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Hong Kong Polytechnic University
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Video
We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by regions in which u > O and u < 0. The classical point of view of regarding the Prandtl equations as an evolution equation in x completely breaks down since u changes sign. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. This is a joint work with Sameer Iyer.
Event date: 14/3/2023
Speaker: Prof. Nader Masmoudi (New York University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Fluid dynamics -- Mathematical models
- Resource Type:
- Video
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Video
In the context of hyperbolic systems of balance laws with dissipative source manifesting relaxation, recent pr"Ogress will be reported in the program of passing to the limit, in 1he BV setting, as the relaxation lime tends to zero.
Event date: 16/2/2023
Speaker: Prof. Constantine Dafermos (Brown University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Equilibrium -- Mathematical models Relaxation Differential equations Hyperbolic
- Resource Type:
- Video
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Video
Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
Event date: 19/1/2023
Speaker: Prof. Benoît Perthame (Sorbonne University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Biology and Mathematics and Statistics
- Keywords:
- Biomathematics Equations
- Resource Type:
- Video
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Video
Universities conduct research for three reasons: to educate students, to contribute to society, and to understand the world. While society often holds a view of the scholar as a solitary and singular genius, in reality scholars today participate in a highly collaborative, worldwide search for shared understandings that stand the test of time and the scrutiny of others. The problems in the 21st century often demand effort by teams of researchers with resources at scale: laboratories and equipment, compute resources, and expert staffing. Working with faculty, students, and other stakeholders to identify the greatest opportunities and the resources needed to address them is both a privilege and a challenge for modern academic administrators. In this talk, I will share three examples: fostering collaborative proposal-writing; planning for shared capabilities in experimental facilities, data, and computation; and transforming academic structures.
Even date: 12/4/2023
Speaker: Prof. Kathryn Ann Moler
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Statistics and Research Methods
- Keywords:
- Research Science
- Resource Type:
- Video
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Video
In this CIHK webinar, we will discuss the material conditions of and historical background to the use of Classical Chinese or Literary Sinitic in writing-mediated brush conversation between literati of Sinitic engaged in cross-border communication within Sinographic East Asia or the Sinographic cosmopolis, which corresponds with today’s China, North Korea, South Korea, Japan (including Okinawa, formerly the Ryukyu Kingdom) and Vietnam. Compared with speech as a modality of communication, real-time writing-mediated interaction between talking humans, synchronously face-to-face, seems uncommon. In any society, speaking is premised on one condition: the interlocutors must have at least one shared spoken language at their disposal, but even then, there are circumstances under which speaking is either physically not feasible or socially inappropriate. Could writing function as an alternative modality of communication when speaking is not an option due to the absence of a shared spoken language, as in cross-border communication settings? Whereas real-time writing-mediated face-to-face interaction is rare where a regional lingua franca was known to exist (e.g., Latin and Arabic), there is ample historical evidence of literati of Classical Chinese or Literary Sinitic from different parts of Sinographic East Asia conducting ‘silent conversation’, synchronously and interactively in writing mode using brush, ink, and paper. Such a pattern of writing-assisted interaction is still practiced and observable in pen-assisted conversation – pen-talk – between Chinese and Japanese speakers today, thanks to the pragma-linguistic affordance of morphographic, non-phonographic sinograms (i.e., Chinese characters and Japanese kanji). We will outline the historical spread of Classical Chinese or Sinitic texts from the ‘center’ to the ‘peripheries’, and the historical background to the acquisition of literacy in Sinitic by the people there. Their shared knowledge of Sinitic helps explain why, for well over a thousand years until the 1900s, literati from these places were able to speak their mind by engaging in ‘Sinitic brush-talk’ 漢文筆談 in cross-border communication.
Even date: 13/5/2022
Speaker: Prof. David C. S. Li
Hosted by: Confucius Institute of Hong Kong, Department of Chinese Culture
- Subjects:
- Chinese Language and Language and Languages
- Keywords:
- Chinese characters History Chinese language -- Written Chinese Written communication China East Asia
- Resource Type:
- Video
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Video
Focusing on tensions and links between national formation and international outlooks, this talk shows how classical world visions persist as China’s modernizers and revolutionaries adopted and revised the Western nation-state and cosmopolitanism. The concepts of tianxia (all under heaven) and datong (great harmony) have been updated into outlooks of global harmony that value unity, equality, and reciprocity as strategies of overcoming interstate conflict, national divides, and social fragmentation. The talk will delve into two debates: the embrace of the West vs. aspirations for a common world, and the difference between liberal cosmopolitanism and socialist internationalism.
Even date: 16/9/2022
Speaker: Prof. Ban Wang
Hosted by: Confucius Institute of Hong Kong, Department of Chinese Culture
- Subjects:
- Chinese Studies
- Keywords:
- Civilization Diplomatic relations World politics China
- Resource Type:
- Video
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Video
Professor Yigong Shi will reflect on the challenges in global higher education, based on his 37 years of learning, scientific research, and teaching experience in academia. He will present Westlake University's educational reforms in university operations, governance, talent recruitment, student development, research and academic evaluation, and interdisciplinary studies, which altogether provide new opportunities for future-oriented higher education.
Even date: 6/12/2022
Speaker: Prof. Yigong Shi
Moderator: Prof. Qingyan Chen (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Keywords:
- Educational change China Education Higher
- Resource Type:
- Video
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Video
Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Convex sets Mathematical optimization Computer science -- Mathematics
- Resource Type:
- Video
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Video
Geospatial information science is a discipline that focuses on using geospatial information technology to understand people, places, nature and processes of the earth. IoT refers to Internet of things, the combination of sensors, software and other technologies to connect and exchange data with other devices and systems over the Internet. The era of IoT brings us opportunities and challenges for geospatial information science. In the keynote, five characteristics and three scientific issues of geo-spatial information science in the era of IoT are summarised.
Even date: 6/9/2022
Speaker: Prof. Daren Li
Moderator: Prof. Christopher Chao (Hong Kong Polytechnic University)
Panel members: Prof. Qingyan Chen, Prof. Qinhao Chen (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Land Surveying and Geo-Informatics
- Keywords:
- Internet of things Geospatial data Spatial data mining
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Sampling (Statistics) Differential equations Partial -- Numerical solutions Mathematical models Adaptive computing systems
- Resource Type:
- Video
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