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En aquest Treball de Fi de Grau estudiem la connexió de Gauss-Manin per Interseccions Completes amb Singularitats Aïllades (ICIS), així com la seva relació amb certs polinomis de Bernstein-Sato. Pel cas d'hipersuperfícies amb singularitats aïllades, aquesta relació s'estableix en un resultat de Malgrange. Per estudiar la possible generalització d'aquest resultat al cas d'ICIS, generalitzem un algorisme de Schulze per calcular la connexió de Gauss-Manin d'una hipersuperfície amb singularitats aïllades al cas d'ICIS. Seguidament, fem ús de la nostra implementació en Magma d'aquest algorisme per calcular alguns exemples. Això ens permet concloure que un candidat per la generalització del resultat de Malgrange és el polinomi de Bernstein-Sato associat al mòdul de cohomologia local d'una ICIS., En este Trabajo Final de Grado estudiamos la conexión de Gauss-Manin para Intersecciones Completas con Singularidades Aisladas (ICIS) y su relación con ciertos polinomios de Bernstein-Sato. Para hipersuperficies con singularidades aisladas, esta relación se establece en un resultado de Malgrange. Para estudiar la posible generalización de este resultado a ICIS, generalizamos un algoritmo de Schulze para el cálculo de la conexión de Gauss-Manin para hipersuperfícies con singularidades aisladas al caso de ICIS. Seguidamente, usamos nuestra implementación en Magma del algoritmo para calcular algunos ejemplos. Esto nos permite concluir que un candidato para la generalización del resultado de Malgrange es el polinomio de Bernstein-Sato asociado al módulo de cohomología local de una ICIS., In this Bachelor thesis we study the Gauss-Manin connection of Isolated Complete Intersection Singularities (ICIS) and its relation with Bernstein-Sato polynomials. For isolated hypersurface singularities, this relation follows from a theorem by Malgrange. To study the possible generalization of this result to ICIS, we generalize an algorithm by Schulze for the computation of the Gauss-Manin connection of isolated hypersurface singularities to the case of ICIS. We then use our Magma implementation of this algorithm to compute some examples, concluding that a candidate for a generalization of Malgrange's result is the Bernstein-Sato polynomial associated to the local cohomology module of an ICIS., Outgoing

En aquest treball de final de grau ens centrarem en el problema de classificació analítica de branques amb un exponent característic. El nostre objectiu és construir una estratificació per un invariant analític concret: el semigrup de valors de l’ideal Jacobià. Aquesta construcció es basa en resultats de Casas-Alvero. Té l’avantatge que cada estrat és un obert afí que està parametritzat per un nombre mínim de paràmetres rellevants: quan varia algun d’aquests paràmetres canvia el tipus analític de la corba, llevat d’un nombre finit de coincidències del mateix tipus analític. Aquesta propietat és ideal per estudiar com varien altres invariants analítics. En particular, refinarem aquesta estratificació amb l’obtinguda pel polinomi de Bernstein-Sato., En este trabajo de final de grado nos centraremos en el problema de clasificación analítica de ramas con un exponente característico. Nuestro objetivo es construir una estratificación por un invariante analítico concreto: el semigrupo de valores del ideal Jacobiano. Esta construcción se basa en resultados de Casas-Alvero. Tiene la ventaja de que cada estrato es un abierto afín que está parametrizado por un número mínimo de parámetros relevantes: cuando varia alguno de estos parámetros el tipo analítico de la curva cambia, salvo un numero finito de coincidencias del mismo tipo analítico. Esta propiedad es ideal para estudiar cómo varia otros invariantes analíticos. En particular, refinaremos esta estratificación con la obtenida por el polinomio de Bernstein-Sato., In this final degree thesis we will focus on the analytic classification problem of branches with one characteristic exponent. Our goal is to construct a stratification by a concrete analytic invariant: the semigroup of values of the Jacobian ideal. This construction is based on results from Casas-Alvero. It has the advantage that each stratum is an afine open set parametrized by a minimum number of relevant parameters: when one of these parameters is modified the analytic type of the curve changes, except for a finite number of coincidences of the same analytic type. This property is ideal for studying how other analytic invariants change. In particular, we will refine this stratification with the one obtained by the Bernstein-Sato polynomial.

K. Saito va formular la pregunta de si una distribució continua és el límit de la distribució dels exponents espectrals de Hodge a l'interval [0,1) d'una hipersuperfície quan aquesta es mou en un sentit que s'ha de precisar. Ell ho va demostrar per a corbes irreductibles amb un límit molt específic. Aquest projecte es centra en el cas de singularitats de corbes planes. S'exploraran les diferents formes d'arribar a una distribució límit d'aquests invariants., K. Saito formuló la pregunta de si una distribución continua es el límite de la distribución de los exponentes espectrales de Hodge en el intervalo [0,1) de una hipersuperficie cuando esta se mueve en un sentido que se ha de precisar. Él lo demostró para curvas irreducibles con un límite muy específico. Este proyecto se centra en el caso de singularidades de curvas planas. Se explorarán las diferentes formas de llegar a una distribución límite de estos invariantes., K. Saito formulated the question whether a continuous distribution is the limit of the distribution of the Hodge spectral exponents in the interval [0,1) of a hypersurface as this hypersurface moves in a sense that has to be made precise. He proved it for irreducible plane curves with a very specific limit formulation. This project will focus on the case of irreducible plane curve singularities. Different formulations of achieving the limit of the distribution of these invariants will be explored.

In this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.

In this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.

In this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.

In this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.

In this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.

In this paper we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and the Tjurina numbers for any irreducible germ of plane curve singularity. This result is based on a closed formula for the minimal Tjurina number of an equisingularity class in terms of the sequence of multiplicities of the strict transform along a resolution. The key points for the proof are previous results by Genzmer, Wall and Mattei., The first and third authors were supported by Spanish Ministerio de Ciencia, Innovación y Universidades MTM2015-69135-P, Generalitat de Catalunya 2017SGR-932 projects, and they are with the Barcelona Graduate School of Mathematics (BGSMath), through the project MDM-2014-0445. The second and fourth authors were supported by Spanish Ministerio de Ciencia, Innovación y Universidades MTM2016-76868-C2-1-P., Peer Reviewed, Postprint (author's final draft)

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the cotangent models in [13] by both considering singular orbits and adding to the cotangent models a model for the prequantum line bundle. These singularities are generic in the sense that are given by Morse-type functions and include elliptic, hyperbolic and focus-focus singularities. Examples of systems admitting such singularities are toric, semitoric and almost toric manifolds, as well as physical systems such as the coupling of harmonic oscillators, the spherical pendulum or the reduction of the Euler’s equations of the rigid body on T *(SO(3)) to a sphere. Our geometric quantization formulation coincides with the models given in [11] and [21] away from the singularities and corrects former models for hyperbolic and focus-focus singularities cancelling out the infinite dimensional contributions obtained by former approaches. The geometric quantization models provided here match the classical physical methods for mechanical systems such as the spherical pendulum as presented in [4]. Our cotangent models obey a local-to-global principle and can be glued to determine the geometric quantization of the global systems even if the global symplectic classification of the systems is not known in general., Peer Reviewed, Postprint (published version)

In this thesis, we study the Kähler-Ricci flow on compact Kähler manifolds. We will begin with reviewing the estimates and known results of the Kähler-Ricci flow, then giving the proofs to the two main results on finite-time singularity of solutions to the Kähler-Ricci flow on a compact Kähler manifold with the maximal existence time T. For the first result, we prove that uniformly equivalent solutions to the Kähler-Ricci flow on a compact Kähler manifold develop the same singularity type (Type I or Type IIa) at the maximal time T. The second result, we assume there are uniformly equivalent solutions to the Kähler-Ricci flow, on a compact Kähler manifold where the eigenvalues of metrics admit a natural lower bound T-t/C . The solutions develop the same singularity type locally. This implies the solutions admit the same Type I singularity set, which is the open set where the solutions converge locally to shrinking solitons after rescaling the metric by 1/T-t.

In this thesis, we study the Kähler-Ricci flow on compact Kähler manifolds. We will begin with reviewing the estimates and known results of the Kähler-Ricci flow, then giving the proofs to the two main results on finite-time singularity of solutions to the Kähler-Ricci flow on a compact Kähler manifold with the maximal existence time T. For the first result, we prove that uniformly equivalent solutions to the Kähler-Ricci flow on a compact Kähler manifold develop the same singularity type (Type I or Type IIa) at the maximal time T. The second result, we assume there are uniformly equivalent solutions to the Kähler-Ricci flow, on a compact Kähler manifold where the eigenvalues of metrics admit a natural lower bound T-t/C . The solutions develop the same singularity type locally. This implies the solutions admit the same Type I singularity set, which is the open set where the solutions converge locally to shrinking solitons after rescaling the metric by 1/T-t.

Moser proved in 1965 in his seminal paper [15] that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group of a manifold coincide. In particular, this yields a classification of compact symplectic surfaces in terms of De Rham cohomology. In this paper we generalize these results for volume forms admitting transversal zeroes. In this case there is also a cohomology capturing the classification: the relative cohomology with respect to the critical hypersurface. We compare this classification scheme with the classification of Poisson structures on surfaces which are symplectic away from a hypersurface where they fulfill a transversality assumption (b-Poisson structures). We do this using the desingularization technique introduced in [10] and extend it to bm-Nambu structures., Peer Reviewed, Postprint (published version)

In this thesis, we study the Kähler-Ricci flow on compact Kähler manifolds. We will begin with reviewing the estimates and known results of the Kähler-Ricci flow, then giving the proofs to the two main results on finite-time singularity of solutions to the Kähler-Ricci flow on a compact Kähler manifold with the maximal existence time T. For the first result, we prove that uniformly equivalent solutions to the Kähler-Ricci flow on a compact Kähler manifold develop the same singularity type (Type I or Type IIa) at the maximal time T. The second result, we assume there are uniformly equivalent solutions to the Kähler-Ricci flow, on a compact Kähler manifold where the eigenvalues of metrics admit a natural lower bound T-t/C . The solutions develop the same singularity type locally. This implies the solutions admit the same Type I singularity set, which is the open set where the solutions converge locally to shrinking solitons after rescaling the metric by 1/T-t.

In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|ß, where x is the position of the single particle and ß is some positive real number., Postprint (published version)

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980., MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE., Bibliography: leaves 112-113., by Barbara R. Peskin., Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980., MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE., Bibliography: leaves 112-113., by Barbara R. Peskin., Ph.D.

Postprint (published version)

Tong, Pun Wai., Thesis (M.Phil.)--Chinese University of Hong Kong, 2009., Includes bibliographical references (leaves 77-78)., also in Chinese., Chapter 1 --- Introduction --- p.6, Chapter 2 --- Basic Terminologies --- p.8, Chapter 3 --- Causality in space-time --- p.12, Chapter 3.1 --- Preliminaries in space-time --- p.12, Chapter 3.2 --- Global causality condition --- p.14, Chapter 3.3 --- Domains of Dependence --- p.23, Chapter 4 --- Conjugate Points --- p.29, Chapter 4.1 --- Space of causal curves --- p.29, Chapter 4.2 --- "Jacobi field, conjugate point and length of geodesic" --- p.35, Chapter 4.3 --- Congruence of causal geodesics --- p.47, Chapter 5 --- Singularity Theorems --- p.57, Chapter 5.1 --- Definition of singularities in space-time --- p.57, Chapter 5.2 --- A singularity theorem of R. Penrose --- p.60, Chapter 5.3 --- A singularity theorem of S.W. Hawking and R. Penrose --- p.64, Appendix --- p.73, Bibliography --- p.77, http://library.cuhk.edu.hk/record=b5894113, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Tong, Pun Wai., Thesis (M.Phil.)--Chinese University of Hong Kong, 2009., Includes bibliographical references (leaves 77-78)., also in Chinese., Chapter 1 --- Introduction --- p.6, Chapter 2 --- Basic Terminologies --- p.8, Chapter 3 --- Causality in space-time --- p.12, Chapter 3.1 --- Preliminaries in space-time --- p.12, Chapter 3.2 --- Global causality condition --- p.14, Chapter 3.3 --- Domains of Dependence --- p.23, Chapter 4 --- Conjugate Points --- p.29, Chapter 4.1 --- Space of causal curves --- p.29, Chapter 4.2 --- "Jacobi field, conjugate point and length of geodesic" --- p.35, Chapter 4.3 --- Congruence of causal geodesics --- p.47, Chapter 5 --- Singularity Theorems --- p.57, Chapter 5.1 --- Definition of singularities in space-time --- p.57, Chapter 5.2 --- A singularity theorem of R. Penrose --- p.60, Chapter 5.3 --- A singularity theorem of S.W. Hawking and R. Penrose --- p.64, Appendix --- p.73, Bibliography --- p.77, http://library.cuhk.edu.hk/record=b5894113, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Summary: The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series., by Mark Wess., Thesis (Ph.D.)--Florida Atlantic University, 2008., Includes bibliography., Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

In this memory we follow the geometric approach of Casas’ boof [1] for studying of the singularities of plane germs of curves, which updates Enriques’ works to modern standards and reviews the modern development of the theorey from the point of view of infinitely near points. This memory has a two sided goal: on one hand, we want to acquire skills with the tools and concepts of the singularity theory and the valuative theory, both the classical ones and the more recent ones. On the other hand, we want to study in depth the different implicit concepts and notions involved in the Favre and Jonsson’s new approach, such as the ultrametric space structure of the set of irreducible germs of plane curves and the tree structure of the valuations.

First, a regularity property for global solutions of some superlinear parabolic problems is established. We obtain some new a priori estimates on the global classical solutions. Applying this property to the blow-up problem, we obtain a general criterion for the occurrence of blow-up. When applied to the study of global weak solutions, we obtain some regularity results, which answers some open questions in this topic., In this thesis, we obtain some new results on the formation of singularities for parabolic problems. We are interested in two typical singularities in parabolic evolution problems: blow-up and quenching., Second, dichotomy properties for some porous medium equations and some semilinear parabolic equations are discussed. Some conditions on universal quenching are also obtained. When the space dimension is one, we establish a new, strong dichotomy property. Bifurcation analysis of some stationary solutions in high dimension is also investigated., by Zheng Gaofeng., "June 2005.", Adviser: Chou Kai-Seng., Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0310., Thesis (Ph.D.)--Chinese University of Hong Kong, 2005., Includes bibliographical references (p. 84-89)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., in English and Chinese., School code: 1307., isbn: 9780542516054, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

First, a regularity property for global solutions of some superlinear parabolic problems is established. We obtain some new a priori estimates on the global classical solutions. Applying this property to the blow-up problem, we obtain a general criterion for the occurrence of blow-up. When applied to the study of global weak solutions, we obtain some regularity results, which answers some open questions in this topic., In this thesis, we obtain some new results on the formation of singularities for parabolic problems. We are interested in two typical singularities in parabolic evolution problems: blow-up and quenching., Second, dichotomy properties for some porous medium equations and some semilinear parabolic equations are discussed. Some conditions on universal quenching are also obtained. When the space dimension is one, we establish a new, strong dichotomy property. Bifurcation analysis of some stationary solutions in high dimension is also investigated., by Zheng Gaofeng., "June 2005.", Adviser: Chou Kai-Seng., Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0310., Thesis (Ph.D.)--Chinese University of Hong Kong, 2005., Includes bibliographical references (p. 84-89)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., in English and Chinese., School code: 1307., isbn: 9780542516054, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Chan Sik Kin., Thesis (M.Phil.)--Chinese University of Hong Kong, 2004., Includes bibliographical references (leaves 38-41)., s in English and Chinese., Chapter 1 --- Introduction --- p.4, Chapter 2 --- Preliminary analysis --- p.11, Chapter 3 --- Liapunov-Schmidt Reduction --- p.19, Chapter 4 --- The reduced problem: A Minimizing Procedure --- p.32, Chapter 5 --- Proof of the theorem 1.2 --- p.35, Bibliography --- p.38, http://library.cuhk.edu.hk/record=b5892097, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Chan Sik Kin., Thesis (M.Phil.)--Chinese University of Hong Kong, 2004., Includes bibliographical references (leaves 38-41)., s in English and Chinese., Chapter 1 --- Introduction --- p.4, Chapter 2 --- Preliminary analysis --- p.11, Chapter 3 --- Liapunov-Schmidt Reduction --- p.19, Chapter 4 --- The reduced problem: A Minimizing Procedure --- p.32, Chapter 5 --- Proof of the theorem 1.2 --- p.35, Bibliography --- p.38, http://library.cuhk.edu.hk/record=b5892097, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

by Lo, Ka-wah., Thesis (M.Phil.)--Chinese University of Hong Kong, 1995., Includes bibliographical references (leaves 76-81 (2nd gp.))., Acknowledgments --- p.i, p.ii, Notations --- p.iii, List of Figures --- p.v, List of Tables --- p.vii, Chapter 1. --- Introduction, Chapter 1.1 --- Motivation --- p.1, Chapter 1.2 --- Literature Review --- p.4, Chapter 1.3 --- Objective --- p.10, Chapter 2. --- Comparison of Different Approaches, Chapter 2.1 --- Sample Manipulator --- p.11, Chapter 2.1.1 --- Force Decomposition Method --- p.12, Chapter 2.1.2 --- Forward Rate Kinematics Base Method --- p.15, Chapter 2.1.3 --- Grassmann Geometry Method --- p.18, Chapter 2.2 --- Comparison Criteria --- p.20, Chapter 2.2.1 --- Computational Complexity --- p.20, Chapter 2.2.2 --- Scope of Application --- p.22, Chapter 2.3 --- Summary --- p.23, Chapter 3. --- Enumeration of Configuration Singularity, Chapter 3.1 --- Novel 6 DOF --- p.25, Chapter 3.1.1 --- Result Analysis --- p.31, Chapter 3.2 --- A 3 DOF with Symmetric Base --- p.33, Chapter 3.2.1 --- Result Analysis --- p.35, Chapter 3.3 --- A 3 DOF with Non-Symmetric Base --- p.36, Chapter 3.3.1 --- Result Analysis --- p.37, Chapter 3.4 --- A New Model of 6-SPS Defined by Kong et al --- p.40, Chapter 3.5 --- A New Class of 6-SPS Platform-Type Parallel Manipulator --- p.45, Chapter 3.5.1 --- The Hexagonal Base --- p.46, Chapter 3.5.2 --- The Pentagonal Base --- p.50, Chapter 3.5.3 --- The Tetragonal Base --- p.52, Chapter 3.5.4 --- The Triangular Base --- p.55, Chapter 3.6 --- Summary --- p.59, Chapter 4. --- Numerical Analysis, Chapter 4.1 --- Parameter Analysis --- p.60, Chapter 4.1.1 --- One Unknown Variable --- p.61, Chapter 4.1.2 --- Two Unknown Variables --- p.63, Chapter 4.2 --- Critical Value of Ratio R/q --- p.69, Chapter 4.3 --- Summary --- p.72, Chapter 5. --- Conclusions and Future Work, Chapter 5.1 --- Conclusions --- p.73, Chapter 5.2 --- Future Work --- p.75, References --- p.76, Appendix --- p.82, http://library.cuhk.edu.hk/record=b5888477, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

by Chu Lap-foo., Thesis (M.Phil.)--Chinese University of Hong Kong, 1994., Includes bibliographical references (leaves 68-69)., Introduction --- p.iii, Chapter 1 --- Basic Properties of Singular Solutions --- p.1, Chapter 1.1 --- An Asymptotic Radial Result --- p.2, Chapter 1.2 --- Local Uniqueness of Radial Solutions --- p.8, Chapter 2 --- Dirichlet Problem : Existence Theory I --- p.11, Chapter 2.1 --- Formulation --- p.12, Chapter 2.2 --- Explicit Solutions on Balls --- p.14, Chapter 2.3 --- The Moser Inequality --- p.19, Chapter 2.4 --- Existence of Solutions in General Domains --- p.24, Chapter 2.5 --- Spectrum of the Problem --- p.26, Chapter 3 --- Dirichlet Problem : Existence Theory II --- p.29, Chapter 3.1 --- Mountain Pass Lemma --- p.29, Chapter 3.2 --- Existence of Second Solution --- p.31, Chapter 4 --- Dirichlet Problem : Non-Existence Theory --- p.36, Chapter 4.1 --- Upper Bound of λ* in Star-Shaped Domains --- p.36, Chapter 4.2 --- Numerical Values --- p.41, Chapter 5 --- The Neumann Problem --- p.42, Chapter 5.1 --- Existence Theory I --- p.43, Chapter 5.2 --- Existence Theory II --- p.47, Chapter 6 --- The Schwarz Symmetrization --- p.49, Chapter 6.1 --- Definitions and Basic Properties --- p.49, Chapter 6.2 --- Inequalities Related to Symmetrization --- p.58, Chapter 6.3 --- An Application to P.D.E --- p.63, Bibliography --- p.68, http://library.cuhk.edu.hk/record=b5888160, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)