Doctoral dissertation in mathematics

The thesis "Stability of some classes of degenerate two-phase difference systems with delay" is to study the stability of degenerate two-phase systems with mixed delay in the direction of variation; Stability and dissipation in finite domain of degenerate 2-D system with variable delay; Evaluation of the gain set and control design for a degenerate 2-D system in the Roesser model with variable delay;... Please refer to it!

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The dissertation is written on the basis of the paper published in Annales Polonici Mathematici, the paper published in Acta Mathematica Vietnamica and the paper published in Results in Mathematics.

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In the dissertation, we consider the problem of finding the shortest path between two points along a sequence of adjacent triangles in a general setting. The sequence of triangles is replaced by a sequence of ordered line segments. The 3D space is replaced by a Euclidean space.

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The thesis mainly aims to solve the following tasks: Firstly, the thesis extensively analyzes a wide range of existing approaches for the ME detection in scientific document images. Then, the thesis investigates and proposes novel methods to improve the detection accuracy of MEs. After enhancing the detection accuracy of MEs, the thesis investigates and pro poses a framework to improve the accuracy of the recognition of MEs in scientific document images.

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The dissertation has five chapters and a list of references. The chapters concentrate on the following issues: In Chapter 1, we recall some classical results of the problem and some basic concepts from variational analysis and nonsmooth analysis. In Chapter 2, we investigate some new models of nonlinear nonlocal regularity; Chapter 3 is devoted to the study of metric perturbation of Milyutin-type regularity on a fixed set under composition of a set-valued mapping and a Lipschitz single-valued mapping;...

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The thesis mainly aims to solve the following tasks: Firstly, the thesis extensively analyzes a wide range of existing approaches for the ME detection in scientific document images. Then, the thesis investigates and proposes novel methods to improve the detection accuracy of MEs. After enhancing the detection accuracy of MEs, the thesis investigates and pro poses a framework to improve the accuracy of the recognition of MEs in scientific document images.

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The research related to this dissertation was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) and Hanoi National University of Education.

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The dissertation has four chapters: Chapter 1 - Background Materials; Chapter 2 - Analysis of an Algorithm in Indefinite Quadratic Programming; Chapter 3 - Qualitative Properties of the Minimum Sum-of-Squares Clustering Problem; Chapter 4 - Some Incremental Algorithms for the Clustering Problem.

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Objectives: The main objective of the dissertation is to research and develop fuzzy clustering techniques on remote sensing image data in order to improve accuracy and improve clustering quality of clustering algorithms.

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The dissertation has four chapters: Chapter 1 - Existence of solutions; Chapter 2 - Stability for global, local and stationary solution sets; Chapter 3 - Continuity and directional differentiability of the optimal value function; Chapter 4 - Stability for extended trust region subproblems.

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The dissertation is divided into four chapters: Chapter 1 - Preliminaries; Chapter 2 - Lyapunov exponents for dynamic equations; Chapter 3 - Bohl exponents for implicit dynamic equations; Chapter 4 - Stability radius for implicit dynamic equations.

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Objectives: The main objective of this thesis is to study the problem of stability analysis and applications in control of discrete-time 2-D systems described by Roesser model with certain types of stochastic parameters. The research includes the methodology development and establishment of analysis and synthesis conditions of the following specified models.

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Aims of the study: Designing a module-based document on Teaching Methods in secondary school Mathematics and to produce a methodology for using those modules in the teacher training process at the Teachers Training College in Lao PDR, to improve the quality of training and contribute to fostering self-study capacity for students of Mathematics Teacher training College.

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Objectives: The main objectives of this thesis is to study the problem of stability analysis and applications in control of discrete-time 2-D systems described by Roesser model with certain types of stochastic parameters. The research includes the methodology development and establishment of analysis and synthesis conditions of the following specified models.

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The objectives of this dissertation are to study the asymptotic behavior of solutions of these nonlocal problems via existence of (its finite dimensional) global attractors, and the existence and exponential stability of stationary solutions.

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The purpose of the study: The dissertation studies how to design learning situations and demonstrates that designed learning situations can support assessing the calculation capacity of senior primary school graders through experiential activities. Accordingly, the dissertation proposes orientations to improve students' calculation capacity in the teaching process, contributing to improving the effectiveness of mathematics teaching in primary school.

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The purpose of the dissertation is to research on the development of new and quality solutions using graph theory and automata, suggesting their applications in, and applying them to steganography and searchable encryption.

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Study on hydraulic stability and structural integrity of RAKUNA-IV armour units when randomly placed on the seaward slope of a rubble mound breakwater by means of experiments on physical models in a wave flume and simulations in mathematical models. The results of the research were later applied to a specific breakwater. Recommendations and solutions were thereby put forward for the design, production and construction of RAKUNA-IV armour units when applied to rubble mound breakwaters in reality.

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The thesis aims to study the problems of image processing under the approach of HA theory. Building a gray level transformation function in S form to enhance the contrast for color images to apply HA. New homogeneity with hedge algebra applies to enhance contrast for color images. Building a photo fading transformation that applies to multi-channel images does not lose image detail.

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Thesis with the aim of focusing on two main issues. The first is time series modeling by states in which each state is a deterministic probability distribution (normal distribution). Based on the experimental results to assess the suitability of the model. Second, combine Markov chains and fuzzy time series into new models to improve forecast accuracy. Expand the model with high-level Markov chains to be compatible with seasonal data.

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