Summary of Applied Mathematics Doctoral Thesis

Purpose of the research: On the basis of identifying necessary metacognitive skills, the role and significance of those metacognitive skills for students of Primary Education, the thesis gives out the procedure and proposes an model of organizing activities, designs specific activities applied in the subjects of mathematics teaching methods to train metacognitive skills for students of Primary Education.

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The research objective: To study the methods used to modeling constraints and improve constraint solving capability. To apply symbolic execution technique in automatic test case generating. To implement proposed methods in automatic test case generating on string constraints and mixed constraints. To analyze and evaluate the obtained results.

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Objectives: The aim of the thesis is to develop Mickens’ methodology to construct NSFD methods for solving some important classes of differential equations arising in fields of science and technology.

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The objectives of the thesis: The thesis focus on the concept of martingale difference for a sequence set-valued random variables (which will then be called a weak set-valued martingale difference), showing some practical examples related to the weak set-valued martingale difference and proving its mathematical properties.

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Aims and objectives of the research: The thesis aims to find out the functions of practical situations, design practical situations, apply designed practical situations to organize cognitive activities for students in the process of teaching mathematics at high school, contribute to improving the quality of mathematics teaching at high schools towards student’s competence development.

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Research objectives: Applying theoretical views to develop competence, meaning and value of ICT application in Education and Training to propose solutions to develop Math teaching competence for Math pedagogical students with the support of ICT.

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Although the research direction on NSFD schemes for differential equations have achieved a lot ofresults shown by both quantity and quality of existing research works, real-world situations have always posednew complex problems in both qualitative study and numerical simulation aspects. On the other hand, there aremany differential models that have been established completely in the qualitative aspect but their correspondingdynamically consistent discrete models have not yet been proposed and studied

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Thesis objectives and tasks: Establishing a mathematical model, putting forward an algorithm applied for seeking the solar system's irradiance equalization configuration under the heterogeneous lighting conditions; establishing a mathematical model, putting forward an algorithm applied for choosing an optimal circuit switching method, from the initial connection configuration to the irradiance equalization configuration.

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This thesis aims to research on overview of automatic test case generating, symbolic execution applied into automatic test case generating. The modeling techniques based on Automata and Bitvector are also studied in this thesis. Apart from that, the analysis and evaluation of available test case generating methods on different constraint are mentioned. The quality and effectiveness of test cases generated by using symbolic execution are assessed.

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The thesis researches and builds an entity search technique based on implicit semantic relations using clustering methods to improve search efficiency. Apply context-aware techniques, build an vertical search engine that applies context-aware in its own knowledge base domain (aviation data). Propose to measure combinatorial similarity in the contextual query suggestion problem to improve the quality of suggestion.

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The objective of the thesis is to develop the iterative method and combining it with other methods to study qualitative and especially the method of solving some two-point boundary problems for the fourth-order differential equations and systems, arising in beam bending theory without using condition of growth rate at infinity, Nagumo condition, etc. of the right-hand side function.

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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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The objective of this thesis is to apply Lagrange equations with multipliers to study dynamics and control of Delta parallel robots. Particularly, mechanical model, mathematical model, and control algorithms for Delta parallel robots are developed as a scientific basis for the research and development of parallel Delta robots.

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