全國中小學科展

2024年

從心開始-三角形的四心到各邊距離和

此研究討論三角形𝐴𝐵𝐶的外心、重心、垂心、內心到三邊之距離,並依銳角、直角及鈍角三角形,去比較各距離總和之大小關係及相互之間的關聯性。其主要結果為: 1.用外接圓半徑𝑅及∠𝐴,∠𝐵,∠𝐶表示各心到三邊之距離。 2.設外心、重心、垂心、內心到三邊之距離總和依序為𝑑1, 𝑑2, 𝑑3, 𝑑4 ,其大小關係為: (1)在銳角∆中,𝑑1 ≥ 𝑑2 ≥ 𝑑4 ≥ 𝑑3,僅當正∆ 時,等號成立。 (2)在直角∆中,𝑑1 > 𝑑2 > 𝑑4 > 𝑑3。 (3)在鈍角∆中,𝑑1 > 𝑑2 > 𝑑4 恆成立。𝑑3與𝑑1、𝑑2、𝑑4比較,並無絕對關係,但在等腰鈍角∆,我們給出其大小順序的臨界值。 (4)在鈍角∆中,若最大內角≥ 120° ,則𝑑3 > 𝑑1 > 𝑑2 > 𝑑4。 3.在銳角∆ 及直角∆ 中,等式𝑑2=2/3 𝑑1+1/3 𝑑3和 𝑑2+1/3 𝑑1-1/3 𝑑3-1/3 𝑑4 = 𝑅 恆成立。

In silico Investigation of Cyclosporine Conjugates as Potential Anti-angiogenic Agents via NFAT Inhibition

Calcineurin (CN) activation is a main cause of cancerous tumor formation, one of the leading causes of death globally. Cyclosporine-A (CsA) is a commercially available oral drug that inhibits CN activation; however, low bioavailability limits its use. Nine patented CsA conjugates are potential alternatives to CsA as they have improved cytotoxicities and bioavailabilities but unknown CN-binding affinity. This study aimed to identify the CNinhibition strength and bioavailability of CsA conjugates in silico drug-likeness evaluation via modified Lipinski’s Rule of Five was done on CsA, voclosporin, and CsA conjugates to test bioavailability. The binding affinities of bioavailable compounds were computed via docking to CN in five trials, and the binding affinities were compared. The Water-soluble, RVal, IIA, Alpha, and MeBmt 2 conjugates showed improved bioavailabilities compared to CsA as they passed the drug-likeness screening. After five trials of computational docking to CN, the IIA and RVal conjugates showed improved binding affinities at -15.8 kcal/mol and -15.2 kcal/mol, respectively, compared to CsA at -14.3 kcal/mol. Notably, IIA also showed an improved binding affinity compared to voclosporin at -15.5 kcal/mol. These results suggest that CsA conjugates may be better oral chemotherapeutic drugs than CsA.

探討高速轉盤風切聲的性質與原理

若使氣流流經轉動的有孔圓盤,將出乎意料產生明顯的聲音。一開始我們假設聲音之來源僅為氣流被圓盤切成一段段的疏密波,並以此基礎進行後續研究。但儘管已使用吸音棉等設備,且對錄下來的聲音傅立葉分析後,卻發現現象並非想像中的簡單。這當中仍有許多無法解釋的現象值得深入探討:包含基頻之相對振幅對比泛音顯得極小、還出現了馬達與氣閥以外的噪音等等。故隨後我們滾動式修正研究方法並尋找更多理論解釋和支持,譬如運用物理引擎 COMSOL 模擬、查詢各方面文獻及理論。 歷經此探究過程,我們最後觀察到顯著的一組諧波,其基頻等為洞數乘以轉動頻率,且第 n 個振幅隨著 n 增加逐漸遞減。我們基於《Siren Harmonics and a Pure Tone Siren 》 (E. A. Milne, R. H. Fowler, 1921)中提到的的諧波模型,加上利用 COMSOL 進行模擬,最後對所觀測的諧音序列提供定性定量解釋,以及證實其他的噪音乃風切現象所貢獻。

聲子晶體結合共振腔與其聲音放大效果之研究

本研究以 zig-zag path 管道自製、設計聲子晶體,並結合空腔(cavity)形成類似電路學的 RLC 共振結構,透過 COMSOL 軟體模擬出其理論之特徵頻率,使空腔中心聲壓達到穩定的放大效果。利用無響室的環境進行實驗,藉由放大電路將聲壓轉為電訊號並以聲源頻率、裝置距離和空腔尺寸作為變因,發現我們自製的聲子晶體可成功將電壓放大約 2.6 倍。此種聲子晶體具有體積小、構造簡單、可擴充為多晶體結構等特性,在未來可結合壓電材料,將其製成兼具發電與降噪功能之環保裝置。

以海源醫材製備新穎有機無機骨組織工程複合支架

膠原蛋白植入人體易降解,在骨組織工程有許多限制,研究用水熱法萃取魚鱗膠原蛋白, 藉GPTMS(3-環氧丙基三甲氧基矽烷)為偶聯劑,交聯四乙基矽酸酯(TEOS)提供的矽網格、魚鱗膠原蛋白、低分子殼聚醣,選擇性添加具黏性多巴胺分子增強機械強度,製備兩種海洋 來源骨組織支架-殼聚醣膠原蛋白複合支架(Collagen Chitosan, CC) 及殼聚醣膠原蛋白多巴胺 複合支架(Collagen Chitosan Dopamine, CCD)。FTIR數據顯示CC支架經GPTMS作用成功產生Si-O-Si基團,CCD樣品中有多巴胺醌化學鍵結產生。NMR結果顯示CC和CCD支架順利開環 反應,證明材料成功合成。SEM可見加入多巴胺會讓CC孔洞變小、多孔結構消失。應力應 變曲線量測結果中知機械性質增強。體外實驗得骨組織支架具良好可控降解性,實驗後一個 月降解40%,支架強度約為人軟骨1/3,無細胞毒性。可嘗試免疫調節劑添加或結合其他生物 相容性材料,擴大骨組織支架應用性。

任意進位制下計數問題的公式解

對於任意正整數m和大於1的正整數p,將集合{m,m+1,...,pm-1}中的每一個元素用p進位制表示。令h為介在1到p-1的正整數,將上述集合在p進位制下有i個h的元素個數記為fh,i(m,p)。本文引進一個創新的想法,讓函數 fh,i(m,p)公式解的推導變得可行且簡單。 再者,當 p=2 時,令 fi(m)= f1,i(m,2),由公式解可以推得對怎樣的正整數n,原像集合the preimage fi-1({n})之元素個數為1。

Quantitative environmental DNA metabarcoding for the enumeration of Pacific salmon (Oncorhynchus spp.)

Understanding species abundance is critical to managing and conserving planetary biodiversity. Pacific salmon (Oncorhynchus spp.) are keystone species of cultural, economic, and ecological importance in Alaska and especially Southwest Alaska. Traditional methods of enumerating salmon such as weirs and visual surveys are often costly, time-intensive, and reliant on taxonomic expertise. Environmental DNA (eDNA), which identifies and quantifies species based on DNA they shed in their habitats, is a potential cost- and time- saving alternative. The relative ease of collecting eDNA samples also enables citizen scientist involvement, expanding research coverage. Currently, more research is required to define eDNA’s potential and limits. This project investigates whether quantitative eDNA metabarcoding can accurately quantify the abundances of six fish species: the five Pacific salmon species plus rainbow trout. Water samples were collected from eight creeks in the Wood River watershed of Southwest Alaska. eDNA metabarcoding and subsequent bioinformatics processing produced a read count for each species. These were compared to visual survey counts, taken to be the true counts for the purposes of this study. Data analyses showed a positive, linear relationship between visual survey count and eDNA count for sockeye salmon. The regressions were significant for both the early (p = 0.089) and late (p = 0.030) sampling dates when 𝛼 = 0.10. eDNA detections of non-sockeye species generally corresponded to visual survey observations of species presence or absence. Overall, the results of this study support eDNA’s potential to be an alternative or supplement to standard methods for the enumeration of fish species.

Unraveling a Transcriptional Enigma: Exploring the Action Model of the Concealed BPC Network on the Circadian Oscillation System玄機暗藏: 深究轉錄因子家族BPC對晝夜節律系統之作用模式

這項研究深入探討阿拉伯芥生理時鐘的轉錄調控機制,關注植物特有 GAGA 結合因子, BASIC PENTACYSTEINEs(BPCs)。通過監測 BPC 突變株和誘導株的葉片運動,及對 BPC 突變株生長缺陷的觀察,推測 BPC 於節律運動和葉形表徵扮演調控要角。藉數學建模和對突變與誘導株的 qRT-PCR 實驗,我揭示第一及第二類 BPC 在協調生物鐘節奏和葉片發育中的多種功能,更描述 BPC 內部調控網絡,了解這些蛋白質如何維持恆定。突變株實驗突顯 BPC 對關鍵時鐘成員 CCA1、ELF4、GI 和 PRR 家族的精確控制,而誘導株實驗則繞離 BPC 家族內部的補救途徑,從不同的尺度提供更直觀的檢驗方法。模擬進一步闡明 BPC 如何微調時鐘,確保振盪最佳化和晝夜間的無縫過渡。此外,我還發現 BPC1 和 BPC3 對第二類 TCP 基因的影響。他們抑制除 TCP5 外的多數 TCP 基因,透過不同下游途徑影響葉緣形態。概括而言,這項研究揭示了 BPC 家族是生理時鐘和葉片發育途徑的關鍵調控者。

探討鐵鎳合金催化劑對電解產氫之影響

目前大部分電解產氫反應(HER)均使用貴金屬,如鉑和鈀,作為催化劑。而我們提出了更便宜的 FexNiyP 金屬磷化物用於經濟製氫。在催化劑的製備中採用不同的化學成分(x/y 比例)和合成條件(氧化溫度)。並將合成樣品通過掃描式電子顯微鏡(SEM)、能量色散 X射線光譜(EDS)和 X光繞射儀(XRD)進行了鑑定,以確認其形態、成分和晶體結構。再通過線性掃描伏安法(LSV)測試了它們的 HER催化效率。實驗結果發現,磷化程度強烈影響催化性能,且可以通過合成條件來適當調整,而 250° C是最佳氧化溫度。此外,電化學測試顯示,FeP 啟動反應所需之能量最低,具有最低的過電位(overpotential);而 NiP 反應路徑最佳,具有最低的塔菲爾斜率(Tafel slope)。我們的結果解決了 HER的反應機構,並對氫燃料生產的發展提供了有用信息。

Silver nanoparticles-loaded titanium dioxide coating towards immobilized photocatalytic reactor for water decontamination and bacterial deactivation under natural sunlight irradiation

The environmental implications of rapid industrialization, including rising pollution, depleted resources, the effects of climate change brought on by global warming, and unrestrained groundwater extraction, are contributing to a growing water scarcity crisis [1-3]. The improvements in quality of life are largely attributable to the innovations in manufacturing technology made possible by the Industrial Revolution, but these innovations also pose risks to the natural world and human health [1-3]. The textile business uses a wide variety of raw materials, including natural fibers like cotton as well as synthetic and woolen fibers, and the chemical components of dyes are just one example. The annual output of synthetic dyes is around 700,000 tons, and there are over 10,000 different varieties available. As much as 200,000 tons of synthetic dyes are released into the environment every year due to the inefficient dyeing technique commonly employed in the textile industry. According to the World Bank, the processing of textiles for dyeing and finishing accounts for between 17 and 20 percent of industrial wastewater [1-3]. Textile wastewaters contain a high biological oxygen demand (BOD), chemical oxygen demand (COD), nitrogen, color, acidity, high suspended particles, high dissolved solids, surfactants, dyestuffs, heavy metals, and other soluble chemicals [3] due to the variety of dyes used to color textile items. In particular, water-soluble reactive and azo dyes are employed to obtain the required color. Ten to twenty percent of the dyes used end up in the effluents, where they might harm wildlife and the ecosystem (carcinogenic or mutagenic). Headaches, nausea, skin irritation, respiratory difficulties, and congenital deformities are only some of the health problems linked to exposure to textile wastewater. There are repercussions for aquatic ecology, environmental biodiversity, and the quality of receiving water bodies. New, low-cost, and highly effective water treatment methods are needed to deal with polluted wastewater. Adsorption and coagulation, two common water purification methods, just concentrate pollutants by shifting them to other phases; they do not "eliminate" or "destroy" them. Sedimentation, filtration, chemical oxidation, and biotechnology are all examples of conventional water treatment methods, but they all have their drawbacks. These include insufficient removal, high chemical reagent consumption, high treatment costs, long treatment times, and the creation of toxic secondary pollutants. New water treatment procedures are needed to improve the quality of treated effluent [1-3]. The use of semiconductor particles in photocatalysis is gaining appeal as a solution to global pollution problems due to its shown efficiency in degrading a wide variety of contaminants. Photocatalyst-coated surfaces-based reactors have proven to be practical for long-term operation over photocatalytic powder-based reactors (i.e., slurry-based reactors) [4-5]. As a promising photo-electrode and photocatalyst, titanium dioxide (TiO2) has enjoyed wider applicability in photocatalytic hydrogen generation, solar cells, and remediation of organic contaminants among other photo-catalytic applications [4-6]. TiO2 has been recognized as one of the low-cost, most effective, and fascinating photo-catalyst as a result of its interesting thermal and chemical stability, desirable electronic features, others, and environmental benignity [6-8]. Pristine TiO2 semiconductor is characterized by a wide band gap that can only utilize the UV part of the light spectrum with a wavelength of less than 385 nm, which is just 5% of the sunlight energy capacity. Spectrum usability extension to visible regions warrants further and extensive research study [8-10]. Additionally, the quickness of the recombination of photo-generated holes and electrons further restricts the practical applicability of the semiconductor [10-12]. It is highly desirable to develop a cost-effective scalable strategy to over these drawbacks toward sustainable development and a clean environment using only natural sunlight irradiation [5-11]. In addition, it is preferred to fabricate them as films rather than powders as photocatalytic immobilized reactors are more practical than powder-based reactors [4-8]. Dye sensitization, supports, magnetic separation, and surface modification by doping with non-metals, metals, and transition metals and coupling with other semiconductors have all been used to enhance the photocatalytic activity of TiO2 photocatalyst. Higher photonic efficiency can be attained through the synergistic fine-tuning of features such as physical, chemical, and electronic, and these composites and hybrid materials based on TiO2 are creating a big trend. Doping has been widely studied as a means of altering the surface of TiO2. Rare earth metals, noble metals, and transition metals are all discussed in the existing literature on the surface modification of TiO2 doped with cations [4-12]. In this study, for the first time, Ag nanoparticles loaded mesoporous TiO2 coating was prepared and applied as an immobilized photocatalytic reactor for water decontamination and bacterial deactivation under natural sunlight irradiation.