Events
Department of Mathematics and Statistics
Texas Tech University
The long-time behavior of solutions of the three-dimensional Navier–Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time t tends to infinity, in a coherent manner. In fact, it is assumed to have a general and complicated asymptotic expansion which involves complex powers of et, t, ln t, or other iterated logarithmic functions of t. We prove that all Leray–Hopf weak solutions admit an asymptotic expansion which is independent of the solutions and is uniquely determined by the asymptotic expansion of the body force. The proof makes use of the complexifications of the Gevrey–Sobolev spaces together with those of the Stokes operator and the bilinear form of the Navier–Stokes equations.
Overweight and obesity have become a global epidemic due to increasing 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 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 parameter conditions for 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 proposed model adequately describes complex epidemic patterns of the overweight and obesity epidemic.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday the 19th via this Zoom link.
Meeting ID: 948 7629 6935
Passcode: 602422
 | Wednesday
Sep. 21
|
| Algebra and Number Theory
No Seminar
|
See PDF.
Watch online via this Zoom link.
In this talk, we present our work on structure-preserving machine learning (ML) moment closure models for the radiative transfer equation. Most of the existing ML closure models are not able to guarantee the stability, which directly causes blow up in the long-time simulations. In our work, with carefully designed neural network architectures, the ML closure model can guarantee the stability (or hyperbolicity). Moreover, other mathematical properties, such as physical characteristic speeds, are also discussed. Extensive benchmark tests show the good accuracy, long-time stability, and good generalizability of our ML closure model.
Please attend this week's Applied Math seminar at 4 PM Wednesday via this Zoom link.
Meeting ID: 976 3095 1027
Passcode: applied
How does import competition from China affect engagement on ESG initiatives by US corporates?
On the one hand, reduced profitability due to import competition and lagging ESG performance of Chinese exporters
can disincentivize US firms to put more resources to ESG initiatives.
On the other hand, the shift from labor-intensive production to capital/technology-intensive
production along with offshoring may improve the US company's ESG performance.
Moreover, US companies have incentives to actively pursue more ESG engagement to differentiate from Chinese imports.
Exploiting a trade policy in which US congress granted China the Permanent Normal Trade Relations and the resulting change
in expected tariff rates on Chinese imports, we find that greater import competition from China leads to an increase in the
US company's ESG performance.
The improvement primarily stems from "doing more positives" and from more involvement on environmental initiatives.
Indirect and direct evidence shows that the improvement is not driven by the change in production process or offshoring,
but is consistent with product differentiation.
Our results suggest that the trade shock from China has significant impact on the US company's ESG performance.