Under a directed leader-follower network structure, this manuscript addresses the cooperative control issue for a class of stochastic upper-triangular nonlinear multi-agent systems (MASs) with unknown growth rates. Initially, by applying time-varying coordinates, the system is converted into an equivalent form with time-dependent gain factors. Subsequently, a time-varying state feedback controller is developed, demonstrating that followers can achieve mean-square bounded output tracking of the leader, with maintaining all the closed-loop system bounded in probability. Lastly, the proposed approach’s effectiveness is confirmed through simulation experiments.
The following semi-linear elliptic equations involving Hardy–Sobolev critical exponents −Δu−μux2=u2*s−2xsu+g(x,u),x∈Ω∖0,u=0,x∈∂Ω have been investigated, where Ω is an open-bounded domain in RNN≥3, with a smooth boundary ∂Ω, 0∈Ω,0≤μ<μ¯:=N−222,0≤s<2, and 2*s=2N−s/N−2 is the Hardy–Sobolev critical exponent. This problem comes from the study of standing waves in the anisotropic Schrödinger equation; it is very important in the fields of hydrodynamics, glaciology, quantum field theory, and statistical mechanics. Under some deterministic conditions on g, by a detailed estimation of the extremum function and using mountain pass lemma with PSc conditions, we obtained that: (a) If μ≤μ¯−1, and λ<λ1μ, then the above problem has at least a positive solution in H01Ω; (b) If μ¯−1<μ<μ¯, then when λ*μ<λ<λ1μ, the above problem has at least a positive solution in H01Ω; (c) if μ¯−1<μ<μ¯ and Ω=B(0,R), then the above problem has no positive solution for λ≤λ*μ. These results are extensions of E. Jannelli’s research (g(x,u)=λu).
本文总结了近海泥沙在波浪、潮流、波流耦合、风暴和陆架环流等动力作用下的输运特点,概述了较为著名的近海海域三维泥沙输运模型的特点及其在港口航道工程、海底地貌演变、海水水质监测等方面的应用进展.泥沙输运数值模型构建需要物理海洋学、沉积学、生态学、计算机科学等多学科理论支撑,现已从泥沙输运路径模拟向多模型耦合方向发展.因此,开展泥沙动力学、环境生态学、地貌动力学等相关理论的研究能够拓宽泥沙数值模拟研究的应用场景,使其服务于更多涉海领域.
城市空气污染问题受到了社会的广泛关注,研究济南市空气质量变化趋势对济南市未来的大气污染防治具有重要意义.基于济南市2018-2022 年空气常规污染物质量浓度的监测数据,采用Sen's斜率估计、MK检验分析、灰色关联分析等方法对济南市空气质量变化趋势和影响因素进行了分析.结果表明:1)近五年来,济南市各项空气污染物质量浓度显著性下降,空气质量总体变好,并且自2021 年下半年,空气质量整体变化趋势更加显著;2)空气污染物质量浓度季节性变化特征明显,除O3 质量浓度随时间变化呈倒"V"型,夏季最高外,其他污染物质量浓度随时间变化呈"V"型,春冬高,夏秋低;3)在冬季供暖时期,除O3 外,其他空气常规污染物质量浓度均有明显升高,其中PM2.5 的质量浓度变化最显著;4)通过灰色关联分析可知,对济南市空气质量影响较大的气象因素和经济因素分别为年平均气温、第二产业占比.
本文对不同种植年限日光温室的土壤活性有机质和腐殖质组成进行了研究,发现随温室种植利用年限的增加,日光温室土壤有机质、腐殖质和活性有机质质量分数均呈升高的趋势.日光温室土壤活性有机质质量分数增幅大于有机质总量的增幅,高龄日光温室0～<20 cm,20～<40 cm土层活性有机质占有机质比例均在20%以上,高于温室外粮田0～<20 cm的表层土壤.随种植利用年限的增加,日光温室土壤中松、稳、紧各级结合态腐殖质质量分数均呈增加的趋势;其中松结合态腐殖质占比大于粮田,稳结合态和紧结合态腐殖质占比小于粮田.日光温室土壤松结合态腐殖质与紧结合态腐殖质的比值(即松紧比)均大于粮田土壤.
