## Monday, 31 May 2010

### 馬肉版孔乙己 (Osu!專用)

Author: Kawashiro Nitori , COPYRIGHT RESERVED

### SIMC Report (3) Challenge 3i

In challenge 3, we are required to create a few models considering real factors.
5)Potential Population Density
Recall the assumption that have been made in Challenge 1,2: They go to the closest shop only; continous and even distribution of potential population and a given map of street.
What can you see that assumption different from the reality?
Going to the closest shop implies that the potential customers are in stationery. In the real society, the population forms a vector field (on a 2D/3D coordinate, whatever), where the peference of cumtomers changes from time to time. For example, we won't go to starbucks in the early morning. Therefore a multiplyer t(x|24) is set to be a cycle of population density in different time.
Consider the given potential population density at a given instant. The vector field of the customers can be ignored since the vector field indicates the rate of change in density and indicates the density in the next moment only. At a given moment there're no population flow. Now the question is: it is impossible for us to create a model and a vector field to compare the marginal influence at every instant. How can we create a easy and reasonable model?
Our solutions will be:
i)A simple model: Consider a street, apart from the closest Starbucks and Coffee Bean from a and b units, then the share of Coffee Bean will be a/(a+b) units. The idea comes from that the closer shops will have a higher probability of selling services to the closer customers. The assumption is that the population is flowing, but there will be a higher chance to walk along the closer shops.
Consider the model on a 2D- plane: (0,0)to (4,0), (0,2) to (4,2), (0,0) to (0,2), (2,0) to (2,2), (4,0) to (4,2), total 14 untis. Assume that the Starbucks located at (2,2) while the Coffee Bean is located at (0,0).
It seems that the location of Starbucks will be much better than the Coffee Bean. Actually in the original model we will get the share as 5/15 units at the proportion of 5:9. But it  is quite weird as they are close to each other. Then how can we improve the result?
In this model, the new share of Coffee Bean will be 6/14 (6:8) which is more reasonable.
We can see that in this model the strategy of "blocking others" is not effective anymore since two close shop will have similar shraes. The new locating strategy is main locating them in the junction point and near to the centre of map which is more close to reality.

Unfinished and we'll discuss a complicated model considering the population flow tomorrow.

## Sunday, 30 May 2010

### SIMC 2010 Report (2): Challenge 2

The aim of tis problem is to maximize the market share within a given budget relating to the position of the shops. Note that the cost is not related to the marginal influence, but the n-junction road,
3)Basic Strategy
Of course we should we most of the budget.
Proof: setting up a new shop shop increase market, so putting more is better.
Another important strategy is that we should bulid more shops in the 2-junction road.
Proof: it's the matter of blocking others and obtaining more "weak" controlling area.
Why obtaining more "weak" area is better? A basic frame is that the area of "strong controlling" is almost the same for every shops. It means that if you bulid a shop in their "strong controlling" area, you will get a little share. Then the "weak" area will be relatively bigger. Now when the number of shops is equal, the brand who controls more "weak" area wins. When three shops nearby forms a close triangle, the area within these three shops is somehow likely a "strong controlled" area so that a large area can be obtained.
comparing the 4-2, buliding two with 2 units of cost is obviously better than buliding one shop in the 4-junction road (even two besides the junction must be better). But how about the 3-2 comparason? It seems that the case of 3-2 is much more complicated since there're too many junction to be drawn and the stright road is undetermined. However we simplify the case for putting two at the end of the junction and the last one in the end of one of the junction. Then the share is also miximized.
Therefore our conclusion about the strategy will be maximized when we bulid as much at 2-junction as possible.
4)Application
Now we go the the core idea of the problem. How can we apply the strategy?
our solution is putting them in front of Starbucks to block them, and we get 27.5/47. however we can see that the optimal solution will be 28/47 where two blocks starbucks below and one above the 4-junction road.
Now we realize that the solution aimed to rule the whole street in the bottom. It seems that it's still the same target: to block Starbucks and acquire a large area. But what's the difference?
The difference is that we are trying to block Starbucks in their "strong" controlling area, and to obtain the whole street in the center. In their solution they tried to obtian the weak area.
Note that when we block starbucks, we can only block one of their way, but they still control the other ways. But acquiring the whole "weak" area is different from that. It will be impossible for Starbucks to go inside the "controlling triangle" such that we can surely win the competition.
Locating near the 40junction road aims at acquiring more market share from different road, then they will have the higher chance the control a "weaker" area. In our solution,
Recall the two strategy : near to the junction road and vlocking others, they have different advantage so how to balance them and maximize the share? That will be the key idea of our report.
Anyway I think this problem is just a further application of Q1, but not very hard if we have solved Q1 in a good way (or many infinite times of trial and of course error?)

### SIMC report (1): challenge

http://www.highsch.nus.edu.sg/SIMC2010/Challenge%20Question%20pdf.htm
Firstly I would like to talk about this problem first since this will be the main propose for us to go to Singapore~
1)Basic analysis and definition
We now simplify the expressions: for X----O with length L, the market share of Coffee Bean (O) will be L/2. Sum of every line segment between two closest Starbucks shop/Cofee Bean shop will be the total share of the whole map.
2)strategy and algorithm
What is the difference of strategy and algorithm? In this problem it's just the same, but dirrerent in score. We have outlined a several strategy (not absolute rule), but we can't obtain enough score here. The main reason will be the difference in complexity and the ensurance of optimal solution.
i)Disperse without overlapping
Proof: Consider X--O1-----O2, XO1= k units, XO2=L units, then market share will be L-k/2 units.
Therefore as O1O2 disperse (L-k increases), our market share increases.
Proof by a 4-junction road. Consider a CB shop near to a cross junction while it market share to the three road will be a,b,c units respectively. If CB shop is 1 units near to the 4 junction road, the market to each road increases 0.5 each which is benificial to CB shop.
iii)Blocking Starbucks shop
Proof: consider the model in (i) again: minimize k to 1 (k≠0, k is non-negative integer), we maximize l(x)=L-k/2.
That's our work to find out the optimal solution.
Greedy algorithm
Marginal influence of a lattice is defined as the increase in market share when a new shop is added there.
Method I: Put the shops in the highest marginal influence.
Method II: Put one shop in the optimal place, re-calculate the marginal influence and to place again.
Obviously Method II is better since optimal three ≠ best combination.
However, we can't show that method II is optimal since it still just a combination of optimal shops, but not an optimal combination.
"I know your method helps to find a better solution. But how can you find such a solution. I mean, is it a modified trial and error?"
Modified trial and error is not avoidable at all. Even a full trial and error will be acceptable. We will that according to our strategy, a few choices will be left as so that we can try all of them.
"How can you determine the optimal solution among them?"
this one is stupid, just by trial and error and comparason.
"Blocking Starbucks is unfeasible. They still have another way to control their markey share. What's the main effect of this strategy?"
First we define "weak" and "strong" of a control of a shop on a particular street. It will be relative concept that is proportional to the distance to the closest shop. Placing a new shop in a "weaker" segments will have a higher market influence.
If we block them is the same direction, the opposite-blocked direction will be "far" from Starbucks so that Even the CB shop is controlling some area somehow "weak",  Then a large piece of area will be in the contrl of CB.
We don't have much to discuss with the solution of (1b), it's just a direct application of our strategy.
4 junction road + blocking the SB on the LHS. The second one located just below the bottom-right SB.
Hmmm, about the City Hall map it's a true hard one. The map is complex and there're far too much combination for us to call it "we 'have fully tried all"....
Let's finish the report for Question 1 here.

## Saturday, 22 May 2010

### 22-5-10

Going to Singapore for SIME 2010.
BTW I found several mistakes in the BAS so I may have to make another version 5.F...

Currently I also find difficulties in typing notes for Physics and Economics. The first one required a lot of experioenced example to deal with, while the second one requries lots of graphs. (I'm a bit lazy to produce graph precisely lol). Anyway I'll try to elaborate them =]

## Wednesday, 19 May 2010

### Osu! 第17話

不過，這些問題或許可以從天才化學家那邊得到解答吧？

haruhiteamsos

「可惡!黑米你這麼做究竟想要幹什麼?」
「哈哈哈!你很快就會知道了! 之前要不是有你阻饒，我的計畫早就成功了。」黑米突然左轉把屋頂當立足點躍身一跳，跳到左邊的大樓窗戶中。
「不好了!快追丟了。」三人各自從大樓不同角度的窗戶跳進去，我眼前的是一個受到驚嚇而坐在地板的辦公員工「剛跳進來的那個黑衣男子在哪裡?」我問道。

「終於把你引到這裡來了。」黑米輕鬆的對我說道。
「你到底想做什麼?」
「拯救世界…」沒想到是站在黑米左邊的黑衣女性先開口用平靜的口吻答道。
「什麼?你不是想毀滅這個世界嗎?」
「無論如何，我們都需要黑米大人的這本理論。」站在黑米右邊的黑衣男性達道。
「沒錯…」黑米露出牙齒笑了一下，然後繼續說「這本黑米理論記載了我過去二十年間對造物者peppy做的研究，這是拯救世界所需要的力量。不過呢…」黑米指向我「你的出現可說是這個計畫最大的阻饒!」

「請進。」

「fish哥，您找我來有什麼急事嗎?」我邊把門關上邊問道。
Fish哥頭沒有回，沉思了一下，接著開始說道:「伊格瑙.莉絲、俠侶、以及當初跟我一同奮戰的夥伴們……了解金Q拉是什麼的人越來越少了。二十年前世界差點因為金Q拉而毀滅，」這時fish哥回過頭來看我，是從沒見過的認真表情，說「如今又有人想要奪取金Q拉了! 」
「什麼!?」我倒抽了一口氣。
「請坐。」fish哥轉過身來坐下，並把手中那包包裹放在辦公桌上。我也抽出椅子，開始聽起事情的經過。
「是黑米。」fish哥很直接得說出了這個名字，並娓娓道來:「他是我以前的學生，並且一直都是最優秀的一個，直到了某一天，他發現了金Q拉的秘密後，就瘋狂得陷入其中。他背著我從事金Q拉的相關研究，也發現了這跟造物者peppy之力之間的關聯。」
「金Q拉是什麼? peppy之力又是什麼?黑米想要這些力量做什麼?」聽到了幾個神秘中帶有巨大危險的關鍵字，我忍不住問道。
「毀滅世界，然後再創造一個，這是我推想後得到的結論。」fish哥只回答了我最後一個問題。
「毀滅世界?這太瘋狂了!」我大叫。
「所以我們必須阻止!這也是我找你來的原因，雖然你沒有經歷過前一次大戰的時代，不過你現在也靠天賦與努力成為了這個世界最強的Beater之一，我需要你的能力，也只有你能擔當這個關鍵要職。」fish哥把那包包裹推到我面前。
「這是什麼?」我看著那包裹上面寫著”把我打開”四個大字，是要我打開嗎?
「不，不是要你打開。這包裹裡面包著一個盒子，是前一次大戰的產物，而外面的包裝是我做的。」

「每當世界面臨毀滅的危機，阻止毀滅的希望也將同時誕生，這是為了世界的平衡，造物者peppy所創造出的定理。上次的大戰的危機使世界的力量創造了這個盒子，雖然最後我阻止了那次的危機，但是並沒有成功摘除最根本的誘因。毀滅世界的力量依然還存在著，而這個盒子仍是拯救世界的關鍵。」
「那盒子裡面是什麼?」為什麼fish哥有著強大的力量，卻不用盒子裡面的東西去除掉世界毀滅的根基。
「裡面什麼都沒有。」fish哥笑著說。
「疑?」我越來越混亂了，難道我被耍了嗎?
「真的~裡面什麼都沒有，但是這個盒子本身充滿了希望!」
「怎麼說。」
「這個盒子誕生於二十年前的大戰。在大戰後，我為了斬草除根，不讓悲劇有機會再發生，我致力於打開這個盒子，花了一年的時間破解了機關、打開了這個盒子。不過打開後我大吃ㄧ驚，裡面什麼都沒有…我很沮喪，難道這個peppy的平衡定理是騙人的?不對，這個盒子確實是peppy的力量創造出來的，因為二十年前得到這個盒子時，上面”osu摻了金Q垃，SS日產一千八”這段話給了我巨大的提示，才得以阻止世界毀滅的危機。當時是這線索給了我拯救世界的唯一機會。那這個空盒子在事後提供了什麼線索? 我百思不得其解，直到了十年前的某一天發生的一個大事件才讓我瞭解。」
「恩。」我發出個無意義的同意，然後繼續聽。
「那次的事件死傷慘重，當時我剛好去了別的城市辦事，有個很巨大的空賊集團就趁機來襲，佔領了城市，城市裡看起來值錢的東西都被搶一搶而空－包括我放在辦公室裡的這個盒子，我在聽到消息後馬上就飛了回來，在空賊把贓物搬上飛船之前我就把他們的飛船通通給擊沉、設下結界包圍這座城市並逮捕整個空賊團，才讓整件事落幕。不過在贓物堆之中我找不到這個盒子，我很緊張。最後我隨著盒子特有的波動在一個房子之中找到了它，不過一進門眼前的景象卻讓我大吃一驚。」

「裡面擠滿藏匿的空賊，我瞬間將它們全部打昏。在裡面的某個房間我看到了…」fish哥停頓了一下，然後接著繼續說「我看到了一個小孩蹲在角落發抖，手上握著這個盒子，在他面前的是為了保護他而犧牲的父母。真可憐，雖然不知道是發生了什麼事使得盒子跑到這孩子手上，但這肯定是個悲劇，這孩子能活下來也算是幸運的了，當時我是這麼想的。決定先把這孩子帶回osu學院安置。我走向那個孩子時，那孩子手中的戒指突然發出一道強光阻擋我，那是peppy的創造之力所發出的光芒。」
「創造之力?難道那就是剛提到黑米想得到的peppy之力?」
「是的，是這個盒子引導我去找到那股光之力的，不幸的是居然是在一場悲劇中找到……不過那確實是被創造之力選上的孩子，是這個世界的希望。那個孩子現在也已經長大了。」
「所以您要我保護那孩子?」我漸漸了解到我在這故事扮演著什麼角色了。
「沒錯!黑米所想得到的是藉由金Q拉所引發的毀滅之力與peppy的創造之力，這樣他就能創造一個在他定的規則下運作的新世界了，這兩者條件缺一不可，你要做的是要防止那孩子落入黑米手中，並阻止他得到金Q拉。不過~」
「不過?」
「那孩子本身還不知道自己擁有這種力量，你必須漸漸帶領他成長茁壯，並在黑米出手的時候適時保護他。你不用給予他過度的保護，因為他是那種能把遇到的人漸漸變成夥伴的那種人，在我的安排下與他既有的特質，一定會有值得信賴又強力的同伴慢慢加入他的。」fish哥示意蘋果帶走包裹。「明天他會來參加畢業的試煉，找個機會把這個包裹交給他，並暗中保護他，因為黑米可能準備找機會對他並出手了，只要你近期不讓黑米得逞，外面的包裝將提供他許多線索，跟隨著這些線索，他遲早會了解這個世界與自己的身世，並在這希望的盒子帶領下，找到拯救這個世界方法。當他解開世界之謎後，這盒子的機關也會跟著打開，我在裡面放了對你們有幫助的東西。」

「另外我也會請yoki、darri這兩位得力助手幫助你們的，他們會適時接近你的，而對抗對抗旅途中強大敵人的工作就敎給你了。」
「我知道了。」我帶著包裹離開了校長室，也了解到我在這環節中佔了多麼重要的地位。

「就是那個!」

「哼哼~這也在預料之中。」黑米也拿出滑鼠擺出戰鬥姿勢。
「你已經逃不掉了!這次我絕對不會再讓你逃走的!束手就擒吧!」我把觸控筆指向他衝了過去…

### Economics -- Firms and production II

Expansion of firms
External expansion (integration) -- combining with another firms, additional inputs may be acquired indirectly from another firm. Example: takeover.
Internal expansiongrow on its own; additional inputs must be acquired from the suppliers of theses inputs directly. Examples: new branch or subsidiary.
Horizontal expansion – the expanded business is engaged in the same production stage of the same product of its original products, including substitutes (related+competing products).
Example: Neway Karaoke Box VS California Red
Advantages: economies of scale (specialisation, discounts), increasing market share/power, reduce competition and reduce duplication of facilities.
Vertical expansion – expand to the different production stage of the same product.
Vertical forward – expand to the business of the later stage of the product.
Example: Frozen meet supplier → Beef restaurant
Vertical backward – expand to the business of the preceding stage of the product.
Example: T-shirt manufacturer → Weaving factory
Advantages: economies of scales (specialisation), secures output (forward) or input (backward) of the product, reduce expenses in transactions like negotiation, contracting, monitoring, packaging and marketing; expand brand name to other products. Note that the risk in losing the whole business is increased.
Lateral expansion -- related but not competing products.
Example: MTR VS KCR
Advantages: economies of scale (lower LRAC by attaining synergy), expand brand name, reducing risk by diversification, more efficient use of resources and attract customers by offering various related products.
Conglomerate expansion – expand to a unrelated products. A conglomerate is a large company composed of different unrelated business.
Example: T-shirt manufacturer → restaurant
Advantages: economies of scale (marketing), reducing risk by diversification, expand brand name, more efficient use of resources and able to invest other more profitable industries.
Market and market structure
Market is the arrangement that enables transactions of a good or services take place. We will only focus the product market here. Note that market may not exist as a matter. It is just an imaginary concept.
Competition forms in scarcity to gain more transactions and hence more profit. Therefore it exists in all markets. Competitions can be further divided as price or non-price competition.
Market structure – describes a typical form of market with specific features and competitive behavior.  It can be divided into perfect or imperfect competition, where the imperfect competition can be further divided into monopolistic, oligopoly or monopoly. # of sellers, ease of entry, and similarity of products and availability of market information will be its indicator.
Perfect competition: large # of small and not associated sellers, free entry, homogeneous (totally identical here) products, and perfect information for both sellers and buyers.
Under perfect competition, all sellers are price takers (must take and sell at market price) since 1)if they rise the price they lose all customers (perfect information); 2)all follow to cut the price if one cuts the price, which led to the profit reduced in the whole industry. Also the profit tends to zero under fierce competition, so there’ll be no competition eventually.
Monopolistic competition: many small and not associated sellers, free entry, heterogeneous products and imperfect information for both buyers and sellers.
Under monopolistic competition, sellers are price searchers since buyers have imperfect information such that the demand isn’t perfectly inelastic. Their price can affect the market price and they will find different price to maximize the profits. They will engage in both price and non-price competition.
Oligopoly: few dominant sellers dominating the market (small sellers can still exist) (main feature), restricted or free entry, homogeneous or heterogeneous products (tends to sell differentiated goods in reality, referring to creating a product’s unique characteristic), imperfect information.
Under oligopoly, sellers are price searchers, interdependent – one dominant seller’s action affect others such as triggering price war, so the price tends to be rigid also since price war led to a great drop of the profit. Also price leadership happens when the main sellers change the price and the small sellers have to follow the suit. Lastly since price rigidity exist, non-price competition is common.
Monopoly: only one (dominant) seller, no entry, homogeneous or heterogeneous products and imperfect information.
Under monopoly, they’re price searchers, engaging in both price or non-price competitions to attract more customers to increase the revenue, and competing with the substitutes too.
The source of monopoly power may come from:
1. Sole ownership of essential resources/techniques required in production – entry is too high or no entry for new sellers
2. Sole ownership of patents or copyrights – having the exclusive rights to produce.
3. Government provision – too strategic for others to supply like national defending system.
4. Natural monopoly – allows no room for another firm to exist (e.g., max. demand fixed)
5. Sole ownership of franchise
6. Integration or collusion – forming cartel and behave collectively like a monopolist.
Profit maximization and output determination
The four main objectives of a firm:
1. Profit (TR-TC) maximization – to satisfy more wants (The major objective)
2. Market share maximization, market share refers to either dollar/unit sales: dollar/unit sales of the firm divided by the dollar/unit sales of the whole industry. Maximising market share gives more market power and enjoy economies of scale, as to earn more profit. Note that highest market share may not make the most money. For example, discount is made to attract customers.
3. Corporate social responsibility (CSR) – responsibility of a firm to all of its stakeholders, who are people who affect or were affected by that firm’s decision and behavior. Obeying laws isn’t enough, but they have to meet the desires and ethical standards of the stakeholders, such as reducing environmental damage and treat their employees fairly.
4. Provide non-profit making good and services to serve the needs of targeted groups.
Methods to determine profit maximizing level:
1. TR—TC approach: recall definition: Profit = TR-TC; TR = PQ; and TC = the cost producing the total amount of output. Profit is maximized when the difference between TR and TC is the largest.
2. MR—MC approach: recall definition: MR of the nth unit = TRn – TRn-1 ; MR = market price for each unit (assume the price for every unit is unique); MC of the nth unit = TCn – TCn-1 , Marginal profit = MR-MC and Total profit of n units = Σ Profits of the ith unit. Note that the profit at zero unit isa negative value which is the TFC (total fixed cost). Now when MR=MC it will be the profit maximizing output level. If the point MR=MC don’t exists, then we say the output level is the level that MR-MC is the closest to zero (positive).
Note that if two output level gives the same TR-TC or MR-MC, we choose the larger output level as to maximize market share as well.
Note that from a marginal cost schedule we can find the profit maximizing output level at each market price. As a result a supply schedule can be deduced. We know that the column of price is equal to the column of MCs while the output column is same as the Qs column.

Recently I found that using MS word → Dreamweaver → blogger is much more effective in bolding sentences (as to avioiding bold two times), and I think the doc. version can be uploaded later (since the supply schedule part may have some problem.)

## Friday, 14 May 2010

### Pilot Ch 2.1

「－－無論如何都不能弄丟。」這是臨走時芷彥留給他的一句話。

「你……是怎、怎麼拿到的？」
「很簡單嘛，剛才你撞到了我，我只是順手拿到這個吧。這個四乘四的扭計骰很漂亮啊！中軸用的是金屬而不是硬膠呢，大概是從外國訂做吧！」
「那，不如借玩兩天吧！」少年說罷便走。
「把我那個扭計體還給我啊啊啊－」子翼立即追上去。
「哈，你是不可能捉到我的～」少年拐進了小街路旁的遊樂場，跟子翼玩起了小孩子的追逐戰。

「嗯，今天就先玩到這裡吧。這個扭計骰就先還給你，我可以保證我沒有看到扭計骰裡面裝了甚麼呢。」說罷，少年就把扭計體拋向子翼。
「你到底是甚麼人？」
「反正你再遲一些也會碰上我，也不用太早知道我的身份吧。可是，我還是要給你一個忠告：你要插手投身裡世界的話，就要做好心理準備，否則你還是快點退出比較好呢。」

「這是純粹的巧合？還是單純的法則？」－－
「他們一定可以幫到我們的－－」

「原來是這樣呢，難怪MSN一直叫你不在……」雪晴若有所思地道。
「這樣啊～彥也要出手了吧？我想＜商會＞也未必會放過她呢。」羽恆忽然拋出了一堆子翼不懂的名詞。
「說得也是呢。子翼，昨天有個男的來陪你玩吧？我想我真的要考慮插手這事情吧，你決定了的話就不能回頭了喔。」
「……就當是玩玩吧。」

## Thursday, 13 May 2010

### Osu! 第16話

wmfchris

「好孩子……」這是我暈倒前聽到的最後一句話。
deepsea

「你們在做什麼？」門外傳來了輕柔的女性嗓音。我回過頭，一股寒氣迎面而來，讓我全身抖了一下。我才發現房間出奇的靜，我只聽到我上下排牙齒交互撞的聲音。這樣的靜，這樣的溫度，讓整個氣氛詭譎的很可怕。我站起身來，邊抖著邊找尋著寒氣和聲音的來源。
媽媽的！
我後退了好幾步，腳在什麼東西上絆了一下。「碰！」頭重重的撞到地面上。本來規律撞擊著的牙齒刺進了嘴巴裡的肉中。媽啊！鬼啊！
朦朧的月光下，一個黑影逐漸的向我靠近，黑影從頭到腳都裹的一片黑，黑衣上面，胸口的位置畫了一個大大的骷髏，骷髏畫的栩栩如生，彷彿想要把我吞噬掉。但是更可怕的是黑影的臉。「如同一張白紙一般」，本來是拿來形容被嚇壞的人，這時拿來形容這個把我嚇到要尿出來的傢伙卻更為貼切。對照著全身的黑，黑影的臉蒼白無比，就像是一張白紙……上面沒畫任何東西的白紙。
黑影的臉上完全沒有五官的輪廓！
「我……我有這麼可怕嗎？」黑影說話了。

廢話！當然有啊！不然我幹麻在這邊翻觔斗？又不是要跟學姐比誰頭比較大！我邊暗暗的咒罵著，邊摸著頭爬起身來，後腦勺腫起了大大的一塊。忽然腿上一癢，我嚇的跳了起來，低頭一看，卻發現學姐坐在地上，用觸手戳著我的腳，臉上露出似笑非笑的神情。
……難道這就是現世報？
算了，這筆帳以後再跟學姐算，我抬起頭來，黑影逐漸的接近，周遭的空氣也越來越冷。我深深的吸了一口氣。
「對不起……」輕柔的聲音帶著一思幽怨。然後是一陣沉默。
我思緒逐漸的平靜了下來，想想她應該也沒什麼惡意，如果她是跟假團長一樣的心思，那她大可直接把我們解決掉，也省的我和學姐在那邊比誰的頭腫比較大。想到這裡，我覺得剛剛的話似乎太過分了。
我把電燈的開關打開，刺眼的光芒讓我流下淚來，我揉揉眼睛看著四周。團長靠在牆上，面無表情的看著前方；學姐張大嘴巴，睜著水汪汪的眼睛望著我們；假團長咬著牙，雙眼直勾勾的望著黑影。
我正要道歉，假團長卻率先打破了沉默。「你來這裡幹什麼？」
「師父要你把他們找來，可沒有要你把他們這樣抓來。」黑影的聲音出奇的冷。「更沒有要你把克溫茵特作成藝術品。」說到這裡，她噗哧一笑。(或是該說傳來了噗哧一聲笑？)聲音隨即恢復冰冷。「如果不是那枚戒指和克溫茵特強大的觸手能力，他們可能早就變成兩具死屍了，你難道不知道嗎？」
「師父只說要找他們，又沒說要怎麼找，也沒說要活的還死的。」假團長一副默不在乎的樣子。「而且我好想吃觸手燒喔。」假團長雙眼直盯著學姐，滴了幾滴口水在地上。我不禁暗暗作嘔。

「啪！」我看到什麼在我眼前晃了一下。「幹！」假團長摀著臉，好像被什麼打中了，黑影卻依然在原地。
「你打我！」
「對啊。還是你比較想被師父打？」黑影冷冷的回應。
「什麼？」
「你出言頂撞師父，還差點搞砸任務。還有……以你的聰明才智，應該不會犯這麼愚蠢的錯誤才是。你恐怕是想背叛師門，獨吞所有東西吧！」
「你……」假團長怒極，站起身來，揮舞著觸手想要攻擊，黑影的動作卻快得多。一道光芒從黑影胸口的骷髏射出，打到了假團長的胸口。偌大的身軀隨即倒了下去。
「闇天使？」
「沒錯……」黑影嘆了口氣。「雖然我們的名字聽起來很美，然而，卻只是個冷冰冰的機器人而已。雖然我們可以思考，可以說話，也有著各種人的個性，卻終究只是機器人而已。」她的聲音十分的哀傷。
「可是你們不是可以隨心所欲的更換器官，還有身體？」我回憶著osu在學園時團長的話，幸好我那天沒有蹺課。「還可以長生不死？」
「你說的對……」她輕輕點頭。「但是你別忘了，機器終究是機器，我們誕生的目的，就只是完成任務而已。除此之外，我們一無是處……」她低著頭望著地板。
沉默。
「你想說什麼嗎？」她顫抖著，彷彿想要說什麼。我選擇先打破沉默，她抬起頭來。
「我……可不可以問你們一個問題？」她猶豫了一陣子，才吞吞吐吐的說。和之前的果斷大不相同。

「我們？」我遲疑了一下，看了團長和學姐一眼，學姐只是張大眼睛看著我(的後腦杓？)，團長輕輕點了點頭。
「說吧。」
「你們願意跟我們合作嗎？」
我一愣，沒想到她會提出這樣的要求。「合作什麼？」
「我不能說。」她搖搖頭。
「那還要我們合作？」我感覺我剛剛對她的一絲同情心正在逐漸消退。「那如果我說不能，你會怎麼做？」
「那你們可以離開。」她的聲音回復了冰冷。「還有，我這裡有你們想要的東西。」答案出乎我的意料，這兩個同門師兄妹還是師姐弟還差真多哪。她的答案卻讓我一時不知道怎麼辦好。
「什麼東西？說來聽聽。」團長看我不知道如何是好，便自己接了下去。
「你們在尋找金Q垃，還有白衣天使的祕密對吧。」
「你怎麼……」我嚇了一跳，黑影卻打斷了我的話。「我這裡有你們需要的資料，如果你們願意跟我們合作的話，那麼這些資料就會全部給你們，我們也會和你們一起合作找到他們。不過你們要答應我的條件。」
「什麼條件？」我有點心動了。
「我不能說。」黑影的回應依然一樣，不過她猶豫了一下，又接了下去。「如果你們不答應也沒關係，我可以給你們其中一份資料，作為我師弟對你們無禮的補償。怎麼樣？」
「嗯……我和團長，學姐個交換了一下眼色。接著三道目光又同時集中在倒在地上的假團長上。」
「不行。」我們異口同聲。「很謝謝你的好意，但是我們不能答應未知的條件。」團長補了一句。
「嗯……我知道了。」黑影冰冷的聲音帶有一絲淡淡的哀愁，雖然她想要盡力的掩飾，我還是不禁替她感到有點難過。不過也是沒辦法的事情。
「那你們要什麼？金Q垃？白衣少女？」
我和團長的目光集中在學姐身上。「要……要我決定呀？」
「只有你有資格決定。」團長點頭。
「我……我不知道要怎麼辦才好呀！」
「看你想怎麼決定呀？不知道怎麼決定的話，就數觸手好了。」我戳了戳學姊的觸手。
「好嘛……金Q垃，白衣少女，金Q垃，白衣少女，金Q垃……」她開始認真的數著觸手，我和團長相對苦笑。
「……金Q垃，白衣少女……啊啊啊！」學姐低下了頭。「怎麼會……應該不會算錯呀……」
「笨蛋克溫茵特，你要金Q垃的那份，直接說不就好了。」黑影渾身顫抖著，像是努力忍著笑。「還有，你忘了算你拿來數觸手的那隻手了啦！哈哈哈哈哈！」說到這裡，黑影，我和團長忍不住哈哈大笑。
「對吼……還有……」學姐一副恍然大悟的表情，我們笑得更厲害了。「還有……怎麼大家都叫我笨蛋啦！」
「因為你是笨蛋。」黑影拿出了一疊文件，塞到了學姐的觸手中。「這裡面是地圖，還有你們要找的，金Q垃化學家的所有資料。」她猶豫了一下，彷彿想說些什麼，卻又搖了搖頭，嘆了口氣。
「後會有期。」她頭也不回的轉身離去。
「再見。對了……」她停下了腳步。「可以問你一個問題嗎？」
「什麼？」
「你叫什麼名字？」
她愣了一下，顯然沒想到我會這樣問。
「波頓安娜˙黑紗」
「嗯……」我不知道要說些什麼，只目送著她漸行漸遠，走向山的更深處，她的身影越來越模糊，身體，輪廓，終於與黑暗合為一體，再也看不見了。
「走吧。我們直接下山。」團長拿出手電筒，從學姐手中接過了文件，唸了出來。
「和傳說中的俠侶一起創造出金Q垃了天才化學家。伊格瑙˙莉絲……」

http://osu.ppy.sh/s/5624
Boten Anna[Normal]

「和傳說中的俠侶一起創造出金Q垃了天才化學家。伊格瑙˙莉絲……她是個變態。」
字到這裡就結束了，剩下的文件都是空白的。媽媽的！

## Tuesday, 11 May 2010

### BAS ver.5 (finalized)

I'm sorry that I forgot to tick the "share to anyone who has the link", and this should be available already.
This version - v5 should be the finalized version, at least I won't add a lot of content into it within a short time.
Comparing with v4.5, a few more inequalities results were mentioned, and harder examples were given.
AM-GM-HM inequality  => Power mean inequality => Maclaurin's Symmetric Mean inequality
Cauchy-Schwarz inequality
Rearrangement inequality
Jensen's inequality

From now on I'll try my best to work on the Phy/Chem/Econ notes...

### Osu! 第15話

wmfchris

「碰」一聲，鎖住我們的木門被觸手搗出了個大洞。「萬歲～」我與學姊擊掌歡呼，卻忘了現在是凌晨三點。

「學姊，我們還在團長家！」我興奮地對學姊說道。

「嘛～老朋友不見那麼久，把小孩都叫出來敘舊不好嗎？」
「你不是我的朋友。」
「哈，隨便你說。反正你兩個失去了其中一個，就成不了事吧！」

http://osu.ppy.sh/b/41442

-失敗路線-

## Friday, 7 May 2010

### Pilot Ch 1.5

「過獎了呢。嗯～這裡也不是對話的好地方，要不要跟我過來？」

「想不到旺角也有這種地方呢。」子翼嘆道。
「是啊，比起街上的喧鬧，我更喜歡這裡的氣氛呢。啊～對了，我還沒正式介紹呢，你叫我芷彥就好了～」
「嗯，那麼關於你找我的事……」
「關於上次委託嗎……真抱歉呢，上次我還沒有等到你來就先跑掉了……還有那個要把你的群組刪掉的事上，那只是我騙你出來的技倆～先說一聲對不起好了。」
「呃……沒關係啦。我跟你原本也不相識，為何是找我而不事其他人呢？」
「嗯，因為你有兩個朋友是大情報商呢。」
「既然你認識她們兩個，為甚麼要找我而不找她們呢？」
「嗯……那我邊走邊解釋好了～」

「那是指黑勢力之類的嗎？」
「也可以這樣說。我們姑且將社會分為表、裡兩層。表面的社會當然就是以政府為代表、律法規管下的社會；裡衽會則可以看成不會出現於表社會，因而不受規限的人。我們所認識的黑勢力，其實是不屬於表、裡社會的人，因此也受到律法的排斥。」

「嗯，裡社會因為不受表社會的律法規限，大部分人也會從事委託、商會之類的工作，他們也會受到裡社會潛藏規則限制呢。」

「啊，怎麼我也沒聽過信和地下有兩層？」
「你沒有聽過才正常呢～歡迎來到阿特拉斯會社呢，子翼。」

「啊，社長回來了呢。」一把男聲響起，「這個就是新找回來的人？」

「……哼。」一臉不爽地走回坐位。

「正如你所看到的，這是一間生意不太好的企業……原本這裡也有不少人的，可是因為一些事情他們都離開了。而這裡接到一星期來第一個委託，就是這個－－」

「這種貨色不是隨便可以在信和找到嗎？為何要執著把它還回去？」
「嘖嘖，你還是沒有了解呢。說不定，裡面也藏了其他東西啊，況且以我們的財政狀況來看也不能不接呢。至於這個骰嘛，我想你兩個朋友能幫上忙呢。」

## Thursday, 6 May 2010

### Basic Algebraic Skills V4.5 publicized~

The file is 561K, which is much smaller than the MS word's product (1.5MB for 22pages, I'll die if I make 86 pages of it)

The isn't "v5.0" since I planned to make the v5 as a temporary end of this set of notes, but I have to publicize this one since a huge amount of new content has been included,

Comparing with v4.0, the following chapters are new:
7.4 A updated list of exercises about finite differences.
7.5 Convergences (A standard pure maths content?)
8.1 System of equation (This is trash. I'll have to amend this later.)
8.2 Roots of unity (Half of pure math syb.)
8.3-8.5 Cubic, quartic equation and discriminants
8.6 Special types of equation (Reference of , maybe need more explaination)
8.7 Application and Riemann's hypothesis -- The most interesting part for me! Linking a problem in integer function with the zeta function, and a brief introduction on the Riemann's hypothesis. However my proof may have some problems. At least we know my f(x) grows same as zeta function.
9.1 Nature of inequality Despite the inequality appeared before, we start from definition.
9.2 Solving inequality, as well as introducing the set notation. Maybe a chance for introducing NZQRC?
9.3 Proving inequality -- staring the olympiad stuffs
9.4 AM-GM-HM inequality
9.5 Cauchy-Schwarz inequality (unfinished)

A new exmaple in old section

P.50 example 6.5.9-11 An extremely hard problem from crazy pure math (AL 1981)

For 9.3 and afterwards I think the difficulty may be harder than problems in HKALE, I will try to find the examples from HKALE, APMO and different MOs. If the examples are too difficult just tell me.
A list of inequality planned to discuss:
1)AM-GM-HM --- and the generalized verion, Power Mean Inequality
2)Cauchy-Schwarz --- and the extended verion (vector and complex numbers)
3)Rearrangement
4)Jensen
5)Holders?...