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 Joe Smith, e-mail, 07.08.2016 01:18I would like to contact CMSgt Isaiah Woods (Woody), if anyone has his address/e-mail. He was my first CMSgt. Isaiah Woods cmsgt (ret), e-mail, 19.06.2016 09:12I served with the 1211 Test Sq/58 WRS from 1962-until I retired in 1973. I was NCOIC of the MET/ARE sampling section most of my time and participated in most of the missions cited on the web page plus others. I would also like info to contact Brig Gen R. Moeller & Col D. Wolfe Emmet Cook, e-mail, 31.05.2016 22:09I attended John Penz'z funeral services. A sad day. He was a great NCO. I worked the Flight line and was the Crew Chief on 295 for a short time before I went to Docks. One of my favorite bosses was CMSgt Houghton. My best to all you guys from the 58th. Those were the good old days. I spent 20 more years in the Army after THE Air Force. Curtis, e-mail, 03.04.2016 01:28TO: Phil Putnam,Yes, I certainly remember your father, Joseph Putnam. If I recall correctly, he was the oldest man flying in the Space suits as an Air Force pilot while I was at Kirtland (68-72). Seems to me he was the Chief of Planning for the 58th WRS at the time I was there. We flew together at times, and he was a great pilot, all business and did it right all the way. I was Chief of the Command Post for a while, Special Assistant to the Commander for Colonel Douglas "Red Dog" Campbell, then Chief Navigator when Colonel Click D. Smith came in. I made a pretty fast exit as he came in. I did not like him, did not trust him, and was ready to go to Vietnam to fly the EC-47 to get away from him. Best move I ever made.I will add that I was fortunate, as a Navigator, to be the first navigator to command a flying Unit in the Military Airlift Command--maybe the Air Force. I was Commander of a Task Force at Albrook AB, Panama for a period with two WB-57Fs, three crews, Life Support Personnel, a medic, and maintenance personnel. General Jack Catton, COMAC, cam into Howard AB, CZ, to visit USAFSO, and sent word that he wanted to be briefed by me on the operation of "his" WB-57Fs out of Panama and Mendoza, Argentina. We also had WB-47s, and WC-135s operating into and out of Howard, while we were operating the F's out of Albrook on the other side of the Canal. So I was alos responsible as senior officer for AWS (MAC) for any support needed from our operation. General Catton came to Albrook for the Briefing. It wasn't fancy as I had flip charts, hand made, but they were well done as I had one NCO who was really great at hand made graphics. I had been told to give him a 12 minute briefing, and a Colonel Whitehead was Wing Commander for USAFSO at Howard. Whitehead was a real jerk and wanted to dictate what I did for the briefing. I declined his directions and created the briefing as seems appropriate. But I did adhere to the 12 minutes as that may have come from Catton. Upon his arrival--with Whitehead in tow--Catton told Whitehead to stay outside. I did the 12 minute briefing, and it was apparently just what Catton wanted. Then he started asking questions about the WC-135 and WB-47 operations, and I was answering everything in detail. Finally, he asked me how I knew all of that just off hand. I told him I had flown the 47 for over 1000 hours, about 2000 hours in the WC-135, and held the record for Polar Missions at that time (eventually 178 polar missions including 87 polar crossings) so I knew exactly what all of the missions were and had flown them. His questions ran that 12 minute meeting far beyond anything I'd imagined. Seemed he just wanted an education on his AWS operation portion of MAC. As I finished, he stood, came forward to thank us, looked at me and said, "I just have one more question. Why the hell is a slick wing navigator commanding one of my flying units?" Without blinking an eye, I said, "Because I know what I'm doing, General!" He replied, "I'd say you're right!" When I arrived back at the 58th some time later, there was a nice letter from Catton to Colonel Campbell telling him of the job I was doing down there. That sure didn't hurt my chances when I came up for Lt. Colonel, I'm sure. Colonel Curtis D. Dale, PhD, USAF (Ret) Joe, e-mail, 21.02.2016 06:47Don't for get reunion is coming up June 15, 16 and 17 in Branson, MO. Joe Devenport, e-mail, 21.02.2016 06:45Just to let you guys know, John Penz passed away Feb 9, 2016. Ted R., 20.09.2015 06:13Did the 58th WRS receive an Outstanding Unit Citation Award in the years 1969-1971? Marty, 22.03.2015 07:49Stationed at Kirtland in 1969 working on the longwings. The most remarkable person I ever met was CMSGT William Frazell along with many other memorable and colorful characters both on base and off. Loved the TDY of course and I can still remember one particularly long trip back from Mendoza on a C-141. Our plane cracked a front window and we dropped pretty far pretty fast and it wasn't even pretty. The plane made an emergency landing somewhere in South Carolina, as I recall, where we went through a rather "entertaining" customs inspection. Also enjoyed Friday's "The General is coming through the Barracks" cleanups (he never did) and the impromptu FOD pickup parties. Raymond Wozniak, e-mail, 24.11.2014 02:27Worked on this aircraft at Yokota AFB in 1971. Great plane. Easy to work on. I was a Sgt from the Pneudraulic Dept John Penz, e-mail, 04.11.2014 02:23Last call you all! Joe Devenport and I have just about finished with the list of identified folks in the yearbook. We are still lacking many, especially the enlisted men in the "mill around" picture on page 14 upper, page 14 lower along with Sam and Pappy, certificate holders on upper left page 15 behind Maj Consta.We will be making an addendum to the book with all the names provided to us, and will furnish it at no cost to those that help ID folks.hanks and Bless.Long Live the Longwings! Clark Wilberg, 03.06.2014 22:05I was an SEO (Special Equipment Operator) with AFTAC and had the pleasure of working with, and flying with, many of the folks listed in these comments. Gordon Blevins--always enjoyed flying with you on the WC-135; had a few flights on WB-47s and thoroughly enjoyed that aircraft as well; 417 was my favorite! I had the privilege of working with -57F navigators--teaching them the operation of the sampling equipment for their sampling operations. Joe Devenport, e-mail, 28.05.2014 04:05For anyone that owns a 58 WRS book: If you can ID anyone in the photos in the sq book, please let us know. contact John Penz or me. Please provide their name, the page and the location on the page, if required. Please use 58 WRS Photos in the subject line. thank you Joe Devenport, e-mail, 08.05.2014 03:25Rodney, if you would like to have a model perhaps you can check this web site out. It's aimhigherjets.com. I have seen some of their work and they do good work. They have a 1 800 number, too. I plan to have them make a model for me soon. As for the helmet, they look better displayed, as for a price, I'm not sure you will make more than a few . Perhaps, we will see you on Pawn Stars some time. Let me know how you make out with it. good luck. Rodney Carroll, e-mail, 07.05.2014 16:20Joe, Thanks for the info. I collect interesting items but this items is a bit large. What I wanted was the RB-57 model. I missed out on that, but I knew the flight helmet was a good deal because I knew what it was related to. I knew about the RB-57 from watching a program of either the History channel or Discovery. I am really into the SR-71 and the U2 missions. I do plan on selling the helmet. That is why I was trying to figure out how it was used. Joe Devenport, e-mail, 06.05.2014 00:26Rodney, not all flights required the pressure suits. We also had the C model. I'm sorry to hear about the Col. He was a good man. So, are you a collector of some kind? Rodney Carroll, e-mail, 03.05.2014 07:11I recently attended the estate sale of Colonel Gene Durden. I acquired a standard style flight helmet that belonged to him. The helmet has "F-Troop" and "58 WRS" stickers on it. This is not a "Space Helmet" like I see in photos of the pilots of the RB 57F. Was this standard style flight helmet used in the unit? Where they used for maintenance flights. Was there other aircraft in the unit that the Colonel could have been flying? John Penz, e-mail, 16.12.2013 01:55Hello all. The 2nd preinting of 10 books is sold out. I have several folks wanting a book, so through the good graces of my neighbor, Joe Herring, owner of Herring Printing in Kerrville, I am going to have 5 more books printed. This will be the last print at the original price, $22 + tax and insured priority mail +/-$5.80, so if you or one of your friends want one, let me know hubba-hubba (WWII term). I will be going to press right after the 1st of the year. email me at jrpenz@windstream.netMerry Christmas and a Happy healthy New Year. JP john holbein, e-mail, 01.11.2013 02:20I was stationed at Kirkland 1962-1965 crewed 837 (short wing)& then 292 rb57f when delivered.Spent time at Johnston atoll'indian springs nev. & Fairbanks.I was there when capt lafoon & maj parr (sadly crashed)I also remember maj red cambell.That was a wonderful time in my life;tw0 of my kids were born there.Chief gullo was the top enlisted man then;I still keep in touch with a few of the guys'nottingham'pastore'I also remember Cassidy he crewed one of the D-models.best regards to all Jeff Powers, e-mail, 17.08.2013 03:34My great uncle, MSG John Supple, helped to develop this beautiful aircraft while working at General Dynamics in Ft. Worth. I still have his "official" Model of the plane as well as his zippo lighter that has the RB-57F Silhouette on it. Gordon Blevins, e-mail, 22.06.2013 02:29I flew the "F" while stationed at Kirtland AFB, NM. I was also the safety officer and part of the accident investigation team for the 292 accident. Of all the airplanes that I flew, the "F" was my favorite. The WC-135B and the WB-47 (my e-mail address is the tail number of the last WB-47E Bob Sprecher, Curt Norden, and I took to the "Bone Yard" at Davis-Monthan. I also took two of the RB-57F's there. THis was/still is I guess (Yea NASA) a fantastic airplane. Hello to those of you who left comments here whom I know!! Lester Johns, e-mail, 18.04.2013 22:03I found these articles while I was looking for a good desktop pic. I was at Rhine Main when the first (F) arrived and until after when we had lost one in the Black Sea. The squadron must have disbanded not too long after I left. It was an awesome aircraft for sure. I can't say what the mission was or my job. I was told to forget, although I have seen articles talking about it since. CMSgt (ret), e-mail, 06.03.2013 07:44Earler I posted my email address wrong. This is to be corrected copy. Anyone wishing to contact me please use this addres: jrpenz@windstream.net Anyone know the address of Dan Templeton,lease give me or h the address above. Thanks for you help in advanceJohn R. Penz John Penz, CMSgt ret, e-mail, 24.02.2013 06:04The F was and still is a most beautiful plane to watch take off and go almost straight up. NASA still has 3 of our planes in their stable (295 renumbered 927 is going through it's final stage of a ramp to ertical stabilzer will be virtually a new aircraft when it is flown to Ellington ready to go to work.If anyone is interested in purcasing repr\\int of the 1974 Squadron book, I have 6 left. These books will be sold for $30 each incuding insured Priority USPS mail. I will be bringing them (if left) to this year's reunion in Branson. MO in June and will wave the postage and handling charge for direct delivery. Chief Snelson (ret) and I have had approximately 100 new patches direct copies of the RB-57F Black ball Patch, the RB57F patch a d the WB-57F patch both in true colors.See post number 2 in this link for prices. These are being sold as a non-profit venture.CMSgt John R Penz,email jrpenz@windstream.net Joe Devenport, e-mail, 31.01.2013 02:27Hello fellow F troopsI was in the 58 WRS from Jan 69 go Aug 72. I didn't know it at the time but the 58 was the best SQ ever with a bunch of good guys. I got out and worked in the Gulf of Mexico for while, made good money at that time. I came back in 2 years later became a flight engineer on C5s and loved it! I remember Basil, E Cook, R Cook, Mike Hong, Wooler, Step, Harroll, Pride, McKey and Short, plus several others. Currently, I live in Oklahoma. I was forced to retire two years ago, the company I worked for lost the contract and my job was done away with. I can't say that I'm broken up about it, I help out around town, church and work in my wood shop and visit family often. CMSGT John R. Penz, e-mail, 24.12.2012 07:00Hi FTroopers all. I must say that the squadron book sale went quite well after the word got out. Matter of fact 2 troops requested books after they were all gone. So I put myself in the hole again and ordered 10 more copies and now have 8 left. The price is$22.00 for the book and priority mail and insurance will total $30.00 if you want one, contact me at jpenz@windstream.net.CMS ret John Snelson came up with a suggestion that maybe their are some folks out there that might like a brand new patch. He and I have put up the front$ so he and I have a limited number of 3 different patches. First was the "Black Ball" patch which I wore from '64- 65/66. The 2nd was the familiar RB57F patch, and the third was the WB57F patch.The "Black ball"patch is $3.00 plus shipping and handling, the other 2 patches will be$4.00each. These patches are true copies of the original. If you are interested emaIl me at jpenx@windstream.net and I will email pictures of the patches. Curtis D. Dale, e-mail, 29.11.2012 11:11I flew in the "Longwing" from Albuquerque for 1968 to 1972. I was Chief Navigator, Chief of Command Post, and Special Assistant to Commander during the period of Don Wolf, Doug Campbell, (and, UGH, Click Smith).It was a wonderful assignnment and airplane, in many ways the ultimate flying assignment of my flying career, even though all the others were terrific. The 58ths was a collection of the finest crews, maintenance, life support, flight surgeons, and civilian tech reps that could possibly be put together. it was my honor to fly with such people Dana Kelly, Vern Duenas, Leroy Gray, Doug "Red Dog" Campbell, Don Wolfe, Ed Wolf, Earl Heal, Gene Durden, Sam Van Dyke and so many other great pilots and to lead the finest collection of navigator/mission director/special equipment operators that could possibly be assembled. These GIBs were able to do what you asked of them, every time, to the very extent the equipment provided was capable of doing. I saw times when their equipment failed, and their innovations still gathered incredibly valuable information, matching or exceeding what the failed equipment provided by the customer was designed to do. Greg Korczak, Rich Wojick, Jack Booth, Larry Champion, Norm Bockledge, and so many others have become legends to me. Flew them out of Albuquerque, Panama, Mendoza Argentina, Alaska and Hawaii. Colonel Curtis D. Dale, PhD, USAF (Ret) RICH, e-mail, 26.10.2012 11:38I was station at Yokota Air base from 1966 to 1968. There were RB-57F's assigned to the 56 WRS and 6091st RS. I worked on the EB-57E's that shared the hanger with the 6091st RB_57F's. There is not much information on their mission in the 60's and I guess it will be lost to history. Emmet Cook, e-mail, 26.09.2012 01:26I was in the 58th from 69 to 72. I worked for Chief Houghton in the Flt Line office for a year and then as a asst Crew Chief on 3295, and then Crew Chief for about a year. After that I went to Docks until I got out in Aug of 72. I went TDY to Alaska, Panama, and Mendoza several times. Loved Panama and Mendoza. In Mendoza I got a back seat ride in a F model. That was a great day. After I got out I went to college on the GI Bill and graduated in 1975 and took a commission and retired as a LTC in the Army in 1995. I am now retired in San Antonio. I remember Denis Davis, Gary Christian, Joe Devenport, Jim Janeway, Dale Heath, Paul Walton, Frank Marguez, Pat Horton, Pat Pastori, Don Gasson, John Penz, Mack, Lt Laird and many others. Hope they are all doing well. Happy trails Tom Hawkins, e-mail, 07.09.2012 22:51Remember the bar races at the O'club? Frank McCabe seemed to have it figured out. Ken Wetzel walked into the head and thought I was in one of the stalls. He said, boy does it stink in here. As he was washing his hands, Good ole' Colonel Click Smith walked out of the stall and said, "yeah, even mine stinks." CMSgt ret John R. Penz, e-mail, 13.08.2012 05:00Hey troops just checking in to see wassup and pass along a little info. Last year I took it upon myself to have the 58th RB57F book reprinted.It was done in a soft cover with all pages done in their original B&W or color. Had a hard time trying to scrape together 40 buyers to get a price of $21.92 + S&H.It was definitely a NOT-FOR- PROFIT undertaing but wound up I think quite successful. I included with the book a cd of the whole book, a cd given to me by NASA JSC with the history of the Longwing at NASA and the 1965/66 Cristmas Card with the F&C inflight together all for only$27.60 which included Priority USPS Mail. I only made the quota with the good graces of several individuals purchasing several copies and donating them to various USAF Museums,Max Schuerebrenn donated a copy to the Air Force Academy Library in memory of Capt Tom Walker, KIA Laos, John Snelson and John Penz copy to Pima Air Musuesm, Richard Wojick to the National Museum of the USAF at WPAFB, George Tash donated his hard cover copy to the Kirtland AFB Museum, Mel Burns donated a copy to the Air Force Historical Center at Maxwell AFB,AL, and a copy was donated to the Warner Robins Air Force Museum by Rich Wojick, and I sent a copy to the fols at NASA JSC Houston thaning them for hosting me last year to watch a suit-up and launch of prior # 503. Yes Bubba, NASA is presently flying (2) two "F"s and 295 is undergoing a wheels up complete rebuild in Colorado to go along with her two sisters. 293 is also in Colorado undergoing some sprucing up but doubtful if she will take to the air again, more likely will be a parts donor. Last month 2 people came outm of the woodwork and snatched the last two books I had. Stange part is I now have two more people wanting books so I stepped in the cow patty and ordered 10 more books at the original price, and another 50 Christmas cards, however unless I get a generous soul that will copy my master CDs for me, they will ot be part of the package this time. Office Max burned me last year when I ran out and needed a few more. I am also having some RB57F "Black Ball" patches made but the will only be availabe to book purchasers. The lady doing the embroidery is the granddaughter of one of my former Life Support troops, and she is doing it for me at her cost, so I will definitely not be trying to even break even on these.Anyone interested in a reunion, a former member of the 58WRS at Eielson and also at Kirtland has been hosting a get to gether ay BRANSON for the past 12 years. We had about a dozen there last year. If you're intersted at:Email CR Layton at: Conradlay@aol.com Great time, great friends, good shows and chow. email me if you or anyone you know want a book. jrp aka FTroopChief Garry Martin, e-mail, 06.06.2012 23:40Tom Cerny,This is Garry Martin, do you remember me? Everything you said was true as I was with the 58th from 1964-67 and worked on 288,289,290,291,292,293, 294&295.I was on a TDY at Eilson AFB in Fairbanks Alaska Dec.Mar.1964-65My home E-Mail is: garmart@camelliacom.com Garry Martin, e-mail, 06.06.2012 22:27Other E-Mail: garmart@camelliacom.com.I forgot to state in my narratice that I was with the 58th WRS, 4300 field, Kirtland AFB from 1964-1967. Garry Martin, e-mail, 06.06.2012 22:22Other E-Mail: garmart@camelliacom.comI noticed that at the top of this page it sayes: Strategic high-altitude reconnaissance aircraft based on B-57 bomber. The first prototype flew in 1966. I was station at Kirtland AFB, N.M. from Jan. 1964 thru 1967. During that time I was on the maintance crew on the RB-57B & F models. From 1964-67 I was on tail # 289,290,291,292,293,294.If you are interested;I have photos. M. L. Shettle, e-mail, 30.05.2012 16:33When Martin built this aircraft it was Top Secret. All flight testing was done at night. Steve Patterson, e-mail, 05.03.2012 02:28Gentleman, I was wondering if any of you had any stories about my father Bob Patterson. I believe he may have flown with Captains Laffon and Lackey out of Kirtland. There are many great memories spending time with the Laffon family on their ranch. My father passed away January 20th, 2009. GEORGE SUTTON, e-mail, 02.02.2012 20:27Was a captain/flight medical officer in F-troop 8/66-8/68, the went to UPT at Williams class 70-01 as Major then the Macdill,Takhli, Kunsan, in F-4E'S until leavinf for civvies as MD as an 0-5. Working on a book, more to follow. Wes Janeway, e-mail, 09.01.2012 09:42My Grandfather was Tsgt Jimmie Janeway. I have heard many stories about this plane and have lots of pictures of it. He passed away and never got to really talk to people about the missions and things he did or met the people he talked about. If any of you have anythings you would like to share or stories of him please try to contact me. My email is wesjaneway@yahoo.com Craig Schneider, e-mail, 13.12.2011 19:35My dad, Maj. Frank Schneider was pilot/maint. officer for the 58th WRS from July '69 to July '70. Lt. Col. Durden was one of his bosses. Loved it there. Wish we could have stayed there longer. Attended Cleveland Jr. High - 8th grade. Where can I get a RB-57F patch? Thanks. Kyle Laffoon, e-mail, 15.10.2011 03:00I've seen many comments about the 'F' first being used in '66.I don't think so. Lester Lackey, of Stepenville Texas, Texas A&M, flew out of Rhine Main in December of 1965. Him and back-seater were taken POW by Soviet Warships after the shot down RB-57 'F' hit the water a distance from Odessa, Ukraine.And, Yes, the 'F' was mostly made in Ft. Worth. As those in Marietta GA. were lucky to assemble a tail correctly. phil putnam, e-mail, 26.08.2011 01:27My father was Lt. Col. Joseph W. Putnam and was in the 1211th and the 58th. He flew out of Avalon AFB in Australia during those years 1962-66. Wonder if you knew him and any stories about those times? I’ve been in contact with quite a few AF buddies that knew and flew with him and am always interested in hearing more. ThanksPhil Will Sutton, e-mail, 23.08.2011 03:37Spent short period at Holloman AFB NM in '74-'75 on F-4D sims and saw some of these, or some modified, long-winged -57's, flying out of there. Bill Basile, e-mail, 05.08.2011 00:13I sure remember Roger Snider---He was my room-mate at Kirtland AFB. I never spent much time in the barracks since I was from Albuquerque. I really lived in downtown Albuquerque with my fiance (now my wife of 42 years). I left the 58th when my enlistment ended (I never thought I was going to live through my military enlistment). I can remember Sgt. Penz telling me that I would probably starve in civilian life (LOL). I guess he was wrong about starving, but I sure didn't end up to be President either. Oh, well, I can honestly say that the one incident I remember most was being so sick one day I did not come to work. I then had to report to Colonel Durden (maybe it was Major Durden)--in any event, he was so nice! However, his Chief Master Sargeant, I forget his name but he told me after meeting the Durden (spelling?) that I did not report to Colonel Durden properly--as if that would have made any difference! That incident taught me that there are those in the military who really care about the troops, and then there are those whose main concern is proper military etiquette (they are, IHMO totally out of it!). I will never forget doing my part in barracks clean ups!The other thing I will never forget was Friday, clean-up days--always using floor wax to both strip and wax the floors--I always thought that was pretty crazy! Roger, if you are still out there--I seemed to always get the Eilson TDY (just as you did) when it was 50 or more below zero! I can also remember how that TDY that Roger got to Mendoza, Argentina went on and on--I think it was for over 100 days--when that crew got back, the word was put out that TDYs would never again last 100 days, even though the Mendoza TDY was a very profitable one--probably the only one where people got paid more than $1 per day---I still wonder what lunatic in the Pentagon dreamed up the idea of sending troops for TDY at a$1 a day per diem! The Pentagon had to be run (probably as is true now of absolutely crazy MBA-type bean counters!) In any event, I went back to school--got my Master's at UNM--the University of New Mexico. My wife and I left Albquerque and went north to Denver. I got hired at the Auraria Higher Education Center. I retired from higher education, however, I am a life-long learner! I play recreational softball and enjoy life!! bill basile Bill Basile, e-mail, 05.08.2011 00:10I sure remember Roger Snider---He was my room-mate at Kirtland AFB. I never spent much time in the barracks since I was from Albuquerque. I really lived in downtown Albuquerque with my fiance (now my wife of 42 years). I left the 58th when my enlistment ended (I never thought I was going to live through my military enlistment). I can remember Sgt. Penz telling me that I would probably starve in civilian life (LOL). I guess he was wrong about starving, but I sure didn't end up to be President either. Oh, well, I can honestly say that the one incident I remember most was being so sick one day I did not come to work. I then had to report to Colonel Durden (maybe it was Major Durden)--in any event, he was so nice! However, his Chief Master Sargeant, I forget his name but he told me after meeting the Durden (spelling?) that I did not report to Colonel Durden properly--as if that would have made any difference! That incident taught me that there are those in the military who really care about the troops, and then there are those whose main concern is proper military etiquette (they are, IHMO totally out of it!). I will never forget doing my part in barracks clean ups!The other thing I will never forget was Friday, clean-up days--always using floor wax to both strip and wax the floors--I always thought that was pretty crazy! Roger, if you are still out there--I seemed to always get the Eilson TDY (just as you did) when it was 50 or more below zero! I can also remember how that TDY that Roger got to Mendoza, Argentina went on and on--I think it was for over 100 days--when that crew got back, the word was put out that TDYs would never again last 100 days, even though the Mendoza TDY was a very profitable one--probably the only one where people got paid more than $1 per day---I still wonder what lunatic in the Pentagon dreamed up the idea of sending troops for TDY at a$1 a day per diem! The Pentagon had to be run (probably as is true now of absolutely crazy MBA-type bean counters!) In any event, I went back to school--got my Master's at UNM--the University of New Mexico. My wife and I left Albquerque and went north to Denver. I got hired at the Auraria Higher Education Center. I retired from higher education, however, I am a life-long learner! I play recreational softball and enjoy life!! bill basile Glenn Wilder, e-mail, 13.05.2011 10:17I was stationed at Yokota AB Japan 1960 – 1961 serving as engine mechanic. My unit was the 3rd Field Maintenance Squadron. We supported the 8th, 13th and 90th Bomb Squadrons, 6091 Recon Squadron. Aircraft were RB57A, and B57B and C models. After Japan I went to 1211 Test Squadron (Sampling), later 58th WRS at Kirtland AFB, Albuquerque, NM from 1961 - 1963. We had RB/WB57B, C and D. Visited Christmas Island and Barber’s Point NAS Hawaii. The squadron received the F models after I was discharged. I will never forget the first time I saw a J65 start –up. CMSgt John R. Penz ret, e-mail, 24.04.2011 07:06I arrived at 58WRS from Iceland, 21 Oct,1964 and assumed Superintendent of Life Support duties. The A/P22s-2 Full Pressure Suits were all over-age hand me downs from ADC and immediately became my biggest challenge. Took some time, a lot of cooperation from MAAMA and 31 damn good troops. I was there until my retirement 1 Sep 1973. I was assigned additional duty of First Term Retention NCO and I'm sure a lot of the younger guys wished I would leave them alone, however I gave them the facts and let them make up their own minds. Called other bases so they could get their base of choice, and the highest bonus allowed. The 58th constantly had the highest reenlistment rate in 9th Weather Wing. Glad to see all the names here, hope everyone reads this: I AM NEGOTIATING A REPRINT OF THE SQUADRON HISTORY BOOK, and prices are dependent on the number of copies ordered. This will be a soft cover edition unless I can get a decent price on a hard cover.Please email me jpenz@stx.rr.com with any questions and be sure to indicate your desires. I will answer all emails received. Example: 20 books will cost $31+/- each, 75 books are$16+/- each and 100 books are \$14.02 each. + S&H.More are cheaper. Please reply ASAP. This is a non-profit venture. :) John P deaftom, e-mail, 05.04.2011 19:53This really should be listed under "General Dynamics" rather than Martin. GD took a B-57 and replaced everything on it except the fuselage, cockpit, horizontal tail, and landing gear. Everything else was totally redesigned, much enlarged, and built from scratch by GD, excepting the engines which were also totally different from the originals. So, both in parts count and in size, the W/RB-57Fs were more General Dynamics than Martin. Joe Smith, e-mail, 18.03.2011 00:05My first assignment was to 58WRS, from sometime in 1969 to sometime in the '70s. I left for Southeast Asia from Kirtland. I enjoyed the outfit and remember Lt Col Rothlisberger, Lt Col Durden, Capt. Powers, CMSgt Woods, SSgt Joe Dino, Col Oliver and many others.God bless you all,Joe Smith Roger Snider, e-mail, 26.02.2011 19:46My first assignment out of basic was the 58th, 68-70.I was a supply troop working in MSL got assigned to 503 than 501. Went to Rhein Main in 69 with 503 using the shuttered 7407th complex. All over the states with 501 for NASA earth resources. I remember my first TDY was to Eilson Alaska it was 67 below in Dec 69. Worked for Msgt Rushing, Lt. Powers, SSgt Lavoie. Many good memories. Robert Kissel, e-mail, 09.02.2011 00:42I WAS ASSIGNED TO 6220 CAMROM Yokota AB FROM 65 TO 68. I was an assistant crew chief working for S/Sgt CAVAZOS ON 503. Also station there was Ron shinn,Pete Baily and Dan Boatright. We all went to school on the RB AT KIRTLAND AB Tom Cerny, e-mail, 06.02.2011 19:16I don't understand the opening remark of the B57-F prototype first flying in 1966. I was with the 58WRS from 62-June of 65 and was the first crew chief on 288 in early 1965. The TDYs with this outfit were not my fondest memories. The last one I was on there was at Eilson in Fairbanks Al. Nov.Dec.Jan.1964-1965. Yeah right, over Christmas, and most the time in temperatures of arond 60 below zero. Some of the troops were great though. Fred Selders, SGT Yonkers, SGT Stutt,Harry Tipton, Mervin Nephew,Cletus Yingling all come to mind,and there were many more. Before the F model I was crew chief on 850 a B57C Tom Cerny, e-mail, 06.02.2011 19:16I don't understand the opening remark of the B57-F prototype first flying in 1966. I was with the 58WRS from 62-June of 65 and was the first crew chief on 288 in early 1965. The TDYs with this outfit were not my fondest memories. The last one I was on there was at Eilson in Fairbanks Al. Nov.Dec.Jan.1964-1965. Yeah right, over Christmas, and most the time in temperatures of arond 60 below zero. Some of the troops were great though. Fred Selders, SGT Yonkers, SGT Stutt,Harry Tipton, Mervin Nephew,Cletus Yingling all come to mind,and there were many more. Before the F model I was crew chief on 850 a B57C Sherman Willden, e-mail, 27.01.2011 17:22Whoops, old age hits again. I was at Kirtland from 1970-1976 Sherman Willden, e-mail, 27.01.2011 17:19I didn't know this site existed and I was glad to find it. I worked with the high-altitude suits from 1970-1984. I really enjoyed the experiences. Stan Martin, e-mail, 22.01.2011 19:20I worked on and recovered samples from the sampling system 1962 to 1966. Remember the D model that lost its wing as it was taxing to a parking place clsoe the the 58th hanger at Kirtland. TDY to Alaska, Johnston Island, Washington State, Panama, Indian Springs and Nellis. Loved the F model. It was great to work on and got a back seat ride out of Panama. Gary Christian, e-mail, 23.12.2010 04:06KAFB 69-71. Jet Engine Tech. I also remember Doug Southwick. Some of the other engine shop guys were Steve Pence, Mike Buell, Frank Marquez, Last name Castro, Pereira, and Clagett. Colonel Wolfe was squadron commander. Colonel Curt Dale, PhD, Ret, e-mail, 19.11.2010 07:08I was in the WB-57F, 58th WRS from 1968 to 1972. It was a marvelous experience. I was the Task Force Alpha Commander at Albrook Air Force Base, Panama for a period, and according to COMAC, General Jack Catton, the first Navigator to command any flying unit in MAC (maybe the AF--no matter!)and he liked the job I was doing and sent a letter of commendation to Col. Doug "Red Dog" Campbell and Col. Don Wolfe. It was a nice touch. It was one of those things that led to me eventually becoming a full colonel. Once, enroute to Panama, we were at 70,100 on my altimeter, and I cross checked it with the pilot. I've had a couple of folks say they got to 71K and another to 72K. Must have been incredibly cold. On one flight from Mendoza, I got down over the Anarctic Peninsula. I flew many missions in it up over the Northern Polar Region adding more to my record of polar missions, since I flew the WB-47E and WC-135 (dual current) in 55WRS, McClellan, and Det 1, 55th WRS, Eielson, as well as the "F" while later on TDY's to Eielson. My total polar missions--178. My North Pole crossings (in WC-135)-87. Hank Brauner, killed over the Trail in a C-130 Specter Bird had 105 North Pole Crossings, and 105 polar missions. So, he held one record and I the other. I did many of the WC-135 missions with him. I recognize many of the names above and some were great friends. I am in contact with many of them on e-mail. I went from there to Vietnam for my third tour. I was Chief of the Command Post for a while in the 58th then Chief Nav for a period until I left for DaNang. It was incredibly good to me. What a group. God Bless all. j. lloyd, e-mail, 08.08.2010 01:04Jet engine mechanic, 58th WRS, Dec64-Jul66. RB-57F and C. I was in the cockpit trimming a J-60. The guy on the ground got too close to the intake. He was sucked up to the intake. His line badge was hanging outside his shirt--the badge was sucked in the intake--one FOD J-60. The trooper survived with bruised ribs. We also got to participate in an overtemp of a J-65 on a "C" model during a jet-cal. Turbine buckets were flying like hornets from a busted nest--narrowly missing fuel cells. Then we got to go TDY to Panama, Australia and Alaska. Survived to make it to the PI to rebuild P-21s from dinosaur F-100s(from SEA) in 66. Changed AFSC and wound up going to Viet Nam and Thailand helping to chase Ho Chi Minh--worked A-26's and B-66's doing NDI.Names I remember from KAFB: Sellers, Rios, Southwick, Smith, Anderson, Dingman, Hillsendigger, Gullo, Rogers, Nestoric. My RAM's from the '60's have a lot of blanks.Chow,j. Lloyd Bernie Nordoff, e-mail, 02.05.2010 18:56I was a back seater in the 58th from 70 to 72. Tom Shull, one of the pilots, told me a 500 series with 2500 lbs of fuel and all 4 engines (110.6% on the 33's) going all out got to 69.9 thousand. It got to 70 but fell back down. The record low temp was -93C or -135F between Panama and the equator. Michael Schaniel, e-mail, 22.04.2010 09:31I was with the 7407th from 1961 - 1966, we had RB-57D's serial numbers 963, 970, 972, 974, 975 & 976. They were replaced with the RB-57F's. Jbaca16@comcast.net, e-mail, 05.04.2010 22:46I am the photographer/reporter that filmed the aircraft coming down in 1972 over Albuquerque. I wonder if that film still exists somewhere. You can read about this event at www.onlyinnewmexico.blogspot.com mike huskey, e-mail, 21.03.2010 18:02I was eng. mec. with the 07th at Rhine Main AB from 67to68when it was disband and have lots of good memories of the long wings and I remember Jim D.I have both patches we used and a few photos of the sq.with RB-57s 500&503.If any of the old 7407th are out there drop me a line some time. Jim Drummond, e-mail, 16.03.2010 17:29I was a crew chief @ Rhine Main AB 66-68We flew 500 503 until the squadron was disbanded in 68I believe it was 286 that spent the night in our hangar on its way back from Pakistan with wing damage Ron Pimentel, e-mail, 25.02.2010 23:56I worked at 58th WRS from 1963 till 1965, in perodic docks was then transfered to vietNam. Marty Martinez and Ralph Iantosca were transfererd with me. We worked on B57's with the 8th bomb squadron and later were transfered to C130's Had a great time at Kirtland with many fond memories. If you want some ariel photos of the RB57F you can find them on google eath at the Air Force boneyard in Arizona. What a sad fate for such a great aircraft. I'm still in contact with Ralph but lost contact with Marty, I last saw him in Viet Nam. Tom Barrolw, e-mail, 03.02.2010 19:24I was a Mission Manager (Backseater) for NASA Houston in the WB-57 until about 1982. On an Airstream air sampling mission for the Department of Energy flying out of Panama, Mike Swann and I reached a max altitude of 68100 feet. The airplane (NASA 928) was fitted with J-60 engines and was flying over the equator where the air at altitude was coldest. At that time, it was the highest altitude attained by a '57F by NASA. The ceiling quoted above (82000 feet) is not possible. Donald A. Brady, e-mail, 04.01.2010 03:45I worked on the air handling systems from 1969 to 1971. Spent many nights in the copit changing the sampler. Was NCOIC on second shift.Went to Panama , Argentina and Alaska. Loved Panama. John Newberry, e-mail, 31.12.2009 04:27I was with the 58th from Mar 62 to Mar 67 then transfered to the 56th WRS. I crewed 291 for 2yrs before going to Job Control. I believe 286 was the lowest tail number. I retired after 28 years. I have a lot of great memories with the 58th and many, many TDY's. Doug Perry, e-mail, 19.12.2009 18:28I saw a RB-57F fly low and slow over my house yesterday. Thought it might be a U2 but the wings were too thick. Had no idea what it was so I researched online and found the it to be the RB-57F. I live on the flight path of the Norfolk Naval Air Station. One online source states that they are now used on "geological survey" missions in Afganistan. There were no markings visible from my perspective. Steve Gulko, e-mail, 16.12.2009 15:47I was a airframe repairman assigned to Yokota Air Base 65,66,and 67. I was in 6220 Camrom, 41st AD. I was one of the tin benders working on the green birds. 501, 502, and 503. We were not air sampling. I am looking for anyone attached to those a/c at that time. Thank you I am also lookin gfor a picture of the radome art of the big nosed cobra in sunglasses named everette. I helped Bob Brandt paint that on when we were tdy to Thailand Emmet Cook, e-mail, 16.12.2009 01:28Hello CMS Davis. I worked for you on the Flight Line. I arrived out of Tech School in Jan 69 and was dischared in Aug 1972. I crewed 295 for about a year before being transferred to Docks. I remember Jim Janeway and Pat Pastori, Chief Houghton. In 2006 Pat Horton, Gary Christian, Frank Marquez and I met in Alq for a reunion. We had a great time and would like to do it again maybe 2011. Would you be interested? After I got out I went back to college and then joined the Army and retired 20 years later as a LTC. Hope to hear from you. I am fully retired and living in San Antonio, Tx. CMS Denis C Davis (RET), e-mail, 11.12.2009 22:18I was assigned to the 58th WRS from September 1968-July 1973.My first job was Crew Chief on aircraft 63-13288. Ronald Ray crewed 63-13286. Another Crew Chief I remember were TSt Jimmy Janeway and SSgt Cook. The Maintenance officer was Capt Mike Laird and the Deputy for maintenance was LT Col Gene Durden. Some of the pilots were Capt Clark, Maj Hoffman, Maj Blevins or safety officer, Lt Col Putnam, and Lt Col Raslisbuger. Not sure of the spelling of their names. We nicknamed Maj Hoffman hydraulic Hoffman as we felt he could smell a hydraulic leak from 100 yards. My second job was Dock Chief. Next I worked in Quality Control and was working their when aircraft 63-13292 crashed. We had been having problems with the horizontal stabilizer actuator and we felt we had the problem fixed. When this aircraft dropped from the sky, we began to second guessing our self. By the way, at the same time this aircraft was falling from the sky, a TV camera man was checking out his camera and captured this on film. I was sent to the site and was able to almost rule out the actuator. After the actuator was removed and sent in for inspection it was found to be in good working order. I was at the crash site when I was told by Lt Col Durden that I had orders to go to the 63rd Mil Airlift Support SQ. Kelly Air Force Base TX. Five days latter I was in TX.If I remember right it was tail number 63-13286 that was returned to the 58th from Pakistan. This aircraft was straddled by two SA-2Guideline missiles as it was descending towards Peshawar.Despite suffering major structural damage and sustaining over 170 holes, the pilot managed to land the aircraft back at Peshawar.The 58th WRS was like a large family. We had personal TDY all over the world 360 days a year. The Commander almost always returned everyone home at Christmas. When you were TDY some one would always check in with your family to make sure they were okay. We always had a picnic in the summer and a very nice Christmas party. The Christmas of 1969, my wife was expecting our last child and she did not have a dress for the Christmas party. LT Col Durdens wife became aware of this and showed up at our house with some of her dresses. She made over one of her dresses to fit my wife. We went on to have one of the best Christmas parties of our life. I could go on and on about how good this unit was but I think you understand by now.I spent the last 10 years at Beale A.F.B. working with the SR-71 and U-2/TR-1 aircraft.I retired from Beale A.F.B. in Oct. 1991 with 30 years service in the Air Force. Tom McLehaney, e-mail, 09.12.2009 20:15I was stationed at Kirtland AFB in the 58th WRS from 1966 until 1970. Steve, I remember you well, we worked together in the Autopilot shop. Sometime between 1966 and 1970, one of our RB-57F's crashed into the north side of Sandia Mountain while attempting to land at night-I don't remember the tail number but it may have been 292. If I remember correctly, the altimeter was found to be faulty leading the pilot to think he was higher than he actually was. The TDY's were definitely an adventure and we got to see and experience some great places-Argentina, Alaska, Panama and Germany are the one's I remember best. Ventura Franco, e-mail, 09.12.2009 08:46I was with the 55th WRS at KMCC and used to assist the turn around of the WB-57F's when they transisted KMCC..Any you guys members of the (Air Weather Recon Association)AWRA?? if not join really interestig stuff there..AWRA @yahoogroups.com also join the AIr Force Band of Brothers... Colin Heatherly, e-mail, 22.11.2009 02:10The serial numbers were 63-13286 through 63-13302 and 63-13500 through 63-13503 (21 Total) I was an aircraft electrician with the 58th at Kirtland from Oct 69 till May 74 when we deactivated. Best outfit of my Air Force career. Those were the days my friend. Loved the travel and the places we went. Mendoza, Panama, Alaska, just to name a few. 287 was lost before I was a member (somewhere over the black sea I’m told) and 292 was lost just south of Albuquerque while I was a member. I think it was either in 72 of 73. NASA still flies two of them. They fly 63-13503 as NASA 926 and 63-13298 as NASA 928. They were here at Nellis back in August and I got to talk to a few of the crew members and revisit my old airplane. Sure brought back a lot of memories. Still one of the most beautiful aircraft ever. Bob Svoboda, e-mail, 19.11.2009 19:17I believe the first tail number was 286. I was stationed at Eielson AFB,AK Det 5/9WRW. HASSAN, e-mail, 30.10.2009 12:11I NEED PAKISTAN AIR FORCE RB-57F IMAGE OR INFORMATION Steve Baker, e-mail, 20.08.2009 08:31I was also assigned to the 58th WRS at Kirtland from 1965 to 1968. I think you are exactly right about the tail numbers. As I remember it was 287. I worked in the auto-pilot shop. We probably went TDY together to either Panama, Alaska, Argentina, or Samoa. Ring a bell with anyone? sb Ken Swick, e-mail, 19.06.2009 01:58The last one flying is operated by NASA at Ellington Field Houston, Texas. I know the sound as the RB-57 before I see it. I live 1 mile from the runway and get to watch this (and many other types) fly diretly overhead on final. What a great place to live! Stan Martin, e-mail, 28.12.2006 00:15I was assigned to the 58th WRS, Kirtland AFB when the first General Dynamics B57's were delivered to us. I can't remeber the lowest tail number. I believe it was 287 or 288. I served from 1962 to 1966. I worked on the air sampling equipment.

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# Week 1

• C : Dmitry Chelkak (École Normale Supérieure, Paris, France)
Planar Ising model: from combinatorics to CFT and s-embeddingscourse page
In theoretical physics, the critical planar Ising model serves as a toy example, in which many precursors of Conformal Field Theory objects and structures exist and can be studied directly in discrete, before passing to the small mesh size limit. Mathematically, a number of results on convergence and conformal invariance of such limits were established during the last decade, both for correlation functions and for interfaces (domain walls) arising in the model. In this mini-course we plan to discuss
• discrete fermions and the Kadanoff-Ceva spin-disorder formalism - crucial tools that allow one to analyse the planar Ising model;
• streamlined version of the classical computation of the magnetization via orthogonal polynomials;
• results on convergence of critical correlation functions (energy densities, spins, ...) in bounded domains to CFT limits;
• recent ideas on appropriate embeddings of weighted planar graphs that play the same role for the planar Ising model as Tutte’s barycentric embeddings do for random walks, allowing one to use discrete complex analysis techniques beyond "regular" lattices.
• W : Ole Warnaar (University of Queensland, Brisbane, Australia)
Schur functions and Schur processescourse page
##### Monday, May 27
• 08:55 - 09:00 Opening remarks
• 9:00 - 10:30 Lecture (C1)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (C1)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:30 Lecture (W1)
• 3:30 - 4:00 Break
• 4:00 - 5:00 TA session (W1)
##### Tuesday, May 28
• 9:00 - 10:30 Lecture (W2)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (W2)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:30 Lecture (C2)
• 3:30 - 4:00 Break
• 4:00 - 5:00 TA session (C2)
##### Wednesday, May 29
• 9:00 - 10:30 Lecture (C3)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (C3)
• Free time / collaboration
##### Thursday, May 30
• 9:00 - 10:30 Lecture (W3)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (W3)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:00 Research talk: Marianna Russkikh (University of Geneva) - Dimers and embeddings
One of the main questions in the context of the universality and conformal invariance of a critical 2D lattice model is to find an embedding which geometrically encodes the weights of the model and that admits “nice” discretizations of Laplace and Cauchy-Riemann operators. We establish a correspondence between dimer models on a bipartite graph and circle patterns with the combinatorics of that graph. We describe how to construct a circle pattern of a dimer planar graph using its Kasteleyn weights. We also introduce the definition of discrete holomorphicity on such an embedding. We discuss the link between these functions and actual continuous holomorphic functions.
Based on:
• “Dimers and Circles” joint with R. Kenyon, W. Lam, S. Ramassamy;
• “Holomorphic functions on t-embeddings of planar graphs” joint with D. Chelkak, B. Laslier.
• 3:00 - 3:30 Break
• 3:30 - 5:00 Lecture (C4)
##### Friday, May 31
• 9:00 - 10:30 Lecture (W4)
• 10:30 - 11:00 Break with snacks
• 11:00 - 12:00 Research talk: Guillaume Barraquand (ENS) - Diffusions in random environment
We will consider the effect of adding a space-time white noise drift to a collection of independent Brownian motions. Using an integrable discretization of the model, we will see that the extreme value behavior for these diffusions is governed by the Kardar-Parisi-Zhang universality class which arises in random growth models and random matrix theory.
This talk is based on joint works with Ivan Corwin and Mark Rychnovsky.
• 12:15 - 1:15 Research talk: Cesar Cuenca (MIT) - Probability measures of representation theoretic origin
We introduce the BC type Z-measures as members of a 4-parameter family of point processes, with origins in the representation theory of the infinite-dimensional orthogonal and symplectic groups. The main result we present is that the BC type Z-measures are determinantal point processes with explicit correlation kernels, in terms of hypergeometric functions. In joint work with Grigori Olshanski, we have defined natural q-analogues of the BC type Z-measures. Our construction is based on the theory of q-hypergeometric orthogonal polynomials, though we hope that these measures can also be constructed from the representation theory of quantum groups. The last part of the talk is a brief overview of the quantization of the BC type Z-measures.
• Free time / collaboration

# Week 2

• S : Tomohiro Sasamoto (Tokyo Institute of Technology, Tokyo, Japan)
Fluctuations of 1D exclusion processes: exact analysis and hydrodynamic approachcourse page
One dimensional exclusion processes are stochastic processes in which many particles perform random walks under exclusion constraint. They have been playing important role in the fields of stochastic interacting systems in probability theory and non-equilibrium statistical mechanics in physics. For the last two decades, fluctuations of the processes have been studied quite intensively, since the seminal work by Johansson[1-1] on totally asymmetric simple exclusion process (TASEP) showing that the current fluctuation of TASEP with step initial condition is described by the GUE Tracy-Widom distribution. There have been a vast accumulation of generalizations and related results, but there are still many intriguing questions and problems to be solved.

In these lectures, we discuss a few new directions in the studies of fluctuations of exclusion processes. We also stress that such studies provide valuable insight to other methods based on hydrodynamic ideas which can be applied to a wider class of interacting particle systems. In the first lecture we review the basics of the subject. After introducing a few models such as the asymmetric simple exclusion process(ASEP) and the Kardar-Parisi-Zhang (KPZ) equation, we explain how one can study their fluctuations for the case of TASEP[1-2]. In the second lecture, we show that an approach introduced in [2] using Frobenius determinant can be applied to a large class of models in a unified manner. In the third lecture we explain our recent result on a two-species exclusion process and connection to the nonlinear fluctuating hydrodynamics[3]. In the last lecture we will consider an application of the techniques to study the large derivation in the symmetric exclusion process[4-1,2].

References
• [1-1] K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. (2009) 437-476. [arXiv:math/9903134]
• [1-2] T. Sasamoto, Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques, J. Stat. Mech. (2007) P07007. [arXiv:0705.2942]
• [2] T. Imamura, T. Sasamoto, Fluctuations for stationary q- TASEP, to appear in Prob. Th. Rel. Fields. [arXiv:1701.05991]
• [3] Z. Chen, J. de Gier, I. Hiki, T. Sasamoto, Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process, Phys. Rev. Lett. 120, 240601 (2018). [arXiv:1803.06829]
• [4-1] T. Imamura, K. Mallick, T. Sasamoto, Large deviations of a tracer in the symmetric exclusion process, Phys. Rev. Lett. 118, 160601 (2017). [arXiv:1701.05991]
• [4-2] T. Imamura, K. Mallick, T. Sasamoto, Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition, arXiv:1810.06131.
• Z : Paul Zinn-Justin (University of Melbourne, Melbourne, Australia)
Quantum integrability and symmetric polynomialscourse page
##### Monday, June 3
• 9:00 - 10:30 Lecture (S1)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (S1)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:30 Lecture (Z1)
• 3:30 - 4:00 Break
• 4:00 - 5:00 TA session (Z1)
##### Tuesday, June 4
• 9:00 - 10:30 Lecture (Z2)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (Z2)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:30 Lecture (S2)
• 3:30 - 4:00 Break
• 4:00 - 5:00 TA session (S2)
##### Wednesday, June 5
• 9:00 - 10:30 Lecture (S3)
• 10:30 - 11:00 Break
• 11:00 - 12:30 Lecture (Z3)
• Free time / collaboration
##### Thursday, June 6
• 9:00 - 10:30 Lecture (Z4)
• 10:30 - 11:00 Break
• 11:00 - 12:00 TA session (Z3)
• 12:00 - 2:00 Lunch time
• 2:00 - 3:30 Lecture (S4)
• 3:30 - 4:00 Break
• 4:00 - 5:00 TA session (S3)
• 6:30 - 9:00 Banquet at Himalayan Fusion ($20/person) # Research talks ##### Friday, June 7 • 9:00 - 9:35 Andrew Ahn (MIT) - Macdonald Plane Partitions and Product Processes The Macdonald plane partitions are a two-parameter family of deformation of the q^vol measure on random plane partitions. It was shown that, under a suitable limit, the Macdonald plane partitions degenerate to products of beta Jacobi ensembles, where the notion of product for arbitrary beta is an extension of free multiplication for unitarily invariant random matrices. We discuss a difference operators method which can be used to access global asymptotics of the Macdonald plane partitions. Under a suitable limit transition, we discuss how this method can be applied to access global asymptotics of products of beta Jacobi ensembles. • 9:40 - 10:15 Jules Lamers (University of Melbourne) - q-deformed Haldane-Shastry spin chain Abstract TBA • 10:15 - 10:50 Break • 10:50 - 11:25 Costanza Benassi (Northumbria University) - Thermodynamic Limit and Dispersive Regularisation in Matrix Models We show that Hermitian Matrix Models support the occurrence of a new type of phase transition characterised by dispersive regularisation of the order parameter near the critical point. Using the identification of the partition function with a solution of a reduction of the Toda hierarchy, known as Volterra system, we argue that the singularity is resolved via the onset of a multi-dimensional dispersive shock of the order parameter in the space of coupling constants. This analysis explains the origin and mechanism leading to the emergence of chaotic behaviours observed in M6 matrix models and extends its validity to even nonlinearity of arbitrary order. Based on a joint work with A. Moro (arXiv:1903.11473). • 11:30 - 12:05 Shalin Parekh (Columbia) - Brownian Meanders in Directed Polymers Stochastic partial differential equations (SPDEs) such as the KPZ equation arise naturally as scaling limits of various probabilistic and physical models which are driven or directed by i.i.d. weights. However, obtaining precise information about the behavior of solutions to these SPDEs poses tremendous difficulties. So far, the most fruitful approach has been to look at exactly solvable models which converge to these SPDEs, and then extract information about the SPDE from the limiting models. One such exactly solvable model is the Log-Gamma directed polymer. In this talk, we will realize a multiplicative-noise stochastic heat equation on a half space as a limit of these Log-Gamma polymers, and we will prove a surprising identity in distribution for such equations using the exact solvability. Our analysis involves obtaining intricate estimates for random walks conditioned to stay positive. • 12:05 - 2:00 Lunch time • 2:00 - 2:35 Yier Lin (Columbia) - KPZ equation limit of the stochastic higher spin vertex model We consider the stochastic higher spin six vertex model introduced by Corwin and Petrov with general integer spin parameter$I, J$. Starting from near stationary initial condition, we prove that the stochastic higher spin six vertex model converges to the KPZ equation under weakly asymmetric scaling. This generalizes a result of Corwin et al. from$I = J =1$(stochastic six vertex model) to general$I, J$. • 2:40 - 3:15 Ryosuke Sato (Nagoya University) - Asymptotic representation theory of quantum groups Asymptotic representation theory means studies of characters and unitary representations of inductive limit groups, for instance, the infinite-dimensional unitary group. A fundamental idea of asymptotic representation theory is to correspond characters to probability measures on a graph giving from branching rules of representations. In this talk, we discuss a natural quantization of this framework, that is, natural character theory of inductive systems of (compact) quantum groups. In particular, we give serious thought when a given inductive system consists of quantum unitary groups. • 3:15 - 3:50 Break • 3:50 - 4:25 Elia Bisi (University College Dublin) - Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation We introduce two families of symmetric polynomials that interpolate between irreducible characters of Sp(2n,C) and SO(2n+1,C) and between irreducible characters of SO(2n,C) and SO(2n+1,C). We then study the last passage percolation model with various symmetries via a number of identities that involve orthogonal/symplectic characters and our interpolating polynomials, thus going beyond the link with classical Schur polynomials originally found by Baik and Rains. We achieve this by applying the Robinson-Schensted-Knuth correspondence to triangular arrays and using a decomposition procedure for Gelfand-Tsetlin patterns. As an application, we provide an explanation of why the Tracy-Widom GOE and GSE distributions from random matrix theory admit formulations in terms of both Fredholm determinants and Fredholm Pfaffians. • 4:30 - 5:05 Yi Sun (Columbia) - Gaussian fluctuations for products of random matrices This talk concerns singular values of M-fold products of i.i.d. right-unitarily invariant N x N random matrix ensembles. As N tends to infinity, the height function of the Lyapunov exponents converges to a deterministic limit by work of Voiculescu and Nica-Speicher for M fixed and by work of Newman and Isopi-Newman for M tending to infinity with N. In this talk, I will show for a variety of ensembles that fluctuations of these height functions about their mean converge to explicit Gaussian fields which are log-correlated for M fixed and have a white noise component for M tending to infinity with N. These ensembles include rectangular Ginibre matrices, truncated Haar-random unitary matrices, and right-unitarily invariant matrices with fixed singular values. I will sketch our technique, which derives a central limit theorem for global fluctuations via certain conditions on the multivariate Bessel generating function, a Laplace-transform-like object associated to the spectral measures of these matrix products. This is joint work with Vadim Gorin. ##### Saturday, June 8 • 9:00 - 9:35 Matteo Mucciconi (Tokyo Tech) - Yang-Baxter Random Fields and Stochastic Vertex Models Starting from the notion of bijectivization of the Yang-Baxter equation [BP] we construct random fields of Young diagrams whose measure is described by spin Hall-Littlewood functions (sHL) and spin q-Whittaker functions (sqW). These are two families of special symmetric functions recently introduced in [B], [BW] that generalize Hall-Littlewood and q-Whittaker functions. The bijectivization formalism uncovers a Schur processes like structure for a number of stochastic integrable vertex models that are obtained as marginals of the fields of Young diagram. Among these we have the six vertex model, the higher spin vertex model or a rather complicated push-type system that generalizes the q-Hahn pushTASEP [CMP]. We also discover q-difference operators acting diagonally on the sHL and sqW functions and we use them to write formulas for observables of the vertex models. The talk is based on collaboration with A. Bufetov and L. Petrov. References: *[B] *A. Borodin, "On a family of symmetric rational functions" *[BP] *A. Bufetov and L. Petrov, "Yang-Baxter field for spin Hall-Littlewood symmetric functions" *[BW] *A. Borodin and M. Wheeler, "Spin q-Whittaker polynomials" *[CMP] *I. Corwin, K. Matveev and L. Petrov, "The q-Hahn pushTASEP" • 9:40 - 10:15 Mikhail Basok (Saint Petersburg State University) - Tau-functions a la Dubedat and cylindrical events in the double-dimer model Double-dimer model on a given graph is a random loop ensemble that is obtained by sampling two independent dimer configurations taken uniformly at random and removing double edges. Given a simplpy-conected domain and a sequence of "discrete" domains, drawn on a square grid, that approximate this domain (we assume that the step of the grid tends to zero) one can consider the corresponding sequence of random loop ensembles induced by the double dimer model in each discrete domain (seen as a subgraph of the square grid). It was predicted by R. Kenyon that this sequence of random loop ensembles converges to Conformal Loop Ensemble with parameter 4 (CLE(4)) sampled in the original domain. Recently his conjecture was deeply supported by a breakthrough work of J. Dubedat: in this work a large family of observables called topological correlators is introduced and it is shown that given sequence of a Temperley discretizations of a simply connected domain topological correlators converge to the corresponding observables for CLE(4). As a biproduct Dubedat showed that topological correlators for CLE(4) coinside with Jimbo-Miwa isomonodromic tau functions; this correspondens seems to be interesting in its own side. It turns out that these results of Dubedat acturally characterize the limit of double-dimer loop ensembles, i.e. the following corollary holds: if the sequence of measures induced by double-dimer ensembles in discrete domains is tight then it converges to CLE(4). We will discuss these results of J. Dubedat and the machinary developed to extract this corollary. Based on a joint work with Dmitry Chelkak (Paris). • 10:15 - 10:50 Break • 10:50 - 11:25 Mark Rychnovsky (Columbia) - Tracy-Widom Fluctuations for a river delta We consider an exactly solvable directed first passage percolation model for a river delta. We prove that asymptotically the width of the river delta of length L is order$L^{2/3}$with Tracy-Widom fluctuations of order$L^{4/9}$. We can also reformulate this result as a Tracy-Widom limit theorem for an interacting particle system sitting above pushTASEP. • 11:30 - 12:05 Guilherme Silva (Michigan) - Properties of the Limiting Distribution for the Periodic TASEP It is now a classical result that the one-point fluctuations of the height function in the TASEP (with step initial data) converge, in a suitable scaling, to the Tracy-Widom distribution$F_2$. In addition to the remarkable universality feature of$F_2\$, appearing in dozens of different models that are seemingly unrelated, this distribution also enjoys several nice different characterizations, for instance it can be given in terms of a somewhat simple Fredholm determinant, or in terms of a solution to the Painlev\'e II equation, or yet expressed via a Riemann-Hilbert problem.

Recently, Baik and Liu found an expression for the limiting distribution for the periodic TASEP. Their formula, somewhat complicated, gives this limiting distribution in terms of a Fredholm determinant. In this talk, after reviewing the just mentioned facts, we plan to explain how to obtain other expressions for Baik-Zhipeng's distribution in terms of a Riemann-Hilbert problem, or yet in terms of a nonlocal PDE, along very much the same spirit of the aforementioned properties of the Tracy-Widom distribution.

This is based on work in progress with Jinho Baik (University of Michigan) and Zhipeng Liu (University of Kansas)

Organizers: Leo Petrov, Axel Saenz

Scientific Committee: Jinho Baik, Alexei Borodin, Ivan Corwin, Vadim Gorin, Leo Petrov


text:
# Competitive Exams: Human Development Index

Only ten years passed since the PQLI was developed, another index came into being. Since 1990, an agency of the United Nations, viz. The United Nations Development Programme (UNDP) has been publishing every year a report called Human Development Report. This report, besides discussing various aspects of human development, has been ranking various countries according to the level of human development index. Before the human development index is described, it would be an interesting idea to look at the GDP/GNP from a fresh angle. It is pointed out that these measures are measures of activity and they concentrate on production of commodities--goods and services. We should, it is suggested, instead focus on capabilities and measure improvement in capabilities of people. Living long and healthy life is a capability and so is to be able to read and write. With rising capabilities, we have wider choices and development is what if not widening of choices! The idea has an added dimension that these capabilities cannot be accumulated. In a way it is close to PQLI except that now the theoretical scaffolding is strong. But at the same time, a non-physical entity will enter in the making of index and it will create problem for international comparison.

The Index

Human Development Index is broadly an average of social aggregates/averages of longevity, knowledge and access to resources. To put it more concretely, it is an equi-weighted average of:

1. Life Expectancy Index (LEI)
2. Education Attainment Index (EAI)
3. Standard of Living Index (SLI)

where the sub-indices were to be calculated by the same old method of the PQLI. In other words.

HDI = (⅓) (LEI + EAI + SLI)

## Components

Life expectancy here refers to life expectancy at birth, not at age one, because infant mortality is not entering this index as a separate indicator. Educational attainment is literacy plus. To begin with, it was only adult literacy. Later on, it became a combination of adult literacy rate and mean years of schooling. In highly developed countries, adult literacy was complete but education level was still rising. This could be reflected through mean years of schooling or enrolment ratio. Now, mean years of schooling have been replaced by combined enrolment ratio. The weight assigned to adult literacy rate (ALR) is ⅔ while that for combined enrolment ratio (CER) is ⅓ Therefore, educational attainment index may be given as:

EAI = (⅔) ALR + (⅓) CER

Standard of living is represented here by a transformation of per capita income. Besides longevity and knowledge, it has been argued, there are many things which people desire. It is difficult to capture them. For living a decent life, people need resources. Per capita national income is the simplest measure of resources at the command of people. Since this exercise has basically been conducted for international comparison, per capita incomes of different nations have per force to be brought to some common denominator. Per capita incomes are first converted into purchasing power parity dollars (PPP$). The second step concerns with the fact that the returns to a dollar of income is not the same throughout the whole range of income. The increase in returns should diminish as income increases and should eventually become zero. This idea was handled by the UNDP in a variety of ways. Presently, standard of living is being captured by the log-transform of per capita income (PCI) in PPP$. In other words.

Standard of living = log (PCI in PPP$) At base 10, logarithms of 10, 100, 1000, and 10000 are 1, 2, 3, and 4 respectively. Thus, returns to additions in income are diminishing as income goes on increasing. There could be many other ways to accomplish this feature. The UNDP has tried other formulae in past but thought it proper to change to simple logarithm conversion. ## Normalisation Since we are using only positive indicators in this index, we can write only one formula for computing the component indices (CI): CI = Actual Value-Minimum Value/Maximum Value-Minimum Value where CI stands for LEI, ALRI, CERI and SLI. It may be noted that ALRI and CERI are just ALR and CER respectively, each divided by 100. ## Minimum and Maximum Values After a lot of debate over years and following the norms for various components, the UNDP has finally fixed the following minimum and maximum values for various components of Human Development Index. ## HDI and India The United Nations Development Programme (UNDP) has been compiling human development indices for different countries for which it had access to relevant data. These indices are published in Human Development Report, brought out annually by the UNDP. Notice that the data compilation takes time. We can also notice Between the last two years, we find, India's rank improved by 13 while number of countries dropped by 12. It is quite possible that most of the countries excluded were above India. We should also notice that India's rank improved by 2 from 123 in 1988 to 121 in 1990 while the HDI value actually fell. It is possible because of change in methodology and components used. Despite these weaknesses, we can see that India's HDI value is improving since 1990 when it recorded its lowest value. Fortunately, HDR 2001 has calculated HDI values for different countries on uniform basis with same methodology by ensuring comparability across nations and over time, at an interval of five years since We should notice that our HDI is improving since the mid-seventies. Perhaps we are improving on all fronts, life expectancy (reflecting health to some extent), education (including literacy) and general standard of living (represented by per capita income). The UNDP has been categorising various countries as countries with high human development, with medium human development and with low human development, depending upon whether a country had HDI value above 0.8, between 0.5 and 0.8 or below 0.5. Prior to 2000, India was considered as low human development nation. In 2000, it has become a country with medium human development. It will not be out of place to inform that some scholars have done interstate comparison for India while some state governments have come out with state-level exercises for human development index. These reports do contain more information on human development than are available in compilation of HDI. Since March 2002, our Planning commission has also come out with a report known as National Human Development Report. ## Quality of Life Index Some economists still feel that, though human development approach talks of many dimensions, the human development index encompasses only very few of them, though important ones. They feel that political and civic dimensions, if not environmental ones, need to be incorporated in any such exercise. In one such contribution ‘On Measuring the Quality of Life’ Dasgupta and Weale have considered six parameters what they have called living standards'indicators or constituents of well-being. These are: • per capita income in PPP$
• life expectancy at birth in years
• infant mortality rate in per thousand live births


text:
Proof that $(A-B)\cup(B-C) = (A\cup B)\cap (A\cup C^c) \cap (B\cap C)^c$

I drew some Venn diagram's and constructed a couple of sets and this claim seems to hold (correct me if I am wrong). I have difficulties proving this however. I have tried to rewrite the lefthandside using the set identities, but no dice so far. Can anyone give me a hint?

Start by simplifying LHS: \begin{align} (A-B) \cup (B-C) &= (A \cap B') \cup (B \cap C') \\ &= ((A \cap B') \cup B) \cap((A \cap B') \cup C') \\ &= ((A\cup B) \cap (B' \cup B)) \cap((A \cup C') \cap (B' \cup C')) \\ &= (A\cup B) \cap (A \cup C') \cap (B\cap C)' \end{align}
• $(A - B) = (A \cap B')$
• Distributive property of $\cap$ and $\cup$
• Demorgon's Law: $(B' \cup C') = (B\cap C)'$


text:
How do you plot -7-i on the complex plane?

draw a straight line $x = - 7$ perpendicular to the real-axis & straight line $y = - 1$ perpendicular to the imaginary axis. The point of intersection of these two straight line will represent the location of point $\left(- 7 - i\right)$ on the complex plane.


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# Tag Info

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### How are mipmap levels computed in Metal?

Mip selection is pretty well standardized across devices today—with the exception of some of the nitty-gritty details of anisotropic filtering, which is still up to the individual GPU manufacturers to ...
• 23.6k
Accepted

### Why use a tent filter in path tracing?

The theoretical ideal antialiasing filter for discretely sampled data is a sinc filter, because it perfectly removes all frequencies higher than the Nyquist frequency, while leaving alone all the ...
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### Anti-aliasing / Filtering in Ray Tracing

There is a great paper from 2006 on this topic, Filter Importance Sampling. They propose your method 2, study the properties, and come out generally in favor of it. They claim that this method gives ...
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### Help me grasp Anisotropic Filtering (AF)

To understand the nature of anisotropic filtering, you need to have a firm understanding of what texture mapping really means. The term "texture mapping" means to assign positions on an object to ...
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### Path tracer - multi layered materials and importance sampling

Wenzel Jakob et al presented a framework for layered Materials at SIGGRAPH 2014. Section 6.2 explains importance sampling. If you prefer code over equations, the method is implemented in the Mitsuba ...
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### Ray tracing - partial derivatives for texture lookup

Yes, ray differentials are the way to go. The Paper by Igehy introduces them for the use case of filtered texture lookups. When generating the primary rays, you initialise the differentials to reflect ...
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### Pixel dispersion (dissolving) algorithms

A very simple low memory approach If you really want to use as little memory as possible, it can be done with not much more memory than that required to store a single image (the first frame) ...
• 5,882

### What does filter mean in glint rendering and texture mapping?

Filtering refers to image processing operations that generate a new image by applying a filter kernel to an existing image. This is used for many purposes, but one of the most common is to resample ...
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### Texture units parameters in OpenGL

Your understanding of the behavior of texture units and state is confused. That's to be expected: OpenGL's pre-DSA API is not making it easy to understand this. As far as core profile OpenGL is ...
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### Kaiser windowed sinc filter for mip mapping

I was curious so I tried it. I used the Kaiser Window from Wikipedia: $\frac{I_0\left(\alpha\sqrt{1-x^2}\right)}{I_0\left(\alpha\right)}$ This page has a slightly different formulation using \$\pi\...
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### Unexpected results from Mitchell-Netravali

Mitchell–Netravali has negative lobes, which are generally not recommended for small sample counts from what I understand; you tend to end up with both the positive and negative areas undersampled. ...
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### Plotting pbrt-v3 Gaussian filter

You probably want to set sigma to be a fraction of the radius, rather than a fixed value. Sigma controls the actual shape of the filter, while radius just controls how far out the filter gets cut off (...
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### Why use a tent filter in path tracing?

I just looked at Wikipedia articles about Bilinear interpolation. A tent filter is a kind of Bilinear interpolation. A Bilinear interpolation interpolates on 2 dimensions. It first linearly ...
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### Help me grasp Anisotropic Filtering (AF)

A few points that you probably already know, but that I just want to put out there for others reading this. Filtering in this case refers to low-pass filtering like you might get from a Gaussian Blur ...
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### Pixel dispersion (dissolving) algorithms

You could do this entirely within an OpenGL/WebGL fragment shader: Attach the image you wish to emerge as a texture/sampler2D. Attach uniforms for the current time, as well as the time you want the ...
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### Does film filter introduce bias in path tracing?

This is an answer to your comment rather than the title of your question. It can be considered as a partial answer. The bias in path tracers are introduced by the estimators. For example, think of the ...
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### How does the GPU know whether to magnify/minify?

Minification vs magnification is an extension of mipmap selection. When you calculate the desired mip level, it can come out to be less than 0 (or in general, less than the sampler's configured ...
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1 vote

### What is a common approach to smooth structures in textures?

I don't have enough rep to add a comment so... You could use a post process based anti-aliasing technique like FXAA or SMAA. Also, if performance is not a priority, you could go for SSAA. Another ...
• 110
1 vote

### Suggested image preprocessing before applying threshold

In your case, I don't think a pre-processing is necessary. You may find the Hough transform useful in your case. Since your image is big, it can be difficult to have a straight line due to the noise ...
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Only top scored, non community-wiki answers of a minimum length are eligible


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accumulation points

• Sep 23rd 2010, 09:10 PM
EmmWalfer
accumulation points
how can you prove this theorem from the book?

A finite set has no accumulation points.

I know that it's true, but fail to show it mathematically :(
• Sep 24th 2010, 06:13 AM
Ackbeet
Are you working in the real numbers? What ideas have you had so far?
• Sep 24th 2010, 11:03 AM
Danneedshelp
Quote:

Originally Posted by EmmWalfer
how can you prove this theorem from the book?

A finite set has no accumulation points.

I know that it's true, but fail to show it mathematically :(

Well, if you construct an epsilon neighborhood around a proposed limit point x in your finite set, then the intersection of your set with the epsilon neighborhood of x must contain points in your finite set other than x for x to be a limit point (accumulation point). If you can show this doesn't hold, then you are done.
• Sep 25th 2010, 05:26 AM
HallsofIvy
The definition of "accumulation point" is: p is an accumulation point of set A if and only if every neighborhood of p contains at least one point of A (other than p itself). Suppose A is finite. Then the set of all distances from p to points in A (other that p itself) is finite and so contains a smallest value. Take the radius of your neighborhood to be smaller than that value.

(I notice now, that is pretty much what Danneedshelp said!)
• Sep 25th 2010, 09:44 AM
Danneedshelp
Quote:

Originally Posted by HallsofIvy
The definition of "accumulation point" is: p is an accumulation point of set A if and only if every neighborhood of p contains at least one point of A (other than p itself). Suppose A is finite. Then the set of all distances from p to points in A (other that p itself) is finite and so contains a smallest value. Take the radius of your neighborhood to be smaller than that value.

(I notice now, that is pretty much what Danneedshelp said!)

I am not a 100% this correct, but I recall a lemma from my intro to real analysis book that stated something along to lines of: a point $x$ is a limit point (accumulation point) of a set $A$ iff for every $\epsilon>0$, the neighborhood $N_{\epsilon}(x)$ contains infinitly many points of the set $A$.

I think you would have to prove this to use it, but it answers your original question rather quickly.


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# Hierarchy of Mathematical Spaces

I really got lost among all those many different spaces in mathematics, and I got really confused what is special case of what.

For example, I knew for long time vector spaces, then Hilbert spaces, that I thought about as infinite dimensional vector spaces, then discovered that there is topological vector spaces, and that Hilbert spaces actually just a special case of, while the "usual" for me vector spaces are actually algebraetic vector spaces... etc.

Are there some visual, or written hierarchy model for those many different space? so one will understand what is the most fundamental object we start from? And what is a special case of what?

Something like Topology=>topological space=> if we equip it with metric we get.. => if we equip it with norm we get ..

Edit

Something like to what is mentioned in Space (Wikipedia) or Connections between metrics, norms and scalar products.. (StackExchange) but with more details and subfields and what is the additional assumed structure.

This is a (probably icomplete) hierarchy of vector spaces from the point of view of functional analysis.

1. Vector spaces: algebraic structure (addition and multiplication by scalars)
2. Topological vector space: vector space with a topology such that addition and multiplication by scalars are continuous.
3. Locally convex topological vector spaces: TVS in which $0$ has a basis of convex neighbourhoods.
4. Fréchet space: LCTVS whose topology is derived from a translation invariant metric, complete.
5. Banach spaces: Fréchet space in which the metric is given by a norm.
6. Reflexive Banach spaces: the cannonical homomorphism between the space and its double dual is an isomorphism.
7. Hilbert space: Banach space in which the norm comes from an inner product.
• On the off chance it's not clear from context, Hilbert spaces are a type of reflexive Banach space. – Theo Bendit Jul 17 '15 at 11:58
• Every Hilbert space is a reflexive Banach space. – Julián Aguirre Jul 17 '15 at 15:49
• Ok good try but it makes me just more confused... for example: Fréchet space has metric, but LCTVS has not? then between them there should be Metric spaces I suppose? or Metric vector spaces? also somewhere between them I suppose should be also complete metric vector spaces also...etc, it is a mess! – TMS Jul 18 '15 at 11:50
• In all these spaces the algebraic structure and the topological structure are related. In TVS addition and multiplication by scalars must be continuous. Other topologies are, as far as I know, of little interest. In Fréchet spaces, the metric is translation invariant. And yes, there are non metrizable LCTVS. – Julián Aguirre Jul 18 '15 at 13:24