全國中小學科展

臺灣

格子點上的三角形

格子點上的三角形表示這個三角形三頂點的座標皆是整數。本研究先探討用平面格子點可以連出哪些三角形的相似形,再推廣到可以連出哪些多邊形的相似形;接著再研究空間中的格子點可以連出哪些三角形及多邊形的相似形,並用研究的結果討論空間中的格子點可以連出哪些正多面體。推廣到四次空間的格子點時,運用一條數論中的恆等式,發現可以做出來的三角形種類(所有相似形為同一種)居然與空間中的格子點一樣,這是個非常神奇的結果。另外,運用四平方和定理可導出,在五維空間中就能夠將所有可能用格子點連出的三角形種類連出來,這也是另一項收穫。When a triangle is formed with grid points, this means the coordinates of the vertices are all integers. This research aims to find out what type of triangles can develop into symmetries with vertices that fall right on 3 grid points on a plane. The same process is further applied to polygons. Based on the results obtained, the researcher moves on to explore what type of triangles can develop into symmetries that can be formed with spatial grid points. By using an equation in number theory to expand the study to a 4-dimension space, it is formed that the kinds of triangles—their symmetries included—which can be formed with 4-dimension grid points can also be formed in a 3-dimension space. In addition, all the possible kinds of triangles which can be formed in a 6-dimension space or up can also be formed in a 5-dimension space.

愛玉愛在結凍時~揭開愛玉神秘面紗

本研究源於暑假製作的愛玉沒有結成像果凍,因此,進行影響愛玉結凍的研究。結果如下: 一、愛玉的種子夾雜一些碎屑,碎屑可以結成愛玉凍。 二、奮起湖愛玉種子,產生的膠質面積最大,野生的愛玉種子,產生的膠質面積最小。 三、熱水讓愛玉凝膠物質產生快,因而熱水結凍較快,冷水較慢。 四、逆滲透水可以讓愛玉子結成凍,推測愛玉碎屑具有離子。 五、攪拌太快或太久,愛玉中的抑制物質產生,導致無法結凍。 六、真假愛玉分辨:碘液試驗法,假愛玉遇到碘液會變成藍黑色,真愛玉黃褐色;透光度法,假愛玉透光度較大,真愛玉透光度較小;軟硬度法,假愛玉較硬,真愛玉較軟;加熱法,假愛玉加熱後融化成液體,冷卻後又凝結成凍。

會旋轉的電解液

本研究主要探討電解液之帶電離子在磁場中的動力行為。為了觀察更細微的結果,共歷經三代裝置改良,第一代用五個電錶及探針測量徑向橫截面上五點的電壓,所測數值電壓有下降趨勢但不足以呈現細微部份的變化。第二代利用電壓感應線、搭配平移台及電腦,呈現連續性且經數位處理之結果,出現電壓升降的電荷堆積現象。第三代為了更精確,將裝置結構及器材上改良。觀察到在磁場作用下有旋轉現象,改變電極極性時,會有順逆時鐘方向的改變,且只有電解質液才會有旋轉。更可以使用帶電質點受到勞倫茲力F=q(VxB)理論解釋。且旋轉中的電解液比沒有旋轉時,析出的銅量少,反應溫度升高快,電解液內電壓分布因電荷堆積造成的高低起伏。經過改變磁場強度、電解液濃度,不銅價離子電解液,結果濃度大、磁場大、離子數較多者,呈現電壓分布圖快速變化,彎曲大。This thesis report is the study of combining the moving charged particles under the perpendicular magnetic field. By using the theory of moving and electrolysis, the electrolytic liquid will swirl through the particular arrangement of the horizontal cylinders enclosed in a circular enclosure container and strong magnet. Then, the researcher observes the force situation of the charge in the magnetic field and discusses the differences of the electrolysis effect, which is experimented under the different conditions, such as, in the magnetic field or no-magnetic field. Furthermore, the researchers discuss the conduction of voltage spreading and interfering when the moving electrons under different position of two electrodes and under the different interaction of electric field and the magnetic field. And the changing reason as follow: (1)the magnetic field strength. (2)the concentration of the electrolytic liquid. (3)electrolytic solution. When the experiment group compared with the comparison group, the result may provide fundamental understanding as follow:(1) The researchers can find out the charged particles rotating in the magnetic field. And it proved the moving condition when the moving electrons in the magnetic field. (2) This experiment can be used in judging the solution, which I electrolytes, or not. (3) This experiment also proved for Arrhenius’s ionic theory. (4) The researchers found out the quantity of Cuprun decrease, the rise in temperature and the reducing in voltage.

超聲波在液體的探討

本實驗一開始主要探討超聲波在水中的基本性質,如:指向性、衰減性…等。實驗發現,超聲波的衰減會同時與其指向性以及衰減性有關。 接著希望利用超聲波在水中的物理性質,近一步測量超聲波在水中的聲速,實驗中則利用駐波以及聲光效應測量。在駐波法測量聲速的實驗中,用洗淨機當作聲源,內部放置量筒,量筒內盛水後放入木屑,並使聲波在其中產生駐波即聲浮現象,求出波長後反推聲速,測量出的聲速誤差值僅有1.13%,而在使用聲光效應測量聲速的實驗中,使1.65 MHz 的超聲波在自製的壓克力容器內部所裝的水中產生駐波後,以波長650 nm 的紅光雷射通過,在遠處屏幕即產生似於光柵繞射現象,藉著屏幕上的繞射條紋反推該液體聲速,測量出聲速誤差均在5%以下。 在觀察聲光效應實驗中,發現過段時間後有氣泡產生,由文獻上,得知此現象為超聲空蝕現象(Acoustic cavitation),就設計實驗測量聲場中聲壓分部,並利用蠟紙觀察氣泡的成長。實驗發現聲場中的聲壓強度以及液體的表面張力和蒸汽壓會影響到產生空蝕的臨界值及產生氣泡的數量。 ;At the beginning this experiment explores the ultrasonic base in the water, including its velocity, the physics property of liquid, direction, and attenuation etc. . . At first, we use methods of standing wave to measure the velocity of sound under the water, using an ultrasonic cleaner as the sound source and putting some wooden powder in the water. As the standing wave accrues/produces, the powder will “stand still.” To measure the length between two grains of powder, in this way we can calculate sound velocity. Another method we use is diffraction of optics. Put 1.65 MHz source and water in a transparent container; then using laser through it. At the board much diffraction light stripes are created. By this way, we can estimate the velocity. Following these ways can calculate velocity precisely. In these experiments, some bubbles create in the container are discovered. We learn it is so-called “Acoustic Cavitation” based on the reference paper. Besides, we design experiment to know the bubbles’ growth and the number of the bubbles is connected to the physics property of liquid. We use different kinds of liquid with different vapor pressure and surface tension. Finally, we know when it has the smaller surface tension and bigger vapor pressure, the liquid makes bubble velocity grow faster and larger amount of bubbles are produced.

以珊瑚蛋白及光頻轉換分子改善太陽能電池效率之研究

能源危機日益嚴重,開發再生能源成為當務之急。在諸多的再生能源之中,太陽能最易於使用,且可源源不絕的不斷取得利用。但目前太陽能電池的效率始終不高。其中重要的原因是太陽本身的頻譜多為短波長,並不適合絕大部分頻譜響應較佳,多為長波長的太陽能電池。目前改善效率方式,多為改變太陽能電池的頻譜響應以配合太陽之頻譜。本研究提出反向思考的概念,藉由頻譜轉換的方法,改變照射在太陽能電池上的太陽光頻譜,以提升太陽能電池的效率。本研究利用一種珊瑚礁的螢光蛋白質(DsRed)以及人工合成的螢光染料(Cy-5)最為本研究的頻譜轉換的材料,加於低成本,目前市場佔有率較大的單晶矽太陽能電池上,經由理論與實驗的結果顯示,增加的發電效率約為3~5%,證實利用頻譜轉換的概念確實可以提升太陽能電池的效率。Energy crisis has become more and more serious in recent years, which makes recycled-energy development is a must. Among different recycled energies, solar power has two advantages, that is, easy-to-use and endless supply. However, the conventional solar cell makes poor use of the solar spectrum because the solar spectrum is mainly composed of short-wavelength, which can’t fit to most of solar cells which is more sensitive to long-wavelength. Currently, the major method to improve the efficiency is change the function of spectral response, such as concentration lens, tracking devices, and antireflection coating. Up to now, no one notices the possibility of changing solar spectrum yet. This research provides an insight into this issue. Instead of changing the function of spectral response, I changed the solar spectrum, which irradiates solar cells through spectrum conversion to improve solar cells’ efficiency. This research uses one kind of coral fluorescence proteins (DsRed) and one kind of artificial fluorescence dyes (Cy-5) as the materials of spectrum conversion. Then coat them on the low-cost and high-market-share mono-crystal-Si. According to the theories I researched and my experiments, the improvement of the efficiency is about 3~5%, which proves it is actually useful to elevate the efficiency of solar cells through spectrum conversion.

以交聯化羊膜為模式探討Wnt路徑保存表皮幹細胞之分子機轉

研究目的:以交聯技術改良羊膜,增進其培養並維持表皮幹細胞的效能;並以其為模式,探討Wnt訊息於基底膜上維持表皮幹細胞之機轉。 研究過程:用EDC交聯羊膜(HLE/CLDAM)、天然羊膜(HLE/DAM)或純化之基底膜蛋白培養角膜表皮幹細胞,以細胞群落形成作用分析幹細胞之保存;以免疫螢光染色法、real-time PCR及西方墨點法觀察幹細胞及分化標記之表現、β-catenin、Tcf4、Lef1、integrin β1及integrin-linked kinase (ILK) 之變化。以ILK SiRNA及cDNA分別下調或上調ILK於HLE之表現,並觀察其對Wnt相關蛋白質及p63表現之影響。 研究結果: HLE/CLDAM組比HLE/DAM組表現更高量的幹細胞群落與標記,並可見β-catenin轉移至細胞核、Tcf4及ILK之表現。加入GSK3-β抑制劑促進表皮細胞之群落形成及p63之表現。調控ILK基因可造成相對應之Wnt訊息及p63蛋白之表現。純化之基底膜蛋白活化Wnt訊息及表現p63蛋白,但產量很少。 結論:交聯化羊膜比天然羊膜更能保存角膜表皮幹細胞,其機轉為ILK活化Wnt路徑,後者再作用於p63基因,從而活化幹細胞相關因子。 運用:交聯化羊膜可取代天然羊膜培養角膜表皮幹細胞;培養基質表面的複雜性可用來調控幹細胞之分化,從而提高體外培養幹細胞之效能。

高分子複合材料的性質、製作與分解

Synthesis of Polymer Material and its Decomposing Processes Because plastic cannot be decomposed naturally by itself, therefore, additives needed to be added to facile the decomposing process. Let us choose one common material: thermoformed Nylon 66. During the formation process, addition of glucose powder and monosaccharide polymerized will result in yielding the products of methyl cellulose, soluble starch and agar powder. Observe whether adding additives would allow changes to occur structurally, or would the elasticity be improved when exist in a linear state, or even it would form a better pH resistance property. According to the experiments, when Nylon 66 contains methyl cellulose, it can sustain the highest tension. Its coefficient of elasticity is 2 times as large as the original one. In terms of the data, we can also observe that when Nylon66 contains soluble starch, it has the lowest ability to sustain tension. Besides, it has the lowest coefficient of elasticity. And when Nylon 66 contains cellulose, it has the highest rate in the process of decomposing.As we look at the surface of polymers under 400 diameters, we can observe that the Nylon 66 with agar powder has some filiferous substance. But we have not confirmed what the matter is. 由於塑膠不能在自然情況下順利分解,所以我們在塑膠中添加其他成分使塑膠可以較易 分解。我們選定常見的塑膠—熱塑性的耐綸-66。在聚合物的製作過程中添加葡萄糖、澱粉、 洋菜粉末以及甲基纖維素,並觀察加入添加物的塑膠在結構上是否有變化?其塑膠在線型時 之張力是否有增強?耐酸鹼性是否有變化?由實驗結果我們可以得知含有甲基纖維素之耐綸 -66 所能承受之張力強度最高,且其彈性係數也比無添加物之耐綸-66 高出近2 倍;而含可溶 性澱粉之耐綸-66 所能承受之張力最小,且彈性係數也最低。此外,進行生物分解的實驗可發 現,含葡萄糖的耐綸-66 分解的速率最快。使用400 倍的光學顯微鏡可發現含有洋菜粉末的耐 綸-66 表面與其他耐綸-66 複合材料差異較大,值得進一步研究。

吸菸、喝酒與嚼檳榔之基因毒性研究

流行病學資料顯示,近年來口腔癌發生率明顯增加。本研究之目的是探討口腔黏膜細胞微核發生頻率及彗星分析法之基因傷害指標是否與菸、酒、檳榔暴露有關,以及是否可以看到菸、酒、檳榔之交互作用。 研究對象為桃園地區山地鄉之民眾,利用問卷收集個人之菸、酒、檳榔及干擾因子之暴露資料,再採集樣本之口腔黏膜細胞及血液樣本,進行基因傷害評估。 結果顯示,口腔黏膜之微核發生率與檳榔之暴露相關性最大,可以解釋12.6%;然而,彗星尾部動量和尾部長度則以香菸暴露解釋力最大;同時,檳榔與香菸的基因傷害交互作用似乎存在。因此我們認為,口腔黏膜細胞之微核發生頻率對於檳榔暴露者應是不錯的基因傷害指標,而香菸暴露則以彗星分析法之指標較為敏感。 ;Epidemiological studies showed that the incidence of oral cancer increased significantly in recent years. The purpose of this study is to evaluate the genotoxicity of cigarette smoke, alcohol and betel quid use as well as the. interaction effect between these three risk factors. The study subjects were selected from residents lived in a mountain area of Tao-Yuan county. We used questionnaire as a tool of exposure measurement. The exfoliated oral buccal cells and blood samples were collected for the assay of micronucleus frequency (MNF) and comet assay. We find that there are higher MNF in smokers, alcohol drinkers, and betel quid users compared with nonusers. However, a significant difference can not be found because of small sample size. The relationship between MNF and three risk factors was strongest in betel quid use, however, for smokers the parameters in comet assay were more sensitive than MNF. There is a tendency of additive effect between cigarette, alcohol and betel quid although without statistical significance. Advanced statistical analysis is suggested to find stronger evidence in the genotoxicity biomarker.

探討生物材料對骨髓間質幹細胞成骨分化效率之影響

本實驗之目的在利用骨髓間質幹細胞 (Bone Marrow Mesenchymal Stem Cells, BMSCs) 培養為平台,篩選能提升BMSCs成骨分化效率的生物材料。實驗中利用osteogenic induction medium (OIM)使BMSCs朝成骨分化路徑進行,分別在第7(前期)、14(中期)、21(後期)天作Alizarin Red Stain assay(ARS assay)測定鈣沉積之效率作為評估標準,而後於平面上塗覆不同生物材料進行測試,根據實驗結果顯示,Gelatin主要在中期就可達到最高成骨分化效率,而PCL與HA到後期亦能顯著提高成骨分化效率。當進入3D立體成骨誘導試驗時,我們發現Gelatin、HA的複合材料能保持平面之特性且結合二者優點,並且更能有效提升成骨分化之效率。

利用雷射光實驗研究液的折射率梯度

溶液和溶劑置於同一容器中,當溶質向上擴散時,會形成濃度梯度及折射率梯度 dn/dy,且dn/dy 對高度y 的關係圖會呈現隨著高度改變的現象。 半徑r 的D形容器,下方置溶液,上方置溶劑,以雷射光照射容器的平面部份時, 雷射光沿著法線出射,受折射率梯度的作用而向下偏Ζ距離,a 為容器至屏的距離, 得到dn/dy=Z/ar 的關係式;改變雷射光的高度y 可得dn/dy 圖。 以硫代硫酸那作實驗,其dn/dy-y 圖為以原始界面為對稱軸,因其擴散係數不隨濃 度改變;甘游水溶液的dn/dy-y 圖呈現不對稱,圖形的極大值往甘油方偏,主要係因 為甘油的擴散係數隨濃度的增大而減少。 我們成功第把不同時間對同一溶液的實驗結果予以模型化,得到的dn/dy-y 曲線隨 時間改變,並發現該曲線所涵蓋的面積為定值。 雷射光經光柵再照射半圓筒,可直接測出各高度的折射率,量出y、 dn/dy、n、及濃度可算出擴散係數。The mixing between a pure liquid and a solutionin a vertical column produced a concentration gradient , which in turn produced the refractive index gradient . As the solute particles diffused upward into the pure liquid , a gradient was generated because of the varying solute concentration . The plot of the refractive index gradient versus vertical position y (dn/dy vs y) is found to vary with time . A D-shape container of radius r is partly filled with a dense solution , and partly filled with solvent which is on the top of the solution. When laser beam pendicularly enters the flat surface of the container, the outgoing beam strikes the container at a normal incidence , and is deflected down a vertical distance Z by the refractive index gradient . We can get dn/dy=Z/ar , where a is the distance between the container and the screen . By changing the vertical position (y)of laser beam , we can get the plot of dn/dy vs y . We have successfully modeled the time dependent experimental gradient curves on the same solution . The area beneath the trace of dn/dy vs y at different time is found to be constant . Additionally, with a grating at the center of the semicircle, we can measure the index of refraction n and get the plot of n vs y. The diffusion coefficient D of the solute can be calculated using the plot of dn/dy,y,and time t.