No description available.

No description available.

No description available.

Cette thèse est consacrée à l’étude du système de Boussinesq stationnaire:-νΔu+(u⋅∇)u+∇π=θg, div u=0,dans Ω(1a)-κΔθ+u⋅∇θ=h,dans Ω (1b)où Ω⊂R^3 est un ouvert, borné et connexe; les inconnues du système sont u,π et θ: la vitesse, la pression et la température du fluide, respectivement; ν>0 est la viscosité cinématique du fluide, κ>0 est la diffusivité thermique du fluide, g est l’accélération de la pesanteur et h est une source de chaleur appliquée au fluide.L’objectif de cette thèse est l’étude de la théorie L^p pour le système de Boussinesq en considérant deux différents types de conditions aux limites du champ de vitesse. En effet, dans une première partie, nous considérons une condition de Dirichlet non homogèneu=u_b, sur Γ (2)où Γ désigne la frontière du domaine. Dans une deuxième partie, nous considérons une condition de Navier non homogèneu⋅n=0,2[D(u)n]_τ+αu_τ=a,sur Γ(3)où D(u)=1/2 (∇u+(∇u)^T ) est le tenseur de déformation associé au champ de vitesse u, n est le vecteur normal unitaire extérieur, τ est le correspondant vecteur tangent unitaire, α et a sont une fonction scalaire de friction et un champ de vecteur tangentiel donnés sur la frontière, respectivement. De plus, la condition aux limites pour la température sera, dans les deux premières parties, une condition aux limites de Dirichlet non homogèneθ=θ_b, sur Γ. (4)Alors, premièrement, nous étudions l’existence et l’unicité d’une solution faible pour le problème (1), (2) et (4) dans le cas hilbertien. Également, l’existence de solutions généralisées pour p≥3/2 et des solutions fortes pour 1<p<∞ est démontrée. De plus, l’existence et l’unicité de la solution très faible sont étudiées. Il est intéressant de noter que puisque une condition de Dirichlet non homogène est considérée pour le champ de vitesse, le fait que la frontière du domaine pourrait être non-connexe joue un rôle fondamental puisque cela apparait de manière explicite dans les hypothèses des principaux résultats.D’autre part, dans la deuxième partie, nous étudions l’existence de solutions faibles dans le cas hilbertien, ainsi que l’existence de solutions généralisées pour p>2 et des solutions fortes pour p≥6/5 pour le problème (1), (3) et (4). Notez que l’hypothèse d’une frontière non-connexe, mentionnée précédemment, ne figurait pas dans cette partie du travail en raison de la restriction d’imperméabilité de la frontière.Enfin, dans la dernière partie de cette thèse, nous étudions la théorie L^p pour les équations de Stokes avec la condition de Navier (3). Plus précisément, nous examinons la régularité W^(1,p) pour p≥2 et la régularité W^(2,p) pour p≥6/5.Mots clés: système de Boussinesq; régularité L^p; solutions faibles; solutions fortes; solutions très faibles / This thesis is dedicated to the study of the stationary Boussinesq system:-νΔu+(u⋅∇)u+∇π=θg, div u=0,in Ω(1a)-κΔθ+u⋅∇θ=h,in Ω (1b)where Ω⊂R^3 is an open bounded connected set; u,π and θ are the velocity field, pressure and temperature of the fluid, respectively, and stand for the unknowns of the system; ν>0 is the kinematic viscosity of the fluid, κ>0 is the thermal diffusivity of the fluid, g is the gravitational acceleration and h is a heat source applied to the fluid.The aim of this thesis is the study of the L^p-theory for the stationary Boussinesq system in the context of two different types of boundary conditions for the velocity field. Indeed, in the first part of the thesis, we will consider a non-homogeneous Dirichlet boundary conditionu=u_b, on Γ (2)where Γ denotes the boundary of the domain; meanwhile in the second part, the velocity field will be prescribed through a non-homogeneous Navier boundary conditionu⋅n=0,2[D(u)n]_τ+αu_τ=a,on Γ(3)where D(u)=1/2 (∇u+(∇u)^T ) is the strain tensor associated with the velocity field u, n is the unit outward normal vector, τ is the corresponding unit tangent vector, α and a are a friction scalar function and a tangential vector field defined both on the boundary, respectively. Further, the boundary condition for the temperature will be, in the first two parts of the thesis, a non-homogeneous Dirichlet boundary conditionθ=θ_b, on Γ. (4)Then, firstly, we study the existence and uniqueness of the weak solution for the problem (1), (2) and (4) in the hilbertian case. Also, the existence of generalized solutions for p≥3/2 and strong solutions for 1<p<∞ is showed. Furthermore, the existence and uniqueness of the very weak solution is studied. It is worth to note that because a non-homogeneous Dirichlet boundary condition is considered for the velocity field, the fact that the boundary of the domain could be non-connected plays a fundamental role since it appears in an explicit way in the assumptions of some of the main results.In the second part, we study the existence of weak solutions in the hilbertian case, as well as the existence of generalized solutions for p>2 and strong solutions for p≥6/5 for the problem (1), (3) and (4). Note that the assumption of a non-connected boundary, which was mentioned before, will not appear here due to the impermeability restriction on the boundary.Finally, in the last part of this thesis, we study the L^p-theory for the Stokes equations with Navier boundary condition (3). Specifically, we deal with the W^(1,p)-regularity for p≥2 and the W^(2,p)-regularity for p≥6/5.Keywords: Boussinesq system; L^p-regularity; weak solutions; strong solutions; very weak solutions

by Chi-Fai Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 53-54). / Abstract also in Chinese. / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter §1.1 --- Polynomial Interpolation --- p.1 / Chapter §1.2 --- Conjugate Gradient Type Methods --- p.6 / Chapter §1.3 --- Outline of the Thesis --- p.10 / Chapter Chapter 2 --- INTEGRAL EQUATIONS --- p.11 / Chapter §2.1 --- Integral Equations --- p.11 / Chapter §2.2 --- Numerical Treatments of Second Kind Integral Equations --- p.15 / Chapter Chapter 3 --- FAST ALGORITHM FOR SECOND KIND INTEGRAL EQUATIONS --- p.20 / Chapter §3.1 --- Introduction --- p.20 / Chapter §3.2 --- The Approximation --- p.24 / Chapter §3.3 --- Error Analysis --- p.35 / Chapter §3.4 --- Numerical Examples --- p.40 / Chapter §3.5 --- Concluding Remarks --- p.51 / References --- p.53

近十年間，離子液體在生物催化和蛋白質化學方面的廣泛應用引起了鑒定蛋白質在離子液體中特性的研究興趣。本研究以古菌Pyrococcus horikoshii的酰基磷酸酶acylphosphatase (PhAcP) 和50% (v/v) 離子液體1-乙基-3-甲基咪唑四氟硼酸鹽 ([EMIM][BF₄]) 作為研究模型，首次利用多維核磁共振譜對蛋白質在離子液體中的結構和穩定性作高解析度的分析。我們首先通過蛋白質主鏈共振歸屬，得出PhAcP每個被歸屬的胺基酸在50% (v/v) [EMIM][BF₄] 中¹³C[superscript α]、¹³C[superscript β]、¹³CO、¹⁵N、H[superscript N]和H[superscript α]原子的化學位移。¹³C的化學位移相對無序纏捲狀態的¹³C化學位移的偏差分析 (¹³C secondary shift)，以及二級結構之間的nuclear Overhauser effect (NOE) 連接顯示PhAcP在50% (v/v) [EMIM][BF₄] 中的二級結構與PhAcP的自然結構大致相同，其三級結構亦無顯著變化。此外，我們以二維的¹H-¹⁵N HSQC實驗觀察在318K、328K和338K這三個溫度下的硫氰酸胍 (GdnSCN) 誘導蛋白質變性，發現同一溫度下無論50% (v/v) [EMIM][BF₄]是否存在，PhAcP的變性曲線都互相重疊，得到的 [GdnSCN]₁[subscript /]₂值也相同，由此可推斷50% (v/v) [EMIM][BF₄] 對PhAcP的穩定性沒有影響。 / The extensive application of ionic liquid in biocatalysis and protein chemistry in the past decade arouses interest in the characterization of protein behavior in ionic liquid. This study demonstrates the use of multi-dimensional nuclear magnetic resonance (NMR) spectroscopy to investigate the structure and conformational stability of protein in ionic liquid at a high resolution for the first time, with Pyrococcus horikoshii acylphosphatase (PhAcP) and 50% (v/v) 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF₄]) as a study model. The backbone amide resonances of PhAcP in 50% (v/v) [EMIM][BF₄] were assigned in order to obtain the chemical shifts of ¹³C[superscript α], ¹³C[superscript β], ¹³CO, ¹⁵N, HN and H[superscript α] of each assigned residue. The estimation of secondary structure by the ¹³C secondary shift analysis and the nuclear Overhauser effect (NOE) connectivities observed within secondary structures together suggest that PhAcP has secondary structures arranged in native-like topology and there is no major alteration in the tertiary structure in 50% (v/v) [EMIM][BF₄]. Guanidine thiocyanate (GdnSCN)-induced denaturation was performed at 318K, 328K and 338K and monitored by 2D ¹H-¹⁵N HSQC experiments to study the conformational stability of PhAcP in 50% (v/v) [EMIM][BF₄]. The overlapping denaturation curves and consistent [GdnSCN]₁[subscript /]₂ values obtained at each temperature indicate no observable trend of stability alteration. / Detailed summary in vernacular field only. / Lee, Tsz Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 57-63). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgements --- p.iii / Contents --- p.iv / Abbreviations --- p.vii / List of Figures --- p.viii / List of Tables --- p.ix / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction to ionic liquid --- p.1 / Chapter 1.1.1 --- Ionic liquid as reaction medium, co-solvent and additive in biocatalysis and protein chemistry --- p.1 / Chapter 1.1.2 --- The impact of ionic liquid on protein structure and stability is poorly understood --- p.3 / Chapter 1.2 --- PhAcP in [EMIM][BF₄] as a model to study the structure and stability of protein in ionic liquid by NMR spectroscopy --- p.6 / Chapter 1.2.1 --- The application of [EMIM][BF₄] with protein --- p.6 / Chapter 1.2.2 --- The background of PhAcP --- p.9 / Chapter 1.2.3 --- Overview of the study --- p.10 / Chapter Chapter 2 --- Materials and Methods --- p.12 / Chapter 2.1 --- Expression and purification of PhAcP --- p.12 / Chapter 2.1.1 --- Expression of PhAcP in Escherichia coli system --- p.12 / Chapter 2.1.2 --- Purification of PhAcP --- p.14 / Chapter 2.2 --- Solubility determination --- p.15 / Chapter 2.3 --- NMR experiments --- p.17 / Chapter 2.3.1 --- General procedures and sample preparation --- p.17 / Chapter 2.3.2 --- ¹H-¹⁵N HSQC spectra in various concentrations of [EMIM][BF₄] --- p.18 / Chapter 2.3.3 --- Structural characterization --- p.18 / Chapter 2.3.4 --- Stability characterization --- p.19 / Chapter Chapter 3 --- Results --- p.21 / Chapter 3.1 --- Can the solubility of PhAcP in [EMIM][BF₄] reach the millimolar range required for NMR study? --- p.21 / Chapter 3.2 --- Determination of the [EMIM][BF₄] concentration for a feasible NMR study --- p.23 / Chapter 3.3 --- Backbone resonance assignment of PhAcP in 50% (v/v) [EMIM][BF₄] --- p.26 / Chapter 3.4 --- Structural characterization of PhAcP in 50% (v/v) [EMIM][BF₄] --- p.29 / Chapter 3.4.1 --- Secondary structure estimation by ¹³C secondary shifts --- p.29 / Chapter 3.4.2 --- NOE connectivities within secondary structures --- p.35 / Chapter 3.5 --- Characterization of the conformational stability of PhAcP in 50% (v/v) [EMIM][BF₄] by guanidine thiocyanate-induced denaturation --- p.40 / Chapter Chapter 4 --- Discussion --- p.46 / Chapter 4.1 --- The structure of PhAcP in 50% (v/v) [EMIM][BF₄] resembles the native conformation --- p.46 / Chapter 4.2 --- The conformational stability of PhAcP has no observable change in 50% (v/v) [EMIM][BF₄] --- p.47 / Chapter 4.3 --- Insight into the application of enzyme in ionic liquid --- p.48 / Chapter 4.4 --- Limitation of the study --- p.49 / Chapter 4.5 --- Insight into future studies --- p.50 / Chapter Chapter 5 --- Conclusions --- p.51 / Appendix --- p.53 / References --- p.57

by Li Jingzhi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 56-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Parameter identification problems --- p.1 / Chapter 1.2 --- Overview of existing numerical methods --- p.2 / Chapter 1.3 --- Outline of the thesis --- p.4 / Chapter 2 --- General Framework --- p.6 / Chapter 2.1 --- Abstract inverse problem --- p.6 / Chapter 2.2 --- Abstract multilevel models --- p.7 / Chapter 2.3 --- Abstract MMC algorithm --- p.9 / Chapter 3 --- Dual Viewpoint and Convergence Condition --- p.15 / Chapter 3.1 --- Dual viewpoint of nonlinear multigrid method --- p.15 / Chapter 3.2 --- Convergence condition of MMC algorithm --- p.16 / Chapter 4 --- Applications of MMC Algorithm for Parameter Identification in Elliptic and Parabolic Systems --- p.20 / Chapter 4.1 --- Notations --- p.20 / Chapter 4.2 --- Parameter identification in elliptic systems I --- p.21 / Chapter 4.3 --- Parameter identification in elliptic systems II --- p.23 / Chapter 4.4 --- Parameter identification in parabolic systems I --- p.24 / Chapter 4.5 --- Parameter identification in parabolic systems II --- p.25 / Chapter 5 --- Numerical Experiments --- p.27 / Chapter 5.1 --- Test problems --- p.27 / Chapter 5.2 --- Smoothing property of gradient methods --- p.28 / Chapter 5.3 --- Numerical examples --- p.29 / Chapter 6 --- Conclusion Remarks --- p.55 / Bibliography --- p.56

Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Ao, Weiwei. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 178-186). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Interior Spike Solutions for Lin-Ni-Takagi Problem --- p.7 / Chapter 1.1.1 --- Background and Main Results --- p.7 / Chapter 1.1.2 --- Sketch of the Proof of Theorem 1.1.1 --- p.12 / Chapter 1.2 --- The A2 and B2 Chern-Simons System --- p.14 / Chapter 1.2.1 --- Background --- p.14 / Chapter 1.2.2 --- Previous Results --- p.19 / Chapter 1.2.3 --- Main Results --- p.20 / Chapter 1.2.4 --- Sketch of the Proof for A₂ Case --- p.21 / Chapter 1.2.5 --- Sketch of the Proof for B₂ Case --- p.26 / Chapter 1.3 --- Organization of the Thesis --- p.27 / Chapter 2 --- The Lin-Ni-Takagi Problem --- p.29 / Chapter 2.1 --- Notation and Some Preliminary Analysis --- p.29 / Chapter 2.2 --- Linear Theory --- p.35 / Chapter 2.3 --- The Non Linear Projected Problem --- p.40 / Chapter 2.4 --- An Improved Estimate --- p.43 / Chapter 2.5 --- The Reduced Problem: A Maximization Procedure --- p.50 / Chapter 2.6 --- Proof of Theorem 1.1.1 --- p.58 / Chapter 2.7 --- More Applications and Some Open Problems --- p.60 / Chapter 3 --- The Chern-Simons System --- p.66 / Chapter 3.1 --- Proof of Theorem 1.2.1 in the A₂ Case --- p.66 / Chapter 3.1.1 --- Functional Formulation of the Problem --- p.66 / Chapter 3.1.2 --- First Approximate Solution --- p.68 / Chapter 3.1.3 --- Invertibility of Linearized Operator --- p.72 / Chapter 3.1.4 --- Improvements of the Approximate Solution: O(ε) Term --- p.76 / Chapter 3.1.5 --- Next Improvement of the Approximate Solution: O(ε²) Term --- p.78 / Chapter 3.1.6 --- A Nonlinear Projected Problem --- p.82 / Chapter 3.1.7 --- Proof of Theorem 1.2.1 for A₂ under Assumption (i) --- p.85 / Chapter 3.1.8 --- Proof of Theorem 1.2.1 for A₂ under Assumption (ii) --- p.94 / Chapter 3.1.9 --- Proof of Theorem 1.2.1 for A₂ under Assumption (iii) --- p.99 / Chapter 3.2 --- Proof of Theorem 1.2.1 in the B₂ Case --- p.100 / Chapter 3.2.1 --- Functional Formulation of the Problem for B₂ Case --- p.100 / Chapter 3.2.2 --- Classi cation and Non-degeneracy for B₂ Toda system --- p.101 / Chapter 3.2.3 --- Invertibility of Linearized Operator --- p.105 / Chapter 3.2.4 --- Improvements of the Approximate Solution --- p.106 / Chapter 3.2.5 --- Proof of Theorem 1.2.1 for B₂ under Assumption (i) --- p.112 / Chapter 3.2.6 --- Proof of Theorem 1.2.1 for B₂ under Assumption (ii) --- p.122 / Chapter 3.2.7 --- Proof of Theorem 1.2.1 for B₂ under Assumption (iii) --- p.127 / Chapter 3.3 --- Open Problems --- p.128 / Chapter 4 --- Appendix --- p.129 / Chapter 4.1 --- B₂ and G₂ Toda System with Singular Source --- p.129 / Chapter 4.1.1 --- Case 1: B₂ Toda system with singular source --- p.130 / Chapter 4.1.2 --- Case 2: G₂ Toda system with singular source --- p.136 / Chapter 4.2 --- The Calculations of the Matrix Q₁ --- p.148 / Chapter 4.3 --- The Calculations of the Matrix Q₁ --- p.169 / Bibliography --- p.178

Ngai To. / "May 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Nous nous intéressons dans cette thèse à l'étude d'une équation parabolique quasilinéaire dans laquelle la diffusion est paramétrée par la longueur des différentes interactions non locales. Pour ce qui est du problème stationnaire associé, après avoir montré des résultats d'existence, d'unicité et de continuité. Nous présentons ensuite un critère général d'inversibilité dépendant du paramètre, ce critère très important va par la suite nous permettre en exemple d'application de retrouver des résultats d'inversibilités déjà connus lorsque le paramètre est égale au diamètre du domaine. Nous donnons ensuite un résultat de principe de comparaison de solutions symétriques radiales et une généralisation du compte du nombre de solutions. Enfin nous donnons quelques applications numériques utilisant une méthode de point fixe et de Newton pour illustrer ces résultats. Pour le problème d'évolution, après avoir montré l'existence d'un attracteur global associé à notre problème, nous démontrons une estimation $L^\infty$ de la solution en fonction d'estimations $L^q$, $q>1$ utilisant des itérations de type Moser.