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Happy New year 2025❤

Nice

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Nice walk, thanks for taking us along. Like 2 from a new friend🙏❤️

Great channel. I'm your Fan.

Loving the street, the video and the people. Thank you!

Loved this video! I noticed a small tweak you could make to your thumbnails to increase clicks

honestly I think it's better than costco

american Goodwill has never looked so organized or clean in my life.

Can I do work in Korea with C3-9 visit visa status

Nice 😊 hope ur channel grows🎉

Wow Gukje Market is big. It is a wonderful place to shop. There are a lot of food stalls. Nice video, friend.

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아름답네요^

Thank you, I love those store walks :) Hope you are doing well.

love this pov, feels like I'm the one driving, with nothing but the wind in my hair and the calmness of the night.

Byexploringtheseproperties,researchersaimtoenhanceourunderstandingofthedynamicsandcharacteristicsoffractionalsemigroups. Definition3.1.ForaBanachspaceU,afamilyofoperators{Q(y)}y≥0⊆(U,U)isreferredtoasafractionalβ-semigroup(orβ-semigroup)ifβ∈(0,∞]anda>0foralla: (i)Q(0)=I, 1 1 1 (ii)Q(s+y)β=Q(sβ)Q(yβ),∀s,y∈[0,∞). Clearly,ifβ =1,then1-semigrouparejusttheusual semigroups. Example3.1.WecandefinethespaceXasC[0,∞),whichrepresentsthesetofreal-valuedcon-tinuousfunctionsontheinterval[0,∞). Now,let’sdefine(Q(y)φ)(s)=φ(s+2√y).ByshowingthatQsatisfiesthepropertiesofa 1-semigroupofoperators,wecaneasilydemonstratethatitisindeeda1-semigroup. 2 2 Definition3.2.Anβ−semigroupQ(y)iscalledaac0−semigroupif,foreachfixedx∈X,Q(y)u→uasy→0+. Thecongormableβ −derivativeofQ(y)aty=0iscalledtheβ −infinitesimalgeneratorofthefractionalβ−semigroupQ(y),withthedomainequals u U:lim y→0+ Mβ(Q(y))uexists. WewillwriteAforsuchgenerator. Theorem3.1.Let{Q(y)}y≥0⊆(U,U)beac0−β−semigroupwithinfinitesimalgeneratorA, 0<β<1.IfQ(y)iscontinuouslyβ−differentiableandu∈Dom(A),then Mβ(Q(y)u=AQ(y)u=Q(y)Ax. Proof. Let’sgetstartedwith β  Q(yg(εy−β)))u−Q(y)u (Q(y))u = lim ε→0 = lim ε→0 ε Q(yβ+(yg(εy−β)))β− ε  yβ)βu -Q(y)u = lim ε→0 Q(yβ+((yg(εy−β)))β− ε yβ))βu -Q(y)u. 1 1 1 IfQ(y)isindeedaβ-semigroupofoperators,thenQ(a+b)β =Q(aβ)Q(bβ).Hence β −β β β Mβ(Q(y))u = lim ε→0 Q(y )βQ((yg(εy ))) −y ))β u−Q(y)u ε = lim ε→0 Q(y)[Q((yg(εy−β)))β− yβ)) β u − Q(0)uε Now,usingtheMeanValueTheoremforconformablefractionalderivative,see[6],weget Q(y)[Q((yg(εy−β))β− yβ)) β u − Q(0)uε forsome0<c<(yg(εy−β))β−yβ.  =Q(y)M  β(Q(c))u (yg(εy−β))β−yββε Ifε 0,thenc 0,andlimMβ(Q(c))=Mβ(Q(0))=A.Consequently, ε→0 Mβ(Q(y))u=Q(y)Aulim ε→0 (yg(εy−β))β yβ . βε UsingL’Hopital’sRule,weget Hence  lim ε→0  (yg(εy−β))β−yββε  =1. Mβ(y)u=Q(y)Au. SimilarlyonecanshowthatQ(y)u∈Dom(A)andMβ(Q(y))u=AQ(y)u. □ Theorem3.2.Theinnitesimalgeneratoroftheabovesemigroupis Aφ(s)= φ′(s), Dom(A) = {φ∈U:φ′existsinU}. Proof. Mβ(Q(y)φ(s) = y1−βQ′(y)φ(s) =y1−β  lim ε→0 Q(y+ε+O(ε2))φ(s)−Q(y)φ(s)ε φ(s+1(y+ε)β)−φ(s+1yβ) = y1−βlim β β ε→0 ε φ(s+1(y+ε)β)−φ(s+1yβ) φ(s+y+ ε)−φ(s +y) = y1−βlim β ε→0 ε β . φ(s+y+ε)−φ(s+y) φ(s+1(y+ε)β)−φ(s+1yβ) φ(s+y+ ε)−φ(s +y) Now, ε→0 φ(s+y+ ε)−φ(s +y) limφ(s+y+ε)−φ(s+y) ε = φ′(s+y), ε→0 ε limφ(s+1(y+ε)β)−φ(s+1yβ)φ(s+y+ε)−φ(s+y) = 0. ε→0 β β 0 UsingL’Hopitalrule(withrespecttoε)toget φ(s+1(y+ε)β)−φ(s+1yβ)  yβ−1φ′(s+ 1yβ) lim β β = β . ε→0 Thustheproductgives φ(s+y+ ε)−φ(s +y) φ′(s+y) Mβ(Q(y))φ(s)=φ′(s+1yβ). β HenceAφ=φ′.

Nice👍🏻 I'll do my best on RUclips, which I just started.

Always amazed at how clean the subway, train, and airport stations are in the big cities. Great Video. Thanks

how beautiful. the lake with the stunning greenery and mountains in the backdrop, absolutely breathtaking.

Was worried and concerned about you! Glad you are back, take care.

2nd

You are doing amazing job. Could plz make some videos about daiso tour near kyungpook national university, primall shopping vlogs and other shopping places near KNU. I think this would help and ease thhe new students life who are coming to korea specially to KNU. I think everyone is exploring Seoul only and we couldn't find any valuable exploration vlogs in daegu except you. I hope Your videos get more recognition, because it deserves.

You really know how to capture the beauty of all your travels big and small. And that’s why I love riding along with you. Thanks for a wonderful road trip, once again. It was amazing. 😻

Thank you, Korea Vagabond, this is really a wonderful spring trip,and,as always,the music you have chosen harmonizes and conveys the blooming mood of the magnificent sakura.I wish you to always be in a good mood🙂

This was adventurous and fun!!😂

Beautiful drive. 😊

You must do this for me :) Everytime it rains, you grab your raincoat, umbrella and start filming. Have a wonderful day.

Love this walk. It must smell amazing with all those blossoms. 😊❤

I want to go here with my bff. Looks amazing. ❤

The cherry blossoms 🌸 are so beautiful to look at, rain or shine 🩷

Very nice morning walk and I love the sound of the waves. Thanks, Vagabond.

Beautiful beach an ocean views. Video 👍

Actually, I watched it a second time and really liked the ride with your music :) Peaceful and relaxing. Stay Healthy

It's raining again???? I would love Daegu! Nice listening to the rain hitting the top of your umbrella and the sounds of people. Thanks.

Ok, you have walked, drove, rode on a bus, drove a scooter and push a shopping cart around.... Next up, it will be a shorter video, but, skydive from 16,000 feet, which will take around six minutes. What a video, you floating in air and fallling towards earth... WOW.. You would be the first to do this.. Don't worry, I will be right by your side, of course, my eyes will be close as I pray... 🤣😅😂😆🤢🤮🤢🤮🤢🤢🤢🤢🤮🤮🤮🤮 Love this video and the scooter ride, but, think Yoon Do Hyun (Sparks Fly) music would of been better (So happy he is cancer free now), love this guy. Your music is just fine

Beautiful! I am running out of things to say about you! I hate repeating myself, but, you are one of the best. Thank you for always taking your time, showing us a different World.

The only thing better than the rain, is the snow for me. Thanks like always... On to the next one. One day, you will have thousands of subscribers and will not have the time to read them all. But, until then, I am here...... Love this video

Outstanding. Love the part with the mom and her little girl, carrying an umbrella bigger than her and not up :) Also, year ago and it's raining. Finally, that is a very long walk to work and so many buses passed you???? Get on the bus 😁🤣😂😜 A Vagabond is a person with no home or job, so, I thought you was rich and living the life. Of course I am joking, my wife tells me all the time, I'm not funny! Hope you are smiling and enjoying your day. Take care. Sorry, I need to go, I am off to a walk on a snowy day by the riverside :)

I think one of my favorite things to do if I was in Korea, would be walking around a Market area watching and listening to the people. Food looks so good, I would want to stop at each stand and eat. Watching the workers work so hard making food. It must be hard work showing up to prepare lunch and dinner. People work so hard to make a living and still keep there sense of pride. I have much respect for the people and you. I found this video just searching your channel. The one lady was buying crabs, can't they pinch you thru the back? Thank you like always. Stay safe and Happy

Awesome! I only cried twice 😁As you got closer to the loop, I started planning my funeral. You must be in great shape... Much appreciation for this video. What does it cost to Space Walk? Thank you, thank you and thank you.....

Did you pay for my seat? I am moving to Daegu and setup an umbrella store :) Thanks the hard work, Vagabond. Take care.

Down in Daegu, it rains alot? I do like the cold rain. I see those subscribers are moving up :) Keep doing what you are doing and you will have many more. Like always, thank you for the time you put into showing us Korea. Take care.

I really enjoy my walks with you, seeing the beauty they call Korea. I wish more people would join this site and see what they are missing. If this is the first time you are visiting this site, Korean Vagabond is out and about during snow, rain or sunshine, providing excellent video's! How about you giving a thumbs up and subscribing, you will not be disappointed. Thanks to all. Great job Vagabond.. Stay healthy and live long :)

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Got it! 4 Hours from Seoul or 1 and half from Busan...

When I first started watching this video, I thought you was at the place they filmed "Undateables" with Namkoong Min, but I was wrong. Great drama! You have out done yourself again, Vagabond! Thanks for the pleasant stroll. Have a wonderful day.

Thank you, Korea Vagabond,it was a very beautiful walk.😊🇰🇷🖐️

Now, Now, Now, you all after my excitement. I am a Two Harley owner and this is my passion! But, sad, no drivers seat on a scooter, so, I was hanging on for my life 🤭😂🤣😁 I might not have to visit Korea, because you are showing me the country. Nah, I am still coming/visiting Korea! The beauty of the country, the great test of the foods and nicest people in the world. Thank you, Vagabond... PS, Lets upgrade to the Harley-Davidson (Road Glide: Unlimted). 🏍🏍🏍