張鎮華教授在文章[4]中介紹威氏遊戲(Wythott’s Game):文章中提到安全殘局所成的集合Sw為 {(1,2),(3,5),(4,7),(6,10),(8,13),(9,15),(11,18),(12,20),(14,23),(16,26),…}。將這個集合中元素第一個座標的數所成的集合命名為A,而將第二個座標的數所成的集合命名為B,設其為A={a1, a2, a3,…}, B={b1, b2, b3, …}, 可以發現集合A和B滿足性質(1) A∪B=N ; 性質(2) A∩B=ψ;性質(3)數列是等差數列 ( bk- ak, k=1, 2, 3,…)。在這個研究計劃中,可以分成數學與遊戲兩部份:(一)數學部份:我們從不同的角度來介紹下列四個集合,並證明它們都相等。1.令{αs |集合S(αs )T(αs )= N?S(α)={[k(αs + s)] | k =1,2,3,…}滿足性質(1), (2), (3)},其中S(αs)={[kαs ] | k =1,2,3,…},T(αs ) = N?S(α)={[k(αs + s)] | k =1,2,3,…}。2.{αs | ([kαs ] ?[(k ?1)αs ] = 2 k=1+ (s ?1)n + [nα]), s=1,2,3,…}。3.{αs | 1/αs +1/(αs + s) = 1, s = 1,2,3,...}。4.{(2- s+√S2+ 4) / 2 | s = 1,2,3,...}。(二)遊戲部份:研究變型(第二型)威氏遊戲和推廣的三排威氏遊戲,利用我們學會的方法來找及證明這兩個遊戲的所有有利位置。下列三個集合都相等,同時它們都和上面的集合有密切的關係5.{X | X ?1/ X = [X ]}。6.{Xs | Xs- 1/Xs= s, s= 1,2,3,...}。7.{(s+√s2+ 4) / 2 | s = 1,2,3,...}。
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太陽短期活動對地球磁場與大氣溫度異常的影響
This study analyzed how short-term solar activities interact with the earth atmosphere, by using two statistic methods: Diffusion Entropy Analysis (DEA), and Standard Deviation Analysis (SDA). Since solar activities influence the Earth atmosphere in its radiating heat and magnetic field, we use DEA and SDA to calculate the exponents, H and δ, of the scaling law in three time series: “the intensity of solar flare” (representing by SOLAR H-alpha flare index), “magnetic anomaly of magnetosphere” and “sea surface temperature anomaly”. The values of H and δ show the time memory and correlative relationship between the event and next event happening in time series. When H = δ = 0.5, events occur in random. When 0.5
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Effects of Macromolecular Crowding on Model in vitro Antigen-Antibody Reactions
Many biological processes in the human body take place in intracellular environments under crowded conditions. This means that such cellular activities occur in the presence of inert macromolecules. These macromolecules are thought to have large effects on reaction rates and equilibria. However, under conventional conditions, these same processes are studied in vitro under uncrowded conditions in dilute buffers and therefore not reflective of physiological conditions. Hence, this project aims to study the effect of macromolecular crowding on antigen-antibody reactions in an attempt to mimic intracellular environments. It also aims to highlight the importance of introducing crowders as a factor of study in conventional in vitro experiments involving cellular reactions. The model reaction investigated involves human collagen type 1 on skin samples and specific antibodies against these antigens. Inert macromolecules of defined hydrodynamic radius and charge were added into the reaction media while quantitative tests are conducted to determine the effect of crowding on the rate and extent of reaction. The macromolecular crowders used were Dextran Sulphate, Ficol170, Ficol1400 and Polyvinylpyrrolidone360. Results were than analysed with the Metamorph 7 imaging system to determine signal strength under crowded and non-crowded conditions. At high primary antibody dilutions, skin samples incubated with a primary antibody solution crowded with a combination of inert macromolecules showed improve signal strength. This could be because crowding tends to shift reaction equilibria such as to minimise the amount of excluded volume, leading to association of the antigen and its specific antibody. This is known as the excluded volume effect. In addition, crowding the primary antibody solution helped increase the rate of reaction. The results also suggest that the addition of crowders may reduce the amount of antibodies needed per sample and decrease the necessary incubation time. Therefore, antigen-antibody reactions can be done more cost-effectively, However, the presence of charged macromolecules such as Dextran Sulphate has an inhibitory effect. Further work is also needed to establish whether macromolecular crowding enhances specificity and thereby reduce autoflourescence of the skin sample.
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