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

An Efficient Method for Generating Synthetic Data for Low-Resource Machine Translation – An empirical study of Chinese, Japanese to Vietnamese Neural Machine Translation

Data sparsity is one of the challenges for low-resource language pairs in Neural Machine Translation (NMT). Previous works have presented different approaches for data augmentation, but they mostly require additional resources and obtain low-quality dummy data in the low-resource issue. This paper proposes a simple and effective novel for generating synthetic bilingual data without using external resources as in previous approaches. Moreover, some works recently have shown that multilingual translation or transfer learning can boost the translation quality in low-resource situations. However, for logographic languages such as Chinese or Japanese, this approach is still limited due to the differences in translation units in the vocabularies. Although Japanese texts contain Kanji characters that are derived from Chinese characters, and they are quite homologous in sharp and meaning, the word orders in the sentences of these languages have a big divergence. Our study will investigate these impacts in machine translation. In addition, a combined pre-trained model is also leveraged to demonstrate the efficacy of translation tasks in the more high-resource scenario. Our experiments present performance improvements up to +6.2 and +7.8 BLEU scores over bilingual baseline systems on two low-resource translation tasks from Chinese to Vietnamese and Japanese to Vietnamese

Développement de formulations intégrales de volume en magnétostatique

In recent years, the Volume Integral Method (VIM) has been received particular attention formodeling of low frequency electromagnetic problems. The main advantage of this method is thatinactive regions do not to be discretized, which makes it light and rapid. Associated with matrixcompression methods, the VIM is a competitive alternative to the finite element method for modelingelectromagnetic devices containing a predominant air volume.This PhD thesis focuses on the development of two volume integral formulations for solvingmagnetostatic problems, in the presence of nonlinear materials, magnets, coils, multiply connectedmagnetic regions, and the presence of magnetic shielding. The first one is a mesh magnetic fluxformulation based on the interpolation of facet elements and the second one is a magnetic vectorpotential formulation based on the interpolation of edge elements. The application of theseformulations provides accurate results even with coarse meshes and allows solving straightforwardnonlinear magnetostatic problems. Methods for computing global magnetic force and magnetic fluxthrough a coil were also implemented as part of this work. Developments performed in the MIPSEplatform were validated on academic case-tests as well as some industrial devices.Ces dernières années, la Méthode Intégrale de Volume (MIV) a reçu une attention particulière pour lamodélisation des problèmes électromagnétiques en basse fréquence. Son intérêt principal est l’absencedu maillage de la région air, ce qui rend la méthode légère et rapide. Associée aux méthodes decompression matricielle la MIV devient aujourd'hui une alternative compétitive à la méthode deséléments finis pour la modélisation de dispositifs électromagnétiques ayant un volume d'airprépondérant.Ce rapport porte sur le développement de deux formulations intégrales de volume pour la résolution deproblèmes magnétostatiques avec prise en compte des matériaux non linéaires, des aimants, desbobines, des circuits magnétiques avec ou sans entrefer et des régions minces magnétiques. Lapremière est une formulation en flux de mailles indépendantes basée sur l'interpolation par éléments defacette. La deuxième est une formulation en potentiel vecteur magnétique basée sur l'interpolation paréléments d'arête. L'application de ces formulations permet d’une part d'obtenir des résultats précismême en présence d’un faible maillage et d’autre part de résoudre aisément des problèmes nonlinéaires. Des méthodes de calcul de la force magnétique globale ainsi que du flux magnétique dansles bobines ont été également mises en oeuvre. Les développements informatiques ont été réalisés dansla plateforme MIPSE et ont été validés sur des problèmes académiques ainsi que sur quelquesdispositifs industriels

Power allocation algorithm in OFDM-based cognitive radio systems

In orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems, the optimized algorithms for sub-carrier power allocation face the problems of complex iterative calculation and difficult realization. In this paper, we propose an exponential power distribution function and derive a sub-optimal power allocation algorithm. This algorithm aims to allocate power of in-band subcarriers of cognitive users according to the numerical characteristics of the power distribution function by using a convex optimization numerical method under linear constraints. This algorithm has the advantages of fast calculation speed and easy realization, and reduces the interference to the authorized users, which is caused by the power leakage of the in-band subcarriers of cognitive users to the out-of-band subcarriers. Simulation results show that the proposed algorithm maximizes the inband channel capacity of the cognitive users under certain interference thresholds of the authorized users, thus increasing their transmission rate

CURRENT SITUATION OF STUDENTS’ PSYCHOLOGICAL STATE BEFORE PRACTICAL COURSES’ FINAL EXAMS

The article aimed to determine the factors influencing students’ psychological state before the final exam of practical courses. The article used conventional scientific research methods in sports and physical training combined with psychological tests studied on fifty students at Ho Chi Minh City University of Physical Education and Sports (UPES). After reviewing related studies and consulting with experts, four tests were employed to assess the psychological state before the test of the research subjects. The results showed that students with a good psychological state to take the exam had good test results. Conversely, students with a feverish or lethargic state will have poor test results. The research results serve as the basis for proposing measures to adjust the psychological state before the exam, contributing to improving the learning results of students.  Article visualizations

Measurement Profile of Surface Revolution by Laser Scan Micrometer Method

Measurement profile of surface revolution by laser scan micrometer method is a non-contact measurement method that allows de-tailed profile measurements with fast measuring speed by using laser scanning and accuracy is much higher than other non-contact scanning methods. This paper presents the mathematical model profile of surface revolution and the application of the laser scan micrometer method for measuring this detailed profile. Fabricating complete equipment model according to the author's proposed method. Compare the results of measuring the profile of surface revolution on a construction measuring device with a roundness meter Jenoptik F315 to prove the feasibility of the construction measurement method

Modelling and Experimental Validation of a VNT Turbocharger for Improving Performances of a Marine Diesel Generator Engine

This paper presents modelling and experimental validation for improving the performances of a marine diesel generator engine. Based on the diesel engine theory, the laws of conservation of energy, and the principle of movement of flow through turbocharger nozzle, a mathematical model of a real turbocharged engine was built, concentrating on the mathematic model of flow through nozzles. This model is simulated by Matlab/Simulink program, the results of simulation showed the relationships between the engine and the turbocharger, the turbine and the compressor, and between the nozzles and the turbocharger. The experiments were carried out to validate this model, the errors between the simulation and measure were acceptable. The measure and simulation results also determined that at the low load conditions (≤50% load) engine performances can be improved by adjusting nozzle opening degree (from fully opening to 90% and 80% opening)