超通用水分子形交換方塊之FPGA設計
本研究提出一個新的超通用、每邊w個端點的四邊形水分子形交換方塊(Water-Molecule-Shaped Switch Block; WMSB)架構,以應用在FPGA之多點連線(multipoint interconnection)和諸多交換網路的設計上。超通用交換方塊(HUSB)的領域中,Fan[2]提出當前唯一一個(4, w)-HUSB,但Fan’s (4, w)-HUSB所需的開關個數大約是6.3w個開關,在接下來的篇幅之中,我們將證明(4, w)-WMSB是只需6w個開關的HUSB;此外,我們還證明沒有(4, w)-HUSB可以使用小於6w個開關。本研究中還使用VPR(一種CAD)及其內建的大量標準線路以證明(4, w)-WMSB不僅是理論上最佳的亦是實用性佳的交換方塊。鑑此,(4, w)-WMSB開關效率高(switch-efficiency)的設計十分適用於其他的交換網路設計,如公共電話網路(Public Switched Telephone Network)。
Application of molecular templates on magnetic particles for adsorption and desorption of heavy metals
This study investigated the production of novel molecular templates, and analyze their adsorption effect on four heavy metal ions (Cu+2, Pb+2, Zn+2, Mn+2), which commonly exist in Taiwan's rivers. Different operating conditions (such as competitive adsorption, pH value and other factors) were explored to compare their adsorption effect of heavy metal ions by using the synthesized template molecules. The molecular templates were found to be specific towards their target metal ions with a high adsorption effect. Then combined with the idea of magnetic particles to produce magnetic molecule templates, a maximum amount of adsorption of heavy metal ions up to 95% through the molecular template was achieved while the effect of heavy metals desorption of up to 83% could be also successfully obtained. Experimental results showed that the magnetic molecule templates did not affect the adsorption of heavy metal ions. Not only can they speed up the recovery time of adsorption but the template molecules can also be collected more efficiently. We also proposed three different applications for the developed molecular templates. The development of magnetic molecular template may provide an affordable, highly-efficient way for dealing with heavy metal pollutions.
二維及三維不完整堆垛方法數之研究
從堆垛金字塔發想,定義了「不完整堆垛」。 一、底列個數n之二維不完整堆疊方法數P(n)=1/√5[(1+√5/2)2n-1-(1-√5/2)2n-1] 且P(n)=3·P(n-1)-P(n-2),其中P(1)=1, P(2)=2。 二、以邊長n之正三角形為底的三維不完整堆垛,方法數T(n)=4T(n-1)-2T(n-2)+T(n-3), 其中T(1)=1, T(2)=2, T(3)=7恰與以正方形為底相同。 三、以邊長n之正六邊形為底的三維不完整堆垛,方法數H(n)=9H(n-1)+3H(n-2)+H(n-3), 其中H(1)=1, H(2)=7, H(3)=67。 四、正三角形與正六邊形的凹洞數有6倍關係,影響方法數。 五、T(n), S(n), H(n)是新發現的數列。 六、本研究討論正三角形、正方形、正六邊形為底。其他正多邊形皆無法研究。 七、以「m列m+K行」長方形為底的三維不完整堆垛,只能橫放方法數 A(m,k)=1+A(1,K)·(m-1)2+A(2,K)·(m-2)2+…+A(m-2,K)·22+A(m-1,K)·12 若能橫放或直放方法數 R(m,k)=4R(m-1,l)-2R(m-2,k)+R(m-3,k)+(2k+1)R(m-1-k,k)-(2K-1)R(m-2-k,k) 八、以股長n之等腰直角三角形為底的三維不完整堆垛,方法數 I(n)=3I(n-1)-2I(n-2)+I(n-3),其中I(1)=I(2)=1,I(3)=2。 九、以邊長n之菱形為底的三維不完整堆垛,方法數r(n)=5r(n-1)-r(n-2)+r(n-3),其中r(1)=1, r(2)=3, r(3)=15。 恰與平行四邊形相同。 十、正三角形與菱形的凹洞數有2倍關係,影響方法數。