格子點的可見性研究
本文的主要結果有兩部分，第一部分，對於固定的𝑏 ∈ 𝑁以原點 O為觀測點，𝑓(𝑥) = 𝑎𝑥𝑏, 𝑎 ∈ 𝑄為觀測視線，觀測目標為格子點陣列𝑉(𝑚) = {(𝑖, 𝑗)|𝑖, 𝑗 ∈ 𝑁, 1 ≤ 𝑖 ≤ 𝑚, 1 ≤ 𝑗 ≤ 𝑚 }，研究其中可見點的數量與機率。我們發現可見點的數量與歐拉函數及默比烏斯函數有關，可見點的機率也與黎曼𝑧𝑒𝑡𝑎函數具有關聯性。第二部分，對於固定的𝑏 ∈ 𝑁，我們在 𝑥軸與𝑦 軸上布置觀測點，以布置的觀測點為新原點，𝑓(𝑥) = 𝑎𝑥𝑏, 𝑎 ∈ 𝑄為觀測視線，研究將目標點集𝑉(𝑚 × 𝑛) = {(𝑖, 𝑗)|𝑖, 𝑗 ∈ 𝑁, 1 ≤ 𝑖 ≤ 𝑚}完整觀測的布點方法與數量。得到重要成果如下，設正整數𝑚 ≥ 6且𝑇 ⊂ {1, … , 𝑚 + 1}為一個 𝐹(𝑚) −覆蓋，𝑟為大於𝑚的最小質數，對於目標點集𝑉(𝑚 × 𝑛)，建構觀測點集 𝑆2 = {(0, 0), (0, 𝑟)}∪{(𝑡, 0) | 𝑡 ∈ 𝑇}，則 𝑉(𝑚 × 𝑛)為𝑆2 −可見。並進一步研究將目標點集改為𝑉(𝑛 × 𝑚) = {(𝑖, 𝑗)|𝑖, 𝑗 ∈ 𝑁, 1 ≤ 𝑗 ≤ 𝑚}，發現其所需要的觀測點數可顯著減少。
Breaking a Caesar Cipher / Vigenère Cipher Encryption for Secure Data Communication
This project had one purpose: creating almost unbreakable encryption by breaking a Caesar – and Vigenère Cipher and getting familiar with how they work. Created a program to encrypt and decrypt messages with a Caesar Cipher and Vigenère Cipher encryption. Breaking these encryptions in these programs will help to identify the factors that contribute to strong and weak encryption systems. A program was created to encrypt messages using Caesar Cipher with a key from 1 to 25 and decrypt messages without knowing the original key by doing different types of “attacks” on the system: a brute force and frequency analysis attack. Created another program to encrypt messages using Vigenère Cipher with a keyword or keyphrase and decrypted messages whilst knowing that original keyword. Tested and compared the two different cyphers when being attacked. This helped identify factors that influenced the strength of encryption and identified the advantages and disadvantages of each Cipher as well as the weaknesses in each attack. Through testing and breaking a Caesar and Vigenère Cipher successfully, multiple factors were identified that influenced the strength of the encryption system. These were used to ensure the new encryption created will be as strong as can be. Comparing the success rate of the different attacks on each Cipher, the similarities, weaknesses and strengths in the Brute Force and Frequency Analysis attacks were found.
HandExo
Stroke is a very common disease, almost a national disease. In terms of stroke frequency, 匈牙利 ranks second in the world. Every year, 40-50 thousand people become paralyzed or permanently injured as a result of cerebrovascular disorders. This number is three to four times higher than in developed countries. Almost every Hungarian family is affected! Of course, saving the life of someone who has a stroke is the most important thing, but rehabilitation is also very important, since only with the help of a physiotherapist will the patient be able to live a full life.
King's Power - The Utilization of Agricultural Waste in the Production of Sustainable Dry Cells
The idea of dramatically reducing the cost of the production dry cell, reducing its carbon footprint, and being able to be an alternative to current materials such as biochars really propels the interest of performing this project research. Biochars from durian husk, bamboo and coconut shell are promising alternative chemical materials of the anodes in the dry cell due to their eco-friendly traits and availability in the trophic areas which covers about 40% of the land on earth. Using the technique of pyrolysis, the latest and the best technique to produce a high carbon content biochars, the dry cell uses the potassium hydroxide as the electrolyte and manganese dioxide as the catalysts that make the biochar mixture to produce maximum voltage of 65% from the dry cell sold in the current market. The voltage analysis of the biochar dry cell was done in our school science laboratory and then, characterization tests analysis was carried out on the products from the specific biomass namely the SEM/EDX analysis, at the Material Characterization Laboratory (MCL), Department of Chemical and Environmental Engineering, Faculty of Engineering, University Putra 馬來西亞. Based on our research, the biochar obtained from the raw materials (Durian Husk, Bamboo and Coconut Shell) had shown different characteristics. The bamboo biochar had shown the most amount of carbon content which is 86.64% more than the durian husk biochar (72.77%) and coconut shell biochar (65.57%). On the other hand, based on the micrograph, we observed that the durian husk biochar had shown much created pores rather than bamboo biochar and coconut shell biochar. In our study, we found out that the average voltage produced by the three different biochars have shown that Durian Husk char dry cell produced the highest voltage which is 0.97V, more than the bamboo char (0.62V) and coconut shell char (0.73V). In conclusion, the biochar dry cell produced are much cheaper in term of its production as our biochar dry cell uses biomass that are freely available and comes from renewable source of energy, the best ingredient for Green Technology.
Observation of volcanic gases with a simple alkaline filter paper method at Sakurajima Volcano in Kagoshima, Japan.
There are many active volcanoes in Kagoshima Prefecture, including Sakurajima Volcano. So, the volcanic disaster prevention is an urgent issue. Also, Hirabayashi of Tokyo Institute of Technology reported that the molar ratio of HCl/SO2 is large during periods of high HCl/SO2 and conversely small during periods of low HCl/SO2 , and that explosions increase one month after the molar ratio of HCl/SO2 increases during periods of no explosions. We decided to determine the composition ratio of volcanic gases (sulfur dioxide, hydrogen chloride, and hydrogen fluoride) emitted from Sakurajima crater in order to understand and predict volcanic activities. Th us, we established a simple collection method for volcanic gases using alkaline filter paper and a quantitative method using a self m ade absorbance photometer so that even high school students could perform the measurement at many points, and we discussed the data from various perspectives. Furthermore, since last year, we have found a correlation between the variation of Cl-/SO2 ratio and the number of eruptions at Sakurajima volcano. Also, a model for the behavior of volcanic gases was developed based on a comparison of the amount of volcanic ash and the number of eruptions.