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The Sylva Gelber Music Foundation
Supporting talented young Canadians embarking on professional music performance careers.
Important deadlines for the 2020 competition!
The timetable for 2020 is:
Call for nominations: December 2019 / January 2020
Nominations due: 07 February 2020
Deadline for applications and supporting materials: 20 March 2020
Pre-selection: March/April 2020
Auditions: 25–27 May 2020 in Ottawa
2019 Award Winners Announced!
The Sylva Gelber Music Foundation held its twelfth annual competition in 2019. As in previous years, we discovered an extraordinary array of Canadian talent in classical music performance displayed by those young musicians who passed to the live audition phase of our awards process. We were extremely grateful for the assistance of our stellar jury, this year made up of Lawrence Ewashko from the University of Ottawa and the Ewashko Singers; David Gillham from UBC, a member of the Archytas Ensemble and the Ridge Piano Trio; Stéphane Lemelin, Chair of the Department of Performance and Professor of Piano at the Schulich School of Music in Montreal; and Nora Shulman, former Principal Flute with the Toronto Symphony and teacher at the University of Toronto and the Glenn Gould School of the Royal Conservatory of Music.
Over three action-packed days at the University of Ottawa's School of Music, which generously provides the Foundation with rehearsal and performance space, we had an opportunity to hear young musicians from every region of the country. Several are engaged in advanced studies at prestigious music schools in Canada, the US, England and Europe, or are working with master teachers, performers and conductors. Some were simply in need of assistance to continue regular lessons or support themselves in extremely expensive European capitals while they make the transition to a full-time professional career. Many award winners are combining their studies with participation in prestigious international competitions; our best wishes go out to them as they prepare to measure themselves against top young artists from around the world!
From among a group of highly talented candidates, the jury recommended awards to 10 young artists, in amounts ranging from $5,000 to $30,000, for a total disbursement this year of approximately $165,000. The Board of Directors of the Foundation is delighted to announce the following winners of the 2018 Sylva Gelber Music Foundation Awards:
Kevin Ahfat, pianist, Toronto
As a pianist that "leaves no question about his riveting presentation and technical finesse" (Seattle Times), Canadian pianist Kevin Ahfat is "poised to become one of the young heirs of the classical piano realm, with a bold, boundary-pushing, millennial style matched by refined execution" (Vanguard Seattle), "summoning plenty of thunderpower in the big moments, but clearly valuing musicianship over mere showmanship" (American Record Guide).
In 2018, Kevin was named one of CBC's 30 hot Canadian classical musicians under 30; he subsequently released a live recording of Brahms from CBC's Studio 211. That same year, Kevin was thrilled to perform the North American premiere of the recently published Third Sonata for Cello & Piano, by Camille Saint-Saëns. In anticipation, he filmed and produced a minidocumentary entitled Soirée pour Camille, a short film documenting the historical context of the work, his artistic partnership with cellist Juliette Herlin, and their exploration of French music. Continuing his dynamic exploration of music and film, he recently partnered with Riddle Films to release a cinematic performance of Mussorgsky's Pictures at an Exhibition, filmed live at Toronto's Koerner Hall.
Highlights of recent seasons include returns to the Seattle Symphony for its first ever Shostakovich Concerto Festival and to the Dame Myra Hess Series in Chicago, and the inaugural masterclass and recital for the Las Vegas Masterclass Series. Ahfat has had the privilege of sharing the stage with renowned artists across many genres, including Jean-Yves Thibaudet, So Percussion, David Finckel, Joshua Roman, and Joaquin Valdepeñas. He enjoyed a new partnership with choreographer Richard Alston and Juilliard Dance in their recreation of Alston's Sheer Bravado (2006). He has also appeared with the ARC Ensemble, Amici Chamber Ensemble, and Art of Time Ensemble throughout North America.
Kevin Ahfat completed principal studies at the Juilliard School in New York under Joseph Kalichstein and Stephen Hough and spent the past year as a Rebanks Fellow at the Royal Conservatory in Toronto. In the coming year, he will use his Sylva Gelber Music Foundation Award to pursue studies with various eminent teachers, prepare for important international competitions, and deepen his skills in film and other visual media as a pathway to enhancing enjoyment and understanding of classical music.
Joel Allison, bass-baritone, Toronto
Canadian Bass-Baritone Joel Allison has been praised for his "beautiful, rich, ringing tone." (Ludwig von Toronto) He has performed in Canada and Europe with the Canadian Opera Company, Saskatoon Opera, Saskatoon Symphony, Tafelmusik Baroque Orchestra and Chamber Choir, the Tilford Bach Festival, and the Newfoundland Symphony.
In the 2019-20 season, Joel is performing the roles of The Mandarin in Turandot and Fiorello in Il Barbiere di Siviglia with the Canadian Opera Company in the Studio Ensemble; he is also giving his debut performance with Symphony Nova Scotia. Last season he debuted with the COC in their Studio Ensemble in the roles of Zaretsky in Eugene Onegin, Superior Senator in the world premiere of Rufus Wainwright's Hadrian, and Schaunard in La Bohème. He also appeared for the first time with the Newfoundland Symphony in the Messiah.
Performance from the University of Toronto. He was the recipient of the 2016/17 Richard Bradshaw Fellowship in Opera, the Norcop Prize in Art Song, and the 2018 Tecumseh Sherman Rogers Graduating Award at the University of Toronto. Joel is an alumnus of the Ontario Youth Choir, Tafelmusik Baroque Summer Institute, and the Toronto Summer Music Festival Art Song Fellowship.
In competitions Joel has won Second Prize at the Christina and Louis Quillico Awards, Second Prize at The Great Lakes regional finals of the Metropolitan Opera National Council Auditions, Second Prize at the COC Centre Stage Competition, and Second Prize at the Brian Law Opera Competition. His Gelber Award has enabled him to participate in the Salzburg Festival Young Singers Project the past summer and will facilitate networking and auditions in Europe, as well as regular lessons back in Toronto.
Joel holds a BMus. in vocal performance from the University of Ottawa and a Master's in Opera
Suren Barry, pianist, Montreal
Suren Barry is well known to audiences across Canada, and his concertizing has brought him overseas as well. He has given numerous solo recitals at La Chapelle Historique du Bon Pasteur in Montreal and has also been invited to perform at the Canadian Opera Company in Toronto, at the George Eastman House in Rochester, NY, at the "Im Hayastan" Festival in Yerevan, Armenia, and at the Ottawa International Chamber Music Festival.
An avid chamber musician, Suren regularly performs in various ensembles at the Ottawa International Chamber Music Festival and at the Festival Pontiac Enchanté. Recently, Suren has been performing with the McGill Percussion Ensemble, whose schedule included a concert at the McCormick Marimba Festival (Tampa, FL).
Suren holds a BMus degree from Carleton University and a Master's in Piano Performance and Literature from the Eastman School of Music; he is currently pursuing his doctorate at the Schulich School of Music in Montreal. He recently received a prestigious Doctoral Fellowship from the Social Sciences and Humanities Research Council (SSHRC) for his research on keyboard improvisation in the 18th century. This project focuses on helping pianists reclaim the rich tradition of improvised classical music. His 2019 Gelber Award will enable him to continue with lessons in Montreal, participate in competitions, and pursue his interest in classical music improvisation through his own performance and in collaboration with esteemed improvisers in the UK and the USA.
Arian Brisson, flûtiste, Montréal
Photo: Annie Éthier
Grand prize winner of the Orchestre symphonique de Trois Rivières' 28th competition and of the 2013 Prix d'Europe, Ariane Brisson has distinguished herself in multiple forums: at the 6th edition of the International Flute Competition in Krakov, at her final public examination at the Montreal Conservatory of Music (Great Distinction), and at the University of Montreal, where she earned her Master's degree (Mention exceptionnelle).
Ariane studied under Mathieu Dufour at DePaul University in Chicago in 2013-14. More recently, her personal reflexions on musical interpretation prompted her to undertake doctoral studies at the University of Montreal.
An accomplished soloist, Ariane is also called upon to perform concertos and other masterworks of the flute repertoire with Les Violons du Roy, the orchestra of the Conservatoire de musique de Montréal and the Orchestre symphonique de Trois-Rivières. A passionate chamber musician, Ariana founded the duo Palladium with pianist Olivier Hébert-Bouchard in 2015; the duo was selected by Jeunesses musicales du Canada to perform in the context of their "Concerts Relève" series in 2017-18.
Drawn by the fluidity and sensitivity of her playing and the richness of her tone, the musicians of Pentaèdre invited Ariana to join their ensemble in 2016.
This year's Gelber Foundation Award is Ariana's second. It will enable her to undertake periods of study in Europe with her mentors, flutists Mathieu Dufour and Philippe Bernold.
Brian Cheng, cellist, Ottawa
© Harald Hoffmann
Laureate of the VI International Paulo Cello Competition, 21-year-old Bryan Cheng is acclaimed worldwide for his "absolutely astonishing" (La Presse, Montréal) command of the cello, "dreamy beauty" (Süddeutsche Zeitung), and "abundant facility, innate musicality, and sense of joy" (New York Concert Review). He made his solo debut at age 10 with the Orchestre de chambre I Musici de Montréal, his Carnegie Hall recital debut at 14, and his Elbphilharmonie solo debut in 2018 with the Deutsche Kammerphilharmonie Bremen and conductor Joshua Weilerstein.
Solo highlights of recent and upcoming seasons include appearances with Finland's Helsinki Philharmonic Orchestra, Lahti Symphony Orchestra, and Tapiola Sinfonietta; Germany's Schleswig-Holsteinisches Sinfonieorchester and Südwestdeutsches Kammerorchester Pforzheim; New York's Adelphi Orchestra; Missouri's Springfield Symphony Orchestra, Canada's National Arts Centre Orchestra, Niagara and Okanagan Symphony Orchestras, and Symphony Nova Scotia, under the baton of such esteemed conductors as Susanna Mälkki, Peter Oundjian, David Geringas, and Jonathan Darlington.
As cellist of the ChengÇ Duo, Bryan has released a trilogy of critically acclaimed albums on the German label audite: Russian Legends (2019), Violonchelo del fuego (2018), and Violoncelle français (2016). He currently studies at the Universität der Künste Berlin with Jens Peter Maintz, and plays on the ca. 1696 Bonjour Stradivari cello with the ca. 1830 Shaw Adam bow, generously on loan from the Canada Council for the Arts Musical Instrument Bank, as First Laureate of their 2018 Competition. Bryan will use his second Gelber Foundation Award to continue a customized program of intensive study, including mentorship from master cellists and conductors; he will also participate in numerous prestigious international competitions, and develop new repertoire for performance.
Kady Evanyshyn
Born in Winnipeg, Kady Evanyshyn joined the International Opera Studio at the Hamburg Staatsoper in September 2019. A competitor in this year's Wigmore Hall/Independent Opera International Song Competition, Ms. Evanyshyn is positioning herself at the crossroads of classical opera and contemporary vocal music. She recently premiered Stefano Gervasoni's Drei Grabschriften for mezzo-soprano and piano and performed Berio's Folk Songs with Jeffrey Milarsky in Alice Tully Hall. Upcoming performances include Claire in Cold Mountain (West Coast premiere), Glascha in Katja Kabanova (German debut), and J.S. Bach's cantata Ich habe genug, conducted by Simone Dinnerstein. Ms. Evanyshyn has received awards from the Gerda Lissner Lieder/Song Competition and the Winnipeg Music Festival.
Past roles include Second Woman in Dido and Aeneas (New York, London, Versailles), Frau Reich in Die Lustigen Weiber von Windsor (Juilliard), and Annio in La clemenza di Tito (Aspen). Kady is an alumnus of the Aspen Music Festival, Music Academy of the West, and Houston Grand Opera's Young Artist Vocal Academy. She earned her Bachelor's and Master's degrees at The Juilliard School, studying with Edith Wiens. She is supported by the Novick Career Advancement Grant in addition to her Sylva Gelber Music Foundation Award, which she will use to assist with travel, vocal lessons and German language training, and other costs that help to build her musical career during her stay in Germany.
Maïthéna Girault
Maïthéna is a first-prize winner of the Canadian Music Competition and winner of the 2017 Golden Violin Award, Canada's largest collegiate music prize. She was the winner in the strings category and of the Québécor Prize at the 2019 Prix d'Europe competition. In 2015, she made her debut in Carnegie Hall as a soloist and chamber musician. A passionate chamber musician,
Maïthéna was a founding member of the Milton String Quartet, Grand Prize winner at the 2017 Fischoff National Chamber Music Competition.
Maïthéna entered the Conservatoire de musique de Montréal at age eight, where she studied with Helmut Lipsky for ten years. She went on to graduate with a Licentiate in Music and a Graduate Diploma of Performance from McGill University, where her primary teachers included Andrew Wan, Alexander Read and Axel Strauss. Maïthéna performs on the 1858 Ex. "Comte Koucheliov" violin by Jean-Baptiste Vuillaume with a bow by François Lotte, both generously loaned to her by Canimex. This is her second Sylva Gelber Music Foundation Award; she plans to use it to continue her studies at the Manhattan School of Music with Lucie Robert and to pursue her involvement in chamber music.
Now 22, pianist Xiaoyu Liu was born in Paris and raised in Montreal. One of the most dynamic and technically gifted pianists of his generation, he is heralded for musical interpretations that are "powerful, polished and emanate from a disciplined spirit" (The Telegram).
His playing has taken him around the world, and he has given recitals in Canada, China, the USA, Japan, France, Italy, Ukraine, Salvador, Poland, Israel, and Switzerland. As a soloist, he has performed with major orchestras such as the Cleveland Orchestra, Israel Philharmonic Orchestra, Montréal Symphony Orchestra, Sendai Philharmonic Orchestra, National Symphony Orchestra of Ukraine, Israel Camerata Jerusalem, Lviv Philharmonic Orchestra, YOA Orchestra of the Americas, among others.
In 2014, he took part in a North-America tour with the China NCPA Orchestra, performing Ravel's G major Concerto, and also appeared with them at the China National Centre for the Performing Arts in Beijing. (National Post) described his interpretation "a subtle range of French colour and feeling ". In 2018, he will be touring with the National Symphony Orchestra of Ukraine in China (Beijing Concert Hall, Shanghai Oriental Art Center, Changsha, and Fuzhou).
Winner of the Prix d'Europe and the Grand Prize at the OSM Competition, Xiaoyu has also won prizes and recognition in various prestigious international competitions, including the Sendai International Piano Competition, the Montreal International Music Competition, the Visue, the Grand Prix Animato in Paris, the Interlaken Classics in Bern, and the Arthur Rubinstein International Piano Master Competition in Tel-Aviv. He has made numerous studio recordings with ICI Radio-Canada featuring works by Bach, Beethoven, Chopin, Ravel, and Satie. This is his second consecutive Gelber Foundation Award; it will assist him in pursuing his studies in Montreal and facilitate his participation in various international competitions.
Xiaoyu received the Prize with Great Distinction from the Conservatoire de musique de Montréal under Richard Raymond and he is continuing his studies with renowned pianist Dang Thai Son at the University of Montreal.
Josh Lovell
Canadian Tenor Josh Lovell is in his first season in the ensemble of the Wiener Staatsoper, performing Lysander in a new production of Britten's A Midsummer Night's Dream, Lurcanio in Ariodante, Don Ramiro in La Cenerentolaand finally, Ernesto in Don Pasquale. Other engagements include Don Ramiro with The New Generation Festival in Florence, Gonsalve in L'Heure Espagnol with Wolf Trap Opera, Poisson in Adriana Lecouvreur as part of the Salzburger Festspiele's Young Singer's Project, Mozart's Requiem with the Vancouver Symphony, and Handel's Messiah with the Victoria Symphony.
Josh was a member of Lyric Opera of Chicago's Patrick G. and Shirley W. Ryan Opera Center, and participated in San Francisco Opera's Merola Opera Program.
Josh is the 2018 Grand Prize and Opera Prize winner of the 52nd Annual International Vocal Competition 's-Hertogenbosch in The Netherlands, the 2nd place winner of the 2018 Dallas Opera Competition, and the 3rd place winner of the Marcello Giordani Foundation competition; in 2017 he was a semi-finalist with the Metropolitan Opera National Council Auditions. From Victoria, British Columbia, he was a student of Benjamin Butterfield at the University of Victoria and graduated from the University of Michigan, where he studied with Stanford Olsen. He currently studies with Julia Faulkner.
Ema Nikolovska
Photo: Kaupo Kikkas
Born in Macedonia and raised in Toronto, Ema earned a coveted place in the Opera Course at The Guildhall School of Music and Drama, where she previously completed a Masters. Her principal teachers include Rudolf Piernay, Susan McCulloch and Helga Tucker. She has an undergraduate degree in violin from The Glenn Gould School, where she studied with Paul Kantor and Barry Shiffman.
Ema is a BBC New Generation Artist and a Young Classical Artist Trust (YCAT) Artist. Her prizes and awards include the Ferrier Loveday Song Prize, the Oxford Lieder Young Artist Platform award, the Guildhall Wigmore Prize, the Gerald Moore Award Singers' Prize, the Susan Longfield Prize, the First and Audience Prizes at the Maureen Lehane Vocal Awards, and Second Prize at the International Helmut Deutsch Lied Competition.
Ema has been part of the Art of Song Program in Toronto, the Britten-Pears Programme, the Music Academy of Villecroze, Les Azuriales, the Franz-Schubert-Institut, Thomas Hampson's Lied Akademie, and the Verbier Festival's Atelier Lyrique.
Recent highlights include a debut recital at Wigmore Hall, the Guildhall Gold Medal Final, and a Schubert Lieder recital with Malcolm Martineau at the Pierre Boulez Saal in Berlin. Upcoming engagements include the Creative Dialogue XI Symposium with Kaija Saariaho, a recital with Joseph Middleton in Glenarm, the role of Celia in Haydn's La fedeltà premiata and Sister Edgar in The Angel Esmeralda, and a premiere by Lliam Paterson (both Guildhall productions).
Ema is grateful to the Shipley Rudge Scholarship, London Syndicate and The Countess of Munster Musical Trust for their support. She will be applying her Gelber Award to the costs associated with living and studying in London.
The Sylva Gelber Music Foundation T: 613.747.4524 Email the Foundation: ed@sylvagelber.ca


By no longer questioning whether or not I "deserved" the same treatment as everyone else and simply asking for it, I gained self-confidence.
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Don't forget what you want or need.
We can't always get what we want in life, but we definitely won't get it if we don't ask.


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CEW Honors Qurate Retail Group at Beauty of Giving Event
December 23, 2019: Qurate Retail Group was recently recognized for our commitment to philanthropy and corporate giving at the Cosmetic Executive Women (CEW)'s Luncheon.
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redpajama_set_name: RedPajamaCommonCrawl


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Q: MYSQL select query including all if not specified In MYSQL, how would I create a select query to show all if the user has not entered anything.
For instance, I have an option where the user can enter a name, in a text box. However if no name is entered, it will return all results.
Example:
select * from names where name=$name
name is the variable the user enters.. however if the user does not enter name, it returns all records.
I have implemented this functionality before, I just cant remember how I did it.

A: You can use this,
select * from names where @parameter IS NULL OR name = @parameter

where @parameter is a variable

redpajama_set_name: RedPajamaStackExchange


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-May
News and Publications / News / News Releases / 2017 / May / Immigration Law Pro Bono Award
HARRISBURG (May 18, 2017) — The Pennsylvania Bar Association (PBA) Immigration Law Pro Bono Award will be presented to York-based Pennsylvania Immigration Resource Center (PIRC) on May 24 at the York Bar Association President's Breakfast.
The award, which is sponsored by the business immigration law firm of Green and Spiegel LLC, was created to annually recognize the pro bono accomplishments of an individual or organization working with the PBA in the area of immigration law. The award is given to individuals or organizations that have provided a unique service resulting in a significant provision of legal services to the neediest of foreign nationals on a pro bono basis or as part of legal aid outreach. The winners are selected in consultation with PBA leadership.
Founded in 1996, PIRC works to provide free access to justice for vulnerable immigrants in detention and in the community through legal services assistance, education and advocacy, protecting their rights to freedom and opportunity in the United States. PIRC does this through educating immigrants in detention and in the community about their legal options; direct representation and coordination of pro bono legal assistance and pro se assistance; and advocating for greater capacity and systems change through language access assistance, partnerships with law schools and universities, and legal training and education.
"In this time of great upheaval for the immigration community, PIRC provides hope to immigrants and their families facing grave challenges within our system," said Jonathan Grode, a partner at Green and Spiegel LLC, who will be presenting the award to PIRC.
"PIRC is honored to be the 2016 recipient of the Pennsylvania Bar Association Immigration Law Pro Bono Award," said Mary Studzinski, executive director of PIRC. "We are fortunate to work alongside many talented pro bono attorneys, volunteers and staff from other nonprofits, who bring their talent and passion to serving the most vulnerable immigrants among us. We are grateful that, in this time of increased need for our services, PIRC's work to ensure access to justice and due process for all persons is recognized."
Green and Spiegel has made a donation of $1,500 in honor of PIRC to the Pennsylvania Bar Foundation, the charitable affiliate of the PBA, to benefit the PBA Pro Bono Office.


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Home	Course Features	Welcome to Maple Chase Golf and Country Club
Course FeaturesFeatured News
Welcome to Maple Chase Golf and Country Club
by TG_Admin01 February 20, 2014
By MARC PRUITT
Say goodbye to Pine Brook Country Club in Winston-Salem as you might know it. No, the club that opened in 1954 isn't shutting its doors. It has a new ownership group that is making plenty of changes, most notably a new name – Maple Chase Golf and Country Club. Initially the ownership announced the name of Maple Plantation but a few weeks later it was changed to Maple Chase.
Longtime members Lynn and Lynette Matthews-Murphy purchased the club and want to do an overhaul to enhance the experience for current and future members. Plans include a complete renovation of the clubhouse, moving the golf pro shop, installing a new practice putting green, upgrading the pool area and expanding the practice area.
They will also be adding tees to several of the holes, but according to General Manager Mark Slawter, the course will largely be untouched.
"We are enlarging a couple of the greens right now, but other than that, we're not going to touch the golf course too much," Slawter said. "We have done some tree removal, but in large part, we think the golf course is pretty good as it is."
The course can play as long as 6,400 yards now, but the addition of the new tees can stretch that to 6,700. New back tees will be added to holes 1, 4, 6, 7, 8, 11, and 16. New front tees have been added on Nos. 1, 3, 6, 7, 8, 11 and 18. The first tee will be moved to accommodate the expansion of the driving range.
"We wanted to stretch the yardage out a little bit because it was a little too condensed," Slawter said. "This will also give us a chance down the road to attract some prestigious events on a regular basis. We're very excited about it."
A new 8,000-square foot practice putting green will be built between the 18th tee and the back patio of the clubhouse. They have also constructed a new stone wall behind the patio with an outdoor fireplace. And there will also be a new cart staging area.
The putting and chipping green will be expanded to make a short-game practice area that will stretch to as many as 70 yards with practice bunkers.
Slawter has also hired a new head pro, Sean Branagan, who began the first week of February.
"Sean's been a club pro for 15 years and brings a strong teaching background, and is an excellent fit for everything we're trying to do here," Slawter said. "He has been at Palisades Country Club and Carolina Lakes Country Club right outside Charlotte."
Changes to the interior of the club were described as "wholesale" by Slawter.
"Every room in the building is getting touched in some form," Slawter said. "The restaurant and bar area are getting a complete overhaul. The pro shop is moving to a brand new location in the center of the building, and the old pro shop space will ultimately become a fitness center. The administrative offices have moved downstairs, which will make it easier on us to interact with our members. And we're excited that Tim Grandinetti, who is one of the partners and executive chef at Spring House Restaurant, will be one of the restaurant's consultants and have input on the menu."
The swimming pool will also be getting some modifications, including new pool furniture and full food service. Slawter also said that he would like to resurrect the swimming team, which would be another potential draw for new members.
Slawter is the younger brother of Sutton Slawter, who is a partner with Lynn Murphy at Signature Real Estate, which is overseeing the project.
Slawter, who played golf for Reynolds High School and later became an All-American at N.C. State in 1994, had been running a college golf placement service in the area for the last four years when his brother afforded him the opportunity to jump on board his latest project.
"It was too good of an opportunity to pass up," Slawter said. ""I love Pine Brook — always have. When they called me about it and said we're going to renovate it and really make a push for membership, it was something that was very appealing to me. It was an easy decision because it's a tremendous opportunity. I played quite a bit here growing up, and the last few years, I've played with my brother in member/guests. The course has a lot of neat characteristics; older greens with a lot of slope in them. Plus, it doesn't take too long to get around out here."
Slawter said the biggest challenge to the timeline of completing the renovation has been the weather, but thinks things have gone about as smoothly as possible.
"I've never personally overseen a project like this, but my brother and Mr. Murphy have with all of their real estate projects, so it's not totally unfamiliar to them," Slawter said. "More than anything this winter, the weather has been our biggest challenge. Other than that, I think everything has gone pretty smooth. With everything we're doing – I mean, you might walk through here one day and get a face full of paint. And sure, everyday has been somewhat of an adventure, but all in all, I think everything's gone pretty smoothly. I know our members will benefit from the changes, and we will have plenty to offer everyone, whether they play golf or not."
Slawter said full-fledged marketing efforts are about to get under way now that the sale of the club is finalized, and they now can officially showcase the new name in all correspondence and advertising efforts.
"We're going to hit things really hard now that all the legal aspects have been squared away," Slawter said. "We're going to get out in the community and tell them about what we've got to offer. We want to reach out to the major industries right around the club. We have some of the best meeting spaces in the county, and we can accommodate 400 bodies in our clubhouse. We think we're well positioned to handle all their needs. We've seen a slight increase in members so far, and we've seen a tremendous amount of interest from the public wanting to join. We feel pretty good that we'll get a push this spring."
Slawter added that the club will still carry the "Pine Brook" name in some form.
"There is a lot of history here," Slawter said. "We might be changing the name, but Pine Brook will live on in some capacity. We'll find an appropriate way to honor the original name."
Maple Chase Golf and Country ClubMaple Plantation Golf and Country ClubMark SlawterPine Brook Country ClubWinston-Salem Golf
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Following the feature on BBC Look North re: Norwood Interiors, a local Kitchen, Bathroom and Bedroom company going into untimely voluntary liquidation, Regal Interiors would like to reassure all our customers that as a member of Which Trusted Traders all work undertaken by us is covered by a Home Improvement Protection Deposit and Work Guarantee Insurance Scheme.
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Fox Woodsum Lumber Co. v. Janes
Harris v. Harris
3. Likewise, a court of record has inherent power to dismiss a cross complaint for lack of diligence in its…
Welden v. Davis Auto Exchange
"Since section 581a is not applicable to the issuance, service and return of summons upon a cross-complaint,…
Full title:FOX WOODSUM LUMBER COMPANY (a Corporation), Respondent, v. OSMONDE W…
Court:Court of Appeal of California, Second District, Division One
Date published: Nov 8, 1946
Court of Appeal of California, Second District, Division One
Docket No. 15317.
APPEAL from an order of the Superior Court of Los Angeles County dismissing a cross-complaint. Ruben S. Schmidt, Judge. Reversed.
A.J. O'Connor and George J. Hider for Appellant.
No appearance for Respondent.
WHITE, J.
No brief having been filed in behalf of respondent, this cause was ordered submitted pursuant to the provisions of rule 17(b) of the Rules on Appeal, which rule further provides that in such cases the court may accept as true the statement of facts in the appellant's opening brief.
The following facts appear therein:
By this action filed May 16, 1945, plaintiff seeks to recover on a check in the amount of $4,300 which was executed and delivered by defendant Janes to defendant J.W. Dimmitt, the latter indorsing and delivering the document to plaintiff. Upon presentation thereof to the drawee bank it was dishonored because payment thereon had been stopped by the maker before presentation.
Defendant Dimmitt in his answer filed June 8, 1945, admitted the execution and delivery to him of said check and his subsequent indorsement, but denied any notice of dishonor.
Defendant and appellant Janes in his answer filed June 9, 1945, in addition to denying generally the allegations of the complaint, affirmatively pleaded (1) a conditional delivery of said check to the payee procured by his fraudulent representations, the payee's breach of said conditions and knowledge of all said facts by plaintiff-indorsee prior to indorsement; (2) want of consideration for said indorsement; (3) failure of consideration passing from payee to maker and a knowledge thereof by indorsee prior to indorsement; and (4) breach by indorsee of his agreement which was a consideration for the indorsement.
In addition to his answer, defendant Janes contemporaneously therewith, on June 9, 1945, filed a cross-complaint for damages against defendant Dimmitt and his copartners individually, and as copartners doing business under the name of Utility Products, wherein it was alleged that the cross-defendants conspired, with the full knowledge of the plaintiff Fox Woodsum Lumber Company, to procure a conditional delivery of said check from defendant Janes by making certain fraudulent representations in order to liquidate a debt due from the said copartnership to plaintiff lumber company, and that the latter took said check by indorsement with full knowledge and notice of said fraudulent representations and conditional delivery.
On June 14, 1945, plaintiff lumber company answered said cross-complaint, denying generally the allegations thereof, and set up by way of affirmative defense substantially the allegations contained in its complaint.
Copies of the summons and cross-complaint were placed in the hands of a professional process server named Fred Ullrich, to serve the same upon Charles H. Harter and John J. Willinger, two of the cross-defendants and members of the above-named copartnership, and a copy of said summons and cross-complaint were sent by mail to Mark Jones, Esq., attorney for defendant Dimmitt.
On July 25, 1945, plaintiff lumber company filed its memorandum setting the cause for trial on September 18, 1945, up to which time the process server had not as yet made service of summons and cross-complaint on the aforesaid two cross-defendants. When the cause was called to trial on September 18, it was permitted to go off calendar because the matter was not then at issue.
On October 12, 1945, plaintiff served upon defendant Janes notice of motion to dismiss said cross-complaint on the ground of want of prosecution, since said process server had not made service of process on the above-mentioned two cross-defendants. This motion came on for hearing on the 26th day of October, 1945, and was by the court granted. From such order defendant Janes prosecutes this appeal.
It is the contention of appellant that the court was without jurisdiction to dismiss the cross-complaint for want of prosecution on the basis of the facts here present, and that said dismissal was in contravention of the provisions of section 581a of the Code of Civil Procedure.
[1] Section 442 of the Code of Civil Procedure provides that whenever a party seeks affirmative relief by way of a cross-complaint, such pleading must be served upon the parties affected thereby, and if any of the parties so affected have not appeared in the action, a summons on the cross-complaint must be issued and served upon them in the same manner as upon the commencement of an original action. In the instant case, therefore, no summons was required as to plaintiff lumber company and defendant J.W. Dimmitt who had theretofore appeared in the action, but a summons was required to be issued and served upon cross-defendants Charles H. Harter and John J. Willinger, who had not theretofore appeared.
[2] Section 581a, relied upon by appellant, does not apply to the issuance, service and return of summons upon a cross-complaint because the section was enacted before the law required summons in such cases ( Seaman v. Superior Court of Marin County, 183 Cal. 47, 48 [ 190 P. 441]).
[3] Since section 581a is not applicable to the issuance, service and return of summons upon a cross-complaint, it manifestly follows that it is within the sound discretion of a trial court in the exercise of its inherent power, to dismiss a cross-complaint for want of prosecution. Therefore, appellant's contention that the trial court was without jurisdiction to dismiss is without merit.
The question presented is whether the trial court abused its discretion in making the order complained of. As heretofore noted, appellant filed his cross-complaint June 19, 1945; plaintiff's motion to dismiss the same was granted October 26, 1945. Some four months only elapsed between the date of filing and the date of dismissal of the cross-complaint.
At the hearing of the motion to dismiss, appellant's attorney presented his affidavit, from which it appears that, prior to the date of September 18, 1945, when the cause was called for trial and ordered off calendar, appellant's attorney had placed in the hands of a professional process server the cross-complaint and summons issued thereon for service upon the two cross-defendants who had not theretofore appeared in the action. Service of the cross-complaint was had upon plaintiff lumber company and defendant Dimmitt who had appeared in the action and plaintiff lumber company filed its answer to the same.
No definite or fixed rule can be laid down for the exercise of discretion in dismissing a cross-complaint for want of prosecution since such action is not regulated by statute, but the discretion to be exercised, under the circumstances of the particular case, is a legal discretion, to be exercised in conformity with the spirit of the law and in such a manner as to subserve and not to impede or defeat the ends of substantial justice.
[4] In the instant case, if we assume that in the affidavit accompanying the motion to dismiss, a prima facie case of lack of diligence was shown, we are impressed that appellant met the burden cast upon him to show circumstances excusing his claimed tardiness in pursuing the two cross-defendants. Four months does not appear to us to be an unseemly or unreasonable delay when appellant had placed the summons with a process server who, in conjunction with plaintiff's attorney, was, according to the latter's affidavit, diligently attempting to locate the two cross-defendants. "Each particular case presents its own peculiar features, and no ironclad rule can justly be devised applicable alike to all." ( First National Bank v. Nason, 115 Cal. 626 [47 P. 595].)
To us it appears that the delay was reasonably accounted for and excused, and that the order of the court did not tend to subserve the ends of substantial justice.
Persuaded as we are that the discretion of the court was improperly exercised, the order appealed from is reversed and the cause remanded.
York, P.J., and Doran, J., concurred.


text:
Q: Proving completeness of $\sigma$-algebra Let $\Omega$ be uncountably infinite, and  $\mathcal{A}=\sigma(\{\omega\}: \omega\in \Omega\setminus\{\omega_0\})$.
I'm supposed to give a characterisation of $\mathcal{A}$ and then prove that $(\Omega,\mathcal{A},\delta_{\omega_0})$ is complete.
My try
For the characterisation: $\mathcal{A}=\{A\subset \Omega\setminus\{\omega_0\}:A \text{ countable or } A^c \text{ countable}\}$
However, to prove completeness, i.e. $N=\{A\subset \Omega:\delta_{\omega_0}(A)=0 \}\subset \mathcal{A}$, since we also have $N=\{A:A\subset \Omega\setminus\{\omega_0\} \}$. This seems to contradict the text of the exercise...

A: I'm not sure your definition of completeness is correct.
You need to show that if

*

*$A \in \mathcal{A}$,

*$\delta_{\omega_0}(A) = 0$,

*$B \subseteq A$,

then $B \in \mathcal{A}$.
This is different than showing that any subset of $\Omega \setminus \{\omega_0\}$ is in $\mathcal{A}$ (in particular because $\Omega \setminus \{\omega_0\} \notin \mathcal{A}$).
Proving the above should be simple, given the [correct] characterization of $\mathcal{A}$; see below.

I should remark that your characterization of $\mathcal{A}$ is slightly incorrect. I think it should be
$$\{A : A \subseteq \Omega \setminus \{\omega_0\}, A \text{ countable}\} \cup \{A : A^c \subseteq \Omega \setminus \{\omega_0\}, A^c \text{ countable}\}$$
For justification, you need to show that this characterization

*

*is a $\sigma$-algebra, and

*any $\sigma$-algebra containing $\{\{\omega\} : \omega \in \Omega \setminus \{\omega_0\}\}$ also contains this characterization.

A: Note that this question concerns Exercise 1.3.2 from Probability Theory: A Comprehensive Course, 3rd edition, by Achim Klenke. This is a long, detailed, hopefully correct answer to the exercise in question.
Discussion
There is a perhaps natural, although totally misguided, desire to characterize $\mathcal{A}$ as $\left\{A \subset \Omega \setminus \{\omega_0\} \colon A \text{ is countable or } A^c \text{ is countable} \right\}$. Eventually you realize that this makes no sense because it cannot contain $\Omega$, so it cannot be a $\sigma$-algebra.
The connection with Exercise 1.1.4 is clearer if you define $\mathcal{B} := \{A \subset \Omega \colon A \text{ is countable}\}$, $\mathcal{C} := \{B^c \colon B \in \mathcal{B}\}$ and $\mathscr{A} := \left\{A \subset \Omega \colon A \text{ is countable or } A^c \text{ is countable} \right\}$ (the latter to reduce clutter, as in Exercise 1.1.4), and then show that
\begin{equation}
    \mathscr{A} = \mathcal{B} \cup \mathcal{C}
\end{equation}
Clearly $\mathscr{A} \supset \mathcal{B} \cup \mathcal{C}$, because we know that $\mathscr{A}$ contains all countable subsets of $\Omega$, and as a $\sigma$-algebra it contains the complements of all those sets. On the other hand, consider $A \in \mathscr{A}$. If $A$ is countable, then $A \in \mathcal{B}$. If $A$ is such that $A^c$ is countable, then $A^c \in \mathcal{B}$, and we must have $A \in \mathcal{C}$. This shows that $\mathscr{A} = \mathcal{B} \cup \mathcal{C}$.
This should make the connection between Exercise 1.1.4 and this exercise clearer, because for this exercise it is then natural to define $\mathcal{B} := \left\{ A \subset \Omega \setminus \{\omega_0\} \colon A \text{ is countable}\right\}$ and $\mathcal{C} := \{B^c \colon B \in \mathcal{B}\}$, and then we try to show that $\mathcal{A} = \mathcal{B} \cup \mathcal{C}$.
Exercise part (i)
Define $\mathcal{B} := \left\{ A \subset \Omega \setminus \{\omega_0\} \colon A \text{ is countable}\right\}$ and $\mathcal{C} := \{B^c \colon B \in \mathcal{B}\}$. We show that $\mathcal{A} = \mathcal{B} \cup \mathcal{C}$.
First, it is clear that $\mathcal{B} \cup \mathcal{C} \subset \mathcal{A}$, because $\mathcal{A}$ will contain countable unions of all elements of $\Omega \setminus \{\omega_0\}$, and all complements of those countable unions. Second, clearly $\left\{\{\omega\} \colon \omega \in \Omega \setminus \{\omega_0\}\right\} \subset \mathcal{B} \cup \mathcal{C}$. Similar to Exercise 1.1.4, we've shown that $\mathcal{A} = \sigma(\mathcal{B} \cup \mathcal{C})$, so if we can show that $\mathcal{B} \cup \mathcal{C}$ is a $\sigma$-algebra, then we're done. We check Definition 1.2.
Definition 1.2 (i)
Clearly $\emptyset \in \mathcal{B}$, so $\Omega \in \mathcal{C}$, and therefore $\Omega \in \mathcal{B} \cup \mathcal{C}$.
Definition 1.2 (ii)
Obviously $\mathcal{B} \cup \mathcal{C}$ is closed under complements by construction.
Definition 1.2 (iii)
First note that $\mathcal{B}$ is stable under countable unions, since the countable union of countable sets is countable. Furthermore, $\mathcal{C}$ is also stable under countable unions, because $\bigcup_{n = 1}^{\infty} B_n^c = \left(\bigcap_{n = 1}^{\infty} B_n\right)^c$, and $\bigcap_{n = 1}^{\infty} B_n \in \mathcal{B}$ because it's the intersection of countable sets and thereore countable, which implies that its complement is in $\mathcal{C}$.
So consider $A_1, A_2, \ldots \in \mathcal{B} \cup \mathcal{C}$, and we might as well assume that we have at least one set in this sequence from $\mathcal{B}$ and at least one from $\mathcal{C}$, because we dealt with the other cases above. We can rearrange $\bigcup_{n = 1}^{\infty} A_n$ into a union of sets from $\mathcal{B}$, unioned with a union of sets from $\mathcal{C}$. Since $\mathcal{B}$ and $\mathcal{C}$ are stable under countable unions, this reduces to showing that if $B \in \mathcal{B}$ and $C \in \mathcal{C}$, then $B \cup C \in \mathcal{B} \cup \mathcal{C}$. Note that $B \cup C \supset C$, hence $(B \cup C)^c \subset C^c \in \mathcal{B}$. Since $(B \cup C)^c$ is a subset of a countable set, it is countable, hence $(B \cup C)^c \in B$, and therefore $B \cup C \in \mathcal{C}$.
We conclude that $\mathcal{B} \cup \mathcal{C}$ is a $\sigma$-algebra, and in particular that $\mathcal{A} = \mathcal{B} \cup \mathcal{C}$.
Exercise part (ii)
To show that $(\Omega, \mathcal{A}, \delta_{\omega_0})$ is complete, we have to show that $\mathcal{A}$ contains all subsets of $\delta_{\omega_0}$-null sets. The $\delta_{\omega_0}$-null sets are those sets $N \in \mathcal{A}$ such that $\omega_0 \notin N$. Looking at our characterization of $\mathcal{A}$ from part (i) above, we see that the only sets meeting these criteria are the sets in $\mathcal{B}$, since all elements of $\mathcal{C}$ contain $\omega_0$. For any $B \in \mathcal{B}$, we know that any $B' \subset B$ is countable and does not contain $\omega_0$, therefore $B' \in \mathcal{B}$. We conclude that $(\Omega, \mathcal{A}, \delta_{\omega_0})$ is complete.


DETROIT -- Ford Motor Credit will cut 20 percent of its U.S. work force as auto sales plunge and the company provides financing for fewer brands.
About 1,200 jobs will be eliminated by the end of July, Ford Credit spokeswoman Margaret Mellott told Automotive New. The move follows a 21.8 percent decline in Ford Motor Co.'s U.S. sales last year, spurred in part by the sale of the Jaguar and Land Rover brands to India's Tata Motors.
"This will help keep our costs in line with the level of receivables we have," Mellott said.
Ford Credit outlined the moves today as it posted a $228 million fourth-quarter net loss on lower loan volumes and higher provisions for credit losses. For the year, the finance unit had a net loss of $1.5 billion, following a profit of $775 million the previous year.
The Ford Credit job cuts will begin in mid-February, Mellott said. The 1,200-position reduction will be achieved primarily through involuntary layoffs and include some planned attrition and retirement. Ford Credit's headquarters in suburban Detroit, regional business centers and field staff will be affected.
In addition to dropping Jaguar and Land Rover, Ford Credit is moving away from writing loans for Mazda. Ford reduced its stake in the Japanese automaker in November to raise cash.
All nine of the finance unit's U.S. business centers will remain open, Mellott said. The credit unit consolidated much of its branch office network into those centers in 2006.
Field operations will be consolidated from seven regions to five, and the number of sales territories will shrink from 64 to 22. The moves will align the field units with those of the Ford Customer Service Division, Mellott said.
Field-position employees, many of whom operated out of home offices, will go from 590 to 340.
Ford Credit currently employs 6,100 in the United States. No cuts are planned for the unit's Canadian operations, Mellott said.
Ford Credit employees were told about the job eliminations on Wednesday.
The credit unit cuts come in addition to the automaker's previously announced 10 percent reduction in North American salaried costs. Those cuts, expected to be the equivalent of roughly 2,300 positions, are scheduled to be completed by Friday.
The automaker reported a quarterly net loss of $5.9 billion and a record $14.6 billion loss for the year as it burned through $5.5 billion in cash in the last three months.


text:
Brentwood teen gunned down while filming rap video
PITTSBURG, Calif.
To his fans the musician was known as Mac Day. He filmed the video with his friends earlier this summer. His real name is Davon George and he was shot to death Friday evening. His uncle, Bobby White, says the family is struggling to understand the brutality of his murder.
"He's a well behaved kid. He just has a lot of love in him. And the sad thing about it is that his little brothers and sisters were there when this all unfolded," White said.
Police tell us George and about five other people were about to begin filming at Buchanan Park. That's when two other people walked up to them and an argument broke out. Investigators say George's group then started running in different directions to get away.
Police tell ABC7 News that George was shot in the back. This is an incident that happened in broad daylight and investigators say they have two suspects they're looking for and they have some pretty good leads.
There are surveillance cameras at Buchanan Park and detectives are now pouring over video from those cameras as part of this investigation. However police have not released any information on their two suspects.
George's uncle says the 18-year-old had been producing music since he was 6-years-old and recently was getting some positive attention.
"Making songs and beats for artists throughout the industry, that's what was starting to happen, they were starting to contact him," White said.
He says George's siblings who witnessed the shooting are now getting counseling because of what happened.


text:
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text:
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\begin{flushright}
{January 1997}\\
{JINR E2-97-37}\\
{solv-int/9701020}
\end{flushright}
\vs{8}
\begin{center}
{\LARGE {\bf The discrete symmetries of the}}\\[0.6cm]
{\LARGE {\bf $N=2$ supersymmetric GNLS hierarchies}}\\[1cm]

\vs{8}

{\large A. Sorin$^{1}$}
{}~\\
\quad \\
{\em {Bogoliubov Laboratory of Theoretical Physics, JINR,}}\\
{\em 141980 Dubna, Moscow Region, Russia}~\quad\\

\end{center}
\vs{8}

\centerline{ {\bf Abstract}}
\vs{4}

The discrete symmetry transformations of the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy are constructed. Their bosonic limit is analyzed
and new discrete symmetries of the modified GNLS hierarchy are
derived. The explicit relations connecting the integrable hierarchy,
produced by the junction of the Lax operators for the $N=2$ supersymmetric
$a=4$ KdV and $(n-1,m)$-GNLS hierarchies, to the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy are established.

\vfill
1){\em e-mail: sorin@thsun1.jinr.ru}

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\noindent{\bf 1. Introduction.}
The goal of the present Letter is to construct the mappings that
act like the discrete symmetry transformations of the $N=2$ supersymmetric
$(n,m)$ Generalized Nonlinear Schr\"{o}dinger ($(n,m)$-GNLS) hierarchy
\cite{bks}. Recently, a variety of $N=2$ supersymmetric integrable
hierarchies, derived by the junction of the Lax operators for the $N=2$
supersymmetric $(n-1,m)$-GNLS and $a=4$ KdV \cite{lm,kst} hierarchies, was
proposed in \cite{ik}. We also explain its origin. We demonstrate that
this variety is gauge related to the variety of $N=2$ supersymmetric
$(n,m)$-GNLS hierarchies.

Let us start with a short summary of the main facts concerning
the $N=2$ supersymmetric $(n,m)$-GNLS hierarchy \cite{bks} and introduce
some new relations which will be useful in what follows.

The Lax operator of the $N=2$ supersymmetric $(n,m)$-GNLS
hierarchy has the following form\footnote{Hereafter, summation over
repeated indices is understood and the square brackets mean that entering
operators act only on superfields inside the brackets, e.g., the fermionic
derivative $D$ in the Lax operator \p{suplax} acts only on the term
${\overline F}_a$ inside the brackets.}:
\begin{eqnarray}
L= \partial - \frac{1}{2}(F_a {\overline F}_a +
F_a {\overline D}\partial^{-1} \left[ D {\overline F}_a\right]), \quad
[D,L]=0,
\label{suplax}
\end{eqnarray}
where $F_a(Z)$ and ${\overline F}_a(Z)$ ($a,b=1,\ldots , n+m$) are chiral
and antichiral $N=2$ superfields
\begin{eqnarray}
D F_a(Z)=0, \quad {\overline D}~{\overline F}_a(Z) = 0,
\label{chiral}
\end{eqnarray}
respectively, which are bosonic for $a=1,\ldots ,n$ and fermionic for
$a=n+1,\ldots , n+m$; $Z=(z,\theta,\overline\theta)$ is a coordinate of
$N=2$ superspace and $D,{\overline D}$ are the $N=2$ supersymmetric
fermionic covariant derivatives
\begin{eqnarray}\label{DD}
D=\frac{\partial}{\partial\theta}
 -\frac{1}{2}\overline\theta\frac{\partial}{\partial z}, \quad
{\overline D}=\frac{\partial}{\partial\overline\theta}
 -\frac{1}{2}\theta\frac{\partial}{\partial z}, \quad
D^{2}={\overline D}^{2}=0, \quad
\left\{ D,{\overline D} \right\}= -\frac{\partial}{\partial z}
\equiv -{\partial}.
\end{eqnarray}
For positive-integer $k$, such a Lax operator provides the consistent flows
\begin{eqnarray}
{\textstyle{\partial\over\partial t_k}}L =[ A , L], \quad
A=(L^k)_{\geq 1}
\label{laxfl1}
\end{eqnarray}
and the infinite number of conserved currents can be obtained as follows:
\begin{eqnarray}
{H}_k = \int d Z (L^k)_{0},
\label{res}
\end{eqnarray}
where the subscripts $\geq 1$ and $0$ mean the sum of the purely
derivative terms and the constant part of the operator, respectively.
There are four additional integrals of motion
\begin{eqnarray}
\tilde{H}_1 = \int d z F_a {\overline F}_a,
\label{nres}
\end{eqnarray}
where we have only space integration due to the equation of motion
\begin{eqnarray}
-\frac{1}{2}{\textstyle{\partial\over\partial t_k}}
(F_a {\overline F}_a)=((L^k)_0)~',
\label{nnn1}
\end{eqnarray}
where the sign $'$ means the derivative with respect to z.

Equations belonging to the $N=2$ supersymmetric $(n,m)$-GNLS hierarchy
admit the complex structure
\begin{eqnarray}
F_a^{*}= (-i)^{d_a-1} {\cal P}_{ab}{\overline F}_b, \quad
{\overline F_a^{*}}=(-i)^{d_a-1}{\cal P}_{ab} F_b, \quad
{\theta}^{*}={\overline {\theta}}, \quad
{\overline {\theta}^{*}}={\theta}, \quad
t^{*}_k= (-1)^{k+1} t_k, \quad
z^{*}= z,
\label{conj}
\end{eqnarray}
where $i$ is the imaginary unity and $d_a$ define the grading
$F_aF_b=(-1)^{d_ad_b}F_bF_a$ with the property $d_a=1$ $(d_a=0)$ for
fermionic (bosonic) superfields; ${\cal P}_{ab}$ is a permutation matrix
(${\cal P}^2=I$) belonging to the discrete permutation subgroup of the
$GL(n|m)$ supergroup, which is the group of invariance of the Lax operator
\p{suplax}.

 From eq. \p{laxfl1} with the Lax operator \p{suplax}, one
can easily extract the equations for the superfields $F_a$,
\begin{eqnarray}
{\textstyle{\partial\over\partial t_k}}F_a = ((L^k)_{\geq 1} F_a)_0.
\label{n1}
\end{eqnarray}
Applying the transformations \p{conj} to eqs. \p{n1}, one can derive
the corresponding equations for the superfields $\overline F_a$,
\begin{eqnarray}
{\textstyle{\partial\over\partial t_k}}\overline F_a =(-1)^{k+1}
((L^{*~k})_{\geq 1} \overline F_a)_0,
\label{nn1}
\end{eqnarray}
where $L^*$ is the complex-conjugate Lax operator
\begin{eqnarray}
L^*= \partial + \frac{1}{2}(F_a {\overline F}_a -
\overline F_a D\partial^{-1} \left[ {\overline D} F_a\right]), \quad
A^*=(L^{*~k})_{\geq 1}, \quad
[\overline D, L^*]=0,
\label{suplaxconj}
\end{eqnarray}
which also provides the consistent flows.
The first nontrivial flow from \p{n1}, \p{nn1} is the
second flow which reads
\begin{eqnarray}
{\textstyle{\partial\over\partial t_2}} F_a =
F_a~'' +  {D}(F_b {\overline F}_b~{\overline D} F_a), \quad
{\textstyle{\partial\over \partial t_2}} {\overline F}_a =
-{\overline F}_a~'' + {\overline D}
(F_b {\overline F}_b {D}{\overline F}_a).
\label{gnls}
\end{eqnarray}
The set of equations \p{gnls} form the $N=2$ supersymmetric GNLS
equations.

{}~

\noindent{\bf 2. Discrete symmetries of the
$N=2$ super-GNLS hierarchies.}
Here, we demonstrate that in addition to the transformations of the
$N=2$ supersymmetry and $GL(n|m)$ supergroup, the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy is invariant with respect to discrete mappings.
In the particular cases corresponding to $n=0,m=1$ and $n=1,m=0$, such
mappings were obtained in \cite{dls,s}. Following the scheme
developed in \cite{s}, we derive their generalizations for arbitrary
values of the discrete parameters $n$ and $m$.

Applying the gauge transformation
\begin{eqnarray}
\widetilde{L} = G^{-1} L G, \quad
\widetilde{A} = G^{-1} A G -
G^{-1} {\textstyle{\partial\over\partial t_k}} G,
\quad {\textstyle{\partial\over\partial t_k}}\widetilde{L} =
[\widetilde{A} , \widetilde{L}]
\label{n2}
\end{eqnarray}
with the gauge function $G$ equal to some given bosonic superfield $F_l$,
\begin{eqnarray}
G= F_l
\label{g1}
\end{eqnarray}
(i.e., the index $l$ is an arbitrary fixed index belonging to the range $1
\leq l \leq n$), substituting the $t_k$-derivative of $F_l$ \p{n1} into
\p{n2}, introducing the new superfield basis $\\$
$\{J(Z), {\widetilde{F_j}}(Z), {\widetilde{{\overline F}_j}}(Z), j=1,
\ldots , l-1, l+1, \ldots , n, \ldots , n+m\}$
\begin{eqnarray}
\widetilde{F_j}=\frac{1}{\sqrt{2}}{F_l}^{-1}F_{j}, \quad
\widetilde{{\overline F}_j}=-
\frac{1}{\sqrt{2}}{\overline D} D {\partial}^{-1}(F_l{\overline F}_{j}),
\quad
J=\frac{1}{2}(\frac{1}{2} F_a {{\overline F}_a} - (\ln F_l)~'~)
\label{n3}
\end{eqnarray}
and making obvious algebraic manipulations in the result, we obtain the
following explicit expressions for the operators $\widetilde{L}$ and
$\widetilde{A}$:
\begin{eqnarray}
\widetilde{L}= \partial -
2J-2 {\overline D}\partial^{-1} \left[ D (J -
\frac{1}{2}{\widetilde F_j} {\widetilde {\overline F}_j})
\right]- {\widetilde F_j} {\overline D}\partial^{-1}
\left[ D {\widetilde {\overline F}_j}\right], \quad
\widetilde{A}=(\widetilde{L}^k)_{\geq 1},
\label{n4}
\end{eqnarray}
which coincide with the LA-pair considered in \cite{ik}.
Thus, the integrable extension of the $N=2$ supersymmetric $a=4$ KdV
hierarchy of Ref. \cite{ik} is gauge related to the $N=2$
supersymmetric $(n,m)$-GNLS hierarchy \cite{bks} and relations \p{n3}
establish their explicit connection. For the particular case $n=1, m=0$,
relation \p{n3} was obtained in \cite{bks}.

In the new basis \p{n3}, the second flow equations \p{gnls} become
\begin{eqnarray}
&&{\textstyle{\partial\over\partial t_2}}{\widetilde F_j} =
{\widetilde F_j}~''+ 4D(J\overline D {\widetilde F_j}), \quad
{\textstyle{\partial\over\partial t_2}}{\widetilde {\overline F}_j} =
-{\widetilde {\overline  F}_j}~''+
4\overline D (J D {\widetilde {\overline F}_j}), \nonumber\\
&&{\textstyle{\partial\over\partial t_2}}J = (-[D,{\overline D}] J-2J^2+
D{\widetilde {\overline F}_j} \cdot \overline D {\widetilde F_j})~',
\label{ngnls}
\end{eqnarray}
and one can observe that they, as well as other equations belonging to the
hierarchy, admit the complex structure
\begin{eqnarray}
&&{\widetilde F_j^{*}}= (-i)^{d_j-1}\widetilde {\cal P}_{jc}
{\widetilde {\overline F}_c}, \quad
{\widetilde {\overline F}_j^{*}}=(-i)^{d_j-1}\widetilde {\cal P}_{jc}
{\widetilde F_c}, \quad
J^{*} = -J, \nonumber\\
&&{\theta}^{*}={\overline {\theta}}, \quad
{\overline {\theta}^{*}}={\theta}, \quad
t^{*}_k= (-1)^{k+1} t_k, \quad
z^{*}= z.
\label{nconj}
\end{eqnarray}
Applying the complex-conjugation transformations \p{conj} and \p{nconj} to
\p{n3}, we observe that in addition to relation \p{n3}, there exists one
more
\begin{eqnarray}
\widetilde{F_j}= -\frac{1}{\sqrt{2}}i D {\overline D} {\partial}^{-1}
({\overline F}_l{\cal P}_{jc} F_{c}), \quad
\widetilde{{\overline F}_j}=-\frac{1}{\sqrt{2}}i{{\overline F}_l}^{-1}
{\cal P}_{jc} {\overline F}_{c}, \quad
J=\frac{1}{2}(\frac{1}{2} F_a {{\overline F}_a} + (\ln {\overline F}_l)~'~),
\label{n5}
\end{eqnarray}
which connects the second flow equations \p{ngnls} to \p{gnls}, as well as
their corresponding hierarchies. Denoting the superfields $F_a$ and
$\overline F_a$ in \p{n3} by the new letters $\r F{}_a$ and $\r {\overline
F}{}_a$, respectively, and equating the corresponding superfields
${\widetilde F_j}$, ${\widetilde {\overline F}_j}$ and $J$ belonging to
the relations \p{n3} and \p{n5}, we derive the mapping
\begin{eqnarray}
&& D {\overline D}{\partial}^{-1}({\overline F}_l F_{j})=
i{\r F{}_l}^{-1}{\cal P}_{jc} \r F{}_{c}, \quad
{\overline D} D {\partial}^{-1} (\r F{}_l\r {\overline F}{}_{j})=
i{{\overline F}_l}^{-1}{\cal P}_{jc} {\overline F}_{c}, \nonumber\\
&&\frac{1}{2} (\r F{}_l \r {\overline F}{}_l +
\r F{}_{j} \r {\overline F}{}_{j} - F_l {{\overline F}_l} -
F_{j} {{\overline F}_{j}}) = (\ln (\r F{}_l {\overline F}_l))~'
\label{n6}
\end{eqnarray}
that acts like the discrete symmetry transformation of the $N=2$
supersymmetric $(n,m)$-GNLS hierarchy. Acting by the fermionic covariant
derivatives $D$ and $\overline D$ on the first line of eqs. \p{n6},
these relations can be rewritten in a slightly different but equivalent
local form
\begin{eqnarray}
{\overline D}~({\overline F}_l F_{j}+
i{\r F{}_l}^{-1}{\cal P}_{jc} \r F{}_{c})=0, \quad
D~ (\r F{}_l\r {\overline F}{}_{j}+
i{{\overline F}_l}^{-1}{\cal P}_{jc} {\overline F}_{c})=0,
\label{nnn6}
\end{eqnarray}
which can be more convenient for applications. Actually, it is easy to
understand that up to an arbitrary permutation ${\cal P}_{jc}$, relation
\p{n6} gives us $n$ different discrete symmetry-mappings if one
remembers that the index $l$ enters \p{n6} like a discrete
parameter\footnote{Let us remember that in \p{n6}, there is no summation
over repeated indices $l$.} taking $n$ values $l=1, \ldots , n$.

Now consider gauge transformation \p{n2} with the gauge function
\begin{eqnarray}
G = (D {\overline F}_f)^{-1},
\label{g2}
\end{eqnarray}
where $\overline F_f$ is some given fermionic superfield
(i.e., the index $f$ is an arbitrary fixed index belonging to the range
$n+1 \leq f \leq n+m$). After introducing the
new superfield basis  $\{J(Z), {\widetilde{F_j}}(Z),
{\widetilde{{\overline F}_j}}(Z),j=1, \ldots , n, \ldots ,
f-1, f+1, \ldots , n+m\}$
according to formulae
\begin{eqnarray}
\widetilde{F_j}=
\frac{1}{\sqrt{2}}(D {\overline F}_f)F_{j}, \quad
\widetilde{{\overline F}_j}=-
\frac{1}{\sqrt{2}}{\overline D}
D ((D {\overline F}_f)^{-1}{\overline F}_{j}),\quad
J=\frac{1}{2}(\frac{1}{2} F_a {{\overline F}_a} +
(\ln D {\overline F}_f)~'~)
\label{nn3}
\end{eqnarray}
we obtain the following expression for the Lax operator
$\widetilde{L}$
\begin{eqnarray}
\widetilde{L}= \partial - 2J+2\left[ D (J - \frac{1}{2}{\widetilde F_j}
\partial^{-1} {\widetilde {\overline F}_j})\right]
{\overline D}\partial^{-1} - {\widetilde F_j} {\overline D}\partial^{-1}
\left[ D \partial^{-1} {\widetilde {\overline F}_j}\right].
\label{nn4}
\end{eqnarray}
We do not present the explicit expression for the operator
$\widetilde{A}$ here, because what we actually need for our purpose is
only the transformation law \p{nn3} in the new basis. For the particular
case $n=0, m=1$, relation \p{nn3} has been discussed in \cite{ks,kst}.

In the new basis \p{nn3}, the second flow equations \p{gnls} become
\begin{eqnarray}
&&{\textstyle{\partial\over\partial t_2}}{\widetilde F_j} =
{\widetilde F_j}~''+ 4D\overline D (J{\widetilde F_j}), \quad
{\textstyle{\partial\over\partial t_2}}{\widetilde {\overline F}_j} =
-{\widetilde {\overline  F}_j}~''+
4\overline D D(J {\widetilde {\overline F}_j}), \nonumber\\
&&{\textstyle{\partial\over\partial t_2}}J =( [D,{\overline D}] J-2J^2-
{\widetilde F_j} {\widetilde {\overline F}_j})~',
\label{nngnls}
\end{eqnarray}
and one can see that they admit the complex structure
\begin{eqnarray}
&&{\widetilde F_j^{*}}= (-i)^{d_j} {\widetilde {\cal P}}_{jc}{\widetilde
{\overline F}_c}, \quad
{\widetilde {\overline F}_j^{*}}=(-i)^{d_j}{\widetilde {\cal P}}_{jc}
{\widetilde F_c}, \quad J^{*} = -J, \nonumber\\
&& {\theta}^{*}={\overline {\theta}}, \quad
{\overline {\theta}^{*}}={\theta}, \quad
t^{*}_2= -t_2, \quad
z^{*}= z.
\label{nnconj}
\end{eqnarray}

Following the above-discussed scheme, we apply the
complex-conjugation transformations \p{conj} and \p{nnconj} to \p{nn3} and
obtain one more mapping,
\begin{eqnarray}
\widetilde{F_j}=
-\frac{i}{\sqrt{2}} D {\overline D}
(({\overline D} F_f)^{-1}{\cal P}_{jc} F_{c}), \quad
\widetilde{{\overline F}_j}=
\frac{i}{\sqrt{2}}({\overline D}F_f){\cal P}_{jc} {\overline F}_{c}, \quad
J=\frac{1}{2}(\frac{1}{2} F_a {{\overline F}_a} -
(\ln {\overline D} F_f)~'~),
\label{nn5}
\end{eqnarray}
connecting the second flow equations \p{nngnls} to \p{gnls}, and,
therefore, the mapping
\begin{eqnarray}
&& i D {\overline D}((\overline D F_f)^{-1} F_{j})=
-(D \r {{\overline F}}{}_f){\cal P}_{jc} \r F{}_{c},\quad
i{\overline D} D ((D \r {{\overline F}}{}_f)^{-1}
\r {\overline F}{}_{j})=
(\overline D F_f){\cal P}_{jc} {\overline F}_{c}, \nonumber\\
&&\frac{1}{2} (F_f {{\overline F}_f} + F_{j} {{\overline F}_{j}}-
\r F{}_f \r {\overline F}{}_f -\r F{}_{j} \r {\overline F}{}_{j}) =
(\ln (\overline D F_f \cdot D \r {{\overline F}}{}_f))~'
\label{nn6}
\end{eqnarray}
acts like the discrete symmetry transformation of the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy. Acting by the fermionic covariant derivatives $D$
and $\overline D$ on the first line of eqs. \p{nn6},
these relations can be represented in the following equivalent form:
\begin{eqnarray}
{\overline D}~ (-i((\overline D F_f)^{-1} F_{j})~' +
(D \r {{\overline F}}{}_f){\cal P}_{jc} \r F{}_{c})=0, \quad
D~ (i((D \r {{\overline F}}{}_f)^{-1} \r {\overline F}{}_{j})~'+
(\overline D F_f){\cal P}_{jc} {\overline F}_{c})=0.
\label{nnnn6}
\end{eqnarray}
Modulo an arbitrary permutation ${\cal P}_{jc}$, relation \p{nn6} gives us
$m$ different discrete symmetry-mappings because the index $f$ takes $m$
different values $l=n+1, \ldots , n+m$.

Let us note that one can rewrite equations (\ref{nngnls}) in a form
similar to (\ref{ngnls}),
\begin{eqnarray}
&&-{\textstyle{\partial\over\partial t_2}}{\Psi_j} =
{\Psi_j}~''+ 4D({\widetilde J}~\overline D {\Psi_j}), \quad
-{\textstyle{\partial\over\partial t_2}}{\overline \Psi}_j =
-{\overline  \Psi}_j~''+
4\overline D ({\widetilde J} D {\overline \Psi}_j), \nonumber\\
&&-{\textstyle{\partial\over\partial t_2}}{\widetilde J} =
(-[D,{\overline D}] {\widetilde J}-2{\widetilde J}^2+
D{\overline \Psi}_j \cdot \overline D {\Psi_j})~',
\label{nnngnls}
\end{eqnarray}
if one introduces the new superfields ${\widetilde J}$, $\Psi_j$ and
${\overline \Psi}_j$ by the following invertible
relations\footnote{Transformations of such kind have been discussed in
\cite{ik}.}
\begin{eqnarray}
&& {\widetilde J}=-J, \quad
\Psi_j = i {\partial}^{-1} D {\widetilde {\overline F}_j}, \quad
{\overline \Psi_j} =i{\partial}^{-1} {\overline D} {\widetilde F_j};
\nonumber\\
&& J=-{\widetilde J}, \quad
{\widetilde F_j} = i D {\overline \Psi}_j, \quad
{\widetilde {\overline F}_j} = i {\overline D} \Psi_j.
\label{tr}
\end{eqnarray}
However the system (\ref{nnngnls}) does not completely coincide with
(\ref{ngnls}): in comparison with (\ref{ngnls}), its time direction is
reversed. Due to this crucial difference, we can not equate the
corresponding superfields entering (\ref{ngnls}) and (\ref{nnngnls}) to
produce new discrete symmetry-mappings for the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy. Nevertheless, the system (\ref{nnngnls}) is
equivalent to (\ref{ngnls}), and relations \p{nn3}, \p{nn5}, and
\p{tr} establish an explicit connection of the integrable hierarchy of
Ref. \cite{ik} to the $N=2$ supersymmetric $(n,m)$-GNLS hierarchy.

{}~

\noindent{\bf 3. Bosonic limit of the mappings.}
Let us briefly discuss the bosonic limit of the mappings \p{n6} and
\p{nn6} in order to generate the discrete symmetries for the
bosonic GNLS and modified GNLS (mGNLS) hierarchies.

To do this, we set all fermionic components of the superfields $F_a$
and $\overline F_a$ equal to zero and define the bosonic
components as \cite{bks}
\begin{eqnarray}
&& b_{\alpha}  = \frac{1}{\sqrt{2}} F_{\alpha}|, \quad
{\overline b}_{\beta} = \frac{1}{\sqrt{2}} {\overline F}_{\beta}|, \quad
1 \leq {\alpha},{\beta} \leq n, \nonumber\\
&& g_s = \frac{1}{\sqrt{2}} {\overline D} F_{s+n}|~
{\exp (-{\partial^{-1}} (b_{\beta} {\overline b}_{\beta}))}, \quad
{\overline g}_p = \frac{1}{\sqrt{2}} D {\overline F}_{p+n}|~
{\exp ({\partial^{-1}} (b_{\beta} {\overline b}_{\beta}))}, \quad
1 \leq s,p \leq m, ~ ~ ~ ~ ~
\label{def}
\end{eqnarray}
where $|$ means the $({\theta}, {\bar\theta})\rightarrow 0$ limit.
In terms of such components, eqs. \p{gnls} for the fields
$b_{\alpha},{\overline b}_{\alpha}$ and $g_s, \overline g_s$ are
completely decoupled:
\begin{eqnarray}
{\textstyle{\partial\over\partial t_2}} b_{\alpha}=
b_{\alpha}~'' -  2 b_{\beta} {\overline b}_{\beta} b_{\alpha}~', \quad
{\textstyle{\partial\over \partial t_2}} {\overline b}_{\alpha} =
-{\overline b}_{\alpha}~'' - 2 b_{\beta}
   {\overline b}_{\beta} {\overline b}_{\alpha}~',
\label{bgnls}
\end{eqnarray}
\begin{eqnarray}
{\textstyle{\partial\over\partial t_2}} g_s=
g_s~'' -  2 g_p {\overline g}_p g_s, \quad
{\textstyle{\partial\over \partial t_2}} {\overline g}_s =
-{\overline g}_s~'' + 2 g_p {\overline g}_p {\overline g}_s.
\label{fgnls}
\end{eqnarray}
The set of equations \p{fgnls} form the bosonic GNLS equations \cite{fk}.
Concerning the set of equations \p{bgnls}, we call them mGNLS
equations, reflecting the name of its first representative---modified NLS
equation \cite{cll} corresponding to the case of $n=1$.

The bosonic limit of the mapping \p{n6} ( \p{nn6} ), acting like
a discrete symmetry transformation of equations \p{bgnls} and \p{fgnls},
also splits into two independent mappings, which one can see from the
explicit expressions
\begin{eqnarray}
&& {\overline b}_l b_{\alpha}~'+
i({\r b{}_l}^{-1}{\cal P}_{{\alpha}{\beta}} \r b{}_{\beta})~' = 0, \quad
\r b{}_l \r {\overline b}{}_{\alpha}~'+
i({{\overline b}_l}^{-1} {\cal P}_{{\alpha}{\beta}}
{\overline b}_{\beta})~'=0, \quad {\alpha} \neq l, \nonumber\\
&& \r b{}_l \r {\overline b}{}_l+
\r b{}_{\alpha} \r {\overline b}{}_{\alpha} -
b_l {\overline b}_l
-b_{\alpha} {{\overline b}_{\alpha}} =
(\ln (\r b{}_l {\overline b}_l))~', \quad
\r b{}_l \r {\overline b}{}_l~'+
\r b{}_{\alpha} \r {\overline b}{}_{\alpha}~' -
b_l {\overline b}_l~'
-b_{\alpha} {\overline b}_{\alpha}~' =
(\ln {\overline b}_l)~'', ~ ~ ~ ~ ~ ~
\label{bn6}
\end{eqnarray}
\begin{eqnarray}
\r g{}_s = {\cal P}_{sp} g_p, \quad
\r {\overline g}{}_s = {\cal P}_{sp} {\overline g}_p
\label{bbn6}
\end{eqnarray}
for the mapping \p{n6}, and
\begin{eqnarray}
\r b{}_{\alpha}{\cal P}_{{\alpha}{\beta}} \r {\overline b}{}_{\beta}~'+
b_{\alpha} {\cal P}_{{\alpha}{\beta}} {\overline b}_{\beta}~'=0, \quad
\r b{}_{\beta} \r {\overline b}{}_{\beta} -
b_{\beta} {{\overline b}_{\beta}} =
-(\ln {\overline b}_{\alpha}~')~' +
(\ln ({\cal P}_{{\alpha}{\beta}} \r {\overline b}{}_{\beta}))~',
\label{fn6}
\end{eqnarray}
\begin{eqnarray}
&& -i(g_f^{-1} g_{s})~' +
\r {{\overline g}}{}_f{\cal P}_{sp} \r g{}_{p}=0, \quad
i(\r {{\overline g}}{}_f^{-1} \r {\overline g}{}_{s})~'+
 g_f {\cal P}_{sp} {\overline g}_{p}=0, \nonumber\\
&& \r {\overline g}{}_f = C_f g_f^{-1}, \quad
\r g{}_f \r {\overline g}{}_f+
\r g{}_s \r {\overline g}{}_s - g_f {\overline g}_f
-g_s {\overline g}_s =
-(\ln {\overline g}_f)~'', \quad s \neq f
\label{ffn6}
\end{eqnarray}
for the mapping \p{nn6}, where there is no summation in eq. \p{fn6} over
repeated indices ${\alpha}$ and $C_f$ in eq. \p{ffn6} is an arbitrary
constant. In the derivation of these expressions, obvious simplifying
transformations, as well as the integration of some intermediate
equations, have been done.

The mapping \p{bbn6} forms the discrete permutation subgroup of the
$GL(m)$ group, which is a group of covariance for the GNLS equations
\p{fgnls}. The mapping \p{ffn6} coincides with the mapping which can be
easily derived using the Darboux-B\"acklund transformations of the GNLS
Lax operators constructed in \cite{a}. Regarding the symmetry
mappings \p{bn6} and \p{fn6} for the mGNLS hierarchy \p{bgnls},
to our knowledge, they are presented for the first time.

In addition to mappings \p{bn6} and \p{fn6}, there are other
symmetries of the mGNLS equations. One can produce them if one remembers
that the GNLS and mGNLS equations are related by the following
transformations \cite{bks}:
\begin{eqnarray}
g_s= b_s~'~ {\exp (-{\partial^{-1}} (b_p {\overline b}_p))}, \quad
{\overline g}_s= {\overline b}_s~ {\exp ({\partial^{-1}}
(b_p {\overline b}_p))}.
\label{trmb}
\end{eqnarray}
Applying the complex-conjugation operation \p{conj} to relations \p{trmb}
for the bosonic components \p{def}, one can obtain one more relation,
\begin{eqnarray}
g_s= i b_s~ {\exp (-{\partial^{-1}} (b_p {\overline b}_p))}, \quad
{\overline g}_s=
i {\overline b}_s~'~{\exp ({\partial^{-1}} (b_p {\overline b}_p))}.
\label{ctrmb}
\end{eqnarray}
Therefore, we can introduce two different relations for the fields
with the arrow:
\begin{eqnarray}
&& \r g{}_s= \r b{}_s~'~ {\exp (-{\partial^{-1}}
(\r b{}_p \r {\overline b}{}_p))}, \quad
\r {\overline g}{}_s=
\r {\overline b}{}_s~ {\exp ({\partial^{-1}}
(\r b{}_p \r {\overline b}{}_p))}, \nonumber\\
&& \r g{}_s= i \r b{}_s~ {\exp (-{\partial^{-1}} (\r b{}_p
\r {\overline b}{}_p))}, \quad
\r {\overline g}{}_s= i \r {\overline b}{}_s~'~{\exp
({\partial^{-1}} (\r b{}_p \r {\overline b}{}_p))}.
\label{atrmb}
\end{eqnarray}
If one takes some fixed combination of the fields without the arrow, $g_s,
\overline g_s$, and the fields with the arrow $\r g{}_s, \r {\overline
g}{}_s$ from the set of relations \p{trmb}--\p{atrmb}, and substitutes
it into the mappings \p{bbn6} and \p{ffn6}, one can generate new
mappings for the mGNLS hierarchies, with different
combinations generating different mappings. Let us only mention that one
such mapping coincides with the mapping \p{fn6}, and, in this way, it is
possible to reproduce the mapping considered in \cite{l} for the modified
NLS equation and to obtain new mappings. It is a simple exercise to derive
their explicit forms, and we do not present them here.

{}~

\noindent{\bf 4. Conclusion.}
In this Letter, we constructed mappings \p{n6} and \p{nn6}, which act
like a discrete symmetry transformations of the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy \p{suplax}, \p{laxfl1}, and produced their bosonic
counterparts \p{bn6}--\p{ffn6}. We also established explicit relations
\p{n3}, \p{n5}, \p{nn3}, and \p{nn5} connecting the integrable hierarchy,
obtained by the junction of the Lax operators for the $N=2$ supersymmetric
$a=4$ KdV and $(n-1,m)$-GNLS hierarchies, to the $N=2$ supersymmetric
$(n,m)$-GNLS hierarchy.

Symmetry mappings contain valuable information about the integrable
hierarchies corresponding to them \cite{lf,ls1,dls,s}. In addition to this,
there is one more reason that stimulates interest in such
mappings---they are usually integrable themselves, i.e., every new mapping
may give us a new example of a one-dimensional integrable system. Thus,
for the $N=2$ supersymmetric f-Toda chain \cite{dls} corresponding to the
case of $n=0, m=1$, the integrability under appropriate boundary
conditions has been proven in \cite{ls}. It is interesting to generalize
this investigation for the case of arbitrary values of the discrete
parameters $n$ and $m$. In this context, it is important to have
Darboux-B\"acklund transformations of the $N=2$ supersymmetric
$(n,m)$-GNLS Lax operators which should generate our mappings and contain
important information about their integrability properties and solutions.
We hope to analyze this complicated problem in future publications.

{}~

\noindent{\bf Acknowledgments.} I would like to thank L. Bonora,
E.A. Ivanov, A.N. Leznov and G.M. Zinovjev for their interest in this work
and useful discussions. This work was partially supported by the Russian
Foundation for Basic Research, Grant No. 96-02-17634, INTAS Grant No.
94-2317, and by a grant from the Dutch NWO organization.

redpajama_set_name: RedPajamaArXiv


Some labels change your life. Their message, sound and energy is so strong it draws you into its own world and helps to characterise your own tastes and where you stand in the endless, bottomless oceans of music. Labels you resonate with personally and musically. Labels you trust with every release. Even if you don't know the artist, you know it's coming from the right place.
We've all got them. And for Amit, one of those labels is Doc Scott's 31.
No happy numbers. But the arrival of any 31 release in Amit's world as he began to cut his teeth as a young junglist definitely did make him happy.
"I've always had a great dialogue with Scott," explains Amit. "He's one of those people who always gets back to you and is very honest and supportive. I created this release with 31 in mind and right from the beginning, I already had a vision for what I wanted the end product to look like. I asked Scott if we could use the old artwork and put it on a 10". This made so much sense to me as I was finding myself as an Artist when those early releases on 31 were being issued. It felt only right that my first release on 31 should have the same look.
This sounds less complicated than it was IRL. The original 31 logo designer John Black had long since lost the font and graphics and a high res version was impossible to find. Eventually they recruited Singapore artist and designer Kiat – a man behind the artwork for many Metalheadz and AMAR releases – who manage to recreate the logo down to the last authentic detail.
This was so different at the time. Built on minimal elements with maximum effect. It was a very powerful release and I'd say that shaped a lot of people's creative direction, witnessing and hearing it in clubs. So simple but it works. Music doesn't have to be overcomplicated.
Neptune is an amazing and beguiling piece of work. Obviously the A-side How You Make Me Feel grabbed everyone, too but this was a personal favourite. Minimal bass, Detrit techno influences, that gradual evolution.
This checked so many things for me. Everything you can say about this record has already been said. Absolutely seminal and still entirely relevant to this day.
Marcus's work was so important to 31. So important to drum & bass jungle. Every slice was a breath of fresh air. One of the most forward-thinking artists there was regardless of any label he's worked on. You can always tell the Marcus cuts. They stood the test of time and you can hear he knew exactly what he wanted to do. He was a visionary.


Our previous three articles1–3 explored the teaching philosophy embodied in our recent book, Accelerated C++: Practical Programming by Example. We have completely rethought how to teach C++. Our classroom experience has been that students learn much more rapidly with our new approach than they do with more traditional techniques. We are reviewing our philosophy in some detail in the hope that others interested in teaching—or learning—C++ can understand the motivation behind our approach and consider adopting it themselves.
Motivate each facility with a problem that uses that facility as an integral part of its solution. The problem must be interesting in its own right, and not merely constructed to demonstrate the facility.
Present the most useful ideas first.
Our strategy so far has led us to describe three fundamental standard-library facilities—vector, string, and struct—before even mentioning built-in arrays or pointers. In doing so, we have shown how to write substantial programs. One example, which appeared in our previous article,3 reads a collection of students' names and corresponding grades, and prints an overall grade report in alphabetical order by name.
At this point, we thought about giving in to the temptation of talking about the low-level ideas of pointers, arrays, and dynamic memory allocation. However, in keeping with the idea of presenting the most useful ideas first, we decided to continue by talking about other types of containers and container operations, and the related—and fundamental—idea of iterators. The lower level ideas are important, of course, but we decided not to discuss them until we really needed them.
An awful lot of programming involves dealing with collections of data, be those collections of strings, files, bitmaps, display lists, URLs, or other collections. Accordingly, one of our aims is to make the reader comfortable working with collections.
So far, we have used only one type of container—a vector—and only a few operations: indexing, push_back, and sorting. Our next pedagogical task, then, was to find problems to motivate additional container operations.
In this example, fgrade is a function, which we wrote separately, that determines whether a student failed the course.
Solving the problem using only familiar facilities helps in two ways: It reinforces the ideas that the students have already learned, and it provides a basis for improvement.
The improvement we pursued in this case came from the observation that the program copies each student record into one of two local variables, pass or fail, and then copies pass on top of its argument and returns fail. To avoid keeping more copies of data around than necessary, we showed examples of several other ways of solving the same problem.
This is a nice example because it lets us explain several useful ideas, and it also gives us an opportunity to show some bad ideas to avoid.
We have observed that people who are learning C++ often have trouble figuring out how to erase the nth element of a vector, so we made sure we showed an example of how to do it. To ensure that the behavior of this statement was clear, we even drew a picture to explain it (see Fig. 1).
Figure 1. Erasing an element from the middle of a vector.
Figure 1 makes plain both what it means to erase an element from the middle of a vector, and that doing so is a lot of work. If we want a program that uses this strategy to be efficient, we must figure out a way of erasing an element from the middle of a container that does not involve copying all the elements that follow.
One straightforward way to avoid the work involved in copying the elements after an erasure is to use a different type of container—one that does not require the excess copying. The most common such container is a list, so we decided to recast our grading program in terms of lists.
Before we could do so, however, we needed to make it stop relying on the random-access properties of vectors. For example, when we evaluated fgrade(students[i]), we were relying on the vector class' ability to give us the ith element efficiently when we supplied the value of i. Moreover, to avoid random access, we would need a different way of accessing the container's elements because, until this point, random access was all we had.
Restricts the available operations in ways that correspond to what the container can handle efficiently.
This program is just as slow as the previous version. However, it has the important property of not using the random-access properties of vectors at all. Instead, it uses an iterator, of a type defined as part of the vector class, to traverse the vector sequentially.
This statement solves another problem that often troubles beginning C++ programmers: It erases an element, identified by an iterator, from a container, and positions the iterator on the element after the erasure.
This example makes an important point: If your program deals with containers by using iterators, it is easy to change the type of container the program uses—as long as the container supports all the operations the program needs. Accordingly, it is wise to write programs that use as small a set of container operations as is reasonably possible, to provide for the possibility of using other container types later.
One reason for choosing one container type over another is efficiency. In Accelerated C++, we reported on informal measurements of the vector and list versions of our program. When we ran both versions on a 735-element input file, the execution time was essentially the same for both versions. However, when the file grew to 73,500 records, the list version took about nine seconds to execute and the vector version took about 10 minutes.
The problem of dealing with student grades offers opportunities to use the language and standard library in several different ways. In this column, we showed how we used this example to explain sequential containers and references, and to make several points about program design and its effect on efficiency.
Not mentioned explicitly, but very much in our minds, was the notion that if it is possible to write two programs that solve the same problem for different types of containers, it should be possible to collapse those programs into one by using a template. In other words, by showing how to solve a single problem in the same way using vectors and lists, we have prepared the ground for generic programming—a notion we have not yet discussed.
Notice that even this far into the book—we are at page 87—we still have not mentioned pointers or built-in arrays. Indeed, the chapter that discusses them does not begin until page 169. Before we get there, we will have shown several more programming examples, introduced more algorithms and container operations, shown how to use templates to write generic functions, explained how to write classes with member functions and protection, and covered iterators in more detail. We find it is more effective for C++ programmers to learn about all of these concepts before they tackle pointers.
Of course, it is essential to discuss pointers eventually. Dynamic binding in C++ comes into play only in the context of pointers or references, and it is much harder to write OO programs using only references than it is to do so using pointers, because only by using pointers is it possible to allocate objects dynamically.
However, our experience is that pointers are a slippery subject to master, and beginners have a much easier time dealing with the value-like classes we have been using until now. Moreover, the notion of iterators turns out to provide a nice basis for explaining pointers.
A programmer who has a thorough understanding of the ideas we have described so far typically has no trouble learning how to use pointers. We therefore think it is right to defer explaining them until they are truly necessary.
Koenig, A., and B. E. Moo. "Rethinking How to Teach C++ Part 1: Goals and Principles," Journal of Object-Oriented Programming, 13(7): 44–47, Nov. 2000.
Koenig, A., and B. E. Moo. "Rethinking How to Teach C++ Part 2: Two Interesting Decisions," Journal of Object-Oriented Programming, 13(8): 36–40, Dec. 2000.
Koenig, A., and B. E. Moo. "Rethinking How to Teach C++ Part 3: The First Data Structures," Journal of Object-Oriented Programming, 13(9): 35–38, Jan. 2001.


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Game of Thrones smashes new piracy record. Here's why HBO isn't concerned.
Did you like watching the latest episode of Game of Thrones, "The Lion and the Rose," where yet another wedding was marred by blood and treachery? So did downloaders - all 1.5 million of them on the first day, alone. According to Hollywood Reporter, "The Lion and the Rose" broke the record for most people sharing a file on BitTorrent simultaneously; 93,418 people were sharing one single torrent within hours of the episode's airing.
As we know, Game of Thrones has also been the most pirated television show for two years in a row. But rather than take a hardline anti-piracy stance, HBO is seemingly unconcerned with their loss of profits - profits that they could be earning by making Game of Thrones available on iTunes (For example, a season pass of HBO's True Blood costs a whopping $46.99).
So why is HBO so blase about losing cash that they could be spending on bonuses and perhaps making more wonderful shows?
"[Piracy] really helps the show's cultural buzz, and it does not impact the bottom line because HBO has more than enough money to keep making the show.
"So what this is, is, this makes HBO the center of a cultural conversation about illegal downloading, about streaming content, about the production of content and distribution of content, which is probably somewhere they really want to be."
That sounds nice, but tapping into the cultural zeitgeist doesn't pay the rent. Do you know who does? Time Warner.
You see, when viewers pay for HBO, an add-on service, they also have to pay for cable television first. HBO—or rather its parent company Time Warner—is happier with downloading than with the alternative: "Cutting the cord" of subscription services.
"[N]ot only are they keeping their HBO subscription, but that the customers are also likely paying Time Warner indirectly via CNN, Cartoon Network, and all of Time Warner's other subsidiaries. That's something the company — financially speaking — shouldn't mess with."
So Time Warner would rather have a few, or even a few million, downloaders rather than have viewers give up on cable altogether.
Obviously, Time Warner knows what it's doing. In 2013, HBO's revenue was $4.9 billion. But parent company Time Warner earned almost $30 billion in revenue.
What do you think? Is piracy going to sink Game of Thrones in the long run, or is this more open-minded model the wave of the future?