關於 remember me心得 ，我們在網路上蒐集到這些相關的討論、資訊與評價

【KidsRead親子共讀分享最終章&明日團購表單預覽】

遠遠近近的朋友們，你們都還好嗎？

💗明早九點(臺灣時間)為期僅四天的KidsRead活動即將開跑，#預覽表單 連結在此先供大家一睹為快👉：https://lihi.tv/gvHSA（此連結明早會轉成正式下單連結）

#大家此團最想購入或曾買過最喜歡的KidsRead商品是什麼呢 ？快來和我們分享吧！

我自己這幾天正經歷著布里斯本的天冷，以及孩子受風寒在家鬧彆扭的疲倦，而這一週的運動計畫也泡湯了。

但縱使外界紛紛擾擾，我們仍可以用音樂洗滌內心的煩憂。今晚，就讓我與你們分享《溫馨的提卡音樂家族》音樂繪本，以及兩張音樂專輯：Jazz for Kids＆《迪士尼音樂點讀專輯》。

因為無論大人或孩子，我們都需要音樂點綴人生。

＊＊

♦️《溫馨的提卡音樂家族》♦️

如果你家孩子喜歡音樂翻翻書，或是你希望向孩子介紹樂器之美，培養美學素養，卻又不知從何開始，《溫馨的提卡音樂家族》音樂繪本便是一個好選擇。

《溫馨的提卡音樂家族》 是由法國知名作家Christelle Saquet 與插畫家Peggy Nille 合作而成的繪本夢幻組合，搭配KidsRead點讀筆，讓可愛的故事插圖更為鮮活，孩子也能選擇書中喜歡的樂器一再回味。這套音樂故事繪本，不僅洗滌心靈，同時為孩子啟蒙音樂的欣賞力。

而這套書細膩之處更在於每本書收錄9-10首樂曲，每首樂曲皆為知名音樂家演奏錄製，非電子合成樂器演奏，並且樂曲都有30秒至一分鐘的長度，用心可見一斑。

＊＊

♦️Jazz for Kids♦️

Jazz for Kids 兒童音樂專輯，是KidsRead與成立30多年、音樂優質的金革唱片合作打造的兒童床邊故事音樂系列（20年前我也是他們的爵士樂CD粉絲呢），歌曲以鋼琴、吉他或顫音琴演奏。

內含12首揉合流行經典、爵士，與兒童音樂的樂曲，是音樂家暨製作人 Michael Janisch 送給女兒的出生禮，怪不得，每個音符都傳遞著滿滿的愛與柔情。

雖說是床邊故事音樂系列，但我也愛在早晨撥放，讓一天的美好隨著音樂於家中緩緩流瀉。它不僅為孩子臉上帶來純真的微笑，也安撫了父母臉上沒睡飽的倦容。

Jazz for Kids點讀版除附有一張光碟，還有兩張可愛的雲朵海報，上頭各有六首曲目，每首曲目都有一位愛睏的台灣黑熊寶寶作陪；此外還有12張點讀小卡，讓孩子外出也能自備小睡音樂。

＊＊

♦️迪士尼音樂點讀專輯♦️

若妳家孩子像我家一樣，覺得拿 Jazz for Kids 當畫畫時的配樂太催眠(人家本來就設計給睡前使用)，那聽聽純音樂的迪士尼音樂點讀專輯會是個不錯的選擇。

專輯中收錄了12首經典的迪士尼動畫電影主題曲，每首歌都以吉他或鋼琴帶出輕快的旋律，就連《可可夜總會》中最催淚的一首Remember Me也成了開心的版本，非常適合平時讓小小孩跟著節奏唱唱跳跳，或是當孩子勞作、看書時的背景樂。Lara時常邊玩樂高邊聽邊讚嘆此專輯：「聽起來好輕鬆喔！」音樂可以調劑身心，果真不假！

《溫馨的提卡音樂家族》音樂繪本，以及兩張音樂專輯：Jazz for Kids＆《迪士尼音樂點讀專輯》的詳細心得文：https://bit.ly/2TEGAq9

張媽媽非常之高興今日超越500,000訂閱了！衷心感謝支持我的觀眾，你們的支持就是我的鼓勵！Thank you so much to all Mama Cheung supporters all over the world, I am so happy that I have reached the half-million subscribers' milestone today!

看影片Click to watch: https://youtu.be/NpZdnCWvF1Y

歡迎大家分享張媽媽廚房的煮食心得，share 我悉心炮製嘅中式食譜給你們的朋友！Please share my authentic Chinese cooking recipes with your foodie friends and cook some at home too for your family and loved ones!

記得俾個LIKE及訂閱張媽媽廚房！重有Follow @mamacheungcooks IG & Facebook喔！Remember to smash the LIKE and SUBSCRIBE button below! Follow me on IG and Facebook as well @mamacheungcooks!

張媽媽廚房頻道裏還有300幾個美味食譜，歡迎瀏覽一下！Mama Cheung YouTube channel has over 300 delicious recipes, happy cooking! #mamacheungcooks #mamacheungrecipe #mamacheungeats #張媽媽 #youtube #hkig #hongkong #chinesecooking #香港 #食譜 #自家製 #湯水#follow #followme #youtuber

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

張媽媽非常之高興今日超越500,000訂閱了！衷心感謝支持我的觀眾朋友，你們的支持就是我的鼓勵！Thank you so much to all Mama Cheung supporters all over the world, I am so happy that I have reached the half-million subscribers' milestone today!

歡迎大家分享張媽媽廚房的煮食心得，share 我悉心炮製嘅中式食譜給你們的朋友！Please share my authentic Chinese cooking recipes with your foodie friends and cook some at home too for your family and loved ones!

記得俾個LIKE及訂閱張媽媽廚房！重有Follow @mamacheungcooks IG & Facebook喔！Remember to smash the LIKE and SUBSCRIBE button below! Follow me on IG and Facebook as well @mamacheungcooks!

張媽媽廚房頻道裏還有300幾個美味食譜，歡迎瀏覽一下！Mama Cheung YouTube channel has over 300 delicious recipes, happy cooking!

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🔖本影片與「碧兒泉」合作。
Collaborate with Biotherm.

嗨大家 這次收到了碧兒泉日夜奇蹟水&特嫩精華的邀請
2月初收到之後就天天使用
都快被我用到空瓶了才來跟大家分享我的心得！
自己最愛就是它能夠撫平我皮膚的粗糙感 又有足夠的保濕度
很推薦有興趣的大家在百貨母親節檔期購入🛍️
免費兌換試用包:https://reurl.cc/4yWrD3
優惠組合參考:https://bit.ly/3wzpkkY

這次去了一直很想去的不然
還有想買很久的龜背芋🌳
雖然很重又必須跑回家一趟
但最近愛上養植物 光看著就太療癒了怎樣都要扛回家xd
之後再慢慢跟大家分享我的植物們!

✿影片中使用的產品
碧兒泉 奇蹟活源晶透露125ml
碧兒泉 奇蹟活源精露125ml
碧兒泉 奇蹟特嫩精華50ml

✿時間軸
00:00 start!
01:09 碧兒泉產品介紹
03:09 使用前皮膚狀況
03:54 短期、中期、長期感受✨
05:04 VLOG : a day with me
07:38 ☕️BRUN不然
106台北市大安區安和路一段7號
10:00 💐建國假日花市
106台北市大安區建國南路一段
13:12 ☕️Remember Me_記得我．Café
105台北市松山區南京東路四段133巷4弄16號
16:45 結尾 母親節優惠分享🛍️

✿Find Me Here
Instagram @4nn8er
https://www.instagram.com/4nn8er/
Facebook @4nn8er
https://www.facebook.com/4nn8er/
Business Inquiries｜ 4[email protected]

✿Music
Epidemicsound https://www.epidemicsound.com/referral/ie63q2/
Music by Fiji Blue - It Takes Two https://thmatc.co/?l=EA80771C

✿FAQ
Camera｜Canon m6 mark ii + 11-22mm
Edit｜Final cut pro X

#頭文字D #specialstage #Root的遊戲心得小舖

這部是網友投稿的影片，提供影片和翻譯給我之後
我再將其字幕合成，做成影片
最費工的地方就是需要對時間軸的字幕，完全是苦力活
而且翻譯上也不是完全正確，或是有語調不順暢的地方
這些都需要重新調整過，我也特地找了原作漫畫來比對
文字上面的編排與呈現，細節部分都是經過特別處理的

我敢肯定的說，會做這種影片的只有我一人！

有兩首歌會有問題，因為版權爭議
一首是SPEEDY SPEED BOY，另一首是REMEMBER ME
我只好設成靜音了，請見諒

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有的影片沒辦法營利，廣告費會被拿走
歡迎用Paypal斗內我「一杯咖啡」的錢喔！
位置是：paypal.me/RootTsou

你 / 妳 想成為Youteber來增加被動收入嗎?
歡迎參考我的簡介喔，下面有詳細介紹
https://www.youtube.com/user/RootTsou/about

也歡迎幫我點讚、分享和訂閱喔 ❤️
點擊右下方X的頭像可以訂閱我，或是結束時P4主角的頭像
如果有訂閱的話請「一定」要開啟小鈴鐺🔔
這樣我上傳新影片的時候才會收到通知~😛

我的巴哈姆特小屋：
https://home.gamer.com.tw/homeindex.php?owner=prettysamy

我的粉絲團網址：
t.me/Root_Tsou

巴哈姆特往日遊戲版的Facebook專頁：
https://www.facebook.com/groups/Baha.OldGames
(優質社團歡迎加入 ww)

Facebook (Root Tsou)：
https://www.facebook.com/root.tsou

電子郵件信箱：
shining383@gmail.com