成果一 刘晓东研究员的论文RECONSTRUCTION OF MULTISCALE ELECTROMAGNETIC SOURCES FROM MULTIFREQUENCY ELECTRIC FAR FIELD PATTERNS AT SPARSE OBSERVATION DIRECTIONS被MULTISCALE MODELING & SIMULATION接收发表。
摘要：
We introduce a multistep scheme for reconstructing multiscale sources from multi -frequency sparse electric far field patterns. The unknown source is a combination of electric dipoles, magnetic dipoles and extended sources. The dipoles are shown to be uniquely identified by the multifrequency electric far field patterns at properly chosen sparse observation directions. Motivated by the constructive uniqueness, two indicator functions are then designed for locating the magnetic dipoles and the electric dipoles. After locating all the dipoles, the formulas for computing the cor-responding polarization strengths are proposed. The stability of the formulas with respect to the frequency band is also derived. Finally, an indicator for the support of the extended sources is intro-duced once the dipoles are identified. Some numerical examples are presented to show the validity and robustness of the proposed algorithm.
成果二
罗德军研究员的论文Enhanced Dissipation for Stochastic Navier-Stokes Equations with Transport Noise被JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS接收发表。
摘要：
The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier-Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier-Stokes equations in vorticity form; in particular, quantitative estimate allows us to choose the parameters of noise, uniformly in initial vorticity bounded in L-2-norm, so that global solutions exist with a large probability sufficiently close to 1.
成果三
朱湘婵研究员的论文Global Existence and Non-Uniqueness for 3D Navier-Stokes Equations with Space-Time White Noise被ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS接收发表。
摘要：
We establish that global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier-Stokes system driven by space-time white noise. In this setting, solutions are expected to have space regularity of at most -1/2-kappa for any kappa >0. Consequently, the convective term is ill-defined analytically and probabilistic renormalization is required. Up until now, only local well-posedness has been known. With the help of paracontrolled calculus we decompose the system in a way which makes it amenable to convex integration. By a careful analysis of the regularity of each term, we develop an iterative procedure which yields global non-unique probabilistically strong paracontrolled solutions. Our result applies to any divergence free initial condition in L2B infinity,infinity -1+kappa, kappa >0, and also implies non-uniqueness in law.
成果四
王长军副研究员的论文Optimally integrating ad auction into e-commerce platforms被THEORETICAL COMPUTER SCIENCE接收发表。
摘要：
Advertising becomes one of the most popular ways of monetizing an online transaction platform. Usually, sponsored advertisements are posted on the most attractive positions to enhance the number of clicks. However, multiple e-commerce platforms are aware that this action may hurt the search experience of users, even though it can bring more incomes. To balance the advertising revenue and the user experience loss caused by advertisements, most e-commerce platforms choose fixing some areas for advertisements and adopting some restrictions on the number of ads, such as a fixed number K of ads or one advertisement for every N organic searched results. Different from these common rules of treating the allocation of ads separately (from the arrangements of the organic searched items), in this work we build up an integrated system with mixed arrangements of advertisements and organic items. We focus on the design of truthful mechanisms to properly list the advertisements and organic items and optimally trade off the instant revenue and the user experience. Furthermore, for different settings and practical requirements, we extend our optimal truthful allocation mechanisms to cater for these realistic conditions. Finally, we exert several experiments to verify the improvement of our mechanism compared to the common-used advertising mechanism. (c) 2023 Elsevier B.V. All rights reserved.
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