text:
module Auto::TransferJournal

  # 費用の自動配賦
  class AllocatedCostFactory < Auto::AutoJournalFactory

    def initialize( auto_journal_param )
      super( auto_journal_param )
      @src_jd = auto_journal_param.journal_detail
      @src_jh = @src_jd.journal
    end

    def make_journals
      jh = @src_jd.transfer_journals.build(auto: true)
      jh.company_id = @src_jh.company_id
      jh.ym, jh.day = calc_ym_and_day(@src_jd)
      jh.slip_type = SLIP_TYPE_AUTO_TRANSFER_ALLOCATED_COST
      jh.remarks = @src_jh.remarks + '【費用配賦】'
      jh.create_user_id = jh.update_user_id = @src_jh.update_user_id

      # 明細作成準備
      # 配賦用の勘定科目を特定
      a = Account.find(@src_jd.account_id)
      if a.path.index(ACCOUNT_CODE_CORPORATE_TAXES)
        # 法人税等
        shared_cost = Account.find_by_code(ACCOUNT_CODE_SHARED_TAXES)
        allocated_cost = Account.find_by_code(ACCOUNT_CODE_ALLOCATED_TAXES)
      else
        shared_cost = Account.find_by_code(ACCOUNT_CODE_SHARED_COST)
        allocated_cost = Account.find_by_code(ACCOUNT_CODE_ALLOCATED_COST)
      end

      # 配賦明細の作成
      JournalUtil.make_allocated_cost(@src_jd).each do |branch, cost|
        # 自身の負担分を作成しない
        next if branch.id == @src_jd.branch_id

        # 本社費用負担
        jd = jh.journal_details.build
        jd.detail_no = jh.journal_details.size
        jd.dc_type = DC_TYPE_DEBIT
        jd.account_id = shared_cost.id
        jd.branch = branch
        jd.amount = cost

        # 本社費用配賦
        jd2 = jh.journal_details.build
        jd2.detail_no = jh.journal_details.size
        jd2.dc_type = DC_TYPE_CREDIT
        jd2.account_id = allocated_cost.id
        jd2.sub_account_id = allocated_cost.get_sub_account_by_code(branch.code).id
        jd2.branch = @src_jd.branch
        jd2.amount = cost
      end
    end

    def calc_ym_and_day(jd)
      ajt = jd.auto_journal_type.to_i

      if ajt == AUTO_JOURNAL_TYPE_PREPAID_EXPENSE
        ym = HyaccDateUtil.next_month(jd.journal.ym)
        [ ym, 1 ]
      elsif ajt == AUTO_JOURNAL_TYPE_ACCRUED_EXPENSE
        ym = HyaccDateUtil.last_month(jd.journal.ym)
        [ ym, HyaccDateUtil.last_day_of_month(ym) ]
      elsif ajt == AUTO_JOURNAL_TYPE_DATE_INPUT_EXPENSE
        [ jd.auto_journal_year.to_i * 100 + jd.auto_journal_month.to_i, jd.auto_journal_day.to_i ]
      else
        [ jd.journal.ym, jd.journal.day ]
      end
    end
  end
end


text:
Search www.buckner.org
Family Hope Centers
Family Pathways
Camp Buckner
Dallas Buckner Center for Humanitarian Aid
Shoes For Orphan Souls®
Art Weiner carries on legacy of caring through Buckner Children's Village
Her picture is the first thing Art Weiner sees when he wakes up each morning and the last thing he sees before nodding off to bed at night. She's his everything and always will be.
She, of course, is his beloved wife Alice.
"She was the most wonderful person I've ever known," Art says. "We were only married 71 years. We were more than the usual married couple. We were friends."
Alice Weiner lost her extended battle with Alzheimer's disease, but Art Weiner carries on fighting for the causes she would have wanted. He's particularly supportive of Alzheimer's research and caring for vulnerable children, including those Buckner serves in Southeast Texas.
Art is financially supportive of the ministry through Buckner Children's Village. His generosity and passion has helped minister to children at their most vulnerable.
He's also sponsored parties that bring the children in Buckner Emergency Shelter together so they can relax and enjoy themselves. Children come to the shelter where Buckner staff members assess their needs so they can best be matched with foster families.
"Children are simply drawn to Mr. Weiner," says Laura May, executive director of Buckner in Southeast Texas. "He's made an incredible difference in their lives when they most need it. They gather near him to hear his stories and soak in his wisdom. He inspires children to do their best in school and reach their full potential."
Time and time again Art creates very special memories for the boys and girls at Buckner. Most notably, the children came together with Art for an Independence Day party that included a local veterans group, as well as guests from Pelican Bay.
"It was a very memorable moment watching the children's faces as two of America's finest demonstrated the folding of the flag," Art said," they shared the meaning of the flag and the ceremony. Most of the boys and girls had never seen this before, and they loved it."
Young people particularly love hearing stories of when Art played baseball.
"They're willing to talk," he says. "They want to talk. We talk about all kinds of things. That's what this is all about – to provide educational materials and meet their needs."
Art has connected with the children and enjoys providing opportunities that allow them to tuck away memories of special events they will never forget. The majority of the children he visits reside in the Emergency Shelter at Buckner for 30-90 days, and though he rarely sees the same child twice, he connects with each group he visits in the same way.
"They are kids who have gone through a tragedy," Art says. "Their lives have been disrupted and they aren't quite sure what's going to happen to them next. I just encourage them to get an education, study, work hard and choose to do something in life that they enjoy doing…then it's not work. The skies the limit to what they can do with their lives."
Looking at the picture of his wife, Art smiles. She would have been proud to see the joy on the children's faces at Buckner.
"Everything I do is in her name," he says. "Everyone knows of her. I have a huge photograph of her in our bedroom. It's what I see before I go to sleep. It's what I see when I wake up. I talk to her. I talk to her all the time. I talk to her about what I'm doing on her behalf."
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to deserialize SAML request in php - Can't install LightSAML I am trying to install LightSAML https://packagist.org/packages/lightsaml/lightsaml, into a Laravel app, to do some very basic deserialization of a HTTP POST request, but getting errors:
 Your requirements could not be resolved to an installable set of packages.

 Problem 1
 - Conclusion: don't install lightsaml/lightsaml 1.3.6
 .....

Installation failed, reverting ./composer.json to its original content.

It does seem a little old so not sure if I can make it work at all - if not, can anyone suggest even simpler means of deserializing and accessing the individual attributes of a SAML request?
I have also seen https://github.com/onelogin/php-saml, however it looks like it does more than I need - I don't need to do the actual auth part using SAML, I merely need to accept a SAML http post and use that data for my own bespoke auth token creation.

A: If the idea is just to decode the SAMLResponse data that's being POST'ed to your endpoint, then you can achieve that easily (as long as it's not encrypted).
The SAMLResponse is base64 encoded, so you just have to decode it. In the controller method where you're receiving the data, you'll do something like:
// Decode the data into the original XML document
$xmlPayload = base64_decode($request->get('SAMLResponse'));

Now, the XML data you've just decoded, needs to be parsed. Given the document is small, using DOMDocument should be enough:
// Load the XML document
$doc = new DOMDocument();
$doc->loadXML($xmlPayload);

// Traverse User elements
foreach ($doc->getElementsByTagName('Attribute') as $attribute) {
    var_dump($attribute->nodeName.'[@'.$attribute->getAttribute('Name').'] -> '.$attribute->nodeValue);
}

That will output something like:
string(34) "saml2:Attribute[@firstName] -> Ray"
string(37) "saml2:Attribute[@lastName] -> Charles"
string(48) "saml2:Attribute[@email] -> ray.charles@music.com"
string(48) "saml2:Attribute[@login] -> ray.charles@music.com"
string(44) "saml2:Attribute[@id] -> 11uboeg2g0bKNxyk01z7"

This is just an example, since the attributes will probably change (depending on how your Single Sign On IdP is set).
I tested with a payload from Okta.

A: I think that the solution is in error:  Your requirements could not be resolved to an installable set of packages. I guess that in your libs must be a conflict with LightSaml. Just incompatible.
Perhaps there's a composer.lock file in /Users/user/.composer or other place that hinders the update.
Try that steps:

*

*got inside global composer folder (C:\Users\your_name\AppData\Roaming\Composer)

*edited the composer.json (added to require : "your_package" : "number.*" )

*in command line: composer global update.

As you wrote, solution might be adding:
"repositories": [
    {
        "type": "vcs",
        "url": "https://github.com/frostieDE/lightSAML"
    }
],

Good luck

A: Sorry I had to add this to composer and update:
"repositories": [
    {
        "type": "vcs",
        "url": "https://github.com/frostieDE/lightSAML"
    }
],

redpajama_set_name: RedPajamaStackExchange


Just stopping by with a glimpse of some new arrivals at Birdhouse Books.
You'll find all these goodies at Birdhouse Books on eBay!
Lovely French postcard, a black and white photo of a cat watching birds from an apartment railing. This charming card would look great framed.
Vintage postcard of cats exploring the patio at the Hemingway House, Key West, Florida.
Lovely vintage New Year postcard with a fireplace and spinning wheel.
This 1910 New Year postcard shows a book and pink flowers. It is a John Winsch postcard.
This vintage B.B. London postcard celebrates the New Year with lovely pink dogwood blossoms in a basket.
What a charming vintage postcard! "Look Pleasant." There is a short verse with daisies and a rural scene.
Alexander and the Wind-Up Mouse is a picture book by Leo Lionni.
The Snowy Day by Ezra Jack Keats is one of my favorite picture books for children. This lovely story is about snow and winter and friendship.
Wee Witches' Halloween is a picture book by Jerry Smath.
The Berenstain Bears and the Prize Pumpkin is a cute Thanksgiving picture book for children.
My kids just love the Wee Witches Halloween and The Berenstein Bears! Great weekend picks!
Thanks! The Wee Witches' Halloween is a cute read aloud. I appreciate the visit!


text:
Dolly Parton makes her first appearance on TV's "The Porter Wagoner Show"
Dolly Parton makes her first in-concert appearance in Porter Wagoner's show in Lebanon, Virginia. She's greeted with boos and chants for Norma Jean, the female singer she replaced
Sevier County holds the first Dolly Parton Day as 7,000 people gather at the courthouse for a show that also features Porter Wagoner and Mel Tillis
Dolly Parton and her uncle, Bill Owens, establish Owepar, a publishing company that owns the copyrights to their songs
Dolly Parton records with Porter Wagoner for the first time
Porter Wagoner & Dolly Parton record "The Last Thing On My Mind"
Dolly Parton replaces Norma Jean on "The Porter Wagoner Show"
Porter Wagoner & Dolly Parton make their first Grand Ole Opry appearance as a duo, performing "The Last Thing On My Mind"
Dolly Parton records as a solo artist for RCA for the first time
Porter Wagoner & Dolly Parton record "Holding On To Nothin'"


And there are a few tell-tale signs.
The tree looks like it has attended too many parties, with baubles and tinsel hanging on by a thread, I can't see the carpet for toys and if I see another mince pie it will be too soon.
Having said that it was a lovely day, complete with too much turkey and a sherry or three.
And the kids only got up at 3am, so that was a bonus.
Now I'm looking towards New Year's Eve. A night where I fall asleep on the sofa and wake up just in time for the clock to strike midnight.
On New Year's Day I'll be full of the joys of January having made lots of resolutions, which will last all of about five minutes.
As we move towards the end of another busy year, we turn our attention to new beginnings.
January is a time where people like to make changes and resolutions. Mine only last about five minutes, but I always have the very best intentions.
It's also the optimum time to start a new business.
At my accountancy firm Stephenson Smart, we offer a free consultation to anyone looking for advice on how to get the ball rolling.
There are lots of small things to consider, but most importantly you obviously need to consider how you are financing it.
Are you applying for a loan, do you have savings, or are you using inheritance money?
And where will you run the business from? A shop, your home, or perhaps you will be on the move and need to invest in a vehicle?
The other important factor is to think about your overheads and profit. Are you going to operate as a sole trader and pay tax, or register as a limited company to separate it from the individuals working within it?
If you are employing people you should think about salaries, dividends and payroll.
It can be a daunting process, but we can make it simpler.
Unlike my Christmas tree lights, which are perhaps the most complicated mess ever.


text:
#pragma once

#include "get_editable_media/v0.hpp"

namespace mf {
namespace api {
/** API action path "system" */
namespace system {
/** API action "system/get_editable_media" */
namespace get_editable_media {

// Default version
using namespace v0;  // NOLINT

}  // namespace get_editable_media
}  // namespace system
}  // namespace api
}  // namespace mf

redpajama_set_name: RedPajamaGithub


In the 2017-2018 academic year, more than 10,000 Pennsylvania students chose to get their education from one of the most successful online public schools in the nation. Find out why.
At The Pennsylvania Cyber Charter School, or PA Cyber, there are as many stories as there are enrollees.
One of the largest, most experienced and successful online public schools in the nation, PA Cyber's online learning environment, personalized instruction, and varied courses meet state standards. Its teachers provide a rich, well-rounded learning experience and there are countless opportunities for enrichment. This year, more than 1,300 PA Cyber students from 63 of Pennsylvania's 67 counties received diplomas. They leave with an exceptional head start.
As her senior class representative, Melanie Hulse joined PA Cyber's DECA chapter her sophomore year and served as its president as a senior. This experience not only inspired her graduation speech, but it also afforded her the chance to gain valuable leadership and presentation skills.
Melanie, who is attending Robert Morris University, where she will study marketing and media arts, recognized she was an independent learner–she was self-motivated. "It's about building opportunities for yourself and knowing how to better your education and what works for you as an individual learner and student," she said.
In the same senior class as Melanie is Isaac Melvin, who enrolled in PA Cyber in ninth grade, after nine years in a homeschool setting. His enrollment in PA Cyber allowed him to stay involved in community activities, while participating in the school's countless extracurricular opportunities. Isaac joined the Raspberry Pi Club, a basic programming group, took part in 3D printing, and served as captain of the Cyber Patriots team, all of which are science, technology, engineering and math, or STEM, related activities and helped shape his interest in aeronautical engineering.
As Isaac prepares to enter the Air Force Academy–an elite prep school that accepts only 125 students nationwide and includes a commission as a Second Lieutenant in the U.S. Air Force upon graduation–he reflects on how crucial being a self-motivated learner is to success.
If you think PA Cyber is a good fit for your child, learn more at one of their upcoming information sessions. You can get more details, and register, by going here.
Do you have a question for a PA Cyber parent? If so, please leave it in the comments section below.
Serving students in kindergarten through 12th grade, the Pennsylvania Cyber Charter School (PA Cyber) is one of the largest, most experienced, and most successful online public schools in the nation. As a public school, PA Cyber is open for enrollment by any school-age child residing in the Commonwealth of Pennsylvania, and does not charge tuition to students or families.


text:
Q: Expression Blend 4 Right to Left Issue I have recently installed Expression Blend 4 and created a test Silverlight 4 project.
When I set the main page FlowDirection to RightToLeft the designer won't change the direction but if I run the application it will be displayed correctly.
Is this a bug or do I have to do something?
Thanks.

A: I believe you were the one who also put the post at the microsoft social site (available here) but since it took me a while to find it, I'll also put the response here:
Unni Ravindranathan - MSFT:

We do not support RTL on the design-surface, so what you are seeing is currently by design (the value that you set is ignored). We hope to be able to support it in the future, however.

Let's hope they would!


text:
Fodor Katalin (1931–1994) pszichológus
 Fodor Katalin (1957) válogatott kosárlabdázó
 Fodor Katalin (1966) válogatott labdarúgó
 Fodor Katalin (?) Harangozó Gyula-díjas táncművész

redpajama_set_name: RedPajamaWikipedia


Raising My Little Superheroes : What Acceptance means to me.
My name is O and Mummy asked me what acceptance meant to me because this month, April, is Autism awareness and acceptance month worldwide.
The word acceptance to me means accepting and respecting other people's differences. Acceptance means that people are embraced by others - differences and all. Acceptance means that I belong - as I am - in the community that I live in. Acceptance means that we shouldn't have to change who we are just so that we can fit into what other people think is normal, even though there really isn't a normal way of being.
When people accept others as they are, they are saying "You are you and I am me, and that's okay. Different is good."
When people accept me and my little brother for who we are, they've made a conscious effort not just to know what we do but also to understand and accept us for who we are and the things that we do. My friends who accept me know that I wear my headphones not to stand out but because too much noise hurts my ears and my brain. They know and understand that sometimes I hide under my desk because my classroom is too busy for my brain.
I want to live in a world in which acceptance is not just a goal, but it is an actual reality. A world in which neurodiversity is just another way which makes people unique. A world in which everyone will agree that diversity is a part of what makes our world a beautiful place. A world in which everyone who is different in some way, feels like they belong. There are too many people and not just people who have Autism, who don't feel like they belong or don't feel like they are welcomed by the communities in which they live.
I think that acceptance will take time. Everyone needs to practice acceptance, especially adults because some adults have forgotten what it is like to be different. Kids, when they are really young, are good at accepting other people for who they are but some adults don't like differences. And some adults are really good at projecting their thoughts onto kids, even the negative thoughts. When this happens, the kids don't accept others when they are different. I've felt this from some kids that I go to school with and it makes me really sad and worried for the future.
I think that everyone, but mostly adults, needs to consciously practice acceptance for it to become part of their everyday routine. Because every time we practice acceptance towards something that makes us uneasy, we will create new neural pathways and strengthen the old neural pathways that are in our brains that tell us difference in others is a good thing. And if kids see adults practising acceptance, then they will also be more accepting of others.
That's what acceptance means to me.


Here is a fun video. Watch the capturing of all of the Villains of Skylanders Trap Team.
And if you like this video check out last years All Bad Guys of Skylanders Swap Force.
Welcome to the final Chapter gameplay video for Skylanders Trap Team. We have played through all 18 chapters, and with this Nightmare Express video we have played through all 4 of the Adventure Packs. Watch as Conner plays as Ka-Boom, and I play as Legendary Deja Vu as we play through an adventure through Flynn's eyes.
Today the boys and I play the new Sunscraper Spire level from the new Light Element Expansion Pack. I play with the new Knight Light, which I thought was the first time I had played with the character, but actually I did play with him for a brief second on the Midnight Museum level. Conner starts with Knight Mare from the Dark Element Expansion Pack so we start with the forces of Light and Dark working together. Overall we found this level and boss battle to be much more interesting than the Midnight Museum. Give it a watch and let us know what you think.
We're back! You might think that once you beat Trap Team that you have nothing else to do. That's never the case in a Skylanders game. Today we dive into the Dark Element Expansion Pack. It comes with one new level called Midnight Museum. Since it is the first extra level we are playing, it's listed for us as Chapter 19. I'm guessing it will be a different chapter for you if it's not your first expansion level. Either way watch as we use our new Knight Mare Dark Element Trap Master and Winterfest Lob-Star (as well as a few others) to tackle this level and try to bring down the new Dark Villain Night Shade.
Here it is! The last chapter of Skylanders Trap Team – The Ultimate Weapon. We reached our goal of finishing the campaign by Christmas. We're about to take a little break for the holidays, but we'll be back soon with a Mega Epic Wave 3 Unboxing, more Arena Battles, Kaos Doom Challenges and a look at each of the four expansion levels, the Mirror of Mystery, Nightmare Express, Midnight Museum and Sunscraper Spire. We'll also have our Trap Team Cutscene Theater video, some character reviews, and maybe a couple other fun videos I'm thinking about doing. But for now, watch as Conner and I use our army of Skylanders to battle Smoke Scream and finally Kaos! I hope the boys don't have any nightmares about Kaos coming through the TV or portal. 🙂 Enjoy watching The Ultimate Weapon and Happy Holidays!
Today we play Chapter 16 of Skylanders Trap Team: The Golden Desert. We make our way through the level trying to get to the Golden Queen's Lair. Along the way we capture Bone Chompy, and Grave Clobber. Eventually we end this level with an Arena Battle thanks to the Golden Queen, who we will most likely catch in the next level.
Today we play Chapter 14 of Skylanders Trap Team: Operation Troll Rocket Steal. I start off as Gearshift as Conner starts with Bushwhack. After we upgrade our characters a little, we head off to try to find and capture Grinnade and Threatpack. On this level we find that we have a couple problems with the co-op jumping puzzles. One of the puzzles may have also been made harder by using Trap Masters. Give it a watch and see how we do.


text:
Tweaker, "Call The Time Eternity"
Call The Time Eternity
True, Chris Vrenna's Tweaker has always carried the reputation of being one of those intermittent "producer's projects", a free-form playground to which a well-known studio wizard returns to in their spare time between work with larger bands, both in the studio and on the road. However, Vrenna's always ducked the major pitfall of most projects of that ilk (wonderful, super-detailed production, but short on memorable tunes) by changing the sound, feel, and even standards by which Tweaker's been judged not with each album, but with each track. Guest appearances and quick flips between breaks, stormy guitar and moody washes made the first two Tweaker records slippery beasts. Third outing Call The Time Eternity feels much more grounded, a tactile and directly percussive record which forthrightly grapples with anxiety and frustration.
What's immediately noticeable about Call The Time is how much more of its spotlight is on the rhythmic dimension of Vrenna's work than before. The swampy guitar and wavering textures which were prominent on The Attraction To All Things Uncertain and 2 A.M. Wakeup Call are present, but muted in comparison to the clanging, jarring, yet often undeniably funky passages cooked up here. The brief, bleepy instrumental "Remorseless" from 2 A.M. Wakeup Call perhaps pointed towards this record's mode: furtive, incessant play between percussion and low-pitched synths that accent more than lead. "A Bit Longer Than Usual" feels like something of a roadmap to the overall aesthetic: a nodding beat grows more angular and menacing as extra kicks and growling pads are overlaid, but the matter-of-fact forward propulsion of the track remains.
As I said, despite the clean, unpretentious presentation of these tunes, there's some swing to the rhythms which keeps things from becoming too clinical despite the dampening of the "organic" elements in Vrenna's toolbox. By the time groovy mid-album interlude "Getting Through A Bad Night" rolls around, instrumental hip hop legends like DJ Shadow and RJD2 are the names which come to mind, rather than the IDM comparisons which you might expect from a "Chris Vrenna gets into deep drum programming" record.
There are a couple of exceptions to Call The Time's central modus operandi. Vrenna concocts richer platters to suit guest vocals from Jessicka Adams (of Scarling) and Karin (of Collide), all woozy strings and filters, but with a surfeit of fluttering drum fills that keep the focus on the album's rhythmic dimension. Less deft is the marriage of the album's core elements and some seething, chuggy guitar on "Areas Of The Brain" (which brings to mind Marilyn Manson, the outfit with whom Vrenna recently finished a tour of duty), which feels like something of a misstep.
While less lush than either previous Tweaker record, Call The Time Eternity is no less considered. Indeed, its themes of stress, insomnia, and general mental disquiet (not new topics of Tweaker work but never so prominent than here) give it a singular focus that makes it far more cohesive listen than its predecessors. This makes for a tense and uneasy record (other track titles: "This Is Ridiculous," "I Don't Care Anymore," "Wasted Time"), but it's by no means an unpleasant one. Vrenna's stripped-down approach holds up from a variety of angles, and it's exciting to hear one of electronic music's most varied producers venting via rhythm.
PreviousAn Interview With Mark Spybey
NextTracks: October 29th, 2012
Necrotek, "Blacklight Magick"
Observer: Antechamber & Autopsie d'une ombre
THYX, "The Way Home"
Replicas: The Birthday Massacre, "Imagica"


text:
Inc. Magazine Unveils Its First-Ever List of the Midwest's Fastest-Growing Private Companies— The Inc. 5000 Series: Midwest
The Negotiator Guru Ranks No. 15 on the inaugural 2020 Inc. 5000 Series: Midwest
NEW YORK, March 25, 2020 – Inc. magazine today revealed that The Negotiator Guru is No.15 on its inaugural Inc. 5000 Series: Midwest list, the most prestigious ranking of the fastest-growing private companies in Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, and Wisconsin. Born of the annual Inc. 5000 franchise, this regional list represents a unique look at the most successful companies within the Midwest economy's most dynamic segment—its independent small businesses.
"We're honored to be recognized in the Inc. 5000 list as one of the fastest growing private companies in the Midwest," said Dan Kelly, Founder and Senior Partner. The Negotiator Guru also ranked #2 in the state of Minnesota and #5 in the category of Business Products and Services. "Our success is a direct result of the value we've delivered with, and for, our global enterprise client base. Congratulations to the TNG team!"
The companies on this list show stunning rates of growth across all industries in the 12 Midwest states. Between 2016 and 2018, these 250 private companies had an average growth rate of 360 percent and, in 2018 alone, they employed more than 27,000 people and added $13 billion to the Midwest's economy. Companies based in the Chicago, Detroit, and Cincinnati areas brought in the highest revenue overall.
Complete results of the Inc. 5000 Series: Midwest, including company profiles and an interactive database that can be sorted by industry, metro area, and other criteria, can be found here starting March 25, 2020.
"The companies on this list demonstrate just how much the small-business sector impacts the economies of each Midwest state," says Inc. editor in chief Scott Omelianuk. "Across every single industry, these businesses have posted revenue and growth rates that are beyond impressive, further proving the tenacity of their founders and CEOs."
About The Negotiator Guru
The Negotiator Guru is the leading advisory firm for Salesforce contract negotiation. Our team of Senior IT Sourcing Experts provides industry leading IT contract negotiation services for a global client base. Clients engage us to source, negotiate, and manage highly complex IT contracts, transactions and suppliers. Through our deep business understanding and senior expert negotiation skills, we work closely with clients to deliver immediate and long-lasting financial impact to all stakeholders.
Founded in 2015, The Negotiator Guru is a private company based in Minneapolis, Minnesota. For more information, visit www.thenegotiator.guru.
More about Inc. and the Inc. 5000 Regional Series
The 2020 Inc. 5000 Regional Series is ranked according to percentage revenue growth when comparing 2016 and 2018. To qualify, companies must have been founded and generating revenue by March 31, 2016. They had to be U.S.-based, privately held, for profit, and independent—not subsidiaries or divisions of other companies—as of December 31, 2018. (Since then, a number of companies on the list have gone public or been acquired.) The minimum revenue required for 2016 is $100,000; the minimum for 2018 is $1 million. As always, Inc. reserves the right to decline applicants for subjective reasons.
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The world's most trusted business-media brand, Inc. offers entrepreneurs the knowledge, tools, connections, and community to build great companies. Its award-winning multiplatform content reaches more than 50 million people each month across a variety of channels including websites, newsletters, social media, podcasts, and print. Its prestigious Inc. 5000 list, produced every year since 1982, analyzes company data to recognize the fastest-growing privately held businesses in the United States. The global recognition that comes with inclusion in the 5000 gives the founders of the best businesses an opportunity to engage with an exclusive community of their peers, and the credibility that helps them drive sales and recruit talent. The associated Inc. 5000 Conference is part of a highly acclaimed portfolio of bespoke events produced by Inc. For more information, visit www.inc.com.
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text:
FP1: Leclerc puts Ferrari on top at Sochi
By Steven De Groote on Fri Sep 27, 2019 11:33 am
Charles Leclerc and Ferrari continue their strong showings by topping the first free practice session at Sochi, Russia. Max Verstappen ended up second fastest for Red Bull as Singapore Grand Prix winner Sebastian Vettel completed the top three.
Leclerc, who vows to put more trust in the team's decisions after a dispute on the team radio, set the fastest time, less than a tenth quicker than Verstappen, but more than half a second up on his team mate Vettel. All three set their best times on the softest Pirelli tyre available this weekend.
Mercedes duo Bottas and Hamilton ended up in 4th and 5th as they chose for longer runs on the medium compound tyres. Bottas's session did however end prematurely, shorly before the scheduled end, as his Mercedes W10 suffered an unusual rear wing failure.
Albon ended FP1 in 6th, ahead of both Renaults who aim to lead the midfield. Hulkenberg was fastest, as he had been in Singapore. Daniel Ricciado ended 6 tenths down, but failed to do a quick lap late in the session as he rear his car into the barriers at Turn 5. Damage appeared relatively minor, so he was able to drive his car back to the pits without much further ado.
Sergio Perez and Romain Grosjean were 9th and 10th respectively, unusually keeping McLaren out of the top 10. The orange cars did however not focus on quick laps, with Sainz completing a long stint on mediums, and Norris focusing on the hard tyre.
1 16 Charles Leclerc Ferrari 1:34.462 - 20
2 33 Max Verstappen Red Bull Racing Honda 1:34.544 +0.082s 25
3 5 Sebastian Vettel Ferrari 1:35.005 +0.543s 20
4 77 Valtteri Bottas Mercedes AMG 1:35.198 +0.736s 28
5 44 Lewis Hamilton Mercedes AMG 1:35.411 +0.949s 22
6 23 Alexander Albon Red Bull Racing Honda 1:35.484 +1.022s 22
7 27 Nico Hulkenberg Renault 1:35.740 +1.278s 21
8 3 Daniel Ricciardo Renault 1:36.287 +1.825s 20
9 11 Sergio Perez Racing Point BWT Mercedes 1:36.321 +1.859s 27
10 8 Romain Grosjean Haas Ferrari 1:36.516 +2.054s 23
11 55 Carlos Sainz McLaren Renault 1:36.523 +2.061s 28
12 10 Pierre Gasly Scuderia Toro Rosso Honda 1:36.538 +2.076s 25
13 20 Kevin Magnussen Haas Ferrari 1:36.596 +2.134s 21
14 18 Lance Stroll Racing Point BWT Mercedes 1:36.714 +2.252s 26
15 7 Kimi Räikkönen Alfa Romeo Racing Ferrari 1:36.770 +2.308s 22
16 4 Lando Norris McLaren Renault 1:36.844 +2.382s 30
17 99 Antonio Giovinazzi Alfa Romeo Racing Ferrari 1:37.328 +2.866s 18
18 63 George Russell Williams Mercedes 1:38.520 +4.058s 27
19 26 Daniil Kvyat Scuderia Toro Rosso Honda 1:38.550 +4.088s 5
20 88 Robert Kubica Williams Mercedes 1:38.670 +4.208s 29
F1: Free practice 1GP Russiaprevious | next
27-09-2019 FP2: Red Bull 'feels alive' as V...
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The Sept. 13 Nintendo Direct for Switch and 3DS games was, in a word, massive. Nintendo's Yoshiaki Koizumi took center stage to walk viewers through nearly 50 upcoming games for those platforms, with several of the most anticipated titles being stamped with a launch window. You can watch for yourself, below.
If you're gaming on a Nintendo platform, then the message from yesterday's Direct was pretty straightforward: You're going to be very busy in the coming months. There was a little something for everyone here, including games from classic Nintendo franchises, indies, sports games and even a couple of major surprises from Bethesda.
Speaking of which, that last one was probably the biggest pull from yesterday's 45-minute Direct. While we don't have release dates yet, Bethesda has announced that both DOOM and Wolfenstein II: The New Colossus will be heading to the Switch. The former was actually shown off briefly and, while the graphics clearly took a bit of a hit, it appears to be the exact same game launched on other platforms last year. So long as it plays the same, we doubt anyone will complain about less sharp textures and a shorter draw distance when Doom arrives for "Holiday 2017." Wolfenstein was announced but not on display, so we figure that one's quite a bit further off. First up, though, is The Elder Scrolls 5: Skyrim, which we have to look forward to on Nov. 17.
Sadly missing the Halloween gaming window, both Resident Evil Revelations games will arrive on Nov. 28 for the Nintendo Switch. Just a few days later, RPG fans will be able to dive into Xenoblade Chronicles 2, arriving Dec. 1. Combine all of that with Super Mario Odyssey on Oct. 27 and it's looking to be a ridiculous holiday season for Switch gamers. Oh, and the last segment of the Direct features a whole bunch of new footage from that very game.
The final dated game for the Switch is Square Enix's new RPG, Lost Sphere, due out Jan. 23. Otherwise, Kirby Star Allies is due out in the spring of next year while Dragon Quest Builders and another Square Enix joint, Project Octopath Traveler, are simply tagged as being out sometime in 2018.
Over to the 3DS and a trio of games were given hard release dates that we were not formerly aware of. For starters, freaking Minecraft is out on the portable console as of today, Sept. 14. Brawler fans will want to check out Kirby: Battle Royale on Jan. 19 but, before that, Mario Party: The Top 100 will combine the 100 most popular Mario Party mini-games into a single collection on Nov. 10.
Again, Koizumi talked about a bunch of other games, so you'll want to at least skim through the entire video to get the full rundown, including new details on the upcoming Pokemon games, Fire Emblem Warriors, some new console skins and amiibo and more.


At Morton & Germany, PLLC, our medical malpractice team is headed by attorney Gary K. Morrell. For more than 30 years, Mr. Morrell has been helping patients and the families of patients in Memphis who have been injured as a result of medical negligence. With years of experience, a keen understanding of the legal and medical issues that factor into these cases, as well as an unwavering commitment to helping clients achieve full and just compensation, Mr. Morrell and the rest of our team will provide you with the support and representation necessary to hold negligent health care providers accountable and help you recover.
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More than just recoveries and recognitions, the testimonials of our current and former clients speak to the personalized service that defines our practice. We encourage you to speak with us, review what our clients have to say, and learn how we can represent you and your family.
Reach out to us at Morton & Germany, PLLC, and speak with attorney Gary K. Morrell. From our office in Memphis, we represent clients throughout Tennessee, Arkansas and Mississippi. Call 901-522-5067 or take a moment to submit an online contact form to schedule your consultation. Se habla español.
Please note our disclaimer below and understand that neither Gary K. Morrell nor Morton & Germany, PLLC, offer any guarantee of case results. Prior results do not guarantee a similar outcome. The success of each claim is directly related to the unique facts and circumstances presented.


text:
\section{Introduction}\label{sec1}
The rotating pulsars are usually associated with strong magnetic field ($B$ on
the order of 10$^{14}$ to 10$^{19}$ G) \cite{Latt07,Bro00,Dex17}, and effects
of the magnetic field on the equation of state (EOS) of neutron star (NS) matter
might not be negligible. This important issue has been investigated by many authors
(see Sec.~9 of Ref. \cite{Latt07} and references therein), and the impact on
the EOS by the magnetic field of a hydrodynamically stable NS was shown to be
essential only if the field intensity $B\gtrsim 10^{18}$ G. In particular,
the complete spin polarization of neutrons likely occurs at $B\gtrsim 4.41\times
10^{18}$ G \cite{Bro00}. Given a common belief that the magnetic field of NS is
usually much weaker than the upper limit of $B\approx 10^{19}$ G, it is often
neglected in numerous mean-field studies of the EOS of NS matter. With the first
direct observation of the binary NS merger GW170817 by the LIGO and
Virgo Scientific Collaborations \cite{Abbott17}, a constraint on the tidal
deformability of NS has been deduced and translated into a constraint on
the radius and mass of NS \cite{Abbott18}. This GW170817 constraint is now
widely used to validate the mass and radius of NS predicted by different models,
which usually neglect the spin polarization of baryons.

Recently, the ``blue" kilonova ejecta observed in the aftermath of the NS merger
GW170817 \cite{Abbott17c,Evan17} have been suggested by Metzger {\it et al.}
\cite{Metzger18} to be caused by both the $\gamma$ decay of the \textit{r}-process nuclei
and magnetically accelerated wind from the strongly magnetized hypermassive NS
remnant. A rapidly rotating hypermassive NS remnant having the magnetic field of
$B\approx (1–3)\times 10^{14}$ G at the surface was found necessary to explain
the velocity, total mass, and enhanced electron fraction of the blue kilonova ejecta
\cite{Metzger18}. Because the strength of magnetic field remains quite strong
in the outer core of magnetar \cite{Fuji14}, partial or full spin polarization
of baryons might well occur during the GW170817 merger.

In general, the spin polarization of baryons can be explicitly taken into account
in a microscopic model of nuclear matter (NM) with proper treatment of the
spin- and spin-isospin dependencies of the in-medium interaction between baryons.
For example, Vida\~na {\it et al.} \cite{Vidana02,Vidana16} have studied the
spin-polarized neutron matter within the Brueckner-Hartree-Fock (BHF) formalism
starting from a free nucleon-nucleon (NN) interaction, to explore the magnetic
susceptibility of high-density neutron matter and possible phase transition
to the ferromagnetic state as origin of the NS magnetic field. Aguirre {\it et al.}
\cite{Agui14} have considered explicitly symmetric NM and neutron matter at finite
temperature embedded in the external magnetic field with $B\simeq 10^{14}$$-$$10^{18}$ G,
and the spin polarization of baryons $\Delta$ was found strongest at low matter
densities and becomes weaker with the increasing baryon density $n_{\rm b}$. A
similar study by Isayev and Yang \cite{Isayev12} shows that high-density neutron
matter embedded in the strong magnetic field might be partially spin-polarized when
$B\gtrsim 10^{18}$ G. Tews and Schwenk have recently considered the EOS of
fully spin-polarized NS matter \cite{Tews20}, and concluded that it is ruled out
by the GW170817 constraint. The complex magnetic-field configuration of the magnetar
has been investigated by Fujisawa and Kisaka \cite{Fuji14}, and the field intensity
was shown to diminish gradually to $B\simeq 0$ from the surface to the center of NS, so
that the baryon matter in the center of NS would not be spin-polarized even for
magnetar. A partial spin polarization of NS matter is, however, not excluded
by these studies, and it is of interest to investigate its impact on the EOS
of NS matter.

Motivated by the magnetar scenario by Metzger {\it et al.} \cite{Metzger18}
for the ``blue" kilonova ejecta of GW170817, we explore in the present work
the EOS of the $\beta$-stable np$e\mu$ matter with different partial
spin polarizations of baryons ($0 \lesssim\Delta\lesssim 1$). Like the isospin asymmetry,
the spin asymmetry of baryons is shown to have a strong impact on the total energy
and pressure of NM. In particular, the total nuclear symmetry energy has a strong
repulsive contribution from the spin-symmetry energy, which in turn can affect
significantly the radius and mass of a magnetar.

\section{Hartree-Fock approach to the spin-polarized nuclear matter}
\label{sec2}
The nonrelativistic Hartree-Fock (HF) method \cite{Loan11} is used in the present
work to study the spin-polarized NM at zero temperature, which is characterized
by the neutron and proton number densities, $n_{\rm n}$ and $n_{\rm p}$, or
equivalently by the total baryon number density $n_{\rm b}=n_{\rm n}+n_{\rm p}$
and neutron-proton asymmetry $\delta=(n_{\rm n}-n_{\rm p})/n_{\rm b}$. The spin
polarization of baryons is treated explicitly for neutrons and protons by using the
densities with baryon spin aligned up or down along the magnetic-field axis
$\Delta_{\rm n,p}=(n_{\uparrow {\rm n,p}}-n_{\downarrow {\rm n,p}})/n_{\rm n,p}$.
The total HF energy density of NM is obtained as
\begin{equation}
\mathcal{E}=\mathcal{E}_{\rm kin}+{\frac{1}{ 2}}\sum_{k \sigma \tau}
\sum_{k'\sigma '\tau '} [\langle{\bm k}\sigma \tau, {\bm k}' \sigma' \tau'
 |v_{\rm D}|{\bm k}\sigma\tau, {\bm k}' \sigma' \tau' \rangle
+ \langle{\bm k}\sigma \tau, {\bm k}'\sigma' \tau' |v_{\rm EX}|
{\bm k}'\sigma \tau, {\bm k}\sigma' \tau' \rangle], \label{eq1}
\end{equation}
where $|{\bm k}\sigma \tau\rangle$ are plane waves, and $v_{\rm D}$ and $v_{\rm EX}$ are
the direct and exchange terms of the effective (in-medium) NN interaction.

We have considered for the present study the density dependent CDM3Y$n$ interaction
that was successfully used in the HF studies of NM \cite{Loan11,Tan16} and the
folding model studies of nucleus-nucleus scattering \cite{Kho97,Kho00}. In fact, the
CDM3Y$n$ interaction is the orginal $G$-matrix based M3Y interaction \cite{Anan83}
supplemented by the realistic density dependences $F_{\rm st}(n_{\rm b})$ of the
spin- and spin-isospin-dependent terms of the M3Y interaction
\begin{align}
& v_{\rm D(EX)}(n_{\rm b}, r)=  F_{00}(n_{\rm b})v_{00}^{\rm D(EX)}(r) +
 F_{10}(n_{\rm b}) v_{\rm 10}^{\rm D(EX)}(r)({\bm\sigma}\cdot {\bm\sigma}') \nonumber \\
& +F_{01}(n_{\rm b}) v_{01}^{\rm D(EX)}(r)({\bm\tau}\cdot {\bm\tau}')+F_{11}(n_{\rm b})
v_{11}^{\rm D(EX)}(r)({\bm\sigma}\cdot {\bm\sigma}') ({\bm\tau}\cdot {\bm\tau}').
\label{eq2}
\end{align}
The radial parts of the direct and exchange terms of the interaction (\ref{eq2})
are determined from the spin singlet and triplet components of the M3Y interaction
\cite{Anan83}, in terms of three Yukawa functions \cite{Kho96} (see Table~\ref{t1}),
$v^{\rm D(EX)}_{\rm st}(r)=\displaystyle\sum_{\nu=1}^3 Y^{\rm D(EX)}_{\rm st}(\nu)
\exp(-R_\nu r)/(R_\nu r)$.
\begin{table} [bht]
\caption{Yukawa strengths of the $G$-matrix based M3Y interaction \cite{Anan83}.}
 \vspace{0cm} \label{t1}
\addtolength{\tabcolsep}{3pt}
\begin{tabular}{cccccccccc}\hline\hline
$\nu$ & $R_{\nu}$ & $Y^{\rm D}_{\rm 00}(\nu)$ & $Y^{\rm D}_{\rm 10}(\nu)$ &
$Y^{\rm D}_{\rm 01}(\nu)$ & $Y^{\rm D}_{\rm 11}(\nu)$ & $Y^{\rm EX}_{\rm 00}(\nu)$ &
$Y^{\rm EX}_{\rm 10}(\nu)$ & $Y^{\rm EX}_{\rm 01}(\nu)$ & $Y^{\rm EX}_{\rm 11}(\nu)$ \\
& (fm$^{-1}$) & (MeV) & (MeV) & (MeV) & (MeV) & (MeV) & (MeV) & (MeV) & (MeV)  \\ \hline
1 & 4.0 & 11061.625 & 938.875 & 313.625 & -969.125& -1524.25 & -3492.75 & -4118.0 & -2210.0 \\
2 & 2.5 & -2537.5   & -36.0   & 223.5 & 450.0 & -518.75 & 795.25 & 1054.75 & 568.75  \\
3 & 0.7072 & 0.0    & 0.0     & 0.0 &   3.4877 & -7.8474 & 2.6157 & 2.6157 & -0.8719 \\
\hline\hline
\end{tabular}
\end{table}

Then the total-energy density (\ref{eq1}) can be obtained as
\begin{equation}
\mathcal{E}=\frac{3}{10}\sum_{\sigma\tau}\frac{\hbar^2 k^2_{F\sigma\tau}}
 {m_\tau}n_{\sigma \tau}+F_{00}(n_{\rm b})\mathcal{E}_{00}
+ F_{10}(n_{\rm b})\mathcal{E}_{10} + F_{01}(n_{\rm b})\mathcal{E}_{01}
+ F_{11}(n_{\rm b})\mathcal{E}_{11} \label{eq3}
\end{equation}
where $\sigma=\uparrow,\downarrow$ and $\tau={\rm n},{\rm p}$. The potential-energy
density of NM is determined by using
\begin{align}
& \mathcal{E}_{00}=\frac{1}{2}\left[n_{\rm b}^2 J^D_{00}+
 \int A^2_{00} v^{\rm EX}_{00}(r) d^3r\right], \nonumber\\
& \mathcal{E}_{10}=\frac{1}{2}\left[n_{\rm b}^2 J^D_{10}
 \left(\Delta_{\rm n}\frac{1+\delta}{2}+\Delta_{\rm p}\frac{1-\delta}{2}\right)^2
 + \int A^2_{10} v^{\rm EX}_{10}(r) d^3r\right], \nonumber \\
& \mathcal{E}_{01}=\frac{1}{2}\left[n_{\rm b}^2 J^D_{01}\delta^2 +
 \int A^2_{01} v^{\rm EX}_{01}(r) d^3r\right], \nonumber \\
& \mathcal{E}_{11}=\frac{1}{2}\left[n_{\rm b}^2 J^D_{11}
 \left(\Delta_{\rm n}\frac{1+\delta}{2}-\Delta_{\rm p}\frac{1-\delta}{2}\right)^2
 + \int A^2_{\rm 11} v^{\rm EX}_{11}(r) d^3r\right]. \label{eq4}
\end{align}
$J^D_{\rm st}=\displaystyle\int v_{\rm st}(r) d^3r$ is the volume integral
of the direct interaction, and the exchange integrals in Eq. (\ref{eq4}) are
evaluated with
\begin{align}
& A_{00}=n_{\uparrow {\rm n}} \widehat{j}_1(k_{F_{\uparrow {\rm n}}}r)+
 n_{\downarrow {\rm n}} \widehat{j}_1(k_{F_{\downarrow {\rm n}}}r)+
 n_{\uparrow {\rm p}} \widehat{j}_1(k_{F_{\uparrow {\rm p}}}r)+
 n_{\downarrow {\rm p}} \widehat{j}_1(k_{F_{\downarrow {\rm p}}}r) \nonumber\\
& A_{10}=n_{\uparrow {\rm n}} \widehat{j}_1(k_{F_{\uparrow {\rm n}}}r)-
 n_{\downarrow {\rm n}} \widehat{j}_1(k_{F_{\downarrow {\rm n}}}r)+
 n_{\uparrow {\rm p}} \widehat{j}_1(k_{F_{\uparrow {\rm p}}}r)-
 n_{\downarrow {\rm p}} \widehat{j}_1(k_{F_{\downarrow {\rm p}}}r) \nonumber\\
& A_{01}=n_{\uparrow {\rm n}} \widehat{j}_1(k_{F_{\uparrow {\rm n}}}r)+
 n_{\downarrow {\rm n}} \widehat{j}_1(k_{F_{\downarrow {\rm n}}}r)-
 n_{\uparrow {\rm p}} \widehat{j}_1(k_{F_{\uparrow {\rm p}}}r)-
 n_{\downarrow {\rm p}} \widehat{j}_1(k_{F_{\downarrow {\rm p}}}r) \nonumber\\
& A_{11}=n_{\uparrow {\rm n}} \widehat{j}_1(k_{F_{\uparrow {\rm n}}}r)-
 n_{\downarrow {\rm n}} \widehat{j}_1(k_{F_{\downarrow {\rm n}}}r)-
 n_{\uparrow {\rm p}} \widehat{j}_1(k_{F_{\uparrow {\rm p}}}r)+
 n_{\downarrow {\rm p}} \widehat{j}_1(k_{F_{\downarrow {\rm p}}}r), \label{eq5}
\end{align}
where $\hat{j}_1(x)=3j_1(x)/x$, and $j_1(x)$ is the first-order spherical Bessel
function. The Fermi momentum of the spin-polarized baryon is determined as
$k_{F\sigma\tau}=(6\pi^2n_{\sigma\tau})^{1/3}$.

\begin{figure}[bht]\vspace{-1cm}
\includegraphics[angle=0,width=1.1\textwidth]{fig1.eps}\vspace{-4cm}
 \caption{Energy per baryon of pure neutron matter with the neutron spin polarization
$\Delta=0$ and 1 given by the HF calculation (\ref{eq5}) using the newly parametrized
CDM3Y8 interaction, in comparison with results of the BHF calculation (squares and
triangles) \cite{Vidana16}. The circles and stars are results of the \textit{ab-initio} calculations
by Akmal, Pandharipande, and Ravenhall (APR) \cite{APR} and microscopic Monte Carlo (MMC)
calculation by Gandolfi {\it et al.} \cite{MMC}, respectively.}
\label{f1}
\end{figure}
One can see that the spin polarization of baryons gives rise to the nonzero
contribution from both the $\mathcal{E}_{10}$ and $\mathcal{E}_{11}$ terms to the total
NM energy density (\ref{eq3}). Therefore, the density dependencies $F_{10}(n_{\rm b})$
and $F_{11}(n_{\rm b})$ of the CDM3Y$n$ interaction (\ref{eq2}) need to be properly
determined for the present HF study. The spin-isospin independent (isoscalar) density
dependence $F_{00}(n_{\rm b})$ was parametrized \cite{Kho97} to correctly reproduce
the saturation properties of symmetric NM at the baryon density $n_0\approx 0.16$ fm$^{-3}$,
and the isospin dependent (isovector) density dependence $F_{01}(n_{\rm b})$ was adjusted
to the BHF results of NM and fine tuned in the coupled-channel study of the charge
exchange $(p,n)$ reaction to isobar analog states in finite nuclei \cite{Kho07,Kho14}.
In the present work we have parametrized the density dependencies $F_{10}(n_{\rm b})$ and
$F_{11}(n_{\rm b})$ of the spin- and spin-isospin-dependent parts of the CDM3Y$n$
interaction in the same functional form as that used earlier for $F_{00}(n_{\rm b})$
and $F_{01}(n_{\rm b})$, and the parameters were adjusted to obtain the HF results
for the spin-polarized neutron matter close to those of the BHF calculation by
Vida\~na {\it et al.} \cite{Vidana16} using the Argonne V18 free NN potential added
by the Urbana IX three-body force. The parameters of $F_{00}(n_{\rm b})$ and
$F_{01}(n_{\rm b})$ were also slightly readjusted for a better agreement of the HF
results with those of the \textit{ab-initio} calculations \cite{APR,MMC} at high baryon densities
(see Fig.~\ref{f1}). This new version of the CDM3Y$n$ interaction is referred to
hereinafter as the CDM3Y8 interaction, with all parameters of the density dependence
given explicitly in Table~\ref{t2}.
\begin{table} [bht]
\caption{Parameters of the density dependence of the CDM3Y8  interaction (\ref{eq2}),\\
 \centerline{$F_{\rm st}(n_{\rm b})=C_{\rm st}[1+\alpha_{\rm st}\exp(-\beta_{\rm st}n_{\rm b})
 +\gamma_{\rm st}n_{\rm b}]$.}}
\vspace{0cm} \label{t2}
\addtolength{\tabcolsep}{3pt}
\begin{tabular}{ccccccc}\\ \hline\hline
$\rm st$ & $C_{\rm st}$& $\alpha_{\rm st}$& $\beta_{\rm st}$ & $\gamma_{\rm st}$ \\
 &  &  & (fm$^3$) & (fm$^3$)  \\ \hline
00 & 0.2658 & 3.8033 & 1.4099  &-4.300  \\
01 & 0.2643 & 6.3836 & 10.2566 & 6.3549 \\
10 & 0.2161 & 3.7510 & -3.3396 & 9.9329 \\
11 & 0.7572 & 1.9967 & 33.2012 & 0.2989 \\ \hline\hline
\end{tabular
\end{table}

\section{Nuclear symmetry energy}
 \label{sec3}
Although the neutron and proton magnetic moments are of different strengths and
of opposite signs, in the presence of strong magnetic field $|\Delta_n|$ and
$|\Delta_p|$ should be of the same order. We have assumed, for simplicity,
the baryon spin polarization $\Delta=\Delta_n\approx -\Delta_p$ in the present
HF study. The total NM energy per baryon $E/A$ is then obtained in the
{\it isospin} symmetry as
\begin{equation}
\frac{\mathcal{E}}{n_{\rm b}}\equiv\frac{E}{A}(n_{\rm b},\Delta,\delta)=
\frac{E}{A}(n_{\rm b},\Delta,\delta=0)+ S(n_{\rm b},\Delta)\delta^2+O(\delta^4)+...
\label{eq6}
\end{equation}
The contribution from $O(\delta^4)$ and higher-order terms in Eq.~(\ref{eq6}) is
small and neglected in the \emph{parabolic} approximation \cite{Kho96}, where the
isospin-symmetry energy $S(n_{\rm b},\Delta)$ equals the energy required per baryon
to change symmetric NM into the pure neutron matter. Governed by the same SU(2)
symmetry, such a parabolic approximation is also valid for the {\it spin} symmetry,
and the total NM energy per baryon can be alternatively obtained as
\begin{equation}
\frac{\mathcal{E}}{n_{\rm b}}\equiv\frac{E}{A}(n_{\rm b},\Delta,\delta)=
\frac{E}{A}(n_{\rm b},\Delta=0,\delta)+ W(n_{\rm b},\delta)\Delta^2+O(\Delta^4)+...
\label{eq7}
\end{equation}
The exact spin-symmetry energy $W$ given by the HF calculation (\ref{eq7}) of
symmetric NM and neutron matter are shown on the right panel of Fig.~\ref{f2},
and one can see that $W$ is approximately $\Delta$-independent, and the
contribution from $O(\Delta^4)$ and higher-order terms to the NM energy
(\ref{eq7}) is indeed negligible.
\begin{figure}[bht!]\vspace{-0.5cm}\hspace*{-1cm}
\includegraphics[angle=0,width=1.2\textwidth]{fig2.eps}\vspace{0cm}
 \caption{The present HF results obtained at different spin polarizations
 $\Delta$ of baryons for the energy per baryon $E/A$  and spin-symmetry energy $W$
 of symmetric NM, panels (a) and (b), respectively,  and those of neutron matter,
 panels (c) and (d), respectively.} \label{f2}
\end{figure}

Given the quadratic dependence of the NM energy on the spin polarization of baryons
and positive strength of the spin-symmetry energy $W$ over the whole range of densities,
it is sufficient to consider only $\Delta\geqslant 0$ in the present HF study.
One can see in the left panel of Fig.~\ref{f2} that the nonzero spin polarization
significantly stiffens the EOS of NM. In particular, the symmetric NM becomes unbound
by the strong interaction at $\Delta\gtrsim 0.75$, in about the same way as the
asymmetric NM becomes unbound by the in-medium NN interaction with the increasing
neutron-proton asymmetry $\delta\gtrsim 0.75$ \cite{Kho96}.
\begin{figure}[bht]\vspace{-1.5cm}
\includegraphics[angle=0,width=1.1\textwidth]{fig3.eps}\vspace{-2.5cm}
 \caption{The nuclear symmetry energy $S(n_{\rm b},\Delta)$ given by the HF calculation
(\ref{eq6}) assuming different spin polarizations of baryons $\Delta$. The shaded
region is the range constrained by the data of HI collisions \cite{Tsang11,Ono03}.
The square and triangle are values suggested by the nuclear structure studies
\cite{Tri08,Fur02}. The vertical bars are the empirical range obtained at the 90\%
confidence level in a statistical Bayesian analysis \cite{Xie19} of the NS radius
$R_{1.4}$ versus the GW170817 constraint \cite{Abbott18}.} \label{f3}
\end{figure}

The isospin-symmetry energy $S(n_{\rm b},\Delta)$, widely discussed in the literature
as the {\bf nuclear symmetry energy}, is a key characteristics of the EOS of neutron-rich
NM. In particular, the knowledge about the density dependence of $S(n_{\rm b})$ is
extremely important for the determination of the nuclear EOS and it has been,
therefore, a longstanding goal of numerous nuclear physics and nuclear astrophysics
studies (see, e.g., Refs.~\cite{BaLi08,Hor14,Latt14}). However, the results of these
studies were mainly obtained for the spin-saturated NM, and describe, therefore,
the behavior of $S(n_{\rm b},\Delta=0)$.

The nuclear symmetry energy is rather well constrained at low baryon densities by
the analyses of the (isospin dependent) data of heavy-ion (HI) collisions
\cite{Tsang11,Ono03} as well as the structure studies of the giant dipole resonance
\cite{Tri08} or neutron skin \cite{Fur02}. Our HF results for $S(n_{\rm b},\Delta)$
are compared with the empirical data in Fig.~\ref{f3}, and a significant increase
of the nuclear symmetry energy is found with the increasing spin polarization
of baryons $\Delta$. At low densities, the calculated $S(n_{\rm b},\Delta)$ values
fall within the empirical range when the baryon spin polarization
$\Delta\lesssim 0.75$. The behavior of the nuclear symmetry energy at high baryon
densities ($n_{\rm b}>n_0$) remains not well determined. However, the mass and radius
of NS (given, e.g., by the Tolman-Oppenheimer-Volkoff equations using different
EOS's of NS matter) are proven to be strongly sensitive to the strength and slope
of $S(n_{\rm b})$ at high densities \cite{Loan11,Xie19}. Recently, Xie and Li
\cite{Xie19} have inferred the symmetry energy at baryon densities up to $3n_0$
from a statistical Bayesian analysis of the correlation of different EOS's of the
np$e\mu$ matter and associated radius $R_{1.4}$ of NS with mass $M\approx 1.4~M_{\odot}$
versus the GW170817 constraint on $R_{1.4}$ imposed by the NS tidal deformability.
In particular, the EOS with the symmetry energy at twice the saturation density
$S(2n_0)\approx 40-60$ MeV give $R_{1.4}$ radii within the range constrained
by the tidal deformability.
The empirical $S(n_{\rm b})$ values suggested for baryon densities up to $3 n_0$
at 90\% confidence level \cite{Xie19} are shown in Fig.~\ref{f3}, and they cover
the symmetry energy predicted by the HF calculation of neutron-rich NM over the whole
range of the spin polarization of baryons $0\lesssim\Delta\lesssim 1$. One can
trace in Fig.~\ref{f3} that the symmetry energy obtained with a narrower uncertainty
(at 68 \% confidence level) $S(2n_0)\approx 39.2^{+12.1}_{-8.2}$ MeV \cite{Xie19}
also covers all possible spin polarizations.

To explore the density dependence of the nuclear symmetry energy, $S$ is often
expanded around the saturation density $n_0$ \cite{BaLi08,Hor14,Latt14} in terms
of the symmetry coefficient $J$, slope $L$ and curvature $K_{\rm sym}$. With the spin
polarization of baryons treated explicitly in the present HF study, these quantities
are now dependent on the spin polarization $\Delta$, and we obtain
\begin{equation}
 S(n_{\rm b},\Delta)=J(\Delta)+\frac{L(\Delta)}{3}\left(\frac{n_{\rm b}-n_0}{n_0}\right) +
 \frac{K_{\rm sym}(\Delta)}{18}\left(\frac{n_{\rm b}-n_0}{n_0}\right)^2+ ... \label{eq8}
\end{equation}
$J(\Delta)$, $L(\Delta)$, $K_{\rm sym}(\Delta)$, and the incompressibility $K_0(\Delta)$
of symmetric NM at the saturation density (which also depends on the spin polarization
of baryons) are the most important characteristics of the EOS of the spin-polarized
NM. The $J,L,K_{\rm sym},K_0$ values given by the present HF calculation using the
CDM3Y8 interaction are given in Table~\ref{t3}.
\begin{table*} [bht]
\caption{The symmetry coefficient $J$, slope $L$, and curvature $K_{\rm sym}$
of the symmetry energy (\ref{eq8}), and incompressibility $K_0$ of symmetric NM
at the saturation density $n_0$ given by the HF calculation of the spin-polarized
NM using the CDM3Y8 interaction.} \vspace{0.5cm} \label{t3}
\addtolength{\tabcolsep}{3pt}
\begin{tabular}{lcccc}\hline \hline
$\Delta$ & $J$ & $L$ & $K_{\rm sym}$ & $K_0$  \\
  &  (MeV)  & (MeV) & (MeV) & (MeV) \\ \hline
 0.0 &  29.5 & 50.6 & -254 & 244  \\
 0.1 &  29.6 & 50.7 & -256 & 243 \\
 0.2 &  29.8 & 51.0 & -264 & 242 \\
 0.3 &  30.1 & 51.6 & -275 & 240 \\
 0.4 &  30.6 & 52.5 & -291 & 238\\
 0.5 &  31.3 & 53.5 & -314 & 234 \\
 0.6 &  32.1 & 54.9 & -340 & 230 \\
 0.7 &  33.1 & 56.6 & -369 & 225 \\
 0.8 &  34.3 & 58.7 & -402 & 219 \\
 0.9 &  35.7 & 61.3 & -450 & 213 \\
 1.0 &  37.5 & 64.7 & -505 & 205 \\ \hline  \hline
\end{tabular} \vspace{0.cm}
\end{table*}
Among these quantities, the incompressibility $K_0$ of symmetric NM has been the
key research topic of numerous structure studies of nuclear monopole excitations
(see, e.g., review \cite{Garg18} and references therein) as well as the studies
of HI collisions and refractive nucleus-nucleus scattering \cite{Kho07r}. These
researches have pinned down this quantity to $K_0\approx 240\pm 20$ MeV.
The symmetry coefficient and slope of the nuclear symmetry energy (\ref{eq8})
were also extensively investigated and inferred independently from different
analyses of terrestrial nuclear physics experiments and astrophysical observations,
and they are now constrained to $J\approx 31.7 \pm 3.2$ MeV and
$L\approx 58.7\pm 28.1$ MeV  \cite{Zhang18}. The $K_{\rm sym}$ value is still not
well determined, and remains within a wide range
$-400$ MeV $\lesssim K_{\rm sym}\lesssim 100$ MeV \cite{Zhang18}. The HF
results for $J, L, K_{\rm sym}$, and $K_0$ of the spin-saturated NM with
$\Delta=0$ agree well with the empirical values, and remain within the empirical
boundaries with the spin polarization of baryons $0\lesssim\Delta\lesssim 0.8$.

\section{Beta-stable neutron star matter}
\label{sec4}
For the EOS of inhomogeneous NS crust, we have adopted that given by the nuclear
energy-density functional (EDF) calculation \cite{Chamel18,Chamel19} using the
BSk24 Skyrme functional, with atoms being fully ionized and electrons forming
a degenerate Fermi gas. At the edge density $n_{\rm edge}\approx 0.076$ fm$^{-3}$,
a weak first-order phase transition takes place between the NS crust and uniform
core of NS. At baryon densities $n_{\rm b}\gtrsim n_{\rm edge}$ the NS core is
described as a homogeneous matter of neutrons, protons, electrons, and negative
muons ($\mu^-$ appear at $n_{\rm b}$ above the muon threshold density
$\mu_e>m_\mu c^2\approx 105.6$ MeV).

\subsection*{Density-independent spin polarization of the np$e\mu$ matter}
To explore the impact of the spin polarization of baryons on the EOS of the
$\beta$-stable np$e\mu$ matter of NS, we have assumed for simplicity that the spin
polarization of baryons $\Delta$ is density independent, and varied $\Delta$
within the range $(0\to 1)$ at each considered density, as done above for the
spin-polarized NM. Then, the total-energy density $\mathcal{E}$ of the np$e\mu$ matter
(including the rest energy) is determined as
\begin{equation}
\mathcal{E}(n_{\rm n},n_{\rm p},n_e,n_\mu,\Delta)=
\mathcal{E}_{\rm HF}(n_{\rm n},n_{\rm p},\Delta)+n_{\rm n}m_{\rm n}c^2
+n_{\rm p}m_{\rm p}c^2+\mathcal{E}_e(n_e)+\mathcal{E}_\mu(n_\mu) \label{eq9},
\end{equation}
where $\mathcal{E}_{\rm HF}(n_{\rm n},n_{\rm p},\Delta)$ is the HF
energy density (\ref{eq3}) of the spin-polarized NM, $\mathcal{E}_e$ and
$\mathcal{E}_\mu$ are the energy densities of electrons and muons given
by the relativistic Fermi gas model \cite{Dou01}. In such a Fermi gas model,
the spin polarization of leptons does not affect the total energy density
$\mathcal{E}$, and the lepton number densities $n_e$ and $n_\mu$ can be determined
from the charge neutrality condition ($n_{\rm p}=n_e+n_\mu$) and the $\beta$-equilibrium
of (neutrino-free) NS matter in the same way as done for the spin unpolarized
NS matter (see Ref.~\cite{Loan11} for more details).

The density-dependent proton fraction $x_{\rm p}(n_{\rm b})$ is a key input for
the determination of the NS cooling rate. In particular, the direct Urca (DU)
process of NS cooling via neutrino emission is possible only if the proton
fraction is above the DU threshold $x_{\rm DU}$ \cite{Loan11}:
\begin{equation}
 x_{\rm DU}(n_{\rm b})=\frac{1}{1+\left[1+r_e^{1/3}(n_{\rm b})\right]^3},
 \label {eq10}
\end{equation}
where $r_e(n_{\rm b})=n_e/(n_e+n_\mu)$ is the leptonic electron fraction at the given
baryon number density. At low densities $r_e=1$, and $x_{\rm DU}\approx 11.1\%$,
which corresponds to the muon-free threshold for the DU process. Because the lepton-baryon
interaction is neglected in the present study, the $x_{\rm DU}$ value determined from
the $\beta$-equilibrium condition depends very weakly on the spin-polarization
of baryons. The proton fraction $x_{\rm p}$ of the spin-polarized $\beta$-stable
np$e\mu$ matter obtained with the HF energy density (\ref{eq3}) using the CDM3Y8
interaction is shown in Fig.~\ref{f4}, and one can see that $x_{\rm p}$ increases
\begin{figure}[bht]\vspace{0cm
\includegraphics[angle=0,width=0.9\textwidth]{fig4.eps}\vspace{-0.5cm}
 \caption{The proton fraction $x_{\rm p}$ determined from the charge neutrality
of the spin-polarized $\beta$-stable np$e\mu$ matter obtained with the HF energy
density (\ref{eq3}) using the CDM3Y8 interaction. The circles are $n_{\rm p}$ values
calculated at the maximum central densities $n_{\rm c}$, and the thin lines are the
DU thresholds (\ref{eq10}).} \label{f4}
\end{figure}
significantly with the increasing spin polarization of baryons, and it exceeds the
DU threshold at densities $n_{\rm b}\gtrsim 2n_0$ if baryons are completely spin
polarized ($\Delta=1$). From the behavior of $n_{\rm p}$ shown in Fig.~\ref{f4}
we find that the electron fraction in the $\beta$-stable np$e\mu$ matter
also increases with the increasing $\Delta$ and might reach up to 20\%$-$30\% at
high densities when $\Delta$ approaches 1. It is remarkable that such a high
electron fraction was found in the blue kilonova ejecta following the NS
merger GW170817 \cite{Abbott17c,Evan17}, and suggested by Metzger \textit{et al.}
\cite{Metzger18} to be of the magnetar origin.

\begin{table} [bht]
\caption{Configuration of NS given by the EOS of the spin-polarized $\beta$-stable
np$e\mu$ matter obtained with the CDM3Y8 interaction. $M_{\rm max}$ and $R_{\rm max}$
are the maximal gravitational mass and radius; $R_{1.4}$, $n_c$, and $P_c$ are
the radius of the NS with $M\approx 1.4~M_\odot$, central baryon number density, and
central total pressure, respectively. $P(2n_0)$ is the total pressure at twice the
saturation density.} \vspace{0.5cm} \label{t4}
\begin{tabular}{ccccccc}\hline\hline
$\Delta$ & $M_{\rm max}$ & $R_{\rm max}$ &$R_{1.4}$& $n_c$ & $P_c$ & $P(2n_0)$  \\
 &($M_\odot$)&(km) & (km)& (fm$^{-3}$)&($10^{35}$dyn/cm$^2$)& ($10^{34}$dyn/cm$^2$)\\ \hline
0.0 & 1.98 & 10.3 & 12.0 & 1.17 & 9.9 & 3.4    \\
0.1 & 1.99 & 10.3 & 12.0 & 1.16 & 10.0 & 3.5    \\
0.2 & 2.00 & 10.4 & 12.1 & 1.16 & 10.2 & 3.6    \\
0.3 & 2.02 & 10.4 & 12.3 & 1.15 & 10.4 & 3.6   \\
0.4 & 2.04 & 10.5 & 12.5 & 1.14 & 10.9 & 3.9    \\
0.5 & 2.06 & 10.6 & 12.8 & 1.11 & 10.3 & 4.1   \\
0.6 & 2.08 & 10.8 & 13.1 & 1.08 & 10.0 & 4.4    \\
0.7 & 2.10 & 11.1 & 13.6 & 1.04 &  9.5 & 4.6   \\
0.8 & 2.12 & 11.3 & 14.1 & 1.01 &  9.0 & 5.0  \\
0.9 & 2.14 & 11.7 & 14.8 & 0.96 &  8.1 & 5.4  \\
1.0 & 2.16 & 12.0 & 15.6 & 0.92 &  7.7 &  5.8  \\ \hline \hline
\end{tabular} \vspace{0.cm}
\end{table}
\begin{figure}[bht]\vspace{-0.5cm
\includegraphics[angle=0,width=0.8\textwidth]{fig5.eps}\vspace{-0.5cm}
 \caption{Pressure $P$ in the unmagnetized ($B_{\rm crust}=0$) and magnetized
($B_{\rm crust}\neq 0$) crust of NS given by the EDF calculation
\cite{Chamel18,Chamel19} using the BSk24 Skyrme functional.} \label{f5}
\end{figure}

The mass density $\rho$ and total pressure $P$ of NS crust given by the EDF
calculation at baryon densities below the edge density
$n_{\rm edge}\approx 0.076$ fm$^{-3}$, and those of the uniform and spin-polarized
np$e\mu$ matter given by the HF calculation at $n_{\rm b}\gtrsim n_{\rm edge}$
have been used as inputs for the Tolman-Oppenheimer-Volkoff (TOV) equations
to determine the hydrostatic configuration of NS (see Table~\ref{t4}).
For a consistent mean-field study of the spin-polarized np$e\mu$ matter of NS,
we have used in this work two versions of NS crust: the unmagnetized crust
($B_{\rm crust}=0$) and crust embedded in the magnetic field of
$B_{\rm crust}=1.323\times 10^{17}$ G \cite{Chamel19}. The effects of magnetic
field on the EOS and the composition of NS crust were shown mainly due to the
Landau quantization of the electron motion, with most protons and neutrons
remaining ``packed" in nuclei with $Z\approx 40\sim 50$ inside in the Wigner-Seitz cell
\cite{Chamel19}. The impact of the magnetic field with $B_{\rm crust}\sim 10^{17}$ G
is strong in the outer crust (see Fig.~\ref{f5}), while the EOS of the inner crust
remains almost unchanged compared to that of the unmagnetized crust at baryon
densities $n_{\rm b}\gtrsim 0.01$ fm$^{-3}$.
As a result, the main properties of NS shown in Table~\ref{t4} are not affected
by the magnetization of the NS crust. We note that the spin polarization of free
baryons and spin-unsaturated nuclei inside the Wigner-Seitz cell has not
been taken into account in the EDF approach \cite{Chamel19}, and it might result
in a stronger impact of the magnetic field on the EOS of the NS crust.

Because NS matter becomes less compressible (see $K_0$ values in Table~\ref{t3})
when the spin polarization of baryons is nonzero, the central density $n_c$ and pressure
$P_c$ decrease with increasing $\Delta$. As a result, the NS expands its size and
the maximal gravitational mass $M_{\rm max}$ and radius $R_{\rm max}$ become larger
with increasing spin polarization of baryons. The LIGO and Virgo data of the NS
merger GW170817 were analyzed by Abbott {\it et al.} \cite{Abbott18} to put constraints
on the tidal deformability of two merging neutron stars, which were then translated into
constraints on NS radius. By requiring that a realistic EOS of NS matter must accommodate
the NS maximal mass $M_{\rm max}\gtrsim 1.97~M_\odot$, Abbott {\it et al.} have obtained
the radius of NS with $M\approx 1.4~M_\odot$ in the range $R_{1.4}\approx 11.9\pm 1.4$
km at the 90\% confidence level \cite{Abbott18}. This analysis has also given a
constraint on the total pressure of NS matter at supra-saturation densities, namely,
$P(2n_0)\approx 3.5^{+2.7}_{-1.7}\times 10^{34}$ dyn/cm$^2$ at the same 90\% confidence
level. One can see from NS properties given by the EOS of the spin-polarized
$\beta$-stable np$e\mu$ matter shown in Table~\ref{t4} that the GW170817 constraints
are fulfilled with the spin polarization of baryons $\Delta \lesssim 0.6$ for
the $R_{1.4}$ radius and $\Delta\lesssim 1$ for the total pressure $P(2n_0)$
of NS matter, respectively. The NS maximal mass $M_{\rm max}$ obtained with the EOS
given by the CDM3Y8 interaction increases from $1.98~~M_\odot$ to $2.16~M_\odot$ with
the spin polarization $\Delta$ increasing from 0 to 1. This range of the $M_{\rm max}$
values covers well the observed NS masses $M\approx 1.908\pm 0.016~M_\odot$,
$2.01\pm 0.04~M_\odot$, and $2.14\pm 0.09~M_\odot$ of the binary pulsars
PSR J1614-2230 \cite{Demorest,Arzou18}, PSR J0348+0432 \cite{Sci340}, and PSR J0740+6620
\cite{Cro19}, respectively. Note that the large NS mass $M\approx 2.14~M_\odot$ seems
possible in the present mean-field scenario only when baryons are completely spin
polarized ($0.9\lesssim\Delta\lesssim 1$).
\begin{figure}[bht]\vspace{-2cm
\includegraphics[angle=0,width=0.9\textwidth]{fig6.eps}\vspace{-3cm}
\caption{The curvature $K_{\rm sym}$ and slope $L$ of the nuclear symmetry energy (\ref{eq8})
versus the radius $R_{1.4}$ of NS with $M\approx 1.4~M_\odot$ shown as solid circles in
panels (a) and (b), respectively, are given by the EOS of the spin-polarized
$\beta$-stable np$e\mu$ matter with $\Delta$ increasing from 0 to 0.9 (see also
Tables~\ref{t3} and \ref{t4}). The shaded areas enclose the range of the $R_{1.4}$
radius constrained by the tidal deformability of NS \cite{Abbott18}.} \label{f6}
\end{figure}

The constraint on the radius $R_{1.4}$ of NS with $M\approx 1.4~M_\odot$ deduced
from the multimessenger observation of GW170817 \cite{Abbott18} has now become
an important reference for the mean-field studies or Bayesian analyses of the EOS
of NS matter to narrow the uncertainty of the symmetry energy (\ref{eq8})
at high baryon densities \cite{Xie19,Tsang19}. For example, Tsang {\it et al.}
 \cite{Tsang19} have shown a systematic correlation of the $J$, $L$, and $K_{\rm sym}$
values with the tidal deformability of NS, using about 200 different sets of Skyrme
interaction in their mean-field study. From the GW170817 constraint on the radius
$R_{1.4}$ and tidal deformability, some correlation between the symmetry energy
at high baryon densities and $R_{1.4}$ radius can be inferred. By comparing the
$J$, $L$, and $K_{\rm sym}$ values given by our HF calculation of the spin-polarized
NM shown in Table~\ref{t3} and $R_{1.4}$ radii obtained at different $\Delta$ values
shown in Table~\ref{t4}, we found that $J$, $L$, and $|K_{\rm sym}|$ are almost linearly
correlated with the $R_{1.4}$ radius (see Fig.~\ref{f6}). In particular, with the
increasing spin polarization of baryons, the larger the slope $L$ of the symmetry
energy, the larger the corresponding $R_{1.4}$ radius. One can see in Fig.~\ref{f6}
that the spin polarization of baryons is confined by the GW170817 constraint to
the range $0\lesssim\Delta\lesssim 0.6$, where $50.6\lesssim L\lesssim 54.9$ MeV
and $12\lesssim R_{1.4}\lesssim 13.1$ km. From the correlation between $L$ and
$R_{1.4}$ shown in Fig.~\ref{f6}, it is not excluded that an EOS of the spin-unpolarized
NS matter with $L\gtrsim 65$ MeV would give a radius $R_{1.4} > 13.1$ km.

\begin{figure}\vspace{-1.5cm}\hspace*{0cm}
\includegraphics[angle=0,width=0.7\textwidth]{fig7.eps}\vspace{-0.5cm}
 \caption{Correlation of the mass and radius of NS given by the EOS of the
 $\beta$-stable spin-polarized np$e\mu$ matter ($\Delta=0\to 1$) obtained with
 the CDM3Y8 interaction (\ref{eq2}). The results obtained with the unmagnetized
 and magnetized NS crust given by the EDF theory \cite{Chamel19} are shown in
 panels (a) and (b), respectively. The GW170817 constraint \cite{Abbott18} is enclosed
 in the colored contours, and circles are the $M,R$ values at the maximum central
 densities $n_c$.} \label{f7}
\end{figure}
Our results obtained for the correlation of the mass and radius of NS given by the EOS
of the $\beta$-stable spin-polarized np$e\mu$ matter with $\Delta$ increasing from
0 to 1 are shown in Fig.~\ref{f7}. The GW170817 constraint for the radius $R_{1.4}$
of NS with $M\approx 1.4~M_\odot$ are plotted in Fig.~\ref{f7} as the shaded contours.
One can see that all mass-radius curves with $\Delta\lesssim 0.6$ go well through
the GW170817 contours. The upper bound of 13.3 km for $R_{1.4}$ \cite{Abbott18}
is exceeded when more than 60\% of baryons are spin polarized. Combined with the
impact on the symmetry energy shown in Figs.~\ref{f3} and \ref{f6}, the upper limit
of $\Delta\approx 0.6$ shown in Fig.~\ref{f7} might well narrow the uncertainty
of the symmetry energy $S$, its slope $L$, and curvature $K_{\rm sym}$ at
supra-saturation baryon densities ($n_{\rm b}>n_0$). As shown in Table~\ref{t4} and
Fig.~\ref{f7}, the maximal gravitional mass $M_{\rm max}$ and radius $R_{\rm max}$
of NS in the hydrostatic equilibrium can be strongly affected by the spin polarization
of baryons. We note that all the calculated $M_{\rm max}$ values are above the
lower limit of $1.97~M_\odot$ that was imposed on the GW170817 constraint for the
$R_{1.4}$ radius by Abbott {\it et al.} \cite{Abbott18}. The results shown in the
upper- and lower panels of Fig.~\ref{f7} confirm that the effect of the magnetization
of the NS crust \cite{Chamel19} on the NS mass and radius is negligible. It remains
uncertain if this conclusion still holds when the spin polarization of free baryons
as well as the spin-unsaturated nuclei in the Wigner-Seitz cell in the NS crust
is treated explicitly.

In conclusion, the present mean-field study shows that the spin polarization
of baryons affects strongly the EOS of the NS matter via the spin- and spin-isospin
dependent channels of the in-medium interaction between baryons. In particular,
the symmetry energy of the spin-polarized  NM (with $\Delta\neq 0$) was found
to be much stiffer at high baryon densities compared with that of the spin-saturated
NM (with $\Delta=0$), and this can affect significantly the hydrostatic configuration
of NS. Based on the GW170817 constraint for the $R_{1.4}$ radius \cite{Abbott18},
baryons in the two merging neutron stars could be partially spin-polarized
with $0\lesssim\Delta\lesssim 0.6$ (see Fig.~\ref{f7}). We found, however, that
the GW170817 constraint excludes the full spin polarization of baryons in NS
matter ($\Delta=1$), and this results agrees well with a recent
conclusion by Tews and Schwenk \cite{Tews20}.

\subsection*{Possible effects by the density dependence of the spin polarization}
We note that the above results have been obtained with the spin polarization
of baryons assumed to be independent of the baryon density $n_{\rm b}$. However,
the magnetic-field distribution in the NS matter is quite complex \cite{Fuji14}, and
the spin polarization of baryons in a magnetar is expected to be gradually weakened
with the increasing baryon density. In particular, with the magnetic-field intensity
diminishing to zero in the NS center \cite{Fuji14}, the spin polarization
of baryons is also expected to decrease to $\Delta\approx 0$ in the central region
of magnetar. Although it is beyond the scope of the present mean-field approach
to properly calculate the density profile $\Delta(n_{\rm b})$ of the spin polarization
of baryons in magnetar, we try to explore this effect by assuming three simple scenarios
(A,B, and C) for the density dependence of $\Delta$ based on the magnetic-field
distribution in magnetar obtained by Fujisawa and Kisaka using the Green's function
relaxation method (see lower panel of Fig.~3 in Ref.~\cite{Fuji14}).

A) The magnetic field is strongly localized in the surface region of magnetar,
around the crust-core transition, and quickly decreases to $B\approx 0$ at the
baryon density $n_{\rm b}\approx 0.18$ fm$^{-3}$. We consider explicitly the spin
polarization of baryons $\Delta=0.6,\ 0.8$, and 1.0, which are assumed
to gradually weaken to $\Delta\approx 0$ at this same density.

B) The distribution of the magnetic-field strength is broader and covers both
the crust and outer core of magnetar, so that $\Delta$ decreases smoothly
to zero at a larger baryon density $n_{\rm b}\approx 0.35$ fm$^{-3}$.

C) The magnetic-field strength is spreading to even higher baryon densities
and decreasing to $B\approx 0$ at $n_{\rm b}\approx 0.5$ fm$^{-3}$. Three
considered strengths of the spin polarization of baryons are gradually weakening
to $\Delta\approx 0$ at this same density.

Thus, the magnetic field in these three scenarios is completely depleted ($B=0$) in
the central region of magnetar where the baryon density $n_{\rm b}$ approaches
$0.6\sim 1$ fm$^{-3}$.
The suggested density-dependent profiles of $\Delta$ are shown together with the
uniform (density independent) spin polarization of baryons (scenarios D) in the upper
panel of Fig.~\ref{f8}. The corresponding TOV results for the mass and radius
of magnetar given by the density-dependent spin polarization of baryons are shown
in the lower panel of Fig.~\ref{f8}, where the GW170817 constraint for the $R_{1.4}$
radius are plotted as the shaded contours. One can see that when the magnetic-field
strength is localized narrowly in the crust-core transition (scenario A), the mass
and radius of magnetar obtained with $\Delta\lesssim 1$ are within the boundaries
of the GW170817 constraint. However, with the magnetic-field strength spreading
more into to the outer core (scenarios A and B) the full spin polarization of baryons
($\Delta=1$) is ruled out, and only a partial spin polarization of baryons with
$\Delta\lesssim 0.8$ is possible. It is noteworthy that the EOS of partially
spin-polarized NS matter with $0\lesssim\Delta\lesssim 0.6$ gives the mass and
radius of magnetar well within the GW170817 boundaries in all three scenarios
(see left panel of Fig.~\ref{f8}).
\begin{figure}\vspace{-0.5cm}\hspace*{-0.5cm}
\includegraphics[angle=0,width=1.1\textwidth]{fig8.eps}\vspace{-0cm}
 \caption{Scenarios A,B,C, and D for the density-dependent spin polarization
 of baryons with $\Delta$ starting from 0.6, 0.8, and 1 are shown in panels (a),
(b), and (c), respectively. The corresponding mass and radius of magnetar given by the
EOS of the $\beta$-stable  spin-polarized np$e\mu$ matter are shown in panels (d), (e),
and (f), respectively. The colored countours enclose the region allowed by the GW170817
constraint \cite{Abbott18}.} \label{f8}
\end{figure}

In general, when the electromagnetic interaction between the magnetic field and
NS matter is taken into account explicitly, the $B$-dependent contribution to the
total energy density of the spin-polarized NS matter (\ref{eq9}) is not negligible
\cite{Agui14,Isayev12}, and the discussed effects of the spin polarization
of baryons to the hydrostatic NS configuration might become even more significant.
Given the results of previous studies \cite{Latt07,Bro00,Agui14,Isayev12,Fuji14}
on the effects of magnetic field, the total impact on the EOS of magnetar
matter by magnetic field might become essential at the moderate field strength,
as found in the magnetar scenario by Metzger {\it et al.} \cite{Metzger18} for
the blue kilonova ejecta of GW170817.

\section*{Summary}
The nonrelativistic HF approach \cite{Loan11} has been extended to study the
spin-polarized NM using the new density-dependent CDM3Y8 version of the M3Y
interaction \cite{Anan83}, with its spin- and spin-isospin dependence adjusted
to obtain the HF results close to those of the BHF calculation of the spin-polarized
neutron matter \cite{Vidana16}. Like for the nuclear (isospin) symmetry energy $S$,
the parabolic approximation was found to be valid also for the spin-symmetry energy $W$,
so that the (repulsive) contribution to the HF energy density of NM from the spin
polarization of baryons is directly proportional to $\Delta^2$, and the EOS of
NM becomes stiffer with the increasing spin polarization of baryons.

The $\Delta$ dependence of the symmetry coefficient $J$, the slope $L$, and
curvature $K_{\rm sym}$ of the nuclear symmetry energy $S$ has been investigated,
and we found that the empirical ranges adopted for these quantities \cite{Zhang18}
include results of the present HF calculation with the spin polarization of baryons
up to $\Delta\approx 0.8$. With the increasing $\Delta$, the $J$, $L$, and $K_{\rm sym}$
values were found to correlate linearly with the radius $R_{1.4}$ of a NS with mass
$M\approx 1.4~M_\odot$.

The total HF energy density of the $\beta$-stable np$e\mu$ matter has been obtained
at different spin polarization of baryons, and the proton fraction $x_{\rm p}$
was found to increase strongly with increasing $\Delta$, which in turn leads
readily to a larger probability of the direct Urca process in the cooling of the magnetar.

The stiffening of the symmetry energy of the $\beta$-stable spin-polarized
np$e\mu$ matter at high baryon densities has been shown to affect significantly
the hydrostatic NS configuration. By subjecting the mass and radius of a NS obtained
at different spin polarizations of baryons to the GW170817 constraint on
the $R_{1.4}$ radius \cite{Abbott18}, we found that up to 60\% of baryons
might have their spins polarized during the NS merger. The same conclusion
can be made when $\Delta$ is assumed to be density dependent, and the spin
polarization of baryons is gradually decreasing from the surface of magnetar
to zero at $n_{\rm b}\lesssim~3n_0$. These results support the magnetar
origin of the blue kilonova ejecta of GW170817 suggested
by Metzger {\it et al.} \cite{Metzger18}.

\section*{Acknowledgement}
The present research was supported, in part, by the National Foundation for
Science and Technology Development of Vietnam (NAFOSTED Project
No. 103.04-2017.317). We also thank Isaac Vida\~na for his helpful communication
on the BHF results of the spin-polarized neutron matter \cite{Vidana16}, and
Nicolas Chamel for providing us with the EOS of the (unmagnetized and magnetized)
NS crust \cite{Chamel18,Chamel19} in the tabulated form.

\bibliographystyle{apsrev4-1}

redpajama_set_name: RedPajamaArXiv


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text:
Calorie Restriction And Red Wine Resveratrol Pills Activate The Same Genes But Measurable Health Benefits May Only Be Evident Among Unhealthy Individuals
July 28, 2013: by Bill Sardi
San Dimas, CA (July 28, 2012) – Researchers report calorie-restricted diets and red wine resveratrol (rez-vair-ah-trol) pills beneficially alter the same array of genes in both healthy and unhealthy individuals but may only produce measurable physiologic improvement in inflammation, blood pressure, blood sugar, insulin sensitivity and weight among individuals with metabolic problems (diabetes, obesity).
Healthy adults taking resveratrol pills aren't wasting their money buying resveratrol pills as researchers surmise this favorable activation of genes will produce future health benefits via "metabolic re-programming effects." Researchers are calling for long-term studies to validate their theory.
Because long-term calorie restricted diets progressively alter more and more genes (831 in laboratory mice) over a lifetime, it is assumed healthy adults who habitually take resveratrol pills will progressively activate more genes over time and derive unparalleled health benefits similar to those observed among laboratory mice on life-long calorie restricted diets. Calorie restriction doubles the lifespan and improves the health span of most animal species.
These revelations, published in a special edition of the Annals of the New York Academy of Sciences dedicated to resveratrol, may provide insight as to why some early short-term studies in the animal lab as well as with human subjects produced null effects.
Plausible explanation
Researchers say a plausible reason why measured health benefits are exclusively observed among the unhealthy is that measures of metabolic fitness simply cannot be improved upon when they fall into the optimal health range.
That was the very same mistake recently made by researchers at the University of Copenhagen who couldn't measure any significant health benefits among healthy senior males who had completed an exercise program and were taking resveratrol pills.
"This research suggests resveratrol does not cause blood pressure or blood sugar to drop too far but rather helps these measures to remain in the "optimal" or "desirable range," says health journalist Bill Sardi who is also managing partner for a red wine pill company.
Sardi says: "It's possible for resveratrol pills to never produce measurable improvements in health parameters if health numbers were never in the unhealthy range in the first place and remain that way thereafter."
How long to wait for benefits?
An earlier report, published in Experimental Gerontology in 2008, demonstrated that short-term (12-week) calorie restriction or resveratrol activated about the same number of longevity genes (198 and 225 respectively). It is assumed life-long consumption of resveratrol pills would, over time, activate the same number of genes (831) as adherence to a long-term calorie restricted diet.
"What these researchers aren't talking about is that their 2008 research study found a commercially available resveratrol pill (Longevinex®), that combines small natural synergistic molecules in a similar array and dosage range to the red wine solids found in 3-5 glasses of red wine (180-300 milligrams), switched 677 of those 831 longevity genes (81%) in laboratory mice in the same direction as calorie restriction in just 12 weeks, not a lifetime as with calorie restriction," says Sardi.
Therefore, health and longevity seekers who habitually adhere to a limited calorie diet or take resveratrol pills, or both, need to know it will take a lifetime to achieve a gene activation profile that favors longevity that could be achieved in just weeks taking Longevinex© says Sardi.
Activation of longevity genes may be an easier task to accomplish in humans than in laboratory mice. While both humans and mice have about the same number of genes (25,000), only about 295 genes are involved in human longevity.
Thousands of people worldwide have tried red wine resveratrol pills since they were first extolled by a Harvard professor in Nature magazine in 2003. The proposed promise of these pills is as a molecular mimic of a calorie-restricted diet and a substitute for the health benefits achieved with modest consumption of red wine.
For many health seekers, they didn't feel any better taking resveratrol pills — didn't notice any beneficial change in markers of health such as inflammation, blood sugar, blood pressure and weight.
"This newly published report suggests resveratrol is favorably re-programming genes regardless of whether resveratrol pills users experience measurable improvement or subjectively feel better," Sardi adds.
What causes longevity genes to be activated?
"Other anti-aging researchers have attempted to attribute the prolonged lifespan and health span observed among calorie restricted animals to what is called "metabolic reprogramming." While their theory may be sound, it only describes what happens metabolically after longevity genes are favorably switched, not what switches longevity genes prior to these measurable effects," says Sardi.
"The scientific literature strongly points toward any method that limits and controls or removes excess minerals as genetic controllers of aging. Whether it is food deprivation (calorie restriction), blood-letting, or use of mineral (iron, copper, calcium) chelating (key-lay-ting) molecules such as those found in red wine, these are all roads that lead to extraordinary longevity," says Sardi. The Overmineralization Theory of Aging, written by Bill Sardi, is available for online reading.
Right dose protects heart and brain
"Even if resveratrol pill users aren't able to feel better or measure any benefits, they should know resveratrol is still on guard, protecting their tissues in an unparalleled way," says Sardi.
This study did not address another desirable biological phenomenon called "preconditioning" that resveratrol activates. Resveratrol and other similar molecules, when given in the right dosage range, are perceived by the body as mild biological stressors that activate internal antioxidant defenses (glutathione, catalase, heme oxygenase, superoxide dismutase) that in turn reduce the need for oxygen in the brain and heart and limit the area of damage in these two critical organs should blood circulation be interrupted by a stroke or heart attack.
This means healthy resveratrol pill users may not feel any better, but should they experience a stroke or heart attack these are likely to be non-mortal events. Only one commercial brand of resveratrol has been demonstrated to produce this effect in the laboratory and worked about twice as well as plain resveratrol. Excessively high dose resveratrol negates these beneficial effects. ©2013 ResveratrolNews.com
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