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

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by-product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory.Comment: 28 page

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

The F@ Framework of Designing Awareness Mechanisms in Instant Messaging

This paper presents our research on awareness support in Instant Messaging (IM). The paper starts with a brief overview of empirical study of IM, using an online survey and face-to-face interviews to identify user needs for awareness support. The study identified a need for supporting four aspects of awareness, awareness of multiple concurrent conversations, conversational awareness, presence awareness of a group conversation, and visibility of moment-to-moment listeners and viewers. Based on the empirical study and existing research on awareness, we have developed the F@ (read as fat) framework of awareness. F@ comprises of the abstract level and the concrete level. The former includes an in-depth description of various awareness aspects in IM, whilst the latter utilises temporal logic to formalise fundamental time-related awareness aspects. F@ helps developers gain a better understanding of awareness and thereby design usable mechanisms to support awareness. Applying F@, we have designed several mechanisms to support various aspect of awareness in IM

Web service interfaces design for e-business applications

University of Technology Sydney. Faculty of Engineering and Information Technology.As a result of the rapid developments in Web Service standards and technologies during the last decade, many organisations are implementing applications using Web Services. Some organisations are making significant commitments to Web Service standards and technology platforms. Successful projects using Web Services will to a large extent depend on the effective design and development methodologies used in the construction of an e-business application. While the importance of application design in general is recognised, so far only limited attention has been paid to design issues for service-oriented e-business applications. Currently there are no comprehensive methodologies for designing service interfaces. The traditional e-business interoperability approach is for business partners to interchange the industry standard business documents or XML messages (i.e. UBL, OTA). This approach is complex and inefficient because the business document is large and results in many optional and repeated elements that are redundant. Developing Web Services for e-business is time-consuming due to the considerable effort required to define the interfaces and maintaining a large volume of standard business documents. This work proposes to use the minimalist design approach to optimise a set of standard business documents and interfaces. The proposed interface is exposed as an abstract layer to the external parties and is able to process multiple actions corresponding to a business document. The method is based on analysing existing business documents, identifying the key elements responsible for an operation, and then exposing the operation interface that corresponds to the business document rather than the business event. This can be achieved by inserting business event action elements into the XML schema. Doing so will not only reduce the number of operation interfaces but also increase the Web Service interface’s flexibility and extendibility. Web Service implementation projects conducted in the absence of a design framework are likely to suffer from poor reuse and extensibility. In order to achieve reusability, this method enables the operation to be invoked based on individual action or multiple actions for the same interface. This is because a single action operation typically represents a fine-grained business task. Consequently, the interface is always extendable due to using multiple actions in the operation. Finally, this thesis will detail the above mentioned methodology to optimise e-business Web Service interface to become more flexible, reusable and extendable. We will illustrate the design methodology using a purchase order business process example based on the Universal Business Language specification in order to demonstrate its effectiveness

An efficient hardware logarithm generator with modified quasi-symmetrical approach for digital signal processing

This paper presents a low-error, low-area FPGA-based hardware logarithm generator for digital signal processing systems which require high-speed, real time logarithm operations. The proposed logarithm generator employs the modified quasi-symmetrical approach for an efficient hardware implementation. The error analysis and implementation results are also presented and discussed. The achieved results show that the proposed approach can reduce the approximation error and hardware area compared with traditional methods

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

EVALUATION OF THE EFFECTIVENESS OF AUTOMATIC SPRINKLING SYSTEM FOR SHALLOT CULTIVATION IN VINH CHAU DISTRICT, SOC TRANG PROVINCE

Shallot is one of the main crops in Vinh Chau district, Soc Trang province where farming techniques are still simply and mainly based on traditional irrigation types. In the district, groundwater is the main water source for daily uses of the local and farming activities. However, this water source increasingly becomes scarity due to over-exploitations. Therefore, this study aims to save water in agricultural production by applying automatic sprinkling irrigation model (Sprinklers system) in shallot farming and Vinh Chau district is selected as the research site. In this study, the amount of irrigation water for Shallot will be determined by CropWat model and the irrigation time will be measured by a soil moisture device (Takemura DM -15). The results show that the automatic sprinkling system model has saved by 43 - 59 % water amount and 85-91 % time of irrigation per 1000 m2 compared to traditional irrigation methods. The input costs of automatic sprinkling system are estimated at about 8 million VND/1000 m2 and it can be applied for many types of plants with its span of 4 years (depending on users’ uses). In conclusion, the automatic sprinkling irrigation model can alter traditional methods of famers in order to improve productivity, reduce negative impacts on groundwater source, and to adapt to water shortage due to climate change impacts