Sliding invariants and classification of singular holomorphic foliations in the plane

By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will show that, in this class, the new invariant is finitely determined. Consequently, the finite determination of the class of isoholonomic non-dicritical foliations and absolutely dicritical foliations that have the same Dulac maps are proved.Comment: 21 pages, 2 figur

Commuting foliations

The aim of this paper is to extend the notion of commutativity of vector fields to the category of singular foliations, using Nambu structures, i.e. integrable multi-vector fields. We will classify the relationship between singular foliations and Nambu structures, and show some basic results about commuting Nambu structures.Comment: New version, with a completely new section which clarifies the relationship between singular foliations and Nambu structures. The size of the paper has doubled from 10 to 20 page

Formes normales de singularités de feuilletages et invariants de glissement

Les objets étudiés dans cette thèse sont les germes de feuilletages holomorphes singuliers dans le plan. Elle est divisée en deux parties: La première partie est consacrée à donner des formes normales formelles de feuilletages topologiquement quasi-homogènes dans des conditions génériques. Toute forme normale est donnée comme la somme de trois termes: un terme générique quasi-homogène initial, un terme hamiltonien et un terme radial. Nous montrons également que le nombre de coefficients libres dans les termes hamiltoniens sont conformes à la dimension de l'espace des modules de Mattei de déploiement. Dans la deuxième partie, par l'introduction d'un nouvel invariant appelé l'ensemble des glissements, nous donnons une classification stricte complète de la classe des germes de feuilletages holomorphes non dicritiques dont les indices de Camacho-Sad ne sont pas rationnels. Par ailleurs, nous allons montrer que, dans cette classe, le nouvel invariant est de détermination finie. Par conséquent, nous obtenons la détermination finie de la classe des feuilletages non dicritiques isoholonomiques et de feuilletages absolument dicritiques qui ont les même applications de Dulac.The objects studied in this thesis are the germs of singular holomorphic foliations in the plan. It is divided into two part: The first part is devoted to the construction of formal normal forms of topologically quasi-homogeneous foliations under generic conditions. Any such normal form is given as the sum of three terms: an initial generic quasi-homogeneous term, a hamiltonian term and a radial term. We also show that the number of free coefficients in the hamiltonian terms are consistent with the dimension of Mattei's moduli space of unfoldings. In the second part, by introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations whose Camacho-Sad indices are not rational. Moreover, we will show that, in this class, the new invariant is finitely determined. Consequently, the finite determination of the class of isoholonomy non-dicritical foliations and absolutely dicritical foliations that have the same Dulac maps are proved

The Use of L1 and the TL in Focus on Form and Its Impact on Uptake, Noticing and Language Development

Since Long's (1991) coinage of the term focus on form (FonF) to refer to brief attention to form in a meaning-oriented classroom, a substantial amount of research has been conducted on the role of FonF in second language learning. Evidence from this research supports the beneficial effects of FonF on learner noticing and language development (e.g. Doughty & Varela, 1998; Ellis, Basturkmen, & Loewen, 2001a; Loewen, 2005; Lyster & Ranta, 1997; Mackey, 2006). However, some other aspects of FonF, especially in an English-as-a-foreign-language (EFL) setting, have received less attention. For example, it has been widely observed that in EFL settings where the teacher and learners usually share the first language (L1), teacher use of L1 to correct learners' errors is frequent (Anton & DiCamilla, 1999; Crawford, 2004; Gabrielatos, 2001; Macaro, 2001; Turnbull & Arnett, 2002). The effect of L1 versus the target language (TL) use on second language learning in the language classroom has long been an issue of concern for both teachers and researchers (Anton & DiCamilla, 1999; E. Chau, 2007; Crawford, 2004; Gabrielatos, 2001; Swain & Lapkin, 2000; Turnbull & Arnett, 2002). However, choice of the language of form-focused episodes (FFEs) by EFL teachers has received little attention in the FonF research literature. This research study investigates teacher use of L1 and the TL in FonF in an EFL setting in Vietnam and its impact on learner uptake, noticing and language development. The research consists of two studies: an observational/descriptive study followed by an experimental study. The observational study sought to identify general patterns of teacher use of L1 and the TL during FFEs in EFL classes through a close analysis of FFEs occurring in EFL classes in two private language institutions in Vietnam. Twelve class sessions across two proficiency levels with six Vietnamese EFL teachers were observed, audio-recorded and analysed. The results revealed that the amount of FonF and uptake in this setting was similar to amounts reported in other research although there was wide variation across the six class groups and the two proficiency levels. Over 18% of the teacher feedback moves were in L1, although again there was wide variety across classes and proficiency levels. When the L1 Vietnamese teachers gave explicit information to learners in multi-move FFEs, particularly on morphosyntax and lexical FFEs, they were more likely to use L1. These findings informed the experimental study which explored the relationship between the use of L1 and the TL in FFEs and learner uptake, noticing and language development. In this study, three interactive dyadic tasks were performed by individuals from two groups of learner participants with the researcher as interlocutor. Learners from one group received feedback in L1 (n= 20), learners from the other group in the TL (n=23). The analysis revealed that, overall, the amount of uptake was similar between the two groups, suggesting that choice of the language of FonF does not influence learner uptake. Furthermore, the results for noticing and learning suggest that the language of FonF (L1 or the TL) does not strongly influence learning outcomes. By shedding light on teacher use of L1 and the TL in FonF and how this affects uptake, noticing, and learning, this research increases our understanding of the efficacy of FonF in the under-researched setting of non-native English teachers teaching in an EFL context

Beam division multiple access for millimeter wave massive MIMO: Hybrid zero-forcing beamforming with user selection

Massive multiple-input multiple-output (MIMO) systems are considered a promising solution to minimize multiuser interference (MUI) based on simple precoding techniques with a massive antenna array at a base station (BS). This paper presents a novel approach of beam division multiple access (BDMA) which BS transmit signals to multiusers at the same time via different beams based on hybrid beamforming and user-beam schedule. With the selection of users whose steering vectors are orthogonal to each other, interference between users is significantly improved. While, the efficiency spectrum of proposed scheme reaches to the performance of fully digital solutions, the multiuser interference is considerably reduced

QUANTUM TELEPORTATION OF ENTANGLED STATES VIA GENERALIZED PHOTON-ADDED PAIR COHERENT STATE

In this paper, we study the quantum teleportation of an unknown atomic state based on the two-photon Jaynes-Cummings model, consisting of an effective two-level atom with a two-mode field in the generalized photon-added pair coherent state (GPAPCS). By applying the detecting method, we use a scheme that includes two two-level atoms and a cavity field to teleport the unknown atomic state from a sender to a receiver. The results show that the number of photons added to the field and the intensity of the initial field influence the average fidelity and success probability of the teleportation process. The time-evolution dependence of the average fidelity is also considered and compared for the field in the pair coherent state and in the GPAPCS

CÁC TÍNH CHẤT ĐỘNG LƯỢNG TỬ CỦA TRẠNG THÁI KẾT HỢP BỘ BA THÊM PHOTON TRONG MÔ HÌNH JAYNES-CUMMINGS HAI MODE

In this paper, we studied the quantum dynamic properties via the two-mode Jaynes-Cummings (JC) model where an effective two-level atom interacts with a field in a photon-added trio coherent state (PATCS). The quantum dynamic properties of the atom and the field were investigated via the photon distribution function, the second-order correlation function of the same and different modes, and the probability of finding the atom in the excited state in the cavity. The results show the dynamic properties of the atom and the non-classical ones of the field in the PATCS. In addition to the factors that affect these dynamic properties, such as the original field strength, the role of adding photons to the modes of the field in the PATCS is important when compared with the field in the original state as the trio coherent state.Trong bài báo này, chúng tôi nghiên cứu các tính chất động lượng tử thông qua mô hình Jaynes-Cummings (JC) hai mode, trong đó một nguyên tử hai mức hiệu dụng tương tác với trường ở trạng thái kết hợp bộ ba thêm photon (PATCS). Các tính chất động lượng tử của nguyên tử và trường ở PATCS đã được khảo sát thông qua các hàm phân bố photon, các hàm tương quan bậc hai cùng mode và khác mode và hàm xác suất tìm nguyên tử ở trạng thái kích thích trong hốc cộng hưởng. Các kết quả khảo sát đã chỉ ra các tính chất động của nguyên tử và tính phi cổ điển của trường ở PATCS. Ngoài các yếu tố ảnh hưởng đến các tính chất động trên như cường độ trường ban đầu thì vai trò của việc thêm photon vào các mode của trường ở PATCS là rất quan trọng khi so sánh với trường ở trạng thái gốc ban đầu là trạng thái kết hợp bộ ba

CAMELLIA SPHAMII (THEACEAE, SECT. PIQUETIA), A NEW TAXON OF YELLOW FLOWER FROM LANGBIANG BIOSPHERE RESERVE, VIETNAM

Camellia sphamii is described and illustrated as a new species of section Piquetia from Hamasin village, D’ran town, Don Duong district, Lam Dong province, Vietnam. C. sphamii is similar to C. proensis (Quach, Luong et al., 2021) but differs from it in several morphological features: mature leaves cordate at base, young leaves purple; pericarp 7–8 mm thick with dense hair on the outer surface, flower buds ovate, ferruginous; sepals 5, hemisphere, concave, finely hairy on the outer surface, sparsely hairy on the inside, petals 7, finely hairy on the outer surface, with translucent margin, concave; style 5, ½ basally united; capsule 5 locular. Information on its phenology, distribution, ecology, and conservation status is also provided

ANALYSIS OF THE POPULARITY OF VOCABULARY USED WHEN PERFORMING SPEAKING ACTIVITIES IN THE CLASS OF FIRST-YEAR ENGLISH LANGUAGE STUDENTS IN THE DIRECTION OF DISCOURSE ANALYSIS

Vocabulary learning is extremely important when learning a foreign language. Fluency in a language depends on vocabulary and its use in specific situations. Speaking well is using vocabulary flexibly and speaking fluently. Researching the popularity of vocabulary is analyzing the prevalence of vocabulary used by linguistics students in communication from discourse analysis. This is a topic the research team is working on. This project will help the researchers learn about common vocabulary that students often use to communicate outside or in the classroom. Thereby understanding whether the vocabulary that students use is diverse, rich, and for the right purpose or not. This study will help students have a more comprehensive view of the ways to use words in communication. In addition, it also helps students improve their communication vocabulary, helps in exams and can be useful for later work. In this study, the research team will investigate the students' ability to use spoken vocabulary, i.e., frequency and extent of vocabulary usage.  Article visualizations