關於1234-，2143-，3412-Avoiding Involution排列的統計量探討
令Sn 為{1,2,…,n}任意排列所成的集合，π ? Sn 為其中的一個元素，我們記π = (π(1), π(2),…, π(n))。今給定π ? Sn ，若對所有i,1? i ? n，都有π (π (i)) = i 時，我們稱π 為involution。假設π ? Sn ，並給定σ ? Sm (m ? n)，當π 中任取m 項，其大小關係的順序都和σ 不同，我們稱π 避開σ，或稱π 是一個σ-avoiding 排列。在這篇報告中，我們主要分析了2143-avoiding involution，1234-avoiding involution，和3412-avoiding involution 中的一些統計量，給出了十數個結果與幾個猜想。Let Sn be the set of permutations on {1,2,…,n} and π ? Sn be an element in Sn. Denote π as π = (π(1), π(2),…, π(n)). We say that π is an involution if π(π(i)) = i for every i, 1? i ? n. Given π ? Sn and σ ? Sm (m ? n) , we say that π avoids σ (or π is an σ-avoiding permutation) if π does not contain any m-term subsequence in the order of σ. In this paper, we discuss some classic statistics on 2143-avoiding involutions, 1234-avoiding involutions and 3412-avoiding involutions. We get many new results in this field and give some interesting conjectures.
巨型小翼效應—未來長程客機經濟省油妙方
本研究主要是探討翼端小翼對飛機飛行的影響，翼端小翼在現在不少的飛機上都有這種設計，假設小翼可以阻止飛機機翼末端的氣流上旋，進而增加升力與推力，讓飛機能提高飛行時的效率，為了驗證這個假設，因此製作了簡易風洞對小翼的升力與阻力進行定性和定量的探討。升力與阻力的定性定量探討是經由10 組主機翼與五個小翼組合，共有2000 次的測試記錄，再轉化成折線圖予以比較研究，而得到一個穩定性數值結果。這測試實驗的數值結果顯示：小翼可以增加升力，但是也會增加阻力，為了降低阻力，小翼的剖面最好是有弧度。The purpose of this research is to find out the effect resulted from the winglet of the plane to the flight. Many a winglet is nowadays designed for the airplane. Assumes the winglet can stop the air of the tail section of the airplane to revolve up, further increase the force of the raise and the push, and uplift the efficiency of the flight. In order to proof this assumption is correct, so makes an easy air hole to do the research of qualitative and quantitative analysis for the force of the raise and resistance. After about 2000 records tested through the combination of ten sets of the main wing and five tiny wings, and transference of curve diagram , we get a steadily value result. This test result appear the first the winglet can increase the force of the raise, and so do the resistance, and the second to have the force of the resistance decreased, it might be better the section of the winglet is not straight but circular.
台灣兒科病人罹患神經母細胞瘤者可檢測到微小病毒B19的存在
罹患神經母細胞瘤的兒科病人，尤其是罹患stage IVs 神經母細胞瘤者，他們有些伴隨著非常嚴重的貧血，但卻檢測不出神經母細胞瘤已經侵犯骨髓；有時病情來勢洶洶，尤其是腫瘤細胞中已可偵測到N-myc 基因增幅者，診斷時腫瘤細胞可能已在腹腔四處擴散並已侵犯大部分的肝臟。但是，某些這種病患，特別是腫瘤細胞中N-myc 基因沒增幅者，即使在沒有治療的狀況下卻可能有自然恢復的現象，也就是腫瘤細胞會自動消退，但原因仍待進一步的證實與探討。可是，這些病人在其病情最嚴重的時候，骨髓內紅血球母細胞形態上的改變顯示可能與病毒感染有關。但是關於病毒來源的研究，現有的資訊仍然十分有限，其中最重要的是，病毒感染與引發其後天之免疫作用是否有關，更需要深層的研究。因此，為更進一步了解罹患神經母細胞瘤之兒科病人的病毒感染及病毒蛋白表現的作用，我們這次研究的目的在檢驗罹患神經母細胞瘤及貧血之兒科病人與微小病毒B19 (PVB19)、Epstein-Barr Virus (EBV)、腸病毒71 型(EV 71)和巨細胞病毒(CMV)的關係，以及病毒蛋白表現對這些病人的作用與臨床意義。In pediatric patients with neuroblastoma, in particular, those with stage IVs neuroblastoma, sometimes the disease was combined with severe anemia. However, no tumor involvement was detected in the bone marrow. Although some of these patients may have N-myc gene amplification, and the disease could have invaded many abdominal organs, especially liver, interestingly, the disease might regress spontaneously in some of these patients. The medical reason of the spontaneous regression, nonetheless, remains to be determined. It is worth noting that morphological changes of erythroid progenitor cells in the bone marrow have suggested virus infection in these pediatric patients. However, the available information of viral origin is limited. Furthermore, it is possible that the virus infection in these patients could be associated with the revocation of immune responses related to the spontaneous regression of the tumor. In this study we will investigate the relationship of parvovirus B19 (PVB19), Epstein-Barr virus (EBV), enterovirus 71 (EV71) and cytomegalovirus (CMV) with neuroblastoma by PCR in Taiwanese pediatric patients. Moreover, we will study the effect and the clinical significance of viral gene expression as well as N-myc gene amplification in these patients.
可表為兩個平方數和的一種特定型式的數及其性質推廣研究~「Concatenating Squa
給定下面範例：\r 058823529411764705882 +235294117647058823532\r =0588235294117647058823529411764705882353，\r 其等式結果與質數17 的倒數結果(1/17)有某種關聯(卻沒有一個決定性的證據)，意即\r 1/17=0.0588235294117647=\r 0.058823529411764705882352941176470588235294117647...... ( Len(17) =16 )\r \r 曾經在下列網站上發現過幾組數字(挑戰試題)，引起我們極大的興趣。\r http://www.domino.research.ibm.com/Comm/wwwr_pondernsf/challenges/March2000.html\r http://www.math.smsu.edu/~les/POW08_96.html\r \r \r The two examples that I have are 0588 2+23532=05882353 and 058823529411764705882+23529411764705882353 2=0588235294117647058823529411764705882353 These were found by the Canadian professor Alf van der Poorten, and he gave a talk on these identities in December at the west coast number theory conference. He was unspecific as to exactly where these identities were coming from, but they are connected with reciprocals of primes:1/17 = 0.0588235294117647= 0.058823529411764705882352941176470588235294117647 ΛΛ ( Len(17) = 16 ) Though not mentioning how to obtain these equations, Prof. Poorten demonstrated the relationship between the above examples and the reciprocal of the prime numbers 17 (1/17 ) without a definitive proof.
Synthesis, Characterisation, and Temperature-sensitivity of Hydroxyl-Terminated Poly(N-isopropylamid
Background:\r Delivery of anticancer drugs in vivo can be achieved by using targetspecific\r drug carriers of various types – e.g. microspheres and liposomes –\r which can be applied intravenously, or subcutaneously via a hypodermal\r patch, etc. as appropriate to the type of drug carrier employed. Recently,\r interest has surged in the usage of amphiphilic polymeric micelles for this\r purpose, as they prove superior to other drug carriers in many ways. They\r have highly-hydrated hydrophilic shells, and hydrophobic cores wherein\r hydrophobic anticancer drugs such as adriamycin can be encapsulated\r during transport in the blood. Their main advantages include their\r smallness of size – enabling them to elude capture by the\r reticuloendothelial system (RES) – their stability in the bloodstream as\r shown in their low critical micelle concentration (CMC) values, their\r passive targeting of tumour sites via the enhanced permeability and\r retention (EPR) effect, and their ability to integrate an active targeting\r mechanism, e.g. antibody-antigen recognition, pH-sensitivity, etc.
由嘉義地區的氣象資料來探討二十四節氣與聖嬰現象
二十四節氣是中國古代對氣象觀測的智慧結晶，由於近幾年來聖\r 嬰與反聖嬰現象的影響，在透過嘉義氣象觀測站的協助之下，利用\r Excel 進行簡易的雨量和氣溫統計，並配合中央氣象局發布的環流型\r 態和農業災害，來探討二十四節氣在嘉義地區的適用性。\r 以陽曆來區分節氣，每年會誤差6 小時，加上四年一閏，剛好彌\r 補差距，農曆則需19 年。至於聖嬰現象對嘉義地區則呈現涼夏和暖\r 冬，但在反聖嬰現象中則變為加強四季之特性，即是熱夏與寒冬。兩\r 者都造成雨量集中夏秋兩季，形成冬春乾旱。至於二十四節氣則是以\r 夏、秋的氣溫和雨量相關的諺語較適合嘉義地區。\r Abstract\r The 24 Solar Terms, is the achievement of weather observation from\r ancient China. Because of the effects from El Nina and La Nina these\r years, we proceed simple statistics of rainfall and temperature by using\r Excel and the assistance from Chia-yi Weather Station. We adopt the\r Circulation Type and the damage of agriculture from Central Weather\r Bureau, to discuss if the 24 Solar Terms for in Chia-yi area.\r To divide the 24 Solar Terms according to the solar calendar, there’ll\r be a six –hour gap every year. The gap could be made up every four years.\r But with the lunar calendar, it takes nineteen years to offset. The El Nina\r shows cool summer and warm winter in Chia-yi area, but the La Nina\r emphasizes the characteristics of the four seasons. It shows hot summer\r and cold winter. Both of them rain mostly in summer and fall, and cause\r the drought in winter and spring. The saying of the 24 Solar Terms is\r suitable for the temperature and the rainfall during summer and fall in\r Chia-yi area.
電解與磁場的秘密.
金屬離子在磁場中的流動速率會略有改變，尤其是在強磁場中時，其影響更是顯著，即 【MHD 磁流動效應】，造成整體電解液中離子的流動，此流動比擴散速率佔優勢。再利用「磁 矩」具有向量性質，探討不同金屬離子（Na+、K+、Fe3+、Al3+、Mg2+）及MnO4 -在磁場角度 相同但強度不同的情況下；及磁場角度不同但強度相同的情況下，對電解速率的影響。 經實驗發現有以下結論： 一、由法拉第電解第一定律出發，加以實驗數據分析，可推導出一關係式： 電解速率Rρ= k ×∫〈∣H 向量∣×∣cosθ∣〉×∣E 向量∣ （k 單位：g / C˙weber˙s） 二、電解效率隨價數增高而增快。 三、較強的電解質，其對磁場的感應也越大，如果就同一族而言，往 下其活性越強，對磁場的感應也越強。 The flowing rate of Metal ion changes slightly in magnetic field. This influence is especially remarkable while the magnetic force is very strong, that’s【MHD (magneto Hydrodynamic Effect ), which gives rise to ionic flowing all over the electrolyte. This flowing rate is superior to expanding rate. Further, basing on the magnetic torque ’s vector trait, this research studies how electrolysis velocity affects different metal ions (Na+、K+、Fe3+、Al3+、Mg2+) and MnO4 － under following situations: Some results are found through the experiment. 1. Begin with Farad Electrolysis First Law, and take the experimental analysis into account, then a relative formula comes out as bellow. Electrolysis Rate Rρ= k ×∫〈∣H∣×∣cosθ∣〉×∣E∣ （k：g / C˙weber˙s） 2. Electrolysis efficiency accelerates by the increasing price amount. 3. Active electrolytes get strong response to the magnetic field. For the same group, the more active the electrolytes are, the stronger it responds to magnetic filed.
無機砷與硒對染色體傷害之交互作用
中文摘要 重金屬對人體傷害的無遠弗屆-人人皆知，根據流行病學的研究指出，長期處在 重金屬含量過高之地區，易造成生理病變。比方說，長期生活在砷含量高的環境中， 易導致肝臟、周邊血管及神經系的損害，各種癌症的發生機率也大為提高。 本實驗以中國倉鼠卵巢細胞（CHO-K1）為材料，利用微核偵測技術(Michronuclei, MN)及姐妹染色分體互換(Sister chromatid exchanges, SCE)之誘引來探討亞硒酸鈉 (Sodium selenite, NaSeO2) 及亞砷酸鈉(Sodium arsenite, NaAsO2) 的交互作用 (interaction)。實驗結果顯示亞硒酸鈉本身不會造成MN 的增加，但讓SCE 頻率增加； 亞砷酸鈉會誘引增加MN 和SCE。亞硒酸鈉前處理不會減少亞砷酸鈉誘引之SCE 和 MN，但可微微降低亞砷酸鈉抑制雙核細胞(Bunucleated cells, BN)的形成，但是不明 顯。本實驗結果未能看出亞硒酸鈉前處理與亞砷酸鈉有明顯的交互作用，但發現亞 硒酸鈉會增加SCE 頻率，因此亞硒酸鈉做為保健食品值得進一步的關切及探討。 英文摘要 It is well-documented that exposure to heavy metals could cause seriously adverse effects to humans. Epidemiological evidence has shown that illness is frequently observed in residents living long-term in heavy metal contaminated area. For example, arsenic exposure was associated with increased incidences of liver diseases, peripheral vascular and neurological diseases, as well as cancers. In this report we investigated the interaction of selenite and arsenite on micronuclei (MN) and sister chromatid exchange (SCE) induction in Chinese hamster ovary-K1 (CHO-K1) cells. The present results demonstrated that sodium selenite by itself did not induce MN, but it did cause the increase of SCE frequency. Sodium arsenite significantly induced MN and SCE in CHO-K1 cells. Pretreatment of CHO-K1 cells with selenite could not reduce MN and SCE frequency induced by arsenite, but slightly prevent the cells from arsenite-induced inhibition of binucleated cell formation. In the present study, no significant interaction between sodium selenite pretreatment and sodium arsenite was observed. However, sodium selenite was unexpectedly found to enhance SCE frequency in CHO-K1 cells. The application of selenite as health protection agent warrants our concerns and further investigation.