S. K. Wong

Bio: S. K. Wong is an academic researcher from State University of New York System. The author has contributed to research in topics: Interquartile range & Equations of motion. The author has an hindex of 1, co-authored 1 publications receiving 449 citations.

Field and particle equations for the classical Yang-Mills field and particles with isotopic spin

Abstract: A complete system of equations describing the interaction between the Yang-Mills field and isotopic-spin-carrying particles in the classical limit is extracted from the equations of motion for the quantum fields. Some simple consequences are derived. The consistency of the equations is investigated.

The Psychological Impacts of COVID-19 Pandemics on Pregnant Women in Hong Kong—Results of a Web-Based Cross-Sectional Survey

Abstract: Background: We sought to assess the anxiety and depression scores of pregnant women in Hong Kong during the COVID-19 pandemic and to evaluate the impact of demographic, economic and social factors on these scores. Methods: This was part of an ongoing worldwide cross-sectional study conducted from 22 May 2020 to 28 February 2021. Data were collected through an anonymous web-based survey. The severity of depression and anxiety was assessed using the Patient Health Questionnaire-9 (PHQ-9) score and the General Anxiety Disorder-7 (GAD-7) score, respectively. Results: A total of 361 participants completed both the GAD-7 and PHQ-9 questionnaires. Participants with psychiatric illness reported a significant higher median GAD-7 score (6.00, interquartile range [IQR] 3.00–7.75 vs. 2.00, IQR 0.00–6.00, p = 0.001), while the median PHQ-9 score was also higher but was not statistically significant (6.50, IQR 3.00–11.00 vs. 5.00, IQR 3.00–8.00, p = 0.066). A higher proportion of participants with psychiatric illness reported moderate-severe depression and anxiety (35.7% vs. 16.5%, p = 0.002, 17.8% vs. 3.6%, p < 0.001 respectively). Multivariate regression analysis demonstrated that financial difficulty, in education and pregnancy by in-vitro fertilization were associated with a higher PHQ-9 score in pregnant women during the COVID-19 pandemic, while underlying psychiatric illness was associated with a higher GAD-7 score. Support from a partner was demonstrated to be associated with a reduced level of depression and anxiety in pregnancy. Conclusions: Pregnant women with underlying psychiatric illness were more vulnerable during the COVID-19 pandemics than the non-psychiatric counterparts. Partner support is important for alleviating depression and anxiety in pregnancy during the COVID-19 pandemic. Clinical Trial Registration: The study was registered at http://www.clinicaltrials.gov, registration number NCT04377412.

A Tour of Subriemannian Geometries, Their Geodesics and Applications

Abstract: Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo of distributions Cartan's approach The tangent cone and Carnot groups Discrete groups tending to Carnot geometries Open problems Mechanics and geometry of bundles: Metrics on bundles Classical particles in Yang-Mills fields Quantum phases Falling, swimming, and orbiting Appendices: Geometric mechanics Bundles and the Hopf fibration The Sussmann and Ambrose-Singer theorems Calculus of the endpoint map and existence of geodesics Bibliography Index.

Lectures on Mechanics

Abstract: Publisher's description: The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule.

Lagrangian Reduction by Stages

Abstract: This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler{Poincare reduction (for the case in which the conguration space is a Lie group) as well as Euler-Poincare reduction for semidirect products. The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange{Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory. We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange{Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory. In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of Marsden, Ratiu and Scheurle [2000], which studies the Lagrange-Routh equations.