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1.
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.  相似文献   
2.
We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.  相似文献   
3.
从教具制作、定量实验探究和教学启示等三方面来探究匀速圆周运动的向心加速度公式,即利用自制教具探究向心加速度a c与圆周运动半径r和角速度ω之间的定量关系.实验发现,结果非常好地符合理论预期.最后讨论了该教具所蕴含的教学启示,可以将其设计成适合高中物理教学的验证性、探究性实验及课外科创活动,从而培养学生的科学探究能力、科学推理能力、动手协作能力和问题解决能力.本教具还提供了测量当地重力加速度的一种新方法.  相似文献   
4.
Hao Wang 《中国物理 B》2022,31(11):114206-114206
As concepts closely related to microwave absorption properties, impedance matching and phase matching were rarely combined with material parameters to regulate properties and explore related mechanisms. In this work, reduction-diffusion method was innovatively applied to synthesize rare earth alloy Y$_{2}$Fe$_{17}$. In order to regulate the electromagnetic parameters of absorbers, the Y$_{2}$Fe$_{17}$N$_{3-\delta }$ particles were coated with silica (Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$) and absorbers with different volume fractions were prepared. The relationship between impedance matching, matching thickness, and the strongest reflection loss peak (${\rm RL}_{\rm min}$) was presented obviously. Compared to the microwave absorption properties of Y$_{2}$Fe$_{17}$N$_{3-\delta }$/PU absorber, Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$/PU absorbers are more conducive to the realization of microwave absorption material standards which are thin thickness, light weight, strong absorbing intensity, and broad bandwidth. Based on microwave frequency bands, the microwave absorption properties of the absorbers were analyzed and the related parameters were listed. As an important parameter related to perfect matching, reflection factor ($\sqrt {ărepsilon_{\rm r}/\mu_{\rm r}}$) was discussed combined with microwave amplitude attenuation. According to the origin and mathematical model of bandwidth, the formula of EAB (${\rm RL}<-10$ dB) was derived and simplified. The calculated bandwidths agreed well with experimental results.  相似文献   
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We provide a representation formula for viscosity solutions to an elliptic Dirichlet problem involving Pucci’s extremal operators. This is done through a dynamic programming principle derived from Denis et al. (2010). The formula can be seen as a nonlinear extension of the Feynman–Kac formula.  相似文献   
7.
The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.  相似文献   
8.
Traditional Chinese medicine (TCM) is the key to unlock treasures of Chinese civilization. TCM and its compound play a beneficial role in medical activities to cure diseases, especially in major public health events such as novel coronavirus epidemics across the globe. The chemical composition in Chinese medicine formula is complex and diverse, but their effective substances resemble “mystery boxes”. Revealing their active ingredients and their mechanisms of action has become focal point and difficulty of research for herbalists. Although the existing research methods are numerous and constantly updated iteratively, there is remain a lack of prospective reviews. Hence, this paper provides a comprehensive account of existing new approaches and technologies based on previous studies with an in vitro to in vivo perspective. In addition, the bottlenecks of studies on Chinese medicine formula effective substances are also revealed. Especially, we look ahead to new perspectives, technologies and applications for its future development. This work reviews based on new perspectives to open horizons for the future research. Consequently, herbal compounding pharmaceutical substances study should carry on the essence of TCM while pursuing innovations in the field.  相似文献   
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10.
杨国武 《化学教育》2022,43(1):118-121
选取了在高中课堂教学中出现的关于速率平衡的几个常见的结论,以阿伦尼乌斯公式为模型讨论了温度对反应速率的影响;推导并梳理了反应物转化率随投料量的变化关系;基于浓度商的单调性证明了平衡状态的“殊途同归”结论在数学上的合理性。在加深对常见结论认识的同时,通过对证明过程中应用的数学方法的总结,实现对几个相似化学问题证明方法的统一,为新问题的证明途径提供了方向。  相似文献   
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