Factors Affecting the Perception of Happiness among Teachers in Vietnam

Vietnam is in the process of implementing education reforms in which teachers play a crucial role in determining success. This study aims to identify the main factors influencing the perception of happiness at work of Vietnamese teachers during the period of educational reform. In any period, teachers are always considered as being the force behind the success of education. Therefore, teachers' happiness is the most vital factor to be taken into consideration when educating students. Identifying the factors that affect teachers' happiness at work is the key to improving their teaching quality and quality of life. This study was conducted to investigate the factors affecting the perceived happiness of secondary school teachers in Vietnam today, thereby objectively assessing the emotional status of teachers in Vietnam in relation to the work they are doing. The results are as follows: 1) Teachers face a lot of pressure from many sides; 2) There is still a large percentage of teachers who do not really attach importance to the teaching profession; 3) State policies have not helped teachers feel secure in their professional activities; 4) Teacher capacity still needs to be greatly improved; 5) It is necessary to strengthen the connection between teachers, educational leaders, policy makers, school administrators and colleagues. This study uses descriptive statistics to present the research results. The survey was carried out in September 2021

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

On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page