Q$ is the cone over $\P^1\times\P^1$ under the projection $\P^{g_m} \dashedarrow \P^3$ from $\Sing Q$. The two rulings of $\P^1\times \P^1$ pull back to $Q$ and cut out on $X$ two divisors $D_1, D_2$, with $h^0(X,D_i)\geq2$, such that $L \sim D_1 + D_2$.
\end{proof}

\section{Computation of the class of $\mathfrak{D}^{\rk (4)}_m$ }\label{tauto}

Let $\mathcal{F}_g^{\mathfrak{N}}$ be the moduli stack of polarized Nikulin surfaces and
\[ \pi \colon \mathcal{X} \longrightarrow \mathcal{F}_g^{\mathfrak{N}} \]
the universal polarized Nikulin surface of genus $g$. Denote by
\[ \mathcal{L}\in\Pic(\mathcal{X}) \]
the universal polarization. The Hodge bundle $\mathbb{E}$ on $\mathcal{F}_g^{\mathfrak{N}}$ is defined by
\[ \mathbb{E}^\vee = R^2 \pi_\ast \O_\mathcal{X} \]
and we denote its first Chern class by
\[ \lambda = c_1(\mathbb{E}) \in \mathrm{CH}^1(\mathcal{F}_g^{\mathfrak{N}}) ,\]
which we refer to as the Hodge class on $\mathcal{F}_g^{\mathfrak{N}}$.

The relative tangent bundle $\mathcal{T}_\pi \longrightarrow \mathcal{X}$ is defined by the short exact sequence
\[ 0 \to \mathcal{T}_\pi \to \mathcal{T}_\mathcal{X} \to \pi^\ast \mathcal{T}_{\mathcal{F}_g^{\mathfrak{N}}} \to 0 . \]
The relative canonical bundle $\omega_\pi = \det(\mathcal{T}_\pi)^{-1}$, which restricts to the canonical (whence trivial) line bundle on each fiber, satisfies
\[ \omega_\pi = \pi^\ast (\pi_\ast \omega_\pi) = \pi^\ast \mathbb{E} .\]
In particular,
\[ c_1(\omega_\pi) = \pi^\ast \lambda .\]

Note that the choice of $\mathcal{L}$ is canonical only up to a twist $\mathcal{L} \mapsto \mathcal{L}\otimes\pi^\ast \alpha$, for some $\alpha\in\Pic(\mathcal{F}_g^{\mathfrak{N}})$. A polarized Nikulin surface $(X,L)$ comes equipped with a distinguished set of $8$ smooth rational curves $R_1,\ldots,R_8$ which form, together with
\[ e = \frac{1}{2} (R_1+\cdots+R_8) ,\]
a basis of the Nikulin lattice $\mathfrak{N}$. We consider the universal bundle
\[ \mathcal{E} \in \Pic(\mathcal{X}) \]
associated to the distinguished class $e\in \Pic(X)$. Again, the choice of $\mathcal{E}$ is canonical only up to a twist $\mathcal{E} \mapsto \mathcal{E} \otimes \pi^\ast \beta$, for some $\beta \in \Pic(\mathcal{F}_g^{\mathfrak{N}})$.

Following \cite[\S 4]{MOP17} we consider in the Chow ring of $\mathcal{F}_g^{\mathfrak{N}}$ the kappa classes
\[ \kappa_{a,b,c} = \pi_\ast \left( c_1(\mathcal{L})^a \cdot c_1(\mathcal{E})^b \cdot c_2( \mathcal{T}_\pi )^c \right) \in \mathrm{CH}^{a+b +2c -2} (\mathcal{F}_g^{\mathfrak{N}}). \]
for some non-negative integers $a,b,c$. The four classes in codimension zero are readily computed by restriction to a fiber $(X,L)$ as follows:
\begin{align*}
\kappa_{2,0,0} &= L^2 = 2g-2 ,\\
\kappa_{0,2,0} &= e^2 = -4 , \\
\kappa_{1,1,0} &= L\cdot e = 0 ,\\
\kappa_{0,0,1} &= \chi_{\textit{top}}(X) = 24.
\end{align*}

In codimension one, we get six classes:
\[ \kappa_{3,0,0}, \, \, \kappa_{0,3,0}, \, \, \kappa_{2,1,0}, \, \, \kappa_{1,2,0}, \, \, \kappa_{1,0,1}, \, \, \kappa_{0,1,1} . \]
By twisting $(\mathcal{L},\mathcal{E}) \mapsto (\mathcal{L}\otimes\pi^\ast \alpha , \mathcal{E}\otimes \pi^\ast\beta)$, these classes will change in general. However, it is straightforward to verify that the following linear combinations are independent from these twists, and thus are canonically defined in $\mathrm{CH}^1(\mathcal{F}_g^{\mathfrak{N}})$,

\begin{align*}
\gamma_0 = \kappa_{3,0,0} - \frac{(g-1)}{4} \kappa_{1,0,1} \, , \quad \gamma_2 = \kappa_{1,0,1} + 6 \kappa_{1,2,0} \, , \\
\gamma_1 = \kappa_{2,1,0} - \frac{(g-1)}{12} \kappa_{0,1,1} \, , \quad \gamma_3 =\kappa_{0,1,1} + 2 \kappa_{0,3,0} \, .
\end{align*}

As in the previous sections, we write
\[ g = 2k^2 + p, \quad k\geq1, \quad 0\leq p < 4k+2 \]
and denote by $g_m = g-2m^2$ the genus of the line bundle $L_m = L\otimes e^{-m}$.

\begin{prop}}\newcommand{\nprop}{\end{prop}\label{GRR} Let $0\leq m\leq k$ and assume $p\geq 2$ if $m=k$. Following the above notations, let $\pi \colon \mathcal{X} \to \mathcal{F}_g^{\mathfrak{N}}$ be the universal polarized Nikulin surface of genus $g = 2k^2+p$,  with universal bundles $\mathcal{L}$ and $\mathcal{E}$, and denote by $\mathcal{L}_m=\mathcal{L}\otimes \mathcal{E}^{\otimes -m}$. For any $n\geq1$, the sheaf $\mathcal{U}_{n,m} := \pi_\ast ( \mathcal{L}_m^{\otimes n})$ is locally free of rank $n^2(g_m -1)+2$ on $\mathcal{F}_g^{\mathfrak{N}}$ with first Chern class
\begin{align*}
c_1(\mathcal{U}_{n,m}) = & \, \, \, \frac{n^3}{6} [ \kappa_{3,0,0} -3m \kappa_{2,1,0} + 3m^2 \kappa_{1,2,0}  -m^3 \kappa_{0,3,0} ] +  \\
& + \frac{n}{12} [\kappa_{1,0,1} -m \kappa_{0,1,1} ] - [1+\frac{n^2}{2} (g_m-1) ] \lambda.
\end{align*}
\nprop

\begin{proof}
For $(X,L)\in \mathcal{F}_g^{\mathfrak{N}}$, we have $h^0(X, L_m^{\otimes n}) = n^2(g_m -1)+2$ and $h^i(X,L_m^{\otimes n})=0 $ for $i=1,2$, whence $\pi_\ast \mathcal{L}_m^{\otimes n}$ is a locally free sheaf of rank $n^2(g_m -1)+2$ and higher direct images vanish $R^i\pi_\ast \mathcal{L}_m^{\otimes n}=0$. By the Grothendieck-Riemann-Roch formula,
\[ \ch \left(  \pi_\ast  \mathcal{L}_m^{\otimes n} \right) = \pi_\ast \left\lbrace \ch (\mathcal{L}_m^{\otimes n} ) \cdot \td(\mathcal{T}_\pi) \right\rbrace . \]

Since $\pi$ is of relative dimension 2, the first Chern class of $\pi_\ast \mathcal{L}_m^{\otimes n}$ equals the push-forward of the degree 3 part of the product on the right-hand side,
\[ c_1(\pi_\ast \mathcal{L}_m^{\otimes n}) = \pi_\ast \left\lbrace \ch (\mathcal{L}_m^{\otimes n} ) \cdot \td(\mathcal{T}_\pi) \right\rbrace_{3} . \]
Recall that the Chern character and Todd class can be expressed in terms of Chern classes as follows:
\begin{align*}
\ch & = \rk + c_1 + \frac{1}{2} (c_1^2 -2c_2) + \frac{1}{6}(c_1^3 -3c_1c_2 +3c_3) + \cdots \\
\td & = 1 + \frac{c_1}{2} + \frac{1}{12}(c_1^2 + c_2) + \frac{1}{24}(c_1c_2) + \cdots
\end{align*}

Now, since $c_1(\omega_\pi) = \pi^\ast \lambda$, we get
\begin{align*}
\pi_\ast( c_1(\omega_\pi) \cdot c_2(\mathcal{T}_\pi))  &= \lambda \cdot \pi_\ast c_2(\mathcal{T}_\pi) = 24 \lambda, \\
\pi_\ast( c_1(\mathcal{L}_m)^2 \cdot c_1(\omega_\pi)) &= \pi_\ast(c_1(\mathcal{L}_m)^2)\cdot \lambda = (2g_m -2)\lambda , \\
\pi_\ast( c_1(\mathcal{L}_m) \cdot c_1(\omega_\pi)^2) &= \underbrace{\pi_\ast( c_1(\mathcal{L}_m))}_{=0} \cdot \lambda^2 =0 .
\end{align*}

Using these and $c_1(\mathcal{T}_\pi)= -c_1(\omega_\pi)$, we get that $c_1(\pi_\ast \mathcal{L}_m^{\otimes n})$  equals
\begin{align*}
 & \pi_\ast\biggl\lbrace \left( 1 + n c_1(\mathcal{L}_m) + \frac{n^2}{2} c_1(\mathcal{L}_m)^2 + \frac{n^3}{6} c_1(\mathcal{L}_m)^3 \right) \cdot  \\
& \phantom{ == } \cdot \left( 1 + \frac{c_1(\mathcal{T}_\pi)}{2} + \frac{c_1(\mathcal{T}_\pi)^2 + c_2(\mathcal{T}_\pi) }{12} + \frac{ c_1(\mathcal{T}_\pi)c_2(\mathcal{T}_\pi) }{24} \right) \biggl\rbrace_3 \\
&= \frac{n^3}{6} \pi_\ast(c_1(\mathcal{L}_m)^3) - \frac{n^2}{4} (2g_m-2)\lambda + \frac{n}{12} \pi_\ast(c_1(\mathcal{L}_m) c_2(\mathcal{T}_\pi) )  - \lambda.
\end{align*}
Substituting $c_1(\mathcal{L}_m)= c_1(\mathcal{L}) - mc_1(\mathcal{E})$ and expanding the last expression yields to the claimed formula.
\end{proof}

We are now ready to prove Theorem \ref{THM-class-of-Dm} from the Introduction.

\begin{proof}[Proof of Theorem.\,\ref{THM-class-of-Dm} ]
We consider the morphism of vector bundles over $\mathcal{F}_g^{\mathfrak{N}}$,
\[ \psi_m \colon \, S^2 \mathcal{U}_{1,m} \to \mathcal{U}_{2,m} . \]
The divisor $\mathfrak{D}^{\rk (4)}_m$ is by definition the locus where $\ker(\psi_m)$ contains quadrics of rank at most four. Applying the formula from \cite[Thm.\,1.1]{FR}, we get
\[ \left[ \mathfrak{D}^{\rk (4)}_m \right] =  A^{g_m-3}_{g_m+1} \left( c_1( \mathcal{U}_{2,m} ) - 2 \left( \frac{ \rk \mathcal{U}_{2,m} }{ \rk \mathcal{U}_{1,m} } \right) c_1( \mathcal{U}_{1,m}) \right) , \]
where the coefficient corresponds to the number $A^r_e$,
\[
A^r_e = \frac{ \binom{e}{r} \binom{e+1}{r-1} \cdots \binom{e+r-1}{1} }{ \binom{1}{0} \binom{3}{1} \binom{5}{2} \cdots \binom{2r-1}{r-1} }
\]
which represents the degree of the variety of symmetric $e\times e$ matrices of corank  at least $r$ inside the projective space of symmetric $e\times e$ matrices.

By Proposition \ref{GRR}, the class
\[ c_1( \mathcal{U}_{2,m} ) - 2 \left( \frac{ \rk \mathcal{U}_{2,m} }{ \rk \mathcal{U}_{1,m} } \right) c_1( \mathcal{U}_{1,m})  \]
is equal to
\begin{align*}
& \frac{2}{ g_m + 1 } [ \kappa_{3,0,0} -3m \kappa_{2,1,0} + 3m^2 \kappa_{1,2,0}  -m^3 \kappa_{0,3,0} ]  \\
& - \frac{ g_m-1}{ 2(g_m+1) } [\kappa_{1,0,1} -m \kappa_{0,1,1} ]  + (2g_m-1) \lambda.
\end{align*}

Plugging into the latter expression the following straightforward identities:
\[
\begin{cases}
2\gamma_0 + m^2\gamma_2  = 2\kappa_{3,0,0} - \frac{g_m-1}{2} \kappa_{1,0,1} +6m^2 \kappa_{1,2,0} , \\
-m^3 \gamma_3 -6m \gamma_1  = -2m^3\kappa_{0,3,0} + \frac{g_m-1}{2} m \kappa_{0,1,1} -6m\kappa_{2,1,0} ,
\end{cases}
\]
one gets

\begin{displaymath}
\frac{ 2 }{ g_m +1 } \gamma_0 - \frac{ 6m }{ g_m +1 } \gamma_1 + \frac{ m^2 }{ g_m +1 } \gamma_2 - \frac{ m^3 }{ g_m +1 } \gamma_3 + (2g_m-1) \lambda .
\end{displaymath} \phantom{.}

The result follows.
\end{proof}

redpajama_set_name: RedPajamaArXiv