變形的橢圓—從距離及距離和談起
給定一平面E，A為平面上一點。取r>0，則我們知道到其距離為定值的點形成一圓，而A為此圓圓心。如果把A改成一平面圖形，則到其距離為定值的點形成的集合會是什麼樣子？類似地，給定平面上兩焦點F1及F2在平面上，則到其距離和為定值的點形成橢圓。同樣的，若把F1及F2改成平面圖形，其圖形會是什麼樣子？藉著GSP的輔助，到目前為止，我們得到了以下的結果： \r 1. 給定一平面E及此平面上的一個凸多邊形, 我們描繪出在此平面上到此凸多邊形之距離為定值的點所形成的圖形。\r 2. 設F1和F2分別為平面E上之點或線段或多邊形（未必是凸多邊形），我們利用包絡線描繪出所有滿足d(P,F1)+d(P,F2)=k（k夠大）的點所形成的圖形。 \r 3. 設C1,C2為平面E上之兩圓，我們討論所有滿足 d(P,C1)+d(P,C2)=k\r （k夠大）的點形成的圖形並討論其性質。 \r 4. 設L1和L2分別為平面E上之兩線段，我們討論所有滿足d(P,L1)+d(P,L2)=k（k夠大）的點形成的圖形並討論其性質。 \r 5. 設A為平面E上之一點，Γ為平面上一凸多邊形，我們討論所有滿足d(P,A)+D(P,Γ)=k（k夠大）的點形成的集合並討論其特性。 \r 6. 藉由和圓作比較，我們研究了變形圓的光學性質；而對變形橢圓也做類似的討論。\r Let E be a plane and A a fixed point on E. Given , it is known that all of the points on E with distance to 0r>rA form a circle and the point A is called the center of this circle. What is the corresponding graph if we replace the point A with a set (for example,a segament or a polygon) contained in FE? Similarly, what is the case when we modify the two focuses and in the definition of an ellcpse to sets and (or example,two segments or two polygons) contained in 1F2F1F2FE ? Taking advantages of GSP and analytic geomety, we research related situations and so far we have obtained the following results:\r 1. Let Γ?E be a segment, a convex polygon or a circle , etc. and r>0 be fixed. We sketch the graph of points on E with distance r to Γ and study properties of such graphs.\r 2. Let F1 and F2 be singletons, line segments , polygons(may not be convex), or circles,etc., on E Taking advantage of envelopes, we sketch the graph of those points P on E satisfying d(P,F1)=k(K>0 is large enough).\r 3. Let C1 and C2 be circles on 1C2CE. We sketch the graph of the points P on E that satisfiy d(P,C1)6d(P,C2)=k (k>0 is large enough) and study properties of this graph.\r 4. Let L1 and L2 be two line segments on E and be a large enough constant. We sketch the graph of points P on E that satisfy d(P,L1)+d(P,L2)=k(k >0is large enough) and research properties of this graph. 0k>\r 5. Let A?E and be a convex polygon on ΓE. We sketch the graph of points on E that satisfy d(P,L1)+d(P,L2)=k(k>0 is large enough) and research properties of this graph.\r 6.We compare the optical properties of metamorphic circles with circles and we deal with metamorphic ellipses similiarly.
吸菸、喝酒與嚼檳榔之基因毒性研究
流行病學資料顯示，近年來口腔癌發生率明顯增加。本研究之目的是探討口腔黏膜細胞微核發生頻率及彗星分析法之基因傷害指標是否與菸、酒、檳榔暴露有關，以及是否可以看到菸、酒、檳榔之交互作用。 研究對象為桃園地區山地鄉之民眾，利用問卷收集個人之菸、酒、檳榔及干擾因子之暴露資料，再採集樣本之口腔黏膜細胞及血液樣本，進行基因傷害評估。 結果顯示，口腔黏膜之微核發生率與檳榔之暴露相關性最大，可以解釋12.6％；然而，彗星尾部動量和尾部長度則以香菸暴露解釋力最大；同時，檳榔與香菸的基因傷害交互作用似乎存在。因此我們認為，口腔黏膜細胞之微核發生頻率對於檳榔暴露者應是不錯的基因傷害指標，而香菸暴露則以彗星分析法之指標較為敏感。 ;Epidemiological studies showed that the incidence of oral cancer increased significantly in recent years. The purpose of this study is to evaluate the genotoxicity of cigarette smoke, alcohol and betel quid use as well as the. interaction effect between these three risk factors. The study subjects were selected from residents lived in a mountain area of Tao-Yuan county. We used questionnaire as a tool of exposure measurement. The exfoliated oral buccal cells and blood samples were collected for the assay of micronucleus frequency (MNF) and comet assay. We find that there are higher MNF in smokers, alcohol drinkers, and betel quid users compared with nonusers. However, a significant difference can not be found because of small sample size. The relationship between MNF and three risk factors was strongest in betel quid use, however, for smokers the parameters in comet assay were more sensitive than MNF. There is a tendency of additive effect between cigarette, alcohol and betel quid although without statistical significance. Advanced statistical analysis is suggested to find stronger evidence in the genotoxicity biomarker.
終端速度
液體中之球體運動與液體的黏滯性有關，本實驗找出球體半徑與終端速度之間的關係。利用攝錄機作為紀錄工具，拍攝三種材質（壓克力、玻璃、水晶）的球體在沙拉油中的自由落體過程。使用電腦影像處理軟體將影像分解成幅影像，時間的解析度為1/30秒。測量球體的高度與時間，分析高度與時間的變化情形，發現終端速度與球體半徑之間的關係。
流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。
再者，在相同半徑的條件下，密度越大的球體終端速度越大，在靜止下落後，越久達到終端速度。
The motion of a sphere which is falling through a fluid is subject to the fluid viscosity. In this study, we find out the relation between the radius of a sphere and the terminal velocity. We used a digital camera to record the sphere's descent in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough estimates of the sphere's location within 1/30 seconds accuracy for statistically consistent results. By measuring the location and time and analyzing them, we find out the relation between the radius of a sphere and the terminal velocity. The expression of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates the expression of the drag force should be Fdrag = -（k1V+ k2V2）. The expression for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is the sphere density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the same, the terminal velocity of a denser sphere is higher and the time to approches the terminal velocity is longer.
Problems of Safe Storage, Collecting and Recycling of Luminescent Lamps
Our research is connected with the problem of the mercurious wasre products (MWP) recycling, luminescent lamps take a great part among them. The problem of recycling MWP is topical not only in Yakutsk, but also in other cities of Russia because of its toxic influence on the human’s body. Mercury is the top among eight the most dangerous metals. I have analyzed the conditions of recycling of luminescent lamps in Yakutsk schools. I have got data on the problem. There is a great amount of the fused luminescent lamps is stored in the territory of schools, it produces danger for the pupils’ health. On the research work I have proposed some ways of solution of the problem.
揭開變化球的神秘面紗 --- 探討丘腦至前額葉的路徑連結
During the evolution of humankind, development of frontal cortex has played a critical role, where higher brain function like emotions, self-consciousness, decisions…etc, were all related to frontal cortex. On the other hand, thalamus is usually associated with relaying the sensory signals from peripheral receptors. In order to understand the functional role of frontal cortex, the signal processing mechanisms in the thalamo-frontal cortical pathway became an important research issue. The aim of this experiment was to find a method to dissect a brain slice that contains a connecting route in vitro between thalamus and frontal cortex with functional activity. Through nerve fibers tracking technique using fluorescent-dye (DiI), it was understood that the 3D-space connection between thalamus and frontal surface was an upward curve with a turn of about 110 degrees and bending inwards from the two sides. If a conventional horizontal section was performed, the route would be cut-off and its integrity lost regardless of the direction. To solve this problem, a novel section method was developed to retain the route. Based on the route direction shown by the fluorescent-dye, a piece of brain block was cut and flattened of about 110 degrees. Other sections were performed as control for studying the effectiveness of the sectioning on the plane of the route. Finally, electrophysiological methods were used to verify the connection route was complete and functional. Thalamus-evoked extracellular field potentials in the frontal cortex were observed by changing stimulation strength, adjusting slice temperature and prepared oxygen supply and administration of drugs like CNQX and picrotoxin in the 110 degree flattened slice but not the others. It was found that the reaction was essentially a neuronal response, indicating the pathway between thalamus and frontal surface was retained substantially. With this novel brain slice technique, we can assess the functional connection between thalamus and frontal cortex and investigate the cellular mechanisms of the signal processing in this connection pathway. It is anticipated that present technique provides an important step to further elucidate the functional role of the frontal cortex. 在人類的演化史上，前額葉的發展扮演了極為重要的角色，凡舉情緒、自我意識、決策等，皆與前額葉有關。而丘腦通常與視覺、聽覺及本體感受如痛覺、觸覺、溫度覺的訊息傳遞有關。要了解前額葉的功能，丘腦到前額葉的徑路及訊息處理機制，便成為一個很重要的研究課題。本實驗的目的是尋找一個方法能在離體的腦切片上維持具有丘腦到前額葉連結的徑路並且有功能的活性。經由螢光染料(DiI)神經束追蹤技術，了解從丘腦至前額葉路徑的三度空間連結為一先向下再向上約110度的角度轉折，並同時先由內向外再轉向內的曲線，若用一般水平之切片方法，無論何種方向，其路徑必定會被切斷，不能保持其完整性。為了解決此問題，發展出一種可以保存其路徑的腦切片方法。依照螢光染料所顯示出的的路徑走向，在腦塊的皮質上切一刻痕，將腦塊以110度的角度展平，使其路徑處在一個平面上再切片。最後利用電生理的方法來證明所切出的連結路徑是完整且具有活性。改變在丘腦的刺激強度、調整腦切片(腦脊髓液)溫度、氧氣的供給以及施予藥物CNQX、picrotoxin，觀察其前額葉之電位變化，發現其反應確實為神經反應，表示從丘腦至前額葉的路徑已在這種特殊的腦切片中被完整保存。藉由這個方法，將有助於研究丘腦至前額葉功能性連結，神經網路結構，及其訊息處理機制，並期待以這樣一個全新的方法將來有助於瞭解前額葉的功能。
Isolation, characterization of β-chitin from squid pens and calcium carbonate crystallization on th
Chitin, a polysaccharide common in biocomposites, has an interwoven organic framework that can act as a scaffold for mineralization in natural systems. Acidic amino acids, namely aspartic (Asp) and glutamic (Glu) acids, are the primary active molecules at biomineralisation interphases in mollusks and play an important role in controlling the polymorph and morphology of the associated mineral.\r In this study, chitin was extracted from squid pens and used as a scaffold for crystallization. The chitin scaffold was functionalized with glutamic acid and aspartic acid separately to create an artificial microenvironment for the study of biomineralization of calcium carbonate. The objective was to investigate the usefulness of the extracted chitin to serve as a scaffold for calcium carbonate crystallization, especially the fidelity of the polymorph nucleated to the amino acids and proteins used.
天空之城耐震設計與隔震技術之探討
我們的研究包括兩部份，第一部份是實地調查訪問。瞭解地震成因、傷害及現有防震方法，並調查坊間各種建築物類型，及常見私自改變建築物結構現象，做為研究的基礎。第二部份為建築物抗震實驗。研究發現：牆面挖空、頂樓加蓋、樓層挑高，建築物會在該處產生弱點，由此斷裂。柱子數量相同下，散開時支撐力較弱。不對稱建築物遇震時會不自然扭轉且易倒。隔震素材恰當，能有效提高耐震力。滑軌、彈珠隔震效果很好，但位移太大，為實際建築所不容許。建物下加裝阻尼材料，能吸收部份地震能量，降低地震對建築物的危害，並有效控制位移問題，是良好的隔震素材。樓頂加裝消能設施亦能減震，但設計極其不易。 The research includes two parts. In the first part the work is concentrated on on-site visiting and investigation such as understanding the cause of earthquake, the damage and the preventive method currently available, investigating the different types of building and the phenomenon of altering the structure of an existing building without permission by government authorities which is popularly seen in Taiwan. These are considered as the basis of the research. The second part is the experimental study of earthquake resistance of a building. The test results showed that weak-point can be caused at the place where the existing wall is moved or an extra building is attached to the roof or the structure of building has extended space between floors, and fracture always occurs at the weak-point. If the number of columns of a building is the same, then the scattering arranged location of columns is weaker than concentrating type of arrangement of columns. The building having unsymmetrical structure will twist in uneven fashion that causes the building apt to collapse in case of earthquake. Employing proper vibration-absorption material can effectively increase earthquake resistance. Sliding rails and balls can provide satisfiable vibration-isolation effect, but can also cause too much displacement of building structure. Install damping material beneath the building can absorb part of the energy of earthquake, and decrease the damage, and can solve the problem of displacement of building, therefore, damping material can be considered as an ideal vibration-isolation material. Install energy-attenuation equipment can also reduce vibration but the design of the equipment is extremely difficult.
總站該設在哪裡？—另類費馬點的研究
The definition of "Fermat Point" is that a dot, which lies in a triangle, has the minimum distance to the three apexes. In other words, "Fermat Point" has the minimum distance to three dots which are not on the same line. In the broad sense, then, in a N polygon, a dot which has the minimum distance to the N apexes could be named "Fermat Point." But what if we link up the N apexes and find out that they cannot make a convex polygon? The above is what we wish to fully discuss. Our inspiration comes from a paper on"Fermat Point." It just describes N convex polygon, so we think of putting the case to naturally polygon. The case may be that it is a concave polygon or part of the apexes which lies on the same line. We would not base our study on the conventional methods. Moreover, strictly defined, the repeated line segment will not be taken into account. That is, if the "Fermat Point" drops on the line with more than two dots on it, we just count the\r line segments except for the shorter line segments which were originally included in other studies. According to the theorem, our conclusions are as follows: 1. If N points lie on the same line segment, then the "Fermat Point"can be any point on the line segment. 2. If (N-1) points are on the same line segment, then the "Fermat Point" is on the point which two lines join together. One is that the line segment, and the other is the one which passes the remaining point and\r perpendicular to the first line segment. 3. Now there are (M+N) points. Among them, M points will make a M jog-polygon. The others all drop in the polygon. As the diagram shown beneath, we know that the "Fermat Point" drops on the point which two lines join together. The two lines must pass as many points as possible. 所謂的「費馬點」是指三角形內到三頂點距離和最小的點。換言之，「費馬點」就是到平面上不共線三點距離和最小的點。因此，我們可定義，廣義的「費馬點」即是n 多邊形內到各頂點距離和最小的點，亦即到平面上不共線n 點距離和最小的點，但若平面上n 點不能恰為n 多邊形的頂點呢？這就是我們所要討論的。由於我們的靈感來自一份關於「費馬點」的科展作品，所以我們想到，當平面上n 點不能恰為n 凸多邊形的頂點，甚或其中有一部分的點共線時，將不能以n邊形的方法來探討，但我們可以將之化為m 邊形內（n-m）個點來討論。而更重要的是，我\r 們增加了另一個限制，重複的線段將不被我們列入計算。亦即當所求點落在某一多點共線的線段上時，我們只計算該線段的總長，而不計其中重複的較短線段。根據這個原則，我們試行證明平面上三點、四點、五點及六點的可能情況，期望能從中找出足以推廣至平面上n 點的一般性。結果雖不完美，但我們總算差強人意的歸納出了下列結論：1.若n 點共線段，所求點可為所共線段上任一點。2.若（n-1）點共線段，則由該不共線點引一線與共線段垂直，其交點即為所求。3.若（n+m）個點中有m 個點為一m 多邊形的頂點，另外n 個點落在該m 多邊形內，則由兩個外頂點引直線盡可能通過最多點，該兩直線的交點即為所求。
芯電感應
Based on Ampere，s Law, the magnetic field intensity of the solenoids is B=μ0μr?n?I, where μ0 is the magnetic permeability of free space, μr is the relative magnetic permeability, n is the number of coils per unit length and I is the solenoidal current. The end magnetic field of the solenoid must multiply by one half. According to the above result, it can be greatly strengthened by the addition of a ferromagnetic core. First, we observe three different inserted materials of coils (wood, iron and magnetite), whose magnetic induction in different solenoidial current. By experiment, when the iron and magnetite materials were inserted into the coil, it would produce larger magnetic induction. The calculated relative magnetic permeabilities of wood, iron and magnetite materials are 0.57, 18.37 and 18.32, which are close to the reported paper (1). When the driving field is removed, the fraction of the saturation magnetization of the magnetite is retained, which is called hysteresis and is related to the existence of magnetic domains in the material. In the second part, we change the frequency of circuit switch, which induced different current. Compared with the result of the first part, it would fit the result, which is the induced magnetic field is proportion to the solenoidal current. 根據安培定律，螺線管的磁場為B=μ0μr?n?I。其中μ0為真空中的導磁率，μr為相對的導磁率，n為單位長度的線圈匝數，I則為通入螺旋管的電流。至於螺旋管的端點磁場須再乘上1/2。所以根據上述的結果，當螺旋管插入鐵磁性物質，會增強螺旋管的磁場。首先，觀察三種不同的芯物質；非鐵磁性材料，軟磁材料，硬磁材料（木棒，低碳鋼棒，磁鐵棒）在不同的外加磁場下的感應磁場，得到芯物質的磁化曲線，而計算出來的相對導磁率分別為0.57, 18.37 和18.32與參考文獻(1)接近。而當外加磁場移走時，硬磁性物質的磁性仍然存在，稱為殘磁現象。在第二部分，我們改變線路開關的頻率。發現不同的開關頻率，會得到不同的螺旋管電流，而造成不同的感應磁場。再度驗證了感應磁場大小是正比於螺旋管電流的大小。