抗癌藥物的研究一直受到重視，吲哚(indole)衍生物可助抵擋自由基，而二吲哚(Di-indole)衍生物已成為抗癌劑。鈣離子/鈣調蛋白依賴性蛋白激酶 (Ca2+/calmodulin-dependent protein kinase II，CaMKII)之抑制劑為癌症標靶藥物重要研究方向之一，抑制CaMKII可降低各種癌細胞增殖和存活，但目前尚無CaMKII抑制劑藥物。本研究以三吲哚為主架構，發展衍生物作為CaMKII抑制劑，期望可應用於抗癌劑。電腦軟體Discovery Studio2016模擬各種三吲哚衍生物分子模型與CaMKII α(PDB: 2VZ6)之結合能，選出結合能較大之化合物3，並延伸結構/活性(SAR)最佳化，進行一系列高效率藥物合成純化工作。經由送測生物細胞活性，其中先導化合物(lead compound) 3-1對癌細胞之毒性高且對CaMKIIα的抑制效果佳，符合癌症治療上的需求，將繼續最佳化此結構，並進行細胞訊號傳送途徑及動物實驗。

阿茲海默症(AD)是導致失智症的主因，影響全球數千萬人。然而，AD目前的藥物大多昂貴且療效有限。目前已知腦內β類澱粉蛋白(Aβ)斑塊為AD的病理特徵，且大腦清除系統被認為對AD的治療具有重要性。先前研究發現非侵入性迷走神經刺激術(nVNS)增加腦脊髓液循環，但在神經退化疾病中的機制和應用尚不明確。本研究旨在探討nVNS增強大腦清除系統來作為AD新療法之成效，使用Aβ誘導之AD小鼠模型，利用巨視顯微鏡和免疫組織化學染色評估其膠淋巴系統功能，並以新奇事物測試評估認知功能。本研究發現於AD小鼠中，給予nVNS使大腦清除系統之水通道蛋白-4顯著增加、促進膠淋巴系統，進而改善認知功能。本研究首次發現nVNS可通過增強大腦清除系統功能，進而改善AD病理引起的失智症狀，支持nVNS作為AD新療法的可行性。

本研究使用柔性PET基板，並將Al2O3沉積於明膠上作為介電層，製作電阻式記憶體-Al/gelatin/ITO-PET元件（AGI柔性元件)，期望提升基板的可撓性，同時維持元件的基本運作模式。為檢測元件性能，本研究分別在平面及彎曲狀態下測量其電性。透過施加循環電壓於AGI元件，測繪其電流變化圖，並分析元件不同操作狀態下（平面、固定彎曲、動態彎曲）的電性穩定度。研究結果顯示，AGI柔性元件在每次循環間電流變化小，且在不同半徑的 動態彎曲測試中，電流－電壓（I－V）疊合圖的開關比均呈現穩定。綜上所述，AGI柔性元件在兩種彎曲狀態下能夠展現低切換電壓與穩定的開關性能，加上明膠的生物相容性和優異性能，表現出其在穿戴式記憶裝置的發展潛力。

本研究先觀察著名的密克定理（Miquel theorem）與密克點（Miquel point），我們創新給出了新的研究項目，關注密克點𝑃與密克三角形的頂點所構成直線和原三角形𝐴𝐵𝐶三邊直線的其餘六個交點，這是前人沒有觸及的研究項目，從而定義旁接三角形與衍伸三角形。 我們先針對特殊型（直角）的構圖，發現滿足兩個衍伸三角形的有向面積 [𝐴1𝐵1𝐶1]=±[𝐴2𝐵2𝐶2] 時，𝑃 點形成的軌跡為原三角形的 Kiepert hyperbola 與外接圓，這個是有趣且重要發現，我們也進一步給出其幾何必然性。進一步考慮 [𝐴1𝐵1𝐶1]=𝑟[𝐴2𝐵2𝐶2] 時，則刻劃出 𝑃 點軌跡為圓錐曲線系。在前面的基礎下，再針對一般型（任意角）的構圖，若 𝑃 點位於原三角形外接圓及Kiepert hyperbola 與 Steiner circumellipse 的線性組合曲線上，此時兩個衍伸三角形 𝐴1𝐵1𝐶1 與 𝐴2𝐵2𝐶2 的有向面積比值為定值，且兩者恆為相反數。

One of the worldwide hidden problems with lack of attention is Bedsores. Simply, These are ulcers, that happen on the areas of the skin that are under pressure while lying on the bed for a prolonged time. This can be infected to anyone in the world. The common group who face these bed sores are..... •Elderly patients, •Spinal cord injury patients, •Stroke patients, •Coma patients, •People who have faced accidents Bed sores develop when the blood supply is cut off for more than 2-3 hours to the skin, (Position changing time depends on the patient's condition) The continuous pressure is the cause for that and also the temperature generated between the skin and the bed surface increases the metabolism of the tissues. When the skin temperature increases by 1°C, the risk of bed sores increases approximately 14 times. So, The skin temperature in the range of 29.4°C to 37.1°C is correlated with the tissue damage score. Not only that shearing and moisture are the other considerable factors for this problem. This infection has 4 stages. Sometimes in the 4th stage of the bed sores can cause death.

本研究在探討數學雜誌《Crux Mathematicorum》2024年公告的題目MA 288.所產生的方格紙圖案分布的規律。我們先解開該題，並透過繪製與分析不同大小的圖形，觀察圖案的規律，並利用此規律求出第 𝑛 列及前 𝑛 列綠色方格數的遞迴關係與一般式。 我們發現在𝑛×(𝑛+1) 的方格紙中，當𝑛為2的次方時，綠色方格圖案會形成一個類似謝爾賓斯基三角形的完整三角形，且每當𝑛增加2的1次方時，綠色方格圖案會利用自我複製的方式形成新的圖案。因此可以把𝑛轉換成二進位的表示法，利用二進位中1的位置與數量推論出方格圖案的樣貌與綠色方格數。 除了利用塗色的方式觀察規律外，本研究還將原問題條件轉換成不同的敘述，方便利用excel繪製圖案，將問題推廣到𝑛×𝑚方格。

Retail inventory management is a crucial part of many businesses due to the high profit associated with it as well as the uncertainty around it, especially for industries with short production cycles and a complex supply chain.Proper management ofretail inventories can lead to decreased inventory costs, prevent spoilage and obsoles- cence, and improve customer satisfaction, all of which lead to increased profits for the company.Inthispaper,wefirstproposeextendingawell-knowninequalityandtry to generalize it to other conditions and similar inequalities.The inequality involves multiple variables and how the maximum/minimum values of a subset of the numbers compare to the maximum/minimum values of the whole set of numbers.Our main contribution is applying such inequality in inventory management to help estimate the total cost of inventory management, which would allow us to determine the shutdown pointforaspecificcompanyusingthegeneralizationsoftheinequality.Lastly,weshow thatourestimatesarereasonableandproposesomefutureareaswheremoreworkcan be done.

An exploration of Pachyrhizus erosus as an option for plant-based milk in the 印尼n market for people with lactose intolerance. With its prevalence in tropical climates, Pachyrhizus erosus is an affordable crop in 印尼. Pachyrhizus erosus is a root vegetable containing a calcium content of 15.6 mg per cup (130g) in its unprocessed form, concentrated in its white flesh. Based on its affordability and calcium content, Pachyrhizus erosus can be transformed into a beverage product with nutritional qualities on par with existing plant-based milk, therefore being a solution for calcium sustenance that is more accessible due to its high capability to be locally grown in 印尼. However, this may be a partial case as Pachyrhizus erosus only thrives in regions with long warm seasons. In this research, three trials of Pachyrhizus erosus-based milk recipe have been conducted Trial 1 consists of a 1:1 ratio of Pachyrhizus erosus to water, Trial 2 consists of a 2:1 ratio of Pachyrhizus erosus to water, and Trial 3 consisting of a 10:10:1 ratio of Pachyrhizus erosus to water, and to a small amount of soybean. Based on the results of 14 organoleptic test respondents, it is concluded that the best ratio of ingredients is 10:10:1 (water: Pachyrhizus erosus: soybean) due to an overall preference of the third trial with this ratio, in terms of taste, aroma, color, and consistency. Pachyrhizus erosus is the dominant ingredient in developing alternate plant-based milk. However, findings from the most preferred trial in the organoleptic test suggest that implementing a minor amount of soybean would stabilize the milk-like consistency and flavor. Pachyrhizus erosus’ ability to retain calcium in its water content has been additionally proven in a calcium test using a reagent solution of ammonium oxalate, as even with the trials’ step of straining the liquid content of Pachyrhizus erosus that had been blended with added water, all three trials tested positive based on the high level of the precipitate. Other tests that tackle the quality of each trial include In Silico Testing, biuret protein test, alcohol test, COB test, and pH level testing.

This study primarily investigates the components of food residues in the stomach of flying squirrels and the metabolism of the intestinal bacteria Floricoccus tropicus. Using nuclear magnetic resonance (NMR) hydrogen spectrum analysis, the signals of long-chain fatty acids were detected in both n-hexane and 75% ethanol extracts of flying squirrel gastric residues and acorns, suggesting that acorns may be a primary food source for the flying squirrels. The study also identified Floricoccus tropicus, one of the lactic acid bacteria, from the intestines of flying squirrels and discovered its role in the metabolism of fatty acids in acorns. Results showed that polyunsaturated fatty acids significantly decreased during fermentation, indicating that they were converted into short-chain fatty acids with anti-inflammatory properties. In the antibacterial activity experiments, the acorn grease showed no inhibitory effects before fermentation, but after fermentation, the acorn grease exhibited inhibitory effects against E. coli. Furthermore, in anti-inflammatory tests, fermented acorn grease samples significantly suppressed the production of NO and TNF-α in LPSinduced RAW 264.7 cells, with greater inhibition at higher concentrations. In conclusion, the lactic acid bacteria Floricoccus tropicus was found to metabolize fatty acids of acorns into compounds with antibacterial and anti-inflammatory effects.

In2013,Adamsintroducedthen-crossingnumberofaknotK,denoted by cn(K).Inequalities between the 2-, 3-, 4-, and 5-crossing numbers have been previously established.We prove c9(K)≤c3(K)−2 for all knots Kthat are not the trivial, trefoil, or figure-eightknot.Weshowthisinequalityisoptimalandobtainpreviouslyunknownvalues for c9(K).

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。

One of the main challenges with today’s batteries is their relatively low volumetric and specific capacities. The highest specific capacity can be achieved with lithium-air batteries, which use metallic lithium as the anode and typically some form of porous carbon as the cathode. To enhance performance, aerogels—among the world’s lightest solid materials—are ideal candidates for cathodes. Resorcinol-formaldehyde (RF)-based carbon aerogels, for example, serve this purpose well. In my work, I utilized two types of carbon aerogels as cathode materials: one derived from pyrolyzed resorcinol-formaldehyde polymer and the other a graphene-oxide-modified version of this carbon gel. I integrated the carbon aerogels I had pyrolyzed into lithium-air batteries to improve the cell’s performance, energy density, and capacity compared to cells using activated carbon. In my research, I examined the pore structure and surface properties of these materials in aqueous media using NMR (nuclear magnetic resonance) relaxometry and cryoporometry, exploring their impact on battery efficiency. I found that the graphene-oxide-containing sample's pores filled with water in a layered manner, indicating a more hydrophilic surface, which suggests a denser arrangement of oxygen-containing functional groups compared to the unmodified carbon aerogel. The pore sizes were reduced after adding graphene oxide, resulting in an increased specific surface area for the sample. Incorporating the reduced graphene-oxide-containing carbon aerogel enabled the creation of a more efficient, higher-capacity battery than with the RF carbon aerogel. This improved performance is likely due to the aerogel’s higher oxygen content and altered morphology. The increased oxygen content provides more active sites for oxygen reduction, meaning that a greater specific power output can be obtained from the battery.