Events
Department of Mathematics and Statistics
Texas Tech University
Obesity has become a global epidemic due to an increase in unhealthy eating habits and sedentary lifestyles. Since excess weight gain can be considered a disease transmitted through social influence, understanding its interpersonal dynamics is crucial for effective intervention and prevention programs. This project proposes a compartment model by considering the social effects on weight gain. We study the local stability of disease-free equilibrium and derive a closed-form formula for the occurrence of backward bifurcation. Moreover, applying fluctuation lemma to prove the global stability of disease-free equilibrium provides a parameter condition to complete elimination of the overweight and obesity epidemic. Due to the fact that the overweight and obesity prevalence in the United States appears to be leveled off, we analyze the global stability of the non-trivial equilibrium by a geometric approach to establish a condition for the plateau of the overweight and obesity epidemic. Numerical simulations support the analytical results and show that the pro-posed model adequately describes complex epidemic patterns of overweight and obesity epidemic.
Please virtually attend this week's Biomath seminar at 4:00 PM Monday the 28th via this zoom link
Meeting ID: 839 9465 7333
Passcode: BfriM6
 | Wednesday
Mar. 30
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| Algebra and Number Theory
No Seminar
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Discontinuous Galerkin (DG) finite element methods are widely used in discretizing hyperbolic conservation laws. Analysis of the linear problems will help understand the properties of the DG methods and shed lights on their further development. In the first part of the talk, we use the two-way wave equations to study how the choice of numerical fluxes can affect the convergence rate of the DG methods. By constructing appropriate global projection operators, we prove optimal error estimates for a family of numerical fluxes on unstructured simplex meshes. In the second part of the talk, we consider the stability of local timestepping schemes with spacetime tents. We analyze a class of the so-called structure-aware Taylor methods and prove their weak stability under a slightly more restrictive time step constraint. Improved stability results are also obtained when coupled with low order spatial polynomials. For both topics we cover, our analysis is sharp, which can be confirmed with numerically.
Please virtually attend this week's Applied Math seminar at 4:00 PM Wednesday the 30th via this zoom link
Meeting ID: 930 3148 4740
no passcode
We describe the AKSZ construction as a geometric method for constructing BV action functionals for topological field theories called sigma-models in the setting of derived geometry, including the well-known special case of a symplectic Lie n-algebroid giving rise to higher Chern-Simons theory, and the possibly lesser-known case of a Leibniz algebroid giving rise to supergravity as a low-energy limit of (type II) string theory.