| 1 | Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations | Weinan, E. | 北京大学;
北京大数据
研究院 | 山东大学;埃默里大学 | (1)In a recent breakthrough paper of E et al [7], they solved the BSDEs from a control perspective by regarding the Z term as a control.
(2)The idea of solving high-dimensional PDEs and control problems with neural networks has been pioneered by the works [33,48,49] and has been further investigated by[77]. |
| 2 | On the birationality of complete intersections associated to nef-partitions | 李 展 | 北京大学 | 德雷塞尔大学;
阿尔伯塔大学;
剑桥大学 | (1)This completes the progress in this direction made by Li’s breakthrough [Li16] by proving the result in full generality and without assumptions
(2)This completes the groundbreaking work of Li [Li16] by removing any need for the assumptions that the Calabi- Yaus and a certain determinantal variety are irreducible.. |
| 3 | The eigencurve over the boundary of weight space | 刘若川 | 北京大学 | 东京城市大学 | (1)However, with recent groundbreaking works including[18,19],we are now gradually revealing what C N looks like globally. |
| 4 | Primitivity, the convergence of the nqz method, and the largest eigenvalue for nonnegative tensors | 张恭庆 | 北京大学;
南开大学 | 杭州电子科技大学 | (1)With these seminal works, Ng et al.[30], Yang and Yang [46,47], as well as Chang et al.[5] further made substantial developments on Perron-Frobenius type theorems for nonnegative tensors. |
| 5 | Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles | 崔 巍
杨静平 | 北京大学 | 香港大学 | (1)Because of their high generality, the results in Cui (2013) arguably represent groundbreaking contributions to the literature of optimal reinsurance and merit further studies. |
| 6 | Image restoration wavelet frame shrinkage, nonlinear evolution pdes, and beyond | 董 彬 | 北京大学 | 慕尼黑理工大学 | (1)This approach rests on breakthroughs of Cai et al. [11] and Dong et al. [16]in which a direct connection between lters and nite difference approximations of differential operators was established. |
| 7 | Flocking of multi-agent dynamical systems with intermittent nonlinear velocity measurements | 温广辉
段志生 | 北京大学 | 伊斯兰阿扎德大学 | (1) Recently, more breakthroughs on Reynolds ocking model have been achieved including a discussion of ocking in case of speed sensor failure in Wen, Duan, Li, and Chen (2012) and ocking control problem of multi-agent systems with connectivity preserving mechanism in another work by Wen, Duan, Su, Chen, and Yu (2012) and the model predictive control ock-ing of a networked multi-agent system is proposed based on position measurements in Zhan and Li (2013). |
| 8 | Consensus of discrete-time linear multi-agent systems with observer-type protocols | 李忠奎
段志生 | 北京大学;
北京理工大学 | 西南交通大学 | (1) In the seminal paper[14],the authors proposed an H∞-type Riccati design method, but the systems have no poles outside the unit circle. |
| 9 | On the base-point-free theorem of 3-folds in positive characteristic | 许晨阳 | 北京大学 | 中国科技大学;
剑桥大学;
东京大学 | (1)Using the recent breakthroughs on the minimal model program for threefolds in characteristic p > 5 [3,5,13,24,59],one can prove nite generation of R(X,D) in some important cases (again in dimension 3,characteristic p > 5). |
| 10 | The nonvanishing hypothesis at infinity for rankin-selberg convolutions | 孙斌勇 | 中国科学院 | 哈尔滨工业大学;印度科学教育与研究学院 | (1)Finally,we remark that although we have followed Sun’s pioneering paper [16] closely for the general approach,there are still many delicate analyses to carry out in our case. |
| 11 | Kahler-einstein metrics and stability | 陈秀雄 | 中国科学院 | 加州大学
伯克利分校 | (1)It plays an essential role in the recent breakthrough of the Yau-Tian-Donalson conjecture [10,45]. |
| 12 | Proof of the fundamental gap conjecture | Andrews, Ben | 中国科学院;
清华大学 | 山西大学 | (1)Luo and the second named author [14] also adapted successfully the coupling method to give a new proof of the fundamental gap conjecture, which was first proved by Andrews and Clutterbuck in the seminal paper [1].
(2)Recently, Sun made a breakthrough by confirming it for GL n (R) × GL n-1 (R) and GL n (C) × GL n-1 (C); see [16]. |
| 13 | Discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method | 刘 耕
Krafczyk, Manfred | 中国科学院 | 伊斯兰阿扎德大学;卡尔斯鲁厄理工学院 | (1)Regarding to historical literatures, Kirk et al. [11] who is the pioneer in the use of LBM for transient fluid flow optimization and Liu et al. [19] successfully pioneered the use of a topology optimization that employed LBM and the objective function corresponding to energy dissipation. |
| 14 | Topology identification and adaptive synchronization of uncertain complex networks with non-derivative and derivative coupling | 徐玉华
周武能 | 中国科学院;上海科技大学;东华大学;云阳师范学院 | 天津理工大学 | (1)In [23,24], Xu et al. pioneered in studying the synchronization of a complex dynamical network with non-derivative and derivative coupling. |
| 15 | Rc-positivity, rational connectedness and yau's conjecture | 杨晓奎 | 中国科学院 | 加州大学圣地亚哥分校;东北大学（日本） | (1)As a new approach to rational connectedness, Xiaokui Yang introduced the notation of RC positivity in the breakthrough paper [Yan17a]. |
| 16 | Carleman estimate for a fractional diffusion equation with half order and application | 徐 翔 | 复旦大学 | 东京大学 | (1)As a pioneer work for the Carleman estimates for fractional diffusion equations, we can refer to Xu, Cheng and Yamamoto [42]. |
| 17 | An analytic grothendieck riemann roch theorem | 郁国梁 | 复旦大学 | 纽约州立大学水牛城分校;马尼托巴大学 | (1)An even bigger breakthrough occurred with the appearance of the two papers [10] and [13], in which the conjecture was confirmed under natural smoothness and transversality conditions. |
| 18 | An iterative algorithm for the stability analysis of dynamic interval systems | 冷慧男
张 奇 | 复旦大学;华东理工大学 | 沙希德·贝赫什蒂大学;德克萨斯大学圣安东尼奥分校 | (1)At present,many researches have made significant breakthroughs in [8,9] in algorithm accuracy in [10] and stability in [11,12]. |
| 19 | Boundary partial regularity for a class of biharmonic maps | 龚华均 | 复旦大学 | 杜伊斯堡-埃森大学;卢万天主教大学;华沙大学 | (1)A boundary regularity theory for stationary biharmonic maps was initiated by Gong et al. [6]. |
| 20 | Stability of fractional-order nonlinear dynamic systems lyapunov direct method and generalized mittag-leffler stability | 李 岩 | 山东大学 | 北京交通大学;加利福尼亚大学美塞德分校;安徽大学 | (1)In the seminal work [1], the Lyapunov direct method is proposed by use of where is the Caputo fractional derivative.
(2)The Mittag-Lefer stability de nition is pro- posed to describe the dynamics of the system, and the fractional direct Lyapunov method is introduced creatively in [15,16],which inspired many scholars and derived a series of pioneering work. |
| 21 | A new face of the branching recurrence of computability logic | Japaridze, Giorgi | 山东大学 | 西安电子科技大学;山东大学 | (1)An impetus to our present investigation was provided by the fact that intro ducing a similar simplication for the ordinary, “non-togg ling” branching recurrence operation ◦ | in [7] almost immediately resulted in a long-awaited and long-overdue breakthrough in syntactically taming that operation ([8,9]), and a number of other interesting, hardly-possible-to-achieve-earlier results ([12,13]). |