text:
The Reluctant RoVer
Thoughts and observations about traveling and living in a recreational vehicle.
An excellent vacation, despite the rain
November 8, 2015--This has been an excellent vacation, despite the weather (rain, rain, and more rain).
When we received the invitation to attend Webster's 90th birthday party, we decided to make a vacation out of the event. Originally, we intended to arrive at Webster's on Friday and leave on Monday morning. From there, we weren't sure where we would go...perhaps to the barrier islands, perhaps to the mountains.
We tried to find camping on the barrier islands (outer banks). All of the state parks are closed for the winter. We found some private RV parks, but their cost was prohibitive. So we canned the idea of camping on the islands.
It was then that Jim remarked that Colerain (the town of 200 in which Webster resides) is close to the Virginia border as well as the outer banks. Also, he said, that whole area was "full of history."
I'm sure I knew it at one time, but I had forgotten that North Carolina was one of the original 13 colonies. The coastal areas of North Carolina are rich in history, dating long before the Revolutionary War.
We decided to make Webster's backyard our home base and explore the coastal area and fish through day trips.
Our first stop was Edenton, a small community of less than 8,000. Sitting on the Albemarle Sound, its quaint colonial downtown stands sentry over the waterfront, complete with a number of cannons from the Revolutionary War era.
Outside of the town is the Edenton National Fish Hatchery, where shad, bass, sturgeon and other species are hatched, raised, and released in area streams and lakes. The biologists had just finished loading some fish into tanks to be transported to other locations, but one of the biologists took time to show us how the fish are hatched and raised. He also showed us some baby sturgeon. I did not realize how prehistoric they look! No scales!
We took a short hike on the 25-acre property. As we were returning to the car, the biologist started to feed the baby fish in the several ponds. Even before the food pellets hit the water, the surface teemed with thousands of fish, waiting for their meal. He said they hear the tractor and the food machine approach and wait to be fed.
From the hatchery, we drove into Edenton and found the visitors' center, which is in the Penelope Barker house, located on the waterfront. The visitors' center also serves as a small, free museum that shows off a number of items, mostly maritime-related.
A half block away from the visitors' center was the Roanoke River Lighthouse, which opened on the Roanoke River, about eight miles away from its current location, in 1866.
Roanoke River Lighthouse, Edenton, N.C.
This lighthouse is believed to be the last remaining square screw-pile lighthouse, which helped guide mariners along the North Carolina shore. The lighthouse was decommissioned by the Coast Guard in 1941. Finally in 1955 a private citizen purchased the lighthouse and had it moved to Edenton, to serve as a private residence. In 2007 the structure was moved to a location on the Edenton Waterfront in Colonial Park. In 2012, it was again moved to its current (permanent) location over the bay, in Edenton Bay. The interior restoration was completed in 2014.
We also drove around Edenton and looked at the historic buildings. During the summer, the town has trolley tours available for tourists.
The next day, we drove up to the coast to see Kitty Hawk and to fish. The biologist we spoke with at the hatchery had told us fishing was really good right now.
The Wright brothers had their historic first flights at Kill Devil Hills, a few miles south of the town of Kitty Hawk. A small museum houses reproductions of their first manned airplane, as well as the glider they used to learn about flying like the birds. A monument stands atop Kill Devil Hill.
Likewise, monuments identify where the first flight took and where it landed (quite a short distance!), as well as the spots where the next three flights landed. Each flight grew progressively longer.
The first flight on December 17, 1903, lasted just a few seconds and covered 120 feet. How awesome is it that we are able to go beyond the moon in manned aircraft, just 112 years after that first humble flight.
Monument commemorating the site of the first flight of the Wright Brothers.
History and museums are interesting, but we wanted fun, too. We headed to the beach, where we lugged our fishing tackle to the shore, determined we would pull in all types of fish.
It was not to be. But we really had fun. Jim changed into shorts and waded into the surf. I tried to stay dry on the beach. The water was chilly; the sun did not come out; the mist threatened to turn into showers. But we had a great time. We also tried our hand fishing off a bridge. People were pulling them in...until we arrived. Then the wind changed, and the fish stopped biting.
Jim got soaked but had a ball surf-casting. He caught one little fish, which he threw back.
We had a great time.
We finally left Webster's on Friday morning and drove down to south of Wilmington, where we hoped to do go to a kite festival and do some fishing. After calculating the time it would take to get to the kite festival, we decided to stay home. Jim wanted to be back in time to watch the FSU game; I wanted to watch IU. Alas, both teams lost heart-breakers.
After the game, we drove into Wilmington. Jim had perused a visitor's guide, which said the city of 89,000 had a river walk. We found the river walk (under construction and not appealing at night). We also discovered that Wilmington has a very vibrant after-dark downtown area on Front Street (near the river walk). Dozens of restaurants attract hundreds of patrons. We ate at a Vietnamese restaurant. We shared a Vietnamese pancake as well as a fried flounder covered with a fruity and vegetable salsa and a tasty sauce (all gluten-free). We've never had such good Vietnamese food.
Today, our plans to fish have been squelched by the weather. The temperature dropped to a high of only 58 today, with rain. I doubt we will wet a hook.
So what that we can't fish here? We can always fish at home. After all, Jacksonville is laced with creeks and rivers and bordered by the Atlantic Ocean, so we can take a "vacation" any time we want.
This vacation, however, has been great.
Until later,
Your Reluctant RoVer,
Posted by Linda No comments:
No opportunities in disguise
November 3, 2015--Some people say that problems are opportunities in disguise. I say (at least in regard to Junior, our motorhome), they are frustrations, plain and simple.
On this trip we have experienced a couple new "challenges"-- the gas furnace hot and the hot water heater.
First, the furnace. The RV has two heating systems: An electric heat strip and a set of two gas furnaces. The furnaces are actually new (installed at no cost by the manufacturer as a beta test three years ago). We've only used them a few times, since we rarely cold-weather camp.
I think the last time we used them was when we camped in Raleigh three years ago. At that time, the temperature fell below freezing. We had attempted to use the heat strips (which work off the AC condensers), but it was too cold for them. (I believe we actually damaged the rear AC condenser at that time.) After that trip, the rear furnace blower would come on by itself occasionally; Jim had to remove the fuse.
The manufacturer of the beta furnaces sent a tech out to identify and fix the intermittent blower problem, but of course, since it was an intermittent problem, he couldn't find the cause. (We're lucky like that.) The furnaces, however, worked fine, last time we used them.
Now? They won't come on. At all.
We can't run the heat strip because it takes too much amperage (we only have 20 amp power from our complimentary plug in at Webster's). This brings us to the second part of the heating problem--our space heater.
We bought a space heater when we purchased our first RV. Although it is five years old, it has only been used a few times. On this trip, the evenings have been chilly and damp, so we needed a source of heat. Since the furnaces don't work and we can't use the electric heat strips, we plugged in the space heater. The first night we had no problem; we were toasty warm running the space heater. The next night was another story. Jim plugged the heater in, and after a few minutes, he saw it arc, then shut off. So long, space heater.
Yesterday, we found a Walmart and purchased a new ceramic space heater.
Now for our second "opportunity"--out hot water heater. It was working fine on both electric and gas power sources, then suddenly it stopped working. No hot water, using either gas or electric heating sources.
Two years ago we had a problem with the hot water heater; the thermostat had gone bad. (That happens, no big deal.) This time, however, we don't think it is the thermostat. We think it is the circuit board, because the heater won't work at all, on electric or gas power.
These are annoying problems, but I am tired of them. Enough, already!
Your frustrated Reluctant RoVer,
Posted by Linda 1 comment:
Don't look a gift horse in the mouth
November 2, 2015--The adage goes, "Don't look a gift horse in the mouth." It means that when someone is kind enough to give a gift, the recipient should be grateful.
We are semi-dry-camping at Webster's, with the RV parked in the back yard near an out-building that has electricity. When we pulled in, Becky (Webster's daughter) said we could plug into a 20 amp circuit if we wanted to. We declined, saying we didn't need to; we had a generator. If we plugged into the electrical circuit, we would not be able to use all of our appliance or electric heat, because we need at least a 30 amp (and preferably a 50 amp) circuit.
So, we opted to run our generator so that we could have all the conveniences of home, on our own terms. However...
After only two days of running the generator (we had driven about 200 miles on the tank of diesel), the generator quit. The generator quits when fuel gets down to a quarter tank. It's a safeguard so that you can still drive to get fuel.
Once the generator quit, the gift of 20 amp electricity looked pretty darn good. We decided to take up the offer. If we care careful, we can watch TV, make coffee, and run the space heater all at the same time, but we can't turn on the microwave. For that we can only watch TV and use the microwave. Figuring out which appliance we can use at one time is like doing a mathematical puzzle: Add up the amps and make sure they don't go over 20.
We had no hesitation in accepting Webster's offer to use his shower. Our water tank was only partially filled when we got here, and the grey water tank was also partially filled. Instead of taking "navy showers" we often use public showers when we dry-camp, so accepting Webster's hospitality was right in keeping with our boondocking. His water pressure is weak, and the water is very hard, but hey! We've learned not to look at gift horse in the mouth.
November 1, 2015--No tricks; all treats yesterday at Webster's 90ths birthday party.
Webster (Jim's uncle--his mother's brother and the only surviving sibling of nine) has lived in this rural northeastern North Carolina community his entire life, except for when he was in the military.
For most of those 90 years, he has lived in the same house!
Webster and Jim after his birthday party
The BIG birthday party
When someone resides and is active in a community that long (he was a successful farmer and an active supporter of education in the area), he becomes well known.
Webster is a genuinely nice man. He still drives (like a bat out of hell); fortunately his eyesight and reflexes still seem good); he still keeps a very large garden. And from that garden he keeps family and friends in vegetables all summer and fall. We will be going home with a huge bagful of green beans, many more sweet potatoes than I'll eat in six months. a bagful of raw peanuts (which are grown in the area), and some pecans from an ancient tree in his front yard.
Webster's birthday party was not a small affair. His five kids (and he) invited more than 175 people. Altogether more than 200 showed up for a luncheon party of fried chicken (really looked good), Carolina barbeque, barbequed potatoes, lima beans, corn, corn bread, and a whole lot of gluten-filled desserts in addition to the birthday cake. (Jim and I ogled the fried chicken and desserts and wished that the gluten could be taken out of it just this once.)
Although all five of Webster's children threw the party for him, his daughter Becky was the primary organizer. I asked her whose idea the party was. "Dad's!" she said. She said about a month or so before the party, he approached her:
"I guess I have a birthday coming up."
"Yes, you do, Dad. It's a big one."
"Guess it is kinda important...so I'd like to have a party."
Although he said he wanted to pay for it himself, she and her brothers refused the offer. A father only turns 90 once.
I'm glad we were here to help him celebrate. It was a great time.
Looking forward to treats, not tricks
October 30, 2015--The last time we went on the road--to the Midwest for four weeks during the summer--we had plenty of tricks waiting for us when we returned.
The first week we were gone, a woman from the neighborhood lost control of her car and turned it over in our adjacent neighbor's yard. The accident took out an electrical transformer and created a significant power surge. So significant that it blew every controller in our house. We lost our refrigerator, the swim-spa controllers, our heated mattress pad, some GFIs, and the sprinkler system.
The refrigerator was the worst: All the food (about $350 worth) was putrified, and the refrigerator had to be replaced. Worst of all were the flies. Where did they come from? I don't even want to think about it.
The good news is we had an early Halloween treat: The auto insurance finally settled the claim--in full. My checkbook is grateful.
So, we hope not to have any more tricks. We are experiencing some treats, however. Yesterday we left home for a trip up to North Carolina. Jim's uncle Webster is celebrating his 90th birthday. It will be a small party...his daughter says she has confirmations from 196 people! Webster is quite popular in this small farming community.
We took our time driving up. We actually stopped in Brunswick, Ga., and had an oil and lube job done on Junior. We then drove another few hours and stayed the night at a Walmart in Florence, S.C. We woke up to chilly weather. We definitely don't need the AC, but we do need some warm blankets.
We are now dry-camping in Webster's backyard. We will be here for a couple of days. We would like to go to North Carolina's barrier islands and fish for a few days, but we are having trouble finding economical RV camping. If we don't go to the islands, then we may go to the mountains. Who knows? It is rather nice not having a schedule and just being able to relax.
I'll let you know where we end up.
Oh...one more thing: I am pleased with my new AT&T hotspot. Until recently, this area of North Carolina was hostage to one small cellular company. None of the big networks worked. I was pleased to find that AT&T now has service here...at least most of the time. And my hotspot works great.
August 21, 2015—We've been back almost a week, and I am finally taking a look back at our 4 1/2 week adventure.
And adventure it was:
We had electrical problems. No AC for the first day. Jim still has to solve the electrical problems with a permanent fix, but at least he had a work-around so that we had lights and AC.
We had limited internet. I will not use T-Mobile any longer for a mobile hotspot. Although I checked ahead of time that I would have 4G connection, I rarely had it—only in big cities or along the interstate.
We had car-battery problems. We anticipated that the battery would die; Jim needs to put some type of trickle charge on the battery to keep it charged while the car is being towed. But we had another problem, too, which turned out to be a bad battery connection. The bright side: We learned how to get a car out of park when the battery is completely dead. And we learned about some fuses on the battery cable that need a good connection. Oh, and yesterday, we replaced the battery in the car. It finally died altogether.
We had a near-accident. When the tow-bar hitch pin broke, the tow bar fell off the car, while we were traveling 60 mph. One of the safety cables also broke. Luckily (very luckily) we had no permanent or bad damage to either the car or the motorhome.
Our trip was "highlighted" at the end by coming home to a dead refrigerator and putrid, month-old spoiled food. The problem was caused by an auto accident outside of my neighbor's yard. A woman from down the street hit the transformer in the front yard, wedged the car between the transformer and the cable box, and turned the car on its side. The accident took out power for the whole neighborhood and caused a surge that took out the fridge. I now have a new refrigerator. I don't know how much I will get back for the fridge and the spoiled food.
We traveled 3,048 miles round trip, spent $840 on diesel and only $587 on RV parks. I did not track our food expenses, but we did not eat out all that often. Neither did I track our amusement expenses. All in all, though, for having spent 34 nights on the road, it was not an expensive vacation.
Most important: We had a good time. My best times, of course, were spent with my family and with my Peru Group friends. But I enjoyed all of the trip.
Jim is ready to go again, but it will probably be October before we head out somewhere, because of medical appointments.
Catchin'
August 15, 2015—Carrabelle, Fla., is a small gulf-coast town on the Forgotten Coast. It is so small—or was so small—that in 1959 there was only one police officer. In the 1960's, the force increased to two, and the police station was a call box bolted on a building at the intersection of two streets. Because the police would get soaked when it rained, the phone company finally built them a phone booth. It was recognized as the "World's Smallest Police Station." The phone booth still exists.
Carrabelle does not offer much in the way of fancy dining, but it offers great gulf fishing.
The old Carrabelle police station--the world's smallest police station.
We are located at HoHum RV Park just outside of the city limits. Our motorhome faces the gulf.
Yesterday, after checking the local charts to find out the best fishing times, and we hit the pier at 3 p.m. when the fish were supposed to be hungry. We had bought some frozen shrimp for bait. I baited my line, cast it, and within minutes I had a strike!
What did I catch? A shark! It was a black-tip. Although these sharks are edible, we unhooked it and threw it back in to grow up a bit more. (I may have seen its mother or father or big brother swimming in front of our coach last night. I saw the shark fin in the water, just yards off the beach.) I caught three or four fish yesterday. Jim caught one or two, I believe.
My first catch--a black-tipped shark!
Today, the charts again said the fish would feed between 3 and 5 p.m., so we headed to the pier. It was a catchin' day, although the catches were not keepers. Almost every cast brought tugs on my line. The fish were very hungry, and we accommodated them. A few also accommodated us.
Altogether I caught about six or seven fish of various species, including a black sea bass (too small to keep), and an ocean catfish. Jim also caught a catfish and a couple other small fish. We were told that the catfish were "trash," not worth keeping.
So we threw them back in.
Probably a mistake. I researched ocean catfish this evening. The species we caught was the hardhead catfish. You have to be careful when touching them, because they have poisonous spines (not fatal, just painful), but everything I read said that these fish are edible and have a mild flavor, similar to snook.
Last night, we also did some night fishing. We didn't have much luck (we'll try again this evening), but it was fun—made even more enjoyable as we watched fish jump and create a phosphorescent swirl in the water. The phosphorescence is created by the bioluminescence of tiny organisms in the water. Cool!
It is our last night here. In a few minutes, we will go out and fish for the last time. Who knows? Maybe we will even catch tomorrow's dinner!
Tomorrow we pack it in and head home. Our vacation will be over, but we have resolved to come back here. It is just so relaxing!
August 15, 2015--The sky sparkled with stars. The Milky Way was visible. In the far distance, we could see lightning; it was far out into the gulf, no threat to us on the fishing pier.
We dipped our lines, but did not have even one nibble. Yet, we had a most enjoyable evening on the pier.The reason: the phosphorescent salt water.
Whenever we cast out our lines, the bait hit the water with a splash that glowed. The hooks sank and waited...and waited. But the fish were not hungry.
They were there, right in front of us, by the hundreds. How did we know? Every time a big one jumped, schools of little fish scurried in the water. Each of them left a trail of luminescence. How cool was that?
Jim and I were mesmerized by the bioluminescence. It was truly entertaining.
I could not take a picture of the phenomena; the trails were sporadic and did not last long enough to capture. Our last fishing adventure in Carrabelle did not give us dinner. Instead, it gave us a memory to last a lifetime--or until the next time we visit HoHum RV Park again.
August 14, 2015—What a way to end a vacation—a vacation of more than four weeks.
We are in paradise, a spot of leisurely heaven located on the Forgotten Coast of Florida. The Forgotten Coast is just that: few tourists, few residents. Lots of coast, water, sun, fun. It is in the panhandle of Florida, away from the hustle and bustle of the big tourist traps.
We found this RV park through a blog. Called HoHum RV Park, it is, well, ho-hum. Its rules say it is only for adults—no kids allowed. It has no amenities to speak of—no pool table, no swimming pool, no clubhouse. What it has is the Gulf of Mexico, free cable TV (with a comprehensive list of channels, none of that basic stuff), and free excellent wifi. It's the best wifi we have experienced in any RV park.
All of the sites in the park have a view of the gulf, but ours is parked front-window-facing the water. I am not one to sit outside, but last night that is what we did, until nightfall. After dinner Jim went out again and stayed outside until a storm threatened. He was looking for meteors. He also enjoyed actually seeing the Milky Way, which is not visible in the light-contaminated skies of Jacksonville.
At one point last night, he came in and showed me his tablet. He called up the weather map, curious to know how far south/southwest lightening strikes were occurring. The map showed they were all the way down by Tampa! Remarkable that we could see the light up here in the Panhandle.
Later, around 2 a.m., Jim came in and asked if I was still awake. He beckoned me to the front of the RV, to look out at the threatening rain storm. The wind was picking up; slightly white-capped waves lapped the rocks below our motorhome. Then the sky opened up with sheet lightening. Spectacular. Finally, rain pelted our fiberglass box. We were cozy as the rain came down.
We are here to fish and to relax. Fishing (as usual) has not been good. But I don't care. If I catch anything, I will post a picture. But no one has been catching. It doesn't matter. It is just nice to sit back and relax.
That's exactly what I plan to do right now.
Mr. Fixit does it again: Let there be shade!
August 12, 2015—Sunshine is delightful. It caresses your skin, makes you feel warm inside. Especially when the temperature hits the 90+ mark and you are sitting in a 40-foot long aluminum box called a motorhome.
We bought our motorhome more than two years ago "as is," which meant that La Mesa (the dealer) did not repair anything that was not functioning, except for safety issues. Before we purchased Junior, however, we talked with the technician, who had gone over the coach from head to toe. He told Jim the things that needed to be fixed. (We now know he had not found everything, but that is par for the course when you buy a pre-owned motorhome.) Included in his list were two awnings—the little one over the entryway and big one over the kitchen slide. Both are products of Carefree of Colorado; both are automatic awnings with anemometers, which measure wind speed and communicate with the awnings electronic boards. When the wind gets too gusty, the awnings are supposed to fold up automatically.
Nice feature, if it works.
The technician had told us that neither of the automatic awning worked: The electronic board in the small awning needed to be replaced, but he said that the automatic feature of the big awning could be by-passed and the awning would work manually.
The awnings have not been a priority issue with Jim, but this week he finally had the opportunity to look at them. The technician was probably correct about the little awning. He was right about the big awning. Jim found wires that were not connected. When he connected them, voila! We have awning!
Mr. Fixit does it again.
The awning will help reduce the load on our air conditioner, and we will enjoy our couple of days at the HoHum RV Park in Carrabelle, Fl., sitting in the shade and looking at the Gulf of Mexico, when we are not fishing.
Huntsville: Lost baggage, rockets, and barbecue
August 11, 2015—It's always nice to be surprised. Huntsville was a surprise to me.
I don't know what I expected—perhaps a southern city filled with antebellum mansions, like Charleston, S.C. (Huntsville is in the south!) Perhaps the city does have these types of homes, and maybe even remnants of plantations, but we did not see them. Instead, we found a clean, modern small city that was not congested with traffic.
Sunday we drove into the city to visit the Welcome Center and get information about area attractions. The downtown area was quiet; most businesses were closed, including most restaurants. The Welcome Center was open from 12-5. We were early, so we stopped at a railroad museum up the street from the center. It was closed, but we walked around and looked into antique train cars and other memorabilia.
The railroad museum in Huntsville was closed on Sunday, but visitors could walk around the grounds and peer into the trains and other antique artifacts, such as this International Harvester truck.
The people at the Welcome Center who greeted us were very friendly and helpful. We left with information on the U.S. Space and Rocket Center (which we intended to visit), as well as brochures on various "trails" such as the barbecue trail. (The area has many other "trails" that we did not pursue.)
Our plans were to visit the Space Center on Monday, then go to the Unclaimed Baggage Center in Scottsboro on Tuesday. We were smart, however, and checked the weather on the way to the Space Center. Good thing: The forecast called for heavy thunderstorms, due to hit just at the time when we would be at the outdoor museum or on a bus tour of the Redstone Arsenal. So, we flipped our plans and headed to the Unclaimed Baggage Center.
Both of us had heard of this "department store." The company buys up all unclaimed baggage from airlines, opens suitcases, sorts and cleans contents, prices items, and displays them just like a discount store.
You would be amazed at what goes unclaimed—from reading and prescription glasses to cell phones to household goods and, of course, clothes. Even underwear.
I wondered, though, if all of the items were actually from unclaimed baggage, or does this store use that handle but buys up goods from other places? Some items appeared brand new.
We both expected bargains. Not so. At least for the cursory shopping we did. I did not look at any women's clothes, but I looked at price tags on many things, including cameras and electronics, such as computers and tablets and i-Pads. Anyone shopping at this store should do homework first and know what goods are going for new and used before buying.
Our decision to visit the store on Monday and the Space Center on Tuesday was a good one. Just as we returned from the Unclaimed Baggage Center, the rain drops started to fall. Then we had a full-blown rain storm with winds up to 30 mph. Several RVers in the campground, including a couple out on their first camping trip in their brand new motorhome, lost their awnings to the wind.
Today we headed back into Huntsville to tour the U.S. Space and Rocket Center, purportedly America's largest space artifact collection.
Jim had been there in the 1970s, but, of course, it was completely different today than it was back then. Rockets greet you from miles off. The Saturn V rocket, which took the astronauts to the moon, was (and still is) the biggest rocket. The Space Center has one standing tall as a 363-foot sentinel to the indoor/outdoor museum. Inside one of the buildings is another Saturn V rocket, mounted horizontally, so that you can see the three-stages of its components.
The Space Center is where kids go to Space Camp. We were told that several hundred may be there at any one time. We saw several groups with their camp leaders touring the grounds.
In addition to learning about the space program, including the shuttle program and the International Space Station, we enjoyed going on the simulators. One carried passengers up a tall tower and dropped them down. Another was like a carnival's tilt-a-whirl—we experienced G-force. I did not care for this particular simulator, because it became difficult to breathe!
The Saturn V rocket is huge!
The Saturn V rocket does not look big from a distance, but it stands 111 meters tall.
We also bought tickets for a tour of the George C. Marshall Space Flight Center, previously known as the Redstone Arsenal. This is where Werner VanBraun and his crew of German scientists developed the first rockets that propelled America into space. It is also the home to the International Space Station's payload operations and integration center, which we saw in operation. Not much going on...but I guess the people in the center get paid well to handle things when there is an emergency.
Our day ended with a trip to an award-winning Alabama barbecue restaurant in Decatur, a suburb west of Huntsville.
The tour of the Marshall Space Center included a visit to the International Space Station Payload Operations Center.
This is where engineers and other experts manage the payload operations of the International Space Station. They are in constant communications with the astronauts on the station.
When Werner von Braun and his team of scientists and engineers designed the first rockets, called Redstone rockets, they tested the rockets at this stand.
In the distance in the center of this picture is the test stand for the Saturn V rocket. When the engineers tests the five engines on the first-stage of the rocket, they fired them up all at once. It is said that the noise and vibration from the blast of these engines could be felt more than 200 miles from Huntsville.
What a disappointment. We have eaten better barbecue at Monroe's and Sticky Fingers in Jacksonville. The meat tasted very smoky, but the choice of sauces was limited.
We had chosen to stay at this resort partially to be able to fish. It is on a huge man-made lake (Lake Guntersville), but the weather has been so hot that the fish have not been biting. We enjoyed the scenery, however. The area around Huntsville is gorgeous.
Tomorrow we are headed toward Florida. We have decided to spend three nights in an RV park that is located directly on the gulf, and we have a front-row spot reserved for us. We will attempt fishing there. Whether the fish will bite is unknown, but I am sure we will have a restful stay.
A near disaster (literally)
August 7, 2015—Stuff happens. And sometimes when it happens, it gets very scary. One of those sometimes was today.
We had spent the night dry-camping at a Walmart in Henderson, Ky., and decided we would head toward Huntsville, Ala., where we would relax, go to the space center, and fish. We found an ideal place on Lake Guntersville, about an hour from Huntsville.
As you enter Alabama from Tennessee on the interstate (or any other highway for that matter), you drive in the mountains. They are not particularly high, but some grades are very steep. At one point, we were behind a truck that must have been carrying a very heavy load. It crept along at about 20 mph. We didn't rush or try to pass, because our own engine was laboring, too. When we got to the top of the mountain and a rest area, we pulled over for the engine to cool off.
Steep grades going up mean steep grades going down. Frequent signs warn trucks (which, in this case, includes motorhomes), to shift into low gear to descend the mountain.
(I don't like mountains. They are nice to look at in the distance, but I don't like to drive in them.)
Finally, the hard climbs seemed to be behind us, as we were traveling along at 60 mph (never higher) on Interstate 24. It was a level area. Suddenly we heard and felt two thumps and simultaneously a car passed us blaring its horn. Jim always drives in the right lane (because we never travel more than 60 mph). He immediately slowed, pulled over onto the shoulder, and stopped.
He said his first thought was that we had blown a tire.
Not so. That would have been bad. What happened could have been worse. We got out and ran to the back of the motorhome to see what had happened.
I did not take a picture of the car butted up to the RV. But after I moved it back, in this picture you can see the broken tow bar and the sheared off safety cable.
The motorhome got scuffed a bit from the car butting into it. Also, the mud flap has a bit of damage, which can be fixed.
In addition to the tow bar, the hitch has two steel safety cables attached to the car. They are supposed to keep the car from running away if the tow bar comes off the car. In this case, the tow bar came off the motorhome. The cable on the left in this picture sheared into two parts.
Just below Jim's hand you can see the frayed wires in the electrical cable. It was unusable.
The pin that held the tow bar to the motorhome's hitch broke!
It was a locking pin; lock sheared off and the pin came out. The tow bar dropped to the ground. One of the two steel safety cables broke. The electrical cable that plugs into the car to work its lights also frayed and was unusable. Fortunately, the car bumped into the motorhome instead of veering off the road. If that had happened, the car would have turned over, been totaled, and possibly would have caused other cars to collide.
We were lucky.
Jim had an extra tow-bar pin and reattached the car. I Googled RV dealers in the area. About 20 miles down the road, we were able to buy a new electrical cable. We finally arrived at the resort about an hour later than planned.
This was a freak accident, but it proved the adage, "Stuff happens."
The moral of the story: Check the tow-bar pin (and every other pin holding the bar and the hitch) before every trip.
Until later, your very grateful,
Reluctant RoVer
Chicago, Chicago!
August 6, 2015—Chicago. As cities go, it's the best. Of course, I am biased, because I was raised a mere 45 miles from the Windy City. I even lived and worked there as an adult, from 1993-1998.
Chicago has so much to offer, especially the food. You could eat in a different restaurant every day of the week (and I don't mean the chain restaurants) and never repeat yourself and barely repeat the ethnicity of the cuisine.
Jim and I settled into our campsite in Elgin, Ill., a western suburb, on Sunday, and then visited with Jennifer and her family. We then decided on how we were going to spend the few days we reserved to "tourist" Chicago: Monday, the Museum of Science and Industry; Tuesday, an architectural riverboat tour; and Wednesday, a visit to the Field Museum of Natural History and the Millennium Park.
As a child, I had visited the Museum of Science and Industry (MSI) many times. We loved going there, because even 50 years ago, the museum was interactive. I remember my favorite exhibits were the development of human life (fetuses in various stages of development); the coal mine; the U-boat; and the television exhibit, where we would walk in front of a huge TV camera (they were BIG back then, and only shot in black and white) and see ourselves on a monitor. Hi, Mom! I'm on TV! It was a blast.
The fetuses are still there, and they are still as interesting to me today as they were when I was a child. The coal mine and the U-boat (German submarine) are now paid exhibits; we chose not to visit them because both Jim and I had been in them before. The television exhibit I knew would not be there. Kids are not impressed with walking in front of a camera and being on television! They do it every day! Such is technology.
Jim had not visited MSI since he was in the Navy in 1955, so he was eager to return. It was the one thing he wanted to do in Chicago.
We were both disappointed.
Interactivity is good, but the museum has too much interactivity, which results in too much noise. Too many things going on at one time. And too many kids. All the kids want to do is pull levers and push buttons; they don't stop to read and learn anything. The science, too, has been dummied down to fit into an abbreviated attention span.
I think we both enjoyed the last thing we visited at the museum: The Silver Streak Pioneer Zephyr. This train had sat outside of the museum for many years. For that reason, I don't think I had ever been in it. When the museum expanded (and also put its parking underground, a surprise to me), the train was brought inside and restored. We had a tour of the train and were able to go into several of the cars.
Architectural Riverboat Tour
While I lived in Chicago, a friend from Michigan visited me. We did the Miracle Mile; we also took a boat tour of the city.
My friend Sharon (a Peru Group 1965 pal) still works as a docent on the Architectural and Historical Cruises out of the North Pier Docks. When she offered complimentary tickets to a boat tour, I took her up on it. I knew we would both enjoy the cruise.
The cruise offers a perspective of the city that few people get. I don't know anything about architecture, but I appreciate the variety and differences in style among the many buildings that make Chicago unique. The docent (it was not Sharon, unfortunately) was excellent. She told us the history of buildings and could name all of the architects who created the high rises we gawked at. It was a wonderful 90 minutes.
Just as I had enjoyed MSI as a kid, I also enjoyed going to the Field Museum. My favorite exhibits were the dinosaurs and the mummies. They are still there, but they have been improved. In fact, the whole museum has been improved.
Although the Field Museum is much more traditional, it has interactivity. And the exhibits have been put together to capture and retain interest. Jim and I felt we could spend days there; our time was too limited. If we return to the city, we will return there.
The Field Museum has a lot of dinasours, but the most famous is Sue, this T-Rex in its central lobby. Sue is the most complete T-Rex ever found.
Everyone told us we needed to visit Millennium Park, which serves as a town center for Chicago, with its free concerts and other events. We were told we needed to see the Bean and the Fountain Faces (Crown Fountain). No one adequately described what these were.
I don't think I can describe the Bean. It is a huge piece of architecture that looks like, well, a bean! Its shiny surface acts a giant concave mirror.
This is the Bean, a piece of architecture that is a centerpiece of Millennium Park, Chicago's new city center for cultural and fitness activities.
The Crown Fountain has two towers--one on either end--that show continuously changing faces. The towers are actually fountains, which spill water into the area between them. Everyone is welcome to wade and splash in the shallow pool.
In the center of the park is a pool fed by two fountains--tall structures on which surface faces continuously appear and change.
The park offers more than these two features, but that was all we had time to see. We headed back to the subway, but made sure we stopped by a Garrett's Popcorn Shop. I needed my "fix" of the Garrett Mix—half caramel corn and half cheddar cheese. Jim was disappointed the shop did not offer more varieties of popcorn. Me? I savored every kernel.
The best part of our visit? Need I say it? It was being with my family—my daughter Jennifer, her husband and my two Chicagoan grandkids. Nothing could beat that.
Jennifer (front) Greg, Campbell, Ben, Linda and Jim. The best part of our Chicago visit.
The challenge of urban camping
August 2, 2015--On our first trip up to Raleigh, N.C., to visit Rob and his family a few years ago, I searched everywhere for a campsite. I found one in state park only about five miles from his house. Beautiful location, right near a lake, in the woods. But camping in North Carolina was problematic: The park closed at dusk and rangers put a chain and lock at the entrance! In Florida, parks close at dusk, but campers are given a code to enter to get back in. In North Carolina, no such luck. You have to park the car outside of the gate and walk to your motorhome (in pitch black darkness). And that can be quite a hike. We did a work-around the first night we were there, by taking the motorhome to Rob's house and parking it on a side street while we went to his birthday party.
The next time we went to Raleigh, I made another search for campgrounds, and this time I discovered we could camp at the State Fair Grounds. I think we had electricity; I can't remember if we had water. It, too, was only a couple of miles from his house, and we could come and go as we pleased. The campgrounds were also policed, so we were secure. No amenities, but who cared? We were there to park our traveling hotel.
I learned from the Raleigh lesson to check local and county fairgrounds and parks for camping facilities. These are not usually listed on ReserveAmerica.com or in the Good Sam Camping Directory.
On our trip to Chicago, I did my research and kept coming up with few alternatives. We wanted to camp near my daughter in Palatine, Ill., (a suburb), and we also wanted an easy commute into Chicago where we could become tourists.
My daughter lives very close to a village park. I even called the parks department to find out if we could dry-camp there. We were told we could, if there were no events going on, but on reflection we decided that because the parking lot was on a busy street and would be unguarded, we did not want to leave our motorhome unattended there.
I finally found four options:
• The truck staging area behind McCormick Place Convention Center. No electricity; no water; no sewer. Just a place to park for $35/night. That would be OK, except or two things: The neighborhood (especially at night) is not what I would call safe. And you have to walk about a mile to catch public transportation. We decided McCormick Place was not a good option.
• Fish Lake Beach Resort. This RV campground is located in Volo, about 45 miles from Chicago, accessible by Metra train. It cost $35/night for electricity and water, no sewer.
• Illinois Beach State Park. This park is located in Zion, way north of Chicago. Like Fish Lake, it is about 45 miles from Chi-town. It would be possible to catch the Metra. But both Fish Lake and Illinois Beach were quite distant from Jennifer's house. I believe the cost was $25/night for non-residents.
• Burnidge Forest Preserve In Elgin, Ill. This was the best option. No sewer hookup, but it did have electricity and water (on some sites). And best of all, it was 30 minutes from Jennifer as well as from the L-station near O'Hare. The only problem: The forest preserve did not take reservations.
We decided to take a chance on getting a spot at the forest preserve in Elgin. I am glad we did. It was convenient and relatively inexpensive ($25/night for non-residents).
If you are traveling to the Chicago area, I recommend this campground. However...be aware that the water has a very harsh iron taste ; there are no community showers, so you will have to take "Navy showers" in your RV, and you may need extra long hose for water hookup. (Not all sites have both electricity and water.) There are two dump stations.
Driving to Chicago can be a nightmare and an expense. (We did drive to the Museum of Science and Industry, because it is so far south. The cost to park was $22.) At my daughter's suggestion, we drove to the Cumberland L-station and parked for $5/day. We bought an all-you-can-ride CTA pass (for the L and city buses) for $10 a day. (You can also get one for $20 for three days, as well as other longer-term options.)
Taking public transportation is an adventure, but CTA drivers/employees are very helpful in advising how to get around the city. The city also posts CTA routes on nearly every block, so it is not difficult to figure out the system.
Although I lived in Chicago for several years, I lived and worked in the fringes of the city. Both my workplace and my apartment were very suburban and were located on the far north side of the city. I rarely ventured into the city center, except when I had company who wanted to visit some of the attractions. Obviously, I am not a "big city" person. I prefer the calmness of the suburbs. But, every few years it is OK to fight the crowds.
We had a good time.
A letter to Mom and Dad
August 2, 2015—I am writing this as a letter to Mom and Dad:
Dear Mom and Dad:
Yesterday we celebrated your lives. Dad, you have been gone for eight years, but we have not forgotten you. All of us got together in Arizona after you left us, and we celebrated your life. Mom, you left us in March. It was now time to say our good-byes to both of you.
According to your wishes, the seven of us (as well as most of your grandchildren and even some great-grandchildren) gathered and had a true celebration of your life. We reflected on how well you raised us to become successful adults and parents.
The Seven Siblings, from the top in order: Judy, Linda, John, Nancy, Michael, Dawn, Sally
We gathered; we ate; some enjoyed wine; and we talked and laughed until late each night.
In honor of our heritage, Dawn arranged for our Friday night dinner to be stuffed cabbage, Polish sausage, and (because you really liked it, Mom) Italian beef. Everything tasted great.
Saturday, we again met at Dawn's in the morning. And we each said our good-byes to you. We made this a happy occasion, Mom. Not because you are gone, but because you gave us each other. No gift could be so great.
When our laughter, our memories, and our tears were done, we climbed into our cars and drove down to Lake Michigan. It was there that we dispersed your ashes. It was a fitting place.
I know that when Dad courted you took you, Mom, to Lake Michigan on dates, although when you were young you did not swim. As we were growing up, it was a special treat when you and Dad took us to Miller Beach or the Dunes State Park. The water was always so cold! We were always faced with the decision: Do we jump in and get wet in one, quick splash, or do we dip our toes in, sink down to our knees, and acclimate ourselves to the cold lake water little by little? I think I usually chose the bold approach.
We loved it when Dad would play with us, throwing us in the water from his shoulders. What great memories!
I always hated, though, walking on that hot sand and getting sand up under my bathing suit. The sand was not any cooler yesterday. I made a beeline over the hot, soft sand to the cool packed sand of the lakeshore.
Each of us, even the grandkids, took part in our private ceremony. We each said our good-byes in our own way.
Afterwards, we went to Innsbrook Country Club, where we had celebrated your 50th wedding anniversary. We had a room to ourselves, and we had a great time.
Finally, we ended up back at Dawn's, where we again ate and talked and talked and ate. It was as you would have wanted it.
Mom, I think you were always concerned that the seven of us would not get along and we would no longer get together after your passing. When we were kids, it was natural for us to bicker and tease. That is the nature of kids; they do that. As adults, we moved away (at your urging).We are scattered throughout the country, from California to Florida. Distance —and the fact that we are separated by age—has made it difficult to be close friends.
But somehow, when we get together, age, different interests, and distance are forgotten. It does not take long to reestablish the natural bond between siblings. We can have our differences, but we respect them. We enjoy each others' company.
So, do not worry, Mom. We are family; we will always be family. Yes, we live our own lives. Yes, we have different interests and goals. And yes, we have different economic bases. But each of us has had a successful life, due in large part to your urging.
We don't want to wait for another funeral to get together again. It is hard to come together, because we are so scattered. You wanted us to be independent and to get away from the Calumet area, and most of us succeeded, to the point that, as you know, we are from coast to coast.
But we will reunite, hopefully without waiting too long.
For now, Mom and Dad, I want to say good-bye one more time. You have left us, but in reality you are not gone. Almost every day I want to share something with you, and I do, in the privacy of my thoughts.
You will always be with us in spirit. We love you. I love you.
RVs, cars, history, and family
July 31, 2015—Visiting attractions in a new area is fun, but when you can do it with family (especially family you have not seen for a long time), the occasion becomes special.
We spent three days in northeastern Indiana (Elkhart area), and then drove up to Marshall, Mich., to visit with Rob, Corky and the grandkids.
I spent the first half of my life as a Hoosier, but I had never really visited the Elkhart area. I had just driven by on the interstate highway.
Jim had done some research, which indicated there were actually a lot of attractions (mostly museums) in the area. Among them, which we visited, were the RV Hall of Fame, the National Military History Center and Kruse Automotive and Carriage Museum (a two-for-one one with admission), the Auburn Cord Duesenberg Automotive Museum in Auburn, Ind., a windmill museum, and Shipshewana Flea Market (open Tuesdays and Wednesdays). (We got "museumed out" and also ran out of time. The area has several other museums.)
Elkhart Museums
The National Military History Center was interesting, but I do not have an optimistic outlook for it to survive. We were the only visitors. The attendance (who, I believe, was a volunteer) said that the museum had been forced to sell off a number of its exhibits a few years ago, but was not acquiring more.
Linda stands with General Eisenhower and his secretary (also his mistress) in front of the car Ike used in WWII.
The exhibits the museum had were interesting, especially the original vehicles used in several wars.
Included with the price of admission was the Kruse Automotive and Carriage Museum, housed in the same building. It, too, was worth seeing, especially if you like old cars. This museum was not dedicated solely to cars; it exhibited some very old carriages and some very new cars.
The Kruse museum displayed many types of vehicles, including this Indy racer. Getting into the racer was not too difficult, but getting out was hard, as Jim discovered.
The RV/MH Hall of Fame displayed an assortment of antique recreational vehicles. We could go into many of them, although the oldest were off-limits. The evolution of the RV, from its earliest days, was intriguing. As technology improved, so did the RVs
One of the first motorhomes
The seats on this antique motorhome don't look too comfortable.
With the history of RVs firmly in mind, we asked the museum docent about tours of RV plants. About 80% of all recreational vehicles in the United States are manufactured in the Elkhart area, and a number of the manufacturers gives tours.
RV Manufacturing Tour
We went to the Thor Company, which manufactures all classes of motorized RVs: A's, B's, and C's. We would have preferred witnessing the assembly of a Class A; however, on the day we visited, the only tour available was for a Class C.
In our journeys, we have toured both the BMW manufacturing plant in Spartanburg, S.C., as well as the Corvette plant in Bowling Green, Ky. Both were highly automated, with probably 80% to 90% of the assembly done by robots. The plants were so clean and tidy that you could almost eat off the floor!
The Thor assembly plant was quite a contrast to the auto plants. About 90% of the RVs are assembled by human labor. And the manufacturing floor showed it. The plant was not as neat as the car manufacturers.
One of the attractions we visited was the Auburn Cord Duesenberg Automobile Museum in Auburn, Ind., about an hour east of Elkhart. This is a world-class museum, one that I have wanted to visit ever since I heard about it more than 25 years ago when I lived in Muncie, Ind. It was worth the time.
The Auburn Auto Manufacturing Company operated in Auburn, Ind., from 1900 to 1937. It manufactured high-end automobiles. Some cost more than $8,000 in the late 1920s! Needless to say, that was a lot of money for that time period. These autos were hand-assembled, unlike Model T Fords. Henry Ford introduced the assembly line in order to make cars affordable to the masses. Auburn Cords and Duesenbergs were meant for the elite—and the workmanship shows, even today in the 126 autos on display.
Some of the cars on display at the Auburn Cord Duesenberg Museum
This photo captures some of the elegance of the art deco building, which was the original showroom for the Auborn Auto Company.
Most of us think antique cars were all painted black. That was Henry Ford's autos. These Cords and Duesenbergs were quite colorful.
The museum is housed in the art deco building that once served as the showroom for these cars. It was an impressive building.
On the way back from Auburn, we saw a sign advertising the Mid-American Windmill Museum. It was an awesome visit.
A fellow who was about 85 years old took our admission, and then proceeded to educate us about windmills. A more knowledgeable docent we would not have been able to find. After learning about why windmills were invented (to mill grain) and the types of windmills, he turned us loose to look at the 55 windmills on the museum's property.
Alas. This museum will probably cease to exist. Again, we were the only visitors. The docent said that the museum relies on volunteers, and few young people are interested in windmills. That is sad, because today, windmills are a great alternative source of energy. When we trekked out west a couple of years ago, we saw miles of huge windmills. We were pleased to see acres of these same types of windmills on our drive through Indiana.
Shipshawana Flea Market
On our final day in Northeastern Indiana, we made a quick trip to Shipshewana Flea Market, advertised as the Midwest's Largest Flea Market. It is open only on Tuesdays and Wednesdays from May through October.
We only had time to browse a couple of aisles, but we were able to purchase some excellent sausage at the Amish meat market. (Incidentally, the Elkhart-Goshen area has a large number of Amish and Mennonite families, who farm, butcher, and handcraft furniture and other items. Drivers must watch out for horse-drawn carriages.)
Family and Greenfield Village
The highlight of our trip, for me, was going to Marshall, Mich., to visit my son, his wife, and my grandchildren. I hadn't seen the kids for almost two years—way too long. We cooked out twice and visited several hours. Corky (my daughter-in-law) and Maddie (my 16-year-old granddaughter), Jim and I made the drive to Greenfield Village, in Dearborn, Mich., on Thursday. (Jack, my grandson opted out of the trip.)
Greenfield Village is another attraction I have wanted to see, ever since I lived in Marshall, more than 20 years ago. Henry Ford built the village—he actually brought in original buildings of significant inventors, scientists, and writers—as a school to preserve the history of America's technological and cultural progress. It originally served as a private school.
A street in Greenfield Village
Corky, Maddie and I try on stylish hats at the millinery shop in Greenfield Village.
An outdoor museum, the 255 acres of exhibits (and a working farm) are divided into five districts.
I learned that Henry Ford had been a protégé of Thomas Edison. As a tribute to Edison, he brought Edison's laboratory to the Village. He dedicated Greenfield Village on the 50th anniversary of the invention of the light bulb. Edison attended the dedication. Ford realized that Edison's days were numbered, so as an additional tribute, he declared that the chair Edison had sat in during the dedication at Edison's relocated laboratory should be nailed down and never moved.
When the floors of the laboratory needed to be redone, the chair was cut out and replaced exactly, in order to keep Ford's declaration true.
Thomas Edison's laboratory
Our visit with Rob and his family was too short, as it always is. But the trip to Greenfield Village was made more memorable because we shared it with family.
Maddie, Jim, Rob, Linda, Jack, and Corky. Family.
November 1, 2015--No tricks; all treats yesterday ...
copyright 2011. Picture Window theme. Powered by Blogger.

redpajama_set_name: RedPajamaCommonCrawl


I"ve just installed it, and perl5 dependency ok.
When I run sendEmail or sendEmail.pl or ./sendEmail.pl I get following error.
All coments and suggestions welcome.
From the directory sendEmail.pl is in, what does perl -v return?
Thanks for the input Rich.
Perhaps the perl5 package needs an update ? Or is this particular pathing requirment unique to sendEmail ?
you'll note it was added back in a couple of times.
Are you saying this is a patch normally done at the OS level ?
My guess is that sendEmail has /usr/bin/perl hardcoded somewhere in it.
A. Extensions should not hardcode paths to system executables (preferable).
B. The perl extension should create the symlink to accommodate those hardcoded paths.
Seems like sendMail needs an alternation.
Then you're in luck. The info file lists you as the maintainer.
Yeah the recommended shebang is "#!/usr/bin/env perl" which doesn't care where perl is.


text:
Division III Regional Track Recap: Crestview's boys 4x800 team qualifies for state
William Kosileski
The Crestview, Lucas, Plymouth and St. Peter's boys track and field teams competed at the first day of the Division III Chillicothe Regional on Wednesday at Southeastern High School.
The standout showing of the day came from Crestview's 4x800-meter relay team, which qualified for state in the event in record-setting fashion. The team of Evan Gibbs, Gabe Smedley, Tommy O'Neill and Ross Kuhn won in a school-record time of 8:04.94.
Crestview athletes advancing to Friday's finals were Chase Shifflet in 300 hurdles (second place, 41.48), Tanner Moore in the 100 meters (fifth, 11.38) and all three relay teams. The 4x400 relay of Gibbs, Evan Hamilton, Kuhn and Smedley took first in 3:31.38. The 4x200 squad of Adison Reymer, Hamilton, Rashaun Barber and Moore (1:32.19) took second, as did the 4x100 relay of Reymer, Hamilton, Shifflet and Moore (44.35).
Wade Bolin (discus) and Payton Eichelberger (pole vault) competed in field event finals for the Cougars. Neither athlete qualified for state, but Bolin placed sixth in the discus with a throw of 136 feet, 3 inches. Bolin edged out Lucas' Grant Barrett, who placed seventh with heave of 135-10.
St. Peter's qualified five athletes for Friday's finals in three events. Senior standout Donovan Duncan won both the 110 hurdles (14.97) and 300 hurdles (40.88), while John Harris was sixth in the 110 hurdles (16.27). The Spartans' 4x200 team of Peyton Bodnar, Ross Pruettmiller, Duncan and Albree Grose placed fourth in the preliminaries with a time of 1:33.71, also advancing to finals.
Missing the cut for finals from Crestview were Reymer (10th) and Barber (15th) in the 200, Hamilton in the 100 (12th) and Gibbs in the 400 (13th).
St. Pete's 4x100 relay team of Bodnar, Pruettmiller, Duncan and Albree Grose failed to qualify for finals with their 10th-place finish. However, the quartet set a new school record with a time of 45.81. Also missing the cut were Bodnar in the 400 (ninth) and Albree Grose in the 200 (11th).
Plymouth's Caiden Allen placed ninth in the 100 in 11.70 seconds, missing the cut for finals by just .03 seconds. The Big Red's 4x800 team of Levi Robinson, Jacob Robinson, Malachi Keefe and Landon Blankenship placed 10th and also missed the cut.
Division III Tiffin Regional
The Lucas and Crestview girls were represented at the first day of the Div. III Tiffin Regional at Tiffin Columbian High School.
Lucas' Shelby Grover advanced to Friday's finals in three events. The sophomore was third in the 100 hurdles (15.54) and second in the 300 hurdles (45.45). She was joined by Alaina Stone, Molly Rannigan and Jamie Grover in the 4x200 relay, which just made the cut for finals with an eighth-place finish (1:50.32).
Crestview's 4x800 team of Abby Rall, Baileigh Cordrey, Tessa Kuhn and Morgan Welch missed the cut for state by placing 10th in 10:20.05.
The Cougars did not qualify any athletes to Friday's finals. The 4x400 team of Emma Aumend, Rall, Emily Weaver and Welch placed 12th, while Aumend and Weaver placed 14th and 15th, respectively, in the 400.
Reach William at wkosileski@gannett.com. On Twitter: @BillKosileski.


text:
Gagea rigida är en liljeväxtart som beskrevs av Pierre Edmond Boissier och Wilhelm von Spruner. Gagea rigida ingår i Vårlökssläktet och i familjen liljeväxter. Inga underarter finns listade.

Källor

Externa länkar

Vårlökar
rigida

redpajama_set_name: RedPajamaWikipedia


An absolutely centrally located apartment is prsented to you here!
An apartment with a view like this is a rarity in Lübeck.
From here, numerous restaurants, cafes with great breakfast and attractions are directly accessible!
1 Person: € 53,- per night, 2nd Person: + € 10,- per night, children up to 4 years of age: free, plus final cleaning: € 30,- (optional). The price includes bedclothes, towels, electricity, heating, warm water and internet access. The minimum rental-time is 2 nights. Gaps from a single night can be booked. We provide special offers for long time rental on request!


text:
Q: calculating the variance of an orthogonal line I have three points $A(x,y) , B(x,y)$ and $C(x,y)$ the $x$ and $y$ coordinates follow a normal distribution with a known mean and variance. I don,t know if $A$ and $B$ are correlated with each other. I know $C$ dont have an correlation with $A$ and $B$.
There is a line made bij $AB$ and the point $C$. i want to calculate the distance from $C$ to the line $AB$. that means there is an orthogonal line from $C$ on $AB$. the length of that line is calculed with the next formule : $det(A)/|a-b|$ $A$ is an matrix made bij $(a-c,a-b)$
Atm i am using a monte carlo simulation to find the variance and mean. with the simulation, i found that the distance follow a normal distribution.
Anyone can help me out?
Is it possible to calculate the variance of the length of the orthogonal line without the use of a simulation?

I am not allowed to upload the plot of the points. the dataframe of the points excist of 4096 points located on the map. i have to find for each point a line with the smallest distence. the points are from an other map. the company want to combine those maps to create an better map

A: The distributions can be wildly varying depending on the distributions of A, B and C.
So I think that it will be difficult to give a simple solution if there is not a clear specification of the distribution, based on which simplifications can be made.
Example for a funny distribution
Let A and B be two distributions centered around $(0,0)$ with A very small variance and B a very large variance.
This makes that the line between A and B is more or less the line through $(0,0)$ and B, or a line through $(0,0)$ with an angle that is homogeneously distributed.
Let C be a distribution far away from $(0,0)$ with small variance. In the computed example below, we used C centered around $(10,0)$

Then the distance of C from the line is more or less equal to
$$d \approx 10 \sin(\theta)$$
Where $\theta$ is the angle between the line through point B and the x-axis.
If we consider the angle is homogenously distributed from $0$ to $\pi$ then you can compute the distribution of $d$ by transformation:
$$\theta = \sin^{-1}(d/10)$$
and the derivative can be used to compute the distribution of the transformed variable
$$f(d) = \frac{2}{\pi \sqrt{100-d^2}}$$
Computation example:

set.seed(1)

### https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_two_points
distance <- function(x0,y0,x1,y1,x2,y2) {
  abs((y2-y1)*x0-(x2-x1)*y0+x2*y1-y2*x1)/sqrt((x2-x1)^2+(y2-y1)^2)
}

n <- 10^4
x0 <- rnorm(n,mean = 10,sd = 0.1)
y0 <- rnorm(n,mean = 0,sd = 0.1)
x1 <- rnorm(n,mean = 0,sd = 2)
y1 <- rnorm(n,mean = 0,sd = 2)
x2 <- rnorm(n,mean = 0,sd = 0.1)
y2 <- rnorm(n,mean = 0,sd = 0.1)

d <- distance(x0,y0,x1,y1,x2,y2)

hist(d, breaks = seq(0,11,0.2), freq = 0, main = "histogram of d \n with theoretic density curve")
ds <- seq(0,10,0.1)
lines(ds , (2/pi)/sqrt(100-ds^2))

redpajama_set_name: RedPajamaStackExchange


Benedict Benjamin takes the stage like a slightly awkward sixth former surprised to be receiving a prize at Speech Day. But he interacts with the audience in the easy, charming and affable manner of one accustomed to the spotlight. His polite soft-spokenness itself commands attention, particularly in the intimate setting of the basement of the Harrison Pub on a Wednesday night.
The songs similarly start in a quietly unassuming manner and you might anticipate some mildly toe-tapping pleasant folk fare, his voice pretty but a little brittle like an overnight frost glittering on a morning field. But then it unexpectedly swells into a potent, full-bodied instrument that soars and swoops like a flock of starlings involved in their mysterious manoeuvres in the sky. The sound is lush and spacious, captivating and other, with choruses that swirl round your head in triumphant crescendos. You're swept up as by a wave crashing on a beach, transported to another realm, carried away on the tide.
The first time I experienced this beguiling effect was when Benjamin supported the North Carolina folk duo Mandolin Orange at the Borderline. It was like witnessing a nightclub act in a David Lynch movie, deep scarlet velvet curtains and all, at times as if he were channelling Roy Orbison or Bobby Vinton in some beautiful and haunting homage, conjuring up adolescent sweethearts clinging to each other for the last dance at some long ago school hop ('I Would Like to See You Tonight', 'Coward').
Melodies edged with melancholy showcase lyrics that demonstrate an honest and mature self-awareness, rather like those of a young (and old) Ray Davies, someone who's recognised and come to reluctant terms with their own weaknesses and foibles.
Benjamin characterises these resonant, passionate, confessional songs as 'depressing' but in fact their very intensity renders them strangely uplifting and cathartic. The refrains of 'Thin Skin', 'Change Your Mind', 'Had What You Had', 'My Feet Have No Need for the Ground' entwine themselves into your memory like cats around your ankles and you find yourself humming them for days after.
The venue in Harrison Street, just off Gray's Inn Road, was an ideal fit for this once a fortnight event, and I couldn't really recommend it more. Three (or even four) acts and it's all free – what's not to like? It's worth getting there an hour or so early to enjoy a vegan stew in the bar beforehand too. Find out more here.
Benedict Benjamin's album Night Songs is on CD now.
He is supporting Slow Dancer and Jack Robert Hardman at the Lock Tavern, Chalk Farm Road on Wednesday 25 May.
Here's a poem about 'Waterloo Sunset', a song tinged with a similar sense of pathos.
Posted by bashfulbadger on May 19, 2016 in blog, Kinks, Music, Ray Davies, vegetarian and tagged badger, bashful, bashfulbadgersblog, benedict benjamin, folk music, folkroom fortnightly, had what you had, Kinks, love that's left behind, night songs, Ray Davies, review.


text:
\section{Introduction and Main Results}

A measure $\mu$ on a locally convex linear space $F$ is called logarithmically concave (log-concave in short)
if for any compact nonempty sets $K,L\subset F$ and $\lambda\in [0,1]$,
$\mu(\lambda K+(1-\lambda)L)\geq \mu(K)^{\lambda}\mu(L)^{1-\lambda}$.
A random vector with values in $F$ is called log-concave if its distribution is logarithmically concave.
The class of log-concave measures is closed under linear transformations, convolutions and weak limits.
By the result of Borell \cite{Bo} a $d$-dimensional vector with a full dimensional support is log-concave
iff it has a log-concave density, i.e. a density of the form $e^{-h}$, where $h$ is a convex function with values
in $(-\infty,\infty]$. A typical example of a log-concave vector is a vector uniformly distributed over a convex body.
Various results and conjectures about log-concave measures are discussed in the recently published monograph \cite{BGVV}.

One of the fundamental properties of log-concave vectors is the Paouris inequality \cite{Pa}
(see also \cite{ALLOPT} for a shorter proof). It states that for a~log-concave vector
$X$ in ${\mathbb R}^n$,
\begin{equation}
\label{eq:Paour}
({\mathbb E}\|X\|_2^{p})^{1/p}\leq
C_1\left(({\mathbb E} \|X\|_2^2)^{1/2}+\sigma_X(p)\right) \quad \mbox{ for }p\geq 1,
\end{equation}
where
\[
\sigma_{X}(p):=\sup_{\|t\|_2\leq 1}\left({\mathbb E}\left|\sum_{i=1}^nt_iX_i\right|^p\right)^{1/p}.
\]
Here and in the sequel by $C_1,C_2,\ldots$ we denote absolute constants.

It is natural to ask whether inequality \eqref{eq:Paour} may be generalized to non-Euclidean norms.
In \cite{La2} the following conjecture was formulated and discussed.

\begin{conj}
\label{conj:ws}
There exists a universal constant $C$ such that for any log-concave vector
$X$ with values in a finite dimensional normed space $(F,\|\ \|)$,
\[
({\mathbb E}\|X\|^p)^{1/p}\leq C\left({\mathbb E}\|X\|+\sup_{\varphi\in F^*,\|\varphi\|_*\leq 1}({\mathbb E}|\varphi(X)|^p)^{1/p}\right)
\quad \mbox{ for }p\geq 1.
\]
\end{conj}

Our main result states that the conjecture holds for spaces that may be embedded in $\ell_r$ for some $r\geq 1$.

\begin{thm}
\label{thm:sublr}
Let $X$ be a log-concave vector with values in a normed space $(F,\|\ \|)$ which may be isometrically
embedded in $\ell_r$ for some $r\in [1,\infty)$. Then for $p\geq 1$,
\[
({\mathbb E}\|X\|^p)^{1/p}\leq C_2r\left({\mathbb E}\|X\|+\sup_{\varphi\in F^*,\|\varphi\|_*\leq 1}({\mathbb E}|\varphi(X)|^p)^{1/p}\right).
\]
\end{thm}

\begin{rem}
Let $X$ and $F$ be as above. Then by Chebyshev's inequality we obtain large deviation estimate for $\|X\|$:
\[
{\mathbb P}(\|X\|\geq 2eC_2rt{\mathbb E}\|X\|)\leq \exp\left(-\sigma_{X,F}^{-1}(t{\mathbb E}\|X\|)\right) \quad \mbox{ for }t\geq 1,
\]
where
\[
\sigma_{X,F}(p):=\sup_{\varphi\in F^*,\|\varphi\|_*\leq 1}({\mathbb E}\varphi(X)^p)^{1/p}  \quad  \mbox{ for } p\geq 1
\]
denotes the weak $p$-th moment of $\|X\|$.
\end{rem}

\begin{rem}
If $i\colon F\rightarrow \ell_r$ is a nonisometric embedding and $\lambda=\|i\|_{F\to \ell_r}\|i^{-1}\|_{i(F)\to F}$,
then we may define another norm on $F$ by $\|x\|':=\|i(x)\|/\|i\|_{F\to \ell_r}$. Obviously $(F,\|\ \|')$
isometrically embeds in $\ell_r$, moreover $\|x\|'\leq \|x\|\leq \lambda\|x\|'$ for $x\in F$. Hence
Theorem \ref{thm:sublr} gives
\begin{align*}
({\mathbb E}\|X\|^p)^{1/p}
&\leq \lambda ({\mathbb E}(\|X\|')^p)^{1/p}\leq
C_2r\lambda\left({\mathbb E}\|X\|'+\sup_{\varphi\in F^*,\|\varphi\|_*^{'}\leq 1}({\mathbb E}|\varphi(X)|^p)^{1/p}\right)
\\
&\leq C_2r\lambda\left({\mathbb E}\|X\|+\sup_{\varphi\in F^*,\|\varphi\|_*\leq 1}({\mathbb E}|\varphi(X)|^p)^{1/p}\right).
\end{align*}
\end{rem}

Since log-concavity is preserved under linear transformations and, by  the Hahn-Banach theorem, any linear functional on
a subspace of $\ell_r$ is a restriction of a~functional on the whole $\ell_r$ with the same norm, it is enough to prove
Theorem \ref{thm:sublr} for $F=\ell_r$. An easy approximation argument shows that we may consider finite dimensional
spaces $\ell_r^n$.
To simplify the notation for an $n$-dimensional vector $X$ and $p\geq 1$ we write
\[
\sigma_{r,X}(p):=\sup_{\|t\|_{r'}\leq 1}\left({\mathbb E}\left|\sum_{i=1}^n t_iX_i\right|^p\right)^{1/p},
\]
where $r'$ denotes the H\"older's dual of $r$, i.e. $r'=\frac{r}{r-1}$  for $r>1$ and $r'=\infty$ for $r=1$.

\begin{thm}
\label{thm:Paourlr}
Let $X$ be a finite dimensional log-concave vector and  $r\in[1,\infty)$. Then
\[
({\mathbb E}\|X\|_r^p)^{1/p}\leq C_2r\left({\mathbb E}\|X\|_r+\sigma_{r,X}(p)\right)\quad \mbox{ for }p\geq 1.
\]
\end{thm}

To show the above theorem we follow the approach from \cite{La3} and establish the following result.

\begin{thm}
\label{thm:cutPaourr}
Suppose that $r\in [1,\infty)$ and $X$ is a log-concave $n$-dimensional random vector. Let
\begin{equation}
\label{eq:defd}
d_i:=({\mathbb E} X_i^2)^{1/2},\quad d:=\left(\sum_{i=1}^n d_i^r\right)^{1/r}.
\end{equation}
Then for $p\geq r$,
\begin{equation}
\label{eq:cutPaour}
{\mathbb E}\left(\sum_{i=1}^n|X_i|^r{\mathbf 1}_{\{|X_i|\geq td_i\}}\right)^{p/r}\leq (C_3r\sigma_{r,X}(p))^{p}
\quad \mbox{ for } t\geq C_4r\log\left(\frac{d}{\sigma_{r,X}(p)}\right).
\end{equation}
\end{thm}

\begin{rem}
Any finite dimensional space  embeds isometrically in $\ell_\infty$, so to show Conjecture~\ref{conj:ws}
it is enough to establish Theorem \ref{thm:sublr} (with a universal constant in place of $C_2r$) for $r=\infty$.
Such  a result was shown for isotropic log-concave vectors (i.e. log-concave vectors with mean zero and identity
covariance matrix), cf.\ \cite[Corollary 3.8]{La4}.
 However a linear image of an isotropic vector does not have to be isotropic, so to establish the conjecture
we need to consider either isotropic vectors and an arbitrary norm or vectors with a general covariance structure
and the standard $\ell_\infty$-norm.
\end{rem}

\section{Proofs}

Let us first discuss the notation. By $C$ we denote universal constants, the value of $C$ may differ
at each occurrence. Whenever we want to fix the value of an absolute constant we use letters $C_1,C_2,\ldots$.
We may always assume that $C_i\geq 1$.
By $|I|$ we denote the cardinality of a set $I$.
For an $n$-dimensional random vector $Z$ and $a\in {\mathbb R}^n$ we write $aZ$ for the vector $(a_iZ_i)_{i}$.
Observe that ${\mathbb E}\|aZ\|_2^2=\sum_{i}a_i^2{\mathbb E} Z_i^2$.

Let us recall some useful facts about log-concave vectors (for details see \cite{La3}).
If $Z$ is log-concave real random variable then
\[
{\mathbb P}(|Z|\geq t)\leq \exp\left(2-\frac{t}{2e({\mathbb E} Z^2)^{1/2}}\right)\quad \mbox{for } t\geq 0.
\]
Moreover, if $f:{\mathbb R}^n \to {\mathbb R}$ is a seminorm, $({\mathbb E} f(Z)^p)^{1/p}\leq C_5\frac{p}{q}({\mathbb E} f(Z)^q)^{1/q}$
for $p\geq q\geq 1$ (see \cite[Theorem 2.4.6]{BGVV}). Therefore for
any log-concave vector $X$ and any $r$,
\[
\sigma_{r,X}(\lambda p)\leq C_5\lambda \sigma_{r,X}(p)\quad \mbox{for } \lambda\geq 1,\ p\geq 2.
\]

The Paouris inequality (\ref{eq:Paour}) together with Chebyshev's inequality imply
\begin{equation}
\label{eq:Paourtail}
{\mathbb P}\left(\|X \|_2\geq eC_1\left(({\mathbb E} \|X \|_2^2)^{1/2}+\sigma_{X}(p)\right)\right)
\leq
e^{-p} \quad \mbox{ for }p\geq 1.
\end{equation}

The next proposition generalizes Proposition 4 from \cite{La3}.

\begin{prop}
\label{conditionalr}
Let $X$, $r$, $d_i$, and $d$ be as in Theorem \ref{thm:cutPaourr}
and $A:=\{X\in K\}$, where $K$ is a convex set in ${\mathbb R}^n$ satisfying $0<{\mathbb P}(A)\leq 1/e$. Then
\\
(i) for every $t\geq r$,
\begin{equation}
\label{eq:cond1r}
\sum_{i=1}^n{\mathbb E} |X_i|^r{\mathbf 1}_{A\cap\{X_i\geq td_i\}}\leq
C_6^r{\mathbb P}(A)\left(r^r\sigma_{r,X}^r(-\log({\mathbb P}(A)))+(dt)^re^{-t/C_7}\right).
\end{equation}
(ii) for every $t>0$, $u\geq 1$,
\begin{align}
\notag
\sum_{k=0}^{\infty}2^{kr}\sum_{i=1}^nd_i^r&{\mathbf 1}_{\{{\mathbb P}(A\cap\{X_i\geq 2^k td_i\})\geq e^{-u}{\mathbb P}(A)\}}
\\
\label{eq:cond2r}
&\leq
\frac{(C_8 u)^r}{t^r}\left(\sigma_{r,X}^r(-\log({\mathbb P}(A)))+d^r{\mathbf 1}_{\{t\leq uC_9\}}\right) .
\end{align}
\end{prop}

\begin{proof}
Let $Y$ be a random vector defined by
\[
{\mathbb P}(Y\in B)=\frac{{\mathbb P}(A\cap\{X\in B\})}{{\mathbb P}(A)}=\frac{{\mathbb P}(X\in B\cap K)}{{\mathbb P}(X\in K)},
\]
i.e. $Y$ is distributed as $X$ conditioned on $A$. Clearly, for every measurable set $B$
one has ${\mathbb P}(X\in B)\geq {\mathbb P}(A){\mathbb P}(Y\in B)$. It is easy to see that $Y$ is log-concave.

To simplify the notation set
\[
p_A:=-\log {\mathbb P}(A)\quad \mbox{ and }\quad c_i:=({\mathbb E} Y_i^2)^{1/2}, \ i=1,\ldots,n.
\]

Let
\[
I=I(v):=\{i\leq n\colon\ {\mathbb E} Y_i^2\geq v^2d_i^2\},
\]
where $v$ is an absolute constant to be chosen later. Let us also fix a sequence $(a_i)_{i\leq n}$.

Put $S=\sum_{i\in I}|a_{i}|c_i^{-1}Y_i^2$. Observe that $S=\|((|a_i|/c_i)^{1/2}Y_i)_{i\in I}\|_2^2$, hence by  the log-concavity
of $Y$, ${\mathbb E} S^2\leq (2C_5)^{4}({\mathbb E} S)^2$, and the Paley-Zygmund inequality yields
\begin{equation}
\label{eq:estY1}
{\mathbb P}\left(\sum_{i\in I}|a_{i}|c_i^{-1}Y_i^2\geq \frac{1}{2}\sum_{i\in I}|a_i|c_i\right)
={\mathbb P}\left(S\geq \frac{1}{2}{\mathbb E} S\right)\geq \frac{1}{4}\frac{({\mathbb E} S)^2}{{\mathbb E} S^2}
\geq \frac{1}{(2\sqrt{2}C_5)^4}.
\end{equation}
We have ${\mathbb E} Y_i^4\leq (2C_5c_i)^4$, so by Chebyshev's inequality we get
\begin{equation}
\label{eq:estY2}
{\mathbb P}\left(\sum_{i\in I} |a_i|c_i^{-3}Y_i^4\geq (2C_5)^4s \sum_{i\in I} |a_i| c_i \right) \leq \frac{1}{s}
\quad \mbox{ for }s>0.
\end{equation}
Combining \eqref{eq:estY1} and \eqref{eq:estY2} we conclude that there exist constants $C_{10},C_{11}$ such that
\[
{\mathbb P}\left(\sum_{i\in I}|a_i|c_i^{-1}Y_i^2\geq \frac{1}{2} \sum_{i\in I} |a_i|c_i,\
\sum_{i\in I}|a_i|c_i^{-3}Y_i^4\leq C_{10}\sum_{i\in I}|a_i|c_i\right)
\geq \frac{1}{C_{11}}
\]
and therefore
\[
{\mathbb P}\left(\sum_{i\in I}|a_i|c_i^{-1}X_i^2\geq \frac{1}{2}\sum_{i\in I}|a_i|c_i,\
\sum_{i\in I}|a_i|c_i^{-3}X_i^4\leq C_{10}\sum_{i\in I}|a_i|c_i\right)
\geq \frac{1}{C_{11}}{\mathbb P}(A)\geq  e^{-C_{12}p_A}.
\]

Let $\tilde{X}$ be the vector $(|a_i|^{1/2}c_i^{-1/2}X_i)_{i\in I}$ conditioned on the set
\[
B:=\left\{\sum_{i\in I}|a_i|c_i^{-3}X_i^4\leq C_{10}\sum_{i\in I}|a_i|c_i\right\}.
\]
Then
\begin{equation}
\label{eq:esttailtildeX}
{\mathbb P}\left(\|\tilde{X}\|_2^2\geq \frac{1}{2}\sum_{i\in I}|a_i|c_i\right)
\geq \frac{1}{{\mathbb P}(B)}e^{-C_{12}p_A}\geq e^{-C_{12}p_A}.
\end{equation}

The random vector $\tilde{X}$ is log-concave and ${\mathbb P}(B)\geq 1/2$ if $v$ is sufficiently large
(since ${\mathbb E} X_i^4\leq Cd_i^4\leq Cv^{-4}c_i^4$ for $i\in I$). Thus
\begin{equation}
\label{eq:estvartildeXunis}
{\mathbb E} \|\tilde{X}\|_2^2=\frac{1}{{\mathbb P}(B)}{\mathbb E}\left(\sum_{i\in I} |a_i|c_i^{-1}X_i^2 {\mathbf 1}_B\right)
\leq
2\sum_{i\in I}{\mathbb E} |a_i|c_{i}^{-1}d_i^2\leq 2v^{-2}\sum_{i\in I}|a_i|c_i.
\end{equation}

Now we will estimate $\sigma_{\tilde{X}}(p)$. To this end fix $t\in {\mathbb R}^I$ with $\|t\|_2\leq 1$.
Let $\alpha,s>0$ be numbers to be chosen later and
\[
J_{\alpha}:=\{i\in I\colon\ |t_i|(|a_i|c_{i})^{-1/2}\leq \alpha\}.
\]
We have
\[
\left\|\sum_{i\in J_\alpha} t_i\tilde{X}_i\right\|_p
\leq {\mathbb P}(B)^{-1/p}\left\|\sum_{i\in J_\alpha} t_i(|a_i|c_{i})^{-1/2}|a_i|X_i\right\|_p\leq
2\alpha\sigma_{1,aX}(p).
\]
Moreover
\[
\left\|\sum_{i\notin J_\alpha} t_i\tilde{X}_i { {\mathbf 1}}_{\{|\tilde{X}_i|\leq s(|a_i|c_i)^{1/2}\}}\right\|_p
\leq \sum_{i\notin J_\alpha} s|t_i|(|a_i|c_i)^{1/2}\leq
s\sum_{i\notin J_\alpha} \frac{|t_i|^2}{|t_i|(|a_i|c_i)^{-1/2}}\leq \frac{s}{\alpha}\sum_{i\in I}t_i^2
\leq \frac{s}{\alpha}.
\]

Observe that by the definition of the set $B$ and the vector $\tilde{X}$ we have
\[
\sum_{i\in I}(|a_i|c_i)^{-1}\tilde{X}_i^4\leq C_{10}\sum_{i\in I}|a_i|c_i.
\]
Thus
\begin{align*}
\left\|\sum_{i\notin J_\alpha} t_i\tilde{X}_i { {\mathbf 1}}_{\{|\tilde{X}_i|>s(|a_i|c_i)^{1/2}\}}\right\|_p
&\leq
\left\|\left(\sum_{i\notin J_\alpha}\tilde{X}_i^2 { {\mathbf 1}}_{\{|\tilde{X}_i|>s(|a_i|c_i)^{1/2}\}}\right)^{1/2}\right\|_p
\\
&
\leq \left\|\frac{1}{s}\left(\sum_{i\in I}(|a_i|c_{i})^{-1}\tilde{X}_i^4\right)^{1/2}\right\|_p
\leq \frac{1}{s}\left(C_{10}\sum_{i\in I}|a_i|c_i\right)^{1/2}.
\end{align*}

Combining the above estimates we obtain
\[
\left\|\sum_{i\in I} t_i\tilde{X}_i\right\|_p\leq 2\alpha\sigma_{1,aX}(p)+\frac{s}{\alpha}+
\frac{1}{s}\left(C_{10}\sum_{i\in I}|a_i|c_i\right)^{1/2}.
\]
Taking the supremum over $t$  and optimizing over $\alpha>0$  we get
\begin{equation}
\label{eq:estsigmatildeXunis}
\sigma_{\tilde{X}}(p)\leq 4(s\sigma_{1,aX}(p))^{1/2}+\frac{1}{s}\left(C_{10}\sum_{i\in I}|a_i|c_i\right)^{1/2}
\quad \mbox{ for }s>0.
\end{equation}

Paouris' inequality \eqref{eq:Paourtail} (applied to $\tilde{X}$ instead of $X$) together with
\eqref{eq:estvartildeXunis} and
\eqref{eq:estsigmatildeXunis} implies that
\begin{align*}
{\mathbb P}\left(\|\tilde{X}\|_2\geq eC_1\left(\left(\frac{2}{v^2}\sum_{i\in I}|a_i|c_i\right)^{1/2}
+4(s\sigma_{1,aX}(C_{12}p_A))^{1/2}
+\frac{1}{s}\left(C_{10}\sum_{i\in I}|a_i|c_i\right)^{1/2}\right)\right)\phantom{a}&
\\
< e^{-C_{12}p_A}&
\end{align*}
Comparing the above with \eqref{eq:esttailtildeX} we get
\begin{align*}
eC_1\left(\left(\frac{2}{v^2}\sum_{i\in I}|a_i|c_i\right)^{1/2}+4(s\sigma_{1,aX}(C_{12}p_A))^{1/2}
+\frac{1}{s}\left(C_{10}\sum_{i\in I}|a_i|c_i\right)^{1/2}\right)\phantom{aaaaaaaaaaaa}&
\\
\geq
\left(\frac{1}{2}\sum_{i\in I}|a_i|c_i\right)^{1/2}&.
\end{align*}
If we choose $s$ and $v$ to be sufficiently large absolute constants we will get
\[
\sum_{i\in I}|a_i|({\mathbb E} Y_i^2)^{1/2}=\sum_{i\in I}|a_i|c_i
\leq C\sigma_{1,aX}(C_{12}p_A)\leq C\sigma_{1,aX}(p_A).
\]

Put $a_i :=( {\mathbb E}|Y_i|^2)^{(r-1)/2}{\mathbf 1}_{i\in I}$.
If $\|t\|_\infty\leq 1$, then $(\sum|t_ia_i|^{r'})^{1/r'} \le \|a \|_{r'}$. Thus the previous inequality implies
\[
\sum_{i\in I} \left({\mathbb E} |Y_i|^2\right)^{r/2}  \leq C\sigma_{1,aX}(p_A) \leq
C\|a\|_{r'} \sigma_{r,X}(p_A) =C  \left( \sum_{i\in I} \left({\mathbb E} |Y_i|^2\right)^{r/2} \right)^{1/r'}  \sigma_{r,X}(p_A) .
\]
This gives
\[
\sum_{i\in I} ({\mathbb E} |Y_i|^2)^{r/2}  \leq C^r  \sigma_{r,X}^r(p_A).
\]

Since $\|Y_i\|_r\leq \max\{1,C_5r/2\}\|Y_i\|_2$ we also get
\[
\sum_{i\in I} {\mathbb E} |Y_i|^r  \leq (Cr)^r  \sigma_{r,X}^r(p_A).
\]

To prove \eqref{eq:cond1r} note that if $i\notin I$, then ${\mathbb P}(|Y_i|\geq sd_i)\leq 2e^{-s/C}$ for $s\geq 0$, hence for $t\geq r$,
${\mathbb E} |Y_i|^r{\mathbf 1}_{\{Y_i\geq td_i\}}\leq (Ctd_i)^r  e^{-t/C}$ and
\[
\sum_{i\notin I}{\mathbb E} |Y_i|^r{\mathbf 1}_{\{Y_i\geq t\}}\leq (Ctd)^re^{-t/C}.
\]
Hence
\begin{align*}
\frac{1}{{\mathbb P}(A)}\sum_{i=1}^n{\mathbb E} |X_i|^r{\mathbf 1}_{A\cap\{X_i\geq td_i\}}
&=\sum_{i=1}^n{\mathbb E} |Y_i|^r{\mathbf 1}_{\{Y_i\geq td_i\}}
\\
&\leq C^r\left(r^r\sigma_{r,X}^r(-\log({\mathbb P}(A)))+(dt)^re^{-t/C}\right).
\end{align*}

To show \eqref{eq:cond2r} note first that for every $i$ the random variable $Y_i$ is log-concave, hence for $s\geq 0$,
\[
\frac{{\mathbb P}(A\cap\{X_i\geq s\})}{{\mathbb P}(A)}=
{\mathbb P}(Y_i\geq s)\leq \exp\left(2-\frac{s}{2e\|Y_i\|_2}\right).
\]
Thus, if ${\mathbb P}(A\cap\{X_i\geq 2^ktd_i\})\geq e^{-u}{\mathbb P}(A)$ and $u\geq 1$, then $\|Y_i\|_2\geq
2^ktd_i/(2e (u+2))\geq 2^ktd_i/(6eu)$.  In particular this cannot happen if $i\notin I$, $k\geq 0$ and $u\leq t/C_9$ with
$C_9$ large enough.
Therefore
\begin{align*}
\sum_{k=0}^{\infty}2^{kr}\sum_{i=1}^nd_i^r&{\mathbf 1}_{\{{\mathbb P}(A\cap\{X_i\geq 2^k td_i\})\geq e^{-u}{\mathbb P}(A)\}}
\\
&\leq
\left(\sum_{i\in I}+{\mathbf 1}_{\{t\leq uC_9\}}\sum_{i\notin I}\right)
d_i^r\sum_{k=0}^{\infty}2^{kr}{\mathbf 1}_{\{({\mathbb E} Y_i^2)^{1/2}\geq 2^ktd_i/(6eu)\}}
\\
&\leq \left(\sum_{i\in I}+{\mathbf 1}_{\{t\leq uC_9\}}\sum_{i\notin I}\right)d_i^r\frac{(Cu)^r}{(td_i)^r}({\mathbb E} Y_i^2)^{r/2}
\\
&\leq \frac{(Cu)^r}{t^r}\left(\sum_{i\in I}({\mathbb E} Y_i^2)^{r/2}+{\mathbf 1}_{\{t\leq uC_9\}}\sum_{i\notin I}d_i^r\right)
\\
&\leq \frac{(Cu)^r}{t^r}\left(\sigma_{r,X}^r(-\log({\mathbb P}(A)))+d^r{\mathbf 1}_{\{t\leq uC_9\}}\right). \qedhere
\end{align*}
\end{proof}

We will also use the following simple combinatorial lemma (Lemma~11 in \cite{La}).

\begin{lem}
\label{combf}
Let $l_0\geq l_1\geq\ldots\geq l_s$ be a fixed sequence of
positive integers and
\[
{\cal  F}:=\left\{f\colon\{1,2,\ldots,l_0\} \rightarrow\{0,1,2,\ldots,s\}\colon\
\forall_{1\leq i\leq s}\ |\{r\colon f(r)\geq i\}|\leq l_i\right\}.
\]
Then
\[
|{\cal F}|\leq\prod_{i=1}^s \left(\frac{e l_{i-1}}{l_i}\right)^{l_i}.
\]
\end{lem}

\begin{proof}[Proof of Theorem \ref{thm:cutPaourr}]
Observe that we may assume that $t\geq C_4 r$. Indeed, if $e\sigma_{r,X}(p)\leq d$ then by our assumption $t\geq C_4 r$.
If $e \sigma_{r,X}(p)> d$  then
\begin{align*}
\Bigg({\mathbb E}\Bigg(\sum_{i=1}^n|X_i|^r&{\mathbf 1}_{\{|X_i|\geq td_i\}}\Bigg)^{p/r}\Bigg)^{1/p}
\\
&\leq
C_4 r \left(\sum_{i=1}^n d_i^r\right)^{1/r}
+\left({\mathbb E}\left(\sum_{i=1}^n|X_i|^r{\mathbf 1}_{\{|X_i|\geq \max\{t,C_4r\}d_i\}}\right)^{p/r}\right)^{1/p}
\\
&\leq
eC_4r\sigma_{r,X}(p)
+\left({\mathbb E}\left(\sum_{i=1}^n|X_i|^r{\mathbf 1}_{\{|X_i|\geq \max\{t,C_4r\}d_i\}}\right)^{p/r}\right)^{1/p}.
\end{align*}

Moreover,  the vector $-X$ is also log-concave, has the same values of $d_i$ and $\sigma_{r,-X}=\sigma_{r,X}$. Hence
it is enough to show that
\[
{\mathbb E}\left(\sum_{i=1}^n X_i^r{\mathbf 1}_{\{X_i\geq td_i\}}\right)^{p/r}\leq (Cr\sigma_{r,X}(p))^{p}
\quad  \mbox{for }t\geq C_4r\max\left\{1 ,\log\left(\frac{d}{\sigma_{r,X}(p)}\right)\right\}.
\]

Observe that for $l=1,2,\ldots$,
\begin{align*}
{\mathbb E}\Bigg(\sum_{i=1}^nX_i^r {\mathbf 1}_{\{X_i\geq td_i\}}\Bigg)^l
& \leq
{\mathbb E}\left(\sum_{i=1}^n\sum_{k=0}^{\infty}2^{(k+1)r}(td_i)^r{\mathbf 1}_{\{X_i\geq 2^ktd_i\}}\right)^l
\\ &
=(2t)^{rl}\sum_{i_1,\ldots,i_l=1}^n\sum_{k_1,\ldots,k_l=0}^{\infty} 2^{(k_1+\ldots+k_l)r}d_{i_1}^r\ldots d_{i_l}^r
{\mathbb P}(B_{i_1,k_1\ldots,i_l,k_l}),
\end{align*}
where
\[
B_{i_1,k_1\ldots,i_l,k_l}:=\{X_{i_1}\geq 2^{k_1}td_{i_1},\ldots,X_{i_l}\geq 2^{k_l}td_{i_l}\}.
\]

Define a positive integer $l$ by
\[
\frac{p}r< l\leq 2\frac{p}r \quad \mbox{ and }\quad l=2^{M} \mbox{ for some positive integer } M.
\]
Then $\sigma_{r,X}(p) \leq \sigma_{r,X}(rl)\leq \sigma_{r,X}(2p)\leq 2C_5\sigma_{r,X}(p)$.
Since for any nonnegative r.v.\ $Z$ we have $({\mathbb E} Z^{p/r})^{r/p}\leq ({\mathbb E} Z^l)^{1/l}$,
it is enough to show that
\begin{equation}
\label{eq:aim}
m(l)
\leq
\left(\frac{Cr\sigma_{r,X}(rl)}{t}\right)^{rl}
\quad \mbox{ for } t\geq C_4r\max\left\{1,\log\left(\frac{d}{\sigma_{r,X}(rl)}\right)\right\},
\end{equation}
where
\[
m(l):=\sum_{k_1,\ldots,k_l=0}^{\infty}\sum_{i_1,\ldots,i_l=1}^n 2^{(k_1+\ldots+k_l)r}d_{i_1}^r\ldots d_{i_l}^r
{\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l}).
\]

We divide the sum in $m(l)$ into several parts.
Define sets
\[
I_{0}:=\left\{(i_1,k_1,\ldots,i_l,k_l)\colon\ {\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l})> e^{-rl}\right\},
\]
and for $j=1,2,\ldots$,
\[
I_{j}:=\left\{(i_1,k_1,\ldots,i_l,k_l)\colon\ {\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l})\in (e^{-rl2^{j}},e^{-rl2^{j-1}}] \right\}.
\]
Then $m(l)=\sum_{j\geq 0}m_j(l)$, where
\[
m_{j}(l)
:= \sum_{(i_1,k_1,\ldots,i_l,k_l)\in I_j} 2^{(k_1+\ldots+k_l)r}d_{i_1}^r\ldots d_{i_l}^r{\mathbb P}(B_{i_1,k_1\ldots,i_l,k_l}).
\]

To estimate $m_{0}(l)$ define for $1\leq s\leq l$,
\[
P_sI_0:=\{(i_1,k_1,\ldots,i_s,k_s)\colon (i_1,k_1,\ldots,i_l,k_l)\in I_0 \mbox{ for some }
i_{s+1},\ldots,k_l\}.
\]
We have (since $t$ is assumed to be large)
\[
{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})\leq {\mathbb P}(B_{i_1,k_1})\leq \exp(2-2^{k_1-1}t/e)\leq e^{-1}.
\]
Thus for $s=1,\ldots,l-1$,
\begin{multline*}
\sum_{(i_1, k_1,\ldots,i_{s+1}, k_{s+1})\in P_{s+1}I_{0}}
2^{(k_1+\ldots+k_{s+1})r}d_{i_1}^r\ldots d_{i_{s+1}}^r{\mathbb P}(B_{i_1,k_1,\ldots,i_{s+1},k_{s+1}})
\\
\leq
\sum_{(i_1,k_1,\ldots,i_s,k_s)\in P_{s}I_{0}}2^{(k_1+\ldots+k_{s})r}d_{i_1}^r\cdots d_{i_{s}}^r
F(i_1,k_1,\ldots,i_s,k_s),
\end{multline*}
where
\begin{align*}
F(i_1&,k_1,\ldots,i_s,k_s):=
\sum_{i=1}^n\sum_{k=0}^{\infty}
2^{kr}d_i^r{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s}\cap\{X_i\geq 2^ktd_i\})
\\
&\leq
\sum_{i=1}^n{\mathbb E} 2t^{-r}|X_{i}|^r{\mathbf 1}_{B_{i_1,k_1,\ldots,i_s,k_s}\cap\{X_i\geq td_i\}}
\\
&\leq
2t^{-r}C_6^r
{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})\left(r^r\sigma_{r,X}^r(-\log{\mathbb P}(B_{i_1, k_1,\ldots,i_s,k_s}))+(dt)^re^{-t/C_7}\right),
\end{align*}
where the last inequality follows by \eqref{eq:cond1r}. Note that for $(i_1,k_1,\ldots,i_s,k_s)\in P_sI_0$ we have
${\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})> e^{-rl}$. Moreover, by our assumptions on $t$
(if  $C_4$ is sufficiently large with respect to $C_7$),
\[
(dt)^re^{-t/C_7}\leq t^re^{-t/(2C_7)}d^re^{-t/(2C_7)}\leq r^r\sigma_{r,X}^r(rl).
\]
Therefore
\begin{multline*}
\sum_{(i_1,k_1,\ldots,i_{s+1},k_{s+1})\in P_{s+1}I_{0}}
2^{(k_1+\ldots+k_{s+1})r}d_{i_1}^r\ldots d_{i_{s+1}}^r{\mathbb P}(B_{i_1,k_1,\ldots,i_{s+1},k_{s+1}})
\\
\leq 4t^{-r}(C_6r\sigma_{r,X}(rl))^r
\sum_{(i_1,k_1,\ldots,i_s,k_{s})\in P_{s}I_{0}}
2^{(k_1+\ldots+k_{s})r}d_{i_1}^r\ldots d_{i_s}^r{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_{s}}).
\end{multline*}

By induction we get
\begin{align*}
m_{0}(l)&
=\sum_{(i_1,k_1,\ldots,i_l,k_l)\in I_{0}}2^{(k_1+\ldots+k_{l})r}d_{i_1}^r\cdots d_{i_l}^r{\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l})
\\
&\leq
\left(\frac{{ 4}C_6r\sigma_{r,X}(rl)}{t}\right)^{r(l-1)}
\sum_{(i_1,k_1)\in P_1I_0}2^{k_1r}d_{i_1}^r{\mathbb P}(B_{i_1,k_1}).
\end{align*}
We have
\begin{align*}
\sum_{(i_1,k_1)\in P_1I_0}2^{k_1r}d_{i_1}^r{\mathbb P}(B_{i_1,k_1}) & \leq
\sum_{i_1=1}^nd_{i_1}^r\sum_{k_1=0}^\infty 2^{k_1r}e^{2-2^{k_1-1}t/e}
\\ &
\leq \sum_{i_1=1}^n d_{i_1}^r2e^{2-t/{ (}2e{)}}\leq \left(\frac{Cr\sigma_{r,X}(rl)}{t}\right)^r,
\end{align*}
where the last two inequalities follow from the assumptions on $t$. Thus
\[
m_0(l)\leq \left(\frac{Cr\sigma_{r,X}(rl)}{t}\right)^{rl} .
\]

Now we estimate $m_j(l)$ for $j>0$.
Fix $j>0$ and define a positive integer $\rho_1$ by
\[
r2^{\rho_1-1}< \frac{t}{C_9}\leq r2^{\rho_1}.
\]
For all $(i_1,k_1,\ldots,i_l,k_l)\in I_j$ define a function
$f_{i_1,k_1,\ldots,i_l,k_l}\colon \{1,\ldots,\ell\}\rightarrow \{0,1,\ldots\}$
by
\[
f_{i_1,k_1,\ldots,i_l,k_l}(s):=
\left\{
\begin{array}{ll}
0 &\mbox{ if } \frac{{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})}{{\mathbb P}(B_{i_1,k_1,\ldots,i_{s-1},k_{s-1}})}>e^{-r},
\\
\rho &\mbox{ if }
e^{-r2^{\rho}}< \frac{{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})}{{\mathbb P}(B_{i_1,k_1,\ldots,i_{s-1},k_{s-1}})}\leq e^{-r2^{\rho-1}},
\ \rho\geq 1.
\end{array}
\right.
\]
Note that for every $(i_1,k_1,\ldots,i_l,k_l) \in  I_j$ one has
\[
1= {\mathbb P}(B_{\emptyset})\geq {\mathbb P}(B_{i_1,k_1}) \geq {\mathbb P}(B_{i_1,k_1,i_2,k_2})\geq \ldots
\geq {\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l}) > \exp(-rl2^{j}).
\]

Denote
\[
{\cal F}_j:=\left\{f_{i_1,k_1,\ldots,i_l,k_l}\colon\ (i_1,k_1,\ldots,i_l,k_l)\in I_j\right\}.
\]
Then for $f=f_{i_1,k_1,\ldots,i_l,k_l}\in {\cal F}_j$ and  $\rho\geq 1$
one has
\begin{align*}
\exp(-r2^{j}l)< {\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l})
&= \prod_{s=1}^{\ell}  \frac{{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})}{{\mathbb P}(B_{i_1,k_1,\ldots,i_{s-1},k_{s-1}})}
\\
&\leq \exp(-r2^{\rho-1}|\{s\colon\ f(s)\geq \rho\}|).
\end{align*}
Hence for every $\rho\geq 1$ one has
\begin{equation}
\label{est_l_r}
|\{s\colon\ f(s)\geq \rho\}| \leq \min\{2^{j+1-\rho}l,l\}=:l_\rho.
\end{equation}
In particular $f$ takes values in $\{0,1,\ldots,j+1+\log_2 l\}$.
Clearly, $\sum_{\rho\geq 1}l_\rho= (j+2)l$ and $l_{\rho-1}/l_\rho\leq 2$,
so by Lemma \ref{combf}
\[
|{\cal F}_j| \leq \prod_{\rho=1}^{j+1+\log_2 l}\left(\frac{e l_{\rho-1}}{l_\rho} \right)^{l_\rho}\leq e^{2(j+2)l}.
\]

Now fix $f\in {\cal F}_j$ and define
\[
I_j(f):=\{(i_1,k_1,\ldots,i_l,k_l)\colon\ f_{i_1,k_1,\ldots,i_l,k_l}=f\}
\]
and for $s\leq l$,
\[
I_{j,s}(f):=\{(i_1,k_1,\ldots,i_s,k_s)\colon\ f_{i_1,k_1,\ldots,i_l,k_l}=f\mbox{ for some }
i_{s+1},k_{s+1}\ldots,i_l,k_l\}.
\]

Recall that for $s\geq 1$, ${\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})\leq e^{-1}$.
Moreover for $s\leq l$,
\begin{align*}
\sigma_X(-\log{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s}))
&\leq \sigma_X(-\log{\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l}))
\leq \sigma_X(rl2^j)
\\
&\leq C_52^{j}\sigma_X(rl).
\end{align*}
Hence estimate \eqref{eq:cond2r} applied with $u=r2^{f(s+1)}$ implies for $1\leq s\leq l-1$,
\begin{multline*}
\sum_{(i_1,k_1,\ldots,i_{s+1},k_{s+1})\in I_{j,s+1}(f)}2^{(k_1+\ldots+k_{s+1})r}d_{i_1}^{r}\ldots d_{i_{s+1}}^{r}
{\mathbb P}(B_{i_1,k_1,\ldots,i_{s+1},k_{s+1}})
\\
\leq g(f(s+1))\sum_{(i_1,k_1,\ldots,i_{s},k_{s})\in I_{j,s}(f)}2^{(k_1+\ldots+k_{s})r} d_{i_1}^{r}\ldots d_{i_{s}}^{r}
{\mathbb P}(B_{i_1,k_1,\ldots,i_{s},k_{s}}),
\end{multline*}
where
\[
g(\rho):=
\left\{
\begin{array}{ll}
(C_8C_5 r)^r t^{-r}2^{jr}\sigma_{r,X}(rl)^r &\mbox{ for } \rho=0,
\\
(C_8C_5r)^r t^{-r}2^{r(\rho+j)}\sigma_{r,X}(rl)^r\exp(-r2^{\rho-1})&\mbox{ for } 1\leq \rho< \rho_1,
\\
(C_8C_5r)^r t^{-r}2^{r\rho}(2^{rj}\sigma_{r, X}(rl)^r+d^r)\exp(-r2^{\rho-1})&\mbox{ for }\rho \geq \rho_1.
\end{array}
\right.
\]

Suppose that $(i_1,k_1)\in I_1(f)$ and $f(1)=\rho$. Then
\[
\exp(-r2^{\rho})\leq {\mathbb P}(X_{i_1}\geq 2^{k_1}td_{i_1})\leq \exp(2-2^{k_1-1}t/e),
\]
hence $2^{k_1}t\leq er2^{\rho+2}$. W.l.o.g.\ $C_9>4e$, therefore $\rho\geq \rho_1$.
Moreover, $2^{rk_1}\leq (4er)^r 2^{r\rho}t^{-r}$, hence
\[
\sum_{(i_1,k_1)\in I_{j,1}(f)}2^{rk_1}d_{i_1}^{r}{\mathbb P}(B_{i_1,k_1})
\leq d^r (8er)^r t^{-r}  2^{r\rho}\exp(-r2^{\rho-1})
\leq g(\rho)=g(f(1)),
\]
since w.l.o.g. $C_8C_5\geq 8e$.
Thus an easy induction shows that
\begin{align*}
m_j(f) &:=  \sum_{(i_1,\ldots,k_{l})\in I_{j}(f)}  2^{(k_1+\ldots+k_{l})r} d_{i_1}^r\ldots d_{i_l}^r
{\mathbb P}(B_{i_1,k_1,\ldots,i_{l},k_{l}})
\\
& \leq \prod_{s=1}^lg(f(s))=\prod_{\rho=0}^{\infty}g(\rho)^{n_\rho},
\end{align*}
where $n_\rho:=|f^{-1}(\rho)|$.

Observe that
\[
e^{-r2^{j-1}l}\geq {\mathbb P}(B_{i_1,k_1,\ldots,i_l,k_l})
=\prod_{s=1}^{l}\frac{{\mathbb P}(B_{i_1,k_1,\ldots,i_s,k_s})}{{\mathbb P}(B_{i_1,k_1,\ldots,i_{s-1},k_{s-1}})}
\geq e^{-lr}\prod_{s\colon f(s)\geq 1}e^{-r2^{f(s)}}.
\]
Therefore
\[
r\sum_{\rho=1}^{\infty}n_\rho2^{\rho-1}=\frac{r}{2}\sum_{s\colon f(s)\geq 1}2^{f(s)}\geq
\frac{r}{2}l(2^{j-1}-1).
\]
Moreover
\[
\sum_{\rho\geq 1} \rho n_\rho\leq (j+1)l+\sum_{\rho\geq j+2}\rho l_\rho= (2j+4)l.
\]
Thus
\[
\prod_{\rho=0}^{\infty}g(\rho)^{n_\rho}
\leq
\left(\frac{C_8C_5r 2^{j}\sigma_{r,X}(rl)}{t}\right)^{rl} 2^{rl(2j+4)}
\left(1+\frac{d^r}{\sigma_{r,X}(rl)^r}\right)^m\exp\left(-\frac{rl}{2}(2^{j-1}-1)\right),
\]
where $m=\sum_{\rho\geq \rho_1}n_\rho\leq l_{\rho_1}\leq 2^{j+1-\rho_1}l$.
By the assumption on $t$ we have $1+d^r/\sigma_{r,X}(rl)^r\leq 2\exp(t/C_4)\leq \exp(r2^{\rho_1-4})$ if $C_4$
is large enough (with respect to $C_9$).
Hence
\[
m_j(l)\leq |{\cal F}_j| \left(\frac{\sqrt{e}C_8C_5 2^{(3j+4)}r\sigma_{r,X}(rl)}{t}\right)^{rl}\exp(-rl2^{j-3}).
\]

We get
\[
m(l)= \sum_{j=0}^{\infty} m_j(l)\leq  \left(\frac{Cr\sigma_{r,X}(rl)}{t}\right)^{rl}+
\sum_{j= 1}^\infty\left(\frac{C2^{5j}r\sigma_{r,X}(rl)}{t}\right)^{rl}\exp(-rl2^{j-3}).
\]
To finish the proof of \eqref{eq:aim}, note that
\begin{align*}
& \sum_{j=1}^\infty \left(2^{5j}\right)^{rl}\exp(-rl2^{j-3}) \leq C^{rl} \sum_{j=1}^\infty \exp(-rl2^{j-4})
\leq C^{rl}. \qedhere
\end{align*}
\end{proof}

\begin{proof}[Proof of Theorem \ref{thm:Paourlr}]
Since $({\mathbb E}\|X\|_r^p)^{1/p}\leq C_5p{\mathbb E}\|X\|_r$, we may assume that
$p\geq r$. Let $d_i$ and $d$ be as in Theorem \ref{thm:cutPaourr}. Then

\begin{equation*}
d=\| ({\mathbb E} X_i^2)^{1/2} \|_r \le { 2C_5 \| ({\mathbb E} |X_i|) \|_r\le 2C_5{\mathbb E}\|X\|_r}.
\end{equation*}
Set
\[
\tilde{p}:=\inf\{q\geq p\colon\ \sigma_{r,X}(q)\geq d\}.
\]
Theorem \ref{thm:cutPaourr} applied with $\tilde{p}$ instead of $p$ and $t=0$ yields
\begin{align*}
({\mathbb E}\|X\|_r^p)^{1/p}&\leq ({\mathbb E}\|X\|_r^{\tilde{p}})^{1/\tilde{p}}\leq C_3r\sigma_{r,X}(\tilde{p})
=C_3r\max\{d,\sigma_{r,X}(p)\}
\\
&\leq Cr({\mathbb E}\|X\|_r+\sigma_{r,X}(p)). \qedhere
\end{align*}
\end{proof}

redpajama_set_name: RedPajamaArXiv