Whose Electors? Our Electors! : Due Process as a Safeguard Against Legislative Direct Appointment of Presidential Electors After an Election

Prior to the 2020 general election, some commentators suggested that President Donald Trump and his allies would attempt to undermine the election’s result by inducing Republican-controlled state legislatures to directly appoint pro-Trump electors to the Electoral College. As predicted, after losing his re-election bid to President Joe Biden, President Trump pressured some leaders in Republican-dominated state legislatures to ignore the election’s result and to appoint electors who would vote for him in the Electoral College. Although these efforts were unsuccessful, the volatility of the current political landscape suggests that this issue might emerge again in a future election. In discussing possible safeguards against such an attempt, many commentators have focused on the Electoral Count Act and other legal measures. Most, however, have not addressed the possibility of a constitutional safeguard. This Note uses the 2020 presidential election as a case study and argues that the Due Process Clause of the Fourteenth Amendment provides a constitutional safeguard that can restrain states from overturning election results through direct appointment of presidential electors

Incidences between points and generalized spheres over finite fields and related problems

Let $\mathbb{F}_q$ be a finite field of $q$ elements where $q$ is a large odd prime power and $Q =a_1 x_1^{c_1}+...+a_dx_d^{c_d}\in \mathbb{F}_q[x_1,...,x_d]$, where $2\le c_i\le N$, $\gcd(c_i,q)=1$, and $a_i\in \mathbb{F}_q$ for all $1\le i\le d$. A $Q$-sphere is a set of the form $\lbrace x\in \mathbb{F}_q^d | Q(x-b)=r\rbrace$, where $b\in \mathbb{F}_q^d, r\in \mathbb{F}_q$. We prove bounds on the number of incidences between a point set $\mathcal{P}$ and a $Q$-sphere set $\mathcal{S}$, denoted by $I(\mathcal{P},\mathcal{S})$, as the following. $$| I(\mathcal{P},\mathcal{S})-\frac{|\mathcal{P}||\mathcal{S}|}{q}|\le q^{d/2}\sqrt{|\mathcal{P}||\mathcal{S}|}.$$ We prove this estimate by studying the spectra of directed graphs. We also give a version of this estimate over finite rings $\mathbb{Z}_q$ where $q$ is an odd integer. As a consequence of the above bounds, we give an estimate for the pinned distance problem. In Sections $4$ and $5$, we prove a bound on the number of incidences between a random point set and a random $Q$-sphere set in $\mathbb{F}_q^d$. We also study the finite field analogues of some combinatorial geometry problems, namely, the number of generalized isosceles triangles, and the existence of a large subset without repeated generalized distances.Comment: to appear in Forum Mat

Error Correction in Teaching Writing Skill:: From Teacher’s Point of View to Practice, A Study at A Pedagogical University in Vietnam

In English learning, writing skill is considered, by many people, the most difficult skill to be mas-tered. In fact, errors and mistakes in writing are unavoidable and a large amount of them has been de-tected with a variety of types. Previous researchers have also proved the significance of error analysis and correction in enhancing the writing skills of English learners, but the beliefs and applications of teachers in error correction methods still differ. Thus, the aim of this paper is to investigate these two factors in the teaching and learning environment of a university in Vietnam. The study is conducted in two phases: teacher interview and class observation in practice, with the participation of two Eng-lish teachers who are in charge of teaching writing skill to two classes of 21 and 28 students. The rec-orded results give emphasis to the need of error correction in writing classes, some commonly effec-tive activities utilized; furthermore, there is a remarkable outcome that teachers seldom have academ-ic basis on error correction but mainly depend on their own experience in teaching practice, and their approaching methods to correcting mistakes on students paper can be both direct and indirect. In ad-dition, some ideal activities for error correction, namely peer feedback, on-going writing quizzes, and error codes, are presente

Motions of a homopolar motor inside a conducting tube

We analyze the physics of a type of homopolar motor comprising an AA battery with two cylindrical neodymium magnets on each end that roll inside a metal cylindrical tube. The motion of the motor results from the interaction between the magnetic field of the magnets and the magnetic field created by the current inside the magnets. We develop a model to describe the dynamics of the system, including the calculation of the terminal velocity of the motor due to eddy currents.Comment: 4 pages, 1 figur

The volatility spillover effects in Chinese, the U.S and Vietnamese stock markets: Implication for portfolio design and hedging strategy

This paper investigates the conditional volatility and shocks transmission among Vietnam, China and the U.S in the context of equity markets; six AR(1)-GARCH(1,1) settings are employed with external regressors (shocks and conditional volatility from another market) in the conditional volatility equation. While the empirical findings for the Vietnam and the U.S markets show significant bidirectional shocks spillover effect, China is out of context as its both shocks and conditional volatility interdependency are insignificant. In addition, the dynamic conditional correlations between the three markets are examined employing DCC-MGARCH model. One noteworthy point from this model estimation is that all conditional correlations are mostly low and mean reverting; however, from 2016 onwards, the correlations between the markets raised at a proportionately significant amount. Drawing from the results from such models, the calculation, suggestion and simulation of optimal portfolio design and hedging ratios are analyzed. The sample data is the returns of Vietnam Index (VNI), Shanghai stock exchange composite index (SHCOMP) and S&P500 composite index (SPCOMP), which are calculated based on the daily close price. The period is between 2005 and 2020, which expectantly illustrates a comprehensive picture of relationship among the markets under study. Based on the empirical findings in this paper, the researcher conducts further analysis on the relationship between the markets, by running a new DCC setting between pairs of markets and new spillover model focusing on the period of 2016 – 2019. By investigating volatility spillover effects and conditional correlation, the paper provides an insight of the relationship between the three markets and determines whether diversification would make sense or not if one (from developed economies) were interested in Vietnamese (developing economy) stocks. Additionally, if one wanted to hedge his/her domestic portfolio (long position), he/she would want to know whether taking short position in Vietnamese stocks effectively would minimize the risk or not