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There are atypical Myeloproliferative Neoplasm Disorders which include molecularly defined PDGFRA-rearranged eosinophilic/mast cell disorders; PDGFRB-rearranged eosinophilic disorders; systemic mastocytosis associated with c-kit mutation; 8p11 Myeloproliferative syndrome; and juvenile myelomonocytic leukemia with recurrent mutations of RAS. MPN also includes the clinicopathologically assigned variants: chronic neutrophilic leukemia; chronic eosinophilic leukemia; hypereosinophillic syndrome, chronic basophilic leukemia, chronic monomyelomonocytic leukemia, systemic mastocytosis; and unclassified myeloproliferative disorder. Chronic myeloid disorders also include myelodysplastic syndrome.
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Changing climatic conditions, increasing energy demands and new market forces will influence the makeup and design of future farming systems in Australia. Part of that redesign is likely to include the adaptation of farming enterprises to incorporate a greater proportion of sustainable and perennial woody crops within their farming business, especially on landscapes (or parts of landscapes) that are no longer viable for annual cropping.
The Future Farm Industries (FFI) CRC has supported research and development to help facilitate this evolution of farming systems in the dryland agricultural regions of southern Australia. The FFICRC's FloraSearch project undertook a detailed screening of Australian native plant species to identify multiple Australian candidates to service current and future woody biomass industries. Potential industries targeted included bioenergy, livestock fodder, wood fibres, Eucalyptus oils, activated carbon and carbon sequestration. Laboratory testing identified those species with characteristics suited to each industry sector and genetic material of the most promising candidates for domestication was sourced from across Australia. However, the productivity of species selected to provide feedstock for new industry types directly influences their future profitability and viability.
To fully evaluate the commercial potential of these new woody crop species it has been necessary to undertake studies on the growth and survival of these plants in lower rainfall environments. Between 2004 and 2005 a series of FloraSearch field trials were established to evaluate the performance of range of species and provenances. In 2006, a more detailed field trial program was initiated at Monarto in South Australia to evaluate different provenances of the highest priority woody crop species. These trials included the national Oldman Saltbush fodder shrub development and domestication trials.
Surveys of the performance of all species and provenances contained these trials will be completed in 2013, and the results will be used to identify species and genetic resources suitable for future woody crop development and domestication/commercialisation.


Portfolio App is a awesome app to anyone to promote their portfolio, bussines, product, or anything else. This app include Native web for user and admin panel. It's easy for customized and running this web into webserver. Include user guide too.
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text:
'Guys and Dolls' comes to Durham's Gala Theatre this January
Fiona Steer in Culture & Arts Drama on 12 January, 2022.
Durham University's largest musical theatre company brings its annual blockbuster musical to Durham's Gala Theatre this January.
Durham University Light Opera Group (DULOG) will be performing the popular tunes from classic musical Guys and Dolls including 'Luck be a Lady', 'If I Were a Bell' and 'Sit Down, You're Rockin' the Boat' from Tuesday 18 to Saturday 22 January.
The annual large-scale DULOG production, is a staple in the city's theatrical calendar and a highlight for the student company. This year's production involves a team of more than 70 students, made up of cast and crew.
Frank Loesser's golden age musical Guys and Dolls is a story of love, loyalty, and gambling in 1950s New York.
Sister Sarah Brown strives to spread goodness as she battles the charms and advances of the mischievous Sky Masterson, whilst Miss Adelaide pines and laments the lack of a wedding ring on her left hand.
Her poor fiancé Nathan Detroit doesn't stand a chance. It quickly becomes clear that these guys and dolls are hopelessly attached to each other, no matter how they roll the dice…
DULOG President, Miriam Templeman, explained why the company has settled on this classic musical for their latest production; "This last year has been a gamble, and we decided the comedic and joyous heart of 'Guys and Dolls' would provide a memorable and entertaining evening of escapism for our audience. We were originally planning to stage the show last spring, so it is a privilege and honour to be able to do so now. It reminds us what a delicate and beautiful living medium theatre is – the spotlights that illuminate the stage can now illuminate our lives, once more. What a gift that is."
Previous collaborations between DULOG and the Gala Theatre including 'Singin' in the rain', and 'Oklahoma!' have been well received over the years.
"We are extremely fortunate to have such exciting opportunities available in theatre, it's exciting for us to be able to perform in a professional venue such as Gala", says Producer Jennifer Leigh.
"Durham has one of the largest student theatre scenes in the country, and DULOG's annual 'Gala musical' always shows off the very best of our talent. I'm thrilled to be working with such a fantastic team of performers, musicians and production team members on something truly special."
The event details and ticket information can be found below:
Venue: Durham Gala Theatre, DH1 1WA
Tickets: £14.50 Standard, £9.50 Concession/Student (£8.50 DST Members)
Dates: 18th-22nd January 2022
Time: 7:30pm all nights, with matinees at 2:30pm on Wednesday 19th and Saturday 22nd
Tickets and more information
https://galadurham.co.uk/galapost/guys-dolls/
All images: Credit to Durham University.
5 + = twelve

redpajama_set_name: RedPajamaCommonCrawl


text:
Apple goes for the jugular with subscription revenue deal
By Mathew Ingram
There have been rumors about a forthcoming Apple News subscription plan for some time now, with the first reports emerging in April last year, when Bloomberg said the company was working on a Netflix-style news service that would include dozens of publishers for one monthly fee. As talks continued, some media companies were said to be reluctant to sign up, and this week it became obvious why: According to a report in The Wall Street Journal, the tech giant wants to keep 50 percent of the revenue from its subscription program, and it also has no plans to share any of the user data it collects with publishers, including credit-card info and email addresses. The 50 percent of revenue publishers share will also be pooled and split up based on whose content gets the most engagement, according to the Journal report.
To say this proposal caused an outcry would be a massive understatement. For an industry that has seen mounting layoffs—more than 2,000 employees have been let go in recent weeks from BuzzFeed, Vice, HuffPost, and the Gannett and McClatchy chains—and even outright closures of newspapers and magazines, the Apple news came as a significant blow. Many were outraged that one of the world's most valuable companies, a behemoth with a staggering $245 billion in cash on its books, would take such a significant chunk of the revenue from its proposed plan, while also saying how much it cares about journalism.
Verge writer Casey Newton called it "obscene," and said the fact Apple could even think of taking a 50 percent share is "a worrying sign about the concentration of tech power in this country." Another journalist said the move amounted to Apple wanting to "twist the knife."
ICYMI: I was plagiarized by Jill Abramson
The deal includes no access to user data. For publishers and media companies eager to build sustainable businesses of their own by appealing to subscribers, access to user names, credit-card numbers and email addresses might make the 50 percent revenue take more palatable. But keeping all of that data just reinforces how all the power is in Apple's hands—and every user who signs up for the bundle just adds to that data hoard.
The unfortunate reality, however, is that some publishers may not have much choice when it comes to deciding whether or not to accept Apple's deal. Giants like The New York Times or the Journal have the heft and the market power to run their own successful subscription businesses, so anything they might get from Apple's plan is gravy. But smaller publishers don't have the brand power and their subscription programs are in most cases significantly smaller, which means they need all the revenue help they can get.
The biggest risk with a plan like Apple's is the same as it was with Facebook's Instant Articles and video projects, both of which came back to bite publishers badly: Namely, that publishers and media companies make a big bet on the platform, and come to rely on the revenue and/or reach that they get from their huge partner—and then that partner either changes the terms of their deal or doesn't come up with the revenue they promised. Dozens of publishers made significant bets on video because of Facebook's pitch about how much it wanted video, and then had to either unwind those investments or in some cases shut down because the promised benefits never emerged.
ICYMI: Mark Zuckerberg seemed "genuinely peeved" during an interview
Part of the reason Mic.com fired its entire staff and sold itself for a fraction of its former value was that it made bets on video that never panned out, and a heavy reliance on Facebook was also part of the driving force behind BuzzFeed's layoffs of more than 200 employees.
Just like Facebook's proposals before it, the Apple deal is a classic Faustian bargain. Apple News has enormous reach (more than 90 million readers, according to recent estimates) and that makes it seem hugely appealing to struggling publishers, many of whom have watched their advertising revenue plummet as Google and Facebook have taken over the industry. But the price of this deal isn't just 50 percent of the revenue; it's also the incalculable cost of yoking your business and potentially your survival to a third party, one that—for all its heart-warming statements about a commitment to journalism—has its own commercial interests in mind. Never build your house on rented land, someone once said.
Here's more on Apple's plan and the reaction to it. There's also an open discussion thread on CJR's Galley forum:
It's insane: It's probably not surprising that the proposed Apple deal would get significant pushback from many journalists, but even veteran Apple blogger John Gruber criticized the proposal, saying taking 30 percent would be "a bit greedy," but that taking half the revenue "is insane."
The Hunger Games: The idea of a "Spotify for news" sounds good, says Alastair Coote, "until you realise the actual comparison is dozens of artists releasing cover versions of the same song every morning and desperately trying to get the algorithm to put their version ahead of everyone else's."
Start running: Apple's proposal should "send publishers running in the other direction," said The Verge's Casey Newton. "Nothing the iPhone can do is worth 50 percent of revenue." Newton also noted that even Facebook, which is not known for being friendly to third parties, let publishers keep 100 percent of their Instant Article revenue.
The Aggregator: Tech analyst Ben Thompson said in his Stratechery newsletter that Apple is doing what aggregators always do: It is using content from others to attract users, "which makes Apple News more attractive, making publishers ever more reticent to leave, even though they aren't getting much out of the deal."
Other notable stories:
Maria Ressa, founder of the Philippines-based news site Rappler, was arrested on Wednesday afternoon by federal agents on charges of breaching that country's digital libel act — an act that Ressa and others have noted was passed months after the article she was arrested for was published. Ressa and her site have been repeated targets of harassment from the government of president Rodrigo Duterte.
After much debate, two controversial proposals for new copyright legislation in the EU are headed to a vote by the EU Parliament. Article 11 would require aggregators like Google News to pay for republishing even small snippets of articles, and Article 13 would require platforms to filter content for copyright violations before it is even uploaded to their networks. Freedom of information advocates argue that both proposals could have significant negative consequences.
Zainab Sultan writes for CJR about how student journalists working for newspapers and magazines published on campuses in many cases do the same kinds of critical investigative stories their peers at mainstream media outlets do, but are subject to far more pressure and even outright intimidation from school officials.
Members of the Newspaper Guild of Pittsburgh have asked that John Robinson Block, publisher of the Pittsburgh Post-Gazette, be banned from entering the newsroom after an incident in which staff said Block went "berserk," ranting and screaming about firing people and "raving like a lunatic." After a statement from the Block family that downplayed the incident, the Guild has released several eyewitness accounts.
A government review of the state of journalism in the UK has recommended tax breaks and other subsidies, but Guardian columnist Owen Jones says that's not enough. He says every citizen should get a stipend of $200, funded by a tax on advertising, and they should be able to give those funds to any nonprofit site.
More than 300 journalists at the Los Angeles Times have signed an open letter to the newspaper's management about its proposed policy on intellectual property. The letter from the LA Times Guild says the policy, which it describes as "draconian," would give the company control over any books written by employees and any movie rights associated with them.
The Agence France-Presse wire service, which has partnered with Facebook to do fact-checking in 17 different countries, says that the relationship is evolving in a positive direction, but that the social network needs to open up more and share data with its partners about how the program is progressing.
Matt Thompson is leaving his current post as executive editor of The Atlantic to become editor-in-chief of the Center for Investigative Reporting and its investigative journalism site RevealNews.org, as well as the organizations public radio show and podcast. Thompson said he will continue to be a contributor editor to The Atlantic.
ICYMI: Photographer behind viral Pelosi photo speaks
Mathew Ingram is CJR's chief digital writer. Previously, he was a senior writer with Fortune magazine. He has written about the intersection between media and technology since the earliest days of the commercial internet. His writing has been published in the Washington Post and the Financial Times as well as by Reuters and Bloomberg.
Why journalists need to think twice about reporting on arrests
AP tackles language about race in this year's style guide


Tim Gruar continues his series about artists coming to Womad in March, this time talking to Dutch/Kiwi three piece My Baby – a group that defies the usual trappings of the music industry machinery, preferring to tour, record and produce entirely under their own steam. Nailing down their sound is a bit of a challenge. They borrow heavily from gospel, blues, soul, voodoo-raves and 60's psychdelica. A recent visit to Wellington gave an opportunity to meet up and discuss the band's origins, music and their upcoming performance at Womad.


text:
Told in fourteen fixed-angle, single shot, individual tableaus that parallel Christ's journey to his own crucifixion, STATIONS OF THE CROSS is both an indictment of fundamentalist faith and the articulation of an impressionable teen's struggle to find her own path in life. Though from the outside Maria lives in the modern world, her family and her heart are faithful to a Catholic radicalism that requires sacrifice and devotion at every turn. As she struggles to balance her own desires with the dictates of her family's faith, she makes ever more perilous sacrifices, attempting to please a God she worships unquestioningly in the pious hopes of curing the autistic younger brother she adores.
DIRECTED BY DIETRICH BRÜGGEMANN
GERMANY | 2014 | GERMAN WITH ENGLISH SUBTITLES
Told in fourteen fixed-angle, single shot, individual tableaus that parallel Christ's journey to his own crucifixion, STATIONS OF THE CROSS is both an indictment of fundamentalist faith and the articulation of an impressionable teen's struggle to find her own path in life. Though from the outside...


Crowd : Suitable for both men and women.
Material : Environmentally friendly high tensile silicone, five claws.
Uses : Suitable for winter crowds to use ice and snow, non-slip, hiking, hiking, fishing to prevent falling.
Features : light weight, natural to wear, easy to carry, convenient and simple, clean water, wear-resistant, strong and strong cold resistance.
Packing : Green plastic bag.
1. Made of high-strength silicone material, self-adhesive Velcro, non-slip, easy to use, can be used on the shoes.
2. Winter climbing or high-altitude mountaineering, used to stand on the slippery ice or snow.
3. Comfortable, comfortable, and excellent crampons. From now on, I am no longer afraid to slip in the snow and ice.
1. You can walk naturally after using this product.
2. It is easy to put on and remove this product.
3. Can avoid injury caused by slipping.
4. You can safely walk in wet places, sand, snow and ice.
-For outdoor climbing activities, outdoor wilderness sruvival activities, outdoor adventures, and used for disaster relief.
-For Climbing, climbing tree, climbing mountain, rock climbing, ice climbing, anchoring, fishing and cleaning up the weeds, ect.


I am unable to run the demo version of NeatIMage on my Linux Mint 18.3 Cinnamon, 64 bit, system.
I have downloaded NeatImageSL.Demo.Intel64.tgz and unpacked it to NeatImageSL.Demo.Intel64.run. When I try to execute this, by double-clicking on the .run file, I am asked for an administration password (which I assume is meant to be my sign-on password). After entering my password nothing else happens, to the best of my knowledge.
Where is the documentation describing how to install and use the demo software under Linux?
Yes, of course, that is intuitively obvious - if you happen to be a technical support employee of ABSoft. For the rest of the population, would it not be a good idea to place this information somewhere on your website? And if it is already there, why not make it somewhere that is less obscure?
Now that we know about this problem with Linux MInt 18.3 Cinnamon, we will this to the list of known issues. Thank you for the great suggestion. You have been the most helpful.


text:
All about BIOFACH 2022
About the exhibition
Patron & supporting organization
Direct flights Pro Sky
Topics & forums
International market prospects
Photos of BIOFACH 2020
26 - 29 July 2022 // Nürnberg, Germany
+++ POSTPONEMENT: BIOFACH and VIVANESS will take place in 2022 from July 26-29. You can find more information HERE. +++
You are here: Home | Newsroom | Press releases
HEYHO: The social muesli attack
BIOFACH Newsroom
12 October 2017 // NürnbergMesse
Young innovative companies pavilion
The HEYHO founders // © HEYHO
HEYHO produces a very special granola, which is handmade by special employees. One adventure wasn't enough for HEYHO's founders, so they simply planned two: a flavour adventure and an adventure of radically different management.
Simply roasting the world's best organic granola is just too little for the socially responsible founders. Firmly convinced that every person can contribute their little bit to society regardless of their past and background, they want to give everyone a good start to the day. In keeping with this belief, a third of the staff who now have a secure job at the company's roasting plant in Lüneburg have a past in which things were not easy for them due to a very turbulent life. "By employing these people at the roasting plant, we want to give them new prospects for the future and show them that social entrepreneurship is possible – while tasting fantastic as well," said Christian Schmidt, one of HEYHO's founders.
With this in mind, the company decided that all its products would be handmade, and so all its granolas are mixed by hand and roasted in the oven on baking trays. The granolas are completely vegan, meaning the factory purposely doesn't use honey and sweetens its products with agave instead. HEYHO wants to add more fun to this market segment with its unconventional flavour combinations.
Frühsportfreunde, for example, is a high-energy granola designed to get consumers going in the morning. The company recommends stretching your masticatory muscles before eating this variety's hand-beaten coconut pieces. For those who enjoy the Late Night Breakfast, its special mixture consists of roasted rolled oats, melted dark chocolate, chocolate salted pretzels, roasted pumpkin seeds, bitter cocoa bean fragments and cocoa moons. The Golden ChaiChai variety, which contains cinnamon, cardamom, ginger, black pepper and turmeric is meant to add a spicy inspiration to the average bowl of muesli. For those in the undecided target group, who don't like having to choose between sweet and salty, the granola specialists have created a variety called Saltcity Original, which includes caramelised almonds, cashews and hazelnuts that have been enhanced with a pinch of real Lüneburg salt. In terms of its packaging designs, HEYHO also wants to move away from the grey mass of muesli boxes and has opted for completely transparent jars.
HEYHO (www.goheyho.com) will be one of the exhibitors in the Pavilion for Young Innovative Companies. This pavilion is being supported by the German Federal Ministry for Economic Affairs and Energy (BMWi) and is aimed at newcomers and start-ups based in Germany. 20 companies altogether will be presenting products there in hall 9 at BIOFACH, the World's Leading Trade Fair for Organic Food (www.biofach.de), which takes place from 14 to 17 February 2018.
Photos: HEYHO
CAPTION: HEYHO founders
Language variants (PDF)
Press team BIOFACH
Further press releases
Leading international fair continues to evolve: What surprises does BIOFACH 2022 have in store? read on
Taste, feel and smell the latest food trends at the newcomer pavilion at BIOFACH 2022 read on
BIOFACH Congress Theme 2022: Organic.Climate.Resilience. read on
Buy tickets for BIOFACH
All FAQ are available here!


text:
Rolling the Dice/ Gambling
Sports betting regulators confront licensing quirks
Applicants say temp licenses, head starts don't make sense
By Shira Schoenberg Gambling, Sports betting 0 Comments Sep 22, 2022
THERE'S AN ODD quirk in the law legalizing sports betting in Massachusetts. The Massachusetts Gaming Commission is allowed to license seven mobile sports betting apps, in addition to mobile apps that are tied to in-person gaming facilities like casinos and racetracks. But the law also lets the commission give an unlimited number of temporary mobile licenses, which would cost a $1 million fee and could last for up to a year.
The temporary licenses were apparently intended to let sports betting begin sooner, while the full regulatory and licensing process is pending. Practically, however, regulators are saying that approach could lead to a scenario where multiple mobile apps are allowed to start operating sports betting, then are forced to shut down months later if they fail to obtain a permanent license. There are 42 companies that have expressed interest in applying to the Gaming Commission for a sports betting license, and all but a handful of them are seeking a mobile or digital license.
At a hearing Thursday, several online betting companies urged regulators not to issue more than seven temporary licenses – if they issue any at all.
Justin Smith, legal counsel for Bally's North American Interactive, said the problem with a short-term license is customers often place wagers on games months in advance. Operators would need to figure out how to manage their operations so they can repay account balances and payments on future bets if they are forced to shut down. "This would be difficult to manage," Smith said.
Several company representatives said it is expensive to set up state-compliant gaming operations and market to consumers. "We don't think it's an effective use of resources by operators or the Commonwealth to offer more temporary licenses than can become final licenses, given the significant investments by the operator and the commission," said Cory Fox, FanDuel's vice president of product and new market compliance.
Cynthia Hays, vice president of compliance for Betfred, said that initial cost can be "prohibitive." A short-term license, she said, would let customers take advance of sign-up offers, but companies won't be around long enough to recoup the money by turning those players into long-term customers.
Fox suggested that the usefulness of temporary licenses would be mainly to let companies that are on track for final licenses get started earlier, while regulators are still conducting their final checks.
Joe Casole, a consultant for NOVABET, said allowing more than seven temporary licenses would give a significant advantage to large established companies that can quickly scale up to add Massachusetts operations, hurting smaller companies that would have to set up equipment testing labs or train staff on the hope that they will be allowed to continue operating.
Casole, speaking on behalf of another consulting client, MaximBet, said if regulators do allow temporary licenses there needs to be a clear timeline from the start, along with clear rules that make customers feel confident they will get any money they are owed back if a company shuts down. "Requiring companies to do everything required to launch only to have a license revoked before a year feels overly draconian," Casole said.
Several companies did say they would apply for a temporary license if one became available. For example, the new app company Betr is trying to get a foothold in the market for its concept of microbetting, which lets players bet on individual moments in a game – a baseball pitch or a football drive. Other larger companies are reluctant to give up the advantage of being among the first to open in Massachusetts, even if that carries a large financial risk.
The Massachusetts Gaming Commission also asked potential license applicants to weigh in on whether there should be a single launch date, where every licensee who is ready can begin operations, or staggered start dates depending on when each company's license application is approved. The commission could also consider having different launch dates for different types of operations – for example, letting on-site sports betting at casinos begin before mobile betting.
Several companies' representatives urged the commission to have a single universal launch date in order to level the playing field and avoid giving the first companies to enter the market an unfair competitive advantage.
Fox, of FanDuel, compared the operations of his company and Boston-based DraftKings in Pennsylvania and Indiana. In Pennsylvania, FanDuel launched three months before DraftKings, and in Indiana, DraftKings launched three months earlier. Three years later, Fox said, the company that launched first remains the market leader in each state – FanDuel in Pennsylvania and DraftKings in Indiana.
"In other states, the operators who launch first have a significant sustained market share versus those that launched a few weeks later," Fox said.
In Virginia, Casole said, FanDuel got a head start of a week or less on two other major sports betting companies – DraftKings and MGM – and even those few days had a material impact on that state's market. "First-mover advantage is a massive leg up and inhibits competition to the detriment of the consumer," Casole said.
A DraftKings representative said his company also favors a simultaneous launch of all companies that are ready.
Tagged in: Gambling/ Sports betting
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Coverage of casino licensing and the gambling referendum
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Sports betting could start in late Jan., maybe


text:
Union: 5 Rooms x 10 Crews x 40+ Artists
This Friday marks the official launch of Los Angeles's brand new mega club and soon-to-be west coast bass music hub, Union, packed with over $250,000 worth of Funktion-One setups and state of the art lighting throughout all FIVE of its spacious rooms. For the opening celebration of such a monstrous venue, it's only fitting that Union commissioned ten of the biggest west coast bass collectives to curate talent for each of its stages for their six hour, bass supershow: Xcellerated & CITY FLOW MUSIC / Heavy Dub Events & CAVITY CULT / Mass LA & Juke Bounce Werk / Cats & Boots Records & FUGITIVE SOUND SESSIONS / and I LOVE LA EVENTS & Wreck-Ignition. Together, these ten collectives will unite over 40 hand-selected bass music artists under one roof, with special surprise guests, the exclusive U.S. debut of Ivy Lab and multiple other U.S. debuts.
Union's launch, taking place Friday, February 19th, is a special 18+ event, with music from 9 pm to 3 am. $20 presales can be purchased here, with an increase in price to $25 tickets at the door.


text:
\section{Introduction}

It is well-known from a number of studies [1-3]
that the Lipkin-Meshkov-Glick (LMG) model [4-6] has a rich phase structure that
is related to a broad range of phenomena in a variety of physical applications,
such as analyses of spin
systems [7], Bose-Einstein condensates [8], etc.
Furthermore, it has been proven [9,10] that the model is exactly solvable.
A special case of the theory is related
to the standard two-site Bose-Hubbard model [11] with a Hamiltonian
that is equivalent to that of a paramagnet of the easy-axis type in
a transverse magnetic field [12]. The quantum dynamics and the energy gap
of the model were studied in [13-14]. The quantum critical behavior
and a special case of the model were discussed in [15-16].
As shown in [9-11, 12-16], exact solutions of the model
can be determined using the Gaudin-Richardson or Bethe ansatz method, in which
eigenstates of the system are written in terms of a product of spectral
parameter-dependent operators. The unknown spectral parameters must satisfy
a set of coupled non-linear equations, called the Bethe ansatz equations (BAEs).
Solutions of the BAEs simultaneously determine the eigenenergies and the
corresponding eigenstates [9-11].

It should be noted that according to
the early work of Stieltjes [17-20] there is an important
one-to-one correspondence between every set of BAEs
and a set of orthogonal polynomials. And furthermore,
as shown by Szeg\"{o} [21], the Stieltjes correspondence
can be used to define a large class of classical orthogonal
polynomials. Roots of these BAEs are zeros of
the corresponding polynomials, which can be interpreted
as stable equilibrium positions for a set of free charges
in an external electrostatic field. This link between Richardson's BCS pairing
model for nuclei and the corresponding electrostatic problem was
established in [22] based on an earlier unpublished preprint of Gaudin,
which was then made clearer in [23]. A much more general approach
to the pairing model was shown in [24] and [25].
The purpose of this paper is
to show that the Stieltjes correspondence related to the solutions of
a special LMG model corresponding to the standard two-site Bose-Hubbard model
gives rise to a new polynomials, which is now called  the
extended Heine-Stieltjes polynomials .

\section{Stieltjes correspondence}

There is a large class of polynomials, called Heine-Stieltjes polynomials $y(z)$,
which satisfy a second-order Fuchsian equation

$$A(x)y^{\prime\prime}(x)+B(x)y^{\prime}(x)+V(x)y(x)=0,\eqno(1)$$\\
where $A(x)$  is a polynomial of degree $m$ with $A(x)=\prod_{i=1}^{m}(x-a_{i})$,
$B(x)$ is a polynomial of degree $m-1$ such that for a set of real
positive parameters $\{\gamma_{i}\}$ and another set of real
parameters $\{a_{i}\}$

$$B(x)/A(x)=\sum^{m}_{i=1}{\gamma_{i}\over{x-a_{i}}},\eqno(2)$$\\
and $V(x)$ is an unknown, but to be determined polynomial of degree
$m-2$ that is allowed to depend on the solution $y(x)$.
The latter are often called Van Vleck polynomials [26].
The case with $m=2$ corresponds to the hypergeometric differential equation,
while the case with $m=3$ corresponds to the Heun equation [27-28].

Such Heine-Sieltjes polynomials and properties of their zeros have been studied
extensively. If the polynomials $A(x)$ and $B(x)$
are algebraically independent, i.e., they do not satisfy any algebraic
equation with integer coefficients, Heine proved that
for every integer $k$ there exist at most
$\sigma(k)=(k+m-2)!/((m-2)! k!)$ different  Van Vleck polynomials $V(x)$
such that $y(x)$ has a polynomial solution of degree $k$.
As summarized in
Szeg\"{o}'s work on orthogonal polynomials [21], for every set of nonnegative integers
$(k_1, k_2,\cdots, k_m)$, there are uniquely determined
real values of the parameters for the Van Vleck polynomials $V(x)$ such that $y(x)$
has a polynomial solution
with $k_j$ simple zeros in the open interval $(a_{j-1}, a_j)$
for each $j=1,2,\cdots, m$. The polynomial
$y(x)$ is uniquely determined  up to a constant factor, and has the degree
$k=k_1+\cdots k_m$.  As noted by Volkmer [29], this existence and uniqueness
theorem can also be derived from the general Klein oscillation theorem for multi-parameter
eigenvalue problems shown in [30].

If $y(x)$ is a polynomial of degree $k$ with simple zeros
$\{x_{1},x_{2},\cdots,x_{k}\}$, one may write $y(x)$ as

$$y(x)=\prod_{j=1}^{k}(x-x_{j}).\eqno(3)$$\\
Thus, one can easily check that $y(x)$
will satisfy

$${y^{\prime\prime}(x_{i})\over{y^{\prime}(x_{i})}}
=\sum_{j\neq i}{2\over{x_{i}-x_{j}}}\eqno(4)$$\\
at any zero $x_{i}$. Combining (1), (2), and (4),
one obtains the following important relations among the zeros:

$$\sum_{j\neq i}^{k}{2\over{x_{i}-x_{j}}}+\sum^{m}_{\mu=1}{\gamma_{\mu}\over{x_{i}-a_{\mu}}}=0\eqno(5)$$\\
for $i=1,2,\cdots, k$. It should be noted that the BAEs frequently appearing in search for
exact solutions of quantum many-body problems, such as those associated with Gaudin type
systems, are similar to the relations shown in (5). The link between Richardson's BCS
pairing model for nuclei and the corresponding electrostatic problem was
investigated in [22] based on an earlier unpublished preprint of Gaudin,
which was then made clearer in [23]. A much more general approach
to the pairing model was shown in [24] and [25].
Roots of the BAEs (5) simultaneously
determine the eigenenergies and eigenstates of the corresponding quantum many-body problem.
As an alternative, roots of the BAEs may also be calculated as zeros of the
corresponding polynomial $y(x)$. In this way, a link between
solutions of the Gaudin type for quantum many-body problems and
the corresponding polynomials is established.

\section{Special LMG model and Bethe ansatz solutions}

As a simple extension of the Stieltjes correspondence, we revisit the Bethe ansatz
solutions for a special LMG model corresponding to the standard two-site Bose-Hubbard model
studied in [11, 13-15], for which the Hamiltonian is

$$\hat{H}=-t(c^{\dagger}d+d^{\dagger}c)+U(c^{\dagger}cc^{\dagger}c+
d^{\dagger}dd^{\dagger}d),\eqno(6)$$\\
where $c^{\dagger}$ ($c$) and $d^{\dagger}$ ($d$) are boson creation
(annihilation) operators, the parameters $t$ and $U$ in the Bose-Hubbard model
are related to the Josephson coupling and the charging energy, respectively.
Following [11, 15], we use the unitary transformation
for the boson operators with

$$c = \sqrt{1\over{2}}(a -\dot{\imath}b),~~~ d =\sqrt{1\over{2}}(a +{\dot{\imath}}b).\eqno(7)$$\\
Then, the Hamiltonian (6) can be rewritten in terms of $a$- and $b$-boson operators
as

$$\hat{H}=t(b^{\dagger}b-a^{\dagger}a)-{1\over{2}}U
S^{+}(0)S^{-}(0)+U\hat{n}^2,\eqno(8)$$\\
where $\hat{n}=a^{\dagger}a+b^{\dagger}b$ is the operator for the total number
of bosons in the system, and

$$S^{+}(0) = b^{\dagger2} + a^{\dagger2},
~~S^{-}(0) = b^{2} + a^{2}\eqno(9)$$\\
are boson pairing operators.

Let $\vert \nu_1,\nu_2\rangle=a^{\dagger\nu_1}b^{\dagger\nu_2}\vert 0\rangle$
with $\nu_{i}=0$ or $1$ for $i=1, 2$
be the $a$- and $b$-boson pairing
vacuum state satisfying

$$a^{2}\vert \nu_1,\nu_2\rangle=b^{2}\vert \nu_1,\nu_2\rangle=0.\eqno(10)$$\\
To diagonalize the Hamiltonian, we use the algebraic Bethe ansatz
which implies that eigenvectors of (8) may be expressed as

$$\vert n,~\zeta,\nu_{1},\nu_{2}\rangle=
S^{+}({x}^{(\zeta)}_{1})S^{+}({x}^{(\zeta)}_{2})\cdots
S^{+}({x}^{(\zeta)}_{k})\vert \nu_1,\nu_2\rangle\eqno(11)$$\\
with $n=2k+\nu_{1}+\nu_{2}$, and

$$S^{+}({x}^{(\zeta)}_{i})={a^{\dagger 2}\over{x_{i}^{(\zeta)}+1}}+{b^{\dagger
2}\over{
x^{(\zeta)}_{i}-1}},\eqno(12)$$\\
in which $x^{(\zeta)}_{i}$ ($i=1,2,\cdots,k$)
are spectral parameters to be determined,
and $\zeta$ is an additional quantum number for distinguishing
different eigenvectors with the same quantum number $k$.
It can then be verified by using the corresponding
eigen-equation that (11) is a solution when the
spectral parameters $x_{i}^{(\zeta)}$ ($i=1,2,\cdots, k$)
satisfy the following set of BAEs:

$$U\left( {2\nu_{1}+1\over{x_{i}^{(\zeta)}+1}}+
  {2\nu_{2}+1\over{x_{i}^{(\zeta)}-1}}\right)+2t
  +4U\sum_{j(\neq i)}{1
  \over{x_{i}^{(\zeta)}-x_{j}^{(\zeta)}}}=0\eqno(13)$$\\
for $i=1,2,\cdots,k$, with the corresponding eigen-energy given by

$$E^{(\zeta)}_{n}=2t\sum_{i=1}^{k}{{x_{i}^{(\zeta)}}}+
t(\nu_2-\nu_1)+Un^{2}.\eqno(14)$$\\
Hence, once the $\zeta$-th roots $\{x_{i}^{(\zeta)}\}$ are obtained
from Eq. (13), the  eigenenergy and the corresponding
eigenstate are thus determined according to (14), (11), and (12).

\section{The extended Heine-Stieltjes polynomials
associated with solutions of the LMG model}

In order to compare to the Stieltjes correspondence,
we assume $t>0$ and $U\neq 0$, and set

$$\alpha=\nu_{1}+1/2,~~~\beta=\nu_{2}+1/2,~~~ \gamma=t/U.\eqno(15)$$\\
Then, the BAEs (13) becomes

$$\left( {\alpha\over{x_{i}^{(\zeta)}-1}}+
  {\beta\over{x_{i}^{(\zeta)}+1}}\right)+\gamma
  +\sum_{j(\neq i)}{2
  \over{x_{i}^{(\zeta)}-x_{j}^{(\zeta)}}}=0.\eqno(16)$$\\
When $U>0$, all parameters $\alpha$, $\beta$ and $\gamma$
are always positive. When $U<0$, we interchange the boson
operator $a^{\dagger}$ with $b^{\dagger}$ in (12). Then, one can easily
verify that such a change is equivalent to interchange $\nu_{1}$ with
$\nu_{2}$ and $t\rightarrow-t$ in the BAEs (13), which leads to
the final BAEs for the $U<0$ case that is the same as (16)
with $\alpha\rightleftharpoons\beta$ and keeping
$\alpha>0$, $\beta>0$, and $\gamma>0$. Hence, it is sufficient
to consider the case for $U>0$ only with BAEs given by (16).

Although the $\gamma=0$ result is trivial for the LMG model,
according to the Stieltjes correspondence, the polynomial
corresponding to (16) in this case is the Jacobi polynomial
$P^{(\alpha-1,\beta-1)}_{k}(x)$  satisfying the well-known
differential equation

$${d^{2}\over{dx^{2}}}P^{(\alpha-1,\beta-1)}_{k}(x)+\left( {\alpha\over{x-1}}+
  {\beta\over{x+1}}\right){d\over{dx}}P^{(\alpha-1,\beta-1)}_{k}(x)
  -{k(k+\alpha+\beta-1)\over{x^{2}-1}}P^{(\alpha-1,\beta-1)}_{k}(x)=0.\eqno(17)$$\\
In this case, the Van Vleck polynomial $V(x)$ is trivially a $k$-dependent
constant. Hence, there is only one set of zeros of $P^{(\alpha-1,\beta-1)}_{k}(x_{i})$
with $i=1,2,\cdots, k$, satisfying the Bethe ansatz equation (16).

The case with $\gamma\neq0$ is non-trivial.
According to (1)-(5), we write a differential
equation corresponding to the Bethe ansatz equation (16) as

$${d^{2}y(x)\over{dx^{2}}}+\left( {\alpha\over{x-1}}+
  {\beta\over{x+1}}+\gamma\right){dy(x)\over{dx}}
 +{V(x)\over{x^{2}-1}}y(x)=0\eqno(18)$$\\
with the corresponding polynomials $A(x)=x^2-1$ and
$B(x)=\gamma x^2+(\alpha+\beta)x+\alpha-\beta-\gamma$
shown in (1). In contrast to the Heine-Sieltjes equation (1),
however, in this case the polynomial $B(x)$ is of the same degree
as that of $A(x)$. Therefore, the polynomials
$y(x)$ determined by (18) should be similar to but different
from those of Heine-Sieltjes type.

In search for polynomial solutions of (18), we write
$$y_{k}(x)=\sum_{j=0}^{k}b_{j}x^{j}.\eqno(19)$$
Substitution of (19) into (18) yields
the condition to determine the corresponding
polynomial $V(x)$ with

$$V(x)=-\gamma kx+f,\eqno(20)$$
where $f$ is an undetermined constant depending on $k$,
together with the expansion coefficients $b_{j}$, satisfying
the following four-term relations:

$$\left( j(\alpha+\beta+j-1)+f\right)b_{j}=
(j+2)(j+1)b_{j+2}+(j+1)(\beta-\alpha+\gamma)b_{j+1}+
\gamma(k-j+1)b_{j-1}\eqno(21)$$\\
with $b_{j}=0$ for $j\leq-1$ or $j\geq k+1$, which is
equivalent to the following eigen-equation for $f$
with

$${\bf F}{\bf b}=f{\bf b},\eqno(22)$$
where

$${\bf F}=\left(
\begin{tabular}{c}
~~0~~~~~~$(\beta-\alpha+\gamma)$~~~~~~~~~~~~2 ~~~~~~~~$0\cdots$~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\
$k\gamma$~~~~$-(\alpha+\beta)$~~~~~~$2(\beta-\alpha+\gamma)$~~~~~~~~$6$~~~~~~~~~$0\cdots$~~~~
~~~~~~~~~~~~~~~~~~~~~~\\\\
~~~~0 ~~~~~~$(k-1)\gamma$~~ ~$-2(\alpha+\beta+1)$ ~~$3(\beta-\alpha+\gamma)$~~$12$~~~$0\cdots$
~~~~~~~~~~~~~~~~~~~~\\\\
~~~~~~~~~~~~~~~$\ddots$~~~~~~~~~~~~~~~~~~~~$\ddots$~~~~~~~~~~~~$\ddots$~~~~~~~~~~~~$\ddots$
~~~~~~~~~~~~\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~$\ddots$~~~~~~~~~~~~~~~~~~$\ddots$~~~~~~~~~~~~~~~$\ddots$~~~~~~$k(k-1)$\\\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$2\gamma$~~~~$-(k-1)(\alpha+\beta+k-2)$~~~$k(\beta-\alpha+\gamma)$ \\\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$\gamma$ ~~~~~~~~~~~~~~~~~~$-k(\alpha+\beta+k-1)$\\
\end{tabular}\right),\eqno(23)$$\\
and the transpose of  ${\bf b}$ is related to the expansion coefficients $\{b_{j}\}$ with
 ${\bf b}^{T}=\left( b_{0},b_{1},\cdots,b_{k-1},b_{k}\right)$.
It is clear that the matrix ${\bf F}$ should have $k+1$ eigenvalues labeled as
$f^{(\zeta)}$ ($\zeta=1,2,\cdots,k+1$), of which
the corresponding eigenvector ${\bf b}^{(\zeta)}$ determines the
polynomial $y^{(\zeta)}_{k}(x)$ according to (19). The number of solutions for $f$
is indeed the same as that of the eigenstates of the standard two-site
Bose-Hubbard Hamiltonian (8) when $\gamma\neq 0$.
The polynomials (19) with $\gamma\neq0$ determined by (21)
are called the extended Heine-Stieltjes polynomials, which,
in general, can also be obtained from the Riccati differential
equation studied in [31-32] or from relevant Bethe ansatz equations
given in [33] though these authors did not intend to do so.
It should be noted that the polynomial approach shown above
is similar to that studied in [34-36] for quasi-exactly solvable sextic anharmonic oscillator problem
and ${\cal PT}$-symmetric quantum mechanics. Since the Bethe ansatz equations
of the quasi-exactly solvable sextic anharmonic oscillator problem
and ${\cal PT}$-symmetric quantum mechanics are different from
those for the special LMG model, the resultants should belong to
different types of extended Heine-Stieltjes polynomials.

As is well known, the advantage of the Bethe ansatz method
for Gaudin type systems lies in the fact that the huge matrix
in the Fock subspace is greatly reduced, especially for the Gaudin-Richardson
pairing model [22-25].
However, the non-linear Bethe ansatz  equations similar to (16)
are very difficult to be solved numerically,
especially for large size systems. There are several attempts to overcome
this difficulty. The approach via Riccati differential
equation shown in [31-32] is one of them.
Actually, if the polynomials can be derived recursively
similar to (21) for the LMG model, it should be much easier to
determine zeros from the polynomials than to solve a set
of BAEs with a set of variables because there is only one
variable in the polynomials. In order to make this point clear,
let us take a simple nontrivial example with $k=2$ and
$\alpha=\beta=\gamma=1/2$ corresponding to $\nu_1=\nu_2=0$
and $t/U=1/2$. In this case, the three polynomials $y_2(x)$ given by (19) with $b_{2}=1$
can easily obtained from the four-term recurrence relations (21)
as listed in Table 1.  Since we set $b_{k}=1$ in $y(x)$,
the coefficient $b_{k-1}$ must equal to
negative sum of zeros of $y(x)$ with
$b_{k-1}=-\sum_{i=1}^{k}x_{i}$.
Therefore, the solution corresponding to the largest $b_{k-1}$
is that for the ground state of the system considered;
that corresponding to the next largest $b_{k-1}$
is that of the first excited state; and so on. One can check
that these are indeed the case as shown in Table 1.

\begin{table}[ht]
\caption{The extended Heine-Stieltjes polynomials $y_2(x)$
for the LMG model with $\alpha=\beta=\gamma=1/2$.}
\label{energy} \vspace*{-6pt}
\begin{center}
\begin{tabular}{cccc}\hline\hline
Zeros of the polynomial &$x_1+x_{2}$ &The Polynomial $y_2(x)$ &$f$ \\ \hline
$x_{1}=-7.2904,~x_{2}=-1.7379$ &$-9.0283$ &$12.6700+9.0283x+x^2$&$~~0.5141$\\
$x_{1}=-5.7052,~x_{2}=~0.5612$ &$-5.1440$ &$-3.2020+5.1440x+x^2$ &$-1.4280$\\
$x_1=-0.6036,~x_{2}=~0.7759$ &$~~0.1723$ &$-0.4684-0.1723x+x^2$&$-4.0861$\\
\hline \hline
\end{tabular}
\end{center}
\end{table}

According to the Stieltjes results, an electrostatic interpretation of the location of
zeros of the new polynomial $y(x)$ may be stated as follows.
Put two positive fixed charges $\alpha/2$ and $\beta/2$ at $-1$ and $+1$
along a real line, respectively,
and allow $k$ positive unit charges to move freely along the real line
under such situation
together with a uniform
electric field with strength $-\gamma/2$. Therefore, up to a constant, the total energy functional
$U(x_{1},x_{2},\cdots, x_{k})$ may be written as

$$U(x_{1},x_{2},\cdots, x_{k})=-{\gamma\over{2}}\sum_{i}x_{i}
-{\alpha\over{2}}\sum_{i}\ln{\vert x_{i}-1\vert}-{\beta\over{2}}\sum_{i}\ln{\vert x_{i}+1\vert}
-\sum_{1\leq i<j\leq k}\ln\vert x_{i}-x_{j}\vert.\eqno(24)$$\\
In this case, there are $k+1$ different configurations for the position
of these $k$ charges $\{x^{(\zeta)}_{1},\cdots, x^{(\zeta)}_k\}$
with $\zeta=1,2,\cdots, k+1$,
corresponding to global minimums of the total energy.
As proven by Stieltjes, there is a unique configuration with
$-1<x_{1}<\cdots<x_{k}<1$ when $\gamma=0$ which corresponds to the
zeros of the Jacobi polynomial $P_{k}^{(\alpha-1,\beta-1)}(x)$. When $\gamma> 0$, however,
one can verify numerically as done in [15] that the range of the positions of these
positive unit charges tends to be along the entire half line except the two
singular points $\pm 1$  with
$\{x_{1},\cdots,x_{k}\}\in (-\infty,-1)~ \bigcup~(-1,+1)$.
Let the positions of these positive charges be arranged as
$x_{1}<x_{2}<\cdots<x_{k}$. The above restriction requires
that these positions must be within the intervals  $(-\infty,-1)$
and $(-1,+1)$ with
$-\infty<x_{1}<x_{2}<\cdots<x_{k_{1}}<-1<x_{k_{1}+1}<\cdots<x_{k}<+1$.
It follows from this that the total number of possible configurations is exactly
the number of ways to put the $k$ positive charges into the two intervals,
which is $\left(\matrix{k+m-1\cr k\cr}\right)=k+1$ for $m=2$.

Some explicit formulas for sums of powers of zeros of the new polynomials
can easily be derived. For example, summing Eq. (16) over $i$, we have

$$(\alpha-\beta)\sum_{i=1}^{k}{1\over{x_{i}^{2}-1}}+
(\alpha+\beta)\sum_{i=1}^{k}{x_{i}\over{x_{i}^{2}-1}}=-k\gamma,\eqno(25)$$
while multiplying Eq. (16) by $x_{i}$ and then summing over $i$, we get

$$(\alpha+\beta)\sum_{i=1}^{k}{1\over{x_{i}^{2}-1}}+
(\alpha-\beta)\sum_{i=1}^{k}{x_{i}\over{x_{i}^{2}-1}}+\gamma\sum_{i=1}^{k}x_{i}=-k(\alpha+\beta+k-1).
\eqno(26)$$
Eqs. (25) and (26) can be combined to express $\gamma\sum_{i=1}^{k}x_{i}$
related to the eigenenergy (14) as

$$\gamma\sum_{i=1}^{k}x_{i}={4\alpha\beta\over{\alpha+\beta}}\sum_{i=1}^{k}{1\over{1-x^{2}_{i}}}
-k(\alpha+\beta+k-1-\gamma{\alpha-\beta\over{\alpha+\beta}}).\eqno(27)$$

    Additional sum rules can be derived from the explicit form
of the new polynomial $y_{k}(x)$ by using the method shown in [37-39] for other
polynomials. Let the polynomial $y_{k}(x)$, up to a constant,
be expressed in terms of its zeros as

$$y_{k}(x)=\prod_{i=1}^{k}(x-x_{i}).\eqno(28)$$\\
Then, the expansion coefficients in (19) can be explicitly written as

$$b_{k}=1,~~b_{k-1}=-\sum_{i=1}^{k}x_{i},~~
b_{k-2}=\sum_{i<j}x_{i}x_{j},~~\cdots,~~
b_{0}=(-)^{k}\prod_{i=1}^{k}x_{i}.\eqno(29)$$\\
Directly using the four-term relation (21) with the explicit expressions shown
in (29), we have, for example,

$$f=\sum_{1\leq i<j\leq k}{2\over{x_{i}x_{j}}}+(\alpha-\beta-\gamma)\sum_{i=1}^{k}
{1\over{x_{i}}}=
\left(\sum_{i=1}^{k}{1\over{x_{i}}}\right)^{2}-(k-1)\sum_{i=1}^{k}{1\over{x_{i}^{2}}}
+(\alpha-\beta-\gamma)\sum_{i=1}^{k}
{1\over{x_{i}}}
\eqno(30)$$\\
for $k\geq2$, and
$$f=-\gamma\sum_{i=1}^{k}x_{i}-k(\alpha+\beta+k-1),\eqno(31)$$\\
which provides a relation among the eigenvalues $f$ in
the differential equation (18) and the eigenenergies (14) of the
special LMG model. Eq. (31) can easily be verified from the results
shown in Table 1.

Sum rules of other higher order
powers and inverse powers of zeros of the new polynomials
may also be derived from the four-term relation (21)
by using explicit expressions shown in (29). Eq. (31)
clearly shows that $f=-k(\alpha+\beta+k-1)$ corresponding
to the Jacobi polynomial with $y_{k}(x)=P^{(\alpha-1,\beta-1)}_{k}(x)$
when $\gamma=0$.

\section{Summary and discussions}

In this paper, new polynomials,
similar to but distinct from those
of the Heine-Stieltjes type, that are associated with a
special LMG model corresponding to the
standard two-site Bose-Hubbard model are derived
based on the Stieltjes correspondence.
It follows that the eigenvalues and corresponding
eigenstates of the special LMG model can be determined
from the zeros of these polynomials. Further, if these polynomials
can be derived recursively, it also follows that it should be much easier to
determine zeros from the polynomials, e. g. the case
considered in [40], than to solve a set
of BAEs with a set of variables because there is only one
variable in the polynomials.
This conclusion applies equally
well to other quantum many-body systems, such as
atomic-molecular Bose-Einstein condensates [41],
the heteronuclear molecular Bose-Einstein condensate model [42],
and the nuclear
pairing problem, when the corresponding polynomials can be
obtained.
It is well known that the Jacobi polynomials $P^{(\alpha,\beta)}_{k}(x)$
are orthogonal with respect to the measure $d\mu(x)=(x-1)^{\alpha}(x+1)^{\beta}dx$
on the interval $x\in (-1,+1)$. Although the orthogonality of the new polynomials
is not addressed, we conjuncture that, similar to the Lam\'{e}
polynomials analyzed in [43-44], there is no sequence of
the new polynomials with $\gamma\neq0$ orthogonal with respect to any measure
supported on the interval $(-\infty, 1)$ when $\gamma\neq 0$.
A rigorous proof of the latter, which requires further work,
is beyond the scope of the present study.
Furthermore, following Stieltjes early work, a one-dimensional
classical electrostatic analogue corresponding to the special LMG model
is established. This shows that any possible configuration of equilibrium
positions of the charges in the electrostatic problem corresponds
uniquely to one set of roots of the BAEs for the LMG model,
and that the number of possible configurations of equilibrium
positions of the charges equals exactly to the number of energy levels
in the LMG model.
Sum rules of powers and inverse powers of zeros of the new polynomials
related to  eigenenergies of the LMG model
are also considered. More complicated sum rules and their relations
may be obtained similarly. The results by extension clearly show a new link
between Bethe ansatz type solutions of large class of quantum many-body problems
and a class of polynomials satisfying second-order differential equations, and
thus opens a new way to get solutions of these BAEs from
zeros of these polynomials.

\vskip .5cm
One of the authors (P. F.) is grateful to Prof. Dr. Hans Volkmer
for providing information about his work on the
Heine-Stieltjes polynomials and related helpful discussions.
The authors are also grateful to the referees for providing
us relevant references to the subject and helpful comments.
Support from the U.S. National Science Foundation
(PHY-0500291 \& OCI-0904874), the Southeastern Universities Research Association, the
Natural Science Foundation of China (11175078),  the Doctoral Program Foundation
of State Education Ministry of China (20102136110002),
and the LSU--LNNU joint research program (9961) is
acknowledged.

redpajama_set_name: RedPajamaArXiv


text:
Freaky (Factual) Tale Friday: The Suspicious Death of Dorothy Kilgallen
(photo @ wikipedia)
From the late 1930's to the early 1960's, Dorothy Kilgallen was something of a journalistic enigma. She was a gossip columnist that rose to a such a degree of notoriety that she became as much (or more) of a celebrity than the people she was writing about. This was in no small part helped by her role as a panelist on the popular game show, 'What's My Line.'
But Kilgallen's writing didn't stay confined to just the entertainment business; she would also break and/or cover major stories in the world of politics and organized crime. A few of her most notable works include:
-Extensive coverage of the Sam Shepard murder trial.
-Being the first journalists to claim that the FBI was working with the Mafia to overthrow Castro.
-Being the first journalist to link Marilyn Monroe to John F. Kennedy.
As you can imagine, a few items on her work history ticked some of the wrong people, which is probably why FBI director J.Edgar Hoover kept a dossier on Kilgallen's activities.
recollectionbooks.com
To be fair, he might have just
been looking for some fashion ideas.
One of Kilgallen's biggest "gets," however, was when she was able to interview Jack Ruby alone. For any of you that don't follow history or watch Oliver Stone movies, Ruby was the man that killed Lee Harvey Oswald (President John F. Kennedy's alleged assassin) on live television...and then died a few years later due to a pulmonary embolism while suffering from lung cancer.
Considering the fact that Ruby told Dallas Deputy Sheriff Al Maddox that he believed he had been injected with cancer cells by the government...and that he told a psychiatrist he was framed for killing Oswald (a murder he willing committed in front of a national audience), Ruby wasn't exactly the most reliable source of information about the JFK assassination. But he had still managed to put himself at the center of it, and Kilgallen was the only reporter that got some one-on-one time with him (although her notes from that interview have yet to have ever been fully revealed).
She also managed to dig up some pretty impressive information from other areas, as well. Through her one of her numerous government contacts, Kilgallen obtained and released the (then classified) transcript of the Warren Commission's questioning of Jack Ruby...which once again, really pissed off some of the wrong people.
She also ran an interview with Acquilla Clemons, who witnessed the killing of Oswald's other victim in Dallas that day, Officer J.D. Tippit...except that according to Clemons (who was never questioned by the Warren Commission), she saw two men fleeing the scene of the shooting, neither of which fit Oswald's description.
Cliché, but surprisingly appropriate.
At this point, Kilgallen was on a mission to get to the bottom of the inconsistencies in the official JFK assassination story, but the desire to profit from it may have been her downfall. She reportedly told some friends of hers that she was "about to blow the JFK case sky high." She hadn't released her findings, however, because according to Ron Pataky (a film critic with whom she was having an affair), Kilgallen was planning to compile all of her findings into a book about the JFK assassination...which surely would have been a big hit for Random House publishing, who at the time had Kilgallen under contract.
But she also just might have been gathering more information to make sure her case (whatever it was going to end up being) was completely solid. She reportedly told her long time make-up man from 'What's My Line', Carmen Gebbia, that she was traveling to New Orleans to meet with a source...and that she would break the real JFK assassination case "if it's the last thing I do."
She never got the chance.
Threats, Death, and Lots of Questions
According to many of people that were around Kilgallen during her final days, she seemed incredibly paranoid and spooked. She also confided in her hairdresser, Marc Sinclaire, that her life had been directly threatened due to her recent work.
On November 8, 1965, Dorothy Kilgallen was found dead in her home, just 12 hours after taping her appearance on 'What's My Line.' The medical examiner determined that she had succumbed to a fatal combination of alcohol and barbiturates. It was eventually ruled as being accidental.
Right off the bat, however, things started smelling funny when the examiner typed "circumstances undetermined" on her death certificate. When interviewed in 1995, the medical examiner whose signature appears on the certificate had no recollection of ever signing it...or how he could have ever signed it at all since he wasn't stationed where Kilgallen had died.
Another very peculiar detail was that according to Sinclair, Kilgallen never slept in the bedroom in which she was found. She was also fully dressed and still in full hair/make-up from taping the show. People that talked with her that evening, including a Western Union rep at 2:00 AM (who she asked to pick up and deliver her latest column to the Journal-American) said she seemed perfectly fine.
Legacy of Silence
According to Lee Israel, who wrote Dorothy Kilgallen' biography, television producer Bob Bach visited with Richard Kollmar (Kilgallen's husband) hours after her funeral. When Bach asked about his late wife's interest in the JFK assassination, Kollmar responded:
"Robert, I'm afraid that will have to go to the grave with me."
Author Mark Lane claims that when he asked Kollmar about her death and its possible ties to her work, he angrily responded that her investigation had "done enough damage already" and that "too many people have suffered as a result." Kollamar died five years later of an apparent suicide.
Killgallen's son, Dickie, claims to have been contacted in 1975 by the FBI, who were searching for his mother's notes on her investigation (which to this day have still not been found).
To date, no other family members or colleagues have come forward with any knowledge about President Kennedy's assassination that has not already been disclosed or declassified.
So...what happened?
Besides the tangled web of characters and a seemingly rational cause of death, there is quite a bit of evidence that suggests Dorothy Kilgallen was murdered. You would think, however, that she would have had some sort of fail safe in the event case she was killed for what she knew...especially since she believed that her life (and subsequently, her story) was in danger.
Enter RamblingBeachCat.com's own crackpot conspiracy theory (please humor us): Dorothy Kilgallen was found dead in the city of New York on November 8, 1965. The very next day, the Northeast Blackout cut power throughout the evening to a large portion of Canada and the northeastern United States...including New York City.
Yes, I know that was part of the plot to an episode
of Dark Skies, but I'm not blaming her death on aliens.
While a lot of conspiracy buffs blamed UFOs for the loss of power (because aliens are jerks, I guess), wouldn't it make more sense for the government (if they were, in fact, responsible for Kilgallen's death) to basically shut down any chance of a "show this to everyone if I'm killed" broadcast occurring?
Also, according to multiple eye witnesses, Kilgallen was seen in a serious/private discussion with an unidentified man until the wee hours of the morning that she died. Maybe she was giving him the scoop (in case she didn't live to see the next day) and the government got to him first...hence why the mystery man has never been identified...
...or maybe she was just cheating on her husband and her boyfriend with another guy. Kigallen had made enough enemies in her lifetime that if she was actually murdered, it may not have been related to the JFK assassination at all. But whatever the case, the death of Dorothy Kilgallen looks very suspicious to even the most ardent of conspiracy skeptics.
And whether it really was an accidental overdose, a suicide, or a conspiracy related murder, the world lost a damn good reporter far too soon.
Dorothy Kilgallen
H/T to DjangoStonereaver of Fark.com for pointing out that Jack Ruby died many months (more like a few years) after meeting with Kilgallen, not "a few months" as I had previously written. My blog sucks, but at least it sucks a little less now :b


text:
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text:
The Danger of Flirtations with First Amendment Violations
by Christina Coleburn | Nov 18, 2021 | Amicus, Courts & Judicial Interpretation, Education & Youth, Establishment Clause, Free Exercise, Freedom of Expression, Legal History, Voting and Elections Rights | 0 comments
Photo Credit: Zimmytws/iStock, via Getty Images Plus
Respect for the Constitution used to be a basic qualification for elected officials. These days, some voters are giddy about campaign promises that would blatantly defy it. More troublingly, some politicians and candidates are ready and willing to give those people want they want — provided that they deliver them electoral gains. Ohio Senate hopeful Josh Mandel is one such person. In October, Mandel courted voters with his insistence that "there's no such thing as separation of church and state" and the prospect of "instilling faith in the classroom, in the workplace, and everywhere in society." While Mandel may calculate that these brazenly unconstitutional ideas are good for his political ambitions, there is no doubt that they are disastrous for the rule of law.
The First Amendment is clear: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." The Constitution puts the government under a crucial constraint. Government officials can neither sponsor religion nor wield state-sponsored control over people's right to practice it. The Establishment Clause is vital to prevent the government from persecuting religious minorities, privileging the faith of some at the expense of the faith of others, and forcing people to conform to the beliefs of the officials that govern them. It is a check against abuses of power that could infringe on the civil liberties of both the faithful and the secular. In totality, the First Amendment grants five core freedoms: speech, religion, petition for redress, press, and assembly. Mandel's stated desire to take a hatchet to the First Amendment plays a dangerous game, especially for someone whose dream job involves carrying out constitutional responsibilities in the job description.
The strategy to gain political capital by appealing to the extreme is not exclusive to Mandel. It has infected politics across the country and carries chilling consequences for Americans' First Amendment rights. The University of Florida, a public school, recently sought to stop its own faculty from testifying on behalf of plaintiffs who were suing the state of Florida over an election law that Governor Ron DeSantis enthusiastically supported. Professor Daniel Smith, a political science expert and nearly 20-year faculty member who was barred from testifying, had previously offered expert testimony and advice about voting rights to Congress, state legislatures, and outside groups. The University of Florida previously praised those activities for providing opportunities for students. Despite past approval, school officials argued that the faculty members' testimony would present "a conflict of interest to the executive branch," and said that because "UF is a state actor, litigation against the state is adverse to UF's interests." A DeSantis spokesperson denied involvement but echoed the university's minimization of the free speech claim because the faculty would be paid for their expert testimony. Compensation for expert testimony is common and would not affect free speech concerns as participation is voluntary. After an uproar, the University of Florida reversed its course.
It is extremely unusual for a public school to forbid academics at public institutions from giving legal testimony. Public schools like the University of Florida are government actors, which are constrained by the First Amendment. The American Association of University Professors, which advocates for academic freedom at colleges, decried the "University of Florida's politically motivated violation of academic freedom" as "undermin[ing] the common good." The Alliance for Academic Freedom, which promotes freedom of speech across the ideological spectrum, offered legal precedents in condemning "the major violation of well-established principles of freedom of speech." Among them is Connick v. Myers (1983), which held that "a public employee does not relinquish First Amendment rights to comment on matters of public interest by virtue of government employment." According to Rankin v. McPherson (1987), "vigilance is necessary to ensure that public employers do not use authority over employees to silence discourse." Garcetti v. Ceballos (2006) also limited when a state entity can impose on employees' speech. The case held that government workers "must face only those speech restrictions that are necessary for their employers to operate efficiently and effectively" when the "employees are speaking as citizens about matters of public concern." Government disagreement with a government employee's private speech is not a constitutionally valid rationale.
Similar First Amendment issues have emerged as controversies over critical race theory engulf school boards. Critical race theory is an academic perspective that interrogates how race has affected social, legal, and institutional structures. Sometimes discussed in law and graduate programs, critical race theory took center stage in the recent Virginia gubernatorial election. Several politicians marketed critical race theory as an indoctrinating staple of K-12 curriculums that teachers force-fed to young children. While many opponents of critical race theory have struggled to define the meaning of the term, others have attempted to define it with an inaccurately broad scope.
Critical race theory is a subgroup of critical legal theory, which holds that the law is necessarily intertwined with inherent social biases to support the interests of people who created the legal system. "The essential claim of CLS is that all law is politics," explained a Touro Law Review piece. "Since there can be no objective way of developing a universal system of jurisprudence, all jurisprudence is, therefore, indeterminate and subjective." Critical race theory critiques constitutional structure and legal ideology. It holds that the First Amendment cannot be neutrally interpreted or objectively applied, that some groups are categorically deprived of legal protection, and that racially oppressive views are codified in America's founding documents. These concepts are difficult for many college students to grasp, never mind children ages five to 17.
Conversations about how race affects institutions in themselves do not amount to critical race theory. On the contrary, many discussions center around ideas that challenge critical race theory's principles. One such stance is that the First Amendment is a valuable tool in fighting bigotry because it protects protest, establishes legal claims for redress, and permits criticism of unjust government actions. Another is that the rule of law is not just a ruse to protect the powerful, but a legitimate principle for constitutional accountability. The belief that the founding documents are aspirational in the pursuit of a "more perfect [u]nion," even when the legal system falls short, also challenges critical race theory. Given these developments, multiple critical race theory bans were proposed by local school boards that have legal problems similar to the ones in the Florida controversy.
In Tinker v. Des Moines Independent Community School District (1969), the Supreme Court held that public students do not "shed" their First Amendment rights "at the schoolhouse gate[,]" notably when student speech does not infringe on other people's rights or create substantial disruptions. Enforcement of a critical race theory ban could infringe on constitutionally protected expression. When the definition of critical race theory is extensive in scope, it could stifle important conversations about tolerance, racism, discrimination, and respect for cultural differences. Public school teachers tasked with educating students also do not forfeit all of their First Amendment protections in the scope of their employment. While teachers' freedom of expression is restricted at the K-12 level, they still have some protections for speech about issues of public concern. In Pickering v. Board of Education (1968), Justice Thurgood Marshall noted that "the interest of the school administration in limiting teachers' opportunities to contribute to public debate is not significantly greater than its interest in limiting a similar contribution by any member of the general public."
Calls to ban Toni Morrison's book Beloved also raise censorship concerns. While the Supreme Court held in Board of Education, Island Trees Union Free School District v. Pico (1982) that public schools can bar books from school library shelves that are "pervasively vulgar" or unsuitable for a curriculum, they cannot remove books from those shelves "simply because they dislike the ideas contained in those books." Beloved details the life of a former slave, who feared her children would be captured. Terrified that her child would be subjected to the horrors of slavery, the protagonist tragically kills her own daughter in the belief that death was preferable to enslavement. "Beloved, she my daughter," Morrison wrote in a haunting passage. "She mine… She come back to me of her own free will and I don't have to explain a thing. I didn't have time to explain before because it had to be done quick. Quick. She had to be safe and I put her where she would be." While Beloved is an emotionally jarring novel and does contain sexual content, the case that a ban was proposed to quell discussion is strong. Although passages about sex may be uncomfortable, the true power to disturb comes from its raw depictions of slavery, brutality, and death. While one could try to claim that Beloved should not be taught in a curriculum because it has sexual material, it can also be persuasively argued that the intellectual gain to older students from teaching it outweighs that concern.
These are only some of the recent examples of how politicians and lawmakers have threatened their constituents' First Amendment rights. Mandel's candidacy opens the door for more infringements. The excuses for Mandel's comments — from dismissing his words as hyperbolic or arguing that he would never actually pass policies that would violate the First Amendment – give cover for inexcusable conduct. Citizens should never tolerate candidates who openly, and proudly in Mandel's case, call for trampling constitutional rights.
In another disturbing turn of events, a candidate running against Mandel used his religion against him. His opponent released an anti-Semitic advertisement in which a voice actor asked, "Are we seriously supposed to believe the most Christian-values Senate candidate is Jewish? I am so sick of these phony caricatures." Another voice in the advertisement adds, "I agree… We keep electing people like this, we'll just keep getting the same terrible results." This smear campaign demonstrates why the First Amendment is so precious and the frightening irony of Mandel's comments. If Mandel's opponent were to prevail, he might implement menacing policies given his evident animosity toward religious minorities. The Constitution was meant to prevent Americans from abdicating their liberties to a zealous government. Voters who turn their cheeks at blatantly unconstitutional pitches like Mandel's make a mockery of this protection, which is a privilege that people who suffer under oppressive regimes in other nations could only dream of having. Fidelity to the Constitution should not be optional for lawmakers, current and aspiring. It is the bare minimum credential for public service. Those who flirt with constitutional violations are unfit.
Christina Coleburn is a J.D. candidate at Harvard Law School.


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text:
Q: replace method in delegate string i have got a little problem i received some data and show it in textbox to invoke it i used
if (textBox1.InvokeRequired)
{
    // this is worker thread
    updatetextBoxDelegate del = new updatetextBoxDelegate(updatetextBox);
    textBox1.Invoke(del, new object[] { data });
}

my data is like
name:sam
age:10
now i want to split it and save these values in array or show in sperate textboxes
i used replace method like
string str = textBox1.text;
str.Replace("name","");

and so on but the problem is replace method is not working on it it doses not replace any thing
tell me what i am doing wrong

A: If you look here: http://msdn.microsoft.com/en-us/library/fk49wtc1.aspx, you'll see the Replace method returns a string you have to "catch" it, so replace:
str.replace("name","");

with
str = str.Replace("name", "");

redpajama_set_name: RedPajamaStackExchange


text:
namespace System.Xml.Schema
{
    using System.Text;
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    using System.Diagnostics;
    using System.Xml.XPath;
    using MS.Internal.Xml.XPath;

    internal class CompiledIdentityConstraint
    {
        internal XmlQualifiedName name = XmlQualifiedName.Empty;
        private readonly ConstraintRole _role;
        private readonly Asttree _selector;
        private readonly Asttree[] _fields;
        internal XmlQualifiedName refer = XmlQualifiedName.Empty;

        public enum ConstraintRole
        {
            Unique,
            Key,
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        public ConstraintRole Role
        {
            get { return _role; }
        }

        public Asttree Selector
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            get { return _selector; }
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        public Asttree[] Fields
        {
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        public static readonly CompiledIdentityConstraint Empty = new CompiledIdentityConstraint();

        private CompiledIdentityConstraint() { }

        public CompiledIdentityConstraint(XmlSchemaIdentityConstraint constraint, XmlNamespaceManager nsmgr)
        {
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            try
            {
                _selector = new Asttree(constraint.Selector.XPath, false, nsmgr);
            }
            catch (XmlSchemaException e)
            {
                e.SetSource(constraint.Selector);
                throw;
            }
            XmlSchemaObjectCollection fields = constraint.Fields;
            Debug.Assert(fields.Count > 0);
            _fields = new Asttree[fields.Count];
            for (int idxField = 0; idxField < fields.Count; idxField++)
            {
                try
                {
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                }
                catch (XmlSchemaException e)
                {
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                _role = ConstraintRole.Unique;
            }
            else if (constraint is XmlSchemaKey)
            {
                _role = ConstraintRole.Key;
            }
            else
            {             // XmlSchemaKeyref
                _role = ConstraintRole.Keyref;
                this.refer = ((XmlSchemaKeyref)constraint).Refer;
            }
        }
    }
}


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text:
Ronda Rousey Says Cris Cyborg Should Be Charged with Attempted Homicide
Ken Pishna
If UFC women's bantamweight champion Ronda Rousey had her way, not only would she never fight Cris "Cyborg" Justino, but the current Invicta FC featherweight champion would also be in jail.
"That girl, in my eyes, should be charged with attempted negligent homicide," Rousey said during Monday's edition of The MMA Hour.
Cyborg has been penalized in the past for using performance-enhancing drugs. After her 16-second knockout of Hiroko Yamanaka, she tested positive for stanozolol, the same anabolic steroid that Olympic sprinter Ben Johnson tested positive for after winning the 100-meter finals in the 1988 Seoul Olympics.
Cyborg was fined $2,500 and had her license suspended for one year.
Though he tried, Johnson never recovered from the failed drug test. Cyborg has continued her career, competing in submission grappling, kickboxing, and mixed martial arts, including capturing the Invicta championship.
"If you are caught with a PED in the Olympics, you are out from the next Olympics and you can't even compete until after that," Rousey commented before her fight with Alexis Davis at UFC 175 in July. "So that's up to an eight-year ban. I think eight years is pretty good.
"I think the reason why (fighters) keep trying to test that border is that there is not really that much punishment afterward. You have to pay a little fine and take a year off? People take a year off and go on vacation all the time. I really do think there should be much more strict enforcement of the rules, possibly career-ending things like that because if people think they might get away with it, they're going to try."
And that's her stance with Cyborg, as well. Rousey says it is not that she's afraid to fight Cyborg, she just fees that her past miscues should have resulted in a much harsher penalty.
"Coming into the cage with performance-enhancing drugs is the equivalent of walking in there with a weapon," Rousey said on The MMA Hour, indicating performance-enhancing drug use could eventually lead to the downfall of the sport.
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Rousey will fight whomever the UFC puts in front of her, but she feels that Cyborg's past transgressions discount her calls for a fight for the UFC championship.
"Do I think that having a big PPV card is worth having that sort of thing for the sport that I've worked so hard to develop? No, I don't think it's worth it," said Rousey. "(But) if you put her in front of me, I'll put her out. But do I think she deserves to be there? No."
Cyborg had intended to make her bantamweight debut and begin her chase of Rousey in December, but a recent injury derailed that plan. So PEDs or not, Cyborg won't be challenging Rousey any time soon, no matter what the champion thinks of her.
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