Monday 31 May 2010

馬肉版孔乙己 (Osu!專用)

Author: Kawashiro Nitori , COPYRIGHT RESERVED

中頻的代充店的格局,是和別處不同的:都是當街一個曲尺形的大櫃台,櫃裡面預備著電鈴,可以隨時叫人代充。MP的人,傍午傍晚散了伙,每每花四文銅錢,買一個月的會員,——這是二十多年前的事,現在每月要漲到四兩銀子,——靠櫃外站著,慢慢的玩Easy圖休息;倘肯多花一兩,便可以買幾個圖,或者幾款皮膚,做附贈物了,如果出到幾十兩,那就能買一個圖包,但這些顧客,多是沙包幫,大抵沒有這樣闊綽。只有BAT,才踱進店面隔壁的房子裡,要會員要圖包,慢慢的玩。

我從十二歲起,便在頻道口的鴨鴨代充店當伙計,鴨鴨說,我樣子太傻,怕侍候不了BAT主顧,就在外面做點事罷。外面的沙包主顧,雖然容易說話,但嘮嘮叨叨纏夾不清的也很不少。他們往往要親眼看著會員從數據庫裡運出,看過會員期限少天數沒有,又親看將會員轉到自己號裡,然後放心:在這嚴重監督下,少天數也很為難。所以過了幾天,鴨鴨又說我干不了這事。幸虧迪西的情面大,辭退不得,便改為專管會員期限的一種無聊職務了。
我從此便整天的站在櫃台裡,專管我的職務。雖然沒有什麼失職,但總覺得有些單調,有些無聊。鴨鴨是一副凶臉孔,主顧也沒有好聲氣,教人活潑不得;只有馬肉到中頻,才可以笑幾聲,所以至今還記得。
馬肉是站著喝酒而是BAT的唯一的人。他身材很高大;青白臉色,皺紋間時常夾些傷痕;一部亂蓬蓬的花白的胡子。穿的雖然是BAT制服,可是又髒又破,似乎十多年沒有補,也沒有洗。他對人說話,總是滿口之乎者也,叫人半懂不懂的。因為他姓馬,別人便從用戶檔案上的這半懂不懂的名字裡,替他取下一個綽號,叫作馬肉。馬肉一到中頻,所有聊天的人便都看著他笑,有的叫道,“馬肉,你臉上又添上新傷疤了!”他不回答,對櫃裡說,“充兩個月會員,要一個東方圖。”便排出九兩白銀。他們又故意的高聲嚷道,“你一定又戳了人家的泡了!”馬肉睜大眼睛說,“你怎麼這樣憑空污人清白……”“什麼清白?我前天親眼見你kill了格拉迪,被中頻的人齊罵SB。”馬肉便漲紅了臉,額上的青筋條條綻出,爭辯道,“懲罰不能算kill……懲罰!……BAT的事,能算kill麼?”接連便是難懂的話,什麼“BAT固窮”,什麼“者乎”之類,引得眾人都哄笑起來:中頻內外充滿了快活的空氣。
聽人家背地裡談論,馬肉原來也做過圖,但終於沒有十星,又不會代充;於是愈過愈窮,弄到將要討飯了。幸而吹得一手好泡,便幫給了錢的人家吹泡,換一碗飯吃。可惜他又有一樣壞脾氣,便是好吃懶做。mod不到幾天,便連人和電腦硬盤OSU,一齊失蹤。如是幾次,叫他mod的人也沒有了。馬肉沒有法,便免不了偶然做些戳泡的事。但他在我們代充店裡,品行卻比別人都好,就是從不拖欠;雖然間或沒有現錢,暫時記在粉板上,但不出一月,定然還清,從粉板上拭去了馬肉的名字。馬肉玩了半個圖,漲紅的臉色漸漸復了原,旁人便又問道,“馬肉,你當真會mod圖麼?”馬肉看著問他的人,顯出不屑置辯的神氣。他們便接著說道,“你怎的連半個十星也撈不到呢?”馬肉立刻顯出頹唐不安模樣,臉上籠上了一層灰色,嘴裡說些話;這回可是全是之乎者也之類,一些不懂了。在這時候,眾人也都哄笑起來:中頻內外充滿了快活的空氣。
在這些時候,我可以附和著笑,鴨鴨是決不責備的。而且鴨鴨見了馬肉,也每每這樣問他,引人發笑。馬肉自己知道不能和他們談天,便只好向孩子說話。有一回對我說道,“河童你mod過圖麼?”我略略點一點頭。他說,“mod過,……我便考你一考。BPM,怎樣測的?”我想,討飯一樣的人,也配考我麼?便回過臉去,不再理會。馬肉等了許久,很懇切的說道,“不能測罷?……我教給你,記著!這些常識應該記著。將來做BAT的時候,rank要用。”我暗想我和BAT的等級還很遠呢,而且我們掌櫃也從不mod圖;又好笑,又不耐煩,懶懶的答他道,“誰要你教,不是一分鐘的節拍數麼?”馬肉顯出極高興的樣子,將兩個指頭的長指甲敲著櫃台,點頭說,“對呀對呀!……BPM有四樣測法,你知道麼?”我愈不耐煩了,努著嘴走遠。馬肉剛用指甲蘸了酒,想在櫃上寫字,見我毫不熱心,便又嘆一口氣,顯出極惋惜的樣子。
有幾回,鄰居孩子聽得笑聲,也趕熱鬧,圍住了馬肉。他便給他們一人一個圖。孩子玩完圖,仍然不散,眼睛都望著Songs文件夾。馬肉著了慌,伸開五指將文件夾罩住,彎腰下去說道,“不多了,我已經不多了。”直起身又看一看圖,自己搖頭說,“不多不多!多乎哉?不多也。”於是這一群孩子都在笑聲裡走散了。
馬肉是這樣的使人快活,可是沒有他,別人也便這麼過。
有一天,大約是中秋前的兩三天,鴨鴨正在慢慢的結賬,取下粉板,忽然說,“馬肉長久沒有來了。還欠十九兩銀子呢!”我才也覺得他的確長久沒有來了。一個SOLO的人說道,“他怎麼會來?……他觸折了腿了。”掌櫃說,“哦!”“他總仍舊是戳。這一回,是自己發昏,竟戳到B姥爺家裡去了。他家的泡,戳的得嗎?”“後來怎麼樣?”“怎麼樣?先寫服辯,後來是觸,觸了大半夜,再觸折了腿。”“後來呢?”“後來觸折了腿了。”“觸折了怎樣呢?”“怎樣?……誰曉得?許是刪游戲了。”鴨鴨也不再問,仍然慢慢的算他的賬。
中秋之後,秋風是一天涼比一天,看看將近初冬;我整天的靠著火,也須穿上棉襖了。一天的下半天,沒有一個顧客,我正合了眼坐著。忽然間聽得一個聲音,“充一個月會員。”這聲音雖然極低,卻很耳熟。看時又全沒有人。站起來向外一望,那馬肉便在櫃台下對了門檻坐著。他臉上黑而且瘦,已經不成樣子;穿一件破夾襖,盤著兩腿,下面墊一個蒲包,用草繩在肩上掛住;見了我,又說道,“充一個月會員。”鴨鴨也伸出頭去,一面說,“馬肉麼?你還欠十九兩銀子呢!”馬肉很頹唐的仰面答道,“這……下回還清罷。這一回是現錢,會員要好。”鴨鴨仍然同平常一樣,笑著對他說,“馬肉,你又戳了泡了!”但他這回卻不十分分辯,單說了一句“不要取笑!”“取笑?要是不戳,怎麼會觸斷腿?”馬肉低聲說道,“跌斷,跌,跌……”他的眼色,很像懇求鴨鴨,不要再提。此時已經聚集了幾個人,便和鴨鴨都笑了。我轉了會員,把號拿出去,密碼紙放在門檻上。他從破衣袋裡摸出四兩銀子,放在我手裡,見他滿手是泥,原來他便用這手走來的。不一會,他玩完圖,便又在旁人的說笑聲中,坐著用這手慢慢走去了。
自此以後,又長久沒有看見馬肉。到了年關,鴨鴨取下粉板說,“馬肉還欠十九兩銀子呢!”到第二年的端午,又說“馬肉還欠十九兩銀子呢!”到中秋可是沒有說,再到年關也沒有看見他。
我到現在終於沒有見——大約馬肉的確刪游戲了。

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

For the quesiton please refer to this link.
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.
ii)Near to junction road
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

我們花了快要半個小時才大略瀏覽完這些資料,並且知道了天才化學家隱居的地點。心裡也生出了不少疑惑。\
  不過,這些問題或許可以從天才化學家那邊得到解答吧?
 
haruhiteamsos
 

我與yoki、darri三人正在屋頂間跳來跳去,追逐在車站搶回[黑米理論]的黑米。
「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。
只見他邊發抖邊指向天花板「在…在上面,你們到底是誰?」我抬頭一看發現天花板被打出一個個大洞,直通屋頂。雖然這條路可能是個幌子,但因為別無選擇只好順著這條通往頂樓的路跳了上去。
我跳上屋頂後擺出一個半跪坐的姿勢落地,抬頭往前一看沒想到黑米真的在頂樓,不過身旁居然還站有兩個人,恩...yoki跟darri還沒上來。
「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!」
黑米一喊完這句,右邊的男性立刻拔出鍵盤與滑鼠、左邊的女性伸出雙手喊出Edit。
恩?具有極強節奏能共鳴能力的Beater與Mapper!?我加強警戒,左手變出了一塊板子,上面的螢幕瞄準了這三人,另一隻手拿著一支細長的觸控筆,擺出準備指揮般美妙的的戰鬥姿勢。
雙方進入了對峙
對方知道我不好對付,不敢輕易露出破綻,而黑米也決定先不動深色。
我或許能用力量壓過對方,但我一有動作的話,黑米也有可能會趁機逃走。
沒有人敢出手之際,我決定先靜觀其變,等yoko跟darri趕到,我才能放心出手。
這時我回想起前幾天從osu學院開始發生的事,以及我任務背後的意義有多麼重大...
「請進。」
打開校長室的門,眼前看到的首先是一個巨大的辦公桌,不過比起巨大的辦公桌,在辦公桌後面傳來的存在感卻更為巨大,一如往常穿著寫了一個”魚”大字的黑襯衫,fish哥背對著門口眺望窗外的風景,手上把玩著一個包裹。
「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。」
我聽的越來越疑惑了,不過fish哥又繼續講了下去。
「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。」
我吞了口口水,然後繼續聽。
「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。」
我接過包裹,轉過身來準備開始任務。
「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。
到了隔天,我尾隨那位繼承創造之力的考生進入森林,一直到看到他打倒了果果妖,得到了金蘋果。
「就是那個!」
我找到了滲透他的機會,便故意把包裹放在他回程的路上,自己寄宿到金蘋果之中,等到黑米正式對他動手時,我就能適時出來幫助他。
後來黑米果真動手了,我現身打倒黑米並保護了一行人,並取得[黑米理論]後也稍微放心了,根據裡面重要的研究內容,黑米一定急著想把這本書要回去,只要我帶在身上,黑米應該會先把目標放在我這,我應該可以放心來到花山(反正往機城那隊跟著依fish哥的提示而找到的那位女僕,應該可以幸賴,而且團長也住在那城市)
接著只要等待黑米出現再把他逮住就沒問題了,只是沒想到他趁人群中偷走[黑米理論],可惡!因為我的疏忽而錯失了良機...
回想到這裡......這次絕對不能再失手!
雙方對峙了幾分鐘,依然找不到機會出手,我也只好拖延時間,先等yoki跟darri趕來幫忙。不久後yoki跟darri終於從大樓邊緣跳了上來,三人的三角陣勢包圍了他們三人,好了,可以出手了!
「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…

關卡名稱: Kachoufuusetsu[hard]
關卡連結: http://osu.ppy.sh/b/26056

失敗路線
三對三的戰鬥中--
黑衣男子阻擋了我對黑米的攻擊,不過他也漸漸被我逼到退路,在最後一擊的時候我把他抓起來甩出去讓他飛出大樓外,不料丟出去卻不小心砸中在旁邊戰鬥的yoki,害yoki掉了下去。而yoki掉下去使得哥哥darri一分心,也被黑米的結界束搏住,完了!我搞砸了…現在變成男子跟女子牽制我的局面,而黑米也從容地逃走了…留下來的只剩迴響在黃昏中的笑聲…

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

子習正在回家的路上。
那個「扭計骰」已經被慎重地放進了他的口袋中,那是芷彥交託他的委託。
「--無論如何都不能弄丟。」這是臨走時芷彥留給他的一句話。
這個「扭計骰」真的有甚麼重要的東西存在裡面嗎?不能弄丟是有不能拒絕的理由,還是這世界單純的法則?
另一方面,這麼大的空間中只是待著兩個人,會不會有點太奇怪了?如果是陷阱的話又何必大費周章呢?
忽然,他有一種不祥的預感。
在這條狹街的小街上,行人就只有他和眼前的少年罷了。這個眼前的少年身穿一套普通的車路士球衣,而且正在意味深長的對他笑著。雖然他這樣子看下去一點也不危險,甚至有點帥的感覺,可是子翼就認定了這少年就是衝他而來的。
然而,他還是作了個最自然的選擇:若無其事地走過去。可是小街還是太窄了,子翼走過時還是撞到了那少年的肩頭。
這時,背後傅來了少年的聲音:「先生,你掉了東西呢。」
子翼猛地回過頭來,發現那少年竟然拿著那「扭計骰」把玩!
「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!」
「啊……這個扭計骰底下的確寫著Made in germany。」
「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。
十五分鐘後,這場追逐還沒有分出勝負,子翼已經有點喘氣了,少年卻沒有露出任何疲態。
少年躍上了滑梯,使子翼無法追下去。
「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。」

學校。
子翼無法理解這接踵而來的怪事,從不不明少女芷彥到昨晚的挑戰,似乎都堅緊地關連著。子翼更想不到任何合理的理由去解釋以上的事情。
「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--」
子翼靈機一動,「他們」所指的當然不是他自己,而是雪晴和羽恆!
子翼立即把那扭計骹拿給兩人看,同時說出這兩晚的事情。
「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。」
羽恆和雪晴聽到後互望了一眼,靈出了惡魔般的笑容--

Thursday 13 May 2010

Osu! 第16話

wmfchris
我隱約看到學姊從背後偷襲得手,偽圃長觸手一鬆,我好像又清醞了一點;我把用盡吃奶的力氣抱住偽團長的腳,他只顧著跟團長和學姊,卻忘記了我。他被我絆倒了。
碩大的身軀壓在我身上當然不好受,但是至少我還能見到學姊,不至於被拐走。
「好孩子……」這是我暈倒前聽到的最後一句話。
deepsea
我睜開眼睛,剛剛撞到地板上的腦袋仍然隱隱作痛。我掙扎著坐起身來,揉一揉眼睛環顧四周。團長,假團長和學姐都癱在地上,學姐的幾隻觸手和假團長的觸手纏繞在一起拉扯著。團長的衣服被扯破了,假團長鼻子流著血,學姐看起來沒受什麼外傷,觸手族的戰鬥力果然驚人。只是……我怎麼覺得她額頭越腫越大了?
  「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]

失敗
「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)

Click here to access the notes

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

靠著學姊強大的觸手,要把門弄開並不是難事。
「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。
原來我們被困在一間雜物室,在房的一側是疊得整整齊齊的木箱。還好學姊沒有走過去,否則那後果真的不堪設想……除了那些木箱外,這間房的另一側放著皮鞭、手銬……還有蠟燭!媽的,偽團長是個變態!
學姊瞪著我,說:「你快看外面啦!要不然看我用這些好好教訓你?」同時也用觸手重重地敲了我一記。
一絲絲月光從洞外面透進來,我趕緊跑到木門那觀察著房內和外面的一切。
是團長家!我心裡的大石已經落下了一半,至少我們沒被拐到荒山野嶺。
「學姊,我們還在團長家!」我興奮地對學姊說道。
學姊卻對此不感興趣,說:「你肯定這裡是團長家?還是擺設差不多而已?」
我不得不沉思起來。再看看外面的擺設,的確跟團長家一模一樣。
這時,手指上的金SS戒指發出了微弱的光芒,我感到手上一陣溫暖,同時,也突然意識到,房間裡好冷……
我看看我手上的金SS戒指,它發出了微弱的光芒,我卻不感覺到寒冷的氣息。我放膽地把手伸出去,一股氣流衝過來,我想把手縮進去時已經太遲了。一隻同樣冰的觸手把我捲住,連人帶門的被拽了出去,我發現,我的手已經不聽我使喚了。
我隱約聽到那個偽團長的笑聲:「唉呀,團長你還是遲了一步呢。這孩子我就要帶走囉!」
身後是團長的怒吼:「你快把他給放了!」
「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!」
學姊從房中跑出來,對偽團長冷笑道:「你能不能離開這裡,還是未知之數呢。」說罷便與團長組成了夾攻之勢,同時把大門堵住。至於我,已經被那幾條觸手凍到不能動彈,頭腦暈呼呼的,金SS戒指也沒有發出光芒。到底我甚麼能幫忙,還是只是他們的負累,我不知道……

關卡: Megpoid Gumi - Final Letter [Normal]
http://osu.ppy.sh/b/41442

-失敗路線-
團長和學姊忌憚偽團長的冰觸手而有所避忌,倒是偽團長越戰越勇,殺敗兩人帶著快結冰的我大笑著滿意地離開了。也許,我再也見不到團長、學姊,還有蘋果,fish哥……對不起了……

Friday 7 May 2010

Pilot Ch 1.5

子翼先是呆了一呆,然後問:「你、你就是疹嗎?」
少女露出陽光般的微笑應道:「嗯啊~你能找到這裡也不簡單呢。」
子翼不好意思地說:「我只是剛好進來逛一下,無意中看到你啊。還有你打太鼓真的好厲害啊,我在youtube也沒有看過你這種神級表演~」
「過獎了呢。嗯~這裡也不是對話的好地方,要不要跟我過來?」
子翼幾乎沒有思考過就已經回應一句「好啊」跟了上去--

旺角某大廈,樓上咖啡室
這間咖啡室的毗鄰是一間日漸衰落的二手書店,為了維持生意,書店便跟咖啡室合作,令顧客有了舒適閱讀的地方,生意也總算維持穩定。而這間咖啡室裝修已經老化,頭頂轉的吊扇已經變得派得,也不知道會不會掉下來,但是整個咖啡室都飄逸著濃郁的咖啡豆香氣,老舊的氣氛成恰好配合了這個環境,因此咖啡室即使身處樓上也經常滿座。
「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~」

信和中心。

子翼奇怪地問:「為甚麼又會回來信和?」
芷彥走到通往地庫的電梯道:「看來她們都沒有告訴你呢。其實,我們身處的社會沒有那麼簡單呢。」
「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。」
子翼幾乎搞不清那突然冒出來的一大串名詞:「照你的說法,裡社會也不是那麼壞囉?」
「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。」
說到這裡,芷彥推開了地庫某道防火門,走過一道窄窄的走廊,走廊的盡頭是一部向下的電梯!
「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。」

電梯門緩緩敞開,映入眼簾的是一間標準的大型辦公室,空調設施也一應俱全。
「啊,社長回來了呢。」一把男聲響起,「這個就是新找回來的人?」
只見工作間一隅有一個比子翼大一點的青年,他有點不屑地說:「彥,我覺得你從裡世界的市場找人不就好了嘛,從外面找人,也不能保證會有用呢。」
芷彥有點不悅地應道:「哥,我做的事我很清楚,他們一定可以幫到我們的!」
「……哼。」一臉不爽地走回坐位。
芷彥轉過頭來跟子翼說:「啊,先不要理他,過來坐吧~」
「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--」
她從抽屜中拿出一個扭計骰,繼續說:「……要把這東西歸還給它的主人。」
「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~

Click here to ascess the note

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?...