该文在函数不一定下半连续,集合不一定是闭集的条件下,利用函数次微分性质,引进新的约束规范条件,等价刻画了鲁棒复合优化问题的最优性条件以及原问题与其松弛型Fenchel-Lagrange对偶问题之间的全对偶。In the case when the functions ...该文在函数不一定下半连续,集合不一定是闭集的条件下,利用函数次微分性质,引进新的约束规范条件,等价刻画了鲁棒复合优化问题的最优性条件以及原问题与其松弛型Fenchel-Lagrange对偶问题之间的全对偶。In the case when the functions are not necessarily lower semicontinuous and the sets are not necessarily closed, by using the properties of subdifferential of functions, we introduce some new weaker constraint qualifications. Under those constraint qualifications, the total duality and optimality condition between the robust composite convex optimization problem and its relaxed Fenchel-Lagrange dual problem are established.展开更多
The aim of this paper is to apply a perturbation approach to deal with Fenchel- Lagrange duality based on weak efficiency to a constrained vector optimization problem. Under the stability criterion, some relationships...The aim of this paper is to apply a perturbation approach to deal with Fenchel- Lagrange duality based on weak efficiency to a constrained vector optimization problem. Under the stability criterion, some relationships between the solutions of primal problem and the Fenchel-Lagrange duality are discussed. Moreover, under the same condition, two saddle-points theorems are proved.展开更多
This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It art...This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It articulates foundational, mathematical axioms (Entanglement, Homogeneity, Emergence, and Measurement) that underpin the dynamics of systems, emphasizing the interconnectedness and emergent behaviors resulting from internal and external interactions. By exploring quantum concepts like coherence, entanglement, and superposition, the paper proposes an interdisciplinary approach termed Quantum Social Mechanics. This approach challenges classical paradigms, advocating for a reevaluation of conventional notions through the lens of quantum principles. The paper argues that understanding the universe’s complexities requires a synthesis of motion states and potential states, suggesting a paradigm shift towards integrating quantum mechanics into the philosophical foundation of social theory. Through this comprehensive framework, the paper aims to foster a deeper understanding of the universe’s interconnected nature and the dynamic processes that govern the emergence of complex systems and behaviors.展开更多
Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We...Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI.Firstly,the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer.Secondly,as the interference pattern is always related to some phase difference,the wave property can be quantified by how well one can estimate the phase parameter of the original state.With QFI as the unified figure of merit for both properties,we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.展开更多
On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by num...On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.展开更多
The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force mu...The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.展开更多
The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force mu...The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.展开更多
双碳政策推动下,乡村农业综合能源系统(integrated energy system,IES)的多能耦合关系更加复杂。为实现农业园区可靠运行,提出面向生态农业IES的多能互补与低碳运行优化调度策略。首先,基于农业园区的能量流动关系,建立沼气生产环节、...双碳政策推动下,乡村农业综合能源系统(integrated energy system,IES)的多能耦合关系更加复杂。为实现农业园区可靠运行,提出面向生态农业IES的多能互补与低碳运行优化调度策略。首先,基于农业园区的能量流动关系,建立沼气生产环节、多能耦合供应环节以及柔性负荷需求响应环节的数学模型。其次,考虑光伏、负荷和沼气的不确定性,建立生态农业IES两阶段鲁棒优化模型。模型引入碳排放成本和启停成本,可降低农业生产碳排放,防止机组频繁启停。然后,采用列与约束生成算法(column-and-constraint generation,C&CG),结合强对偶定理与线性化理论实现模型求解。最后,基于江西省某生态牧场IES进行算例仿真,验证所提策略的有效性。仿真结果表明,所提策略可实现生态农业IES的协调运行,提高系统经济性、低碳性和能效性。展开更多
文摘该文在函数不一定下半连续,集合不一定是闭集的条件下,利用函数次微分性质,引进新的约束规范条件,等价刻画了鲁棒复合优化问题的最优性条件以及原问题与其松弛型Fenchel-Lagrange对偶问题之间的全对偶。In the case when the functions are not necessarily lower semicontinuous and the sets are not necessarily closed, by using the properties of subdifferential of functions, we introduce some new weaker constraint qualifications. Under those constraint qualifications, the total duality and optimality condition between the robust composite convex optimization problem and its relaxed Fenchel-Lagrange dual problem are established.
基金Supported by the National Natural Science Foundation of China (Grant No.10871216)Innovative Talent Training Project,the Third Stage of "211 Project"Chongqing University (Grant No.S-0911)
文摘The aim of this paper is to apply a perturbation approach to deal with Fenchel- Lagrange duality based on weak efficiency to a constrained vector optimization problem. Under the stability criterion, some relationships between the solutions of primal problem and the Fenchel-Lagrange duality are discussed. Moreover, under the same condition, two saddle-points theorems are proved.
文摘This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It articulates foundational, mathematical axioms (Entanglement, Homogeneity, Emergence, and Measurement) that underpin the dynamics of systems, emphasizing the interconnectedness and emergent behaviors resulting from internal and external interactions. By exploring quantum concepts like coherence, entanglement, and superposition, the paper proposes an interdisciplinary approach termed Quantum Social Mechanics. This approach challenges classical paradigms, advocating for a reevaluation of conventional notions through the lens of quantum principles. The paper argues that understanding the universe’s complexities requires a synthesis of motion states and potential states, suggesting a paradigm shift towards integrating quantum mechanics into the philosophical foundation of social theory. Through this comprehensive framework, the paper aims to foster a deeper understanding of the universe’s interconnected nature and the dynamic processes that govern the emergence of complex systems and behaviors.
文摘Quantum Fisher information(QFI) plays an important role in quantum metrology,placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract.We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI.Firstly,the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer.Secondly,as the interference pattern is always related to some phase difference,the wave property can be quantified by how well one can estimate the phase parameter of the original state.With QFI as the unified figure of merit for both properties,we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.
文摘On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.
文摘The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.
文摘The question of what magnetism is vital to quantum physics. We know what all other quantum phenomenon is, but we did not know what magnetism is. It is not enough to say it is a force because of a charge. That force must be something, for consistencies sake it had to be tested. This paper was written in order to confirm the results that were received in the experiments that took place that led to the paper “Magnetism: Insights from the Thomas Young Experiment” where it was concluded the magnetic phenomenon is both a particle and a wave. Will different interference patterns confirm a khumalon and wave like behaviour? The khumalon is the name of the particle associated with magnetic phenomenon. This paper concludes by confirming what was discovered in mentioned paper. Magnetism organizes into a wave no matter the interference. Understanding this reality, it allows us to understand what is happening with simple magnetic interactions. When like poles meet because they can not occupy the same space they push each other. Opposite poles are antiparticles to each other and annihilate each other. South pole scientifically speaking is not attracted to the north pole, the reason why the magnets slam each other is because they are closing a magnetic vacuum caused by the particles annihilating each other. We can now start theorizing on why a lodestone attracts iron because we now know we are dealing with a particle.
文摘双碳政策推动下,乡村农业综合能源系统(integrated energy system,IES)的多能耦合关系更加复杂。为实现农业园区可靠运行,提出面向生态农业IES的多能互补与低碳运行优化调度策略。首先,基于农业园区的能量流动关系,建立沼气生产环节、多能耦合供应环节以及柔性负荷需求响应环节的数学模型。其次,考虑光伏、负荷和沼气的不确定性,建立生态农业IES两阶段鲁棒优化模型。模型引入碳排放成本和启停成本,可降低农业生产碳排放,防止机组频繁启停。然后,采用列与约束生成算法(column-and-constraint generation,C&CG),结合强对偶定理与线性化理论实现模型求解。最后,基于江西省某生态牧场IES进行算例仿真,验证所提策略的有效性。仿真结果表明,所提策略可实现生态农业IES的协调运行,提高系统经济性、低碳性和能效性。
