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

Environmental allergen reduction in asthma management: an overview

Asthma is a prevalent non-communicable disease that affects both children and adults. Many patients with severe, uncontrolled asthma could not achieve total control despite using anti-asthmatic drugs. There is increasing evidence that allergy to environmental allergens, including both indoor and outdoor allergens, is associated with asthma symptoms and severe asthma. Frequently reported sensitized allergens were dust mites, cockroaches, grass pollens, molds, pets, and rodents in allergic asthma patients, although the patterns of widespread allergens differed from each country. Allergen avoidance is the cornerstone of asthma management, especially in sensitized subjects. This review summarizes environmental allergen avoidance and clarifies their effects on asthma control. Despite contrasting results about the impact of allergen exposure reduction on asthma control, several studies supported the beneficial effects of reducing asthma-related symptoms or risk of exacerbations as a nondrug therapy. Identifying environmental allergens is helpful for asthma patients, and further studies on clinically effective avoidance methods are required

Architecture Parallel for the Renewable Energy System

This chapter present one possible evolution is the parallel topology on the high-voltage bus for the renewable energy system. The system is not connected to a chain of photovoltaic (PV) modules and the different sources renewable. This evolution retains all the advantages of this system, while increasing the level of discretization of the Maximum Power Point Tracker (MPPT). So it is no longer a chain of PV modules that works at its MPPT but each PV module. In addition, this greater discretization allows a finer control and monitoring of operation and a faster detection of defects. The main interest of parallel step-up voltage systems, in this case, lies in the fact that the use of relatively high DC voltages is possible in these architectures distributed

Nanocomposite Thin Film TiO2/CdS Electrodes Prepared by Thermal Evaporation Process for Photovoltaic Applications

The incorporation of cadmium sulfide (CdS) into TiO2 nanoparticle thin films was investigated. The nanoparticle TiO2 thin film onto an indium doped–tin oxide (ITO) substrate was deposited by Electron Beam Deposition (EBD) combined with thermal process. Then a CdS thin film was vacuum-deposited onto the pre-deposited TiO2 film by a thermal evaporation technique. The obtained TiO2/CdS was characterized by X-ray diffraction (XRD), field emission scanning electron microscope (FE-SEM). The TiO2/CdS nanocomposite film was used in a photo-electrochemical (PEC) cell as a working electrode and a platinum electrode as a counter electrode. The electrolyte solution contains 1 M KCl and 0.1M Na2S. The results show that the cell with TiO2/CdS composite film electrode has significantly improved photoelectric capability in comparison with that of the pure TiO2 thin films

Vietnamese children and adults' perceptions of genealogy's role in family tradition education

When one studies their ancestors, they acquire information and documentation about their marriages, births, and deaths as far back as possible, through their parents, grandparents, and great grandparents, as well as information and documentation about their children and grandchildren. In particular, the purpose of this study is to examine the perspectives of Vietnamese children and adults regarding the significance of genealogy in traditional family education in the country of Vietnam. One hundred and ninety-nine persons participated in the survey. In a questionnaire, they answered eight questions regarding the lives of their forefathers and foremothers. When this research came to a close, it was determined that the perceptions of Vietnamese children and adults about the function of genealogy in traditional family education fell into one of two categories: "below average" and "above average." All of the findings from this research are critical in terms of establishing family traditions in the minds of future generations

Effect of Annealing Temperature on the Li+^{ + } Ionic Conductivity of La0.67−x_{0.67 - x}Li3x_{3x}TiO3_{3 }

Perovskite La0.67-xLi3xTiO3 with x = 0.10, 0.11, 0.12 and 0.13 were firstly annealed at 800 oC then treated by reactive milling, followed by post-annealing at temperatures from 1100 to 1200oC. The crystalline structure of grain and grain-boundary were characterized by XRD and SEM. The impedance measurements showed that nanocrystalline La0.67-xLi3xTiO3 after being annealed at 1150 oC possessed a grain conductivity as high as 1.3×10-3 S.cm-1. The grain-boundary conductivity was enhanced one order in magnitude after annealing at temperature higher 1100oC and consists of 5.8×10-5 S.cm-1. The results have also showed the limitation of the adiabatic thermal treatment for the improvement of the grain-boundary conductivity and suggested the way to overcome the limitation by rapidly cooling the samples from the high temperature to room temperature