電腦科學與資訊工程

此研究的目的是要設計出一套完整編輯顯現數學式、加以計算，並求出解的一套方法與成品。而這項工作的執行者，在此稱之Equatetor 。一般的數學式子，若要計算的話，普通的計算機是不足夠的。原因是它們沒有辦法表現出數學式的「原貌」，例如分號、指數、函數、根號等數學符號混在一起時的情況。於是，我便擬定了一個研究，希望設計出一套更方便且實用的方法。換句話說，我要設計出一個功能強大的工程計算機程式。其中，自然牽扯到數學式子的顯現方式（以MathML 實現），以及計算機科學的演算法及資料結構。我主要的目的有四：(1) 顯示數學式(2) 方便編輯數學式(3) 計算數學式(4) 處理可以以不同形式輸出解答的計算（如輸出分數、根號、函數解等）。研究結果中，成功地運用XML 中的MathML 與二分逼近分數等演算法及若干資料結構，達到了以下實用的幾點：(1) 結構化的數學式編輯(2) 完整地顯示數學式(3) 正確運算並輸出運算式的答案(4) 提供一般數學形式之解（非小數之解）;The object of this study is to design a method and processor which is able to edit, display a mathematical expression representing a number, calculate and output the answer. The executor of this task is called Equatetor. Normal calculators are not adequate for this kind of task. The main reason is that they can’t reveal the original expression, such as fractions, radicals, exponents or mathematic functions. Therefore, a simple and convenient method is needed. To perform the possible way of handling those tasks, a computer program has been written. Several techniques were used, such as MathML, computing algorithms, data structures, and so on. Following are main purposes: (1) Displaying mathematical expressions. (2) Editing mathematical expressions simply. (3) Calculating mathematical expressions. (4) Outputting the answers(in different expressions). And the achievements:(1) Structured methods of editing of mathematical expressions. (2) Displaying mathematical expressions completely. (3) Calculating mathematical expressions precisely. (4) Offering answers in different expressions.

台灣通史「婆娑之洋，美麗之島」，身為台灣人，應知台灣事，本研究本維 基百科（Wikipedia）所揭示的「海納百川，有容乃大」精神，以Apache 網頁伺 服器為平台，MySQL 為資料庫，利用AJAX、PHP 網頁技術，並使用Google Maps 提供之服務，建立符合Web 2.0 精神的的b04地理資訊共享系統。在此系統下， 我們允許教師(編輯者)以合作方式上網提供與課程相關的地理資訊，並可進行資 訊修改或刪除，希望集合所有教師之力，提供給學生最豐富、最正確的b04地理 資訊系統。 In this paper, we propose a new map-based collaboration environment “MyGIS” for geographical information distribution. In MyGIS, the publishers/teachers can easily collaborate to annotate a spot with contents such as messages and links. The annotations of a spot are updated on the map in real-time which enables the receivers/students to correctly study at anywhere and anytime. To ensure the trustfulness of the content, the publishers are authenticated using login mechanism. In this study, several technologies inc lu ding Apache, PHP, MySQL, Ajax are involved. Finally, We implemented MyGIS on Google Maps and evaluated its feasibility and usefulness.

This study investigates the possibility that “Digital Buses” would actually be used in real life. In addition to the basic mathematics knowledge that I have acquired over the years, I have used “Microsoft Visual Basic” and “LEGO ROBOLAB SOFTWARE” to implement the idea as a program. It simulates the way in which a digital bus travels in a city with a rectangular grid. Various plans are tested to find the best paths for providing the most efficient, convenient and speedy transportation. This study has not only shown that “Digital Buses” are sure to be used in a modern city when wireless communication networks has developed to a certain point, but also supplied a framework for future researchers who may wish to study the optimal way in which more than one digital buses could efficiently run in cities according to their population distributions and road arguments, in order to overcome the traffic problems from the current bus systems. 本研究探討數位公車在人類未來生活中實際運行的可行性。本人以所學的數學知識進行公車路徑規劃，並透過「樂高機器人控制系統」以及Microsoft Visual Basic 軟體程式之撰寫，在棋盤式城市區域中模擬公車行駛情境，靈活搭配各種方案找出最佳路徑，達到便利快捷的高運輸效能。本研究顯示當現代化都市無線通訊網路發達到一定的程度時，數位公車的發展是可以預期的。本研究之結果可提供後續研究者繼續探討多台數位公車在實際都市中依人口分佈、道路狀況來規劃最佳行駛路徑，以解決現今機械公車無法克服之繁雜交通困境。

在這篇報告中，我們探索了「將錯就錯的Knuth 河內塔問題」。傳統河內塔問題在電腦科學上佔有重要的地位，是一個極具內涵的模型。由於這個模型的深厚數學內涵，使其和巴斯卡三角形建立了緊密的連結，且利用這個緊密的數學連結，設計出復原任意起始狀態的良好演算法。Knuth 河內塔起因於數學家Knuth 在論文[3]中，描述傳統的河內塔問題時所發生的一次筆誤。在這個新的規則之下，我們意外發現Knuth 河內塔存在著一個和傳統河內塔平行的模型，此模型在電腦科學及數學上有著完全不同於傳統河內塔的內涵。我們的研究主要如下：(分別為內文中的四大段)(一) 結構分析。移動環所需要的次數，如何移動環並分析每一次動作所動的環，及每個環何時被動到並給出演算法。(二) 正整數的分割。所有的移動步驟將正整數做了一個新的分割(Partition)；此分割模k之後有良好的循環性質。(三) 費波那契真分數的排序。這個正整數的分割形成一張表，這張表恰好就是分子分母皆為費波那契真分數之排序。(四) 隨意亂排的Knuth 河內塔復原演算法。在Knuth 河內塔的規定下將起始狀態改變，找出良好的復原演算法，並分析。 In this project we study the "Knuth Hanoi Tower", which is motivated by a typo in a paper of Knuth. This inadvertently typo leads to a new rule of moving the discs on the Hanoi Tower (see introduction below for definition). Although seemingly similar to the traditional Hanoi-Tower problem, it turns out that under this rule the "Knuth Hanoi Tower" problem consists of amazing properties, and is totally different from the traditional one. Our study focuses on the following directions: (1) Structure analyzing: We analysis the sequences recording the disc moving and offer enumeration results and recurrsive/non-recurrsive algorithms. (2) Partition of N: The moving sequence forms a partition (a table) of N, which has an amazing congruence property. (3) The order of Fibonacci proper fraction: The row/column of the partition table is, even more amazing, exactly the order when sorting the Fibonacci proper fraction with fixed denominator/numerator. (4) The Restoration of an arbitrary initial state: We offer an efficient algorithm for restoring any initial state of discs. We hope that our study on the "Knuth Hanoi Tower" offers a simple, neat, and new example on the theory of Algorithm, Number theory and Combinatorics.

對數位、光電的初步了解是在小三的科展，當時我是利用一個大型的凸透\r 聚光鏡，匯聚太陽光照射在不同的金屬導線之一端，而另一端接在冰冷的地\r 板上，用不同的金屬材料來做比較。利用微電流計測得不同的材料有不同大\r 小的電流，而且有不同的熱量。到國中的電學時了解到電阻熱功率的關係，\r P=IV 才知道，除非有『超傳導系統』否則任何物體必有電阻。進入國中時，\r 在電工課程中了解了數位的控制，產生了這方面的興趣。\r

The larceny is always annoys our family and our society. They usually steal on the day when people working in the office or studding in the school. They always wait for people leave the house, and try the bell until them confirm the owner of the house leaved and nobody at home. Then they will open the door or break the lock of door. So we can find that if any body home or the lock is very hoard to open or to break. Then the thief is always choice to give up. That prove if we con let the thief think the house is some body home. Then it can to avoid larceny. This project is about how to design a system which is used AI technology to be a robot that is like a human. That robot can talk to the thief and can be a special lock when the thieves try to break the lock of door. The goal of this project is to design a robot that will be a door angel. It will let thief thinks that is some people always in the house. So they can not to steal in this house. We use the AI speech recognition & house environment control I/O system to be a robot which is setup in the door. It is like an angel to protect our home and family. And can stop the larceny. 「住宅竊盜犯罪」一直持續困擾著人類社會，住宅竊案最常發生於大白天，小偷常趁著家中成員上班、上學等時機，稍加觀察，再加以測試（按門鈴） ，確定家中無人，下手破壞鎖具侵入搜括；小偷只要遇到非常難開的鎖或認為有人在家就不會進一步的行竊。所以這證明只要讓小偷認為家裡有人，就能防止竊案的發生，而我們的研究目的就是如何在小偷還在徘徊尋找目標時，就要讓他感到這一家不能偷，如何讓他感覺家裡有人，進而打消入侵行竊的意念。我們希望能設計一套系統，利用AI人工智慧語音辨識及家庭環境控制，來建立一個充滿智慧的門神機器人，來事先嚇阻小偷的行動，就像門神一樣，可以預防竊案的發生，並整合大門門鎖內鎖與家電，形成智慧型的門神機器人，來保佑我們的家庭，也讓竊盜率降低，作為竊盜犯罪防治的利器。

In the fast-paced environment of a hospital intensive care unit (ICU), good doctor-patient communication is essential. However, medical conditions and devices often inhibit a patient’s ability to speak, write or type. Current assistive communication devices are either prohibitively expensive or cumbersome and time-consuming, creating a gap in communication during a patient’s first days in the ICU. This project applies computer vision to develop a low-cost software solution that bridges this gap by enabling patients to generate words with eye movements. In the system, a webcam acquires an image of the patient, and an image processing algorithm classifies patient’s gaze as pointing in one of eight directions. Each direction corresponds to an option on a graphical menu presented to the patient on the computer’s display. The patient can use the menu to select a preformed phrase from a list of common phrases. Patients desiring to express more complex ideas can type custom words using the menu as an ambiguous keyboard (similar to a phone keypad). In either case, the patient-generated text will be displayed on screen and read aloud through the computer’s audio system. The only hardware requirements are an existing computer and a $6 webcam. The program can process and respond to an image in 148ms. A new user can be trained in approximately 10 minutes, and after training can type a simple phrase such as “hello world” in 40 seconds. While further testing and improvement is required before the system will be ready for implementation, the project shows promise as a low-cost solution to ICU communication.

Video compression is indispensable to web streaming and memory storage.Most video\r compression technology has difficulty to achieve high quality video at lower bit\r rates.Apparently,limited transmission bandwidth and network resources often degrade\r video signals.Thus the goal of my research was to enhance video degrade video\r signals.Thus the goal of my research was to enhance video compression performance and\r to improve visual quality.It is hypothesized that the reduction in neighboring pixels\r coding,and humans perceptual mechanisms(psychovisual)redundancy could produce a\r low-complexity geometry streams for animated visual objects.A set of algorithms is\r developed to parse bidirectional interpolation pixels into their characteristic cells,which\r vary in spectral energy and wavelength.The bits contained in these cells are vectorized and\r transformed recursively to identify lower correlations among vector arrarys for blocks\r filtering.DCT function calculates energy ratios between high spatial frequency and low\r spatial frequency,to devote most of the highest spatial frequency bits with the calculated\r energy ratios.A variable quantization method is used to measure the sensitivity of colors\r and its intensity ratios to restore any missing high spatial frequency pixels.presnted in\r mathematical intrinsic.This approach leads to the ability to compress video data that\r normally require a large amount of memory to store and high bandwidth to\r transmit,Results form the enhanced video compression experiment have attained\r 0.1bpp(256kbps,25fps)without noticeable effects comparable to the video compression\r technique that achieved 0.5bpp(1.5Mbps,25fps)in use today.

Now Artificial Neural Networks using on the basic math is fewer. This paper is to suggest the Linear equation of the basic math using the BP Artificial Neural Networks. The BP Neural Networks have power ability for learning and can approximate any function, and regularity can be found to solve the linear equation. A good sample is one of the important elements for learning of Artificial Neural Networks. Generally, the samples are a lot of amount for the resolution of Linear equation. This paper is to use the principle of two points decide one line for the samples. The experiment shows that this method curtails many samples. Furthermore we also use Artificial Neural Networks to solve the problem of point-slope form. The experiment result is very satisfactory, and it offers some idea for the basic math using Artificial Neural Networks.目前人工神經網路較少用於基礎數學方面的求解，本文針對基礎數學直線方程式提出BP 人工神經網路應用於求解直線方程式，運用其很強的學習能力、(輸入向量和其對應的目標向量來訓練網路、逼近函數)，尋求規律來求解直線方程式；而良好的樣本是人工神經網路學習的重要條件之一，一般解決直線方程式需要大量樣本，本文利用二點決定一直線的原理來解決樣本問題，實驗結果顯示，這一方法成功的縮短了可觀的學習樣本，此外我們也運用BP 人工神經網路來求解點斜式的直線方程式問題，實驗結果是可行的，並且為人工神經網路用於基礎數學提供了一些思考方向。