圓周上跳躍回歸問題之研究
圓周上相異n個點,將圓周分割成n段弧,每次每個點沿逆時針方向變換成與下一點所成弧之中點,若某點經m次變換後回到初始點,則m的最小值以及m的所有可能值為何?我們發現,m的最小值為n+2。更進一步發現,m的充要條件為m≧n+2且m≠kn-1, kn, kn+1,其中k為正奇數。接著,我們將問題一般化,圓周上相異n個點,沿逆時針方向變換成與下一點所成弧之p:q處,若某點經m次變換後回到初始點,則m的最小值以及m的所有可能值為何?我們發現,若p, q∈N,(p,q)=1,當變換次數r足夠大時,此n個點的位置會收斂至圓周上n等分點,同時,此n個點會在變換T=n(p+q)/(n,p)次後再次收斂至相同的位置。在這篇研究中,我們推導出任意點Pi變換r次後的點之位置坐標Ai(r)的一般式,不失一般性,我們針對P0求出A0(r)的最小極端值Lr與最大極端值Ur,在變換次數r足夠大時,透過觀察Lr與Ur對應到圓周上的收斂位置所形成的區間是否涵蓋原點,可預期P0變換r次後可否回歸。此外,我們也針對n個點具特殊初始位置座標來研究其回歸性質。
Removal of Nutrients by Chlorella Vulgaris Microalgae in Bandar Abbas Municipal Wastewater
The entry of nutrients into the environment can cause the creation of eutrophication of aquatic ecosystems. One of the methods of removing nutrients from effluents is the use of algae. Algal purification is a new and inexpensive technology for this purpose. The present study investigated the rate of cell growth and nutrient removal of urban wastewater in Bandar Abbas in winter 2020 by the Chlorella vulgaris microalgae in the phycolab of Fisheries Research. Treatments with different dilutions (0%, 25%, 50% and 75%) were prepared; in addition, specific growth rate, cell density and removal efficiency of phosphate, nitrate, nitrite were examined during a 14 day period with initial constant density (1×10⁶ cells / ml ) of microalgae. The results indicated that 0% and 75% dilution had the highest and lowest cell densities (8.675×10⁶ and 56.633×10⁶), respectively; moreover, they had the specific growth rate (0.166 and 0.311). Furthermore, there was a significant difference between them (P≥ 0.05). The highest nitrate and nitrite removal efficiencies were -40.75 and -79.84 in effluent dilution of 50%; in addition, the lowest were 1.26 and -40.26 in dilution of 75% and 25% respectively. Phosphate had the highest removal efficiency at 0% dilution with a mean of -79.65 that showed a significant difference with the lowest at 25% dilution (P≥ 0.05). Therefore, high or low levels of nutrients can affect the removal efficiency and growth rate of microalgae.
Chlorella vulgaris chlorophyll a fluorescence as a potential indicator for zinc and nickel detection
Heavy metals contaminate many bodies of water, posing a health risk to not only organisms that live and use the water in these areas, but also to the humans that live nearby. Chlorella vulgaris, a microalga, is one organism whose chlorophyll a fluorescence can indicate the presence of these substances, detecting any changes in concentrations using fluorescence microscopy and other fluorescence devices. The study explores the sensitivity of C. vulgaris to the heavy metal zinc where the algae was exposed to five concentrations of zinc: 0 ppm, 5 ppm, 10 ppm, 50 ppm, and 100 ppm. The fluorescence of the samples was observed with a fluorescence microscope on days 0, 4, 7, and 12, where the algal samples were adapted to the dark for 5 minutes, then exposed to light for 90 seconds. The values of the minimal and maximal fluorescence of the samples in the dark were noted. There is a significant difference in the values of the minimal fluorescence, maximal fluorescence, and maximum quantum yield, a value derived from the minimal and maximal fluorescence, at the highest concentration, 100 ppm, from the other treatments for the entirety of the experiment. The significantly low values at 100 ppm and the calculated EC50 of 75.70 ppm indicate that C. vulgaris is indeed a viable indicator for zinc detection at this and higher concentrations of zinc.
Using EEG Neuro-Feedback technology to control a prosthetic hand
Unaffordable healthcare and excessive plastic waste are both alarming issues that are plaguing modern society. Recent studies conducted by the World Health Organisation (WHO) report that about 15% of the world's population suffer from a form of disability, of which 50% of the demographic cannot afford adequate health care. Furthermore, 8 million metric tons of plastic annually enter our oceans (apart from the 150 metric tons that currently circulate our oceans!). In conjunction to the global plastic pollution crisis, unnecessary invasive surgery is currently being done on amputees. Many of these desperate patients are forced to pay exorbitant prices in order to live a normal life with bionic prosthetics. The solution… Project Limbs - an EEG, 3D printed prosthetic printed from recycled plastic. Signal processors will be implemented to build an affordable and easy-to-use ‘mind controlled prosthetic hand’, that requires no invasive surgery.