Uniform lower bound for the least common multiple of a polynomial sequence

Let $n$ be a positive integer and $f(x)$ be a polynomial with nonnegative integer coefficients. We prove that ${\rm lcm}_{\lceil n/2\rceil \le i\le n} \{f(i)\}\ge 2^n$ except that $f(x)=x$ and $n=1, 2, 3, 4, 6$ and that $f(x)=x^s$ with $s\ge 2$ being an integer and $n=1$, where $\lceil n/2\rceil$ denotes the smallest integer which is not less than $n/2$. This improves and extends the lower bounds obtained by Nair in 1982, Farhi in 2007 and Oon in 2013.Comment: 6 pages. To appear in Comptes Rendus Mathematiqu

Using Battery Storage for Peak Shaving and Frequency Regulation: Joint Optimization for Superlinear Gains

We consider using a battery storage system simultaneously for peak shaving and frequency regulation through a joint optimization framework which captures battery degradation, operational constraints and uncertainties in customer load and regulation signals. Under this framework, using real data we show the electricity bill of users can be reduced by up to 15\%. Furthermore, we demonstrate that the saving from joint optimization is often larger than the sum of the optimal savings when the battery is used for the two individual applications. A simple threshold real-time algorithm is proposed and achieves this super-linear gain. Compared to prior works that focused on using battery storage systems for single applications, our results suggest that batteries can achieve much larger economic benefits than previously thought if they jointly provide multiple services.Comment: To Appear in IEEE Transaction on Power System

An Image Never Reaching the Perfect

My thesis seeks to take several concrete texts to examine this ΓÇ£new womenΓÇ¥ genealogy in modern Chinese literature, analyze the differences and development of such an image, and argue that because all the new women images in modern Chinese literature are created with the writersΓÇÖ certain purpose, they can never be ideal or perfect. They all have some drawbacks, and we could not even find one till today

Study of II-VI Colloidal Semiconductor Magic-size Nanoclusters and Crystalline Quantum Platelets

The main objective of this project is to prepare and isolate the smallest, discrete, magic-size nanoclusters of cadmium selenide (CdSe) and to grow crystalline, wurtzite CdSe quantum platelets (QPs) at room temperature. The achievement of these goals enables us to provide a general synthesis of II-VI semiconductor magic-size nanoclusters and low-temperature routes to well-passivated nanocrystals having a range of compositions and morphologies. The magic-size nanocluster (CdSe)13 is grown in a lamellar-bilayer soft template at room temperature. The results described in this thesis strongly suggest that [(CdSe)13(n-octylamine)13] is the most thermodynamically stable nanocluster and serves as a key intermediate in the formation of CdSe quantum belts. Upon ligand exchange, sheet-like structures of [(CdSe)13(n-octylamine)x(oleylamine)13-x] and free clusters of [(CdSe)13(oleylamine)13] are released from the template. The kinetically stabilized magic-size nanolcusters prefer to grow to larger sizes once the steric protection of the primary-amine ligation is compromised by small-ligand substitution. Several discrete [(CdSe)13(RNH2)13] derivatives (R = n-propyl, n-pentyl, n-octyl, and oleyl) are prepared in the corresponding primary amine solvent. For the first time, the soft-template method has been employed on the gram scale to prepare pure (CdSe)13 as a solid, isolable derivative. This achievement enables us to study the intrinsic physical properties of (CdSe)13, like size and melting points. The access to preparative quantities of (CdSe)13 will promote further experimental studies of its structure, reactivity, and use as a nanocrystal precursor. A novel method is introduced to synthesize crystalline wurtzite, two-dimensional CdSe quantum platelets (QPs) by employing primary amine and secondary amine cosolvent mixtures. This is the first preparation of thickness-controlled CdSe nanocrystals under mild conditions. The thickness of the QPs is dependent on temperature, and the length is affected by the nature of secondary amine. Reaction monitoring establishes that the magic-size nanocluster (CdSe)34 is a key intermediate in the formation of the QPs. [(CdSe)34(n-octylamine)16(di-n-pentylamine)2] is isolated, which functions as critical size crystal nuclei that may be stored in a bottle

Monitoring and modeling of diurnal and seasonal odour and gas emissions from different types of swine rooms

The issue of odour, greenhouse gas emissions and indoor air quality in swine buildings have become a great concern for the neighbouring communities as well as governments. Air dispersion models have been adopted widely as an approach to address these problems which determine science-based distance between livestock production site and neighbours. However, no existing model considers the diurnal and seasonal variations of odour, gas (ammonia, hydrogen sulphide, greenhouse gas), and dust concentrations and emissions, which may cause great uncertainty. The primary objective of this project is to monitor and model the diurnal and seasonal variations of odour, gases, and dust concentrations and emissions from nursery, farrowing, and gestation rooms. Additionally, this study tried to quantify the greenhouse gas contribution from swine buildings and evaluate the indoor air quality of swine barns. Strip-block experimental design was used to measure the diurnal variation of odour and gas concentrations and emissions in PSC Elstow Research Farm. It was found that: 1) odour and gas concentrations in winter were significantly higher than those in mild and warm weather conditions for all three rooms (P0.05); 3) significant diurnal variations occurred in August and April (P0.05); 4) apparent diurnal variation patterns were observed in August and April for NH3, H2S and CO2 concentrations, being high in the early morning and low in the late afternoon; 5) positive correlation was found between odour concentrations and NH3, H2S, and CO2 concentrations, respectively. A whole year ( August 2006 to July 2007) monitoring of odour, gas and dust concentrations and emissions revealed that: 1) significant seasonal effect on odour and gas concentrations and emissions, total dust concentrations and dust depositions were observed (