text:
Tournaments > 2017 > United States > 48th World Series of Poker (WSOP) 2017
Tournament: 48th World Series of Poker (WSOP) 2017
Date: May 30 - Jul 22, 2017
Venue: Rio Hotel and Casino Las Vegas, NV, United States
Event: No Limit Hold'em - Tag Team (Event #10) (Jun 5 - 7, 2017)
Buy-in: $1,000
Prize: $758,700
May 31, 2017 No Limit Hold'em Casino Employees (Event #1) $565
May 31 - Jun 1, 2017 No Limit Hold'em - Tag Team Championship (Event #2) $10,000
Jun 1 - 3, 2017 Omaha Hi/Lo (Event #4) $1,500
Jun 1 - 3, 2017 No Limit Hold'em - Shootout (Event #3) $3,000
Jul 7 - 9, 2017 Seven Card Stud Championship (Event #72) $10,000
Jun 2 - 6, 2017 No Limit Hold'em - The Colossus III (Event #5) $565
Jun 3, 2017 No Limit Hold'em - WSOP.com Online (Event #8) $333
Jun 3 - 5, 2017 Limit Mixed Triple Draw Lowball (Event #7) $2,500
Jun 4 - 6, 2017 Omaha Hi/Lo Championship (Event #9) $10,000
Jun 5 - 7, 2017 No Limit Hold'em - Tag Team (Event #10) $1,000
Jun 5 - 7, 2017 Dealers Choice - 6 Handed (Event #11) $1,500
Jun 6 - 8, 2017 No Limit 2-7 Lowball Draw (Event #13) $1,500
Jun 6 - 8, 2017 No Limit Hold'em (Event #12) $1,500
Jun 7 - 9, 2017 No Limit Hold'em - Heads-Up Championship (Event #15) $10,000
Jun 7 - 9, 2017 H.O.R.S.E. (Event #14) $1,500
Jun 8 - 10, 2017 No Limit Hold'em - 6 Handed (Event #16) $1,500
Jun 8 - 10, 2017 Dealers Choice - 6 Handed Championship (Event #17) $10,000
Jun 9 - 11, 2017 Pot Limit Omaha (Event #18) $565
Jun 9 - Jul 8, 2017 No Limit Hold'em - The Giant (Event #19) $365
Jun 10, 2017 Eight Game Mix - 6 Handed (Event #21) $1,500
Jun 10 - 14, 2017 No Limit Hold'em - Millionaire Maker (Event #20) $1,500
Jun 11 - 13, 2017 No Limit 2-7 Lowball Draw Championship (Event #22) $10,000
Jun 12 - 14, 2017 Limit Hold'em (Event #24) $1,500
Jun 12 - 16, 2017 No Limit Hold'em - The Marathon (Event #23) $2,620
Jun 13 - 15, 2017 Pot Limit Omaha (Event #25) $1,000
Jun 13 - 15, 2017 Razz Championship (Event #26) $10,000
Jun 14 - 16, 2017 No Limit Hold'em - 6 Handed (Event #27) $3,000
Jun 14 - 16, 2017 Limit 2-7 Lowball Triple Draw (Event #28) $1,500
Jun 15 - 17, 2017 No Limit Hold'em (Event #29) $2,500
Jun 15 - 17, 2017 H.O.R.S.E. Championship (Event #30) $10,000
Jun 16 - 18, 2017 No Limit Hold'em - Seniors Championship (Event #31) $1,000
Jun 16 - 18, 2017 Pot Limit Omaha Hi/Lo/ Limit Omaha Hi/Lo (Event #32) $1,500
Jun 17 - 19, 2017 Limit 2-7 Lowball Triple Draw Championship (Event #34) $10,000
Jun 18 - 20, 2017 No Limit Hold'em - Super Seniors (Event #35) $1,000
Jun 19 - 21, 2017 Limit Hold'em Championship (Event #38) $10,000
Jun 20, 2017 Seven Card Stud Hi/Lo (Event #40) $1,500
Jun 20, 2017 No Limit Hold'em - Super Turbo Bounty (Event #39) $1,000
Jun 21 - 23, 2017 No Limit Hold'em - 6 Handed Championship (Event #42) $10,000
Jun 22 - 24, 2017 H.O.R.S.E. (Event #44) $3,000
Jun 22 - 24, 2017 No Limit Hold'em - Shootout (Event #43) $1,500
Jun 23, 2017 Pot Limit Omaha Hi/Lo (Event #46) $1,500
Jun 23, 2017 No Limit Hold'em (Event #45) $5,000
Jun 24 - 26, 2017 Seven Card Stud Hi/Lo Championship (Event #48) $10,000
Jun 24 - 28, 2017 No Limit Hold'em - Monster Stack (Event #47) $1,500
Jun 25 - 27, 2017 Pot Limit Omaha - 6 Handed (Event #49) $3,000
Jun 26 - 28, 2017 No Limit Hold'em - Bounty (Event #50) $1,500
Jun 26 - 28, 2017 Pot Limit Omaha Hi/Lo - Championship (Event #51) $10,000
Jun 27 - 29, 2017 Limit Hold'em - 6 Handed (Event #53) $3,000
Jun 28 - 30, 2017 Pot Limit Omaha - 8 Handed Championship (Event #54) $10,000
Jun 28 - 30, 2017 Seven Card Stud (Event #55) $1,500
Jun 29 - Jul 1, 2017 Omaha Hi/lLo/ Seven Card Stud Hi/Lo Mixed (Event #57) $2,500
Jun 29 - Jul 2, 2017 No Limit Hold'em (Event #56) $5,000
Jun 30 - Jul 2, 2017 Mixed Big Bet (Event #59) $2,500
Jul 1, 2017 No Limit Hold'em High Roller - WSOP.com Online (Event #61) $3,333
Jul 1 - 4, 2017 No Limit Hold'em - Crazy Eights (Event #60) $888
Jul 2 - 6, 2017 Poker Players Championship - 6 Handed (Event #62) $50,000
Jul 3 - 5, 2017 No Limit Hold'em/Pot Limit Omaha - 8 Handed (Event #64) $1,500
Jul 3 - 5, 2017 No Limit Hold'em (Event #63) $1,000
Jul 5 - 8, 2017 Pot Limit Omaha - High Roller (Event #67) $25,000
Jul 6 - 8, 2017 Razz (Event #69) $1,500
Jul 7, 2017 No Limit Hold'em - WSOP.com Online Championship (Event #71) $1,000
Jul 7 - 8, 2017 No Limit Hold'em - Ladies Championship (Event #70) $1,000
Jun 2 - 5, 2017 No Limit Hold'em - High Roller for One Drop (Event #6) $111,111
Jul 8 - 22, 2017 No Limit Hold'em - Main Event Championship (Event #73) $10,000
Jul 11 - 15, 2017 No Limit Hold'em - The Little One for One Drop (Event #74) $1,000 + 111
1st Nipun Java	 $75,318	 — —
1st Aditya Sushant	 $75,319	 — —
2nd David Guay	 $46,537	 — —
2nd Pablo Mariz	 $46,537	 — —
3rd Michael Semenov	 $32,595	 — —
3rd Kiryl Radzivonau	 $32,595	 — —
4th Georgios Zisimopoulos	 $23,159	 — —
4th Charalampos "Babis" Lappas	 $23,159	 — —
5th Mukul Pahuja	 $16,696	 — —
5th Jonas Wexler	 $16,695	 — —
6th Esther "ETAY" Taylor	 $12,215	 — —
6th DJ MacKinnon	 $12,215	 — —
7th Samantha Cohen	 $9,072	 — —
7th Ryan Laplante	 $9,071	 — —
8th Austin Buchanan	 $6,840	 — —
8th Lanie Foster	 $6,840	 — —
9th James Gibson	 $3,492	 — —
9th Rafael Lopez	 $3,492	 — —
9th Joseph Choueiri	 $3,491	 — —
10th Joe Tehan	 $4,074	 — —
10th Benton Blakeman	 $4,074	 — —
11th Barry Shulman	 $2,716	 — —
11th Allyn Jaffrey Shulman	 $2,716	 — —
11th Jessica Horan	 $2,716	 — —
12th Ramon Bartsch	 $2,037	 — —
12th Brian McCann	 $2,037	 — —
12th Dimitry Novek	 $2,037	 — —
12th Jan Bruhns	 $2,037	 — —
13th Ryan Hughes	 $3,220	 — —
13th Ben Landowski	 $3,219	 — —
14th Deepinder Singh	 $3,219	 — —
14th John Hulett	 $3,220	 — —
15th Clayton Kalisek	 $3,220	 — —
15th Joseph Kalisek	 $3,219	 — —
16th Morgan Davies	 $2,586	 — —
16th Daniel Dawson	 $2,586	 — —
17th Michael Bartalotta	 $1,724	 — —
17th Justus Marsico	 $1,724	 — —
17th AJ Gillette	 $1,724	 — —
18th Eric Polerecky	 $1,293	 — —
18th David Barnett	 $1,293	 — —
18th Louis Diesch	 $1,293	 — —
18th Matthew Diesch	 $1,293	 — —
19th John Green	 $1,408	 — —
19th William McClain	 $1,407	 — —
19th Jake Abdalla	 $1,408	 — —
20th John "Hank" Sitton	 $1,408	 — —
20th Heather Landay	 $1,408	 — —
20th Nathan Dowland	 $1,407	 — —
21st Thomas Zanot	 $2,112	 — —
21st Gregory Milliron	 $2,111	 — —
22nd Brian Yoon	 $2,112	 — —
22nd Michael Gagliano	 $2,111	 — —
23rd Riley Fuller	 $2,112	 — —
23rd Keith Ingham	 $2,111	 — —
24th Matthew Wakeman	 $2,111	 — —
24th Thomas Miller	 $2,112	 — —
25th Donald Otto	 $2,111	 — —
25th John Volpe	 $2,112	 — —
26th Alison Senycz	 $2,112	 — —
26th John Senycz	 $2,111	 — —
27th Jason Bolte	 $2,112	 — —
27th James Davis	 $2,111	 — —
28th Maksim Semisoshenko	 $1,753	 — —
28th Konstantin Maslak	 $1,753	 — —
29th Christopher Godfrey	 $1,169	 — —
29th Shane Abbott	 $1,168	 — —
29th Joel Micka	 $1,169	 — —
30th Terry Grimes	 $1,753	 — —
30th Yuliya Makarova	 $1,753	 — —
31st Blair Miller	 $1,169	 — —
31st Steven Palmer	 $1,168	 — —
31st Jamie Kerstetter	 $1,169	 — —
32nd Daniel Healey	 $1,753	 — —
32nd Thomas Kearney	 $1,753	 — —
33rd Daniel Thomas	 $1,753	 — —
33rd Michael Sortino	 $1,753	 — —
34th James Rann	 $1,753	 — —
34th Andrew Hedley	 $1,753	 — —
35th Aron Dermer	 $1,169	 — —
35th Jeremy Williams	 $1,168	 — —
35th David Harmon	 $1,169	 — —
36th Nathaniel Janda	 $1,753	 — —
36th Darren Wong	 $1,753	 — —
37th Brian Pinkus	 $1,481	 — —
37th Michael Pinkus	 $1,480	 — —
38th Sheng Ye	 $1,481	 — —
38th Federico Butteroni	 $1,480	 — —
39th Daniel "DJ" Buckley	 $1,480	 — —
39th Ryan Hartman	 $1,481	 — —
40th Paul Balzano	 $1,481	 — —
40th Devin Shalmi	 $1,480	 — —
41st Kevin Eyster	 $1,481	 — —
41st Andrew Bulliard	 $1,480	 — —
42nd Rodolfo Avalos	 $987	 — —
42nd Thomas Wheeler	 $987	 — —
42nd Douglas Foust	 $987	 — —
43rd Randy Gonzales	 $1,481	 — —
43rd Rick Schwartz	 $1,480	 — —
44th Anthony Leshnack	 $1,481	 — —
44th Justin Priscilla	 $1,480	 — —
45th Antonio Miramontes	 $741	 — —
45th Raymond Ho	 $741	 — —
45th Adam Volen	 $740	 — —
45th Peter Hengsakul	 $740	 — —
46th David Novak	 $1,272	 — —
46th Aditya "Intervention" Agarwal	 $1,272	 — —
47th Jennifer Miller	 $1,272	 — —
47th Ricardo Alvarado	 $1,272	 — —
48th Aaron Mccormack	 $848	 — —
48th Cy Williams	 $848	 — —
48th Peter Lewis	 $848	 — —
49th Theresa Juliusson	 $1,272	 — —
49th Ronald Juliusson	 $1,272	 — —
50th Robert Brown	 $848	 — —
50th Kelly Webb	 $848	 — —
50th Larry Gurney	 $848	 — —
51st Nicholas Marsh	 $1,272	 — —
51st Amanda Hruska	 $1,272	 — —
52nd Jacob Miller	 $1,272	 — —
52nd Joshua Abady	 $1,272	 — —
53rd Andrew Winkler	 $848	 — —
53rd Robert Ettore	 $848	 — —
53rd Bruno "Da Butcher" Fiorenza	 $848	 — —
54th Sean Dower	 $1,272	 — —
54th Mark Stenger	 $1,272	 — —
55th Blake Bohn	 $1,112	 — —
55th Aalok Arora	 $1,113	 — —
56th James Cavanaugh	 $1,113	 — —
56th Garrett Greer	 $1,112	 — —
57th Unknown Player	 $1,112	 — —
58th Maria Ho	 $742	 — —
58th Philipp Zukernik	 $741	 — —
58th Rainer Kempe	 $742	 — —
59th Timothy Rhoda	 $1,112	 — —
59th Melanie Banfield	 $1,113	 — —
60th Travis Maly	 $556	 — —
60th Joshua Williamson	 $556	 — —
60th Eric Maier	 $557	 — —
60th David Skilling	 $556	 — —
61st Vernon Bigham	 $1,113	 — —
61st Christopher Capone	 $1,112	 — —
62nd Benjamin Yu	 $1,113	 — —
63rd Vini Bjazevich	 $1,112	 — —
63rd Franklin Connell	 $1,113	 — —
64th Chris Back	 $990	 — —
64th Aaron Durzak	 $991	 — —
65th Jose Andres Guzman	 $990	 — —
65th David Garcia	 $991	 — —
66th John Hauskins	 $990	 — —
66th Eric Cain	 $991	 — —
67th Steven Thompson	 $990	 — —
67th Jose Severino	 $991	 — —
68th Jonathan Harrington	 $991	 — —
69th Daniel Ott	 $990	 — —
69th Dillon Ott	 $991	 — —
70th Gaurav Raina	 $990	 — —
70th Nicholas Salimbene	 $991	 — —
71st Fred Goff	 $990	 — —
71st Fredrick Goff	 $991	 — —
72nd James Eads	 $496	 — —
72nd William Fierro	 $495	 — —
72nd Chase Reynolds	 $495	 — —
72nd Christian Larsen	 $495	 — —
73rd Ivaylo Mitrev	 $898	 — —
73rd Daniel Raiff	 $898	 — —
74th Stephen Hawley	 $449	 — —
74th Christopher Holbrook	 $449	 — —
74th Brian Dryer	 $449	 — —
74th Spencer Chasteen	 $449	 — —
75th Stephen Dees	 $898	 — —
75th James Kinney	 $898	 — —
76th Joseph Ogden	 $599	 — —
76th Nicholas Hart	 $599	 — —
76th Richard Humphrey	 $598	 — —
77th Vincent Moscati	 $898	 — —
77th Kyle Cartwright	 $898	 — —
78th Matthew Wantman	 $898	 — —
78th Asher Conniff	 $898	 — —
78th William Alex Foxen	 $598	 — —
79th Terry Schumacher	 $898	 — —
79th Laurent Manderlier	 $898	 — —
80th Leyla Rogers	 $599	 — —
80th Jon "PearlJammed" Turner	 $599	 — —
80th Steve McNally	 $598	 — —
81st Andy Bloch	 $898	 — —
81st Chris "Jesus" Ferguson	 $898	 — —
82nd Peter Morris	 $830	 — —
82nd Alfred Giles	 $829	 — —
83rd Roger Matfeld	 $415	 — —
83rd Gerd Schumacher	 $415	 — —
83rd Volker Zimmer	 $414	 — —
83rd Jochen Pfeifer	 $414	 — —
84th Damien Dreyer	 $553	 — —
84th Larry Serebryany	 $553	 — —
84th Michael S Harris	 $553	 — —
85th Douglas Carli	 $829	 — —
85th Benjamin Carli	 $830	 — —
86th Michael Pariso	 $414	 — —
86th Stuart Marshak	 $415	 — —
86th Lisa Hamilton	 $415	 — —
86th Scott Bohlman	 $414	 — —
87th Park Yu "Sparrow" Cheung	 $830	 — —
87th Lee Wai Kiat	 $829	 — —
88th Jose "Nacho" Ignacio Barbero	 $830	 — —
88th Nick Yunis	 $829	 — —
89th Arthur Goltz	 $415	 — —
89th Andrew Hangarter	 $415	 — —
89th Jeffrey Daniels	 $414	 — —
89th Nicholas Gibson	 $415	 — —
90th Jacqueline Bailey	 $553	 — —
90th Tom "Captain" Franklin	 $553	 — —
90th Timothy Burt	 $553	 — —
91st Jorden Fox	 $390	 — —
91st Mark Cohen	 $391	 — —
91st Levi Fox	 $391	 — —
91st Yosef Fox	 $390	 — —
92nd Jeffrey Mulder	 $781	 — —
92nd Kevin "ImALuckSack" MacPhee	 $781	 — —
93rd Adrian Buckley	 $781	 — —
93rd Cosima "Mina" Greco	 $781	 — —
94th Jeffrey Berneathy	 $390	 — —
94th Benjamin Kantor	 $391	 — —
94th Andrew Adelson	 $390	 — —
94th Tyler Young	 $391	 — —
95th Matthew Lambrecht	 $781	 — —
95th Cody Wiegmann	 $781	 — —
96th Bryan Rosen	 $781	 — —
96th Michael Spiegel	 $781	 — —
97th Luke Yerby	 $781	 — —
97th Jay Yerby	 $781	 — —
98th Jonathan Gilliam	 $781	 — —
98th Daniel Aviles	 $781	 — —
99th Todd Brunson	 $390	 — —
99th Matt Glantz	 $390	 — —
99th Robert Mizrachi	 $391	 — —
99th Michael "The Grinder" Mizrachi	 $391	 — —
100th Michael Lech	 $749	 — —
100th Darius Tamulevicius	 $750	 — —
101st Adam Bromley	 $750	 — —
101st Natalie Bromley	 $749	 — —
102nd Michael Souza	 $749	 — —
102nd Leo Gianulis	 $750	 — —
103rd Alexandre Blanc	 $749	 — —
103rd Remi Blanc	 $750	 — —
104th Ralph Smith	 $749	 — —
104th Denny Axel	 $750	 — —
105th Barny Boatman	 $750	 — —
105th John "Mr Big" Duthie	 $750	 — —
106th Zachary Pierce	 $749	 — —
106th John Pierce	 $750	 — —
107th Bradley Rhodes	 $750	 — —
107th Aaron Steury	 $749	 — —
108th Thomas Woolums	 $500	 — —
108th Mason Moore	 $499	 — —
108th Robert Covert	 $500	 — —
109th Timothy Jurkiewicz	 $499	 — —
109th Christoph Brand	 $500	 — —
109th Zachary Gruneberg	 $500	 — —
110th Josh Lohrke	 $749	 — —
110th Bryan Berc	 $750	 — —
111th Tony Cheng	 $375	 — —
111th Thai Ha	 $374	 — —
111th Marc Goldhaber	 $375	 — —
111th Wen Shu Zhang	 $375	 — —
112th Valentin Vornicu	 $750	 — —
113th Alexis Gavin	 $749	 — —
114th Terrance Eischens	 $749	 — —
114th Chris Dombrowski	 $750	 — —
115th David Finkelstein	 $499	 — —
115th Harry Frankel	 $500	 — —
115th Thomas Mcardle	 $500	 — —
116th Ryan McNeel	 $750	 — —
116th Saya Ono	 $749	 — —
117th Xu Jin Zhu	 $499	 — —
117th Meng Lu	 $500	 — —
117th Cheng Dong	 $500	 — —
118th Florencio Acevedo	 $750	 — —
118th Brad Sailor	 $749	 — —
119th Greg McCurry	 $750	 — —
119th Kurt Jewell	 $749	 — —
120th Hui "Kitty" Chen-Kuo	 $750	 — —
120th Russell Thomas	 $749	 — —
121st Robin Wasserbauer	 $374	 — —
121st Daniel Schausberger	 $375	 — —
121st Markus Ganglbauer	 $375	 — —
121st Peter Hanke	 $375	 — —
122nd Matthew Kaplan	 $750	 — —
122nd Robert Miller	 $749	 — —
123rd Lisa Costello	 $749	 — —
123rd Anthony Gargano	 $750	 — —
124th Thomas Lindell	 $749	 — —
124th Jay Dagnenica	 $750	 — —
125th Brian Breidenbach	 $749	 — —
125th Michael Marek	 $750	 — —
126th Jesse James Sylvia	 $749	 — —
126th Ashley Sleeth	 $750	 — —
127th Steven Penner	 $374	 — —
127th Blair Miller	 $375	 — —
127th Doug Polk	 $375	 — —
127th Ryan Fee	 $375	 — —


text:
class QtWebThreadController : public QObject
{
        Q_OBJECT
    public:
        explicit QtWebThreadController(QObject *parent = 0);

    Q_SIGNALS:
        void connectionToHandle();
};

#endif // QTWEBTHREADCONTROLLER_H

redpajama_set_name: RedPajamaGithub


text:
Graphplan is an algorithm for automated planning developed by Avrim Blum and Merrick Furst in 1995. Graphplan takes as input a planning problem expressed in STRIPS and produces, if one is possible, a sequence of operations for reaching a goal state.

The name graphplan is due to the use of a novel planning graph, to reduce the amount of search needed to find the solution from straightforward exploration of the state space graph.

In the state space graph:
 the nodes are possible states,
 and the edges indicate reachability through a certain action.

On the contrary, in Graphplan's planning graph:
 the nodes are actions and atomic facts, arranged into alternate levels,
 and the edges are of two kinds:
 from an atomic fact to the actions for which it is a condition,
 from an action to the atomic facts it makes true or false.
the first level contains true atomic facts identifying the initial state.

Lists of incompatible facts that cannot be true at the same time and incompatible actions that cannot be executed together are also maintained.

The algorithm then iteratively extends the planning graph, proving that there are no solutions of length l-1 before looking for plans of length l by backward chaining: supposing the goals are true, Graphplan looks for the actions and previous states from which the goals can be reached, pruning as many of them as possible thanks to incompatibility information.

A closely related approach to planning is the Planning as Satisfiability (Satplan). Both reduce the automated planning problem to search for plans of different fixed horizon lengths.

References

A. Blum and M. Furst (1997). Fast planning through planning graph analysis. Artificial intelligence. 90:281-300.

External links

Avrim Blum's Graphplan home page
PLPLAN: A Java GraphPlan Implementation
NPlanner: A .NET GraphPlan Implementation
Emplan and JavaGP: C++ and Java implementations of Graphplan
MIT OpenCourseWare lecture on GraphPlan and making planning graphs
Python/SQL Courses

Automated planning and scheduling
Search algorithms

redpajama_set_name: RedPajamaWikipedia


text:
Хуан Цзюйцай (*黃居寀, 933 —993) — китайський художник часів царства Пізня Шу та династії Сун.

Життєпис
Народився у 933 році у м. Ченду (сучасна провінція Сичуань). Був молодшим сином відомого художника Хуан Цюаня. Від нього отримав основу художнього майстерності. Згодом Хуан Цзюйцай працював при дворі володаря царства Пізня Шу Мень Чана. У 965 році цю державу було захоплено арміями сун. Незабаром після цього Хуан Цзюйцая перевозять до Кайфена. Тут він стає придворним художником сунських імператорів — Тайцзу та Тай-цзуна. Водночас зробити чудову службову кар'єру — отримує посаду дайчжао («чекаючий імператорських вказівок»), члена Академії живопису (Хуа-юань). Помер у Кайфені у 993 році.

Творчість
Працював у жанрі «квіти і птахи». Наслідував стилю свого батька, який вдосконалив й розвинув. Його роботи характеризуються яскравістю, виточеністю, безперервним контуром, дещо увігнутим, використання тіней, підкресленням об'єктів. Хуан Цзюйцай сприяв народженю академічного стилю живопису епохи Північна Сун. Найвідомішими творами художника є сувій «Фазан та дрібні птахи біля зізіфуса», «Горобці грають в очереті», «Папуга на гілці персикового дерева», «Дві білих квітки камелії і пташка на гілці», «Фазани і колючі чагарники».

Джерела
 Laing E. J. The Development of Flower Depiction and the Origin of the Bird-and-Flower Genre in Chinese Art//Bulletin of the Museum of Far Eastern Antiquities. Stockholm. 64 (1992)

Китайські художники


text:
Home Local News Stolen Vehicle Recovered, Suspects Arrested
Stolen Vehicle Recovered, Suspects Arrested
Source: BPS News Release
On March 6, 2022, at 10:00 pm, police located the stolen red Chevrolet Cobalt parked in the 300 block of 18th street N. Suspects had removed the licence plate, and replaced it with a different stolen licence plate, but police were able to verify it was the stolen vehicle from the VIN number.
Further investigation led police to locate and arrest two suspects nearby. One of the suspects, a 42-year-old male, was found with the keys from the stolen vehicle in his possession. He was later released and will appear in court on May 2, 2022 on charges of Possession of Property Obtained by Crime, and Fail to Comply with Release Order. The second suspect, a 43-year-old female was also released to appear in court on May 2, 2022 on a charge of Possess Property Obtained by Crime
Original release from March 2, 2022 –
On March 1, 2022, police received a report of a stolen vehicle from the 700 block of 10th street. The suspect stole the vehicle, which was left running and unattended shortly after 9:00 pm. The vehicle is described as a red Chevrolet Cobalt with Manitoba licence KTW633.
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redpajama_set_name: RedPajamaCommonCrawl


Nehemiah was a gifted leader who lived around 425 BC. As Jerusalem lay in ruins he rallied his people together to rebuild the walls of the great city. In doing so though he also helped rebuild their hearts and minds to follow God. Using Scripture, Nehemiah would build the people up spiritually to help them learn to turn to God for their ultimate source of help and wisdom. There is much to learn from this intriguing and action-packed book, so join us as we journey through Nehemiah.


text:
News 01 Oct 2019
The Band / 50th anniversary reissue
Super deluxe box • 5.1 surround mix • New stereo mix • Previously unreleased bonus tracks • 2LP vinyl • 2CD deluxe
Universal Music will reissue The Band's self-titled second album for its 50th anniversary. Three physical editions are on offer, including a six-disc super deluxe box set with a 5.1 surround mix.
The super deluxe edition of the 1969 album consists of two CDs, a blu-ray audio, a 2LP vinyl set and a bonus seven-inch single. Like with last year's Music From Big Pink reissue, Bob Clearmountain has created a new stereo mix of The Band album and this features on the box is various places including the first CD and the 2LP vinyl.
The first disc also features six previously unreleased bonus tracks, while the seven studio bonus tracks previously issued in 2000 are also included on the second CD after a Live at Woodstock performance.
The blu-ray audio includes a 5.1 surround sound mix and a hi-res stereo mix of the album (the latter is presumably the new stereo mix). In addition the six bonus tracks from the first CD are also included and mixed to 5.1.
The box concludes with a 2LP black vinyl pressing of The Band, along with a seven-inch single that features 'Rag Mama Rag' b/w 'The Unfaithful Servant'.
A 2LP black vinyl edition of the new stereo mix will also be available, along with a 2CD deluxe that is effectively discs one and two from the big box.
This set has been overseen by Robbie Robertson and will be released on 15 November 2019.
The Band - super deluxe box
Amazon de 100.88 Order
Amazon usa 112.95 Order
Amazon fr 129.4 Order
Amazon es 102.63 Order
Amazon ca 158 Order
Amazon jp 11976.00 Order
JPC de 135.99 Order
the SDE shop uk 89.99 pre-order
The Band - 2LP vinyl
Amazon it 28.8 Order
The Band - 2CD deluxe
Amazon uk 9.46 Order
Amazon fr 9.99 Order
Disc 1 (CD)
The Band new stereo mix
1. Across The Great Divide
2. Rag Mama Rag
3. The Night They Drove Old Dixie Down
4. When You Awake
5. Up On Cripple Creek
6. Whispering Pines
7. Jemima Surrender
8. Rockin' Chair
9. Look Out Cleveland
10. Jawbone
11. The Unfaithful Servant
12. King Harvest (Has Surely Come)
13. Up On Cripple Creek (Earlier Take) *
14. Rag Mama Rag (Alternate Version) *
15. The Unfaithful Servant (Alternate Version) *
16. Look Out Cleveland (Instrumental Mix) *
17. Rockin' Chair (A Cappella / Stripped Down) *
18. Up On Cripple Creek (Instrumental Mix) *
Live At Woodstock (1969)
1. Chest Fever
2. Tears Of Rage
3. We Can Talk
4. Don't Ya Tell Henry
5. Baby Don't You Do It
6. Ain't No More Cane On The Brazos
7. Long Black Veil
8. This Wheel's On Fire
9. I Shall Be Released
10. The Weight
11. Loving You Is Sweeter Than Ever
Studio Bonus Tracks (from 2000 reissue)
12. Get Up Jake (Outtake – Stereo Mix)
13. Rag Mama Rag (Alternate Vocal Take – Rough Mix)
14. The Night They Drove Old Dixie Down (Alternate Mix)
15. Up On Cripple Creek (Alternate Take)
16. Whispering Pines (Alternate Take)
17. Jemima Surrender (Alternate Take)
18. King Harvest (Has Surely Come) (Alternate Performance)
Disc 3 (Blu-ray audio)
1. Across The Great Divide (Stereo and 5.1 Surround)
2. Rag Mama Rag (Stereo and 5.1 Surround)
3. The Night They Drove Old Dixie Down (Stereo and 5.1 Surround)
4. When You Awake (Stereo and 5.1 Surround)
5. Up On Cripple Creek (Stereo and 5.1 Surround)
6. Whispering Pines (Stereo and 5.1 Surround)
7. Jemima Surrender (Stereo and 5.1 Surround)
8. Rockin' Chair (Stereo and 5.1 Surround)
9. Look Out Cleveland (Stereo and 5.1 Surround)
10. Jawbone (Stereo and 5.1 Surround)
11. The Unfaithful Servant (Stereo and 5.1 Surround)
12. King Harvest (Has Surely Come) (Stereo and 5.1 Surround)
13. Up On Cripple Creek (Earlier Version) (Stereo and 5.1 Surround)
14. Rag Mama Rag (Alternate Version) (Stereo and 5.1 Surround)
15. The Unfaithful Servant Alternate Version) (Stereo and 5.1 Surround)
16. Look Out Cleveland (Instrumental Mix) (Stereo and 5.1 Surround)
17. Rockin' Chair (A Cappella / Stripped Down) (Stereo and 5.1 Surround)
18. Up On Cripple Creek (Instrumental Mix) (Stereo and 5.1 Surround)
Disc 4 (The Band vinyl LP) The Band new stereo mix
3. Look Out Cleveland [Side A]
4. Jawbone
5. The Unfaithful Servant
6. King Harvest (Has Surely Come)
Disc: 6 (seven-inch single)
1. Rag Mama Rag (Side A, Original 1969 7″ Capitol Single)
2. The Unfaithful Servant (Side B, Original 1969 7″ Capitol Single)
The Band / 2CD deluxe
The Band 2LP vinyl
The Band / Stage Fright 50th anniversary reissue
Box set, 2CD and vinyl LP • New Bob Clearmountain remixes
David Bowie / Conversation Piece review
SDE takes a close look at the new box set and comes away impressed
Frank Zappa / Hot Rats Sessions box
Frank Zappa's second album Hot Rats is being reissued for its 50th anniversary and…
The Beatles / Abbey Road reissued for its 50th anniversary across six formats
3CD+blu-ray box • 3LP vinyl • 2CD deluxe • vinyl picture disc • 5.1 & Dolby Atmos surround mixes • Two discs of outtakes in both CD and vinyl sets


Great news for McLean Hamlet home owners! The home at 8113 Birnam Wood Drive has sold for $1,1600,000. The sale price should move the price point higher for home sales in the McLean Hamlet, as this home lacked renovations that most high priced homes feature. The home featured hardwood floors throughout and large room sizes, but it had not been renovated in key rooms such as the kitchen or master suite. As a matter of fact, this home had many original elements in it, an unfinished basement, dated kitchen cabinets, bathroom floors of inch colored tile, and wallpaper in the two-story foyer. Many recent homes sold in the Hamlet at this price feature new kitchens with top of the line appliances, fine cabinetry, and granite counters, or master suites that have been renovated with tile and glass enclosed steam-showers, and master closets with built in shelves and drawers. Yet, the buyers of this home paid above list price and were represented by a buyer broker experienced in the neighborhood, so indications are strong for prices to trend upward in the Hamlet.


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How the CPA Examination Is Changing
Jan 12, 2022 | Education, HR/Talent, Training
In 2021, the National Association of State Boards Accountancy (NASBA) and the American Institute of CPAs (AICPA) announced a joint effort to remodel the Uniform CPA examination.
The effort is fueled by changing technology and the drive for CPAs to adapt to the dynamic needs of businesses. Changes to the Uniform CPA examination will take effect in January 2024.
The CPA Evolution Initiative instigated by NASBA and the AICPA found a number of gaps between standard accounting curriculums and the needs of businesses.
For example, companies have found that knowledge of traditional IT concepts such as cybersecurity, data analytics, and IT governance are increasingly relevant in today's accounting workforce. Therefore, both NASBA and the AICPA are pushing universities to include these topics in their accounting courses.
The Current Uniform CPA Exam
Under the current Uniform CPA Exam, four topics are covered in separate 4-hour testing windows. These topics include:
Auditing and Attestation (AUD)
Business Environment and Concepts (BEC)
Financial Accounting and Reporting (FAR)
Regulation (REG)
The examination is available in approved testing locations throughout the United States and around the world. Testing windows occur during the first two months of each quarter. If a candidate fails an exam in one quarter, they must wait until the following quarter to retake the test.
Once all four tests are passed, the candidate must meet additional requirements set forth by their state accounting board to become a fully licensed CPA. Those requirements typically include a set number of educational hours, usually between 120 and 150 hours of university-level courses. There may also be a set number of accounting-related courses that must be passed.
In addition to the academic requirements, there are usually a number of years of experience in an accounting position that must be attained before a license will be granted. Experience must be obtained under the supervision of a licensed CPA.
Future Uniform CPA Exams
While the AICPA and NASBA have not yet released the full scope of changes to the Uniform CPA exam, it is expected that there will be changes to the content of the tests. In particular, you can expect a Core + Discipline model. This will result in three key core tests and a choice of a discipline. The three core tests will include the following:
In addition to the three core tests, CPA candidates will need to select a discipline for their final test. Disciplines can include any one of the options below:
Business Analysis and Reporting (BAR)
Information Systems and Controls (ISC)
Tax Compliance and Planning (TCP)
Currently, the AICPA and NASBA are working to understand the types of skills and knowledge that CPAs will need. Once they have decided upon those skills, the test will be adapted to cover the requisite topics.
Universities will need to change their current curriculums to remain competitive and meet the needs of aspiring CPA candidates.
Business Analysis and Reporting
The Business Analysis and Reporting discipline will be encouraged for accountants who are interested in financial reporting, operations management, and assurance or advisory services.
Content will likely focus on financial planning and risk management, assessment of revenue recognition, and hedges or business combinations.
Information Systems and Controls will focus on IT-related concepts, such as business processes, information security and governance, and IT audits.
Anticipated content includes a focus on network security, software access, and information system security from an accounting and business perspective.
Tax Compliance and Planning
The Tax Compliance and Planning discipline will be a continuation of the tax core exam, but will cover additional advanced topics such as individual and entity tax compliance. Other potential subject matters include entity planning, multijurisdictional taxation, and liquidation of business entities.
With more companies expanding overseas, this discipline may cover certain international taxation concepts, as well.
Transition Period for the Uniform CPA Exam
If you are currently studying for the Uniform CPA exam and plan to pass all four sections prior to January 2024, your path to the CPA license will not change.
If you are unable to pass all four sections prior to January 2024, you may proceed under the old examination structure if you have passed at least one of the prior exams. However, this transition period will likely be limited.
Final Thoughts on the New Uniform CPA Exam
While the exact nature and content of the new exams won't be known for at least a few months, you can expect to see some significant changes. Both NASBA and the AICPA will work hand in hand with universities to ensure that they incorporate new content into their accounting curriculums.
You can also expect course providers who assist CPA candidates in studying for the CPA exam to update their content to fit the new topics. The most common CPA course providers include Becker CPA Review, UWorld Roger CPA Review, and Gleim CPA Review. All three have indicated that their exam preparation materials will be updated to meet the changes to the new Uniform CPA examination.
Learn More about CPA Examinations in Our Community
Looking to learn more about CPA examinations? Controllers Council is a national community and platform of Controllers, Accounting and Finance professionals focused on accounting best practices, information and resources, recognition and networking. Membership has many features and benefits to propel your career and expertise, and to be an active participant in our exciting community. The Controllers Council Forum allows members to pose questions about technology and other topics. Become a member today.


This Microsoft Volume Licensing exam was launched in November 2017. If you need an overview of the 70-705 exam then you can find Microsoft's official exam page here.
We have a range of resources to help you to prepare for and pass the 70-705 exam which you can read about below, and if you want to be kept up to date with new resources as we release them and other news about the 70-705 exam then subscribe to our dedicated mailing list below.
We offer both online and on-site training courses to make sure you're in the best possible position to pass the 70-705 exam.
Contact info@licensingschool.co.uk if you would like to discuss running a course for your organisation.
Take our FREE Taster Test – coming soon!


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Business Survey: High Freight Costs Raising Prices | National Review
Posted By: Tony Beasley December 9, 2021
Logistics company Freightos conducted a survey of over 300 importers who use its services. They sent the first survey in January, another in June, and the most recent one was from November. It's not a scientific survey, so results can't be generalized to the whole country. But it gives a useful perspective on how businesses are responding to supply-chain challenges.
Here are some of the results:
In January 77% of respondents answered that they've encountered supply chain challenges since the pandemic began and in June 79% answered the same. However, in our most recent survey, nearly all respondents (93%) reported experiencing supply chain difficulties.
In January and June, less than half of importers reported raising prices on their goods in response to higher freight costs, while in November 64% of importers increased prices.
In November's survey, nearly a third of businesses who responded that they recently raised prices did so by more than 20%, compared to only a fifth of businesses who reported similar price increases in June.
We found that pre-pandemic, ocean shipping costs per unit for smaller items ranged from $0.30 to $0.40, or about half a percent of the sticker price.
But elevated freight rates have pushed costs to $4-5 per unit. Even with increased sticker prices, ocean shipping contributions have climbed to 5% of the current inflated price tags.
For bulkier items like large TVs, per-unit freight costs climbed from $3.66 to more than $48 and from 1.2% to more than 8% of the consumer price. This explains why more businesses are raising prices even higher than earlier in the year.
Compared to large businesses, small importers were twice as likely (36% vs. 17%) to have reduced their margins to accommodate rising costs. They were also less likely to have benefited from an increase in demand for their products (55% vs. 68%) and were twice as likely to be shipping less volume than before the pandemic (39% vs. 16%), mostly due to rising shipping costs (80%).
Check out the full write-up from Freightos.com here.
#Business #Survey #High #Freight #Costs #Raising #Prices #National #Review
Nick Wright: At worst LeBron is the second best player in the league, we've never seen anything like him I THE HERD
First Things First Host Nick Wright joins Colin Cowherd to discuss the greatness of Los Angeles Lakers All-Star LeBron James in his 19th season. Nick…
Ric Bucher on Lakers-Westbrook: The issue is that you can't win with him, but will he contribute differently? I UNDISPUTED
Chicago Drivers Get Speeding Tickets Every Eleven Seconds | National Review
Bioethicists OK Human Extinction to Eliminate Suffering | National Review
Biden Withdraws Nomination of Former Agent to Head ATF


As a Realtor in Ottawa for more than 30 years, I often find myself working with clients who are new to our city and have asked for help in buying a home.
Article 13 is a new piece of legislation passed in the European Union Parliament. The new law has a significant impact on the way copyright is administered in the digital space.
The high tech sector in Ottawa is thriving. Tech companies are once again dominating the business landscape.
Are you a new, or perhaps confused, business owner who isn't clear on what Canada Revenue Agency (CRA) requires at tax time?
Growing a strong and relevant corporate culture today means making some bold moves - and one of the highest impact ways to do this is by cultivating safety and trust in the workplace.


Today's guest just brings the biggest smile to my face and heart - artist, creative entrepreneur and self-proclaimed Mandala Magic Geometer, Julie Gibbons. My response to this whole conversation internally was, yes yes yes.
You can visit Julie RIGHT HERE.
A mandala journey to the sacred heart of you, this workshop invites you to undertake an artful self-discovery quest from the comfort of your creative space! We shall begin by creating the most basic of all mandalas, the circle, and bring it into physical form by way of a mandala disc. Our next task will be to seek out our symbolic nature by means of some journaling, before weaving this colourful fabric back into the welcoming embrace of the mandala. Completing our adventure together, we will activate the mandala magic in some unexpected ways.
For more Holistic Creative Chats, go HERE.
Join the Holistic Creative mailing list, to receive insider peeks + musings + updates + special offers for your Holistic Creative discovery, right in your inbox, 1-2 x per month.


Beauty surgical treatment is getting to be more and far more well-known by the day and the advantages of this medical procedures are widely accepted by one particular and all. Hundreds of thousands of individuals both males and girls endure this surgical procedure every single yr. Plastic surgery can change almost any element of your bodily look. This is exactly why it performs an crucial position in developing self esteem and helping individuals regain self-confidence specially if the surgical treatment was carried out for medical factors. Apart from that, if the surgical treatment is done for aesthetic charm, it will help in creating a optimistic frame of mind and improves self esteem too.
For some people, undergoing beauty medical procedures is vital to enhancing self-assurance amounts. At times, you stay with a bodily characteristic that you want was diverse and want to change it to improve your general aesthetic charm. A easy surgical procedure can support you restore it to standard and give you the self confidence to wander with it. If it is a recognizable deformity, there is all the much more reason to endure a medical procedures to appropriate it.
For individuals obtaining overall health problems because of to a deformity and many others. that is bothering them, it gets all the far more critical that the surgical procedure be carried out. For example a nose work could help reduce the signs and symptoms of sinus and removal of breast tissue can greatly minimize the prospective of cancer.
Like any other surgical procedure, this surgery ought to not be taken lightly. Likely difficulties exist in this variety of medical procedures as well. A single main drawback of this surgery is that it requires all around six months to recover and see the final results of the treatment. Some clients encounter the adverse effects of the anesthesia used and some may well produce bacterial infections on the web site of incision. The even bigger the procedure, the greater the threat of issues in the course of surgery so, make confident that your adhere to the doctor's recommendations and in no way skip a adhere to up appointment.
The most important element of a cosmetic surgery is that you need to established your anticipations right. The surgical procedure may possibly not always flip out the way you imagine. Most typically, the dilemma is with the expectations and not with the surgical treatment. It is essential to established practical anticipations from a surgery. Unrealistic expectations these kinds of as anticipating to look like Cosmetic Surgery Directory The Bronx after the operate is carried out can be a fantastic established back again. So, make positive you discuss about your surgery with your medical doctor and realize all the implications of what to assume and what not to.
The most essential component of plastic surgery is the restoration time. You need to program your time to mend completely and be witnessed in community once again. The therapeutic time differs from patient to affected person and the type of treatment carried out.
Whether you are undergoing a huge surgical method or a straightforward 1 to erase some wrinkles, to come to feel youthful, make confident that you discuss to a certified surgeon and discuss the achievable outcomes and difficulties prior to going through surgical treatment.


List of Macclesfield based printers offering colour digital photo and business printing services - cards, brochures, flyers & leaflets.
For the highest quality of printing and individual design at a reasonable price. For a superb selection of office stationery, supplies and personal stationery products. For the best quality mono & colour Photocopying and Digital Print in the Macclesfield area. For excellent deals on all office equipment, computers and consumables.
We are based in Stockport, Cheshire in the North West of England and are one of the UK's leading designers, manufacturers and suppliers of a wide range of cardboard point of sale packaging including, skin pack boards, blister pack cards, folding cartons and our own environmentally friendly patented PeelAway skin boards.
A quality Printer, based in the North West. A company with a wealth of experience and the equipment to get the job done right. Knowledge and expertise across a host of services including; 5 & 6 Colour Heidelberg printing presses; Direct Mail; Digital and Web-to-Print Solutions. Account Managers who know what they're talking about but who can listen as well as talk.
R.A. Smart has over 30 years experience supplying screenprint and digital equipment to the Graphics and Textile Industries. With the customer brief as our focus, we can offer a complete bespoke turnkey solution for any Screenprint or Digital Print application, from a small design house or an educational facility, through to a complete industrial installation.


text:
List of The Simple Life episodes
Airline (1982 TV series)
An airline is a company that provides air transport services for traveling passengers and freight. Airlines lease or own their aircraft with which to supply these services and may form partnerships or alliances with other airlines for mutual benefit. Generally, airline companies are recognized with an air operating certificate or license issued by a governmental aviation body.
Airlines vary from those with a single aircraft carrying mail or cargo, through full-service international airlines operating hundreds of aircraft. Airline services can be categorized as being intercontinental, domestic, regional, or international, and may be operated as scheduled services or charters.
The first airlines
DELAG, Deutsche Luftschiffahrts-Aktiengesellschaft was the world's first airline. It was founded on November 16, 1909 with government assistance, and operated airships manufactured by The Zeppelin Corporation. Its headquarters were in Frankfurt. The first fixed wing scheduled air service was started on January 1, 1914 from St. Petersburg, Florida to Tampa, Florida. The four oldest non-dirigible airlines that still exist are Netherlands' KLM, Colombia's Avianca, Australia's Qantas, Polish AeroTarg, and the Czech Republic's Czech Airlines. KLM first flew in May 1920, while Qantas (which stands for Queensland and Northern Territory Aerial Services Limited) was founded in Queensland, Australia, in late 1920.
This page contains text from Wikipedia, the Free Encyclopedia -	https://wn.com/Airline
This is a complete list of episodes from the TV series The Simple Life starring Paris Hilton and Nicole Richie. The series included 54 episodes and 2 specials that aired between January 20, 2004 and August 5, 2007 in the United States.
List of seasons
Season 1: 2003–2004
Road Trip: 2004
Interns: 2005
'Till Death Do Us Part: 2006
Goes to Camp: 2007
This page contains text from Wikipedia, the Free Encyclopedia -	https://wn.com/List_of_The_Simple_Life_episodes
Airline is a British television series produced by Yorkshire Television for the ITV network in 1982.
The series starred Roy Marsden as Jack Ruskin, a pilot demobbed after the end of the Second World War who starts his own air freight business.
Airline was created by Wilfred Greatorex and lasted for one series of nine episodes broadcast in January & February 1982, with a repeat in the summer of 1984. Other leading cast members were Polly Hemingway, Richard Heffer, Nicholas Bond-Owen, Sean Scanlan and Terence Rigby, while noted guest-stars included Anthony Valentine and Walter Gotell (better-known for his numerous guest stints as KGB General Gogol in a string of James Bond films during the Cold War era).
It was partially filmed at the former RAF Rufforth in Yorkshire.
Series 1: ITV, 1982
Airline at the Internet Movie Database.
This page contains text from Wikipedia, the Free Encyclopedia -	https://wn.com/Airline_(1982_TV_series)
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Turkish sultana raisin production is expected to increase by 35 percent in MY2014/15 to 328,167 MT, thereby rebounding from last year's poor crop. Sultana raisin exports are forecast at 280,000 MT in MY 2014/15, up from 215,000 MT last year.
After a bad season of freeze and hail in MY 2013/14 that resulted in a 20-percent in production, Turkish sultana raisin production is forecast to increase to a record high level of 328,167 MT in MY 2014/15. Favorable weather conditions and increased area are the reasons for the expected increase. Among European countries, the UK is the leading export destination, receiving 28 percent of all Turkish raisin exports with 42,000 tons between September 2013 and June 14, 2014. UK is followed by Germany, Holland, Italy and Australia. This trend is expected to continue similarly in the upcoming years.
Turkey is the world's second largest raisin producer after the United States and the leading exporter, accounting to 25 percent of the world's total raisin production and 40-45 percent of total raisin exports. Grapes are grown throughout Turkey, and there are over 1,200 different grape varieties in Turkey. Nearly two-thirds of these grapes have seeds, and one-third are seedless.
Turkey produces approximately 4.2 MMT of grapes annually. Table grapes make up approximately 30 percent of the production, drying grapes make up 35 percent, grapes for traditional products such as pekmez (molasses) make up 25 percent, and grapes used for alcoholic beverage production make up approximately 10 percent of this total.
Harvest season starts around August 15, so the marketing years in this report refer to the period between September 1st of the first year until August 30th of the next year. Seedless grape production expanded significantly in Turkey in the 1990s due to more intensive cultivation and adaption of better irrigation techniques. Seedless grapes constitute about 40 percent of Turkey's total grape crop and are grown only in the Aegean (western) part of Turkey. While the Aegean region produces seedless grapes, the Marmara, Central Anatolia and Southeast Anatolia regions produce table and wine grapes. Sultanas are indigenous to the Aegean Region and are the raisin variety referred to in this report.
Despite's Turkey's leading role in the production of raisins, domestic consumption is comparatively low, and most of the production (generally around 90 percent) is exported. Human and industry consumption is around 20-25,000 MT and the alcoholic beverages sector (lead by raki - a strong anise based Turkish alcoholic drink, and followed by wine and brandy) use about the same amount. Alcoholic beverage industry has been under the pressure of the conservative government actions such as restricting sales and marketing activities, heavy taxation, etc. which eventually reflected in a decrease of consumption. The Raki industry usually demands 350,000 MT of grapes, and the brandy and wine industries demand about 80,000 MT of grapes annually, and the wine grape production barely meets this demand.
Domestic consumption of sultanas is forecast at 45,000 MT for 2014/15.


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Events Practice makes Practice
|PMP| Stuff to Handle the Human Condition: Scientology, William S. Burroughs and the Counterculture
Sat 16th July 2016 Studios
Stuff to Handle the Human Condition: Scientology, William S. Burroughs and the Counterculture
Talk by Dr. Mark Jackson
William S. Burroughs has been recognised as a hugely influential figure of the 20th Century counterculture who is responsible for bringing a diverse range of alternative materials into the vocabulary of contemporary writers, artists, filmmakers and musicians. – This talk explored one of the most forceful, and yet least discussed, of these influences: L Ron Hubbard's Dianetics and Church of Scientology. Drawing on his unpublished interview with the late head of the Church of Scientology in the UK, and responding to Scientologist! David Wills' recent book on Burroughs, Mark Jackson looked at the way Burroughs reworked Hubbard's ideas in a collision of countercultures and in the context of a somewhat hostile yet ultimately critical moment for both Burroughs and the Church.
Dr. Mark Jackson is a curator and Senior Lecturer in Art History and Critical Theory at Northumbria University. Exhibitions include Dead Fingers Talk: The Tape Experiments of William S. Burroughs at IMT Gallery, London.
The talk ran in connection with Freaks! The Alternative Press & The Psychedelic Underground An Archive // Exhibition
This event is part of Practice makes Practice, an artist development programme run by artists for artists, initiated by The NewBridge Project.
Practice makes Practice focuses on developing artistic talent and equipping artists with the necessary skills to manage their practice, bridging the gap between art school, studio practice, the gallery and beyond.
The programme is open to our Studio Members, and to the wider arts community through an associate Artist Membership. To become an Artist Member please click here.
IMAGE: Orphée listening to messages from the dead in the static of the car radio


The deadline for public comments regarding school admission policy for the 2020 school year has been extended.
The Gauteng Department of Education has extended the deadline for public comments regarding school admission policy for the 2020 school year.
Gauteng Education MEC, Panyaza Lesufi, officially tabled the proposed amendments to the school admissions policy at a public meeting held at Sutherland High school, in Centurion on August 21.
Lesufi, addressing parents on the draft amendments highlighted how the changes were instituted to ensure the department was aligned with the National legislation and complied with a Constitutional court judgment of determining feeder zones.
He said these would also clarify ambiguity following the court battles the department had faced most recently.
These included challenges to admission of learners at schools such as Overkruin, Montana and Afrikaanse Hoër Meisieskool.
Steve Mabona, Education spokesperson, said the department was eager to hear concerns from parents and education stakeholders regarding the proposed amendments.
"We urge parents to participate in this process, as it is of utmost importance to receive public input.
Mabona said the amendments were still available for download on the departments website.
Written comments may be submitted until September 14, and may be posted to the departments head offices in Johannesburg or hand delivered.


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April 2015 - Booster Minutes
The regular meeting of the Raymore-Peculiar Band Boosters Club was held on April 14, 2015 in the South High School band room. Those in attendance were: Mike McIntosh, Kellie Norton, Kim Roberts, Caren Homer, Lisa Hatfield, Kim Sickler, Scott Bradley, Denise Staudinger, Trina Tygret, Alex Adolphson, Jeff McDowell, Melissa Hogan, Holli Berry, Dana Wilhite, Dillion Jarrott, Jennifer Gibson and Sandi McIntosh.
The meeting was called to order at 7:00pm.
Meeting Minutes Approval: The February 10, 2015 minutes were reviewed and a motion to approve was made by Mike McIntosh and seconded by Jim Johnson. Motion carried.
Director's Report – John Wilson
Marching Band tryout dates:
April 21st – Marching Band Fundamentals 6:00-8:00pm
April 23rd – Drum Major and Section Leader Auditions
April 28th – Marching Band Fundamentals 6:00-8:00pm
May 5th – March Band Auditions 6:00-8:00pm
Scott Lang Conference – 31 students attended this motivational conference which is designed to help students learn to take ownership/leadership in the band. The Scott Lange Leadership Application is due on April 20th.
Color Guard Try-outs – dates for tryouts are April 22nd – 24th for clinics and auditions will be held on April 24th. The 2015 Color Guard will be announced on April 27th. There is a Color Guard Parent Meeting at 6:00pm on April 23rd.
State May 1st Columbia schedule is not out yet
May 7th and May 8th are the dates for this year's Band extravaganza at 7:00pm both nights.
May 7th is Eagle Glen, 7th Grade, 8th Grade and Wind Symphony
May 8th is Bridle Ridge, Concert Band, Symphonic Band and Wind Symphony
Wind Symphony will play different songs both nights
May 12 is schedule banquet – there was discussion about whether to have the band awards after the May 8th Band Extravaganza Concert or leave it as scheduled for May 12th. The students are split on this issue. After discussion, it was decided to leave the Band Awards on May 12th.
There were 38 "1" ratings at District Band this year. INCREDIBLE.
All 3 bands received a "1" rating at State Large Group Ensemble.
Mattress sale a huge success. Special thanks to Brian Kincaid, Chris and Carter Wilhite for helping clean up and Mike McIntosh who was at the event from 8:00am-6:15pm to set up and clean up. A total of $5,500 was made - $1,100 goes to the student accounts and $4,400 goes to the Band Booster account. There were 39 referrals and 41 mattresses were sold.
A motion was made by the band directors for approval for $1,000 to purchase medals for the Band Awards. This may not be needed if the school is willing to make the purchase for us. Mike McIntosh made the motion and Kim Roberts seconded. Motion carried.
New newsletter to be sent out each week. The directors will be doing a weekly newsletter that will be sent out to parents with updates about the High School Band Program. This will eliminate multiple e-mails being sent out each week.
Communication's Report – Dillon Jarrett
Vice President Report – Dana Wilhite
Treasurer's Report – Jeff McDowell
Checking Balance: $13,750.18
Savings Balance: $24,677.11
The Father/Daughter Dance fundraiser has been finalized. A total of $10,049.31 was made and after expenses paid of $3,028.60, the net profit was $7,020.71 which will go into the students' accounts. The student accounts have been credited.
Fundraising – Mary Fambraugh
Truck Raffle Fundraiser – the drawing for the truck has been extended to May 8th (Band Extravaganza). We have officially sold 32 tickets. A minimum of 140 tickets have to be sold to go forward with the fundraiser. There are a total of 200 tickets that can be sold. There will be a table set up at Landmark South Dodge to sell tickets on Saturday, April 18th from 10:00am to 1:00pm. Parents are encouraged to spread the word about the raffle. Volunteers may be recruited to do ticket tables at other locations on other days.
April 24th is the Pancake Breakfast, Rummage Sale and Flower Sale which will be located on the parking lot of the Peculiar Methodist Church.
Kellie Norton requested $300.00 to purchase food for April 24th pancake breakfast and concession stand. The motion was made by Jim Johnson made the motion and Sandi McIntosh seconded. Motion carried.
Kellie Norton also requested $600.00 to purchase food for Band Extravaganza. . The motion was made by Mike McIntosh made the motion and Kim Roberts seconded. Motion carried.
For Band Extravaganza, Kellie advised they are looking into doing a concession stand which could possibly have Chick-Fil'A sandwiches and Sonic hamburgers. A sandwich, chips and
drink would cost $5.00. Kim Sickler volunteered to get the hamburgers and buns at Sam's Club if we wanted to cook them ourselves. In addition to a concession stand, there are also plans for a dessert bar. Kellie also advised they are looking into doing a Reverse Raffle.
Popcorn sales began on April 13th.
The cookbook fundraiser will begin soon. Caren Homer is heading this fundraiser.
Various other fundraisers are in the works.
Uniform Chair Report – Tracey Caskey
Hospitality Chair Report – Kim Sickler
Band Dad's Chair Report – Mike McIntosh
Jim Johnson advised the semi-trailer needs to be sent for painting if we want it done in time to showcase at Band Extravaganza. He advised the painting would cost approximately $3,300 and latches are also needed that would cost approximately $150.00. A motion for $3,500 for these expenses was made by Mike McIntosh and seconded by Scott Bradley. The motion carried.
Band Trailer Workday is scheduled for April 24th in the school parking lot.
Jennifer Gibson advised that the Nominating Committee met in early April to begin seeking candidates for the 2015-2016 Band Booster Board. The positions being voted on will be President, Vice President, Secretary and Treasurer. The following are the recommendations for the positions to be voted on at the May Band Booster meeting:
Dana Wilhite – President
Alec Adolphson – Vice President
Debbie Elrod – Secretary
Tracy Caskey - Treasurer
For Committee Chairpersons, the recommendations are as follows:
Kellie Norton – Fundraising
Jim Johnson – Head Band Dad
Kim Sickler – Hospitality
TBD – Uniforms
On the night of the elections, nominations can be taken from the floor for the 4 elected positions.


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text:
\section{Introduction}
Let $\ensuremath{{\mathcal H}}$ be a real Hilbert space with scalar product
$\scal{\cdot}{\cdot}$ and associated norm $\|\cdot\|$. The best
approximation to a point $z\in\ensuremath{{\mathcal H}}$ from a nonempty closed convex
set $C\subset\ensuremath{{\mathcal H}}$ is the point $P_Cz\in C$ that satisfies
$\|P_Cz-z\|=\min_{x\in C}\|x-z\|$. The induced best approximation
operator $P_C\colon\ensuremath{{\mathcal H}}\to C$, also called the projector onto $C$,
plays a central role in several branches of applied
mathematics \cite{Deut01}.
If we designate by $\iota_C$ the indicator function of $C$, i.e.,
\begin{equation}
\label{e:iota}
\iota_C\colon x\mapsto
\begin{cases}
0,&\text{if}\;\;x\in C;\\
\ensuremath{{+\infty}},&\text{if}\;\;x\notin C,
\end{cases}
\end{equation}
then $P_Cz$ is the solution to the minimization problem
\begin{equation}
\label{e:proj}
\underset{x\in\ensuremath{{\mathcal H}}}{\mathrm{minimize}}\;\;\iota_C(x)+\frac12\|x-z\|^2.
\end{equation}
Now let $\Gamma_0(\ensuremath{{\mathcal H}})$ be the class of lower semicontinuous convex
functions $f\colon\ensuremath{{\mathcal H}}\to\ensuremath{\left]-\infty,+\infty\right]}$ such that
$\ensuremath{\operatorname{dom}} f=\menge{x\in\ensuremath{{\mathcal H}}}{f(x)<\ensuremath{{+\infty}}}\neq\ensuremath{{\varnothing}}$. In \cite{Mor62b}
Moreau observed that, for every function $f\in\Gamma_0(\ensuremath{{\mathcal H}})$,
the proximal minimization problem
\begin{equation}
\label{e:prox}
\underset{x\in\ensuremath{{\mathcal H}}}{\mathrm{minimize}}\;\;f(x)+\frac12\|x-z\|^2
\end{equation}
possesses a unique solution, which he denoted by $\ensuremath{\operatorname{prox}}_fz$.
The resulting proximity operator $\ensuremath{\operatorname{prox}}_f\colon\ensuremath{{\mathcal H}}\to\ensuremath{{\mathcal H}}$
therefore extends the notion of a best approximation operator
for a convex set. This fruitful concept has become a central tool
in mechanics, variational analysis, optimization, and signal
processing, e.g., \cite{Alar06,Banf10,Rock09}.

Though in certain simple cases closed-form expressions are available
\cite{Banf10,Smms05,More65}, computing $\ensuremath{\operatorname{prox}}_fz$ in numerical
applications is a challenging task. The objective of this paper is
to propose a splitting algorithm to compute proximity operators in
the case when $f$ can be decomposed as a sum of composite functions.

\begin{problem}
\label{prob:1}
Let $z\in\ensuremath{{\mathcal H}}$ and let $(\omega_i)_{1\leq i\leq m}$ be reals in
$\left]0,1\right]$ such that $\sum_{i=1}^m\omega_i=1$.
For every $i\in\{1,\ldots,m\}$, let $(\ensuremath{{\mathcal G}}_i,\|\cdot\|_{\ensuremath{{\mathcal G}}_i})$ be
a real Hilbert space, let $r_i\in\ensuremath{{\mathcal G}}_i$, let $g_i\in\Gamma_0(\ensuremath{{\mathcal G}}_i)$,
and let $L_i\colon\ensuremath{{\mathcal H}}\to\ensuremath{{\mathcal G}}_i$ be a nonzero bounded linear operator.
The problem is to
\begin{equation}
\label{e:prob1}
\underset{x\in\ensuremath{{\mathcal H}}}{\mathrm{minimize}}\;\;
\sum_{i=1}^m\omega_ig_i(L_ix-r_i)+\frac12\|x-z\|^2.
\end{equation}
\end{problem}

The underlying practical assumption we make is that the proximity
operators $(\ensuremath{\operatorname{prox}}_{g_i})_{1\leq i\leq m}$ are implementable
(to within some quantifiable error). We are therefore aiming
at devising an algorithm that uses these operators separately.
Let us note that such splitting algorithms are already available
to solve Problem~\ref{prob:1} under certain restrictions.
\begin{enumerate}
\item[A)]
Suppose that $\ensuremath{{\mathcal G}}_1=\ensuremath{{\mathcal H}}$, that $L_1=\ensuremath{\operatorname{Id}}\,$, that the functions
$(g_i)_{2\leq i\leq m}$ are differentiable everywhere with a
Lipschitz continuous gradient, and that $r_i\equiv 0$. Then
\eqref{e:prob1} reduces to the minimization of the sum of
$f_1=g_1\in\Gamma_0(\ensuremath{{\mathcal H}})$ and of the smooth function
$f_2=\sum_{i=2}^m\omega_ig_i\circ L_i+\|\cdot-z\|^2/2$,
and it can be solved by the forward-backward
algorithm \cite{Smms05,Tsen91}.
\item[B)]
The methods proposed in \cite{Joca09} address the case
when, for every $i\in\{1,\ldots,m\}$, $\ensuremath{{\mathcal G}}_i=\ensuremath{{\mathcal H}}$, $L_i=\ensuremath{\operatorname{Id}}\,$,
and $r_i=0$.
\item[C)]
The method proposed in \cite{Svva10} addresses the case
when $m=2$, $\ensuremath{{\mathcal G}}_1=\ensuremath{{\mathcal H}}$, and $L_1=\ensuremath{\operatorname{Id}}\,$, and $r_1=0$.
\end{enumerate}
The restrictions imposed in A) are quite stringent since many
problems involve at least two nondifferentiable potentials.
Let us also observe that since, in general, there is no explicit
expression for $\ensuremath{\operatorname{prox}}_{g_i\circ L_i}$ in terms of
$\ensuremath{\operatorname{prox}}_{g_i}$ and $L_i$, Problem~\ref{prob:1} cannot be
reduced to the setting described in B). On the other hand,
using a product space reformulation, we shall show that the setting
described in C) can be exploited to solve Problem~\ref{prob:1}
using only approximate implementations of the operators
$(\ensuremath{\operatorname{prox}}_{g_i})_{1\leq i\leq m}$.
Our algorithm is introduced in Section~\ref{sec:2}, where we also
establish its convergence properties.
In Section~\ref{sec:3}, our results are applied to best
approximation and image recovery problems.

Our notation is standard.
$\ensuremath{\EuScript B}\,(\ensuremath{{\mathcal H}},\ensuremath{{\mathcal G}})$ is the space of bounded linear operators from $\ensuremath{{\mathcal H}}$
to a real Hilbert space $\ensuremath{{\mathcal G}}$. The adjoint of $L\in\ensuremath{\EuScript B}\,(\ensuremath{{\mathcal H}},\ensuremath{{\mathcal G}})$ is
denoted by $L^*$. The conjugate of $f\in\Gamma_0(\ensuremath{{\mathcal H}})$
is the function $f^*\in\Gamma_0(\ensuremath{{\mathcal H}})$ defined by
$f^*\colon u\mapsto\sup_{x\in\ensuremath{{\mathcal H}}}(\scal{x}{u}-f(x))$. The
projector onto a nonempty closed convex set $C\subset\ensuremath{{\mathcal H}}$
is denoted by $P_C$. The strong relative interior of a
convex set $C\subset\ensuremath{{\mathcal H}}$ is
\begin{multline}
\label{e:sri}
\ensuremath{\operatorname{sri}} C=\menge{x\in C}{\ensuremath{\operatorname{cone}} (C-x)=\ensuremath{\overline{\operatorname{span}}\,} (C-x)},\\
\quad\text{where}\quad
\ensuremath{\operatorname{cone}} C=\bigcup_{\lambda>0}\menge{\lambda x}{x\in C},
\end{multline}
and the relative interior of $C$ is
$\ensuremath{\operatorname{ri}} C=\menge{x\in C}{\ensuremath{\operatorname{cone}} (C-x)=\ensuremath{{\operatorname{span}}\,} (C-x)}$.
We have $\ensuremath{\operatorname{int}} C\subset\ensuremath{\operatorname{sri}} C\subset\ensuremath{\operatorname{ri}} C\subset C$ and, if $\ensuremath{{\mathcal H}}$ is
finite-dimensional, $\ensuremath{\operatorname{ri}} C=\ensuremath{\operatorname{sri}} C$.
For background on convex analysis, see \cite{Zali02}.

\section{Main result}
\label{sec:2}

To solve Problem~\ref{prob:1}, we propose the following algorithm.
Its main features are that each function $g_i$ is activated
individually by means of its proximity operator, and that the
proximity operators can be evaluated simultaneously. It is important
to stress that the functions $(g_i)_{1\leq i\leq m}$ and the operators
$(L_i)_{1\leq i\leq m}$ are used at separate steps in the algorithm,
which is thus fully decomposed. In addition, an error $a_{i,n}$ is
tolerated in the evaluation of the $i$th proximity operator at
iteration $n$.

\begin{algorithm}
\label{algo:2}
For every $i\in\{1,\ldots,m\}$, let $(a_{i,n})_{n\in\ensuremath{\mathbb N}}$ be a sequence
in $\ensuremath{{\mathcal G}}_i$.
\begin{equation}
\label{e:main2}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
\rho=\big(\max_{1\leq i\leq m}\|L_i\|\big)^{-2}\\[1mm]
\varepsilon\in\left]0,\min\{1,\rho\}\right[\\[1mm]
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,0}\in\ensuremath{{\mathcal G}}_i\\
\end{array}
\right.\\[1mm]
\end{array}
\right.\\[10mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
x_n=z-\sum_{i=1}^m\omega_iL_i^*v_{i,n}\\[1mm]
\gamma_n\in\left[\varepsilon,2\rho-\varepsilon\right]\\[1mm]
\lambda_n\in\left[\varepsilon,1\right]\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,n+1}=v_{i,n}+\lambda_n\Big(\ensuremath{\operatorname{prox}}_{\gamma_n g_i^*}
\big(v_{i,n}+\gamma_n(L_ix_n-r_i)\big)+a_{i,n}-v_{i,n}\Big).
\end{array}
\right.\\[2mm]
\end{array}
\right.\\[2mm]
\end{array}
\end{equation}
\end{algorithm}

Note that an alternative implementation of \eqref{e:main2}
can be obtained via Moreau's decomposition formula in a real
Hilbert space $\ensuremath{{\mathcal G}}$ \cite[Lemma~2.10]{Smms05}
\begin{equation}
\label{e:2010-06-15b}
(\forall g\in\Gamma_0(\ensuremath{{\mathcal G}}))(\forall\gamma\in\ensuremath{\left]0,+\infty\right[})(\forall v\in\ensuremath{{\mathcal G}})
\quad\ensuremath{\operatorname{prox}}_{\gamma g^*}v=v-\gamma\ensuremath{\operatorname{prox}}_{\gamma^{-1}g}(\gamma^{-1}v).
\end{equation}
We now describe the asymptotic behavior of Algorithm~\ref{algo:2}.

\begin{theorem}
\label{t:2}
Suppose that
\begin{equation}
\label{e:hanoi2010-05-27a}
(r_i)_{1\leq i\leq m}\in\ensuremath{\operatorname{sri}}
\menge{(L_ix-y_i)_{1\leq i\leq m}}{x\in\ensuremath{{\mathcal H}},
(y_i)_{1\leq i\leq m}\in\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^m\ensuremath{\operatorname{dom}} g_i}
\end{equation}
and that
\begin{equation}
\label{e:2010-06-15a}
(\forall i\in\{1,\ldots,m\})\quad\sum_{n\in\ensuremath{\mathbb N}}\|a_{i,n}\|_{\ensuremath{{\mathcal G}}_i}<\ensuremath{{+\infty}}.
\end{equation}
Furthermore, let $(x_n)_{n\in\ensuremath{\mathbb N}}$, $(v_{1,n})_{n\in\ensuremath{\mathbb N}}$, \ldots,
$(v_{m,n})_{n\in\ensuremath{\mathbb N}}$ be sequences generated by
Algorithm~\ref{algo:2}.
Then Problem~\ref{prob:1} possesses a unique solution $x$ and
the following hold.
\begin{enumerate}
\item
\label{t:2i}
For every $i\in\{1,\ldots,m\}$, $(v_{i,n})_{n\in\ensuremath{\mathbb N}}$ converges
weakly to a point $v_i\in\ensuremath{{\mathcal G}}_i$. Moreover, $(v_i)_{1\leq i\leq m}$
is a solution to the minimization problem
\begin{equation}
\label{e:prob2}
\underset{v_1\in\ensuremath{{\mathcal G}}_1,\ldots,\, v_m\in\ensuremath{{\mathcal G}}_m}
{\mathrm{minimize}}\;\;\frac12\left\|z-\sum_{i=1}^m
\omega_iL_i^*v_i\right\|^2+\sum_{i=1}^m\omega_i
\big(g_i^*(v_i)+\scal{v_i}{r_i}\big),
\end{equation}
and $x=z-\sum_{i=1}^m\omega_iL_i^*v_i$.
\item
\label{t:2ii}
$(x_n)_{n\in\ensuremath{\mathbb N}}$ converges strongly to $x$.
\end{enumerate}
\end{theorem}
\begin{proof}
Set $f\colon\ensuremath{{\mathcal H}}\to\ensuremath{\left]-\infty,+\infty\right]}\colon x\mapsto\sum_{i=1}^m\omega_ig_i(L_ix-r_i)$.
The assumptions imply that, for every $i\in\{1,\ldots,m\}$, the
function $x\mapsto g_i(L_ix-r_i)$ is convex and lower semicontinuous.
Hence, $f$ is likewise. On the other hand, it follows from
\eqref{e:hanoi2010-05-27a} that
\begin{equation}
(r_i)_{1\leq i\leq m}\in\menge{(L_ix-y_i)_{1\leq i\leq m}}{x\in\ensuremath{{\mathcal H}},
(y_i)_{1\leq i\leq m}\in\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^m\ensuremath{\operatorname{dom}} g_i}
\end{equation}
and, therefore, that
$\ensuremath{\operatorname{dom}} f\neq\ensuremath{{\varnothing}}$. Thus, $f\in\Gamma_0(\ensuremath{{\mathcal H}})$ and, as seen in
\eqref{e:prox}, Problem~\ref{prob:1} possesses a unique
solution, namely $x=\ensuremath{\operatorname{prox}}_f z$.

Now let $\ensuremath{\boldsymbol{\mathcal H}}$ be the real Hilbert space obtained by endowing
the Cartesian product $\ensuremath{{\mathcal H}}^m$ with the scalar product
$\scal{\cdot}{\cdot}_{\ensuremath{\boldsymbol{\mathcal H}}}\colon(\boldsymbol{x},\boldsymbol{y})\mapsto
\sum_{i=1}^m\omega_i\scal{x_i}{y_i}$, where
$\boldsymbol{x}=(x_i)_{1\leq i\leq m}$ and
$\boldsymbol{y}=(y_i)_{1\leq i\leq m}$ denote generic
elements in $\ensuremath{\boldsymbol{\mathcal H}}$. The associated norm is
\begin{equation}
\label{e:palawan-mai2008}
\|\cdot\|_{\ensuremath{\boldsymbol{\mathcal H}}}\colon\boldsymbol{x}\mapsto
\sqrt{\sum_{i=1}^m\omega_i\|x_i\|^2}.
\end{equation}
Likewise, let $\ensuremath{\boldsymbol{\mathcal G}}$ denote the real Hilbert space obtained by
endowing the Cartesian product $\ensuremath{{\mathcal G}}_1\times\cdots\times\ensuremath{{\mathcal G}}_m$
with the scalar product and the associated norm respectively
defined by
\begin{equation}
\label{e:palawan-mai2008-}
\scal{\cdot}{\cdot}_{\ensuremath{\boldsymbol{\mathcal G}}}
\colon(\boldsymbol{y},\boldsymbol{z})\mapsto
\sum_{i=1}^m\omega_i\scal{y_i}{z_i}_{\ensuremath{{\mathcal G}}_i}
\quad\text{and}\quad\|\cdot\|_{\ensuremath{\boldsymbol{\mathcal G}}}\colon
\boldsymbol{y}\mapsto\sqrt{\sum_{i=1}^m\omega_i\|y_i\|_{\ensuremath{{\mathcal G}}_i}^2}.
\end{equation}
Define
\begin{equation}
\label{e:fgL}
\begin{cases}
{\boldsymbol f}=\iota_{\boldsymbol D},
\quad\text{where}\quad\boldsymbol{D}=\menge{(x,\dots,x)\in\ensuremath{\boldsymbol{\mathcal H}}}{x\in\ensuremath{{\mathcal H}}}\\
{\boldsymbol g}\colon\ensuremath{\boldsymbol{\mathcal G}}\to\ensuremath{\left]-\infty,+\infty\right]}\colon\boldsymbol{y}\mapsto
\sum_{i=1}^m\omega_ig_i(y_i)\\
{\boldsymbol L}\colon\ensuremath{\boldsymbol{\mathcal H}}\to\ensuremath{\boldsymbol{\mathcal G}}\colon\boldsymbol{x}\mapsto
(L_ix_i)_{1\leq i\leq m}\\
\boldsymbol{r}=(r_1,\ldots,r_m)\\
\boldsymbol{z}=(z,\ldots,z).
\end{cases}
\end{equation}
Then $\boldsymbol{f}\in\Gamma_0(\ensuremath{\boldsymbol{\mathcal H}})$,
$\boldsymbol{g}\in\Gamma_0(\ensuremath{\boldsymbol{\mathcal G}})$, and
$\boldsymbol{L}\in\ensuremath{\EuScript B}\,(\ensuremath{\boldsymbol{\mathcal H}},\ensuremath{\boldsymbol{\mathcal G}})$. Moreover, $\boldsymbol{D}$
is a closed vector subspace of $\ensuremath{\boldsymbol{\mathcal H}}$ with projector
\begin{equation}
\label{e:PD}
\ensuremath{\operatorname{prox}}_{\boldsymbol{f}}=
P_{\boldsymbol{D}}\colon\boldsymbol{x}\mapsto
\bigg(\sum_{i=1}^m\omega_ix_i,\ldots,\sum_{i=1}^m\omega_ix_i\bigg)
\end{equation}
and
\begin{equation}
\label{e:L*}
\boldsymbol{L}^*\colon\ensuremath{\boldsymbol{\mathcal G}}\to\ensuremath{\boldsymbol{\mathcal H}}\colon\boldsymbol{v}\mapsto
\big(L_i^*v_i\big)_{1\leq i\leq m}.
\end{equation}
Note that \eqref{e:palawan-mai2008-} and \eqref{e:palawan-mai2008}
yield
\begin{align}
\label{e:2010-06-09e}
(\forall\boldsymbol{x}\in\ensuremath{\boldsymbol{\mathcal H}})\quad
\|\boldsymbol{L}\boldsymbol{x}\|_{\ensuremath{\boldsymbol{\mathcal G}}}^2
&=\sum_{i=1}^m\omega_i\|L_ix_i\|_{\ensuremath{{\mathcal G}}_i}^2\nonumber\\
&\leq\sum_{i=1}^m\omega_i\|L_i\|^2\|x_i\|^2\nonumber\\
&\leq\Big(\max_{1\leq i\leq m}\|L_i\|^2\Big)
\sum_{i=1}^m\omega_i\|x_i\|^2\nonumber\\
&=\Big(\max_{1\leq i\leq m}\|L_i\|^2\Big)\|\boldsymbol{x}\|^2_{\ensuremath{\boldsymbol{\mathcal H}}}.
\end{align}
Therefore,
\begin{equation}
\label{e:2010-06-09f}
\|\boldsymbol{L}\|\leq\max_{1\leq i\leq m}\|L_i\|.
\end{equation}
We also deduce from \eqref{e:hanoi2010-05-27a} that
\begin{equation}
\label{e:1938}
\boldsymbol{r}\in\ensuremath{\operatorname{sri}}\big(\boldsymbol{L}(\ensuremath{\operatorname{dom}} \boldsymbol{f})-
\ensuremath{\operatorname{dom}}\boldsymbol{g}\big).
\end{equation}
Furthermore, in view of \eqref{e:palawan-mai2008} and
\eqref{e:fgL}, in the space $\ensuremath{\boldsymbol{\mathcal H}}$,
\eqref{e:prob1} is equivalent to
\begin{equation}
\label{e:prob4}
\underset{\boldsymbol{x}\in\ensuremath{\boldsymbol{\mathcal H}}}{\mathrm{minimize}}\;\;
{\boldsymbol f}(\boldsymbol{x})+
{\boldsymbol g}({\boldsymbol L}\boldsymbol{x}-\boldsymbol{r})+
\frac12\|\boldsymbol{x}-\boldsymbol{z}\|_{\ensuremath{\boldsymbol{\mathcal H}}}^2.
\end{equation}
Next, we derive from \cite[Proposition~3.3]{Svva10} that the dual
problem of \eqref{e:prob4} is to
\begin{equation}
\label{e:prob5}
\underset{\boldsymbol{v}\in\ensuremath{\boldsymbol{\mathcal G}}}{\mathrm{minimize}}\;\;
\widetilde{\boldsymbol{f}^*}(\boldsymbol{z}-
\boldsymbol{L}^*\boldsymbol{v})+\boldsymbol{g}^*(\boldsymbol{v})
+\scal{\boldsymbol{v}}{\boldsymbol{r}}_{\ensuremath{\boldsymbol{\mathcal G}}},
\end{equation}
where $\widetilde{\boldsymbol{f}^*}\colon\boldsymbol{u}\mapsto
\inf_{\boldsymbol{w}\in\ensuremath{\boldsymbol{\mathcal H}}}\big(\boldsymbol{f}^*(\boldsymbol{w})+
(1/2)\|\boldsymbol{u}-\boldsymbol{w}\|_{\ensuremath{\boldsymbol{\mathcal H}}}^2\big)$ is
the Moreau envelope of $\boldsymbol{f}^*$.
Since ${\boldsymbol f}=\iota_{\boldsymbol D}$, we have
$\boldsymbol{f}^*=\iota_{\boldsymbol{D}^\bot}$.
Hence, \eqref{e:palawan-mai2008} and \eqref{e:PD} yield
\begin{equation}
\label{e:2010-06-09a}
(\forall\boldsymbol{u}\in\ensuremath{\boldsymbol{\mathcal H}})\quad
\widetilde{\boldsymbol{f}^*}(\boldsymbol{u})
=\frac12\|\boldsymbol{u}-P_{\boldsymbol{D}^\bot}\boldsymbol{u}\|_{\ensuremath{\boldsymbol{\mathcal H}}}^2
=\frac12\|P_{\boldsymbol{D}}\boldsymbol{u}\|_{\ensuremath{\boldsymbol{\mathcal H}}}^2
=\frac12\left\|\sum_{i=1}^m\omega_iu_i\right\|^2.
\end{equation}
On the other hand, \eqref{e:palawan-mai2008-} and \eqref{e:fgL} yield
\begin{equation}
\label{e:2010-06-09b}
(\forall\boldsymbol{v}\in\ensuremath{\boldsymbol{\mathcal G}})\quad
\boldsymbol{g}^*(\boldsymbol{v})=
\sum_{i=1}^m\omega_ig_i^*(v_i)\quad\text{and}\quad
\ensuremath{\operatorname{prox}}_{\boldsymbol{g}^*}\boldsymbol{v}
=\big(\ensuremath{\operatorname{prox}}_{g_i^*}v_i\big)_{1\leq i\leq m}.
\end{equation}
Altogether, it follows from \eqref{e:L*}, \eqref{e:2010-06-09a},
\eqref{e:2010-06-09b}, and \eqref{e:palawan-mai2008-}, that
\begin{equation}
\label{e:2010-06-09c}
\text{\eqref{e:prob5} is equivalent to \eqref{e:prob2}.}
\end{equation}
Now define
\begin{equation}
\label{e:2010-06-09d}
(\forall n\in\ensuremath{\mathbb N})\quad
\begin{cases}
\boldsymbol{x}_n=(x_n,\ldots,x_n)\\
\boldsymbol{v}_n=(v_{1,n},\ldots,v_{m,n})\\
\boldsymbol{a}_n=(a_{1,n},\ldots,a_{m,n}).
\end{cases}
\end{equation}
Then, in view of \eqref{e:fgL}, \eqref{e:PD}, \eqref{e:L*},
\eqref{e:2010-06-09f}, and \eqref{e:2010-06-09b}, \eqref{e:main2}
is a special case of the following routine.
\begin{equation}
\label{e:main1}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
\rho=\|{\boldsymbol L}\|^{-2}\\[1mm]
\varepsilon\in\left]0,\min\{1,\rho\}\right[\\[1mm]
{\boldsymbol v}_0\in\ensuremath{\boldsymbol{\mathcal G}}\\[1mm]
\end{array}
\right.\\[5mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
{\boldsymbol x}_n=\ensuremath{\operatorname{prox}}_{\boldsymbol f}({\boldsymbol z}-
{\boldsymbol L}^*{\boldsymbol v}_n)\\[1mm]
\gamma_n\in\left[\varepsilon,2\rho-\varepsilon\right]\\[1mm]
\lambda_n\in\left[\varepsilon,1\right]\\
{\boldsymbol v}_{n+1}={\boldsymbol v}_n
+\lambda_n\big(\ensuremath{\operatorname{prox}}_{\gamma_n {\boldsymbol g}^*}({\boldsymbol v}_n
+\gamma_n({\boldsymbol L}{\boldsymbol x}_n
-{\boldsymbol r}))+{\boldsymbol a}_n-{\boldsymbol v}_n\big).
\end{array}
\right.\\[2mm]
\end{array}
\end{equation}
Moreover, \eqref{e:2010-06-15a} implies that
$\sum_{n\in\ensuremath{\mathbb N}}\|{\boldsymbol a}_n\|_{\ensuremath{\boldsymbol{\mathcal G}}}<\ensuremath{{+\infty}}$.
Hence, it follows from \eqref{e:1938} and
\cite[Theorem~3.7]{Svva10} that the following hold,
where $\boldsymbol{x}$ is the solution to
\eqref{e:prob4}.
\begin{itemize}
\item[(a)]
$({\boldsymbol v}_n)_{n\in\ensuremath{\mathbb N}}$ converges weakly to a solution
$\boldsymbol{v}$ to \eqref{e:prob5} and ${\boldsymbol x}=
\ensuremath{\operatorname{prox}}_{\boldsymbol f}({\boldsymbol z}-{\boldsymbol L}^*{\boldsymbol v})$.
\item[(b)]
$({\boldsymbol x}_n)_{n\in\ensuremath{\mathbb N}}$ converges strongly to
${\boldsymbol x}$.
\end{itemize}
In view of \eqref{e:palawan-mai2008}, \eqref{e:palawan-mai2008-},
\eqref{e:fgL}, \eqref{e:PD}, \eqref{e:L*}, \eqref{e:2010-06-09c},
and \eqref{e:2010-06-09d}, items (a) and (b) provide respectively
items \ref{t:2i} and \ref{t:2ii}.
\end{proof}

\begin{remark}
\label{r:2010-06-18}
Let us consider Problem~\ref{prob:1} in the special case when
$(\forall i\in\{1,\ldots,m\})$ $\ensuremath{{\mathcal G}}_i=\ensuremath{{\mathcal H}}$, $L_i=\ensuremath{\operatorname{Id}}\,$, and $r_i=0$.
Then \eqref{e:prob1} reduces to
\begin{equation}
\label{e:prob24}
\underset{x\in\ensuremath{{\mathcal H}}}{\mathrm{minimize}}\;\;
\sum_{i=1}^m\omega_ig_i(x)+\frac12\|x-z\|^2.
\end{equation}
Now let us implement Algorithm~\ref{algo:2} with
$\gamma_n\equiv 1$, $\lambda_n\equiv 1$,
$a_{i,n}\equiv 0$, and $v_{i,0}\equiv 0$.
The iteration process resulting from \eqref{e:main2} can be
written as
\begin{equation}
\label{e:main23}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
x_0=z\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,0}=0\\
\end{array}
\right.\\[1mm]
\end{array}
\right.\\[4mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,n+1}=\ensuremath{\operatorname{prox}}_{g^*_i}(x_n+v_{i,n}).
\end{array}
\right.\\[1mm]
x_{n+1}=z-\sum_{i=1}^m\omega_iv_{i,n+1}.
\end{array}
\right.\\[2mm]
\end{array}
\end{equation}
For every $i\in\{1,\ldots,m\}$ and $n\in\ensuremath{\mathbb N}$, set
$z_{i,n}=x_n+v_{i,n}$. Then \eqref{e:main23} yields
\begin{equation}
\label{e:main24}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
x_0=z\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
z_{i,0}=z\\
\end{array}
\right.\\[1mm]
\end{array}
\right.\\[5mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
x_{n+1}=z-\sum_{i=1}^m\omega_i\ensuremath{\operatorname{prox}}_{g^*_i}z_{i,n}\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
z_{i,n+1}=x_{n+1}+\ensuremath{\operatorname{prox}}_{g^*_i}z_{i,n}.
\end{array}
\right.\\[0mm]
\end{array}
\right.\\[6mm]
\end{array}
\end{equation}
Next we observe that
$(\forall n\in\ensuremath{\mathbb N})$ $\sum_{i=1}^m\omega_iz_{i,n}=z$.
Indeed, the identity is clearly satisfied for $n=0$ and,
for every $n\in\ensuremath{\mathbb N}$, \eqref{e:main24} yields
$\sum_{i=1}^m\omega_iz_{i,n+1}=x_{n+1}+\sum_{i=1}^m\omega_i
\ensuremath{\operatorname{prox}}_{g^*_i}z_{i,n}=(z-\sum_{i=1}^m\omega_i\ensuremath{\operatorname{prox}}_{g^*_i}z_{i,n})
+\sum_{i=1}^m\omega_i\ensuremath{\operatorname{prox}}_{g^*_i}z_{i,n}=z$.
Thus, invoking \eqref{e:2010-06-15b} with $\gamma=1$,
we can rewrite \eqref{e:main24} as
\begin{equation}
\label{e:main25}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
x_0=z\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
z_{i,0}=z\\
\end{array}
\right.\\[1mm]
\end{array}
\right.\\[5mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
x_{n+1}=\sum_{i=1}^m\omega_i\ensuremath{\operatorname{prox}}_{g_i}z_{i,n}\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
z_{i,n+1}=x_{n+1}+z_{i,n}-\ensuremath{\operatorname{prox}}_{g_i}z_{i,n}.
\end{array}
\right.\\[0mm]
\end{array}
\right.\\[6mm]
\end{array}
\end{equation}
This is precisely the Dykstra-like algorithm proposed in
\cite[Theorem~4.2]{Joca09} for computing
$\ensuremath{\operatorname{prox}}_{\sum_{i=1}^m\omega_ig_i}z$ (which itself extends the
classical parallel Dykstra algorithm for projecting $z$ onto an
intersection of closed convex sets \cite{Baus94,Gaff89}). Hence,
Algorithm~\ref{algo:2} can be viewed as an extension of
this algorithm, which was derived and analyzed with different
techniques in \cite{Joca09}.
\end{remark}

\section{Applications}
\label{sec:3}

As noted in the Introduction, special cases of Problem~\ref{prob:1}
have already been considered in the literature under certain
restrictions on the number $m$ of composite functions, the
complexity of the linear operators $(L_i)_{1\leq i\leq m}$,
and/or the smoothness of the potentials $(g_i)_{1\leq i\leq m}$
(one will find specific applications in
\cite{Cham05,Svva10,Banf10,Smms05,Demo09,Pott93}
and the references therein). The proposed framework makes it
possible to remove these restrictions simultaneously. In this
section, we provide two illustrations.

\subsection{Best approximation from an intersection of composite
convex sets}

In this section, we consider the problem of finding the best
approximation $P_Dz$ to a point $z\in\ensuremath{{\mathcal H}}$ from a closed convex
subset $D$ of $\ensuremath{{\mathcal H}}$ defined as an intersection of affine inverse
images of closed convex sets.

\begin{problem}
\label{prob:3}
Let $z\in\ensuremath{{\mathcal H}}$ and, for every $i\in\{1,\ldots,m\}$, let
$(\ensuremath{{\mathcal G}}_i,\|\cdot\|_{\ensuremath{{\mathcal G}}_i})$ be a real Hilbert space, let
$r_i\in\ensuremath{{\mathcal G}}_i$, let $C_i$ be a nonempty closed convex subset of
$\ensuremath{{\mathcal G}}_i$, and let $0\neq L_i\in\ensuremath{\EuScript B}\,(\ensuremath{{\mathcal H}},\ensuremath{{\mathcal G}}_i)$. The problem is to
\begin{equation}
\label{e:prob3}
\underset{x\in D}{\mathrm{minimize}}\;\|x-z\|,
\quad\text{where}\quad
D=\bigcap_{i=1}^m\menge{x\in\ensuremath{{\mathcal H}}}{L_ix\in r_i+C_i}.
\end{equation}
\end{problem}

In view of \eqref{e:iota}, Problem~\ref{prob:3} is a special case of
Problem~\ref{prob:1}, where $(\forall i\in\{1,\ldots,m\})$
$g_i=\iota_{C_i}$ and $\omega_i=1/m$.
It follows that, for every
$i\in\{1,\ldots,m\}$ and every $\gamma\in\ensuremath{\left]0,+\infty\right[}$, $\ensuremath{\operatorname{prox}}_{\gamma g_i}$
reduces to the projector $P_{C_i}$ onto $C_i$. Hence, using
\eqref{e:2010-06-15b}, we can rewrite Algorithm~\ref{algo:2}
in the following form, where we have set
$c_{i,n}=-\gamma_n^{-1}a_{i,n}$ for simplicity.

\begin{algorithm}
\label{algo:3}
For every $i\in\{1,\ldots,m\}$, let $(c_{i,n})_{n\in\ensuremath{\mathbb N}}$ be a sequence
in $\ensuremath{{\mathcal G}}_i$.
\begin{equation}
\label{e:main3}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
\rho=\big(\max_{1\leq i\leq m}\|L_i\|\big)^{-2}\\[1mm]
\varepsilon\in\left]0,\min\{1,\rho\}\right[\\[1mm]
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,0}\in\ensuremath{{\mathcal G}}_i\\
\end{array}
\right.\\[1mm]
\end{array}
\right.\\[10mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
x_n=z-\sum_{i=1}^m\omega_iL_i^*v_{i,n}\\[1mm]
\gamma_n\in\left[\varepsilon,2\rho-\varepsilon\right]\\[1mm]
\lambda_n\in\left[\varepsilon,1\right]\\
\operatorname{For}\;i=1,\ldots,m\\
\left\lfloor
\begin{array}{l}
v_{i,n+1}=v_{i,n}+\gamma_n\lambda_n\Big(
L_ix_n-r_i-
P_{C_i}\big(\gamma_n^{-1}v_{i,n}+L_ix_n-r_i\big)-c_{i,n}\Big).
\end{array}
\right.\\[2mm]
\end{array}
\right.\\[2mm]
\end{array}
\end{equation}
\end{algorithm}

In the light of the above, we obtain the following application of
Theorem~\ref{t:2}\ref{t:2ii}.

\begin{corollary}
\label{c:2010-07-07a}
Suppose that
\begin{equation}
\label{e:2010-07-07a}
(r_i)_{1\leq i\leq m}\in\ensuremath{\operatorname{sri}}
\menge{(L_ix-y_i)_{1\leq i\leq m}}{x\in\ensuremath{{\mathcal H}},
(y_i)_{1\leq i\leq m}\in\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^m C_i}
\end{equation}
and that $(\forall i\in\{1,\ldots,m\})$
$\sum_{n\in\ensuremath{\mathbb N}}\|c_{i,n}\|_{\ensuremath{{\mathcal G}}_i}<\ensuremath{{+\infty}}$.
Then every sequence $(x_n)_{n\in\ensuremath{\mathbb N}}$ generated by
Algorithm~\ref{algo:3} converges strongly to the
solution $P_Dz$ to Problem~\ref{prob:3}.
\end{corollary}

\subsection{Nonsmooth image recovery}

A wide range of signal and image recovery problems can be modeled
as instances of Problem~\ref{prob:1}. In this section, we focus on
the problem of recovering an image $\overline{x}\in\ensuremath{{\mathcal H}}$ from
$p$ noisy measurements
\begin{equation}
\label{e:model}
r_i=T_i\overline{x}+s_i,\quad 1\leq i\leq p.
\end{equation}
In this model, the $i$th measurement $r_i$ lies in a Hilbert space
$\ensuremath{{\mathcal G}}_i$, $T_i\in\ensuremath{\EuScript B}\,(\ensuremath{{\mathcal H}},\ensuremath{{\mathcal G}}_i)$ is the data formation operator,
and $s_i\in\ensuremath{{\mathcal G}}_i$ is the realization of a noise process. A typical
data fitting potential in such models is the function
\begin{equation}
\label{e:2010-07-14s}
x\mapsto\sum_{i=1}^p\omega_ig_i(T_ix-r_i),\quad\text{where}\quad
0\leq g_i\in\Gamma_0(\ensuremath{{\mathcal G}}_i)\quad\text{and $g_i$ vanishes only at $0$}.
\end{equation}
The proposed framework can handle $p\geq 1$ nondifferentiable functions
$(g_i)_{1\leq i\leq p}$ as well as the incorporation of additional
potential functions to model prior knowledge on the original image
$\overline{x}$. In the illustration we provide below,
the following is assumed.
\begin{itemize}
\item
The image space is $\ensuremath{{\mathcal H}}={\mathrm H}_0^1(\Omega)$, where
$\Omega$ is a nonempty bounded open domain in $\ensuremath{\mathbb{R}}^2$.
\item
$\overline{x}$ admits a sparse decomposition in an orthonormal
basis $(e_k)_{k\in\ensuremath{\mathbb N}}$ of $\ensuremath{{\mathcal H}}$.
As discussed in \cite{Demo09,Zouh05} this property can be promoted
by the ``elastic net'' potential
$x\mapsto\sum_{k\in\ensuremath{\mathbb N}}\phi_k(\scal{x}{e_k})$, where
$(\forall k\in\ensuremath{\mathbb N})$
$\phi_k\colon\xi\mapsto\alpha|\xi|+\beta|\xi|^2$, with
$\alpha>0$ and $\beta>0$. More general choices of suitable functions
$(\phi_k)_{k\in\ensuremath{\mathbb N}}$ are available \cite{Siop07}.
\item
$\overline{x}$ is piecewise smooth. This property is promoted
by the total variation potential
$\operatorname{tv}(x)=\int_\Omega|\nabla x(\omega)|_{2}d\omega$,
where $|\cdot|_2$ denotes the Euclidean norm on $\ensuremath{\mathbb{R}}^2$
\cite{Rudi92}.
\end{itemize}

Upon setting $g_i\equiv\|\cdot\|_{\ensuremath{{\mathcal G}}_i}$ in \eqref{e:2010-07-14s},
these considerations lead us to the following formulation (see
\cite[Example~2.10]{Svva10} for more general nonsmooth potentials).

\begin{problem}
\label{prob:9}
Let $\ensuremath{{\mathcal H}}={\mathrm H}_0^1(\Omega)$, where $\Omega\subset\ensuremath{\mathbb{R}}^2$ is
nonempty, bounded, and open, let $(\omega_i)_{1\leq i\leq p+2}$ be
reals in $\left]0,1\right]$ such that $\sum_{i=1}^{p+2}\omega_i=1$,
and let $(e_k)_{k\in\ensuremath{\mathbb N}}$ be an orthonormal basis of $\ensuremath{{\mathcal H}}$.
For every $i\in\{1,\ldots,p\}$, let $0\neq T_i\in\ensuremath{\EuScript B}\,(\ensuremath{{\mathcal H}},\ensuremath{{\mathcal G}}_i)$,
where $(\ensuremath{{\mathcal G}}_i,\|\cdot\|_{\ensuremath{{\mathcal G}}_i})$ is a real Hilbert space,
and let $r_i\in\ensuremath{{\mathcal G}}_i$. The problem is to
\begin{equation}
\label{e:prob11}
\underset{x\in\ensuremath{{\mathcal H}}}{\mathrm{minimize}}\;\;
\sum_{i=1}^p\omega_i\|T_ix-r_i\|_{\ensuremath{{\mathcal G}}_i}+
\sum_{k\in\ensuremath{\mathbb N}}\bigg(\omega_{p+1}|\scal{x}{e_k}|
+\frac12|\scal{x}{e_k}|^2\bigg)
+\omega_{p+2}\operatorname{tv}(x).
\end{equation}
\end{problem}

It follows from Parseval's identity that Problem~\ref{prob:9}
is a special case of Problem~\ref{prob:1} in
$\ensuremath{{\mathcal H}}={\mathrm H}_0^1(\Omega)$ with $m=p+2$, $z=0$, and
\begin{equation}
\label{e:2010-07-14f}
\begin{cases}
g_i=\|\cdot\|_{\ensuremath{{\mathcal G}}_i}\;\text{and}\;L_i=T_i,\:
\text{if}\;\;1\leq i\leq p;\\
\ensuremath{{\mathcal G}}_{p+1}=\ell^2(\ensuremath{\mathbb N}),\,g_{p+1}=\|\cdot\|_{\ell^1},\,
r_{p+1}=0,\,\text{and}\;L_{p+1}\colon x\mapsto(\scal{x}{e_k})_{k\in\ensuremath{\mathbb N}};\\
\ensuremath{{\mathcal G}}_{p+2}={\mathrm L}^2(\Omega)\oplus {\mathrm L}^2(\Omega),\,
g_{p+2}\colon y\mapsto\int_\Omega|y(\omega)|_2d\omega,\,
r_{p+2}=0,\,\text{and}\;L_{p+2}=\nabla.
\end{cases}
\end{equation}

To implement Algorithm~\ref{algo:2}, it suffices to note that
$L_{p+1}^*\colon(\nu_k)_{k\in\ensuremath{\mathbb N}}\mapsto\sum_{k\in\ensuremath{\mathbb N}}\nu_ke_k$ and
$L_{p+2}^*=-\operatorname{div}$, and to specify the proximity
operators of the functions $(\gamma g^*_i)_{1\leq i\leq m}$,
where $\gamma\in\ensuremath{\left]0,+\infty\right[}$.
First, let $i\in\{1,\ldots,p\}$. Then $g_i=\|\cdot\|_{\ensuremath{{\mathcal G}}_i}$
and therefore $g_i^*=\iota_{B_i}$, where $B_i$ is the closed unit
ball of $\ensuremath{{\mathcal G}}_i$. Hence $\ensuremath{\operatorname{prox}}_{\gamma g_i^*}=P_{B_i}$.
Next, it follows from \eqref{e:2010-06-15b} and
\cite[Example~2.20]{Smms05} that
$\ensuremath{\operatorname{prox}}_{\gamma g^*_{p+1}}\colon(\xi_k)_{k\in\ensuremath{\mathbb N}}\mapsto
(P_{[-1,1]}\xi_k)_{k\in\ensuremath{\mathbb N}}$.
Finally, since $g_{p+2}$ is the support function of
the set \cite{Merc80}
\begin{equation}
\label{e:K}
K=\menge{y\in\ensuremath{{\mathcal G}}_{p+2}}{|y|_2\leq 1~\text{a.e.}},
\end{equation}
$g_{p+2}^*=\iota_K$ and therefore $\ensuremath{\operatorname{prox}}_{\gamma g_{p+2}^*}=P_K$,
which is straightforward to compute.
Altogether, as $\|L_{p+1}\|=1$ and $\|L_{p+2}\|\leq 1$,
Algorithm~\ref{algo:2} assumes the following form
(since all the proximity operators can be implemented with
simple projections, we dispense with the errors terms).

\begin{algorithm}
\label{algo:4}
\begin{equation}
\label{e:main9}
\begin{array}{l}
\operatorname{Initialization}\\
\left\lfloor
\begin{array}{l}
\rho=\big(\max\{1,\|T_1\|,\ldots,\|T_p\|\}\big)^{-2}\\[1mm]
\varepsilon\in\left]0,\min\{1,\rho\}\right[\\[1mm]
\operatorname{For}\;i=1,\ldots,p\\
\left\lfloor
\begin{array}{l}
v_{i,0}\in\ensuremath{{\mathcal G}}_i\\
\end{array}
\right.\\[1mm]
v_{p+1,0}=(\nu_{k,0})_{k\in\ensuremath{\mathbb N}}\in\ell^2(\ensuremath{\mathbb N})\\
v_{p+2,0}\in{\mathrm L}^2(\Omega)\oplus{\mathrm L}^2(\Omega)\\
\end{array}
\right.\\[12mm]
\operatorname{For}\;n=0,1,\ldots\\
\left\lfloor
\begin{array}{l}
x_n=z-\sum_{i=1}^p\omega_iT_i^*v_{i,n}
-\omega_{p+1}\sum_{k\in\ensuremath{\mathbb N}}\nu_{k,n}e_k
+\omega_{p+2}\operatorname{div}v_{p+2,n}\\[1mm]
\gamma_n\in\left[\varepsilon,2\rho-\varepsilon\right]\\[1mm]
\lambda_n\in\left[\varepsilon,1\right]\\
\operatorname{For}\;i=1,\ldots,p\\
\left\lfloor
\begin{array}{l}
v_{i,n+1}=v_{i,n}+\lambda_n\Big(
{\displaystyle\frac{v_{i,n}+\gamma_n(T_ix_n-r_i)}
{\max\{1,\|v_{i,n}+\gamma_n(T_ix_n-r_i)\|_{\ensuremath{{\mathcal G}}_i}\}}}-v_{i,n}\Big)
\end{array}
\right.\\[4mm]
\operatorname{For~every}\;k\in\ensuremath{\mathbb N},\:
\nu_{k,n+1}=\nu_{k,n}+\lambda_n\Big(
{\displaystyle\frac{\nu_{k,n}+\gamma_n\scal{x_n}{e_k}}
{\max\{1,|\nu_{k,n}+\gamma_n\scal{x_n}{e_k}|\}}}-\nu_{k,n}\Big)\\[2mm]
\operatorname{For~almost~every}\;\omega\in\Omega,\\
\qquad v_{p+2,n+1}(\omega)=v_{p+2,n}(\omega)+\lambda_n\Big(
{\displaystyle\frac{v_{p+2,n}(\omega)+\gamma_n\nabla x_n(\omega)}
{\max\{1,|v_{p+2,n}(\omega)+\gamma_n\nabla x_n(\omega)|_2\}}}
-v_{p+2,n}(\omega)\Big).
\end{array}
\right.\\[2mm]
\end{array}
\end{equation}
\end{algorithm}

Let us establish the main convergence property of this algorithm.
\begin{corollary}
\label{c:2010-07-21}
Every sequence $(x_n)_{n\in\ensuremath{\mathbb N}}$ generated by
Algorithm~\ref{algo:4} converges strongly to the
solution to Problem~\ref{prob:9}.
\end{corollary}
\begin{proof}
In view of the above discussion and of Theorem~\ref{t:2}\ref{t:2ii},
it remains to check that \eqref{e:hanoi2010-05-27a} is satisfied.
Set $S=\menge{(L_ix-y_i)_{1\leq i\leq m}}{x\in\ensuremath{{\mathcal H}},
(y_i)_{1\leq i\leq m}\in\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^m\ensuremath{\operatorname{dom}} g_i}$.
We have $\ensuremath{\operatorname{dom}} g_i=\ensuremath{{\mathcal G}}_i$ for every $i\in\{1,\ldots,p\}$,
$\ensuremath{\operatorname{dom}} g_{p+1}=\ell^1(\ensuremath{\mathbb N})$, and
$\ensuremath{\operatorname{dom}} g_{p+2}={\mathrm L}^2(\Omega)\oplus {\mathrm L}^2(\Omega)$.
Consequently,
\begin{align}
S
&=\Big\{(T_1x-y_1,\ldots,T_px-y_p,(\scal{x}{e_k}-\eta_k)_{k\in\ensuremath{\mathbb N}},
\nabla x-y_{p+2}~\Big|~\nonumber\\
&\mbox{}\hskip 28mm x\in\ensuremath{{\mathcal H}},
(y_i)_{1\leq i\leq p}\in\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^p\ensuremath{{\mathcal G}}_i,
(\eta_k)_{k\in\ensuremath{\mathbb N}}\in\ell^1(\ensuremath{\mathbb N}),
y_{p+2}\in{\mathrm L}^2(\Omega)\oplus {\mathrm L}^2(\Omega)\Big\}
\nonumber\\
&=\big(\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^p\ensuremath{{\mathcal G}}_i\big)\times\ell^2(\ensuremath{\mathbb N})
\times\big({\mathrm L}^2(\Omega)\oplus {\mathrm L}^2(\Omega)\big)
\nonumber\\
&=\ensuremath{\raisebox{-0.5mm}{\mbox{\LARGE{$\times$}}}}\!_{i=1}^m\ensuremath{{\mathcal G}}_i.
\end{align}
Hence, we trivially have $(r_1,\ldots,r_p,0,0)\in\ensuremath{\operatorname{sri}} S$.
\end{proof}

Let us emphasize that a novelty of the above variational framework is
to  perform total variation image recovery in the presence of several
nondifferentiable composite terms, with guaranteed strong convergence
to the solution to the problem, and with elementary steps in the form
of simple projections.
The finite-dimensional version of the algorithm can easily be obtained
by discretizing the operators $\nabla$ and $\operatorname{div}$ as
in \cite{Cham05} (see also \cite[Section~4.4]{Svva10} for variants
of the total variation potential).

redpajama_set_name: RedPajamaArXiv