Fluorine-containing compounds gained significant attention during the past decade1. About 20% of novel pharmaceuticals and 40% of novel agrochemicals every year contain at least one fluorine atom in the molecule. For a long time the most frequently used was trifluoromethyl group, but nowadays the most promising is the chemistry of partially-fluorinated groups. For example, the difluoromethyl substituent (CHF2) exhibits unique pharmacoforic properties capable of serving as lipophilic hydrogen bond donor thus being bioisosteric to hydroxyl group2. There are several general approaches for the formation of a required fluorinated fragment, one of them is direct nucleophilic fluoroalkylation. This approach is well-developed for trifluoromethylation reactions, such as addition of CF3-anion equivalents to C=O, C=N and electron-deficient C=C bonds or metal-catalyzed substitution in haloarenes3. However the similar difluoromethylation processes are still quite challenging. Herein we present a novel and convenient protocol for the synthesis of β-CF2H functionalized carbonyl compounds and carbinols by nucleophilic difluoromethylation of electron-deficient olefines. The process is based on a 1,4-addition of in situ generated4 phosphorus ylide Ph3P=CF2 2 to the arylidene Meldrum's acid conjugates 1. The resulting phosphobetaines 3 are hydrolized/protodephosphorilated without isolation, giving β-CF2H substituted carboxylic acids 4. The latter may be easily transformed to the corresponding ethers 5 and alcohols 6 without preliminary purification.

Photochromism is determined as reversible transformation between two chemical species, induced by action of light [1]. Herewith, initial form and photoinduced isomer have different properties, first of all, spectral. The phenomenon is attractive for the design of hi-tech materials for different applications, including optical memory elements and molecular switches. Diarylethenes are the most promising class of organic photochromic compounds due to outstanding thermal stability of both isomers and high photostability [2, 3]. Photochromism of diarylethenes explained by reversible electrocyclic reaction of hexatriene system, provoked by UV light, back reaction is induced by visible light. In this work we have proposed a new class of photochromic diarylethenes with cyclohexenone ethene “bridge” 4. The key stage of the synthesis is “one-pot” reaction of ketoesters 1 and chalkones 2 in ethanol in the presence of sodium ethoxide that includes Michael reaction and subsequent intramolecular condensation of the resulting product. The final decarboxylation of semi-product 3 results in target diarylethenes 4. We have prepared a wide range of photochromic diarylethenes with thiophene, oxazole, imidazole and benzene derivatives as aryl moieties. The spectral characteristics of compounds obtained have also been discussed.

This project aims to create the polar equations from the relation of the points on the centre line of the water twisted from Butterfly sprinkler heads. The water path includes inner rim, outer rim and centre line laying in the middle of the water path is used Rhombus’s property. The diagonals are perpendicular bisectors of each other to create the centre line. Then we create the polar equation of the centre line of water that twists from 4 types of the Butterfly sprinkler heads: edge frame, curve frame, STL and STL rotary. The polar equation of outer rim and inner rim is created by adding and removing the “ f ” value ( ; is the distance between the outer rim and the centre line, and is the geometric sequence that is ) of the coefficient (a) of the polar equation respectively. The results show that the formal equation of the centre line is which can explain the different properties of Butterfly sprinkler heads. If “ f ” value is increasing the water path and the blade will be wider that affects droplets distributing thoroughtly. Furthermore the relationship between the volume of water and the radius of water distribution can be processed to find the least time that can increase the appropriate moisture level of soil.

這篇報告要探討下列的「轉沙發的問題」是否有解？有一個長方形的沙發，如圖一，若要求每次只能以「四個頂點逆時針或順時針連續旋轉90度」的方式轉動，請問當長寬具備何種關係時，沙發經數次轉動後，剛好可以「轉」到相鄰的位置，如圖一，而且沙發坐人的正面方向仍保持不變呢？ 我們把原問題看成「平面座標上長方形旋轉的數學問題」，再利用「平面座標、三角函數、複數、複數的極式表示及向量」等數學工具，導出符合題目要求的方程式，最後證出當長與寬的比值為正實數時，有下列的結果： 1.當長與寬比值為無理數時，此問題無解。 2.當長與寬比值是最簡分數時，若分子為奇數，此問題無解。 3.當長與寬比值是最簡分數時，若分子為偶數，分母為奇數，此問題有解。 4.在有解的情況下，我們可以找出特定轉法的最小值。 5.當長與寬比值是最簡分數時，若分子為偶數，分母為奇數，沙發可轉至A點座標為(αp,0) 的位置，其中 α∈Z，且沙發坐人的正面方向保持不變。 6.當長與寬比值是最簡分數時，若分子為奇數，分母為偶數，沙發可轉至A點座標為(0,βq) 的位置，其中 β∈Z，且沙發坐人的正面方向保持不變。 7當的長與寬比值為正實數時，可將沙發轉至A點的座標為(2αp + 2βq,2γp + 2qω)的位置，其中 α,β,γ,ω∈Z，且沙發坐人的正面方向保持不變。 In this paper we discuss the solution of rotating sofa problem as follows : The condition is : Merely allow to rotate the sofa several times by rotating 90 degrees clockwise or counterclockwise around the vertex. (maybe A, B, C, or D in Fig. 1) The question is : What’s the relationship between the length and the width of the sofa, if we request the sofa translated next to the original position with direction unchanged. (as shown in Fig. 1 with A’B’C’D’). We take this problem as a mathematical one of rotating a rectangle in plane coordinates. Then we derive the desired equations by using the tools of plane coordinates, trigonometric functions, complex number, polar form of complex number, and vector. Finally, we prove that： 1. When the ratio of length and width is irrational, the problem has no solution. 2. When the length of sofa is odd in the ratio of length and width, the problem has no solution. 3. When the ratio of length and width is even, the problem has solutions. 4. When the solutions exist , we can find the minimum of the number of rotations. 5. When the ratio of length and width is an irreducible fraction, which has the even numerator and the odd denominator, the sofa can be rotated to the coordinate (αp,0)(α∈Z)which is the new position of A and keep the original position with direction unchanged. 6. When the ratio of length and width is an irreducible fraction, which has the odd numerator and the even denominator, the sofa can be rotated to the coordinate (0,βq)(β∈Z) which is the new position of A and keep the original position with direction unchanged. 7. When the ratio of length and width is a real positive number, the sofa can be rotated to the coordinate (2αp + 2βq,2γp + 2qω)(α,β,γ,ω∈Z)which is the new position of A and keep the original position with direction unchanged.

在物理馬戲團這本書中提到：「當你泡即溶咖啡或攪拌奶精的時候，用湯匙輕敲杯壁看看，添加奶精後攪拌時，敲擊的聲音與添加前明顯不同，為什麼？」這本書的解答是：「當粉末溶解的時候，藏在粉末裡的空氣就會跑出來。因為空氣裡的音速低於水裡的音速，在空氣與水混合的環境裡，音速也比在水裡低。當水裡不斷有空氣混進去時，這個容器的共振頻率和它裡面的音速有關，所以也會降低。因此你會聽到較低的音調，直到空氣全部跑光。」我們利用指向性麥克風以電腦錄音後以Adobe Audition 軟體分析聲波頻率，覺得這個說法有點問題。例鹽水溶液音速較水高，敲擊時的音調卻較水低。由敲擊一黏於裝水水盆中之空杯，與敲擊杯內裝同一水位之水之杯子，頻率非常接近。告訴我們影響頻率的是靠近杯壁一層有效質量。因鹽水溶液密度較高有效質量較大，所以頻率較低。以密度的觀念檢視裝有溶液之杯子被敲後的頻率是對的。但對杯中有懸浮物就不然，例如流體中含有氣泡，則混合體之密度必定變低，有效質量變小頻率應變高。但實驗發現含有氣泡時頻率是變低的。可見氣泡還有其他的影響力高於密度對音調的影響。 流體的振動應是會壓縮到氣泡，氣泡與流體間之力學交互作用為何會使頻率下降，正是我們要找出的。 The Flying Circus of Physics has a question “As you stir instant cream or instant coffee into a cup of water, tap the side with your spoon. The pitch of the tapping changes radically as the powder is added and during the stirring. Why?” The answer is, “The air trapped in the powder is released as the powder dissolves. Since the speed of sound is lower in air than that in water, the speed of sound in the air-water mixture is lower than that in pure water. During that period while the air escapes the container, the resonant frequencies of the water, which depend directly on the speed of sound, will also be lower. Hence, you hear a lower tone until the air escapes. “We then tap the coffee cup and generate an audible tone. The signal picked up by the microphone . The same signal is also studied using Adobe Audition, a waveform processing and analyzing software. We find the assumption is wrong, the speed of sound is higher in sugar solution than that in water, but we hear a lower tone. An effective layer of fluid adjacent to the glass wall is set into motion when we gently rub the rim of the wineglass. The thickness is about the same whether the fluid is inside or outside the glass. This explains why the frequency drops when the liquid is added to the system. When the density of the sugar solution is higher, the mass of the effective layer is higher. But what the presence of the bubbles and the theoretical explanations must NOT rely on are: Use effective density argument: One should not just use a change in the main density to try to explain why the frequency is lower. I would think that the bubbles are compressed a little bit by the vibrational motion of the glass communicated to them through the fluid. But how do the bubbles interact with the fluid under this setting? This is what we need to work out.

Millions of people worldwide suffer from aphasia, a disorder that severely inhibits language comprehension. Medical professionals suggest that individuals with aphasia have a noticeably greater understanding of pictures than of the written or spoken word. Accordingly, we design a text-to-image converter that augments lingual communication, overcoming the highly constrained input strings and predefined output templates of previous work. This project offers four primary contributions. First, we develop an image processing algorithm that finds a simple graphical representation for each noun in the input text by analyzing Hu mo-ments of contours in images from The Noun Project and Bing Images. Next, we construct a da-taset of 700 human-centric action verbs annotated with corresponding body positions. We train support vector machines to match verbs outside the dataset with appropriate body positions. Our system illustrates body positions and emotions with a generic human representation created using iOS’s Core Animation framework. Third, we design an algorithm that maps abstract nouns to concrete ones that can be illustrated easily. To accomplish this, we use spectral clustering to iden-tify 175 abstract noun classes and annotate these classes with representative concrete nouns. Fi-nally, our system parses two datasets of pre-segmented and pre-captioned real-world images (Im-ageClef and Microsoft COCO) to identify graphical patterns that accurately represent semantic relationships between the words in a sentence. Our tests on human subjects establish the system’s effectiveness in communicating text using im-ages. Beyond people with aphasia, our system can assist individuals with Alzheimer’s or Parkin-son’s, travelers located in foreign countries, and children learning how to read.

Diarrhoea is an infectious disease that claims many lives (particularly among infants) and is known among many other infectious diseases, to have a relationship with climate. This projects quantifies this relationship by comparing health insurance treatment claims for diarrhoea and anti-diarrheal drug sales data from the private health sector with temperature and rainfall data provided by the South African Weather Service. The data were then analysed and show that incidence is highly seasonal and varies among regions with different seasonal climates. The results show that climate variability can explain 73% of diarrhea incidence variation with rainfall explaining 8% and minimum temperature explain the other 65 %. Preliminary predictions of future monthly percentage increases in incidence were then made for a series of time ranges. This project demonstrates that with predicted climate data one can predict future variations of diarrhoea allowing the health sector to be adequately prepared.

The objective of the project is to develop a novel biomimetic membrane and/or a scaffold for the said membrane. The approach of the project is to use animal skin from the domesticated pig or fish as a scaffold material for the adherence and growth of human skin fibroblasts to create a biomimetic membrane that can be used in medical applications as an alternative to today’s gold standards of Xenograft, Allograft and Autograft procedures. The biomimetic skin membrane can be used to treat victims of burns or scarring with a natural material that would be eliminated via natural bodily functions while eliminating the side effects and drawbacks such as scarring, secondary infections and tissue damage resulting from the current gold standard graft procedures on donor sites. Pig and fish skins were treated with ethanol and dehydrated followed by perfusion with Phosphate buffer solution and Cell culture media. Human skin fibroblasts (NF3 cells) were seeded on the animal skin scaffold. The human skin fibroblasts were then observed to determine their morphology and membrane formation properties. It was observed that the human skin fibroblasts were able to adhere to the non-human skin scaffolding and proliferate. More research is needed to determine their viability as a biomimetic membrane.

Retinoblastoma (RB) is a childhood retinal cancer caused by mutations in the RB1 gene. Molecular diagnosis is crucial for early detection and treatment. Current DNA diagnostic screening requires substantial amounts of tumour and blood samples. However current screening methods face the challenges of limited DNA templates from minute retinal tumours and too much blood samples drawn from young patients. In addition, the starting DNA template amount and quality are important to ensure confident detection of disease-causing mutations. As the majority of RB1 mutations are unique and distributed throughout the RB1 gene with no real hot spots, the entire gene needs to be thoroughly analysed. This investigation proposes to enrich DNA samples using a whole genome amplification (WGA) step prior to RB1 mutation screening by RB1 gene-specific PCR amplification as well as high resolution melt (HRM) analysis and sequencing. It also identifies RB1 mutations in two RB patients and explores whether WGA and saliva products can be a source of DNA templates for RB1 analysis. In addition, this study was conducted based on the hypotheses that RB1 mutations were the underlying cause of the disease in the two patients, and that the products from WGA could be used specifically for RB1 gene analysis to overcome the constraint of insufficient DNA samples. Two anonymised genomic DNA samples from two unrelated RB patients and five normal healthy DNA samples were used in this project. WGA kits were compared according to three criteria, namely amplification yield, product fragment size and whether DNA is amplifiable. Prior to and after amplification, the optical density of two normal samples was measured to determine the increase in DNA yield. The amplicons were subjected to gel electrophoresis to determine the product fragment size. Exons 6, 14 and 25 of the original and amplified samples undergone PCR, and were examined again using gel electrophoresis to ascertain that the amplicons were amplifiable. Mutation analysis using HRM was carried out with pre-existing primers for all 27 exons and the promoter of RB1. Samples from patients were analysed against 83 saliva DNAs extracted using Oragene•DNA (OG-500) Kit. REPLI-g was observed to produce higher yield and products of reliable fragment size. Single distinct bands were also seen for exons amplified using REPLI-g, indicating that REPLI-g is more accurate and suitable in the amplification of DNA. Abnormal melt profiles were obtained for exon 6 in RB477 and exon 14 in RB572 for HRM. These exons were sequenced to determine the exact mutation. Exon 6 was found to have a splice-site mutation g.607+1G>T, while a point mutation, g.1363C>T (p.Arg455X) was identified in exon 14. Both the uses of saliva as a non-invasive DNA source and the WGA approach for enriching DNA sample for application in RB1 gene analysis have never been reported for RB. Although HRM analysis has been used for other diseases, this is its first instance applied in work on RB1 gene. In short, this report offers novel and promising approaches which would contribute significantly to the molecular analysis of mutations in RB.

EXPERIMENT 1---The effect of NaCl and Glucose Concentration on the efficiency of the cell I. Introduction Experiment on different concentrations of standard glucose solution (ranged from 0.125 M to 1.000 M) and standard sodium chloride solution (ranged from 0.250 M to 4.000 M) were done. We investigated the full concentration effect, which included both concentration of glucose solution and sodium chloride solution on the fuel cell’s output voltage, current and power. II. Procedures 1. Add 25.0 cm3 of Glucose solution of the tested concentration to the beaker representing the anode, and add 25.0 cm3 of distilled water to the beaker representing the cathode. 2. Add 50.0 cm3 of 0.250 M NaCl (aq) to both beakers representatively. 3. Fold a piece of filter paper and soak in fully into NaCl (aq) at cathode. 4. Clean and place the silver wires into the beakers representatively, and connect the air pump to the cathode. 5. Connect the cell to two multi-meters, each acting as a voltmeter and an ammeter respectively 6. Take the readings of multi-meters after 30 seconds. 7. Repeat steps 1 to 6 twice for the second and third reading of the cell. 8. Take average value among three values as the final reading of the cell. 9. Repeat steps 1 to 8 by replacing the NaCl (aq) with concentrations of 0.000 M, 0.500 M, 1.000 M, 2.000 M and 4.000 M, and the standard glucose solution with concentrations of 0.000 M, 0.125 M, 0.250 M, 0.500 M, 0.750 M and 1.000 M. III. Result of Experiment 1 When glucose concentration is increased from 0.000 M to 0.250 M, the output power increases, it is found that power generated is maximized at glucose concentrations between 0.125 M and 0.250 M. However, with further increase in glucose concentration from 0.250 M to 1.000 M, the power generated decreases. This shows that high concentration of glucose inhibits the generation of electricity, while higher concentration of sodium chloride solution can increase the output. EXPERIMENT 2---The effect of temperature on the efficiency of the cell I. Introduction In this experiment, the second effect - temperature on the fuel cell’s output voltage, current and power was investigated. In order to get a significant result, the effect of temperature on these measures with fixed 0.250 M glucose solution and sodium chloride solution concentrations varied from 0.500 M to 4.000 M had been investigated. II. Procedures 1. Add 25.0 cm3 of Glucose solution of the tested concentration (0.25 M) to the beaker representing the anode, and add 25.0 cm3 of distilled water to the beaker representing the cathode. 2. Add 50.0 cm3 of 0.500 M NaCl (aq) to both beakers representatively. 3. Fold a piece of filter paper and soak in fully into NaCl (aq) at cathode. 4. Clean and place the silver wires into the beakers respectively, and connect the air pump to the cathode. 5. Connect the cell to two multi-meters, each acting as a voltmeter and an ammeter respectively 6. Take the readings of multi-meters after 30 seconds. 7. Repeat steps 1 to 6 twice for the second and third reading of the cell. 8. Take average value among three values as the final reading of the cell. 9. Repeat steps 1 to 8 by varying the temperature from 42℃ to 32℃. 10. Repeat steps 1 to 9 by replacing the NaCl solution of 0.000 M, 1.000 M, 2.000 M, and 4.000 M respectively. III. Result of Experiment 2 The results showed a consistent trend and relationship of the effect of temperature on the output current, voltage and power of the fuel cell for 4 different concentrations of sodium chloride solution with fixed 0.25 M glucose solution. Generally, the results showed that the output power increases with temperature. EXPERIMENT 3---The effect of dialysis tubing and Nafion 117 on the efficiency of the cell I. Introduction Semi-permeable membrane separating glucose and oxygen, ensure the glucose oxidation only occurs at the anode, and preventing glucose oxidation occurs at the cathode, responds to maximize power output. Experimental study on two kinds of membranes, dialysis membranes and Nafion 117 films were done, by studying their fuel cell output voltage, current and power effects. Previous experiments showed that the optimal output of the battery is at 0.250 M glucose solution, Therefore, experimental conditions for glucose concentration is fixed on 0.250 M and sodium chloride solution concentration varies from 0.500 to 4.000 M. II. Procedures The Effect of Dialysis Tubing on voltage and current of the fuel cell 1. Pour 50 cm3 1.000 M NaCl (aq) to each compartment of the beaker separated by dialysis tubing. 2. Pour 0.250 M Glucose Solution into the compartment representing anode. 3. Connect the cell to two multimeters, which act as a voltmeter and ammeter respectively 4. Take the reading of the multimeters after 30 seconds 5. Repeat steps 1 to 4 twice for the second and third reading of the cell. 6. Take average value among three values as the final reading of the cell. 7. Repeat steps 1 to 6 with NaCl (aq) with concentration of 0.000 M, 0.250 M, 0.500 M, 2.000 M and 4.000 M to obtain the remaining data. The Effect of Nafion 117 on voltage and current of the fuel cell 1. Add 50 cm3 1.000 M NaCl (aq) and 50 cm3 of 0.250 M of glucose solution to the beaker. 2. Add 1.000 M NaCl (aq) to the Nafion 117 membrane pouch, and silver plate was put inside to become the anode. 3. Connect the cell to two multimeters, which act as a voltmeter and ammeter respectively 4. Take the reading of the multimeters after 30 seconds 5. Repeat steps 1 to 4 twice for the second and third reading of the cell. 6. Take average value among three values as the final reading of the cell. 7. Repeat steps 1 to 6 with NaCl (aq) with concentration of 0.000 M, 0.250 M, 0.500 M, 2.000 M and 4.000 M to obtain the remaining data. III. Result of Experiment 3 The result had shown that when the solution does not contain glucose (i.e. Glucose concentration equals to 0.000 M), Nafion 117 Membrane Cells have similar power outputs compared to the dialysis tubing cells. However, in 0.250 M glucose solution, the output of Nafion 117 membrane cell is about 1 to 5 times more compared to that of dialysis tubing cell. According to the experiment results, it was found out that the power output was maximized when the concentration of glucose solution and NaCl (aq) are 0.250 M and 4.000 M respectively. Under this concentration, the out of Nafion 117 membrane cell was 1336.68 nW which was 5 times higher than that of dialysis tubing cell. Hence, adopting Nafion 117 as the selectively membrane can greatly enhance the output of cell. It is believed that the special structure of Nafion 117 has limited the movement of glucose molecules, and prevented their oxidation at cathode. This has enhanced the oxidation of glucose at anode, and thus increased the power output of the cell.

本作品為環球數學城市競賽的考題之推廣（ International Mathematics Tournament of the Towns, Senior A-Level Paper, Fall 2009, No. 7 ），然而此題目本身比較接近Scientific American （ Feb 1979 ）中 Martin Gardner 的文章 The Rotating Table 所提出的問題。 而此問題的多邊形版已被數學家解決(Ted Lewis & Stephen Willard, 1980, The Rotating Table,Mathematics Magazine, 53,Page 174-175.)。然而此份作品採用簡潔的初等數學歸納法證明了原本的多邊形情形，且專注於探討條件改變為m=n-1時的多邊形情形。 m=n-1時的情形是前人所沒有做出結果的，且m=n-1的情形遠遠比m=n 的情況來得複雜多變，其中估計上下界所使用的許多組合技巧相當特別。然而其中當n為3 和5的倍數時有比較特殊的情況，這一個部分僅能給出目前得出的k值上界。而其他情況則能夠找出所有的k值。

The aim of our research is to produce superhydrophobic coatings on both glass and cloth substrates in order to achieve high contact angles and low sliding angles for self-cleaning. In addition, we aim to modify these coatings to be as transparent as possible so as not to interfere with the aesthetics of the objects which will be coated. To achieve this goal, we synthesised a solution using 1H, 1H, 2H, 2H-perfluorooctyltriethoxysilane (a type of FAS), silica nanoparticles (SiO2), tetraethyl orthosilicate (TEOS), (3-glycidyloxypropyl) trimethoxysilane (Glymo) and deionised water. Using the convenient sol-gel method, coatings of 20% and 30% by weight of FAS-SiO2 nanoparticles were prepared on glass and cotton substrates. It was found that coatings containing 30% by weight of FAS-modified SiO2 nanoparticles on glass slide produced coatings with water contact angle as high as 162.8° and sliding angle as low as 4°. It can also be seen that for glass substrates, the hydrophobicity increased with an increase in percentage of FAS-modified SiO2 nanoparticles. Although the highest percentage transmittance was about 30%, texts and pictures beneath the coated glass slides were clearly readable. The cotton substrates also exhibited excellent hydrophobicity, with a water contact angle of 150° and sliding angle of 22°. Furthermore, the substrates showed good retention of colour and durability after simulated washing and 72 hours of ultraviolet (UV) weathering chamber test. These results show that the effects of washing and UV on the important properties of the cloth were insignificant.