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Thermal-Mechanical Effect Analysis of Structures under Intensive Laser Irradiation
The coupled thermal—mechanical breakage effect of structures induced by intensivelaser irradiation is an important research topic of the laser breakage mechanism. In thisdissertation, the thermal—mechanical effects of structures irradiat....
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Geometry of Lagrangian Submanifolds and Related Problems
In this thesis, we mainly study geometry of Lagrangian submanifolds and related problems, including Bernstein type theorems, construction of special Lagrangian submanifolds, Hamiltonian minimal Lagrangian submanifolds and Lagrangian submanif....
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Distributions of Closed Orbits and Statistical Properties of Some Hyperbolic Dynamical Systems
In Chapter 1, We consider the billiard flows on the plane with finitely many scatters with smooth boundary satisfying the visibility assumption and describe the asymptotics of the distribution of closed orbits with an even collision number.....
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Martingale Transform and Related Problems
The present Ph.D. thesis mainly deals with the the martingale transform for right processes and related problems. Firstly, we consider the problem of the representation formula for the transition probability density of a right process under....
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Statistical Inference for Discretely Sampled Processes of Ornstein-Uhlenbeck Type
Processes of Ornstein-Uhlenbeck type are an important special case of Markov processes with jumps. Recently, they are widely used in describing the connections between branching processes and Levy processes, the stochastic volatilities of fi....
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Some Problems of Estimating a Distribution Function with Missing Data
The missing data phenomenon is universal: Respondents in a household survey may refuse to report private information, In an industrial process some results are missing because of mechanical breakdowns, Some data are missing with or without i....
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Learning on Riemannian Manifold: Online Classification and Multi-Kernel Algorithms
With the development of modern science and technology, we are confronted with a mass of data every day. How to understand and deal with these data and then make use of them become an important research topic in modern science and technology.....
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Testing Serial Correlation and Heteroscedasticity in Partial Linear Models
Testing serial correlation and heteroscedasticity in residuals (errors) for regressionmodels are important practice in econometric data analysis. We generally assume thatthe errorsε_i's are mutually independent and homoscedastic in regressi....
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Properties of Solutions for One Dimensional Compressible Navier-Stokes Equations
In this thesis, we are concerned with some properties of solutions for one dimensional compressible Navier-Stokes equations.In Chapter one, we study the global stability of strong rarefaction waves for compressible Navier-Stokes equationswit....
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Results on Existence and Regularity of Solutions for Some Quasilinear Equations
In this paper, we consider the existence, regularity and decay of weak solutionsfor the following pH.S.Zhou [46], by Vanishing, Nonvanishing and variable scaling we prove theboundedness of the corresponding (PS)-sequences, then get the exist....
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Semilinear Elliptic Systems and Schr(?)dinger Equations
In this paper,we are concerned with the existence of solutions of semilinear ellipticsystems on bounded domain and the nonlinear Schro¨dinger equations on RN.In chapter two, we consider the semilinear elliptic systems of the formwhere ? ? R....
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The Mathematical Analysis on Element Energy Projection Method
The finite element method is one of the efficient numerical methods to solve partial different equations. But in general the derivatives of the finite element solution are not continuous across the boundary of elements and have low global ac....
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Long-Time Behaviors of Solutions for Some Classes of Nonlinear Evolution Equations
In this thesis we deal with the existence and stability of periodic or almostperiodic solutions for some classes of nonlinear evolution equations related to PDEwith delay or not. Meanwhile, we consider the existence of global attractors, ine....
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Conservation and Symplectic Properties of Continuous Finite Element Methods for Hamiltonian Systems
Hamiltonian system is the most important dynamic system. Feng Kang has pointed out, all the real physical processes with negligible dissipation can be expressed, in some way or orther, in suitable Hamiltonian forms. They are ordinary differe....
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Large-Sample Theory of the Maximum Likelihood Estimate in Generalized Linear Models
We address in this thesis some important topics in the large-sample theory forgeneralized linear models (GLM). They are weak consistency, strong consistencyand asymptotic normality of the maximum likelihood estimate (MLE) of the para-meters.....
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Study on Several Models for Correlated Data Analysis
Based on the theory of generalized estimating equations(GEE), this thesisstudies the parameter estimation in several statistical models for longitudinal data.Firstly, the parameter estimation in a typical hierarchical generalized linearmodel....
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The Discrete-Time Risk Models with Dividends and the Applications of Transition Probabilities for Mar
The risk theory has been developed in a so long period that the theory about the classical risk model has almost been perfected, especially, about the classical continuous time risk model. Beyond all doubt, the theory is playing am important....
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Fuzzy Relation Posynomial Geometric Programming
In 1965, Zadeh, a well-known expert from the United States in cybernetics, produced the concept of fuzzy sets. It symbolized the birth of the fuzzy math-ematics academics. Through decades of efforts by the researchers all over theworld, the....
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A Study of Preemptive Scheduling on Parallel Machines
This thesis mainly concerns design and analysis of approximation algorithms forpreemptive (semi-)online parallel machine scheduling problems. For each problemconsidered in this thesis, both lower bound and online approximation algorithm arep....
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A Study of Scheduling on Parallel Machines with Activation Cost
This thesis mainly concerns design and analysis of approximation algorithms for(semi-)online parallel machine scheduling problems with machine activation cost. Foreach problem considered in this thesis, both lower bound and (semi-)online app....
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A Study of Partitioning Problems with Matroid Constraint
Partitioning problem is one of the classical combinatorial optimization problems. Many combinatorial optimization problems can be transformed to partitioning problem, therefore, it has many application and has received many researcher's atte....
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Controllability and Regularity for Partial Differential Equations
In this dissertation, we discuss the controllability and regularity for some control systemsgoverned by partial differential equations.We study the controllability of two classes of important quasilinear degenerate parabolicequations (Newton....
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Projection Methods for Problems in Control Theory and Computation
The present Ph.D. dissertation is concerned with projection methods for large-scale problems in control theory and computation. We propose Galerkin method and minimal residual method for iteratively solving generalized Sylvester equations. T....
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Optimal Control Problems Governed by a Parabolic System with k-approximate Periodic Solutions
This dissertation is concerned with several problems related to the optimal control andidentification of intrinsic parameters of a parabolic system. The system is assumed to havethe so-called k-approximate periodic solutions. A k-approximate....
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A Study of Some New Problems Arising from the Field of Minimum Cost Network Flows
Everywhere we look in our daily lives, networks are apparent. Network flows areof growing interest over the last few decades from the point of view of both applica-tions and theory. The topic of network flows has applications in such wide fi....
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A Study of Some Three-stage Clos Network Nonblocking Problems
The switching network problem is an combinatorial optimization problem originated from the connection of telephone network. At first, the study on the switching network is in the classical circuit switching model. However, with the developme....
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Linearly Constrained Matrix Least Squares Problems: Theory and Algorithms
In the recent decades, with the development of society and the progress of science, more and more new problems which are urgent to be solved arise from the engineer technology and many other domains. Many of these problems can be reduced to....
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Finite Element Modelling and Simulations of Carbon Nanotubes Based on Atomic Potentials
Carbon nanotubes (CNTs) have very amazing mechanical, electronic, thermal and optical properties, which enable them many potential applications. Since the discovery of CNTs, great attention has been paid to the prediction of their mechanical....
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Inverse Eigenvalue Problems in Structural Dynamics
This dissertation studies the inverse eigenvalue problems in structural dynamics, including vibration inverse problems for the spring-mass system, the discrete beam, damped systems and the damage detection in rods. The main contribution is a....
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Modling, Identification and Topology Optimization of Damped Structural
Damping is a difficult field in structural dynamic analysis. The proportional damping assumption used in dynamical analysis does not match the requirement of accuracy. It is difficult to design the structural modal damping ratio. Although (f....