本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论...
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本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振.利用分数阶Shapiro-Loginov公式和Laplace变换技巧,本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益(Output Amplitude Gain, OAG)的解析表达式,然后讨论了分数阶、时滞和噪声参数对OAG的影响.结果显示:各参数对OAG的影响均呈现非单调变化的特点,表明系统出现广义随机共振.特别地,分数阶与时滞的协同作用可能诱导随机共振的多样化.这就为在一定范围内调控随机共振提供了可能.
人工智能在当前社会有着极为广泛的应用,随着人工智能的快速发展,在国家发展中占据了重要高地。众所周知,数学与人工智能密切相关,数学不仅是人工智能的理论基础,还在其算法、模型和应用中发挥着关键作用,人工智能又能将数学理论应用在实际生活中。数学与人工智能相辅相成,互相促进。因此,数学和人工智能的交叉融合成为当前和未来高校教育的一个重要方向。鉴于此,本文聚焦于数学与人工智能交叉融合教育及学生创新能力培养,面对当前学科融合的复杂性、课程设计与教学方法的整合以及缺乏跨学科项目实践与创新机会三方面挑战,提出数学基础与人工智能的交叉点分析、跨学科课程融合与设计以及跨学科科研实践与创新的应对策略。Artificial intelligence has a very wide range of applications in today’s society, and with its rapid development, it occupies an important position in national development. It is well known that mathematics is closely related to artificial intelligence;not only is mathematics the theoretical foundation of AI, but it also plays a key role in its algorithms, models, and applications. In turn, artificial intelligence can apply mathematical theories to real-life situations. Mathematics and artificial intelligence complement and promote each other. Therefore, the integration of mathematics and artificial intelligence has become an important direction for education in universities both now and in the future. In light of this, this paper focuses on the education and cultivation of innovative capabilities at the intersection of mathematics and artificial intelligence. It addresses three challenges: the complexity of interdisciplinary integration, the integration of course design and teaching methods, and the lack of interdisciplinary project practice and innovation opportunities. The paper proposes strategies for analyzing the intersections of mathematical foundations and artificial intelligence, integrating and designing interdisciplinary courses, and promoting interdisciplinary research practice and innovation.
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